Benefit of PARMA Modeling for Long-Term Hydroelectric Scheduling Using Stochastic Dual Dynamic Programming

Abstract

In the long-term management of large hydropower systems, operators generally have to maximize the benefits from energy production while ensuring they satisfy a minimal energy profile throughout the year. Enhanced hydrological information can be critical to improving the operations of the system. This need encourages the use of a more complex representation of inflow series. Stochastic dual dynamic programming (SDDP) is a commonly used method for optimizing multireservoir operations of hydropower systems. Within SDDP, inflow uncertainty is usually modeled using statistical time-series models such as the family of periodic autoregressive (PAR) models, which have the required linear structure to implement SDDP. Although often used in hydrological modeling for its ability to represent long-term spatiotemporal relationships, periodic autoregressive and moving average (PARMA) has yet been little used in a SDDP framework. The additional moving average component of PARMA models over PAR models provides PARMA with a deeper memory than PAR, thanks to a more complex correlation structure. This paper compares policies generated by PARMA and PAR to manage the Manicouagan hydropower system in Quebec, Canada. The comparison is made between PAR and PARMA models of the same autoregressive order to illustrate the advantages of including the moving average component. Simulations over historical scenarios are performed and reveal that PARMA derives policies that can better manage the interannual capacity present in the system.