Professor, today's topic is about transformer hot-spot analysis, correct? What exactly is it?

It refers to the localized temperature rise in windings and its impact on insulation lifespan. The analysis is conducted in accordance with IEC 60076.

What kind of equations are involved in transformer hot-spot analysis?

The analysis involves solving the heat conduction equation.

How is this equation actually solved using a computer?

We use spatial discretization via the Finite Element Method (FEM). This involves assembling the element stiffness matrices and constructing the global stiffness equation.

What specifically is meant by the matrix solution algorithm?

It involves solving the system of equations using either direct methods (LU decomposition, Cholesky decomposition) or iterative methods (Conjugate Gradient method, GMRES method). For large-scale problems, preconditioned iterative methods are particularly effective.

Hot Spot Analysis of Transformers

Category: 解析 | Integrated 2026-04-06

Theory and Physics

🎓

Local temperature rise in windings. Impact on insulation lifespan. Compliant with IEC 60076.

🧑‍🎓

Wait, wait, so local temperature rise in windings... does that mean it can be used in cases like this too?

Governing Equations

$$ \theta_h=\theta_o+\Delta\theta_{hs} $$

$$ \Delta\theta_{hs}=H\cdot I^2 R_{dc}(1+\alpha\Delta T) $$

🧑‍🎓

I see. So if a transformer has a hot spot, it's basically okay for now?

Discretization Method

🧑‍🎓

How do you actually solve this equation on a computer?

🎓

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrices and construct the global stiffness equation.

🎓

We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

Matrix Solution Algorithms

🧑‍🎓

What exactly do you mean by matrix solution algorithms?

🎓

We solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Solution Method	Classification	Memory Usage	Applicable Scale
LU decomposition	Direct Method	O(n²)	Small to Medium Scale
Cholesky decomposition	Direct Method (Symmetric Positive Definite)	O(n²)	Small to Medium Scale
PCG Method	Iterative Method	O(n)	Large Scale
GMRES method	Iterative Method	O(n·m)	Large Scale / Non-symmetric
AMG Preconditioning	Preprocessing	O(n)	Very Large Scale

🧑‍🎓

So if you cut corners on the finite element method part, you'll pay for it later. I'll keep that in mind!

Implementation in Commercial Tools

🧑‍🎓

So, what software can be used to perform hot spot analysis for transformers?

Tool Name	Developer/Current	Main File Format
JMAG-Designer	JSOL Corporation	.jmag, .jproj
Ansys Maxwell	Ansys Inc.	.aedt, .maxwell
COMSOL Multiphysics	COMSOL AB	.mph
Ansys Mechanical (formerly ANSYS Structural)	Ansys Inc.	.cdb, .rst, .db, .ans, .mac

Vendor Lineage and Product Integration History

🧑‍🎓

Is the background of each software quite dramatic?

JMAG-Designer

🧑‍🎓

What exactly is JMAG?

🎓

Developed by Japan's JSOL Corporation. An electromagnetic field analysis tool specialized for electrical equipment design.

Current Affiliation: JSOL Corporation

Ansys Maxwell

🧑‍🎓

Tell me about "Ansys Maxwell"!

🎓

Ansoft Maxwell. Low-frequency electromagnetic field analysis. Integrated into Ansys in 2008.

Current Affiliation: Ansys Inc.

🧑‍🎓

After hearing all this, I finally understand why the Japanese one is important!

COMSOL Multiphysics

🧑‍🎓

Tell me about "COMSOL Multiphysics"!

🎓

Founded in Sweden in 1986. Started as FEMLAB with MATLAB integration, later renamed to COMSOL. Strong in multiphysics.

Current Affiliation: COMSOL AB

File Formats and Interoperability

🧑‍🎓

Are there any points to note when transferring data between different software?

Format	Extension	Type	Overview
STEP	.stp/.step	Neutral CAD	ISO 10303 compliant 3D CAD data exchange format. Supports geometry + PMI.
IGES	.igs/.iges	Neutral CAD	Early CAD data exchange standard. Has issues with surface data compatibility. Transition to STEP is progressing.

🎓

When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.

🧑‍🎓

I see... formats seem simple at first glance, but they're actually quite deep, aren't they?

Practical Considerations

🧑‍🎓

Are there things like "field wisdom" that aren't covered in textbooks?

🎓

Verifying mesh convergence, validating the appropriateness of boundary conditions, and performing sensitivity analysis of material parameters are extremely important.

🎓

Mesh Dependency Verification: Confirm convergence with at least three levels of mesh density.

Boundary Condition Validity: Setting physically meaningful constraint conditions.

Result Verification: Comparison with theoretical solutions, experimental data, and known benchmark problems.

🎓

Yeah, you're on the right track! Actually getting your hands dirty is the best way to learn. If you have any questions, feel free to ask anytime.