Reinitialization for a piecewise-defined DAE set of equations

I am trying to model an electrical thyristor, which has the following switching equations:

ON-status: Vak >= Vf & vg > Vgt; or when Iak > Il

OFF-status: Else

For this, I am modelling a piecewise function as follows:

sCond = piecewise(Vak >= Vf & vg > Vgt | Iak > Il, 1, 0);

So, when sCond is 1, the status is ON; and when sCond is 0, the status is OFF.

By having such piecewise-defined function, I can use it to multiply it in my electric system's equations, which are strategically defined so that when sCond = 1, I will obtain a DAE system for the ON topology, and when sCond = 0, I will obtain a different DAE system which represents the OFF topology.

e =

 piecewise(1/10000 < i_L2(t) | 0 <= u_KL1(t) - u_KL2(t), (50*sin(100*pi*t))/pi + i_L1(t)/(100*pi) + (91*i_L2(t))/(100*pi) - (20*u_KL1(t))/pi + (10*u_KL2(t))/pi, (50*sin(100*pi*t))/pi + i_L1(t)/(100*pi) - (10*u_KL1(t))/pi)
                           piecewise(1/10000 < i_L2(t) | 0 <= u_KL1(t) - u_KL2(t), i_L3(t)/(10*pi) - (91*i_L2(t))/(100*pi) + (10*u_KL1(t))/pi - (20*u_KL2(t))/pi, i_L3(t)/(10*pi) - (91*i_L2(t))/(100*pi) - (20*u_KL2(t))/pi)
                                                                                                                                                                                    u_KL1(t) - i_L1(t)/1000 - 5*sin(100*pi*t)
                                                                                             piecewise(1/10000 < i_L2(t) | 0 <= u_KL1(t) - u_KL2(t), u_KL1(t) - (91*i_L2(t))/1000 - u_KL2(t), - (91*i_L2(t))/1000 - u_KL2(t))
                                                                                                                                                                                                       u_KL2(t) - i_L3(t)/100

                                                                                                      
%Thus, when the sCond = 0, e would be:  

                           L1*diff(i_L1(t), t) + RL1*i_L1(t) == u_KL1(t) - US*sin(phiS + 2*pi*f*t)
                                                    L2*diff(i_L2(t), t) + RL2*i_L2(t) == -u_KL2(t)
                                                     L3*diff(i_L3(t), t) + RL3*i_L3(t) == u_KL2(t)
         u_KL1(t)/(2*L1*f*pi) == (US*sin(phiS + 2*pi*f*t))/(2*L1*f*pi) + (RL1*i_L1(t))/(2*L1*f*pi)
 u_KL2(t)*(1/(2*L2*f*pi) + 1/(2*L3*f*pi)) == (RL3*i_L3(t))/(2*L3*f*pi) - (RL2*i_L2(t))/(2*L2*f*pi)
 
%Otherwise, when sCond = 1, e would be:

L1*diff(i_L1(t), t) + RL1*i_L1(t) == u_KL1(t) - US*sin(phiS + 2*pi*f*t)
                                                                                                         L2*diff(i_L2(t), t) + RL2*i_L2(t) == u_KL1(t) - u_KL2(t)
                                                                                                                    L3*diff(i_L3(t), t) + RL3*i_L3(t) == u_KL2(t)
 u_KL1(t)*(1/(2*L1*f*pi) + 1/(2*L2*f*pi)) - u_KL2(t)/(2*L2*f*pi) == (US*sin(phiS + 2*pi*f*t))/(2*L1*f*pi) + (RL1*i_L1(t))/(2*L1*f*pi) + (RL2*i_L2(t))/(2*L2*f*pi)
                                         u_KL2(t)*(1/(2*L2*f*pi) + 1/(2*L3*f*pi)) - u_KL1(t)/(2*L2*f*pi) == (RL3*i_L3(t))/(2*L3*f*pi) - (RL2*i_L2(t))/(2*L2*f*pi)
    
    

It's all working well, except for one thing.

I am not being able to correctly reinitialize the variables when an event is detected (when sCond changes from 0 to 1 or viceversa). In fact, my code is only works when I manually change the initial values at each event-reinitialization using the values that I previously know that should be consistent, but I need to do it automatically for when I expand my problem. Is there a formal way to do this? I tried using decic() by giving it the previous's step values but apparently it does not recognize that the DAE set of equations e is changing from ON to OFF, thus it tries to use these previous's step values and thus says that it needs a better guess.

[Nicolas Mira Gebauer]

I forgot to mention that the change of state (from ON to OFF) produces a discontinuity on the variables.