An MMC contains many switching submodules, but the transformer sees the voltage produced at its connected AC port through the station network. A spectrum measured at one submodule or arm cannot simply be assigned to the transformer winding. Apply the HVDC transformer specification framework of IEC/IEEE 60076-57-129 to the stated liquid-immersed equipment [1].
Mark the transformer terminal plane in the model. Identify the converter AC nodes, arm inductors, cables or buswork, filters and grounding connections between that plane and the switching sources. The chosen boundary determines what becomes an imposed voltage and what remains part of the circuit response.
Keep voltage modes separate
| Quantity | Definition at the model boundary | Path to verify |
|---|---|---|
| Differential phase voltage | Voltage between specified AC nodes | Winding terminal-to-terminal excitation |
| Common-mode voltage | Shared displacement relative to the defined earth reference | Capacitive and grounded paths to tank/earth |
| Arm or submodule voltage | Internal converter node waveform | Transfer through arms and connected network |
| Transformer internal voltage | Distributed winding response | Not identical to terminal spectrum at high frequency |
Use the waveform that reaches the terminal
Retain modulation state, submodule arrangement and operating point in the converter model. Extract the terminal waveform under that case, then inspect its spectral content using a stated time window and frequency resolution. A spectrum during startup or control recovery may differ from the settled operating spectrum.
For a linear interconnecting network, frequency-domain transfer functions can help show which components reach the transformer. If switching behavior, saturation or time-varying controls dominate, a fixed linear transfer function is only a limited approximation.
Separate a common-mode harmonic from differential excitation
Assume simultaneous 10 kHz node components vₐ = 30 sin(ωt) kV and vᵦ = 10 sin(ωt) kV relative to the same earth. Their differential peak is 20 kV and their pair common-mode peak, defined as (vₐ + vᵦ)/2, is also 20 kV. Treating the 30 kV node peak as differential duty overstates this example by 50% while discarding a real earth-related component. Export both modes at the transformer plane and retain their separate coupling paths.
Grounding determines part of the exposure
Common-mode voltage and current depend on grounding and capacitances, including the transformer and valve-hall connections. Leaving these out can remove the very stress under investigation. State the reference node rather than calling every waveform “phase voltage.”
Derive differential and common-mode terminal waveforms from the actual MMC connection and control case. Retain the modeled boundary because a valve-hall connection can change the duty. Introduce an LCC-like DC offset only if this topology independently produces it.
Use an EMT model that retains the MMC controls and connected network [2].
References
- IEC/IEEE, IEC/IEEE 60076-57-129:2017, Power transformers – Part 57-129: Transformers for HVDC applications.
- CIGRE WG B4.70, Guide for electromagnetic transient studies involving VSC converters, ELECTRA No. 316, June 2021, technical-brochure summary.