How is the theta_e transformation angle calculated for the Asynchronous Machine block in SimPowerSystems?

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I am trying to understand how the transformation angle theta_e (synchrounous reference frame) is calculated for the Asynchronous Machine block. Which phase is used as reference phase?

Accepted Answer

MathWorks Support Team
MathWorks Support Team on 27 Jun 2009
The documentation describes theta_e as the position of the synchronous rotating reference frame. The governing equations for the Asynchronous Machine block are complicated. The best way to understand the underlying model is to take a look inside the Asynchronous Machine block to see how the theta_e is calculated.
You can try the following to look inside the model:
1. Open powerlib_models
2. Open Continuous
3. Look under the mask of the asynchronous_machine block
4. Open the sin,cos block
You will see two enabled subsystems. The upper one is enabled when the user select the 'rotor' or 'stationary' Reference Frame in the mask of the ASM block. The second enabled subsystem is enabled when the 'synchronous' reference frame is selected.
5. Open the second enabled subsystem
The enabled subsystem will calculate the right sin(th) and cos(th) signals to use in another part of the model, that we will visit now: Since the Reference Frame option is used to convert ABC input voltages of the machine to dq reference frame we have to look at the following block.
6. In the powerlib_models/continuous/asynchronous_machine/ block open the abc2dq block.
You will see three enabled subsystems that are used to define the reference frame depending on the choice the user made in the general mask of the machine. The third subsystem is the one that is used to calculate the synchronous reference frame.
7. Open the third enabled subsystem to see how theta_e is used in the reference frame calculations

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