coordination between medium-term generation planning and short-term operation in electricity markets

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 1, FEBRUARY 2006 43

Coordination Between Medium-TermGeneration Planning and Short-Term

Operation in Electricity MarketsJavier Reneses, Efraim Centeno, and Julián Barquín, Member, IEEE

Abstract—This paper analyzes the coordination betweenmedium-term generation planning and short-term operation inelectricity markets. This coordination is particularly importantfrom a practical point of view in order to guarantee that certainaspects of the operation that arise in the medium-term level areexplicitly taken into account: limited-energy resources and oblig-atory-use resources. Three different approaches are proposed inorder to guarantee that short-term decisions made by a generationcompany are consistent with its operation objectives formulatedfrom a medium-term perspective. These approaches make use oftechnical and economic signals to coordinate both time scopes:primal information, dual information, and resource-valuationfunctions. This paper presents the main advantages and draw-backs of the three approaches and applies them to a case study thatuses a conjectural-variation-based representation of the market.

Index Terms—Electricity markets, medium-term planning,medium- and short-term coordination, short-term operation.

I. INTRODUCTION

THE operation of power generation systems has tradition-ally been organized following a hierarchical structure.

Planning decisions belong to a long-, medium-, or short-termlevel according to their horizon of influence [1]. Typically,the long-term decision level considers more than three yearsof operation, the medium-term level encompasses from a fewmonths up to two years, and the short-term level includes atmost the following week. The detail with which the powersystem and the time intervals are represented diminishes as thetime horizon of interest increases.

Longer-term decision levels yield resource allocation re-quirements that must be incorporated into shorter-term decisionlevels. This coordination between different decision levels isparticularly important in order to guarantee that certain aspectsof the operation that arise in the medium-term level (e.g.,hydrothermal coordination, annual or monthly take-or-pay con-tracts with minimum-fuel-consumption requirements, annualemission allowances, etc.) are explicitly taken into account.

In a traditional framework, the coordination between dif-ferent time scopes is developed by a system operator tryingto minimize the total cost of the system. Several works haveaddressed this problem. Some of them can be found in [2],

Manuscript received March 8, 2004; revised April 8, 2005. Paper no.TPWRS-00129-2004.

The authors are with the Instituto de Investigación Tecnológica, School ofEngineering, Universidad Pontificia Comillas, 28015 Madrid, Spain (e-mail:[email protected]).

Digital Object Identifier 10.1109/TPWRS.2005.857851

which is a review of optimization for water resources systems.In [1], the medium- and short-term scheduling are referred toas a decomposition problem, and the coordination between thetwo levels is performed as an iteration of the Benders decompo-sition technique. In [3], the short-term operation makes use ofdual information (the derivative of valuation functions aroundthe actual levels) in order to include hydro signals from themedium-term planning. Longer-term energy constraints are in-corporated in [4] using dual information (pseudo prices), whilein [5], the coordination procedure makes use of primal infor-mation (forcing the allocation of energy). An iterative coordi-nation procedure is proposed in [6], using dual information, inorder to coordinate SO emission allowance trading, energy andspinning reserve transactions, and consumption or take-or-payfuels. In [7], primal and dual information are used in a hierar-chical simulation model. Finally, in [8], there is a discussionconcerning the use of primal and dual coordination betweenannual resource allocations and short-term operation, but it isnot implemented.

Recently, reorganizations have been taking place in the elec-tricity sector of many countries. There is a pronounced trendtoward liberalization and decentralization. This paper addressesthe coordination between medium-term planning and the short-term operation in electricity markets in this new framework. Theabove-mentioned approaches (based on primal and dual infor-mation) are adapted to competitive environments. Furthermore,a decomposition-inspired method is proposed in order to im-prove their performance in practice.

Different approaches are presented in order to deal withthis problem. In addition, a practical implementation of theproposed approaches is carried out, considering medium-termmarket equilibrium and a short-term detailed operation, usingan explicit market representation.

When a company faces the coordination between its medium-term planning and its short-term operation, the following twodifferent issues have to be considered.

• Allocation of limited-energy resources throughout thewhole medium-term horizon, e.g., hydro resources ormaximum production levels for thermal units with limitedemission allowances;

• Minimum production levels due to technical, economic,or strategic reasons. Examples of these issues area minimum-fuel-consumption requirement due to atake-or-pay contract or a minimum market share for thecompany in order to maintain its market position. These

0885-8950/$20.00 © 2005 IEEE

44 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 1, FEBRUARY 2006

minimum productions can be renamed as obligatory-useresources.

Both issues will be represented and discussed in this paper.The natural way to analyze an oligopolistic market (the case

of a perfect-competition market can be represented through costminimizations, as has been widely studied in the literature) isby computing the market equilibrium. This is to say, computingthe set of decisions that make a company obtain a lower profitif it unilaterally changes its behavior. The market equilibriumis the result to be expected from market clearing when compa-nies have gained knowledge of the market rules and behavior,and collusion does not exist. Hence, theoretically, the coordi-nation between medium-term planning and short-term opera-tion could be seen as an iteration in the framework of the de-composition theory for optimization problems [9]. Thus, co-ordination strategies can be derived from decomposition tech-niques. However, the models adopted in practice to representmedium- and short-term operation differ significantly. One usesa market equilibrium model, but the other is normally a unilat-eral profit-maximization model. This means that the medium-and the short-term models do not result from the decompositionof a single larger model. In spite of this, decomposition tech-niques can provide an inspiration for practical coordination pro-cedures, as will be shown in this paper.

The organization of this paper is such that Section II providesa description of the medium-term decision stage, expressing itas the computation of market equilibrium among the existinggeneration companies. The equilibrium problem is formulatedwith a conjectural-variation-based approach. Section III corre-sponds to the short-term decision stage, which is formulated asa profit-maximization problem, including a detailed representa-tion of the spot market and the company’s generation portfolio.Section IV suggests three alternative methods in order to coor-dinate both stages and guarantee that the company’s resourceallocation is optimally carried out: primal information, dual in-formation, and resource-valuation functions. Finally, Section Vincludes a case study, in which all the methodology is imple-mented and illustrated, and in Section VI, the main conclusionsof the paper are summarized.

II. MEDIUM-TERM MODEL

This section describes the medium-term decision stage as amarket equilibrium problem. The market is represented using aconjectural-variation-based approach [10]–[12]. The single-pe-riod case is addressed first, and then it is extended to the multi-period case.

A. Single-Period Case

The market equilibrium model used in this paper is pro-posed in [13]. It is a model based on conjectural variations1

that represents the strategic behavior of a number of firmscompeting in an oligopolistic market.

1Conjectural variation models suppose as known the derivative of other sup-pliers’ production with respect to changes in one supplier’s production. An inter-esting advantage of the proposed model is the capacity of dealing with inelasticdemand.

The conjectured variation of the clearing price with respectto each firm production is assumed to be known

(1)

Each firm is the owner of a number of generating units, so its output in megawatts is given by .

In addition, demand is considered to be inelastic (the ex-tension to a linear decreasing demand is developed in [13], aswell as the consideration of contracts signed by the companies).

Generation and demand are linked through the power balanceequation

(2)

The profit that firm obtains when being remunerated atthe marginal price is (disregarding contracts)

(3)

The equilibrium is obtained by expressing the first-orderprofit-maximization condition for every firm

(4)

The conjectured variation of the clearing price with respectto each firm production leads to

(5)

Under these assumptions, the market equilibrium can be com-puted by solving an equivalent quadratic optimization problem

s.t.

Technical Constraints (6)

where denotes a term called effective cost function

(7)

Under the hypothesis of continuous and convex cost func-tions, it can be proved (see [13] and [14]) that this optimiza-tion problem is equivalent to the market equilibrium problemdefined by (2) and (5).2 The first- and second-order optimalityconditions are the same for both approaches. Note that the dualvariable of the demand constraint is the system’s marginal price.

2An additional assumption is to consider all constraints as linear inequalities(this is to say, a convex feasible region), which exclude, for instance, the utiliza-tion of integer variables.

RENESES et al.: MEDIUM-TERM GENERATION PLANNING AND SHORT-TERM OPERATION 45

B. Multiperiod Case

The extension of previous results to the multiperiod case isimmediate. The generation planning in the medium term con-siders time periods (typically, weeks), each oneof them comprising load levels.

A demand and firm’s output is considered for eachperiod and load level.

The market equilibrium is computed through the followingoptimization problem:

s.t.

Technical Constraints (8)

C. Medium-Term Resource Allocation and MinimumProduction Constraints

When a company faces its medium-term planning, it hasto take into account the allocation of 1) its limited-energyresources throughout the whole medium-term horizon and 2)its obligatory-use resources.

As shown in [13], the proposed medium-term model caninclude all these constraints when computing the equilibriumpoint, simply by adding them to the constraint set of (8).

Finally, the proposed medium-term model can be extendedto consider contracts (either bilateral or financial) signed by thefirms [13], as well as stochasticity in some parameters (e.g.,water resources or demand) [15].

III. SHORT-TERM MODEL

A model oriented to the optimization of the short-term op-eration of a certain company must provide the following twodifferent types of results:

1) anticipated generation schedule that observes the units’operating constraints;

2) hourly offers complying with the rules of the spot marketin which company is operating.

The short-term model considered in this paper represents indetail both the company’s decisions in the spot market and theoperation of the company’s generating units [16]. This modeldoes not represent each of the company’s rivals but rather han-dles them in an aggregate manner.

It is assumed that the company of interest makes its short-termdecisions within a time scope that ranges from one day to oneweek. In other words, the short-term horizon comprises at mostthe first time period , considered from the medium-termperspective.

The model must decide the amount of energy that the com-pany should sell in each of the hourly uniform-price multiunitdouble auctions that typically constitute the daily sessions of thespot market. The amount sold by the company in the auction forhour exerts an influence on that auction’s clearing price

. This influence is represented by means of the company’s in-verse residual demand curve .

The objective function that guides the search for the com-pany’s best offering strategy in each auction can be formulatedas follows:

(9)

where is the cost function of the company’s generatingportfolio in hour .

The short-term model must include constraints to guaranteethat the offers submitted by the company to the spot market areconsistent with the spot market rules. Additionally, the energysold by the company in the spot market must lead to a gener-ation schedule that complies with the operating constraints ofeach of its units, such as maximum and minimum power output,ramp-rate limits, available hydro resources, etc. A descriptionof all these constraints can be found in [16]. With the aim ofsimplifying the formulation, the following expression is used toindicate that company ’s short-term decisions must belong tothe set of company ’s feasible decisions :3

(10)

Hence, we suggest the following compact formulation for theproblem faced by the generation company in the short term:

s.t. (11)

The solution of this optimization problem provides the op-timal generation schedule for the company. The hourly offersfor the spot market will be constructed under the considerationof uncertainty in the company’s residual demand curve [16].

The coordination methodology described in this paper canalso be applied with a stochastic short-term model that explicitlyconsiders uncertainty [17], [18].

IV. SIGNALS BETWEEN MEDIUM- AND SHORT-TERM MODELS

A. Decisions Hierarchy

As mentioned, the operation of power generation systems hastraditionally been organized following a hierarchical structure.In the new liberalized framework, this hierarchy is maintainedand a company competing in an electricity market divides itsoperation planning into different time scopes. In order to maxi-mize its present and future profit, different constraints have to beconsidered, such as resource constraints (e.g., minimum or max-imum fuel consumption limits) or hydro management. Whena constraint is defined over the short-term scope, it can be di-rectly included in the short-term model. Nevertheless, when aconstraint is defined over a long- or medium-term scope, it isnecessary to apply a methodology to properly consider it in theshort-term operation planning.

Traditional short-term operation-planning tools such as unit-commitment or economic-dispatch models include guidelines

3Generally, this feasible region will be nonconvex, due to the use of binaryvariables.


in order to direct their results toward the objectives previouslyidentified by medium-term models. For example, a volume ofavailable hydro resources can be specified for the short-termdecision stage according to the results of a medium-term hy-drothermal-coordination model. Alternatively, instead of speci-fying a fixed amount of available water for the short term, a costfunction can be defined for this water, namely, the water-valuecurve. These guidelines prevent short-term models from makinguse of all available hydro resources.

It is important to note that the models adopted in practiceto represent medium- and short-term operation differ signifi-cantly. Usually, medium-term models to represent oligopolisticmarkets state an equilibrium problem with linear constraints. Incontrast, short-term models represent in detail the problem for acompany facing a residual demand function (normally causingthe problems to be nonconvex). There exist two main reasonsfor not adopting a market-equilibrium model in the short term:1) they would become computationally unaffordable, and 2) it isvery rare for a company to own detailed data about its competi-tors generation units.4 However, both approaches are based ona maximization of the profit for the companies. Furthermore, itmust be noted that in the real operation performed by generationcompanies (GENCOs), medium-term models’ results are not al-ways calculated every week, so therefore, short-term modelsface a different problem, in which some of the variables havea reduced degree of uncertainty.

This paper considers the following two kinds of situationsfaced by a company when addressing the coordination betweenits medium-term planning and its short-term operation.

• The allocation of limited-energy resources throughoutthe whole medium-term horizon. Two examples of thissituation are 1) the allocation of hydro resources and2) the allocation of the thermal production for someunits, which are subject to maximum-annual-productionconstraints (due to, e.g., emission allowances or fuelsupply limits).

• The allocation of obligatory-use resources throughout thewhole medium-term horizon. Two examples of this situa-tion are 1) a minimum-fuel-consumption requirement dueto a take-or-pay contract and 2) a minimum market sharefor the company in order to maintain its market position.

In the following three subsections, three different approachesto coordinate medium- and short-term models are proposed andexplored.

1) The primal-information approach, which strictly imposesupon the short-term model the production levels obtainedin the medium-term model. In this sense, the primal-in-formation approach is inspired in the Bender’s decompo-sition technique [9].

2) The dual-information approach, which makes use of thevaluations obtained from the medium-term model to ex-plicitly valuate the resource’s use in the short-term model.This approach is inspired by the Dantzig–Wolfe decom-position technique [9].

4A company can estimate medium-term model data from its knowledge oftheir own units. Nevertheless, short-term model data include real-time charac-teristics, which can differ significantly among different units.

3) The marginal resource-valuation function, which providesthe short-term model with a continuous valuation of theresource, for all the different operation points that the firmcan face. Hence, this function brings to mind the so-calledrecourse function in decomposition techniques [9].

B. Primal-Information Approach

This is the approach that has been mostly used in practice tosend signals from medium-term generation-planning models toshort-term operation models.

Once the market equilibrium is computed with the medium-term model, a resource production level will result for each timeperiod considered in the medium-term scope (either for lim-ited-energy resources or obligatory-use resources). The strategyfollowed by the primal-information approach is to strictly im-pose these production levels of resources (primal signals) asconstraints on the short-term operation of the company.

The main advantage of the primal coordination is that it iseasily obtained from the medium-term models and not difficultto implement in the short-term models. Furthermore, the sig-nals provided with this approach are very easy to understand,since they are mere short-term-scope production levels of theresources. Finally, the primal-information approach assures thatthe medium-term objective will be satisfied.

However, this methodology has important drawbacks. Themain one is the lack of flexibility in the decisions that the com-pany can make in the short term. The resource usage levels pro-vided by the medium-term model may be not optimal, mainlydue to two reasons: the time aggregation in the models and thepresence of uncertainty.

The results obtained with the medium-term model are basedon a forecast of the future market conditions that in the endmay not occur. Furthermore, the medium-term model deals withaggregated load levels that may distort short-term results.

Hence, when facing the short-term operation, the companymay find a market situation considerably different from the oneforecasted, and the primal signals may not be consistent or eco-nomically efficient.

C. Dual-Information Approach

The dual-information approach is based on valuing thecompany’s resources in the medium-term horizon. As shownin [19], the proposed medium-term model allows computingmarginal valuations of the resources (either limited-energyresources or obligatory-use resources). These valuations aregiven by the dual variables of the corresponding constraints.For a limited-energy resource, the valuation is the dual variableof the maximum-medium-term-production constraint. For anobligatory-use resource, the valuation is the dual variable of theminimum-medium-term-production constraint.

Once the medium-term planning provides these valuations(dual signals), they can be incorporated into the short-term oper-ation. The short-term model used in this paper incorporates theexplicit valuation of the company’s resources into its objectivefunction, depending on the kind of resource.

• In the case of a limited-energy resource, a new term is in-corporated into the objective function, penalizing its use.


• In the case of an obligatory-use resource, a new termis incorporated into the objective function, considering abonus for its use.

Equation (12) illustrates an example of an objective function,considering two resources: 1) hydro production for a generatingunit valuated through the dual variable of the medium-term-model constraint and 2) an annual minimum productionfor a thermal unit , valuated through the dual variable of themedium-term-model constraint

(12)

Note that is nonpositive and is non-negative. Thus, thereis a penalty on the use of hydro production for unit and a bonusfor the use of thermal production for unit . Consequently, thesign of dual variables directly takes into account the penalty orbonus for different resources.

As can be seen, the dual approach is more flexible than theprimal one, as it allows choosing different resources’ uses ac-cording to the current market conditions or the current situationof the company’s generating portfolio. Hence, it economicallyvalues the higher or lower use of the resources.

An interesting aspect of the dual approach is the interpretationof the dual signals. They should not be considered as a reflec-tion of how much it “costs” the company to use the resource inthe short-term scope. The correct interpretation is how much it“costs” in the rest of the medium-term scope. This is to say, fora limited-energy resource, the dual signal is not the variationin the present short-term-operation cost when modifying theshort-term use of the resource. Rather, it is the forecasted vari-ation in the medium-term cost when modifying the short-termuse of the resource.

It is important to note that, if the forecasted market condi-tions used in the medium-term model match up with the currentmarket conditions, the primal and dual approaches lead to thesame short-term operation.

The main disadvantage of the dual coordination is the lack ofrobustness. A small change in the medium-term valuation canlead to important changes in the short-term operation. Anotherproblem of the dual approach arises when the actual market con-ditions are considerably different from the forecasts used in themedium-term planning. In this situation, the valuation providedby the medium term may be incorrect. Furthermore, the use ofdual information may make it necessary to include some addi-tional constraints in order to precisely fulfill the medium-termobjective (e.g., in the last weeks of a year, the generation of aunit with a limited annual production has to be controlled inorder to fulfill the annual constraint).

One way to avoid these undesirable effects is to combine theprimal and dual approaches. The valuation of the resource is in-cluded, but the deviation from the medium-term results is lim-ited to a selected range.

Another relevant observation is that medium-term modelsgenerally represent in less detail the operation of the generatingunits (e.g., ramp-rate constraints are usually not represented)and consider larger time steps. Due to this, the valuation pro-vided by a medium-term model may not correspond exactlywith the perspective adopted for the short-term model. This

Fig. 1. Marginal valuation function for a limited-energy resource.

effect should be examined and corrected in practice, and it isusually a point of friction between different departments of acompany.

D. Marginal Resource-Valuation Functions

This section suggests an alternative approach that could beused to coordinate the medium-term planning and the short-termoperation. It consists in the calculation of marginal resource-valuation functions in the medium term and its use in the shortterm. A marginal resource-valuation function is a continuousvaluation of a resource (either a limited-energy resource or anobligatory-use resource) for a range of operating points that thecompany could face. This is to say, for an operation point, thefunction provides the marginal valuation of the resource.

The valuation function is an extension of the dual-informationapproach, which only provides one point of the function. Fig. 1shows an example of the absolute value (because it is nonposi-tive) of a marginal valuation function for a limited-energyresource .

The independent variable of the function is the total use ofthe resource in the short-term scope. is the absolute value ofthe valuation for the resource used in the dual-information ap-proach, and is the resource level used in the primal-informa-tion approach.

Note that the absolute value of the function is nondecreasing,because the forecasted valuation in the medium term will not belower and in fact will usually be higher if the use of the resourceis higher in the short-term operation (and, consequently, lowerin the rest of the medium-term scope). On the contrary, the mar-ginal valuation for an obligatory-use resource is a nonincreasingfunction.

The coordination based on marginal-resource-valuation func-tions improves the dual coordination, because it eliminates itstwo main disadvantages. On the one hand, the valuation func-tion provides robustness, since significant changes in short-termoperation are discouraged. On the other hand, the function pro-vides information for all the values of the independent variable,even for those far from the medium-term forecast. Fig. 2 com-pares the use of marginal valuation functions and the dual-in-formation approach for an obligatory-use resource.

It can be seen how, if the actual conditions make the use of theresource higher than the forecasted use , the valuation of thedual approach will be higher than that provided by the marginal-valuation function (MVF). Hence, the use of the resource willbe higher with the MVF approach than with the dual approach.This is to say, the dual approach overvalue the resource (and,consequently, makes a lower use of it) with respect to the MVF


Fig. 2. Comparison of marginal valuation function with dual approach.

Fig. 3. Marginal valuation function for an obligatory-use resource.

approach. On the contrary, if the conditions make the actual useof the resource lower than its forecast, the dual approach willprovide a lower valuation and, consequently, a higher use thanthe MVF approach.

The MVFs are incorporated into the short-term operationthrough new terms in the objective function of the short-termmodel. Each term corresponds to the total valuation ofa resource, computed as the integral of the marginal valuationfunction

(13)

Fig. 3 shows the marginal valuation function for an obliga-tory-use resource and the total valuation for the resource level

(as the area under the function).The main drawback of this method is its practical implemen-

tation. The computation of the function may be difficult withthe medium-term model, although the medium-term model pro-posed in this paper allows obtaining different points of the func-tion through different executions of the model (the case studyshows an example for an obligatory-use resource). The compu-tation of this set of points leads to the incorporation of the inte-gral of (13) as a piecewise-linear function, as will be shown inthe study case.

Finally, it should be noted that marginal resource-valuationfunctions are actually multidimensional. This is to say, the val-uation of every resource depends not only on its use but alsoon the use of the rest of the resources. Hence, marginal valua-tion functions are really an approximation of these multidimen-sional functions. The computation and implementation of mul-tidimensional valuation functions is an immediate extension ofthe proposed methodology. Nevertheless, the computer time re-quirements could not justify their use. An alternative is makinguse of approximate techniques that are well known in cost-min-imization frameworks. As an example, dynamic programming

Fig. 4. Scheme of comparison of the proposed approaches.

by successive approximations is used in [20] in the long-termoperation of a large multireservoir system.

E. Comparison of Different Coordination Approaches

A methodology is proposed to compare the results obtainedusing the three above-mentioned approaches. This methodologyintends to simulate the real use of medium- and short-termmodels in the following three steps.

1) Elaborate medium-term signals by executing the medium-term planning model, including the different constraintsfor companies’ resources. Three results have to beobtained:• primal signals: use of the resources for the first time

period;• dual signals: dual variables of the resources’ con-

straints;• MVFs for all the resources.

2) Simulate the actual operation by executing the short-termoperation model for the first time period , using thethree proposed approaches. In order to conduct a thoroughcomparison of the approaches, several market conditionsand several situations of the company’s generating port-folio have to be considered in the short-term operation.

3) Execute again the medium-term planning model, in orderto estimate a likely operation for the rest of the year, be-ginning in the second time period. These executions takeinto account the actual conditions that the firm has facedin short-term operation. Compare the results obtained forthe three proposed approaches. The comparison will beperformed through the total profit obtained in the wholetime horizon: the actual short-term-operation profit andthe forecasted medium-term-planning profit, beginning inperiod . These comparisons will permit the perfor-mance of the different approaches to be assessed.

In Fig. 4, a scheme for the comparison methodology is shown.If the conditions faced in the short term are similar to those

forecasted in the medium-term planning, the results obtainedwith the three approaches should be almost the same. The maindifferences will arise in the cases in which a) market conditions


TABLE IINSTALLED GENERATION CAPACITY (MW) AND GENERATION COSTS (C=/MWh)

are far from the forecasted by the medium-term planning, or b)the detail used in the medium-term model is not enough to copewith situations that take place in the short-term operation.

The next section includes a small-size case study, in whichthe three approaches are compared under different marketconditions.

V. CASE STUDY

The case study represents an application of the describedmethodology, using a single resource: a minimum market-shareconstraint for a company in the medium term. The comparisonis performed according to the proposed scheme in three steps.The first step is medium-term planning and includes the min-imum market-share objective for a company. The second step isthe simulation of the short-term operation for different marketconditions. The third step is the updating of the medium-termplanning model with the actual short-term market conditions, toestimate the operation for the rest of the year. Finally, a compar-ison of the results obtained with primal information, dual infor-mation, and MVF is performed.

Although the proposed case study does not represent a real-size system, the methodology could be naturally extended. Theexecution either of the medium- or the short-term model takesonly a few seconds in a Pentium IV processor, and real-sizesystems can be solved in a few minutes [14].

A. Medium-Term Planning

The case study represents a system with two generation com-panies. GENCO owns ten generation units: – , whileGENCO owns eight units: – . Table I shows the in-stalled generation capacity and the production cost for each gen-eration unit.

The time horizon for the medium-term planning is consideredto be ten weeks, corresponding to time periods .Each period is supposed to be split into five load levels

. Table II shows the duration of the load levels inevery week.

Finally, the inelastic demand for each time period and loadlevel and the conjectured variation of the price with respect to

TABLE IILOAD LEVEL DURATION (HOURS)

TABLE IIIINELASTIC DEMAND (MW)

TABLE IVCONJECTURED VARIATION OF THE PRICE WITH RESPECT TO THE FIRM’S

PRODUCTION ((C=/MWh)/GW)

TABLE VPRODUCTION OF GENCO x’s UNITS IN THE FIRST WEEK (GWh)

each firm production are shown in Tables III and IV, respec-tively.

The computation of the market equilibrium without con-sidering any additional constraint yields a total production of6647 GWh (which corresponds to a market share of 54.63%)for GENCO in the medium-term horizon. Nevertheless, inthis case study, it has been supposed that GENCO wantsto assure its market position with a 60% market share (cor-responding to a 7301-GWh production with the forecasteddemand of Table III). This constraint has been included in themarket-equilibrium model.

Table V shows the production for all generation units be-longing to GENCO in the first week .

In order to fulfill the minimum market-share objective in theshort-term operation, primal and dual information are required.As was said before, the primal information is the company’smarket-share objective for the first week. In the case study, thevalue obtained is 60.53% (corresponding to 732.2 GWh). Onthe other hand, the dual information needed is the valuation ofthe minimum production objective for GENCO . In the casestudy, this valuation is 15.48 /MWh. This dual variable can be


Fig. 5. Approximation of the marginal valuation function.

interpreted as the internal bonus that GENCO has to considerfor its production in order to fulfill the medium-term objective.

Finally, the marginal valuation function for the market-shareobjective has been approximated by four points, correspondingto the forecasted first-week production (732.2 GWh) and thisproduction incremented in 1% (739.5 GWh), 2% (746.8 GWh),and 3%(754.2 GWh). These points have been selected byknowing that, under actual market conditions (5% incrementin demand), the actual generation in the first week will behigher than the forecasted. In a real situation, the MVF has tobe computed in a range including points either higher or lowerthan the forecasted production. The range in which these pointsare computed and the number of points have to be adjustedbased on experience, to accurately approximate the MVF.

These four points have been computed through the executionof the medium-term model for weeks 2 to 10 .In each of them, a minimum production constraint has been im-posed corresponding to a 7301-GWh total medium-term pro-duction. In Fig. 5, the approximated marginal valuation functionis represented, and it can be seen that the committed error in thepiecewise approximation is low. With these results, the next stepis the short-term operation under different situations.

B. Short-Term Operation

Two cases have been considered in the short-term operation.The first one (case ) corresponds to a market situation similarto that forecasted in the medium term. The second one (case )corresponds to a situation significantly different from the fore-cast used in the medium-term planning.

In case , the only deviation considered from the medium-term forecast is the hourly demand shape. A maximum devi-ation of 5% has been implemented, considering a total weeklydemand equal to the medium-term forecast. Table VI shows howprimal, dual, and MVF approaches lead to similar results for theweekly generation of generation units.

In case , the situation is considerably different from the fore-casted. On the one hand, the hourly demand has been considered5% higher than in case . On the other hand, the unit is un-available due to a failure.

Table VII shows how, in this case, the results obtained usingthe three approaches differ significantly in marginal units.

The total production with the primal approach (768.8 GWh)corresponds to a market share of 60.53% with the actual de-mand. The use of the dual approach makes the GENCO incre-

TABLE VIPRODUCTION OF GENCO x’s UNITS IN THE FIRST WEEK WITH A SIMILAR

SITUATION TO THE FORECASTED-CASE A (GWh)

TABLE VIIPRODUCTION OF GENCO x’s UNITS IN THE FIRST WEEK WITH A DIFFERENT

SITUATION FROM THE FORECASTED—CASE B (GWh)

ment its total generation (747.9 GWh) with respect the fore-cast (732.2 GWh) but significantly under the primal-approachproduction. Finally, the MVF-approach production (745 GWh)is still lower than the dual-approach one, since the dual-ap-proach-resource valuation is higher than the MVF valuation, asshown in Section IV.

C. Medium-Term Planning Updating: Comparison

Once the short-term operation has faced the proposed situ-ations, the medium-term model has to be executed beginningin the second period to estimate the operation for therest of the year. In these executions, the results obtained in theshort-term operation have to be taken into account in order tofulfill the medium-term market-share objective. Due to the sim-


TABLE VIIITOTAL PRODUCTION OF GENCO x’s UNITS CONSIDERING SHORT-TERM

OPERATION AND UPDATED MEDIUM-TERM PLANNING (GWh)

TABLE IXTOTAL BENEFIT OF GENCO X CONSIDERING SHORT-TERM OPERATION AND

UPDATED MEDIUM-TERM PLANNING (MC=)

ilarity of the results obtained in case , this step will only beperformed with case .

Table VIII shows the total production of each generation unitbelonging to GENCO in the medium term, considering theshort-term operation and the updated medium-term planning(periods – ). Note that the total production is 7337.6 GWhin all the cases, greater than the 7301 GWh mentioned above.This is due to the increment in the demand supposed in the firstperiod, which forces GENCO to increment its production inorder to fulfill the 60% market-share objective.

Finally, Table IX shows the obtained profit for GENCO inthe medium-term scope (periods – ).

It can be seen how with the primal approach, the total gen-eration of units and is higher, decreasing the generationof and . Thus, the total cost for GENCO has increased,since the total generation is the same for all the approaches, and

and are the most expensive units owned by . The totalproduction in the medium-term horizon is the same for the threeapproaches, as the minimum market-share constraint is binding.

The cost reduction, along with an increment in the obtainedrevenues, leads to a higher profit with the dual-information andMVF approaches. It is important to note that, although the profitincrement does not seem to be very high, we are dealing witha repeated situation (typically, the company faces its short-termoperation every week).

Even though this result cannot be expected to be absolutelygeneral, it is not unreasonable either, so far as the dual-in-formation approach is the first-order approximation of themarginal valuation function. Furthermore, if the complete

multidimensional marginal valuation function were includedin the short-term objective function, it is reasonable to expectthat the obtained solution would improve the one-dimensionalMVF approach.

The MVF approach slightly increases the profit with respectto the dual-information approach. This is because this approachmakes use of a more accurate approximation of the actualmarginal valuation function. Nevertheless, when dealing with asmall-size problem, the differences between dual-informationand MVF approaches are not very big.

VI. CONCLUSION

The operation of power generation systems has traditionallybeen organized following a hierarchical structure. Longer-termdecision levels yield resource allocation requirements that mustbe incorporated into shorter-term decision levels. This coordina-tion between different decision levels is particularly importantin order to guarantee that certain objectives of the operation thatarise in the medium-term level are explicitly taken into accountin the short-term operation.

In the new liberalized framework, the coordination betweendecision levels has become an important issue for generationcompanies in order to increase their profitability.

This paper has focused on the coordination between themedium-term planning and short-term operation of a GENCOcompeting in an electricity market. Three different strategiesto deal with this coordination have been described, as wellas their implementation and comparison. The first one is theprimal-information approach, in which the coordination is per-formed strictly imposing the production levels of the resourcesas constraints in the short-term operation. The dual-informationapproach is based on valuing the company’s resources in themedium-term horizon and including these valuations into theshort-term operation. The dual approach is more flexible thanthe primal, allowing the short-term operation to better adapt toactual conditions faced by the generation company.

Finally, the marginal resource-valuation functions are con-tinuous valuations of the resources, for all the different oper-ation points that the company could face. With this approach,the short-term operation must include the total valuation of theresources, calculated as the integral of the marginal valuations.

An extensive case study has illustrated the methodologies,and the better adequacy of the MVF and the dual-informationapproach with respect to the primal, especially in cases wherethe actual short-term operation is considerably different thanthat forecasted in the medium-term planning.

ACKNOWLEDGMENT

The authors would like to thank the valuable comments ofthe two anonymous reviewers, which have greatly improved thefirst version of the manuscript.

REFERENCES

[1] M. V. F. Pereira and L. M. V. G. Pinto, “Application of decompositiontechniques to the mid- and short-term scheduling of hydrothermalsystems,” IEEE Trans. Power App. Syst., vol. PAS-102, no. 11, pp.3611–3618, Nov. 1983.


[2] W. W. G. Yeh, “Reservoir management and operation models, a state-of-the-art review,” Water Resources Res., vol. 21, pp. 869–883, 1985.

[3] A. Renaud, “Daily generation management at Electricité de France:From planning toward real time,” IEEE Trans. Autom. Control, vol. 38,no. 7, pp. 1080–1093, Jul. 1993.

[4] J. Handke, E. Handschin, K. Linke, and H.-H. Sanders, “Coordinationof long- and short-term generation planning in thermal power systems,”IEEE Trans. Power Syst., vol. 10, no. 2, pp. 803–809, May 1994.

[5] E. Handschin and H. Slomski, “Unit commitment in thermal power sys-tems with long-term energy constraints,” IEEE Trans. Power Syst., vol.5, no. 4, pp. 1470–1477, Nov. 1990.

[6] F. N. Lee, J. Liao, and A. M. Breipohl, “Coordination of SO emissionallowance trading, energy and spinning reserve transactions, and con-sumption of take-or-pay fuels,” IEEE Trans. Power Syst., vol. 9, no. 3,pp. 1243–1252, Aug. 1994.

[7] E. Centeno, A. Ramos, and F. Cuadra, “Chronological stochastic sim-ulation of medium- and long-term optimal operation using a multilevelhierarchical model,” presented at the 6th PMAPS, Madeira, Portugal,2000.

[8] J. Gardner, W. Hobbs, F. N. Lee, D. Leslie, D. Streiffert, and D. Todd,“Summary of the panel session ’Coordination Between Short-Term Op-eration Scheduling and Annual Resource Allocations’,” IEEE Trans.Power Syst., vol. 10, no. 4, pp. 1879–1889, Nov. 1995.

[9] M. Minoux, Mathematical Programming: Theory and Algorithms.Chichester, U.K.: Wiley, 1986.

[10] C. J. Day, B. F. Hobbs, and J. S. Pang, “Oligopolistic competition inpower networks: A conjectured supply function approach,” IEEE Trans.Power Syst., vol. 17, no. 3, pp. 597–607, Aug. 2002.

[11] A. García-Alcalde, M. Ventosa, M. Rivier, A. Ramos, and G. Relaño,“Fitting electricity market models. A conjectural variations approach,”presented at the 14th PSCC, Sevilla, Spain, 2002.

[12] Y. Song, Y. Ni, F. Wen, Z. Hou, and F. F. Wu, “Conjectural variationbased bidding strategy in spot markets: Fundamentals and comparisonwith classical game theoretical bidding strategies,” Elect. Power Syst.Res., vol. 67, pp. 45–51, 2003.

[13] J. Barquín, E. Centeno, and J. Reneses, “Medium-term generation pro-gramming in competitive environments: A new optimization approachfor market equilibrium computing,” Proc. Inst. Elect. Eng., Gener.,Transm., Distrib., vol. 151, no. 1, pp. 119–126, Jan. 2004.

[14] J. Reneses, “Medium-Term operation analysis of generation electricitymarkets,” Ph.D. dissertation, Dept. Industrial Organization, Univ. Pon-tificia Comillas, Madrid, Spain, 2004. (in Spanish).

[15] J. Barquín, E. Centeno, and J. Reneses, “Stochastic market equilibriummodel for generation planning,” presented at the 8th PMAPS, Ames, IA,2004.

[16] Á. Baíllo, “A methodology to develop optimal schedules and offeringstrategies for a generation company operating in a short-term electricitymarket,” Ph.D. dissertation, Dept. Industrial Organization, Univ. Ponti-ficia Comillas, Madrid, Spain, 2002.

[17] Á. Baíllo, M. Ventosa, M. Rivier, and A. Ramos, “Optimal offeringstrategies for generation companies operating in electricity spot mar-kets,” IEEE Trans. Power Syst., vol. 19, no. 2, pp. 745–753, May 2004.

[18] S. Takriti, B. Krasenbrink, and L. S.-Y. Wu, “Incorporating fuel con-straints and electricity spot prices in the stochastic unit commitmentproblem,” Oper. Res., vol. 48, pp. 268–280, 2000.

[19] J. Reneses, E. Centeno, and J. Barquín, “Medium-term marginal costsin competitive power markets,” Proc. Inst. Elect. Eng., Gener., Transm.,Distrib., vol. 151, no. 5, pp. 604–610, Sep. 2004.

[20] J. E. Giles and W. O. Wunderlich, “Weekly multipurpose planning modelfor TVA reservoir system,” in Proc. ASCE J. Water Resources PlanningManagement Division, vol. 107, 1981, pp. 495–511.

Javier Reneses received the degree in industrial engineering in 1996 and thePh.D. degree in industrial engineering in 2004 from the Universidad PontificiaComillas, Madrid, Spain, and the degree in mathematics from the UniversidadNacional de Educación a Distancia, Madrid, in 2005.

Currently, he is a Research Fellow at the Instituto de Investigación Tec-nológica, Universidad Pontificia Comillas. His areas of interest includeoperation, simulation models, and planning of electric energy systems and riskmanagement strategies in electricity markets.

Efraim Centeno received the degree in industrial engineering in 1991 and thePh.D. degree in industrial engineering in 1998 from the Universidad PontificiaComillas, Madrid, Spain.

Currently, he is part of the research staff at the Instituto de Investigación Tec-nológica, Universidad Pontificia Comillas. His areas of interest include planningand development of electric energy markets and systems.

Julián Barquín (M’94) received the degree in industrial engineering in 1988and the Ph.D. degree in industrial engineering in 1993 from the UniversidadPontificia Comillas, Madrid, Spain, and the degree in physics from the Univer-sidad Nacional de Educación a Distancia, Madrid, in 1994.

Currently, he is part of the research staff at the Instituto de Investigación Tec-nológica, Universidad Pontificia Comillas. His present interests include control,operation, and planning of power systems.

coordination between medium-term generation planning and short-term operation in electricity markets

Documents