In simscape electrical PMSMDriveExample: what is the abc2dq0 theta_offset value when change the winding type from Y to delta.

Hi all,

I am doing the delta-IPMSM motor control simulation, and I already know that there will be a theta offset (maybe -30 degrees electrical Angle?)in the park transformation while changing the motor winding type from Y to delta. But in simscape electrical PMSMDriveExample, I found that the theta_offset is '-(120/p)*pi/180'.why the value is this?

Answer 1

[Prem Manoj Mule]

Hello! 👋 @Chenyang

This above equation is used because changing the motor winding type from Y (Star) to Delta introduces a 120° phase shift in the electrical angle. The negative sign indicates a change in rotation direction.

The factor 120/p120/p120/p adjusts the phase shift based on the number of pole pairs (p). The conversion π/180\pi/180π/180 changes degrees to radians.

This formula ensures correct alignment of the rotating reference frame after switching from Star to Delta configuration.

The offset value changes with the number of pole pairs to maintain synchronization in the rotating reference frame. The formula ensures that the electrical angle adjustment is accurate for proper motor control and simulation results.

[Chenyang]

Dear Prem Manoj Mule,

I sincerely appreciate your insightful response to my question. Your explanation regarding the 120° phase shift introduced when changing the motor winding type from Y (Star) to Delta was particularly helpful.

I have two follow-up questions that I would like to understand more deeply:

1. You mentioned that changing the motor winding configuration introduces a 120° phase shift in the electrical angle. Do you have any references or literature that explain this in detail? I would like to explore the theoretical background further.
2. Since the 120° phase shift is already in electrical degrees, why is it still necessary to divide by the pole pair number when performing the Park transformation? Conceptually, I would expect the electrical angle shift to be directly used, but I assume there is a deeper reasoning behind the additional division.

Looking forward to your insights, and once again, thank you for your valuable help!

[Prem Manoj Mule]

Hello @Chenyang, Refer this....

1. Phase Shift Introduced by Changing Motor Winding Configuration from Y (Star) to Delta:

When transitioning from a Y (Star) to a Delta configuration in three-phase systems, a phase shift occurs between the line-to-neutral voltages of the primary and secondary windings. Specifically, the line-to-neutral voltages on the star side lead the corresponding voltages on the delta side by 30°. This phase shift is crucial in transformer applications to ensure proper synchronization and operation.

https://www.eeeguide.com/phase-shift-in-star-delta-transformer/

2. Necessity of Dividing by the Number of Pole Pairs in the Park Transformation:

The Park transformation is a mathematical tool used to simplify the analysis of three-phase electrical machines by transforming the three-phase stationary reference frame (abc) into a two-axis rotating reference frame (dq). This transformation relies on the electrical angle, which is related to the mechanical angle by the number of pole pairs (p) of the machine. The relationship is given by:

θe​ = p × θm

Where:

θe​ is the electrical angle.

θm​ is the mechanical angle.

p is the number of pole pairs.

This relationship ensures that the transformation accurately reflects the machine's electrical behavior relative to its mechanical position.

https://en.wikipedia.org/wiki/Direct-quadrature-zero_transformation

3. Incorporating Phase Shift into the Park Transformation:

The Park transformation is a mathematical tool used to simplify the analysis of three-phase electrical machines by transforming the three-phase stationary reference frame (abc) into a two-axis rotating reference frame (dq). When changing the motor winding configuration from Y to Delta, the inherent 30° phase shift must be accounted for in the transformation.Given the relationship between electrical and mechanical angles, the phase shift in electrical degrees is:

θshift​=30 / p.

This adjustment ensures that the Park transformation aligns correctly with the motor's actual operating conditions, maintaining accurate representation of the machine's behavior.

The 120/p​ phase offset in the Park transformation arises from the need to account for the inherent phase shift introduced by the Delta winding configuration and the relationship between electrical and mechanical angles in the machine.​

https://dspace.mit.edu/bitstream/handle/1721.1/123557/Final_Submission__Open_Access.pdf?sequence=1&isAllowed=y

[Chenyang]

Thank you very much, Prem Manoj Mule. Your insightful explanation helps a lot!