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題名 | 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 Model |
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作者 | 劉佳明; | 書刊名 | 農業工程學報 |
卷期 | 54:4 2008.12[民97.12] |
頁次 | 頁1-15 |
分類號 | 443.96 |
關鍵詞 | 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; Reservoir capacity planning; Multipurpose reservoir; Network algorithm; Linear decision rule; Linear programming; |
語文 | 中文(Chinese) |
中文摘要 | 水庫線性供水決策規則設定供水量與已知或預測資料(如水庫的蓄水量、進水量、蒸發散與滲漏等)之間的線性關係,這個模式能以一般線性規劃方法解析,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、貯水與蓄洪為目標的多功能水庫,這些功能的需求與進水皆為確定的時間序列。為推求能使水庫容量最小的決策規則參數值,本文建立其模式,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,其變數為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。 |
英文摘要 | This paper concerns a reservoir capacity planning model with a linear decision rule for operation and its efficient algorithm. A multipurpose reservoir with known inflow sequence It, 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 St, Ft≡ Sv-St≥ Ft(superscript min), (2) minimal pondage, or the difference of water storage St and dead storage So, Lt≡ St-So ≥ St(superscript min), and (3) net release ∆Yt, or the difference of release Yt and inflow It, ∆Yt≡ Yt-It (= St-St+1)≥ ∆Yt(superscript min)≡ Yt(superscript min)- It, where the equality Yt- It= St- St+1 is the water balance condition at period t and the release Yt is a linear function of the initial storage St, or Yt=St- bt with an operating policy parameter bt. Our problem is to minimize the reservoir capacity Sv 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= Sv, subject to Sv-St≥ Ft(superscript min), St-So≥ St(superscript min), St-St+1≥ ∆Yt(superscript min), Yt-It= St-St+1, Yt= St-bt. [I] : Min z= Sv, subject to Sv-St≥ Ft(superscript min), St-So≥ St(superscript min), St-St+1≥ ∆Yt(superscript min). [II] : Yt=St- St+1+ It, bt= St+1- It, the solution of the last 2 constraints of [O] for Yt and bt. Subproblem [I] can be solved for St, Sv, and So 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 obtainYt and bt. |
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