Optimal stochastic scheduling of hydropower-based compensation for combined wind and photovoltaic power outputs

This paper examines and quantifies the evolution of the uncertainty in forecasting solarand wind-based electricity generation compensated with hydroelectric power, based on the forecast uncertainties of the three constituents. We used the generalized martingale model of forecast evolution to separately describe the uncertainties of power outputs of wind and photovoltaic systems in the same region. We then superimposed the separate power outputs to obtain the combined power output from these variable renewable energies (VRE). Furthermore, we developed a stochastic recourse model for optimally scheduling hydropower dispatch to compensate VRE and meet scheduled power demands. We applied the new model to hourly performance data obtained from photovoltaic, wind, and hydropower plants with power outputs of 3.1 GW, 2.7 GW, and 3.3 GW, respectively, in the Yalong River Basin in China. Based on the variance of hourly power outputs during spring days with different weather patterns, we found that the uncertainty of the forecasted combined power output of wind and photovoltaic systems is 46% less than that of the forecasted wind power output, and approximately 2% greater than that of the forecasted photovoltaic power output. After hydropower compensated for the power shortage in the combined VRE power output, the uncertainty of meeting prescheduled hourly demand during each of the considered days was reduced by 90%, compared with that without hydropower compensation. When the forecasts were updated dynamically, the uncertainties of the forecasts of the separate power outputs, of the combined power output, and of the power shortage decreased substantially. Thus, the approach proposed in this study offers a scheduling plan for hydropower compensation of VRE on a daily time scale and can also be used to evaluate the risk of power shortage.