Power Systems, IEEE Transactions on - IIT

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003

Optimal Energy Management of an Industrial Consumer in Liberalized Markets Emilio Gómez-Villalva, Member, IEEE, and Andrés Ramos

Abstract—This paper presents an optimization model for mid-term management of a thermal and electricity supply system of an industrial consumer under liberalized energy markets. Electricity is supplied from the electric grid or from a gas engine, while thermal energy is satisfied through a boiler or the mentioned gas engine. The objective is to minimize the overall annual energy supply costs in order to make optimal contracting decisions. Mixed-integer linear programming is applied to solve the problem since binary decision and operation variables have been employed. A realistic case is presented to illustrate the model capabilities. Index Terms—Cogeneration, contracts, industrial plants, liberalized energy markets, mixed-integer linear programming (MILP).

I. INTRODUCTION

T

HE liberalization of energy markets has brought with it significant changes in the energy supply management of industrial consumers. A scheme based on fixed annual tariffs for electric and thermal energy consumers existed prior to the current situation. Nowadays, new contracting opportunities have arisen under liberalized markets. In this new framework, an optimal management is needed to take advantage of these new contracting possibilities, and therefore, minimize the energy supply costs. In this context, retailers have understood the need to build and deliver more sophisticated offerings to their clients such as global energy cost optimization [1]. In this paper, we present an optimization model devoted to solving the mid-term decision problem of an industrial consumer with different energy supply alternatives. The industrial consumer analyzes and decides some months before the expiration of the current contracts which contract of each type to sign for the following year among the proposed by retailers. Four contract sets are modeled: i) electricity acquisition from the grid; ii) sale of surplus electricity generated by the cogeneration facility; iii) natural gas acquisition for the cogeneration facility; and iv) oil acquisition for the boiler. Each of these sets is composed by different contract types containing contracts of the same format. The scope of the model is a year because of the usual duration of the different contracts. A cogeneration system fed by natural gas is used as a high performance alternative for electricity and thermal production. Electric and thermal energy can also be supplied by the electric Manuscript received November 25, 2002. E. Gómez-Villalva is with Iberdrola Ingeniería y Consultoría (IBERINCO), Madrid, 28036, Spain (e-mail: [email protected]). A. Ramos is with the Instituto de Investigación Tecnológica, Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, Madrid, 28015, Spain (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRS.2003.811197

grid and by an oil boiler, respectively. Thus, the minimization of the energy supply costs involves system operation and contracting decisions. Cogeneration systems or combined heat and power (CHP) systems have been broadly modeled by optimization models as helpful tools for making decisions in operation, sizing and investment. Daily operation schedule is the most extended problem solved by optimization models concerning cogeneration systems (e.g., [2] and [3]). In [4] and [5], a one period economic dispatch handling nonlinear functions is solved. Doztauer [6] and Doztauer et al. [7] treat the economic dispatch and the unit commitment problems simultaneously considering nonlinear cost functions as well. Few publications combine operation optimization and contract decisions as a whole, as the model presented in this paper does. Illerhaus et al. [8] propose a short-term operation model of a CHP where optimal contracts are to be chosen. Fleten [9] combines hydropower reservoirs management and financial products to mitigate inflow and electricity price uncertainty. As far as existing types of electricity contracts are concerned, most publications are mainly oriented to wholesale markets (see, for example, [10] and [11]). However, some of these bilateral contracts, which are not traded through a market, can be adapted to bilateral contracts between retailers and consumers, which correspond to the kind of contracts formulated in the model presented in this paper. Treating specifically retail contracts, Richter [12] classify them attending to consumer risk exposure in his discussion about pricing in retail electricity. The exposition is organized as follows: modeling issues concerning the proposed model are discussed in Section II. The problem formulation is stated in Section III as a mixed-integer linear programming (MILP) problem. Section IV shows a realistic case study. Finally, the main conclusions are presented in Section V.

II. MODELING ISSUES The cogeneration system addressed in this paper, see Fig. 1, is integrated with a gas engine, a heat recovery boiler that makes use of exhaust gases for steam production, and a refrigeration system (e.g., heat exchanger) to regulate the heat released by the high temperature refrigeration circuit which satisfies the hot water demand. Alternatively, an oil boiler can produce the steam and hot water needed. The problem constraints are related to equipment modeling (i.e., cogeneration system and boiler), the thermal and the electricity balance (i.e., demand supply), and the four contract sets

0885-8950/03$17.00 © 2003 IEEE

GÓMEZ-VILLALVA AND RAMOS: OPTIMAL ENERGY MANAGEMENT OF AN INDUSTRIAL CONSUMER

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Only constraints related to electricity purchase contracts among the four modeled sets are presented, since the other contract types can be considered analogous. For readability purposes, some specific constraints imposed by the Spanish law concerning efficiency and limits in sales of surplus electricity, which have been included into the computer model, have been omitted in the problem formulation presented in the paper. The list of notations used throughout the paper is compiled in the Appendix. A. Objective Function The total cost of energy supply ( ), which is to be minimized, is composed of the operating costs of the boiler ( ) and the cogeneration facility ( ), excluding costs of fuel acquisition, and those corresponding to contracts for acquisition of natural gas ( ), oil ( ), electricity ( ), and the sale of surplus electricity generated by the cogeneration facility ( ). Fig. 1.

Block diagram of the thermal balance as formulated in the problem.

(1) quoted in the previous section. The model can be easily extended in each of the mentioned types of constraints. On one hand, the main decision to be made with this model is the contract choice for the whole scope and, therefore, contracts are modeled in detail. On the other hand, some simplifications in the annual operation modeling can be allowed as they significantly reduce the problem size without losing relevant information. The simplifications considered are mentioned. • Linear relations among variables are used for equipment modeling. Gas engines have a quite linear behavior along their operating range, as do the boilers. Thus, this representation can be acceptable, furthermore, taking into account that operation variables represent average values for each period with duration of several hours. • Temperature and pressure variations are not significant for average values of thermal energy as considered in the presented mid-term problem and, therefore, these variations have been neglected. Consequently, variables that represent thermal energy are exclusively functions of mass flow. • Start-up and shut-down costs can be neglected in gas engines for mid-term problems. Other characteristics of the model are: • Only surplus electricity produced by the cogeneration facility can be sold. • Oil tanks have no storage capacity. • The unused thermal energy is lost, it cannot be sold. • Binary variables are used for equipment (i.e., cogeneration system and boiler) commitment, electricity balance, and contract modeling.

III. PROBLEM FORMULATION The objective function consists of minimizing the total cost of energy supply. The constraints are related to the boiler and the cogeneration system operation, the electric and thermal energy balance, and the electricity contracts.

B. Boiler Operation Oil consumption by the boiler ( ) is represented as a linear function of the thermal energy produced ( and ) (2) where represents each period of the model scope, and boiler commitment status. Boiler operation limits

the

(3) Operation costs of the boiler excluding oil consumption (4)

C. Cogeneration System Operation Electricity ( ), thermal energy generated by exhaust gases ( ), and thermal energy produced by the high temperature refrigeration circuit ( ), can be expressed as linear functions of the fuel consumed by the cogeneration facility ( ) (5) Cogeneration system operation limits (6) Thermal energy produced by the exhaust gas recovery boiler is used to supply steam ( ) and/or hot water demand ( ). Surplus exhaust gases are released into the atmosphere (7) Thermal energy produced by the high temperature refrigeration circuit is used to supply hot water demand ( ). Surplus

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Electricity acquisition cost is derived from the chosen contract among the proposed ( ) (15) Only one of the proposed contracts can be chosen if electricity is consumed from the grid, otherwise no contract is signed (16)

Fig. 2. Block diagram of the electricity balance as formulated in the problem.

Electricity consumed is equal to the imputed energy to the ) chosen contract (

energy contribution through this circuit is dispelled through a refrigeration system

(17)

(8) Electricity generated by the cogeneration facility is supplied to the industrial consumer ( ) and/or sold to the electricity market ( ), if surplus energy exists

Relation between the binary decision variable of each con) and the electricity consumed under this contract tract ( (18)

(9) Operating costs of the cogeneration facility excluding natural gas consumption (10)

In the following sections, only a few representative contracts have been modeled, even though generalization to several contract types can be easily done. 1) Type 1: Three Sections TOU Rate: The cost of this contract is derived from the electricity consumption at a price which varies from one period to another

D. Energy Balance Figs. 1 and 2 depict thermal and electricity balance, respectively. 1) Electricity Balance: Electricity demand ( ) is supplied by the cogeneration facility or by the grid ( ) (11) It is only allowed to sell the surplus electricity not consumed by the industrial consumer

(19) 2) Type 2: Fixed Annual Price Plus Bonus/Penalty by Consumption: The cost of this contract is derived from the annual energy consumption at a price which varies from the reference as a stepwise function of the annual consumption devia(see Fig. 3) tion from the reference

(12) 2) Thermal Balance: Steam demand ( ) can be supplied via the boiler and/or the exhaust gas recovery boiler (13)

(20)

Thermal energy needed for water heating ( ) can be supplied via the boiler and/or the cogeneration facility. In this last case, energy can be supplied either through the exhaust gas recovery boiler or the high temperature refrigeration circuit

It determines in which segment of the annual consumption deviation (in relation to what has been specified in the contract) lies the industrial customer consumption

(14) to E. Electricity Purchase Contracts The next constraints are common to all electricity purchase contracts.

to

(21)


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Fig. 4. Type 4 of electricity purchase contract.

price, or at the market price if this price is located between the cap and the floor prices (see Fig. 4). Fig. 3.

Type 2 of electricity purchase contract.

The binary variable ( ) associated with segment in which annual consumption deviation is located, takes value 1 if the contract is formalized (22)

(26)

Annual consumption deviation in relation to the reference consumption belongs to only one of the defined segments. Thus, if a contract is chosen, the binary variable associated with that consumption segment takes value 1, which allows energy imputation to that contract

), which shows if segment is The binary variable ( active according to the relative position among the spot, floor and cap prices at each period, is 0 if the spot price is not in segment . See equation (27) at the bottom of the page. ) is 0 if the market Energy consumed at segment ( price does not belong to that segment

(23)

Electricity imputed to the chosen contract is equal to that ) which corresponds to the active consumption segment (

(28) Electricity market price at each period can only be greater than the cap price, lower than the floor price, or be located between both

(24)

(29)

3) Type 3: Spot Price: The cost of this contract type is derived from the annual consumption at a final spot market price ( )

If the contract is formalized, there is a binary variable whose value differs from 0, and permits energy consumption at a price indicated by segment . (30)

(25) 4) Type 4: Spot Price Plus Cap and Floor: The cost of this ) plus the contract type consists of an annual premium ( energy consumption cost. The electricity consumption is paid at ) if this price is lower than the market price, a cap price ( ) if this price is higher than the market at a floor price (

Electricity imputed to the chosen contract is equal to the one that corresponds to the active consumption segment at each period (31)

(27)

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IV. IMPLEMENTATION AND CASE STUDY The presented model has been tested with realistic data from a paper cellulose factory located in Spain. The cogeneration system employed is a gas engine which is widely spread in Spain due to its small size (around 2 MW of electric output), operation flexibility, demand structure of consumers, etc. [13], [14]. An oil boiler with enough capacity to supply the total steam and hot water demand is also available. The goal pursued by the industrial consumer is to minimize the global energy supply cost of the factory. The decision concerning which contracts to sign for the following year among those proposed by the retailers has to be made. One contract of each of these types has to be chosen: i) electricity acquisition; ii) oil acquisition for feeding the boiler; iii) natural gas for feeding the gas engine; and iv) surplus electricity sale. The energy supply system (e.g., boiler and cogeneration system) operates in an optimal way. Thus, overall optimization involving contracting decisions and energy supply system operation must be done. The scope of the model is one year since this is the duration of the contracts. The factory has a flat load shape in working days so, in order to reduce the number of periods of the problem, four representative days per month are used. These are the combination of weekend and working days according to the Spanish calendar for electricity tariffs, and factory on/off status. Four periods per representative day are used for the working days and three for the others. The total number of periods modeled is 112 of 168 possible, since the factory production does not stop every month. Monthly prices have been considered for oil and natural gas, while for electricity acquisition and surplus sale prices differ from one period to another. Fig. 5 shows the oil and the natural gas prices implemented in the model. In this figure, electricity prices depicted are monthly average prices of maximum, average, and minimum daily prices. Steam at 170 C and 8 kg cm supplies digesters and paper dryer machines, while hot water at 90 C is demanded for sodium hydroxide heating. The thermal peak demand including steam and hot water is 1.9 MW, while the thermal production capacity is the following: i) boiler with 2.2 MW; ii) heat recovery boiler with 1.6 MW; and iii) high temperature refrigeration circuit with 0.9 MW. The maximum electricity produced by the gas engine is 2.8 MW whereas the industrial peak load is 1.2 MW, so surplus electricity can be sold. One contract per type is modeled as shown in Tables I–IV. Oil and natural gas contracts have the same format as types 2 and 4 of electricity acquisition, while surplus sale contracts have the same format as types 1 and 3 of electricity acquisition. The MILP problem formulated has been implemented via an algebraic modeling language called GAMS [15], and has been solved by the solver CPLEX which uses branch and bound algorithm as the solution method. The first binary variables branched by the solver have been the decision variables corresponding to contract selection. This choice reduces time execution because of its main importance in the optimal solution. The resulting optimization problem contains 6162 variables, 881 of which are binary, 3969 restrictions and 40 690 non zero elements. It takes

Fig. 5.

Oil, natural gas, and electricity spot market monthly prices. TABLE I ELECTRICITY PURCHASE CONTRACT PARAMETERS

TABLE II SURPLUS SALE CONTRACT PARAMETERS

42 s to solve the proposed case study obtaining the optimal solution. The model has been executed on a 1.7-GHz Pentium 4 personal computer running under Microsoft Windows 2000.


TABLE III OIL PURCHASE CONTRACT PARAMETERS

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of these optimal contracts are shown in Table V. The optimal output values of the main operation variables are outlined in Table VI. To show the decision change capabilities of the presented model, a 6% drop in cap and floor prices in natural gas type 2 contract is performed. This variation makes the modified contract to be chosen among the optimal ones, resulting in an objective function value of 593.1. V. CONCLUSION

TABLE IV NATURAL GAS PURCHASE CONTRACT PARAMETERS

TABLE V OBJECTIVE FUNCTION TERMS [k]

TABLE VI CUMULATIVE MONTHLY ENERGY RESULTS [MWh]

This paper presents a mid-term MILP model for the overall optimization of the operation of an energy supply system, and the contracting policies related to energy purchase/sale of an industrial consumer under liberalized energy markets. Contracts are formalized at the beginning of the problem horizon. Global energy supply cost, which is to be minimized, includes operation and maintenance costs. The high level of detail shown in the modeling for the type of problem presented in this paper represents an improvement from previous works. Mainly, a significant set of contracts is rigorously modeled. Despite the increased complexity of the problem formulation compared with previous models, the problem can be solved with standard methods in a reasonable time. The proposed model can be a useful tool for industrial consumers with electric and/or thermal energy demand supplied by the electric grid and/or a cogeneration system and/or a boiler when deciding among different energy contract offers. Retailers can also take advantage of the proposed tool for evaluating the best integrated contracting solution for a particular consumer, as well as for testing new contract types of electricity and/or fuels. Cogeneration facility investment analysis based on the operation results given by the model can also be a useful application. A realistic case study has been successfully implemented and analyzed to validate the presented model. Future works will focus on modeling issues concerning uncertainty derived from fuel and electricity price forecasting. Risk management will be taken into account in decision policies involving contracts under uncertainty. APPENDIX The list of notations used throughout the paper consists of the following A. Sets

The optimal contracts obtained with the mentioned input data have been: type 4 for electricity acquisition, type 2 for surplus electricity sale, and type 1 for oil and natural gas purchase. Costs

periods ( ); electricity purchase contracts of type ( ); types of electricity purchase contracts ( ); period indexes corresponding to each time-of-use (TOU) rate period ; periods corresponding to peak, plateau, and off-peak ); load, of a three sections TOU rate ( periods ( ) corresponding to the twelve months of the year; segment indexes ( ) corresponding to type 2 of electricity purchase contracts; segment indexes corresponding to type 4 of electricity purchase contracts.

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B. Constants

,

,

• Global , ,

• , , , • , ,

,

, •

•

steam, hot water, and electricity demand at period [MWh/h]; , oil and natural gas market prices at period in [ kg] and [ therm], respectively; , electricity market purchase and sale prices, respectively, at period [ kWh]. The sale price is indexed to the electricity market price; duration of period [h]. Boiler operation production design constants in [ton/h] and [ton/MWh], respectively; fixed and variable operating costs, excluding oil costs in [ ] and [ ton], respectively; maximum and minimum oil consumption, respectively [ton/h]. Cogeneration system operation , Electricity, exhaust gases, and high tempera, , ture refrigeration circuit design constants in [km N h]1 and [km N MWh], respectively; fixed and variable operating costs excluding natural gas costs in [ ] and [ MWh], respectively; heat recovery boiler performance; maximum production of electricity generated and exported to the electric grid [MWh/h]; maximum and minimum natural gas consumption, respectively [km N h]. Energy balance maximum electricity consumed from the grid [MWh/h]. Electricity purchase contracts fixed term of electricity purchase contract of [ ]; type electricity price at period for contract of type 1 [ kWh]; annual price for contract of type 2 corre[ ]; sponding to consumption annual consumption for contract of type 2 [MWh]; , price and consumption increment in relation and , respectively, for segment to of contract of type 2; premium of contract of type 4 [ ]. , cap and floor prices, respectively, for contract of type 4 [ kWh].

C. Variables Binary variables are represented by Greek letters. • Objective function total energy supply cost [ ]; 1kilo

normal cubic meter of natural gas per hour

,

•

•

•

•

cost of the acquisition contract of oil for the boiler, electricity to supply the industrial consumer demand, and natural gas for the cogeneration facility, respectively [ ]; operating costs of the boiler, excluding oil costs, and of the cogeneration facility, excluding natural gas costs, respectively [ ]; income of the electricity sale contract derived from the exported surplus electricity produced by the cogeneration facility [ ]. Boiler operation oil consumed at period [ton/h]; , thermal energy produced to supply steam and hot water demand respectively, at period [MWh/h]; boiler commitment status 1 on/0 off at period . Cogeneration system operation natural gas consumed at period [km N h]; electricity generated at period [MWh/h]; , electricity generated, exported to the grid and consumed by the industrial consumer respectively, at period [MWh/h]; thermal energy produced by exhaust gases at period [MWh/h]; , thermal energy produced by exhaust gas recovery employed to supply steam and hot water demand respectively, at period [MWh/h]; thermal energy produced by the high temperature refrigeration circuit of the gas engine at period [MWh/h]; thermal energy produced by the high temperature refrigeration circuit of the gas engine employed to supply hot water demand at period [MWh/h]; cogeneration system commitment status 1 on/0 off at period . Energy Balance electricity consumed from the electric grid at period [MWh/h]; , binary variable which is 1 if electricity produced by the cogeneration facility is exported (or consumed from the electric grid) at period , otherwise it takes value 0. Electricity purchase contracts cost of contract of type [ ]; binary variable which is equal to 1 if contract of type is chosen, otherwise it takes value 0; electricity consumed from the grid in contract of type at period [MWh/h]; binary variable which is equal to 1 if the annual energy consumption from the grid is located in segment for contract of type 2; electricity consumed from the grid in segment for contract of type 2 at period [MWh/h];


binary variable which indicates whether the market price is in segment or not (1/0) for contract of type 4 at period ; electricity consumed from the grid in segment for contract of type 4 at period [MWh/h]. ACKNOWLEDGMENT The authors would like to acknowledge Juan Bautista Cobo and Francisco Acosta de los Reyes from COTTON SOUTH S.A. for all the data provided and the suggestions made. REFERENCES [1] C. Lewiner, “Business and technology trends in the global utility industries,” IEEE Power Eng. Rev., pp. 7–9, Dec. 2001. [2] B. N. Venkatesh and V. Chankong, “Decision models for ma na gement of cogeneration plants,” IEEE Trans. Power Syst., vol. 10, pp. 1250–1256, Aug. 1995. [3] L. L. Lai and J. T. Ma, “Multitime-interval scheduling for daily operation of a two cogeneration system with evolutionary programming,” Elect. Power Energy Syst., vol. 20, no. 5, pp. 305–311, 1998. [4] B.-K. Chen and C.-C. Hong, “Optimum operation for a back-pressure cogeneration system under time-of-use rates,” IEEE Trans. Power Syst., vol. 11, pp. 1074–1082, May 1996. [5] T. Guo, M. I. Henwood, and M. V. Ooijen, “An algorithm for combined heat and power economic dispatch,” IEEE Trans. Power Syst., vol. 11, pp. 1778–1784, Nov. 1996. [6] E. Dotzauer, “Algorithms for Short-Term Production-Planning of Cogeneration Plants,” Ph.D., Linköping University, Linköping, Sweden, 1997. [7] E. Dotzauer, K. Holmström, and H. F. Ravn, “Optimal unit commitment and economic dispatch of cogeneration systems with a storage,” in Proc. 13th PSCC Conf., Trondheim, Norway, 1999. [8] S. W. Illerhaus and J. F. Verstege, “Optimal operation of industrial chpbased power systems in liberalized energy markets,” in IEEE Power Tech. Conf., vol. BPT99–352-13, Aug./Sept. 29–2, 1999. [9] S.-E. Fleten, “Portfolio Management Emphasizing Electricity Market Applications. A Stochastic Programming Approach,” Ph.D., Norwegian University of Science and Technology, Trondheim, Norway, 2000. [10] R. Green, The Electricity Contract Market. Cambridge, MA: Department of Applied Economics and Fitzwilliam College, 1996.

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[11] G. Michalik and W. Mielczarski, “Contracts for electrical energy,” Int. J. Energy, Environment and Econ., vol. 7, no. 4, pp. 383–393, 1998. [12] R. Richter, “Pricing desings in retail electricity: How to get out of price wars and get into profitability,” Electric Light and Power, pp. 27–28, Aug. 2000. [13] P. de la Pezuela, “La cogeneración en españa, evolución y futuro,” Energía, pp. 105–111, Mar./Apr. 1999. [14] J. M. Sala, Cogeneración. Aspectos termodinámicos, tecnológicos y económicos, Tercera ed: Universidad del País Vasco, 1999. [15] A. Brooke, D. Kendrick, A. Meeraus, and R. Raman, GAMS. A User’s Guide. Washington, D.C., USA: GAMS Development Corporation, 1998.

Emilio Gómez-Villalva (S’98–A’00–M’02) was born in Granada, Spain, in 1973. He received the electrical engineer degree from the Universidad Pontificia Comillas (ICAI), Madrid, Spain, in 1997. He is currently pursuing the Ph.D. degree at the Universidad Pontificia Comillas (ICAI). From July 1998 to November 1999 he was a junior consultant on SCADA’s applications to power systems at NorSistemas (Unión Fenosa). He joined Iberdrola Ingeniería y Consultoría in November 1999 where he is currently performing power system analysis. His main areas of interest are power system operation, planning, and economics.

Andrés Ramos was born in Guadramiro, Spain, in 1959. He received the Electrical Engineer degree from the Universidad Pontificia Comillas (ICAI), Madrid, Spain, in 1982 and the Ph.D. degree in electrical engineering from the Universidad Politécnica de Madrid, Madrid, Spain, in 1990. Currently, he is a Full Professor in the Departamento de Organización Industrial (DOI), ICAI, Madrid, Spain. From 1982 to 1984, he was a Junior Research Staff at the Instituto Tecnológico para Postgraduados. From 1984 to now he is Senior Research Staff at the Instituto de Investigación Tecnológica, ICAI. His areas of interest include operations, planning and economy of electric power systems, operation research applied to power systems and software development.