How are the L and R matrices derived from the parameters of the per unit synchronous machine in SimPowerSystems?

I am trying to understand how the L and R matrices  derived from the parameters of the per unit synchronous machine in SimPowerSystems. 

I went through the reference papers  in order to understand how to get from the standard pu parameters to the matrices L and R.

 

Yet, the formulas I got (and verified with the books I have) from these papers would not lead to an unrealistic L matrix in case of Xl = 0.01 in my example.

 

Hence, I wonder which parameters does the SimPowerSystem algorithms compute realistic values and similar values to those I'd get with my simpler formulas from your references? 

Answer 1

[MathWorks Support Team]

Here are the steps that we are using to calculate Xmd:

 

1.      From Td’ and Td’’,  the open-circuit time constant Tdo’ and Tdo’’ are estimated base on Ref.[1].

2.      From Xd, Xd’, Xd’’, Xl, and Td’’, the d-axis damper time constant Tkd is estimated base on Ref.[2].

3.      From Td’, Td’’, Tdo’, Tdo’’, Tkd, and Xd, Xmd is calculated based on Ref.[3].

 

References:

[1].   I. M. Canay, “Modelling of alternating-current machines having multiple rotor circuits”

[2].   Y. Takeda and B. Adkins, “Determination of Synchronous Machine Parameters Allowing for Unequal Mutual Inductances”

[3].   L. Salvatore, M. Savino, “Exact relationship between parameters and test data for models of synchronous machines”