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1、word同步电机三相短路电流和电磁转矩计算 编写 佘名寰本文是按照陈珩教授所著的同步电机运行根本理论与计算机算法一书介绍的算法和例题计算同步电机的三相短路电流。计算程序用MATLAB语言编写，计算结果与书中结果根本一致。本文可供电力系统电气技术人员和大专院校电力专业学生参考。1 计算方法1.1初始数据计算由短路前的机端电压u0, 定子绕组电流io, 和功率因数角0 求得短路前的功率角0=从而得u0, i0 的正、交轴分量ud0=u0sin0uq0=u0cos0id0=i0sin(0+0)iq0=i0cos(0+0)短路前的空载电势是Eq0=uq0+riq0+xdid0励磁电流为if0= Eq0
2、/xaf式中 xd为同步电机正轴同步电抗xq同步电机交轴同步电抗 xaf定子绕组与劢磁绕组间的互感电抗r 定子绕组电阻1.2电流变化量的状态空间方程式同步电机突然短路时各绕组电流的变化量的计算可运用以派克分量表示的状态空间方程式方程中各下标变量的含义为d-纵轴，q-横轴，f-励磁绕组，D-纵轴阻尼绕组，Q-横轴阻尼绕组，a-定子绕组上式可简化为化作电流变化量的常系数一阶微分方程组形式在三相短路时假如励磁电压不可调，如此由于电流不能突变，t=0瞬间电流变化量的初值将电压变化量和电流变化量的初值代入微分方程，用数值计算的龙格-库塔法即可求出t=0+h 时刻的各电流变化量，反复计算如此可求得各个时刻
3、的，叠加短路前绕组电流可得短路时电流全量用派克逆变换可得定子三相电流，以a相为例 ia=短路t=0时转子位置角2.同步电机三相短路电流计算例题与程序电机参数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原始运行条件为额定负载U0=1, i0=1, 0=0.5548 (单位为弧度，相对于cos=0.8)短路时的转子位置角0=3.1416 三相短路计算程序：CMSHORT3.M% part 1ra=0
4、.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,-0.45,0.0,0.0,0.70; z1=-0.00
5、5,0.6,0.0,0.0,-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; fi0=eq0/xaf; du=-ud
6、0,-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)*(-xd*di(1)+xaf*fi(1)+xazd*zd
7、i(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); end dy=z2*(y).+i1; % k=k+1;% part 3
8、 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(ia); title(3-phase fault of synchronous machine); grid3程序说
9、明：X1为状态空间方程的 Xdq0 矩阵Z1 为状态空间方程的 Zdq0 矩阵X2=I1=程序 % part 1 第一局部输入初始数据，建立状态空间方程；程序 % part 2 第二局部用定步长四阶龙格-库塔法解一阶微分方程组，计算 tn+1=tn+h 时刻各绕组电流的变化量。时间步长 h用标么值，单位为弧度,h 取1/6 定步长四阶龙格-库塔法解一阶微分方程组的根本公式：y1=f1(t,y1,y2,ym), y1(t0)=y10y2=f2(t,y1,y2,ym), y2(t0)=y20.Ym=fm(t,y1,y2,ym), ym(t0)=ym0微分方程组由 tj 积分一步到 tj+1=tj+
10、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程序 % part 3 第三局部输出计算结果，tm 为转矩Tm =iqd+idqd=-xdid+xafif+xaDiDq=-xqiq+xaQiQ本程序计算时间周期为t=010X1/6,绘画取2
11、04.程序计算结果：T=0-10X1/6,取10个点纵轴短路电流didi = Columns 1 through 7 0.796619004726714 2.236713099343222 4.447862637592319 6.826397836640811 8.736932238288684 9.681343663919698 9.427860674567469 Columns 8 through 10 8.066892631590545 5.980344929918005 3.734356462313833A相短路电流aiai = Columns 1 through 7 -0.79661
12、4563934470 -0.964424160320735 0.040406125009780 2.449668621343802 5.677720481984181 8.417251517142065 9.427882627330178 Columns 8 through 10 8.362265350144739 5.918432557900433 3.227399551484802横轴短路电流qiqi = Columns 1 through 7 0.604481729507368 1.945204362140078 2.614573311556660 2.449593397214421 1
13、.511700429332145 0.065795066843252 -1.494184215750709 Columns 8 through 10 -2.752315328026902 -3.381332555555734 -3.227468137315201励磁绕组电流fifi = Columns 1 through 7 2.038931795592884 2.517817424546951 3.254850977730984 4.050131846860924 4.692501533033596 5.015716266153790 4.941547215637447 Columns 8 through 10 4.498664026601245 3.812805524243933 3.071441629933557纵轴阻尼绕组电流zdizdi = Columns 1 through 7 0 0.8597117
