Modeling Electrical Daily Demand in Presence of PHEVs in Smart Grids with Supervised Learning

Replacing a portion of current light duty vehicles (LDV) with plug-in hybrid electric vehicles (PHEVs) offers the possibility to reduce the dependence on petroleum fuels together with environmental and economic benefits. The charging activity of PHEVs will certainly introduce new load to the power grid. In the framework of the development of a smarter grid, the primary focus of the present study is to propose a model for the electrical daily demand in presence of PHEVs charging. Expected PHEV demand is modeled by the PHEV charging time and the starting time of charge according to real world data. A normal distribution for starting time of charge is assumed. Several distributions for charging time are considered: uniform distribution, Gaussian with positive support, Rician distribution and a non-uniform distribution coming from driving patterns in real-world data. We generate daily demand profiles by using real-world residential profiles throughout 2014 in the presence of different expected PHEV demand models. Support vector machines (SVMs), a set of supervised machine learning models, are employed in order to find the best model to fit the data. SVMs with radial basis function (RBF) and polynomial kernels were tested. Model performances are evaluated by means of mean squared error (MSE) and mean absolute percentage error (MAPE). Best results are obtained with RBF kernel: maximum (worst) values for MSE and MAPE were about 2.89 10-8 and 0.023, respectively.