梯级水电站群联合优化调度规则制定的投影寻踪回归法

Derivation of optimal operating rules for cascade hydropower stations based on projection pursuit regression model

为了客观反映梯级水电站群联合调度过程中各调度因子之间的非线性关系,引入了投影寻踪回归模型,用相关分析和多元逐步回归分析相结合的方法筛选调度因子,建立了基于Hermite多项式的梯级水电站群调度函数的投影寻踪回归模型,并采用实数编码遗传算法对模型进行了求解。算例结果表明,投影寻踪回归模型能很好地反映调度函数中决策变量与自变量之间的非线性关系,与BP人工神经网络模型相比,其对最优运行轨迹的拟合效果提高明显,稳健性更好。

To better understand complicated nonlinear relationships between the input and output variables of optimal operation for cascade hydropower stations, this study develops a projection pursuit regression model using a ridge function of nonlinear Hermite polynomials and optimizes the operation with a real accelerating genetic algorithm. This model combines correlation analysis with multivariate stepwise regression analysis method to select the independent variables of dispatching function, obtaining a better way to determine the dispatching factors in formulating optimal operation rules for the cascade stations. Application of the model to one example shows that its fitting accuracy and robustness in solving dispatching function are superior to BP artificial neural network model.