Markov chain monte Carlo sampling based Bayesian multivariate linear spline load forecasting agent for smart microgrid energy management system

This paper proposes a load forecasting agent for a multi-agent based energy management system (EMS) in a smart microgrid. EMS in a microgrid is responsible for providing dispatch strategies for the generation units requiring both the renewable resource forecast and load forecast. The efficiency of the EMS significantly relies on the accuracy of the forecasting. Classical piecewise linear models use single optimized parameters according to cross-validation score or penalized likelihood. They fail to accommodate the uncertainty of parameter values, which results in the regression surface become non-smooth. The proposed model considers a Bayesian analysis of the piecewise linear model, which has been assembled by the basis function approach. The basis function approach generalizes the univariate linear splines to higher dimensions, which naturally enforces the mean level continuity at the boundaries of regions. The posterior distribution of the response variable is achieved by integrating the posterior model space by altering numbers and locations of planes. As a result, a Bayesian local linear model with predictive distribution and a group of local linear parameters are achieved, which quantifies the forecast uncertainty imposed in the model. The proposed model shows better forecasting accuracy of 97.0559%, and therefore implemented as an agent for microgrid EMS.