Abstract: In the market environment, cascade load is allocated at both the inter-plant level and the in-plant level of different generating units. Its targets are to maximize cascade benefit at the inter-plant level and minimize water consumption under security constraints at the in-plant level. This paper develops and integrates two hierarchical allocation models for the two levels. The inter-plant allocation is aimed at maximum power output profit, which is solved using a progressive optimal algorithm. The model of load allocation over the in-plant units is solved by a two-step dynamic programming to achieve the objective of minimum water consumption. It uses dynamic programming to solve the optimal allocation under security constraints in successive periods, and then in the second step to optimize the procedure to start up and shut down the units. Calculations at the two levels are coordinated and optimized through a comprehensive output coefficient as the coordination variable, and solved iteratively at the first and second stages, respectively, producing optimal results of the inter-plant and in-plant allocations. A case study shows that the algorithm is efficient and fast in achieving a unified dispatching between the load allocations, thus improving the competitiveness of cascade hydropower stations in the market.

Key words: optimal scheduling, cascade hydropower stations, inter-plant and in-plant load allocation, dual dynamic programming, two stage iteration