Interior-point linear programming algorithm for auction methods

Interior-point programming (IP) has been applied to many power system problems because of its efficiency for big problems. This paper illustrates application of interior-point linear programming (IPLP) to auction methods. An extended algorithm of IPLP is developed and used in this paper. This extended IPLP algorithm can find the exact optimal solution (i.e., exact optimal vertex) and can recover the optimal basis. Sensitivity analysis can be performed after the optimal basis is found. The sensitivity analysis performed in this paper is increase in the bid price and increase in the flow limit of the transmission line. This extended algorithm is expanded from the affine-scaling primal algorithm. The concept used in this extended algorithm to find the optimal vertex and optimal basis is simple     

Auction implementation problems using Lagrangian relaxation

Lagrangian relaxation (LR) is used as an auction method for bidding in a deregulated environment. This paper focuses on the problems that occur while using LR as an auction method. Identical or similar units can prevent LR from finding the optimal solution. If the units are similar, LR may have trouble selecting some of them for the optimal solution. A feasible solution may thus not be found. Since a heuristic selection of which unit data to alter has to be applied, this is inequitable to the unit(s) not selected and may result in lawsuit(s). Because the dispatcher has to use heuristic selection, there is no “fair” solution to these problems. The authors suggest previously published methods to implement auctions. Sensitivity analysis has also been applied in this paper to show that the percentage difference of similarity between units may affect the solution found