电气工程学报, 2015, 10(6): 67-70 doi:

理论研究

分布式发电接入主动配电网的全局优化与研究

沈鑫, 曹敏

云南电力试验研究院(集团)有限公司电力研究院 昆明 650217

Global Optimization and Research on Distributed Generation Integration to Active Distribution Network

Shen Xin, Cao Min

Yunnan Electric Power Research Institute Kunming 650217 China

责任编辑: 陈大立

收稿日期: 2015-05-11   网络出版日期: 2015-06-25

基金资助: 国家高技术研究发展计划(863计划)资助项目.  2011AA05A120

Received: 2015-05-11   Online: 2015-06-25

作者简介 About authors

沈 鑫 男 1981年生,高级工程师,博士研究生,研究方向为电能计量和智能电网。

曹 敏 男 1961年生,教授级高级工程师,云南电网公司一级技术专家,云南省技术带头人,研究方向为电能计量和智能电网。

摘要

主动配电网是实现大规模间歇式新能源并网运行和控制、电网与充放电设施互动、智能配用电等电网分析与运行关键技术的有效解决方案,针对分布式发电规划问题,建立主动配电网线损最小、电压偏差最小、投资成本最小的多目标分布式发电规划模型。采用模糊集将多目标优化转换为单一目标优化,使总体满意度最大化,提升整体性能。同时采用改进多种群遗传算法对建立的模型进行求解,在一定程度上克服了多种群遗传算法容易较早收敛的问题,并对某城市小区主动配电网系统上进行计算、仿真和试验,验证了该模型和算法的有效性。

关键词: 分布式发电 ; 主动配电网 ; 全局优化

Abstract

Active distribution network is an effective approach to solutions such as the high-penetration of intermittent renewable energy, interaction between grid ,charge and discharge facilities,and also the analysis and operation of smart grid. In allusion to the planning of distributed generators,a multi-objective programming model, which takes into account the least active power loss, the best voltage level and the smallest investment cost, is established. Using the fuzzy set theory to transform the multi-objective optimization into mono-objective optimization and maximizing the overall satisfaction improves the overall performance. At the same time, the modified multi-population genetic algorithm is used to solve the model. To a certain extent, this algorithm overcomes the premature convergence caused by multi-population genetic algorithm. The 35 node power system of certain city community is checked the effectiveness of the model and algorithm.

Keywords: Distributed generation ; active distribution network ; global optimization

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本文引用格式

沈鑫, 曹敏. 分布式发电接入主动配电网的全局优化与研究. 电气工程学报[J], 2015, 10(6): 67-70 doi:

Shen Xin. Global Optimization and Research on Distributed Generation Integration to Active Distribution Network. Journal of Electrical Engineering[J], 2015, 10(6): 67-70 doi:

1 引言

主动配电网是实现大规模间歇式新能源并网运行和控制、电网与充放电设施互动、智能配用电等电网分析与运行关键技术的有效解决方案[1]。分布式发电是一种重要的新能源,与大电网的结合是普遍公认的节能减排、绿色环保且安全可靠的电力系统运行方式,是电力发展的方向[2]

分布式发电(Distributed Generation,DG)是直接接在用户附近或配电网中向用户供电的小型发电装置,其不但能够缓解能源危机,而且可以补充大电源、远距离输电,解决大电网互联存在的无法灵活跟踪负荷变化、局部事故易扩散等问题,并可在一定程度上调节电网负荷的峰谷差,改善电能质量,因此在配电网中得到了广泛的应用。

在配电网中引入DG后,其安装位置和容量对配电网的规划和运行会产生一定的影响,合理确定DG的容量和位置对配电网的效益具有非常重要的作用[2]。本文从经济性、电压质量和电压稳定性多方面考虑,建立了网损最小、节点电压偏差最小及电压稳定裕度最大的多目标DG规划模型,运用模糊集理论将多目标转换为单一目标优化,并采用改进的多种群遗传算法对多目标数学模型进行优化,解决传统多种群遗传算法早熟的问题,并最终得到了接入DG后的最优规划方案。

2 分布式电源接入数学模型

2.1 目标函数

在满足配电网安全约束的前提下,配电网DG规划是对DG进行最优选址和定容[3],本文评估DG效益的指标选用系统网损指标、静态电压稳定裕度指标和电压偏差指标,数学模型表示如下。

2.1.1 网络损耗最小

由于配电网电压等级较低,R/X值较大,功率在馈线中流动造成的网损较大,以网损作为优化目标,能获得较好经济效益,配电网网损最小目标函数为

式中,Ploss为配电网网损;Nl为支路数;Gl(i,j)为支路l的电导;ij分别为支路两端节点号;UiUj为节点ij的电压幅值;δij为节点ij的相位差。

2.1.2 分布式发电的投资成本

包括设备综合成本和安装成本,投资成本最小的目标函数为

式中,Xi取0、1,Xi = 0表示节点i不接入DG,Xi = 1表示节点i接入DG;n为设备的使用年限;r为贴现率;Caz,iCOM,i为节点i DG运行维护和安装成本;PDGi为节点i DG的额定安装容量。

2.1.3 电压偏差最小

传统的DG规划,往往将节点电压看成约束条件进行限制,这样优化后的结果往往使节点电压非常接近其限定值。而节点电压幅值是系统安全和电能质量的重要指标,幅值过低将影响用户正常工作,过高影响系统安全,电压偏差最小目标函数为

式中,Ui为节点i电压幅值;Uispec为期望电压;ΔUimax为最大允许偏差;N为配电网节点数。

2.2 约束条件

(1)等式约束为潮流方程。

(2)不等式约束为:

1)电压约束: ;

2)支路功率最大值约束: ;

3)分布式发电容量限制: ;

4)旋转备用约束: ;

5)DG有功总量上限约束:

式中, 为节点电压幅值上、下限;Pl为支路有功功率;PDGimaxPDGimin为DG注入有功的上、下限;Psmax为配电系统实际购电的最大功率;Ps为配电系统购电的实际功率;PLGi为节点负荷有功;NDG为安装DG总数;N为节点数;η为DG有功总量占系统负荷总量的比例上限。

2.3 基于模糊集理论的多目标单一化

由于网损、投资成本及电压偏差优化目标具有不同量纲,相互之间可能存在矛盾,难以使各个子目标同时达到最优[6]。本文采用模糊理论将3个优化子目标转化为单一目标,引入通用的线性分段函数来表示各子目标的模糊隶属度函数

式中,μi为对应子目标的隶属度,i = 1,2,3; 为对应子目标函数值的上限,由决策者在规划过程中根据系统状况给定;fi*为对应子目标进行优化得到的最佳目标值。

经过模糊化处理后原多目标规划问题就转化为单一规划问题

式中,λ表示总体满意度。

3 改进的多种群遗传算法

对于多目标函数的遗传算法,多种群的并行算法是很具吸引力的[7],且结果更优,本文对传统的多种群遗传算法进行两方面的改进。

3.1 引入自适应交叉和变异算子

交叉率和变异率过小难以产生新个体,使得搜索过程缓慢甚至停滞;交叉率和变异率过大又会使算法变成随机搜索算法,破坏优良个体[7]。本文采用自适应变异和交叉算子:当前一代种群中个体的适应度值低于平均值时,提高交叉率和变异率来增大其转变为优良个体的几率;反之则降低变异率和交叉率来保存优良个体,自适应调整公式如下

式中,t = 1,2,3,…对应多目标规划中的各个子目标函数;Fmaxt为适应度函数最大值;Favgt为适应度函数平均值;Fdt为交叉个体中适应度函数的较大值;Fbt为变异个体的适应度函数值,取Pm,max = 0.1,Pm,min = 0.001,Pc,max = 0.9,Pc,min = 0.5。

3.2 算法结构的改进

为改善传统多种群遗传算法算子取值的不同结果易波动的不足,对算法进行改进,改进多种群遗传算法的如图1所示。第1~m个种群为子种群,对应独立的目标函数f1,f2,…,fm。第m + 1个种群为父种群,对应综合目标函数Z。精华种群则保留其他两类种群一定数量的最优个体。迁徙算子决定父、子种群的联系频度,子种群仅与父种群进行直接的信息交换,交换的充分程度决定算法的性能和收敛速度。人工算子将父子种群中的最优个体及时地保存在精华种群中,保证进化过程中的良好信息不被破坏。

图1

图1   改进的多种群遗传算法结构示意图

Fig.1   Improved multiple population genetic algorithm


父子种群间的进化过程是相互独立的,每个种群可以引入自适应遗传算子,自动地求解不同阶段的交叉率和变异率,使种群高效地朝着最优解收敛,摆脱传统算法受控于固定交叉率和变异率的束缚。精华种群(J)可作为收敛依据之一,进化终止后,将精华种群中的个体排序,可得到最优和若干次优方案。

改进的多种群遗传算法的流程图如图2所示。

图2

图2   改进的多种群遗传算法的流程图

Fig.2   Improve multiple population genetic algorithm


3.3 仿真试验及计算

对某城市小区配电网进行分布式电源的选址和定容计算,35节点网架结构如图3所示,有功负荷为337MW,无功负荷为116Mvar,DG规划总容量不超过系统总负荷的10%,功率因数为0.91,群体规模为60,最大迭代次数为100,保留率为0.1。

图3

图3   某城市小区的主动配电网络拓扑图

Fig.3   A city district of active power distribution network topology


为了将单目标优化与多目标优化进行比较分析,首先对单目标进行优化,然后进行多目标优化,并对接入DG 前后网损、投资成本、电压偏差进行比较,结果见表1

表1   仿真结果对比

Tab.1  The simulation results

规划
方案
规划结果f1 / kWf2 /万元f3(pu)
1未接入DG194.600.432
210(8.2),13(5.7),21(6.1),25(4.6),30(6.8)153.48750.342
38(5.4),10(6.4),19(5.2),22(7.1),26(6.9)183.58020.397
42(9.7),11(4.8),17(7.6),22(8.2)171.78900.287
52(8.7),10(6.3),25(8.3),32(4.1),28(5.7)162.58600.328
62(7.3),14(6.5),16(5.2),26(6.7),33(7.3)158.28170.312

注:方案1未接入DG;方案2、3、4为采用改进算法得到的系统网损、投资成本、电压偏差3个子目标的DG规划结果;方案5、6为采用多种群遗传算法和改进算法得到的多目标优化结果。规划结果中,括号外为接入DG的节点编号,括号内为优化接入DG容量,单位为MV·A。

新窗口打开| 下载CSV


表1可知,在配电网中接入分布式电源可以减小网损和电压偏差,为电网经济、稳定运行创造有利条件。比较方案2~6得到满意度的值,结果见表2

表2   单目标和多目标比较总体满意度比较

Tab.2  Compare single objective and multi-objective overall satisfaction

规划方案目标隶属度总体满意度λ
μ1μ2μ3
21.000.250.530.25
30.091.000.470.09
40.190.781.000.19
50.670.580.830.58
60.780.820.890.78

新窗口打开| 下载CSV


单目标优化和多目标优化时各目标的隶属度对比可以看出,虽然单目标优化以得到很高的模糊函数隶属度,但是其他两个目标的隶属度较低,总体的满意度较差。多目标优化时,各个子目标隶属度比较平均,总体满意度好于单目标优化,很好的协调了各优化目标之间的关系。与多种群算法相比,改进算法在收敛准确度方面更高,总体满意度也更为优越。

4 结论

本文建立配电网网损最小、投资成本且电压偏差最小的多目标分布式规划模型,运用模糊集理论,将多目标问题单一化,通过最大化总体满意度来提高整体性能,仿真验证结果表明采用多目标优化能够获得比单目标更好的总体满意度,使各子目标达到相对最优,很好的协调了各目标函数之间的关系。模型采用改进多种群遗传算法进行求解,克服多种群遗传算法早熟陷入局部最优的缺点,获得了更好的收敛准确度,通过实例验证了模型和算法的有效性。

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