基于牛頓拉夫遜法潮流計(jì)算的matlab實(shí)驗(yàn)報(bào)告定稿

基于牛頓拉夫遜法潮流計(jì)算的matlab實(shí)驗(yàn)報(bào)告一、實(shí)驗(yàn)?zāi)康膽?yīng)用MATLAB語(yǔ)言編寫(xiě)具有一定通用性的牛頓-拉夫遜法潮流計(jì)算程序。要求：（1）潮流計(jì)算方法為牛頓-拉夫遜法。（2）編程語(yǔ)言為MATLAB。（3）程序具有較強(qiáng)通用性。二、程序流程圖所用公式其中開(kāi)始形成節(jié)點(diǎn)導(dǎo)納矩陣開(kāi)始形成節(jié)點(diǎn)導(dǎo)納矩陣輸入原始數(shù)據(jù)設(shè)節(jié)點(diǎn)電壓，i=1,2…,n,is置迭代次數(shù)置節(jié)點(diǎn)號(hào)i=1按式（3-3），（3-4）計(jì)算雅克比矩陣元素按式（3-2）計(jì)算節(jié)點(diǎn)的，，節(jié)點(diǎn)的，求解修正方程式，得，雅克比矩陣是否已全部形成？計(jì)算平衡節(jié)點(diǎn)及PV節(jié)點(diǎn)功率求，迭代次數(shù)k=k+1i=i+1？潮流計(jì)算完成計(jì)算各節(jié)點(diǎn)電壓的新值：求解問(wèn)題及其結(jié)果IEEE-美國(guó)新英格蘭10機(jī)39節(jié)點(diǎn)測(cè)試系統(tǒng)系統(tǒng)單線圖二、系統(tǒng)參數(shù)1）系統(tǒng)容量基準(zhǔn)值為100MVA。2)負(fù)荷數(shù)據(jù)見(jiàn)表D-1表D-1負(fù)荷數(shù)據(jù)節(jié)點(diǎn)號(hào)有功（MW）無(wú)功（Mvar）節(jié)點(diǎn)號(hào)有功（MW）無(wú)功（Mvar）BUS-3BUS-4BUS-7BUS-8BUS-12BUS-15BUS-16BUS-18BUS-20322.0500.0233.8522.08.5320.0329.0158.0680.02.4184.084.0176.088.0153.032.330.0103.0BUS-21BUS-23BUS-24BUS-25BUS-26BUS-27BUS-28BUS-29BUS-39274.0247.5308.0224.0139.0281.0206.0283.51104.0115.084.6-75.527.626.93）發(fā)電機(jī)數(shù)據(jù)見(jiàn)表D-2表D-2發(fā)電機(jī)數(shù)據(jù)發(fā)電機(jī)節(jié)點(diǎn)號(hào)有功（MW）無(wú)功（Mvar）電壓（p.u.）PVPQPQPVPVPQPVPVPVBUS-30BUS-32BUS-33BUS-34BUS-35BUS-36BUS-37BUS-38BUS-39250.00650.00632.00508.00650.00560.00540.00830.001000.00175.90103.3596.881.047501.012301.049301.027801.026501.03000平衡節(jié)點(diǎn)BUS-310.0(電壓幅角)1.0（幅值）4）線路參數(shù)見(jiàn)表D-3表D-3線路參數(shù)序號(hào)節(jié)點(diǎn)I節(jié)點(diǎn)JR(p.u.)X(p.u.)B/2(p.u.)LN1LN2LN3LN4LN5LN6LN7LN8LN9LN10LN11LN12LN13LN14LN15LN16LN17LN18LN19LN20LN21LN22LN23LN24LN25LN26LN27LN28LN29LN30LN31LN32LN33LN34BUS-2BUS-39BUS-3BUS-25BUS-4BUS-18BUS-5BUS-14BUS-6BUS-8BUS-7BUS-11BUS-8BUS-9BUS-39BUS-11BUS-13BUS-14BUS-15BUS-16BUS-17BUS-19BUS-21BUS-24BUS-18BUS-27BUS-22BUS-23BUS-24BUS-26BUS-27BUS-28BUS-29BUS-29BUS-1BUS-1BUS-2BUS-2BUS-3BUS-3BUS-4BUS-4BUS-5BUS-5BUS-6BUS-6BUS-7BUS-8BUS-9BUS-10BUS-10BUS-13BUS-14BUS-15BUS-16BUS-16BUS-16BUS-16BUS-17BUS-17BUS-21BUS-22BUS-23BUS-25BUS-26BUS-26BUS-26BUS-280.003500.001000.001300.007000.001300.001100.000800.000800.000200.000800.000600.000700.000400.002300.001000.000400.000400.000900.001800.000900.000700.001600.000800.000300.000700.001300.000800.000600.002200.003200.001400.004300.005700.001400.041100.025000.015100.008600.021300.013300.012800.012900.002600.011200.009200.008200.004600.036300.025000.004300.004300.010100.021700.009400.008900.019500.013500.005900.008200.017300.014000.009600.035000.032300.014700.047400.062500.015100.349350.37500.128600.073000.110700.106900.067100.069100.021700.073800.056500.069450.039000.190200.600000.036450.036450.086150.183000.085500.067100.152000.127400.034000.065950.160800.128250.092300.180500.256500.119800.390100.514500.12450LN35:BUS-4接有并聯(lián)電容器，B4＝1.0000LN36:BUS-5接有并聯(lián)電容器，B4＝2.00005)變壓器參數(shù)見(jiàn)表D-4表D-4變壓器參數(shù)序號(hào)節(jié)點(diǎn)I節(jié)點(diǎn)JR(p.u.)X(p.u.)變比(%)TR37TR38TR39TR40TR41TR42TR43TR44TR45TR46TR47TR48BUS-11BUS-13BUS-30BUS-31BUS-32BUS-34BUS-33BUS-35BUS-36BUS-37BUS-38BUS-20BUS-12BUS-12BUS-2BUS-6BUS-10BUS-20BUS-19BUS-22BUS-23BUS-25BUS-29BUS-190.001600.001600.000000.000000.000000.000900.000700.000000.000500.000600.000800.000700.043500.043500.018100.025000.020000.018000.014200.014300.027200.023200.015600.01380100.6100.6102.5107.0107.0100.9107.0102.5100.0102.5102.5106.0%IEEE-美國(guó)新英格蘭10機(jī)39節(jié)點(diǎn)測(cè)試系統(tǒng)%123456%busvoltanglepqtypebus=[11.00000.000.000.00121.00000.000.000.00131.00000.00-3.22-0.024141.00000.00-5.00-1.84151.00000.000.000.00161.00000.000.000.00171.00000.00-2.338-0.84181.00000.00-5.22-1.76191.00000.000.000.001101.00000.000.000.001111.00000.000.000.001121.00000.00-0.085-0.881131.00000.000.000.001141.00000.000.000.001151.00000.00-3.20-1.531161.00000.00-3.29-0.3231171.00000.000.000.001181.00000.00-1.58-0.301191.00000.000.000.001201.00000.00-6.80-1.031211.00000.00-2.74-1.151221.00000.000.000.001231.00000.00-2.475-1.151241.00000.00-3.08-0.9221251.00000.00-2.24-0.4721261.00000.00-1.39-0.171271.00000.00-2.81-0.7551281.00000.00-2.06-0.2761291.00000.00-2.835-0.2691301.04750.002.500.002311.00000.000.000.003321.00000.006.501.7591331.00000.006.321.03351341.01230.005.080.002351.04930.006.500.002361.00000.005.600.96881371.02780.005.400.002381.02650.008.300.002391.03000.00-1.040.002];%1234567%line:frombustobusR,X,G,B/2Kline=[2 1 0.00350 0.04110 00.349350;39 1 0.00100 0.02500 00.375000;3 2 0.00130 0.01510 00.128600;25 2 0.00700 0.00860 00.073000;4 3 0.00130 0.02130 00.110700;18 3 0.00110 0.01330 00.106900;5 4 0.00080 0.01280 00.067100;14 4 0.00080 0.01290 00.069100;6 5 0.00020 0.00260 00.021700;8 5 0.00080 0.01120 00.073800;7 6 0.00060 0.00920 00.056500;11 6 0.00070 0.00820 00.069450;8 7 0.00040 0.0046000.039000;9 8 0.00230 0.03630 00.190200;39 9 0.00100 0.02500 00.600000;11 10 0.00040 0.00430 00.036450;13 10 0.00040 0.00430 00.036450;14 13 0.00090 0.01010 00.086150;15 14 0.00180 0.02170 00.183000;16 15 0.00090 0.00940 00.085500;17 16 0.00070 0.00890 00.067100;19 16 0.00160 0.01950 00.152000;21 16 0.00080 0.01350 00.127400;24 16 0.00030 0.00590 00.034000;18 17 0.00070 0.00820 00.065950;27 17 0.00130 0.01730 00.160800;22 21 0.00080 0.01400 00.128250;23 22 0.00060 0.00960 00.092300;24 23 0.00220 0.03500 00.180500;26 25 0.00320 0.03230 00.256500;27 26 0.00140 0.01470 00.119800;28 26 0.00430 0.04740 00.390100;29 26 0.00570 0.06250 00.514500;29 28 0.00140 0.01510 00.124500;400001.00000;500002.00000;11 12 0.00160 0.04350 00100.60000/100;13 12 0.00160 0.04350 00100.60000/100;30 2 0.00000 0.01810 00102.50000/100;31 6 0.00000 0.02500 00107.00000/100;32 10 0.00000 0.02000 00107.00000/100;34 20 0.00090 0.01800 00100.90000/100;33 19 0.00070 0.01420 00107.00000/100;35 22 0.00000 0.01430 00102.50000/100;36 23 0.00050 0.02720 00100.00000/100;37 25 0.00060 0.02320 00102.50000/100;38 29 0.00080 0.01560 00102.50000/100;20 19 0.00070 0.01380 00106.00000/100];計(jì)算結(jié)果牛頓－拉夫遜法潮流計(jì)算結(jié)果節(jié)點(diǎn)計(jì)算結(jié)果：n節(jié)點(diǎn)節(jié)點(diǎn)電壓節(jié)點(diǎn)相角（角度）節(jié)點(diǎn)注入功率11.049185-8.8749910.000000+j0.00000021.053167-6.3671800.000000+j0.00000031.041493-9.207297-3.220000+j-0.02400041.036574-10.042585-5.000000+j-1.84000051.044652-8.9592370.000000+j0.00000061.043883-8.2931040.000000+j0.00000071.032645-10.342431-2.338000+j-0.84000081.031177-10.811816-5.220000+j-1.76000091.042715-10.5956480.000000+j0.000000101.046426-6.0104760.000000+j0.000000111.044322-6.7924620.000000+j0.000000121.030736-6.795388-0.085000+j-0.880000131.042351-6.6754910.000000+j0.000000141.036310-8.2323370.000000+j0.000000151.018517-8.519794-3.200000+j-1.530000161.025492-7.051856-3.290000+j-0.323000171.032750-8.0771180.000000+j0.000000181.034779-8.936485-1.580000+j-0.300000191.044862-2.3821690.000000+j0.000000200.988148-3.811032-6.800000+j-1.030000211.024926-4.596980-2.740000+j-1.150000221.042650-0.0705120.000000+j0.000000231.032952-0.245457-2.475000+j-1.150000241.021125-6.906503-3.080000+j-0.922000251.060163-4.952002-2.240000+j-0.472000261.052697-6.205207-1.390000+j-0.170000271.037683-8.217337-2.810000+j-0.755000281.050444-2.695196-2.060000+j-0.276000291.0501630.063077-2.835000+j-0.269000301.0043921.5947816.500000+j1.759000310.9916322.8925726.320000+j1.033500321.0505397.7977865.600000+j0.968800331.047500-3.9575982.500000+j1.211174341.0123001.3857745.080000+j1.826359351.0493004.9253246.500000+j2.637566361.0278001.8194765.400000+j-0.108224371.0265007.1255798.300000+j0.214225381.030000-10.390696-1.040000+j-2.291639391.0000000.0000005.628660+j1.384403線路計(jì)算結(jié)果：n節(jié)點(diǎn)I節(jié)點(diǎn)J線路功率S(I,J)線路功率S(J,I)線路損耗dS(I,J)211.178698+j-0.360055-1.174311+j-0.3604810.004386+j-0.7205363916.405845+j-2.096152-6.361848+j2.4082870.043997+j0.31213532-3.633961+j-0.5426133.649983+j0.4465770.016021+j-0.0960362522.370242+j-1.109311-2.328681+j0.9973560.041562+j-0.11195543-0.750370+j-0.3071720.751094+j0.0800140.000724+j-0.2271591830.337560+j-0.663855-0.337133+j0.4385990.000427+j-0.225256541.635254+j0.499000-1.633054+j-0.6091190.002200+j-0.1101191442.621711+j-0.216428-2.616576+j0.1507770.005135+j-0.065651654.826035+j-0.675350-4.821682+j0.6846070.004353+j0.00925785-3.178130+j-1.0418363.186428+j0.9989890.008297+j-0.04284776-4.249274+j-0.9695594.259899+j1.0106570.010625+j0.0410981163.465003+j-0.270003-3.457273+j0.2091360.007730+j-0.06086687-1.909893+j-0.1967321.911274+j0.1295590.001381+j-0.067173980.132235+j0.116464-0.131977+j-0.5214320.000258+j-0.4049683997.617154+j-1.902126-7.557438+j2.1426870.059717+j0.2405611110-3.483660+j-0.2030643.488121+j0.1713520.004461+j-0.0317121310-3.008372+j-0.7304893.011879+j0.6886800.003508+j-0.0418091413-2.934129+j-0.4114632.941429+j0.3072640.007300+j-0.1041991514-0.311115+j-0.9985560.312417+j0.6278910.001303+j-0.37066516152.896296+j0.430232-2.888885+j-0.5314440.007411+j-0.1012121716-2.048841+j0.9507402.052282+j-1.0491220.003441+j-0.09838319164.542969+j0.681545-4.511670+j-0.6258730.031300+j0.05567221163.324778+j-0.302389-3.316338+j0.1770060.008440+j-0.12538324160.410793+j-0.811601-0.410571+j0.7447570.000222+j-0.0668441817-1.917560+j0.3638551.920087+j-0.4752080.002527+j-0.1113532717-0.128621+j0.1326480.128754+j-0.4755310.000133+j-0.34288422216.093176+j1.070437-6.064778+j-0.8476110.028398+j0.2228262322-0.406149+j-1.1160630.406824+j0.9280400.000675+j-0.1880242423-3.490793+j-0.1103993.516516+j0.1388370.025723+j0.0284382625-0.771398+j-0.4428810.773189+j-0.1115800.001791+j-0.5544602726-2.681379+j-0.8876482.691475+j0.7319000.010096+j-0416063+j-0.565082-1.408178+j-0.2107470.007885+j-0.77583029261.921038+j-0.679443-1.901899+j-0.2482720.019138+j-0.92771529283.491624+j-0.395924-3.476063+j0.2890820.015561+j-0.106842400.000000+j-1.0744850.000000+j0.0000000.000000+j-1.074485500.000000+j-2.1825960.000000+j0.0000000.000000+j-2018656+j0.473066-0.018327+j-0.4641260.000329+j0.00894013120.066943+j0.423225-0.066673+j-0.4158740.000270+j0.0073513027.897633+j-0.731582-7.897633+j1.8602770.000000+j1.1286953167.506817+j1.371343-7.506817+j0.1091530.000000+j1.480496321012.260592+j5.296517-12.260592+j-2.0640070.000000+j3.23250934205.080000+j1.826359-5.054406+j-1.3144730.025594+j0.5118863319-1.716763+j5.3489101.736896+j-4.9405040.020133+j0.40840535226.500000+j2.637566-6.500000+j-1.9984770.000000+j0.63908936231.402814+j-0.195113-1.401865+j0.2467630.000949+j0.05165037259.586236+j0.419689-9.533808+j1.6075170.052428+j2.0272063829-12.165903+j2.10659312.280860+j0.1350620.114957+j2.2416552019-1.745594+j0.2844731.747837+j-0.2402650.002242+j0.044208結(jié)果分析：此程序的運(yùn)行結(jié)果和試驗(yàn)程序給出的結(jié)果是一致的。說(shuō)明程序無(wú)誤，但在精確度上有微小差異，這主要是和導(dǎo)納矩陣的精確度以及顯示精度有關(guān)。心得：本程序分模塊進(jìn)行，先是排序，再是求導(dǎo)納陣，然后求雅閣比，再進(jìn)行迭代運(yùn)算，程序本身很簡(jiǎn)潔明了，運(yùn)行的時(shí)候只需要在matlab里輸入main就行了，然后打開(kāi)BUS和line所在的.m文件，結(jié)果就會(huì)自動(dòng)存在result文件中了，通過(guò)編寫(xiě)牛頓拉夫遜法matlab潮流計(jì)算程序復(fù)習(xí)了潮流計(jì)算的知識(shí)，也實(shí)現(xiàn)了計(jì)算機(jī)算法附錄：實(shí)驗(yàn)源程序：Main函數(shù)：clear[dfile,pathname]=uigetfile('*.m','SelectDataFile');ifpathname==0error('youmustselectavaliddatafile')elselfile=length(dfile);%stripoff.meval(dfile(1:lfile-2));end[nb,mb]=size(bus);[nl,ml]=size(line);%計(jì)算bus和line矩陣的行數(shù)和列數(shù)[bus,line,nPQ,nPV,nodenum]=Num(bus,line);%對(duì)節(jié)點(diǎn)重新排序的子程序Y=y(bus,line)%計(jì)算節(jié)點(diǎn)導(dǎo)納矩陣的子程序myf=fopen('Result.m','w');fprintf(myf,'計(jì)算結(jié)果');fclose(myf);%在當(dāng)前目錄下生成“Result.m”文件，寫(xiě)入節(jié)點(diǎn)導(dǎo)納矩陣formatlongEPS=1.0e-10;%設(shè)定誤差精度f(wàn)ort=1:100%開(kāi)始迭代計(jì)算，設(shè)定最大迭代次數(shù)為100，以便不收斂情況下及時(shí)跳出[dP,dQ]=dPQ(Y,bus,nPQ,nPV);%計(jì)算功率偏差dP和dQ的子程序J=Jac(bus,Y,nPQ);%計(jì)算雅克比矩陣的子程序UD=zeros(nPQ,nPQ);fori=1:nPQUD(i,i)=bus(i,2);%生成電壓對(duì)角矩陣endenddAngU=J\[dP;dQ];dAng=dAngU(1:nb-1,1);%計(jì)算相角修正量dU=UD*(dAngU(nb:nb+nPQ-1,1));%計(jì)算電壓修正量bus(1:nPQ,2)=bus(1:nPQ,2)-dU;%修正電壓bus(1:nb-1,3)=bus(1:nb-1,3)-dAng;%修正相角if(max(abs(dU))<EPS)&(max(abs(dAng))<EPS)breakend%判斷是否滿足精度誤差，如滿足則跳出，否則返回繼續(xù)迭代endbus=PQ(bus,Y,nPQ,nPV);%計(jì)算每個(gè)節(jié)點(diǎn)的有功和無(wú)功注入的子程序[bus,line]=ReNum(bus,line,nodenum);%對(duì)節(jié)點(diǎn)恢復(fù)編號(hào)的子程序YtYm=YtYm(line);%計(jì)算線路的等效Yt和Ym的子程序，以計(jì)算線路潮流bus_res=bus_res(bus);%計(jì)算節(jié)點(diǎn)數(shù)據(jù)結(jié)果的子程序S_res=S_res(bus,line,YtYm);%計(jì)算線路潮流的子程序myf=fopen('Result.m','a');fprintf(myf,'牛頓－拉夫遜法潮流計(jì)算結(jié)果節(jié)點(diǎn)計(jì)算結(jié)果：n節(jié)點(diǎn)節(jié)點(diǎn)電壓節(jié)點(diǎn)相角（角度）節(jié)點(diǎn)注入功率\n');fori=1:nbfprintf(myf,'%2.0f',bus_res(i,1));fprintf(myf,'%10.6f',bus_res(i,2));fprintf(myf,'%10.6f',bus_res(i,3));fprintf(myf,'%10.6f+j%10.6f\n',real(bus_res(i,4)),imag(bus_res(i,4)));endfprintf(myf,'n線路計(jì)算結(jié)果：n節(jié)點(diǎn)I節(jié)點(diǎn)J線路功率S(I,J)線路功率S(J,I)線路損耗dS(I,J)\n');fori=1:nlfprintf(myf,'%2.0f',S_res(i,1));fprintf(myf,'%2.0f',S_res(i,2));fprintf(myf,'%10.6f+j%10.6f',real(S_res(i,3)),imag(S_res(i,3)));fprintf(myf,'%10.6f+j%10.6f',real(S_res(i,4)),imag(S_res(i,4)));fprintf(myf,'%10.6f+j%10.6f\n',real(S_res(i,5)),imag(S_res(i,5)));endfclose(myf);%迭代結(jié)束后繼續(xù)在“Result.m”寫(xiě)入節(jié)點(diǎn)計(jì)算結(jié)果和線路計(jì)算結(jié)果程序結(jié)束"Num.m"作用為對(duì)節(jié)點(diǎn)重排序，并修改相應(yīng)的線路數(shù)據(jù)function[bus,line,nPQ,nPV,nodenum]=Num(bus,line)[nb,mb]=size(bus);[nl,ml]=size(line);nSW=0;%numberofswingbuscounternPV=0;%numberofPVbuscounternPQ=0;%numberofPQbuscounterfori=1:nb,%nb為總節(jié)點(diǎn)數(shù)type=bus(i,6);iftype==3,nSW=nSW+1;%incrementswingbuscounterSW(nSW,:)=bus(i,:);elseiftype==2,nPV=nPV+1;%incrementPVbuscounterPV(nPV,:)=bus(i,:);elsenPQ=nPQ+1;%incrementPQbuscounterPQ(nPQ,:)=bus(i,:);endend;bus=[PQ;PV;SW];newbus=[1:nb]';nodenum=[newbusbus(:,1)];bus(:,1)=newbus;fori=1:nlforj=1:2fork=1:nbifline(i,j)==nodenum(k,2)line(i,j)=nodenum(k,1);breakendendendend"y.m"作用為計(jì)算節(jié)點(diǎn)導(dǎo)納矩陣functionY=y(bus,line)[nb,mb]=size(bus);[nl,ml]=size(line);Y=zeros(nb,nb);fork=1:nlI=line(k,1);%讀入線路參數(shù)J=line(k,2);Zt=line(k,3)+j*line(k,4);Yt=1/Zt;Ym=line(k,5)+j*line(k,6);K=line(k,7);if(K==0)&(J~=0)%普通線路:K=0;Y(I,I)=Y(I,I)+Yt+Ym;Y(J,J)=Y(J,J)+Yt+Ym;Y(I,J)=Y(I,J)-Yt;Y(J,I)=Y(I,J);endif(K==0)&(J==0)%對(duì)地支路:K=0,J=0,R=X=0;Y(I,I)=Y(I,I)+Ym;endifK>0%變壓器線路:Zt和Ym為折算到i側(cè)的值,K在j側(cè)Y(I,I)=Y(I,I)+Yt+Ym;Y(J,J)=Y(J,J)+Yt/K/K;Y(I,J)=Y(I,J)-Yt/K;Y(J,I)=Y(I,J);endifK<0%變壓器線路:Zt和Ym為折算到K側(cè)的值,K在i側(cè)Y(I,I)=Y(I,I)+Yt+Ym;Y(J,J)=Y(J,J)+K*K*Yt;Y(I,J)=Y(I,J)+K*Yt;Y(J,I)=Y(I,J);endend"dPQ.m"作用為計(jì)算功率偏差function[dP,dQ]=dPQ(Y,bus,nPQ,nPV)%nPQ、nPV為相應(yīng)節(jié)點(diǎn)個(gè)數(shù)n=nPQ+nPV+1;%總節(jié)點(diǎn)個(gè)數(shù)dP=bus(1:n-1,4);dQ=bus(1:nPQ,5);%對(duì)dP和dQ賦初值PV節(jié)點(diǎn)不需計(jì)算dQ平衡節(jié)點(diǎn)不參與計(jì)算fori=1:n-1forj=1:ndP(i,1)=dP(i,1)-bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3)));ifi<nPQ+1dQ(i,1)=dQ(i,1)-bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3)));endendend%利用循環(huán)計(jì)算求取dP和dQ"Jac.m"作用為計(jì)算雅克比矩陣functionJ=Jac(bus,Y,nPQ)[nb,mb]=size(bus);H=zeros(nb-1,nb-1);N=zeros(nb-1,nPQ);K=zeros(nPQ,nb-1);L=zeros(nPQ,nPQ);%將雅克比矩陣分塊，即：J=[HN;KL]，并初始化Qi=zeros(nb-1,1);Pi=zeros(nb-1,1);fori=1:nb-1forj=1:nbPi(i,1)=Pi(i,1)+bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3)));Qi(i,1)=Qi(i,1)+bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3)));endend%初始化并計(jì)算Qi和Pifori=1:nb-1forj=1:nb-1ifi~=jH(i,j)=-bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3)));elseH(i,j)=Qi(i,1)+imag(Y(i,j))*((bus(i,2))^2);end%分別計(jì)算H矩陣的對(duì)角及非對(duì)角元素ifj<nPQ+1ifi~=jN(i,j)=-bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3)));elseN(i,j)=-Pi(i,1)-real(Y(i,j))*((bus(i,2))^2);endend%分別計(jì)算N矩陣的對(duì)角及非對(duì)角元素ifi<nPQ+1ifi~=jK(i,j)=bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3)));elseK(i,j)=-Pi(i,1)+real(Y(i,j))*((bus(i,2))^2);end%分別計(jì)算K矩陣的對(duì)角及非對(duì)角元素ifj<nPQ+1ifi~=jL(i,j)=-bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3)));elseL(i,j)=-Qi(i,1)+imag(Y(i,j))*((bus(i,2))^2);endend%分別計(jì)算L矩陣的對(duì)角及非對(duì)角元素endendendJ=[HN;KL];%生成雅克比矩陣"PQ.m"作用為計(jì)算每個(gè)節(jié)點(diǎn)的功率注入functionbus=PQ(bus,Y,nPQ,nPV)n=nPQ+nPV+1;%n為總節(jié)點(diǎn)數(shù)fori=nPQ+1:n-1forj=1:nbus(i,5)=bus(i,5)+bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3)));endend%利用公式計(jì)算PV節(jié)點(diǎn)的無(wú)功注入forj=1:nbus(n,4)=bus(n,4)+bus(n,2)*bus(j,2)*(real(Y(n,j))*cos(bus(n,3)-bus(j,3))+imag(Y(n,j))*sin(bus(n,3)-bus(j,3)));bus(n,5)=bus(n,5)+bus(n,2)*bus(j,2)*(real(Y(n,j))*sin(bus(n,3)-bus(j,3))-imag(Y(n,j))*cos(bus(n,3)-bus(j,3)));end%計(jì)算平衡節(jié)點(diǎn)的無(wú)功及有功注入"ReNum.m"作用為對(duì)節(jié)點(diǎn)和線路數(shù)據(jù)恢復(fù)編號(hào)function[bus,line]=ReNum(bus,line,nodenum)[nb,mb]=size(bus);[nl,ml]=size(line);bus_temp=zeros(nb,mb);%bus_temp矩陣用于臨時(shí)存放bus矩陣的數(shù)據(jù)k=1;fori=1:nbforj=1:nbifbus(j,1)==kbus_temp(k,:)=bus(j,:);k=k+1;endendend%利用bus矩陣的首列編號(hào)重新對(duì)bus矩陣排序并存入bus_temp矩陣中bus=bus_temp;%重新賦值回bus，完成bus矩陣的重新編號(hào)fori=1:nlforj=1:2fork=1:nbifline(i,j)==nodenum(k,1)line(i,j)=nodenum(k,2);breakendendendend%恢復(fù)line的編號(hào)"YtYm.m"作用為計(jì)算線路的等效Yt和Ym，以計(jì)算線路潮流functionYtYm=YtYm(line)[nl,ml]=size(line);YtYm=zeros(nl,5);%對(duì)YtYm矩陣賦初值0YtYm(:,1:2)=line(:,1:2);%矩陣前兩列為線路兩段節(jié)點(diǎn)編號(hào)，后三列分別為線路等效Yt，i側(cè)的等效Ym，j側(cè)的等效Ymj=sqrt(-1);fork=1:nlI=line(k,1);J=line(k,2);Zt=line(k,3)+j*line(k,4);ifZt~=0Yt=1/Zt;endYm=line(k,5)+j*line(k,6);K=line(k,7);if(K==0)&(J~=0)%普通線路:K=0YtYm(k,3)=Yt;YtYm(k,4)=Ym;YtYm(k,5)=Ym;endif(K==0)&(J==0)%對(duì)地支路:K=0,J=0,R=X=0YtYm(k,4)=Ym;endifK>0%變壓器線路:Zt和Ym為折算到i側(cè)的值,K在j側(cè)YtYm(k,3)=Yt/K;YtYm(k,4)=Ym+Yt*(K-1)/K;YtYm(k,5)=Yt*(1-K)/K/K;endifK<0%變壓器線路:Zt和Ym為折算到K側(cè)的值,K在i側(cè)YtYm(k,3)=-Yt*K;YtYm(k,4)=Ym+Yt*(1+K);YtYm(k,5)=Yt*(K^2+K);endend"bus_res.m"計(jì)算并返回節(jié)點(diǎn)數(shù)據(jù)結(jié)果functionbus_res=bus_res(bus)[nb,mb]=size(bus);bus_res=zeros(nb,4);%bus_res矩陣儲(chǔ)存著節(jié)點(diǎn)計(jì)算結(jié)果bus_res(:,1:2)=bus(:,1:2);bus_res(:,3)=bus(:,3)*180/pi;%相角采用角度制bus_res(:,4)=bus(:,4)+(sqrt(-1))*bus(:,5);%注入功率end"S_res.m"計(jì)算并返回線路潮流functionS_res=S_res(bus,line,YtYm)[nl,ml]=size(line);S_res=zeros(nl,5);%S_res矩陣儲(chǔ)存著線路潮流計(jì)算結(jié)果S_res(:,1:2)=line(:,1:2);%前兩列為節(jié)點(diǎn)編號(hào)fork=1:nlI=S_res(k,1);J=S_res(k,2);if(J~=0)&(I~=0)S_res(k,3)=bus(I,2)^2*(conj(YtYm(k,3))+conj(YtYm(k,4)))-bus(I,2)*bus(J,2)*(cos(bus(I,3))+j*sin(bus(I,3)))*(conj(cos(bus(J,3))+j*sin(bus(J,3))))*conj(YtYm(k,3));S_res(k,4)=bus(J,2)^2*(conj(YtYm(k,3))+conj(YtYm(k,5)))-bus(I,2)*bus(J,2)*(conj(cos(bus(I,3))+j*sin(bus(I,3))))*(cos(bus(J,3))+j*sin(bus(J,3)))*conj(YtYm(k,3));S_res(k,5)=S_res(k,3)+S_res(k,4);%利用公式計(jì)算非接地支路的潮流elseif(J==0)S_res(k,3)=bus(I,2)^2*conj(YtYm(k,4));S_res(k,5)=S_res(k,3)+S_res(k,4);elseS_res(k,4)=bus(J,2)^2*conj(YtYm(k,5));S_res(k,5)=S_res(k,3)+S_res(k,4);%利用公式計(jì)算接地支路的潮流endendendend作業(yè)y=pifun(10000)y=3.1415>>clearall>>tic;>>y=pifun(100000);>>toc;Elapsedtimeis0.014727seconds.functiony=pifun(n)y=0;fori=1:ny=y+(-1)^(i-1)*1/(2*i-1);endy=y*4;end>>a=0:pi/12:2*pi;>>x=5*cos(a);>>y=3*sin(a);>>plot(x,y)clearformatlongmax1=100;eps1=1.0e-10;eps2=1.0e-10;>>x0=[1.01.01.0]';x=x0;fori=1:max1,A=Fd(x);b=F(x);dx=A\b;%矩陣左除，即b除以Ax=x-dx;sprintf('第%d次迭代結(jié)果：\n',i)[xdxF(x)]%在屏幕上輸出每次的x(i),dx(i),F(x(i))if(max(abs(dx))<eps1)&(max(abs(F(x)))<eps2)breakendendans=第1次迭代結(jié)果：ans=0.9271660275216500.0728339724783501.3111821259085110.4608255403622090.539174459637791-24.062491382655779-0.5300540795902311.5300540795902310.147573280945995ans=第2次迭代結(jié)果：ans=0.5018641043912150.4253019231304350.0104813987548680.1873147780763010.273510762285908-5.878576435100477-0.528121534118709-0.0019325454715220.013528291912525ans=第3次迭代結(jié)果：ans=0.5005844096414050.0012796947498100.0022669049922680.0610447317778920.126270046298410-1.291470136051974-0.525085549559423-0.0030359845592860.002837480507536ans=第4次迭代結(jié)果：ans=0.5001071124267420.0004772972146630.0003396889614650.0115643149629220.049480416814970-0.198312653023639-0.523882243946242-0.0012033056131810.000407361167536ans=第5次迭代結(jié)果：ans=0.5000054898064050.0001016226203370.0000165185979270.0005989530207930.010965361942129-0.009739343772851-0.523613482331101-0.0002687616151410.000019534404784ans=第6次迭代結(jié)果：ans=0.5000000162962940.0000054735101110.0000000488893170.0000017817132920.000597171307501-0.000028885