Probabilistic Assessment and Sensitivity Analysis of Marginal Price of Different Services in Power Markets

Different sources of uncertainty in power systems, i.e., the uncertainties associated with bus loading and component availability is reflected in uncertainties in different system variables through system physical and economical relationships. A stochastic power flow algorithm can be used to model the stochastic nature of power systems. The algorithm introduced in this paper calculates the probability density function (pdf) of marginal prices of different market services. These pdfs provide the market participant with some valuable information to reduce the risk of their decisions and actions. The algorithm linearizes the optimal power flow formulation and uses the Gram-Charlier method to find the pdf of the marginal prices based on the statistical moments of these prices. The market clearing equation is linearized instead of the power flow equations. It is essential for different market participants to reduce the risk of their actions in both planning and operation modes. Application of the mentioned PDFs can help them in this way. The great advantage of the proposed method is that the program execution time is very short. The proposed method is illustrated using the IEEE Reliability Test System and the results are presented and discussed in detail to show the effectiveness of the proposed method.