The numerical probabilistic analysis of optimization problems hydropower

The paper considers the problem of optimizing the hydroelectric power generation in the face of uncertainty of the input data. To solve optimization problems with random hydropower input data we used numerical probability analysis. The numerical probabilistic analysis is a new section of Computational Mathematics, for applying to different tasks with random input data. The probabilistic extensions and numerical operations on the probability densities of the random variables are the base of numerical probabilistic analysis. We explore the sources of the emergence of various types of uncertainty and their methods of presentation. To demonstrate the NPA methods we present an optimization problem example of hydroelectric power generation which depends on the prediction of lateral inflow into the reservoir provided in the form of stochastic functions. It is shown that in the discrete case the problem reduces to solving a system of linear algebraic equations with random coefficients. The results of numerical simulation are presented in the graphic form of probability density histograms approximating the joint probability density function as the optimal amount of water passing through the turbines at different times.