Parametric Modeling of Electric Vehicle Charging Profiles

Nicole Ng


The power used by electric vehicles (EVs) has a significant impact on the electric grid. It is important to know the probabilistic and statistical characteristics of charging demand, as they can improve load forecast accuracy and electric grid operation. In this research, we identified and evaluated parametric models of the electrical power used by EV charging stations. The models are based on charging station data in the Seattle, Washington and San Diego, California areas. To generate these models, we organized the data in both 15-minutely and hourly intervals. We then created and visually inspected the histograms of the data to select parametric distributions that are the most promising. The best candidates were the Weibull, General Extreme Value, Gamma, Inverse Gaussian, Log Logistic, Normal and Lognormal. We estimated the parameters for each distribution using the maximum likelihood estimation procedure. To evaluate the parametric models, we used the chi-squared test, which evaluates the goodness-of-fit of a considered parametric distribution to the data set. A criticism of the chi-squared test is that the number of bins to use is subjective. To mitigate this, we selected three different numbers of bins to evaluate. First we used Log2(N) to determine the number of bins—Sturges’ rule of thumb—where N is the number of samples for either the 15-minutely or hourly interval, and a plus/minus 3 bin sensitivity. The results of the analysis indicate that the Weibull and Generalized Extreme Value distributions are good candidates for EV charging station load modeling. However, the distribution that was the best fit for Seattle was different than for San Diego. This is likely due to time-of-use pricing that San Diego utilizes. Time-of-use pricing encourages energy consumption to be concentrated into a smaller interval by charging people less money for electricity during non-peak hours. Hence the energy draw is more concentrated in San Diego than Seattle. The results can be used to help analyze the impact of increased energy demand caused by EVs, and enable load forecasters to better understand how to plan and operate the grid.


Electric Vehicles; Load Profiles; Parametric Model

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