Ansys Maxwell: 3PH Transformer Inductance Calculations
Hello everyone, David Giglio here with Ozen Engineering, Inc. In this video, I will show you how to use the ANSYS Maxwell ED current solver to compute self-inductances, mutual inductances, and leakage inductances.
Introduction to Inductance
Inductance is measured in Henrys, which in base units is expressed as Webers per ampere. This indicates how much magnetic flux (in Webers) is produced in a material for a given current (in amperes). The higher the flux produced per ampere, the higher the inductance. Higher inductance means it is easier to produce magnetic flux in a material per unit ampere.
Types of Inductance
- Self Inductance: Represents how much flux is produced in a winding divided by the operating current flowing through that winding. It can be computed as:
- Apparent Inductance: Total flux leakage value divided by the operating current.
- Differential Inductance: Derivative of flux linkage at the operating point divided by the operating current.
- Leakage Inductance: Represents how much flux does not link with another winding, divided by the operating current in the winding producing the flux.
- Mutual Inductance: Total flux produced by one winding that links with another winding, divided by the current in the winding producing the flux.
Inductance Calculations in a Three-Phase Transformer
For a six-winding system, such as a three-phase transformer, there are:
- 6 Self Inductances
- 30 Permutations for Mutual Inductance
- 30 Permutations for Leakage Inductance
This results in a 6x6 matrix showing self-inductances along the diagonal and mutual inductances elsewhere. In total, there are 18 relevant inductances, including self, mutual, and leakage inductances.
Example: Excitation Circuit
For an open circuit test, we determine self and mutual inductance by exciting the low voltage phase A winding. All other windings are open circuit. The self-inductance is the total flux produced by this winding divided by the current flowing in it. The mutual inductance is the total flux linking the high voltage winding divided by the operating current in the excited winding.
Expressions for Inductance
ANSYS Maxwell automatically provides self and mutual inductance values. However, leakage inductance must be computed using expressions. Here are some key expressions:
- Self Inductance:
- Magnitude of flux linkage in winding divided by operating current.
- Imaginary part of impedance of the excited winding divided by operating frequency (Omega).
- Total magnetic energy times two divided by the magnitude of the current squared.
- Mutual Inductance:
- Magnitude of flux linking high voltage phase A divided by current in low voltage phase A, divided by the turns ratio.
- Imaginary part of impedance of induced voltage in high voltage phase A divided by current in low voltage phase A, divided by operating frequency.
- Leakage Inductance:
- Self-inductance of low voltage phase A plus self-inductance of high voltage phase A divided by turns ratio squared minus two times mutual inductance between high and low voltage phase A divided by turns ratio.
Conclusion
All these results match, confirming the validity of the expressions used. Contact Ozen Engineering, Inc. for consulting services, mentoring, and training on ANSYS tools, or for purchasing ANSYS software. Check out our YouTube channel for more content, and find links to our blogs in the video descriptions.
Thank you very much and have a nice day.
Hello everyone, David Giglio here with Ozen Engineering. In this video, I will show you how to use the ANSYS Maxwell ED current solver to compute self-inductances, mutual inductances, and leakage inductances. Here, I have a blog prepared where I go over fundamental inductance definitions.
Inductance has units of Henry, which is expressed in base units as Webers per amp. So, this reveals to us how much flux, representing Webers, is produced in material for a given value of current in unit amps. The higher the flux produced for a given amp, the higher the inductance.
Higher inductance means easier to produce magnetic flux in a material per unit amp, and there are various inductance types. Self-inductance represents how much flux is produced in a winding divided by the operating current flowing through that winding.
It can be computed as an apparent inductance, which is the total flux value divided by the operating current in that winding, or as a differential inductance calculated as the derivative of flux linkage at the operating point divided by the operating current in that winding at that point.
Leakage inductance represents how much flux is not linking another winding divided by the operating current in the winding producing the flux. Mutual inductance is the total flux produced by one winding that links with another winding divided by the current in the winding producing the flux.
For a six-winding system, such as a three-phase transformer, there are 18 relevant inductances, which include the six self-inductances, the six mutual inductances, and the six leakage inductances. Here's an example of an excitation circuit.
For an open-circuit test, we want to determine the self-inductance and mutual inductance. We excite one winding, and some of the flux links with another winding. The self-inductance is the total flux produced by this winding divided by the current flowing in this winding.
The mutual inductance is the total flux linking the second winding divided by the operating current in the excited winding. Once the simulation is done, we have data to post-process.
We can use expressions to determine the self-inductance, which is equal to the magnitude of the flux linkage in winding levels phase a divided by the operating current. It's also equal to the imaginary part of the impedance of the excited winding divided by the operating frequency omega.
Leakage inductance is equal to the total magnetic energy times two divided by the magnitude of the current squared. It's also equal to the leakage inductance plus the mutual inductance, where L represents inductance, and the subscripts represent which winding with respect to another winding.
The mutual inductance from the open-circuit test is equal to the magnitude of the flux flux linking the second winding divided by the current flowing in the excited first winding divided by the turns ratio.
It's also equal to the imaginary part of the impedance of the second winding divided by the current flowing in the excited first winding divided by the operating frequency omega.
Leakage inductance is equal to the magnitude of the flux linkage in the first winding divided by the current in that winding.
It's also equal to the self-inductance of the first winding plus the self-inductance of the second winding divided by the terms ratio squared minus two times the mutual inductance between the first and second windings divided by the terms ratio.
For the short-circuit test, we only short the second winding while all other windings are open circuit. The open circuits are represented by very high resistance, and the short circuit is represented by very low resistance.
The leakage inductance is equal to the flux linkage of the first winding divided by the current in that same first winding. It's also equal to the leakage inductance computed using the coupling coefficient with respect to the second winding and the first winding squared.
We use the self-inductance of the first winding times one minus the coupling coefficient squared with respect to the second and first winding based on the load of the current.
We use the expression again on the right side, the expression using self-inductance of the first and second windings and the terms ratio and the neutral inductance between these windings. All these results match. They're identical, almost identical. And there you have it.
You have multiple ways to compute leakage inductance, and we confirm that all these expressions work and they match. Contact us, Ozen Engineering Inc. for information on how we can help you with your technological goals.
We can help you with consulting services, mentoring, and training of how to use ANSYS tools, and for sales on purchasing ANSYS software. Please check out our Ozen Engineering YouTube video, YouTube channel for content that we create and we publish.
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