How to solve equations with the warning "Unable to find explicit solution".

I need to find an expression for tzvs_p.

clc
clear

syms Vp Ip2 ws wp Ie theta_e Rp Vg real

Bp = atan2( ( -Ip2 - ( ( ws^2 / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * sin( theta_e ) ) ), ( ( -Vp / Rp ) + ( Vg / Rp ) + ( ( wp * ws / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * cos( theta_e ) ) ) ) ;
Ap = ( -Vp + Vg + ( ( wp * ws * Rp / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * cos( theta_e ) ) ) / cos( Bp ) ;

syms tzvs_p real 
tzvs_p_equation = Vp == ( Ap * cos( wp * tzvs_p + Bp ) ) - Vg - ( ( wp * ws * Rp / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * cos( ws * tzvs_p - theta_e ) ) ;
tzvs_p = solve( tzvs_p_equation, tzvs_p ) 

Warning: Unable to find explicit solution. For options, see help.

 
tzvs_p =
 
Empty sym: 0-by-1
 

[Torsten]

I need to find an expression for tzvs_p

It might be possible to get a numerical value for tzvs_p if you specify numerical values for the other symbolic parameters.

But a general solution looks impossible for me (and MATLAB).

[Aditya Zade]

Is there a way to get a solution as an expression by mentioning some assumptions or boundaries for the symbolic parameters?

[Torsten]

I think the only assumption for which you will get a solution is

wp = ws 
Bp = - theta_e

But this case is excluded since you divide by wp^2 - ws^2.

[Aditya Zade]

Vp = 480 ;

Ip2 = 7.296 ;

ws = 6.2832e+05 ;

wp = 8.6986e+06 ;

Ie = 14.137 ;

theta_e = 0.5924 ;

Rp = 328.4596 ;

Vg = 521.5385 ;

These are the actual values where wp >> ws.

Could any assumptions be made to get an expression?

[Dyuman Joshi]

There are periodic solutions for the values mentioned -

Vp = 480 ;
Ip2 = 7.296 ;
ws = 6.2832e+05 ;
wp = 8.6986e+06 ;
Ie = 14.137 ;
theta_e = 0.5924 ;
Rp = 328.4596 ;
Vg = 521.5385 ;

Bp = atan2( ( -Ip2 - ( ( ws^2 / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * sin( theta_e ) ) ), ( ( -Vp / Rp ) + ( Vg / Rp ) + ( ( wp * ws / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * cos( theta_e ) ) ) ) ;
Ap = ( -Vp + Vg + ( ( wp * ws * Rp / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * cos( theta_e ) ) ) / cos( Bp ) ;

syms tzvs_p real 
tzvs_p_equation = Vp == ( Ap * cos( wp * tzvs_p + Bp ) ) - Vg - ( ( wp * ws * Rp / ( wp^2 - ws^2 ) ) * ( Ie / 2 ) * cos( ws * tzvs_p - theta_e ) ) ;

for k=-2*pi:pi:2*pi
sol = vpasolve( tzvs_p_equation, tzvs_p, k)
end

sol = 

sol = 

sol = 

0.000000048208036616102117891601212689647

sol = 

3.1415927017978298545647612748807

sol = 

6.2831853553876230930274046581602