﻿ 智能水滴算法与SQP相混合的电力环境经济调度
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 智能系统学报  2018, Vol. 13 Issue (3): 346-351  DOI: 10.11992/tis.201705002 0

### 引用本文

ZHAO Wenqing, QIN Zhibu. Hybrid intelligent water drops algorithm and sequential quadratic programming for electric power economic emission dispatch[J]. CAAI Transactions on Intelligent Systems, 2018, 13(3): 346-351. DOI: 10.11992/tis.201705002.

### 文章历史

Hybrid intelligent water drops algorithm and sequential quadratic programming for electric power economic emission dispatch
ZHAO Wenqing, QIN Zhibu
School of Control and Computer Engineering, North China Electric Power University, Baoding 071003, China
Abstract: Economic dispatch in an electric power environment is critical to reducing the cost of coal consumption and the emission of air pollutants during power generation. We propose a hybrid methodology that combines an intelligent-water-drops (IWD) algorithm with sequential quadratic programming (SQP) to improve the economic dispatch. Because of SQP’s weak global search capability, we use IWD to seek a global solution. In addition, the solution generated by the water droplets in each iteration is then taken as the initial solution of SQP, which is also slightly adjusted to improve the solution. We test the proposed approach by using a ten-unit system. In comparison with other methods that consider the valve-point effect, the proposed IWD-SQP method is feasible and effective.
Key words: intelligent water drops algorithm    sequential quadratic programming    electric power environment    economic dispatch    valve-point effect    continuous optimization    hybrid algorithm    standard test function

1 电力环境经济调度问题模型

 ${\text{Cost}} = \sum\limits_{i = 1}^{i = N} {{a_i} + {b_i}{P_i} + {c_i}{{({P_i})}^2} + \left| {{e_i}\sin ({f_i}({P_i}^{{\text{min}}} - {P_i}))} \right|}$ (1)
 ${\text{Emission}} = \sum\limits_{i = 1}^{i = N} {{\alpha _i} + {\beta _i}{P_i} + {\gamma _i}{{({P_i})}^2} + {\eta _i}\exp ({\delta _i}{P_i})}$ (2)

 $\sum\limits_{i = 1}^{\text{N}} {{P_i}} = {P_D}{\text{ + }}{P_L}$ (3)
 ${P_i^{\min}} \leqslant P_i \leqslant {P_i^{\max}}$ (4)

 ${P_L}{\text{ = }}\sum\limits_{i{\text{ = }}1}^N {\sum\limits_{j{\text{ = }}1}^N {{P_i}{B_{ij}}{P_j}} }$ (5)

 $T = w \cdot {\text{Cost}} + (1 - w){\text{Emission}} + \lambda \left| {\sum\limits_{i = 1}^N {{P_i} - ({P_D} + {P_L})} } \right|$ (6)
2 智能水滴算法与SQP相混合的算法 2.1 智能水滴算法

2.1.1 算法初始化

2.1.2 水滴选择

 $P_i^{{\text{iwd}}}(j) = \left\{ {\begin{array}{*{20}{l}} {\displaystyle\frac{{f({\text{soil}}(i,j))}}{{\sum {f({\text{soil}}(i,k))} }}}, \quad k \in {J_{{\text{iwd}}}}(i) {0}, \quad {\text{其他}} \end{array}} \right.$ (7)

 ${J_{{\text{iwd}}}}(i) \in {C_{x,y}},\;\;\;\;x \notin {\text{VCX}}({\text{iwd}})$ (8)

2.1.3 局部信息更新

 ${\text{soil}}({\text{idw}}) = {\text{soil}}({\text{idw}}) + \Delta {\text{soil}}(i,j)$ (9)
 ${\text{velocity}}(j) = {\text{velocity}}(i) + \frac{{a_v}}{{b_v + c_v \cdot {\text{soil}}(i,j)}}$ (10)
 ${\text{soil}}(i,j) = (1 - \rho n) \cdot {\text{soil}}(i,j) - {\rho _n} \cdot \Delta {\text{soil}}(i,j)$ (11)
 $\Delta {\text{soil}}(i,j) = \frac{{a_s}}{{b_s + c_s \cdot {\text{time}}(i,j)}}$ (12)

2.1.4 参数确定

 ${{\text{x}}_i} = \sum\limits_{j = 1 + (i - 1){P_i}}^{i \cdot {P_i}} {{y_j} \cdot {{10}^{{m_i} - \left[ {j - \left( {i - 1} \right)P} \right]}}}$ (13)

 ${P_i}{\text{ = }}{P_{i,{\text{min}}}}{\text{ + (}}{P_{i,{\text{max}}}} - {P_{i,{\text{min}}}}{\text{)}} \cdot {{{x_i}}/{{x_{i,{\text{max}}}}}}$ (14)
2.1.5 全局更新操作

 ${\text{soil}}(i,j) = 1.1 \times {\text{soil}}(i,j) - 0.01 \times \frac{{{\text{soil}}_{{\text{IB}}}^{{\text{iwd}}}}}{n}, \,\, \forall (i,j) \in T_{\text{IB}}$ (15)

2.2 SQP方法

 $\begin{array}{c}{\rm{min }}\nabla F{({{{P}}_k})^{\rm{T}}}{{{d}}_k} + \displaystyle\frac{1}{2}{{d}}_k^{\rm{T}}{{{H}}_k}{{{d}}_k}\\[5pt]{\rm{s.t.}}\;{g_i}({{{P}}_k}) + \left| {\nabla g{{({{{P}}_k})}^{\rm{T}}}} \right|{d_k} = 0, \,\, {{ i}} = 1,2,\cdots,{m_e}\\[5pt]\;\;\;{g_i}({{{P}}_k}) + \left| {\nabla g{{({{{P}}_k})}^{\rm{T}}}} \right|{d_k} \leqslant 0, \,\, {{i}} = 1,2,\cdots,m\end{array}$ (16)

2.3 智能水滴算法与SQP相混合的算法

1)初始化静态参数。确定智能水滴数目 ${N_{{\text{iwd}}}}$ ，每条路径上的初始泥土量、最大迭代次数、速度更新参数 ${a_v}$ ${b_v}$ ${c_v}$ ，泥土量更新参数 ${a_{\text{s}}}$ ${b_s}$ ${c_s}$ ，根据机组的出力上下限设置参数的范围。

 Download: 图 1 IWD-SQP算法流程图 Fig. 1 Flow chart of the IWD-SQP algorithm

2)初始化动态参数和水滴初始位置。设置水滴的初始速度以及携带的初始泥土量，水滴访问过的节点集。对每个水滴的初始位置进行随机初始化。

3)水滴选择并更新局部信息。水滴根据路径中的泥土量大小，按照式(7)概率大小选择下一个节点；水滴根据被选择的节点更新局部信息，按式(9)~(12)局部更新水滴的信息。

4)重复3)，直到所有的水滴都完成流动，即所有的水滴都有一条路径形成完整的解。

5)确定参数的值。根据各水滴所形成的流动路径，将其分别按式(13)、(14)计算出各个参数的值，得到本次迭代水滴的解。

6)应用SQP微调各参数值。将5)中本次迭代水滴所产生的解作为SQP的初始点进行计算，得到本次迭代的解与目标值。

7)确定本次迭代的最优解，更新全局量。确定本次迭代最优解并根据本次迭代最优解更新全局最优解，同时根据式(15)更新全局泥土量。

8)判断是否满足终止条件。当所有的水滴都收敛到同一路径上或者算法达到设定的最大迭代次数时转到9)，否则转到2)。

9)保存结果。将最优解与目标值保存，算法结束。

3 实验分析 3.1 实验对象与环境

3.2 算法参数设置

3.3 混合的IWD-SQP算法性能分析

3.4 10机组测试系统实验结果分析

4 结束语

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