An Analytical Model to Evaluate the Effects of Wind Turbine Parameters and the Probabilistic Characteristic of Wind Speed on the Average LMP of the Power Market

With the increase of wind penetration in the power systems, analysis of the probabilistic production on the market prices becomes more essential. Researches in this field are often focused on the simulation tools and analytical modeling is rarely used. The aim of this paper is to provide an analytical method for assessing the effects of wind power plants on the Locational Marginal Price (LMP) based on some strong mathematical foundation. In order to achieve this goal, we utilize the LMP decomposition in the transmission-constrained electricity market. In this regard, using Rayleigh distribution for wind speed, nonlinear relationship between the wind power output and the wind speed and mathematical principles of probability, the probability density function of the wind power is determined analytically. Then, the average wind power with a precise mathematical formulation is obtained in a closed form and as a function of the wind turbine parameters and the probabilistic characteristic of wind speed. Finally, for the average LMP of each bus, an exact analytical relationship is determined. The proposed method is tested on the IEEE 24 bus system. The results show the efficiency of the proposed model.