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Reinitialization for a piecewise-defined DAE set of equations

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Nicolas Mira Gebauer
关闭： MATLAB Answer Bot 2021-8-20
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.
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Nicolas Mira Gebauer
Nicolas Mira Gebauer 2020-10-20
I forgot to mention that the change of state (from ON to OFF) produces a discontinuity on the variables.

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