energy and reserve co-optimization of a combined f. a

F. A. CamposInstitute for Research in Technology (IIT),

Technical School of Engineering (ICAI),

Comillas Pontifical University,

Santa Cruz de Marcenado 26,

Madrid 28015, Spain

e-mail: [email protected]

J. RenesesInstitute for Research in Technology (IIT),

Technical School of Engineering (ICAI),

Comillas Pontifical University,

Santa Cruz de Marcenado 26,

Madrid 28015, Spain

e-mail: [email protected]

Energy and ReserveCo-optimization of a CombinedCycle Plant Using Mixed IntegerLinear ProgrammingThe growth in the importance of interruptible sources of energy is increasing the con-cerns of many electricity market regulators with respect to the reliability and stability ofelectricity supply. Decisions such as that to increase the number of reserve markets, theirreserve requirements, or the role of reserve prices in the final electricity price have meantthat generation plants are currently often operating with strategies to obtain not onlylarge energy market quotes but also reserve ones. In this paper, a mixed integer linearprogramming (MILP) model is proposed to obtain the energy and reserve dispatch of areal combined cycle plant (CCP) to optimize its use on a weekly or annual basis. The dis-patch is optimal in the sense that it maximizes the joint energy and reserve profits, includ-ing an estimation of the energy and reserve prices. The detailed technical and economiccharacteristics of the plant have been considered, such as start-ups, shut-downs, mini-mum hours for steam generation, supplementary firing, or natural gas contracts. Thecases studies validate the main features of the mathematical model and analyze the com-putational efficiency in a realistic simulation. [DOI: 10.1115/1.4028002]

1 Introduction

Over recent years, the increasing investment in interruptibleenergy sources, such as renewable energy, has emphasized theneed for new market mechanisms to guarantee that the supply ofelectricity meets the demand within a stable electricity supply net-work. Examples of such mechanisms are the establishment ofhigher reserve requirements for generation companies (GENCOs)in existing ancillary reserve markets or the creation of new auc-tions to ensure a system’s reliability (such as the upward reservemarket recently created in Spain for power plants that have notbeen cleared in the day-ahead market). Ancillary reserve servicesmust respond almost simultaneously to system load fluctuationsand restore the generation and load balance in the event of a con-tingency such as the loss of a generator or a line, the correction ofdemand, or solar or wind generation forecasting errors. Reservesare usually classified according to their technical characteristics:The response timescale in which they must be provided, the con-trol mechanisms that ensure their coordination, and the type ofevent they must respond to. In Europe, for example, these servicesare classified into three different types: primary, secondary, andtertiary. Primary is a virtually instantaneous service for frequencyvariations controlled by an automatic generation control that coor-dinates multiple generators at different power plants. Secondaryreserve responds basically to small load changes that must becompensated in a period ranging from a few seconds to a fewminutes. Finally, tertiary reserve must be supplied within minutesand it is used to replace the secondary energy that is being used(see Ref. [1] for a review of the current types of reserves and for aclassification of these services implemented in various countries).

Prior to the existence of large amounts of interruptible energy,fossil-fuel power plants with high variable costs were mainly rele-gated to running only in peak hours, particularly in oversized gen-eration capacity systems. With the significant penetration of windor other nondispatchable energy, these fossil plants will have tostop for very long time periods, compromising their capacity to

recover their investments. Nevertheless, the fact that renewableenergy is subject to multiple uncertainties (mainly related toweather conditions) increases the importance of reserve marketsand brings new opportunities for such fossil plants, especially forthose with the ability to provide a large quantity of reserve in avery short period of time. This is precisely the case of CCPs, sincethey have fast ramp-rates due to the physicochemical properties ofthe natural gas burned and their gas/steam cycles [2].

In this new scenario, new powerful models which representCCP operation and take into account both energy and reserve sup-ply services have become increasingly necessary. Consequently,the majority of the research presented in the literature related toCCP modeling focuses on the representation of the process ofselecting and facilitating the control strategies of CCPs in realtime. This research models the technical aspects of the maindesign components of CCPs, such as air compressors, boilers, gasturbines (GTs), heat recovery steam generators (HRSGs), steamturbines (STs), or alternators, and even circuitry, shafts, valves,pipes, and so on. It also analyzes CCP operating modes and con-trol characteristics. The main resolution methodology of theseapproaches is based on the application of dynamic simulation bymeans of the use of different standard commercial simulators (see,for example, Ref. [3] for a steady-state simulation of a CCP,applying software from Lehigh University) or by using soft com-puting methods (see, for example, Ref. [4] for the optimization ofthe start-up costs of a CCP using fuzzy-logic and evolutionarycomputation).

Nevertheless, few CCP models optimize the operation decisionsof CCPs in larger time frames. Economic dispatch (ED) and unitcommitment (UC) are the main approaches used in these cases.ED provides the optimal electricity production for all scheduledgenerating units (including CCPs) in order that the system loadcan be supplied in the most economical way, subject to transmis-sion and operational constraints [5]. In Ref. [6], the theoreticalaspects of applying constrained optimization to obtain the ED ofCCPs are discussed, and a maximum level of greenhouse gasemissions is proposed (though CCPs can be considered to be envi-ronmentally friendly). The resolution of the UC problem, on theother hand, determines the generation schedule for a given combi-nation of generating units, satisfying a set of dynamic operational

Contributed by the Cycle Innovations Committee of ASME for publication in theJOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received October15, 2013; final manuscript received June 24, 2014; published online July 29, 2014.Assoc. Editor: Paolo Chiesa.

Journal of Engineering for Gas Turbines and Power OCTOBER 2014, Vol. 136 / 101702-1Copyright VC 2014 by ASME

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and environmental constraints at minimum cost. In particular, UCoptimizes the multiple operating configurations of CCPs, that is,the different modes in which certain elements or functions ofCCPs are turned on or off (such as the state of the ST, see Ref.[7]). The objective of the UC approach is to supply a fixed genera-tion program that has been assigned to each CCP as well as com-puting the optimal CCP operating configurations, and usually forlarger planning periods than in ED (typically 1 week for UC, seeRef. [8]). Since the operating configurations involve discrete deci-sions, UC always entails integer variables that complicate the re-solution. In Refs. [7] and [9], a UC is solved by means of usingdynamic programming to analyze a state-transition diagram inwhich each node represents a particular configuration. Reservecommitments and network constraints are included in Ref. [7] andsolved applying Bender decomposition [10] to minimize thenetwork violation in each Bender subproblem. Nevertheless,suboptimal solutions can be obtained, especially if interhourlyconstraints, such as ramps, are included. In addition, large compu-tational times are sometimes obtained if a large number of statesare considered (as occurs when modeling start-up and shut-downdecisions, or minimum on/off time constraints). These conditionsare included in Ref. [11], where a very interesting UC model ispresented. This model optimizes the operating modes by using ajoint energy and reserve MILP model, while taking into accountother complex conditions such as ramping constraints and limitson the number of turbines running. In addition, computational effi-ciency is not compromised, thank to the use of the powerful opti-mizer Cplex [12] in one of its latest versions.

This paper proposes a price-based UC model for the optimiza-tion of generation and secondary reserve operations, using a simi-lar MILP to Ref. [11]. Instead of minimizing costs, GENCOprofits in the day-ahead and reserve markets are maximized by

considering energy and reserve prices to be input data. This meansthat no demand meeting constraints are required, and only theCCP to be analyzed is represented. In contrast to Ref. [11], gascontracts, daily and monthly gas capacities (tolls), and CO2 emis-sions costs have been taken into account. Several peculiarities ofCCP operation are also considered, such as the minimum time andthe minimum production levels required in order to start-up theST or supplementary firing processes; however, network con-straints are omitted. As in the CCC model of Ref. [11], the tur-bines have been represented as individual components rather thanby means of a finite number of operation modes. Spinning reserveis also represented but for the CCP under study there is nonecessity to include additional ramps constraints in an hourlyschedule, since the ramp-rates of the CCP are sufficiently high(today’s fast start CCPs can reach full load in 18 min or less, seeRef. [13]). See Ref. [14] to include ramp constraints when model-ing CCPs.

This document is organized as follows. In Sec. 2, an overviewof the analyzed CCP is presented. Section 3 describes the mainassumptions and modeling issues with respect to CCPs and gascontracts. The detailed mathematical formulation of the proposedMILP is also presented. Finally, several case studies and conclu-sions will end this paper.

2 General Description of the CCP

The CCP modeled in this paper has four GT and four HRSG,but only one ST. Figure 1 shows the basic scheme of the CCPstudied here, avoiding, for the sake of simplicity, the detailed rep-resentation of the high pressure (HP) and the low pressure (LP)water/steam circuitry, or other more specific components such aspumps, drums, or economizers.

Fig. 1 CCP design

101702-2 / Vol. 136, OCTOBER 2014 Transactions of the ASME


The CCP in this study can operate with any combination ofGTs turned on or off, and each supplementary burner in theHRSG for the ST running can also be turned on or off. EachHRSG introduces two streams of steam that are expanded by theST: HP and LP flows. These gas volumes depend on whether thesupplementary burner is used or not. If the burner is turned on, thetotal electricity generated in the ST is increased at a certain cost,since some quantity of additional natural gas is consumed. In fact,these supplementary burners are often utilized only in peak hours.Finally, each GT has a bypass stack that allows the turbine to runin simple cycle mode, isolating the HRSG used in combinedcycle.

3 CCP Modeling With MILP

This section describes the main assumptions and the mathemat-ical formulation of the proposed MILP problem. Super index� re-fers to the ST, capital letters are used for the decision variables,and small letters for the parameters.

3.1 Decision Variables. The main decisions to be optimizedin the CCP operation provide answers to the following questions:

• Considering a time horizon of 1 yr, is it necessary to turn onthe ST in addition to GTs (that is, in this last case the CCPrunning in combined cycle)?

• Binary variables Uu,h indicate if each GT u is turned on athour h and U�h indicate if the ST is running.

• When does the ST have to be turned on, started up or shutdown, in addition to each GT?

• In this case, binary variables (Uu,h and U�h ) indicate if eachGT and the ST are turned on, respectively, while (Yu,h andY�h ) and (Zu,h and Z�h ) are the corresponding binary variablesfor start-up and shut-down decisions, respectively.

• Is the CCP running in a combined cycle and is it necessary toapply supplementary firing to the gases resulting from thecombustion in each HRSG of each GT?

• The binary variable Ui;�u;h indicates whether each GT is in

combined cycle and whether it is generating without (i¼ 0)or with supplementary firing (i¼ 1).

• With supplementary firing, what is the degree U2;�u;h � [0,1]

of supplementary firing?

It is also necessary to quantify

• The gross (Qu,h and Q�h ) and net (Pu,h and P�h ) energy gener-ated by each GT and by the ST (and therefore to know whatthe total energy sold by the CCP in the day-ahead market is).

• The upward (URu,h and UR�h ) and downward reserve (DRu,h

and DR�h ) provided by each GT and the ST and sold in thereserve market.

• The total consumption Gu,h of natural gas by each GT, takinginto account the supplementary firing process (if this isapplicable).

• The monthly Jm and daily Jd capacities of gas contracted bythe GENCO to be able to deal with unpredictable closer-in-time gas demands by the CCP.

Some other less significant variables are described in the No-menclature section of this paper.

3.2 Objective Function. The objective function consists inthe maximization of the company’s margin as the differencebetween revenues and costs. The total revenues of the companyconsist of the following items (see Nomenclature for a betterunderstanding of their formulations).

(1) Revenues from the day-ahead energy marketXh

Ph � phf g (1)

(2) Revenues from the secondary reserve marketXh

URh þ DRhð Þ � psh

� �(2)

(3) Revenues from the energy bought or sold within the reserveXh

ph � PURh � nur � PDRh � ndr� ��

(3)

When considering Eq. (3), it is important to remember that themodel optimizes the remuneration of the reserve in terms of pro-viding opportunities to sell or buy energy, taking into account theenergy finally sold or bought within such a reserve (here calledregulating energy). This is especially relevant in the Spanish case,in which regulating energy is remunerated using the marginalprice of the tertiary market (see Ref. [15] for more details).

The cost function to be considered consists of the following:

(1) Through a forward natural gas supply contract, GENCOsare required to pay the gas supplier an agreed price, cng,for the natural gas burned in his CCP, instead of a fluctuat-ing spot price. This allows GENCOs to manage the riskassociated with the highly volatile pricing of natural gasand produces the following fuel cost (natural gas cost):X

h

cng � Gh þ GURh � GDRhð Þf g (4)

(2) The maintenance cost computed through the number ofhours of each turbine being committedX

u;h

cmu � Uu;h

� �þX

h

cm� � U�h� �

(5)

(3) Start-up and shut-down costs

Xu;h

cstu � Yu;h

� �þX

h

cst� � Y�h� �

þXu;h

cshu � Zu;h

� �þX

h

csh� � Z�h� � (6)

(4) CO2 emissions costsXu;h

pemis � cemisu � Gu;h þ GURu;h � GDRu;h

� �� (7)

(5) By means of another contract, GENCOs also pay the net-work operator (who is also normally the pipeline company,as in most European countries), for the use of the infrastruc-ture needed in the delivery. The unit cost in this case,referred to as “variable tariff” (v), depends on the quantityof natural gas to be delivered and is as follows:

Xh

Gh þ GURh � GDRhð Þ � vf g (8)

(6) The main flaw in these contracts is that v may not be suffi-cient for the recovery of the investment in pipeline. A fur-ther problem is inflexibility in demand and fluctuation insupply. To mitigate this, the network operator and theGENCO usually agree on some specific clauses in con-tracts. One of these consists in a commitment on the part ofthe GENCO to specify not only monthly capacities Jm forthe gas pipeline but also daily ones Jd, to deal with thedemand for gas, the corresponding daily tariffs being higherthan the monthly ones. Daily and monthly tariffs are repre-sented in this paper by monthly coefficients (dm and mm,

Journal of Engineering for Gas Turbines and Power OCTOBER 2014, Vol. 136 / 101702-3


respectively) with respect to a base annual tariff (f), called“fixed tariff.” These tariffs result in the following fixedcosts: X

d;m:d2m

Jd � dm � ff g þX

m

Jm � mm � ff g (9)

3.3 Constraints. The objective function described abovemust be optimized subject to the following constraints.

GT Modeling. Relation between gross and net power

Pu;h ¼ Qu;h � 1� cauð Þ (10)

Each GT is required to reach different minimum power genera-tion levels, depending on whether the GT is running without pro-

ducing steam (minimum denoted as qminu ), producing steam

without supplementary firing (qmin;0;�u ), or producing steam and

applying supplementary firing (qmin;1;�u ). The first constraint of

Eq. (11) models the relationship between the final minimum gross

power QV;minu;h and the different minimum power limits qmin

u ,

qmin;0;�u , and qmin;1;�

u for each of the mentioned three states, by

using their corresponding binary variables Uu,h, U0;�u;h , and U1;�

u;h .

The second constraint represents the power Qminu;h above QV;min

u;h ,

and the last constraint defines the total gross power Qu,h generated

QV;minu;h ¼

qminu � Uu;h

þ qmin;0;�u � qmin

u

� �� U0;�

u;h

þ qmin;1;�u � qmin;0;�

u

� �� U1;�

u;h

8>><>>:

9>>=>>;

Qminu;h � qmax

u;h � Uu;h � QV;minu;h

� �� du;h

Qu;h ¼ Qminu;h þ QV;min

u;h � du;h

(11)

The gas consumption GWu,h (without taking into account the con-sumption in the HRSG) is modeled as a linear function of thegross power Qu,h, and considering a minimum gas consumptiongmin

u necessary to turn on the CCP (this linear function, see Fig. 2,have been estimated based on a linear regression using experimen-tal data directly obtained from the CCP operation and with a coef-ficient of determination not lesser than 0.92)

GWu;h ¼ gminu � Uu;h þ au � Qu;h (12)

Unlike the CCP under study in this paper, Ref. [16] introducesnonlinear equations for the modeling of these performance curvesfor other CCPs and proposes an approximation of these curves bymeans of piecewise linear functions, which leads to a MILP opti-mization model, as in this research.

Limits on the upward and downward spinning reserves

URu;h � qmaxu;h � du;h � 1� cauð Þ � Uu;h � Pu;h

DRu;h � Pu;h � QV;minu;h � du;h � 1� cauð Þ

URu;h þ DRu;h � bmaxu

(13)

Apart from the use of supplementary firing mode, there are occa-sions, especially when the reserve price is high and the day-aheadprice is low, when some GTs may be configured in order to pro-vide only upward reserve without being turned on for a wholehour. This is called the “fast start” operation mode. The relationbetween the upward reserve and the binary variable UFu,h for thismode is represented as

URu;h � bsmaxu � Uu;h þ UFu;h

� �Uu;h þ UFu;h � 1

(14)

The first two constraints of Eq. (15) model the cleared energywithin the upward and downward reserves by using the percen-tages qur and qdr of energy cleared within each type of reserve.Equation (15) also includes the relationship between the gross andthe net cleared energy within each reserve by means of the auxil-iary services coefficient cau

PURu;h ¼ URu;h � qur

PDRu;h ¼ DRu;h � qdr

QURu;h ¼ PURu;h= 1� cauð ÞQDRu;h ¼ PDRu;h= 1� cauð Þ

(15)

Definition of the gas consumed within the reserve

GURu;h ¼ au � QURu;h

GDRu;h ¼ au � QDRu;h

(16)

Coherency between the start-up, shut-down, and turn-on decisions

Yu;h � Zu;h ¼ Uu;h � Uu;h�1 (17)

HRSG Modeling. In this paper, there are assumed to be threemain operation modes for each HRSG, depending on if the sup-plementary burner is turned off (no supplementary firing, i¼ 0); itis turned on, burning a minimum natural gas quantity (minimumsupplementary firing mode, i¼ 1); or it is turned on and burning aquantity above the minimum quantity mentioned above (supple-

mentary firing mode, i¼ 2). Thus, if Ui;�u;h is a binary variable indi-

cating mode i activation for i2{0,1}, and U2;�u;h a continuous

variable in [0,1] graduating the natural gas burned between theseminimum and maximum quantities, then the total natural gas con-sumption in terms of the gas used in the HRSG (without supple-mentary firing, i¼ 0 or additional consumption) is represented as

Gu;h ¼ GWu;h þXi¼1;2

Ui;�u;h � gc�i þ fsu � gmin

u � UFu;h (18)

Note that Eq. (18) includes the gas consumed during the fast startmode. This consumption is estimated for each hour using the frac-tion fsu of the hour in which the GT will actually be turned on(because the system operator requires the use of the upwardreserve). As mentioned, the unit gas consumption decreases as theoutput gross power increases and, thus, for this fraction of thehour, the corresponding minimum gas consumption gmin

u (see Fig.2) has to be taken into account.

In addition, in Eq. (18), it is assumed that gas consumed gc�i isan incremental value with respect to the previous mode i� 1 andtherefore,Fig. 2 Gas consumption as a linear function of gross power



Ui�1;�u;h � Ui;�

u;h (19)

If the GT is not turned on, then it cannot provide steam

U0;�u;h � Uu;h (20)

However, once it has been decided that a GT must apply supple-

mentary firing, i.e., U1;�u;h ¼ 1, the next important issue is to opti-

mize the level of supplementary firing. In this paper, it is assumed

that the continuous variable U2;�u;h in [0,1] represents this level,

from a minimum firing (with U2;�u;h ¼ 0 and Qu,h¼ qmin;1;�

u ) to a

maximum firing (with U2;�u;h ¼ 1 and Qu,h¼ qmax

u;h ). Intermediate

values of U2;�u;h (in (0,1)) are assumed to be proportional to

Qu,h� qmin;1;�u in a linear way, that is

U2;�u;h ¼

Qu;h � qmin;1;�u

qmaxu;h � qmin;1;�

u

(21)

Since this expression must be true only when U1;�u;h ¼ 1, Eq. (22)

presents the linear formulation as a function of U1;�u;h . Note that if

U1;�u;h ¼ 0, Eq. (22) does not constrain

U2;�u;h �



u

� 1� U1;�u;h

� �� 1

U2;�u;h �



u

� 1� U1;�u;h

� �� 1ð Þ

(22)

Another technical requirement is that if a GT provides reserve,

that is, URu,hþDRu,h> 0, and steam, i.e., U0;�u;h ¼ 1, at the same

time supplementary firing is necessary, that is, U1;�u;h ¼ 1, which is

modeled as

U1;�u;h � U0;�

u;h � 1� �

þ URu;h þ DRu;h

bmaxu

(23)

One important technical constraint (on each GT) is the need toproduce above an amount of power during a number of hours t�

previous to the production of steam. It is also necessary that theGT is turned on (above its minimum technical power) 1 h beforethis time period. If the amount of power to be supplied during thisperiod is imposed in terms of a load u�, Eq. (24) uses the binaryvariable V�u;h as an auxiliary variable such that V�u;h¼ 1 if the loadof each GT is above u� in h and turned on in h� 1

2 � V�u;h �Qu;h=qmax

u;h

� �u�

þ Uu;h�1 (24)

Using V�u;h, Eq. (25) means that if a GT is producing steam(U0;�

u;h ¼ 1), then the previous t� variables V�u;h�1, …, V�u;h�t� mustbe equal to 1

t� � U0;�u;h �

Xh�t��h0<h

V�u;h0 (25)

ST Modeling. Relation between the net and gross powers

P�h ¼ Q�h � 1� ca�ð Þ (26)

Maximum and minimum power

qmin;� � U�h � Q�h � qmax;�h � U�h (27)

Coherency between the binary variables which indicate if a GT isproducing steam and the status of the ST

U�h �X

u

U0;�u;h � 4 � U�h (28)

In this paper, it has been assumed that the total generated grossproduction at each hour by the ST can be characterized as a linearregression of the HP and LP flows, that is

Q�h hpfh; lpfhð Þ ¼ k0 þ k1 � hpfh þ k2 � lpfh (29)

the estimation of coefficients ki being based on historical informa-tion. The HP and LP flows are at the same time expressed usingincremental flows hpfi,u,h and lpfi,u,h depending on the three opera-tion modes described in the HRSG modeling (no supplementaryfiring, i¼ 0; minimum supplementary firing mode, i¼ 1; orsupplementary firing mode, i¼ 2)

hpfh ¼Xi;u

Ui;�u;h � hpfi;u;h

lpfh ¼Xi;u

Ui;�u;h � lpfi;u;h

(30)

Flows hpfi,u,h and lpfi,u,h are also modeled via linear regressions,1

in this case using the gross production generated by each GT asthe explanatory variable

hpfi;u Qu;h

� �¼ ahp

i;u þ bhpi;u � Qu;h

lpfi;u Qu;h

� �¼ alp

i;u þ blpi;u � Qu;h

(31)

Since the three operation modes described are incremental,Eq. (30) can be expressed using Eq. (31) as

hpfh ¼Xi;u

Ui;�u;h � ahp

i;u � ahpi�1;u

� �þ bhp

i;u � bhpi�1;u

� �� Qu;h

n o

lpfh ¼X

i;u

Ui;�u;h � alp

i;u � alpi�1;u

� �þ blp

i;u � blpi�1;u

� �� Qu;h

n o(32)

Equation (29) is therefore equivalent to

Q�h ¼ k0 þXi;u

Ui;�u;h � kai;u;h þ kbi;u;h � Qu;h

� �(33)

being

kai;u ¼ k1 � ahpi;u � ahp

i�1;u

� �þ k2 � alp

i;u � alpi�1;u

� �kbi;u ¼ k1 � bhp

i;u � bhpi�1;u

� �þ k2 � blp

i;u � blpi�1;u

� � (34)

Finally, Eq. (35) is the linear formulation of the ST total powerdefined in Eq. (33) and included in the proposed MILP

Q�h ¼ k0 � U�h þX

i

Qi;�u;h

Qi;�u;h � kai;u � Ui;�

u;h þ kbi;u � Qu;h

Qi;�u;h � kai;u þ kbi;u � qmax

u;h

n o� Ui;�

u;h

(35)

Limits on the upward and downward spinning reserves are alsoimposed

1Statistical analyses using real data taken directly from the CCP confirm that allthe regressions are very accurate, with coefficients of determination always higherthan 0.9 even in pessimistic scenarios.



UR�h � qmax;�h � 1� ca�ð Þ � U�h � P�h

DR�h � P�h � qmin;� � 1� ca�ð Þ � U�hUR�h þ DR�h � bmax;�

(36)

The definition of the cleared energy within the reserve is

PUR�h ¼ UR�h � qur

PDR�h ¼ DR�h � qdr(37)

Coherency between the start-up, shut-down, and turn-on decisionsis represented as

Y�h � Z�h ¼ U�h � U�h�1 (38)

Modeling of Gas Contracts. Apart from the specific price provi-sions modeled in Eqs. (8) and (9), a nonpricing clause that reducesthe supplier’s risk and that has received much attention is thetake-or-pay clause. This clause requires GENCOs to pay for a spe-cific minimum quantity of natural gas, even if this is not burned.Therefore, GENCOs either use the product or simply pay the sup-plier for such a minimum quantity. Take-or-pay clauses are repre-sented in this paper using the minimum daily and monthly naturalgas quantities (cmin

d and cminm ) to be supplied. Maximum quantities

may also be imposed

cmind �

Xh2d

Gh þ GURh þ GDRhð Þ � cmaxd

cminm �

Xh2m

Gh þ GURh þ GDRhð Þ � cmaxm

(39)

Daily consumption is limited by the total daily contractedcapacity X

h2d

Gh þ GURh � GDRhf g � Jd þX

m:d2m

Jm (40)

Other Constraints. Definition of aggregated variables

Qh ¼X

u

Qu;h þ Q�h

Gh ¼X

u

Gu;h

URh ¼X

u

URu;h þ UR�h

DRh ¼X

u

DRu;h þ DR�h

GURh ¼X

u

GURu;h

GDRh ¼X

u

GDRu;h

PURh ¼X

u

PURu;h þ PUR�h

PDRh ¼X

u

PDRu;h þ PDR�h

(41)

If this model is used to represent a Spanish CCP (as occurs in thecase studies), a single reserve price must be considered sinceupward and downward reserves are related

URh ¼ DRh � urdrh (42)

A certified maximum net power can be also considered

Xu

Pu;h þ URu;h

� �( )þ P�h þ UR�h� �

� cqmax (43)

An upper bound cbmax over the total reserve generated with theCCP is required to be certified by the system operator. Equation(44) models cbmax taking into account the fact that it is given byeach GT turned on

URh þ DRh � cbmax �X

u

Uu;h þ UFu;h

� �(44)

4 Case Studies

This section presents several executions of the proposed MILPmodel to simulate the day-ahead and secondary reserve markets inSpain [17] for the whole of 2013.

Execution Modes. Three execution modes for the whole yearwere tested:

• Weekly optimization (WO): one representative week for eachmonth is optimized and the results are extrapolated to the restof weeks of the month, taking into account the day of theweek.

• Monthly optimization (MO): each month is sequentially opti-mized, the CCP state at the end of previous executed monthsbeing considered as an output.

• Joint optimization (JO): with all the hours of the year opti-mized at the same time.

The executions were run on a 64-bit intercore CPU at 3.4 GHz,programmed in GAMS

2 and solved using Cplex solver. Interiorpoint methods for the linear problems [18] and the branch andbound algorithm [19] available in Cplex with the default cut iden-tification strategies have been applied.

Input Data. A real Spanish CCP with the structure presentedin Fig. 1 is analyzed. The following is a set of technical inputsused in the analysis with slight differences with respect to the realvalues used in the real operation, for reasons of confidentiality:

• The nominal output of the CCP with the ST turned off isPu qmin

u;h ¼ 200 MW, while the ST is able to increase thepower by an extra qu

max,�¼ 100 MW.• Total minimum gross power for the GT with the ST turned

off and on areP

u qminu;h ¼ 52 and

Pu qmin;0;�

u;h ¼ 50 MW,respectively. Minimum gross power when generating withthe ST and with supplementary firing is

Puqu

min,1,�

¼ 75 MW.• Maximum secondary reserve is bmax

u ¼ 48.2 MW andbmax,�¼ 80 MW for the ST.

• Auxiliary services coefficients are cau¼ 1.8% and ca�¼ 5%,respectively.

• CO2 emission factors have been established to 0.2 tCO2/MWht.• Minimum monthly gas consumption cmin

m,T is 600 MWht.

• To produce steam, each GT must be above a load u� duringt�¼ 3 h.

The actual day-ahead and secondary reserve Spanish prices forJan. 2013 are depicted in Fig. 3.

High Price Scenario Analyses. Profiles of Fig. 3 have beenmodified to test how the CCP operates in a high price scenario.The baseline case corresponds to the real market prices of 2013(first month in Fig. 3), while the scenario labeled as “IncP”assumes an increase of 25% in energy prices, maintaining thereserve price fixed at its base value. Scenario “IncPs” is similarlydefined but with an increase in the reserve price of 50%. ScenarioIncP is reasonable741 given that renewable technologies are tolose their current regulated incentives and given a possible growthin demand after the current economic crisis. IncPs is also reason-able given the premise of increasing reserve requirements and

2http://www.gams.com/.



http://www.gams.com/

prices that encourage CCPs to run as a backup for intermittenttechnologies.

For Jan. 2013, Fig. 4 shows the CCP final revenues and costsfor each scenario in euros applying the MO execution mode. Thelabels used and their significance are as follows:

• Rev_md: revenues in the day-ahead market• Rev_ms: revenues in the reserve market• Rev_rs: revenues due to regulating energy• Cost_vac: maintenance costs• Cost_ng: cost of natural gas• Cost_sud: start-up and shut-down costs• Cost_emis: cost of emissions• Cost_peajv: variable cost of contracted capacities of gas• Cost_peajfm: cost of monthly contracted capacities of gas• Cost_peajfd: cost of daily contracted capacities of gas

Table 1 presents the number of hours and the CCP efficiencyfor each operation mode, in which

• Cycle denotes if the CCP is running with the ST turned on(CC) or not (CS).

• Postc indicates whether the HRSG is running with (CP) orwithout (SP) supplementary firing.

• Numgt indicates the number of GTs turned on and not run-ning in fast start mode (GTi indicating i GT turned on).

• Fasts indicates the number of GTs turned on in fast startmode.

• Func indicates whether the CCP is providing reserve (REG)or not (running at PEAKS).

• STOP stands for the number of hours where the CCP istotally turned off.

• Efic (%) indicates the efficiency of each operation mode asthe ratio between the total net energy generated and the ther-mal energy used in this generation. As average value approxi-mations, the plant’s thermal efficiency is approximately30–35% in its single cycle, with an overall efficiency of40–45% using the combined cycle. This efficiency is reducedto 35–40% with supplementary firing but compensated by ahigher reserve generation which enables the plant to respondto fluctuations in electricity load.

• Nhours (h) indicates the number of hours running in eachoperation mode.

The total gas consumption (Cons_gas), the net and gross pro-ductions (Prod and Prodg), and the upward and downwardreserves (Reser_uw and Reser_dw) are depicted in Fig. 5 for Jan.2013.

As can be seen, since the CCP has been running for very fewhours at the current energy and reserve prices (see the baselinescenario in Table 1), revenues are almost null (see Fig. 4, which iscompletely in line with the actual operation of many SpanishCCPs). Revenues in the IncP and IncPs scenarios rise and fuelcosts are almost covered by the day-ahead market, reserve marketrevenues being a key issue for the economic survival of the CCP.An increase in reserve revenues would be justified by a scenarioin which high penetration of renewable energy meant that CCtechnology played a decisive role as backup generation to providereserve in Spain (unlike other conventional technologies, CCPramp-rates are faster when regulating). Furthermore, delivered gascosts are higher in IncP than at IncPs (see Cost_ng in Fig. 4) sincein the former a greater quantity of fuel is burned in the energymarket due to the opportunity energy price (see Fig. 5). In Fig. 5,it can be seen that reserves provided at IncP and IncPs are similar,but the CCP operation also achieves energy production goals atIncP. Table 1 also shows that efficiency increases from values of23% to 40–43% when the two thermodynamic cycles of the CCPare combined, increasing the efficiency of the process.

Figure 6 shows the evolution of the net production, gas con-sumption, upward and downward reserves, and turn-on and start-up binary decisions, during 6 h on Jan. 3, 2013 and for the IncPscenario. It depicts the operation of the CCP from a turned-offoperation mode (hour h14) to a full operation mode with everyGT turned on (hour h17 onwards), with the exception of two GTs(un2 and un3) that are providing upward reserve but they are notturned on (fast start mode).

For Jan. 3, 2013, the evolution of the net production and thetotal reserve provided by all the GTs (GT.Prod and GT.Reser) andby the ST (ST.Prod and ST.Reser) in relation to the energy andreserve prices is depicted in Fig. 7.

For the first hours of the day (from h01 until h09), the CCPruns in regulation mode since reserve prices are high. In particu-lar, two GTs are in fast start mode and another GT at maximumpower to provide downward reserve. When the reserve pricedecreases, the CCP shuts down (from h10 to h14) until the energyprice begins to increase (from h15 onwards). More specifically,

Fig. 3 Day-ahead and reserve prices for Jan. 2013

Fig. 4 Economic results for Jan. 2013



from h15 to h17, the CCP progressively starts up three GTs, pro-viding reserve during this starting. From h18 to h24, the CCPoperation aims to take advantages of high energy prices, relegat-ing reserves to lower levels. Note that the ST satisfies the mini-mum number t�¼ 3 h (from h15 to h17) to be turned on.

Sensitivity to Gas Contracts. This subsection presents the sen-sitivity of the proposed model with respect to daily and monthlytariffs (v and f). Scenario IncP, with an increase of 50% in energyprices, has been executed to turn on the CCP during a longer pe-riod of time.

Table 1 Number of hours and efficiency for each operation mode and for Jan. 2013

Scenario Cycle Postc Numgt Fasts Func Efic (%) Nhours (h)

Baseline CS SP GT1 2 REG 25.60 47STOP STOP GT0 0 STOP 0 697

IncP CC CP GT0 1 REG 31.20 52 REG 30.20 1463 REG 27.50 18

GT2 1 REG 39.20 122 REG 34.91 115

GT3 1 REG 34.80 5SP GT1 0 PEAKS 40.40 25

GT2 1 REG 40.00 482 REG 32.68 51

GT3 0 PEAKS 43.80 231 REG 38.04 26

CS SP GT1 1 REG 26.60 92 REG 25.60 973 REG 23.00 4

GT2 2 REG 26.77 29STOP STOP GT0 0 STOP 0 131

IncPs CC CP GT1 1 REG 30.60 42 REG 30.20 201

SP GT2 1 REG 35.10 4CS SP GT1 1 REG 27.40 37

2 REG 25.60 163GT2 2 REG 26.42 14

STOP STOP GT0 0 STOP 0 321

Fig. 5 Production, reserve and gas consumption for Jan. 2013

Fig. 6 Dispatch results for 6 h on Jan. 2013



Applying WO execution mode, Fig. 8 shows the daily andmonthly contracted capacities (Jd and Jm) of natural gas corre-sponding to Jan. 2013 for three different scenarios: The baselinescenario, with reference daily and monthly tariffs; scenario“Incd,” doubling the daily reference tariff; and “Decd,” with thereference tariff halved. Pd_“esc” and Pm_“esc” in Fig. 8 refer tothe daily and monthly capacities mentioned above for scenario“esc.”

It can be seen that only monthly capacities are contracted whenthe daily reference tariff is increasing (Pd_Incd is null), whilst theopposite occurs when it is decreasing (scenario Decd). In this lastcase, monthly capacity is 600 MWht, since this is exactly the min-imum amount of gas that must be consumed according to thetake-or-pay signed contract. An intermediate situation between

these two extreme behaviors is the baseline scenario, where themonthly toll is above 600 MWht and the Pd_baseline is not null.Applying MO execution mode, Fig. 9 shows the monthly anddaily contracted capacities for this last scenario. Gas consumptionis also depicted.

Note that a base monthly capacity of gas is contracted as wellas an additional daily capacity for those days with a gas consump-tion over that base capacity (see, for example, days D3, D4, andD5; in contrast, the consumption on some other days is below thismonthly capacity; see, for example, day D1).

Computational Results. For each of the execution modes, thetotal number of continuous variables, binary variables, constraints,

Fig. 7 Dispatch results for Jan. 3, 2013

Fig. 8 Daily and monthly contracted capacities of gas for Jan. 2013

Fig. 9 Gas consumption, and daily and monthly contracted capacities, for Jan. 2013



and the total execution times are presented in Table 2. In the caseof the MO execution mode, these results solved sequentially.

As Table 2 shows, JO cannot be solved because the Cplexresource limit was exceeded. Indeed, only WO and MO modes arecurrently being executed by one price-taker electricity generatorin Spain, with satisfactory results in terms of accuracy and execu-tion time requirements for 1 yr planning.

5 Conclusions

This paper has proposed a price-based UC model for the opti-mization of the generation and reserve operation of a CCP, usinga MILP model. Its objective function consists in the maximizationof energy and reserve joint profits, while the main technical con-straints represent several peculiarities of the CCP operation, suchas the Brayton and Rankine cycles, the minimum time, and pro-duction levels to start-up the ST or supplementary firing processesin the HRSG.

Flexible and take-or-pay contracts can also be modeled, as wellas CO2 emissions costs. The proposed MILP model can be used toestimate the behavior of a CCP on the basis of energy and reserveprices forecasted using statistical and econometric models forshort-term planning [20]. It would also be suitable for use withmore fundamental representations (such as those set up on Nashgames [21]) with longer horizons.

The cases studies are focused on the Spanish day-ahead andsecondary reserve markets. The operation of a real Spanish CCPis simulated, showing that, with the current electricity and reserveprices, the CCP is turned off a large amount of time, whichreflects the current operation of this kind of CCPs in Spain. Aprincipal conclusion is that an increase of 50% in the reserve pricewould imply a higher utilization rate for this type of CCPs, whichcould be a stimulus for the creation of new regulatory frameworksthat improve the remuneration of reserve, ensuring the recovery ofthe CCP investment costs. Furthermore, this could also encouragenew investments in renewable technologies since the CCP may berunning as a backup for these technologies.

The examples also show the improvement in the overall effi-ciency of the CCP as a result of the application of the combinedoperation mode, as well as the behavior of gas contracts in differ-ent daily and monthly tariff scenarios. Several operation modes,such as the fast start mode, have also been tested in addition tocompliance with minimum start-up times for STs. Though thecomputational efficiency in real applications can be subject to dis-cussion for large temporal scopes, because of the large number ofbinary decisions, execution times are acceptable for monthly orweekly sequential executions.

Future developments will focus on the inclusion of more oper-ating modes for the HRSG and also stochasticity in the ST opera-tion when modeled as a function of the output HP and LP flows.

Nomenclature

CCP ¼ combined cycle plantsED ¼ economic dispatchGT ¼ gas turbineHP ¼ high pressure

HRSG ¼ heat recovery steam generatorLP ¼ low pressure

MILP ¼ mixed integer linear programmingST ¼ steam turbineUC ¼ unit commitment

Indexes

d ¼ daysh ¼ hoursi ¼ HRSG state (without applying supplementary

firing: i¼ 0, with minimum supplementary fir-ing: i¼ 1, and above minimum supplementaryfiring, i¼ 2)

m ¼ monthsu ¼ gas turbines

System Data Parameters

cng ¼ cost of the natural gas (e/MWht)nur, ndr ¼ coefficients to obtain the energy reserve price

with respect to ph (pu)ph ¼ day-ahead energy price (e/MWh)

pemis ¼ CO2 emission price (e/TCO2)ph

s ¼ reserve price (e/MW)qur, qdr ¼ percentage of reserve energy cleared (pu)

urdrh ¼ upward/downward reserve relation (pu)

GT and ST Technical and Economic Data Parameters

bumax, bmax,� ¼ maximum reserve (MW)

cau, ca� ¼ auxiliary services coefficient (pu)cmu, cm� ¼ maintenance cost (e/h)cshu, csh� ¼ shut-down cost (e)

cstu, cst�¼ start-up cost (e)cbmax ¼ maximum certified net reserve per GT turned

on (MW/GT)cqmax ¼ maximum certified net power (MW)

qumin, qmin,� ¼ minimum gross power (MW)

qu,hmax, qh

max,� ¼ maximum gross power (MW)

Other GT Data Parameters

bsumax ¼ maximum upward reserve (MW)

cuemis ¼ CO2 emission factor (TCO2/MWht)du,h ¼ availability coefficient (pu)fsu ¼ percentage of qu

min,T in fast start (%)gmin

u ¼ gas consumed at minimum gross power(MWht)

qumin,I,� ¼ minimum gross power providing steam with-

out (i¼ 0) or with supplementary firing (i¼ 1)(MW)

au ¼ consumed gas per gross MW (MWht/MW)

Other ST Data Parameters

t� ¼ minimum number of hours above u� to runthe ST (h)

u� ¼ minimum load to test if the ST can run (pu)fsu ¼ fraction of hour in which the GT u is turned

on in fast start mode (pu)

Combined Cycle Data Parameters

ahpi,u, alp

i,u ¼ HP/LP independent regression coefficientsbetween the HP/LP flow and each GT grosspower (kg/s)

Table 2 Computation results

#Continuousvariables

#Binaryvariables #Constraints

Executiontime (min)

WO 149,508 46,320 270,420 72MO 661,284 205,296 1196,916 408JO 680,722 169,412 1142,179 na



bhpi,u, blp

i,u ¼ HP/LP regression coefficients between theHP/LP flow and each GT gross power((kg/s�MW)

gc�i ¼ gas consumed with minimum (i¼ 1) andmaximum (i¼ 2) supplementary firing(MWht)

hpfh, lpfh ¼ total HP and LP flows (kg/s)hpfi,u,h, lpfi,u,h ¼ HP and LP flows per HRSG state (kg/s)

ki ¼ regression coefficients between the ST grosspower and the total HP and LP flows (MW fori¼ 0, and (MW/(kg/s)) for i> 0)

Gas Contracts Data and Tariffs

cmind , cmax

d ¼ minimum and maximum daily gasconsumption (MWht)

cminm , cmax

m ¼ minimum and maximum monthly gasconsumption (MWht)

dm, mm ¼ monthly coefficients for the fixed tariff (pu)v, f ¼ variable and fixed tariffs (e/MWht)

Gas Consumption Continuous Variables

Gh ¼ total (MWht)Gu,h ¼ by each GT (MWht)

GURh, GDRh ¼ upward/downward regulating energy (MWht)GURu,h, GDRu,h ¼ by each GT (MWht)

GWu,h ¼ without supplementary firing (MWht)

Energy and Power Continuous Variables

Pu,h, P�h, Ph ¼ net power (MW)PURh, PDRh ¼ net energy within the reserve (MW)

PURu,h, PDRu,h ¼ net energy within the reserve by each GT(MW)

PUR�h, PDR�h ¼ net energy of the ST within the reserve (MW)Qu,h, Q�h, Qh ¼ gross power (MW)

Qi�u,h ¼ additional gross power with or without

supplementary firing (MW)Qmin

u;h ¼ gross power above the minimum (MW)

QV;minu;h ¼ minimum gross power (MW)

QURu,h, QDRu,h ¼ gross energy within the reserve by each GT(MW)

Reserve Continuous Variables

URh, DRh ¼ upward and downward reserves (MW)URu,h, DRu,h ¼ by each GT (MW)

UR�h DR�h ¼ by the ST (MW)

Contract Continuous Variable

Jd, Jm ¼ maximum daily and monthly quantity of natu-ral gas contracted (MWht)

HRSG Continuous Variables

Qi,�u,h ¼ gross power with or without supplementary

firing (MWh)

U2,�u,h ¼ percentage of gross power in relation to the

maximum and the minimum gross power pro-duced with supplementary firing (pu)

Binary Variables

Uu,h, U�h ¼ turn-on decision

Ui;�u;h ¼ steam generation decision without (i¼ 0) or

with minimum supplementary firing (i¼ 1)UFu,h ¼ fast start decision

V�u;h ¼ if the load is above u� in h and the GT is onin h� 1

Yu,h, Y�h ¼ start-up decisionZu,h, Z�h ¼ shut-down decision

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