潮流計(jì)算的計(jì)算機(jī)算法

1、高等電力系統(tǒng)分析（潮流計(jì)算的計(jì)算機(jī)算法）PQ分解法潮流計(jì)算（ IEEE14）目錄一、MATLAB源程序二、對支路參數(shù)（ B1）、節(jié)點(diǎn)參數(shù)（ B2）的說明三、帶入數(shù)據(jù)，運(yùn)行結(jié)果、 MATLAB 源程序clearclose alln=input('請輸入節(jié)點(diǎn)數(shù) :n=');n1=input('請輸入支路數(shù) :n1=')isb=input('請輸入平衡節(jié)點(diǎn)號(hào):isb=')pr=input('請輸入誤差精度 :pr=');B1=input('請輸入支路參數(shù) :B1=');B2=input('請輸入節(jié)點(diǎn)參數(shù) :B2=

2、');n2=input('請輸入 PQ節(jié)點(diǎn)個(gè)數(shù) :n2=');Y=zeros(n);for i=1:n1p=B1(i,1);q=B1(i,2);Y(p,q)=Y(p,q)-1/(B1(i,3)+B1(i,4)*1j); %Y(q,p)=Y(p,q);Y(p,p)=Y(p,p)+1/(B1(i,3)+B1(i,4)*1j)+B1(i,6)*1j; %Y(q,q)=Y(q,q)+1/(B1(i,3)+B1(i,4)*1j)+B1(i,6)*1j; end非對角元對角元disp(' 導(dǎo)納矩陣 Y=');disp(Y)% 下面是求 P,Q,V,O 矩陣 V=ze

3、ros(1,n);O=zeros(1,n);P=zeros(1,n);Q=zeros(1,n);G=real(Y);B=imag(Y);for i=1:nP(i)=B2(i,3);Q(i)=B2(i,4);V(i)=B2(i,5);O(i)=B2(i,6);endB3=B(1:n-1,1:n-1); %B4=B(1:n2,1:n2); % %不含平衡節(jié)點(diǎn)，由節(jié)點(diǎn)導(dǎo)納虛部構(gòu)成所有 PQ節(jié)點(diǎn)% 下面是求 P, Q矩陣 DX=0;ICT=1;Mp=1;Mq=1;while ICT=0m1=1;m2=1;for i=1:n所有節(jié)點(diǎn)數(shù)節(jié)點(diǎn)數(shù)求DP,DQ對V矩陣求逆P/VP/V/B3 角 =- P/V/V

4、/B3 V=- Q/V/Bif i=isbC(i)=0;D(i)=0;for j1=1:nC(i)=C(i)+V(i)*V(j1)*(G(i,j1)*cos(O(i)-O(j1)+B(i,j1)*sin(O(i)-O( j1);D(i)=D(i)+V(i)*V(j1)*(G(i,j1)*sin(O(i)-O(j1)-B(i,j1)*cos(O(i)-O( j1);endDP(m1)=P(i)-C(i); m1=m1+1;if B2(i,2)=1 DQ(m2)=Q(i)-D(i); m2=m2+1;endend end m1=m1-1; % m2=m2-1; %PQ DPQ=DP'DQ&

5、#39; % V1=V(:,1:m1); V2=diag(V1); V3=inv(V2); % H=V3*DP' % K=-inv(B3)*H; %- deltO=V3*K; % max1=max(abs(DP); for i=1:m1if max1<prMp=0;elseO(i)=O(i)+deltO(i)'Mq=1;end end V4=V(:,1:m2); V5=diag(V4); V6=inv(V5); L=V6*DQ' N=-inv(B4)*L; deltV=N; % max2=max(abs(DQ);for i=1:m2if max2<prMq=

6、0;elseif B2(i,2)=1;V(i)=V(i)+deltV(i)'Mp=1;endendendif Mp=0&&Mq=0ICT=0;elseICT=1;endDX=DX+1;end% 迭代結(jié)束，開始輸出結(jié)果disp('');disp(' 迭代次數(shù)為： '); disp(DX);for i=1:nE(i)=V(i)*cos(O(i)+1j*V(i)*sin(O(i); o(i)= 180*angle(E(i)/pi;enddisp('');disp(' 修正后各節(jié)點(diǎn)電壓標(biāo)么值為(節(jié)點(diǎn)號(hào)從小到大排列) :&#

7、39;); disp(V);disp('');disp(' 修正后各節(jié)點(diǎn)電壓相角為(節(jié)點(diǎn)號(hào)從小到大排列) :'); disp(o);% 計(jì)算各個(gè)節(jié)點(diǎn)的功率disp('');disp(' 各節(jié)點(diǎn)的功率為 :');for p=1:nC(p)=0;for q=1:nC(p)=C(p)+conj(Y(p,q)*conj(E(q); endS(p)=E(p)*C(p);enddisp(S);% 計(jì)算各支路的功率 for i=1:n1 p=B1(i,1);q=B1(i,2);Si(p,q)=E(p)*(conj(E(p)*conj(Y(p,p

8、)-Y(p,q)+(conj(E(p)-conj(E(q )*conj(Y(p,q);disp('');disp(' 各條支路的首端功率為 :'); disp(Si(p,q);Si(q,p)=E(q)*(conj(E(q)*conj(Y(q,q)-Y(p,q)+(conj(E(q)-conj(E(p )*conj(Y(p,q);disp('');disp(' 各條支路的末端功率為 :'); disp(Si(q,p);DS(i)=Si(p,q)+Si(q,p);disp('');disp(' 各條支路的功率損

9、耗為 :');disp(DS(i);end% 計(jì)算平衡節(jié)點(diǎn)功率 Sp=0;for i=1:nSp=Sp+V(n)*conj(Y(n,i)*conj(V(i);enddisp('');disp(' 平衡節(jié)點(diǎn)功率為 :');disp(Sp);、對支路參數(shù)（ B1）、節(jié)點(diǎn)參數(shù)（ B2）的說明1. 節(jié)點(diǎn)數(shù)： 142. 支路數(shù)： 203. 支路矩陣 B1 的各支路參數(shù)：起點(diǎn)編號(hào)，終點(diǎn)編號(hào)，電阻，電抗，電導(dǎo)，電納120.01335 0.04211 00 ;130 0.20912 0 0140 0.55618 0 01100.05811 0.17632 00.0341

10、110.06701 0.17103 00.01282100.05695 0.17388 00.03462120 0.25202 0 02140.05403 0.22304 00.0492340 0.11001 0 03130 0.17615 0 0450.03181 0.0845 00 ;490.12711 0.27038 00 ;560.08205 0.19207 00 ;6120.09498 0.1989 00 ;780.22092 0.19988 00 ;7120.12291 0.25581 00 ;890.17093 0.34802 00 ;8120.06615 0.13027 00

11、;10110.04699 0.19797 00.043810140.01938 0.05917 00.05284. 節(jié)點(diǎn)參數(shù)矩陣 B2 的各節(jié)點(diǎn)參數(shù)：（對應(yīng)的每一列為） 節(jié)點(diǎn)編號(hào)，類型，注入有功，注入無功，電壓幅值，電壓相位 其中節(jié)點(diǎn)類型： 1=PQ節(jié)點(diǎn)， 2=PV節(jié)點(diǎn)， 0=平衡節(jié)點(diǎn)1 1 -0.478 2 1 -0.0763 1 0 04 1 -0.2955 1 -0.096 1 -0.0357 1 -0.0618 1 -0.1359 1 -0.14910 2 0.18311 2 -0.94212 2 -0.11213 214 00.039 1 0;-0.016 1 0;1 0;-0.16

12、6 1 0;-0.058 1 0;-0.018 1 0;-0.016 1 0;-0.058 1 0;-0.05 1 0;0 1.045 0;0 1.01 0;0.047 1.7 0;0 0.174 1.9 0;0 0 1.06 0;三、帶入數(shù)據(jù)，運(yùn)行結(jié)果>> clearclose alln=input（' 請輸入節(jié)點(diǎn)數(shù) :n='）; n1=input（' 請輸入支路數(shù) :n1='）; isb=input（' 請輸入平衡節(jié)點(diǎn)號(hào) :isb='）; pr=input（' 請輸入誤差精度 :pr='）;B1=input（

13、9; 請輸入支路參數(shù) :B1='）;B2=input（' 請輸入節(jié)點(diǎn)參數(shù) :B2='）; n2=input（' 請輸入 PQ 節(jié)點(diǎn)個(gè)數(shù) :n2='）;Y=zeros（n）;for i=1:n1p=B1(i,1);q=B1(i,2);Y(p,q)=Y(p,q)-1/(B1(i,3)+B1(i,4)*1j); %非對角元Y(q,p)=Y(p,q);Y(p,p)=Y(p,p)+1/(B1(i,3)+B1(i,4)*1j)+B1(i,6)*1j; %對角元Y(q,q)=Y(q,q)+1/(B1(i,3)+B1(i,4)*1j)+B1(i,6)*1j;enddis

14、p(' 導(dǎo)納矩陣 Y=');disp(Y)%下面是求 P,Q,V,O矩陣 V=zeros(1,n);O=zeros(1,n);P=zeros(1,n);Q=zeros(1,n);G=real(Y);B=imag(Y);for i=1:nP(i)=B2(i,3);Q(i)=B2(i,4);V(i)=B2(i,5);O(i)=B2(i,6); endB3=B（1:n-1,1:n-1）; %不含平衡節(jié)點(diǎn)，由節(jié)點(diǎn)導(dǎo)納虛部構(gòu)成B4=B（1:n2,1:n2）;%所有 PQ 節(jié)點(diǎn)%下面是求 P, Q矩陣 DX=0;ICT=1;Mp=1;Mq=1;while ICT=0m1=1;m2=1;fo

15、r i=1:nif i=isbC(i)=0;D(i)=0;for j1=1:nC(i)=C(i)+V(i)*V(j1)*(G(i,j1)*cos(O(i)-O(j1)+B(i,j1)*sin(O(i)-O(j1);D(i)=D(i)+V(i)*V(j1)*(G(i,j1)*sin(O(i)-O(j1)-B(i,j1)*cos(O(i)-O(j1); endDP(m1)=P(i)-C(i); m1=m1+1;if B2(i,2)=1 DQ(m2)=Q(i)-D(i); m2=m2+1;end end end m1=m1-1; m2=m2-1; DPQ=DP'DQ' V1=V(:,

16、1:m1); V2=diag(V1); V3=inv(V2); H=V3*DP' K=-inv(B3)*H; deltO=V3*K;%所有節(jié)點(diǎn)數(shù)%PQ節(jié)點(diǎn)數(shù)%求 DP,DQ%對 V 矩陣求逆%P/V%-P/V/B3% 角 =-max1=max(abs(DP);for i=1:m1if max1<prMp=0;elseO(i)=O(i)+deltO(i)'Mq=1;endendV4=V(:,1:m2);V5=diag(V4);V6=inv(V5);L=V6*DQ'N=-inv(B4)*L;deltV=N;%V=- Q/V/Bmax2=max(abs(DQ);for

17、i=1:m2if max2<prMq=0;else if B2(i,2)=1; V(i)=V(i)+deltV(i)' Mp=1;endendendif Mp=0&&Mq=0ICT=0;elseICT=1;endDX=DX+1;end% 迭代結(jié)束，開始輸出結(jié)果disp('');disp(' 迭代次數(shù)為： '); disp(DX);for i=1:nE(i)=V(i)*cos(O(i)+1j*V(i)*sin(O(i);o(i)= 180*angle(E(i)/pi;enddisp('');disp(' 修正后

18、各節(jié)點(diǎn)電壓標(biāo)么值為(節(jié)點(diǎn)號(hào)從小到大排列) :'); disp(V);disp('');disp(' 修正后各節(jié)點(diǎn)電壓相角為(節(jié)點(diǎn)號(hào)從小到大排列) :'); disp(o);%計(jì)算各個(gè)節(jié)點(diǎn)的功率 disp('');disp(' 各節(jié)點(diǎn)的功率為 :');for p=1:nC(p)=0;for q=1:nC(p)=C(p)+conj(Y(p,q)*conj(E(q);endS(p)=E(p)*C(p); end disp(S);%計(jì)算各支路的功率 for i=1:n1 p=B1(i,1);q=B1(i,2);Si(p,q)=E(

19、p)*(conj(E(p)*conj(Y(p,p)-Y(p,q)+(conj(E(p)-conj(E(q)*conj(Y(p,q); disp('');disp(' 各條支路的首端功率為 :');disp(Si(p,q);Si(q,p)=E(q)*(conj(E(q)*conj(Y(q,q)-Y(p,q)+(conj(E(q)-conj(E(p)*conj(Y(p,q);disp('');disp(' 各條支路的末端功率為 :');disp(Si(q,p);DS(i)=Si(p,q)+Si(q,p);disp(''

20、);disp(' 各條支路的功率損耗為 :');disp(DS(i);end% 計(jì)算平衡節(jié)點(diǎn)功率 Sp=0;for i=1:nSp=Sp+V(n)*conj(Y(n,i)*conj(V(i);enddisp('');disp(' 平衡節(jié)點(diǎn)功率為 :');disp(Sp);請輸入節(jié)點(diǎn)數(shù) :n=14請輸入支路數(shù) :n1=20請輸入平衡節(jié)點(diǎn)號(hào) :isb=14請輸入誤差精度 :pr=0.00001請輸入支路參數(shù) :B1=1 2 0.01335 0.04211 0 0 ;130 0.20912 00140 0.55618 001100.058110.176

21、3200.0341110.067010.1710300.01282100.056950.1738800.03462120 0.25202 002140.054030.2230400.0492340 0.11001 00 ;3130 0.17615 00450.031810.084500 ;490.127110.2703800 ;560.082050.1920700 ;6120.094980.198900 ;780.220920.1998800 ;7120.122910.2558100 ;890.170930.3480200 ;8120.066150.1302700 ;10110.046990.

22、1979700.0438 ;10140.019380.0591700.0528 ;請輸入節(jié)點(diǎn)參數(shù) :B2=1 1-0.478 0.03921-0.076-0.01610;310 01 0;41-0.295-0.16610;51-0.09-0.05810;61-0.035-0.01810;71-0.061-0.01610;81-0.135-0.05810;91-0.149-0.0510;1020.1830 1.0450;112-0.9420 1.010;122-0.1120.0471.70;1320 0.174 1.90;1400 01.06 0;請輸入 PQ 節(jié)點(diǎn)個(gè)數(shù) :n2=9導(dǎo)納矩陣Y=1

23、Columns 1 through 50;10.5130 -38.2963i-6.8410 +21.5786i0.0000 + 4.7819i0.0000 + 1.7980i0.0000 +0.0000i-6.8410 +21.5786i9.5680 -34.8916i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 +0.0000i0.0000 + 4.7819i0.0000 + 0.0000i0.0000 -19.5490i0.0000 + 9.0901i0.0000 +0.0000i0.0000 + 1.7980i0.0000 + 0.0000i0.0000

24、+ 9.0901i5.3261 -24.2825i-3.9020+10.3654i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-3.9020 +10.3654i5.7829-14.7683i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-1.8809 +4.4029i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 +Columns 6 through 100.0000

25、+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +-1.6860 +-1.7011 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +9.5213-1.1350 +0.0000 +0.0000 +-4.99910.0000 + 0.0000i0.0000i0.0000 + 0.0000i0.0000i-1.6860 + 5.1158i0.0000i-1.9860 + 5.0688i0.0000i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i0.0000

26、i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i5.1158i0.0000 + 0.0000i5.1939i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i0.0000i-1.8809 + 4.4029i0.0000i3.8359 - 8.4970i0.0000i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i -30.1895i0.0000 + 0.0000i4.7819i-1.9550 + 4.0941i0.

27、0000i0.0000 + 0.0000i0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-1.7011 + 5.1939i0.0000 + 0.0000i0.0000 + 3.9679i0.0000 + 0.0000i-1.0259 + 4.2350i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i4.0150 - 5.4279i-2.4890 + 2.2520i0.0000 + 0.00

28、00i0.0000 + 0.0000i0.0000 + 0.0000i-1.5260 + 3.1760i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 5.6770i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-2.4890

29、+ 2.2520i6.7249 -10.6697i-1.1370 + 2.3150i0.0000 + 0.0000i0.0000 + 0.0000i-3.0989 + 6.1028i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-1.4240 + 3.0291i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-1.4240 + 3.0291

30、i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i-1.1370 + 2.3150i2.5610 - 5.3440i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i+15.2631iColumns 11 through 14-1.9860 + 5.0688i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.

31、0000i0.0000 + 0.0000i0.0000 + 0.0000i-1.1350 + 4.7819i3.1210 - 9.7941i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 3.9679i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i -1.9550 + 4.0941i -1.5260 + 3.1760i -3.0989 + 6.1028i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i

32、6.5799 -17.3407i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 5.6770i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 - 5.6770i0.0000 + 0.0000i0.0000 + 0.0000i-1.0259 + 4.

33、2350i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i -4.9991 +15.2631i0.0000 + 0.0000i0.0000 + 0.0000i0.0000 + 0.0000i6.0250 -19.3961i迭代次數(shù)為：42修正后各節(jié)點(diǎn)電壓標(biāo)么值為Columns 1 through 10（節(jié)點(diǎn)號(hào)從小到大排列）1.2128 1.21481.5809 1.04501.56271.53641.56021.6264

34、1.67921.6654Columns 11 through 141.0100 1.70001.90001.0600修正后各節(jié)點(diǎn)電壓相角為（節(jié)點(diǎn)號(hào)從小到大排列）Columns 1 through 10-13.1377 -11.9998-14.4540-15.0006-15.3011-15.7590-16.4954-16.3362-16.0220 -5.2081Columns 11 through 14-12.1568 -16.1918 -14.4540各節(jié)點(diǎn)的功率為 :Columns 1 through 5-0.0475 -1.4718 - 1.8800i 0.9041 - 1.1423i0.

35、0000 - 0.0000i -0.1314 + 0.1399i0.0646iColumns 6 through 10-1.5950 -0.0300 + 0.0035i 0.0039 - 0.1228i -0.0656 - 0.0724i -0.0352 - 0.1437i 1.3905iColumns 11 through 14-0.4870 - 1.2396i 3.2005 + 3.0414i 1.7586 + 3.1847i -2.7057 + 0.3992i各條支路的首端功率為26.1711 +87.9128i各條支路的末端功率為23.5667 +83.4812i各條支路的功率損耗為

36、:4.9738e+01 + 1.7139e+02i各條支路的首端功率為15.2545 +65.3872i各條支路的末端功率為0.2082 +56.8008i各條支路的功率損耗為 :1.5463e+01 + 1.2219e+02i各條支路的首端功率為15.3538 +59.6752i各條支路的末端功率為12.6813 +60.6685i各條支路的功率損耗為 :2.8035e+01 + 1.2034e+02i各條支路的首端功率為18.4735 +62.4536i各條支路的末端功率為11.6194 +39.6840i各條支路的功率損耗為 :3.0093e+01 + 1.0214e+02i各條支路的首端功率為18.0012 +62.4930i各條支路的末端功率為5.5097 +16.2405i各條支路的功率損耗為23.5109 +78.7335i各條支路的首端功率為17.0452 +57.7870i各條支路的末端功率為11.7622 +39.7706i各條支路的功率損耗為28.