How I can resolve this system of equations?

Hi,

I have a system of equation of 15 unknown variables, define like next.

I get first a warning that even I have 15 variables the program see 14 and then says that I donot get any solution. It is quite a big system:

syms Ra Xdssec Xqssec Rfd Lfd Ladssec R1d L1d R1q L1q Laqssec R2q L2q id0 iq0 
[sol_Ra,sol_Xdssec, sol_Xqssec, sol_Rfd,  sol_Lfd,  sol_Ladssec, sol_R1d, sol_L1d, sol_R1q, sol_L1q, sol_Laqssec,  sol_R2q, sol_L2q, sol_id0, sol_iq0]=solve(-(1*((Ra+0)*sin(-38.96)+(1.7+Xdssec)*cos(-38.96))*(0.6709+Laqssec*id0)-1*((1.7+Xqssec)*sin(-38.96)-(Ra+0)*cos(-38.96))*(-0.1217+Ladssec*iq0))/(2*11.2*((Ra+1.7)^2+(1.7+Xdssec)*(1.7+Xqssec)))/(2*11.2)==-0.0001198,-((((Ra+0)*Ladssec*(0.6709+Laqssec*id0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1d))-(((1.7+Xqssec)*Ladssec*(-0.1217+Ladssec*iq0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1d))+((Ladssec*iq0)/L1d))/(2*11.2)==0.00001019, -((((1.7+Xdssec)*Laqssec*(0.6709+Laqssec*id0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L1q)))+(((Ra+0)*Laqssec*(-0.1217+Ladssec*iq0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L1q)))-((Laqssec*id0)/L1q))/(2*11.2)==0.00001632, -((((1.7+Xdssec)*Laqssec*(0.6709+Laqssec*id0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L1q)))-(((Ra+0)*Laqssec*(-0.1217+Ladssec*iq0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L2q)))-((Laqssec*id0)/L2q))/(2*11.2)==-0.00001416, -(1*Rfd*1*Ladssec*((1.7+Xqssec)*sin(-38.96)-(0+Ra)*cos(-38.96))/(Lfd*((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))))==5.96, -(1*Rfd*(1-(Ladssec/Lfd)+((1.7+Xqssec)*(Ladssec^2)/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*Lfd)))/Lfd)==0.01679, -((((1*Rfd)/Lfd))*(((1.7+Xqssec)*(Ladssec^2))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1d)-(Ladssec/Lfd)))==-0.2445, -((((1*Rfd*Ladssec)/Lfd))*((-(Ra+0)*Laqssec)/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1q)))==1.71, -((((1*Rfd*Ladssec)/Lfd))*((-(Ra+0)*Laqssec)/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L2q)))==-6.077,-((((1*R1d*1*Ladssec)/L1d))*(((1.7+Xdssec)*sin(-38.96)-(Ra+0)*cos(-38.96))/((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))))==0.1549, -((((1*R1d)/L1d))*(((1.7+Xqssec)*(Ladssec^2))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*Lfd)-(Ladssec/Lfd)))==0.2681, -((((1*R1d)/L1d))*(1+((1.7+Xqssec)*(Ladssec^2))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*L1d)-(Ladssec/Lfd)))==-0.05322, -((((1*R1d*Ladssec)/L1d))*((-(0+Ra)*(Laqssec))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*L1q)))==2.152, -((((1*R1d*Ladssec)/L1d))*((-(0+Ra)*(Laqssec))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*L2q)))==-7.458, -((((1*R1q*Laqssec*1)/L1q))*(((Ra+0)*sin(-38.96)+(1.7+Xdssec)*cos(-38.96))/((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))))==0.3381)

Answer 1

[Walter Roberson]

Your equations do not use R2q

In sin(-38.96) and cos(-38.96) are you sure that those numbers are radians and not degrees? sin() and cos() operate on radians; you can use sind() and cosd() for degrees (Note: MuPAD will not recognize sind() or cosd() within a quoted string.)

[Traian Preda]

Hi, You are right. I will try it again Thank you

[Traian Preda]

Hi,

I've made the change but what I get is this warning

Warning: Explicit solution could not be found. > In solve at 169

sol_Ra =

[ empty sym ]

The new system is:

syms Ra Xdssec Xqssec Rfd Lfd Ladssec R1d L1d R1q L1q Laqssec L2q id0 iq0 [sol_Ra,sol_Xdssec, sol_Xqssec, sol_Rfd, sol_Lfd, sol_Ladssec, sol_R1d, sol_L1d, sol_R1q, sol_L1q, sol_Laqssec, sol_R2q, sol_L2q, sol_id0, sol_iq0]=solve(-((((Ra+0)*Ladssec*(0.6709+Laqssec*id0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1d))-(((1.7+Xqssec)*Ladssec*(-0.1217+Ladssec*iq0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1d))+((Ladssec*iq0)/L1d))/(2*11.2)==0.00001019, -((((1.7+Xdssec)*Laqssec*(0.6709+Laqssec*id0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L1q)))+(((Ra+0)*Laqssec*(-0.1217+Ladssec*iq0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L1q)))-((Laqssec*id0)/L1q))/(2*11.2)==0.00001632, -((((1.7+Xdssec)*Laqssec*(0.6709+Laqssec*id0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L1q)))-(((Ra+0)*Laqssec*(-0.1217+Ladssec*iq0))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec)*L2q)))-((Laqssec*id0)/L2q))/(2*11.2)==-0.00001416, -(1*Rfd*1*Ladssec*((1.7+Xqssec)*sind(-38.96)-(0+Ra)*cosd(-38.96))/(Lfd*((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))))==5.96, -(1*Rfd*(1-(Ladssec/Lfd)+((1.7+Xqssec)*(Ladssec^2)/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*Lfd)))/Lfd)==0.01679, -((((1*Rfd)/Lfd))*(((1.7+Xqssec)*(Ladssec^2))/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1d)-(Ladssec/Lfd)))==-0.2445, -((((1*Rfd*Ladssec)/Lfd))*((-(Ra+0)*Laqssec)/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L1q)))==1.71, -((((1*Rfd*Ladssec)/Lfd))*((-(Ra+0)*Laqssec)/(((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))*L2q)))==-6.077,-((((1*R1d*1*Ladssec)/L1d))*(((1.7+Xdssec)*sind(-38.96)-(Ra+0)*cosd(-38.96))/((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))))==0.1549, -((((1*R1d)/L1d))*(((1.7+Xqssec)*(Ladssec^2))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*Lfd)-(Ladssec/Lfd)))==0.2681, -((((1*R1d)/L1d))*(1+((1.7+Xqssec)*(Ladssec^2))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*L1d)-(Ladssec/Lfd)))==-0.05322, -((((1*R1d*Ladssec)/L1d))*((-(0+Ra)*(Laqssec))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*L1q)))==2.152, -((((1*R1d*Ladssec)/L1d))*((-(0+Ra)*(Laqssec))/(((Ra+0)^2+(1.7+Xqssec)*(1.7+Xdssec))*L2q)))==-7.458, -((((1*R1q*Laqssec*1)/L1q))*(((Ra+0)*sind(-38.96)+(1.7+Xdssec)*cosd(-38.96))/((Ra+0)^2+(1.7+Xdssec)*(1.7+Xqssec))))==0.3381)

[Walter Roberson]

Quick question: all those 1.7's: are they representing sqrt(2) ?

[Traian Preda]

Hi,

No there are only some numbers.

[Walter Roberson]

I can remove 5 variables out without much difficulty, but then it starts getting slow and memory intensive. In the approaches I have tried so far, back-substituting in "Ra" especially tends to get messy.

[Traian Preda]

Ok, do you think I can resolve this one in the end?

Thank you very much

[Walter Roberson]

It turns out that it cannot be resolved.

Eliminate Xqssec from #14, backsubstitute, then Xdssec from #13, backsubstitute, then L2q from #12, backsubstitute, then R1q from #11, backsubstitute, then R1d from #10, and backsubstitute. Then skip one in the working backwards from the end, and eliminate Rfd from #8 and backsubstitute. At this point, #7 will have become numeric on both sides, but the two sides are not equal, 1634713/932250 = 171/100 being false. Therefore your equations are inconsistent.

[Traian Preda]

Do you know which can be the source of this problem? and if any way to resolve it? Can you please send me the system which gave you the numeric results in a m file? Thank you

[Walter Roberson]

You have not given us any information as to what the equations represent or how you derived them, so we cannot say anything about the source of the problem. Either your equations are wrong or the system you are trying to solve has no solution.

After the eliminations and backsubstitutions I list above, the system becomes this:

[
(1/224000)*(1076000000*((2681/21520)*Laqssec*iq0*Lfd+(6709/10000+Laqssec*id0)*L1q)*(L1d-Lfd)*Ladssec^2-1076000000*Lfd*L1d*((2681/21520)*Laqssec*iq0*Lfd+(9776161/538000000+id0*L1q)*Laqssec+(6709/10000)*L1q)*Ladssec+16313885*Laqssec*Lfd^2*L1d)/(L1d*Lfd*(13405*Lfd+2661*L1d)*Ladssec*Laqssec) = 82/8047105,

(1/807731680000)*(-4492350625*Ra*Laqssec^2*id0*Lfd^4*Ladssec*L1d+36059450000*((-L1q*Laqssec*id0-(6709/10000)*L1q)*Ladssec^3+((iq0*L1q+(8033/53800)*Laqssec*id0)*Ra-L1q*Laqssec*id0-(6709/10000)*L1q)*L1d*Ladssec^2+((-(2661/107600)*Laqssec*id0+iq0*L1q)*L1d+id0*(-1+L1q)*Ra-(1217/10000)*L1q)*L1d*Ra*Ladssec+(id0*(-1+L1q)*Ra-(1217/10000)*L1q)*L1d^2*Ra)*Laqssec*Lfd^3-79276990000*Ladssec*((16066/29471)*L1q*((-(5372/8033)*Laqssec*id0-9010187/20082500+Ra*iq0)*Laqssec*L1d-(53800/8033)*(6709/10000+Laqssec*id0)*L1q*Ra)*Ladssec^2+(16066/29471)*((29471/16066)*((-(21375813/1585539800)*Laqssec*id0+iq0*L1q)*Ra+(2661/29471)*(6709/10000+Laqssec*id0)*L1q)*Laqssec*L1d+(id0*Laqssec*(-1+L1q)*Ra+(-(1217/10000)*L1q-(107600/8033)*id0*L1q^2)*Laqssec-(1804721/200825)*L1q^2)*Ra)*L1d*Ladssec+(id0*Laqssec*(-1+L1q)*Ra+(-(107600/29471)*id0*L1q^2-(1217/10000)*L1q)*Laqssec-(1804721/736775)*L1q^2)*L1d^2*Ra)*Lfd^2+43217540000*Ladssec^2*((((2661/16066)*Laqssec*id0+Ra*iq0+17852649/160660000)*Laqssec*L1d-(107600/8033)*(6709/10000+Laqssec*id0)*L1q*Ra)*L1q*Ladssec+(id0*Laqssec*(-1+L1q)*Ra+(-(1217/10000)*L1q-(107600/8033)*id0*L1q^2)*Laqssec-(1804721/200825)*L1q^2)*L1d*Ra)*L1d*Lfd+289444000000*Ladssec^3*(6709/10000+Laqssec*id0)*L1q^2*L1d^2*Ra)/((-(2681/21520)*Ladssec*Lfd^2*Laqssec+((-(2661/107600)*L1d*Laqssec+Ra*(-1+L1q))*Ladssec+Ra*(-1+L1q)*L1d)*Lfd-Ra*L1d*Ladssec*(-1+L1q))*L1q*(-(16066/13405)*Ladssec+Lfd)*Lfd*L1d*Ra) = 51/3125000,

(1/93517235354368000000)*(-224560231317778125*Laqssec^3*Ra*Lfd^6*Ladssec^2*id0*L1d+3605025123430500000*Ladssec*((538/3729)*(6709/10000+Laqssec*id0)*L1q*Ladssec^3-(1/2)*((iq0*L1q-(8033/53800)*Laqssec*id0)*Ra-(1076/3729)*(6709/10000+Laqssec*id0)*L1q)*L1d*Ladssec^2+L1d*Ra*((-(2661/107600)*Laqssec*id0-(1/2)*iq0*L1q)*L1d+(L1q+2653/2152)*id0*Ra+(1217/20000)*L1q)*Ladssec+((L1q+2653/2152)*id0*Ra+(1217/20000)*L1q)*L1d^2*Ra)*Laqssec^2*Lfd^5-14468508141780000000*(-(8033/53800)*((-(4348654/29955057)*Laqssec*id0-14587559843/149775285000+Ra*iq0)*Laqssec*L1d-(115777600/29955057)*(6709/10000+Laqssec*id0)*(L1q+3729/2152)*Ra)*L1q*Ladssec^4-L1d*((2681/10760)*(((21375813/721189000)*Laqssec*id0+iq0*L1q)*Ra+(954412/16662415)*(6709/10000+Laqssec*id0)*L1q)*Laqssec*L1d+((-(8033/26900)*(L1q+2653/2152)*id0*Laqssec+L1q*iq0*(-1+L1q))*Ra-(4304/3729)*L1q*((36455304369/2315552000000+id0*L1q+(3729/2152)*id0)*Laqssec+(6709/10000)*L1q+25017861/21520000))*Ra)*Ladssec^3+((2661/107600)*((2661/107600)*Laqssec*id0+iq0*L1q)*Laqssec*L1d^2+(((2681/5380)*(L1q+2653/2152)*id0*Laqssec-2*L1q*iq0*(-1+L1q))*Ra+(2152/3729)*(((3729/2152)*id0+12166895433/231555200000+id0*L1q)*Laqssec+(6709/10000)*L1q+25017861/21520000)*L1q)*L1d+(-1+L1q)*((L1q+3729/1076)*id0*Ra+(1217/10000)*L1q)*Ra)*L1d*Ra*Ladssec^2+2*(((-(2661/107600)*(L1q+2653/2152)*id0*Laqssec-(1/2)*L1q*iq0*(-1+L1q))*Ra-(3238437/2152000000)*L1q*Laqssec)*L1d+(-1+L1q)*((L1q+3729/1076)*id0*Ra+(1217/10000)*L1q)*Ra)*L1d^2*Ra*Ladssec+(-1+L1q)*((L1q+3729/1076)*id0*Ra+(1217/10000)*L1q)*L1d^3*Ra^2)*Laqssec*Lfd^4+46277639320176000000*Ladssec*(-(8033/21438)*((1343/13450)*((5762023847/53639522068)*Laqssec*id0+Ra*iq0+38657417989523/536395220680000)*Laqssec^2*L1d^2+(iq0*(-1+L1q)*Ra-(25984324/29955057)*(6709/10000+Laqssec*id0)*(L1q+3729/2152))*Laqssec*Ra*L1d-(57888800/29955057)*(L1q+3729/1076)*(6709/10000+Laqssec*id0)*L1q*Ra^2)*L1q*Ladssec^3+(8033/21438)*((78422331/1728701600)*(((21375813/1585539800)*Laqssec*id0+iq0*L1q)*Ra+(954412/36632453)*(6709/10000+Laqssec*id0)*L1q)*Laqssec^2*L1d^2-(29471/8033)*((-(10788319/198192475)*(L1q+2653/2152)*id0*Laqssec+L1q*iq0*(-1+L1q))*Ra-(23121088/109897359)*L1q*((36455304369/2315552000000+id0*L1q+(3729/2152)*id0)*Laqssec+(6709/10000)*L1q+25017861/21520000))*Laqssec*Ra*L1d+((L1q+3729/1076)*(-1+L1q)*id0*Laqssec*Ra+(57888800/9985019)*((-12151768123/578888000000+id0*L1q^2+((3729/1076)*id0+12151768123/578888000000)*L1q)*Laqssec+(6709/10000)*(L1q+3729/1076)*L1q)*L1q)*Ra^2)*L1d*Ladssec^2+(29471/21438)*(-(21438/29471)*(((26140777/768909600)*(L1q+2653/2152)*id0*Laqssec+L1q*iq0*(-1+L1q))*Ra+(477206/13323717)*L1q*((133745085903/2315552000000+id0*L1q+(3729/2152)*id0)*Laqssec+(6709/10000)*L1q+25017861/21520000))*Laqssec*L1d+((L1q+3729/1076)*(-1+L1q)*id0*Laqssec*Ra+(57888800/36632453)*L1q*((-44581695301/578888000000+id0*L1q^2+(44581695301/578888000000+(3729/1076)*id0)*L1q)*Laqssec+(6709/10000)*(L1q+3729/1076)*L1q))*Ra)*L1d^2*Ra*Ladssec+((L1q+3729/1076)*(-1+L1q)*id0*Laqssec*Ra+(28944400/39971151)*((-48644890767/289444000000+id0*L1q^2+((3729/1076)*id0+48644890767/289444000000)*L1q)*Laqssec+(6709/10000)*(L1q+3729/1076)*L1q)*L1q)*L1d^3*Ra^2)*Lfd^3-49149754215012000000*Ladssec^2*(-(32132/45537)*L1q*(-(2661/215200)*((477206/9985019)*Laqssec*id0+1600787527/49925095000+Ra*iq0)*Laqssec^2*L1d^2+(iq0*(-1+L1q)*Ra-(4348654/29955057)*(6709/10000+Laqssec*id0)*(L1q+3729/2152))*Laqssec*Ra*L1d-(28944400/9985019)*(L1q+3729/1076)*(6709/10000+Laqssec*id0)*L1q*Ra^2)*Ladssec^2+(32132/45537)*(-(45537/32132)*(((7125271/408315100)*(L1q+2653/2152)*id0*Laqssec+L1q*iq0*(-1+L1q))*Ra+(3817648/56602491)*L1q*((36455304369/2315552000000+id0*L1q+(3729/2152)*id0)*Laqssec+(6709/10000)*L1q+25017861/21520000))*Laqssec*L1d+((L1q+3729/1076)*(-1+L1q)*id0*Laqssec*Ra+(57888800/9985019)*((-12151768123/578888000000+id0*L1q^2+((3729/1076)*id0+12151768123/578888000000)*L1q)*Laqssec+(6709/10000)*(L1q+3729/1076)*L1q)*L1q)*Ra)*L1d*Ra*Ladssec+((L1q+3729/1076)*(-1+L1q)*id0*Laqssec*Ra+(115777600/56602491)*L1q*((-68885231547/1157776000000+id0*L1q^2+((3729/1076)*id0+68885231547/1157776000000)*L1q)*Laqssec+(6709/10000)*(L1q+3729/1076)*L1q))*L1d^2*Ra^2)*L1d*Lfd^2+17340623036616000000*Ladssec^3*(-L1q*(Laqssec*(iq0*(-1+L1q)*Ra+(954412/9985019)*(6709/10000+Laqssec*id0)*(L1q+3729/2152))*L1d-(57888800/9985019)*(L1q+3729/1076)*(6709/10000+Laqssec*id0)*L1q*Ra)*Ladssec+((L1q+3729/1076)*(-1+L1q)*id0*Laqssec*Ra+(57888800/9985019)*((-12151768123/578888000000+id0*L1q^2+((3729/1076)*id0+12151768123/578888000000)*L1q)*Laqssec+(6709/10000)*(L1q+3729/1076)*L1q)*L1q)*L1d*Ra)*L1d^2*Ra*Lfd-33511131654400000000*Ladssec^4*(L1q+3729/1076)*(6709/10000+Laqssec*id0)*L1q^2*L1d^3*Ra^2)/((-(2681/21520)*Ladssec*Lfd^2*Laqssec+((-(2661/107600)*L1d*Laqssec+Ra*(-1+L1q))*Ladssec+Ra*(-1+L1q)*L1d)*Lfd-Ra*L1d*Ladssec*(-1+L1q))*L1q*(-(2681/21520)*Ladssec*Lfd^2*Laqssec+((-(2661/107600)*L1d*Laqssec+(L1q+3729/1076)*Ra)*Ladssec+Ra*(L1q+3729/1076)*L1d)*Lfd-Ladssec*(L1q+3729/1076)*L1d*Ra)*(-(16066/13405)*Ladssec+Lfd)*Lfd*L1d*Ra) = -177/12500000,

(1/745800000)*(653885200*L1q*((Lfd-L1d)*Ladssec+L1d*Lfd)*Ladssec*cos((487/1125)*Pi)-81462185*Lfd*Laqssec*(-(16066/13405)*Ladssec+Lfd)*L1d*sin((487/1125)*Pi)[phone]*L1q*((Lfd-L1d)*Ladssec+L1d*Lfd)*Ladssec)/(((Lfd-L1d)*Ladssec+L1d*Lfd)*Laqssec*Ladssec*cos((487/2250)*Pi)) = 149/25,

(-81462185*Lfd^2+(65291288*L1d+81462185*Ladssec)*Lfd-81462185*Ladssec*L1d)/((372900000*L1d+372900000*Ladssec)*Lfd-372900000*Ladssec*L1d) = 1679/100000,

((16170897*L1d-16170897*Lfd)*Ladssec+81462185*Lfd^2)/((-372900000*L1d+372900000*Lfd)*Ladssec+372900000*L1d*Lfd) = -489/2000,

1634713/932250 = 171/100,

-6077/1000 = -6077/1000,

(578888/5)*L1q*((-(2681/21520)*Ladssec*Lfd^2*Laqssec+((L1q*Ra-(2661/107600)*L1d*Laqssec)*Ladssec+L1d*L1q*Ra)*Lfd-L1q*Ra*Ladssec*L1d)*Ladssec*sin((487/1125)*Pi)+(2681/21520)*L1d*Laqssec*(-(16066/13405)*Ladssec+Lfd)*Ra*(1+cos((487/1125)*Pi))*Lfd)/(L1d*Lfd*Ra*(-16066*Ladssec+13405*Lfd)*cos((487/2250)*Pi)*Laqssec^2) = 1549/10000,

2681/10000 = 2681/10000,

-2661/50000 = -2661/50000,

269/125 = 269/125,

-3729/500 = -3729/500,

3381/10000 = 3381/10000
]

The eliminations proceeded as:

Xqssec = -(1/33810)*(1700000*R1q*Laqssec*cos((487/2250)*Pi)+1000000*R1q*Laqssec*cos((487/2250)*Pi)*Xdssec-1000000*R1q*Laqssec*Ra*sin((487/2250)*Pi)+338100*L1q*Ra^2+977109*L1q+574770*L1q*Xdssec)/(L1q*(17+10*Xdssec))

Xdssec = (1/24860)*(1127*R1d*Ladssec*L1q*Ra-42262*L1d*R1q*L2q*cos((487/2250)*Pi)+24860*L1d*R1q*L2q*Ra*sin((487/2250)*Pi))/(L1d*R1q*L2q*cos((487/2250)*Pi))

L2q = -(1076/3729)*L1q

R1q=3381/21520*R1d*Ladssec*Ra*Laqssec*(-50000*R1d*Lfd+50000*Ladssec*R1d+2661*L1d*Lfd)/(-50000*R1d*Laqssec*L1d*Lfd*Ra*sin(487/2250*Pi)+50000*R1d*Ladssec*Laqssec*L1d*Ra*sin(487/2250*Pi)-50000*R1d*Ladssec^2*Lfd*Laqssec*cos(487/2250*Pi)+107600*Ladssec*L1q*Lfd*cos(487/2250*Pi)*L1d*Ra+2661*Laqssec*L1d^2*Lfd*Ra*sin(487/2250*Pi))

R1d = -(1/50000)*(13405*Lfd+2661*L1d)*Lfd*L1d/(-L1d*Lfd+Ladssec*L1d-Ladssec*Lfd)

Rfd = -(6077/372900000)*(13405*Lfd+2661*L1d)*Lfd^2/(-L1d*Lfd+Ladssec*L1d-Ladssec*Lfd)

Answer 2

[Traian Preda]

Hi,

The system describes the operation of a synchronous generator and it is done by identification between two matrices.

However the documentation is quite big, but I will send you the equations via this support window

Answer 3

[Traian Preda]

Here is the original system of equations with the variables

>> w0=1; H=11.2; phi0=-0.68; %rads Ra=0.01; Re=0; Xe=1.7; Eb=1; Psiad0=0.6709; Psiaq0=-0.1217; >> syms Rfd Lfd Ladssec R1d L1d R1q L1q Laqssec R2q L2q Ra Xdssec Xqssec id0 iq0 S=solve(-(((Eb*((Ra+Re)*sin(phi0)+(Xe+Xdssec)*cos(phi0)))*((Psiad0+Laqssec*id0))-(Eb*((Xe+Xqssec)*sin(phi0)-(Re+Ra)*cos(phi0))))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*(2*H))==-0.0001198,-((((Ra+Re)*Ladssec*(Psiad0+Laqssec*id0))-((Xe+Xqssec)*Ladssec*(Psiaq0+Ladssec*iq0)))/(((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*Lfd*(2*H))+((Ladssec*iq0)/(2*H*Lfd)))==0.00051,-((((Ra+Re)*Ladssec*(Psiad0+Laqssec*id0))-((Xe+Xqssec)*Ladssec*(Psiaq0+Ladssec*iq0)))/(((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L1d*(2*H))+((Ladssec*iq0)/(2*H*L1d)))==0.00001019,-((((Xdssec+Xe)*Laqssec*(Psiad0+Laqssec*id0))+((Ra+Re)*Laqssec*(Psiaq0+Ladssec*iq0)))/(((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L1q*(2*H))-((Laqssec*id0)/(2*H*L1q)))==0.00001632,-((((Xdssec+Xe)*Laqssec*(Psiad0+Laqssec*id0))+((Ra+Re)*Laqssec*(Psiaq0+Ladssec*iq0)))/(((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L2q*(2*H))-((Laqssec*id0)/(2*H*L2q)))==-0.00001416,-((w0*Rfd*Eb*Ladssec*((Xe+Xqssec)*sin(phi0)-(Re+Ra)*cos(phi0)))/(Lfd*((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))))==5.96,-((((w0*Rfd)/Lfd))*(1-(Ladssec/Lfd)+((Xe+Xqssec)*(Ladssec^2))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*Lfd))==0.01679,-((((w0*Rfd)/Lfd))*(-(Ladssec/Lfd)+((Xe+Xqssec)*(Ladssec^2))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L1d))==0.01679,-((((w0*Rfd)/Lfd))*(-((Ra+Re)*(Ladssec*Laqssec))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L1q))==-0.2445,-((((w0*Rfd)/Lfd))*(-((Ra+Re)*(Ladssec*Laqssec))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L2q))==1.71,-((((w0*R1d)/L1d))*(Eb*Ladssec*(((Xe+Xdssec)*sin(phi0)-(Ra+Re)*cos(phi0)))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))))==-6.077,-((((w0*R1d)/L1d))*(-(Ladssec/Lfd)+((Xe+Xqssec)*(Ladssec^2))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*Lfd))==0.1549,-((((w0*R1d)/L1d))*(1-(Ladssec/Lfd)+((Xe+Xqssec)*(Ladssec^2))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*L1d))==0.2681,-(((Eb*((Ra+Re)*sin(phi0)+(Xe+Xdssec)*cos(phi0)))*(w0*R1q*Laqssec))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*(L1q))==0.3381,-((((w0*R2q)/L2q))*(((Ra+Re)*(Ladssec*Laqssec))/((Ra+Re)^2+(Xe+Xdssec)*(Xe+Xqssec))*Lfd))==1)

Warning: Explicit solution could not be found. > In solve at 179

S =

[ empty sym ]