Optimal Control of Cascade Hydro Plants as a Prosumer-Oriented Distributed Energy Depot

Abstract

For political and economic reasons, renewable sources of energy have gained much importance in establishing a sustainable energy economy. By their very nature, however, their benefits depend on changeable weather conditions, and are unrelated to the generation and consumption patterns in industrial or home environments. This generation–dissipation disparity induces price fluctuations and threatens the stability of the supply system, yet can be alleviated by installing energy depots. While the classic methods of energy storage are hardly cost-effective, they may be supplemented, or replaced, by a distributed system of small-scale hydropower plants with ponds used as energy reservoirs. In this paper, following a rigorous mathematical argument, a dynamic model of a multi-cascade of hydropower plants is constructed, and a cost-optimal controller, with formally proven properties, is designed. On the one hand, it allows for an increase in the owners’ revenue by as much as 30% (compared to a free-flow state); on the other hand, it reduces the load fluctuation imposed on the grid and the legacy supply system. Moreover, the risk of floods and droughts downstream resulting from inappropriate use of the plants is averted.