Volterra equation based models for energy storage usage based on load forecast in EPS with renewable generation

High penetration of renewable energy under condition of the free electricity market leads to the need of creating new methods for maintaining balance between load and generation, in particular, energy storage usage in modern power systems. However, most of the proposed models of energy storage do not take into account some important parameters, such as the nonlinear dependence of efficiency on life time and changes in capacity over time, the distribution of load between several independent storages and others. In order to solve this problem models based on Volterra integral equations of the first kind with kernels presented in the form of discontinuous functions are proposed. Such models allows to determine the alternating power function at known values of load and generation. However, to effectively solve this problem, an accurate forecast of the electrical load is required, therefore, several forecasting models based on machine learning was exploited. Forecasting models use different kind of features such as average daily temperature, load values with time shift, moving averages and others. In the paper comparison of the forecasting results is provided, including random forest, gradient boosting over the decision trees, the support vector machine, and also multiparameter linear regression. Effectiveness of the proposed forecasting models and storage model is demonstrated on the real data of Germany power system.