多目標水庫序率最佳操作模式之建立與應用

本研究介紹一新的水庫最佳操作模式，此模式乃藉由控制學之分離理論結合卡門濾波與限制型可微分動態規劃法。對於如何求得序率最佳水庫操作規則，本文主要是計算當狀態變數滿足機率型限制條件及控制變數滿足其限制式時之序率目標函數之最佳條件期望值，此模式之特性是將複雜之序率系統轉換成定率型態，並且求得多水庫系統在考慮入流量之不確定因素時之較佳操作策略。其中限制型可微分動態規劃是結合可微分動態規劃與狀態變數可行解集合之觀念，故能考慮狀態變數、控制變數之上下限制條件與狀態變數之終端限制等限制式，並能處理二次以上目標函數之定率演算法。而對於求目標函數最佳期望值所產生之狀態變數條件期望值，則以卡門濾波演算法推估之。本研究以簡化之淡水河流域水庫系統驗證其收歛效率與可靠度。

關鍵字

卡門濾波；微分動態規劃；分離理論；水庫操作

並列摘要

This paper presents a new algorithm which employs a separation theorem in optimal control in order to combine with kalman filter and constrained differential dynamic programming (CDDP). The new algorithm can provide a suboptimal strategy in multireservoir system operation, which exhibits intrinsic uncertainties in reservoir inflow. CDDP is a deterministic algorithm which was developed by coupling differential dynamic programming (DDP) with a feasible set of state variables; hence, it is capable of modeling the following constraints: the upper and lower constraints on the state and control variables, and the fixed terminal state on the state variables. In addition, the objective function is modeled in a non-quadratic form. As for determining the stochastic optimal operation rules, the model maximizes the expected benefits of the system objective function while satisfying the remaining objectives at pre-specified reliability levels. Furthermore, the kalman filter is utilized to estimate the estimated expectation, which are required prior to determining the expectation of the system objective function. This computation procedure allows the reformulation of a complex stochastic formulation into simplified deterministic state equations. Subsequently, the aforementioned CDDP algorithms are applied to solve the deterministic model. The model reliability and convergence are verified with an application in the frame work of a multi-reservoir system of the Tanshui River Basin in northern Taiwan.

並列關鍵字

Kalman filter ； Differential dynamic programming ； Separation theorem ； Reservoir operation

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