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🔥 内容介绍
本文提出了一种两阶段的启发式计算方法,可以在最小的计算时间内重新配置一个径向分布网络。所有的网络交换机在操作的初始阶段都是关闭的,并提出了一个顺序的开关开闸策略,以获得一个接近最优的径向配置。在随后的阶段中,从径向网络中选择一对开关来交换其开/关状态。提出了一种利用总线注入分支电流矩阵的数学模型,选择一对交换机,目的是减少每次交换操作后网络的功率损耗。该方法在 33 总线、69 总线、84 总线、136 总线和 417 总线的配电网上进行了测试,结果表明,所提的方法有助于在明显较低的运行时间下实现径向配电网的最佳配置。
配电网在向电力系统的终端能源消费者提供电力方面起着至关重要的作用。然而,低电抗和电阻的比值和配网的径向性质导致了热能形式的高有源功率损失。配网重构(DNR)是在保证系统可靠运行的同时,尽量减少网络有功功率损耗的可能解决方案之一。配电网中有两种类型:常闭分段开关和常开连接开关。DNR 通过修改网络中交换机的开/关状态,提出了一种新的配电网拓扑结构。文献中用于解决 DNR 问题的方法可以大致分为三种类型:进化算法、数学规划和启发式方法[1]、[2]、[3]。然而,由于进化算法和数学规划的高计算要求,研究人员更倾向于 DNR 的启发式方法。对于快速重构,启发式算法考虑了两种策略:分支交换策略和顺序开开关策略。[4]首先提出了分支交换策略,通过交换开关对的开/关状态来重新配置最初的径向网络。然而,由于作者在分析中忽略了分支电流的反应性分量,因此所提出的方法的准确性较低。作为一种解决方案,在[5]中引入了初始网格网络的顺序开关打开策略,其中环路中的开关被策略性地打开,直到获得最优的径向配置。但该方法未能达到对大型系统的最优配置。此后,在文献中引入了几种 DNR 的启发式方法。在[6]中引入了一种最小电流循环更新机制,该机制旨在绕过局部最优点,实现全局最优结果。在[7]中,提出了一种结合分支交换和开开关策略的启发式方法。虽然文献中可用的技术是非常精确的,但它需要大量的计算时间来实现最佳配置。本文提出了一种新的两阶段启发式算法,可以在更短的时间内解决一个DNR 问题。与其他启发式方法相比,该方法减少了在操作过程中进行负载流分析(LFA)的需要,从而减少了计算时间。
📣 部分代码
function [BD,LD,TL]=data136()Vbase=13.8; %%---Base Voltage in kV---%%Sbase=1; %%---Base Power in MVA---%%Zbase=Vbase*Vbase/Sbase; %%---Base impedance in ohms---%%%% ----Line Data (or Branch data) of the system----- %%%%--- Line From To R X Line Charging Tap Angle----%% %%---Number Bus Bus (in ohms) (in ohms) (in ohms) Ratio Shift----%%LD = [ 1 1 2 0.33205 0.76653 0.0 1.0 0 2 2 3 0.00188 0.00433 0.0 1.0 0 3 3 4 0.22324 0.51535 0.0 1.0 0 4 4 5 0.09943 0.22953 0.0 1.0 0 5 5 6 0.15571 0.35945 0.0 1.0 0 6 6 7 0.16321 0.37677 0.0 1.0 0 7 7 8 0.11444 0.26417 0.0 1.0 0 8 7 9 0.05675 0.05666 0.0 1.0 0 9 9 10 0.52124 0.27418 0.0 1.0 0 10 9 11 0.10877 0.10860 0.0 1.0 0 11 11 12 0.39803 0.20937 0.0 1.0 0 12 11 13 0.91744 0.31469 0.0 1.0 0 13 11 14 0.11823 0.11805 0.0 1.0 0 14 14 15 0.50228 0.26421 0.0 1.0 0 15 14 16 0.05675 0.05666 0.0 1.0 0 16 16 17 0.29379 0.15454 0.0 1.0 0 17 1 18 0.33205 0.76653 0.0 1.0 0 18 18 19 0.00188 0.00433 0.0 1.0 0 19 19 20 0.22324 0.51535 0.0 1.0 0 20 20 21 0.10881 0.25118 0.0 1.0 0 21 21 22 0.71078 0.37388 0.0 1.0 0 22 21 23 0.18197 0.42008 0.0 1.0 0 23 23 24 0.30326 0.15952 0.0 1.0 0 24 23 25 0.02439 0.05630 0.0 1.0 0 25 25 26 0.04502 0.10394 0.0 1.0 0 26 26 27 0.01876 0.04331 0.0 1.0 0 27 27 28 0.11823 0.11805 0.0 1.0 0 28 28 29 0.02365 0.02361 0.0 1.0 0 29 29 30 0.18954 0.09970 0.0 1.0 0 30 30 31 0.39803 0.20937 0.0 1.0 0 31 29 32 0.05675 0.05666 0.0 1.0 0 32 32 33 0.09477 0.04985 0.0 1.0 0 33 33 34 0.41699 0.21934 0.0 1.0 0 34 34 35 0.11372 0.05982 0.0 1.0 0 35 32 36 0.07566 0.07555 0.0 1.0 0 36 36 37 0.36960 0.19442 0.0 1.0 0 37 37 38 0.26536 0.13958 0.0 1.0 0 38 36 39 0.05675 0.05666 0.0 1.0 0 39 1 40 0.33205 0.76653 0.0 1.0 0 40 40 41 0.11819 0.27283 0.0 1.0 0 41 41 42 2.96288 1.01628 0.0 1.0 0 42 41 43 0.00188 0.00433 0.0 1.0 0 43 43 44 0.06941 0.16024 0.0 1.0 0 44 44 45 0.81502 0.42872 0.0 1.0 0 45 44 46 0.06378 0.14724 0.0 1.0 0 46 46 47 0.13132 0.30315 0.0 1.0 0 47 47 48 0.06191 0.14291 0.0 1.0 0 48 48 49 0.11444 0.26417 0.0 1.0 0 49 49 50 0.28374 0.28331 0.0 1.0 0 50 50 51 0.28374 0.28331 0.0 1.0 0 51 49 52 0.04502 0.10394 0.0 1.0 0 52 52 53 0.02626 0.06063 0.0 1.0 0 53 53 54 0.06003 0.31858 0.0 1.0 0 54 54 55 0.03002 0.06929 0.0 1.0 0 55 55 56 0.02064 0.04764 0.0 1.0 0 56 53 57 0.10881 0.25118 0.0 1.0 0 57 57 58 0.25588 0.13460 0.0 1.0 0 58 58 59 0.41699 0.21934 0.0 1.0 0 59 59 60 0.50228 0.26421 0.0 1.0 0 60 60 61 0.33170 0.17448 0.0 1.0 0 61 61 62 0.20849 0.10967 0.0 1.0 0 62 48 63 0.13882 0.32047 0.0 1.0 0 63 1 64 0.00750 0.01732 0.0 1.0 0 64 64 65 0.27014 0.62362 0.0 1.0 0 65 65 66 0.38270 0.88346 0.0 1.0 0 66 66 67 0.33018 0.76220 0.0 1.0 0 67 67 68 0.32830 0.75787 0.0 1.0 0 68 68 69 0.17072 0.39409 0.0 1.0 0 69 69 70 0.55914 0.29412 0.0 1.0 0 70 69 71 0.05816 0.13425 0.0 1.0 0 71 71 72 0.70130 0.36890 0.0 1.0 0 72 72 73 1.02352 0.53839 0.0 1.0 0 73 71 74 0.06754 0.15591 0.0 1.0 0 74 74 75 1.32352 0.45397 0.0 1.0 0 75 1 76 0.01126 0.02598 0.0 1.0 0 76 76 77 0.72976 1.68464 0.0 1.0 0 77 77 78 0.22512 0.51968 0.0 1.0 0 78 78 79 0.20824 0.48071 0.0 1.0 0 79 79 80 0.04690 0.10827 0.0 1.0 0 80 80 81 0.61950 0.61857 0.0 1.0 0 81 81 82 0.34049 0.33998 0.0 1.0 0 82 82 83 0.56862 0.29911 0.0 1.0 0 83 82 84 0.10877 0.10860 0.0 1.0 0 84 84 85 0.56862 0.29911 0.0 1.0 0 85 1 86 0.01126 0.02598 0.0 1.0 0 86 86 87 0.41835 0.96575 0.0 1.0 0 87 87 88 0.10499 0.13641 0.0 1.0 0 88 87 89 0.43898 1.01338 0.0 1.0 0 89 89 90 0.07520 0.02579 0.0 1.0 0 90 90 91 0.07692 0.17756 0.0 1.0 0 91 91 92 0.33205 0.76653 0.0 1.0 0 92 92 93 0.08442 0.19488 0.0 1.0 0 93 93 94 0.13320 0.30748 0.0 1.0 0 94 94 95 0.29320 0.29276 0.0 1.0 0 95 95 96 0.21753 0.21721 0.0 1.0 0 96 96 97 0.26482 0.26443 0.0 1.0 0 97 94 98 0.10318 0.23819 0.0 1.0 0 98 98 99 0.13507 0.31181 0.0 1.0 0 99 1 100 0.00938 0.02165 0.0 1.0 0 100 100 101 0.16884 0.38976 0.0 1.0 0 101 101 102 0.11819 0.27283 0.0 1.0 0 102 102 103 2.28608 0.78414 0.0 1.0 0 103 102 104 0.45587 1.05236 0.0 1.0 0 104 104 105 0.69600 1.60669 0.0 1.0 0 105 105 106 0.45774 1.05669 0.0 1.0 0 106 106 107 0.20298 0.26373 0.0 1.0 0 107 107 108 0.21348 0.27737 0.0 1.0 0 108 108 109 0.54967 0.28914 0.0 1.0 0 109 109 110 0.54019 0.28415 0.0 1.0 0 110 108 111 0.04550 0.05911 0.0 1.0 0 111 111 112 0.47385 0.24926 0.0 1.0 0 112 112 113 0.86241 0.45364 0.0 1.0 0 113 113 114 0.56862 0.29911 0.0 1.0 0 114 109 115 0.77711 0.40878 0.0 1.0 0 115 115 116 1.08038 0.56830 0.0 1.0 0 116 110 117 1.09923 0.57827 0.0 1.0 0 117 117 118 0.47385 0.24926 0.0 1.0 0 118 105 119 0.32267 0.74488 0.0 1.0 0 119 119 120 0.14633 0.33779 0.0 1.0 0 120 120 121 0.12382 0.28583 0.0 1.0 0 121 1 122 0.01126 0.02598 0.0 1.0 0 122 122 123 0.64910 1.49842 0.0 1.0 0 123 123 124 0.04502 0.10394 0.0 1.0 0 124 124 125 0.52640 0.18056 0.0 1.0 0 125 124 126 0.02064 0.04764 0.0 1.0 0 126 126 127 0.53071 0.27917 0.0 1.0 0 127 126 128 0.09755 0.22520 0.0 1.0 0 128 128 129 0.11819 0.27283 0.0 1.0 0 129 128 130 0.13882 0.32047 0.0 1.0 0 130 130 131 0.04315 0.09961 0.0 1.0 0 131 131 132 0.09192 0.21220 0.0 1.0 0 132 132 133 0.16134 0.37244 0.0 1.0 0 133 133 134 0.37832 0.37775 0.0 1.0 0 134 134 135 0.39724 0.39664 0.0 1.0 0 135 135 136 0.29320 0.29276 0.0 1.0 0];%% ----Bus Data of the system---- %%%%--- Type 1 - PQ Bus ; Type 2 - PV Bus; Type 3 - Swing Bus%%----Bus Bus V theta Pg Qg Pl Ql Qgmax Qgmin----%% %%---Number Type (in pu) (in rad) (in kW)(in kVAR)(in kW)(in kVAR)(in pu) (in pu)----%%BD = [ 1 3 1.0 0 0 0 0 0 0 0 2 1 1.0 0 0 0 0 0 0 0 3 1 1.0 0 0 0 47.780 19.009 0 0 4 1 1.0 0 0 0 42.551 16.929 0 0 5 1 1.0 0 0 0 87.022 34.622 0 0 6 1 1.0 0 0 0 311.310 123.855 0 0 7 1 1.0 0 0 0 148.869 59.228 0 0 8 1 1.0 0 0 0 238.672 94.956 0 0 9 1 1.0 0 0 0 62.299 24.786 0 0 10 1 1.0 0 0 0 124.598 49.571 0 0 11 1 1.0 0 0 0 140.175 55.768 0 0 12 1 1.0 0 0 0 116.813 46.474 0 0 13 1 1.0 0 0 0 249.203 99.145 0 0 14 1 1.0 0 0 0 291.447 115.952 0 0 15 1 1.0 0 0 0 303.720 120.835 0 0 16 1 1.0 0 0 0 215.396 85.695 0 0 17 1 1.0 0 0 0 198.586 79.007 0 0 18 1 1.0 0 0 0 0 0 0 0 19 1 1.0 0 0 0 0 0 0 0 20 1 1.0 0 0 0 0 0 0 0 21 1 1.0 0 0 0 30.127 14.729 0 0 22 1 1.0 0 0 0 230.972 112.920 0 0 23 1 1.0 0 0 0 60.256 29.458 0 0 24 1 1.0 0 0 0 230.972 112.920 0 0 25 1 1.0 0 0 0 120.507 58.915 0 0 26 1 1.0 0 0 0 0 0 0 0 27 1 1.0 0 0 0 56.981 27.857 0 0 28 1 1.0 0 0 0 364.665 178.281 0 0 29 1 1.0 0 0 0 0 0 0 0 30 1 1.0 0 0 0 124.647 60.939 0 0 31 1 1.0 0 0 0 56.981 27.857 0 0 32 1 1.0 0 0 0 0 0 0 0 33 1 1.0 0 0 0 85.473 41.787 0 0 34 1 1.0 0 0 0 0 0 0 0 35 1 1.0 0 0 0 396.735 193.96 0 0 36 1 1.0 0 0 0 0 0 0 0 37 1 1.0 0 0 0 181.152 88.563 0 0 38 1 1.0 0 0 0 242.172 118.395 0 0 39 1 1.0 0 0 0 75.316 36.821 0 0 40 1 1.0 0 0 0 0 0 0 0 41 1 1.0 0 0 0 1.254 0.531 0 0 42 1 1.0 0 0 0 6.274 2.660 0 0 43 1 1.0 0 0 0 0 0 0 0 44 1 1.0 0 0 0 117.88 49.971 0 0 45 1 1.0 0 0 0 62.668 26.566 0 0 46 1 1.0 0 0 0 172.285 73.034 0 0 47 1 1.0 0 0 0 458.556 194.388 0 0 48 1 1.0 0 0 0 262.962 111.473 0 0 49 1 1.0 0 0 0 235.761 99.942 0 0 50 1 1.0 0 0 0 0 0 0 0 51 1 1.0 0 0 0 109.215 46.298 0 0 52 1 1.0 0 0 0 0 0 0 0 53 1 1.0 0 0 0 72.809 30.865 0 0 54 1 1.0 0 0 0 258.473 109.570 0 0 55 1 1.0 0 0 0 69.169 29.322 0 0 56 1 1.0 0 0 0 21.843 9.260 0 0 57 1 1.0 0 0 0 0 0 0 0 58 1 1.0 0 0 0 20.527 8.702 0 0 59 1 1.0 0 0 0 150.548 63.819 0 0 60 1 1.0 0 0 0 220.687 93.552 0 0 61 1 1.0 0 0 0 92.384 39.163 0 0 62 1 1.0 0 0 0 0 0 0 0 63 1 1.0 0 0 0 226.693 96.098 0 0 64 1 1.0 0 0 0 0 0 0 0 65 1 1.0 0 0 0 294.016 116.974 0 0 66 1 1.0 0 0 0 83.015 33.028 0 0 67 1 1.0 0 0 0 83.015 33.028 0 0 68 1 1.0 0 0 0 103.770 41.285 0 0 69 1 1.0 0 0 0 176.408 70.184 0 0 70 1 1.0 0 0 0 83.015 33.028 0 0 71 1 1.0 0 0 0 217.917 86.698 0 0 72 1 1.0 0 0 0 23.294 9.267 0 0 73 1 1.0 0 0 0 5.075 2.019 0 0 74 1 1.0 0 0 0 72.638 28.899 0 0 75 1 1.0 0 0 0 405.99 161.523 0 0 76 1 1.0 0 0 0 0 0 0 0 77 1 1.0 0 0 0 100.182 42.468 0 0 78 1 1.0 0 0 0 142.523 60.417 0 0 79 1 1.0 0 0 0 96.042 40.713 0 0 80 1 1.0 0 0 0 300.454 127.366 0 0 81 1 1.0 0 0 0 141.238 59.873 0 0 82 1 1.0 0 0 0 279.847 118.631 0 0 83 1 1.0 0 0 0 87.312 37.013 0 0 84 1 1.0 0 0 0 243.849 103.371 0 0 85 1 1.0 0 0 0 247.750 105.025 0 0 86 1 1.0 0 0 0 0 0 0 0 87 1 1.0 0 0 0 89.878 38.101 0 0 88 1 1.0 0 0 0 1137.280 482.108 0 0 89 1 1.0 0 0 0 458.339 194.296 0 0 90 1 1.0 0 0 0 385.197 163.290 0 0 91 1 1.0 0 0 0 0 0 0 0 92 1 1.0 0 0 0 79.608 33.747 0 0 93 1 1.0 0 0 0 87.312 37.013 0 0 94 1 1.0 0 0 0 0 0 0 0 95 1 1.0 0 0 0 74.001 31.370 0 0 96 1 1.0 0 0 0 232.05 98.369 0 0 97 1 1.0 0 0 0 141.819 60.119 0 0 98 1 1.0 0 0 0 0 0 0 0 99 1 1.0 0 0 0 76.449 32.408 0 0 100 1 1.0 0 0 0 0 0 0 0 101 1 1.0 0 0 0 51.322 21.756 0 0 102 1 1.0 0 0 0 59.874 25.381 0 0 103 1 1.0 0 0 0 9.065 3.843 0 0 104 1 1.0 0 0 0 2.092 0.887 0 0 105 1 1.0 0 0 0 16.735 7.094 0 0 106 1 1.0 0 0 0 1506.522 638.634 0 0 107 1 1.0 0 0 0 313.023 132.694 0 0 108 1 1.0 0 0 0 79.831 33.842 0 0 109 1 1.0 0 0 0 51.322 21.756 0 0 110 1 1.0 0 0 0 0 0 0 0 111 1 1.0 0 0 0 202.435 85.815 0 0 112 1 1.0 0 0 0 60.823 25.784 0 0 113 1 1.0 0 0 0 45.618 19.338 0 0 114 1 1.0 0 0 0 0 0 0 0 115 1 1.0 0 0 0 157.07 66.584 0 0 116 1 1.0 0 0 0 0 0 0 0 117 1 1.0 0 0 0 250.148 106.041 0 0 118 1 1.0 0 0 0 0 0 0 0 119 1 1.0 0 0 0 69.809 29.593 0 0 120 1 1.0 0 0 0 32.072 13.596 0 0 121 1 1.0 0 0 0 61.084 25.894 0 0 122 1 1.0 0 0 0 0 0 0 0 123 1 1.0 0 0 0 94.622 46.260 0 0 124 1 1.0 0 0 0 49.858 24.375 0 0 125 1 1.0 0 0 0 123.164 60.214 0 0 126 1 1.0 0 0 0 78.350 38.304 0 0 127 1 1.0 0 0 0 145.475 71.121 0 0 128 1 1.0 0 0 0 21.369 10.447 0 0 129 1 1.0 0 0 0 74.789 36.564 0 0 130 1 1.0 0 0 0 227.926 111.431 0 0 131 1 1.0 0 0 0 35.614 17.411 0 0 132 1 1.0 0 0 0 249.295 121.877 0 0 133 1 1.0 0 0 0 316.722 154.842 0 0 134 1 1.0 0 0 0 333.817 163.199 0 0 135 1 1.0 0 0 0 249.295 121.877 0 0 136 1 1.0 0 0 0 0 0 0 0]; %% ----Tie Line Data of the system---- %%%%--- Line From To R X %%---Number Bus Bus (in ohms) (in ohms)TL = [ 136 8 74 0.13132 0.30315 0 1.0 0 137 10 25 0.26536 0.13958 0 1.0 0 138 16 84 0.14187 0.14166 0 1.0 0 139 39 136 0.08512 0.08499 0 1.0 0 140 26 52 0.04502 0.10394 0 1.0 0 141 51 97 0.14187 0.14166 0 1.0 0 142 56 99 0.14187 0.14166 0 1.0 0 143 63 121 0.03940 0.09094 0 1.0 0 144 67 80 0.12944 0.29882 0 1.0 0 145 80 132 0.01688 0.03898 0 1.0 0 146 85 136 0.33170 0.17448 0 1.0 0 147 92 105 0.14187 0.14166 0 1.0 0 148 91 130 0.07692 0.17756 0 1.0 0 149 91 104 0.07692 0.17756 0 1.0 0 150 93 105 0.07692 0.17756 0 1.0 0 151 93 133 0.07692 0.17756 0 1.0 0 152 97 121 0.26482 0.26443 0 1.0 0 153 111 48 0.49696 0.64567 0 1.0 0 154 127 77 0.17059 0.08973 0 1.0 0 155 129 78 0.05253 0.12126 0 1.0 0 156 136 99 0.29320 0.29276 0 1.0 0]; BD(:,5:8)=BD(:,5:8)/(1000*Sbase); %%---Conversion of P and Q in pu quantity---%%LD(:,4:5)=LD(:,4:5)/Zbase; %%----Conversion of R and X in pu quantity---%%TL(:,4:5)=TL(:,4:5)/Zbase; %%----Conversion of R and X in pu quantity---%%
⛳️ 运行结果
🔗 参考文献
[1] 李国胜,华泽玺,苗轶如.基于MATLAB与VC++混合编程实现配电网重构算法[J].贵州大学学报:自然科学版, 2012, 29(3):4.DOI:10.3969/j.issn.1000-5269.2012.03.014.
[2] 易波.基于二次协作优化方法的配电网重构[D].长沙理工大学,2013.DOI:10.7666/d.Y2306157.