肖永江，于永進(jìn)，張桂林

基于改進(jìn)烏燕鷗算法的分布式電源優(yōu)化配置

肖永江，于永進(jìn)，張桂林

(山東科技大學(xué)電氣與自動(dòng)化工程學(xué)院，山東 青島 266590)

對(duì)分布式電源(DG)接入配電網(wǎng)進(jìn)行合理規(guī)劃配置，能夠在兼顧運(yùn)營(yíng)商和用戶(hù)利益的同時(shí)，提高系統(tǒng)電壓穩(wěn)定性。在考慮經(jīng)濟(jì)指標(biāo)的情況下，提出了一種新的系統(tǒng)電壓增強(qiáng)指標(biāo)，改善了系統(tǒng)整體電壓分布。建立了多目標(biāo)優(yōu)化模型，利用層次分析法確定各目標(biāo)函數(shù)的權(quán)重，進(jìn)而轉(zhuǎn)化成單目標(biāo)函數(shù)規(guī)劃問(wèn)題。針對(duì)烏燕鷗算法全局搜索能力較強(qiáng)和局部搜索能力較弱的缺點(diǎn)，提出了一種新穎的改進(jìn)烏燕鷗算法。將遺傳算法的變異思想融入其中，進(jìn)行DG的優(yōu)化配置，提高了收斂速度和收斂精度。通過(guò)算例驗(yàn)證了改進(jìn)的烏燕鷗算法對(duì)改善系統(tǒng)電壓分布效果明顯，所建立的模型有很好的實(shí)際意義。

分布式電源；配電網(wǎng)；多目標(biāo)優(yōu)化；層次分析法；改進(jìn)烏燕鷗算法

0 引言

本文構(gòu)造的目標(biāo)函數(shù)在考慮運(yùn)營(yíng)商利益的同時(shí)，還考慮了用戶(hù)購(gòu)電成本。為了改善系統(tǒng)整體節(jié)點(diǎn)電壓水平，本文提出了一種新的系統(tǒng)電壓增強(qiáng)指標(biāo)，然后將它加入到目標(biāo)函數(shù)當(dāng)中。由于經(jīng)濟(jì)指標(biāo)和系統(tǒng)電壓增強(qiáng)指標(biāo)量綱不同，需要進(jìn)行無(wú)量綱化然后歸一化處理，根據(jù)層次分析法確定各個(gè)目標(biāo)函數(shù)的權(quán)重，得到綜合目標(biāo)函數(shù)。在此基礎(chǔ)上，針對(duì)DG的選址定容問(wèn)題對(duì)烏燕鷗算法做出了相應(yīng)的改進(jìn)，并將其應(yīng)用到DG的規(guī)劃問(wèn)題上。

1 分布式電源的優(yōu)化配置模型

首先建立DG的優(yōu)化配置模型，以有功網(wǎng)損、年投資運(yùn)行費(fèi)用、用戶(hù)購(gòu)電成本和系統(tǒng)電壓增強(qiáng)指標(biāo)來(lái)構(gòu)造目標(biāo)數(shù)函數(shù)，以功率平衡、電壓、配電線路極限傳輸和DG裝置容量為約束條件，進(jìn)而規(guī)劃合適的優(yōu)化配置方案。

1.1 目標(biāo)函數(shù)

1) 網(wǎng)損費(fèi)用

以系統(tǒng)的有功網(wǎng)損最低構(gòu)造目標(biāo)函數(shù)，如式(1)所示。

將系統(tǒng)的有功網(wǎng)損轉(zhuǎn)化成經(jīng)濟(jì)指標(biāo)，如式(2)所示。

2) 分布式電源的投資成本

3) 用戶(hù)購(gòu)電成本

4) 系統(tǒng)電壓增強(qiáng)

為了使系統(tǒng)電壓增強(qiáng)指標(biāo)更大，以及方便多目標(biāo)的歸一化，定義目標(biāo)函數(shù)為

1.2 約束條件

1) 節(jié)點(diǎn)功率平衡約束

2) 節(jié)點(diǎn)電壓約束

3) 線路的極限功率約束

2 多目標(biāo)函數(shù)權(quán)重系數(shù)確定

2.1 無(wú)量綱化

2.2 層次分析法

1) 構(gòu)造判斷矩陣

2) 求特征值即特征向量

3) 一致性檢驗(yàn)

2.3 多目標(biāo)歸一化

各個(gè)子目標(biāo)由式(14)無(wú)量綱化之后，使用層次分析法對(duì)各個(gè)目標(biāo)函數(shù)主觀賦權(quán)，然后確定子目標(biāo)的權(quán)重，因此把多個(gè)子目標(biāo)函數(shù)統(tǒng)一為

3 改進(jìn)烏燕鷗算法

3.1 標(biāo)準(zhǔn)烏燕鷗算法

3.1.1遷徙行為(全局搜索)

算法通過(guò)模擬烏燕鷗群體的遷徙過(guò)程來(lái)實(shí)現(xiàn)全局搜索，在遷徙階段需要滿(mǎn)足3個(gè)條件。

1) 避免沖突

2) 聚集

烏燕鷗個(gè)體在移動(dòng)過(guò)程中避免與其他烏燕鷗位置發(fā)生沖突以后，會(huì)向最佳位置所在的方向進(jìn)行移動(dòng)。其公式為

3) 更新

烏燕鷗向著最佳位置所在方向進(jìn)行移動(dòng)的軌跡，其公式為

3.1.2攻擊行為(局部搜索)

烏燕鷗在遷徙過(guò)程中依靠翅膀和重量來(lái)保持高度，并且可以不斷調(diào)整攻擊角度和速度。在要攻擊獵物時(shí)，烏燕鷗在空中的盤(pán)旋行為可被定義為如下數(shù)學(xué)模型。

烏燕鷗的攻擊位置根據(jù)式(24)—式(27)可得：

3.2 烏燕鷗算法的改進(jìn)

本文根據(jù)建立的模型，為了減少配電網(wǎng)的網(wǎng)損以及降低費(fèi)用，對(duì)傳統(tǒng)烏燕鷗算法做出以下三點(diǎn)改進(jìn)。

1) 種群個(gè)體位置優(yōu)化

2) 最優(yōu)解微調(diào)策略

3) 增強(qiáng)局部搜索能力

3.3 算法流程

圖1 改進(jìn)STOA算法流程圖

4 算例分析

4.1 基本參數(shù)

圖2 IEEE33節(jié)點(diǎn)配電系統(tǒng)

4.2 仿真算例分析

根據(jù)上述參數(shù)仿真，對(duì)歸一化之后的目標(biāo)函數(shù)進(jìn)行最小值尋優(yōu)。采用改進(jìn)自適應(yīng)遺傳算法[7]、烏燕鷗算法和改進(jìn)烏燕鷗算法進(jìn)行對(duì)比，結(jié)果如表1所示。

表1 不同算法結(jié)果對(duì)比

圖3 IEEE33各節(jié)點(diǎn)的電壓幅值

圖4 不同算法網(wǎng)損對(duì)比

表2 不同算法優(yōu)化結(jié)果對(duì)比

由表2可以看出：3種智能算法在迭代精度方面相近，但是本文改進(jìn)的烏燕鷗算法尋優(yōu)精度更好。在尋優(yōu)效率方面，本文算法平均迭代次數(shù)為64次，而其他兩種算法的收斂次數(shù)為87次和135次，相比較而言，本文所改進(jìn)算法的迭代次數(shù)最少。上述3種算法在各運(yùn)行100次以后，本文算法的尋優(yōu)效率最高，平均耗時(shí)最少，尋優(yōu)精度和效率上更為優(yōu)越。

5 結(jié)論

2) 提出改進(jìn)烏燕鷗算法，針對(duì)選址定容問(wèn)題進(jìn)行了相應(yīng)的改進(jìn)，初次迭代尋優(yōu)的結(jié)果優(yōu)于其他算法。融入了遺傳算法的變異環(huán)節(jié)，提出了最優(yōu)解微調(diào)策略，加快了算法收斂速度，通過(guò)算例仿真，驗(yàn)證了本文改進(jìn)的烏燕鷗算法具有很好的適應(yīng)性。

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Optimal configuration of distributed power generation based on an improved sooty tern optimization algorithm

XIAO Yongjiang, YU Yongjin, ZHANG Guilin

(College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China)

Reasonable planning and configuration of distributed power generation (DG) accessing the distribution network can improve system voltage stability while taking into account the interests of operators and users. In this paper, considering economic indicators, a new system voltage enhancement indicator is proposed to improve the overall voltage distribution of the system. A multi-objective optimization model is established, and an analytic hierarchy process is used to determine the weight of each objective function, which is then transformed into a single objective function programming problem. Given the problem that the sooty tern optimization algorithm has relatively strong global search ability but its local search ability is weak, a novel and improved sooty tern optimization algorithm is proposed. It incorporates the genetic algorithm's mutation idea and optimizes the configuration of DG. This improves convergence speed and accuracy. The calculation example verifies that the improved sooty tern optimization algorithm has a good effect on improving the system voltage distribution, and the established model has good practical significance.

This work is supported by the Key Research and Development Program of Shandong Province (No. 2019GGX103049).

distributed generation;distribution network;multi-objective optimization; analytic hierarchy process; improved sooty tern optimization algorithm

10.19783/j.cnki.pspc.210381

山東省重點(diǎn)研發(fā)計(jì)劃資助(2019GGX103049)

2021-04-10；

2021-07-06

肖永江(1996—)，男，碩士研究生，研究方向?yàn)殡娏ο到y(tǒng)運(yùn)行與控制；E-mail: 1785897859@qq.com

于永進(jìn)(1980—)，男，通信作者，博士，副教授，主要研究方向?yàn)殡娏ο到y(tǒng)運(yùn)行與控制；E-mail: yaydjto@163.com

張桂林(1983—)，男，博士，副教授，研究方向?yàn)闇h(huán)非線性建模與控制。E-mail: zhangguilin@sdust.edu.cn

(編輯 葛艷娜)