Winding Temperature Rise Calculator – IEEE, IEC

Accurate winding temperature rise calculations are critical for transformer design and operation safety. These calculations ensure transformers operate within thermal limits, preventing insulation damage and failures.

This article explores winding temperature rise calculators based on IEEE and IEC standards. It covers formulas, tables, and real-world examples for precise thermal analysis in transformers.

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• Calculate winding temperature rise for a 100 MVA transformer with 65°C ambient temperature.
• Determine temperature rise using IEEE standard for a 50 MVA transformer with 40°C ambient.
• Find IEC winding temperature rise for a 200 MVA transformer with 55°C ambient temperature.
• Compute temperature rise for a 75 MVA transformer with 45°C ambient and 30°C oil temperature.

Common Values for Winding Temperature Rise According to IEEE and IEC Standards

Fundamental Formulas for Winding Temperature Rise Calculation

Understanding the thermal behavior of transformer windings requires precise formulas. Below are the key equations used in IEEE and IEC standards for calculating winding temperature rise.

1. Top-Oil Temperature Rise Calculation

The top-oil temperature rise above ambient is calculated using the following formula:

• T_oil: Top-oil temperature rise above ambient (°C)
• ΔT_oil,R: Rated top-oil temperature rise above ambient (°C)
• K: Per unit load (load / rated load)
• n: Oil exponent, typically 0.8 (IEC) or 0.9 (IEEE)

This formula models how the oil temperature rise varies with load, reflecting the nonlinear heat dissipation characteristics.

2. Winding Hot-Spot Temperature Rise Calculation

The winding hot-spot temperature rise above top-oil temperature is given by:

• ΔT_hs: Hot-spot temperature rise above top-oil (°C)
• ΔT_hs,R: Rated hot-spot temperature rise above top-oil (°C)
• K: Per unit load
• m: Winding exponent, typically 1.6 (IEC) or 1.7 (IEEE)

This formula accounts for the increased heating effect at the winding hot-spot due to load.

3. Total Hot-Spot Temperature Calculation

The total hot-spot temperature is the sum of ambient temperature, top-oil temperature rise, and hot-spot temperature rise:

• T_hs,total: Total hot-spot temperature (°C)
• T_a: Ambient temperature (°C)
• T_oil: Top-oil temperature rise above ambient (°C)
• ΔT_hs: Hot-spot temperature rise above top-oil (°C)

4. Transient Temperature Rise Calculation

Transformer temperature does not change instantaneously. The transient temperature rise is modeled as:

• θ(t): Temperature at time t (°C)
• θ_final: Final steady-state temperature (°C)
• θ_initial: Initial temperature (°C)
• t: Time elapsed (minutes)
• τ: Thermal time constant (minutes)

This exponential model is used for both top-oil and winding temperature transient calculations, with their respective time constants.

5. Per Unit Load Calculation

Per unit load is the ratio of actual load to rated load:

• K: Per unit load (dimensionless)
• P: Actual load (MVA or kW)
• P_rated: Rated load (MVA or kW)

Detailed Real-World Examples of Winding Temperature Rise Calculation

Example 1: IEEE-Based Calculation for a 100 MVA Transformer

A 100 MVA, 230 kV transformer operates at 80% load with an ambient temperature of 40°C. The rated top-oil temperature rise is 55°C, and the rated hot-spot temperature rise above top-oil is 30°C. Calculate the total hot-spot temperature.

Step 1: Calculate per unit load (K)

Step 2: Calculate top-oil temperature rise (T_oil)

Using IEEE exponent n = 0.9:

Step 3: Calculate hot-spot temperature rise above top-oil (ΔT_hs)

Using IEEE exponent m = 1.7:

Step 4: Calculate total hot-spot temperature (T_hs,total)

The total hot-spot temperature is approximately 105.5°C, which is within typical insulation class limits.

Example 2: IEC-Based Calculation for a 50 MVA Transformer

A 50 MVA transformer operates at 1.1 per unit load with an ambient temperature of 35°C. The rated top-oil temperature rise is 50°C, and the rated hot-spot temperature rise above top-oil is 25°C. Calculate the total hot-spot temperature.

Step 1: Calculate per unit load (K)

Step 2: Calculate top-oil temperature rise (T_oil)

Using IEC exponent n = 0.8:

Step 3: Calculate hot-spot temperature rise above top-oil (ΔT_hs)

Using IEC exponent m = 1.6:

Step 4: Calculate total hot-spot temperature (T_hs,total)

The total hot-spot temperature is approximately 118.1°C, which may require checking against insulation class ratings.

Additional Technical Details and Considerations

• Thermal Time Constants: The thermal time constants for oil and winding (τ_oil and τ_w) are essential for transient temperature calculations. Typical values range from 30 to 180 minutes depending on transformer size and cooling method.
• Cooling Modes: Different cooling modes (ONAN, ONAF, OFAF, etc.) affect temperature rise and exponents n and m. IEEE and IEC provide guidelines for adjusting these values accordingly.
• Insulation Classes: The maximum allowable hot-spot temperature depends on insulation class (A, B, F, H). For example, Class A insulation limits hot-spot temperature to 105°C, while Class F allows up to 155°C.
• Ambient Temperature Variations: Ambient temperature significantly impacts winding temperature rise. Calculations should consider site-specific ambient conditions for accurate thermal assessment.
• Load Cycling: For transformers with variable load, transient temperature rise calculations using thermal time constants provide more realistic temperature profiles than steady-state assumptions.
• Standards References: For detailed guidelines, refer to IEEE Std C57.91-2011 and IEC 60076-7:2018, which provide comprehensive methodologies for temperature rise calculations and transformer thermal evaluation.

Authoritative External Resources

• IEEE Std C57.91-2011 – Guide for Loading Mineral-Oil-Immersed Transformers
• IEC 60076-7:2018 – Power Transformers – Part 7: Loading Guide for Mineral-Oil-Immersed Transformers
• Transformers Magazine – Temperature Rise in Transformers