Modeling and analysis of renewable energy obligations and technologybandings in the UK electricity market

Gül Gürkan, Romeo Langestraat n

CentER, Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands

H I G H L I G H T S

� We model and analyze three renewable obligation policies in a mathematical framework.� We provide revenue adequate pricing schemes for the three policies.� We carry out a simulation study via sampling.� The UK policy cannot guarantee that the original obligation target is met.� Cost reductions can lead to more pollution or higher prices under banding policies.

a r t i c l e i n f o

Article history:Received 25 October 2013Received in revised form15 March 2014Accepted 17 March 2014Available online 13 April 2014

Keywords:Renewable energy obligationsGreen certificatesMathematical programmingUK electricity market

a b s t r a c t

In the UK electricity market, generators are obliged to produce part of their electricity with renewableenergy resources in accordance with the Renewable Obligation Order. Since 2009 technology bandinghas been added, meaning that different technologies are rewarded with a different number ofcertificates. We analyze these two different renewable obligation policies in a mathematical representa-tion of an electricity market with random availabilities of renewable generation outputs and randomelectricity demand. We also present another, alternative, banding policy. We provide revenue adequatepricing schemes for the three obligation policies. We carry out a simulation study via sampling. A keyfinding is that the UK banding policy cannot guarantee that the original obligation target is met, hencepotentially resulting in more pollution. Our alternative provides a way to make sure that the target ismet while supporting less established technologies, but it comes with a significantly higher consumerprice. Furthermore, as an undesirable side effect, we observe that a cost reduction in a technology with ahigh banding (namely offshore wind) leads to more CO2 emissions under the UK banding policy and tohigher consumer prices under the alternative banding policy.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In decentralized electricity markets, firms are mainly focusedon maximizing their profits while competing with other firms.Investments in cheap and often polluting technologies tend toserve these goals well. This is in conflict with the goals set bygovernments as they aim at reducing pollution and want thereforeto create financial incentives to make investments in cleanertechnologies more attractive. One way of creating these incentivesis by means of a renewable energy obligation. This is a target on

the proportion of electricity that should come from renewableresources and is imposed on one group of operators in the market.In several US states and in European countries like Belgium,Poland, Romania, Sweden, Italy, and UK, a renewable obligationis in effect.1 The so-called green certificates are used to showcompliance to the target, and typically one such certificaterepresents 1 MWh of renewable electricity production. At theend of each obligation period, often a year, each seller or producershould submit a certain number of certificates to the regulator. Whennot satisfying the target, typically a buy-out fine has to be paid.

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/enpol

Energy Policy

http://dx.doi.org/10.1016/j.enpol.2014.03.0220301-4215/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail addresses: ggurkan@tilburguniversity.edu (G. Gürkan),

r.langestraat@tilburguniversity.edu (R. Langestraat).

1 For overviews of different support mechanisms across Europe, see Fouquetand Johansson (2008) and Koster et al. (2011).

Energy Policy 70 (2014) 85–95

The latter comes with an opportunity cost that puts a value on eachcertificate, which forms the price that a seller is willing to pay to arenewable generator. The reward that generators receive adds to theshort-term profits in a way that high long-term investment costs canbe covered. Certificates can also be traded on a secondary market andas a consequence the renewable obligation does not oblige individualgenerators to produce a certain part of their electricity generationwith renewable resources.

The UK and Italy form an exception to the system where onecertificate represents 1 MWh of renewable electricity. In thesecountries certificates are banded according to technology, meaningthat for different (renewable) technologies a different number ofcertificates is handed out per MWh of production. These so-calledbanding systems in the UK2 and Italy3 can help in encouraginginvestments in less developed technologies as to make them morecompetitive in the long run. This way it can overcome one of theshortcomings of the regular renewable obligation which is knownto single out the most developed technologies, namely onshorewind power and to a lesser extent landfill gas (see Meyer, 2003;Wood and Dow, 2011; Verbruggen and Lauber, 2012). Althoughthese technologies may be financially attractive, due to all kinds ofgeographical constraints and opposition against onshore windfarms, it is unlikely that the renewable obligation target can bemet in the long run without investments in other renewabletechnologies like offshore wind, as emphasized by Toke (2011)and Wood and Dow (2011). As technology banding may result ina discrepancy between the total MWh of renewable electricityproduced and the total number of certificates, in the UK theobligation shifted from one on renewable production to one oncertificates. In the Italian system however, the regulator buysexcess certificates.

We investigate the effects and side effects of both a standardrenewable energy obligation and the UK banding system, usinga mathematical model of the electricity market. In addition,we introduce an alternative banding policy in which the obligationis on renewable production and where certificate prices aremodified to deal with the discrepancy between production andcertificates. We model these three policies in a mathematicalframework, by extending the stochastic version of the two stageinvestment model of the electricity market as introduced inGürkan et al. (2013). In the model, investments are considered aslong-term decisions (for example yearly) which take place at thefirst stage. Production, transmission, and market clearing areshort-term decisions (for example hourly or daily) that take placein the spot market, referred to as the second stage. At the secondstage, both demand and availability of renewable productioncapacity are subject to uncertainty. We assume perfect competi-tion at both stages meaning that firms are price takers.

In order to make our model a good representation of reality andto keep results analytically tractable, we will make two simplifyingassumptions with respect to the UK system. First of all, in the UK therenewable obligation is imposed on total electricity sales. Weassume though that the firms producing power are selling theirpower directly to consumers, meaning that the obligation will be onelectricity production. The second simplifying assumption concernsthe trading of certificates. In reality, certificates can be traded dailyon a secondary market and will have a certain value determined bythe short term demand for certificates. Trading would be done on adaily basis and result in day-to-day variations in the value of acertificate. We overlook the micro details of the secondary tradingmarket and therefore ignore the daily trading possibilities. Instead,

we consider the average certificate value that holds over the year,which is directly related to the yearly obligation target. This averagevalue is the reward that the regulator pays firms per certificate.

Typically, regulators strive for a certificate system to be revenueadequate, meaning that the system is self-financing without anyloss or gain for the regulator. Therefore, for each policy we proposea way to price certificates and to adjust consumer prices such thatthe regulator's expenses on certificate payments are covered bymark-ups that consumers pay on top of the electricity price.

The three obligation policies are analyzed in a numerical study.We consider a market with two non-renewable technologies (coaland combined cycle gas turbine (CCGT)) and three renewabletechnologies (onshore wind (ONW), offshore wind (OFFW), andlandfill gas (LFG)) and obtain investment quantities, prices, andCO2 emissions for all three policies. A key observation is that ineach policy, CO2 emissions are curbed both by the increasedrenewable capacity and by the replacement of coal by the cleanerCCGT. Comparing the original obligation with the banding policies,we find that technology banding fails to create the right incentivesfor the less established OFFW when the obligation target is set toolow. On the other hand, somewhat as a surprise, once OFFW isin the technology mixture, the UK banding system may resultin higher levels of CO2 emissions than the other systems. Thealternative banding system proposes a possible solution for thisundesirable side effect, albeit with relatively higher and less stableconsumer prices.

Finally we analyze the effect of a decrease in the investmentcost of OFFW. This leads to increased levels of CO2 emissions in theUK banding system and increased consumer prices in the alter-native system. These are obviously negative side effects of bandingsystems, implying that as costs reduce, financial support andhence bandings should be reduced accordingly.

This paper is organized as follows. In Section 2 we present theelectricity market investment model, and subsequently proposemodifications that account for the renewable obligation, the UKbanding system, and an alternative banding system. For each system,we present a self-financing pricing scheme. The numerical methodsand experimental data used for obtaining numerical results arepresented in Section 3. Results are discussed in Section 4. Section 5concludes and summarizes the policy implications.

2. The mathematical framework

2.1. The electricity market

We first provide a brief description of the electricity market.Given is an electricity grid with supply nodes at which firmsowning generation plants produce electricity using their technol-ogies that are renewable or non-renewable, and demand nodes atwhich consumers with, by assumption, inelastic random demandare located. Consumer demand is subject to uncertainty, caused byfor example seasonality and daily changes in weather patterns.The output of renewable power plants may also vary from day today and hour to hour. For example wind turbines are dependingon daily weather conditions and influenced by the actual windspeed. A unit investment in wind energy does not mean that wecan produce a given amount of power at all times. We refer to thisuncertainty as the uncertainty in availability of capacity.

Firms make decisions in two stages. At the first stage all firmssimultaneously maximize their profits while determining theiroptimal production capacity. Investment decisions can be seen aslong-term decisions that are made once in every year. First stageprofits of firms are dependent on the expected equilibrium out-come at the second stage, which in return is dependent onthe investment decisions of all firms at the first stage. At the first

2 For a description of the UK (banding) system, see Constable and Barfoot(2008) and Clark (2008).

3 For a description of the Italian system, see Giovannetti (2009).

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–9586

stage, only the underlying probability distributions (which can besimply based on past empirical data) of the second stage demandand availability of capacity are known; firms have to makedecisions on their optimal investment quantities without knowingthe outcome of the random variables.

At the second stage, all firms maximize their profits whileproducing electricity given their production capacity in the firststage. In addition, a transmission system operator (TSO) owningthe transmission grid is maximizing its own profits and taking careof the flows between supply and demand nodes. Finally, themarket is cleared by two types of market clearing conditions,namely an imposed price cap when there is unsatisfied demand,and a condition guaranteeing that demand is satisfied in all nodes.Second stage decision making and market clearing can be seen asa short-run process that repeats itself over and over again.Realizations of the random variables are revealed to the firmsand are thus realizations associated with a particular day (or hour).We assume perfect competition, and hence at both stages firmsare not aware of the fact that they can influence prices. Since at themarket equilibrium investment decisions of firms (indirectly)depend on decisions of other firms, we have a two stage gamebetween the firms. When the first stage is solved to optimality andthe second stage is at equilibrium, for none of the entities it isprofitable to deviate and thus a perfectly competitive equilibriumis obtained.

2.2. A two-stage model of the electricity market

A suitable mathematical framework for a two-stage game inthe electricity market is presented in Gürkan et al. (2013). Theymodel the electricity market in a two-stage setting and show thatunder perfect competition the resulting two-stage game with(demand) uncertainty at the second stage can be written as eithera standard two stage stochastic program or as a mixed comple-mentarity problem (MCP). In this paper, we will need to utilize thelatter formulation, since introducing one of the banding systems(the Alternative Banding System of Section 2.5) will induce non-linearities in the model. Furthermore, in order to understand thedirect effects of banding systems, we work with the followingsimplifying assumption: there is a single node. In effect, having asingle node means that we are focusing on a network withunlimited transmission capacities and that we can omit the TSO'sproblem dealing with the flows and associated constraints. Just fornotational convenience, we also assume that each firm has its owntechnology. The sets, parameters, and variables are given below.Sets:

KN the set of non-renewable technologiesKR the set of renewable technologiesK the set of all technologies ðK≔KN [ KRÞ.

Parameters:

ck unit production cost for technology kAKκk unit investment cost for technology kAKd demandMR

k ceiling on investments in renewable technology kAKR

VOLL value of unserved energy or lost load.

Variables:

xk generation capacity investment in technology kAKyk quantity of power generated by using technology kAKδ unserved demandpc consumer price

pNk price non-renewable technology kAKN gets per unit soldpRk price renewable technology kAKR gets per unit sold.

We additionally introduce ωAΩ, a random vector in the spaceof possible outcomes Ω, containing the outcomes of both randomavailable capacities and random demand. To incorporate uncertainavailability of capacity, for kAKR, we define Fkðx;ωÞ as somedifferentiable random function of the investment amount x oftechnology k at realization ωAΩ.4 For given ωAΩ, Fkðx;ωÞ is therealized available capacity in technology kAKR. Uncertain demandat realization ωAΩ is denoted by dðωÞ. In addition, all secondstage variables will get an ω attached to them to indicate that foreach ωAΩ their equilibrium value needs to be determined. It isworth to emphasize that Fkðx;ωÞ s and dðωÞ s may be obtainedfrom historical data or, for instance, computer-based simulations.

In the remainder of the paper, variables may get superscripts N andR depending on their corresponding technology in KN and KR,respectively. We next formulate the second stage problem as anumber of optimization problems combined with twomarket clearingconditions, and then present the first stage problem in MCP form.

2.2.1. The second stage problemRecall that at the first stage each firm kAK determines its

optimal investment quantity xk, in order to maximize its profit,defined as the expected optimal second stage profit minus theinvestment cost. At the second stage, each firm determines at anyrealization its optimal production quantity while maximizing itssecond stage profit, subject to the capacity constraint. The invest-ment quantities from the first stage and the price for which theelectricity is sold are taken as given and treated as parameters.Each non-renewable firm kAKN determines at any realizationωAΩ and for given xN and pNk ðωÞ a solution to

ΠNk ðxNk ;ωÞ≔max

yNkðωÞ

ðpNk ðωÞ�cNk ÞyNk ðωÞ

s:t: yNk ðωÞrxNk ðβNk ðωÞÞ

yNk ðωÞZ0: ð1ÞHere, βN

k ðωÞ, kAKN , ωAΩ, is the dual variable to the capacityconstraint and can be interpreted as the scarcity rent of technologyk at realization ω. Scarcity rents are key in determining the optimalinvestment quantities at the first stage, as we explain in Section 2.2.2.

Similarly, each renewable firm kAKR determines at any reali-zation ωAΩ and for given xR and pRk ðωÞ a solution to

ΠRk ðxRk ;ωÞ≔max

yRkðωÞ

ðpRk ðωÞ�cRk ÞyRk ðωÞ

s:t: yRk ðωÞrFkðxRk ;ωÞ ðβRk ðωÞÞ

yRk ðωÞZ0: ð2ÞAgain, βR

k ðωÞ, kAKR, ωAΩ, is the dual variable to the capacityconstraint and can be interpreted as the scarcity rent of technologyk at realization ω.

In addition, there are two market clearing conditions thatshould hold at a second stage equilibrium:

0rVOLL�pcðωÞ ? δðωÞZ00r ∑

kAKN

yNk ðωÞþ ∑kAKR

yRk ðωÞþδðωÞ�dðωÞ ? pcðωÞZ0: ð3Þ

The first condition indicates that there may be unsatisfieddemand, which we denote by δðωÞ. Whenever the unsatisfieddemand is positive, the consumer price is set to VOLL, the Value Of

4 One must use some caution here, since many differentiable functions maylead to problems as the profit functions for renewable generators would notnecessarily be concave as a function of x. A strong enough condition on Fk would forinstance be that it is affine as a function of x; this is also what we used in ournumerical experiments in Sections 3 and 4.

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–95 87

Lost Load, or to a high price-cap. In other words, VOLL canessentially serve as a price-cap and is in general taken as a highnumber, compared to regular consumer prices. When there is nounsatisfied demand, the second condition balances electricityproduction from all firms and consumer demand, and the con-sumer price pcðωÞ is set accordingly. In particular, the conditionensures that whenever there is excess production, the price is setat level zero.

Summarizing, the second stage problem at any realizationconsists of (1) for all kAKN , (2) for all kAKR, and two marketclearing conditions given by (3). For given xN and xR, a secondstage equilibrium can be determined only when the relationbetween the prices pN and pR and the consumer price pc is given.This relation is fixed in a pricing scheme imposed by a regulator.Details are further discussed in Sections 2.3.1, 2.4.1, and 2.5.1. Afterfixing such a relation by means of a pricing scheme, we will restatethe second stage problem as the set of KKT-optimality conditionsto (1) and (2) along with (3); see below in Section 2.3.2.

2.2.2. The first stage problemGiven an equilibrium at the second stage, firms determine their

optimal first stage investment quantities based on informationfrom the second stage. An optimal investment decision maximizesa firm's long term profits, consisting of the expected optimalsecond stage profit minus the investment cost. These optimizationproblems can be found in Appendix A. Since the remainder of thispaper relies on a complementarity formulation, in this section weformulate the first stage as an MCP by deriving the KKT-optimalityconditions of the underlying optimization problems. The KKT-optimality condition for the first stage problem of non-renewablefirm kAKN is given by

0r�Eω½βnNk ðωÞ�þκNk ? xnNk Z0: ð4Þ

This condition follows from writing the Lagrangian function of theunderlying optimization problem (A.1) of firm kAKN and takingthe derivative with respect to xNk , kAKN . A detailed derivation offirst stage conditions can be found in Gürkan et al. (2013); here weonly give an interpretation. xnNk is the optimal investment quantityin non-renewable technology kAKN and βnN

k ðωÞ is the optimalscarcity rent taken from the second stage in ωAΩ when x¼ xn.For every kAKN , at least one of the two sides in (4) should holdwith equality, and hence there can only be a positive investmentin technology kAKN if the corresponding expected scarcity rentcovers the investment cost κNk . For any ωAΩ, βnN

k ðωÞ can now beinterpreted as the value of an additional unit investment intechnology kAKN .

Firms with renewable technologies solve similar problems.However, there can be a ceiling on capacity investments due tofor example regulation or physical limitations. This is typical forsome renewable technologies like landfill gas. Hence, the follow-ing constraint would be added to the optimization problems ofeach renewable technology kAKR, in Appendix A:

xRk rMRk ðζRk Þ;

where ζRk is the nonnegative dual price associated with the ceiling;below we provide an interpretation of this dual price. Then, theKKT-optimality conditions for the first stage problem of renewablefirm kAKR are given by

0r�Eω∂FkðxnRk ;ωÞ

∂xRkβnRk ðωÞ

" #þκRk þζnR

k ? xnRk Z0

0rMRk�xnRk ? ζnR

k Z0: ð5ÞThese conditions follow from writing the Lagrangian function ofthe underlying optimization problem (A.2) subject to (A.3), andtaking derivatives with respect to xRk and ζRk, kAKR. xnRk is the

optimal investment quantity in renewable technology kAKR andβnRk ðωÞ is the optimal scarcity rent taken from the second stage in

ωAΩ when x¼ xn. The first condition in (5) implies that at leastone of the two sides should hold with equality and hence thatthere can only be a positive investment in technology kAKR ifEω½ð∂FkðxnRk ;ωÞ=∂xRk Þβ

nRk ðωÞ� covers the sum of the investment cost

κRk and the dual price, ζnRk , associated with the ceiling. Here, βnR

k ðωÞis the optimal scarcity rent corresponding to a unit production atrealization ωAΩ, and ð∂FkðxnRk ;ωÞ=∂xRk Þ is the change in productioncorresponding to a unit change in investment. Hence, ð∂FkðxnRk ;ωÞ=∂xRk Þβ

nRk ðωÞ represents the scarcity rent of a unit investment in

ωAΩ when x¼ xn. ζnRk can be seen as the additional scarcity

rent that comes with the ceiling, MRk. When the ceiling becomes

binding, another, more expensive technology will be used tosatisfy demand. As a consequence prices, and hence scarcity rents,increase with the additional rent ζnR

k . The second condition in (5)guarantees that ζnR

k is zero whenever the ceiling is not binding.The entire two-stage game now consists of the first stage

optimality conditions (4) for all kAKN and (5) for all kAKR, andfor all ωAΩ a second stage problem consisting of (1) for all kAKN ,(2) for all kAKR, and two market clearing conditions (3). We nextintroduce a renewable obligation and a system of tradable greencertificates, before going into more detail about the second stageequilibrium.

2.3. A renewable obligation and tradable green certificates

A renewable obligation target, denoted by ϕ, is set by theregulator. ϕA ½0;1� is the minimum proportion of total electricityproduction that should come from renewable resources. Let YN

ω ¼Eω½∑kAKN yNk ðωÞ� and YR

ω ¼ Eω½∑kAKRyRk ðωÞ� be the total expectedproduction using non-renewable and renewable plants, respec-tively. Given the obligation target it should hold that

YRω

YRωþYN

ω

Zϕ: ð6Þ

Production with renewable resources is in general more expensive(when considering both investment and production cost) thanproduction with non-renewable resources. The obligation (6)forces producers to replace non-renewable production withrenewable production and thus comes with a certain additionalcost. Rewriting (6) with ν as its dual variable leads to the followingcomplementarity condition that is imposed on the first stage ofthe problem:

0rEω ∑kAKR

ð1�ϕÞyRk ðωÞ" #

�Eω ∑kAKN

ϕyNk ðωÞ" #

? νZ0: ð7Þ

The dual variable to (7), ν, will be the mark-up that renewablegenerators get. These mark-ups are given to the firms throughcertificates. For each unit production, a renewable certificate isobtained and thus ν is going to be the value of such a certificate.Certificates can either be traded on a secondary market, or sold tothe regulator to show compliance to the obligation. When tradingis considered, the value of ν at equilibrium gives us the fair pricefor each certificate. When, like we assume, the regulator rewardsfirms for owning certificates, ν will be the reward per certificatefirms get paid at the end of each period, typically a year. Thus,we may refer to ν as the certificate price (from the regulator'sperspective) or reward (from the firm's perspective).

2.3.1. Pricing, financial incentives, and revenue adequacyWe consider the effect of rewards on the prices determined at

each realization. The electricity price is usually set by the technol-ogy that produces with the highest marginal production cost.Since the fuel cost and hence the unit production cost (as opposed

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–9588

to the unit investment cost) of renewable technologies will ingeneral be very low, without loss of generality we can assume thatthe electricity price will be set by a non-renewable technology. Werefer to this price as the base price of electricity and denote it bypeðωÞ. When power is bought from a non-renewable generatorkAKN , the price paid per unit thus equals pNk ðωÞ ¼ peðωÞ, ωAΩ.When a renewable generator kAKR sells power, it sells both thepower (at price peðωÞ) to the consumer and the certificate (at price ν)to the regulator, and should therefore be paid pRk ðωÞ ¼ peðωÞþν.

The rewards paid by the regulator should be financed in certainway, in order for the system to be revenue adequate. As such, wesuggest a way to cover the regulator's expenses on rewards byadjusting the consumer price via a pricing scheme. More specifi-cally, we let consumers pay a mark-up on top of the electricityprice. The mark-up is determined in such a way that the additionalexpected income of a certain period covers the expected rewardspaid to firms for owning certificates, taking into account that inelectricity markets consumers typically pay a fixed consumer pricethat is independent of the resource.

If consumers would only pay the electricity price peðωÞ, therewards paid to the firms could not be covered. Since a part ϕ ofthe total production should come from renewable resources, giventhat the total expected production equals Yωð ¼ YN

ωþYRωÞ, the total

expected renewable production should be ϕYω. This is also thenumber of times a reward should be paid to the firms. Hence, themark-ups for the consumer price should cover ϕYων. Assumingthat all the produced power will be sold, it should hold that themark-up Δpc is the solution of ΔpcYω ¼ϕYων, resulting in aconsumer price equal to pcðωÞ ¼ peðωÞþϕν, ωAΩ. The mark-upis thus equal in all realizations ωAΩ, and per realization it ispossible that rewards paid to firms do not equal mark-ups paid byconsumers; in expectation however, they are equal. Summarizing,we impose the following pricing scheme in every ωAΩ:

pNk ðωÞ ¼ peðωÞ; 8kAKN

pRk ðωÞ ¼ peðωÞþν; 8kAKR

pcðωÞ ¼ peðωÞþϕν: ð8Þ

2.3.2. Equilibrium conditionsGiven the pricing (8), we can express both pNk ðωÞ and pRk ðωÞ

respectively in (1) and (2) in terms of pcðωÞ; that is,pNk ðωÞ ¼ pcðωÞ�ϕν for kAKN and pRk ðωÞ ¼ pcðωÞþð1�ϕÞν forkAKR. Now for any ωAΩ, a solution of the entire second stageproblem can be obtained by solving the KKT conditions of (1) and(2), and the market clearing conditions (3) for given x and ν and atany ωAΩ:

0rβnNk ðωÞ�pncðωÞþϕνþcNk ? ynN

k ðωÞZ0; 8kAKN

0rβnRk ðωÞ�pncðωÞ�ð1�ϕÞνþcRk ? ynR

k ðωÞZ0; 8kAKR

0rxNk �ynNk ðωÞ ? βnN

k ðωÞZ0; 8kAKN

0rFkðxRk ;ωÞ�ynRk ðωÞ ? βnR

k ðωÞZ0; 8kAKR

0rVOLL�pncðωÞ ? δnðωÞZ0

0r ∑kAKN

ynNk ðωÞþ ∑

kAKR

ynRk ðωÞþδnðωÞ�dðωÞ ? pncðωÞZ0: ð9Þ

The entire two-stage investment problem can now be solved bysimultaneously solving the first stage optimality conditions con-sisting of (4) for all kAKN , (5) for all kAKR, and the obligationconstraint (7), and the second stage conditions (9) for any ωAΩand with x¼ xn and ν¼ νn.

2.4. The UK banding system

The previously introduced model was applicable to the UKsystem until the 1 April 2009, when the Renewable Obligation

Order 2009 became effective.5 In this regulatory document abanding system was added to the renewable obligation. In theold system, a unit production with a renewable technology waseligible for one renewable energy certificate and hence wouldreceive the certificate price for each unit production. In the newsystem, renewable certificates are banded according to technology.This means that different renewable technologies are eligible for adifferent number of certificates. The main reason for introducingbandings is to encourage investments in less established technol-ogies (by giving them more certificates per unit production). Theoriginal renewable obligation failed to give the right financialincentives as it tended to mainly benefit onshore wind power andlandfill gas, as noted by Meyer (2003). As argued by Toke (2011)and Wood and Dow (2011), investments in these more establishedtechnologies are limited not by the lack of financial incentives, butmostly because of landscape protection, public opposition, andspace. Therefore, investment in less developed technologies willbe necessary in order to be able to achieve the ambitious renew-able energy targets.

In the new system onshore wind is used as the reference forbandings. A unit production with onshore wind is rewarded withone certificate, less established technologies like offshore wind andgeothermal are rewarded with 1.5 and 2 certificates, respectively,and more established technologies like sewage gas and landfillgas are rewarded with only 0.5 and 0.25 certificates, respectively.The regulator may change these coefficients from time to timewhen a different support is desirable. This has recently been done foroffshore wind, which now will get 2 certificates per unit productionuntil 2014.

With the banding system as introduced in the UK, the obliga-tion shifts from one on the renewable production to one that isexpressed as the number of certificates that should be presentedby the entire market at the end of each period. Hence, with thenew system, obligation constraint (7) should be replaced by acondition of the following form:

0rEω ∑kAKR

αkyRk ðωÞ

" #�R ? νZ0; ð10Þ

where R is the number of certificates all firms together have topresent, and αk is the number of certificates firm kAKR receives forproducing one unit of electricity with renewable technologykAKR.

As explained in great detail in the Renewable Obligation Order2009, in order to determine R, the UK regulator performs twocalculations estimating the number of certificates that should orcan potentially be issued. Whichever calculation gives the highestestimate will be set as the obligation target R. The first calculation,Calculation A, is based on a fixed target representing the numberof certificates that firms should produce per unit of electricityproduced. This target is in fact the original obligation target ϕ thatwas used in system (7). The total number of certificates thatshould be issued based on this fixed target is simply ϕ times theexpected total electricity production and will be defined as A.

In the second calculation, Calculation B, the number of certifi-cates that is likely to be issued, given the existing renewableproduction capacity and the expected new built capacity, isestimated. In addition a headroom of 8% is added. The outcomeis defined as B.

In practice this means that if A4B, it is expected that theexisting and expected new built capacity will not be sufficient toreach the original obligation target ϕ that was used for CalculationA. The target number of certificates is set at R¼A to oblige firms to

5 See url http://www.legislation.gov.uk/uksi/2009/785/contents/made?view=plain.

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–95 89

install additional renewable capacity. If B4A, it means that thereis already sufficient existing plus expected new built capacity inthe system. When this happens, the original target ϕ may be metquite easily and as a consequence the value of certificates maydrop to zero, resulting in an unfavorable situation for the renew-able generators. The obligation target is set at R¼B in an attemptto avoid this.

After determining the target R, the regulator expresses theobligation as the number of certificates that should be presentedper unit production; we define this number as ϕUK . If R¼A, firmsare obliged to submit ϕUK ¼ϕ certificates per unit production.If R¼B, firms are obliged to submit ϕUK ¼ϕB=A certificates perunit production. Rewriting (10) with ν as its dual variable, weobtain

0rEω ∑kAKR

ðαk�ϕUK ÞyRk ðωÞ� ∑kAKN

ϕUKyNk ðωÞ" #

? νZ0: ð11Þ

Note that ideally it would hold that, with the obligation oncertificates, a fraction ϕUK of the total production comes fromrenewable resources like in the old obligation system. However,since there is no one-to-one relationship between renewableproduction and certificates anymore, this is not necessarily thecase. In case a major part of the obligation is satisfied by atechnology with a high banding coefficient, the actual renewableproduction may be (much) lower than the desired target onproduction and as a consequence the banding system could resultin a more polluting mixture of technologies. In general, CalculationB may set the target on certificates a bit higher than the originalobligation ϕ, but when there are technologies with a high bandingcoefficient, one may not guarantee that the original target onrenewable production is met unless the target on certificates isincreased accordingly. We will come back on this issue in ourdiscussion of numerical results.

2.4.1. Pricing, financial incentives, and revenue adequacySince different technologies are rewarded with a different

number of certificates, prices paid to the generators will dependon the technology used. Therefore we will have to adjust thepricing (8) introduced under the original renewable obligation.Per unit production, a renewable technology kAKR is given αk

certificates. Since, when selling the electricity, firms also sell theircertificates, at any ωAΩ renewable technology kAKR is then paidthe base price, peðωÞ, plus αk times the certificate price ν. In thecorresponding pricing scheme, at any ωAΩ, we set pNk ðωÞ ¼ peðωÞ,kAKN and pRk ðωÞ ¼ peðωÞþαkν, kAKR. With a consumer pricesimilar to the one in (8), namely pcðωÞ ¼ peðωÞþϕUKν, it turnsout that, in expectation, mark-ups paid by consumers equal therewards paid to firms for owning certificates. That is, renewabletechnologies are paid

νEω ∑kAKR

αkyRk ðωÞ

" #;

which by (11) equals νϕUKYω. It can easily be seen that νϕUKYω isthe total mark-ups paid by consumers, and hence rewards paid tofirms are covered. This means that the pricing scheme is revenueadequate. Summarizing, the adjusted pricing scheme for the UKbanding system becomes, at any ωAΩ,

pNk ðωÞ ¼ peðωÞ; 8kAKN

pRk ðωÞ ¼ peðωÞþαkν; 8kAKR

pcðωÞ ¼ peðωÞþϕUKν: ð12Þ

2.4.2. Equilibrium conditionsThe second stage equilibrium conditions are similar to (9), but

with pricing (12) replacing pricing (8). At the first stage, (7) isreplaced by (11).

2.5. An alternative banding system

As the UK banding system does not necessarily guarantee thatthe obligation target on renewable production (7) is satisfied andmay even result in a more polluting mixture, we propose analternative banding system. Unlike in the UK banding systemwhere the obligation shifted to one on certificates, the obligationwill be imposed on production in the same way it was done in theoriginal renewable obligation (that is, as in (7) as opposed to (11)).On the other hand, certificates will still be handed out based onthe pre-specified banding coefficients. Since in this case we haveno one-to-one correspondence between a unit of renewableproduction and a certificate, and since the target is not oncertificates like in the UK banding system, we can no longerguarantee revenue adequacy when firms receive the dual price νin (7) as the certificate price. Instead, as discussed in detail inSection 2.5.1, firms will receive an adjusted price that is based onthe number of certificates on the market and the total renewableproduction.

Although this alternative system guarantees that the originalobligation target on production is satisfied, there may be a fewdrawbacks to this system. First of all, the price of a certificate is nolonger determined by the secondary trading market. The regulatorhas to intervene and buy certificates from firms at an adjustedprice that is influenced by the technology mixture. The interven-tion in the trading process is likely to come with a certainadministrative burden. Second, as we will see in more detail inour numerical study, the consumer price is much more sensitive tothe technology mixture and in particular is higher when a largeshare of the production is done with a technology with a bandingcoefficient higher than 1. Furthermore, the consumer price couldeven increase as a result of a cost reduction (due to for exampleinnovation) of a technology; this, we do not observe in the UKbanding system. However, as we will show numerically, in the UKbanding system cost reductions can potentially lead to morepolluting technology mixtures.

2.5.1. Pricing, financial incentives, and revenue adequacyAs we have seen, under the previously discussed obligation

policies consumers pay a mark-up that covers the rewards that theregulator pays to the firms for owning certificates; in other words,the proposed pricing schemes are revenue adequate for theregulator. We would like this revenue adequacy to hold inthe alternative system as well. In the UK banding system, in thepricing (12), the consumer price was set at pcðωÞ ¼ peðωÞþϕν.We adopt this price in our alternative system as this price does notdepend on the αks and hence on the technologies used, which istypically the case in electricity markets. With this price the totalexpected income from mark-ups paid by consumers equals

ϕνEω ∑kAKN

yNk ðωÞþ ∑kAKR

yRk ðωÞ" #

¼ νEω ∑kAKR

yRk ðωÞ" #

:

The latter equality holds by (7); that is, either ν¼ 0 or the left-hand side inequality in (7) holds with equality. The total expectedincome has to be divided by the total expected amount ofcertificates on the market, which is Eω½∑kAKRαkyRk ðωÞ�. Therefore,instead of ν, we are going to pay firms an adjusted certificate price

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–9590

~ν, which is determined as follows:

~ν ¼ νEω½∑kAKRyRk ðωÞ�Eω½∑kAKRαkyRk ðωÞ�:

We deal with the above condition by imposing the followingequality condition at the first stage:

Eω ∑kAKR

ð ~ναk�νÞyRk ðωÞ" #

¼ 0: ð13Þ

This condition contains both primal and dual variables andinduces a nonlinearity in the model.

The resulting pricing scheme at any ωAΩ then becomes

pNk ðωÞ ¼ peðωÞ; 8kAKN

pRk ðωÞ ¼ peðωÞþαk ~ν; 8kAKR

pcðωÞ ¼ peðωÞþϕν: ð14ÞIt can easily be seen with (7) and (13) that this new scheme isrevenue adequate for the alternative banding system.

2.5.2. Equilibrium conditionsThe second stage equilibrium conditions are similar to (9), but

with pricing (14) replacing pricing (8). At the first stage we impose(7) along with the additional condition (13).

3. Numerical methods and data

3.1. Numerical framework

In a numerical study, we are going to analyze effects on invest-ments, prices, and CO2 emissions of three different renewable obliga-tion policies:

� No banding: There is no banding mechanism, meaning that allαks for renewable technologies are equal to 1.

� UK banding: The banding mechanism that is currently appliedin the UK is imposed, under the assumption that Calculation Asets the target; the obligation is expressed as the number ofcertificates per MWh of power produced.

� Alternative banding: The banding mechanism as proposed inSection 2.5 is imposed; the obligation is expressed as theamount of power that should come from a renewable resourceper MWh of power produced, and rewards are adjusted inorder to guarantee long term revenue adequacy.

We utilize the MCPs consisting of the first and second stage KKToptimality conditions as introduced in Section 2. In order to dealwith uncertainty, we use a sampling technique. Given probabilitydistributions for random demand and random availabilities ofrenewable capacities, we generate random samples using a pseu-dorandom number generator. We obtain realization vectors, sim-ply referred to as realizations. For each realization there is asecond stage problem that needs to be solved. At the first stage,expectations are replaced by sample averages. Then we obtain alarge sized MCP that we program in GAMS and solve using thePATH solver, see Ferris and Munson (2000, 2008). This solver,which can be seen as a generalization of Newton's method forsolving MCPs, finds an equilibrium solution to the set of KKToptimality conditions of the sampled first and second stageproblems. We use samples of size 3000, which we established tobe sufficiently large by subsequently solving the model for 3, 100,1000, 3000, 5000, 8000, and 10 000 samples. In all models, thereis a significant difference between the solutions for 100 and 1000samples. However, increasing the sample size to 3000 does notreveal significant changes, nor does increasing the sample size any

further. We solve the MCP for a range of obligation targets.Computation times are around 2 h per instance.

3.2. Experimental data

We consider five firms, each having a unique technology at theirdisposal. Non-renewable technologies coal and closed cycle gasturbine (CCGT) are used by firms 1 and 2, respectively. Renewabletechnologies onshore wind (ONW), offshore wind (OFFW), andlandfill gas (LFG) are used by firms 3, 4, and 5, respectively. Inaddition, there are two aggregate consumers, indexed by 6 and 7.Table 1 contains the characteristics of the technologies, consisting ofper unit production costs (ck), investment costs (κk), tons of CO2

emission per unit production (ek), and the banding coefficient (αk).The CO2 emission per unit production, ek, is given to indicate

how polluting the technologies are. The cost figures are in Poundsand based on data in MottMacDonald (2010). It is quite common innumerical studies to work with levelized cost of investment; thatis, the investment cost that is needed to produce 1 MWh ofelectricity, taking into account that not every MW installed willbe available at all times. We ignore this when defining theinvestment costs that play a role at the first stage, and will thuswork with the real investment cost that is involved with having1 MW of capacity installed. The fact that not all installed capacityis available for the full 8760 h in the year is taken into account atthe second stage via the function Fð�Þ that we specify below.

Demand dnðωÞ, n¼6,7, by the aggregate consumers are inde-pendent and are sampled from uniform distributions with lowerbound an and upper bound bn as in Table 2.

The available wind and landfill gas capacities are also randomlydistributed. As a function representing the realized available capa-city of technology k we take Fkðx;ωÞ ¼ θkðωÞx, where for eachrenewable technology θkðωÞ is sampled from a uniform distributionwith lower bound ak and upper bound bk, k¼ 3;4;5, as in Table 3.We assume that onshore and offshore wind are fully correlated, butassume independence between wind and landfill gas realizations.We chose uniform distributions out of convenience; one can choose

Table 1Characteristics of the technologies.

Parameters Coal CCGT ONW OFFW LFG

ck(d) 22.1 50.2 0 0 21.1κk(d) 30.24 12.96 25.62 53.48 24.78ek 1 0.35 0 0 0.2αk 0 0 1 2 0.25

Table 2Parameters for uniform demand distribution.

dn an bn

6 8 127 15 20

Table 3Parameters for uniform renewable output distribution.

Technologies ak bk

ONW .2 .36OFFW .33 .45LFG .5 .774

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–95 91

alternatives which may fit the empirical data closely or even useempirical data itself.6

Finally, as investment in landfills in the UK is limited by law, weimpose a maximum investment in LFG of 5 units.

4. Results and discussion

4.1. Effects of varying the obligation target

We compare the three obligation systems in terms of invest-ment quantities, consumer prices, and CO2 emissions for variousobligation targets; that is, we let the obligation target range from0 to 0.5 with increments of 0.01.

In Figs. 1, 2, and 3 the effects of an increasing obligation targetϕ on investments are depicted for the standard renewableobligation, the UK banding system, and the alternative bandingsystem, respectively. In all three systems we observe thatthe obligation reduces CO2 emissions in two ways: directly, viathe replacement of coal by ONW or OFFW, and indirectly, via thereplacement of coal by the cleaner CCGT.7

Investments in the less established OFFW only occur in thepresence of technology banding and for high levels of the obliga-tion target. Neither banding system succeeds in giving incentivesto invest in OFFW for low target levels. The UK banding systemneeds a target of at least ϕUK ¼ 0:33, while the alternative bandingsystem needs a target of at least ϕ¼ 0:41.

Fig. 4 shows the average consumer prices. Since we may havedifferent prices at each realization, we look at the average price, pc ,over all realizations. We observe that in all three systems theaverage consumer price increases with ϕ. Another key finding isthat when OFFW enters the optimal technology mixture, (average)consumer prices in the alternative banding system increase andexceed those obtained in the other systems.

The realized renewable production as fractions of total produc-tion in the three scenarios is depicted in Fig. 5. Depending on ϕ,it is possible that the UK banding system overshoots or violates theoriginal obligation target. For ϕo0:45 overshooting occurs due tothe substantial amount of LFG, which has a banding coefficient lessthan 1, in the optimal mixture. For ϕ40:45 violation occurs due tothe substantial amount of OFFW, which has a banding coefficientgreater than 1, in the optimal mixture.

In Fig. 6 the average CO2 emissions over all realizations aredepicted. We see that, as one would expect, CO2 emissions aredecreasing with ϕ. For high levels of ϕ (above 0.45), when asignificant amount of OFFW is in the mixture, we find that the UKbanding system leads to higher levels of CO2 emission comparedto the other systems.

To summarize, a renewable obligation leads to more financialincentives for investments in renewable resources. When OFFW isgiven more support in the form of a higher banding, for relativelyhigh obligation levels this support becomes effective. However,this may come at the cost of more CO2 emissions in the UKbanding system and significantly higher consumer prices in thealternative banding system.

4.2. Sensitivity to decreasing investment costs

One goal of a banding system is to encourage development in lessestablished technologies like offshore wind power. As technologies get

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

Obligation target φ

Opt

imal

inve

stm

ent q

uant

ity

CoalCCGTONWOFFWLFG

Fig. 1. Investment quantities in the no banding system.

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

Obligation target φUK

Opt

imal

inve

stm

ent q

uant

ity

CoalCCGTONWOFFWLFG

Fig. 2. Investment quantities in the UK banding system.

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

Obligation target φ

Opt

imal

inve

stm

ent q

uant

ity

CoalCCGTONWOFFWLFG

Fig. 3. Investment quantities in the alternative banding system.

6 As one would expect, numerical experiments indicate that the results couldbe sensitive to the choice of probability distribution. In this regard, in a real worldapplication, it may be worth using the numerical tools we provide here inconnection with historical data.

7 From our numerical output data we conclude that CCGT acts as a peak loadtechnology, as it is mainly used for producing electricity in cases of high demandand/or low wind. In the literature it is also often argued or even assumed that CCGTand gas in general are suitable technologies for dealing with intermittency due toits low capital cost and relatively fast start-up times (see for example DeCarolis andKeith, 2006; Strbac, 2002; Strbac et al., 2007).

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–9592

more established, investment costs are likely to go down in the longrun (learning by doing). We now assume that due to the extra supportfor offshore wind that is given by the banding systems, the investment

cost of OFFW is going to decrease. In this section we will thereforeanalyze the effect of a small decrease (0.42) in the unit investment costof OFFW down to κ4 ¼ 53:06. Assuming that operating and manage-ment costs remain the same, this means a decrease of 32.5 per kW ofinstalled capacity (which is approximately 1% of the original buildingcost per kW).

In Figs. 7 and 8 the investment quantities in the UK andalternative banding systems, respectively, are shown. Investmentdecisions in the original obligation system will be the same as inFig. 1. Comparing Figs. 2–7, it is obvious that a small decrease inOFFW investment cost can have quite an impact on investmentstrategies. In Fig. 2 a target of 0.33 is needed for OFFW to come intothe mixture, whereas with the lower investment cost a ϕUK of 0.22is sufficient. The same comparison can be done for Figs. 3 and 8.

Fig. 9 shows the average consumer prices after the costreduction in OFFW. While in the no banding and UK bandingsystems we observe nearly the same average prices as thoseobserved in Fig. 4, in the alternative banding system the averageconsumer price is significantly increased compared to pricesbefore the cost reduction.

Figs. 10 and 11 contain the fraction of renewable productionand the expected CO2 emissions, respectively. Our main observa-tion is that in the UK banding system the fraction of renewableproduction and the expected CO2 emissions are significantly

0 0.1 0.2 0.3 0.4 0.550

55

60

65

70

75

80

Obligation target φ

Ave

rage

con

sum

er p

rice

No BandingUK BandingAlternative Banding

Fig. 4. The average consumer price.

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

Obligation target φ

Ren

ewab

le p

rodu

ctio

n as

frac

tion

of to

tal p

rodu

ctio

n No BandingUK BandingAlternative Banding

Fig. 5. The renewable production as a fraction of total production.

0 0.1 0.2 0.3 0.4 0.512

14

16

18

20

22

24

26

28

Obligation target φ

Ave

rage

CO

2 em

issi

ons

No BandingUK BandingAlternative Banding

Fig. 6. The average CO2 emissions.

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

Obligation target φUK

Opt

imal

inve

stm

ent q

uant

ity

CoalCCGTONWOFFWLFG

Fig. 7. Investment quantities in the UK banding system.

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

Obligation target φ

Opt

imal

inve

stm

ent q

uant

ity

CoalCCGTONWOFFWLFG

Fig. 8. Investment quantities in the alternative banding system.

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–95 93

affected by the cost reduction; that is, the cost reduction has led toa more polluting technology mixture. There is more investment inOFFW, but since each unit investment in OFFW contributes 2

to satisfying the obligation on certificates, overall there is lessinvestment in renewable technologies.

To summarize, when a technology with a high banding man-ages to reduce its cost, banding mechanisms may cause unwantedside effects. In the UK banding system a cost reduction in OFFWmay lead to increased levels of CO2 emission, whereas in thealternative system it may lead to increased consumer prices.

5. Conclusions and policy implications

In this paper, we modeled and analyzed three different renew-able obligation policies in a mathematical framework. The original(UK) renewable obligation, the renewable obligation including theUK banding system, and a proposal for an alternative bandingsystem have been modeled in the electricity market investmentmodel that was introduced by Gürkan et al. (2013). For each policywe proposed a way to adjust the consumer prices and to pricecertificates in order for the policy to be self-financing. These so-called revenue adequate pricing schemes guarantee that regula-tor's expenses on certificate payments are covered by mark-upspaid by consumers. Finally, a numerical study shed light on thepossible advantages and disadvantages of each system.

The main goal of the renewable obligation is to reduce CO2

emissions by reducing investments in polluting technologies and tohave them replaced by renewable ones. As we observed in ournumerical study, CO2 emissions are curbed both directly by thereplacement of coal by onshore wind, and indirectly by thereplacement of coal by the cleaner CCGT. While we see an increas-ing investment in onshore wind and to a lesser extent landfill gas,a major concern is that in the long term targets may not be metwithout investment in less developed technologies like offshorewind. As observed in our numerical study, the original renewableobligation fails to give the right financial incentives to these lessdeveloped technologies. This is the main reason why a bandingsystem was introduced in the UK in 2009. Rather than rewardingeach unit production with a renewable resource with the sameamount of certificates, more certificates and hence more support isgiven to the technologies that needed additional incentives.

We find that the UK banding system can be successful in givingincentives to OFFW, but that rather high targets are needed in orderto do so. Once there is a substantial amount of investment in OFFW,we observe that the original obligation target on production maynot be met. This problem may be magnified when less developedtechnologies like tidal and wave power enter the optimal mixture.They need more support as stressed out by Allan et al. (2011), andtherefore they have banding coefficients of 3 and 5.

We also proposed an alternative banding system which guaran-tees that the original obligation target on production is alwayssatisfied. On the downside, based on our numerical study it isexpected that in the alternative system prices will significantly rise.

It is expected that more support for OFFW is going to causemore development in OFFW and hence will result in a downwardshift in OFFW investment cost in the long run. We analyzed theconsequences of such a cost decrease and found that investmentlevels in different technologies are in general very sensitive. Weconcluded that technology banding, besides its positive effects onless established technologies, can have certain negative sideeffects in the long run. When technologies succeed in reducingtheir costs as a result of the given support (learn by doing), thefinancial support may have to be therefore reduced accordingly.

Acknowledgments

In early stages, our research was sponsored by the NetherlandsOrganization for Scientific Research (NWO). We would like to

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

Obligation target φ

Ren

ewab

le p

rodu

ctio

n as

frac

tion

of to

tal p

rodu

ctio

n No BandingUK BandingAlternative Banding

Fig. 10. The renewable production as a fraction of total production.

0 0.1 0.2 0.3 0.4 0.512

14

16

18

20

22

24

26

28

Obligation target φ

Ave

rage

CO

2 em

issi

ons

No BandingUK BandingAlternative Banding

Fig. 11. The average CO2 emissions.

0 0.1 0.2 0.3 0.4 0.550

55

60

65

70

75

80

85

90

Obligation target φ

Ave

rage

con

sum

er p

rice

No BandingUK BandingAlternative Banding

Fig. 9. The average consumer price.

G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–9594

thank Özge Özdemir, Yves Smeers, and two anonymous refereesfor sharing their ideas and constructive comments. We are alsograteful to Peter Kort and Dolf Talman for their constructivefeedback on earlier versions of this work. Finally, we would liketo thank the participants in seminars at the 20th Meeting of theInternational Symposium for Mathematical Programming (ISMP)in Chicago, the INFORMS Annual Meeting 2009 in San Diego, the12th International Conference on Stochastic Programming inHalifax, the 35th conference on the mathematics of operationsresearch in Lunteren, and at Tilburg University for their usefulcomments.

Appendix A. First stage optimization problems

At the first stage, each firm kAK determines its optimalinvestment quantities xk, in order to maximize the expectedoptimal second stage profit minus the investment cost. At eachωAΩ, the optimal second stage profit of technology kAK is theprice pkðωÞ minus unit production cost ck, times the optimalsecond stage production ykðωÞ as a function of investments xk.Unit investment costs for technology kAK are κk. The first stageoptimization problem for a non-renewable firm kAKN looks asfollows:

maxxNkZ0

Eω½ðpNk ðωÞ�cNk ÞyNk ðxNk ;ωÞ��κNk xNk : ðA:1Þ

yNk ðxNk ;ωÞ is the optimal production quantity of non-renewabletechnology kAKR at realization ωAΩ at the second stage if xNk arethe investment quantities. Since firms are assumed to be pricetakers, for kAKN , pNk ðωÞ is taken as a parameter. For a renewablefirm kAKR the first stage problem looks similar, namely

maxxRkZ0

Eω½ðpRk ðωÞ�cRk ÞyRk ðxRk ;ωÞ��κRkxRk : ðA:2Þ

Again, yRk ðxRk ;ωÞ is the optimal production quantity of renewabletechnology kAKR at realization ωAΩ at the second stage if xRk arethe investment quantities. The price pRk ðωÞ is taken as a parameter.The constraint on capacity investments for renewable technologykAKR is formulated as

xRkrMRk ðζRk Þ; ðA:3Þ

where ζRk is the nonnegative dual price associated with the ceilingMk.

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G. Gürkan, R. Langestraat / Energy Policy 70 (2014) 85–95 95