Incorporated Multi-Stage Nash Equilibriums for the Generation Allocation Problem Considering Ramp Rate Effects

This paper presents a novel method to find the profit-maximizing Nash equilibriums in allocating generation amounts with consideration of ramp-rates under competitive market environment. In order to find the Nash equilibriums it is necessary to search all the feasible combinations of generators´ outputs which satisfy various constraints. The procedure to eliminate the dominated strategies can be formulated using Bellman´s optimality principle of dynamic programming problem and hence the backward or forward search algorithm of dynamic programming can be easily applied. Therefore, the Nash equilibriums are found using dynamic programming method and we found that there exist several Nash equilibriums in the generation allocation problem. Individual generators participate in a game to maximize its profit through competitions and play aa game with bidding strategies of its generation quantities in a spot market. The ramp-rate physically or technically limits generators to increase or decrease outputs in its range and restricts the number of bidding strategies of each generator. We suggest the dynamic programming to find the Nash equilibriums while removing the dominated strategies in each stage (or each time). In the case studies, we analyzed the generation allocation game for a 12-hour multi-stage and compared it with the results of dynamic economic dispatch. Both of the two cases were considered generator´s ramp-rate effects.