Analysis of Mathematical Models for Electricity Demand Concentration due to Price Fluctuations

Abstract

If power providers introduce more renewable energy power plants in the future, they may control the electricity price in order to fit demand to fluctuating supply. However, it was recently indicated using a mathematical model that price changes may cause an excessive demand concentration. In the present study, we modify this model to analyze the robustness of its property, and show that it is conserved robustly for prices following a Gaussian distribution and a Langevin equation. Also, we analyze a demand distribution theoretically, and confirm that the result is consistent with numerical experiments.