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AC Side Harmonics in VSC-HVDC Systems

1. VSC Harmonics

Harmonic Generation: VSC can be considered a harmonic voltage source behind internal impedance because it generates harmonic voltages independent of the load. The primary control strategy of VSC generates a 3-phase reference voltage in a continuous sinusoidal function. Then, the converter switching action (modulation techniques and switching of capacitors) happens that can produce output voltage in a stepped function. If there is a deviation in stepped output voltage from the continuous 3-phase reference voltage, then the harmonics are generated.

Integer Harmonics: If the deviation in stepped output voltage from continuous 3-phase reference voltage is the same pattern for every fundamental period, the integer harmonics (i.e., characteristic harmonics) can be generated. The integer harmonics are integer multiples of the fundamental frequency. If the AC supply at the Point of Common Coupling (PCC) is balanced, the VSC generates higher-order harmonics near the switching frequency and a few low-order harmonics. It depends on the type of converter topology, modulation techniques, and switching frequency.

Inter-Harmonics: If the deviation in stepped output voltage from continuous 3-phase reference voltage is not the same pattern for every fundamental period, the inter-harmonics (i.e., non-characteristic harmonics) can be generated. The inter-harmonics are non-integer multiples of the fundamental frequency. If the AC system is unbalanced or the VSC contains background harmonics, the VSC generates inter-harmonics that may have both positive and negative sequence components. The zero sequence harmonics generated at the converter side can be blocked by the converter transformer configuration (either Y-Δ or Y-Y without grounding on the converter side). An unbalanced AC network can cause VSC to produce inter-harmonics in the low-frequency range.

2. Frequency Range Consideration for VSC Harmonics

The frequency range consideration for VSC harmonics can be grouped into the following categories (refer to Fig. 1):

Converter Imperfections & Unbalanced AC System: The converter imperfections are measurement tolerances, component tolerances, and non-idealities in the control system which can generate harmonics in the low-frequency range. The VSC can generate inter-harmonics in the low-frequency range when it is connected to an unbalanced AC system.
Switching Pattern: The converter topology and modulation techniques are the main consideration for these harmonics. For MMC, the harmonic frequencies are depending on the number of submodules. If the MMC has more submodules, the frequencies of the spectrum are higher. For 2-level VSC, the switching frequency and its integer harmonics are the primary considerations for the harmonic spectrum.
Non-ideal Switching: The non-ideal switching of the power electronic devices is the main consideration for these harmonics. The commutation of current from one device to another will lead to an overshoot in voltage and current response in the higher frequency content.

Fig. 1. Frequency range consideration for VSC harmonics.

3. Sources of VSC Harmonics Generation

The following sources are the primary considerations for VSC harmonic generation:

Type of VSC topology.
Control strategy of the VSC (reference voltage generation and switching pattern generation).
Power electronics hardware (interlocking time and semiconductor voltage drop).
Unbalanced AC network.

VSC Topology: According to IEC 62747, the VSC topologies can be divided into two categories such as switch-type valves and controllable voltage source-type valves. The switch type valves are 2-level converter and 3-level converter. The controllable voltage source type valves are modular multi-level converter (MMC) and cascaded 2-level converter. The converter topology has a significant impact on the VSC harmonic generation.

VSC Control Strategy: According to CIGRE TB 604, the control strategy of the VSC can be divided into upper-level control, lower-level control, and valve building block. The upper-level controls can be divided into outer loop (i.e., active power/DC voltage and AC voltage/reactive power control) and inner-loop current control. The upper-level control generates a 3-phase reference voltage signal. The lower-level controls are pulse width modulation (PWM), phase-shifted PWM, nearest level control (NLC), and capacitor voltage balancing. The lower-level control generates switching pulses (i.e., switching pattern) and is fed to the VSC semiconductors. The characteristic nature of the 3-phase reference voltage, type of modulation techniques, and switching frequency consideration have a huge impact on the VSC harmonic generation. In the valve building block, the semiconductor switching may generate noise in a high-frequency range.

Power Electronics Hardware: The harmonics generation due to power electronics hardware depends on the VSC valve voltage and current. In this stage, the effects of interlocking time and semiconductor voltage drop are the primary considerations. The interlocking time is the time delay between the switching instant of individual IGBTs in a particular module. The current flow through each module can lead to a voltage drop across the IGBT and diode terminals. The total voltage drop depends on the number of IGBTs and diodes in the module and the operating point of the VSC.

Unbalanced AC Network: The unbalanced AC system can exist if there are asymmetrical transmission lines and loads, or any unbalanced faults or unbalanced current injection to the AC grid due to the asymmetries in the phase reactance (of the transformers and reactors) between the phases because of the different manufacturer tolerances. The unbalanced AC network can contribute to the VSC harmonics generation especially low-order inter-harmonics which have both positive and negative sequence components. The VSC control strategy can handle negative sequence control as well.

4. Calculation of Harmonics at Point of Common Coupling (PCC)

The total harmonic distortion (THD) at the PCC is the combination of:

VSC generated harmonics.
Background harmonics along with VSC influence.

Fig. 2 shows a simple example of VSC harmonic distortion calculation. The harmonics generated by the VSC are less significant. The harmonic voltage distortion at the PCC due to the VSC can be determined using equation (1). The background harmonics along with the VSC influence are the significant part. The harmonic voltage distortion due to background harmonics can be determined using equation (2). The total harmonic distortion (THD) at the PCC is the summation of VSC-generated harmonics and background harmonics. Note that there is no fixed phase relationship between VSC-generated harmonics and background harmonics.

Fig. 2. Simple example for VSC Harmonics calculation, (a) Harmonics generated by converter, (b) background harmonics along with VSC influence.

References:

CIGRE Working Group B4.67, TB 754, AC side harmonics and appropriate harmonic limits for VSC HVDC, 2019.
Zhong, Qing, et al. "Harmonic analysis model for voltage source converter under unbalanced conditions." IET Generation, Transmission & Distribution, 2015.
Han, Minxiao, Phuchuy Nguyen, and Wenli Yan. "Inter-harmonics in multi-terminal VSC-based HVDC systems." Journal of Modern Power Systems and Clean Energy, 2016.