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A SIMULATION TOOL FOR SHORT TERM ELECTRICITY MARKETS

A. Martini, P. Pelacchi (Member, IEEE), L. PellegriniDept. of Electrical Systems and Automation

University of Pisa, Pisa, Italy

M.V. Cazzol, A. Garzillo, M. InnortaCESI/T&D Network

Milan, Italy

Abstract: In a competitive electricity market, generatingcompanies (GENCOs) have to sell their output by presenting bids

on the market. A pure operating costs optimization will not beenough as bidding strategies definition requires GENCO toconsider other factors such as market structure and its inter-relationships, demand forecast level and competitor behavior.Hourly supply curves are the final output of an operation planningdecision support model, which is hierarchically articulated in long,medium and short-term components. This paper presentsDESPOT (DEcision-support Simulator for POwer Trading), ashort-term wholesale electricity market simulation tool that

provides unit commitment, system hourly prices, profit andexpected bid for a GENCO. The model provides a detailed Italiangeneration system representation and a market structure based onthe rules established by the Italian decree 79/99, which hasintroduced competition in Italy. A simplified version of the globalmodel is presented and results of the simulations are also

provided. Notwithstanding the generation capacity reduction of the dominant GENCO imposed by the Italian law, preliminaryresults seem to show that the market power of the generationcompanies is still considerable and this might strongly influencethe energy prices.

Keywords: Deregulation, Italian Electricity Market, Power System Management, Hydro-Thermal Scheduling, Simulation,Quadratic Programming, Dynamic Programming.

I. INTRODUCTION A. Paper overviewThis paper presents a model – DESPOT - for short-term

decisions that a generation firm (GENCO) must face inthe new competitive framework. This tool is a complexcombination of modules as the determination of the hourlyenergy production by each unit, self Unit Commitmentand hourly bidding curves to submit, necessarily requiresadditional information to the old way of doing business.With no revenue regulation, competitor behavior anddemand level expectation become extremely relevant for GENCO to decide.

Considering electricity trading complexity (differentmarkets to operate, uncertainty, etc.) and the embryonicstage of the industry restructuring process in Italy, agradual model implementation of new features is greatlyrecommended in order to achieve more effective learning.The model addressed here is a simplified version as onlyday-ahead energy market decisions are considered.

DESPOT provides a detailed generation systemrepresentation and electricity market structure based onthe Italian deregulation law - decree 79/99 - which hasopened to a completely new regulatory framework.Therefore, the simulations we present are carried outunder realistic assumptions. The weekly module is

presented here in detail.

B. Literature reviewThe introduction of competition in the electricity industry

undertaken in a wide range of countries, although withdifferent patterns, involves many problems regarding market

power, competitive performance of the market and inevitablyaffects the generators’ way of doing business. These power industry changes worldwide are causing a great reseachstreams development with contributions ranging fromenginnering to economics, decision science andmultidisciplinary. This literature extension makes it difficultfor both academics and pratictioners to understand the state-of-the art regarding short-term models to be used by generationfirms (GENCOs) in day-ahead electricity market as well as theemergent trend in this research stream. In particular, there aremany simulation models incorporating the new features and

using different methods but they do not address the same goal.For this reason, models with different goals from DESPOThave not been reviewed.

We divided GENCO short-term models on the base of twoitems:• model’s goal: some models perform a what if analysis [1,

2, 3, 4] while others are ‘operating focused’ [5, 6, 7];• competitors’ behavior formulation: some works use a

‘sensitive’ approach (historical DB use, marketinformation) [6, 7, 8] while others use theoretical models(Cournot, Bertrand [1, 4, 9], supply-function approach[10]).

Following this literature classification, DESPOT is a modeldesigned to adopt a ‘sensitive’ approach to competitor

behavior determination and with an ‘operative’ focus.Similarly to [5, 7], our model has a weekly optimiser module.

An overview of DESPOT is presented in section II, whilesection III describes the Weekly optimiser Module (WeM)which solves the self UC problem in a deregulated contextand provides expected hourly schedule for each unit of theconsidered generation firm. Sections IV and V state themathematical formulation of the module and the notationused for its expression. Results of the WeM application to anumerical example on the Italian electricity framework are

presented in section VI and, finally, conclusions are

presented in section VII.II. MODEL OVERVIEW

Operation planning for generation firms has beentraditionally decomposed in different time scopes: long,medium and short term. This temporal division ishierarchically organized as decisions with a shorter time scopedirectly or indirectly depend on longer-term results [1].Fulfilling this decision scheduling, DESPOT focuses on short-

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term analysis and receives input from the medium termupstream model.

Two modules hierarchically working compose themodel: a weekly-based optimiser (WeM) and a daily-basedone (Fig.1). In addition, information on competitor behavior and hourly demand level are exploited by two other modules. Upstream, a medium-term model suppliesinformation on group maintenance, water reservoir annualmanagement, and fuel consumption as well as long runmarket strategy.

The weekly optimizer performs both hourly UC anddispatching for each generating units as well as expectedhourly prices. Obviously, the shifting from monopolisticmarkets to competition necessarily requires a weekly profit-maximization UC instead of a cost-minimization one.

Fig. 1. DESPOT architecture

The daily optimizer receives the firm’s hourly optimal

productions as input data, together with expected hourly prices - previous module results - and designs the biddingcurve for each hour of the day.

This model is a simplified version of DESPOT as onlyday-ahead energy market decisions are considered.

III. WEEKLY SIMULATOR MODULEDESCRIPTION

The weekly optimiser module (WeM) estimates hourlyenergy prices, self UC and scheduling of each unit of the

considered GENCO in order to maximise weekly profit, and atthe same time respects, both operation efficiency(minimization of thermal plants shutdowns and start-ups, water spills avoidance, etc.) and market aspects (medium termstrategy, expected market prices).

A. Objective functionAs revenue is no longer regulated, operation efficiency can

no longer be guided by weekly cost-minimisation but theobjective function has to take into account the expected energymarket prices. To gain insight in this new way of operatingonly profit maximisation will be considered. Risk exposuredegree and portfolio management should be added in futuredevelopments of the model [11,12].

B. Generation systemsThe generation system is modeled in great detail as both

hydro and thermal systems are represented.The hydraulic system is composed of a certain number ( NC )

of hydroelectric plants distributed over the territory that, froma topological point of view, can be grouped into hydraulicallylinked subsets, called valleys. Each plant is fed by a reservoir geographically located upstream and its discharge is collected

by a second reservoir downstream or is dispersed into a water stream. Spillage outflows are accepted for natural or artificialreservoirs; should the level in those reservoirs reach excessivelevels, it is possible to discharge water in the reservoirsdownstream without using it to produce electric energy.

In Fig. 2 a simple example of a valley model composed of three basins and three power plants is represented. For thegeneric basin j the volume l ij, the natural inflows F ij, thespillage outflows sij and the turbine discharge qij relevant to the

period i are shown.

Fig. 2. Val Gerola (Italy) hydraulic system

The thermal generation system is represented by a set of NG power plants. Initial state, upward and downward ramp limits,minimum and maximum power levels and outage period aredefined. Production cost is analytically described by aquadratic curve; start-up and shutdown costs are alsorepresented. Moreover, for each thermal plant, the hours inwhich it is allowed to perform a start-up or a shut down areassumed to be fixed. This assumption greatly simplifies thesolution procedure since it allows to implicitly handle a lot of complex constraints typical of Unit Commitment formulationsuch as minimum up/down time constraints, maximum number

Medium term marketstrategy

MEDIUMTERM MODEL

Maintenance plans

Weekly water spills

SHORT-TERMMODEL

Expected hourly prices

Unit Commitment

Scheduling

Weekly OptimiserModule

Daily OptimiserModule

Hourly bidding curves

Competitors’ behaviouModule

Competitor biddingcurves

Historicalload curveDB

DemandforecastModule

HistoricalDB

REGOLEDO

s i3

TRONA

PEDESIN

PANIGAIGEROLA

PEDESIN

F i1

F i2

s i1

s i2

l i1

l i2

l i3

q i1

q i2

q i3

F i3

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of start-up/shutdown allowed during the simulation periodand crew constraints.

C. Market systemThe adopted market model assumes as input (from an

ad hoc module) the competitors’ behaviours analyticallyrepresented by their aggregated bidding curves (see Fig.1). These curves relate the market price P i with the

competitors production iΠ for each period i by means of a linear function: P i = P i (∏ i). (1)

The load level a GENCO has to face is expressed by itsresidual demand curve for each hour (RD) that is totaldemand minus the sum of all the competitor’s bids. RDdetermination requires data from both the competitors’

behavior module and the demand forecaster one.

Moreover, short-term decisions must be in-line withmedium term strategy. An ad hoc model providesinformation on maintenance plans, weekly water spillsand medium term market strategy. Several constraints can

be designed for this latest guideline: a minimum marketshare goal, a price target, a risk aversion rate, up to a

portfolio strategy.

IV. MODEL FORMULATIONThe thermal system consists of power plants with

assigned production limits, and quadratic cost curves.The hydro system is modelled representing the power

plants, the reservoirs and the relevant hydraulicconnections in detail. For the sake of simplicity, the

problem formulation is referred to the hydraulic systemshown in Fig. 2. Its extension to the general case ishowever immediate.

The electric transmission system is not represented

(bus-bar model). A. Objective functionThe objective of the problem is to determine the value

of the market price and the operative program for hydraulic and thermal plants in order to maximize the

profit of the producer over the whole week (divided in N time intervals).

From an analytical point of view we obtain thefollowing objective function to be maximized:

( )( )∑ ∑

∑ ∑∑

= =

= ==

++−

+

+=

N

i

NG

j ji jiijij

N

i

NG

jij

NC

jij ji

CSDCSU pCost

pq P OF

1 1,,

1 11

κ

where:

( ) 2210 ij jij j jijij pc pcc pCost ++= is the quadratic cost

function of thermal generator j in interval i; c0, c1, c2 arecoefficient values.

jiCSU , ( jiCSD , ) is the start-up (shutdown) cost of thermal

generator j if it starts up (or shuts down) in interval i, and it isequal to zero otherwise.

The first term of the objective function is the income due toselling energy (produced by both hydraulic and thermal plants)at the market price, while the second term represents theoperation costs due to thermal plants.

B. ConstraintsThe problem is subject to equality constraints related to

mass and energy balances, to inequality constraints relevant tothe lower and upper bounds on problem variables and tological constraints due to the rules for the start-up and the shutdown which are implicitly and efficiently handled by the

proposed solution procedure.

- Equality constraints are:mass balance equations relevant to each basin in eachinterval: such equations relate water volumes in each

basin in two successive time intervals. For the hydraulicsystem in Fig. 2 and considering the simulation period

divided in N intervals, the mass balance equations can bewritten as follows:

−−+++=−−+++=

−−+=

−

−

−

332233,13

221122,12

1111,11

iiiiiii

iiiiiii

iiiii

sq sq F l l

sq sq F l l

sq F l l

i=1,...,N

in particular, in (4), the equations relevant to the firsttime interval l 01 , l 02 , l 03 indicate the starting water volumesin basins 1, 2 and 3.

electric power balance equations in each period: suchequations require that in each period the sum of theelectric power produced by the hydraulic and thermal

systems of the producer and the total competitor productions satisfies the load demand:

∑ ∑= =

=Π++ NC

ji

NG

jiijij j CAR pqk

1 1

i=1,...,N

where k j is the energy coefficient of hydraulic plant j,

ij p is the power produced by the thermal plant j in interval

i and CARi is the total load in interval i.- Inequality constraints are:

basins capacity constraints: in each period the water volume in each basin cannot exceed its maximumcapacity and, in the last interval, it must be higher or

equal to the imposed final volume:k ik l l max0 ≤≤ k=1,...,3 i=1,...,N-1 ;

k Nk k l l l maxfin ≤≤ k=1,...,3

technical constraints on hydraulic plants and thermalgroups: in each period the used water flow of eachhydraulic plant and the power generated by each thermalgroup must satisfy the technical constraints:

(2)

(3)

(4)

(5)

(6)

(7)

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jij j qqq maxmin ≤≤ j=1,...,NC i=1,...,N

jij jij p p p p maxmin0 ≤≤∨= j=1,...,NG

i=1,...,N

V. PROPOSED SOLUTION PROCEDURE

The model is formulated as a mixed integer quadratic programming problem with a sparse constraints matrix,which can reach a remarkable size due to the large number of the discrete intervals and to the consideredhydro-thermal system’s complexity.

However, it can be successfully solved by using aniterative procedure based on a de-coupling betweencontinuous and logical variables of the scheduling

problem. Going into further detail, the procedure starts bychoosing an initial Unit Commitment and by solving therelated hydrothermal weekly dispatching. This is aquadratic programming problem, which has beenefficiently solved [13, 14, 15] by the non-linear extensionof the primal dual interior point method [16,17]. In asuccessive step the procedure fixes the hydro productionsand looks for a more convenient Unit Commitment for each thermal group. This problem has been efficientlysolved by a dynamic programming approach [18]. If theabove step leaves the previous Unit Commitmentunchanged, the current solution is assumed to be theoptimal one and the procedure ends; otherwise the

procedure once more solves a new hydrothermal weeklydispatching by using the last computed Unit Commitment.Fig. 3 synthesizes the solution procedure.

VI. CASE STUDIESA practical case study is presented in order to illustrate

the tool efficiency.

A. Input dataIn the performed simulations, the main Italian

integrated system generation units constitute theconsidered hydrothermal production system.

The thermal system is characterised by 165 thermalgroups with a total installed power of about 36000 MW.All thermal groups can start-up in the morning when theload grows and can shut down at the end of day when theload decreases (daily flexibility).

The hydro generation system is characterised by 195 power plants and about the same number of basins divided

in 70 subsets (valleys) with a total installed power of about 13000 MW.The considered simulation interval starts at 06.00 a.m.

of a Friday and ends at 06.00 a.m., ten days later (onMonday) in order to join the obtained weekly operationscheduling to the next one.

Therefore the load to be supplied is constituted by 240hourly values; the minimum load is about 9400 MW andthe load peak is about 28500 MW (see Fig. 4).

Initial UC

Hydro-thermal scheduling with fixed UC

(interior point algorithm)

UC with fixed hydro generation

(dynamic programming approach)

STOP

Is UC changed?

YES

NO

Fig. 3. Solution procedure scheme

Fig. 4. Load curve

Referring to the Italian decree 79/1999, which has broken

down the former monopoly setting, in the considered hydro-thermal production system two generation groups have beenidentified: the model user and its competitors. In the secondsimulation the user is PRODUCER1, the main Italian GENCOwith an installed power of about 34000 MW (22800 MW of thermal power and 11900 MW of hydraulic power) whilecompetitors are a set of new GENCOs with an overall installed

power of about 7000 MW (6200 MW of thermal power and600 MW of hydraulic power). In simulation 3 the user isPRODUCER2, which is one of the new GENCOs.

The following simulations have been performed:1. the integrated operation scheduling on the whole system

in order to minimise production costs;

2. the operation scheduling of PRODUCER1 in order tomaximise its profit, considering the new GENCOs ascompetitors;

3. the operation scheduling of PRODUCER2 in order tomaximise its profit; the others are competitors.

In the last two simulations, competitor behaviour has beenconsidered by means of their aggregated bidding curves.Because of historical data unavailability, competitors have

been assumed to offer energy at their marginal costs. In this

(8)(9)

0

5000

10000

15000

20000

25000

30000

35000

1 25 49 73 97 121 145 169 193 217

Periodi

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context, the interaction between players is modelled asPrice Leadership behaviour: the leader firm acts asOligopolistic firm, while the followers act as marginal

players.

B. ResultsWeM determines the hourly power output for each of

the GENCO’s generating units. We assume that eachgenerating firm deals with the maximisation of its profitinstead of individual profits of its units (co-ordinatedsimulation case in [1]).

Referring to simulation 3, the hourly energy to be produced by PRODUCER2 with thermal and hydro unitshas been presented in Fig. 5. Hydro generation is placed in

peak hours as hydro units can obtain larger profits.

0

500

1000

1500

2000

2500

3000

3500

1 26 51 76 101 126 151 176 201 226

Hour

Fig. 5. PRODUCER’S 2 hourly energy output (case study 3)

0

10

20

30

40

50

60

70

80

1 24 47 70 93 116 139 162 185 208 231

Hour

0

500

1000

1500

2000

2500

3000

3500

Fig. 6. Hourly energy price and output of PRODUCER 2

Fig. 6 shows both the hourly firm’s energy outputs andthe expected market prices obtained. Computation timefor solving the optimisation problem was 26 sec. in aPentium II, 128 MB and 133 MHz.

In Table 1 a comparison between the operationscheduling of PRODUCER2 in open market context andintegrated system is performed.

In Table 2 some results of the first two simulations aresummarised. In particular, a comparison betweenPRODUCER1 operation scheduling both in open marketcontext and in integrated system is performed.

Table 1

M ARKET PARTICIPANTS E NERGY (GWh)

COSTS (MLIT)

PRODUCER2 600 24736

COMPETITORS 3977 156374 O P E N

M A R K E T

TOTAL 4577 178110

PRODUCER2 672 27811

COMPETITORS 3905 147631

I N T E G R A T E D

S Y S T E M

TOTAL 4577 175442

Table 2

M ARKET PARTICIPANTS E NERGY (GWh)

COSTS (MLIT)

PRODUCER1 2842 104924

COMPETITORS 1735 71191 O P E N

M A R K E T

TOTAL 4577 176115

PRODUCER1 3047 113329

COMPETITORS 1530 62113

I N T E G R A T E D

S Y S T E M

TOTAL 4577 175442

Total production costs in the integrated system are quitelower than in the open market framework (-0.4 %). In fact, anintegrated operation scheduling leads to an optimal utilisationof the whole production system. On the contrary, the marketleads PRODUCER1 to maximise its profit by reducing its

production. In this way, competitors have to supply load byusing their more expensive plants and, consequently,determining higher market prices.

VII. CONCLUSIONSThis paper has addressed the short-term problems that

GENCOs must deal with in a deregulated framework. Adecision support tool - DESPOT - has been presented and theweekly optimizer module - WeM - has been explained indetail. WeM has been applied to the Italian case and threesimulations have been carried out. A comparison between theoperation scheduling in a deregulated framework and in the

past-integrated context, for the main Italian GENCO, hasdemonstrated that total production costs in the integratedsystem are lower than in the open market framework (-0.4 %).The performed tests have demonstrated the adequacy of the

proposed model and the efficiency of the solution algorithm.

Future development of the model regards competitor behavior module implementation and additional marketmechanisms incorporation (hour-ahead market, ancillaryservices, bilateral contracts and derivative) in order to have areal operative decision tool devoted to the portfoliomanagement.

PRODUCER’s 2 outputEnergy price

Thermal output Hydro output

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VIII. ACKNOWLEDGEMENTSThe authors gratefully acknowledge the contributions of M. Gallanti,

A. Gelmini and M. Benini for their work on the original version of thisdocument. This work was supported by the ENTRADE/RET/01/002funds.

IX. REFERENCES[1] I. Otero-Novas, C. Meseguer, C. Battle and J.J. Alba, “A

Simulation Model for a Competitive Generation Market”,IEEE Transaction on Power Systems, vol. 15, no. 1, 2000,

pp. 250-256.[2] C. Li, A. J. Svoboda, X. Guan and H. Singh, “Revenue

Adeguate Bidding Strategies in Competitive ElectricityMarkets”, IEEE Transactions on Power Systems, vol. 14,no. 2, May 1999, pp. 492-497.

[3] G. Gross and D. J. Finlay, “Optimal Bidding Strategies inCompetitive Electricity Markets”, Proceedings of the 12 th Power Systems Computation Conference (PSCC), Dresden,August 1996, vol. 2, pp. 815-823.

[4] M. Ventosa, A. Ramos and M. Rivier, “ModellingCompetition in Electric Markets by EquilibriumConstraints”, Utilities Policy, vol. 7, no. 4, April 1999, pp.233-242.

[5] A. Baíllo, M. Ventosa, A. Ramos, M. Rivier and A. Canseco,“Strategic Unit Commitment for Genetarion Companies inDeregulated Electricity Markets”, Proceedings of the 1999DIMACS/EPRI Workshop.

[6] C. W. Richter and G. B. Sheblé, “Building Fuzzy BiddingStrategies for the Competitive Generator”, North AmericanPower Symposium, Laramie, WY, 1997.

[7] J. García, J. Román, J. Barquín, A. González, “StrategicBidding in Deregulated Power Systems”, 13 th PSCC 1999Conference, Norway, vol. 1, pp. 258-264.

[8] D. Zhang, Y. Wang and P. B. Luh, “Optimization basedBidding Strategies in the Deregulated Market“, IEEETransactions on Power Systems, vol. 15, no. 3, August2000, pp. 981-986.

[9] A. Maiorano, Y. H. Song and M. Trovato, “ImperfectCompetition: Modeling and Analysis of OligopoliElectricity Markets”, IEEE Power Engineering Review, vol.19, no. 5, May 1999, pp. 56-58.

[10] J. I. Del Castillo and N. J. Barquín, “Oligopolistic ElectricalMarket Competition, Stranded Costs and Uncertainty: aSupply Function Appoach”, 6 th International Conference onProbabilistic Methods Applied to Power Systems (PMAPS),Portugal, September 2000.

[11] G. B. Sheblé, “Decision Tools for GENCO Dispatchers”,IEEE Transaction on Power Systems, vol. 14, no. 2, May1999, pp. 745-750.

[12] S. N. Siddiqi, “Project Valuation and Power PortfolioManagement in a Competitive Market”, IEEE Transactionson Power Systems, vol. 15, no. 1, February 2000, pp. 116-121.

[13] P. Burelli, G. D'Amora, M. Innorta, P. Marannino, “ShortTerm Hydrothermal Generation Scheduling with Inter-AreaPower Flow Constraints”, PSCC 1990, Graz.

[14] J. Medina, V. H. Quintana, A. J. Conejo, F. Perez Thoden, “AComparison of Interior Point Codes for Medium-term Hydro-Thermal Coordination”, IEEE Transactions on Power Systems,1997, pp. 224-231

[15] M.V. Cazzol, A. Garzillo, M. Innorta, M. Ricci, “Short TermHydro-Thermal Generation Scheduling with Network Power Flow Constraints”, EPSOM 1998, Zurich, September 23-25, pp.20-1, 20-6.

[16] N. Megiddo, “Pathways to the optimal set in linear programming” in Progress in Mathematical Programming:Interior Point and Related Methods, New York: Springer Verlag.

[17] S. Mehrotra, “On the Implementation of a Primal-dual Interior Point Method”, SIAM Journal on Optimization, vol. 2, no. 4,1992, pp. 575-601

[18] Wood A. J., Wollenberg B. F., Power Generation, Operation andControl, New York: Wiley & Sons, 1996.

X. BIOGRAPHIESMaria Vittoria Cazzol received her degree in Mathematics from theUniversity of Milan, Italy in 1987. Since 1991 she has been involvedat CESI in research activities in the field of applied optimization.She is now working on the design of new optimization tools for power

system analysis in an open energy market environment.Angelo Garzillo received his degree in Electronic Engineering fromthe University of Naples, Italy in 1974. In 1975 he joined theAutomation and Computation Research Center of ENEL where he has

been responsible for research activities in the field of power systemanalysis, optimization and control. Recently he joined CESI where heis working on the design of new optimization tools for power systemanalysis in an open energy market environment.

Mario Innorta received his degree in Mathematics from theUniversity of Catania, Italy in 1969. In 1970 he joined the Automationand Computation Research Center of ENEL where he has beenresponsible for research activities in the field of applied optimization.Recently he joined CESI where he is working on the design of newoptimization tools for power system analysis in an open energy marketenvironment.

Antonella Martini was born in Fivizzano, Italy on 1969. Shegraduated in Business Economics at the University of Pisa andobtained her PhD degree in Managerial Engineering in 2000. In 1999she received a grant from Dept. of Electrical Systems and Automation,University of Pisa, for research on electricity industry regulation andmodeling of power markets. Her research interests regard electricitymarkets liberalization processes with a particular attention to theItalian situation.

Paolo Pelacchi received his electrical engineering degree from PisaUniversity, Italy, in 1976. In 1979 he joined the Electrical ResearchCenter of ENEL. Since 1983 he has worked in the Department of Electrical Systems and Automation at Pisa University; currently he is

full professor of electric power systems. His recent research interestsregard electricity markets liberalisation processes focusing on theItalian situation.

Luisa Pellegrini was born in Pisa, Italy, on 1970. She graduated inBusiness Economics at the University of Pisa and obtained her PhDdegree in Managerial Engineering in 1999. Since 1998 she has beenassistant professor at the University of Pisa.

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A 1052001