How I can resolve this system of equations?
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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)
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Respuesta aceptada
Walter Roberson
el 21 de Ag. de 2013
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.)
9 comentarios
Walter Roberson
el 22 de Ag. de 2013
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)+653885200*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)
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