PDF estimation of gridable vehicles for self-healing purpose

In this paper, a novel method is proposed, which detects the stochastic characteristics of vehicles connected to the network. Using statistical and machine learning formulas, a method to find the probability density function of random variables for each gridable vehicle is provided. The final purpose is to exploit these vehicles for self-healing characteristic of the Smart grid. The defined important random variables for this purpose are times that each vehicle connects to and disconnects from the network, and battery state of charge at the time of connection. For this purpose, the Bayesian inference algorithm and the expectation - maximization method have been modified. In this method, the parameters of distribution function are amended with respect to the evidenced behavior of the vehicle. Due to the learning ability of algorithms, by changing the usage pattern of the vehicle, the probability density function will also change gradually. After obtaining the values of parameters of distribution functions for each vehicle, by using them in combination with each other, the overall probability density functions can be obtained. Finally, we can combine these functions to find the probability density function of several other variables. In this paper, the random variables, which represent the energy of batteries of vehicles that can help on emergencies of the network in a probabilistic manner in different hours of afternoon, are obtained.