The Supply Function Equilibrium Economics Essay

Supply Function Equilibrium ( SFE ) is a better theoretical account of competition in oligopoly as it includes both Cournot and Bertrand theoretical accounts as one of its particular instances. It helps ISO ( Independent System Operator ) and allows other genco ‘s to construct optimum command schemes. Most of the earlier researches of SFE trade with individual period and individual market theoretical account which did non see the facts that the genco ‘s clasp a combination of portions or other investings in electricity and fuel markets. In this paper a proper SFE has been recognized which can be applied to multiple-period state of affairs, so by utilizing Two-Settlement Approach maximization of genco ‘s societal public assistance and pay off of each genco for a specified period is done.

The undertaking work comprises of five chapters:

Chapter 1 a brief debut of market competition has been provided with some debut to the of import characters playing function in the selling environment which makes the understanding simple.

Chapter 2 specifies function of economic sciences in the electricity market with different ways through which command takes topographic point has been specified, this chapter smoothens the way to understand the undertaking work easy.

Chapter 3 is the anchor of the undertaking work, it deals with SFE and its development and function in the undertaking work and it farther incorporates two-settlement attack used in LSFE so as to obtain equilibrium parametric quantities of the market.

Chapter 4 trades with the simulation and consequences of the undertaking work and Chapter 5 Concludes the work with a subdivision of Appendix to follow.

Chapter 1


What is Competition:

Competition leads to the betterment of trade good in many Fieldss of human enterprise. It is permeant ; every organisation needs a scheme to present superior value to its client. Today the competition has intensified dramatically over last several decennaries in about all spheres.

Competition in electric industry by and large means competition merely in the production ( coevals ) of electricity and in the commercial maps of wholesaling and retailing.

Fig.1.1. Physical maps of electricity market

The transit map ( transmittal and distribution ) can non be competitory as they are natural monopolies, because it does non do economic sense to construct up multiple sets of viing transmittal system. Furthermore, the system operations besides have to be a monopoly, since the system operator has to command all the workss in the control country.

Dramatis Personae

Coevals Companies ( Gencos ) produce and sell electrical energy, they may besides sell services such as ordinance, electromotive force control and modesty. These services are required by the system operator to keep the quality and security of electrical supply. A bring forthing company can have a individual works or portfolio of workss of different engineerings.

Distribution Companies ( Discos ) ain and operate distribution webs, in a traditional environment they have a monopoly for the sale of electrical energy to all consumers connected to their web.

Retailers buy electrical energy from the sweeping market and resell it to consumers who do non wish or are non allowed to take part in sweeping market. They do non hold to have any power coevals, transmittal and distribution assets.

Market Operator ( MO ) typically runs a computing machine system that matches the commands and offers that purchaser and marketer of electrical energy have submitted. It besides takes attention of the colony of the recognized commands and offers ; this means that it forwards payments from purchaser to Sellerss following bringing of the energy. The Independent system operator ( ISO ) is normally responsible for running the market of last resort, which is the market in which burden and coevals are balanced in existent clip.

Independent System Operator ( ISO ) has the primary duty of keeping the security of the power system, it is called independent because in a competitory environment the system must be operated in a mode that does non prefer or punish one market participant over another. An ISO would usually have merely the computer science and communicating assets required to supervise and command the power system.

Transmission Companies ( TransCo ) ain transmittal assets such as lines, overseas telegrams, transformers and reactive compensation devices, they operate this equipment harmonizing to the instructions of the independent system operator. Transmission companies are sometimes subordinates of companies that besides own bring forthing workss.

Regulator is the authorities organic structure responsible for guaranting the just and efficient operation of the electricity sector ; it determines or approves the regulations of the electricity market and investigates suspected instances of maltreatment of market power.

Small Consumers buy electrical energy from a retail merchant rental a connexion to the power system from their local distribution company, their engagement in the electricity market normally amounts to no more than taking one retail merchant among others when they have this option.

Large Consumers on the other manus will frequently take an active function in electricity markets by purchasing their electrical energy straight through the market, some of them may offer their ability to command their burden as a resource that the ISO can utilize to command the system ; the largest consumers are sometimes connected straight to the transmittal system.

Models of Competition:

1.3.1 Monopoly: The figure shown here is a theoretical account of a monopoly public-service corporation. It deals with the instance where integrating of coevals, transmittal and distribution of electricity takes topographic point through a individual public-service corporation. In this the coevals and transmittal are handled by one public-service corporation, which sells the energy to local monopoly distribution companies.

Fig.1.2. Monopoly theoretical account of electricity market

Buying Agency: A possible first measure towards the debut of competition in the electricity supply industry has been shown in ( fig.1.2 ) . In instance of buying bureau the integrated public-service corporation no longer owns all the coevals capacity ( Fig.1.3 ) . Here in ( Fig.1.4 ) Independent power manufacturers ( IPP ) are the connected to the web, they sell their end product to the public-service corporation that acts as a buying agent.

Fig.1.3. Integrated version of public-service corporation

Fig.1.4. Disaggregated version of public-service corporation

In this theoretical account the public-service corporation no longer owns any coevals capacity and purchases all its energy from the IPP ‘s, the distribution and retail activities are besides disaggregated. Discos so purchase the energy consumed by their client from the sweeping buying bureau.

Sweeping Competition: In this theoretical account ( Fig.1.5 ) disco purchase the electrical energy straight from bring forthing companies. These minutess take topographic point in a sweeping electricity market ; this market can take the signifier of pool or bilateral minutess. At the sweeping degree the lone map that remain centralised are the operation of the topographic point market and the operation of transmittal web. At the retail degree the system remains centralised because each disco non merely run the distribution web in its country but besides buy electrical energy on behalf of the consumer located in its service district.

Fig.1.5. Sweeping competition market

Retail Competition: In this signifier of competitory electricity market ( Fig.1.6 ) all consumers can take their provider, merely big consumer chooses sweeping market as provider. Most little and average consumers purchase energy from the retail merchants. The retail merchants buy energy from the sweeping market and provide it to the consumers. In this the distribution companies are usually separated from their retail activities because they no longer keep monopoly for the supply of electrical energy in the country covered by the web. The lone monopoly held in this competition is by transmittal and distribution webs.

When such a market gets established so no farther ordinance of retail monetary value takes topographic point, because little consumers can alter their retail merchant when offered better monetary value.

Fig.1.6. Retail Competition theoretical account of electricity market

From economic sciences perspective this theoretical account is most satisfactory because in this energy monetary values are set through interactions. Implementing this theoretical account nevertheless requires considerable sum of metering, communicating and information processing.

Chapter 2


2.1. Supply and Demand: Supply and Demand is an economic theoretical account of monetary value finding in the market, it includes that in a competitory market the unit monetary value of a peculiar good will change until it settles at a point where the measure demanded by the consumer is equal to the measure supplied by the manufacturer, ensuing to economic equilibrium between monetary value and measure.

Graphic Representation:

Fig.2.1. Supply-Demand Curve

Here the graph shown is the supply demand curve it is discernible from the above graph that when demand increases from D1 to D2 so monetary value and measure both addition P1 to P2 and Q1 to Q2 severally, supply staying same.

When supply curve additions from S1 to S2 so monetary value lessenings from P2 to P2 ‘ and measure additions from Q2 to Q2 ‘ conversely is besides true for both instances.

Supply agenda:

Graph depicted above besides has supply curve, which represents the sum of some goods that the manufacturer is willing and able to sell at assorted monetary values presuming ceteris paribus, that is presuming all determiners of supply other than the monetary value of goods in inquiry staying same. Under the premise of perfect competition, supply is determined by fringy cost, the houses will bring forth extra end product every bit long as cost of bring forthing an excess unit of end product is less than the monetary value they will have.

Demand agenda:

Graph depicted above besides has demand curve ; it represents the sum of some goods that the purchasers are willing and able to buy at assorted monetary values. Assuming all determiners of demand other than the monetary value of the good in inquiry, such as income, personal gustatory sensation, remain the same. Following the jurisprudence of demand that if the monetary value will diminish the buyer will purchase more goods, hence ever a downward sloping.


Elasticity refers to how strongly the measure supplied and demanded respond to assorted factors including monetary value and other determiners. It can besides be stated as the per centum alteration in one variable ( measure supplied or demanded ) to per centum alteration in causative variable in simple words it is step of comparative alterations, it is measured as per centum alteration in measure to the per centum alteration in monetary value.

If the measure demanded or supplied alteration by a larger per centum than the alteration in monetary value so the demand or supply is said to be elastic, conversely inelastic, in instance of zero snap that is no per centum alteration in measure supplied or demanded so supply is absolutely inelastic.

Here we model an oligopoly facing unsure demand in which each house chooses as its scheme a “ supply map ” associating its measure to its monetary value, by coercing each house ‘s supply map to be optimum against a scope of possible residuary demand curves.

There are two sorts of patterning which were used for taking a supply map that is

Cournot patterning in this theoretical account measure were fixed and monetary value was varied ( steep supply map )

Bertrand mold in this theoretical account measure were varied and monetary value was fixed ( horizontal supply map )

Further it has been analyzed that the house may accomplish higher net income by perpetrating to a supply map than by perpetrating to fixed monetary value or fixed measure, because a supply map allows better adaptability to the uncertainness [ 1 ] .

In this we develop a formal theoretical account of supply map competition in oligopoly under demand uncertainness, before a demand daze is realized, each house commits to a map stipulating the measure it will bring forth as a map of its monetary value. After the daze is realized, all markets clear: each house produces at the point on its supply map which intersects its accomplished residuary demand curve ( intersection of demand curve and supply map ) [ 1 ] .

An electricity market has its ain features which are different from other trade good markets, electricity can non be stored and its demand is about inelastic and varies with seasons and day-to-day conditions conditions. Supply of electricity besides varies with clip as a consequence of planned care and forced outages, old research has shown that bing electricity markets are non absolutely competitory and that generators have some market power.

Previous surveies refering the market power issues provide several indices, such as the Lerner index and HHI index to place the being of market power. The generators can exercise their market power in progress by taking into consideration both the available coevals capacity or entire supply and the demand degree. It is suggested that a demand supply ratio will bespeak such conditions. Once this status does be, generators might be able to strategically offer into market and harvest their excess net incomes in day-to-day trading. The term ‘market power ‘ refers to an ability of a house to raise monetary value above the competitory degree without a rapid loss of ability to sell. Similarly, market power is an ability to productively keep monetary values above competitory degree by curtailing end product above competitory degree.

There are two chief mechanisms, i.e. strategic command and capacity withholding by which bring forthing houses may exert market power in the widely used command based pool markets, both of these strive to coerce up the market glade monetary value. The cardinal factors that determine the extent of market power include provider ‘s concentration, demand snap and manner of competition.

In recent old ages many equilibrium theoretical accounts have been used in the analysis of strategic interaction between participants in an electricity market, including oligopoly theoretical accounts of Cournot, Betrand, Stackelberg, Supply map equilibrium ( SFE ) and Collusion. Among them the Cournot and SFE theoretical accounts are the most extensively used theoretical accounts for analysing pool- based electricity markets. The general SFE theoretical account was introduced by Klemperer and Meyer [ 1 ] and the first analyzed by Green and Newbery [ 2 ] , in which each house chooses as its scheme a “ supply map ” associating its measure to its monetary value. The consequence of three policies that could increase the sum of competition has been modeled in the electricity topographic point market in England and Wales through SFE attack [ 3 ] . The ( MPEC ) has been used to explicate the job of ciphering SFE in the presence of transmittal restraints [ 4 ] , it presents an analysis that estimates the monetary value of electricity dispatched and sold utilizing a closed house mathematical expression derived from the analytical construct of SFE. An illustration to compare Cournot and SFE theoretical accounts of command based electricity markets with and without transmittal restraints has been done and a presentation of the consequence by parameterization of SFE on the deliberate consequences has been shown [ 5 ] . A conjectured supply map ( CSF ) theoretical account of competition among power generators on a linearized District of Columbia web been presented in [ 6 ] . Coevolutionary Computation attack has been used to obtain close signifier solutions when practical issues in electricity market are considered such as non convexness and discontinuity of cost map and inter temporal programming of generators [ 7 ] . Another new attack has been presented utilizing agent based market simulation technique [ 8,9 ] .

The exercising of market power may be facilitated by some feature of electricity markets including inelastic demand, limited transmittal capacity, and the demands that supply and demand of the power systems must equilibrate continuously. A batch of work has been done on market power analysing different economic theoretical accounts ; a study of electricity market patterning particularly the equilibrium theoretical accounts has been presented. Non-cooperative game theoretical attacks such as the Cournot and SFE theoretical accounts are widely used for power market simulation. The electricity topographic point markets modeled by SFE and Cournot theoretical accounts have been extended to include contract markets in, the English electricity market is modeled by SFE theoretical account with a contract market, and the entry status of the contract market. It has been shown that competition in contract market could take the generators to sell contracts and increase their end products and besides hedge the topographic point market monetary value in England and Wales. Furthermore it proposes an asymmetric additive supply map equilibrium ( LSFE ) theoretical account to develop house ‘s optimum command schemes given their forward contracts and market power extenuation consequence of forward contracts have besides been evaluated [ 10 ] . To analyze the interaction between the topographic point market and forward markets, it is normally assumed that the Gencos are risk impersonal two colony electricity market with transmittal line restraints is studied and compared with a individual colony market. It is shown that topographic point market monetary values will diminish when the supplies enter frontward contracts.

Market Equilibrium: In ( fig.2.2 ) consumer and manufacturer excess has been shown when a market reaches equilibrium.

Fig.2.2. Consumer & A ; Producer surplus in market equilibrium

Consumer excess equals the country above the monetary value and under demand curve, where as Producer excess equals the below the monetary value and above supply curve. The entire country between the supply and demand up to the point of equilibrium represents the entire excess in the market. In ( fig.2.3 ) if the measure is less than the equilibrium measure such as Q1, the value to purchaser exceeds the cost to Sellerss.

Fig.2.3. Efficiency of equilibrium measure

If the measure is greater than equilibrium measure such as Q2, the cost to Sellerss exceeds the value to purchasers. Therefore, the market equilibrium maximizes the amount of manufacturer and consumer excess.

Offering Scheme:

Command schemes trades with set of programs taking to offering of a monetary value one is willing to pay for something so as to maximise its net income or carry through its demand. In electricity market command plays a critical function, where a set of supply maps are offered as commands by figure of Genco ‘s so as to run into the demand, consequently each Genco receives its net income by the usage of the construct of supply map equilibrium which helps them in doing their commands, by the usage of Two-settlement attack the sum of measure, monetary value and net income of each Genco can be obtained.

Previous researches on command schemes can be divided into three subdivisions.

Optimization theoretical account:

This theoretical account pays attending over a individual participant that is the participant under survey in which figure of mathematical scheduling theoretical accounts has been developed in this subdivision to happen optimum command scheme ; some of them are Fuzzed Linear Programming, Dynamic Programming, and Stochastic Dynamic Programming etc. The proposed command scheme like Markov Decision Process ( MDP ) in which effects of market portion and production bound has been discussed on optimum command scheme, peak/off-peak burden ; peak/off-peak monetary value has been used to cut down the figure of provinces [ 11 ] . It has been proposed so as to back up in determination devising for hedge and programming in power portfolio optimisation. In this theoretical account inputs such as electricity demand, electricity frontward monetary value, gas frontward monetary value and electricity topographic point monetary value are done through several stochastic procedures, the draw back in this theoretical account is that it does non pattern behavior facet of participants.

2.3.2 Game Theory Model:

In this theoretical account command schemes has been discussed which incorporates the characteristic of interaction between participants. The whole intent of this theoretical account is to analyse economic equilibria of the system hence frequently called as equilibrium theoretical account. The common interaction is represented by Game Theory. It is further divided into two areas- Concerted Game Theory and Non-cooperative Game Theory. In another theoretical account named, Stackelberg game assumes that the house with the largest market power can pull strings monetary values but houses holding less market power can non impact monetary values. This game can be modeled through mathematical plan with equilibrium restraints ( MPEC ) job [ 4 ] . There are more competitory theoretical accounts like Cournot and Bertrand but these theoretical accounts besides have a draw back as Cournot trades with fixed measure and variable monetary value and Bertrand trades with fixed monetary value and variable measure far different from existent market supply maps where both measure and monetary value can be varied, it gave rise to a much better theoretical account SFE which has been used in this undertaking work.

Agent and heuristic Model:

This theoretical account incorporates computing machine scientific discipline techniques to pattern human being intelligence to imitate optimum command schemes [ 12 ] , Genetic Algorithm based model has been proposed in a dual side auction market topographic point through Pascal linguistic communication [ 13 ] . Bidding scheme has besides been discussed in an evolutionary scheduling [ 14 ] . Simulation in Genco ‘s command has been analyzed and compared via pros and cons of familial algorithm, evolutionary scheduling and atom drove optimisation has discussed issues on patterning electricity market as Multi-Agent System ( MAS ) both practical and theoretical facets.

This full chapter dealt with the engagement of economic sciences in the electricity market, it proposes the constructs of supply and demand which is necessary in understanding the capable affair. It farther specifies market equilibrium conditions and travel on to discourse different command schemes which are taken up by gencos in the competitory market.

Now, the following chapter trades with SFE theoretical accounts which are utile in topographic point markets, this theoretical account has besides been incorporated in this undertaking work, a brief cognition of this construct has been discussed in this chapter itself.

Chapter 3


3.1 Reappraisal:

The general supply map equilibrium ( SFE ) theoretical account was introduced by Klemperer and Meyer and applied to the electricity industry reform in England & A ; Wales ( E & A ; W ) [ 1,2 ] . A additive SFE theoretical account has been used to measure the old market public presentation of ERCOT BES. A survey has been made on command scheme of market participants in ERCOT within the same period and showed that several major participants with largest market portion behave near to what a SFE predicts. These illustrations prove that SFE theoretical account is a valuable tool to imitate current electricity market. In SFE theoretical account, functional signifiers such as demand map, quadratic cost map, and additive supply map are specified. It is simpler to presume a additive demand map, quadratic cost map, and additive supply map. Assuming SFE with additive functional signifiers is more advantageous for analytical solubility.

Suppose there are Gencos ( providers ) in the electricity market where each Genco is risk impersonal and has a generator characterized by following cost map


and be the measure generated by genco ; and are the coefficients of the generator cost map, the fringy cost map of genco is as follows:

, where

When there is negligible transmittal loss the aggregative demand which is opposite of additive demand map will be equal to the entire end product of gencos ( market uncluttering status ) , that is ( 3.3 )

where is the topographic point market monetary value ; and coefficients of demand map and, where is the incline of system demand map.

Besides presuming that each genco command a additive increasing supply map, holding two strategic parametric quantities ; stop ( ) and incline ( ) where.

Supply map bided by genco be

In this undertaking work the affect of transmittal web has non been considered as a consequence the market glade monetary value is same for all gencos. Each genco changes its parametric quantities in signifier of intercept and incline so as to maximise its net income. Supply map equilibrium means that no genco can increase its net income by one-sidedly altering its command supply map.

3.2 Multiple Period SFE:

It is assumed that demand curve can see any random daze, which meant that the command map needed to be optimum for any realisation of the demand [ 1 ] . It is assumed that the command map is consistent across all clip periods. A individual period, individual market theoretical account restricts the flexibleness of command scheme compared to true flexibleness in these markets. A wholly different mentality has been proposed in which supply map is non assumed to be same across multiple pricing periods ; they can merely be changed by changing the intercept of the command map non their incline. The advantage of utilizing intercept as strategic parametric quantity is that it leads to a additive equation whose equilibrium can be easy proved in footings of being, uniqueness, and stableness.

In this study two-settlement game theoretical account has been used to explicate the two colony market dwelling of a topographic point market. The Linear Supply Function Equilibrium ( LSFE ) theoretical accounts have been used in topographic point market.

The optimisation job faced by each genco is to maximise its expected entire net income, where it is equal to

LSFE Model: Genco take part in the topographic point market by subjecting their commands in signifier of LSF, through different parameterization studied in [ 5 ] which can be represented as:

Different parameterizations of LSF are:

-parameterization in this the genco can take in ( 3.4 ) arbitrary but is required to stipulate a fixed, normally.

-parameterization in this the genco can take in ( 3.4 ) arbitrary but is required to stipulate a fixed, normally.

The optimum value of can be obtained by distinguishing ( 3.5 ) with regard to and utilizing equations ( 3.4 ) and ( 3.3 ) the undermentioned equation is obtained

By comparing above equation to zero optimum value of is obtained as [ 16 ]

3.3 SFE with Resource Constraint:

Sing its place in the fuel market genco makes a command determination in a twenty-four hours a caput type electricity market. At a peculiar twenty-four hours genco submits a series of command maps for the undermentioned T periods on the following twenty-four hours, there by maximising societal public assistance of ISO and its ain wage off. If transmission congestion is considered so market glade monetary value is non same for all gencos.

In this we are planing a theoretical account which is good to be analyzed in staying scheme with multiple period restraints, which genco face in the existent universe such as fuel stock list, energy bound group, volume of reservoir etc. Genco ‘s usually keep a portfolio of assets in both electricity and fuel markets, a individual market theoretical account badly restricts the flexibleness of command scheme compared to the true flexibleness in these markets.

The additive SFE theoretical account requires participants to repair a parametric quantity of command map in order to work out a alone equilibrium, the chief advantage to take incline as scheme parametric quantity is that most electricity markets worldwide allow genco to offer a different supply map at each period and the incline parameterization theoretical account can non be applied to multiple period state of affairs. Another cardinal advantage is that since intercept parameterization leads to a additive equation system, the being, uniqueness, and stableness of the equilibrium are easy to turn out, and a batch of computational troubles will be reduced compared to the incline parameterization theoretical account.

It is assumed that a genco makes offering determination in a twenty-four hours a caput type electricity market sing its place in a fuel market. The twenty-four hours a caput market construction is assumed to hold a unvarying non discriminatory pricing regulation. Every forenoon on twenty-four hours D, genco are required to subject a series of command maps for the undermentioned T periods on the following twenty-four hours D+1. After a market glade mechanism, ISO maximizes its societal public assistance. Each genco is informed of the market monetary values and awarded MW measures for every period “ T ” , so gencos can settle with ISO on their profits/ losingss for the following twenty-four hours.

Multiple clip command can be applied to two separate systems

1 ) the system that deals with individual genco multiple clip command, in this we use PIPA ( Penalty Interior Point Algorithm ) to work out for individual genco

2 ) the system in which multiple genco can be dealt harmonizing to different clip periods, this is the instance we are traveling to work out.

Fig.3.1. Two-level optimisation

The -parameters can be obtained through the equation, the derivation of this equation has been shown in the appendix.

Charter 4


To understand the proposed constructs a instance survey covering with 3 genco and 5 genco has been done. In this subdivision and, where is the intercept and is the incline of the reverse demand map. Here costate variable and mutual of fuel cost of genco has been provided as which is fixed for all gencos.

Here Table 1 nowadayss which denotes intercept of reverse demand map, incline of reverse demand map, reciprocal of fuel cost map, costate variable severally.

Table I

Constants for Gencos

( GWh )

( GWh/ ( $ /MWh ) )






Cost Coefficients of 3 Gencos

Genco no.




Cost parametric quantity ( $ /MWh )




Cost parametric quantity ( $ /MWh )




Table II trades with coefficients of cost map for 3 genco, where as Table III shows the simulation consequences for 3 genco, Table IV trades with coefficients of cost map for 5 genco and Table V shows the simulation consequences for 5 genco.

Strategic parametric quantities set up to single genco have been obtained utilizing the construct of multiple genco command scheme. Furthermore, power supplied, net income earned, and monetary value per MW has been obtained for single genco utilizing the construct of two-settlement theoretical account discussed above.

Costate variable proposed in this theoretical account are invariables, because fuel monetary value is estimated by the gencos before subjecting a set of commands in a multi period, twenty-four hours a caput market. The estimated forward monetary value does impact gencos command schemes. The impacts are represented by the parametric quantity which is included into.

Some of import observations can be made from the Table III and Table V, i.e. in their several instances the strategic parametric quantity of SFE obtained is about equal to other gencos offering strategic parametric quantity. It confirms that the electricity market proposed here is an oligopoly market holding few Numberss of big houses.

Table III

Simulation Results for 3 Genco

( $ /MWh )


( $ /MWh )


( $ /MWh )


( GWh )


( GWh )


( GWh )


1.0e+005 *1.4224

1.0e+005 *1.0296

1.0e+005 *0.7982

( $ /MWh )


Table Four

Cost Coefficients of 5 genco

genco no.






Cost parametric quantity ( $ /MWh )






Cost parametric quantity ( $ /MWh )






Table Volt

Simulation Results for 5 Genco

( $ /MWh )


( $ /MWh )


( $ /MWh )


( $ /MWh )


( $ /MWh )


( GWh )


( GWh )


( GWh )


( GWh )


( GWh )


1.0e+003 *1.9681

1.0e+003 *1.1696

1.0e+003 *3.0621

1.0e+003 *2.8649

1.0e+003 *1.1696

( $ /MWh )


Chapter 5


In this undertaking a proper SFE theoretical account has been discussed which can be applied to multiple period and multiple market state of affairs, compared to the incline parameterization the intercept parameterization require less computational attempts, furthermore genco ‘s determinations in both fuel and electricity market has been incorporated.

A Two-settlement attack has been successfully applied to find market equilibrium parametric quantities in signifier of monetary value, net income, power delivered by each of the genco. It has been found that the proposed attack is really effectual in finding the market equilibrium in all the instances. Simulation consequences further confirms that there is no consequence of forward contract in the intercept parameterization as inducements in intercept parameterization are zero. It has besides been justified from the simulation consequences that electricity market are oligopoly market consisting of few big houses as the strategic parametric quantities are really near to each other in both the instances of 3 genco and 5 genco.

Optimum command scheme is determined sing parametric quantities at peculiar clip. The parametric quantities so obtained depend on other rival genco determination at clip. It is noted that the work done employs the normally used premise of hazard neutrality on all gencos and sufficient arbiters in the market.

There could be a possibility to look into the command behaviours of gencos when the hazard antipathy for gencos is considered. The work may be extended by sing hazard direction in gencos determination affecting a portfolio of direction theory.


[ 1 ]

P. D. Klemperer and M. A. Meyer, “ Supply map equilibrium in oligopoly under uncertainness, ” Econometrica 57, pp. 1243-1277, 1989.

[ 2 ]

R. Green, D. M. Newbery, “ Competition in the British electricity topographic point market, ” J. Political Econ. 100, pp. 929-953, 1992.

[ 3 ]

R. Green, “ Increasing competition in the British electricity topographic point market, ” J. Ind. Econ. 44, pp. 205-216, 1996.

[ 4 ]

B. F. Hobbs, C. B. Metzler, and J. Pang, “ Strategic gambling analysis for electric power systems: an MPEC attack, ” IEEE Trans. Power Syst. , vol. 15, no. 2, pp. 638-645, 2000.

[ 5 ]

R. Baldick, “ Electricity market equilibrium theoretical accounts: The consequence of parametrization, ” IEEE Trans. Power Syst. , vol. 17, no. 4, pp. 1170-1176, 2002.

[ 6 ]

C. J. Day and B. F. Hobbs, “ Oligopolistic competition in power webs: A conjectured supply map attack, ” IEEE Trans. Power Syst. , vol. 17, no. 3, pp. 597-607, 2002.

[ 7 ]

H. Chen, K. P. Wong, D. H. M. Nguyen, and C. Y. Chung, “ Analyzing oligopolistic electricity market utilizing coevolutionary calculation, ” IEEE Trans. Power Syst. , vol. 21, no. 1, pp. 143-152, Feb. 2006.

[ 8 ]

D.W. Bunn and F. S. Oliveira, “ Agent-based simulation-an application to the new electricity trading agreements of England and Wales, ” IEEE Trans. Evol. Comput. , vol. 5, no. 5, pp. 493-503, 2001.

[ 9 ]

J. Nicolaisen, V. Petrov, and L. Tesfatsion, “ Market power and efficiency in a computational electricity market with prejudiced double-auction pricing, ” IEEE Trans. Evol. Comput. , vol. 5, no. 5, pp. 504-523, 2001.

[ 10 ]

H. Niu, R. Baldick, and G. D. Zhu, “ Supply map equilibrium command schemes with fixed forward contracts, ” IEEE Trans. Power Syst. , vol. 20, no. 4, pp. 1859-1867, Nov. 2005.

[ 11 ]

H. Song, C. C. Liu, and J. Lawarree, “ Optimum electricity supply command by Markov determination procedure, ” IEEE Trans. Power Syst. , vol. 15, no. 2, 2000.

[ 12 ]

T. Sueyoshi, and G. R. Tadiparthi, “ A sweeping power trading simulator with larning capablenesss, ” IEEE Trans. Power Syst. , vol. 20, no. 3, 2005.

[ 13 ]

C. W. Richter Jr. , G. B. Sheble, and D. Ashlock, “ Comprehensive command schemes with familial programming/finite province zombi, ” IEEE Trans. Power Syst. , vol. 14, no. 3, pp. 1207-1212, 1999.

[ 14 ]

G. Xiong, “ An evolutionary calculation for provider command scheme in electricity auction market, ” IEEE Power Eng. Soc. , pp. 83-88, 2002.

[ 15 ]

F. Gao and G. B. Sheble, “ Electricity Market Equilibrium Model with resource restraint and transmittal congestion, ” Electric Power Syst. Research 80, pp. 9-18, 2010.

[ 16 ]

S. X. Zhang, C. Y. Chung, K. P. Wong, and H.Chen, “ Analyzing Two-Settlement Electricity Market Equilibrium by Coevolutionary Computation Approach, ” IEEE Trans. Power Syst. , vol. 24, no. 4, pp. 1155-1164, 2009.