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1、实用同步电机三相短路电流和电磁转矩计算编与 佘名寰本文是按照珩教授所著的同步电机运行基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基本一致。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从而得Uo, i0的正、交轴分量Ud0=U0Sin S oUq0=U0 cos 8 0ido =i0sin( 8 0+ $【0】)iq0=i 0cos( 8 0+ $ 0)短路前的空载电势是Eq0 =Uq0 +ri q0
2、 +Xdid0励磁电流为if0 = Eq0/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？id ?iq ?if ?iD ?iQ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?Udq0 = go ?Idq0 + Zd3) ?Idq0化作电流变化量的常系数一阶微分方程组形式?
3、I dq0=-X（3）-1dq0+xdqo）-1?U dq0在三相短路时若励磁电压不可调，则?udq0 =卜u d0 -u q0000 f由于电流不能突变，t=0瞬间电流变化量的初值?idqo 0 = 0 0 0 0 0 1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，反复计算则可求得各个时刻的？idq0 ,叠加短路前绕组电流idq0 0=:id0 iq0 if0 00t可得短路时电流全量idq0 ：=idiq if iD iQ t用派克逆变换可得定子三相电流，以a相为例ia=idcos(t + 0 0) - iq sin(t +
4、0 0)0 0 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, o=O.5548 （单位为弧度，相对于 cos =0.8） 短路时的转子位置角0 0=3.1416三相短路计算程序：CMSHORT3.M% part 1 ra=0.005;rf=.000656;rzd=.00151;rzq
5、=.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=-0.005,0.6,0.0,0.0,-0.45;-1.0,-0.005,0.
6、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*si n(phas)+xq*i0)/(u0*cos(phas)+ra*i0);g0=ata n( g0)-phas;ud0=u0*si n( g0);uq0=u0*cos(g0);di0=i0*si n(g0+phas);qi0=i0*cos(g0+phas);eq0=uq0+ra*qi0+xd*di0;fi0=eq0/xaf;du=-ud0,-uq0,0.0,0.0,0.0;x2=i nv(x1);z2=-x2
7、*z1;i1=x2*du;y=0.0,0.0,0.0,0.0,0.0;% part 2t=0.0 ;for i=1:5b(i)=y(i);enddy=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+citaO)-qi(1)*s in (t+citaO);tm(1)=qi(1)*(-xd*di(1)+xaf*fi(1)+xazd*zdi(1)-di(1)*(-xq*qi(1)+xazq*zqi(1);% while (tt( n)v
8、p)%k=0;for n=2:10a(1)=h/2;a(2)=a(1);a(3)=h;a(4)=h;for k=1:3for i=1:5c(i)=b(i)+a(k)*dy(i);y(i)=y(i)+a(k+1)*dy(i)/3.0;enddy=z2*(c).+i1;endfor i=1:5y(i)=y(i)+h*dy(i)/6.0;endt=t+h;for i=1:5b(i)=y(i);enddy=z2*(y).+i1;%k=k+1;% part 3tt(n )=t;di( n)=y(1)+di0;qi( n)=y(2)+qi0;fi( n)=y(3)+fi0;zdi(n)=y( 4);zqi
9、(n )=y(5);ai( n)=di( n)*cos(t+cita0)-qi( n)*s in (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 syn chro nous machi ne);grid3 程序说明：X1为状态空间方程的Xdq0矩阵Z1为状态空间方程的Zdq0矩阵文档x2=Xdq；)-1I1=X(3) -1 dq0?U
10、 dq0程序% part 1第一部分输入初始数据，建立状态空间方程;tn+1=tn + h 时刻程序% part 2第二部分用定步长四阶龙格-库塔法解一阶微分方程组，计算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 n定步长四阶龙格-库塔法解一阶微分方程组的基本公式：y1 二f1(t,y1,y2,ym), y1(to)=yey2 =f2(t,y1,y2,ym), y2(to)=y2oYm 二fm(t,y1,y2,ym), ym(t0)=ym0微分方程组由tj积分一步到tj+1 =tj+hYi,j+1 二yij+(k1i+2k2i+2k3i+k4i)h/6, i=1,2,m心二
11、鮒创也,ymj),i=1,2,mk2i=fi(tj+h/2,y1j+knh/2,ymj+k1mh/2), i=1,2,mk3i=fi(tj+h/2,y1j+k21 h/2,ymj+k2mh/2), i=1,2,mk4i=fi(tj+h,y1j+k31h,ymj+k3mh),i=1,2,m程序% part 3第三部分输出计算结果，tm为转矩Tm =iq d + id q d=-Xdid +Xafif+XaDiD q=-Xqiq+XaQiQ本程序计算时间周期为 t=0 10X1/6 n ,绘画取20 n4程序计算结果：T=0-10X1/6 n 取 10个点纵轴短路电流didi =Colu mns
12、1 through 70.7966190047267142.2367130993432224.4478626375923196.8263978366408118.736932238288684Colu mns 8 through 108.066892631590545A相短路电流aiai =Colu mns 1 through 7-0.7966145639344705.677720481984181Colu mns 8 through 108.362265350144739横轴短路电流qiqi =Colu mns 1 through 70.6044817295073681.5117004293
13、32145Colu mns 8 through 10-2.752315328026902励磁绕组电流fifi =Colu mns 1 through 72.0389317955928844.692501533033596Colu mns 8 through 104.4986640266012459.6813436639196985.980344929918005-0.9644241603207358.4172515171420655.9184325579004339.4278606745674693.7343564623138330.0404061250097809.4278826273301783.2273995514848022.4496686213438021.9452043621400782.6145733115566600.065795066843252-1.494184215750709-3.3813325555557342.5178174245469515.0157162661537903.812805524243933-3.2274681373152013.2548509777309844.9415472156374473.071441629933557
