In particular, if (A, u)is the optimal Lagrange multipliers the profits I (Bi, A'(i), u(Bi))of bidder i are equal to the revenues less the costs incurred with 中(2’D,B)=max{4(△;D,B):AH≥0}(1) I(G;'G),()=∑()+(, then, L(DP)全中(A,D,R) c(p:)-c(r:H)(1-t:-)u (15) The optimal bidding strategy calls for the maximization of provides a tighter lower bound on the optimal cost P(D, R)of I(Bi, A(Bi), u(B ) )over the set of admissible bids, i.e the primal problem P(D,R)≥L(D,R) b(),b(),g (c(p)+c(rt-1)(1 As a by-product of the process of maximizing P(A,A; D,R), we obtain the optimal Lagrange multipliers 2 and A:(B)p; t-i(o)ri t ]ui, t system schedule >=fy, p,r) resulting from the solution to the Lagrangian relaxation for A= a.and u= u.The bEClp?m,P1,6;ec[, oo),:20(16) given in Equation(3),i.e, >i=ui,P,ti]en (ai )for all i 1, M. In certain cases, does satisfy the demand and re- serve constraints making it feasible for the primal problem. If in addition,> satisfies the complementary slackness condi- 卫;r ∑()+(4-)(1-;-)-A(B) ∑=∑ the optimal schedule to the primal probler 9]. Practical approaches for computing a near-optimal sched- (1)r;wt:{u;;ren()} (17) ule have been developed [7].[8]. For all practical purposes the with a (gi )as defined in equation(4) difference between 2 and the near optimal schedule >"is We next introduce the assumption of perfect competition in assumed to be negligible. Moreover we also assume that the the CEM. Under such a condition, no single bidder may affect optimal Lagrange multiplier A'(u*), associated with demand prices and is consequently a price taker. In other words, any (reserve)in time period t, differs negligibly from the marginal change in the bid submitted by bidder i will have a small effect price(reserve price)in the same period on the prices determined by the CEMP. Formally, we state the Strategic Bid Formulation ny bidder has a negligible effect on the system marginal and reserve prices We use the CEM framework to solve the bidder's problem: This assumption holds when ne bidder controls a signifi. formulation of a bidding strategy to earn maximum profit. We cant portion of the total CEM tion and capacity. The nsider the problem of bidder i who submits bid Bi. For market price is determined by ds of the set of competing dder i, the bids Pi,j=1, 2. 1,i+1,.,M of the other bidders. From the viewpoint of bidder i, the market clearing bidders are fired but unknown. The CEMP determines the prices are independent of Bi so that optimal system price pair('A), the optimal system schedule X'(日)=2°and'()= (18) The prices depend on the bid of all generators in the CEM, B,, j=1,.M. However, bidder i It is convenient to define the loss function A2-II and re- place equation(16)by the 4.(Bi). The dependence of 2 on the bid B: is of Ai. We restate the problem relaxation of the CEMP b(),b(),g ∑c!()+(1-n-)- b!(p;)+b(r,t)( 1)-A:(B -r:bCpm,n],eC,∞),a;≥0}(19) Li,P: ri where ui,p*r i minimizes the proble where the set ni (a )is a defined in equation(4).The bidder generation costs incurred in c!()u;+c(r-)(1 u;t-1)u,. We use cf((c1(]to denote the fuel and variable operations and maintenance costs(start-up costs]of unit i. We Given the structural similarity between the minimizations in sume both functions to be continuous. The total costs of unit equations(19)and(20)we make use of the [e(p2)+c(r-1)(1 paid to generato time period is Ai(Pi)per MWh of 1 In effect collaboration among bidders, i. e,gener- tors behave noncooperatively and there is ergy and ui(P:)per MW of no cartel of generators re served. It follows that who act together to set prices