Low-frequency electrical heating can introduce heat within the winding rather than only at its outer surface. The heat source follows the conductor path, while the core sees the applied induced-voltage history. The two effects require separate checks. [1]
Define the actual connected winding, supply waveform and return circuit. Use the facility’s qualified equipment and process. Frequency alone does not specify the heating method, current distribution or safe operating condition.
Account for the electrical heat source
A first winding term is PR = Irms²R(T), with amperes and ohms giving watts. Include temperature-dependent resistance. Additional losses and unequal currents need the appropriate model. Total power can include losses outside the intended winding. [2]
| Constraint | Evidence | Unresolved by current alone |
|---|---|---|
| Winding heating | Current, resistance and section temperatures | Local heat transfer into thick insulation |
| Core excitation | Induced voltage, turns and waveform | Flux excursion and added core temperature |
| Terminal and connection heating | Actual conductor/joint path | External losses near instrumentation |
| Drying response | Representative moisture evidence | Heat input is not a direct dryness measurement |
Low frequency makes voltage history important
For sinusoidal induced voltage, Erms = 4.44fNABpk. Thus, at fixed turns and effective core area, flux scales with induced E/f. Allow for winding resistance and leakage when deriving E from the terminal waveform. [2]
The heating current and magnetic excitation are coupled through the circuit. An arrangement that produces the intended Joule heat may still need a separate core-temperature assessment.
Preserve the return-winding circuit and current phase relationships as well as terminal voltages; independent heat and flux screens do not design a complete LFH operating circuit.
Check induced volts per hertz separately from heat
Assumptions: the heated winding carries 500 A RMS and has 0.020 Ω resistance at 80 °C, giving 5 kW. In the connected circuit, assume sinusoidal induced E = 20 V RMS, N = 100 turns, effective area A = 0.010 m², and an approved flux ceiling of 0.80 T. At 10 Hz, Bpk = 0.450 T; at 5 Hz it doubles to 0.901 T and exceeds the assumed ceiling by 0.101 T. At 5 Hz, E must be at most 17.76 V for that ceiling. Hold the 20 V/5 Hz condition and resolve the coupled circuit, current and thermal history. These are induced voltages after winding drops. [2]
References
- Y. Brahami, A. Betie, F. Meghnefi, I. Fofana and Z. Yeo, Development of a Comprehensive Model for Drying Optimization and Moisture Management in Power Transformer Manufacturing, Energies 18, 789, 2025. DOI: 10.3390/en18040789.
- U.S. Department of Energy, DOE-HDBK-1011/4-92, Electrical Science, Volume 4, 1992.