Improvements to Modern Portfolio Theory based models applied to electricity systems
Gabriel Malta Castro, Claude Klöckl, Peter Regner, Johannes Schmidt, Amaro Olímpio Pereira
Abstract
With the increase of the share of variable renewable energies in electricity systems, many studies were developed in order to determine their optimal technological and spatial mix. Modern Portfolio Theory (MPT) has been frequently applied in this context. However, some crucial aspects, important in energy planning, are not addressed by these analyses. We, therefore, propose several improvements and evaluate how each change in formulation impacts results. More specifically, we use generation cost instead of installed capacity as one of the objectives; we consider the correlation between demand and generation profiles; and we limit shortage risks via the inclusion of a CVaR measure. These modifications are presented in a formal model which is also applied to the case of Brazil. We found that, after including our proposed modifications, the resulting efficient frontier differs strongly from the one obtained in the original formulation. The main difference is that the new efficient frontier has a much shorter range of acceptable standard deviation values. Therefore, many of the portfolios obtained from the traditional formulation have a much higher probability of under-production, especially portfolios located at regions with standard deviation either too low or too high. Furthermore, we show that diversification plays an important role in smoothing output from portfolios of variable renewable sources.