1、同步電機(jī)三相短路電流和電磁轉(zhuǎn)矩計算 編寫 佘名寰本文是按照陳珩教授所著的同步電機(jī)運(yùn)行基本理論與計算機(jī)算法一書介紹的算法和例題計算同步電機(jī)的三相短路電流。計算程序用MATLAB語言編寫，計算結(jié)果與書中結(jié)果基本一致。本文可供電力系統(tǒng)電氣技術(shù)人員和大專院校電力專業(yè)學(xué)生參考。1 計算方法1.1初始數(shù)據(jù)計算由短路前的機(jī)端電壓u0, 定子繞組電流io, 和功率因數(shù)角0 求得短路前的功率角0=tan-1u0sin0+xqi0u0cos0+ri0-0從而得u0, i0 的正、交軸分量ud0=u0sin0uq0=u0cos0id0=i0sin(0+0)iq0=i0cos(0+0)短路前的空載電勢是Eq0=uq0

2、+riq0+xdid0勵磁電流為if0= Eq0/xaf式中 xd 為同步電機(jī)正軸同步電抗xq 同步電機(jī)交軸同步電抗 xaf 定子繞組與勱磁繞組間的互感電抗 r 定子繞組電阻1.2電流變化量的狀態(tài)空間方程式同步電機(jī)突然短路時各繞組電流的變化量 id iq if iD iQ 的計算可運(yùn)用以派克分量表示的狀態(tài)空間方程式uduquf00=-xdxafxaD-xqxaQ-xafxfxfD-xaDxfDxD-xaQxQidiqifiDiQ+-rxq-xaQ-xd-rxafxaDrfrDrQidiqifiDiQ方程中各下標(biāo)變量的含義為d-縱軸，q-橫軸，f-勵磁繞組，D-縱軸阻尼繞組，Q-橫軸阻尼繞組，a

3、-定子繞組上式可簡化為udq0=Xdq0(3)Idq0+Zdq0(3)Idq0化作電流變化量的常系數(shù)一階微分方程組形式Idq0=-Xdq0（3）-1Zdq0(3)Idq0+Xdq0（3）-1udq0在三相短路時若勵磁電壓不可調(diào)，則udq0=-ud0 -uq0 0 0 0 t由于電流不能突變，t=0瞬間電流變化量的初值idq0 0= 0 0 0 0 0 t將電壓變化量和電流變化量的初值代入微分方程，用數(shù)值計算的龍格-庫塔法即可求出t=0+h 時刻的各電流變化量，反復(fù)計算則可求得各個時刻的idq0 ，疊加短路前繞組電流idq0 0= id0 iq0 if0 00t可得短路時電流全量idq0= id

4、 iq if iD iQ t用派克逆變換可得定子三相電流，以a相為例 ia=idcost+0-iqsint+0 0 短路t=0時轉(zhuǎn)子位置角2.同步電機(jī)三相短路電流計算例題與程序電機(jī)參數(shù)r=0.005, rf=0.000656，rD=0.00151, rQ=0.00159xd=1,0, xq=0.60, xf=1.03, xD=0.95, xQ=0.70xaf=0.85, xaD=0.85, xfD=0.85, xaQ=0.45原始運(yùn)行條件為額定負(fù)載 U0=1, i0=1, 0=0.5548 (單位為弧度，相對于cos=0.8) 短路時的轉(zhuǎn)子位置角 0=3.1416 三相短路計算程序：CMSHO

5、RT3.M% part 1ra=0.005;rf=.000656;rzd=.00151;rzq=.00159;xd=1.0; xq=.60;xf=1.03;xzd=.95;xzq=.70;xaf=.85;xazd=.85;xfzd=.85;xazq=.450; u0=1.0;i0=1.0;phas=.5548;cita0=3.1416;p=31.4160;h=.5236; x1=-1.0,0.0,0.85,0.85,0.0;0.0,-0.60,0.0,0.0,0.45;-0.85,0.0,1.03,0.85,0.0; -0.85,0.0,0.85,0.95,0.0;0.0,-0.45,0.0,

6、0.0,0.70; z1=-0.005,0.6,0.0,0.0,-0.45;-1.0,-0.005,0.85,0.85,0.0;0.0,0.0,0.000656,0.0,0.0; 0.0,0.0,0.0,0.00151,0.0;0.0,0.0,0.0,0.0,0.00159; g0=(u0*sin(phas)+xq*i0)/(u0*cos(phas)+ra*i0); g0=atan(g0)-phas; ud0=u0*sin(g0); uq0=u0*cos(g0); di0=i0*sin(g0+phas); qi0=i0*cos(g0+phas); eq0=uq0+ra*qi0+xd*di0;

7、fi0=eq0/xaf; du=-ud0,-uq0,0.0,0.0,0.0; x2=inv(x1); z2=-x2*z1; i1=x2*du' y=0.0,0.0,0.0,0.0,0.0;% part 2 t=0.0 ; for i=1:5 b(i)=y(i); end dy=z2*(y).'+i1; tt(1)=t; di(1)=y(1)+di0; qi(1)=y(2)+qi0; fi(1)=y(3)+fi0; zdi(1)=y(4); zqi(1)=y(5); ai(1)=di(1)*cos(t+cita0)-qi(1)*sin(t+cita0); tm(1)=qi(1)*

8、(-xd*di(1)+xaf*fi(1)+xazd*zdi(1)-di(1)*(-xq*qi(1)+ xazq*zqi(1); % while (tt(n)<p)% k=0; for n=2:10 a(1)=h/2; a(2)=a(1); a(3)=h; a(4)=h; for k=1:3 for i=1:5 c(i)=b(i)+a(k)*dy(i); y(i)=y(i)+a(k+1)*dy(i)/3.0; end dy=z2*(c).'+i1; end for i=1:5 y(i)=y(i)+h*dy(i)/6.0; end t=t+h; for i=1:5 b(i)=y(i)

9、; end dy=z2*(y).'+i1; % k=k+1;% part 3 tt(n)=t; di(n)=y(1)+di0; qi(n)=y(2)+qi0; fi(n)=y(3)+fi0; zdi(n)=y(4); zqi(n)=y(5); ai(n)=di(n)*cos(t+cita0)-qi(n)*sin(t+cita0); tm(n)=qi(n)*(-xd*di(n)+xaf*fi(n)+xazd*zdi(n)-di(n)*(-xq*qi(n)+ xazq*zqi(n); endplot(tt,ai); xlabel('t(rad)');ylabel('

10、ia'); title('3-phase fault of synchronous machine'); grid3程序說明：X1為狀態(tài)空間方程的 Xdq0 矩陣Z1 為狀態(tài)空間方程的 Zdq0 矩陣X2=Xdq0（3）-1I1=Xdq0（3）-1udq0程序 % part 1 第一部分輸入初始數(shù)據(jù)，建立狀態(tài)空間方程；程序 % part 2 第二部分用定步長四階龍格-庫塔法解一階微分方程組，計算 tn+1=tn+h 時刻各繞組電流的變化量。時間步長 h用標(biāo)么值，單位為弧度,h 取1/6 定步長四階龍格-庫塔法解一階微分方程組的基本公式：y1=f1(t,y1,y2,ym)

11、, y1(t0)=y10y2=f2(t,y1,y2,ym), y2(t0)=y20.Ym=fm(t,y1,y2,ym), ym(t0)=ym0微分方程組由 tj 積分一步到 tj+1=tj+h Yi,j+1=yij+(k1i+2k2i+2k3i+k4i)h/6, i=1,2,mk1i=fi(tj,y1j,y2j,ymj), i=1,2,mk2i=fi(tj+h/2,y1j+k11h/2,ymj+k1mh/2), i=1,2,mk3i=fi(tj+h/2,y1j+k21h/2,ymj+k2mh/2), i=1,2,mk4i=fi(tj+h,y1j+k31h,ymj+k3mh), i=1,2,m程

12、序 % part 3 第三部分輸出計算結(jié)果，tm 為轉(zhuǎn)矩Tm =iqd+idqd=-xdid+xafif+xaDiDq=-xqiq+xaQiQ本程序計算時間周期為t=010X1/6,繪畫取204.程序計算結(jié)果：T=0-10X1/6,取10個點縱軸短路電流didi = Columns 1 through 7 Columns 8 through 10 8.066892631590545 5.980344929918005 3.734356462313833A相短路電流aiai = Columns 1 through 7 Columns 8 through 10橫軸短路電流qiqi = Columns 1 through 7 Columns 8 through 10勵磁繞組電流fifi = Columns 1 through 7 Columns 8 through 10縱軸阻尼繞組電流zdizdi = Columns 1 through 7 Columns 8 through 10橫軸阻力尼繞組電流zqizqi = Columns 1 through 7 Columns 8 through 10電磁轉(zhuǎn)矩tmtm = Columns 1 through 7 C