Cascade Reservoir Scheduling Using Float-Discrete Dynamic Programming
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Solution Overview
Problem
Existing methods for cascade reservoir group scheduling, such as dynamic programming successive approximation (DPSA) and intelligent algorithms, face high computational workload and instability in achieving optimal solutions, failing to effectively utilize the relationship between hydropower station output and water head.
Innovation Solution
A float-discrete differential dynamic programming successive approximation method that raises water levels in cascade reservoirs based on surface areas, generates electricity, and iteratively optimizes water level trajectories to maximize total power generation, using discrete differential dynamic programming to reduce invalid calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If dynamic programming successive approximation algorithm is used to calculate each reservoir multiple times, then a better optimal solution can be obtained, but the calculation workload is large and the calculation time is long
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing the water level-area relationship curves for each reservoir before the main optimization process. This preliminary preparation allows the algorithm to quickly retrieve area values during successive approximations without performing repeated calculations, thereby reducing calculation time while maintaining solution quality
Solution Approach 2:
The patent implements partial action by performing dynamic programming calculations only on the necessary water level trajectories that are relevant to the optimization, rather than calculating all possible trajectories. The method focuses computational effort on the most promising paths while using the pre-stored water level-area relationships to avoid redundant calculations
2Power
If intelligent algorithms such as genetic algorithm and particle swarm optimization are used, then massive computing can be performed, but the algorithm is easy to fall into local optimal solution and the obtained solution is unstable
Solution Approach 1:
The patent applies feedback by implementing an iterative successive approximation process where each iteration uses the results from the previous iteration to refine the water level trajectories. The algorithm continuously compares the current solution with the previous solution and adjusts the trajectories based on the feedback from the objective function evaluation, ensuring convergence to a stable optimal solution rather than getting trapped in local optima
Solution Approach 2:
The patent implements dynamics by allowing the water level trajectories to evolve and adjust dynamically through the successive approximation iterations. The method adapts the search direction and intensity based on the current state of the system, transitioning from broad exploration to focused refinement as the solution converges, thereby maintaining both computational power and solution stability
3Ease of manufacture
If traditional mathematical methods are used for solving, then calculations can be performed, but the methods do not take into account the change law of cascade reservoirs' water energy, so a large number of calculations are useless
Solution Approach 1:
The patent applies parameter changes by transforming the physical relationship between water level and reservoir area into a usable mathematical form. The method changes the parameters from raw water level measurements to pre-calculated water level-area relationship curves, which capture the change laws of cascade reservoirs' water energy. This transformation makes the calculations both feasible and efficient by encoding the physical characteristics directly into the computational model
Solution Approach 2:
The patent introduces an intermediary element in the form of pre-calculated water level-area relationship curves that mediate between the physical system (cascade reservoirs) and the mathematical optimization algorithm. These curves serve as an intermediary data structure that encodes the change laws of water energy, allowing the algorithm to efficiently query area values without directly modeling the complex physical relationships during each calculation iteration
Data Source
AI summary
The invention provides a float-discrete differential dynamic programming successive approximation method for cascade reservoir group scheduling, comprising the following steps: water levels of cascade reservoir group are raised from small to large according to water surface areas of reservoirs; the cascade reservoir group generates electricity after raising the water level according to incoming water; at the end of calculation period, and initial water level trajectory is obtained when the raised water level of the cascade reservoir group falls back to the set water level; based on the initial water level trajectory obtained, discrete differential dynamic programming calculation of each reservoir is carried out from upstream to downstream with the goal of maximizing the cascade total power generation, and the improved water level trajectory of each cascade reservoir is obtained; taking the improved water level trajectory of each cascade reservoir as the initial trajectory, and the iterative optimization is carried out.