model whose slope and intercept of the bidding curve vary with the same scale is employed to analyze the bidding strategy of suppliers, where the influence of contracts for difference CFDs [7] (CFDs means that if the spot price rises above the strike price, which is the price level at vz,LF=s2
which the contract can be called, suppliers compensate retailers for the difference, but if the spot price falls below the strike price, then the retailers compensate suppliers for the difference) on market equilibrium is considered. In Ref. [8], the concept of virtual rival and the method of parameter estimation are introduced to study the bidding strategy of suppliers based on game theory, where the slope and intercept of the bidding curve is also assumed to vary with the same scale. vz,LF=s2
Forward contracts are one of the efficient means for risk management, and it is applied in the power market of many countries. The power pool will plan the electricity of suppliers according to the market rules, the bidding price of suppliers and forward contracts while there are forward vz,LF=s2
contracts between suppliers and buyers. The bidding strategy of suppliers will vary with the forward contracts to achieve maximum profit. In this paper, a supply function model is used to simulate the bidding strategy of suppliers in a power pool. Firstly, a supply function model with forward vz,LF=s2
contracts is presented. Accordingly, it is proved that only one of the parameters between the slope and intercept of the bidding curve can be strategy variable in order to achieve definite equilibrium (the Nash equilibrium is a strategy profile in which each player’s part is as good a response to what the others are meant to do as any other strategy available to that player [9]). Secondly, the equilibria of the market are studied when different intercepts of the bidding curve are chosen. Finally, the effect of different future contracts on the equilibrium strategies of suppliers in various bidding strategy models is analyzed. Besides, the bidding strategies are also studied while generation constraints are active. vz,LF=s2
2. Supply function equilibrium model with forward contracts vz,LF=s2
It is supposed that the inverse demand function is a linear function, that is vz,LF=s2
(1) vz,LF=s2
where p is market price, r and s are the intercept and slope of the inverse demand function, respectively, is the generation of the supplier i and N is the number of suppliers. Eq. (1) can be transformed into the electricity demand function, vz,LF=s2
(2) vz,LF=s2
, vz,LF=s2
The bidding curve of the supplier is assumed as a linear function, vz,LF=s2
(3) vz,LF=s2
where and are the intercept and slope of the bidding curve, respectively, both of which are larger than zero, and i = 1,. . . ,N. vz,LF=s2
The electricity price is assumed to clear at the uniform price in the power pool, and then, the generations of the suppliers are calculated according to Eqs. (2) and (3). vz,LF=s2
If the forward contracts is while the dealing price is , the equilibrium state of the suppliers can be obtained by maximizing an individual profit function of each supplier. vz,LF=s2
vz,LF=s2
(i=1……N) (4) vz,LF=s2
vz,LF=s2
Without loss of generality, the cost function of a supplier is assumed to be a quadratic function of active power generation. That is: vz,LF=s2
vz,LF=s2
Then, the generation of supplier i is vz,LF=s2
vz,LF=s2
Correspondingly, the system marginal price is vz,LF=s2