The comparisons between pricing methods on pool ... - IEEE Xplore

2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DRPT2004) April 2004 Hong Kong

The Comparisons Between Pricing Methods On Pool-Based Electricity Market using Agent-Based simulation

Zou Bin',' IEEE member Yan maosong'

Xie Xianya'

1.

Shanghai University, Automation department, Shanghai China, 200072

2.

Southem Yangtze University, electric engineering laboratory, Wuxi China, 2 1'4036, room for a power supplier to raise the market price by his strategic bidding and he is induced to bid in accordance with his cost and the market becomes robust in some sense. And also EVE provides an intrinsic and reasonable mechanism to compensate the capacity investment automatically. This paper is organized as follows. The notations are arranged in section 2, the simulation model is described in section 3, and the simulation result is reported in section 4. Finally, the market characteristics of the various pricing methods are summarized in section 5.

Abstract: Because of the existences of market power and economies of scale, there have been various pricing methods proposed for pool-based electricity market, for example, uniform clearing pricing method (UCP), pay as bid pricing (PAB) and the Electricity Value Equivalent (EVE) pricing method. An agent-based simulation model is developed in this paper to compare the market characteristics under different pricing methods. In this model the generators leam bidding strategy using reinforced leaming algorithm in repeated bidding game to seek for their maximum profits. Simulation result is presented based on the data from IEEE Reliability Test System, showing that the EVE pricing method has many market characteristics better than other pricing methods. For example, when EVE is used in market pricing, there exists little room for a power supplier to raise the market price by his strategic bidding and the market becomes robust in some sense. And also EVE provides an intrinsic and reasonable mechanism to compensate the capacity investment automatically. Key Word: Pool-based electricity market pricing method agent-based simulation

2.

Notations

A the action set of the unit

[AI

the elements number of the action set

B,, the quotation of the m-th unit of firm i K the number of the block in units' quotation

KIlePthe normal coefficient, equal to 20-100.

M , the unit number of the firm i &,j(n)

1.

Introduction The marginal cost pricing methods, such as those of uniform clearing pricing (UCP) and node pricing prevail in electricity auction. Despite that microeconomics tell us that the perfect competitive market would achieve the equilibrium that is Pareto efficient under the conditions that films' production function is convex, continuous and their profits are bounded below from zero ['I, the actual electricity market, however, tends to be characterized by an oligopoly of generators ['I. Besides, there is very little demand-side elasticity in the short term, and the economies of scale do not vanish. In the various national electricity markets, the generators' market power persecutes the power pool and the reserve margin has continually declined because of uncertainties about cost recovery for new generation investment [31[41. So new pricing methods have been proposed to overcome these problems, for instance, the discrimination method----pay as bid (PAB), which was expected to restrain the generators' market power. And in China the electricity value equivalent (EVE) pricing methods [51-[71 have been developed to improve market efficiency, to adequately and reasonably retum investment and to adequately and reasonably restrain the price peak in pool-based market. There are various game models to discuss the generators' strategic behavior in electricity market [81-['41. But conventional economic modeling approaches have shown a very limited ability in dealing with electricity auction, especially when PAB or EVE are employed as pricing method in the market. It is obviously important to provide concrete evidences to forecast the market characteristic before the pricing rules are put in use in practice. In this paper, agent-based simulation method is employed to estimate the market price and generators' strategic behavior in pool-based electricity market for various pricing method, such as UCP, PAB and EVE. In this simulation method the agents and the market clearing mechanisms, together with the reinforced leaming algorithm used by the agents provide a computational framework to estimate the equilibrium price. A simulation result based on the data of IEEE Reliability Test System ["I is presented, which shows that the EVE pricing method has many market characteristics better than others. For example, when EVE is used in market pricing, there exists little 0-7803-8237-4/04/$17.0002004IEEE

the choice probability of the m-th unit of firm i to

select action j in n round q,,(n) the propensity of the m-th unit of firm

i

in n round

the production energy of the m-th unit of firm i

Q,,, R, leaming excitement of the firm i

R,,,, leaming excitement of the m-th unit of firm i

&''

the k -th capacity block's capacity in the quotation of the m-th unit of firm i x,,"" the total capacity of the k -th capacity block's capacity in the quotation of the m-th unit of firm i x,,.,~ the purchased capacity of the k -th capacity block's capacity in the quotation of the m-th unit of firm i x:, the k -th capacity block's capacity in the cost based bid of the m-th unit of firm i ai,,pi,,yim the coefficient of the quadratic cost function of the m-th unit of firm i bid

, k = 1,2,...,K

the k -th capacity block's price in the

quotation of the m-th unit of firm i P,",,~ the purchased price of the k -th capacity block in the

quotation of the m-th unit of firm i the k -th capacity block's price in the cost based bid of the m-th unit of firm i the k -th capacity block's shadow capacity value of the m-th unit of firm i the k -th capacity block's capacity value of the m-th unit offirm i n, the profit of the firm i , : : I

-

n, the average profit of the firm i over all round

The electricity auction models in agent-based simulation 3.1 simulation frame In day-ahead electricity auction, the system operator is the unique one buyer, and he forecasts the next day load demand. 3.

285

2004 JEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DRPT2004) April 2004 Hong Kong

Generator's firms bid their selling price for each unit, together with their capacity. Each unit's capacity can be divided into several blocks. These blocks' biding prices can be different, but the prices must ascend accordingly as capacity increasing. The quotation of the m -th unit of firm i can be expressed as: ( 1.1 4, = {(x ,Pid, (X$? P:::2 ' ' ' ,( X Z P& )}

1

1

y

7

p:;:) I p y 2 I ...I pi$

( 1.2)

K

CX,"?.k

5X

( 1.3 1

Z

k=l

Suppose the unit's cost function can be written as quadratic function, it is Cm (Qzm

I=

a;mQfn + Pim ' Qim + ~

i

(2.1)

m

K Qim

(2.2)

=C X i m . k k=l

and it can be expressed as discrete formulation, named cost-based bid, it is: (3.1 B,:?' = x:', ( ~ 2 ~2:; : ; ~ ,(p:mOyL1 .:m":i )}

{b:mOy,,' 1

1

t..

The relationship between actual bids with cost based bid is (4.1)

PKk = P:m"?j+

X K k =x:; (4.2) The aim of generators firm's strategy is to select for each unit the different price A P , ~from the action set A to seek for their maximal profits. The action set is A={AP,,AP~,-,AP,} (5) 0 E A is essential that means biding by cost. Though each unit has it own cost function it is acceptable to suppose that all units have the same action set A , because the action means the difference between price with the cost. The profit of the firm i 's m -th unit is

The firm i seeks for his maximum total profits, that is el ectri c i t y aucti on si ml ati on

I

A i n i t i a l i z e the choice probability i t e r a t i v e nuher$)

with their choice probability, and

Glculate price and firm'

profits

out cone accor di ng t o the pr i ci ng mt hod F i r m uses t h i s p r o f i t t o update the new choice probability f w the next round

c

I

s Iterat i ve nuntoer add 1

I

I t erati ve nunber i s over?

Figure 1 the simulation flow chart

286

M,

max

=I

=

-pd

(7)

",=I

In (6), the actual selling prices are determined by pricing method and all units' bids. In this paper we investigate three pricing methods, UCP, PAB and EVE, which will be discussed in section 2.2. It is obvious that all the optimization problems (7) of each firm and the pricing method compose a game. Solving the game by optimization method is difficult, especially when PAB or EVE is used as the pricing method. In agent-based simulation, the firm select Ap,,,, from the And the action set according to a choice probability, 4m,s. choice probabilities are updated according to firm's profit obtained by the action s through reinforced learning (this will be discussed in section 2.3). Figure 1 shows the simulation flow chart. At the beginning of the first round of the auction, each unit assigns a uniform probability to each possible action among the action set. Then it chooses the action from the action set by its probability, and forms the quotation according to (1)-(4). At the end of the auction round, each unit then calculate and update the choice probabilities for the next round according to the profit obtained in last round. The choice probability will converge to equilibrium position along with the repeated auction, if the learning is rational enough. 3.2 Clearing mechanism The uniform clearing pricing method is well known. After firms submitting their units' bid, system operator arranges the capacity blocks in the order of their bidding prices, then purchases the blocks from the cheapest one until the sum of the purchased capacities equals the load demand. The last capacity block's price is the marginal price, and all purchased capacities are paid off by marginal price. The clearing mechanism of the pay as bid pricing method is similar to that of uniform clearing pricing method, except that all purchased capacities are paid off by their bidding price, rather than the marginal price. In UCP and PAB auction, the daily load demand is expressed by load level in time sequence, and in each period of time, the generator firms should submit their bids. In EVE auction, however, things are different. Comparing with UCP and PAB, the basic concept of EVE has the following specialties (see [5]-[7] for details): 1, Any unit only submits its bid once a day, including number of blocks and their capacity sizes as well as their operational costs. 2 , The daily load demands is expressed in load duration curve, based on which the system operator (SO) arranges all the bids in merit loading order and then determines which blocks with how many hours are to be purchased. 3, According to the Capacity Cost Reference Systems (CCRS), which are given by the govemment and composed by sets of reasonable average capacity cost and corresponding average operational cost, the SO determines for each purchased block the purchase price, which consists in two parts: one corresponds to the operational cost, which is equal to the bidding price of this block, and another is corresponding to the shadow capacity cost and employed time interval of this block, which is to be used to compensate the capacity investment. Another important role played by CCRS is to restrain the skyrocket of the price (price peak) in the case of high load demand. It is obvious that under the condition of identical distribution of the bids, the purchased capacity will be the same in all the three pricing method, but their payments will not be identical, The total payment in PAB auction seems the lowest, and the highest seems that in EVE auction. But it cannot be confirmed that the (average) market price in PAB auction is the lowest, because the pricing rule will result in specific agent behavior and the market status. This must be investigated in the equilibrium status.

2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DRPT2004) April 2004 Hong Kong

Table 1 the generator type, the cost function and bidding based on cost cost based bid

cost function

2;

capacity MW a.1000 unit

block 1

P'lOO

~1

~2

capacity

U400

400

0.0039

3.4459

0

1.2

U350

350

0.013

2.9841

0

0.98

U197

197

0.0199

3.0645

0

0.47

68.95

U155

155

0.022

3.039

0

0.31

54.25

U100

100

0.0477

3.0014

0

0.17

U76

76

0.1227

3.2743

0

0.11

U20

20

1.3816

0.1651

0

0.02

U12

12

0.6266

3.5997

0

0.01

block 2

price

block 3

block 4

capacity

pricc

capacity

price

capacity

MW

$/kWh

MW

$kwh

MW

price $kwb

200

0.036

320

0.037

400

0.0335

227.5

0.0357

280

0.0371

350

0.0389

0.0334

118.2

0.0353

157.6

0.0369

197

0.0385

0.0376

0.0328

93

0.0345

124

0.0359

155

0.0372

0.0324

50

0.0348

80

0.0376

100

0.0396

15.2

0.0365

38

0.0421

60.8

0.0477

76

0.0514

15.8

0.0453

I8

0.0514

19.8

0.0564

20

0.0569

nnw

6

0.0435

9.6

0.048

12

0.051

Do j=1 t o S

I

3.3 Reinforced leaming algorithm The reinforced leaming algorithm applied in this paper was developed in [I61 and [ 171, which was shown to be able to seek the unique equilibrium over a wide variety of multi-agent repeated games. The key idea is the 'law of effect principle' that has been widely accepted in the psychological learning literatures. For the aspect of the calculation, the action's result (profit) is used to form the excitement for leaming, and the learning excitement was employed to calculate the propensity, then the choice probability was updated by the propensity. At the beginning of the first round of the repeated game, the choice probability is uniform, and can be written as

Calculating the new choice probability by (14)

1

I 4.

Casestudy In this section, the results based on the IEEE-RTS data are to be reported. Table 1 is the unit type in the system, the coefficients of their cost functions, and cost based bid. Note the coefficient of the quadratic cost function, y . For which there are 2 cases: the one y l is zero that ensures the marginal cost being always bigger than the average price which implies no economies of scale in this case, and the other y 2 is a positive number that means the marginal cost may be less than the

At the nth round, after the firm's profit is obtained by (6), then his leaming excitement can be calculated by 8 =.,-? (9)

022

I

I

,

,

I

,

I

I

I

I

02 0 18

.

-

016-

Because M,units are in possession of the firm i , the learning excitement must be assigned to each unit in the light of the units' capacity, that is

E

01-

\the

Suppose the selected action of unit im at the nth round is s, then the propensity of the action among the action set is

q,,",j ( n + 1) =

.IR,,nl.