Dynamic Interactions of TGC and Electricity Markets to Promote Wind Capacity Investment

46 IEEE SYSTEMS JOURNAL, VOL. 6, NO. 1, MARCH 2012

Dynamic Interactions of TGC and ElectricityMarkets to Promote Wind Capacity Investment

Masoud Hasani-Marzooni and Seyed Hamid Hosseini, Member, IEEE

Abstract—This paper proposes a time simulation model forlong-term wind capacity investment decisions in the presenceof electricity market and tradable green certificate (TGC)market. Investment decisions and wind capacity developmentare fundamentally based on incentives gained from both thesemarkets. In TGC market, the tradable certificates are issuedto renewable generation companies for each megawatt-hour ofelectricity generation. Distribution companies are obligated tosupport fraction of their electricity consumptions from renewablesources. The dynamics of prices in both markets are simulatedin a system dynamics model to trace the dynamics of windcapacity investment. Such a decision model enables both thewind generation investors and the regulators to gain perfectinsight into finding possible consequences of different decisionsthat they should make under different policies and marketsconditions particularly in the preliminary design of TGC market.The impacts of regulatory policies, trading strategies of players,and uncertainties in both markets are examined in a case study.

Index Terms—Electricity market, investment decision, systemdynamics, tradable green certificate (TGC) market, tradingstrategies.

Nomenclature

i Subscript referring to technology (1, . . . , I).j Subscript referring to vintage (1, . . . , J).k Subscript referring to year.e Superscript referring to variables expectation.�t Model time step.EPR(t) Electricity price.TPR(t) TGC price.CPR(t) Consumer total price.TGCShare(t) TGC share.D(t) Electricity demand.DGR(t) Electricity demand growth rate.v(t) Wind speed time series.ov(t) Observed wind speed.sv(t) Simulated wind speed.μ(t) Mean value of observed wind speed at time t.σ(t) Standard deviation of observed wind speed.FP(t) Fuel price.

Manuscript received September 9, 2010; revised December 14, 2010;accepted May 25, 2011. Date of publication August 30, 2011; date of currentversion February 23, 2012.

The authors are with the Department of Electrical Engineering, SharifUniversity of Technology, Tehran 11155, Iran (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSYST.2011.2162891

EP(t) Emission price.MC(t) Marginal cost of generation.η Thermal efficiency.r Emission rate.CF (t; �t) Capacity factor in the time interval [t − �t, t].P(t) Installed capacity.T Production time.TGc(t; �t) Total generation of conventional technologies.QN (t; �t) Net electricity demand.TD(t) TGC demand.TT (t) TGC target.ρ Discount rate.T a Amortization time.T c Construction time.TGCDes

Sale(t) TGC desired sale rate.

TGCDesPur (t) TGC desired purchase rate.

TPRb(t) Fundamental TGC price.

TGCExpIssued(t) Expected issued TGC.

TGCAdjGenCo(t) Adjustment for GenCo’s TGC holding.

TGCAdjDisCo(t) Adjustment for DisCo’s TGC holding.

PES Price elasticity of TGC sale.PEP Price elasticity of TGC purchase.�(t) Total profit in planning time horizon.π(t) Operating profit.OMC(t) Operational and maintenance costs.IC(t) Investment cost.πe

wind(t) Expected operating profit of wind power.T p Perceived time.IRR(t) Internal rate of return.PI(t) Profitability index.m Aggregated capacity level.mmax Saturation capacity level.β, γ Fixed parameters of investment function.I(t) Investment rate.P re(t) Capacity retirement rate.D(t) Capacity addition to cover maximum demand.Pc(t) Capacity under construction.Pca(t) Construction accomplishing rate.P in

i,j(t) Capacity rate entering a vintage.Pout

i,j (t) Capacity rate departing a vintage.T age Aging time of vintages.

I. Introduction

THE POWER electricity industries have been experiencinga process of deregulation in order to introduce commer-

1932-8184/$26.00 c© 2011 IEEE

HASANI-MARZOONI AND HOSSEINI: DYNAMIC INTERACTIONS OF TGC AND ELECTRICITY MARKETS 47

cial incentives in generation, transmission, and distributioninvestments. In addition to these changes, the environmentalconcerns in electricity generation have been considered inmany nations. To prevent mortal effects of greenhouse gas(GHG) emissions and global warming, some countries haveadopted the energy and environmental policies. The mostrelevant policies are those derived from Kyoto Protocol for thereduction of GHG emissions as well as those promoting re-newable energy sources (RESs) [1]. The energy/environmentalpolicies have at least these two major and interrelated goalswhich can be also in conflict [2]. The agreement of Europeancountries for GHG reduction by the years 2008–2012 is 8%of the GHGs produced in 1990 [3].

The emission allowance taxes have been employed to reducethe GHG in power industries. Also, tradable emission permitmarkets have been developed for this purpose by establishing aset of national permits that can be traded [4]. These policies areemployed directly to improve the environmental performanceof power industries.

In addition to these environmental policies, the other poli-cies corresponding with the Kyoto Protocol have been usedto increase the role of renewable technologies in the future ofelectricity generation. The incentives gained from these poli-cies should insure the profitability of investment in renewableresources. The renewable generation supporting policies alsohave obviated the challenges facing the market regulators tokeep the option for these capital-intensive technologies suchas wind power technology. Some regulatory incentives suchas utility direct subsidies (e.g., feed-in-tariff in Europe orfederal production tax credit in the U.S.) and fixed premiumas well as indirect incentives (e.g., tax exemption policies)have been used to promote RESs and cause these technologiescompetitive with the conventional generation resources. Somemarket oriented instruments to achieve targets for renewableelectricity generation in deregulated electricity market havealso been developed. The TGC market has been regarded asa market-based environmental subsidy. It is used to increasethe share of renewable generations at costs below the costs ofdirect subsidies and to make promotion of a diverse mix ofRESs, some of which may be more attractive from social, eco-nomical and ecological perspectives [5]. With these incentives,the regulatory body tries to reduce the long-run marginal cost(LRMC) of RESs below the LRMC of conventional units [6].

The TGC markets have been implemented in the U.S. tocomply with renewable portfolio standard which is a state re-quirement for RESs’ electricity generation [5]. Such regulatorypolicies are used in other regions of the world. Australia has amandatory renewable energy target which imposes electricityretailers and large consumers to purchase a percentage of theirelectricity requirement from RESs [7]. A national tradablerenewable energy credits scheme for achieving the renewableportfolio targets in India has been proposed [8], [9]. The TGCmarket as national policy in some European countries likeScandinavian countries [6], [10], [11], Netherland [12], Italy[13], and U.K. [14] have been employed. The potential ofgreen certificates application in China has been also studied[15]. Investigations have been done to establish a scheme withharmonized national electricity support systems for renewable

energy certificates in Europe. Soderholm [16] analyzed thepolitical economy of establishing bilateral trade in greencertificate markets as one step toward this harmonization. TGCmarket has been also bundled with emission permits marketfor simultaneous attainment of energy goals [17]–[19].

Some references deal with modeling of TGC market as aneconomic mechanism. Deterministic equilibrium models todescribe interaction between the power and green certificatemarkets have been proposed in [20] and [21]. The impactof renewable energy certificates on generation planninghas been also studied [22]. Some challenges facing theRESs investors and regulators such as financial risks andconstraints, overinvestment risk, and the role of long-termcontracts in TGC market modeling and implementation havebeen also introduced in previous studies [23]–[26]. A closedmathematical TGC market model that describes behaviorof market functions both in the long-term (development ofgenerating capacities) and short-term (demand and supplybalance) periods is proposed in [27]. The TGC market inan imperfect environment and the relation with feed-in tariffscheme were assessed in [28] using U.K. market data.

The static aspects of TGC and electricity markets wereconsidered in the models proposed by most of the aforemen-tioned literatures. The models are generally based on long-runequilibrium state. Dynamic aspects of TGC and electricitymarkets such as specific time delays and feedback structureof the processes, strategic behaviors of TGC market playersin time domain, stochastic nature of some RESs, and pricevolatilities due to dynamic nature of these markets were rarelyconsidered [6]. Ford et al. [5] and Vogstad [29] proposed timesimulation models of TGC market to capture these dynamicswith modeling an idealized electricity market in which priceswere fixed at the total levelized cost of new combined cyclegas turbine (CCGT) units. Only the internal dynamics of TGCmarket is focused in these models.

In this paper, a long-term system dynamics model ispresented to consider the dynamics of the combined TGCand electricity markets in a time simulation framework. Re-ciprocal dynamics (dynamic interactions of electricity andTGC markets with considering price oscillations of each)are considered. Detailed modeling of wind power generationsand wind capacity investments are done using wind speedforecast method in system dynamics modeling. Therefore, thewind capacity factor is dynamically changed depending onthe wind speed unlike the models which consider the windcapacity factor to be fixed. The wind capacity investment isalso assessed due to dynamic features mentioned above andprice volatilities in both markets. The effects of uncertainty infuel price of conventional units, gas emission tax employmentin electricity market, as well as trading strategies of TGCmarket players are assessed using sensitivity analysis.

The remainder of this paper is organized as follows. InSection II, the system dynamics model based on combinationof electricity and TGC markets beside the main principleof each market is described. The detail of the methodologyand some of the mathematical framework of the model arepresented in Section III. In Section IV, simulation of a casestudy including both markets with different scenarios will be


Fig. 1. Causal loop model for long-term assessment of investments in conventional and wind capacities using incentives from electricity and TGC markets.

Fig. 2. Causal loop model for certificate trading strategies and price definition in TGC market.

carried out to demonstrate the effectiveness of the model.Finally, conclusions are outlined in Section V.

II. Model Description

Three conventional generation technologies including hardcoal (HC), CCGT, and gas turbine (GT) are considered forsupplying base, middle, and peak loads, respectively. Windpower technology is regarded as the sole renewable generationtechnology which is taken into the system as the base loadsupplier when it is available. So, wind generators are paidreal-time electricity market price plus the TGC market price.

The system dynamics approach is used to comprehendthe dynamics of the interaction between the components ofelectricity and TGC markets. Dynamics of an economicalsystem arises from two types of feedback loops: positive orreinforcing loops and, negative or balancing loops [30]. Thefeedback structure of coupled electricity and TGC markets andthe relationship between variables are shown in causal loopdiagrams of Figs. 1 and 2. The balancing loops are determinedin these diagrams. In Fig. 1, investments in conventional andwind power capacities using incentives gained from both elec-

tricity and TGC markets are assessed. There are four negativefeedback loops in this diagram. Loop L1 defines the long-termprice elasticity of electricity consumption. Consumers respondto both electricity and TGC prices. Loop L2 characterizesthe price elasticity of conventional electricity generation. Inthese types of units, marginal cost of generation and electricityspot price are considered for defining their capacity factor. Onthe other hand, they are committed in electricity market interms of their marginal costs and the marginal cost of themost expensive committed generation technology determinesthe spot price. Wind power technology is not considered to beprice-dispatched and is not involved in this balancing loop.

Balancing loops L3 and L4 limit the capacity investments innew conventional and wind power generation technologies, re-spectively. They state that when generation capacity and there-fore electricity reserve increase, more electricity generation isdispatched and eventually electricity market price is likely tofall after a short time period. This decreases the expectationsof future electricity prices which in turn reduces the likelihoodof profitability expected by capacity investors. So, investmentdecisions will be restricted and after a time delay, the construc-tions proposals will be lower resulting in much lower conven-


tional and wind power installed capacities. Investors have thepossibility to defer or cancel the project if they conclude thatthe investment was not economically reversible for them. Themain time delays shown in this diagram are time intervals forconstruction permit acquiring and construction time.

The main principle of TGC market is based on tradingof virtual megawatt-hours of renewable generation that canbe regarded as certificates. An issuing body issues greencertificates when wind power generating company (GenCo)produces actual megawatt-hour of green electricity [6]. Windpower GenCos can sell these certificates to distribution compa-nies (DisCos) or hold these certificates as a buffer against theuncertainties especially price uncertainty. In Fig. 2, a causalloop model of certificate trading strategies as well as pricedefinition in TGC market is shown. If the wind speed is high,wind power generation will be high and the TGCs quantitywhich is issued will increase. So, the TGC price will decrease.GenCos can wait to see higher prices and then sell their TGCsto DisCos. Holding of TGCs by GenCos is a tool for theirprofitability in TGC market, but they are not generally allowedto hold them extensively. Indefinite time holding of TGCs byGenCos is called extensive banking [5]. After definite coveragetime of TGCs holding, they will expire.

Obligations are usually imposed on DisCos to support somefraction of electricity consumptions from RESs. This fractionis called TGC target [6] which is specified by regulatorypolicies. In this model, the TGC target grows over the timeand wind power capacity should be invested in the wayfollowing this target. The certificates are withdrawn fromcirculation when DisCos present the certificates to the re-demption authority to account for their obligations or whenthe certificates period of validity expires. If the TGC price islow, DisCos will purchase more TGCs (even more than theirpresent obligation) from wind power GenCos and hold themto guarantee their future obligations. DisCos may hold TGCstill their periods of validity expire. In some TGC markets,the possibility of deferring the obligation for future existswhenever the TGCs are deficient. This is called borrowing [5],[6]. In this model, DisCos are allowed to borrow the fractionof their obligations. If they do not possess sufficient TGCs andborrowing is impossible, they will pay penalty price to ISOfor the remaining part of their obligations.

Balancing loop L5 defines the adjustment of TGCs holdingvolume by wind power GenCos. Desired sale rate of TGCs byGenCos depends on expected wind power generation whichin turn relates to available wind power capacity and theforecasted wind speed. This loop prevents overflowing ofTGC volume which is held by GenCos. Loop L6 makesthe possibility of TGC volume adjustment for DisCos. If theborrowing rate of TGC increases due to shortage of TGCsvolume held by DisCos, they will attempt to buy more fromGenCos. The desired purchase rate depends on the TGCdemand or target.

Loop L7 describes the TGC price elasticity of desired salerate. Wind power GenCos are assumed to be fundamentaltraders [5], i.e., if the TGC price exceeds their estimate of thefundamental price, they will tend to sell TGCs. DisCos are alsoassumed to be fundamental traders, i.e., if the TGC price is

below the fundamental price, they will be more inclined to buy.This TGC price elasticity of DisCos’ purchase rates is includedin loop L8. Strategic behaviors of GenCos and DisCos besidethe delays and uncertainties in the system make imbalancesbetween TGC desired sale and purchase rates and extractthe TGC price from equilibrium state. TGC price is adjustedproportional to TGC excess demand in this dynamic model(loops L7 and L8 in Fig. 2). End-consumers also respondto TGC price directly. If the TGC price and consequentlyconsumer price increase, the electricity consumption and theTGC demand will decrease and DisCos will buy less TGCs.This will eventually cause the TGC price to be reduced aftera time span (loop L9 in Fig. 2).

The market share of renewable generation technology suchas wind power affects the consumer price. The electricityconsumption and TGC demand will decrease as long as theTGC share increases. Then, this will reduce the TGC purchaserate and TGC price after a time delay. Finally, GenCos willlower the TGC sale rate and this will diminish the TGC sharewhich is denoted by balancing loop L10.

If the causal loop diagrams of Figs. 1 and 2 are linked, twoother balancing loops can be found regarding the relationshipsamong the variables of combined diagrams. One of themassociates the investment in wind power capacity with theTGC price. With increasing the TGC price, the profitability ofwind power GenCos will increase, so they will decide to investmore and after a time delay, more wind power capacity will beinstalled. Therefore, the electricity generation from wind willrise resulting in more TGC issuing. This will finally decreasethe TGC price. The other balancing loop relates the electricityconsumption to TGC share in consumer price. If the shareof wind power in consumer price increases, the electricityconsumption will decrease. This will cause the electricity spotprice to be reduced. Afterward, less wind power capacity willbe installed and finally the TGC share will decrease.

Some reinforcing loops (which are not described here for thesake of brevity) can be seen in this model. The transmissionnetwork effects are ignored. Stock and flow diagrams whichare not depicted here have been used to model the de-tailed relationships between variables. Some sets of nonlineardynamical differential equations were produced using theserelationships and the stock and flow structures which willbe presented in the following section. These equations aregenerally complicated and too long in order to be presented.The numerical methods like Euler algorithm are used tosolve them in the system dynamics software. The modelingrequirements and some of the mathematical relationships willbe presented in the next section.

III. Modeling Requirements

A. Electricity Market Modeling

In the proposed model, electricity market implementationtime step or time resolution of the model is assumed tobe one week in order to capture the short-term variationsof demand and wind speed. So, the electricity price iscleared from balancing the weekly energy consumption andgeneration. For considering the economical aspects of electric


power consumption, end-consumers are assumed to be ableto respond or modify their electrical energy consumptionwith price feedbacks. The consumer total price (containingelectricity price and the fraction of TGC prices) is as follows:

CPR(t) = EPR(t) + TGCshare(t). TPR(t). (1)

The same exogenous annual demand growth rate is assumedfor base, middle, and peak loads in load duration curve andthe electricity demand will be

D(t + �t) = D(t) +

t+�t∫t

DGR(τ).dτ. (2)

The wind speed real data fitted by Weibull samplingexpression was gathered and the weekly average of windspeed was extracted from it. For modeling the wind powergeneration in entire planning time horizon, wind speed timeseries simulation technique based on auto-regressive movingaverage (ARMA) model is employed as the wind speedforecast method regarding the autocorrelation nature of windspeeds observed in consecutive time intervals [31]. Then, theMonte Carlo technique as a stochastic simulation processwas applied to establish different wind speed time seriesfor future. Random samples in this technique were producedcorresponding with Weibull sampling expression. Initial timeseries of wind speed can be established using data samplingor real observed data. The wind speed time series can becomputed using observed data in each time step

v(t) = (ov(t) − μ(t))/σ(t). (3)

Then, the ARMA model is applied. The model consists oftwo parts, an auto-regressive part and a moving average partand is usually referred to as the ARMA(M, N) model whereM is the order of the auto-regressive part and N is the orderof the moving average part, as defined below

v(t) = c +M∑

m=1

φm.v(t − m) + α(t) −N∑

n=1

θn.α(t − n). (4)

In this series, normal white noise process α(t) can besampled randomly. Using the least square of errors criterionand trial and error for different M and N, the best estimatesof �m and θn were found. After calculating the coefficients,v(t) for future time horizon will be determined and finallythe simulated wind speed will be defined using the followingequation:

sv(t) = μ(t) + σ(t).v(t). (5)

After the wind speed simulation, an available output powerof a wind turbine generator at any time can be calculatedusing a typical turbine’s power output curve [32]. In this case,it is assumed that all wind capacity is concentrated in only onewind farm while full correlation exists among the wind speedsof turbines’ hub. Finally, the generation amount of wind poweris calculated.

The electricity market is assumed to be perfectly compet-itive. So, generation companies cannot strategically influencethe market price. It has been proved that in perfect electricity

market the optimal mix of generations will be obtained whendifferent generation technologies earn the exact amount tocover their fixed and operational costs [33]. Market priceequals the marginal cost of the most expensive running gener-ation technology. Therefore, we assume that each generationcompany is represented by an individual generation technologyto reflect the competition among several technologies. Windpower technology is assumed to be the base load supplier andthe wind power generation depends on the wind availability.The net electricity demand which is the difference betweenelectricity demand and wind power generation is calculatedfor each time step and is assumed to be supplied by totalgeneration of conventional technologies. We also assume thatthe conventional generation technologies make bid accordingto the electricity price signal and also their marginal costs ofgeneration which is assumed to be the sum of fuel cost andemission cost as follows:

MCi,j(t) = FPi(t)/ηi,j + ri,j.EP(t) (6)

in which the vintage modeling [33]–[35] is considered torepresent the technological development in marginal cost re-duction of newer generating units.

Using aforementioned assumptions, the commitment modelused in [6] and [35] is employed. In this method, the supplycurve for each generation technology and an aggregated supplycurve are used. These curves can be obtained as the resultof performing regular unit commitment in the network. Thesupply curve for each generation technology demonstrates thestraight relation between the capacity factor (in each timeinterval) and the ratio of electricity market price to marginalcost of that technology. Thus, the electricity generation ofeach technology can be calculated using this typical curveand the electricity price signal feedback. By combinationof all conventional technologies’ curves which are obtainedfrom unit commitment, an aggregated supply curve can bespecified which is the result of plotting the cumulative capacityof aggregated conventional units against the sorted marginalcost of generation. Finally, the total electricity generation ofconventional technologies in time interval [t − �t, t], can bedefined as follows:

TGc(t; �t) =I∑

i=1

J∑j=1

Pi,j(t).CFi,j(t; �t).Ti,j. (7)

The total production time in each time step is the productof availability factor of the related technology and the timestep. As mentioned previously, the net demand should besupplied by the total generation of conventional technologies.In dynamic aspects of electricity market, the excess demandfunction (EDF) is used to define the price variations at eachtime. In this way, the electricity price variation is adjusted ineach time step proportional to the imbalances or discrepanciesbetween net demand and the total generation of conventionaltechnologies using an EDF [34]

�EPR(t)=(EPR(t)/�t) · (QN (t; �t)−TGc(t; �t))/QN (t; �t).(8)


These electricity price fluctuations continuously trace thedirection of imbalances, i.e., if the net demand is more thanthe total electricity generation of conventional technologies,the electricity price will increase and vice versa. The value ofelectricity price in the next time interval of market implemen-tation is defined using price variation and the stock and inflowstructure of the process

EPR(t + �t) = EPR(t) +

t+�t∫t

�EPR(τ).dτ. (9)

B. TGC Market Modeling

In most TGC markets in the world, TGC obligations are usu-ally met annually and TGC market implementation in a shortertime is a price adjustment process which controls the TGCobligations [6]. In our proposed model, the TGC market runsmonthly and the TGC obligations in each year are distributeduniformly among the months. The monthly TGC market is runafter every four weekly electricity market runs and TGC pricewill be provided for wind power GenCos. So, the seasonalstochastic variations of wind speed are appropriately capturedby the model. The TGC target is usually set by regulators forthe planning time horizon. The linear curve is used in thismodel, i.e., the DisCos are imposed to serve some percentageof their consumptions from wind power generation which in-creases linearly over time. Therefore, the TGC demand will be

TD(t) = TT (t).D(t). (10)

The relative economic attractiveness of wind power gener-ation versus conventional power plant generation is the basisof the incentive mechanism used as a subsidy for wind powertechnology [5]. Although the variable cost of this technologyis trivial, it is capital intensive due to its high investment costsespecially in offshore type. The fundamental price of TGC isset to the difference of LRMC of wind power technology andthe LRMC of the most expensive conventional technology inorder to make wind power competitive with others. The LRMCof each technology can be calculated as follows:

LRMCi,j =1

8760 CFi,j

(ρ.ICi

1 − e−ρT ai

+ OMCi,j

)+ MCi,j.

(11)The TGC price in this market is cleared from balancing of

TGC desired sale rate by GenCos and TGC desired purchaserate by DisCos. An excess demand function [similar to (8)in electricity market] is defined for showing the relationshipbetween TGC price changes and the discrepancies betweenTGC desired sale and purchase rates. Then, the TGC pricewill be defined by using the following stock and flow relation:

TPR(t + �t) = TPR(t) +

t+�t∫t

�TPR(τ).dτ. (12)

Assuming both the wind power GenCos and DisCos arefamiliar with the fundamental TGC price and are value traders,

they can respond in order to modify their desired sale andpurchase rates by the following relations [5]:

TGCDesSale(t)=[TGC

ExpIssued(t) + TGC

AdjGenCo(t)].(TPR(t)/TPRb(t))PES

(13)

TGCDesPur (t) = [TD(t) + TGC

AdjDisCo(t)].(TPR(t)/TPRb(t))PEP

(14)in which GenCos incline to modify their desired sale rates byTGC price to accord with expected value of issuing TGCsor expected wind power generation. DisCos also tend toachieve TGCs to fulfill their obligations. The TGC adjustmentvalues defined in these formulations are the modifications ofGenCos and DisCos to reach their desired amounts of salesor purchases.

Two stock variables represent the volume of TGCs whichare held by GenCos and DisCos. The inflow of GenCo’sstored TGC is the issuing rate of TGCs and its outflowis the TGC sale rate. On the other hand, the inflow ofDisCo’s stored TGC is the TGC purchase rate and its out-flow is the TGC redemption rate turned in for TGC tar-get. The stock and flow diagrams and their formulationsare not presented here for brevity. GenCos should considerthe validation lifetime of TGCs in their sale rates. Thiscoverage time can be extensive or limited due to the policiesmade by regulators. GenCos can decide to hold TGCs duringthe valid time period to wait and see higher prices or tosell immediately depending on their trading strategies. Thesame consideration is for DisCos in holding of TGCs beforeredemption.

If adequate TGCs exist in the property of DisCos, the TGCswill be turned in on-time. Otherwise, DisCos can borrow up tothe fraction of their monthly obligation with the possibility ofborrowing established by the regulator. The borrowed TGCsenter a backlog and are due later than the specified obligationtime depending on the borrowing time. If no sufficient TGCsand borrowing authority exist, they will pay the penalty priceto ISO on the remaining part of obligation. Modeling of TGCborrowing is described in [5].

C. Expectation Modeling and Profitability Assessment

An approach presented in [30] has been employed formodeling expectation of variables in electricity and TGCmarkets. The model is based on bounded rationality hypothesisfor market players in which model parameters are estimatedinstead of optimization due to lack of knowledge.

For assessing the project economics, the net present valuemethod is used. The cash-flows in different years of the projectare brought to a common reference time which is commonlytermed as the time of decision. Applying this method for newinvestments in conventional and wind power technologies, wecan evaluate the present worth of the total economic profit foreach technology at time t as follows:

�i(t) =T a

i∑k=1

(πei,k(t) − OMCi,k(t)).e−ρ(k+T c

i) − ICi(t). (15)


Subject to uncertainties, investors improbably know theright expectation of annual price and profit primarily in thetime of decision. Olsina proposed the common aggregatedexpectation of profit in all periods of lifetime [33]. The main-tenance cost may also vary from year to year depending on thetechnology and unit age. Therefore, an average of maintenancecost is assumed per unit of capacity in the lifetime. So, in thiscase, the common expected term of operating profit πe

i (t) andaverage term of maintenance cost OMCav

i (t) replace πei,k(t)

and OMCi,k(t), respectively, and both terms can be emittedfrom sigma notation in (15). The expected operating profit ofconventional generation technologies depends on the capacityutilization, i.e., if the expected electricity price exceeds themarginal cost of generation in some time periods in a year, theunit will gain benefit in these time intervals and is expectedto be committed for generation. Therefore, for conventionalgeneration technologies, we can write

πei (t) =

t∫t−T p

(EPRe(τ) − MCei (τ)).dτ ∀ EPRe(t) ≥ MCe

i (t).

(16)But for wind power technology, both the electricity and

TGC prices are used as incentives while the marginal costof generation is zero. Therefore, we have

πewind(t) =

t∫t−T p

(EPRe(τ) + TPRe(τ)).dτ. (17)

Equations (16) and (17) are the expectation of economicoperating profits with perceived time which is typically oneyear. By replacement of expected operating profit in thepresent worth of total profit for each technology in (15),investors can check the profitability of their investment. Onthe other hand, solving the equation �i(t) = 0 for ρ yieldsa value which is termed internal rate of return (IRR). Thisparameter can be used to define a dimensionless profitabilityindex

PIi(t) = IRRi(t)/ρ. (18)

The long-run economic equilibrium in an electricity marketis achieved when entering different types of generating unitsinto the market has brought the economic profit of eachindividual generation firm to zero while the sum of averagecosts of all generation firms is minimized [36]. In this state,the profitability index value of each generation technologywill be unity since its operating profit will exactly cover theamortized fixed cost. So, there is no incentive for investment.But the investors’ behavior does not track necessarily the long-run equilibrium. Investment will be performed if considerableprofit is reached while negative profit results in not investingat all. Greater profitability index makes more incentive forinvestors. Moreover, capacity retirement and demand growthshould be recovered by introducing new generating units.These factors should be considered to convert the profitabilitycriterion to the investment level. Olsina has proposed anS-shaped function with definite saturation level to describe

the aggregated capacity investment in each technology [33]

mi(PIi) = mmaxi /(1 + Exp(−(βi.PIi + γi))). (19)

The constant parameters can be computed by satisfying thecondition m(1) = 1. Finally, the investment rate is expressedusing the above logistic function, retired capacity rate, and therelated capacity addition to cover the maximum demand

Ii(t) = mi(PIi).(Prei (t) + Di(t)). (20)

D. Capacity Development

The capacity development modeling refers to the processof investment decision making, permission acquiring, newcapacity constructing, vintage modeling of existing capacities,and capacity retiring. All of these procedures can simply bemodeled using stock and flow structures of the processes. Therelated capacities in each stage play the role of stock variableswith some flow variables such as investment rate, permissionrate, construction completion rate, vintage transferring rate,and retirement rate. Important time delays in the model arepermission acquiring time, permit expiration time, constructiontime, vintage time, and unit lifetime. The related stock andflow equations are presented as follows [34].

The capacity under construction for each technology, com-prising the conventional and wind power capacities, is an ac-cumulation depending on the investment rate and constructionaccomplishing rate

Pci (t + �t) = Pc

i (t) +

t+�t∫t

(Ii(τ) − Pcai (τ)).dτ (21)

in which the accomplishing rate depends on the capacity underconstruction and construction time in the following way:

Pcai (τ) = Pc

i (t)/T ci . (22)

For any technology, the construction time may vary dueto project size, location, and facilities accommodation. Thus,an average value is hypothesized for the construction time.The vintage modeling is appointed for capacity developmentof conventional and wind capacities. The installed capacity ofeach technology can be described through an accumulation

Pi,j(t + �t) = Pi,j(t) +

t+�t∫t

(P ini,j(τ) − Pout

i,j (τ)).dτ (23)

in which the capacity rate entering a vintage of each generationtechnology is equal to the rate of departing the previous one

P ini,j+1(t) = Pout

i,j (t). (24)

In this paper, three vintages are assumed for all conventionaland wind power technologies. The aging times of vintages areequal and are calculated by dividing the technology’s lifetimeby the number of vintages. The departure rate is defined usingthe installed capacity of that vintage and the vintage agingtime

Pouti,j (t) = Pi,j(t)/T

Agei . (25)


TABLE I

Electricity Demand Characteristics

Initial peak demand (GW) 15Initial minimum demand (GW) 10Expected annual growth rate (%/year) 1.2Standard deviation of growth rate (%) 1Long-term price elasticity of demand −0.3

The entrance rate into the newest vintage is logically equiva-lent to the construction accomplishing rate [33]

P ini, 1(t) = Pca

i (t) (26)

and the departure rate of the oldest vintage is the same as theretired rate of the capacity

Pouti, 3 (t) = P re

i (t). (27)

IV. Simulation Results and Analysis

A case study is presented in order to investigate the impactof introducing TGC market and its dynamic interaction withelectricity market. The TGC target is assumed to increaselinearly from 5% to 25% during the 20 years of planningtime horizon. Some of the most important characteristics ofelectricity demand, generation technologies, and the behaviorsof wind power GenCo and DisCo in the TGC market aretabulated in Tables I–III. The penalty price of DisCos is setat twice the fundamental TGC price.

The values of parameters presented in all these tables areused for the base case scenario and some of them will bevaried to perform sensitivity analysis for other scenarios.The discount rate for investment process is assumed to be12.5 %/year for all technologies. The initial condition of thesystem is the long-run equilibrium. Therefore, the system is ina resting state at the beginning of the simulations. Using thisassumption means that we will avoid any exogenous sourcesof dynamics that might happen in the past and may affect thesystem operating in the future.

The study includes four parts. The first part includes simula-tions performed for the base case scenario which is character-ized by the values of the parameters in Tables I–III. The secondpart is stochastic simulation considering uncertain nature ofwind power generation due to the wind speed uncertainty.The third part is the sensitivity analysis of the investmentvariables to the exogenous parameters in the electricity market.Finally, trading strategies in TGC market and sensitivity ofthe investment variables to them are assessed in the fourthpart. Since the competition is among generation technologiesin our system dynamics model, all generating units of the sametechnology in our simulations are assumed to be a sole GenCo.The same consideration is also assumed for all DisCos.

A. Base Case Scenario

As the base scenario, the case study is simulated using thebase data presented above. Results are illustrated in Fig. 3. InFig. 3(a), the electricity price, the yearly average electricity

TABLE II

Generation Technologies Characteristics

HC CCGT GT WindAverage construction time (year) 3 1.5 0.75 1Lifetime (year) 40 30 20 20Amortization period (year) 25 20 15 15Investment cost ($/kW) 1000 600 500 1500Fuel price ($/MWh) 5 13 13 –Emission price ($/Ton of CO2) 0 0 0 –Maintenance cost ($/kW/year) 16 16 16 12

TABLE III

Parameters to Describe the GenCo and DisCo Behaviors

in TGC Market

Wind GenCo Variables ValuesObligation time (year) 1Price elasticity of TGC sale 0.8TGC validation lifetime (year) ExtensiveDisCo Variables ValuesObligation time (year) 1Price elasticity of TGC purchase −0.8TGC validation lifetime (year) 1Borrowing fraction allowed 0Penalty price ($/MWh) 30

price, and future expected electricity price are shown. TheTGC price is depicted in Fig. 3(b). Investment rate of eachtechnology is the consequence of investors’ behaviors in priceexpectation and profitability assessment. Sensible upward anddownward trends in invested and installed capacities andconsequently in the reserve margin make business cycles. Thegrowth of electricity price in initial and last years of simulationtime as well as the low prices in intermediate years is theconsequence of investment booms and busts. The TGC priceis cleared from TGC sale rate by wind power GenCo and TGCpurchase rate by DisCo. In initial years, the small amount ofTGC causes the TGC price to increase and hit its cap. Aninclination of wind power GenCo to hold or sell the TGCs andDisCo to purchase them makes the TGC price to oscillate.

The TGC target and the share of wind power generation(or wind energy penetration) in DisCo’s electrical demand areshown in Fig. 3(c). The wind energy penetration is 5% inthe first year of simulation time and it is desired to increaselinearly to reach 25% at the end of simulation time interval inorder to meet the regulated TGC target.

In initial years, the deficiency of TGC causes the windenergy penetration to be less than the TGC target. Afterwards,whenever the TGC price is low, DisCo tends to buy moreTGCs and present them to redemption authority before theirexpiration, so that the wind energy penetration meets and thenexceeds the requirement (even more than 30%). In contrast,when the TGC price is high, wind energy penetration is low.In final years, the TGC amount is high enough that DisCowill learn to purchase in such a way to modify the TGCtarget. The TGC price remains at the bottom price in the endof simulation time horizon.

Fig. 3(d) illustrates the TGC volumes which are held bywind power GenCo and DisCo. When the TGC price increases,


Fig. 3. Simulation results of basic scenario. (a) Electricity price, yearly average, and expected electricity prices. (b) TGC price. (c) TGC target and windgeneration share in electricity demand. (d) TGC volume held by wind GenCo and DisCo. (e) Investment rate of each technology. (f) Installed capacity ofeach technology.

GenCo tends to sell more and hold less and vice versa. Whenthe TGC prices are decreasing at the end of the simulationtime, GenCo tends to sell less and hold more TGCs to wait andsee higher TGC prices. So, the TGC holding volume of GenCohas an increasing pattern. Besides, the DisCo tends to buymore in this time interval. Therefore, the TGC holding volumeof DisCo has also an ascending pattern until the year 2026when the TGC obligation is met by DisCo and consequently,it is not necessary to buy more after this time. So, the TGCvolume held by DisCo is decreasing at the final years.

The wind capacity investment is the consequence of in-centives obtaining from both TGC and electricity markets.Two investment waves in wind capacity can be seen inFig. 3(e). Wind power investment rate increases till 2023due to high TGC price. After the year 2026, the electricitymarket dominates the TGC market with respect to investmentsso that the wind capacity investment (like investments inother technologies) increases due to electricity price spikes.In Fig. 3(f), the installed capacities for three conventional andwind power technologies are depicted. Forever, the installationrate of wind capacity is more than its retirement rate. So, thewind power installed capacity has an increasing pattern.

B. Stochastic Simulation

In this section, the results of stochastic simulation usinguncertain wind speed are presented. The Weibull distributionfunction with related parameters is selected for wind speed.Using Monte Carlo method, several scenarios based on thisdistribution function are generated that each of them deter-mines a track of random time series using ARMA method. Inour case study, 1000 scenarios are simulated in order to coveralmost all values of wind speed and the results are reflected inseveral curves of some output variables. The 100% percentilesshow the upper and lower curves to bind all simulation runsand the narrow band of these two curves is referred to asconfidence interval. For instance, the confidence intervals ofTGC price and wind installed capacity due to wind speeduncertainty are shown in Fig. 4.

Wind speed uncertainty has low effect on TGC price inthe first years of simulation time due to TGC shortage. Then,high wind speed causes more wind power generation, sothat more TGCs are issued. Later on, the TGC price willdecrease and as a result it drops below from its cap verysoon. Primarily enough capacity is existed in the market andthe electricity price does not depend on the variations of wind


Fig. 4. Confidence interval for (a) TGC price and (b) wind installed capacity due to uncertainty in wind speed.

TABLE IV

Sensitivity of Parameters to Fuel Price Variations in Electricity Market

Fuel price (fossil fuel, gas fuel) ($/MWh) (3, 11) (4, 12) (5, 13) (6, 14) (7, 15)Electricity price spike ($/MWh) in first decade 82.2 89.5 96.7 106.6 109.8Electricity price spike ($/MWh) in second decade – 182.2 200.0 162.2 –Average of TGC price ($/MWh) 19.3 17.5 17.2 16.9 16.8Average of wind investment rate (MW/year) 1040 1190 1320 1060 870Wind installed capacity (MW) 18 540 21 420 23 970 18 840 14 890

GenCo’s cumulative profit from electricity market (×109$) 8.33 12.13 14.19 12.35 8.32

GenCo’s cumulative revenue from TGC market (×109$) 5.24 4.71 4.56 4.51 4.49

GenCo’s total profit from both markets (×109$) 13.57 16.84 18.75 16.86 12.81

TABLE V

Sensitivity of Parameters to Emission Tax Variations in Electricity Market

Emission tax ($/Ton of CO2) 0 5 10 15 20Electricity price spike ($/MWh) in first decade 96.7 100.1 103.3 106.8 111.2Electricity price spike ($/MWh) in second decade 200.0 92.3 – – –Average of TGC price ($/MWh) 17.2 16.6 16.5 16.5 16.4Average of wind investment rate (MW/year) 1320 1035 980 950 850Wind installed capacity (MW) 23 970 18 120 16 970 16 345 14 335

GenCo’s cumulative profit from electricity market (×109$) 14.19 10.30 8.50 8.20 7.43

GenCo’s cumulative revenue from TGC market (×109$) 4.56 4.42 4.34 4.34 4.33

GenCo’s total profit from both markets (×109$) 18.75 14.72 12.84 12.54 11.76

power generation due to wind uncertainty. No changes of TGCand electricity prices due to uncertainty in initial years makethe confidence interval of wind installed capacity to be smallin this time period.

C. Electricity Market Parameters Assessment

In this section, the sensitivities of electricity price spikesin first and second decades of simulation time, average ofTGC price, average of wind investment rate, wind powerinstalled capacity, GenCo’s cumulative profit in electricitymarket, GenCo’s cumulative revenue in TGC market, andGenCo’s total profit to fuel price and emission tax variationsare studied. For different fuel (fossil fuel and gas) prices,Table IV gives the values of the aforementioned quantities.

The effect of TGC market implementation on electricityprice can be suitably reflected in the second decade. If the fuelprice increases, the LRMC of most expensive conventionaltechnology will increase, so that lower TGC price will besufficient to motivate wind power generation and make it asdominant technology for investing. This can be seen from the

decrease of the average of TGC price and TGC revenues inTable IV. In this way, the TGC price drops earlier from itscap value and hit the bottom price. Initial electricity pricespikes will be more intensive if the fuel becomes expensive.Electricity prices in the following years are influenced fromadequacy or shortage of installed capacities. In the case of(7, 15) fuel prices, the initial electricity price spikes are sohigh that no capacity shortage happens in the following yearsdue to adequate investment.

The same sensitivity studies are illustrated in Table V fordifferent values of emission tax. Applying higher taxes foremission also increases the LRMC of conventional technolo-gies. So, the TGC price will be lower and as a result, therevenues of wind power GenCo will decrease. In this case,the initial electricity price spikes are extended when the taxis higher. More severe initial electricity price spikes willresult in sufficient investment and no other price spikes willlikely to happen. The results from Tables IV and V showthat the increase in electricity price will decrease the TGCprice.


TABLE VI

Sensitivity of Parameters to GenCo’s Maximum Holding Time of TGC in TGC Market

TGC validation lifetime for GenCo (year) 5 3 1.5 1 0.5 0.25Average of TGC price ($/MWh) 17.2 17.1 17.1 17.0 16.7 16.6Average of wind investment rate (MW/year) 1320 1170 1155 1160 1315 1320Wind installed capacity (MW) 23 970 20 905 20 630 20 790 23 960 24 070

GenCo’s cumulative profit from electricity market (×109$) 14.19 12.05 11.92 12.06 14.38 14.30

GenCo’s cumulative revenue from TGC market (×109$) 4.56 4.66 4.75 4.74 4.54 4.41

GenCo’s total profit from both markets (×109$) 18.75 16.71 16.67 16.80 18.92 18.71

DisCo’s cumulative penalty payment (×109$) 3.77 3.75 3.71 3.69 3.65 3.61

DisCo’s total payment (×109$) 22.52 20.46 20.38 20.49 22.57 22.32

TABLE VII

Sensitivity of Parameters to DisCo’s TGC Maximum Borrowing Fraction Allowed in TGC Market

TGC validation lifetime for GenCo (year) 5 5 5 0.5 0.5 0.5Maximum fraction of TGC allowed for borrowing 0 0.3 0.8 0 0.3 0.8Average of TGC price ($/MWh) 17.0 20.3 22.32 16.7 19.9 22.80Average of wind investment rate (MW/year) 1320 1110 1189 1315 1160 1165Wind installed capacity (MW) 23 970 19 500 20 980 23 960 20 480 20 525

GenCo’s cumulative profit from electricity market (×109$) 14.19 11.62 11.07 14.38 11.69 11.04

GenCo’s cumulative revenue from TGC market (×109$) 4.56 5.63 7.17 4.54 5.79 7.55

GenCo’s total profit (×109$) 18.75 17.25 18.24 18.92 17.48 18.59

DisCo’s cumulative penalty payment (×109$) 3.77 2.42 0.86 3.65 2.38 0.76

DisCo’s total payment (×109$) 22.52 19.67 19.10 22.57 19.86 19.35

D. TGC Market Parameters Assessment

In this part, the sensitivity analysis to some strategic behav-iors in TGC market is investigated. First, the values of someimportant parameters in both electricity and TGC marketsdue to variations of maximum TGC holding time of GenCoare presented in Table VI. The DisCo’s cumulative penaltypayment and total payment were added in this table. The TGCvalidation lifetime of five years represents the banking whichis the extensive holding time of TGCs for GenCo.

Limited holding time restricts the possibility of TGCspeculation for GenCo and consequently prevents from highprices. It can be seen from the table that the average of TGCprice increases with the extension of holding time. But thisdoes not necessarily mean that the GenCo’s revenue in TGCmarket will increase. When the holding time exceeds the1.5 year, the cumulative revenues of GenCo from TGC marketbehaves in opposite direction. The reason is that the DisCoprefers to pay penalty to ISO instead of buying expensiveTGCs from GenCo. The greatest penalty payment is in thecase of banking. In the case of limited holding time, the timegraph of TGC price (which is not shown here for brevity)has more volatility than the TGC price in the case of banking[Fig. 3(b)]. The TGC price in the case of limited holdingtime also remains in the price cap for fewer years than thatof Fig. 3(b). The least revenue of GenCo in electricity markethappens in the case of 1.5 year holding time. In the viewpointof DisCo, this holding time of GenCo is favorable due to itsleast total payment. Although this case is desirable for GenCoin TGC market, but the total revenues from both markets arethe most in the case of 0.5 year holding time.

Finally, the last analysis is the evaluation of borrowingeffects. Table VII shows the values of the same parametersas in Table VI for different fractions of borrowing allowed to

DisCo. This case can be assessed in both situation of GenCo’sextensive or limited holding time. Borrowing fractions of0, 0.3 and 0.8 were tested for both situations of five yearand 0.5 year holding times. The cumulative penalty paymentof DisCo is considerably reduced with the introduction ofborrowing possibility. This affects directly on the cumulativerevenue of GenCo in the TGC market. Since the DisCotends to buy TGCs from GenCo instead of paying penalties,the TGC market prosperity will increase and the averageTGC price will be higher than the case of no borrowing.It was seen from time graphs that the TGC price remainsat the cap somewhat longer. The value of penalty reductionis dominated over the value of GenCo’s revenue growth.So, the borrowing affects are particularly important forDisCo.

Adequate installation of wind capacity due to TGC marketincentives makes the electricity price in the following yearsslightly smaller and this will reduce subsequently the revenueof wind power GenCo in the electricity market.

V. Conclusion

A dynamic simulation model that helps to get insights intohow the combined competitive electricity and TGC marketscan make investment incentives for renewable technology hasbeen presented. In the proposed system dynamics model,numbers of balancing loops model the electricity and TGCmarkets behaviors and interactions between them. Some regu-lated policies and strategic behaviors in TGC market includingthe extensive or limited TGC holding and TGC borrowinghave been described and included in the model. Conventionalgenerating technologies were modeled price-dispatched whilethe wind power was assumed to be available according to thestochastic nature of wind speed.


A case study exhibits the effectiveness of the proposedmodel for wind capacity expansion in this dynamic frameworkusing the incentives gained from both markets. In addition tothe base case scenario simulation and stochastic simulationconsidering the wind speed uncertainty, sensitivity analysisto important market parameters, regulations, and strategicbehaviors in both electricity and TGC markets have beendone. Those which cause the electricity price to becomeexpensive make the average TGC price to reduce. Differentholding time of TGCs for GenCo and the possibility ofborrowing for DisCo also make some changes in TGC price,penalty payment and total payment of DisCo, TGC marketrevenues and electricity market profits of GenCo.

The TGC market design is relatively new. Moreover, notmany TGC markets have yet experienced the trend of fullrenewable capacity investment and requirements to follow theTGC target. Therefore, using such a simulation tool can helpthe regulators to choose appropriate policies and analyze theinteractions of electricity and TGC markets in the phase ofmarket preliminary design.

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Masoud Hasani-Marzooni received the B.Sc. andM.Sc. degrees in electrical engineering from theSharif University of Technology, Tehran, Iran, in2001 and 2004, respectively. He is currently pursu-ing the Ph.D. degree with the Department of Electri-cal Engineering, Sharif University of Technology.

His current research interests include restructuredpower system planning and operation, and powersystem economics.

Seyed Hamid Hosseini (M’89) received the B.S.degree from the University of Oklahoma, Norman,in 1983, and the M.S. and Ph.D. degrees fromIowa State University, Ames, in 1985 and 1988,respectively, all in electrical engineering.

Since 1988, he has been with the Department ofElectrical Engineering, Sharif University of Technol-ogy, Tehran, Iran. He is currently an Associate Pro-fessor. His current research interests include powersystem operation, optimization, and planning.

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Dynamic Interactions of TGC and Electricity Markets to Promote Wind Capacity Investment

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