Ali Movahednasab, Masoud Rashidinejad, and Amir Abdollahi
[1], [4]; HRj denotes requiredthermal energy for power generation by a technology inBtu/KWh and decreases every year [4]:MCj = (Fj·HRj + O&Mj + CO2j)(1 + rr)y. (3)Investment cost is settled through the construction pe-riod and must be recovered during the operation. Validreports have expressed the investment cost in $/KW [1],[4], which is convertible into $/KWh using life time ofeach technology in (4). The offers are adjusted using themarginal cost and the investment cost must be recovered23under the influence of market condition during the opera-tion period:ICj($/KWh) =ICj($/KW)LTj × 8760(1 + rr)y. (4)3.2 Electric DemandDemand of electric energy is modelled by load durationcurve (LDC) for base, middle and peak sections, whichare supplied by coal-fired, CCGT and GT, respectively; itgrows in each section with a constant growth rate everyyear and the average amount by (5) is offered to the marketas market demand. Market price affects the demand viademand elasticity:D(t) =ki=1δi·Li·eg·y− λ·Δρ. (5)3.3 Power MarketThis paper considers an energy-only market with pay-as-bid structure, in which the lowest offers are dispatched andreceive their offers from the market and market price isequal to average offer. The superiority of this structure ineliminating price spikes persuaded some markets to preferit over the uniform price. The firms should adjust theiroffers properly, above the MC and below their predictionof price via the TREND function; they should make abalance between their profit and the chance to win in themarket [3], [45].3.4 ProfitabilityClearing the market specifies the generation of each firm,which is applicable in computing their costs and profits.Total generation cost, in (6), is the sum of firm’s expensesfor generating electric energy until studied time t:Φj =t0Gj·MCjdt (6)By subtracting the generation and investment costsfrom the income, the total profit of the firms is given byΠj =t0Gj·χj − Gj·MCj − CPj·ICjdt (7)Profitability index is defined in (8), as the ratio ofprofit to generation cost, for normalizing the profits to asame quantity [46]. This parameter is helpful in investingin a technology rather than its profit:PIj =ΠjΦj(8)3.5 Stable StateA market can become stable by recovering its generationand investment costs of the firms [45]. This condition isequivalent to PIj = 0, as both costs are considered in PIj.The firms can reach the stable state by offering a priceequal to MC plus a multiple of forecasted price [3], namedas stable price.3.6 Capacity ExpansionThe PIs of firms are converted into investment rate viaS-shaped curves in (9), which limit the rate of variationsand final values in each firm [46]. The coefficients mj max,αj and βj differ in each technology, but mj is equal to 1 forPIj = 1 in the whole, as indicated in Fig. 6. The coefficientmj is influenced by reliability policy and profitability forproviding enough capacity:mj =mj max1 + e−(αj P Ij −βj )(9)Figure 6. The coefficient m for different technologies vs. PI.Equation (10) gives investment rate in each technologyas a function of demand growth rate and retirement rateof the firms weighted by the coefficient mj:IRj = mj·( ˙Li + ˙REj) (10)Reliability policy in (11) forms an internal loop inlaunching process, named as launch scale [9] that changesrate of investment in each technology for holding reserveratio at a proposed level:Res.Rat =TCP − D(t)D(t)(11)The investment rate is converted into capacity af-ter a construction delay. Equation (12) indicates underconstruction capacity, which is the difference between in-vestment rate and construction rate in each technology.Exploited capacity in (13) is the difference between con-structed capacity and retired amount after a life time.A part of GT capacity is converted into CCGT by a change24ratio and change delay that influences the pattern of ex-pansion. Operational capacity is declared to the marketand creates the main feedback loop in this process; besides,it is used for providing reliability as an internal loop:UCj =t0IRj − IRj(t − CTj)dt (12)CPj =t0CNj − CNj(t − LTj)dt (13)3.7 Wind TechnologyThe wind technology competes with other participants inthe market, while previous studies subtracted its capacityfrom the demand [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [3]. The studyis followed via three scenarios, namely stable state, naturalgas price variation and access of demand to natural gasand electricity. The first scenario enlarges market stability,which is known by recovering generation and investmentcosts. At the second scenario the effect of natural gascharge variation is analysed in low, medium and highcharges and the third scenario analyses the demand accessto both natural gas and electricity via seasonal factors.Unlike other researches, the wind participates at the en-ergy market beside the thermal firms, instead of decreasingits capacity from the demand. The applied data are frompublished reports by EIA about generation and investmentcosts of different technologies, natural gas hub price, natu-ral gas city gate price and etc., summarized in Appendix A.The rest of paper is organized as follows; Section 2 de-scribes the concept of system dynamics briefly by introduc-ing employed and important tools in this paper. Section 3explains general model and its different parts. The resultsof model simulation in defined scenarios are represented inSection 4 and Sections 5 and 6 discuss about the resultsand pluralize them, respectively. Appendix A summarizesthe applied data in this study.2. Concept of System DynamicsSystem dynamics was approached by Sterman for analysingcomplex systems and system thinking in a practicalmethod. Growing the dynamic complexity in business, in-dustrial and social systems increases the role of modelling,predicting and analysing their complex behaviour for un-derstanding its reasons. System dynamics is a method for21understanding and analysing the complex behaviours by aset of conceptual tools and modelling methods, which arehelpful in simulating the long-run behaviour of a system indifferent policies and making better decision.Feedback control theories and nonlinear dynamicsfound the base of system dynamics. For long-run analysisof a system, it is necessary to understand different effectivefactors and their causal relation. Moreover, identifyingfeedbacks, delays and other linearity which leads the sys-tem to instability and modelling them by stocks and flowsis the main art in analysing a system.Simulation is the only reliable way for testing the valid-ity of the models because of complexity of relations amongdifferent nonlinear parameters, which makes understand-ing the behaviour of the model in a long time period im-possible. Without simulation techniques, the system hardbehaviour can be improved using feedbacks through thereal world which is very slow and inefficient due to delays,nonliterary and costs of testing the ideas [46].2.1 Causal DiagramFor simulating a dynamic system, different tools areneeded. Causal loops are important tools for showing thestructure of the feedbacks in the system and their effects.A causal diagram, in Fig. 2, consists of arrows which con-Figure 2. The causal representation of a variable.Figure 3. The stock and flow variable.Figure 4. Casual diagram of the TREND function.nects related variables together and shows the influencesamong them. The positive sign on the arrow shows in-creasing Y by increment of X and negative sign indicatesdecreasing of Y .2.2 Stocks and FlowsOne of the most limitations of casual loops is their inabilityin capturing the stocks and flows structure of the system.Stock structures are other tools in studying the systemdynamics, which accumulate difference between inflow andoutflow of a variable as shown in Fig. 3. Equation (1)expresses the relation of stocks, which create inertia inthe system and provide memory for it; they are helpfulfor creating delays in a system by accumulating the differ-ence between the inflow and outflow of a parameter in aprocess:Y (t) =t0X1(τ) − X2(τ)dτ + Y (t0) (1)2.3 ForecastingBounded rationality hypothesis (BRH) is a forecastingalgorithm formed by adaptive expectation, in which cur-rent expectations are related to the current and past val-ues as in (2). Expectations on the value of variablesfor time T are revised with adjustment rate κ, if fore-casted value in previous periods is different from the actualamount [49]:ξe(t, T) = ξe(t, T − 1) + κ[ξ(T − 1) − ξe(t, T − 1)] (2)Sterman has proposed an expectational model basedon the system dynamics, called TREND function; he hasused needed times for measuring, collecting and analysingdata, historic time horizon and required time for perceivingand reacting to variable changes. Figure 4 representsthe structure of TREND function, which is usable forestimating fractional growth rate in input variable [46].22Figure 5. Process of capacity expansion in a power market.3. Model DescriptionFigure 5 represents an overview of developed model. Thefirms adjust their offers considering their marginal costand forecasted market price. Offers, existent capacityand average of demand are submitted to the power mar-ket for clearing market price and generation amount byeach firm. Clearing the market facilitates calculation ofprofits and generation costs, considering the investmentcosts. The profits are normalized and converted into in-vestment through some multipliers, which create underconstruction and generation capacities after some delays.The existent capacities return to the market via offer,which forms main feedback loop in this process. Re-serve ratio makes an internal loop by changing the launchscale for providing the proposed reliability level. Hubprice of natural gas acts on fuel cost of natural gas-based technologies and affects city gate price via seasonalfactors. Details of different parts of the model are asfollows.3.1 CostsMarginal and investment costs are two expenses for gener-ating electricity. The firms settle the marginal cost for gen-erating each MWh of electric energy including fuel, CO2and O&M costs, which grows with constant rate of returnevery year as indicated in (3) [1], [4]; HRj denotes requiredthermal energy for power generation by a technology inBtu/KWh and decreases every year [4]:MCj = (Fj·HRj + O&Mj + CO2j)(1 + rr)y. (3)Investment cost is settled through the construction pe-riod and must be recovered during the operation. Validreports have expressed the investment cost in $/KW [1],[4], which is convertible into $/KWh using life time ofeach technology in (4). The offers are adjusted using themarginal cost and the investment cost must be recovered23under the influence of market condition during the opera-tion period:ICj($/KWh) =ICj($/KW)LTj × 8760(1 + rr)y. (4)3.2 Electric DemandDemand of electric energy is modelled by load durationcurve (LDC) for base, middle and peak sections, whichare supplied by coal-fired, CCGT and GT, respectively; itgrows in each section with a constant growth rate everyyear and the average amount by (5) is offered to the marketas market demand. Market price affects the demand viademand elasticity:D(t) =ki=1δi·Li·eg·y− λ·Δρ. (5)3.3 Power MarketThis paper considers an energy-only market with pay-as-bid structure, in which the lowest offers are dispatched andreceive their offers from the market and market price isequal to average offer. The superiority of this structure ineliminating price spikes persuaded some markets to preferit over the uniform price. The firms should adjust theiroffers properly, above the MC and below their predictionof price via the TREND function; they should make abalance between their profit and the chance to win in themarket [3], [45].3.4 ProfitabilityClearing the market specifies the generation of each firm,which is applicable in computing their costs and profits.Total generation cost, in (6), is the sum of firm’s expensesfor generating electric energy until studied time t:Φj =t0Gj·MCjdt (6)By subtracting the generation and investment costsfrom the income, the total profit of the firms is given byΠj =t0Gj·χj − Gj·MCj − CPj·ICjdt (7)Profitability index is defined in (8), as the ratio ofprofit to generation cost, for normalizing the profits to asame quantity [46]. This parameter is helpful in investingin a technology rather than its profit:PIj =ΠjΦj(8)3.5 Stable StateA market can become stable by recovering its generationand investment costs of the firms [45]. This condition isequivalent to PIj = 0, as both costs are considered in PIj.The firms can reach the stable state by offering a priceequal to MC plus a multiple of forecasted price [3], namedas stable price.3.6 Capacity ExpansionThe PIs of firms are converted into investment rate viaS-shaped curves in (9), which limit the rate of variationsand final values in each firm [46]. The coefficients mj max,αj and βj differ in each technology, but mj is equal to 1 forPIj = 1 in the whole, as indicated in Fig. 6. The coefficientmj is influenced by reliability policy and profitability forproviding enough capacity:mj =mj max1 + e−(αj P Ij −βj )(9)Figure 6. The coefficient m for different technologies vs. PI.Equation (10) gives investment rate in each technologyas a function of demand growth rate and retirement rateof the firms weighted by the coefficient mj:IRj = mj·( ˙Li + ˙REj) (10)Reliability policy in (11) forms an internal loop inlaunching process, named as launch scale [9] that changesrate of investment in each technology for holding reserveratio at a proposed level:Res.Rat =TCP − D(t)D(t)(11)The investment rate is converted into capacity af-ter a construction delay. Equation (12) indicates underconstruction capacity, which is the difference between in-vestment rate and construction rate in each technology.Exploited capacity in (13) is the difference between con-structed capacity and retired amount after a life time.A part of GT capacity is converted into CCGT by a change24ratio and change delay that influences the pattern of ex-pansion. Operational capacity is declared to the marketand creates the main feedback loop in this process; besides,it is used for providing reliability as an internal loop:UCj =t0IRj − IRj(t − CTj)dt (12)CPj =t0CNj − CNj(t − LTj)dt (13)3.7 Wind TechnologyThe wind technology competes with other participants inthe market, while previous studies subtracted its capacityfrom the demand [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [9] that changesrate of investment in each technology for holding reserveratio at a proposed level:Res.Rat =TCP − D(t)D(t)(11)The investment rate is converted into capacity af-ter a construction delay. Equation (12) indicates underconstruction capacity, which is the difference between in-vestment rate and construction rate in each technology.Exploited capacity in (13) is the difference between con-structed capacity and retired amount after a life time.A part of GT capacity is converted into CCGT by a change24ratio and change delay that influences the pattern of ex-pansion. Operational capacity is declared to the marketand creates the main feedback loop in this process; besides,it is used for providing reliability as an internal loop:UCj =t0IRj − IRj(t − CTj)dt (12)CPj =t0CNj − CNj(t − LTj)dt (13)3.7 Wind TechnologyThe wind technology competes with other participants inthe market, while previous studies subtracted its capacityfrom the demand [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [8] gives the seasonal factorsas shown in Fig. 7. These factors adapt to additive modelthat makes the real variable by adding a seasonal factor.Figure 7. The seasonal factors of the city gate natural gasprice.4. Simulation and ResultsThis section analyses the results of simulating differentstates of natural gas consumption in the power systemin three scenarios including firms stability, changes in thenatural gas charge and access of demand to the natural gasand electricity. Some results such as the profitability index,reserve ratio, and capacity expansion are represented andcompared with the base state in each scenario. The appliedparameters in the simulation are from the published databy the EIA on the generation costs by different technolo-gies, natural gas city gate prices and natural gas hub prices.The results represent the statue of the parameters in 1,200months for indicating the stability of the developed model.4.1 Base ScenarioIn this scenario, the firms stay on the stable state by ad-justing the offers for recovering the generation and invest-ment costs [45] that is achievable by PIj = 0 in (8), due toits association to these costs. They adjust their offers byadding multiples of the forecasted price to their marginalcost, which are 0.13, 0.083, 0.058 and 0.45 for the coal-fired, CCGT, GT and wind, respectively. The technologieswith higher investment cost need a greater coefficient forgetting to the stability.Figure 8 represents the profitability index of the firmsin this scenario, which tends to zero during the studiedhorizon. The variation of the PI around zero is a moti-vation for expanding the capacity by different technologiesbeside the growing demand.Table 1 summarizes the total present profit of the firmsin this scenario. The coal-fired earns the most profit bysupplying the base load and the CCGT and GT are at thenext places. The wind earns the least profit in the stablestate.Figure 9 represents the reserve ratio of the powersystem calculated by (11) for providing the reliability ofthe power system, which swings around 0.2 with a limitedvariation between 0.18 and 0.22.The reliability level is achieved by the pattern of gener-ation capacity, shown in Fig. 10. The capacity of the coal-fired, CCGT and GT gets to 8.8 × 104MW, 4.8 × 104MWand 3.3 × 104MW for supplying the base, middle and peakloads, respectively and the wind technology expands itscapacity to 1,400 MW in the stable state.25Figure 8. The profitability index of the firms in the base scenario: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 1Total Present Profit of the Firms at the Base ScenarioTechnology Profit ($)Coal-fired 3 × 106CCGT 0.94 × 106GT 0.33 × 106Wind 0.085 × 106Figure 9. The reserve ratio of the power system in the basescenario.4.2 Natural Gas Price VariationThe second scenario investigates the influence of the vari-ations in the natural gas price on the long-run investmentin the capacity expansion. The variations are modelled aslow-price, medium-price and high-price outlines, summa-rized in Table A.1 [6], [48], [38]. The results of the high andFigure 10. The capacity of different technologies in thebase scenario.Figure 11. The price of electric energy for different outlinesof natural gas price.low prices of natural gas are compared with the mediumprice as base scenario.Figure 11 represents the price of electric energy fordifferent outlines of natural gas price. The electric price26Figure 12. The profitability index of the firms at the high price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 2Total Present Profit of the Firms at the High Price ofNatural GasTechnology Profit ($)Coal-fired 24 × 106CCGT 4.3 × 106GT −1.3 × 106Wind 3.4 × 106increases by growing the natural gas price and decreasesby its decline, compared with the medium price.Figure 12 indicates the profitability index of the firmsat the high price of natural gas. The PI increases to0.04, 0.01 and 0.33 for the coal-fired, CCGT and wind,respectively, but decreases to −0.0002 for the GT, due tothe loss of opportunity for generation by this technology.Reducing the heat rate of the GT, increases its PI tozero on month 900 by raising its generation chance anddecreases the PI of the coal-fired in Figs. 12(a) and (c).The present profit of the firms changes by their devi-ation from the stable state, summarized in Table 2. Theprofit of the coal-fired, CCGT and wind increases , com-pared with Table 1, but the high price is disadvantageousfor the GT and causes its negative profit in Table 2.The average of the reserve ratio does not change signif-icantly at the high price and grows to the average of 0.21with a pattern same as Fig. 9. Compared with Fig. 10, theFigure 13. The capacity of different technologies at thehigh price of natural gas.capacity of different firms changes as indicated in Fig. 13;the capacity of the coal-fired and the wind increases to9 × 104MW and 7,300 MW, respectively, but it decreasesto 4.4 × 104MW and 3 × 104MW for the CCGT and GT,which shows the reduced share of the natural gas consumersin the market and the great ratio of capacity expansion bythe wind at high prices.Decreasing the charge of the natural gas, drops theelectric price in the market, which leads to the loss of thefirms at the stable offer, due to irretrievable investmentcosts. The profitability index of the firms drops to −0.0073,−0.007, −0.0035 and −0.49 for the coal-fired, CCGT, GTand wind in Fig. 14.Table 3 summarizes the present profit of the firms atthe low charge of natural gas, which is negative for thewhole and results in their loss by offering the stable price.27Figure 14. The profitability index of the firms at the low price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 3Total Present Profit of the Firms at the Low Price ofNatural GasTechnology Profit ($)Coal-fired −2.8 × 106CCGT −1.3 × 106GT −0.58 × 106Wind −0.15 × 106Figure 15. The capacity of different technologies at the lowprice of natural gas.Low-price natural gas does not influence the reliabilityof the power system remarkably and decreases the aver-age of the reserve ratio to the amount 0.19 with the be-haviour same as Fig. 9. The pattern of generation capacitychanges at low charge of natural gas as shown in Fig. 15.The capacity of the CCGT and the GT increases to4.9 × 104MW and 3.4 × 104MW, while the amount of thecoal-fired and the wind decreases to 8.7 × 104MW and540 MW, respectively. This variation increases the share oftechnologies in the market that consume the natural gas.4.3 Natural Gas Consumption by the DemandThis section analyses the access to the electricity and nat-ural gas as two separate energy resources by 10% of thedemand. The demand switches between these energy re-sources by comparing the electric market price and naturalgas city gate price and choosing the cheapest one.Figure 16 represents the PI of the firms, when 10%of the demand selects between two energy resources. ThePI of the coal-fired decreases to −0.033 in Fig. 16a, but itdoes not change for the other technologies significantly.Table 4 summarizes the present profit of the firms atthe selection of the natural gas by the demand. The loss ofthe profit by the coal-fired is severe, due to the variations inthe base demand, which enforces it to increase its coefficientin the offer. The present profit of the other technologiesdoes not change a lot in this scenario, compared withTable 1.The resource selection by the demand enforces thefirms to expand the capacity for a discontinuous demand,which is detectable in the capacity of different technologiesin Fig. 17. The capacity of the coal-fired, CCGT and GTincreases with swings to 10 × 104MW, 5.8 × 104MW and3.7 × 104MW, respectively. The wind capacity decreasesto 1,047 MW in this scenario.28Figure 16. The profitability index of the firms at the natural gas consumption by the demand scenario: (a) coal-fired;(b) CCGT; (c) GT; and (d) wind.Table 4Total Present Profit of the Firms at the Natural GasConsumption by the Demand ScenarioTechnology Profit ($)Coal-fired −23.1 × 106CCGT 1 × 106GT 0.31 × 106Wind 0.072 × 106Figure 17. The capacity of different technologies at thenatural gas consumption by the demand scenario.Figure 18. The reserve ratio of the power system at thenatural gas consumption by the demand scenario.This pattern of capacity has a negative influence onthe reserve ratio of the power system for providing thereliability as shown in Fig. 18. The average of the reserveratio swings around the average amount of 0.35 and variesbetween 0.15 and 0.6 in this figure. Increasing the accessof the demand to both energy resources from 10% createsundesirable effects on the profitability and reserve ratio.The efficiency of the natural gas consumption by thedemand is an effective factor for keeping the stability ofthe electric market. Growing the efficiency of the naturalgas consumption to above 50%, restores the stable stateof the firms in the market by keeping the PI of the firmsat the zero and the reserve ratio on 0.2 with a little swingsame as Figs. 8 and 9. High efficient natural gas demands29are dismissed form the electric market, which decreases theinstalled capacity at the stable state and its swings.5. DiscussionThe natural gas affects the power market in generationand consumption levels. Based on the hub price of naturalgas, three scenarios can be defined including, low, mediumand high charges. The access of demand to the natural gasaffects the market via the seasonal factors.The stable state (PI = 0) which is considered as thebase scenario compensates the generation and investmentcosts of the firms and keeps the reserve ratio on about0.2 for providing the reliability. This state is achieved byadding a multiple of the forecasted price to the MC by thefirms, which is 0.13, 0.083, 0.058 and 0.45 for the coal-fired,CCGT, GT and wind, respectively; the technologies withhigher investment cost adjust their offer with a greatercoefficient. The Medium price of natural gas is consideredin the base scenario.High-charge natural gas increases the market price andthe firms offers, which increases the profitability index ofthe coal-fired, CCGT and wind from zero to 0.04, 0.01 and0.33, respectively; however, this charge decreases the gener-ation opportunity for GT and decreases its PI to −0.0002.So, the GT should decrease its coefficient during high priceof natural gas for creating generation opportunity. Byincreasing the natural gas price reaches the capacity of GTand CCGT increases from 4.8 × 104MW and 3.3 × 104MWto 4.4 × 104MW and 3 × 104MW and the share of naturalgas-based technologies in the market decreases. However,increasing the profit creates the opportunity for the coal-fired and wind to expand their capacity and increase theirshare from 8.8 × 104MW and 1,400 MW at the stable stateto 9 × 104MW and 7,300 MW. The average of reserve ratiogrows from 0.2 to 0.21 in this situation.Low-charge natural gas decreases the average pricein the market and reduces the PI of coal-fired, CCGT,GT and wind to −0.0073, −0.007, −0.0035 and −0.49,respectively, which results in the loss of the firms. Theshare of CCGT and GT increases to 4.9 × 104MW and3.4 × 104MW in the market, while the capacity ofthe coal-fired and wind decreases to 8.7 × 104MW and540 MW. The capacity expansion is due to the effects ofdemand growth rate and retirement rate on the invest-ment rate for providing the proposed reliability level ofabout 0.19.The charge of natural gas at the consumption level isinfluenced by seasonal factors, which has additive patternand its amount is greater in colder months. Natural gasconsumption by demand decreases the profitability indexof the coal-fired to −0.033 as base supplier. This conditionenforces the firms to expand their capacity, while theirgeneration is not consumed by the demand continuously,which hardens recovering the investment. Choosing thecheapest energy resource by the demand keeps the PIof the CCGT, GT and wind at zero and increasing thepercentage of demand access decreases the PI of CCGTand GT. The capacity of coal-fired, CCGT, GT and windreaches to 10 × 104MW, 5.8 × 104MW, 3.7 × 104MW and1,047 MW. Switching between the energy resources by thedemand causes the swing of the reserve ratio, which isresolved by increasing the efficiency of the natural gasconsumers.6. ConclusionThis paper analyses the effect of the natural gas on thecapacity expansion by the firms in a pay-as-bid energy-only market using the system dynamics. Natural gas-basedtechnologies and demand selection between the electricityand natural gas are two considered tie points between theseresources. This subject is studied via three scenarios,namely, (1) the firms stability, (2) changes in the naturalgas charge and (3) access of demand to natural gas andelectricity. Four generation technologies including coal-fired, CCGT, GT and wind participate in an energy-onlymarket using the published data in the reports of EIA.At the first scenario, the firms adjust their offersabove the marginal cost for recovering the generation andinvestment costs as stable state, which is known by PIj = 0.The firms adjust their offers by adding a multiple of theforecasted price to the marginal cost, which is greater forthe technologies with higher investment cost. The stablestate can recover the costs of the firms and provide thetargeted reliability level of the power system.The natural gas price as assumed to fluctuate betweenlow, medium and high prices, where the medium priceis applied at the base scenario. High-price natural gasincreases the offers of the firms and the market price, whichincreases the profit of the coal-fired, CCGT and wind, butcauses the loss of the profit by the GT, as it loses theopportunity for generation. More profit increment by coal-fired and loss of GT reduces the share of natural gas-basedtechnologies in the market at high charges of natural gas.Low-price natural gas decreases the offers and market priceto an amount, which cannot recover the investment costsand causes the loss of the whole. The capacity is expandedfor supplying the demand and compensating the retirementwith a less ramp. The loss of coal-fired and wind in lowcharge is more severe due to their higher investment costs,which increases the share of natural gas-based technologiesin the market. The reserve ratio of the power systemdoes not change remarkably by changing the natural gasprice.Selecting the natural gas as resource of energy by aportion of demand causes the loss of profit by the coal-firedand does not influence on the revenue of the rest. Thisbehaviour of demand expands the generation capacity andincreases the average of reserve ratio, but creates swing init. Increasing the per cent of demand access to the naturalgas intensifies the unstable condition in the market. Thegrowth of efficiency in the natural gas demand dismisses itfrom the power market and restores it to the stability.Appendix ATable A.1 summarizes the parameters of the simulation,which are from the published report by EIA [4].30Table A.1The Parameters of the SimulationTechnology Coal-Fired CCGT GT WindParameterFuel Cost 65 ($/ton) Low Price = 3.8 $/MMBtuThermal Value Medium Price = 4.6 $/MMBtu= 6080 kcal/kg High price = 6 $/MMBtuHeat rate (Btu/KWh) 9,200 6,752 9,289Heat rate changes (Btu/KWh year) −30 −28 −50O&M costs ($/MWh) 7.7 3.3 4.3 3.4CO2 costs ($/MWh) 24 10.5 16Investment costs ($/MWh) 3.7 3.3 2.3 10.97Construction time (months) 48 36 24 6Life time (months) 720 360 360 240Rate of return (%/year) 5%Peak demand (MW) 1,200Peak duration 0.2Middle demand (MW) 1,000Middle duration 0.6Base demand (MW) 700Base duration 0.2Demand growth rate (%/year) 5%Rated wind speed (m/s) 7Product wind speed (m/s) 4Cut out wind speed (m/s) 13References[1] “Projected Costs of Generating Electricity , International En-ergy Agency, 2010 Edition.[2] S. Macmillan, A. Antonyuk, and H. Schwind, Gas to CoalCompetition in the U.S. Power Sector, International EnergyAgency, May, 2013.[3] S.F. Tierney, T. Schatzki, and R. Mukerji, Uniform-Pricingversus Pay-as-Bid in Wholesale Electricity Markets: Does itMake a Difference?, Analysis Group & New York ISO, March2008.[4] R. Tidball, J. Bluestein, N. Rodriguez, and S. Knoke, Cost andPerformance Assumptions for Modeling Electricity GenerationTechnologies, ICF International Fairfax, Virginia, November2010, 96–102.[5] Life Data Analysis Reference, Worldwide Headquarters, AZ,USA, May 22, 2015.[6] A. Sieminski, Annual Energy Outlook 2015, U.S. EnergyInformation Administration, May, 2015.[7] Indepndent Statics and Data Analysis, US Natural Gas Citygate Price, U.S. Energy Information Administration, May,2016.[8] Guide to Seasonal Adjustment with X-12-ARIMA, TSAB,March, 2007.[9] A.S. Cui, M. Zhao, and T. Ravichandran, Market uncertaintyand dynamic new product launch strategies: A system dynam-ics model, IEEE Transactions on Engineering Management,58(3), 2011, 530–550. [10] A. Ford, System dynamics and the electric power industry,System Dynamics Review, 13(1), 1997, 57–85. [11] F. Olsina, F. Garce, and H.J. Haubrich, Modeling long-termdynamics of electricity markets, Energy Policy, 34(12), 2006,1411–1433. [12] A. Movahednasab, M. Rashidinejad, and A. Abdollahi, A sys-tem dynamics analysis of the long run investment in market-based electric generation expansion with renewable resources,International Transactions on Electrical Energy Systems, 2017.DOI: 10.1002/etep.2338. [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [8] gives the seasonal factorsas shown in Fig. 7. These factors adapt to additive modelthat makes the real variable by adding a seasonal factor.Figure 7. The seasonal factors of the city gate natural gasprice.4. Simulation and ResultsThis section analyses the results of simulating differentstates of natural gas consumption in the power systemin three scenarios including firms stability, changes in thenatural gas charge and access of demand to the natural gasand electricity. Some results such as the profitability index,reserve ratio, and capacity expansion are represented andcompared with the base state in each scenario. The appliedparameters in the simulation are from the published databy the EIA on the generation costs by different technolo-gies, natural gas city gate prices and natural gas hub prices.The results represent the statue of the parameters in 1,200months for indicating the stability of the developed model.4.1 Base ScenarioIn this scenario, the firms stay on the stable state by ad-justing the offers for recovering the generation and invest-ment costs [45] that is achievable by PIj = 0 in (8), due toits association to these costs. They adjust their offers byadding multiples of the forecasted price to their marginalcost, which are 0.13, 0.083, 0.058 and 0.45 for the coal-fired, CCGT, GT and wind, respectively. The technologieswith higher investment cost need a greater coefficient forgetting to the stability.Figure 8 represents the profitability index of the firmsin this scenario, which tends to zero during the studiedhorizon. The variation of the PI around zero is a moti-vation for expanding the capacity by different technologiesbeside the growing demand.Table 1 summarizes the total present profit of the firmsin this scenario. The coal-fired earns the most profit bysupplying the base load and the CCGT and GT are at thenext places. The wind earns the least profit in the stablestate.Figure 9 represents the reserve ratio of the powersystem calculated by (11) for providing the reliability ofthe power system, which swings around 0.2 with a limitedvariation between 0.18 and 0.22.The reliability level is achieved by the pattern of gener-ation capacity, shown in Fig. 10. The capacity of the coal-fired, CCGT and GT gets to 8.8 × 104MW, 4.8 × 104MWand 3.3 × 104MW for supplying the base, middle and peakloads, respectively and the wind technology expands itscapacity to 1,400 MW in the stable state.25Figure 8. The profitability index of the firms in the base scenario: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 1Total Present Profit of the Firms at the Base ScenarioTechnology Profit ($)Coal-fired 3 × 106CCGT 0.94 × 106GT 0.33 × 106Wind 0.085 × 106Figure 9. The reserve ratio of the power system in the basescenario.4.2 Natural Gas Price VariationThe second scenario investigates the influence of the vari-ations in the natural gas price on the long-run investmentin the capacity expansion. The variations are modelled aslow-price, medium-price and high-price outlines, summa-rized in Table A.1 [6], [48], [38]. The results of the high andFigure 10. The capacity of different technologies in thebase scenario.Figure 11. The price of electric energy for different outlinesof natural gas price.low prices of natural gas are compared with the mediumprice as base scenario.Figure 11 represents the price of electric energy fordifferent outlines of natural gas price. The electric price26Figure 12. The profitability index of the firms at the high price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 2Total Present Profit of the Firms at the High Price ofNatural GasTechnology Profit ($)Coal-fired 24 × 106CCGT 4.3 × 106GT −1.3 × 106Wind 3.4 × 106increases by growing the natural gas price and decreasesby its decline, compared with the medium price.Figure 12 indicates the profitability index of the firmsat the high price of natural gas. The PI increases to0.04, 0.01 and 0.33 for the coal-fired, CCGT and wind,respectively, but decreases to −0.0002 for the GT, due tothe loss of opportunity for generation by this technology.Reducing the heat rate of the GT, increases its PI tozero on month 900 by raising its generation chance anddecreases the PI of the coal-fired in Figs. 12(a) and (c).The present profit of the firms changes by their devi-ation from the stable state, summarized in Table 2. Theprofit of the coal-fired, CCGT and wind increases , com-pared with Table 1, but the high price is disadvantageousfor the GT and causes its negative profit in Table 2.The average of the reserve ratio does not change signif-icantly at the high price and grows to the average of 0.21with a pattern same as Fig. 9. Compared with Fig. 10, theFigure 13. The capacity of different technologies at thehigh price of natural gas.capacity of different firms changes as indicated in Fig. 13;the capacity of the coal-fired and the wind increases to9 × 104MW and 7,300 MW, respectively, but it decreasesto 4.4 × 104MW and 3 × 104MW for the CCGT and GT,which shows the reduced share of the natural gas consumersin the market and the great ratio of capacity expansion bythe wind at high prices.Decreasing the charge of the natural gas, drops theelectric price in the market, which leads to the loss of thefirms at the stable offer, due to irretrievable investmentcosts. The profitability index of the firms drops to −0.0073,−0.007, −0.0035 and −0.49 for the coal-fired, CCGT, GTand wind in Fig. 14.Table 3 summarizes the present profit of the firms atthe low charge of natural gas, which is negative for thewhole and results in their loss by offering the stable price.27Figure 14. The profitability index of the firms at the low price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 3Total Present Profit of the Firms at the Low Price ofNatural GasTechnology Profit ($)Coal-fired −2.8 × 106CCGT −1.3 × 106GT −0.58 × 106Wind −0.15 × 106Figure 15. The capacity of different technologies at the lowprice of natural gas.Low-price natural gas does not influence the reliabilityof the power system remarkably and decreases the aver-age of the reserve ratio to the amount 0.19 with the be-haviour same as Fig. 9. The pattern of generation capacitychanges at low charge of natural gas as shown in Fig. 15.The capacity of the CCGT and the GT increases to4.9 × 104MW and 3.4 × 104MW, while the amount of thecoal-fired and the wind decreases to 8.7 × 104MW and540 MW, respectively. This variation increases the share oftechnologies in the market that consume the natural gas.4.3 Natural Gas Consumption by the DemandThis section analyses the access to the electricity and nat-ural gas as two separate energy resources by 10% of thedemand. The demand switches between these energy re-sources by comparing the electric market price and naturalgas city gate price and choosing the cheapest one.Figure 16 represents the PI of the firms, when 10%of the demand selects between two energy resources. ThePI of the coal-fired decreases to −0.033 in Fig. 16a, but itdoes not change for the other technologies significantly.Table 4 summarizes the present profit of the firms atthe selection of the natural gas by the demand. The loss ofthe profit by the coal-fired is severe, due to the variations inthe base demand, which enforces it to increase its coefficientin the offer. The present profit of the other technologiesdoes not change a lot in this scenario, compared withTable 1.The resource selection by the demand enforces thefirms to expand the capacity for a discontinuous demand,which is detectable in the capacity of different technologiesin Fig. 17. The capacity of the coal-fired, CCGT and GTincreases with swings to 10 × 104MW, 5.8 × 104MW and3.7 × 104MW, respectively. The wind capacity decreasesto 1,047 MW in this scenario.28Figure 16. The profitability index of the firms at the natural gas consumption by the demand scenario: (a) coal-fired;(b) CCGT; (c) GT; and (d) wind.Table 4Total Present Profit of the Firms at the Natural GasConsumption by the Demand ScenarioTechnology Profit ($)Coal-fired −23.1 × 106CCGT 1 × 106GT 0.31 × 106Wind 0.072 × 106Figure 17. The capacity of different technologies at thenatural gas consumption by the demand scenario.Figure 18. The reserve ratio of the power system at thenatural gas consumption by the demand scenario.This pattern of capacity has a negative influence onthe reserve ratio of the power system for providing thereliability as shown in Fig. 18. The average of the reserveratio swings around the average amount of 0.35 and variesbetween 0.15 and 0.6 in this figure. Increasing the accessof the demand to both energy resources from 10% createsundesirable effects on the profitability and reserve ratio.The efficiency of the natural gas consumption by thedemand is an effective factor for keeping the stability ofthe electric market. Growing the efficiency of the naturalgas consumption to above 50%, restores the stable stateof the firms in the market by keeping the PI of the firmsat the zero and the reserve ratio on 0.2 with a little swingsame as Figs. 8 and 9. High efficient natural gas demands29are dismissed form the electric market, which decreases theinstalled capacity at the stable state and its swings.5. DiscussionThe natural gas affects the power market in generationand consumption levels. Based on the hub price of naturalgas, three scenarios can be defined including, low, mediumand high charges. The access of demand to the natural gasaffects the market via the seasonal factors.The stable state (PI = 0) which is considered as thebase scenario compensates the generation and investmentcosts of the firms and keeps the reserve ratio on about0.2 for providing the reliability. This state is achieved byadding a multiple of the forecasted price to the MC by thefirms, which is 0.13, 0.083, 0.058 and 0.45 for the coal-fired,CCGT, GT and wind, respectively; the technologies withhigher investment cost adjust their offer with a greatercoefficient. The Medium price of natural gas is consideredin the base scenario.High-charge natural gas increases the market price andthe firms offers, which increases the profitability index ofthe coal-fired, CCGT and wind from zero to 0.04, 0.01 and0.33, respectively; however, this charge decreases the gener-ation opportunity for GT and decreases its PI to −0.0002.So, the GT should decrease its coefficient during high priceof natural gas for creating generation opportunity. Byincreasing the natural gas price reaches the capacity of GTand CCGT increases from 4.8 × 104MW and 3.3 × 104MWto 4.4 × 104MW and 3 × 104MW and the share of naturalgas-based technologies in the market decreases. However,increasing the profit creates the opportunity for the coal-fired and wind to expand their capacity and increase theirshare from 8.8 × 104MW and 1,400 MW at the stable stateto 9 × 104MW and 7,300 MW. The average of reserve ratiogrows from 0.2 to 0.21 in this situation.Low-charge natural gas decreases the average pricein the market and reduces the PI of coal-fired, CCGT,GT and wind to −0.0073, −0.007, −0.0035 and −0.49,respectively, which results in the loss of the firms. Theshare of CCGT and GT increases to 4.9 × 104MW and3.4 × 104MW in the market, while the capacity ofthe coal-fired and wind decreases to 8.7 × 104MW and540 MW. The capacity expansion is due to the effects ofdemand growth rate and retirement rate on the invest-ment rate for providing the proposed reliability level ofabout 0.19.The charge of natural gas at the consumption level isinfluenced by seasonal factors, which has additive patternand its amount is greater in colder months. Natural gasconsumption by demand decreases the profitability indexof the coal-fired to −0.033 as base supplier. This conditionenforces the firms to expand their capacity, while theirgeneration is not consumed by the demand continuously,which hardens recovering the investment. Choosing thecheapest energy resource by the demand keeps the PIof the CCGT, GT and wind at zero and increasing thepercentage of demand access decreases the PI of CCGTand GT. The capacity of coal-fired, CCGT, GT and windreaches to 10 × 104MW, 5.8 × 104MW, 3.7 × 104MW and1,047 MW. Switching between the energy resources by thedemand causes the swing of the reserve ratio, which isresolved by increasing the efficiency of the natural gasconsumers.6. ConclusionThis paper analyses the effect of the natural gas on thecapacity expansion by the firms in a pay-as-bid energy-only market using the system dynamics. Natural gas-basedtechnologies and demand selection between the electricityand natural gas are two considered tie points between theseresources. This subject is studied via three scenarios,namely, (1) the firms stability, (2) changes in the naturalgas charge and (3) access of demand to natural gas andelectricity. Four generation technologies including coal-fired, CCGT, GT and wind participate in an energy-onlymarket using the published data in the reports of EIA.At the first scenario, the firms adjust their offersabove the marginal cost for recovering the generation andinvestment costs as stable state, which is known by PIj = 0.The firms adjust their offers by adding a multiple of theforecasted price to the marginal cost, which is greater forthe technologies with higher investment cost. The stablestate can recover the costs of the firms and provide thetargeted reliability level of the power system.The natural gas price as assumed to fluctuate betweenlow, medium and high prices, where the medium priceis applied at the base scenario. High-price natural gasincreases the offers of the firms and the market price, whichincreases the profit of the coal-fired, CCGT and wind, butcauses the loss of the profit by the GT, as it loses theopportunity for generation. More profit increment by coal-fired and loss of GT reduces the share of natural gas-basedtechnologies in the market at high charges of natural gas.Low-price natural gas decreases the offers and market priceto an amount, which cannot recover the investment costsand causes the loss of the whole. The capacity is expandedfor supplying the demand and compensating the retirementwith a less ramp. The loss of coal-fired and wind in lowcharge is more severe due to their higher investment costs,which increases the share of natural gas-based technologiesin the market. The reserve ratio of the power systemdoes not change remarkably by changing the natural gasprice.Selecting the natural gas as resource of energy by aportion of demand causes the loss of profit by the coal-firedand does not influence on the revenue of the rest. Thisbehaviour of demand expands the generation capacity andincreases the average of reserve ratio, but creates swing init. Increasing the per cent of demand access to the naturalgas intensifies the unstable condition in the market. Thegrowth of efficiency in the natural gas demand dismisses itfrom the power market and restores it to the stability.Appendix ATable A.1 summarizes the parameters of the simulation,which are from the published report by EIA [4].30Table A.1The Parameters of the SimulationTechnology Coal-Fired CCGT GT WindParameterFuel Cost 65 ($/ton) Low Price = 3.8 $/MMBtuThermal Value Medium Price = 4.6 $/MMBtu= 6080 kcal/kg High price = 6 $/MMBtuHeat rate (Btu/KWh) 9,200 6,752 9,289Heat rate changes (Btu/KWh year) −30 −28 −50O&M costs ($/MWh) 7.7 3.3 4.3 3.4CO2 costs ($/MWh) 24 10.5 16Investment costs ($/MWh) 3.7 3.3 2.3 10.97Construction time (months) 48 36 24 6Life time (months) 720 360 360 240Rate of return (%/year) 5%Peak demand (MW) 1,200Peak duration 0.2Middle demand (MW) 1,000Middle duration 0.6Base demand (MW) 700Base duration 0.2Demand growth rate (%/year) 5%Rated wind speed (m/s) 7Product wind speed (m/s) 4Cut out wind speed (m/s) 13References[1] “Projected Costs of Generating Electricity , International En-ergy Agency, 2010 Edition.[2] S. Macmillan, A. Antonyuk, and H. Schwind, Gas to CoalCompetition in the U.S. Power Sector, International EnergyAgency, May, 2013.[3] S.F. Tierney, T. Schatzki, and R. Mukerji, Uniform-Pricingversus Pay-as-Bid in Wholesale Electricity Markets: Does itMake a Difference?, Analysis Group & New York ISO, March2008.[4] R. Tidball, J. Bluestein, N. Rodriguez, and S. Knoke, Cost andPerformance Assumptions for Modeling Electricity GenerationTechnologies, ICF International Fairfax, Virginia, November2010, 96–102.[5] Life Data Analysis Reference, Worldwide Headquarters, AZ,USA, May 22, 2015.[6] A. Sieminski, Annual Energy Outlook 2015, U.S. EnergyInformation Administration, May, 2015.[7] Indepndent Statics and Data Analysis, US Natural Gas Citygate Price, U.S. Energy Information Administration, May,2016.[8] Guide to Seasonal Adjustment with X-12-ARIMA, TSAB,March, 2007.[9] A.S. Cui, M. Zhao, and T. Ravichandran, Market uncertaintyand dynamic new product launch strategies: A system dynam-ics model, IEEE Transactions on Engineering Management,58(3), 2011, 530–550.[10] A. Ford, System dynamics and the electric power industry,System Dynamics Review, 13(1), 1997, 57–85.[11] F. Olsina, F. Garce, and H.J. Haubrich, Modeling long-termdynamics of electricity markets, Energy Policy, 34(12), 2006,1411–1433.[12] A. Movahednasab, M. Rashidinejad, and A. Abdollahi, A sys-tem dynamics analysis of the long run investment in market-based electric generation expansion with renewable resources,International Transactions on Electrical Energy Systems, 2017.DOI: 10.1002/etep.2338.[13] D. Eager, B.F. Hobbs, and J.W. Bialek, Dynamic modelingof thermal generation capacity investment: Application tomarkets with high wind penetration, IEEE Transactions onPower Systems, 27(4), 2002, 2127–2137.[14] M. Hasani-Marzooni and S.H. Hosseini, Short-term marketpower assessment in a long-term dynamic modeling of capacityinvestment, IEEE Transactions on Power Systems, 28(2),2013, 626–638. [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [8] gives the seasonal factorsas shown in Fig. 7. These factors adapt to additive modelthat makes the real variable by adding a seasonal factor.Figure 7. The seasonal factors of the city gate natural gasprice.4. Simulation and ResultsThis section analyses the results of simulating differentstates of natural gas consumption in the power systemin three scenarios including firms stability, changes in thenatural gas charge and access of demand to the natural gasand electricity. Some results such as the profitability index,reserve ratio, and capacity expansion are represented andcompared with the base state in each scenario. The appliedparameters in the simulation are from the published databy the EIA on the generation costs by different technolo-gies, natural gas city gate prices and natural gas hub prices.The results represent the statue of the parameters in 1,200months for indicating the stability of the developed model.4.1 Base ScenarioIn this scenario, the firms stay on the stable state by ad-justing the offers for recovering the generation and invest-ment costs [45] that is achievable by PIj = 0 in (8), due toits association to these costs. They adjust their offers byadding multiples of the forecasted price to their marginalcost, which are 0.13, 0.083, 0.058 and 0.45 for the coal-fired, CCGT, GT and wind, respectively. The technologieswith higher investment cost need a greater coefficient forgetting to the stability.Figure 8 represents the profitability index of the firmsin this scenario, which tends to zero during the studiedhorizon. The variation of the PI around zero is a moti-vation for expanding the capacity by different technologiesbeside the growing demand.Table 1 summarizes the total present profit of the firmsin this scenario. The coal-fired earns the most profit bysupplying the base load and the CCGT and GT are at thenext places. The wind earns the least profit in the stablestate.Figure 9 represents the reserve ratio of the powersystem calculated by (11) for providing the reliability ofthe power system, which swings around 0.2 with a limitedvariation between 0.18 and 0.22.The reliability level is achieved by the pattern of gener-ation capacity, shown in Fig. 10. The capacity of the coal-fired, CCGT and GT gets to 8.8 × 104MW, 4.8 × 104MWand 3.3 × 104MW for supplying the base, middle and peakloads, respectively and the wind technology expands itscapacity to 1,400 MW in the stable state.25Figure 8. The profitability index of the firms in the base scenario: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 1Total Present Profit of the Firms at the Base ScenarioTechnology Profit ($)Coal-fired 3 × 106CCGT 0.94 × 106GT 0.33 × 106Wind 0.085 × 106Figure 9. The reserve ratio of the power system in the basescenario.4.2 Natural Gas Price VariationThe second scenario investigates the influence of the vari-ations in the natural gas price on the long-run investmentin the capacity expansion. The variations are modelled aslow-price, medium-price and high-price outlines, summa-rized in Table A.1 [6], [48], [38]. The results of the high andFigure 10. The capacity of different technologies in thebase scenario.Figure 11. The price of electric energy for different outlinesof natural gas price.low prices of natural gas are compared with the mediumprice as base scenario.Figure 11 represents the price of electric energy fordifferent outlines of natural gas price. The electric price26Figure 12. The profitability index of the firms at the high price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 2Total Present Profit of the Firms at the High Price ofNatural GasTechnology Profit ($)Coal-fired 24 × 106CCGT 4.3 × 106GT −1.3 × 106Wind 3.4 × 106increases by growing the natural gas price and decreasesby its decline, compared with the medium price.Figure 12 indicates the profitability index of the firmsat the high price of natural gas. The PI increases to0.04, 0.01 and 0.33 for the coal-fired, CCGT and wind,respectively, but decreases to −0.0002 for the GT, due tothe loss of opportunity for generation by this technology.Reducing the heat rate of the GT, increases its PI tozero on month 900 by raising its generation chance anddecreases the PI of the coal-fired in Figs. 12(a) and (c).The present profit of the firms changes by their devi-ation from the stable state, summarized in Table 2. Theprofit of the coal-fired, CCGT and wind increases , com-pared with Table 1, but the high price is disadvantageousfor the GT and causes its negative profit in Table 2.The average of the reserve ratio does not change signif-icantly at the high price and grows to the average of 0.21with a pattern same as Fig. 9. Compared with Fig. 10, theFigure 13. The capacity of different technologies at thehigh price of natural gas.capacity of different firms changes as indicated in Fig. 13;the capacity of the coal-fired and the wind increases to9 × 104MW and 7,300 MW, respectively, but it decreasesto 4.4 × 104MW and 3 × 104MW for the CCGT and GT,which shows the reduced share of the natural gas consumersin the market and the great ratio of capacity expansion bythe wind at high prices.Decreasing the charge of the natural gas, drops theelectric price in the market, which leads to the loss of thefirms at the stable offer, due to irretrievable investmentcosts. The profitability index of the firms drops to −0.0073,−0.007, −0.0035 and −0.49 for the coal-fired, CCGT, GTand wind in Fig. 14.Table 3 summarizes the present profit of the firms atthe low charge of natural gas, which is negative for thewhole and results in their loss by offering the stable price.27Figure 14. The profitability index of the firms at the low price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 3Total Present Profit of the Firms at the Low Price ofNatural GasTechnology Profit ($)Coal-fired −2.8 × 106CCGT −1.3 × 106GT −0.58 × 106Wind −0.15 × 106Figure 15. The capacity of different technologies at the lowprice of natural gas.Low-price natural gas does not influence the reliabilityof the power system remarkably and decreases the aver-age of the reserve ratio to the amount 0.19 with the be-haviour same as Fig. 9. The pattern of generation capacitychanges at low charge of natural gas as shown in Fig. 15.The capacity of the CCGT and the GT increases to4.9 × 104MW and 3.4 × 104MW, while the amount of thecoal-fired and the wind decreases to 8.7 × 104MW and540 MW, respectively. This variation increases the share oftechnologies in the market that consume the natural gas.4.3 Natural Gas Consumption by the DemandThis section analyses the access to the electricity and nat-ural gas as two separate energy resources by 10% of thedemand. The demand switches between these energy re-sources by comparing the electric market price and naturalgas city gate price and choosing the cheapest one.Figure 16 represents the PI of the firms, when 10%of the demand selects between two energy resources. ThePI of the coal-fired decreases to −0.033 in Fig. 16a, but itdoes not change for the other technologies significantly.Table 4 summarizes the present profit of the firms atthe selection of the natural gas by the demand. The loss ofthe profit by the coal-fired is severe, due to the variations inthe base demand, which enforces it to increase its coefficientin the offer. The present profit of the other technologiesdoes not change a lot in this scenario, compared withTable 1.The resource selection by the demand enforces thefirms to expand the capacity for a discontinuous demand,which is detectable in the capacity of different technologiesin Fig. 17. The capacity of the coal-fired, CCGT and GTincreases with swings to 10 × 104MW, 5.8 × 104MW and3.7 × 104MW, respectively. The wind capacity decreasesto 1,047 MW in this scenario.28Figure 16. The profitability index of the firms at the natural gas consumption by the demand scenario: (a) coal-fired;(b) CCGT; (c) GT; and (d) wind.Table 4Total Present Profit of the Firms at the Natural GasConsumption by the Demand ScenarioTechnology Profit ($)Coal-fired −23.1 × 106CCGT 1 × 106GT 0.31 × 106Wind 0.072 × 106Figure 17. The capacity of different technologies at thenatural gas consumption by the demand scenario.Figure 18. The reserve ratio of the power system at thenatural gas consumption by the demand scenario.This pattern of capacity has a negative influence onthe reserve ratio of the power system for providing thereliability as shown in Fig. 18. The average of the reserveratio swings around the average amount of 0.35 and variesbetween 0.15 and 0.6 in this figure. Increasing the accessof the demand to both energy resources from 10% createsundesirable effects on the profitability and reserve ratio.The efficiency of the natural gas consumption by thedemand is an effective factor for keeping the stability ofthe electric market. Growing the efficiency of the naturalgas consumption to above 50%, restores the stable stateof the firms in the market by keeping the PI of the firmsat the zero and the reserve ratio on 0.2 with a little swingsame as Figs. 8 and 9. High efficient natural gas demands29are dismissed form the electric market, which decreases theinstalled capacity at the stable state and its swings.5. DiscussionThe natural gas affects the power market in generationand consumption levels. Based on the hub price of naturalgas, three scenarios can be defined including, low, mediumand high charges. The access of demand to the natural gasaffects the market via the seasonal factors.The stable state (PI = 0) which is considered as thebase scenario compensates the generation and investmentcosts of the firms and keeps the reserve ratio on about0.2 for providing the reliability. This state is achieved byadding a multiple of the forecasted price to the MC by thefirms, which is 0.13, 0.083, 0.058 and 0.45 for the coal-fired,CCGT, GT and wind, respectively; the technologies withhigher investment cost adjust their offer with a greatercoefficient. The Medium price of natural gas is consideredin the base scenario.High-charge natural gas increases the market price andthe firms offers, which increases the profitability index ofthe coal-fired, CCGT and wind from zero to 0.04, 0.01 and0.33, respectively; however, this charge decreases the gener-ation opportunity for GT and decreases its PI to −0.0002.So, the GT should decrease its coefficient during high priceof natural gas for creating generation opportunity. Byincreasing the natural gas price reaches the capacity of GTand CCGT increases from 4.8 × 104MW and 3.3 × 104MWto 4.4 × 104MW and 3 × 104MW and the share of naturalgas-based technologies in the market decreases. However,increasing the profit creates the opportunity for the coal-fired and wind to expand their capacity and increase theirshare from 8.8 × 104MW and 1,400 MW at the stable stateto 9 × 104MW and 7,300 MW. The average of reserve ratiogrows from 0.2 to 0.21 in this situation.Low-charge natural gas decreases the average pricein the market and reduces the PI of coal-fired, CCGT,GT and wind to −0.0073, −0.007, −0.0035 and −0.49,respectively, which results in the loss of the firms. Theshare of CCGT and GT increases to 4.9 × 104MW and3.4 × 104MW in the market, while the capacity ofthe coal-fired and wind decreases to 8.7 × 104MW and540 MW. The capacity expansion is due to the effects ofdemand growth rate and retirement rate on the invest-ment rate for providing the proposed reliability level ofabout 0.19.The charge of natural gas at the consumption level isinfluenced by seasonal factors, which has additive patternand its amount is greater in colder months. Natural gasconsumption by demand decreases the profitability indexof the coal-fired to −0.033 as base supplier. This conditionenforces the firms to expand their capacity, while theirgeneration is not consumed by the demand continuously,which hardens recovering the investment. Choosing thecheapest energy resource by the demand keeps the PIof the CCGT, GT and wind at zero and increasing thepercentage of demand access decreases the PI of CCGTand GT. The capacity of coal-fired, CCGT, GT and windreaches to 10 × 104MW, 5.8 × 104MW, 3.7 × 104MW and1,047 MW. Switching between the energy resources by thedemand causes the swing of the reserve ratio, which isresolved by increasing the efficiency of the natural gasconsumers.6. ConclusionThis paper analyses the effect of the natural gas on thecapacity expansion by the firms in a pay-as-bid energy-only market using the system dynamics. Natural gas-basedtechnologies and demand selection between the electricityand natural gas are two considered tie points between theseresources. This subject is studied via three scenarios,namely, (1) the firms stability, (2) changes in the naturalgas charge and (3) access of demand to natural gas andelectricity. Four generation technologies including coal-fired, CCGT, GT and wind participate in an energy-onlymarket using the published data in the reports of EIA.At the first scenario, the firms adjust their offersabove the marginal cost for recovering the generation andinvestment costs as stable state, which is known by PIj = 0.The firms adjust their offers by adding a multiple of theforecasted price to the marginal cost, which is greater forthe technologies with higher investment cost. The stablestate can recover the costs of the firms and provide thetargeted reliability level of the power system.The natural gas price as assumed to fluctuate betweenlow, medium and high prices, where the medium priceis applied at the base scenario. High-price natural gasincreases the offers of the firms and the market price, whichincreases the profit of the coal-fired, CCGT and wind, butcauses the loss of the profit by the GT, as it loses theopportunity for generation. More profit increment by coal-fired and loss of GT reduces the share of natural gas-basedtechnologies in the market at high charges of natural gas.Low-price natural gas decreases the offers and market priceto an amount, which cannot recover the investment costsand causes the loss of the whole. The capacity is expandedfor supplying the demand and compensating the retirementwith a less ramp. The loss of coal-fired and wind in lowcharge is more severe due to their higher investment costs,which increases the share of natural gas-based technologiesin the market. The reserve ratio of the power systemdoes not change remarkably by changing the natural gasprice.Selecting the natural gas as resource of energy by aportion of demand causes the loss of profit by the coal-firedand does not influence on the revenue of the rest. Thisbehaviour of demand expands the generation capacity andincreases the average of reserve ratio, but creates swing init. Increasing the per cent of demand access to the naturalgas intensifies the unstable condition in the market. Thegrowth of efficiency in the natural gas demand dismisses itfrom the power market and restores it to the stability.Appendix ATable A.1 summarizes the parameters of the simulation,which are from the published report by EIA [4].30Table A.1The Parameters of the SimulationTechnology Coal-Fired CCGT GT WindParameterFuel Cost 65 ($/ton) Low Price = 3.8 $/MMBtuThermal Value Medium Price = 4.6 $/MMBtu= 6080 kcal/kg High price = 6 $/MMBtuHeat rate (Btu/KWh) 9,200 6,752 9,289Heat rate changes (Btu/KWh year) −30 −28 −50O&M costs ($/MWh) 7.7 3.3 4.3 3.4CO2 costs ($/MWh) 24 10.5 16Investment costs ($/MWh) 3.7 3.3 2.3 10.97Construction time (months) 48 36 24 6Life time (months) 720 360 360 240Rate of return (%/year) 5%Peak demand (MW) 1,200Peak duration 0.2Middle demand (MW) 1,000Middle duration 0.6Base demand (MW) 700Base duration 0.2Demand growth rate (%/year) 5%Rated wind speed (m/s) 7Product wind speed (m/s) 4Cut out wind speed (m/s) 13References[1] “Projected Costs of Generating Electricity , International En-ergy Agency, 2010 Edition.[2] S. 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[35]–[44] studied the role of naturalgas in the power system via optimization problems andsolved it by different techniques. However, there is a gap inlong-run analysis of natural gas effect on the power systemfor accessing to a real-time view about this subject. Inthis regard, system dynamics is applied, which is a newidea in this field. The effect is studied in generation andconsumption levels.Four generation technologies including coal-fired,CCGT, GT and wind participate in a pay-as-bid energy-only market, which is chosen by some markets due toelimination of price spikes in this structure [3]. The studyis followed via three scenarios, namely stable state, naturalgas price variation and access of demand to natural gasand electricity. The first scenario enlarges market stability,which is known by recovering generation and investmentcosts. At the second scenario the effect of natural gascharge variation is analysed in low, medium and highcharges and the third scenario analyses the demand accessto both natural gas and electricity via seasonal factors.Unlike other researches, the wind participates at the en-ergy market beside the thermal firms, instead of decreasingits capacity from the demand. The applied data are frompublished reports by EIA about generation and investmentcosts of different technologies, natural gas hub price, natu-ral gas city gate price and etc., summarized in Appendix A.The rest of paper is organized as follows; Section 2 de-scribes the concept of system dynamics briefly by introduc-ing employed and important tools in this paper. Section 3explains general model and its different parts. The resultsof model simulation in defined scenarios are represented inSection 4 and Sections 5 and 6 discuss about the resultsand pluralize them, respectively. Appendix A summarizesthe applied data in this study.2. Concept of System DynamicsSystem dynamics was approached by Sterman for analysingcomplex systems and system thinking in a practicalmethod. Growing the dynamic complexity in business, in-dustrial and social systems increases the role of modelling,predicting and analysing their complex behaviour for un-derstanding its reasons. System dynamics is a method for21understanding and analysing the complex behaviours by aset of conceptual tools and modelling methods, which arehelpful in simulating the long-run behaviour of a system indifferent policies and making better decision.Feedback control theories and nonlinear dynamicsfound the base of system dynamics. For long-run analysisof a system, it is necessary to understand different effectivefactors and their causal relation. Moreover, identifyingfeedbacks, delays and other linearity which leads the sys-tem to instability and modelling them by stocks and flowsis the main art in analysing a system.Simulation is the only reliable way for testing the valid-ity of the models because of complexity of relations amongdifferent nonlinear parameters, which makes understand-ing the behaviour of the model in a long time period im-possible. Without simulation techniques, the system hardbehaviour can be improved using feedbacks through thereal world which is very slow and inefficient due to delays,nonliterary and costs of testing the ideas [46].2.1 Causal DiagramFor simulating a dynamic system, different tools areneeded. Causal loops are important tools for showing thestructure of the feedbacks in the system and their effects.A causal diagram, in Fig. 2, consists of arrows which con-Figure 2. The causal representation of a variable.Figure 3. The stock and flow variable.Figure 4. Casual diagram of the TREND function.nects related variables together and shows the influencesamong them. The positive sign on the arrow shows in-creasing Y by increment of X and negative sign indicatesdecreasing of Y .2.2 Stocks and FlowsOne of the most limitations of casual loops is their inabilityin capturing the stocks and flows structure of the system.Stock structures are other tools in studying the systemdynamics, which accumulate difference between inflow andoutflow of a variable as shown in Fig. 3. Equation (1)expresses the relation of stocks, which create inertia inthe system and provide memory for it; they are helpfulfor creating delays in a system by accumulating the differ-ence between the inflow and outflow of a parameter in aprocess:Y (t) =t0X1(τ) − X2(τ)dτ + Y (t0) (1)2.3 ForecastingBounded rationality hypothesis (BRH) is a forecastingalgorithm formed by adaptive expectation, in which cur-rent expectations are related to the current and past val-ues as in (2). Expectations on the value of variablesfor time T are revised with adjustment rate κ, if fore-casted value in previous periods is different from the actualamount [49]:ξe(t, T) = ξe(t, T − 1) + κ[ξ(T − 1) − ξe(t, T − 1)] (2)Sterman has proposed an expectational model basedon the system dynamics, called TREND function; he hasused needed times for measuring, collecting and analysingdata, historic time horizon and required time for perceivingand reacting to variable changes. Figure 4 representsthe structure of TREND function, which is usable forestimating fractional growth rate in input variable [46].22Figure 5. Process of capacity expansion in a power market.3. Model DescriptionFigure 5 represents an overview of developed model. Thefirms adjust their offers considering their marginal costand forecasted market price. Offers, existent capacityand average of demand are submitted to the power mar-ket for clearing market price and generation amount byeach firm. Clearing the market facilitates calculation ofprofits and generation costs, considering the investmentcosts. The profits are normalized and converted into in-vestment through some multipliers, which create underconstruction and generation capacities after some delays.The existent capacities return to the market via offer,which forms main feedback loop in this process. Re-serve ratio makes an internal loop by changing the launchscale for providing the proposed reliability level. Hubprice of natural gas acts on fuel cost of natural gas-based technologies and affects city gate price via seasonalfactors. Details of different parts of the model are asfollows.3.1 CostsMarginal and investment costs are two expenses for gener-ating electricity. The firms settle the marginal cost for gen-erating each MWh of electric energy including fuel, CO2and O&M costs, which grows with constant rate of returnevery year as indicated in (3) [1], [4]; HRj denotes requiredthermal energy for power generation by a technology inBtu/KWh and decreases every year [4]:MCj = (Fj·HRj + O&Mj + CO2j)(1 + rr)y. (3)Investment cost is settled through the construction pe-riod and must be recovered during the operation. Validreports have expressed the investment cost in $/KW [1],[4], which is convertible into $/KWh using life time ofeach technology in (4). The offers are adjusted using themarginal cost and the investment cost must be recovered23under the influence of market condition during the opera-tion period:ICj($/KWh) =ICj($/KW)LTj × 8760(1 + rr)y. (4)3.2 Electric DemandDemand of electric energy is modelled by load durationcurve (LDC) for base, middle and peak sections, whichare supplied by coal-fired, CCGT and GT, respectively; itgrows in each section with a constant growth rate everyyear and the average amount by (5) is offered to the marketas market demand. Market price affects the demand viademand elasticity:D(t) =ki=1δi·Li·eg·y− λ·Δρ. (5)3.3 Power MarketThis paper considers an energy-only market with pay-as-bid structure, in which the lowest offers are dispatched andreceive their offers from the market and market price isequal to average offer. The superiority of this structure ineliminating price spikes persuaded some markets to preferit over the uniform price. The firms should adjust theiroffers properly, above the MC and below their predictionof price via the TREND function; they should make abalance between their profit and the chance to win in themarket [3], [45].3.4 ProfitabilityClearing the market specifies the generation of each firm,which is applicable in computing their costs and profits.Total generation cost, in (6), is the sum of firm’s expensesfor generating electric energy until studied time t:Φj =t0Gj·MCjdt (6)By subtracting the generation and investment costsfrom the income, the total profit of the firms is given byΠj =t0Gj·χj − Gj·MCj − CPj·ICjdt (7)Profitability index is defined in (8), as the ratio ofprofit to generation cost, for normalizing the profits to asame quantity [46]. This parameter is helpful in investingin a technology rather than its profit:PIj =ΠjΦj(8)3.5 Stable StateA market can become stable by recovering its generationand investment costs of the firms [45]. This condition isequivalent to PIj = 0, as both costs are considered in PIj.The firms can reach the stable state by offering a priceequal to MC plus a multiple of forecasted price [3], namedas stable price.3.6 Capacity ExpansionThe PIs of firms are converted into investment rate viaS-shaped curves in (9), which limit the rate of variationsand final values in each firm [46]. The coefficients mj max,αj and βj differ in each technology, but mj is equal to 1 forPIj = 1 in the whole, as indicated in Fig. 6. The coefficientmj is influenced by reliability policy and profitability forproviding enough capacity:mj =mj max1 + e−(αj P Ij −βj )(9)Figure 6. The coefficient m for different technologies vs. PI.Equation (10) gives investment rate in each technologyas a function of demand growth rate and retirement rateof the firms weighted by the coefficient mj:IRj = mj·( ˙Li + ˙REj) (10)Reliability policy in (11) forms an internal loop inlaunching process, named as launch scale [9] that changesrate of investment in each technology for holding reserveratio at a proposed level:Res.Rat =TCP − D(t)D(t)(11)The investment rate is converted into capacity af-ter a construction delay. Equation (12) indicates underconstruction capacity, which is the difference between in-vestment rate and construction rate in each technology.Exploited capacity in (13) is the difference between con-structed capacity and retired amount after a life time.A part of GT capacity is converted into CCGT by a change24ratio and change delay that influences the pattern of ex-pansion. Operational capacity is declared to the marketand creates the main feedback loop in this process; besides,it is used for providing reliability as an internal loop:UCj =t0IRj − IRj(t − CTj)dt (12)CPj =t0CNj − CNj(t − LTj)dt (13)3.7 Wind TechnologyThe wind technology competes with other participants inthe market, while previous studies subtracted its capacityfrom the demand [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [8] gives the seasonal factorsas shown in Fig. 7. These factors adapt to additive modelthat makes the real variable by adding a seasonal factor.Figure 7. The seasonal factors of the city gate natural gasprice.4. Simulation and ResultsThis section analyses the results of simulating differentstates of natural gas consumption in the power systemin three scenarios including firms stability, changes in thenatural gas charge and access of demand to the natural gasand electricity. Some results such as the profitability index,reserve ratio, and capacity expansion are represented andcompared with the base state in each scenario. The appliedparameters in the simulation are from the published databy the EIA on the generation costs by different technolo-gies, natural gas city gate prices and natural gas hub prices.The results represent the statue of the parameters in 1,200months for indicating the stability of the developed model.4.1 Base ScenarioIn this scenario, the firms stay on the stable state by ad-justing the offers for recovering the generation and invest-ment costs [45] that is achievable by PIj = 0 in (8), due toits association to these costs. They adjust their offers byadding multiples of the forecasted price to their marginalcost, which are 0.13, 0.083, 0.058 and 0.45 for the coal-fired, CCGT, GT and wind, respectively. The technologieswith higher investment cost need a greater coefficient forgetting to the stability.Figure 8 represents the profitability index of the firmsin this scenario, which tends to zero during the studiedhorizon. The variation of the PI around zero is a moti-vation for expanding the capacity by different technologiesbeside the growing demand.Table 1 summarizes the total present profit of the firmsin this scenario. The coal-fired earns the most profit bysupplying the base load and the CCGT and GT are at thenext places. The wind earns the least profit in the stablestate.Figure 9 represents the reserve ratio of the powersystem calculated by (11) for providing the reliability ofthe power system, which swings around 0.2 with a limitedvariation between 0.18 and 0.22.The reliability level is achieved by the pattern of gener-ation capacity, shown in Fig. 10. The capacity of the coal-fired, CCGT and GT gets to 8.8 × 104MW, 4.8 × 104MWand 3.3 × 104MW for supplying the base, middle and peakloads, respectively and the wind technology expands itscapacity to 1,400 MW in the stable state.25Figure 8. The profitability index of the firms in the base scenario: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 1Total Present Profit of the Firms at the Base ScenarioTechnology Profit ($)Coal-fired 3 × 106CCGT 0.94 × 106GT 0.33 × 106Wind 0.085 × 106Figure 9. The reserve ratio of the power system in the basescenario.4.2 Natural Gas Price VariationThe second scenario investigates the influence of the vari-ations in the natural gas price on the long-run investmentin the capacity expansion. The variations are modelled aslow-price, medium-price and high-price outlines, summa-rized in Table A.1 [6], [48], [38]. The results of the high andFigure 10. The capacity of different technologies in thebase scenario.Figure 11. The price of electric energy for different outlinesof natural gas price.low prices of natural gas are compared with the mediumprice as base scenario.Figure 11 represents the price of electric energy fordifferent outlines of natural gas price. The electric price26Figure 12. The profitability index of the firms at the high price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 2Total Present Profit of the Firms at the High Price ofNatural GasTechnology Profit ($)Coal-fired 24 × 106CCGT 4.3 × 106GT −1.3 × 106Wind 3.4 × 106increases by growing the natural gas price and decreasesby its decline, compared with the medium price.Figure 12 indicates the profitability index of the firmsat the high price of natural gas. The PI increases to0.04, 0.01 and 0.33 for the coal-fired, CCGT and wind,respectively, but decreases to −0.0002 for the GT, due tothe loss of opportunity for generation by this technology.Reducing the heat rate of the GT, increases its PI tozero on month 900 by raising its generation chance anddecreases the PI of the coal-fired in Figs. 12(a) and (c).The present profit of the firms changes by their devi-ation from the stable state, summarized in Table 2. Theprofit of the coal-fired, CCGT and wind increases , com-pared with Table 1, but the high price is disadvantageousfor the GT and causes its negative profit in Table 2.The average of the reserve ratio does not change signif-icantly at the high price and grows to the average of 0.21with a pattern same as Fig. 9. Compared with Fig. 10, theFigure 13. The capacity of different technologies at thehigh price of natural gas.capacity of different firms changes as indicated in Fig. 13;the capacity of the coal-fired and the wind increases to9 × 104MW and 7,300 MW, respectively, but it decreasesto 4.4 × 104MW and 3 × 104MW for the CCGT and GT,which shows the reduced share of the natural gas consumersin the market and the great ratio of capacity expansion bythe wind at high prices.Decreasing the charge of the natural gas, drops theelectric price in the market, which leads to the loss of thefirms at the stable offer, due to irretrievable investmentcosts. The profitability index of the firms drops to −0.0073,−0.007, −0.0035 and −0.49 for the coal-fired, CCGT, GTand wind in Fig. 14.Table 3 summarizes the present profit of the firms atthe low charge of natural gas, which is negative for thewhole and results in their loss by offering the stable price.27Figure 14. The profitability index of the firms at the low price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 3Total Present Profit of the Firms at the Low Price ofNatural GasTechnology Profit ($)Coal-fired −2.8 × 106CCGT −1.3 × 106GT −0.58 × 106Wind −0.15 × 106Figure 15. The capacity of different technologies at the lowprice of natural gas.Low-price natural gas does not influence the reliabilityof the power system remarkably and decreases the aver-age of the reserve ratio to the amount 0.19 with the be-haviour same as Fig. 9. The pattern of generation capacitychanges at low charge of natural gas as shown in Fig. 15.The capacity of the CCGT and the GT increases to4.9 × 104MW and 3.4 × 104MW, while the amount of thecoal-fired and the wind decreases to 8.7 × 104MW and540 MW, respectively. This variation increases the share oftechnologies in the market that consume the natural gas.4.3 Natural Gas Consumption by the DemandThis section analyses the access to the electricity and nat-ural gas as two separate energy resources by 10% of thedemand. The demand switches between these energy re-sources by comparing the electric market price and naturalgas city gate price and choosing the cheapest one.Figure 16 represents the PI of the firms, when 10%of the demand selects between two energy resources. ThePI of the coal-fired decreases to −0.033 in Fig. 16a, but itdoes not change for the other technologies significantly.Table 4 summarizes the present profit of the firms atthe selection of the natural gas by the demand. The loss ofthe profit by the coal-fired is severe, due to the variations inthe base demand, which enforces it to increase its coefficientin the offer. The present profit of the other technologiesdoes not change a lot in this scenario, compared withTable 1.The resource selection by the demand enforces thefirms to expand the capacity for a discontinuous demand,which is detectable in the capacity of different technologiesin Fig. 17. The capacity of the coal-fired, CCGT and GTincreases with swings to 10 × 104MW, 5.8 × 104MW and3.7 × 104MW, respectively. The wind capacity decreasesto 1,047 MW in this scenario.28Figure 16. The profitability index of the firms at the natural gas consumption by the demand scenario: (a) coal-fired;(b) CCGT; (c) GT; and (d) wind.Table 4Total Present Profit of the Firms at the Natural GasConsumption by the Demand ScenarioTechnology Profit ($)Coal-fired −23.1 × 106CCGT 1 × 106GT 0.31 × 106Wind 0.072 × 106Figure 17. The capacity of different technologies at thenatural gas consumption by the demand scenario.Figure 18. The reserve ratio of the power system at thenatural gas consumption by the demand scenario.This pattern of capacity has a negative influence onthe reserve ratio of the power system for providing thereliability as shown in Fig. 18. The average of the reserveratio swings around the average amount of 0.35 and variesbetween 0.15 and 0.6 in this figure. Increasing the accessof the demand to both energy resources from 10% createsundesirable effects on the profitability and reserve ratio.The efficiency of the natural gas consumption by thedemand is an effective factor for keeping the stability ofthe electric market. Growing the efficiency of the naturalgas consumption to above 50%, restores the stable stateof the firms in the market by keeping the PI of the firmsat the zero and the reserve ratio on 0.2 with a little swingsame as Figs. 8 and 9. High efficient natural gas demands29are dismissed form the electric market, which decreases theinstalled capacity at the stable state and its swings.5. DiscussionThe natural gas affects the power market in generationand consumption levels. Based on the hub price of naturalgas, three scenarios can be defined including, low, mediumand high charges. The access of demand to the natural gasaffects the market via the seasonal factors.The stable state (PI = 0) which is considered as thebase scenario compensates the generation and investmentcosts of the firms and keeps the reserve ratio on about0.2 for providing the reliability. This state is achieved byadding a multiple of the forecasted price to the MC by thefirms, which is 0.13, 0.083, 0.058 and 0.45 for the coal-fired,CCGT, GT and wind, respectively; the technologies withhigher investment cost adjust their offer with a greatercoefficient. The Medium price of natural gas is consideredin the base scenario.High-charge natural gas increases the market price andthe firms offers, which increases the profitability index ofthe coal-fired, CCGT and wind from zero to 0.04, 0.01 and0.33, respectively; however, this charge decreases the gener-ation opportunity for GT and decreases its PI to −0.0002.So, the GT should decrease its coefficient during high priceof natural gas for creating generation opportunity. Byincreasing the natural gas price reaches the capacity of GTand CCGT increases from 4.8 × 104MW and 3.3 × 104MWto 4.4 × 104MW and 3 × 104MW and the share of naturalgas-based technologies in the market decreases. However,increasing the profit creates the opportunity for the coal-fired and wind to expand their capacity and increase theirshare from 8.8 × 104MW and 1,400 MW at the stable stateto 9 × 104MW and 7,300 MW. The average of reserve ratiogrows from 0.2 to 0.21 in this situation.Low-charge natural gas decreases the average pricein the market and reduces the PI of coal-fired, CCGT,GT and wind to −0.0073, −0.007, −0.0035 and −0.49,respectively, which results in the loss of the firms. Theshare of CCGT and GT increases to 4.9 × 104MW and3.4 × 104MW in the market, while the capacity ofthe coal-fired and wind decreases to 8.7 × 104MW and540 MW. The capacity expansion is due to the effects ofdemand growth rate and retirement rate on the invest-ment rate for providing the proposed reliability level ofabout 0.19.The charge of natural gas at the consumption level isinfluenced by seasonal factors, which has additive patternand its amount is greater in colder months. Natural gasconsumption by demand decreases the profitability indexof the coal-fired to −0.033 as base supplier. This conditionenforces the firms to expand their capacity, while theirgeneration is not consumed by the demand continuously,which hardens recovering the investment. Choosing thecheapest energy resource by the demand keeps the PIof the CCGT, GT and wind at zero and increasing thepercentage of demand access decreases the PI of CCGTand GT. The capacity of coal-fired, CCGT, GT and windreaches to 10 × 104MW, 5.8 × 104MW, 3.7 × 104MW and1,047 MW. Switching between the energy resources by thedemand causes the swing of the reserve ratio, which isresolved by increasing the efficiency of the natural gasconsumers.6. ConclusionThis paper analyses the effect of the natural gas on thecapacity expansion by the firms in a pay-as-bid energy-only market using the system dynamics. Natural gas-basedtechnologies and demand selection between the electricityand natural gas are two considered tie points between theseresources. This subject is studied via three scenarios,namely, (1) the firms stability, (2) changes in the naturalgas charge and (3) access of demand to natural gas andelectricity. Four generation technologies including coal-fired, CCGT, GT and wind participate in an energy-onlymarket using the published data in the reports of EIA.At the first scenario, the firms adjust their offersabove the marginal cost for recovering the generation andinvestment costs as stable state, which is known by PIj = 0.The firms adjust their offers by adding a multiple of theforecasted price to the marginal cost, which is greater forthe technologies with higher investment cost. The stablestate can recover the costs of the firms and provide thetargeted reliability level of the power system.The natural gas price as assumed to fluctuate betweenlow, medium and high prices, where the medium priceis applied at the base scenario. High-price natural gasincreases the offers of the firms and the market price, whichincreases the profit of the coal-fired, CCGT and wind, butcauses the loss of the profit by the GT, as it loses theopportunity for generation. More profit increment by coal-fired and loss of GT reduces the share of natural gas-basedtechnologies in the market at high charges of natural gas.Low-price natural gas decreases the offers and market priceto an amount, which cannot recover the investment costsand causes the loss of the whole. The capacity is expandedfor supplying the demand and compensating the retirementwith a less ramp. The loss of coal-fired and wind in lowcharge is more severe due to their higher investment costs,which increases the share of natural gas-based technologiesin the market. The reserve ratio of the power systemdoes not change remarkably by changing the natural gasprice.Selecting the natural gas as resource of energy by aportion of demand causes the loss of profit by the coal-firedand does not influence on the revenue of the rest. Thisbehaviour of demand expands the generation capacity andincreases the average of reserve ratio, but creates swing init. Increasing the per cent of demand access to the naturalgas intensifies the unstable condition in the market. Thegrowth of efficiency in the natural gas demand dismisses itfrom the power market and restores it to the stability.Appendix ATable A.1 summarizes the parameters of the simulation,which are from the published report by EIA [4].30Table A.1The Parameters of the SimulationTechnology Coal-Fired CCGT GT WindParameterFuel Cost 65 ($/ton) Low Price = 3.8 $/MMBtuThermal Value Medium Price = 4.6 $/MMBtu= 6080 kcal/kg High price = 6 $/MMBtuHeat rate (Btu/KWh) 9,200 6,752 9,289Heat rate changes (Btu/KWh year) −30 −28 −50O&M costs ($/MWh) 7.7 3.3 4.3 3.4CO2 costs ($/MWh) 24 10.5 16Investment costs ($/MWh) 3.7 3.3 2.3 10.97Construction time (months) 48 36 24 6Life time (months) 720 360 360 240Rate of return (%/year) 5%Peak demand (MW) 1,200Peak duration 0.2Middle demand (MW) 1,000Middle duration 0.6Base demand (MW) 700Base duration 0.2Demand growth rate (%/year) 5%Rated wind speed (m/s) 7Product wind speed (m/s) 4Cut out wind speed (m/s) 13References[1] “Projected Costs of Generating Electricity , International En-ergy Agency, 2010 Edition.[2] S. 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Ford, Cycles in competitive electricity markets: A simulationstudy of the western United States, Energy Policy, (27), 1999,637–658.[30] J.D.M. Bastidas, C.J. Franco, and F. Angulo, Delays inelectricity market models, Energy Strategy Reviews, (16), 2017,24–32. DOI: 10.1016/j.esr.2017.02.004.[31] Y. Liu, Y.X. Ni, and F.F. Wu, A novel framework for thestudy of strategic bidding impacts on power market stabilityand equilibrium, International Journal of Power and EnergySystems, 2007. DOI: 10.2316/Journal.203.2007.3.203-3640.[32] Q. Jiang, Y. Wang, and H. Lin, Analysis on relation-ship between electricity wholesale market and retail marketbased on system dynamics method, 2016. DOI: 10.7500/AEPS20160627004.[33] A. Gholizad, L. Ahmadi, E. HassanNayebi, and M. Shak-ibayifar, A system dynamics model for the analysis of thederegulation in electricity market, 2017, DOI: 10.4018/IJSDA.2017040101.[34] X. Zhang, Y. Liang, and W. Liu, Pricing model for the chargingof electric vehicles based on system dynamics in Beijing, Energy,(119), 2017, 218–234. DOI: 10.1016/j.energy.2016.12.057.[35] T.J. Hammons, L.A. Barroso, and H. Rudnick, Integratednatural gas-electricity resources adequacy planning in LatinAmerica, International Journal of Power and Energy Systems,2010. DOI: 10.2316/Journal.203.2010.1.203-3894. [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6], [38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [8] gives the seasonal factorsas shown in Fig. 7. These factors adapt to additive modelthat makes the real variable by adding a seasonal factor.Figure 7. The seasonal factors of the city gate natural gasprice.4. Simulation and ResultsThis section analyses the results of simulating differentstates of natural gas consumption in the power systemin three scenarios including firms stability, changes in thenatural gas charge and access of demand to the natural gasand electricity. Some results such as the profitability index,reserve ratio, and capacity expansion are represented andcompared with the base state in each scenario. The appliedparameters in the simulation are from the published databy the EIA on the generation costs by different technolo-gies, natural gas city gate prices and natural gas hub prices.The results represent the statue of the parameters in 1,200months for indicating the stability of the developed model.4.1 Base ScenarioIn this scenario, the firms stay on the stable state by ad-justing the offers for recovering the generation and invest-ment costs [45] that is achievable by PIj = 0 in (8), due toits association to these costs. They adjust their offers byadding multiples of the forecasted price to their marginalcost, which are 0.13, 0.083, 0.058 and 0.45 for the coal-fired, CCGT, GT and wind, respectively. The technologieswith higher investment cost need a greater coefficient forgetting to the stability.Figure 8 represents the profitability index of the firmsin this scenario, which tends to zero during the studiedhorizon. The variation of the PI around zero is a moti-vation for expanding the capacity by different technologiesbeside the growing demand.Table 1 summarizes the total present profit of the firmsin this scenario. The coal-fired earns the most profit bysupplying the base load and the CCGT and GT are at thenext places. The wind earns the least profit in the stablestate.Figure 9 represents the reserve ratio of the powersystem calculated by (11) for providing the reliability ofthe power system, which swings around 0.2 with a limitedvariation between 0.18 and 0.22.The reliability level is achieved by the pattern of gener-ation capacity, shown in Fig. 10. The capacity of the coal-fired, CCGT and GT gets to 8.8 × 104MW, 4.8 × 104MWand 3.3 × 104MW for supplying the base, middle and peakloads, respectively and the wind technology expands itscapacity to 1,400 MW in the stable state.25Figure 8. The profitability index of the firms in the base scenario: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 1Total Present Profit of the Firms at the Base ScenarioTechnology Profit ($)Coal-fired 3 × 106CCGT 0.94 × 106GT 0.33 × 106Wind 0.085 × 106Figure 9. The reserve ratio of the power system in the basescenario.4.2 Natural Gas Price VariationThe second scenario investigates the influence of the vari-ations in the natural gas price on the long-run investmentin the capacity expansion. The variations are modelled aslow-price, medium-price and high-price outlines, summa-rized in Table A.1 [6], [48], [38]. The results of the high andFigure 10. The capacity of different technologies in thebase scenario.Figure 11. The price of electric energy for different outlinesof natural gas price.low prices of natural gas are compared with the mediumprice as base scenario.Figure 11 represents the price of electric energy fordifferent outlines of natural gas price. The electric price26Figure 12. The profitability index of the firms at the high price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 2Total Present Profit of the Firms at the High Price ofNatural GasTechnology Profit ($)Coal-fired 24 × 106CCGT 4.3 × 106GT −1.3 × 106Wind 3.4 × 106increases by growing the natural gas price and decreasesby its decline, compared with the medium price.Figure 12 indicates the profitability index of the firmsat the high price of natural gas. The PI increases to0.04, 0.01 and 0.33 for the coal-fired, CCGT and wind,respectively, but decreases to −0.0002 for the GT, due tothe loss of opportunity for generation by this technology.Reducing the heat rate of the GT, increases its PI tozero on month 900 by raising its generation chance anddecreases the PI of the coal-fired in Figs. 12(a) and (c).The present profit of the firms changes by their devi-ation from the stable state, summarized in Table 2. Theprofit of the coal-fired, CCGT and wind increases , com-pared with Table 1, but the high price is disadvantageousfor the GT and causes its negative profit in Table 2.The average of the reserve ratio does not change signif-icantly at the high price and grows to the average of 0.21with a pattern same as Fig. 9. Compared with Fig. 10, theFigure 13. The capacity of different technologies at thehigh price of natural gas.capacity of different firms changes as indicated in Fig. 13;the capacity of the coal-fired and the wind increases to9 × 104MW and 7,300 MW, respectively, but it decreasesto 4.4 × 104MW and 3 × 104MW for the CCGT and GT,which shows the reduced share of the natural gas consumersin the market and the great ratio of capacity expansion bythe wind at high prices.Decreasing the charge of the natural gas, drops theelectric price in the market, which leads to the loss of thefirms at the stable offer, due to irretrievable investmentcosts. The profitability index of the firms drops to −0.0073,−0.007, −0.0035 and −0.49 for the coal-fired, CCGT, GTand wind in Fig. 14.Table 3 summarizes the present profit of the firms atthe low charge of natural gas, which is negative for thewhole and results in their loss by offering the stable price.27Figure 14. The profitability index of the firms at the low price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 3Total Present Profit of the Firms at the Low Price ofNatural GasTechnology Profit ($)Coal-fired −2.8 × 106CCGT −1.3 × 106GT −0.58 × 106Wind −0.15 × 106Figure 15. The capacity of different technologies at the lowprice of natural gas.Low-price natural gas does not influence the reliabilityof the power system remarkably and decreases the aver-age of the reserve ratio to the amount 0.19 with the be-haviour same as Fig. 9. The pattern of generation capacitychanges at low charge of natural gas as shown in Fig. 15.The capacity of the CCGT and the GT increases to4.9 × 104MW and 3.4 × 104MW, while the amount of thecoal-fired and the wind decreases to 8.7 × 104MW and540 MW, respectively. This variation increases the share oftechnologies in the market that consume the natural gas.4.3 Natural Gas Consumption by the DemandThis section analyses the access to the electricity and nat-ural gas as two separate energy resources by 10% of thedemand. The demand switches between these energy re-sources by comparing the electric market price and naturalgas city gate price and choosing the cheapest one.Figure 16 represents the PI of the firms, when 10%of the demand selects between two energy resources. ThePI of the coal-fired decreases to −0.033 in Fig. 16a, but itdoes not change for the other technologies significantly.Table 4 summarizes the present profit of the firms atthe selection of the natural gas by the demand. The loss ofthe profit by the coal-fired is severe, due to the variations inthe base demand, which enforces it to increase its coefficientin the offer. The present profit of the other technologiesdoes not change a lot in this scenario, compared withTable 1.The resource selection by the demand enforces thefirms to expand the capacity for a discontinuous demand,which is detectable in the capacity of different technologiesin Fig. 17. The capacity of the coal-fired, CCGT and GTincreases with swings to 10 × 104MW, 5.8 × 104MW and3.7 × 104MW, respectively. The wind capacity decreasesto 1,047 MW in this scenario.28Figure 16. The profitability index of the firms at the natural gas consumption by the demand scenario: (a) coal-fired;(b) CCGT; (c) GT; and (d) wind.Table 4Total Present Profit of the Firms at the Natural GasConsumption by the Demand ScenarioTechnology Profit ($)Coal-fired −23.1 × 106CCGT 1 × 106GT 0.31 × 106Wind 0.072 × 106Figure 17. The capacity of different technologies at thenatural gas consumption by the demand scenario.Figure 18. The reserve ratio of the power system at thenatural gas consumption by the demand scenario.This pattern of capacity has a negative influence onthe reserve ratio of the power system for providing thereliability as shown in Fig. 18. The average of the reserveratio swings around the average amount of 0.35 and variesbetween 0.15 and 0.6 in this figure. Increasing the accessof the demand to both energy resources from 10% createsundesirable effects on the profitability and reserve ratio.The efficiency of the natural gas consumption by thedemand is an effective factor for keeping the stability ofthe electric market. Growing the efficiency of the naturalgas consumption to above 50%, restores the stable stateof the firms in the market by keeping the PI of the firmsat the zero and the reserve ratio on 0.2 with a little swingsame as Figs. 8 and 9. High efficient natural gas demands29are dismissed form the electric market, which decreases theinstalled capacity at the stable state and its swings.5. DiscussionThe natural gas affects the power market in generationand consumption levels. Based on the hub price of naturalgas, three scenarios can be defined including, low, mediumand high charges. The access of demand to the natural gasaffects the market via the seasonal factors.The stable state (PI = 0) which is considered as thebase scenario compensates the generation and investmentcosts of the firms and keeps the reserve ratio on about0.2 for providing the reliability. This state is achieved byadding a multiple of the forecasted price to the MC by thefirms, which is 0.13, 0.083, 0.058 and 0.45 for the coal-fired,CCGT, GT and wind, respectively; the technologies withhigher investment cost adjust their offer with a greatercoefficient. The Medium price of natural gas is consideredin the base scenario.High-charge natural gas increases the market price andthe firms offers, which increases the profitability index ofthe coal-fired, CCGT and wind from zero to 0.04, 0.01 and0.33, respectively; however, this charge decreases the gener-ation opportunity for GT and decreases its PI to −0.0002.So, the GT should decrease its coefficient during high priceof natural gas for creating generation opportunity. Byincreasing the natural gas price reaches the capacity of GTand CCGT increases from 4.8 × 104MW and 3.3 × 104MWto 4.4 × 104MW and 3 × 104MW and the share of naturalgas-based technologies in the market decreases. However,increasing the profit creates the opportunity for the coal-fired and wind to expand their capacity and increase theirshare from 8.8 × 104MW and 1,400 MW at the stable stateto 9 × 104MW and 7,300 MW. The average of reserve ratiogrows from 0.2 to 0.21 in this situation.Low-charge natural gas decreases the average pricein the market and reduces the PI of coal-fired, CCGT,GT and wind to −0.0073, −0.007, −0.0035 and −0.49,respectively, which results in the loss of the firms. Theshare of CCGT and GT increases to 4.9 × 104MW and3.4 × 104MW in the market, while the capacity ofthe coal-fired and wind decreases to 8.7 × 104MW and540 MW. The capacity expansion is due to the effects ofdemand growth rate and retirement rate on the invest-ment rate for providing the proposed reliability level ofabout 0.19.The charge of natural gas at the consumption level isinfluenced by seasonal factors, which has additive patternand its amount is greater in colder months. Natural gasconsumption by demand decreases the profitability indexof the coal-fired to −0.033 as base supplier. This conditionenforces the firms to expand their capacity, while theirgeneration is not consumed by the demand continuously,which hardens recovering the investment. Choosing thecheapest energy resource by the demand keeps the PIof the CCGT, GT and wind at zero and increasing thepercentage of demand access decreases the PI of CCGTand GT. The capacity of coal-fired, CCGT, GT and windreaches to 10 × 104MW, 5.8 × 104MW, 3.7 × 104MW and1,047 MW. Switching between the energy resources by thedemand causes the swing of the reserve ratio, which isresolved by increasing the efficiency of the natural gasconsumers.6. ConclusionThis paper analyses the effect of the natural gas on thecapacity expansion by the firms in a pay-as-bid energy-only market using the system dynamics. Natural gas-basedtechnologies and demand selection between the electricityand natural gas are two considered tie points between theseresources. This subject is studied via three scenarios,namely, (1) the firms stability, (2) changes in the naturalgas charge and (3) access of demand to natural gas andelectricity. Four generation technologies including coal-fired, CCGT, GT and wind participate in an energy-onlymarket using the published data in the reports of EIA.At the first scenario, the firms adjust their offersabove the marginal cost for recovering the generation andinvestment costs as stable state, which is known by PIj = 0.The firms adjust their offers by adding a multiple of theforecasted price to the marginal cost, which is greater forthe technologies with higher investment cost. The stablestate can recover the costs of the firms and provide thetargeted reliability level of the power system.The natural gas price as assumed to fluctuate betweenlow, medium and high prices, where the medium priceis applied at the base scenario. High-price natural gasincreases the offers of the firms and the market price, whichincreases the profit of the coal-fired, CCGT and wind, butcauses the loss of the profit by the GT, as it loses theopportunity for generation. More profit increment by coal-fired and loss of GT reduces the share of natural gas-basedtechnologies in the market at high charges of natural gas.Low-price natural gas decreases the offers and market priceto an amount, which cannot recover the investment costsand causes the loss of the whole. The capacity is expandedfor supplying the demand and compensating the retirementwith a less ramp. The loss of coal-fired and wind in lowcharge is more severe due to their higher investment costs,which increases the share of natural gas-based technologiesin the market. The reserve ratio of the power systemdoes not change remarkably by changing the natural gasprice.Selecting the natural gas as resource of energy by aportion of demand causes the loss of profit by the coal-firedand does not influence on the revenue of the rest. Thisbehaviour of demand expands the generation capacity andincreases the average of reserve ratio, but creates swing init. Increasing the per cent of demand access to the naturalgas intensifies the unstable condition in the market. Thegrowth of efficiency in the natural gas demand dismisses itfrom the power market and restores it to the stability.Appendix ATable A.1 summarizes the parameters of the simulation,which are from the published report by EIA [4].30Table A.1The Parameters of the SimulationTechnology Coal-Fired CCGT GT WindParameterFuel Cost 65 ($/ton) Low Price = 3.8 $/MMBtuThermal Value Medium Price = 4.6 $/MMBtu= 6080 kcal/kg High price = 6 $/MMBtuHeat rate (Btu/KWh) 9,200 6,752 9,289Heat rate changes (Btu/KWh year) −30 −28 −50O&M costs ($/MWh) 7.7 3.3 4.3 3.4CO2 costs ($/MWh) 24 10.5 16Investment costs ($/MWh) 3.7 3.3 2.3 10.97Construction time (months) 48 36 24 6Life time (months) 720 360 360 240Rate of return (%/year) 5%Peak demand (MW) 1,200Peak duration 0.2Middle demand (MW) 1,000Middle duration 0.6Base demand (MW) 700Base duration 0.2Demand growth rate (%/year) 5%Rated wind speed (m/s) 7Product wind speed (m/s) 4Cut out wind speed (m/s) 13References[1] “Projected Costs of Generating Electricity , International En-ergy Agency, 2010 Edition.[2] S. 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Salazar, A holisticapproach for planning natural gas and electricity distributionnetworks, IEEE Transactions on Power Systems, 28(4), 2013,4052–4063. [40] S. Spiecker, Modeling market power by natural gas producersand its impact on the power system, IEEE Transactions onPower Systems, 28(4), 2013, 3737–3746. [41] T. Li, M. Eremia, and M. Shahidehpour, Interdependencyof natural gas network and power system security, IEEETransactions on Power Systems,23(4), 2008, 1817–1824. [42] M. Shahedipour, Y. Fu, and T. Wiedman, Impact of naturalgas infrastructure on electric power systems, Proceedings ofthe IEEE, 93(5), 2005, 1042–1056. [44] studied the role of naturalgas in the power system via optimization problems andsolved it by different techniques. However, there is a gap inlong-run analysis of natural gas effect on the power systemfor accessing to a real-time view about this subject. Inthis regard, system dynamics is applied, which is a newidea in this field. The effect is studied in generation andconsumption levels.Four generation technologies including coal-fired,CCGT, GT and wind participate in a pay-as-bid energy-only market, which is chosen by some markets due toelimination of price spikes in this structure [3]. The studyis followed via three scenarios, namely stable state, naturalgas price variation and access of demand to natural gasand electricity. The first scenario enlarges market stability,which is known by recovering generation and investmentcosts. At the second scenario the effect of natural gascharge variation is analysed in low, medium and highcharges and the third scenario analyses the demand accessto both natural gas and electricity via seasonal factors.Unlike other researches, the wind participates at the en-ergy market beside the thermal firms, instead of decreasingits capacity from the demand. The applied data are frompublished reports by EIA about generation and investmentcosts of different technologies, natural gas hub price, natu-ral gas city gate price and etc., summarized in Appendix A.The rest of paper is organized as follows; Section 2 de-scribes the concept of system dynamics briefly by introduc-ing employed and important tools in this paper. Section 3explains general model and its different parts. The resultsof model simulation in defined scenarios are represented inSection 4 and Sections 5 and 6 discuss about the resultsand pluralize them, respectively. Appendix A summarizesthe applied data in this study.2. Concept of System DynamicsSystem dynamics was approached by Sterman for analysingcomplex systems and system thinking in a practicalmethod. Growing the dynamic complexity in business, in-dustrial and social systems increases the role of modelling,predicting and analysing their complex behaviour for un-derstanding its reasons. System dynamics is a method for21understanding and analysing the complex behaviours by aset of conceptual tools and modelling methods, which arehelpful in simulating the long-run behaviour of a system indifferent policies and making better decision.Feedback control theories and nonlinear dynamicsfound the base of system dynamics. For long-run analysisof a system, it is necessary to understand different effectivefactors and their causal relation. Moreover, identifyingfeedbacks, delays and other linearity which leads the sys-tem to instability and modelling them by stocks and flowsis the main art in analysing a system.Simulation is the only reliable way for testing the valid-ity of the models because of complexity of relations amongdifferent nonlinear parameters, which makes understand-ing the behaviour of the model in a long time period im-possible. Without simulation techniques, the system hardbehaviour can be improved using feedbacks through thereal world which is very slow and inefficient due to delays,nonliterary and costs of testing the ideas [46].2.1 Causal DiagramFor simulating a dynamic system, different tools areneeded. Causal loops are important tools for showing thestructure of the feedbacks in the system and their effects.A causal diagram, in Fig. 2, consists of arrows which con-Figure 2. The causal representation of a variable.Figure 3. The stock and flow variable.Figure 4. Casual diagram of the TREND function.nects related variables together and shows the influencesamong them. The positive sign on the arrow shows in-creasing Y by increment of X and negative sign indicatesdecreasing of Y .2.2 Stocks and FlowsOne of the most limitations of casual loops is their inabilityin capturing the stocks and flows structure of the system.Stock structures are other tools in studying the systemdynamics, which accumulate difference between inflow andoutflow of a variable as shown in Fig. 3. Equation (1)expresses the relation of stocks, which create inertia inthe system and provide memory for it; they are helpfulfor creating delays in a system by accumulating the differ-ence between the inflow and outflow of a parameter in aprocess:Y (t) =t0X1(τ) − X2(τ)dτ + Y (t0) (1)2.3 ForecastingBounded rationality hypothesis (BRH) is a forecastingalgorithm formed by adaptive expectation, in which cur-rent expectations are related to the current and past val-ues as in (2). Expectations on the value of variablesfor time T are revised with adjustment rate κ, if fore-casted value in previous periods is different from the actualamount [49]:ξe(t, T) = ξe(t, T − 1) + κ[ξ(T − 1) − ξe(t, T − 1)] (2)Sterman has proposed an expectational model basedon the system dynamics, called TREND function; he hasused needed times for measuring, collecting and analysingdata, historic time horizon and required time for perceivingand reacting to variable changes. Figure 4 representsthe structure of TREND function, which is usable forestimating fractional growth rate in input variable [46].22Figure 5. Process of capacity expansion in a power market.3. Model DescriptionFigure 5 represents an overview of developed model. Thefirms adjust their offers considering their marginal costand forecasted market price. Offers, existent capacityand average of demand are submitted to the power mar-ket for clearing market price and generation amount byeach firm. Clearing the market facilitates calculation ofprofits and generation costs, considering the investmentcosts. The profits are normalized and converted into in-vestment through some multipliers, which create underconstruction and generation capacities after some delays.The existent capacities return to the market via offer,which forms main feedback loop in this process. Re-serve ratio makes an internal loop by changing the launchscale for providing the proposed reliability level. Hubprice of natural gas acts on fuel cost of natural gas-based technologies and affects city gate price via seasonalfactors. Details of different parts of the model are asfollows.3.1 CostsMarginal and investment costs are two expenses for gener-ating electricity. The firms settle the marginal cost for gen-erating each MWh of electric energy including fuel, CO2and O&M costs, which grows with constant rate of returnevery year as indicated in (3) [1], [4]; HRj denotes requiredthermal energy for power generation by a technology inBtu/KWh and decreases every year [4]:MCj = (Fj·HRj + O&Mj + CO2j)(1 + rr)y. (3)Investment cost is settled through the construction pe-riod and must be recovered during the operation. Validreports have expressed the investment cost in $/KW [1],[4], which is convertible into $/KWh using life time ofeach technology in (4). The offers are adjusted using themarginal cost and the investment cost must be recovered23under the influence of market condition during the opera-tion period:ICj($/KWh) =ICj($/KW)LTj × 8760(1 + rr)y. (4)3.2 Electric DemandDemand of electric energy is modelled by load durationcurve (LDC) for base, middle and peak sections, whichare supplied by coal-fired, CCGT and GT, respectively; itgrows in each section with a constant growth rate everyyear and the average amount by (5) is offered to the marketas market demand. Market price affects the demand viademand elasticity:D(t) =ki=1δi·Li·eg·y− λ·Δρ. (5)3.3 Power MarketThis paper considers an energy-only market with pay-as-bid structure, in which the lowest offers are dispatched andreceive their offers from the market and market price isequal to average offer. The superiority of this structure ineliminating price spikes persuaded some markets to preferit over the uniform price. The firms should adjust theiroffers properly, above the MC and below their predictionof price via the TREND function; they should make abalance between their profit and the chance to win in themarket [3], [46].2.1 Causal DiagramFor simulating a dynamic system, different tools areneeded. Causal loops are important tools for showing thestructure of the feedbacks in the system and their effects.A causal diagram, in Fig. 2, consists of arrows which con-Figure 2. The causal representation of a variable.Figure 3. The stock and flow variable.Figure 4. Casual diagram of the TREND function.nects related variables together and shows the influencesamong them. The positive sign on the arrow shows in-creasing Y by increment of X and negative sign indicatesdecreasing of Y .2.2 Stocks and FlowsOne of the most limitations of casual loops is their inabilityin capturing the stocks and flows structure of the system.Stock structures are other tools in studying the systemdynamics, which accumulate difference between inflow andoutflow of a variable as shown in Fig. 3. Equation (1)expresses the relation of stocks, which create inertia inthe system and provide memory for it; they are helpfulfor creating delays in a system by accumulating the differ-ence between the inflow and outflow of a parameter in aprocess:Y (t) =t0X1(τ) − X2(τ)dτ + Y (t0) (1)2.3 ForecastingBounded rationality hypothesis (BRH) is a forecastingalgorithm formed by adaptive expectation, in which cur-rent expectations are related to the current and past val-ues as in (2). Expectations on the value of variablesfor time T are revised with adjustment rate κ, if fore-casted value in previous periods is different from the actualamount [49]:ξe(t, T) = ξe(t, T − 1) + κ[ξ(T − 1) − ξe(t, T − 1)] (2)Sterman has proposed an expectational model basedon the system dynamics, called TREND function; he hasused needed times for measuring, collecting and analysingdata, historic time horizon and required time for perceivingand reacting to variable changes. Figure 4 representsthe structure of TREND function, which is usable forestimating fractional growth rate in input variable [46].22Figure 5. Process of capacity expansion in a power market.3. Model DescriptionFigure 5 represents an overview of developed model. Thefirms adjust their offers considering their marginal costand forecasted market price. Offers, existent capacityand average of demand are submitted to the power mar-ket for clearing market price and generation amount byeach firm. Clearing the market facilitates calculation ofprofits and generation costs, considering the investmentcosts. The profits are normalized and converted into in-vestment through some multipliers, which create underconstruction and generation capacities after some delays.The existent capacities return to the market via offer,which forms main feedback loop in this process. Re-serve ratio makes an internal loop by changing the launchscale for providing the proposed reliability level. Hubprice of natural gas acts on fuel cost of natural gas-based technologies and affects city gate price via seasonalfactors. Details of different parts of the model are asfollows.3.1 CostsMarginal and investment costs are two expenses for gener-ating electricity. The firms settle the marginal cost for gen-erating each MWh of electric energy including fuel, CO2and O&M costs, which grows with constant rate of returnevery year as indicated in (3) [1], [4]; HRj denotes requiredthermal energy for power generation by a technology inBtu/KWh and decreases every year [4]:MCj = (Fj·HRj + O&Mj + CO2j)(1 + rr)y. (3)Investment cost is settled through the construction pe-riod and must be recovered during the operation. Validreports have expressed the investment cost in $/KW [1],[4], which is convertible into $/KWh using life time ofeach technology in (4). The offers are adjusted using themarginal cost and the investment cost must be recovered23under the influence of market condition during the opera-tion period:ICj($/KWh) =ICj($/KW)LTj × 8760(1 + rr)y. (4)3.2 Electric DemandDemand of electric energy is modelled by load durationcurve (LDC) for base, middle and peak sections, whichare supplied by coal-fired, CCGT and GT, respectively; itgrows in each section with a constant growth rate everyyear and the average amount by (5) is offered to the marketas market demand. Market price affects the demand viademand elasticity:D(t) =ki=1δi·Li·eg·y− λ·Δρ. (5)3.3 Power MarketThis paper considers an energy-only market with pay-as-bid structure, in which the lowest offers are dispatched andreceive their offers from the market and market price isequal to average offer. The superiority of this structure ineliminating price spikes persuaded some markets to preferit over the uniform price. The firms should adjust theiroffers properly, above the MC and below their predictionof price via the TREND function; they should make abalance between their profit and the chance to win in themarket [3], [45].3.4 ProfitabilityClearing the market specifies the generation of each firm,which is applicable in computing their costs and profits.Total generation cost, in (6), is the sum of firm’s expensesfor generating electric energy until studied time t:Φj =t0Gj·MCjdt (6)By subtracting the generation and investment costsfrom the income, the total profit of the firms is given byΠj =t0Gj·χj − Gj·MCj − CPj·ICjdt (7)Profitability index is defined in (8), as the ratio ofprofit to generation cost, for normalizing the profits to asame quantity [46]. This parameter is helpful in investingin a technology rather than its profit:PIj =ΠjΦj(8)3.5 Stable StateA market can become stable by recovering its generationand investment costs of the firms [45]. This condition isequivalent to PIj = 0, as both costs are considered in PIj.The firms can reach the stable state by offering a priceequal to MC plus a multiple of forecasted price [3], namedas stable price.3.6 Capacity ExpansionThe PIs of firms are converted into investment rate viaS-shaped curves in (9), which limit the rate of variationsand final values in each firm [46]. The coefficients mj max,αj and βj differ in each technology, but mj is equal to 1 forPIj = 1 in the whole, as indicated in Fig. 6. The coefficientmj is influenced by reliability policy and profitability forproviding enough capacity:mj =mj max1 + e−(αj P Ij −βj )(9)Figure 6. The coefficient m for different technologies vs. PI.Equation (10) gives investment rate in each technologyas a function of demand growth rate and retirement rateof the firms weighted by the coefficient mj:IRj = mj·( ˙Li + ˙REj) (10)Reliability policy in (11) forms an internal loop inlaunching process, named as launch scale [9] that changesrate of investment in each technology for holding reserveratio at a proposed level:Res.Rat =TCP − D(t)D(t)(11)The investment rate is converted into capacity af-ter a construction delay. Equation (12) indicates underconstruction capacity, which is the difference between in-vestment rate and construction rate in each technology.Exploited capacity in (13) is the difference between con-structed capacity and retired amount after a life time.A part of GT capacity is converted into CCGT by a change24ratio and change delay that influences the pattern of ex-pansion. Operational capacity is declared to the marketand creates the main feedback loop in this process; besides,it is used for providing reliability as an internal loop:UCj =t0IRj − IRj(t − CTj)dt (12)CPj =t0CNj − CNj(t − LTj)dt (13)3.7 Wind TechnologyThe wind technology competes with other participants inthe market, while previous studies subtracted its capacityfrom the demand [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds [47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [49]:ξe(t, T) = ξe(t, T − 1) + κ[ξ(T − 1) − ξe(t, T − 1)] (2)Sterman has proposed an expectational model basedon the system dynamics, called TREND function; he hasused needed times for measuring, collecting and analysingdata, historic time horizon and required time for perceivingand reacting to variable changes. Figure 4 representsthe structure of TREND function, which is usable forestimating fractional growth rate in input variable [46].22Figure 5. Process of capacity expansion in a power market.3. Model DescriptionFigure 5 represents an overview of developed model. Thefirms adjust their offers considering their marginal costand forecasted market price. Offers, existent capacityand average of demand are submitted to the power mar-ket for clearing market price and generation amount byeach firm. Clearing the market facilitates calculation ofprofits and generation costs, considering the investmentcosts. The profits are normalized and converted into in-vestment through some multipliers, which create underconstruction and generation capacities after some delays.The existent capacities return to the market via offer,which forms main feedback loop in this process. Re-serve ratio makes an internal loop by changing the launchscale for providing the proposed reliability level. Hubprice of natural gas acts on fuel cost of natural gas-based technologies and affects city gate price via seasonalfactors. Details of different parts of the model are asfollows.3.1 CostsMarginal and investment costs are two expenses for gener-ating electricity. The firms settle the marginal cost for gen-erating each MWh of electric energy including fuel, CO2and O&M costs, which grows with constant rate of returnevery year as indicated in (3) [1], [4]; HRj denotes requiredthermal energy for power generation by a technology inBtu/KWh and decreases every year [4]:MCj = (Fj·HRj + O&Mj + CO2j)(1 + rr)y. (3)Investment cost is settled through the construction pe-riod and must be recovered during the operation. Validreports have expressed the investment cost in $/KW [1],[4], which is convertible into $/KWh using life time ofeach technology in (4). The offers are adjusted using themarginal cost and the investment cost must be recovered23under the influence of market condition during the opera-tion period:ICj($/KWh) =ICj($/KW)LTj × 8760(1 + rr)y. (4)3.2 Electric DemandDemand of electric energy is modelled by load durationcurve (LDC) for base, middle and peak sections, whichare supplied by coal-fired, CCGT and GT, respectively; itgrows in each section with a constant growth rate everyyear and the average amount by (5) is offered to the marketas market demand. Market price affects the demand viademand elasticity:D(t) =ki=1δi·Li·eg·y− λ·Δρ. (5)3.3 Power MarketThis paper considers an energy-only market with pay-as-bid structure, in which the lowest offers are dispatched andreceive their offers from the market and market price isequal to average offer. The superiority of this structure ineliminating price spikes persuaded some markets to preferit over the uniform price. The firms should adjust theiroffers properly, above the MC and below their predictionof price via the TREND function; they should make abalance between their profit and the chance to win in themarket [3], [45].3.4 ProfitabilityClearing the market specifies the generation of each firm,which is applicable in computing their costs and profits.Total generation cost, in (6), is the sum of firm’s expensesfor generating electric energy until studied time t:Φj =t0Gj·MCjdt (6)By subtracting the generation and investment costsfrom the income, the total profit of the firms is given byΠj =t0Gj·χj − Gj·MCj − CPj·ICjdt (7)Profitability index is defined in (8), as the ratio ofprofit to generation cost, for normalizing the profits to asame quantity [46]. This parameter is helpful in investingin a technology rather than its profit:PIj =ΠjΦj(8)3.5 Stable StateA market can become stable by recovering its generationand investment costs of the firms [45]. This condition isequivalent to PIj = 0, as both costs are considered in PIj.The firms can reach the stable state by offering a priceequal to MC plus a multiple of forecasted price [3], namedas stable price.3.6 Capacity ExpansionThe PIs of firms are converted into investment rate viaS-shaped curves in (9), which limit the rate of variationsand final values in each firm [46]. The coefficients mj max,αj and βj differ in each technology, but mj is equal to 1 forPIj = 1 in the whole, as indicated in Fig. 6. The coefficientmj is influenced by reliability policy and profitability forproviding enough capacity:mj =mj max1 + e−(αj P Ij −βj )(9)Figure 6. The coefficient m for different technologies vs. PI.Equation (10) gives investment rate in each technologyas a function of demand growth rate and retirement rateof the firms weighted by the coefficient mj:IRj = mj·( ˙Li + ˙REj) (10)Reliability policy in (11) forms an internal loop inlaunching process, named as launch scale [9] that changesrate of investment in each technology for holding reserveratio at a proposed level:Res.Rat =TCP − D(t)D(t)(11)The investment rate is converted into capacity af-ter a construction delay. Equation (12) indicates underconstruction capacity, which is the difference between in-vestment rate and construction rate in each technology.Exploited capacity in (13) is the difference between con-structed capacity and retired amount after a life time.A part of GT capacity is converted into CCGT by a change24ratio and change delay that influences the pattern of ex-pansion. Operational capacity is declared to the marketand creates the main feedback loop in this process; besides,it is used for providing reliability as an internal loop:UCj =t0IRj − IRj(t − CTj)dt (12)CPj =t0CNj − CNj(t − LTj)dt (13)3.7 Wind TechnologyThe wind technology competes with other participants inthe market, while previous studies subtracted its capacityfrom the demand [14], [16]. Different effective factors suchas generation and investment costs, construction time andlife time are considered for analysing long-run behaviour ofwind technology [1], [4]. Wind speed, which is modelled byWeibull probability distribution function in (14), perturbsoutput power of wind technology [5]:Vw(t) =γη·tηη−1·e−( tη )γ(14)Wind generation in (15) is affected by wind perturba-tion and restriction of facilities in low and high wind speeds[47]. The CCGT compensates the lack of wind planed gen-eration, due to its continuous generation and fast response,which increases its income in the market [37]:Gw =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, Vw < VciVwVr3CPrw, Vci ≤ Vw < VrCPrw, Vr ≤ Vw < Vco0, Vw ≥ Vco.(15)3.8 Natural GasNatural gas affects the power system in generation anddemand parts. This fuel reaches to the consumer with90% efficiency, while the efficiency decreases to about 35%through the electric generation. The natural gas-basedtechnologies provide their fuel from hubs with a hub price,which is a source of uncertainty in the power systems.Different references have modelled the uncertainty of nat-ural gas hub price by low, medium and high scenarios [6],[38], [48].Price of natural gas for demand is known by city gateprice, which is affected by hub price and seasonal factors [2].Analysing published data by EIA about city gate price [7]via X-12-ARIMA time series [8] gives the seasonal factorsas shown in Fig. 7. These factors adapt to additive modelthat makes the real variable by adding a seasonal factor.Figure 7. The seasonal factors of the city gate natural gasprice.4. Simulation and ResultsThis section analyses the results of simulating differentstates of natural gas consumption in the power systemin three scenarios including firms stability, changes in thenatural gas charge and access of demand to the natural gasand electricity. Some results such as the profitability index,reserve ratio, and capacity expansion are represented andcompared with the base state in each scenario. The appliedparameters in the simulation are from the published databy the EIA on the generation costs by different technolo-gies, natural gas city gate prices and natural gas hub prices.The results represent the statue of the parameters in 1,200months for indicating the stability of the developed model.4.1 Base ScenarioIn this scenario, the firms stay on the stable state by ad-justing the offers for recovering the generation and invest-ment costs [45] that is achievable by PIj = 0 in (8), due toits association to these costs. They adjust their offers byadding multiples of the forecasted price to their marginalcost, which are 0.13, 0.083, 0.058 and 0.45 for the coal-fired, CCGT, GT and wind, respectively. The technologieswith higher investment cost need a greater coefficient forgetting to the stability.Figure 8 represents the profitability index of the firmsin this scenario, which tends to zero during the studiedhorizon. The variation of the PI around zero is a moti-vation for expanding the capacity by different technologiesbeside the growing demand.Table 1 summarizes the total present profit of the firmsin this scenario. The coal-fired earns the most profit bysupplying the base load and the CCGT and GT are at thenext places. The wind earns the least profit in the stablestate.Figure 9 represents the reserve ratio of the powersystem calculated by (11) for providing the reliability ofthe power system, which swings around 0.2 with a limitedvariation between 0.18 and 0.22.The reliability level is achieved by the pattern of gener-ation capacity, shown in Fig. 10. The capacity of the coal-fired, CCGT and GT gets to 8.8 × 104MW, 4.8 × 104MWand 3.3 × 104MW for supplying the base, middle and peakloads, respectively and the wind technology expands itscapacity to 1,400 MW in the stable state.25Figure 8. The profitability index of the firms in the base scenario: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 1Total Present Profit of the Firms at the Base ScenarioTechnology Profit ($)Coal-fired 3 × 106CCGT 0.94 × 106GT 0.33 × 106Wind 0.085 × 106Figure 9. The reserve ratio of the power system in the basescenario.4.2 Natural Gas Price VariationThe second scenario investigates the influence of the vari-ations in the natural gas price on the long-run investmentin the capacity expansion. The variations are modelled aslow-price, medium-price and high-price outlines, summa-rized in Table A.1 [6], [48], [38]. The results of the high andFigure 10. The capacity of different technologies in thebase scenario.Figure 11. The price of electric energy for different outlinesof natural gas price.low prices of natural gas are compared with the mediumprice as base scenario.Figure 11 represents the price of electric energy fordifferent outlines of natural gas price. The electric price26Figure 12. The profitability index of the firms at the high price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 2Total Present Profit of the Firms at the High Price ofNatural GasTechnology Profit ($)Coal-fired 24 × 106CCGT 4.3 × 106GT −1.3 × 106Wind 3.4 × 106increases by growing the natural gas price and decreasesby its decline, compared with the medium price.Figure 12 indicates the profitability index of the firmsat the high price of natural gas. The PI increases to0.04, 0.01 and 0.33 for the coal-fired, CCGT and wind,respectively, but decreases to −0.0002 for the GT, due tothe loss of opportunity for generation by this technology.Reducing the heat rate of the GT, increases its PI tozero on month 900 by raising its generation chance anddecreases the PI of the coal-fired in Figs. 12(a) and (c).The present profit of the firms changes by their devi-ation from the stable state, summarized in Table 2. Theprofit of the coal-fired, CCGT and wind increases , com-pared with Table 1, but the high price is disadvantageousfor the GT and causes its negative profit in Table 2.The average of the reserve ratio does not change signif-icantly at the high price and grows to the average of 0.21with a pattern same as Fig. 9. Compared with Fig. 10, theFigure 13. The capacity of different technologies at thehigh price of natural gas.capacity of different firms changes as indicated in Fig. 13;the capacity of the coal-fired and the wind increases to9 × 104MW and 7,300 MW, respectively, but it decreasesto 4.4 × 104MW and 3 × 104MW for the CCGT and GT,which shows the reduced share of the natural gas consumersin the market and the great ratio of capacity expansion bythe wind at high prices.Decreasing the charge of the natural gas, drops theelectric price in the market, which leads to the loss of thefirms at the stable offer, due to irretrievable investmentcosts. The profitability index of the firms drops to −0.0073,−0.007, −0.0035 and −0.49 for the coal-fired, CCGT, GTand wind in Fig. 14.Table 3 summarizes the present profit of the firms atthe low charge of natural gas, which is negative for thewhole and results in their loss by offering the stable price.27Figure 14. The profitability index of the firms at the low price of natural gas: (a) coal-fired; (b) CCGT; (c) GT; and (d) wind.Table 3Total Present Profit of the Firms at the Low Price ofNatural GasTechnology Profit ($)Coal-fired −2.8 × 106CCGT −1.3 × 106GT −0.58 × 106Wind −0.15 × 106Figure 15. The capacity of different technologies at the lowprice of natural gas.Low-price natural gas does not influence the reliabilityof the power system remarkably and decreases the aver-age of the reserve ratio to the amount 0.19 with the be-haviour same as Fig. 9. The pattern of generation capacitychanges at low charge of natural gas as shown in Fig. 15.The capacity of the CCGT and the GT increases to4.9 × 104MW and 3.4 × 104MW, while the amount of thecoal-fired and the wind decreases to 8.7 × 104MW and540 MW, respectively. This variation increases the share oftechnologies in the market that consume the natural gas.4.3 Natural Gas Consumption by the DemandThis section analyses the access to the electricity and nat-ural gas as two separate energy resources by 10% of thedemand. The demand switches between these energy re-sources by comparing the electric market price and naturalgas city gate price and choosing the cheapest one.Figure 16 represents the PI of the firms, when 10%of the demand selects between two energy resources. ThePI of the coal-fired decreases to −0.033 in Fig. 16a, but itdoes not change for the other technologies significantly.Table 4 summarizes the present profit of the firms atthe selection of the natural gas by the demand. The loss ofthe profit by the coal-fired is severe, due to the variations inthe base demand, which enforces it to increase its coefficientin the offer. The present profit of the other technologiesdoes not change a lot in this scenario, compared withTable 1.The resource selection by the demand enforces thefirms to expand the capacity for a discontinuous demand,which is detectable in the capacity of different technologiesin Fig. 17. The capacity of the coal-fired, CCGT and GTincreases with swings to 10 × 104MW, 5.8 × 104MW and3.7 × 104MW, respectively. The wind capacity decreasesto 1,047 MW in this scenario.28Figure 16. The profitability index of the firms at the natural gas consumption by the demand scenario: (a) coal-fired;(b) CCGT; (c) GT; and (d) wind.Table 4Total Present Profit of the Firms at the Natural GasConsumption by the Demand ScenarioTechnology Profit ($)Coal-fired −23.1 × 106CCGT 1 × 106GT 0.31 × 106Wind 0.072 × 106Figure 17. The capacity of different technologies at thenatural gas consumption by the demand scenario.Figure 18. The reserve ratio of the power system at thenatural gas consumption by the demand scenario.This pattern of capacity has a negative influence onthe reserve ratio of the power system for providing thereliability as shown in Fig. 18. The average of the reserveratio swings around the average amount of 0.35 and variesbetween 0.15 and 0.6 in this figure. Increasing the accessof the demand to both energy resources from 10% createsundesirable effects on the profitability and reserve ratio.The efficiency of the natural gas consumption by thedemand is an effective factor for keeping the stability ofthe electric market. Growing the efficiency of the naturalgas consumption to above 50%, restores the stable stateof the firms in the market by keeping the PI of the firmsat the zero and the reserve ratio on 0.2 with a little swingsame as Figs. 8 and 9. High efficient natural gas demands29are dismissed form the electric market, which decreases theinstalled capacity at the stable state and its swings.5. DiscussionThe natural gas affects the power market in generationand consumption levels. Based on the hub price of naturalgas, three scenarios can be defined including, low, mediumand high charges. The access of demand to the natural gasaffects the market via the seasonal factors.The stable state (PI = 0) which is considered as thebase scenario compensates the generation and investmentcosts of the firms and keeps the reserve ratio on about0.2 for providing the reliability. This state is achieved byadding a multiple of the forecasted price to the MC by thefirms, which is 0.13, 0.083, 0.058 and 0.45 for the coal-fired,CCGT, GT and wind, respectively; the technologies withhigher investment cost adjust their offer with a greatercoefficient. The Medium price of natural gas is consideredin the base scenario.High-charge natural gas increases the market price andthe firms offers, which increases the profitability index ofthe coal-fired, CCGT and wind from zero to 0.04, 0.01 and0.33, respectively; however, this charge decreases the gener-ation opportunity for GT and decreases its PI to −0.0002.So, the GT should decrease its coefficient during high priceof natural gas for creating generation opportunity. Byincreasing the natural gas price reaches the capacity of GTand CCGT increases from 4.8 × 104MW and 3.3 × 104MWto 4.4 × 104MW and 3 × 104MW and the share of naturalgas-based technologies in the market decreases. However,increasing the profit creates the opportunity for the coal-fired and wind to expand their capacity and increase theirshare from 8.8 × 104MW and 1,400 MW at the stable stateto 9 × 104MW and 7,300 MW. The average of reserve ratiogrows from 0.2 to 0.21 in this situation.Low-charge natural gas decreases the average pricein the market and reduces the PI of coal-fired, CCGT,GT and wind to −0.0073, −0.007, −0.0035 and −0.49,respectively, which results in the loss of the firms. Theshare of CCGT and GT increases to 4.9 × 104MW and3.4 × 104MW in the market, while the capacity ofthe coal-fired and wind decreases to 8.7 × 104MW and540 MW. The capacity expansion is due to the effects ofdemand growth rate and retirement rate on the invest-ment rate for providing the proposed reliability level ofabout 0.19.The charge of natural gas at the consumption level isinfluenced by seasonal factors, which has additive patternand its amount is greater in colder months. Natural gasconsumption by demand decreases the profitability indexof the coal-fired to −0.033 as base supplier. This conditionenforces the firms to expand their capacity, while theirgeneration is not consumed by the demand continuously,which hardens recovering the investment. Choosing thecheapest energy resource by the demand keeps the PIof the CCGT, GT and wind at zero and increasing thepercentage of demand access decreases the PI of CCGTand GT. The capacity of coal-fired, CCGT, GT and windreaches to 10 × 104MW, 5.8 × 104MW, 3.7 × 104MW and1,047 MW. Switching between the energy resources by thedemand causes the swing of the reserve ratio, which isresolved by increasing the efficiency of the natural gasconsumers.6. ConclusionThis paper analyses the effect of the natural gas on thecapacity expansion by the firms in a pay-as-bid energy-only market using the system dynamics. Natural gas-basedtechnologies and demand selection between the electricityand natural gas are two considered tie points between theseresources. This subject is studied via three scenarios,namely, (1) the firms stability, (2) changes in the naturalgas charge and (3) access of demand to natural gas andelectricity. Four generation technologies including coal-fired, CCGT, GT and wind participate in an energy-onlymarket using the published data in the reports of EIA.At the first scenario, the firms adjust their offersabove the marginal cost for recovering the generation andinvestment costs as stable state, which is known by PIj = 0.The firms adjust their offers by adding a multiple of theforecasted price to the marginal cost, which is greater forthe technologies with higher investment cost. The stablestate can recover the costs of the firms and provide thetargeted reliability level of the power system.The natural gas price as assumed to fluctuate betweenlow, medium and high prices, where the medium priceis applied at the base scenario. High-price natural gasincreases the offers of the firms and the market price, whichincreases the profit of the coal-fired, CCGT and wind, butcauses the loss of the profit by the GT, as it loses theopportunity for generation. More profit increment by coal-fired and loss of GT reduces the share of natural gas-basedtechnologies in the market at high charges of natural gas.Low-price natural gas decreases the offers and market priceto an amount, which cannot recover the investment costsand causes the loss of the whole. The capacity is expandedfor supplying the demand and compensating the retirementwith a less ramp. The loss of coal-fired and wind in lowcharge is more severe due to their higher investment costs,which increases the share of natural gas-based technologiesin the market. The reserve ratio of the power systemdoes not change remarkably by changing the natural gasprice.Selecting the natural gas as resource of energy by aportion of demand causes the loss of profit by the coal-firedand does not influence on the revenue of the rest. Thisbehaviour of demand expands the generation capacity andincreases the average of reserve ratio, but creates swing init. Increasing the per cent of demand access to the naturalgas intensifies the unstable condition in the market. Thegrowth of efficiency in the natural gas demand dismisses itfrom the power market and restores it to the stability.Appendix ATable A.1 summarizes the parameters of the simulation,which are from the published report by EIA [4].30Table A.1The Parameters of the SimulationTechnology Coal-Fired CCGT GT WindParameterFuel Cost 65 ($/ton) Low Price = 3.8 $/MMBtuThermal Value Medium Price = 4.6 $/MMBtu= 6080 kcal/kg High price = 6 $/MMBtuHeat rate (Btu/KWh) 9,200 6,752 9,289Heat rate changes (Btu/KWh year) −30 −28 −50O&M costs ($/MWh) 7.7 3.3 4.3 3.4CO2 costs ($/MWh) 24 10.5 16Investment costs ($/MWh) 3.7 3.3 2.3 10.97Construction time (months) 48 36 24 6Life time (months) 720 360 360 240Rate of return (%/year) 5%Peak demand (MW) 1,200Peak duration 0.2Middle demand (MW) 1,000Middle duration 0.6Base demand (MW) 700Base duration 0.2Demand growth rate (%/year) 5%Rated wind speed (m/s) 7Product wind speed (m/s) 4Cut out wind speed (m/s) 13References[1] “Projected Costs of Generating Electricity , International En-ergy Agency, 2010 Edition.[2] S. 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