# Mismatch between theoretical equation and simulink simulation

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Joaquín Rebled Lluch on 4 May 2017
Answered: Joel Van Sickel on 21 May 2021
Hi,
Context: I am building a thyristor converter small-signal model for HVdc studies. In order to validate the small-signal models, I use a simulink simscape model and verify the concordancies. However, I detected significative differences between the small-signal model and the simulink results. Of course, I initially assumed that my small-signal model must contain some errors. However, in order to be completely sure that Simulink was functionning as the theoretical equations, I did some testing and found differences between the pure theoretical equations and the simulink block outputs. I simplified the simulink model in order to be able to test the theoretical equations against the simplest possible case, and still found a mismatch. The equation I am trying to verify is:
Vdc=3*sqrt(2)/pi*cos(alfa)*Vline-line - 3*w*Lac*Idc/pi
Problem: When I run the model with an ideal ac grid (that is Lac=0) the equations and the model results have a perfect match. However, when I consider an inductance between the ideal voltage sources and the thyristor bridge (which represents the transformer) the equations do not match the results. That seems to indicate that the problem is related with the second part of the equation.
Considerations: I have done a consistent litterature review in order to be sure I was considering the correct terms for the above equation. For example, the line-to-line voltage must be the voltage before the inductances. Moreover, this equations has been used for a long time as the thyristor HVdc converter is quite a mature technology.
Possible solutions: -There is something I am not understanding about the equations, or there is some assumptions I am not considering. -The simulink built-in blocks have some characteristics that somehow modify the behaviour of the system -The equation is wrong (highly improbable)
Any help is extremelly welcomed! Of course, I attach the model which I am currently using to verify the concordances between equations and the simulink blocks.
PD: The comparation between simulink results and theoretical equations is done in the double-input scopes at the bottom right of the model.
Thank you very much!
##### 2 CommentsShowHide 1 older comment
Rauf Laghari on 22 Apr 2021
Thank you for the post. I just went through your thesis on the small signal model and I really loved it. Can I reach out to you via email or something? I am working on a similar project and any discussion with you would be really insightful. Thank you.

Joel Van Sickel on 21 May 2021
Solved! The mismatch was due to the solver. Surprisingly, the recommended solver (Ode23tb), which yields the highest simulation speed for this particular case, is the one causing the mismatch. Ode 23s yields accurate results according to the equations. I hope it can help anyone with the same issue.