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⛄ 内容介绍
电力系统无功优化是保证系统安全,经济运行的有效手段,是提高电力系统电压质量的重要措施之一。无功优化的目的在于确定系统中无功设备的合理配置,以保证电网在满足一定的安全约束条件下,使系统的技术经济性能指标最好,即无功补偿设备的安装投资及电网的运行费用最小。 电力系统无功优化是一个多变量、多约束的混合非线性规划问题,其操作变量既有连续变量又有离散变量,其优化过程比较复杂。本文采用粒子群优化算法求解无功优化问题,给出了运用粒子群优化算法的相应求解步骡,并对部分参数的取值进行了讨论和调整。计算表明,该算法能够同时处理问题中的连续变量和离散变量,能够较好地协调全局搜索和局部搜索,并具有并行计算的特性以及较强的鲁棒性,可以取得令人满意的结果。 本文对IEEE30,IEEE57节点试验系统和石家庄高邑县电网进行了无功优化计算,取得了令人满意的结果,表明用粒子群优化算法求解该问题是可行的、更有效的
⛄ 部分代码
function [baseMVA, bus, gen, branch, areas, gencost] = case_ieee30
% CASE_IEEE30 Power flow data for IEEE 30 bus test case.
% Please see 'help caseformat' for details on the case file format.
% This data was converted from IEEE Common Data Format
% (ieee30cdf.txt) on 20-Sep-2004 by cdf2matp, rev. 1.11
% See end of file for warnings generated during conversion.
%
% Converted from IEEE CDF file from:
% http://www.ee.washington.edu/research/pstca/
%
% 08/20/93 UW ARCHIVE 100.0 1961 W IEEE 30 Bus Test Case
% MATPOWER
% $Id: case_ieee30.m,v 1.3 2007/09/17 16:07:48 ray Exp $
%%----- Power Flow Data -----%%
%% system MVA base
baseMVA = 100;
%% bus data
% bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vmin
bus = [
1 3 0 0 0 0 1 1.06 0 132 1 1.06 0.94;
2 2 21.7 12.7 0 0 1 1.043 -5.48 132 1 1.06 0.94;
3 1 2.4 1.2 0 0 1 1.021 -7.96 132 1 1.06 0.94;
4 1 7.6 1.6 0 0 1 1.012 -9.62 132 1 1.06 0.94;
5 2 94.2 19 0 0 1 1.01 -14.37 132 1 1.06 0.94;
6 1 0 0 0 0 1 1.01 -11.34 132 1 1.06 0.94;
7 1 22.8 10.9 0 0 1 1.002 -13.12 132 1 1.06 0.94;
8 2 30 30 0 0 1 1.01 -12.1 132 1 1.06 0.94;
9 1 0 0 0 0 1 1.051 -14.38 1 1 1.06 0.94;
10 1 5.8 2 0 19 1 1.045 -15.97 33 1 1.06 0.94;
11 2 0 0 0 0 1 1.082 -14.39 11 1 1.06 0.94;
12 1 11.2 7.5 0 0 1 1.057 -15.24 33 1 1.06 0.94;
13 2 0 0 0 0 1 1.071 -15.24 11 1 1.06 0.94;
14 1 6.2 1.6 0 0 1 1.042 -16.13 33 1 1.06 0.94;
15 1 8.2 2.5 0 0 1 1.038 -16.22 33 1 1.06 0.94;
16 1 3.5 1.8 0 0 1 1.045 -15.83 33 1 1.06 0.94;
17 1 9 5.8 0 0 1 1.04 -16.14 33 1 1.06 0.94;
18 1 3.2 0.9 0 0 1 1.028 -16.82 33 1 1.06 0.94;
19 1 9.5 3.4 0 0 1 1.026 -17 33 1 1.06 0.94;
20 1 2.2 0.7 0 0 1 1.03 -16.8 33 1 1.06 0.94;
21 1 17.5 11.2 0 0 1 1.033 -16.42 33 1 1.06 0.94;
22 1 0 0 0 0 1 1.033 -16.41 33 1 1.06 0.94;
23 1 3.2 1.6 0 0 1 1.027 -16.61 33 1 1.06 0.94;
24 1 8.7 6.7 0 4.3 1 1.021 -16.78 33 1 1.06 0.94;
25 1 0 0 0 0 1 1.017 -16.35 33 1 1.06 0.94;
26 1 3.5 2.3 0 0 1 1 -16.77 33 1 1.06 0.94;
27 1 0 0 0 0 1 1.023 -15.82 33 1 1.06 0.94;
28 1 0 0 0 0 1 1.007 -11.97 132 1 1.06 0.94;
29 1 2.4 0.9 0 0 1 1.003 -17.06 33 1 1.06 0.94;
30 1 10.6 1.9 0 0 1 0.992 -17.94 33 1 1.06 0.94;
];
%% generator data
% bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin
gen = [
1 260.2 -16.1 10 0 1.06 100 1 360.2 0;
2 40 50 50 -40 1.045 100 1 140 0;
5 0 37 40 -40 1.01 100 1 100 0;
8 0 37.3 40 -10 1.01 100 1 100 0;
11 0 16.2 24 -6 1.082 100 1 100 0;
13 0 10.6 24 -6 1.071 100 1 100 0;
];
x=[1.06
%% branch data
% fbus tbus r x b rateA rateB rateC ratio angle status
branch = [
1 2 0.0192 0.0575 0.0528 9900 0 0 0 0 1;
1 3 0.0452 0.1652 0.0408 9900 0 0 0 0 1;
2 4 0.057 0.1737 0.0368 9900 0 0 0 0 1;
3 4 0.0132 0.0379 0.0084 9900 0 0 0 0 1;
2 5 0.0472 0.1983 0.0418 9900 0 0 0 0 1;
2 6 0.0581 0.1763 0.0374 9900 0 0 0 0 1;
4 6 0.0119 0.0414 0.009 9900 0 0 0 0 1;
5 7 0.046 0.116 0.0204 9900 0 0 0 0 1;
6 7 0.0267 0.082 0.017 9900 0 0 0 0 1;
6 8 0.012 0.042 0.009 9900 0 0 0 0 1;
6 9 0 0.208 0 9900 0 0 0.978 0 1;
6 10 0 0.556 0 9900 0 0 0.969 0 1;
9 11 0 0.208 0 9900 0 0 0 0 1;
9 10 0 0.11 0 9900 0 0 0 0 1;
4 12 0 0.256 0 9900 0 0 0.932 0 1;
12 13 0 0.14 0 9900 0 0 0 0 1;
12 14 0.1231 0.2559 0 9900 0 0 0 0 1;
12 15 0.0662 0.1304 0 9900 0 0 0 0 1;
12 16 0.0945 0.1987 0 9900 0 0 0 0 1;
14 15 0.221 0.1997 0 9900 0 0 0 0 1;
16 17 0.0524 0.1923 0 9900 0 0 0 0 1;
15 18 0.1073 0.2185 0 9900 0 0 0 0 1;
18 19 0.0639 0.1292 0 9900 0 0 0 0 1;
19 20 0.034 0.068 0 9900 0 0 0 0 1;
10 20 0.0936 0.209 0 9900 0 0 0 0 1;
10 17 0.0324 0.0845 0 9900 0 0 0 0 1;
10 21 0.0348 0.0749 0 9900 0 0 0 0 1;
10 22 0.0727 0.1499 0 9900 0 0 0 0 1;
21 22 0.0116 0.0236 0 9900 0 0 0 0 1;
15 23 0.1 0.202 0 9900 0 0 0 0 1;
22 24 0.115 0.179 0 9900 0 0 0 0 1;
23 24 0.132 0.27 0 9900 0 0 0 0 1;
24 25 0.1885 0.3292 0 9900 0 0 0 0 1;
25 26 0.2544 0.38 0 9900 0 0 0 0 1;
25 27 0.1093 0.2087 0 9900 0 0 0 0 1;
28 27 0 0.396 0 9900 0 0 0.968 0 1;
27 29 0.2198 0.4153 0 9900 0 0 0 0 1;
27 30 0.3202 0.6027 0 9900 0 0 0 0 1;
29 30 0.2399 0.4533 0 9900 0 0 0 0 1;
8 28 0.0636 0.2 0.0428 9900 0 0 0 0 1;
6 28 0.0169 0.0599 0.013 9900 0 0 0 0 1;
];
%%----- OPF Data -----%%
%% area data
areas = [
1 1;
];
%% generator cost data
% 1 startup shutdown n x1 y1 ... xn yn
% 2 startup shutdown n c(n-1) ... c0
gencost = [
2 0 0 3 0.038432 20 0;
2 0 0 3 0.25 20 0;
2 0 0 3 0.01 40 0;
2 0 0 3 0.01 40 0;
2 0 0 3 0.01 40 0;
2 0 0 3 0.01 40 0;
];
return;
% Warnings from cdf2matp conversion:
%
% ***** Qmax = Qmin at generator at bus 1 (Qmax set to Qmin + 10)
% ***** area data conversion not yet implemented (creating dummy area data)
% ***** MVA limit of branch 1 - 2 not given, set to 9900
% ***** MVA limit of branch 1 - 3 not given, set to 9900
% ***** MVA limit of branch 2 - 4 not given, set to 9900
% ***** MVA limit of branch 3 - 4 not given, set to 9900
% ***** MVA limit of branch 2 - 5 not given, set to 9900
% ***** MVA limit of branch 2 - 6 not given, set to 9900
% ***** MVA limit of branch 4 - 6 not given, set to 9900
% ***** MVA limit of branch 5 - 7 not given, set to 9900
% ***** MVA limit of branch 6 - 7 not given, set to 9900
% ***** MVA limit of branch 6 - 8 not given, set to 9900
% ***** MVA limit of branch 6 - 9 not given, set to 9900
% ***** MVA limit of branch 6 - 10 not given, set to 9900
% ***** MVA limit of branch 9 - 11 not given, set to 9900
% ***** MVA limit of branch 9 - 10 not given, set to 9900
% ***** MVA limit of branch 4 - 12 not given, set to 9900
% ***** MVA limit of branch 12 - 13 not given, set to 9900
% ***** MVA limit of branch 12 - 14 not given, set to 9900
% ***** MVA limit of branch 12 - 15 not given, set to 9900
% ***** MVA limit of branch 12 - 16 not given, set to 9900
% ***** MVA limit of branch 14 - 15 not given, set to 9900
% ***** MVA limit of branch 16 - 17 not given, set to 9900
% ***** MVA limit of branch 15 - 18 not given, set to 9900
% ***** MVA limit of branch 18 - 19 not given, set to 9900
% ***** MVA limit of branch 19 - 20 not given, set to 9900
% ***** MVA limit of branch 10 - 20 not given, set to 9900
% ***** MVA limit of branch 10 - 17 not given, set to 9900
% ***** MVA limit of branch 10 - 21 not given, set to 9900
% ***** MVA limit of branch 10 - 22 not given, set to 9900
% ***** MVA limit of branch 21 - 22 not given, set to 9900
% ***** MVA limit of branch 15 - 23 not given, set to 9900
% ***** MVA limit of branch 22 - 24 not given, set to 9900
% ***** MVA limit of branch 23 - 24 not given, set to 9900
% ***** MVA limit of branch 24 - 25 not given, set to 9900
% ***** MVA limit of branch 25 - 26 not given, set to 9900
% ***** MVA limit of branch 25 - 27 not given, set to 9900
% ***** MVA limit of branch 28 - 27 not given, set to 9900
% ***** MVA limit of branch 27 - 29 not given, set to 9900
% ***** MVA limit of branch 27 - 30 not given, set to 9900
% ***** MVA limit of branch 29 - 30 not given, set to 9900
% ***** MVA limit of branch 8 - 28 not given, set to 9900
% ***** MVA limit of branch 6 - 28 not given, set to 9900
function [baseMVA, bus, gen, branch, areas, gencost] = case_ieee30
% CASE_IEEE30 Power flow data for IEEE 30 bus test case.
% Please see 'help caseformat' for details on the case file format.
% This data was converted from IEEE Common Data Format
% (ieee30cdf.txt) on 20-Sep-2004 by cdf2matp, rev. 1.11
% See end of file for warnings generated during conversion.
%
% Converted from IEEE CDF file from:
% http://www.ee.washington.edu/research/pstca/
%
% 08/20/93 UW ARCHIVE 100.0 1961 W IEEE 30 Bus Test Case
% MATPOWER
% $Id: case_ieee30.m,v 1.3 2007/09/17 16:07:48 ray Exp $
%%----- Power Flow Data -----%%
%% system MVA base
baseMVA = 100;
%% bus data
% bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vmin
bus = [
1 3 0 0 0 0 1 1.06 0 132 1 1.06 0.94;
2 2 21.7 12.7 0 0 1 1.043 -5.48 132 1 1.06 0.94;
3 1 2.4 1.2 0 0 1 1.021 -7.96 132 1 1.06 0.94;
4 1 7.6 1.6 0 0 1 1.012 -9.62 132 1 1.06 0.94;
5 2 94.2 19 0 0 1 1.01 -14.37 132 1 1.06 0.94;
6 1 0 0 0 0 1 1.01 -11.34 132 1 1.06 0.94;
7 1 22.8 10.9 0 0 1 1.002 -13.12 132 1 1.06 0.94;
8 2 30 30 0 0 1 1.01 -12.1 132 1 1.06 0.94;
9 1 0 0 0 0 1 1.051 -14.38 1 1 1.06 0.94;
10 1 5.8 2 0 19 1 1.045 -15.97 33 1 1.06 0.94;
11 2 0 0 0 0 1 1.082 -14.39 11 1 1.06 0.94;
12 1 11.2 7.5 0 0 1 1.057 -15.24 33 1 1.06 0.94;
13 2 0 0 0 0 1 1.071 -15.24 11 1 1.06 0.94;
14 1 6.2 1.6 0 0 1 1.042 -16.13 33 1 1.06 0.94;
15 1 8.2 2.5 0 0 1 1.038 -16.22 33 1 1.06 0.94;
16 1 3.5 1.8 0 0 1 1.045 -15.83 33 1 1.06 0.94;
17 1 9 5.8 0 0 1 1.04 -16.14 33 1 1.06 0.94;
18 1 3.2 0.9 0 0 1 1.028 -16.82 33 1 1.06 0.94;
19 1 9.5 3.4 0 0 1 1.026 -17 33 1 1.06 0.94;
20 1 2.2 0.7 0 0 1 1.03 -16.8 33 1 1.06 0.94;
21 1 17.5 11.2 0 0 1 1.033 -16.42 33 1 1.06 0.94;
22 1 0 0 0 0 1 1.033 -16.41 33 1 1.06 0.94;
23 1 3.2 1.6 0 0 1 1.027 -16.61 33 1 1.06 0.94;
24 1 8.7 6.7 0 4.3 1 1.021 -16.78 33 1 1.06 0.94;
25 1 0 0 0 0 1 1.017 -16.35 33 1 1.06 0.94;
26 1 3.5 2.3 0 0 1 1 -16.77 33 1 1.06 0.94;
27 1 0 0 0 0 1 1.023 -15.82 33 1 1.06 0.94;
28 1 0 0 0 0 1 1.007 -11.97 132 1 1.06 0.94;
29 1 2.4 0.9 0 0 1 1.003 -17.06 33 1 1.06 0.94;
30 1 10.6 1.9 0 0 1 0.992 -17.94 33 1 1.06 0.94;
];
%% generator data
% bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin
gen = [
1 260.2 -16.1 10 0 1.06 100 1 360.2 0;
2 40 50 50 -40 1.045 100 1 140 0;
5 0 37 40 -40 1.01 100 1 100 0;
8 0 37.3 40 -10 1.01 100 1 100 0;
11 0 16.2 24 -6 1.082 100 1 100 0;
13 0 10.6 24 -6 1.071 100 1 100 0;
];
x=[1.06
%% branch data
% fbus tbus r x b rateA rateB rateC ratio angle status
branch = [
1 2 0.0192 0.0575 0.0528 9900 0 0 0 0 1;
1 3 0.0452 0.1652 0.0408 9900 0 0 0 0 1;
2 4 0.057 0.1737 0.0368 9900 0 0 0 0 1;
3 4 0.0132 0.0379 0.0084 9900 0 0 0 0 1;
2 5 0.0472 0.1983 0.0418 9900 0 0 0 0 1;
2 6 0.0581 0.1763 0.0374 9900 0 0 0 0 1;
4 6 0.0119 0.0414 0.009 9900 0 0 0 0 1;
5 7 0.046 0.116 0.0204 9900 0 0 0 0 1;
6 7 0.0267 0.082 0.017 9900 0 0 0 0 1;
6 8 0.012 0.042 0.009 9900 0 0 0 0 1;
6 9 0 0.208 0 9900 0 0 0.978 0 1;
6 10 0 0.556 0 9900 0 0 0.969 0 1;
9 11 0 0.208 0 9900 0 0 0 0 1;
9 10 0 0.11 0 9900 0 0 0 0 1;
4 12 0 0.256 0 9900 0 0 0.932 0 1;
12 13 0 0.14 0 9900 0 0 0 0 1;
12 14 0.1231 0.2559 0 9900 0 0 0 0 1;
12 15 0.0662 0.1304 0 9900 0 0 0 0 1;
12 16 0.0945 0.1987 0 9900 0 0 0 0 1;
14 15 0.221 0.1997 0 9900 0 0 0 0 1;
16 17 0.0524 0.1923 0 9900 0 0 0 0 1;
15 18 0.1073 0.2185 0 9900 0 0 0 0 1;
18 19 0.0639 0.1292 0 9900 0 0 0 0 1;
19 20 0.034 0.068 0 9900 0 0 0 0 1;
10 20 0.0936 0.209 0 9900 0 0 0 0 1;
10 17 0.0324 0.0845 0 9900 0 0 0 0 1;
10 21 0.0348 0.0749 0 9900 0 0 0 0 1;
10 22 0.0727 0.1499 0 9900 0 0 0 0 1;
21 22 0.0116 0.0236 0 9900 0 0 0 0 1;
15 23 0.1 0.202 0 9900 0 0 0 0 1;
22 24 0.115 0.179 0 9900 0 0 0 0 1;
23 24 0.132 0.27 0 9900 0 0 0 0 1;
24 25 0.1885 0.3292 0 9900 0 0 0 0 1;
25 26 0.2544 0.38 0 9900 0 0 0 0 1;
25 27 0.1093 0.2087 0 9900 0 0 0 0 1;
28 27 0 0.396 0 9900 0 0 0.968 0 1;
27 29 0.2198 0.4153 0 9900 0 0 0 0 1;
27 30 0.3202 0.6027 0 9900 0 0 0 0 1;
29 30 0.2399 0.4533 0 9900 0 0 0 0 1;
8 28 0.0636 0.2 0.0428 9900 0 0 0 0 1;
6 28 0.0169 0.0599 0.013 9900 0 0 0 0 1;
];
%%----- OPF Data -----%%
%% area data
areas = [
1 1;
];
%% generator cost data
% 1 startup shutdown n x1 y1 ... xn yn
% 2 startup shutdown n c(n-1) ... c0
gencost = [
2 0 0 3 0.038432 20 0;
2 0 0 3 0.25 20 0;
2 0 0 3 0.01 40 0;
2 0 0 3 0.01 40 0;
2 0 0 3 0.01 40 0;
2 0 0 3 0.01 40 0;
];
return;
% Warnings from cdf2matp conversion:
%
% ***** Qmax = Qmin at generator at bus 1 (Qmax set to Qmin + 10)
% ***** area data conversion not yet implemented (creating dummy area data)
% ***** MVA limit of branch 1 - 2 not given, set to 9900
% ***** MVA limit of branch 1 - 3 not given, set to 9900
% ***** MVA limit of branch 2 - 4 not given, set to 9900
% ***** MVA limit of branch 3 - 4 not given, set to 9900
% ***** MVA limit of branch 2 - 5 not given, set to 9900
% ***** MVA limit of branch 2 - 6 not given, set to 9900
% ***** MVA limit of branch 4 - 6 not given, set to 9900
% ***** MVA limit of branch 5 - 7 not given, set to 9900
% ***** MVA limit of branch 6 - 7 not given, set to 9900
% ***** MVA limit of branch 6 - 8 not given, set to 9900
% ***** MVA limit of branch 6 - 9 not given, set to 9900
% ***** MVA limit of branch 6 - 10 not given, set to 9900
% ***** MVA limit of branch 9 - 11 not given, set to 9900
% ***** MVA limit of branch 9 - 10 not given, set to 9900
% ***** MVA limit of branch 4 - 12 not given, set to 9900
% ***** MVA limit of branch 12 - 13 not given, set to 9900
% ***** MVA limit of branch 12 - 14 not given, set to 9900
% ***** MVA limit of branch 12 - 15 not given, set to 9900
% ***** MVA limit of branch 12 - 16 not given, set to 9900
% ***** MVA limit of branch 14 - 15 not given, set to 9900
% ***** MVA limit of branch 16 - 17 not given, set to 9900
% ***** MVA limit of branch 15 - 18 not given, set to 9900
% ***** MVA limit of branch 18 - 19 not given, set to 9900
% ***** MVA limit of branch 19 - 20 not given, set to 9900
% ***** MVA limit of branch 10 - 20 not given, set to 9900
% ***** MVA limit of branch 10 - 17 not given, set to 9900
% ***** MVA limit of branch 10 - 21 not given, set to 9900
% ***** MVA limit of branch 10 - 22 not given, set to 9900
% ***** MVA limit of branch 21 - 22 not given, set to 9900
% ***** MVA limit of branch 15 - 23 not given, set to 9900
% ***** MVA limit of branch 22 - 24 not given, set to 9900
% ***** MVA limit of branch 23 - 24 not given, set to 9900
% ***** MVA limit of branch 24 - 25 not given, set to 9900
% ***** MVA limit of branch 25 - 26 not given, set to 9900
% ***** MVA limit of branch 25 - 27 not given, set to 9900
% ***** MVA limit of branch 28 - 27 not given, set to 9900
% ***** MVA limit of branch 27 - 29 not given, set to 9900
% ***** MVA limit of branch 27 - 30 not given, set to 9900
% ***** MVA limit of branch 29 - 30 not given, set to 9900
% ***** MVA limit of branch 8 - 28 not given, set to 9900
% ***** MVA limit of branch 6 - 28 not given, set to 9900
⛄ 运行结果
⛄ 参考文献
[1] 董淑华.基于改进粒子群优化算法的电力系统无功优化[D].中南大学,2010.DOI:10.7666/d.y1719172.
[2] 陶国正,徐志成.基于粒子群优化算法的电力系统无功优化[J].计算机工程, 2010, 36(20):3.DOI:10.3969/j.issn.1000-3428.2010.20.069.
[3] 耿彦波.基于粒子群算法的电力系统无功优化[D].华北电力大学（北京）,2009.DOI:10.7666/d.D518246.
[4] 周敏,王劲草,吴刚.基于粒子群算法的电力系统无功优化[J].电工技术, 2014, 000(005):34-35.DOI:10.3969/j.issn.1002-1388.2014.05.018.
