【摘要】 本文在开机组合业已给定的情况下运用运筹学中的分数规划建立了梯级水电站有功功率最优分配的数学模型,提出了梯级水电站经济调度新的最优准则——梯级各电站全日各时段水头加权平均耗水率为最小。分数规划的目标函数为 其中Q=(Q₁₁,…,Q_1T,Q₂₁,…,Q_2T,…,Q_n1,…,Q_nT)′为nT维流量矢量。我们探讨了约束条件（出力平衡、梯级水电站日流量限制、水头限制、水电站出力限制和流量限制）的数学表达式。本文用“移动截断法”MTM将此分式目标函数化为一系列等价的非分式目标函数,再用混合罚函数法SUMT解这一系列非分式目标函数及其约束组成的约束非线性规划问题,确定了增广目标函数φ_k,导出了梯度分量的计算公式,这些公式能比较全面深刻地揭示出梯级水电站之间存在的固有规律与内在联系。这将有助于人们利用它来控制调度和管理梯级水电站经济运行,为“四化”服务。更多还原

【Abstract】 In this paper we use fractional programming of OR to establish a mathematical model for optimization of active power dispatch of cascade hydroelectric power stations under the condition that the combination of water-turbine dynamos has been given, and propose a new optimum criterion for economical scheduling of cascade hydroelectric power stations-the water rate weighted average with respect to water heads of all hours of the day for each power station of cascade be minimum, i. e., the objective function of the the fractional programming is where Q = (Q11 ,…,Q1T,Q2l,…,Q2T. …,Qn1 , …,QnT)’ is an nT-dimensional flow vector, we have studied the mathematical expressions of the constraints (power balance, the restrictions of flow of cascade hydroelectric power stations in all hours of the day, bounds on the water heads, bounds on the power and bounds on the flow of hydroelectric power stations). Using moving truncation method MTM we transform the fractional objective function into a series of equivalent non-fractional objective functions, then we solve these constrained nonlinear programming problems by mixed penalty function method SUMT. The augmented objective functions <pk are defined, the formulas for calculating the components of the gradient of <pk,i.e.,are derived. These formulas can reveal the proper regularitiesand inherent relations between cascade hydroelectric power stations very deeply and all-sidedly. It may be utilized to control, schedule and manage the economical operations of cascade hydroelectric power stations. It may be served for the "four modernizations".更多还原