水电优化中的四边形法则与准单调收敛

QUADRANGLE RULER AND QUASI-MONOTONIC CONVERGENCE IN OPTIMIZATION OF HYDROPOWER STATIONS

短期水电优化是过程问题 ,应该用泛函极值的变分法即欧拉方程求解。但由于有各种复杂的耦合而难以实现。即使是最简单问题的协调方程 λ=γ.q也因其解算方法过于繁复且物理意义不明确而无实用价值。曾有作者建议使用网流法来克服这个困难 ,但却受到其模型未将实际问题的求解视为一个过程的限制。由于天然来水具有随机性和测不准性而必须由中期滚动跟踪调整来平衡水量 ,而细节问题由实时调度负责 ,所以短期里使用水电平均耗水率特性 (是过原点的一簇直线 [4 ] )是合理的 ,相当于是一种估计 ,因此提出一种新的基于欧拉方程的网流法来将 γ与 λ以及 γ与 β解耦。在此基础上给出了具有线性形式的四边形法则 [3]和 2 nd、3rd费用网络并构造了具有准单调收敛性的最短路径算法。由于每一步都使用基于四边形法则的“绝对判据”,所以能保证“一步步用小的流量来计算的方式”具有“准单调收敛性”

Short term optimization of hydroelectric generation is a procedure problem and should be solved by the variational method of functional extreme value, i.e., the famous Eulerian equation. But the solution is difficult to acquire because of the existence of various complicated couples. Even the coordinative equation λ=γ·q for the simplest problem does not possess practicality due to the complicated solving process and absence of explicit physical meaning. To solve this optimal problem the Network Flow Method (NFM) was proposed to attempt conquering that difficulty. But this method is restricted by its own model which does not consider the solution of practical problem as a procedure. Because the quantity of naturally inflow is random and uncertain it should be balanced by mid term adjustment based on recursive tracking, as for its details are processed by real time dispatching. Thus, applying the average water consumption ratio in a short term is rational, and it corresponds to a sort of estimation. Consequently, a new NFM approach based on Eulerian equation is proposed which decouples the Lagrangian factor γ with λ and βrespectively. Then a quadrangle rule which is of linear form, the 2nd cost and the 3rd cost network are given and the shortest path algorithm which possesses quasi monotonic convergence can be constructed. Because in each step the quadrangle rule based absolute criterion is used, so it is ensured that the calculation mode which uses small water flow step by step has quasi monotonic convergence.