Application of hierarchical clustering on electricity demand of electric vehicles for GEP problems

Abstract

Increasing fossil fuel consumption and consequently the effects of greenhouse gases (GHGs) on the environment and economy are a major concern for all nations and governments. Electric vehicles (EVs) with plug-in capabilities have the potential to ease such problems. However, the extracted power from the grid for charging the EVs' batteries will significantly impact daily power demand. To satisfy the increasing demand and ensure generation capacity adequacy, the generation expansion planning (GEP) problem is solved to determine the investment decisions for electricity generation sources. Even though there are no centralized utilities for generation planning in most markets, there is still a need to realistically solve the GEP problems and find the optimal investment decisions to tailor the incentives used by most governments to guide the market. There is also a need for a tool to analyze the effect of different charging power levels, charging policies, and penetration levels. The main goal of this paper is to provide a tool to determine realistic optimal investment plans and evaluate different cases. It is also very important to consider the stochastic nature of the electricity demand in GEP problems. We propose a scenario-based stochastic programming model to incorporate the variability in the electricity demand due to EV charging through a set of scenarios generated by Monte Carlo Simulation. The methodology starts with applying a simulation method to generate the electricity demand of EVs by considering all the possible factors affecting EVs' demand. Each iteration of this simulation represents a possible demand profile as a result of penetrating the EVs into the market. Using all these demand profiles in GEP is preferable, but it is not computationally efficient. Computational tractability is achieved by using the clustering technique to reduce the size of such scenarios. We propose clustering methods to select a representative set from the data sets generated by the simulation and integrate EVs into GEP problems by using the selected set. The GEP models are defined to represent EVs' demand explicitly and then solved to imply the benefit of the suggested methods. The results show that GEP models with a representative set produce more realistic solutions than the GEP models including only average EVs demand. To select representative sets, different clustering techniques and distance measurements are used and compared with respect to their performances. Two different methods are defined to choose the best number of clusters: the silhouette coefficient method and the elbow method. For each method, five different distance measurement techniques are used. In each of these techniques, three approaches are evaluated for the representative point: Min, Max, and Average. A key contribution of this article is to explore and evaluate the quality of GEP models for each case according to how close the total cost obtained from the GEP model by using clustered load curves to the total cost obtained by using the full data sets generated by simulation.