How to solve two equations two unknowns for the equations with syms?

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Aditya Zade
Aditya Zade 2023-5-20
回答： Dinesh 2023-6-7
Ran in:
I am trying to calculate solutions for the two equation two unknown type scenario. But, the solver is not able to give any explicit solution. The unknows are syms type transfer functions H_mi_thetadcap and H_mi_vtest.
clc
clear
%% Parameters
Vm = 277 * sqrt(6) ;
ws = 2 * pi * 85000 ;
Lp = 28.3e-6 ;
RLp = 77.55e-3 ;
Zpss = ( ws * Lp * 1i ) + RLp ;
Cpp = 123.13e-9 ;
RCpp = 13.55e3 ;
Zppss = RCpp / ( 1 + RCpp * Cpp * ws * 1i ) ;
Cps = 160.32e-9 ;
RCps = 8e3 ;
Zpsss = RCps / ( 1 + RCps * Cps * ws * 1i ) ;
Ll = 37.45e-6 ;
RLl = 25.85e-3 ;
Zlss = ( ws * Ll * 1i ) + RLl ;
Lm = 996.2e-6 ;
Zmss = ( ws * Lm * 1i ) ;
Cdc = 161.466e-6 ;
RCdc = 20e3 ;
Zdcss = RCdc ;
Rload = 500e3 ; % 128.94 ;
Vbat = 730 ;
Rbat = 0.045 ;
Kp1ss = ( Zmss + Zpsss + Zlss ) / Zmss ;
Kp2ss = Zpsss + Zlss ;
Kp3ss = 1 + ( Zpss / Zppss ) + ( Zpss / ( Zpsss + Zlss ) ) ;
Kp4ss = Zpss / ( Zpsss + Zlss ) ;
Ko1ss = ( 1 / Zdcss ) + ( 1 / Rload ) ;
Ko2ss = 1 + ( Rbat / Rload ) ;
%% Steady State
Mi = 0.975 ;
Vtt = ( 2 * sqrt(3) / pi ) * Mi * Vm ;
thetad = 1.263077326 ;
Vdc = Vbat ;
Vd = ( 4 / pi ) * Vdc * ( cos( thetad ) - 1i * sin( thetad ) ) ;
Id = abs( ( Vtt - ( Vd * ( Kp1ss * Kp3ss - Kp4ss ) ) ) / ( Kp2ss * Kp3ss ) ) * ( cos( thetad ) - 1i * sin( thetad ) ) ;
for iterations = 1 : 1 : 10
Iout = ( 2 / pi ) * abs( Id ) ;
Idc = Iout ;
Vdc = ( Vbat + Idc * Rbat ) / ( 1 + Rbat / Rload ) ;
Vd = ( 4 / pi ) * Vdc * ( cos( thetad ) - 1i * sin( thetad ) ) ;
Id = abs( ( Vtt - ( Vd * ( Kp1ss * Kp3ss - Kp4ss ) ) ) / ( Kp2ss * Kp3ss ) ) * ( cos( thetad ) - 1i * sin( thetad ) ) ;
end
Pdc = Vdc * Idc ;
Rd = ( 8 / pi^2 ) * ( Vdc / Idc ) ;
Vtest = 339.254 ;
%% Small Signal
syms s H_mi_thetadcap H_mi_vtest real
mi = Mi ;
vtt = ( 2 * sqrt(3) / pi ) * mi * Vm ;
Zp = ( s * Lp ) + ( ws * Lp * 1i ) + RLp ;
Zpp = RCpp / ( 1 + ( s * Cpp * RCpp ) + ( ws * Cpp * 1i * RCpp ) ) ;
Zps = RCps / ( 1 + ( s * Cps * RCps ) + ( ws * Cps * 1i * RCps ) ) ;
Zl = ( s * Ll ) + ( ws * Ll * 1i ) + RLl ;
Zm = ( s * Lm ) + ( ws * Lm * 1i ) ;
Zdc = RCdc / ( 1 + ( s * RCdc * Cdc ) ) ;
Kp1 = ( Zm + Zps + Zl ) / Zm ;
Kp2 = Zps + Zl ;
Kp3 = 1 + ( Zp / Zpp ) + ( Zp / ( Zps + Zl ) ) ;
Kp4 = Zp / ( Zps + Zl ) ;
Ko1 = ( 1 / Zdc ) + ( 1 / Rload ) ;
Ko2 = 1 + ( Rbat / Rload ) ;
H_mi_idcap_V = ( ( 4 * sqrt(3) * Vtest ) + ( 4 * sqrt(3) * Mi * H_mi_vtest ) + ( 1i * Vdc * 4 * ( Kp1 * Kp3 - Kp4 ) * ( cos( thetad ) - 1i * sin( thetad ) ) * H_mi_thetadcap ) ) / ( pi * Kp2 * Kp3 ) ;
H_mi_idcap_real = real( H_mi_idcap_V ) ;
H_mi_idcap_imag = imag( H_mi_idcap_V ) ;
Id_real = real( Id ) ;
Id_imag = imag( Id ) ;
Id_abs = abs( Id ) ;
equation_one = H_mi_thetadcap + ( ( H_mi_idcap_imag * Id_real ) - ( H_mi_idcap_real * Id_imag ) ) / Id_abs^2 ;
equation_two = H_mi_idcap_real - ( ( -Id_imag / Id_real ) * H_mi_idcap_imag ) ;
solution = solve( [equation_one, equation_two], [H_mi_thetadcap, H_mi_vtest] )
Warning: Unable to find explicit solution. For options, see help.
solution = struct with fields:
H_mi_thetadcap: [0×1 sym] H_mi_vtest: [0×1 sym]
H_mi_thetadcap = getfield( solution, 'H_mi_thetadcap' )
H_mi_thetadcap = Empty sym: 0-by-1
H_mi_vtest = getfield( solution, 'H_mi_vtest' )
H_mi_vtest = Empty sym: 0-by-1

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采纳的回答

Dinesh
Dinesh 2023-6-7
Hi
The warning: unable to find explicit solution is because your equation is too complicated to solve. One way to solve this question would be to use numerical approach (vpasolve or fsolve).
Please refer to the following MATLAB documentations.
  1. https://www.mathworks.com/help/symbolic/sym.vpasolve.html
  2. https://www.mathworks.com/help/optim/ug/fsolve.html
Also refer to this MATLAB answer thread for more details on solving two equations with two unknowns.
https://www.mathworks.com/matlabcentral/answers/395460-how-can-i-solve-two-equations-with-two-unknown-variable-using-matlab
Hope this helps,
Thank you!

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