Question about Algeb diag_eps

[jinningwang]

Hi Hantao,

I'm curious about the diag_eps=True in the Algeb definition, may I ask what's it?

Regards,
Jinning

[jinningwang]

Answer from Hantao:

diag_eps adds an additional small element to the diagonal element in the Jacobian matrix corresponding to this equation and variable. It is needed when the derivative of this equation w.r.t this variable may not be zero to avoid singularity.

For example:

self.vi = Algeb(info='Total input voltages',
                tex_name='V_i',
                unit='p.u.',
                e_str='ue * (-v + vref - WF_y - vi)',
                v_str='-v + vref',
                diag_eps=True,
                )

Here if we compute the derivative of vi (consider e_str as a function g(vi) = 0 and compute dg / d (vi)), we get -ue. If the device is tripped during the simulation, the connection status flag ue switches to 0 and thus dg / d(vi)=0. Then we will have 0 appear on the diagonal of the Jacobian matrix, which will cause the matrix to be singular.

Therefore, adding a small value avoids the singularity in such cases.

If diag_eps = True, the default diag_eps value in the config file will be used. If supplied with a specific value, say diag_eps = 1e-6, the specific value will be used. Still, there is no difference in simulation.

Note:
ue is the connectivity status.

Jinning

[cuihantao]

Thanks! Just edited.