Analysis of the Probability Distribution of LMP by Central Limit Theorem

The main goal of this paper is to provide an analytical study on the statistical behaviors of the electricity price at various conditions of the load and the network. In order to achieve this goal, a novel two-step modeling is proposed for the electricity price. At the first step, it is proved that there is a linear relationship between the locational marginal prices (LMP) and the strategies of generating companies (GenCos). In this linear relationship, the LMP is decomposed to the weighted summation of the strategies of marginal units plus constant value. At the second step, the LMP is modeled by classic central limit theorem (CLT). Using this model an analytical relationship is derived between the price discovery mechanism and characteristics of its probability density function (pdf). As a result, this paper shows analytically that increasing system load causes the price pdf deviates from the normal distribution. On the other hand, by decreasing system load, the electricity price distribution tends toward the normal distribution. The statistical studies on the real power markets data confirm these analytical results. Furthermore, the simulation results of the IEEE 300-bus test system illustrate the efficiency of the proposed model.