# 基于三步优化的多目标水资源配置研究及应用Multi-Objective Water Resources Allocation Based on Three-Step Method

• 全文下载: PDF(1809KB)    PP.433-444   DOI: 10.12677/JWRR.2018.75049
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A multi-objective water resources optimal allocation model for transboundary region is established after an overall consideration of national economic water demand, water balance and eco-environmental water consumption. In order to ensure the equality among stakeholders, the index and benefit ratio is introduced, and the multi-objective problem is transformed into several single-objective problems by adopting the three-step method, which can greatly simplify the solution process. The proposed model and method are verified through the case study in the middle and lower reaches of Han River. The outputs of Highest Water Profit (HWP) model show that the allocation benefits of subdivisions located in Tangbai River basin have more effects on each other while the cities that are located downstream of Danjiangkou Reservoir do not depend upon the allocated water to others. The Highest Ratio of Highest Water Profit (HRHWP) model presents that the benefit ratio is lowest in summer, mainly due to the largest water demand in this period. In spring, autumn and winter, the indices all exceed 0.9. The results of Final Water Profit (FWP) model show that the water shortage rates are 3.11%, 3.69% and 3.94% at frequency of 50%, 75% and 95%, respectively. The domestic water consumption is basically satisfied at the planning year, but there are relatively larger shortages in agricultural irrigation and ecological environment water consumption. The water shortage in Tangbai River basin is more serious than that in the main stream area below Danjiangkou Reservoir.

1. 引言

2. 研究方法

2.1. 水资源优化配置模型

$\mathrm{max}\text{}{Z}_{k}=\underset{t}{\sum }\left({p}_{k}^{a}×{x}_{kt}^{a}+{p}_{k}^{d}×{x}_{kt}^{d}+{p}_{k}^{u}×{x}_{kt}^{u}\right)$ (1)

 (2)

$\underset{j\in DN}{\sum }{y}_{k\to j,t}\ge {\alpha }_{kt}^{e}×E{D}_{kt}\text{}\forall k,t$ (3)

${\alpha }_{kt}^{e}=\left\{\begin{array}{l}1\text{}生态需水满足要求\\ 0\text{}生态需水不满足要求\end{array}\text{}\forall k,t$ (4)

${x}_{kt}^{a}\le A{D}_{kt}\text{}\forall k,t$ (5)

${x}_{kt}^{d}\le D{D}_{kt}\text{}\forall k,t$ (6)

${x}_{kt}^{u}\le U{D}_{kt}\text{}\forall k,t$ (7)

${x}_{kt}^{a}\ge 0\text{}\forall k,t$ (8)

${x}_{kt}^{d}\ge 0\text{}\forall k,t$ (9)

${x}_{kt}^{u}\ge 0\text{}\forall k,t$ (10)

${y}_{i\to k,t}\ge 0\text{}\forall k,t$ (11)

${y}_{k\to j,t}\ge 0\text{}\forall k,t$ (12)

2.2. 多目标优化的三步法

$\mathrm{max}\text{}{f}_{1}^{\ast }=\underset{t}{\sum }\left({p}_{1}^{a}×{x}_{1t}^{a}+{p}_{1}^{d}×{x}_{1t}^{d}+{p}_{1}^{u}×{x}_{1t}^{u}\right)$ (13)

$\mathrm{max}\text{}Y=\underset{t}{\sum }{\lambda }_{t}$ (14)

${p}_{k}^{a}×{x}_{kt}^{a}+{p}_{k}^{d}×{x}_{kt}^{d}+{p}_{k}^{u}×{x}_{kt}^{u}\ge {\lambda }_{t}×{f}_{kt}^{*}\text{}\forall k,t$ (15)

$\mathrm{max}\text{}W=\underset{k}{\sum }\underset{t}{\sum }\left({p}_{k}^{a}×{x}_{kt}^{a}+{p}_{k}^{d}×{x}_{kt}^{d}+{p}_{k}^{u}×{x}_{kt}^{u}\right)$ (16)

3. 汉江中下游水资源优化配置

3.1. 研究区概况

3.2. 水资源分区及水系概化

3.3. 模型参数

Figure 1. Sketch map of study area and location in the middle and lower Han River basin

Figure 2. Conceptual diagram for water resources system in the middle and lower Han River basin

Table 1. Divisions for water resources allocation in the middle and lower Han River basin

Table 2. Comparison of water consumptions in current year and planning year in the middle and lower Han River basin

${P}_{a}={\gamma }_{a}\underset{i=1}{\overset{m}{\sum }}{A}_{i}\left({Y}_{i}-{Y}_{oi}\right){P}_{i}-{C}_{a}/{W}_{a}$ (17)

Figure 3. Danjiangkou Reservoir operation chart in normal water supply operation period

Table 3. Percentage of lowest ecological water demand in the rivers

${P}_{i}=\frac{10000×{\gamma }_{i}}{{q}_{i}}-{C}_{i}$ (18)

4. 结果与讨论

4.1. 三步法求解结果及分析

HWP模型是让单个分区的效益最大化，据此求得各分区的配置水量。如模型1即代表进行水资源配置时，随州市取最大经济效益。从表4中数据分析可知，位于唐白河流域的分区，其配置效益受其它分区配水影响较大，而丹江口干流以下区域由于受到水库调蓄优化，配置效益不受其它分区的配水影响。

4.2. 不同频率配置结果及分析

2020规划水平年取农业灌溉需水频率分别为50%，75%和95%，采用各计算分区1956~2000年逐月长

Table 4. Optimal benefit for each division in 2020 in the middle and lower Han River basin (Unit: 0.1 billion yuan)

Table 5. Benefit ratio of each month calculated by the HRHWP model

Table 6. Optimal allocation water for each division in 2020 (50%) in the middle and lower Han River basin

Table 7. Water resources supply and demand balance at different frequency in the middle and lower Han River basin

(a) 随州 (b) 襄阳 (c) 神农架林区 (d) 十堰 (e) 荆门 (f) 天门潜江仙桃

Figure 4. Water shortage for each division in the middle and lower Han River basin

5. 结论

1) HWP模型结果表明，位于丹江口水库以上的分区，包括随州市和襄阳市，其配置效益受其它用水分区配水影响较大，而丹江口干流以下区域由于受水库调蓄优化，配置效益不受其他分区配水影响，全区总配置效益可达2150.55亿元。

2) 从HRHWP模型结果得到的效益比看出，由于夏季需水量最大，效益比值相对较小，而春、秋和冬季的效益比均超过0.9，表明夏季用水满足程度低于其它季节。

3) FWP模型结果表明，2020水平年在50%频率下，汉江中下游湖北区域河道外的总缺水量为3.47亿m3，其中农业和工业缺水量分别为3.37亿m3和972万m3，生活用水基本满足要求。

4) 当频率分别为50%、75%和95%时，2020年汉江中下游湖北地区缺水率分别为3.11%、3.69%和3.94%。其中，城镇和农村生活用水基本得到满足，而农业灌溉和河道内生态环境用水缺口较大。随着频率增高，需水缺口逐步增大。

5) 从三级水资源分区来看，由于缺少丹江口水库的调节，唐白河流域的缺水情况明显较丹江口以下干流地区严重，三种频率下总体缺水率分别达到24.84%，27.86%和29.75%。而丹江口以下地区总体缺水率分别仅为0.49%，0.57%和0.65%。

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