Risk‐Constrained Optimal Scheduling in Water Distribution Systems Toward Real‐Time Pricing Electricity Market

Abstract In recent years, as a result of emerging renewable energy markets, several developed regions have already launched Real‐Time Pricing (RTP) strategies for electricity markets. Establishing optimal pump operation for water companies in RTP electricity markets presents a challenging problem. In a RTP market, both positive and negative electricity prices are possible. These negative prices create economically attractive opportunities for Water Distribution System (WDS) to dispatch their energy consumption. On the other hand, excessively high prices may put WDS at risk of supply disruptions and reduced service levels. However, the continuous development of wind power and photovoltaics results in more volatile and unpredictable fluctuations in the price of renewable energy. The risk arising from uncertainty in electricity prices can lead to a significant increase in actual costs. To address this issue, this paper develops an a posteriori random forest (AP‐RF) approach to forecast the probability density function of electricity prices for the next day and provide a risk‐constrained pump scheduling method toward RTP electricity market. The experimental results demonstrate that the developed method effectively addresses the issue of increased costs caused by inaccurate electricity price forecasting.