# An AC fault ride-through control of modular multilevel converters for HVDC systems

Sidlawendé Ouoba, Florent Morel

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Sidlawendé Ouoba, Florent Morel. An AC fault ride-through control of modular multilevel converters for HVDC systems. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0174. hal-05107549

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# An AC fault ride-through control of modular multilevel converters for HVDC systems

Sidlawendé V. M. Ouoba

SuperGrid Institute

23 rue Cyprian

Villeurbanne, France

Tel.: +33 (0)7 62 20 16 65

Email: sidlawende.ouoba@supergrid-institute.com

URL: https://www.supergrid-institute.com

Florent Morel

SuperGrid Institute

23 rue Cyprian

Villeurbanne, France

Tel.: +33 (0)7 63 42 14 34

Email: sidlawende.ouoba@supergrid-institute.com

URL: https://www.supergrid-institute.com

## Acknowledgements

This work has been supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" Program (ANE-ITE-002-01).

## Keywords

«HVDC», «Modular multilevel converter», «Fault ride-through», «Current control», «Voltage control».

## Abstract

This paper proposes a modified threshold virtual impedance (MTVI) control to ensure an AC fault ride-through (FRT) for modular multilevel converters (MMCs). The proposal limits the AC current of the MMC by virtually increasing its output impedance. It prevents to trigger its protection systems when a fault occurs. Compared with conventional TVI control, the proposed method avoids not only MMC blocking but also increases its power quality by providing undistorted voltage and current waveforms in the case of asymmetrical faults. Simulations in MATLAB/Simulink are carried out to validate the effectiveness of the proposed MTVI control, which is compared with the conventional TVI control. The results show the ability of the MTVI control to limit voltage and current perturbations in the MMC and to provide better voltage and current profiles compared to the classical TVI during unbalanced faults.

## Introduction

High-voltage direct current (HVDC) links are a cost-effective option for transferring energy and integrating renewable energy over long distances [1], [2]. Currently, voltage sourced converters (VSCs), notably modular multilevel converters (MMCs), are commonly deployed and will be used for future HVDC multiterminal systems. Indeed, VSCs offer black start capability and better active and reactive power control performances than line-commutated converters (LCC) and MMCs offer lower switching losses than two- or three-level VSCs [2], [3].

When an overcurrent occurs, in case of fault for example, all the IGBTs in the MMC are opened, to protect them from being damaged. The MMC is said to be in a blocked state. In the event of an AC fault, grid codes require MMCs to remain connected and control current to enable detection and isolation of the fault [2]. It is then needed to avoid blocking the MMC in case of AC faults. MMC fault ride-through control has been the subject of numerous research projects in recent years.

An extended limiting method was developed in [2] for the MMC under unbalanced fault conditions. During onshore fault events, this method maximises the currents injected into the faulted phases by making better use of the capacity of the converter than the normal limiting method. As a result, the proposed concept also shows an improved voltage profile in the offshore grid. In [4], a grid forming control for MMCs was proposed to cope with different faults scenarios (symmetrical or asymmetrical) while ensuring that AC-side currents are limited to a predefined value. This is achieved by using a voltage
controller and elliptical voltage limiting with a feedforward signal in series with a current controller and elliptical current limiting. Both above methods provide FRT using PI regulators and the elliptical current or voltage limiter which could have an impact on the system stability. This article focuses on a simple method where FRT can be provided without introducing PI regulators. One control that can provide FRT control for inverters without introducing PI regulators is the TVI control [5]. However, classical TVI control for MMC FRT generates distorted voltage and current waveforms in case of asymmetrical faults, which decreases the power quality.

In this paper, an enhanced TVI control is developed to ensure MMC fault ride-through for balanced and unbalanced faults. The proposed MTVI control is based on the TVI method which is well known for inverter current limitation [6]. Here, an improved version of the TVI control is designed to limit the output current of the MMC by virtually increasing the output impedance of the MMC when its AC current exceeds a preselected threshold value ($I_{thresotd}$). Limiting the fault current prevents the protection systems of the MMC from being activated and then the converter blocking.

The rest of the paper is organized as follows. First, the studied system is presented. Secondly, the proposed MTVI method for MMC FRT is investigated. Finally, simulations and results are presented and a conclusion is highlighted.

## System description

The general scheme of the HVDC system studied in this paper is illustrated in Fig. 1. The HVDC system consists of an MMC connected to a symmetrical DC voltage source and a variable load. The general structure of the MMC consists of three legs, each with an upper and a lower arm. Each arm is formed by a stack of N switchable half-bridge submodules (SM) and an arm inductance ($L_{arm}$). In this paper, the MMC is modelled with the average arm model (Type 4-based model) with blocked state proposed in [7], as shown in Fig. 2, to minimize the simulation time while representing the dominant transient behaviour [7]. Individual SM switching, SM voltages and SM capacitor voltage balancing are not implemented in the MMC model.

The MMC control used in this case study implements the control presented in [3]. The simplified MMC control strategy is shown in Fig.

3, where energy is controlled per leg ($W_{vertical}$), the difference between legs ($W_{horizontal}$) and the total energy in the converter ($W_{total}$). This control scheme introduces $I_{diff}$ which is a linear combination of upper and lower arm currents and is defined as follows:

$$I_{diff} = 0.5(I_{armU} - I_{armL}) \quad (1)$$

More information on the MMC control (energy, power, voltage and current controllers) can be found in [3].

<figure><img src="image_2.png" /><figcaption>Fig. 1: Simplified scheme of the studied HVDC system</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2: Modelling of the MMC</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3: Simplified control scheme of the MMC</figcaption></figure>
The MMC is implemented with a fault detection algorithm that blocks the converter when it operates outside its normal operating zones to avoid its degradation. In this study, the MMC is blocked when an overcurrent occurs in the MMC (arm currents and AC output currents). A further criterion monitors the slope of the arm current and trigger the blocking signal when its value exceeds a maximum value (CS<sub>max</sub>).

<table><caption>Table I: MMC normal operating zones</caption><thead><tr><th>Parameters</th><th>Operating zones</th></tr></thead><tbody><tr><td>MMC arm current</td><td>|i<sub>arm</sub>| ≤ I<sub>arm_max</sub> = 1.15 I<sub>arm rated</sub></td></tr><tr><td>MMC AC current</td><td>|i<sub>ac</sub>| ≤ I<sub>ac_max</sub> = 1.15 I<sub>ac rated</sub></td></tr><tr><td>MMC current slope</td><td>|d<i>ac</i>|/dt ≤ CS<sub>max</sub></td></tr></tbody></table>

The converter normal operating zones are summarised in Table I. I<sub>arm rated</sub> and I<sub>ac rated</sub> represent respectively, the magnitude of the MMC rated arm current and the amplitude of the MMC rated AC current. DC voltage (overvoltage and undervoltage) is also a criterion for blocking the MMC, but it has no impact on this study. The following section explains the process of calculating the MMC reference voltage (V<sub>dq_FRT</sub>), considering fault ride-through control (see Fig. 3).

## Proposed Modified Threshold Virtual Impedance Control

In this section, the MTVI control is designed to limit the MMC AC currents in the event of balanced and unbalanced faults thanks to a virtual impedance (Z<sub>v</sub> = R<sub>v</sub> + jX<sub>v</sub>). The virtual impedance is inserted when an overcurrent is detected, i.e. when the calculated value hereunder named I<sub>max</sub>) exceeds the trigger value (I<sub>max</sub> > I<sub>threshold</sub>) and bypassed otherwise (I<sub>max</sub> ≤ I<sub>threshold</sub>).

For the conventional TVI control, I<sub>max</sub> = I<sub>amp</sub> with I<sub>amp</sub> the current amplitude defined in (2).

$$I_{amp} = \sqrt{I_{d}^{2} + I_{q}^{2}} \qquad (2)$$

However, for the proposed MTVI method, I<sub>max</sub> corresponds to the maximal value of the current amplitude (I<sub>amp</sub>) and of the maximum current (I<sub>SSM</sub>) estimated using the Sequence Separation

Method (SSM) proposed in [8]. I<sub>max</sub> is described below.

$$I_{max} = max(I_{amp}, I_{SSM}) \qquad (3)$$

The SSM is used to separate the positive and negative sequences of the current and estimate its maximum value for each phase. This ensures that the maximum current value is always obtained in the event of both symmetrical and asymmetrical faults. The methodology for calculating I<sub>max</sub> is illustrated in Fig. 4.

To ensure a smoother transition between normal operation and fault operation, the resistance (R<sub>v</sub>) and reactance (X<sub>v</sub>) values are adjusted to increase with the overcurrent (i.e. the higher the current magnitude, the greater the value of the virtual impedance). R<sub>v</sub> and X<sub>v</sub> are defined as follows:

$$R_{v} = K_{Zv} (I_{max} - I_{threshold}) \qquad (4)$$

$$X_{v} = K_{Zv} \sigma_{Zv} (I_{max} - I_{threshold}) \qquad (5)$$

K<sub>Zv</sub> represents the virtual impedance proportional gain and is related to steady state current limitation; σ<sub>Zv</sub> denotes the virtual impedance ratio and is related to dynamics. Tuning method of the virtual impedance proportional gain K<sub>Zv</sub> and ratio σ<sub>Zv</sub> can be found in [9].

Once the virtual impedance is estimated, the voltage references (V<sub>d_ref</sub>, V<sub>q_ref</sub>) of the MMC are reduced virtually to limit the current of the converter as presented in Fig. 5.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Maximum AC current calculation</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Current limitation control scheme</figcaption></figure>
Simulation and results

To study the proposed MTVI control during AC faults, a MATLAB/Simulink simulation is performed on the HVDC system depicted in Fig. 1 with parameters given in Table II.

A test is carried out to validate the effectiveness of the proposed control, which is compared with the classical TVI control. An unbalanced phase-to-phase fault, as shown in Fig. 6, is simulated with both controls (MTVI and TVI) when the MMC is supplying the nominal power (1 p.u.) to the load. The fault is simulated at 1.8 s and is cleared at 1.9 s. Both controls have the same virtual impedance parameters for this test.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Phase-to-phase fault on the HVDC system</figcaption></figure>

The obtained results are illustrated in Fig. 7 and Fig. 8. Results include AC voltages, AC currents, arm currents, equivalent capacitor voltages and the output power of the MMC. It can be seen from Fig. 7 (c), (d), (e) and (f) that the AC currents and arm currents of the MMC remain within the operational zones defined in Table I for both controls.

<table><caption>Table II: HVDC system parameters</caption><thead><tr><td>Parameters</td><td>Designation</td><td>Value</td></tr></thead><tbody><tr><td>Line inductance</td><td>L<sub>ac</sub></td><td>5.22 mH</td></tr><tr><td>Line resistance</td><td>R<sub>ac</sub></td><td>0.2 Ω</td></tr><tr><td>DC voltage</td><td>V<sub>dc</sub></td><td>640 kV</td></tr><tr><td>MMC AC RMS voltage</td><td>U<sub>ac</sub></td><td>226.2 kV</td></tr><tr><td>MMC rated power</td><td>P<sub>nom</sub></td><td>700 MW</td></tr><tr><td>Virtual impedance ratio</td><td>σ<sub>Zv</sub></td><td>0.7</td></tr><tr><td>Virtual impedance proportional gain</td><td>K<sub>Zv</sub></td><td>0.16</td></tr><tr><td>Maximum AC current of the MMC SyM</td><td>I<sub>max</sub></td><td>1.22 p.u.</td></tr><tr><td>AC Current magnitude trigger value</td><td>I<sub>threshold</sub></td><td>1 p.u.</td></tr><tr><td>MMC frequency</td><td>f<sub>F2F</sub></td><td>50 Hz</td></tr></tbody></table>

The currents in faulted phases a and b are limited to 1 p.u. in both controls. This allows power to continue to be injected from the HVDC system (admittedly with a power lower than before the fault) despite the phase-to-phase fault. However, it can easily be noticed that the proposed MTVI method introduces significantly fewer disturbances in the AC side of the network than the classical TVI method during the fault.

In fact, AC voltages (Fig. 7 (a)) and currents (Fig. 7 (c)) of the MMC obtained with the MTVI control remain sinusoidal after the phase-to-phase fault, whereas AC voltages (Fig. 7 (b)) and currents (Fig. 7 (d)) of the TVI method have distorted waveforms close to the triangular shape. Note that once the fault has been cleared, the AC voltages, AC currents and arm currents of the converter return to their pre-fault operating values.

Fig. 8 (a) and (b) show that, during the fault, the converter AC and DC powers drop to 0.25 p.u. and 0 p.u. respectively for the MTVI strategy and to 0.4 p.u. and 0.15 p.u. respectively for the TVI control. Furthermore, the largest ripples are observed in the AC power supplied by the MMC with the TVI control. Once the fault is eliminated, the MMC AC and DC powers are restored to 1 p.u. for both controls. The MMC equivalent capacitor voltages fluctuate (see Fig. 8 (c) and (d)) between 0.60 p.u. and 1.35 p.u. during the fault for both methods and return to steady state at approximately 2.1 s (0.2 s after the fault is cleared). It is worth mentioning that the MMC should also be blocked if the voltages of the equivalent capacitors are outside the operating range, but in this case these voltages remain within permissible limits. It is important to note that whatever the value of the virtual impedance parameter, the MTVI control shows better results than the TVI for the phase-to-phase fault case. However, a higher value of this parameter would increase the dynamics of the control, which would cause the MMC to block during the fault for both controls due to the slope of the arm current exceeding the maximum value (CS<sub>max</sub>).

The results obtained in this section demonstrate that the MTVI control limits disturbances in the MMC and in the AC side of the system by providing better voltage and current profiles than the classical TVI strategy in the event of unbalanced faults. For a balanced fault (three-phase fault), the proposed MTVI and TVI have similar results.
<figure><img src="image_8.png" /><figcaption>Fig. 7: Results with the TVI (on the left) and MTVI (on the right) controls after a phase-to-phase fault: (a), (b) AC voltages of the MMC; (c), (d) AC currents of the MMC; (e), (f) arm currents of the MMC.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8: Results with the TVI (on the left) and MTVI (on the right) controls after a phase-to-phase fault: (a), (b) AC and DC powers of the MMC; (c), (d) equivalent capacitor voltages of the MMC.</figcaption></figure>
Conclusion

This work introduces an AC fault ride-through control for MMCs under balanced and unbalanced fault. The proposed modified threshold virtual impedance control is an improved version of the TVI control and is designed to limit the output current of the MMC thanks to a virtual impedance while ensuring better voltage and current profiles during the fault event. The efficiency of the proposed MTVI approach for MMC is validated using MATLAB/Simulink and compared to the conventional TVI control. Results demonstrate that the MTVI control limits the fault current and thus prevents the converter from blocking. Results also highlight the fact that the proposed control scheme introduces fewer perturbations into the grid AC side, in case of asymmetrical faults, resulting in enhanced voltage and current profiles compared with conventional TVI control. Future work will focus on validating the proposed MTVI control with more realistic models of the AC and DC systems.

References

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