How to solve equations with the warning "Unable to find explicit solution".
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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 )
5 Comments
Dyuman Joshi
on 29 Dec 2023
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
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