Study on the mutual feedback relation among water supply-power generation- environment of reservoir group in the upper reaches of the Yangtze River based on gradient analysis method

The optimal regulation of the coupled system of water resources in the upper reaches of the Yangtze River involves the competing and incommensurable objectives of water supply, power generation and ecological water requirements. It is difficult to analyse and describe the mutual feedback covariance mechanism of the water supply, power generation and environment and to balance and optimize the regulation of multiple objective benefits. Based on the theory and method of multi-objective optimization and operational research, a method to study the mutual feed relationship among water supply, power generation and the environment is proposed using gradient analysis. The multi-objective constrained optimization method is used to obtain the Pareto optimal solution set of the joint optimal operation of the reservoir group in the upper reaches of the Yangtze River within the objective space of the water supply-power generation-environment, and the multi-objective space surface of the mutual feed relationship of the water supply-power generation-environment is constructed by interpolation. Thus, the first-order difference approximation is used to acquire the partial derivative function values of the water supply to the environment and power generation to quantify the gradient of the environmental response to changes in the water supply and power generation. Then, the mutual feed covariance relationship of the water supply-power generation-environment is analysed. This method provides a new approach for studying the multi-objective mutual feed relationship of the optimal operation of the reservoir group.