论文：Multi-Objective Modified Grey Wolf Optimizer for Optimal Power Flow-最优潮流

论文来源：

Multi-objective Modified Grey Wolf Optimizer for ..._百度学术 http://xueshu.baidu.com/s?wd=Multi-Objective+Modified+Grey+Wolf+Optimizer+for+Optimal+Power+Flow&rsv_bp=0&tn=SE_baiduxueshu_c1gjeupa&rsv_spt=3&ie=utf-8&f=8&rsv_sug2=1&sc_f_para=sc_tasktype%3D%7BfirstSimpleSearch%7D

关于OPF的介绍的链接---东南大学

【图文】六、最优潮流汇总._百度文库 https://wenku.baidu.com/view/dafe8d4749d7c1c708a1284ac850ad02de8007ea.html

1. Optimal Power Flow：

https://baike.baidu.com/item/%E6%9C%80%E4%BC%98%E6%BD%AE%E6%B5%81/11003211?fr=aladdin

最优潮流 [1] (Optimal Power Flow，OPF)是指当系统的结构参数和负荷情况都已给定时，调节可利用的控制变量(如发电机输出功率、可调变压器抽头等)来找到能满足所有运行约束条件的，并使系统的某一性能指标(如发电成本或网络损耗)达到最优值下的潮流分布。优潮流是一个典型的非线性优化问题，且由于约束的复杂性使得其训一算复杂，难度较大。虽然人们已经提出了许多种方法，并且在部分场合有所应用，但是要大规模实用化，满足电力系统的运行要求还有不少问题要解决。

潮流计算：确定电网的电压和功率分布

实际电网中往往只知道负荷功率和供电节点的电压，怎样确定各点电压和功率？？

2.OPF问题表述： 论文中和PPT中的，并不是电气工程专业，所有有些纠结那个定义更好，而且后续的内容只是看懂了一些参数设置的界限以及定义

下载了文档：是真的不懂在干啥

3.GWO 算法改进：

文中作者的论点是灰狼算法中a是约束整个勘探阶段的，它的值也不应当是一个单纯的随机数，故而在文中提出了这种概念：

但是我觉的GWO算法在思想上的根据等级确定了三个最好的，三个最好的会同时的分布在不同的方向吗？每个根据Agent中的三个最优的最为每一次的更新方向，感觉没有依据可言啊。三头狼都在一个方向上则均值也是在哪一个方向，没有更多的多样性啊，觉的在使用的时候是不适合多目标的，而且很容易陷入局部最优，我自是这么想，没有code 没有依据

4. 多目标优化句子

（1） Pareto Optimization is used to make a decision in a multiobjective problem, in which case there are no solution for enhancement any objective without sacrificing the others[33,34].
（2）In order to efficiently and effectively obtain the solution, the search for the best solution is executed in two stages. The
first stage, is to find a set of non-dominated solutions, and the second stage, is to obtain the best compromise solution

(3)

(4) dominance comparison strategy adopted for updating the archive: 1) In case the new solution obtained is
infeasible or dominated by other members in the population, the solution will not be saved into the repository. 2) If a
nondominated member in the population cannot be dominated by any solution in the current repository, the solution will be
saved into the repository. 3) Any dominated solution in the current repository by this nondominated member will be
removed from the repository.

最佳折中方案的模糊决策

（1）归一化：The fuzzy method has been implemented to normalize the　objective functions which are not in the same range.
（２）ＭＯAlgorithms utilizing the aforementioned objective functions, which does not give a single optimal solution, but rather a set of Pareto optimal solutions that cannot improve one objective without being unfair to the rest of objectives.

(3) However, the requirement of the practical applications is to chose just one solution called best compromise solution (Utopia solution) which satisfy various optimization goals.

5. 多目标GWO算法-----学习的地方，学习人家如何的去表述

1. Representation of Solution.
a) Read the original data of power system and the control parameters of MOGWO shown in Table I.
b) Each search agents, are coded by real number and takes its positions (as a trial solution vector) to compose OPF control variables as in Eq.(5)

2. Initialization

The first search agent takes its positions randomly using sets of uniform random number distribution ranging within the
range of the boundaries as in the following equation:

3. Start the improvision . set iteration = 0

4. Power Flow solution

During iterations, for each wolf, the full Newton-Raphson (NR) power flow analysis is performed to evaluate the objective
function .

5. Non-dominate solutions based on Pareto strategy

a) Calculate the value of objective functions using Eqs. (26,27) based on the results of the NR power flow calculations.
b) The Pareto method as in Eqs.(37,38) is applied to obtain all non-dominated solutions which are stored in the Paret set repository.
6. Best compromise solution based Fuzzy Decision-Making.
a) Utilize Eq. (39) to convert each objective function value into corresponding fuzzy membership function values.
b) Choose the weight factor ߱௜ for all non-dominated solutions and sort μ୩ in Eq.(40) from the largest to the smallest.
The best compromise solution is that having the highest cardinal priority ranking.
7. Update the contents of the Pareto-set in each iteration.
That is done by inserting all the currently non-dominated positions into the repository. Any dominated positions from the
repository are eliminated in the process.
8. Save the first three best the global solutions obtained so far from the pareto-set.
9. In line with “winner-take-all” rule for the leader's wolf[39],

alpha wolves take the best global compromise solution with highest rank, while beta and delta wolves will take the
second and third one.

10. Encircling prey: grey wolves encircle prey during the hunt using Eqs.(29-32, 36)
11. Hunting: oblige the omegas search agents to update their values according to the position of the leaders search
agents using Eqs.(33-35).
12. Verify the boundary limits.
If there are any violations in the inequality constraints, then the position of the responsible wolf will be fixed using Eq.(28).
13. Stop the process: If the maximum number of iterations is satisfied then go to Step 14, else go back to step 4.
14. Attacking prey: The hunting process of grey wolves will be stopped when the prey stops. Then the final Pareto-optimal
set from the repository is available.

6. 图表实验：

自己觉得有借鉴的：

[33] S. M. Mazhari, H. Monsef, R. Romero, “A Multi-Objective Distribution System Expansion Planning Incorporating Customer Choices on Reliability”, IEEE Trans. Power Syst., vol. 31, no. 2, pp. 1330–1340, 2016.DOI: 10.1109/TPWRS.2015.2430278
[34] Paterakis et al., “Multi-objective reconfiguration of radial distribution systems using reliability indices”, IEEE Trans. Power Syst., vol. 31, no. 2, pp. 1048–1062, 2016. DOI: 10.1109/TPWRS.2015.2425801

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