A framework for multi-interval optimal power flow under solar energy penetration

Abstract

The increasing penetration of renewable energy introduces variability and uncertainty into power system operations, thus requiring accurate forecasting methods to ensure reliable and economical scheduling. This study presents a multi-interval day-ahead optimal power flow (OPF) analysis integrated with photovoltaic (PV) generation, where hourly PV forecasts are obtained using the seasonal autoregressive integrated moving average (SARIMA) (1,0,1)(4,0,3)24 model. The forecast results achieved low error values (root mean square error (RMSE)=0.354, normalized RMSE (NRMSE)=4.192%, mean absolute error (MAE)=0.202), successfully capturing the daily PV generation pattern and providing sufficiently accurate input for the OPF simulation. The forecasted PV profiles were then integrated into a multi-interval OPF framework using the MATPOWER interior point solver (MIPS) solver. Results show that PV integration reduces system operating costs compared to cases without PV, with cost savings observed at various time intervals (e.g., reduction from $802.22/hour to $780.65/hour during PV peak hours). Compared to the conventional single-interval OPF benchmark based on Weibull distribution assumptions for PV, the proposed framework achieves lower average costs ($790.97/hour vs. $869.70/hour) while also reflecting the real variability of solar dynamics and load. Overall, the integrated forecasting-optimization framework demonstrates that SARIMA-based PV forecasting provides reliable inputs for OPF and offers a practical tool to support future system planning and operation with higher renewable energy penetration.