﻿ 隔河岩水电站最优运行方式研究

隔河岩水电站最优运行方式研究Research on Optimal Operation Mode of Geheyan Hydropower Station

Abstract: The mid-long term reservoir operation mainly focuses on the construction and solution of models, and few studies discuss the optimal dispatch results. A mid-long term reservoir operation model which takes the maximum energy generation as objective function is established and uses discrete differential dynamic programming method (DDDP) to obtain optimal scheduling results. Taking Geheyan Reservoir as a Case study, 4 types of hydropower station operation modes and 6 types of reservoir operation modes are proposed and analyzed. The results show that the hydropower operation mode is mainly based on minimum output and increased output, while the operation mode of the reservoir is mainly based on “V-shaped type” and “upper-limit water level type”. Moreover, in the “V-shaped type” and “storage type” operation mode, the failure output operation mode of hydropower station does not appear. In the “upper limit water level type” operation mode, the minimum output operation mode of hydropower station does not appear.

1. 引言

Bellman [1] 针对多阶段最优决策问题的特点，创立了著名的动态规划(DP)方法。DP是一种全局搜索法，可求出状态变量给定离散精度下的全局最优解。然而随着离散精度和水库数的增加，遍历寻优的方式会导致“维数灾”问题 [2]。针对该问题，国内外学者相继提出了一系列改进措施，其改进思路主要有三种：其一，改进初始轨迹的选取方式，进而加快收敛速度，如冯仲恺等 [3] 结合均匀试验设计，提出了均匀动态规划。其二，分析各项约束间的关系，从而缩减搜索空间，如明波等 [4] 基于发电调度模型中水电站最小出力以及下泄流量约束，提出了搜索空间缩减法；其三，通过多核计算技术缓解维数灾难题，如张忠波等 [5] 将并行计算与动态规划相结合，用OpenMP编程模式实现动态规划的并行计算。同时，随着计算机科学的发展，现代智能算法也逐渐应用于水库优化调度问题中 [6] [7] [8] [9] [10]，但智能算法普遍存在优化机理不明晰、计算结果不稳定、泛化能力差等问题，因而目前还缺乏实用性。另一方面，部分学者基于最优调度结果开展了水库优化调度的研究，丰富了水库调度领域的研究思路和成果：Yoo等 [11] 采用线性规划计算水库优化调度结果，并基于最优调度结果分析了弃水和库容之间的影响和敏感性；周研来等 [12] 以大渡河梯级为研究对象，基于模拟调度结果采用非线性规划法修正调度函数。

2. 水库中长期发电优化调度数学模型

2.1. 模型构建

$\left\{\begin{array}{l}\begin{array}{l}\mathrm{max}\text{}F\left(\text{X}\right)\hfill \\ \text{s}\text{.t}\text{.}|\begin{array}{l}{h}_{i}\left(\text{X}\right)=0\text{}\left(i=1,2,\cdots ,s\right)\\ \text{}{g}_{j}\left(\text{X}\right)\le 0\text{}\left(j=1,2,\cdots ,m\right)\end{array}\hfill \end{array}\hfill \\ \text{X}=\left({x}_{1},{x}_{2},\cdots ,{x}_{n}\right)\in {E}_{n}\hfill \end{array}$ (2-1)

1) 选取发电量最大为目标函数

${E}_{T}^{*}=\mathrm{max}\left\{\underset{t=1}{\overset{T}{\sum }}\left[{N}_{t}\Delta t\right]\right\}=\mathrm{max}\left\{\underset{t=1}{\overset{T}{\sum }}\left[K{Q}_{t}^{fd}{H}_{t}\Delta t\right]\right\}$ (2-2)

2) 等式约束包括：水库水量平衡约束；库容曲线约束；下游水位流量关系约束；发电水头约束；水电站预想出力约束；初、末水位约束等。

$\left\{\begin{array}{l}{V}_{t+1}={V}_{t}+{\delta }_{t}\left({Q}_{t}^{in}-{Q}_{t}^{out}\right)\hfill \\ {Z}_{t}={f}_{ZV}\left({V}_{t}\right)\hfill \\ {Z}_{t}^{xy}={f}_{ZQ}\left({Q}_{t}^{out}\right)\hfill \\ {H}_{t}=\left({Z}_{t}+{Z}_{t+1}\right)/2-{Z}_{t}^{xy}-{h}_{ss,t}\hfill \\ {N}_{t}^{yx}={f}_{yx}\left({H}_{t}\right)\hfill \\ {Z}_{0}={Z}_{beg},\text{}{Z}_{T}={Z}_{end}\hfill \end{array}$ (2-3)

3) 不等式约束包括：水位约束；出力约束；非负约束等。

$\left\{\begin{array}{l}{Q}_{t}^{fd}\ge \text{}0\hfill \\ {Z}_{t}^{\mathrm{min}}\le {Z}_{t}\le {Z}_{t}^{\mathrm{max}}\hfill \\ {N}_{t}^{\mathrm{min}}\le {N}_{t}\le {N}_{t}^{\mathrm{max}}\hfill \end{array}$ (2-4)

${N}_{t}=\left\{\begin{array}{l}{N}_{t}+\gamma \left({N}_{t}-{N}_{\mathrm{min}}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\left({N}_{t}<{N}_{\mathrm{min}}\right)\\ {N}_{t}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\left({N}_{t}\ge {N}_{\mathrm{min}}\right)\end{array}$ (2-5)

2.2. 求解方法

3. 中长期发电优化最优运行方式研究

3.1. 水电站运行方式

1) 破坏运行方式：时段出力小于最小出力，称为破坏运行方式(图1(a))，记为 ${N}_{d}$

${N}_{d}:\text{\hspace{0.17em}}\text{\hspace{0.17em}}{N}_{t}<{N}_{t}^{\mathrm{min}}$ (3-1)

2) 最小出力运行方式：时段出力等于最小出力，称为最小出力运行方式(图1(b))，记为 ${N}_{\mathrm{min}}$

${N}_{\mathrm{min}}:\text{\hspace{0.17em}}\text{\hspace{0.17em}}{N}_{t}={N}_{t}^{\mathrm{min}}$ (3-2)

3) 加大出力运行方式：时段出力介于最小、最大出力间，称为加大出力运行方式(图1(c))，记为 ${N}_{c}$

${N}_{c}:\text{\hspace{0.17em}}\text{}{N}_{t}^{\mathrm{min}}<{N}_{t}<{N}_{t}^{\mathrm{max}}$ (3-3)

4) 最大出力运行方式：时段出力等于最大出力，称为最大出力运行方式(图1(d))，记为 ${N}_{\mathrm{max}}$

${N}_{\mathrm{max}}:\text{}\text{\hspace{0.17em}}{N}_{t}={N}_{t}^{\mathrm{max}}$ (3-4)

(a) 破坏运行方式 (b) 最小出力运行方式 (a) 加大出力运行方式 (b) 最大出力运行方式

Figure 1. Diagram of hydropower station operation mode

3.2. 水库运行方式

1) “V型”运行方式：水库由上限水位开始，经若干时段，最终回到上限水位，称为“V型”运行方式(如图2(a))，其水位过程满足式(3-5)。

$\left\{\begin{array}{l}{Z}_{b}={Z}_{b}^{\mathrm{max}}\hfill \\ {Z}_{b+j}^{\mathrm{min}}<{Z}_{b+j}<{Z}_{b+j}^{\mathrm{max}}\begin{array}{cc},& 0 (3-5)

2) “倒V型”运行方式：水库由下限水位开始，经若干时段，最终回到下限水位，称为“倒V型”运行方式(如图2(b))，其水位过程满足式(3-6)。

$\left\{\begin{array}{l}{Z}_{b}={Z}_{b}^{\mathrm{min}}\hfill \\ {Z}_{b+j}^{\mathrm{min}}<{Z}_{b+j}<{Z}_{b+j}^{\mathrm{max}}\begin{array}{cc},& 0 (3-6)

3) “消落型”运行方式：水库从上限水位开始，经若干时段，最终消落到下限水位，称为“消落型”运行方式(如图2(c))，其水位过程满足式(3-7)。

$\left\{\begin{array}{l}{Z}_{b}={Z}_{b}^{\mathrm{max}}\hfill \\ {Z}_{b+j}^{\mathrm{min}}<{Z}_{b+j}<{Z}_{b+j}^{\mathrm{max}}\begin{array}{cc},& 0 (3-7)

4) “蓄水型”运行方式：水库从下限水位开始，经若干时段，最终蓄水到上限水位，称为“蓄水型”运行方式(如图2(d))，其水位过程满足式(3-8)。

$\left\{\begin{array}{l}{Z}_{b}={Z}_{b}^{\mathrm{min}}\hfill \\ {Z}_{b+j}^{\mathrm{min}}<{Z}_{b+j}<{Z}_{b+j}^{\mathrm{max}}\begin{array}{cc},& 0 (3-8)

5) “上限水位型”运行方式：水库水位始终保持在上限水位，称为“上限水位型”运行方式(如图2(e))，其水位过程满足式(3-9)。

${Z}_{b+j}={Z}_{b+j}^{\mathrm{max}}\begin{array}{cc},& 0\le j\le e-b\end{array}$ (3-9)

6) “下限水位型”运行方式：水库水位始终保持在下限水位，称为“下限水位型”运行方式(如图2(f))，其水位过程满足式(3-10)。

${Z}_{b+j}={Z}_{b+j}^{\mathrm{min}}\begin{array}{cc},& 0\le j\le e-b\end{array}$ (3-10)

(a) 倒V型 (b) V型 (c) 消落型 (d) 蓄水型 (e) 上限水位型 (f) 下限水位型

Figure 2. Diagram of reservoir operation mode

4. 实例研究

4.1. 研究对象概况

Table 1. Characteristics table of Geheyan Hydropower Station

4.2. 隔河岩中长期发电优化调度方式

1) 隔河岩水电站运行方式分析

Figure 3. Statistics of operation mode of Geheyan Hydropower Station

2) 隔河岩水库运行方式分析

Table 2. Statistics of operation mode of Geheyan Reservoir

3) 隔河岩水库运行方式的出力特性

(a) V型 (b) 消落型(c) 蓄水型 (d) 上限水位型

Figure 4. Characteristics of different operation modes of Geheyan Reservoir

5. 结论

1) 隔河岩水电站运行方式以最小出力( ${N}_{\mathrm{min}}$ )和加大出力运行方式( ${N}_{c}$ )为主，两者总占比达到92.55%。

2) 隔河岩水库存在“V型”、“消落型”、“蓄水型”和“上限水位型”4种运行方式，其中以“V型”和“上限水位型”运行方式为主，两者出现次数总占比为89.43%。并且，“消落型”运行方式后一定接“蓄水型”运行方式，两者出现次数相等，而后者持续的时段数一般较短，最长不超过10旬。

3) 隔河岩的“V型”和“蓄水型”运行方式中，不存在水电站的破坏出力运行方式( ${N}_{d}$ )的时段；而“上限水位型”运行方式中，不存在最小出力运行方式( ${N}_{\mathrm{min}}$ )的时段。

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