Warning: Solutions are parameterized by the symbols: [z, z1], z1.

Could I please get help in solving the equtions given below?

clc
clear

V1 = 480 ;
V2 = 587 * ( 1 / 1.36 ) ;
V3 = 400 * ( 1 / 0.85 ) ;

Ld = 30e-6 ;
w = 2 * pi * 100e3 ;

syms phi_grid phi_ev real

P12 = ( V1 * V2 / ( w * Ld ) ) * phi_grid * ( 1 - ( phi_grid / pi ) ) ;
P13 = ( 8 * V1 * V3 / ( pi^2 * w * Ld ) ) * sin( phi_ev ) ;
P32 = ( 8 * V2 * V3 / ( pi^2 * w * Ld ) ) * sin( phi_grid - phi_ev ) ; 

P1 = 4000 ;
P2 = -4000 ;
P3 = 0 ;

P2_eq = -P12 - P32 == P2 ;
P3_eq = -P13 + P32 == P3 ;
phi_grid_eq1 = phi_grid < pi / 2 ;
phi_grid_eq2 = phi_grid > 0 ;
phi_ev_eq1 = phi_ev < pi / 2 ;
phi_ev_eq2 = phi_ev > 0 ;

Equations = [ P2_eq P3_eq phi_grid_eq1 phi_grid_eq2 phi_ev_eq1 phi_ev_eq2 ] ;
Solution = solve( Equations, [ phi_grid phi_ev ],'ReturnConditions',1 ) 

Solution = struct with fields:
      phi_grid: z
        phi_ev: z1
    parameters: [z    z1]
    conditions: - (4801746272469333*sin(z1 - z))/549755813888 - (2669999971608161*sin(z1))/274877906944 == 0 & (4801746272469333*sin(z1 - z))/549755813888 + (6042395358318913*z*(z/pi - 1))/549755…

Solution.phi_grid

ans = 

z

Solution.phi_ev

ans = 

Answer 1

[Torsten]

The "solution" you obtain with the code from above is just a repetition of your equations. Use instead

clc
clear
V1 = 480 ;
V2 = 587 * ( 1 / 1.36 ) ;
V3 = 400 * ( 1 / 0.85 ) ;
Ld = 30e-6 ;
w = 2 * pi * 100e3 ;
syms phi_grid phi_ev real
P12 = ( V1 * V2 / ( w * Ld ) ) * phi_grid * ( 1 - ( phi_grid / pi ) ) ;
P13 = ( 8 * V1 * V3 / ( pi^2 * w * Ld ) ) * sin( phi_ev ) ;
P32 = ( 8 * V2 * V3 / ( pi^2 * w * Ld ) ) * sin( phi_grid - phi_ev ) ; 
P1 = 4000 ;
P2 = -4000 ;
P3 = 0 ;
P2_eq = -P12 - P32 == P2 ;
P3_eq = -P13 + P32 == P3 ;
%phi_grid_eq1 = phi_grid < pi / 2 ;
%phi_grid_eq2 = phi_grid > 0 ;
%phi_ev_eq1 = phi_ev < pi / 2 ;
%phi_ev_eq2 = phi_ev > 0 ;
%Equations = [ P2_eq P3_eq phi_grid_eq1 phi_grid_eq2 phi_ev_eq1 phi_ev_eq2 ] ;
%Solution = solve( Equations, [ phi_grid phi_ev ],'ReturnConditions',1 ) 
Solution = solve([P2_eq,P3_eq])

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

Solution = struct with fields:
      phi_ev: 0.12950879328358872805311501776301
    phi_grid: 0.27363106526757571046547973834901

[Aditya Zade]

Thank you.