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Electric power bidding model for practical utility system
Alexandria Engineering Journal (2017) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Electric power bidding model for practical utility system M. Prabavathi *, R. Gnanadass Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pondicherry 605 014, India Received 21 March 2014; revised 26 September 2016; accepted 15 December 2016
KEYWORDS Bidding strategy; Day ahead electricity market; Market clearing price; Market clearing volume; Block bid; Intermediate value theorem
Abstract A competitive open market environment has been created due to the restructuring in the electricity market. In the new competitive market, mostly a centrally operated pool with a power exchange has been introduced to meet the offers from the competing suppliers with the bids of the customers. In such an open access environment, the formation of bidding strategy is one of the most challenging and important tasks for electricity participants to maximize their profit. To build bidding strategies for power suppliers and consumers in the restructured electricity market, a new mathematical framework is proposed in this paper. It is assumed that each participant submits several blocks of real power quantities along with their bidding prices. The effectiveness of the proposed method is tested on Indian Utility-62 bus system and IEEE-118 bus system. Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction The electricity industry around the world has been undergoing through a change from regulated to restructuring market structure and the government owned utilities have become privatized. In this environment, introduction of competitive energy market, unbundling electricity services and open access to the network have been created. In order to have the competitive market, market operator and policy makers need to study, analyze and monitor the behavior of market participants. In a competitive electricity market, both power suppliers and consumers are allowed to participate in the market. Due to limited number of power producers, long period of * Corresponding author. E-mail addresses: [email protected] (M. Prabavathi), [email protected] (R. Gnanadass). Peer review under responsibility of Faculty of Engineering, Alexandria University.
power plant construction, large size of capital investment, transmission constraints and transmission losses, the restructured power market behaves more like an imperfect competition. In such oligopolistic markets, an individual generator can exercise market power and manipulate the market price via its strategic bidding behavior and generating companies may achieve benefits by bidding at a price higher than their marginal production cost. This is called as a strategic bidding problem. In order to maximize the profit for suppliers and minimize the payments of customers, the building of bidding strategies is a major concern in the restructured power market because their profits depend on their bids. In recent years, a number of strategic bidding models have been proposed by many researchers. There are three main methods to model the strategic bidding problems based on the estimation of market clearing price, probability of rival’s bidding behavior and game theory approach [1]. The market clearing price (MCP) plays a significant role in the strategic bidding problem since it determines what blocks will be nom-
http://dx.doi.org/10.1016/j.aej.2016.12.002 1110-0168 Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
2 inated by the market clearing mechanism. The MCP is determined by the following process. In the competitive electricity market, the sellers submit the offers to sell the energy and the buyers submit the bids to buy the energy. After accepting the offers and bids from the sellers and buyers, the market operator ranks the selling offers with buying bids. The stacked supply curve for seller and demand curve for buyer are formed by market operator. The point of intersection of the two curves sets the MCP. The determination of market clearing price is main operating function for a market operator in energy trading market. Still now, a wide research work has been done on developing bidding strategies for generation side market participant only and little work on demand side participants. The problem of developing optimal bidding strategies for competitive generation companies was first introduced by David [2] and then surveyed by several researchers. Most of the researchers have used a linear bid function or quadratic bid function to build the bidding strategy for the electricity market participant. In [3,4], a linear bid function is assumed to build the bidding strategies for participant and the system is dispatched to maximize the social welfare. In [5], Market clearing price with and without wind power has been evaluated in double sided bidding for linear bid and block bid trading model. Using Graphical analysis, the MCP and schedules are determined under different market conditions in which quadratic bid function from both generating side and consumer side is considered [6]. In [7], a conceptual study is carried out on optimal bidding strategies of power suppliers in the operating Zhejiang provincial electricity market in which the step-wise bidding protocol is used. A normal probability distribution function is used to describe the bidding behaviors of rivals. The problem of building optimal bidding strategies for GENCOs is formulated as stochastic optimization problem which is solved by MonteCarlo simulation method and the optimal bidding block price of GENCO is searched by Genetic Algorithm. Based on the stepwise bidding protocol in electricity markets, the impact of different numbers of bidding segments on the bidding strategies of generation companies is calculated in [8]. The published research work regarding solution methodology for bidding strategies can be grouped as optimization method, game theory based and evolutionary based model. In [9,10], strategic bidding problem has been formulated as an optimization problem in which producers try to maximize their profit based on the market clearing price. An analytical formulation was developed for building the optimal bidding strategy in England and Wales type electricity markets under an assumption that the MCP is independent of the bid of any supplier [11]. Some mathematical programming models [12] such as linear and nonlinear integer programming models were established to build optimal building problem for power producers in day ahead electricity auction markets. In [13], the bidding decision problem is formulated for GENCO with considering risk management and unit commitment. Using Graphical analysis, MCP and schedules are determined under different market conditions in double sided auction [14]. Li et al. [15] have presented a mathematical model to find out MCP in the electricity markets. In [16], a strategic bidding procedure based on stochastic programming is decomposed using the Benders technique. Zou [17] has designed bidding strategy model to maximize social welfare in the spot market. In [18],
M. Prabavathi, R. Gnanadass the supply function models of various bidding strategies with forward contracts are employed to simulate the bidding strategy of suppliers in the power pool. An improved PSO algorithm is proposed to solve the optimal bidding problem for GENCO’s in a uniform price spot market [19]. Richter and Sheble have applied GA [20] and GP - Automata [21] to evolve appropriate bidding strategies in double auctions for electric utilities which trade electricity competitively. Strategic bidding has been addressed by many researchers for a wide variety of market players. Researchers utilized many different modeling approaches and different solution methods. By analyzing the strategic bidding behavior of generating companies, a specific MLNB decision model for day-ahead electricity markets is created in [22]. Soleymani [23] has proposed a new method that was the combination of PSO and simulated annealing to predict the bidding strategy of generating companies in an electricity market where they have incomplete information about their opponents and market mechanism of payment is pay as bid. In [24], discrete cosine transforms based neural network approach is used to classify the electricity markets of Mainland Spain and New York. Agent based simulation is employed to study the power market operation under different pricing methods in [25]. The JAVA based power trading simulator is proposed to find out the market clearing price in single sided auction market in [26]. For the price-maker hydro-electric producers bidding problem, the most recent developments and a path for future efforts are illuminated in [27]. Jain et al. [28] have developed an optimal bidding strategy for a supplier considering double sided bidding, rivals bidding behavior, and unconstrained and constrained market scenario. A number of strategic bidding models have been proposed by different researchers in recent years. In this paper, a mathematical model is developed for step bidding function for a day ahead market in the competitive environment. In most of the research work, a linear supply function model was presented to investigate strategic bidding behavior. However actual implementation of electricity markets requires the representation of supply offers and demand bids that aggregated into distinct steps. This paper presents mathematical model for stepwise bidding protocol for both supplier offer functions and customer bid functions of real power. Conventional method is used to solve this mathematical model for step bidding function. This proposed method is tested on Indian Utility-62 bus system and IEEE-118 bus system. The Indian Energy Exchange actually uses piecewise-linear bids that are strict functions from price to quantity. Bidders in practice use these functions almost exclusively to closely approximate step functions with constant quantities for a range of prices. In this paper, bids to be assumed of a true step form throughout and do not use the linear interpolation of the exchange. In the developing electricity markets, a suitable trading mechanism is required for all participants in order to achieve the profit. This paper employs conventional method to solve the bidding function of both suppliers and customers. The pricing mechanism in double side auction is uniform pricing method. The social welfare generated by the double auction will be improved greatly. The different case studies with block bids models are illustrated. It has been found that MCP may be higher when demand is increased. Case studies show that
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model such a structure allows all power market participants to empower with more information about the market settlement. This method is more consistent than other simulation model. This paper is organized as follows. Section 2 explains the mathematical formulation of the strategic bidding problem for double sided auction in a day ahead market. Section 3 describes the solution algorithm. Section 4 illustrates conceptual analysis for a practical utility system and results are presented. Conclusive remarks are given in Section 5. 2. Mathematical formulation To realize the economic dispatch, maximize the profits of suppliers and minimize the customer payments, it is very important to create reasonable matching rule for the electricity auction market. In a day ahead electricity market, every electricity supplier and customer submits bids to the power market for every hour. Market operator sorts bids of customers and suppliers by their price offers in descending and ascending order respectively and the customer with the highest bid price is first matched with the lowest offer price of supplier. For that, the aggregated hourly supply and demand bid curves are constructed from the offers and bids submitted by participants. The point of intersection between aggregated demand and supply curve sets the market clearing price (MCP). Every supplier whose offering price is below or equal to the MCP will be allowed to sell the electricity at that hour. Similarly every customer whose bidding price is above or equal to the MCP will be accepted to buy the energy. All accepted participants will be paid at the same clearing price for the electricity, but not the price offered. Thus a system dispatch levels are fixed by a market operator by making maximize the profit of suppliers and minimize the customer payments. In this paper, it is assumed that each participant (supplier and customer) in day ahead electricity market submits its own bid as pairs of price and quantity with several blocks. Stepwise bidding is considered. Mathematical model is developed for bidding function of suppliers and customers. The solution methodology is also proposed for this mathematical model. The plant ramping, transmission and system security constraints and reserve have been ignored. 2.1. Mathematical model for suppliers In a competitive electricity market, the participants can be allowed to bid their outputs and demands as blocks. The sales bid of suppliers are expressed in the following way. Suppose that a system consists of ‘m’ independent power suppliers. Each supplier is required to submit a block bid function. Each supplier has ki ði ¼ 1; 2; . . . ; mÞ blocks of power to sell which are arranged in ascending order of their cost of production as shown below. 8 psi1 ai0 6 q 6 ai1 ; > > > > > ai1 6 q 6 ai2 ; p > > < si2 p ai2 6 q 6 ai3 ; si3 ð1Þ Si ðqÞ ¼ > > . . . . .. >. . > . . . . > > > : psiki aiki 1 6 q 6 aiki ; i ¼ 1; 2; . . . m
3 where psi1 denotes offering price of first block for the ith supplier between the power quantity ai0 and ai1 . The electricity supply curve is upward sloping curve which can be obtained by summing of all net sales bids of suppliers. The cumulative blocks of power for all suppliers can be written as 8 ps1 a0 6 q 6 a1 ; > > > > > > ps2 a1 6 q 6 a2 ; > > > < SðqÞ ¼ ps3 a2 6 q 6 a3 ; ð2Þ > > > . . . . > .. . . .. .. > > > > > : psk ak1 6 q 6 ak where ps1 denotes offering price of first block for the ‘m’ suppliers between the power quantity a0 and a1 . Using Heaviside’s unit step function, these equations are expressed as a single equation and are given by the equation. SðqÞ ¼ ps1 þ ðps2 ps1 Þua1 ðqÞ þ ðps3 ps2 Þua2 ðqÞ þ þ ðpsk psk1 Þuak 1 ðqÞ
ð3Þ
2.2. Mathematical model for customers The demand bid of customers are expressed in the following way. Let there are ‘n’ independent customers and each customer has lj ; ðj ¼ 1; 2; . . . nÞ blocks of power to purchase the energy which is given by the equations. 8 pdi1 bj0 6 q 6 bj1 ; > > > > > > > > pdi2 bj1 6 q 6 bj2 ; > > < Dj ðqÞ ¼ pdi3 bj2 6 q 6 bj3 ; ð4Þ > > > . . . . >. .. . . .. > . > > > > > :p bjlj1 6 q 6 bjlj ; j ¼ 1; 2; . . . n djlj where pdj1 denotes offering price of first block for the jth customer between the power quantity bj0 and bj1 . The electricity demand curve is downward sloping curve which can be obtained by summing up of all purchase bids of customers. The cumulative blocks of power for all customers can be written as 8 pd1 b0 6 q 6 b1 ; > > > > > p b1 6 q 6 b2 ; > > < d2 p b2 6 q 6 b3 ; d3 DðqÞ ¼ ð5Þ > > . . . . .. >. . > > . . . . > > : pdl bl1 6 q 6 bl where pd1 indicates the bidding price of first block for ‘n’ customers between the power quantity b0 and b1 . Using Heaviside’s unit step function, these equations are expressed as a single equation and are given by the equation. DðqÞ ¼ pd1 þ ðpd2 pd1 Þub1 ðqÞ þ ðpd3 pd2 Þub2 ðqÞ þ þ ðpdl pdl1 Þubl 1 ðqÞ
ð6Þ
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
4
M. Prabavathi, R. Gnanadass Optimization models are involved with profit maximization problem for a single participant in electricity market. Equilibrium models represent the market behavior taking into consideration competition between all participants. Simulation models aim to model complexity of electricity market as collection of rule based agents interacting with one another dynamically. Optimization models generally focus on one specific market participant in system by simplifying rest of the system as a set of exogenous variables. It is well established by mathematical foundation and difficult to model complex and dynamic system. This model is used to describe the players in electricity market with the objective of finding optimal solution [29,30]. Equilibrium models represent the overall market behavior taking into consideration and competition among all participants. The approach assumes that each player in the market tries to maximize its profit. Hence performance of market participant is affected by other participant behaviors. All players are assumed to be rational which does not generally hold in reality. This model is developed with aim of improving economic efficiency [31,32]. Simulation models are an alternative to equilibrium models when the problem under consideration is too complex to be addressed within a formal equilibrium frame work. Only few simple rules are followed by various agents participated in the network and interacting with one another intelligently and dynamically. It is based on agents that allow developing models to represent in more realistic way electricity markets. But actual performance of the system is limited by mathematical or logical relationship foundation [33,34]. In this research work, conventional method is used to find the solution of supply and demand equation. Intermediate value property is used to solve this mathematical model of step bidding function. The solution for this mathematical function is found by equating aggregated suppliers function and aggregated customers function. The MCP of the system is obtained by the intersection of the aggregated supply curve and the aggregated demand curve. SðqÞ ¼ DðqÞ
Figure 1
Step by step algorithm.
2.3. Solution methodology Strategic bidding has been addressed in many research literature and different solution methods are proposed. From an organization point of view and according to bidding models for market participants’ behavior taking into account, electricity market modeling can be classified into three main areas:
ð7Þ
Eq. (7) is nothing but the solution of FðqÞ ¼ 0 where FðqÞ ¼ SðqÞ DðqÞ. The solution of FðqÞ ¼ 0 can be found by using intermediate value property. The intermediate value theorem was first proved by Bernard Bolzano [35]. This theorem states that let ‘a’, ‘b’ real numbers with a < b and let ‘f’ be a continuous function defined on the interval ½a; b to R such that fðaÞ < 0 and fðbÞ > 0. Then there is some number ‘c’ between ‘a’ and ‘b’ such that fðcÞ ¼ 0. According to this theorem, it is easy to see that, if we find two values qr and qr1 such that Fðqr ÞFðqr1 Þ < 0 (i.e. one value is positive and another one is negative) then there exists a ‘q’ which lies between qr and qr1 such that FðqÞ ¼ 0. The iteration process is used to find value of qr and qr1 such that Fðqr ÞFðqr1 Þ < 0. In this connection while finding the values of FðqÞ for q ¼ 0; 10; 20; 30; . . . at one stage we will have qr and qr1 such that Fðqr ÞFðqr1 Þ < 0. We note the value of ‘q’ at which the sign of FðqÞ changes. By intermediate value theorem we can find a ‘q’ in between qr and qr1 such that FðqÞ ¼ 0. The corresponding price for this ‘q’ is known as market clearing price.
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model
5
Figure 2
Table 1
Matching of aggregated suppliers and customers curve.
The effect of load variation.
Load demand
MCP (INR/MWh)
MCV (MW)
6200 6400 6000
2570 3000 2210
Base load Increase in load Decrease in load
ascending order of price from the 19 supplier’s offers and descending order of price from 29 consumer’s bids which is given in appendix. The supplier curve and customer curve are obtained and illustrated in Fig. 2. The point of intersection of two curves gives the market clearing price and corresponding quantity is called as market clearing volume. The market clearing price and transaction volume are given in Table 1. 4.1.2. The effect of load variation
In this paper, MCP for market participants in practical utility system is found by using step bidding function of suppliers and customers. MCP is set by the intersection of demand and supply at the market. In case of linear bidding, the exercise of market power creates an economic dead weight loss. It causes loss of benefit to society. In step bidding, the exercise of market power could not create an economic dead weight loss. This is the most efficient output because the exercise market power can be avoided. This paper also employs conventional method to solve this mathematical model. This proposed solution methodology gives unique solution. The optimal price and quantity occur at the intersection of supply curve and demand curve. This proposed method is an exact and efficient method. 3. Step by step algorithm The step by step procedure to evaluate market settlement in double auction electricity market is illustrated in Fig. 1. 4. Results and discussion Case 1 4.1. Indian Utility-62 bus system A case study has been carried on Indian Utility 62 bus system with 19 generators and 29 customers interconnected by 89 transmission lines [36]. The different case studies are analyzed in this section. 4.1.1. Base load condition In this case, under the base load condition the Market Clearing Price is determined. The bidding data are aggregated in
In this case the load is varied with 20% increase and decrease from the base case. For these loads, the consolidated offer curve for suppliers and bid curve for customers are obtained and given in Fig. 3. By comparing the graphs with those of base load, it can be observed that the demand curve shifts upward or downward when the load is increased or decreased from the base load. The market clearing price and clearing volume for each case are listed in Table 1. From the table, it can be clearly seen that when the load is 20% more than the base case the estimated market clearing price is higher than the base case and 20% less than the base case the expected market clearing price is less than the base case. The market clearing price and market clearing volume for various load conditions are given in Table 1. 4.1.3. MCP and MCV for various system demands The volume of system demand at various percentages is given in Fig. 4. In this case, the transaction of volume and market clearing price under different market conditions is obtained which is given in Fig. 5. The scheduling quantity of all 19 generators obtained by proposed method is shown in Fig. 6. After determining the market clearing price in base load condition, the offering price below and equal to MCP of suppliers is measured. For each offering price, the contributed generators and their clearing volume of each generator are given in Table 2. Case 2 4.2. IEEE-118 bus system This test case consists of 118-bus, 19 generators, 35 synchronous condensers, 177 lines, 9 transformers, and 91 loads. For this practical utility system, MCP is determined by assuming linear bid and as well as step bid function under base load conditions. Economic welfare between linear bid and step bid
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
6
M. Prabavathi, R. Gnanadass
Figure 3
Matching of aggregated suppliers and customers curve in different load conditions.
Figure 4
Figure 5
The volume of system demand.
MCP and MCV for different system demands.
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model
7
Clearing volume of each generator.
Figure 6
Table 2
Clearing volume of competitive generator.
Bid price (INR/MWh) 4000 4200 4500 5000 5300 5500 5700 6200
Contributed generators G1 G2 G1 G2 G3 G3 G3 G3
G3 G6 G3 G4 G6 G4 G5 G5
G9 G10 G10 G9 G7 G7 G8 G7
G14 G16 G14 G10 G11 G9 G10 G9
G18 – G17 G16 G17 G10 G13 G10
– – G18 G19 G18 G12 – G16
Clearing volume of generators (MW) – – – – G19 G15 – G19
Figure 7
– – – – – G19 – –
50 50 50 50 50 100 80 150
50 60 50 60 50 50 60 40
75 100 75 50 50 25 75 25
50 30 50 50 95 50 35 55
25 – 35 30 45 50 100 25
– – 30 95 25 80 – 30
– – – – 30 25 – 35
Total volume (MW) – – – – – 20 – –
250 240 290 335 345 400 350 360
Linear bid curve.
is also analyzed. We assume that each generator specifies an offer function is equal to its marginal cost. For base load condition, suppliers offer function and customers bid function are aggregated and illustrated. Figs. 7 and 8 show matching of aggregated suppliers and customers curve for linear bid and step bid function. Under base load conditions, MCP is found as 8100 INR/MWh.
An individual supplier can exercise market power and manipulate the market price via strategic bidding behavior. Each market participant will maximize their profit at a point where marginal revenue (MR) equals to marginal cost (MC). Since demand curve is downward sloping, profit maximization level of output (MR) lies below the demand curve. Because of this market produces less than socially output amount. It
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
8
M. Prabavathi, R. Gnanadass
Step bid curve.
Figure 8
Figure 9
Table 3
Dead weight loss.
Bidding block and simulation result of optimization based method [7]. Ref. [7]
GENCOs
Max. available capacity (MW)
Bidding block
MCP
I
II
III
$/MWh
200 200 200 200 200
200 200 200 200 200
200 200 200 200 200
49.99
Rival bidding block
800
800
800
Bidding price
10$
30$
50$
GENCO X R1 R2 R3 R4
600 600 600 600 600
causes dead weight loss. There is a loss in economic surplus within the market. Dead weight loss is the lined triangle shown in Fig. 9. In case of step bidding, the profit maximization output line (MR) is the same as the demand curve. Marginal revenue curve is the first order derivative of total revenue curve. Marginal revenue of step bidding function is the same as the total revenue function (i.e.) demand function. So marginal rev-
Dispatched amount (MW)
Benefit $
400
8698
enue curve lies on the demand curve, that is marginal revenue curve will be the same as the actual quantity demand curve illustrated in Fig. 8. Hence there is no dead weight loss on step bidding. Case 3 In this case, we compare the results of dispatched power of GENCOs and their surplus amount. Both participants (suppli-
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model Table 4
9
Bidding block and simulation result of proposed method. Proposed method
GENCOs
Max. available capacity (MW)
G1 G2 G3 G4 G5
600 600 600 600 600
Bidding block
Bidding price
MCP
I
II
III
IV
V
VI
I
II
III
IV
V
VI
100 100 200 150 100
100 150 200 150 150
100 150 200 100 150
100 100 – 100 200
100 100 – 100 –
100 – – – –
10 15 20 15 10
20 20 35 30 30
35 30 55 40 50
52 45 – 55 60
58 54 – 60 -
65 – – – -
ers and customers) are considered in our proposed method. The registered capacities of all five GENCOs are same as those of Ref. [7] (i.e.) 600 MW each. Each participant can bid at more than one block with different prices for each period in power market. The solution of the system is obtained by intermediate value property. The MCP of the system obtained using proposed method is same for all GENCOs (i.e.) 50 $. Table 4 gives the simulation results obtained by proposed method against those given in optimization based method [7]. Table 3 shows the values of dispatched power and benefit of GENCO X. The dispatched output for all GENCOs and their benefit are given in Table 4. It is seen that the dispatched level for each participant in each period is based on the bidding prices and load forecast. Profits of generation companies depend on their bidding strategies. This trading mechanism maximizes the total value of the transactions between the participants by making each customer maximize its savings and each supplier maximize its gains. 5. Conclusion In competitive electricity market, power suppliers and customers are required to bid stepwise bidding protocol function. For that a new mathematical model is proposed in this paper to build bidding strategies for power suppliers and customers in a day ahead electricity market. The solution methodology for the proposed mathematical model is also discussed. This methodology has been tested on Indian Utility-62 bus system and IEEE-118 bus system. The case studies are analyzed for different load conditions. References [1] A.K. David, F. Wen, Strategic bidding in competitive electricity markets: a literature survey, Proceedings of IEEE Power Engineering Society Summer Meeting, vol. 4, 2000, pp. 2168– 2173. [2] A.K. David, Competitive bidding in electricity supply, IEE Proc. Gener. Transm. Distrib. 140 (5) (1993) 421–426. [3] A.K. David, F. Wen, Optimal bidding strategies and modeling of imperfect information among competitive generators, IEEE Trans. Power Syst. 16 (1) (2001) 15–21. [4] J. Vijaya Kumar, D.M. Vinod Kumar, Optimal bidding strategy in an open electricity market using Genetic Algorithm, Int. J. Adv. Soft Comput. Appl. 3 (2011) 55–67. [5] S.N. Singh, I. Erlich, Strategies for wind power trading in competitive electricity markets, IEEE Trans. Energy Convers. 23 (2008) 249–256.
$/ MWh
50
Dispatched amount (MW)
Benefit
300 500 400 400 400
8500 9000 9000 9250 9500
$
[6] Tanay Joshi, Gagan Uberoi, Graphical scheme for determination of market clearing price using quadratic bid function, Int. J. Adv. Eng. Technol. 1 (2011) 144–150. [7] Li Ma, Wen Fushuan, A.K. David, A preliminary study on strategic bidding in electricity markets with step-wise bidding protocol, IEEE/PES on Transmission and Distribution Conference and Exhibition, Asia Pacific, vol. 3, Dover, 2002, pp. 1960–1965. [8] L. Wang, C.W. Yu, F.S. Wen, The impacts of different bidding segment numbers on bidding strategies of generation companies, Electr. Power Syst. Res. 78 (2008) 458–463. [9] D. Zhang, Y. Wang, P.B. Luh, Optimization based bidding strategies in the deregulated market, IEEE Trans. Power Syst. 15 (2000) 981–986. [10] J.D. Weber, T.J. Overbye, A two-level optimization problem for analysis of market bidding strategies, in: Proceedings of IEEE Power Engineering Society Summer Meeting, 1999, pp. 682–687. [11] G. Gross, D.J. Finlay, Optimal bidding strategies in competitive electricity markets, in: Proceedings of 12th Power Systems Computation Conference (PSCC-96), Dresden, 1996, pp. 815– 823. [12] Roy H. Kwon, Daniel Frances, Optimization-based bidding in day-ahead electricity auction markets: a review of models for power producers, Handbook of Networks in Power Systems I, Springer, Berlin Heidelberg, 2012, pp. 41–59. [13] Azmi Saleh, Takao Tsuji, Tsutomu Oyama, Optimal bidding strategies for generation companies in a day-ahead electricity market with risk management taken into account, Am. J. Eng. Appl. Sci. 2 (2009) 8–16. [14] S. Prabhakar Karthikeyan, Sathish K. Kumar, Y. Janakinadh, V.V. Raviteja, I. Jacob Raglend, P. Kothari, Determining market clearing price using graphical analysis - impact of loss as a case study, in: International Conference and Utility Exhibition on Power and Energy Systems: Issues & Prospects for Asia (ICUE), 2011, pp. 1–8. [15] Zuyi Li, Hossein Daneshi, Some observations on market clearing price and locational marginal price, IEEE Power Engineering Society General Meeting, vol. 2, 2005, pp. 2042– 2049. [16] Alvaro Baillo, Mariano Ventosa, M. Rivier, A. Ramos, Strategic bidding in a competitive electricity market: a decomposition approach, IEEE Power Tech Proc. 1 (2001) 8–13. [17] Xiaoyan Zou, Double-sided auction mechanism design in electricity based on maximizing social welfare, Energy Policy 37 (2009) 4231–4239. [18] Zhiqiang Yuan, Dong Liu, Chuanwen Jiang, Analysis of equilibrium about bidding strategy of suppliers with future contracts, Energy Convers. Manage. 48 (2007) 1016–1020. [19] Karim Afshar, Saeedeh Ahmadi, Nooshin Bigdeli, Bidding strategy based on improved particle swarm optimization algorithm for a generation company, International Conference on Power and Energy Systems, vol. 13, 2012, pp. 157–162.
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10 [20] C.W. Richter, G.B. Sheble, Genetic algorithm evolution of utility bidding strategies for the competitive market place, IEEE Trans. Power Syst. 15 (1998) 256–261. [21] C.W. Richter, G.B. Sheble, D. Ash lock, Comprehensive bidding strategies with genetic programming/finite state automata, IEEE Trans. Power Syst. 14 (1999) 1207–1212. [22] Guangquan Zhang, Guoli Zhang, Ya Gao, Jie Lu, Competitive strategic bidding optimization in electricity markets using bilevel programming and swarm technique, IEEE Trans. Power Syst. 58 (6) (2011). [23] S. Soleymani, Bidding strategy of generation companies using PSO combined with SA method in the pay as bid markets, Electr. Power Energy Syst. 33 (2011) 1272–1278. [24] S. Anbazhagan, N. Kumarappan, Day-ahead deregulated electricity market price classification using neural network input featured by DCT, Electr. Power Energy Syst. 37 (2012) 103–109. [25] Hossein Haghighat, Hossein Seifi, Ashkan RahimiKian, Pay-asbid versus marginal pricing: the role of suppliers strategic behaviour, Electr. Power Energy Syst. 42 (2012) 350–358. [26] Sumit Saroha, Amit Rathee, Rohit Verma, JAVA based power trading simulator in electricity market, Int. J. Comput. Appl. 44 (2012) 8–13. [27] Gregory Steeger, Luiz Augusto Barroso, Steffen Rebennack, Optimal bidding strategies for hydro-electric producers: a literature survey, IEEE Trans. Power Syst. 29 (4) (2014) 1758– 1766. [28] Arvind Kumar Jain, Suresh Chandra Srivastava, Sri Niwas Singh, Laxmi Srivastava, Bacteria foraging optimization based
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H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Electric power bidding model for practical utility system M. Prabavathi *, R. Gnanadass Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pondicherry 605 014, India Received 21 March 2014; revised 26 September 2016; accepted 15 December 2016
KEYWORDS Bidding strategy; Day ahead electricity market; Market clearing price; Market clearing volume; Block bid; Intermediate value theorem
Abstract A competitive open market environment has been created due to the restructuring in the electricity market. In the new competitive market, mostly a centrally operated pool with a power exchange has been introduced to meet the offers from the competing suppliers with the bids of the customers. In such an open access environment, the formation of bidding strategy is one of the most challenging and important tasks for electricity participants to maximize their profit. To build bidding strategies for power suppliers and consumers in the restructured electricity market, a new mathematical framework is proposed in this paper. It is assumed that each participant submits several blocks of real power quantities along with their bidding prices. The effectiveness of the proposed method is tested on Indian Utility-62 bus system and IEEE-118 bus system. Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction The electricity industry around the world has been undergoing through a change from regulated to restructuring market structure and the government owned utilities have become privatized. In this environment, introduction of competitive energy market, unbundling electricity services and open access to the network have been created. In order to have the competitive market, market operator and policy makers need to study, analyze and monitor the behavior of market participants. In a competitive electricity market, both power suppliers and consumers are allowed to participate in the market. Due to limited number of power producers, long period of * Corresponding author. E-mail addresses: [email protected] (M. Prabavathi), [email protected] (R. Gnanadass). Peer review under responsibility of Faculty of Engineering, Alexandria University.
power plant construction, large size of capital investment, transmission constraints and transmission losses, the restructured power market behaves more like an imperfect competition. In such oligopolistic markets, an individual generator can exercise market power and manipulate the market price via its strategic bidding behavior and generating companies may achieve benefits by bidding at a price higher than their marginal production cost. This is called as a strategic bidding problem. In order to maximize the profit for suppliers and minimize the payments of customers, the building of bidding strategies is a major concern in the restructured power market because their profits depend on their bids. In recent years, a number of strategic bidding models have been proposed by many researchers. There are three main methods to model the strategic bidding problems based on the estimation of market clearing price, probability of rival’s bidding behavior and game theory approach [1]. The market clearing price (MCP) plays a significant role in the strategic bidding problem since it determines what blocks will be nom-
http://dx.doi.org/10.1016/j.aej.2016.12.002 1110-0168 Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
2 inated by the market clearing mechanism. The MCP is determined by the following process. In the competitive electricity market, the sellers submit the offers to sell the energy and the buyers submit the bids to buy the energy. After accepting the offers and bids from the sellers and buyers, the market operator ranks the selling offers with buying bids. The stacked supply curve for seller and demand curve for buyer are formed by market operator. The point of intersection of the two curves sets the MCP. The determination of market clearing price is main operating function for a market operator in energy trading market. Still now, a wide research work has been done on developing bidding strategies for generation side market participant only and little work on demand side participants. The problem of developing optimal bidding strategies for competitive generation companies was first introduced by David [2] and then surveyed by several researchers. Most of the researchers have used a linear bid function or quadratic bid function to build the bidding strategy for the electricity market participant. In [3,4], a linear bid function is assumed to build the bidding strategies for participant and the system is dispatched to maximize the social welfare. In [5], Market clearing price with and without wind power has been evaluated in double sided bidding for linear bid and block bid trading model. Using Graphical analysis, the MCP and schedules are determined under different market conditions in which quadratic bid function from both generating side and consumer side is considered [6]. In [7], a conceptual study is carried out on optimal bidding strategies of power suppliers in the operating Zhejiang provincial electricity market in which the step-wise bidding protocol is used. A normal probability distribution function is used to describe the bidding behaviors of rivals. The problem of building optimal bidding strategies for GENCOs is formulated as stochastic optimization problem which is solved by MonteCarlo simulation method and the optimal bidding block price of GENCO is searched by Genetic Algorithm. Based on the stepwise bidding protocol in electricity markets, the impact of different numbers of bidding segments on the bidding strategies of generation companies is calculated in [8]. The published research work regarding solution methodology for bidding strategies can be grouped as optimization method, game theory based and evolutionary based model. In [9,10], strategic bidding problem has been formulated as an optimization problem in which producers try to maximize their profit based on the market clearing price. An analytical formulation was developed for building the optimal bidding strategy in England and Wales type electricity markets under an assumption that the MCP is independent of the bid of any supplier [11]. Some mathematical programming models [12] such as linear and nonlinear integer programming models were established to build optimal building problem for power producers in day ahead electricity auction markets. In [13], the bidding decision problem is formulated for GENCO with considering risk management and unit commitment. Using Graphical analysis, MCP and schedules are determined under different market conditions in double sided auction [14]. Li et al. [15] have presented a mathematical model to find out MCP in the electricity markets. In [16], a strategic bidding procedure based on stochastic programming is decomposed using the Benders technique. Zou [17] has designed bidding strategy model to maximize social welfare in the spot market. In [18],
M. Prabavathi, R. Gnanadass the supply function models of various bidding strategies with forward contracts are employed to simulate the bidding strategy of suppliers in the power pool. An improved PSO algorithm is proposed to solve the optimal bidding problem for GENCO’s in a uniform price spot market [19]. Richter and Sheble have applied GA [20] and GP - Automata [21] to evolve appropriate bidding strategies in double auctions for electric utilities which trade electricity competitively. Strategic bidding has been addressed by many researchers for a wide variety of market players. Researchers utilized many different modeling approaches and different solution methods. By analyzing the strategic bidding behavior of generating companies, a specific MLNB decision model for day-ahead electricity markets is created in [22]. Soleymani [23] has proposed a new method that was the combination of PSO and simulated annealing to predict the bidding strategy of generating companies in an electricity market where they have incomplete information about their opponents and market mechanism of payment is pay as bid. In [24], discrete cosine transforms based neural network approach is used to classify the electricity markets of Mainland Spain and New York. Agent based simulation is employed to study the power market operation under different pricing methods in [25]. The JAVA based power trading simulator is proposed to find out the market clearing price in single sided auction market in [26]. For the price-maker hydro-electric producers bidding problem, the most recent developments and a path for future efforts are illuminated in [27]. Jain et al. [28] have developed an optimal bidding strategy for a supplier considering double sided bidding, rivals bidding behavior, and unconstrained and constrained market scenario. A number of strategic bidding models have been proposed by different researchers in recent years. In this paper, a mathematical model is developed for step bidding function for a day ahead market in the competitive environment. In most of the research work, a linear supply function model was presented to investigate strategic bidding behavior. However actual implementation of electricity markets requires the representation of supply offers and demand bids that aggregated into distinct steps. This paper presents mathematical model for stepwise bidding protocol for both supplier offer functions and customer bid functions of real power. Conventional method is used to solve this mathematical model for step bidding function. This proposed method is tested on Indian Utility-62 bus system and IEEE-118 bus system. The Indian Energy Exchange actually uses piecewise-linear bids that are strict functions from price to quantity. Bidders in practice use these functions almost exclusively to closely approximate step functions with constant quantities for a range of prices. In this paper, bids to be assumed of a true step form throughout and do not use the linear interpolation of the exchange. In the developing electricity markets, a suitable trading mechanism is required for all participants in order to achieve the profit. This paper employs conventional method to solve the bidding function of both suppliers and customers. The pricing mechanism in double side auction is uniform pricing method. The social welfare generated by the double auction will be improved greatly. The different case studies with block bids models are illustrated. It has been found that MCP may be higher when demand is increased. Case studies show that
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model such a structure allows all power market participants to empower with more information about the market settlement. This method is more consistent than other simulation model. This paper is organized as follows. Section 2 explains the mathematical formulation of the strategic bidding problem for double sided auction in a day ahead market. Section 3 describes the solution algorithm. Section 4 illustrates conceptual analysis for a practical utility system and results are presented. Conclusive remarks are given in Section 5. 2. Mathematical formulation To realize the economic dispatch, maximize the profits of suppliers and minimize the customer payments, it is very important to create reasonable matching rule for the electricity auction market. In a day ahead electricity market, every electricity supplier and customer submits bids to the power market for every hour. Market operator sorts bids of customers and suppliers by their price offers in descending and ascending order respectively and the customer with the highest bid price is first matched with the lowest offer price of supplier. For that, the aggregated hourly supply and demand bid curves are constructed from the offers and bids submitted by participants. The point of intersection between aggregated demand and supply curve sets the market clearing price (MCP). Every supplier whose offering price is below or equal to the MCP will be allowed to sell the electricity at that hour. Similarly every customer whose bidding price is above or equal to the MCP will be accepted to buy the energy. All accepted participants will be paid at the same clearing price for the electricity, but not the price offered. Thus a system dispatch levels are fixed by a market operator by making maximize the profit of suppliers and minimize the customer payments. In this paper, it is assumed that each participant (supplier and customer) in day ahead electricity market submits its own bid as pairs of price and quantity with several blocks. Stepwise bidding is considered. Mathematical model is developed for bidding function of suppliers and customers. The solution methodology is also proposed for this mathematical model. The plant ramping, transmission and system security constraints and reserve have been ignored. 2.1. Mathematical model for suppliers In a competitive electricity market, the participants can be allowed to bid their outputs and demands as blocks. The sales bid of suppliers are expressed in the following way. Suppose that a system consists of ‘m’ independent power suppliers. Each supplier is required to submit a block bid function. Each supplier has ki ði ¼ 1; 2; . . . ; mÞ blocks of power to sell which are arranged in ascending order of their cost of production as shown below. 8 psi1 ai0 6 q 6 ai1 ; > > > > > ai1 6 q 6 ai2 ; p > > < si2 p ai2 6 q 6 ai3 ; si3 ð1Þ Si ðqÞ ¼ > > . . . . .. >. . > . . . . > > > : psiki aiki 1 6 q 6 aiki ; i ¼ 1; 2; . . . m
3 where psi1 denotes offering price of first block for the ith supplier between the power quantity ai0 and ai1 . The electricity supply curve is upward sloping curve which can be obtained by summing of all net sales bids of suppliers. The cumulative blocks of power for all suppliers can be written as 8 ps1 a0 6 q 6 a1 ; > > > > > > ps2 a1 6 q 6 a2 ; > > > < SðqÞ ¼ ps3 a2 6 q 6 a3 ; ð2Þ > > > . . . . > .. . . .. .. > > > > > : psk ak1 6 q 6 ak where ps1 denotes offering price of first block for the ‘m’ suppliers between the power quantity a0 and a1 . Using Heaviside’s unit step function, these equations are expressed as a single equation and are given by the equation. SðqÞ ¼ ps1 þ ðps2 ps1 Þua1 ðqÞ þ ðps3 ps2 Þua2 ðqÞ þ þ ðpsk psk1 Þuak 1 ðqÞ
ð3Þ
2.2. Mathematical model for customers The demand bid of customers are expressed in the following way. Let there are ‘n’ independent customers and each customer has lj ; ðj ¼ 1; 2; . . . nÞ blocks of power to purchase the energy which is given by the equations. 8 pdi1 bj0 6 q 6 bj1 ; > > > > > > > > pdi2 bj1 6 q 6 bj2 ; > > < Dj ðqÞ ¼ pdi3 bj2 6 q 6 bj3 ; ð4Þ > > > . . . . >. .. . . .. > . > > > > > :p bjlj1 6 q 6 bjlj ; j ¼ 1; 2; . . . n djlj where pdj1 denotes offering price of first block for the jth customer between the power quantity bj0 and bj1 . The electricity demand curve is downward sloping curve which can be obtained by summing up of all purchase bids of customers. The cumulative blocks of power for all customers can be written as 8 pd1 b0 6 q 6 b1 ; > > > > > p b1 6 q 6 b2 ; > > < d2 p b2 6 q 6 b3 ; d3 DðqÞ ¼ ð5Þ > > . . . . .. >. . > > . . . . > > : pdl bl1 6 q 6 bl where pd1 indicates the bidding price of first block for ‘n’ customers between the power quantity b0 and b1 . Using Heaviside’s unit step function, these equations are expressed as a single equation and are given by the equation. DðqÞ ¼ pd1 þ ðpd2 pd1 Þub1 ðqÞ þ ðpd3 pd2 Þub2 ðqÞ þ þ ðpdl pdl1 Þubl 1 ðqÞ
ð6Þ
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
4
M. Prabavathi, R. Gnanadass Optimization models are involved with profit maximization problem for a single participant in electricity market. Equilibrium models represent the market behavior taking into consideration competition between all participants. Simulation models aim to model complexity of electricity market as collection of rule based agents interacting with one another dynamically. Optimization models generally focus on one specific market participant in system by simplifying rest of the system as a set of exogenous variables. It is well established by mathematical foundation and difficult to model complex and dynamic system. This model is used to describe the players in electricity market with the objective of finding optimal solution [29,30]. Equilibrium models represent the overall market behavior taking into consideration and competition among all participants. The approach assumes that each player in the market tries to maximize its profit. Hence performance of market participant is affected by other participant behaviors. All players are assumed to be rational which does not generally hold in reality. This model is developed with aim of improving economic efficiency [31,32]. Simulation models are an alternative to equilibrium models when the problem under consideration is too complex to be addressed within a formal equilibrium frame work. Only few simple rules are followed by various agents participated in the network and interacting with one another intelligently and dynamically. It is based on agents that allow developing models to represent in more realistic way electricity markets. But actual performance of the system is limited by mathematical or logical relationship foundation [33,34]. In this research work, conventional method is used to find the solution of supply and demand equation. Intermediate value property is used to solve this mathematical model of step bidding function. The solution for this mathematical function is found by equating aggregated suppliers function and aggregated customers function. The MCP of the system is obtained by the intersection of the aggregated supply curve and the aggregated demand curve. SðqÞ ¼ DðqÞ
Figure 1
Step by step algorithm.
2.3. Solution methodology Strategic bidding has been addressed in many research literature and different solution methods are proposed. From an organization point of view and according to bidding models for market participants’ behavior taking into account, electricity market modeling can be classified into three main areas:
ð7Þ
Eq. (7) is nothing but the solution of FðqÞ ¼ 0 where FðqÞ ¼ SðqÞ DðqÞ. The solution of FðqÞ ¼ 0 can be found by using intermediate value property. The intermediate value theorem was first proved by Bernard Bolzano [35]. This theorem states that let ‘a’, ‘b’ real numbers with a < b and let ‘f’ be a continuous function defined on the interval ½a; b to R such that fðaÞ < 0 and fðbÞ > 0. Then there is some number ‘c’ between ‘a’ and ‘b’ such that fðcÞ ¼ 0. According to this theorem, it is easy to see that, if we find two values qr and qr1 such that Fðqr ÞFðqr1 Þ < 0 (i.e. one value is positive and another one is negative) then there exists a ‘q’ which lies between qr and qr1 such that FðqÞ ¼ 0. The iteration process is used to find value of qr and qr1 such that Fðqr ÞFðqr1 Þ < 0. In this connection while finding the values of FðqÞ for q ¼ 0; 10; 20; 30; . . . at one stage we will have qr and qr1 such that Fðqr ÞFðqr1 Þ < 0. We note the value of ‘q’ at which the sign of FðqÞ changes. By intermediate value theorem we can find a ‘q’ in between qr and qr1 such that FðqÞ ¼ 0. The corresponding price for this ‘q’ is known as market clearing price.
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model
5
Figure 2
Table 1
Matching of aggregated suppliers and customers curve.
The effect of load variation.
Load demand
MCP (INR/MWh)
MCV (MW)
6200 6400 6000
2570 3000 2210
Base load Increase in load Decrease in load
ascending order of price from the 19 supplier’s offers and descending order of price from 29 consumer’s bids which is given in appendix. The supplier curve and customer curve are obtained and illustrated in Fig. 2. The point of intersection of two curves gives the market clearing price and corresponding quantity is called as market clearing volume. The market clearing price and transaction volume are given in Table 1. 4.1.2. The effect of load variation
In this paper, MCP for market participants in practical utility system is found by using step bidding function of suppliers and customers. MCP is set by the intersection of demand and supply at the market. In case of linear bidding, the exercise of market power creates an economic dead weight loss. It causes loss of benefit to society. In step bidding, the exercise of market power could not create an economic dead weight loss. This is the most efficient output because the exercise market power can be avoided. This paper also employs conventional method to solve this mathematical model. This proposed solution methodology gives unique solution. The optimal price and quantity occur at the intersection of supply curve and demand curve. This proposed method is an exact and efficient method. 3. Step by step algorithm The step by step procedure to evaluate market settlement in double auction electricity market is illustrated in Fig. 1. 4. Results and discussion Case 1 4.1. Indian Utility-62 bus system A case study has been carried on Indian Utility 62 bus system with 19 generators and 29 customers interconnected by 89 transmission lines [36]. The different case studies are analyzed in this section. 4.1.1. Base load condition In this case, under the base load condition the Market Clearing Price is determined. The bidding data are aggregated in
In this case the load is varied with 20% increase and decrease from the base case. For these loads, the consolidated offer curve for suppliers and bid curve for customers are obtained and given in Fig. 3. By comparing the graphs with those of base load, it can be observed that the demand curve shifts upward or downward when the load is increased or decreased from the base load. The market clearing price and clearing volume for each case are listed in Table 1. From the table, it can be clearly seen that when the load is 20% more than the base case the estimated market clearing price is higher than the base case and 20% less than the base case the expected market clearing price is less than the base case. The market clearing price and market clearing volume for various load conditions are given in Table 1. 4.1.3. MCP and MCV for various system demands The volume of system demand at various percentages is given in Fig. 4. In this case, the transaction of volume and market clearing price under different market conditions is obtained which is given in Fig. 5. The scheduling quantity of all 19 generators obtained by proposed method is shown in Fig. 6. After determining the market clearing price in base load condition, the offering price below and equal to MCP of suppliers is measured. For each offering price, the contributed generators and their clearing volume of each generator are given in Table 2. Case 2 4.2. IEEE-118 bus system This test case consists of 118-bus, 19 generators, 35 synchronous condensers, 177 lines, 9 transformers, and 91 loads. For this practical utility system, MCP is determined by assuming linear bid and as well as step bid function under base load conditions. Economic welfare between linear bid and step bid
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6
M. Prabavathi, R. Gnanadass
Figure 3
Matching of aggregated suppliers and customers curve in different load conditions.
Figure 4
Figure 5
The volume of system demand.
MCP and MCV for different system demands.
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Electric power bidding model
7
Clearing volume of each generator.
Figure 6
Table 2
Clearing volume of competitive generator.
Bid price (INR/MWh) 4000 4200 4500 5000 5300 5500 5700 6200
Contributed generators G1 G2 G1 G2 G3 G3 G3 G3
G3 G6 G3 G4 G6 G4 G5 G5
G9 G10 G10 G9 G7 G7 G8 G7
G14 G16 G14 G10 G11 G9 G10 G9
G18 – G17 G16 G17 G10 G13 G10
– – G18 G19 G18 G12 – G16
Clearing volume of generators (MW) – – – – G19 G15 – G19
Figure 7
– – – – – G19 – –
50 50 50 50 50 100 80 150
50 60 50 60 50 50 60 40
75 100 75 50 50 25 75 25
50 30 50 50 95 50 35 55
25 – 35 30 45 50 100 25
– – 30 95 25 80 – 30
– – – – 30 25 – 35
Total volume (MW) – – – – – 20 – –
250 240 290 335 345 400 350 360
Linear bid curve.
is also analyzed. We assume that each generator specifies an offer function is equal to its marginal cost. For base load condition, suppliers offer function and customers bid function are aggregated and illustrated. Figs. 7 and 8 show matching of aggregated suppliers and customers curve for linear bid and step bid function. Under base load conditions, MCP is found as 8100 INR/MWh.
An individual supplier can exercise market power and manipulate the market price via strategic bidding behavior. Each market participant will maximize their profit at a point where marginal revenue (MR) equals to marginal cost (MC). Since demand curve is downward sloping, profit maximization level of output (MR) lies below the demand curve. Because of this market produces less than socially output amount. It
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8
M. Prabavathi, R. Gnanadass
Step bid curve.
Figure 8
Figure 9
Table 3
Dead weight loss.
Bidding block and simulation result of optimization based method [7]. Ref. [7]
GENCOs
Max. available capacity (MW)
Bidding block
MCP
I
II
III
$/MWh
200 200 200 200 200
200 200 200 200 200
200 200 200 200 200
49.99
Rival bidding block
800
800
800
Bidding price
10$
30$
50$
GENCO X R1 R2 R3 R4
600 600 600 600 600
causes dead weight loss. There is a loss in economic surplus within the market. Dead weight loss is the lined triangle shown in Fig. 9. In case of step bidding, the profit maximization output line (MR) is the same as the demand curve. Marginal revenue curve is the first order derivative of total revenue curve. Marginal revenue of step bidding function is the same as the total revenue function (i.e.) demand function. So marginal rev-
Dispatched amount (MW)
Benefit $
400
8698
enue curve lies on the demand curve, that is marginal revenue curve will be the same as the actual quantity demand curve illustrated in Fig. 8. Hence there is no dead weight loss on step bidding. Case 3 In this case, we compare the results of dispatched power of GENCOs and their surplus amount. Both participants (suppli-
Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002
Electric power bidding model Table 4
9
Bidding block and simulation result of proposed method. Proposed method
GENCOs
Max. available capacity (MW)
G1 G2 G3 G4 G5
600 600 600 600 600
Bidding block
Bidding price
MCP
I
II
III
IV
V
VI
I
II
III
IV
V
VI
100 100 200 150 100
100 150 200 150 150
100 150 200 100 150
100 100 – 100 200
100 100 – 100 –
100 – – – –
10 15 20 15 10
20 20 35 30 30
35 30 55 40 50
52 45 – 55 60
58 54 – 60 -
65 – – – -
ers and customers) are considered in our proposed method. The registered capacities of all five GENCOs are same as those of Ref. [7] (i.e.) 600 MW each. Each participant can bid at more than one block with different prices for each period in power market. The solution of the system is obtained by intermediate value property. The MCP of the system obtained using proposed method is same for all GENCOs (i.e.) 50 $. Table 4 gives the simulation results obtained by proposed method against those given in optimization based method [7]. Table 3 shows the values of dispatched power and benefit of GENCO X. The dispatched output for all GENCOs and their benefit are given in Table 4. It is seen that the dispatched level for each participant in each period is based on the bidding prices and load forecast. Profits of generation companies depend on their bidding strategies. This trading mechanism maximizes the total value of the transactions between the participants by making each customer maximize its savings and each supplier maximize its gains. 5. Conclusion In competitive electricity market, power suppliers and customers are required to bid stepwise bidding protocol function. For that a new mathematical model is proposed in this paper to build bidding strategies for power suppliers and customers in a day ahead electricity market. The solution methodology for the proposed mathematical model is also discussed. This methodology has been tested on Indian Utility-62 bus system and IEEE-118 bus system. The case studies are analyzed for different load conditions. References [1] A.K. David, F. Wen, Strategic bidding in competitive electricity markets: a literature survey, Proceedings of IEEE Power Engineering Society Summer Meeting, vol. 4, 2000, pp. 2168– 2173. [2] A.K. David, Competitive bidding in electricity supply, IEE Proc. Gener. Transm. Distrib. 140 (5) (1993) 421–426. [3] A.K. David, F. Wen, Optimal bidding strategies and modeling of imperfect information among competitive generators, IEEE Trans. Power Syst. 16 (1) (2001) 15–21. [4] J. Vijaya Kumar, D.M. Vinod Kumar, Optimal bidding strategy in an open electricity market using Genetic Algorithm, Int. J. Adv. Soft Comput. Appl. 3 (2011) 55–67. [5] S.N. Singh, I. Erlich, Strategies for wind power trading in competitive electricity markets, IEEE Trans. Energy Convers. 23 (2008) 249–256.
$/ MWh
50
Dispatched amount (MW)
Benefit
300 500 400 400 400
8500 9000 9000 9250 9500
$
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Please cite this article in press as: M. Prabavathi, R. Gnanadass, Electric power bidding model for practical utility system, Alexandria Eng. J. (2017), http://dx.doi. org/10.1016/j.aej.2016.12.002