Physical Meanings Analysis of Price Multiplicity Based on Mortzkin's Theorem

This paper analyzes the physical meanings of price multiplicity in real-time market, i.e. the characteristics of market clearing model when price multiplicity happens, in detail. Based on the allowable variation ranges of the corresponding multipliers, buses and transmission lines are divided into three types respectively. The classification is further applied to the formula of locational marginal price, and the variation equations are obtained. By adopting Mortzkin's theorem, the physical meanings of price multiplicity at quasi-marginal buses and non-marginal buses are derived. When price multiplicity happens at a bus, the variations of the objective function of market clearing model for an extra injection and extraction power at this bus must be unequal. In particular, for quasi-marginal buses, the price multiplicity also means that there are no marginal units or marginal loads at these buses in all the optimal solutions of the clearing problem. Numerical examples are provided to illustrate and verify the above theoretical analyses.