IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 1

Renewable Energy Integration in Zonal MarketsIgnacio Aravena,Student, IEEE,and Anthony Papavasiliou,Member, IEEE

Abstract—In this paper we investigate the impact of zonalnetwork management in the operation of power systems withsignificant levels of renewable energy integration. Our study isinspired by the current state of the European energy market, andwe focus on a case study of the Central Western European (CWE)system. First, we present a hierarchy of models that account forunit commitment, the separation of energy and reserves, andthe simplified representation of transmission constraints in azonal market, in order to examine the impact of these factors onefficiency in a regime of large-scale renewable energy integration.Second, we simulate operations of the CWE system under thezonal market design using a detailed instance that consists of656 thermal generators, 679 nodes and 1073 lines, with multi-area renewable energy production and 15-minute time resolution.Zonal market operations are compared against deterministic andstochastic unit commitment using high performance computingin order to tackle the scale of the resulting models. We find thatmarket design can have an influence on cost efficiency whichfar exceeds the benefits of stochastic unit commitment relative todeterministic unit commitment. We conduct a detailed analysis ofthe numerical results in order to explain the relative performanceof the different models.

I. I NTRODUCTION

EUROPE has adhered to an ambitious renewable energyintegration agenda as a key pillar of its energy and cli-

mate objectives. Over the past 5 years, the growth of renewablecapacity has been especially significant in the CWE system(comprising Austria, Belgium, France, Germany, Luxembourg,the Netherlands and Switzerland). Approximately 40 GW ofsolar photovoltaic (PV) panels and 17 GW of wind turbineshave been installed in the system between 2008 and 2013 [1].This trend is expected to continue at the same pace towardsmeeting the 2020 European Union (EU) emissions targets [2].Even further development is expected moving forward to 2050,as a result of ambitious environmental targets set by numerouscountries [3].

Renewable resources cause various complications in opera-tions, including congestion resulting from uncontrollable fluc-tuations of renewable energy [4] and the need to carry adequatereserves in the system. The management of unscheduled flowshas been especially challenging in Europe, as evidenced forexample by the externalities of renewable power integration onneighboring networks (e.g. Poland and other zones [5]). Theneed for European Transmission System Operators (TSOs)to pool reserves in order to better deal with the uncertaintyand variability of renewable resources has been recognizedrecently [6] and efforts are underway for harmonizing thedefinition and management of reserves in Europe. Ultimately,

Manuscript received XXX; revised XXX.I. Aravena and A. Papavasiliou are with the Center for Operations Research

and Econometrics (CORE), Universite catholique de Louvain, Belgium. e-mail: ignacio.aravena@uclouvain.be, anthony.papavasiliou@uclouvain.be

the introduction of renewable resources induces spatial andtemporal coordination requirements on operators.

The European electricity market has favored a zonal marketdesign, known as Market Coupling (MC) [7], over locationalmarginal pricing (LMP) on the basis of simplicity and liq-uidity. There is a long-standing debate about the relativemerits of the two designs, and the implementation of themarket coupling design in Europe has generated considerablecontroversy (see [8] and references therein for a detaileddiscussion). European zonal markets are characterized by threefeatures that differentiate them substantially from centralizednodal markets in the context of renewable energy integration:(i) the simplified representation of transmission at the day-ahead time stage, (ii ) the sequential clearing of reserves andenergy, and (iii ) the limited real-time coordination amongzones for relieving congestion and imbalances.

Several US electricity markets, such as PJM [9], MISO[10], CAISO [11] and NYISO [12], have adopted LMP andcentralized operations under a single Independent SystemOperator (ISO). Zonal prices continue to be used for billingloads in certain markets such as NYISO [13]. Nevertheless,in contrast to market coupling, zonal prices are computedafter scheduling production with a nodal model [12], hencethe use of zonal prices does not create unscheduled flows onthe transmission network.

The market coupling design is, to some extent, the counter-part of bilateral market-to-market operations in US power sys-tems. Market coupling uses uniform pricing within eachbid-ding zone1 (commonly, national markets) and clears market-to-market interchanges within the European wide day-aheadenergy market, implicitly allocating transmission capacity be-tween zones [7]. US markets use LMP within each balancingauthority area [14], however market-to-market interchangesare usually arranged prior to clearing of the day-ahead marketin a bilateral fashion and they must to be approved byevery affected ISO [14], [15]. Approved interchanges are thenconsidered fixed and unscheduled flows caused by them aretaken into account in day-ahead market operations [11].

In addition to day-ahead market design challenges, real-timeoperation posses several coordination challenges in systemswith multiple operators [16]. Similar coordination mechanismsare used both in market coupling and wide US intercon-nections. In the market coupling design, balance responsibleparties are entitled to maintain their schedulednet position2

in real time [17]. Likewise, in US markets each balancingauthority (ISO) must maintain its area control error (a measure

1A bidding zone is defined as a geographical area within which marketparticipants are able to exchange energy without allocating transmissioncapacity [1].

2The net position is the netted sum of electricity exports andimports foreach market time unit in a certain bidding zone [1].

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consisting of the difference between scheduled and real areanet position, and the area frequency deviation) below certainestablished limits [18].

In this policy analysis paper we present a framework formodeling the market coupling design as currently implementedin the CWE system at an operational level. In addition, we usethe proposed framework to revisit the question of the relativemerits of zonal and nodal markets in the context of systemswith high levels of renewable energy.

A. Literature review

The impact of the simplified representation of transmissionconstraints in day-ahead energy markets on operational effi-ciency was recognized in early work by Bjørndal and Jornsten[19] and Ehrenmann and Smeers [8], whom illustrate a numberof challenges in zonal markets, including efficiency lossesandthe difficulties of defining zones. The authors use dispatchmodels in order to obtain analytical insights on systems withup to 6 nodes. Van der Weijde and Hobbs [20] introduce unitcommitment in the study of zonal systems. They focus onquantifying the benefits of zonal coordination in balancing,and use a two-stage model that represents the sequencingof unit commitment and dispatch decisions. Their study isfocused on a 4-node system. Recent work by Oggioniet al.[21], [22] further refines zonal models. In [21] the authors usegeneralized equilibrium models in order to study the effectof coordination among TSOs on operational efficiency. Theauthors use a standard 6-node network and a 15-node modelof the CWE system. They estimate the welfare gains of LMPpricing over zonal pricing in the CWE system at0.001%.The authors do not account for reserves or unit commitmentin their analysis. In [22] the authors evaluate the impacts ofpriority dispatch of wind in Germany using a zonal modelof the CWE system. Uncertainty is accounted for using ascenario-based formulation, however the authors ignore unitcommitment decisions in their analysis.

Studies that focus on renewable energy integration in Eu-rope commonly ignore zonal network management either bydirectly assuming a nodal market [23] or by considering azonal transportation network without addressing congestionwithin zones [24]–[27]. Nevertheless, a number of studies haveestimated the potential efficiency gains of LMP in Europerelative to a zonal design, in the context of renewable energyintegration. Leutholdet al. [28] estimate the welfare gains ofLMP over uniform pricing at 0.8% using a model of Germanyand its neighboring countries that consists of 309 nodes. Barthet al. [29] study the effect of international unscheduled flowsusing a regional model for the entire EU. The authors usea transportation model for transmission and estimate costsavings of0.1% of nodal relative to zonal pricing. Neuhoffet al. [30] estimate the operating cost savings of LMP relativeto zonal pricing between1.1% − 3.6%. The authors use asingle-period unit commitment model of the UCTE-STUMsystem (4300 nodes, 6000 lines) which is simulated for twoextreme operational snapshots (no wind and maximum wind).Abrell and Kunz [31] present a framework for day-ahead andintraday operation in a receding horizon scheme, emulating

the sequential operation of day-ahead and intraday markets.Abrell and Kunz study a detailed model of the German gridfor which they estimate efficiency losses of zonal markets at0.6%. The authors do not consider uncertainty, assume thatall thermal generators can update their commitment in realtime and include topology control as a congestion managementmeasure in the zonal market design.

An emerging aspect that results from the large-scale in-tegration of renewable resources is the sub-hourly rampingcapacity of a system. The state of the art in renewable energyintegration often employs hourly time resolution for day-aheadand real-time operations [32]–[35]. Recent work by Deaneetal. [36] and Gangammanavaret al. [37] underscores the im-portance of sub-hourly time resolution in accurately estimatingthe costs of integrating renewable energy. Bakirtziset al. [38]propose a receding horizon model with 5-minute resolutionfor simulating real-time operation under large-scale renewableenergy integration. In this study we develop a hybrid modelthat employs hourly resolution for the commitment of units,and 15-minute resolution for dispatch. This is in line withoperating practice in European markets (hourly day-aheadmarkets [39] and a quarterly real-time balancing mechanism[6]).

This paper contributes to the existing literature by devel-oping a detailed model of the market coupling design andanalyzing a detailed instance of the CWE region, which leadsto novel insights about the performance of zonal marketsin a regime of large-scale renewable energy integration. Interms of modeling, we develop a hierarchy of models for themarket coupling design that includes a model for availabletransfer capacity computation that is guaranteed to outperformpreviously proposed models [30], a power exchange modelthat accounts for unit commitment and the treatment of non-convexities by European power exchanges, and a model thatemulates the decentralized process of nominations of produc-tion and reserves after the day-ahead exchange has cleared.The latter two elements are largely absent from the currentliterature [20]–[22], [29]–[31]. We use the proposed hierarchyof models to compare the market coupling design to deter-ministic and stochastic unit commitment models (centralizednodal designs). Numerical results provide novel policy insightsby demonstrating that the conjunction of zonal managementand unit commitment decisions, in a regime of large-scalerenewable energy integration, produces effects that deviatesubstantially from assumptions of fully coordinated systems.

B. Paper organization

The paper is organized as follows. Section II presents theproposed model for the market coupling design, starting froman overview and introducing a hierarchy of mathematicalprograms to model day-ahead and real-time operations in thesubsequent subsections. Section III presents the CWE systeminstance used in this study and the simulation setup. SectionIV compares the results of the market coupling model to theactual performance of the CWE system over the reference yearof the simulation. Section V compares the performance ofthe various policies that were investigated and analyzes the

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 3

obtained results. Finally, section VI concludes the paper andpoints to directions of future research.

II. A M ODEL OF EUROPEANMARKET COUPLING

The market coupling design has become the uniformparadigm for operating the European electricity markets.Through the price coupling of regions (PCR) project, themarket coupling design is now present in most countries ofwestern, central and northern Europe [40].

From an operational point of view, market coupling consistsof sequential steps that are executed or supervised by powerexchanges or by system operators, with some differencesamong countries due to local regulatory frameworks. Thesteps involved in the day-ahead energy market (namely, thecomputation of transfer capacities and the clearing of theenergy market) are nearly standardized among countries. Incontrast, there is substantial diversity in the definition ofreserves. The procedures governing re-dispatch and balancingand the definitions of products are often incompatible amongcountries. These incompatibilities have already been resolvedbetween Germany and Switzerland, and the TSOs of Belgium,Germany and the Netherlands are currently working towardsharmonizing the definition and sharing of their reserve re-sources [6]. Further standardization is expected in the mediumterm following the ENTSO-Enetwork codes[17], [41]. Inanticipation of this harmonization, in this paper we assumethat system operators adhere to a common definition of reserveproducts among zones.

Following the standardization of reserve products, it isexpected that bidding zones will increasingly interchangesecondary and tertiary reserves as is currently the case forprimary reserves3. As opposed to primary reserves, for whichshared volumes are in the order of tens of MW, the inter-change of secondary and tertiary reserves might involve largevolumes of power, which would require the reservation ofcross-border transmission capacity between zones, as analyzedby Gebrekiroset al. [43]. The reservation of transmissioncapacity for reserve provision is currently under debate amongEuropean regulators, hence we do not include this element inour analysis in order to focus on the status quo.

Throughout the paper, we model the transmission networkusing a lossless DC power flow model. We assume that alldispatch decisions (production, flows) are updated every 15minutes, whereas commitment (on/off) decisions of thermalgenerators are updated on an hourly basis. Thermal generatorswith commitment decisions are divided into two groups:slowgenerators, whose commitment must be determined in the day-ahead time frame, andfast generators, whose commitmentcan be modified in real-time operations. Following theseassumptions, we model the market coupling design as depictedin Fig. 1.

At day ahead, the TSOs compute the available transfercapacities (ATCs) between the different physically connectedzones in the system, for each hourτ of the next day. Then,

3Switzerland, for example, is currently sourcing primary reserve fromFrance and Germany [42].

power exchanges collect bids from firms and clear the day-ahead energy market, modeling the exchanges between zonesthrough a transportation network limited by the ATCs. Theday-ahead energy market is cleared with hourly resolution,andit determines a net position∆QMC

a,τ for each zonea for eachhour τ of the next day, as well as a preliminary commitmentfor slow generatorsuMC .

After the energy market clears and before firms commu-nicate their final schedule to the corresponding TSO, firmswithin each zone can trade among each other their productionand reserve obligations [44], [45]. We model this decentralizedprocess as a cost minimizing scheduling that aims at meetingsecurity targets for real-time operation. This procedure resultsin final commitment decisions for slow generators,uR, thatcomply with the energy balance and reserve requirements ofeach zone. Note that reserve obligations of firms are deter-mined in monthly or weekly tenders, prior to day-ahead energymarket clearing [6]. We assume that the forward positions ofthe reserve tendering process are adjusted by firms after theday-ahead exchange clears, hence we do not represent theseforward auctions explicitly in our analysis.

Finally, the resolution of congestion (referred to as re-dispatch) and the resolution of imbalances due to outagesand forecast errors (referred to as balancing) take place inreal time on 15-minute intervals, while respecting the netposition of each zone∆QMC [17] and the commitment ofreservesuR. At this stage, we assume that TSOs in chargeof the possibly multiplecontrol areas4 within each biddingzone fully coordinate their operations and that they net outtheir scheduled net positions for balancing purposes [46].Thisassumption allows us to model each individual bidding zoneas if it were operated by a single TSO in real time.

A. Computation of available transfer capacity

Power exchanges use the simplified transportation networkpresented in Fig. 2 for representing transmission constraintsamong zones in the CWE system. The topology of this zonalnetwork is determined by the topology of the real network andit includes an interconnector between each pair of adjacentzones. Flows on the zonal network are limited by the ATCs,which must be computed on a daily basis by the TSOs andcommunicated to power exchanges.

The first step in the computation of ATCs is the determi-nation of total transfer capacities (TTC) among zones. TheENTSO-E Operational Handbook [47] defines TTC as “themaximum exchange program between two adjacent controlareas that is compatible with operational security standardsapplied in each system if future network conditions, generationand load patterns are perfectly known in advance”. Followingthis definition, we propose the following model for computingthe TTC from exporting zonea to importing zoneb in hour

4A control area is defined as a coherent part of the interconnected system,operated by a single system operator which includes connected physical loadsand/or generation units if any [1]. In the CWE system almost every biddingzone corresponds to a single control area, with the exception of the German-Austrian zone which is divided into five control areas, each one operated bya different system operator.

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ATCcomputation TSOs

Energy auction Power Exchanges

Reservescommitment

and nominationsTSOs

Re-dispatchand balancing TSOs

Firms

ATC

∆QMCuMC

∆QMCuR

bids

nominations

↑ Day-ahead

↓ Real time

Fig. 1. Market coupling organization model overview.

France Switzerland

Belgium Germany

Austria

Luxembourg

Netherlands

Fig. 2. Zonal model of the CWE network used by the power exchanges toclear the day-ahead energy market. Each zone is represented as a single nodeand exchanges between zones are limited by the ATC values.

τ , TTC+ab,τ . The notation used in the present and subsequent

mathematical formulations is described in Appendix A.

maxq,u,f,θ

∑

l∈L×(a,b)

fl −∑

l∈L×(b,a)

fl (1)

s.t.∑

l∈L×(c,d)

fl −∑

l∈L×(d,c)

fl = nBCE(c,d),τ ∀(c, d) ∈ K \ {(a, b)}

(2)∑

g∈G(n)

qg +1

4

∑

t∈T15(τ)

ξn,t +∑

l∈L(·,n)

fl =

1

4

∑

t∈T15(τ)

Dn,t +∑

l∈L(n,·)

fl ∀n ∈ N (3)

fl = Bl

(

θn(l) − θm(l)

)

, − F−l ≤ fl ≤ F

+l ∀l ∈ L (4)

Q−g ug ≤ qg ≤ Q

+g ug , ug ∈ {0, 1} ∀g ∈ G (5)

∑

l∈L×(c,·)

fl −∑

l∈L×(·,c)

fl ≤

∑

g∈G(N(c))

Q+g −

(

RFCRc +R

aFRRc +R

mFRRc

)

−

1

4

∑

n∈N(c)t∈T15(τ)

(

Dn,t − ξn,t

)

∀c ∈ {a, b} (6)

The objective function (1) corresponds to the cross-borderflow (exchange program) from zonea to zoneb, determined asthe sum of individual flows over cross-border lines. Constraint(2) enforces the exchanges between other pairs of areasto correspond to a baseline value, referred to as the basecase exchange (BCE). Constraint (3) enforces hourly energybalance assuming renewable supplyξ, constraint (4) modelsthe network assuming that all lines are available, constraint(5) models generating unit output limits, considering minimumstable and maximum production.

Constraint (6) models theoperational security standardsforeach control area. The left-hand-side of (6) corresponds tothenet position of zonec in terms of cross-border flows, whilethe right-hand-side corresponds to the maximum net positionfor zone c such that primary, secondary and tertiary reservetargets,RFCR

c , RaFRRc andRmFRR

c , respectively, can be met.This constraint limits the exports of each area to a level thatensures that there is enough internal capacity to satisfy theinternal demand for energy and reserves.TTC−

(a,b),τ (a importing, b exporting) is computed in ananalogous way toTTC+

(a,b),τ , by minimizing the objectivefunction (1). Note that in order to compute all the TTCs, prob-lem (1)–(6) needs to be solved twice for each interconnectorand hour, i.e.2 · |K| · |T60| times.

Problem (1)–(6) directly maximizes the cross-border flowbetweena and b in a one-shot optimization problem, whichoutperforms iterative methods, such as the one describedin [47], and methods based on net position manipulation,proposed by Neuhoffet al. [30].

Once the TTC value is available, the net transfer capacityNTC+

(a,b),τ is computed by discounting the determined valuefor TTC+

(a,b),τ by the Transmission Reliability Margin5 TRM

[47]. Considering a proportionalTRM (0 < TRM < 1),common to all interconnectors,NTC+

(a,b),τ is computed usingequation (7).

NTC+k,τ :=TTC+

k,τ − TRM ·∣

∣TTC+k,τ

∣

∣·

1TTC

+

k,τ−TTC

−

k,τ≥TRM ·

(

|TTC+

k,τ|+|TTC

−

k,τ|)

(7)

The indicator function in equation (7) ensures that the TRMis applied only when a sufficient margin between transfercapacities in forward and backward directions exists, i.e.itguarantees thatNTC+

(a,b),τ ≥ NTC−(a,b),τ . For computing

NTC−(a,b),τ , theTRM is added in equation (7).

NTCs are required to be simultaneously feasible, in otherwords, any cross-border exchange configuration respectingtheNTC values must be feasible for the real network [48]. In geo-metric terms, the set of exchange configurations respectingtheNTC values for hourτ defines a subset ofR|K|, specificallyan NTC hyper-rectangleNNTC

τ := {n ∈ R|K| | NTC−

k,τ ≤

nk ≤ NTC+k,τ ∀k ∈ K}. Simultaneous feasibility of NTCs

5The transmission reliability margin is defined as a security margin thatcopes with uncertainties on the computed TTC values arising from: (i)inadvertent deviations of physical flows during operation due to the physicalfunctioning of secondary control; (ii) emergency exchangesbetween TSOs tocope with unexpected unbalanced situations in real time; (iii) inaccuracies,e.g. in data collection and measurements [1].

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demands thatNNTCτ is fully contained within the region

defined by feasible exchanges for the real network,NOPFτ

(a |K|-dimensional polyhedron). In practice, however, thisrequirement is relaxed and replaced by vertex feasibility6,which demands that all vertices ofNNTC

τ are contained withinNOPF

τ [48].Vertex feasibility is not necessarily satisfied by NTC values

computed using equation (7), NTC values computed usingother procedures proposed in the literature [30], or the proce-dure used in practice [47]. The technical documentation [48]states that if NTC values do not comply with vertex feasibilitythen “reductions are applied to the NTC levels in a coordinatedway with a view to eliminating overloads”. We model thisprocess by computing a new set of NTC valuesχ+, χ−, as thesolution of problem (8)–(14), which aims at achieving vertexfeasibility with the minimum possible total reduction on theNTCs.

minχ,q,f,θ

∑

k∈K

(

(

NTC+k,τ − χ

+k

)

+(

χ−k −NTC

−k,τ

)

)

(8)

s.t. χ+k ≤ NTC

+k,τ , χ

−k ≥ NTC

−k,τ , χ

+k ≥ χ

−k ∀k ∈ K

(9)∑

l∈L×(a,b)

fil −

∑

l∈L×(a,b)

fil =

1iab χ+(a,b) + (1− 1iab)χ

−(a,b) ∀(a, b) ∈ K, i ∈ Ξ

(10)∑

g∈G(n)

qig +

1

4

∑

t∈T15(τ)

ξn,t +∑

l∈L(·,n)

fil =

1

4

∑

t∈T15(τ)

Dn,t +∑

l∈L(n,·)

fil ∀n ∈ N, i ∈ Ξ (11)

fil = Bl

(

θin(l) − θ

im(l)

)

, −F−l ≤ f

il ≤ F

+l ∀l ∈ L, i ∈ Ξ

(12)

0 ≤ qig ≤ Q

+g ∀g ∈ G, i ∈ Ξ (13)

∑

l∈L×(a,·)

fil −

∑

l∈L×(·,a)

fil ≤

∑

g∈G(N(a))

Q+g −

(

RFCRa +R

aFRRa +R

mFRRa )−

1

4

∑

n∈N(a)t∈T15(τ)

(

Dn,t − ξn,t

)

∀a ∈ A, i ∈ Ξ (14)

The objective function (8) corresponds to the total NTCreduction, i.e. the difference between the preliminary NTCvaluesNTC± and the vertex feasible NTC valuesχ±. Theconstants in this objective function drop out of the optimizationand can therefore be ignored, but are included here for clarityof the exposition. Constraints (9) establish the bounds forχ±

for all interconnectors.Each vertexi ∈ Ξ of NNTC

τ can be mapped to an arrayof directions for cross-border flows, e.g. [forward on (a, b),backwardon (c, d), . . .], hence it can be represented using anindicator 1iab for each interconnector(a, b) with 1iab = 1 ifflow on (a, b) goes in the forward direction in vertexi and1iab = 0 otherwise. Using these indicators, constraints (10)

6Note that vertex feasibility corresponds to a relaxation ofsimultaneousfeasibility if NOPF

τ is not convex.

force the cross-border flow on interconnector(a, b) at vertexi ∈ Ξ to be equal to the corresponding vertex feasible NTC.

The requirement that all verticesi ∈ Ξ of NNTCτ are

contained withinNOPFτ is enforced through constraints (11)–

(14), which correspond to the linear relaxation of constraints(3)–(6) for each vertex. As the formulation employed is basedon the vertices ofNNTC

τ , we have that in general the size ofthe problem is exponential in the number of interconnectors(|Ξ| = 2|K|). For the CWE system the number of vertices to beconsidered is26, which results in a large-scale linear problemthat is still tractable using state-of-the-art linear solvers.

Since our market coupling model does not consider pre-viously contracted transmission capacity, available transfercapacities are equal to the optimal simultaneously feasibleNTCs, ATC±

k,τ := (χ±k )

∗ ∀k ∈ K. As a final remark, notethat the solution to problem (8)–(14) might not be unique.In such a case, an auxiliary quadratic problem can be solvedto obtain unique simultaneously feasible NTCs, following themethodology used in [40] to compute unique prices.

B. Day-ahead energy market clearing

Day-ahead energy market clearing in CWE is carried outby power exchanges. Exchanges collect bids from participantsand determine the acceptance/rejection decisions that maxi-mize social welfare. Energy is cleared using a strict linearpricing scheme, which results in a series of rules regardingthe acceptance/rejection of different types of bids, dependingon whether they are in-the-money (bid acceptance would yielda strictly positive profit), at-the-money (bid acceptance wouldyield zero profit) or out-of-the-money (bid acceptance wouldyield strictly negative profit). Currently two main types ofbidsare allowed by power exchanges in the CWE system:

• Continuous bids: bids that can be accepted partially.Continuous bids that are in-the-money must be fullyaccepted, at-the-money continuous bids can be partiallyaccepted and out-of-the-money continuous bids must berejected.

• Block bids: bids that can be either fully accepted orrejected (fill-or-kill condition, which gives rise to integervariables in the clearing model). Block bids that are in-the-money or at-the-money can be accepted or paradox-ically rejected, while out-of-the-money block bids mustbe rejected.

Block bids can be arranged in linked families, in whichthe acceptance/rejection of certain bids is conditional ontheacceptance of other bids, or in exclusive groups, in which atmost one block order within the group can be accepted.

Once the bids have been collected, the power exchangeclears the market using the simplified network model providedby the TSOs (Fig. 2) in order to represent cross-borderexchanges.

The CWE power exchange uses the EUPHEMIA algorithm[40] to clear the energy market, based on the bids submittedby firms. In the following we present an equivalent model ofEUPHEMIA proposed by Madani and Van Vyve [49], whichhas been modified in order to account for exclusive groups.

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Consider that buy bids (e.g. loads) correspond to bids withpositive quantitiesQ > 0, while sell bids (e.g. generators)correspond to bids with negative quantitiesQ < 0. Then,the welfare maximization (market clearing) problem can beformulated as the mathematical program (15)–(21), whereconstraints have been grouped in primal-dual pairs.

maxx,y,ns,p,λ

∑

i∈I

(

∑

τ∈T60

QiτP

i)

xi +∑

j∈J

(

∑

τ∈T60

QjτP

j)

yj (15)

s.t.∑

i∈I

(

∑

τ∈T60

QiτP

i)

xi +∑

j∈J

(

∑

τ∈T60

QjτP

j)

yj ≥

∑

i∈I

si +∑

g∈G

sg +∑

k∈Kτ∈T60

(

ATC+k,τλ

+k,τ −ATC

−k,τλ

−k,τ

)

(16)∑

i∈I(a)

Qiτxi +

∑

j∈J(a)

Qjτyj =

∑

k∈K(·,a)

nk,τ −∑

k∈K(a,·)

nk,τ ∀a ∈ A, τ ∈ T60 (17)

ATC−k,τ ≤ nk,τ ≤ ATC

+k,τ , pa(k),τ − pb(k),τ+

λ+k,τ − λ

−k,τ = 0 ∀k ∈ K, τ ∈ T60 (18)

xi ≤ 1 , si +∑

τ∈T60

Qiτpa(i),τ ≥

∑

τ∈T60

QiτP

i ∀i ∈ I

(19)∑

j∈JE(g)

yj ≤ 1 ∀g ∈ G , sg(j) +∑

τ∈T60

Qjτpa(j),τ ≥

∑

τ∈T60

QjτP

j −Mj(1− yj) ∀j ∈ J (20)

x, s,λ ≥ 0 ; y ∈ {0, 1}|J| (21)

The objective function (15) corresponds to total welfare.Constraint (16) enforces strong duality at the solution, i.e. itenforces equality of the total welfare with the total surplus(surplus minimization is the dual of welfare maximization). Asa consequence of Theorem 2 of [49], constraint (16) guaran-tees that a solution to (15)–(21) will satisfy (i) complementaryslackness between the acceptance of bids and the surplusfor continuous bids and accepted block bids, as well as (ii)complementary slackness between exchanges and congestionprices.

Energy balance at each area is expressed through constraints(17). Relation (18) corresponds to primal and dual constraintsfor exchanges in the simplified (transportation) network pro-vided by the TSOs.

Constraints (19)–(20), together with constraint (16), estab-lish primal restrictions and dual conditions for the acceptanceof different types of bids. Constraints (19) and complementaryslackness (si ⊥ 1 − xi and xi ⊥ si +

∑

τ∈T60Qi

τpa(i),τ −∑

τ∈T60Qi

τPi, ∀i ∈ I) ensure that continuous bids are

accepted (xi = 1) if they are in-the-money (si > 0), partiallyaccepted (0 ≤ xi ≤ 1) if they are at-the-money (si = 0 and∑

τ∈T60Qi

τpa(i),τ =∑

τ∈T60Qi

τPi), and rejected (xi = 0)

otherwise.Constraints (20) deal with block bids within exclusive

groups. Among the bidsJE(g) of groupg, at most one can beaccepted and that bid must be in-the-money or at-the-money.

qg

Cg(qg)

Qg1 Q

g2 Q

g3

Cg1

Cg2

Cg3

Fig. 3. Production cost function discretization. Each production levelQgj is

associated with a production costCgj through the cost functionCg(·).

ProvidedMj are sufficiently large constants, the surplus ofthe groupsg is determined by the accepted bid only. Theaccepted bid is not necessarily the one with the maximumsurplus within the group, i.e. the maximum surplus bid can beparadoxically rejected, and it is also true that the entire groupcan be paradoxically rejected.

C. Firm bids and energy market clearing reformulation

The solution of the market clearing model (15)–(21) com-plies with the rules of the CWE exchange that govern theacceptance/rejection of bids. Nevertheless, the model presumesa finite set of bids that have been bid by agents to the exchange.

In order to construct bids for all participants, we assumethat they place bids in the energy market that approximateas closely as possible their feasible production/consumptionpossibilities7 and their true costs/valuations. Following thisassumption, loads, renewable producers and certain thermalproducers can be easily modeled as submitting continuousbids.

Other thermal generators, for which we consider commit-ment decisions, cannot represent their constraints using con-tinuous bids. They are modeled as submitting large exclusivegroups (one group per generator) containing a discretizedversion of their generation possibilities for the next day.To construct this discrete set of production possibilities, thegenerator output is first discretized inmg levels {Qg

j}mg

j=1.The computation of production cost is accordingly discretized,as shown in Fig. 3. The first level of production correspondsto the technical minimum, the last level corresponds to thegenerator capacity andmg must be large enough in order toallow the generator to ramp between different levels of outputwithout violating its ramp rate.

The generator output at each hourτ can then be expressed as∑mg

j=1 Qgjω

gj,τ , whereωg

j,τ is an auxiliary binary variable suchthat

∑mg

j=1 ωgj,τ ≤ 1, ∀τ ∈ T60 [50]. Any production profile

within the discrete set is then defined by a certainωg. In orderto be a feasible production profile, the production, commitmentand startup associated with a certain production profile mustcomply with the generator constraints: technical minimum,maximum capacity, minimum up/down times and ramp rate

7Bidding infeasible production/consumption bids would conflict with therules of the power exchange [39].

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constraints. These constraints define the hourly productiondomainD60

g .Considering that each feasible production profile of gener-

ator g is included in groupg, we can reformulate the energyclearing model as problem (22)–(27), wherehg(ωg,vg) cor-responds to the total cost of the production profile associatedwith ωg andvg, and wherevg corresponds to the startup in-dicator variable. Problem (22)–(27) explicitly includes hourlyapproximations of the unit commitment constraints for thermalgenerators while respecting the rules of the power exchangefor the treatment of non-convexities.

maxx,ω,v,ns,p,λ

∑

i∈I

(

∑

τ∈T60

QiτP

i

)

xi −∑

g∈G

hg(ωg,vg) (22)

s.t.∑

i∈I

(

∑

τ∈T60

QiτP

i

)

xi −∑

g∈G

hg(ωg,vg) ≥∑

i∈I

si+

∑

g∈G

sg +∑

k∈Kτ∈T60

(

ATC+k,τλ

+k,τ −ATC

−k,τλ

−k,τ

)

(23)

∑

i∈I(a)

Qiτxi −

∑

g∈G(N(a))

mg∑

j=1

Qgjω

gj,τ =

∑

k∈K(·,a)

nk,τ −∑

k∈K(a,·)

nk,τ ∀a ∈ A, τ ∈ T60 (24)

mg∑

j=1

ωgj,τ ≤ 1 ∀g ∈ G, τ ∈ T60 ,

sg ≥∑

τ∈T60

mg∑

j=1

Qgjω

gj,τpa(g),τ − hg(ωg,vg) ∀g ∈ G

(25)(

mg∑

j=1

Qgjω

gj ,

mg∑

j=1

ωgj , vg

)

∈ D60g ∀g ∈ G (26)

(18)–(19); x, s,λ ≥ 0 ; ωg ∈ {0, 1}mg×|T60| ∀g ∈ G(27)

Problem (22)–(27) is analogous to (15)–(21), with thedifference that block bids that were explicitly enumeratedin(20) are now implicitly enumerated by (25)–(26). Constraint(25) ensures that each generator recovers at least its productioncost, while constraint (26) enforces that the accepted pro-duction profile is feasible. We define the total cost functionhg(ωg,vg) according to equation (28).

hg(ωg,vg) :=∑

τ∈T60

(

mg∑

j=1

Cgj ω

gj,τ +Kg

mg∑

j=1

ωgj,τ +Sgvg,τ

)

(28)

Notice that constraint (25) includes a product of two vari-ables,ωg

j,τpa(j),τ , which can be linearized by using a big-Mformulation sinceωg

j,τ is binary [50].The solution of the energy clearing model of equations (22)–

(27) determines the preliminary commitmentuMCg for slow

generators and net positions∆QMCa for each zone. The net

position can be computed using equations (29) and (30).

uMCg,τ :=

mg∑

j=1

(ωgj,τ )

∗ ∀g ∈ GSLOW , τ ∈ T60 (29)

∆QMCa,τ :=

∑

g∈G(N(a))

mg∑

j=1

Qgj (ω

gj,τ )

∗ −∑

i∈I(a)

Qiτx

∗i ∀a ∈ A, τ ∈ T60

(30)

We conclude this subsection by pointing out that the solu-tion of (22)–(27) represents an optimistic situation in which thepower exchange can decide among a large number of possibleschedules in order to maximize welfare. Limits on the numberof profiles that each unit can bid into the market can also beincluded in the formulation or during the solution of the energyclearing problem.

D. Reserves

Reserves in the CWE region can be classified into threecategories: (i) primary reserves (also referred as FrequencyContainment Reserve or FCR) are responsive to frequency andmust be delivered within 30 seconds; (ii) secondary reserves(also referred to as automatic Frequency Restoration Reservesor aFRR) are activated following the activation of FCR, andmust be delivered within 5-15 minutes; and (iii) tertiaryreserves (also referred to as manual Frequency RestorationReserves or mFRR) must be delivered within 15-30 minutes.

Following the assumption of harmonization in the definitionof reserve products across zones [6], we model the reserveallocation and nomination process [44], [45] as a simulta-neous cost minimizing scheduling that aims at securing therequisite FCR, aFRR and mFRR capacity. This scheduling isconducted at day ahead in each zone, after the clearing of theenergy market, where firms can also trade their productionobligations. This is in line with current operating practice inBelgium, France, Germany and Switzerland. Given that bal-ancing responsible parties are required to offer reserve whilemaintaining a balanced position [17], [41], we assume that thereserve scheduling must honor the net positions determinedby the power exchange∆QMC

a,τ for each zone and period.Additionally, we assume that slow generators committed bythe power exchange cannot be shut down when reserves areallocated.

Considering these assumptions, the commitment of reservecapacity for each 15-minute interval of the following dayis formulated as the optimization problem (31)–(35), whichneeds to be solved separately for each zone in the system.

minq,r,u,v

∑

g∈G(N(a))

(

1

4

∑

t∈T15

C(qg,t) +∑

τ∈T60

(

Kgug,τ + Sgvg,τ)

)

(31)

s.t.∑

g∈G(a)

rFCRg,t ≥ R

FCRa ,

∑

g∈G(a)

(rFCRg,t + r

aFRRg,t ) ≥ R

FCRa +R

aFRRa ,

∑

g∈G(a)

(

rFCRg,t + r

aFRRg,t + r

mFRRg,t

)

≥

RFCRa +R

aFRRa +R

mFRRa ∀t ∈ T15 (32)

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∑

g∈G(N(a))t∈T15(τ)

qg,t +∑

n∈N(a)t∈T15(τ)

(

ξn,t −Dn,t

)

= 4∆QMCa,τ ∀τ ∈ T60

(33)

ug,τ ≥ uMCg,τ ∀g ∈ GSLOW(N(a)), τ ∈ T60 (34)

(

qg, rFCRg , r

aFRRg , r

mFRRg ,ug,vg

)

∈ D15,Rg ∀g ∈ G(N(a))

(35)

The objective function (31) corresponds to the total cost ofthe planned operation of zonea. Constraint (32) enforces thereserve requirements for each period. Constraint (33) requiresthat each zone maintains its day-ahead position in the energymarket, and constraint (34) requires that slow units committedby the energy exchange remain ON during the commitment ofreserves. Constraint (35) corresponds to generator constraintsfor providing energy and reserves that must be respected witha 15-minute time resolution.

The reserve allocation (31)–(35) can modify the output ofthe energy market clearing model by turning on additionalslow generators to supply reserves. Consequently, the outputof the reserve allocation is a new vector of commitment forslow generatorsuR,vR, which guarantees the availability ofthe required reserves for each zone and for each period of thenext day.

E. Redispatch and balancing

During real-time operations, Kirchhoff’s laws determine theflows on the network. Moreover, renewable energy supply candiffer from its forecastξ. To mitigate the effects of networkcongestion and forecast errors, the system operator can modifydispatch decisions and the commitment of fast generators withthe objective of minimizing the real-time operating cost.

In order to evaluate the real-time cost performance ofthe day-ahead commitment decisions, the actual renewableinjection is assumed to be modeled by the random vectorζ.The real-time operating cost of the system is then estimatedby solving the redispatch and balancing model (36)–(42). Theaverage performance of the system is estimated through MonteCarlo simulation, i.e. problem (36)–(42) is solved for eachζs, s ∈ Ssim, whereSsim is the set of random samples.

minq,u,v,δf,θ,e,o

∑

g∈G

(

1

4

∑

t∈T15

Cg(qg,t) +∑

τ∈T60

(

Kgug,τ + Sgvg,τ)

)

+

V∑

n∈N

∑

t∈T15

en,t + CL∑

a∈A

∑

τ∈T60

δa,τ (36)

s.t. δa,τ ≥

∣

∣

∣

∣

∣

4∆QMCa,τ −

(

∑

l∈L×(a,·)t∈T15(τ)

fl,t −∑

l∈L×(·,a)t∈T15(τ)

fl,t

)∣

∣

∣

∣

∣

∀a ∈ A, τ ∈ T60

(37)

∑

g∈G(n)

qg,t + ζn,s,t +∑

l∈L(·,n)

fl,t + en,t =

Dn,t +∑

l∈L(n,·)

fl,t + on,t ∀n ∈ N, t ∈ T15 (38)

fl,t = Bl

(

θn(l),t − θm(l),t

)

,

− F−l ≤ fl,t ≤ F

+l ∀l ∈ L, t ∈ T15 (39)

0 ≤ on,t ≤∑

g∈G(n)

qg,t + ζn,s,t ,

0 ≤ en,t ≤ Dn,t ∀n ∈ N, t ∈ T15 (40)

(qg,ug,vg) ∈ D15g ∀g ∈ G (41)

ug = uRg , vg = v

Rg ∀g ∈ GSLOW (42)

Problem (36)–(42) commits fast units, with the additionalrequirement of respecting day-ahead zonal net positions andthe commitment schedule of slow generators. The requirementof respecting the zonal day-ahead net positions is imposed asa soft constraint, the violation of which is penalized throughan L1 penalty term defined by equation (37). Assuming that,in practice, TSOs prefer to redispatch any generator instead ofviolating their net position, the penaltyCL can be establishedas the maximum marginal cost of any generator within azone. In contrast, the requirement of respecting the day-aheadcommitment of slow generators is imposed as a hard constraintin equation (42).

By maintaining day-ahead zonal net positions, the redis-patch and balancing model (36)–(42) captures the partialcoordination of system operators in real time.

III. N UMERICAL SIMULATION SETTINGS

A. The Central Western European system

A number of studies have focused on developing representa-tive models for the European grid. Leuthold [51] and Hutcheonand Bialek [52] model the European transmission grid basedon study models and maps published by ENTSO-E [1] and bynational TSOs, while Egereret al. [53] document the existingavailable information on transmission, generation and demandin Europe.

We use the transmission network model of Hutcheon andBialek [52] for the CWE system, presented in Fig. 4. Thermalratings for cross-border lines were updated to their currentvalues, as published in [54]. Thermal ratings for internal lineswithin the Netherlands were established as published in [55].Thermal ratings for internal lines within other countries wereestimated through an iterative process of simulating systemoperations and correcting internal capacities, with the objectiveof approximating the congestion management costs for theyear 2015 [1].

The network was populated using an industrial databaseof thermal generators, provided by ENGIE, which includestechnical and economic characteristics of 656 generating units.Thermal generators were assigned to network buses accordingto their approximate geographical location [56]. These unitsare classified intofive groups: 87 nuclear units (85G W), 144combined heat and power (CHP) units (40 GW), 272 slow

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 9

France

Belgium

Switzerland

Netherlands

Germany

Austria

Fig. 4. Nodal model of the CWE network [52]. The model comprises thehigh voltage networks of the 7 countries in the CWE system, it includes 679nodes and 1073 lines.

units (conventional thermal units that are neither nuclearnorCHP, and obey a minimum up and down time greater than 3hours, totaling 99 GW), 126 fast units (conventional thermalunits that are neither nuclear nor CHP, and obey a minimumup and down time less than or equal to 3 hours, totaling 14GW) and 27 aggregated small generators (10 GW).

The capacity of thermal generators within Germany, Franceand Belgium was reduced in order to account for scheduledmaintenance and large outages. A different outage de-ratingfactor was computed for each generator and each season basedon the outage information published by national TSOs [57],[58] and Power Exchanges (PX) [59] for the year 2014.

Zonal reserve targets were obtained from [6] for Belgium,Germany and the Netherlands, and from national TSOs forother countries [42], [57], [60]. We assume that FCR needs tobe delivered within 30 seconds of activation (current specifi-cation in all CWE countries), that aFRR needs to be deliveredwithin 5 minutes of activation (current product specificationin Germany), and that mFRR needs to be delivered within15 minutes of activation (current product specification inBelgium, Germany, the Netherlands and Switzerland).

Historical 15-minute demand profiles for 2014 were col-lected from national TSOs for Austria [60], France [57],Belgium [58] and the Netherlands [61], and hourly demandprofiles for Germany and Switzerland were collected fromENTSO-E [1]. Demand profiles were distributed across thebuses of the network within the relevant area using the par-ticipation factors included in [52]. Exchanges between CWEcountries and non-CWE countries are collected from [1] andare modeled as fixed flows of power at the correspondingborders.

Regional 15-minute production profiles and day-ahead fore-casts for wind and solar PV for years 2013-2014 were also col-lected from national TSOs and power exchanges. The spatialresolution of renewable production data varies from countryto country. There are 4 geographical regions in Germany,

Time [hours]

Stoch.REproduction[G

W]

010

20

30

40

0 2 4 6 8 10 13 16 19 22

120

130

140

150

160

Determ.netdem

and[G

W]

RE max. energy RE max. ramp

RE min. energy Demandg

Fig. 5. Stochastic renewable energy production (wind and solar) and determin-istic net demand (demand minus hydro power) for a typical autumn weekday.The shaded gray area, included in the background, shows the variation rangeof renewable energy production.

21 regions in France, 2 regions in Belgium and 1 region inAustria. Profiles for the Netherlands and Switzerland wereestimated by averaging data of neighboring regions. Offshorewind power profiles were associated to offshore wind connec-tion buses in the transmission system. Onshore wind and solarPV capacity was distributed uniformly among generation andload buses within each administrative region of each country(12 states of Germany, 21 regions of France, 2 regions ofBelgium, Austria, Switzerland and the Netherlands). Each buswith renewable capacity was then assigned a wind and asolar PV production profile according to its location, thereforethe spatial information of renewable resource dispersion ispreserved in our data set.

Hydro power resources are modeled as fixed injections orwithdrawals from the transmission system. Hydro productionprofiles for seasonal storage, pumped storage and run of riverwere collected from RTE [57] for each power plant in France.Hydro plants in other countries were assigned productionprofiles based on profiles of French hydro plants and by takinginto account the characteristics of these plants (technology,size and location).

We used clustering to select 8 representative day types ofload for 2014, corresponding to one weekday and one weekendday for each season. We used the forecast errors of 2013-2014to generate samples of real-time renewable energy production.Fig. 5 presents the resulting deterministic net demand anduncertainty faced by the system in the day ahead. The netload forecast error can span more than 15 GW and canexhibit ramps of up to 3 GW in 15 minutes. Renewableproduction ramps of this magnitude already occur in Germany,for instance in May 11, 2014, between 17:45 and 18:00 [59].

B. Simulation setup

We simulate system operation of the CWE system underthree major policy designs: (i) the market coupling policy,which is the current zonal design in the CWE system, (ii )deterministic unit commitment, which is the current nodal

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design in several US markets, and (iii ) stochastic unit com-mitment, which is an ideal benchmark. Operations under thesethree designs are modeled in two stages. The first stage takesplace in the day ahead and determines the commitment ofthe slow thermal generators based on a forecast for renewableenergy supply. The second stage takes place in real time andcorresponds to the re-dispatch and balancing performed by thesystem operator given the realization of multi-area renewablesupply. The second stage must respect the commitment de-termined for slow thermal generators in the first stage in allpolicies.

Thermal generators, other than slow generators, are mod-eled as follows. The commitment of nuclear generators isdecided prior to the day ahead, therefore it is considered asbeing fixed in the simulations. Similarly, CHP production isdetermined based on heat demand and CHP units can adjusttheir production only within a limited range, therefore we fixtheir output and allow an adjustment of±5% of their capacityin the simulations. fast units adjust both their commitmentand production in real time. Aggregated generators correspondto small producers, therefore no commitment decision isassociated with them and it is assumed that they can adjusttheir production in real time.

The market coupling policy is simulated using the modeldescribed in section II. Note that while day-ahead markets arecleared using the zonal network of Fig. 2, real-time operationis simulated using the nodal network of Fig. 4. We considertwo variants of the market coupling design, representingdifferent levels of coordination in real-time redispatch andbalancing: (i) MC Net Positionpenalizes deviations from day-ahead zonal net positions at the maximum marginal cost ofany generator in the system [8], representing the operationalpractice whereby balancing responsible parties are requiredto balance their resources in real time, which implies thateach zone should maintain its trading position on the day-ahead market. (ii ) MC Free allows for adjustments in zonalnet positions at no penalty (CL = 0). This approximates theeffect of intra-day markets that allow balancing responsibleparties to adjust their positions as real time approaches andthe conditions of the system are gradually revealed, as wellasthe effect of coordinating balancing among zones.

Deterministic and stochastic unit commitment are modeledfollowing [34]. Deterministic unit commitment correspondsto a centralized nodal market design with full coordina-tion of the various products of the market (energy, reservesand transmission) and full coordination among zones. Thestochastic unit commitment model additionally endogenizesthe uncertainty faced by the system in order to optimallyadapt the commitment of reserves to multi-area renewablesupply uncertainty. We selected 25 scenarios for the stochasticunit commitment model from the real-time renewable energyproduction samples, by resorting to the scenario selectionalgorithm of Heitsch and Romisch [62]. For these two modelswe used a hybrid time resolution with hourly commitmentdecisions and quarterly dispatch decisions.

In order to estimate the performance of each policy, weperform a Monte Carlo simulation over a set of 120 samplesof multi-area renewable production. We resort to high per-

formance computing in order to parallelize the Monte Carlosimulations. The relative performance of stochastic unit com-mitment, deterministic unit commitment andMC Free is dueto the difference in their day-ahead commitment schedules.The performance ofMC Net Positionis additionally affectedby the requirement of adhering, in real time, to day-aheadfinancial positions.

Mathematical programs are implemented in Mosel/XPress[63] and solved on the Sierra cluster at the Lawrence Liver-more National Laboratory. Given that we model productioncost as a piece-wise linear convex function, all mathematicalprograms correspond either to LPs or MILPs. Most mathemat-ical programs are solved directly by XPress, with two excep-tions. (i) Stochastic unit commitment is solved within a 1%optimality gap using the distributed asynchronous algorithmproposed in [64] on 4 nodes. Solution times range from 44minutes to 1 hour and 56 minutes. Each scenario subproblemconsists of 444 thousand continuous variables, 539 thousandconstraints and 9.5 thousand integer variables. (ii ) The marketclearing model is solved using an enumeration heuristic basedon column-and-constraint generation. The heuristic achievesa cost which is within 1% of the optimal cost, and optimalwelfare which is within10−4% of optimal.

IV. M ODEL VALIDATION

In order to validate the accuracy of the market couplingmodel, we compare the results ofMC Net Positionagainstthe historical performance of the CWE system, as reportedin publicly accessible statistics. Table I presents the actualproduction mix of 2014 [57], [58], [65], [66] and the resultingproduction mix of our model, which is obtained by averagingall samples, seasons and day types (where the contributionof each day type is weighted by the relative frequency ofoccurrence of each day type).

These results present a reasonable approximation to theactual production mix. The most notable differences appearin the coal production of Germany, the nuclear production ofFrance and the conventional thermal production of the Nether-lands. These differences can arise from a number of factors:(i)we simulate 960 days of operations over 8 representative daytypes in our simulation in order to exploit high performancecomputing and keep the study computationally tractable; (ii )the observed estimates of 2014 are subject to statistical error(since they correspond to 365 daily samples of operation,rather than a long-run average); (iii ) we derate units by seasoninstead of modeling unit-by-unit maintenance and outages,in order to capture their average effect in a season whileusing representative day types; (iv) we compute ATC valuesendogenously within our model, instead of using the ATCs thatwere used in the exchange. Notable differences between ourmodel and the ATC values have been observed in the borderbetween Germany and the Netherlands. In order to test theinfluence of ATC value differences, we have also simulatedthe operation of theMC Net Positionmodel using the actualATCs [1]. The results better approximate the production mixfor the Netherlands and France, however the approximation ofthe German fuel mix worsens and the average operating cost

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 11

TABLE IANNUAL ENERGY PRODUCTION BY PRIMARY SOURCE

CountryPrimary MC Net Pos. Systemsource results [TWh] statistics [TWh]

Germany Coal 234.2 274.1Nuclear 87.0 97.1Gas 11.2 59.8Wind 44.4 57.3Solar 39.4 35.1Hydro 13.1 19.6Oil 0.2 6.1Other 64.3 75.9

France Nuclear 468.0 415.5Hydro 55.0 67.3Wind 16.0 17.1Gas 3.0 13.1Coal 11.6 6.7Solar 5.9 5.8Oil 0.0 2.6Other 27.2 7.4

Netherlands Thermal 38.0 91.1Wind 6.2 5.8Nuclear 4.1 4.1Hydro 0.1 0.1Solar 0.8 –

Switzerland Hydro 32.4 37.5Nuclear 22.3 25.4Thermal 5.2 3.7Wind & Solar 0.9 –

Belgium Nuclear 26.7 32.1Thermal 13.2 23.9Solar 3.4 2.8Wind 4.7 2.5Hydro 0.3 1.4

Austria Hydro 34.5 40.2Thermal 13.2 13.8Wind 4.0 3.0Solar 0.5 –

Total 1291.2 1447.8

increases by 8.4%, due to a significant shift in production fromFrance-Germany (where energy is produced at a low marginalcost) to Belgium-Netherlands (where energy is produced ata higher marginal cost). We therefore use the ATC valuescomputed endogenously by our model, in order to maintainATC values that are internally consistent with the CWEtransmission model that we use in our simulations.

In addition to fuel mix, we compare the congestion man-agement costs estimated by our model to those publishedby national TSOs. We estimate the congestion managementcosts as the difference between the cost ofMC Net Positionwith and without thermal limits on lines. Table II presentsa comparison between the estimated congestion managementcosts and the actual congestion management costs of the CWEsystem8 [1] (values correspond to January-December 2015).The congestion management costs estimated by our modelcorrectly approximate the current situation of the Germany-Austria bidding zone, although they are greater than thoseobserved in reality for Belgium and France. We note thatour model does not account for the active control of trans-mission networks for relieving congestion (e.g. the use ofFACTS devices at the borders and transmission switching inBelgium [67]). The integration of active transmission network

8Congestion management costs that cover most of the CWE area were notavailable for 2014.

TABLE IICONGESTION MANAGEMENT COSTS

ZoneMC Net Pos. results System statistics

[MMe/year] [MMe/year]DE/AT/LX 679.2 688.2Belgium 118.4 0.0France 66.4 1.1Netherlands 19.4 –Switzerland 8.7 –

TABLE IIIEXPECTED POLICY COSTS AND EFFICIENCY LOSSES WITH RESPECT TO

DETERMINISTIC UC

Policy Expected cost Efficiency losses[MMe/d] [%] [MM e/year]

MC Net Position 30.42 6.2 650MC Free 29.45 2.8 294Deterministic UC 28.64 – –Stochastic UC 28.49 –0.5 –55Perfect Foresight 28.32 –1.1 –117

management in our model is an area of future research.

V. POLICY ANALYSIS RESULTS

We proceed with a comparison of the cost performance ofthe four policies described in section III-B: stochastic unitcommitment, deterministic unit commitment,MC Free andMC Net Position.

The average cost of each policy is presented in TableIII. In addition, the cost of perfect foresight is provided forcomparison. The difference betweenMC Net PositionandMC Free quantifies the benefits of intra-day markets and thecoordination of TSOs in balancing. These efficiency gainsare estimated at3.4% of operating costs. The differencebetweenMC Free and deterministic unit commitment quan-tifies the efficiency gains of nodal market design relative tozonal markets, and is estimated at2.8% of operating cost.Finally, the difference between deterministic and stochasticunit commitment corresponds to the benefits of endogenizinguncertainty relative to using fixed requirements for the com-mitment of reserves. This gain amounts to 0.5%. Even whenconsidering the perfect foresight model, gains of perfectlyforecasting uncertainty are no larger than 1.1%. These gainsare notably lower than the aforementioned cost differencesbetween deterministic unit commitment,MC FreeandMC NetPosition.

The breakdown of operating costs is presented in Table IV,where SLOW+ corresponds to the set of nuclear, CHP, slowand aggregated units. We note that the differences betweenpolicies are largely driven by the production cost of fastunits, with the market coupling policies incurring substantiallyhigher costs from fast units relative to deterministic unitcommitment. Differences between deterministic and stochasticunit commitment are driven largely by differences in thecommitment cost of slow units.

Table V presents the expected production of each generatortype along with the production-weighted average marginal costof units providing energy. We note that even though productionfrom fast units is limited to 0.7–1.4% of the total production,

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TABLE IVCOMPOSITION OF THE EXPECTED OPERATING COST

Commitment cost Production cost LoadPolicy [MMe/d] [MMe/d] shedding

SLOW+ FAST SLOW+ FAST [MMe/d]MC Net Pos. 2.83 0.28 25.60 1.61 0.10MC Free 2.83 0.20 25.39 0.97 0.05Determ. UC 2.81 0.07 25.45 0.31 0.00Stoch. UC 2.60 0.12 25.21 0.56 0.00

TABLE VPRODUCTION AND AVERAGE MARGINAL COST OF THERMAL GENERATORS

PER POLICY

Production Production Av. marginal costPolicy [TWh/year] curtailment [e/MWh]

SLOW+ FAST [TWh/year] SLOW+ FASTMC Net Pos. 1014.9 14.6 6.5 9.21 40.14MC Free 1014.1 11.3 2.4 9.14 31.34Determ. UC 1016.8 7.4 1.2 9.14 15.29Stoch. UC 1015.4 9.0 1.3 9.06 22.99

the production cost of fast units corresponds to 1.2–6.3% ofthe total production cost. This table highlights the fact thatthe market coupling policies often resort to the activationof a substantial amount of fast units that are found at thefar right of the fast unit supply stack. This large increasein the production costs of fast units is accompanied by anincreasing amount of production curtailment that is requiredfor alleviating congestion and balancing zones inMC NetPosition.

We proceed with analyzing a number of factors that couldexplain the substantial observed cost differences among deter-ministic unit commitment,MC FreeandMC Net Position9. Inorder to better understand the results, we compare the modelsin pairs, moving from the most efficient to the least efficientpolicy.

A. Relative performance of deterministic unit commitment andMC Free

The MC design and deterministic unit commitment schedulesimilar amounts of slow capacity within each area, in all daytypes. The amount of committed capacity is mostly driven bythe net demand of each area. Nevertheless, the units committedby MC Free are less useful in real time, as can be seenin Fig. 6. Units that are committed byMC Free and notby deterministic unit commitment remain at their technicalminimum for more than 85% of the time, and are used atfull capacity for less than 5% of the time. Units committedby deterministic unit commitment and not byMC Free, incontrast, are used significantly more.

The commitment decisions ofMC Free are mainly drivenby the merit order of different units within each area, whileig-noring intra-zonal flows and misrepresenting the physical lawsgoverning cross-border exchanges. This leads to schedulesthatare not necessarily feasible when considering the full network,as shown in Fig. 7. Slow units that are committed byMC Freeand result in congestion need to be re-dispatched down in real

9Differences between the stochastic and deterministic UC have beenanalyzed in the literature [34].

100 80 70 60 50 40 30 20 10 0

020

4060

8010

0

Ocurrences [%]

Pro

duct

ion

[%of

oper

atio

nal

rang

e]

DetermUCMCFree

Fig. 6. Production duration curves of slow units that are exclusivelycommitted by deterministic unit commitment andMC Free. For any onlineunit, 0% of the operational range corresponds to its technical minimum while100% corresponds to its maximum capacity. In green, slow unitsthat werecommitted by deterministic unit commitment but not byMC Free. In red(dashed), slow units committed by the market coupling model but not bydeterministic unit commitment.

D-100

0–50 e/MWh

≥ 50 e/MWh

[0,50)% load

[50,100)% load

100% load

overloaded

Fig. 7. Day-ahead schedule determined byMC Free for a spring weekdayat the 17:00–18:00 interval. Flows implied by the productionschedule areinfeasible for the real network since they overload lines inthe west ofGermany. This infeasible schedule is altered in real time by re-dispatchingall generators at D-100 down to their technical minimum and starting up fastunits in the surrounding area in order to relieve congestion.

time in order to prevent overloading transmission lines. Thisresults in the activation of more expensive units in real timerelative to deterministic unit commitment.

Fig. 8 demonstrates that congestion management after day-ahead market clearing results in a more frequent use of high-cost fast units in the case ofMC Free. Deterministic unitcommitment, on the other hand, does not require a substantialmodification of the day-ahead schedule in real time since thephysical constraints of the transmission network are accountedfor when committing slow generators (the same is true forstochastic unit commitment), as it is the case in nodal USmarkets [11]. This highlights the need to account for unitcommitment when analyzing zonal market designs, a feature

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 13

0 50 100 150 200 250

-0.5

0.0

0.5

050

100

150

200

Production [GW]

fD

eter

mU

C−

fM

CF

ree

[-]

Mar

gina

lco

st[e

/MW

h]Fig. 8. Difference in the frequency of use of supply curve increments betweendeterministic unit commitment and theMC Freepolicy for autumn weekdays.The frequency of use of each supply increment, for a given policy andday type, corresponds to the proportion of the increment thatis used onaverage over all quarterly periods and all samples of real-time operation. Inthe plot, green stripes represent the frequency of use of supply incrementscorresponding to SLOW+ generators, while red stripes correspond to fastgenerators. The marginal cost function of the system (which is measuredin the right vertical axis) is presented for reference in black.

MC

Net

Pos

MC

Fre

e

MC

Net

Pos

MC

Fre

e

MC

Net

Pos

MC

Fre

e

MC

Net

Pos

MC

Fre

e

MC

Net

Pos

MC

Fre

e

Belgium

Switzerla

nd

DE/AT/LX

France

Netherlands

-400

00

2000

4000

Net

posi

tion

adju

stm

ent

[MW

h]

Fig. 9. Adjustment of zonal net position in real time with respect to theday-ahead net position. A positive adjustment corresponds to a real-time netposition that is larger than the day-ahead net position, andvice versa. Netposition adjustments of DE/AT/LX range between -6 GW and 5 GW.

that has been largely overlooked in existing literature.

B. Relative performance of MC Free and MC Net Position

The comparison ofMC Net PositionandMC Freeprovidesan indication about the value of intra-day adjustments andthe coordination of TSOs in balancing operations [6]. Fig. 9demonstrates thatMC Freecontinuously alters the day-aheadnet position due to the coordination among zones, whereasMC Net Positiononly deviates from the day-ahead zonal netpositions in extreme situations (these correspond to outliers inthe box plots).

The behavior of theMC Net Positionmodel is largelydriven by the renewable supply forecast error of DE/AT/LX(more specifically Germany), since adjustment in other zonesis driven by adjustments in DE/AT/LX. This is demonstrated

-3 -2 -1 0 1 2

-3-1

12

Fitted adjustment [GWh]

Actualadjustment[G

Wh] Autumn

-2 -1 0 1

-3-1

12

Fitted adjustment [GWh]

Actualadjustment[G

Wh] Winter

Fig. 10. Linear regression of the adjustment of the real-time net position ofDE/AT/LX under MC Freerelative toMC Net Positionfor autumn weekdays(best fit) and winter weekdays (worst fit). The explanatory variables are theforecast error of DE/AT/LX and the day-ahead net positions of the zones. A45 degree line is drawn in red along with the data for comparison.

0 20 40 60 80 120

-0.6

0.0

0.4

Production [GW]

fM

CF

ree−

fM

CN

etP

os[-

] DE/AT/LX

0 20 60 100 140

050

150

Production [GW]

Mar

gina

lco

st[e

/MW

h]

FR/NL/BE/CH

Fig. 11. Difference in use of zonal supply function increments betweenMCFreeandMC Net Position, for samples and periods with an adjustment of thenet position of DE/AT/LX below the 87.5% quantile (12.5% larger reductionsin net position of DE/AT/LX), for autumn weekdays.

in Fig. 10. The figure presents the linear regression of theadjustments in the DE/AT/LX zone, using the forecast errorin renewable production and the day-ahead net positions asindependent variables. Across all day types, the forecast error(with positive correlation) and the day-ahead net positionofDE/AT/LX (with negative correlation) are the factors withthe greatest coefficients and highest significance levels. Thisindicates that when DE/AT/LX is short on its prediction ofrenewable supply (negative forecast error) and has availableimport capacity (large day-ahead net position), theMC Freepolicy will decrease the real-time net position of the zone byimporting more power from other areas. Instead, according tothe MC Net Positionpolicy the forecast error is corrected byre-dispatching within the zone, which results in significantlyhigher cost, as can be observed in Fig. 11. This highlights amajor weakness of partial real-time coordination in systemswith substantial levels of renewable supply, which can resultin major efficiency losses. Note that this type of efficiencyloss affects both the continental European system as well asthe wide interconnections in US systems [16].

VI. CONCLUSIONS

In this paper we propose a hierarchy of mathematical pro-grams that model the sequential clearing of products in zonalelectricity markets, in particular, the market coupling designcurrently present in continental Europe. Our model accounts

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 14

for the simplified representation of transmission in the day-ahead time frame, the separation of energy and reserves, theseparation of day-ahead unit commitment decisions from real-time dispatch and balancing, and the uncertainty stemmingfrom renewable forecast errors. The market coupling designiscompared to two centralized nodal designs: deterministic andstochastic unit commitment.

Our study finds that market design can exert an influ-ence on physical operations, which far exceeds the benefitsof stochastic unit commitment relative to deterministic unitcommitment. A decentralized zonal market can underminesystem performance in two ways: (i) by leading to subopti-mal commitment of slow generators and creating significantunscheduled flows in day-ahead markets, and (ii ) by applyingsuboptimal balancing strategies due to partial coordinationamong multiple system operators in real time. The first type ofproblem affects only the European market, where institutionalbarriers have blocked the implementation of LMPs and thesplitting of wide zones into smaller ones. In contrast, thesecond type of problem currently affects both the continentalEuropean system and the wide interconnections in US systems.Moreover, the lack of real-time coordination can harm opera-tional security in extreme situations. This has motivated systemoperators of both systems to study alternatives for bettercoordination in balancing, for instance, imbalance netting andthe harmonization of balancing products in Europe.

Future extensions of the present work include (i) a recedinghorizon model of real-time operations that represents theinfluence of ramp rate constraints more accurately, (ii ) thestudy of the impact of ramp rate constraints in a finer timescale (e.g. 5 minutes), (iii ) the representation of resources(e.g. CCGT, hydro and nuclear) in greater detail, and (iv) therepresentation of active transmission network management.

ACKNOWLEDGMENT

The authors would like to thank Pr. (E.) Yves Smeers(UC Louvain), Pr. Matheiu Van Vyve (UC Louvain) andDr. Andreas Ehrenmann (ENGIE) for their comments andthoughtful discussions during the development of this work.

The authors would also like to thank the Fair Isaac Cor-poration FICO for providing licenses for Xpress, and theLawrence Livermore National Laboratory for granting accessand computing time at the Sierra cluster.

This research was funded by the ENGIE Chair on EnergyEconomics and Energy Risk Management and by the Uni-veriste catholique de Louvain through an FSR grant.

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APPENDIX ANOMENCLATURE

SetsT60 hourly periods,T60 = {1, . . . , 24}T15 15 minute periods,T15 = {1, . . . , 96}A zonesN busesL linesK interconnectorsG thermal generatorsT15(τ) 15 minute periods within hourτN(a) nodes in zoneaL(n,m) lines between busesn andm, directed fromn

to m

L×(a, b) cross-border lines connecting zonesa and b,directed froma to b

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, MMM YYYY 16

K(a, b) interconnectors between zonesa andb, directedfrom a to b

Ξ corners of NTC hyper-rectangleG(n) thermal generators at noden (or set of nodesn)NNTC

τ set of feasible exchanges with respect to NTCsNOPF

τ set of feasible exchanges with respect to DCOPF

GSLOW slow generatorsGFAST fast generatorsI continuous bidsJ block bidsG exclusive groupsI(a) continuous bids in zoneaJ(a) block bids in zoneaJE(g) block bids within exclusive groupgD60

g set of feasible generator production decisions forhourly resolution

D15,Rg set of feasible generator production and reserve

decisions for 15-minute resolutionD15

g set of feasible production decisions for 15-minute resolution

Parametersτ(t) corresponding hour of quartertF±l flow bounds, linel

Bl susceptance, lineln(l),m(l) departing and arrival buses, linelDn,t demand at busn on periodtξn,t forecast renewable supply at busn, periodtnBCEk,τ Base Case Exchange through interconnectork

in hour τRFCR

a FCR requirement in zonea (similarly definedfor aFRR and mFRR)

TTC±k,τ total transfer capacity, interconnectork, hour τ

NTC±k,τ net transfer capacity, interconnectork, hour τ

ATC±k,τ available transfer capacity, interconnectork,

hour τa(k), b(k) departing and arrival zones, interconnectork

Qiτ quantity offered, bidi, hour τ

P i unitary price, bidiMj big-M parameter, block bidja(i) area of bidiCg(q) hourly production cost function, generatorgQ

gj discrete output quantities, generatorg

Cgj discrete production costs, generatorg

mg number of discrete production bins, generatorg

Kg no load cost, generatorgSg startup cost, generatorghg(ω,v) total cost of production profile(ω,v), generator

g

∆QMCa,τ day-ahead net position of zonea, hour τ

uMCg,τ day-ahead preliminary commitment, generator

g, hour τuRg,τ , v

Rg,τ day-ahead definitive commitment and startup,

generatorg, hour τV value of lost loadCL day-ahead net position update penalty

ζn,s,t renewable supply at busn, Monte Carlo samples, periodt

Variablesqg, q

ig, qg,t quantity produced, generatorg

fl, fil , fl,t flow through linel

θn, θin, θn,t voltage angle, busn

xi acceptance/rejection continuous bidiyj acceptance/rejection block bidjnk,τ exchange through interconnectork, hour τpa,τ energy price in zonea, hour τsi, sg surplus of bidi (exclusive groupg)λ±k,τ congestion price, interconectork, hour τ

ug,τ , vg,τ commitment and startup, generatorg, hour τωgj,τ acceptance of production binj, generatorg,

hour τrFCRg,t FCR provision, generatorg, periodt (similarly

defined for aFRR and mFRR)on,t production shedding at busn, periodten,t load shedding at busn, periodtδa,τ day-ahead net position update, zonea, hour τ

Ignacio Aravena (M’13) obtained his B.Sc. andM.Sc. degrees in Electrical Engineering from Uni-versidad Tecnica Federico Santa Marıa (UTFSM),Chile, where he also served as lecturer. He is cur-rently a Ph.D. student on Applied Mathematics atUniversite Catholique de Louvain (UCL), Belgium.

Anthony Papavasiliou (M’06) received the B.S.degree in electrical and computer engineering fromthe National Technical University of Athens, Greece,and the Ph.D. degree from the Department of Indus-trial Engineering and Operations Research (IEOR)at the University of California at Berkeley, Berkeley,CA, USA. He holds the ENGIE Chair at the Uni-versite catholique de Louvain, Louvain-la-Neuve,Belgium, and is also a faculty member of the Centerfor Operations Research and Econometrics. He hasserved as a consultant for N-SIDE, Pacific Gas and

Electric, Quantil and Sun Run and has interned at the FederalEnergyRegulatory Commission, the Palo Alto Research Center and the Energy,Economics and Environment Modelling Laboratory at the National TechnicalUniversity of Athens.