用最小范数法解三峡梯级水电站短期经济调度问题

本文主要研究三峡梯级水电站与华中、华东和川东电网联网的短期经济调度问题,利用泛函分析和运筹学相结合的方法建立了三峡梯级水电站日负荷最优分配的数学模型。本文扩充和推广了Hawary和Christensen的最小范数法用来求解这个具有等式和不等式约束的高维非线性含时滞的动态最优化问题,最优策略由一组动态的非线性代数、微分方程确定。引入适当的变量并进行适当化简,最终可将三峡梯级水电系统的经济调度问题转化为一个最小范数问题,并给出了最优解的具体表达式.用Lagrange乘子和Kuhn-Tucker乘子将约束条件并入目标函数中形成一个增广价格函数。通过变换可将该无约束优化问题转化为求解非线性代数方程组的问题。本文选用Fletcher-Reeves共轭梯度法求解无约束极值问题.在IBM-PC型微机上进行了试算。试算结果表明用最小范数法求解三峡梯级水电站日负荷最优分配问题是完全可行的,梯级水耗率有明显下降,能获得一定的经济效益。

SOLVING THE SHORT TERM ECONOMIC SCHEDULING PROBLEM OF THE THREE GORGES CASCADE HYDROPOWER STATIONS BY THE MINIMUM NORM APPROACH

The paper aims mai nly at researching the short term economic scheduling problem of the Three Gorges Cascade Hydropower Stations connected with the power networks in Central-China, East-China and East-Sichuan. The mathematical model of optimal daily load dispatch of the Three Gorges Cascade Hydropower Stations is built by the methods of functional analysis combined with operations research. This paper extends and generalizes the Hawary-Christensen minimum norm approach for solving high dimensional nonlinear dynamic optimization problem with equality and inequality constraints containing time delay. The optimal strategy is determined by a dynamic systemof nonlinear algebraic and differential equations. This problem may be finally converted into aminimum norm problem and a concrete optimal solution is given. This unconstrained optimization problem may be transformed into nonlinear algebraic system of equations. We select the Fletcher-Reeves conjugate gradient method to solve the unconstrained extremum problem, and take test computations on the microcomputer IBM-PC. The trial computation shows that the minimum norm approach is completely feasible to solve the optimal daily load dispatch of the Three Gorges Cascade Hydropower Stations. The water consumption rate of the Cascade is obviously decreased and the Cascade may obtain a certain economic benefit.