線性供水規則下水庫容量規劃模式－位勢網絡解釋與算法

A Potential Network Interpretation and Algorithm for a LDR Reservoir Capacity Planning Mode

劉佳明(Chia-Ming Liu)

《農業工程學報》 54卷4期 (2008/12) Pp. 1-15

https://doi.org/10.29974/JTAE.200812.0001

摘要

水庫線性供水決策規則設定供水量與已知或预测资料（如水庫的蓄水量、進水量、蒸發散與滲漏等）之间的線性關係，這個模式能以一般線件規劃方法解析，適合當作水庫初步規劃的分析工具。本文探討相關模式的一個高效率演算法。
本文考慮一個以供水、貯水與蓄洪爲目標的多功能水庫，這些功能需求與進水皆爲確定的時間序列。爲推求能使水庫饗量殼小的決策規則參數值，本文建左其模式，又將它轉換並劃分成可以依序解算的二個區段：[Ⅰ]單純規劃模式，具有位勢網絡結構，其變數爲水庫容量與各時期蓄水量等狀態值：[Ⅱ]操作參變數公式：供水量與決策規則參數以模式[Ⅰ]的狀態變數表示。因此，前段模式[Ⅰ]能以高效率網絡法求解狀態變數，所得代入後段公式[Ⅱ]即得供水量與參數。
上述單純水庫容量規劃模式具下列有位勢網絡特性：(1)圖像直觀，自然傳達供需時程觀念，(2)結構簡明，有效發揮演算分析效率。

關鍵字

水庫容量規劃 ； 多目標水庫 ； 網絡演算法 ； 位勢網路 ； 線性決策規則 ； 線性規劃

並列摘要

This paper concern a reservoir capacity planning model with a linear decision rule for operation and its efficient algorithm. A multipurpose reservoir with known inflow sequence I(subscript t), where time period t-1, 2,……,n, is required to meet the following three minimal demand conditions: (1) reserved buffered space for flood, or the difference of reservoir capacity Sv and water storage S(subscript t) F(subscript t)=S(subscript tv) S(subscript t)≥F(subscript t) (superscript min), (2) minimal pondage, or the difference of water storage St and dead storage S(subscript o) L(subscript t)=S(subscript t)-S(subscript o)≥S(subscript t) (superscript min), and (3) net release △Y(subscript t), or the difference of release Y(subscript t) and inflow I(subscript t) △Y(subscript t)=Y(subscript t)-I(subscript t) (=S(subscript t)-S(subscript t-1)≥△Y(subscript t) (superscript min)=Y(subscript t) (superscript min)-It, where the equality Y(subscript t)-I(subscript t)=S(subscript t)-S(subscript t-1) is the water balance condition at period t and the release Y(subscript t) is a linear function of the initial storage S(subscript t), or Y(subscript t)=S(subscript t)-b(subscript t) with an operating policy parameter b(subscript t). Our problem is to minimize the reservoir capacity S(subscript v) while all demand conditions are satisfied.
The problem is formulated as a linear program [O] which is partitioned into two subproblems [Ⅰ] and [Ⅱ].
[O]: Min z=S(subscript v), subject to S(subscript v)-S(subscript t)≥F(subscript t) (superscript min), S(subscript t)-S(subscript o)≥S(subscript t) (superscript min), S(subscript t)-S(subscript t-1)≥△Y(subscript t) (superscript min).
[Ⅰ]: Min z=S(subscript v), subject to S(subscript v)-S(subscript t)≥F(subscript t) (superscript min), S(subscript t)-S(subscript o)≥S(subscript t) (superscript min), S(subscript t)-S(subscript t-1)≥△Y(subscript t) (superscript min), Y(subscript t)-I(subscript t)=S(subscript t)-S(subscript t-1), Y(subscript t)=St-b(subscript t)
[Ⅱ]: Y(subscript t)=S(subscript t)-S(subscript t-1)+I(subscript t), b(subscript t)=S(subscript t+1)-I(subscript t), the solution of the last 2 constraints of [O] for Y(subscript t) and b(subscript t). Subproblem [Ⅰ] can be solved for S(subscript t), S(subscript v), and S(subscript o) with a potential network algorithm which is more than a few hundred times faster than with a linear programming method, The solution of [Ⅰ] is then substituted into [Ⅱ] to obtain Y(subscript t), and b(subscript t).

並列關鍵字

Reservoir capacity planning ； Multipurpose reservoir ； Network algorithm ； Linear decision rule ； Linear programming