Detection of Price Multiplicity Based on Rank of Submatrix

Linear programming model is usually used to solve the real-time market clearing problem in electricity markets around the world. Locational marginal price (LMP) is widely used for its effect to reflect the network congestion cost and the marginal cost of power generation. However, in the actual solution process, it is faced with price multiplicity, which affects market fairness. Changing the pricing process to solve it will lead to a large number of redundant calculations. Therefore, accurate and efficient detection of price multiplicity is needed. In this paper, a detection method of price multiplicity based on rank of submatrix is proposed. On the basis of a set of solutions obtained by using KKT conditions, the variable equation in the form of a matrix is further obtained. By simplifying rank of coefficient matrix, a price multiplicity detection method is obtained. Numerical examples are given to test the effect of the above price multiplicity detection method.