Comparative Evaluation of Transient Stability in MMCs: Grid-Forming vs. Grid-Following Strategies

Abstract

This paper explores how different control strategies—grid-forming and grid-following—impact the transient stability of modular multilevel converters (MMCs) interfacing with AC power grids. By employing electromagnetic transient simulation tools (PSCAD/EMTDC) on an adapted IEEE three-machine, nine-bus system, various scenarios are analyzed, including faults of differing types and locations. In the simulation, traditional synchronous generators (SGs) are replaced by MMCs configured under distinct control modes. Results indicate that grid-forming (GFM) control enhances the receiving-end grid’s transient stability by providing superior phase support and extended fault-clearing times compared to grid-following (GFL) control, with hybrid approaches yielding intermediate performance. These findings underline the importance of converter control selection in achieving robust dynamic operation in modern power systems with a high penetration of renewable energy.

1. Introduction

The Jiangsu Power Grid, renowned for its extensive load requirements and intricate network structure, is among the most developed regional AC systems in China. As a receiving-end grid, it heavily relies on imported electricity; external power makes up approximately 20–30% of the province’s total demand. In addition, the load distribution is uneven, with the southern region experiencing higher demands, thereby leading to a consistent “north-to-south” pattern in power transmission throughout the network.

Historically, the Jiangsu AC Power Grid was built upon a densely interconnected transmission network that was predominantly expanded through the addition of large-scale conventional generation sources. However, with the rapid development and construction of large-scale renewable energy installations, the grid is now confronted with new challenges. The intermittent and uncertain nature of renewable energy generation introduces complexities in power flow management, system stability, and voltage regulation. These challenges necessitate the reconsideration of traditional control strategies and the integration of advanced concepts to ensure reliable operation under more dynamic conditions.

Against the backdrop of significant renewable energy developments in regions such as the “Sand and Gobi Deserts”, long-distance, ultra-high-voltage (UHV) DC transmission has emerged as a highly beneficial technology for delivering power across vast regions with high capacity. While UHVDC technology facilitates the efficient allocation of distributed energy resources, it also brings about operational intricacies and introduces new technical and managerial challenges that must be addressed to ensure system robustness.

According to the perspective presented in References [1,2], the synchronization issue encountered by an MMC feeding into a receiving-end grid can be classified under the framework of generalized synchronization stability. Within this framework, one of the necessary conditions for synchronous operation between the converter stations and the AC grid is ensuring that the phase-locked loop (PLL) maintains a constant phase-lock.

MMCs can be operated using two primary control strategies: grid-following and grid-forming. In the case of grid-following control, converter stations achieve synchronization by employing a PLL that measures the actual phase of the sampled AC voltage [3]. Since grid-following converter stations react passively to the variables of the receiving-end grid, they are generally less effective when supplying power to weak or passive grids [4]. In contrast, grid-forming converter stations are capable of self-synchronization by generating their own reference signals either through the PLL or by utilizing a power synchronization loop (PSL). Consequently, the conditions required for achieving generalized synchronization stability in an MMC-fed receiving-end grid are explicitly linked to maintaining phase lock in the PLL and avoiding a step-out condition in the PSL.

In order to overcome the limitations inherent in pure PLL-based operation, several self-synchronization control methods have been proposed. These include power synchronization control [5], droop control [6], and DC voltage synchronization control [7]. Control strategies that rely on self-generated phase information for coordinate transformation are categorized as grid-forming (GFM) control, which establishes a clear distinction from grid-following (GFL) control [8].

In recent years, the transition of traditional receiving-end grids toward systems that incorporate MMC–HVDC systems has underscored the importance of grid-forming control. Compared with grid-following control, grid-forming control offers a stronger support to the grid by actively contributing to stability [9]. For example, under power synchronization control, a grid-forming converter station can behave like a virtual synchronous generator, effectively mimicking the inertia and damping characteristics of a conventional synchronous generator [5,10]. This inherent capability makes grid-forming converter stations particularly suitable for grids with a high proportion of DC feed-in or for offshore isolated substations [11,12]. Further, Reference [13] utilizes an improved Heffron–Phillips model to analyze the low-frequency oscillation phenomenon in a single-machine infinite-bus (SMIB) system following the integration of a modular multilevel converter (MMC) and attributes these oscillations mainly to the voltage controller of the nearby MMC. In addition, studies such as Reference [14] have compared the synchronization characteristics between grid-forming controllers and synchronous generator power sources in hybrid systems, showing that such systems possess a larger synchronization stability region and achieve faster dynamic convergence. Moreover, Reference [15] investigates a system in which a synchronous generator power source and a grid-following controller are connected in parallel to an infinite bus, indicating that the grid-following controller can modify the power angle characteristic curve of the synchronous generator and thereby impact its overall synchronization stability. Finally, in Reference [16], a gradual replacement of synchronous generator power sources in a four-machine system with renewable energy sources was performed using a combination of grid-forming and grid-following control, and the study examined how varying the proportions of these control strategies affects system synchronization stability.

To improve the transient stability of power systems with 100% renewable energy, a voltage-adaptive strategy considering the current limits of RESs is proposed in [17,18], where a novel adaptive control method is developed based on Lyapunov theory and the Lie derivative. A comprehensive submodule fault management scheme for MMCs under nearest level modulation is proposed in [19], including detection, location, and fault-tolerant control based on circulating current characteristics.

It is important to note that the vast majority of previous studies have primarily focused on the impact of grid-forming and grid-following control strategies on the transient stability of synchronous machines. They have not extensively addressed the synchronization stability characteristics pertinent to MMCs feeding into a receiving-end grid. When comparing traditional receiving-end grid scenarios with those that are fed by MMCs, several distinct differences emerge that may significantly affect synchronization characteristics:

(1)

Dependence on Control Versus Physical Properties:

• In conventional receiving-end grids, synchronization is largely governed by the inherent physical properties of the network. In contrast, for MMC-fed grids, the synchronization behavior is predominantly determined by the control strategies employed by the converter stations;

(2)

Overcurrent Capacity and Fault Characteristics:

• Traditional receiving-end grids are designed with high overcurrent capacities and tend to exhibit pronounced voltage source characteristics during fault events. On the other hand, MMCs have limited overcurrent capabilities, and, once current saturation is reached, they tend to behave as current sources. This results in fundamentally different residual voltage characteristics during fault conditions;

(3)

Diverse Control Modes and Interactions:

• Beyond the conventional V/f control mode, MMCs can operate under various control strategies. The interaction among converter stations with different control modes can further influence the overall synchronization characteristics of the receiving-end grid.

Both analytical methods and simulation methods are widely used to analyze transient stability issues in power systems. However, when dealing with MMCs feeding into receiving-end grids, analytical approaches encounter significant obstacles due to the large number of converter stations, the high number of state variables associated with each station, and the presence of notable nonlinearities and switching elements in the converter control mechanisms. Moreover, it is noteworthy that the input signal for the PLL is derived from the positive-sequence q-axis component of the instantaneous voltage at the grid connection point, while electromechanical transient simulations typically consider only the positive-sequence fundamental phasors of the power system. For these reasons, the present study adopts the electromagnetic transient simulation software PSCAD/EMTDC v4.6 to investigate the transient stability characteristics of MMC-fed receiving-end grids.

This paper first introduces the fundamental control principles underpinning voltage support in MMCs. In order to simulate a realistic operating scenario, all synchronous generator power sources in an IEEE three-machine, nine-bus system were replaced with MMCs, thereby constructing an MMC that feeds into a receiving-end grid. A series of precise simulations were then conducted, considering multiple factors such as the control strategies of the converter stations, the types of faults, and the fault locations. The Critical Clearing Time (CCT) was employed as a quantitative evaluation metric in this study to analyze how these different factors influence the transient stability characteristics of the receiving-end grid.

2. Control Structure Model of MMCs

According to Ref. [20], converter stations can be categorized into four types based on their equivalent external characteristics under normal operating conditions: Vθ grid-forming, PV grid-forming, PV grid-following, and PQ grid-following converter stations. It should be pointed out that because the PV systems have intermittent characteristics, they need to incorporate energy storage on the DC side to function as PV grid-forming. It is worth noting that, under standard operating conditions, the equivalent circuit representations for both PV grid-forming and PV grid-following converter stations are the same since they both function as voltage sources with a fixed magnitude and phase angle.

The grid-following type is usually connected to a strong power grid, selecting either constant DC voltage or constant active power based on DC-side control requirements. The grid-forming type is typically connected to a weak power grid to avoid phase-locked loop (PLL) loss of synchronization. This paper mainly discusses the differences between the grid-following and grid-forming types.

Figure 1 presents a schematic diagram of a grid-connected MMC. In this configuration, the MMC provides the voltage support needed by the receiving-end grid. To guarantee adequate voltage support within the system, one can choose any of the first three types of converter stations.

In Figure 1, a typical MMC station consists of three main components: the grid-connected converter, the converter controller, and the remaining parts (DC side and AC side). In practice, the DC voltage U_dc, input DC current I_dcin, and output DC current I_dcout can fully reflect the influence of the remaining parts on the grid-connected converter and the AC system.

The converter directly impacts the voltage phasor on the valve side ${\overline{U}}_{\mathrm{V}}$ and the current phasor ${\overline{i}}_{\mathrm{V}}$, which can be used to control U_dc, active power P_s, reactive power Q_s, or the system-side voltage amplitude U_s. Additionally, θ_s is the angle of the system-side voltage phasor.

From a macroscopic viewpoint and considering the phase generation method of the grid-connected converter, MMCs can be grouped into two main categories: grid-following converter stations and grid-forming converter stations. Moreover, when taking into account the station’s capability to regulate the AC voltage, grid-following units can be further subdivided into grid-following PV converter stations and grid-following PQ converter stations.

Similarly, if one considers both the flexibility in controlling the input active power and the provision of a system reference frequency, grid-forming power sources can be distinguished as either grid-forming Vθ converter stations or grid-forming PV converter stations. The characteristics that define these four types of converter stations are detailed in

Table 1. Four types of MMCs based on the characteristics of grid-connected converters.

Types	Phase Generation Methods	Control the AC Voltage or Not	Adjustability of the Input Active Power	Provide the Reference Frequency or Not
PQ-GFL	Sampling by the PLL	No	Relatively weak	No
PV-GFL	Sampling by the PLL	Yes	Relatively weak	No
PV-GFM	Self-generating	Yes	Relatively weak	No
Vθ-GFM	Self-generating	Yes	Very strong	Yes

.

In essence, the ancillary components of an MMC primarily influence the DC side—namely, the voltage, current, and power—without altering the mathematical model of the grid-connected converter or its controller, and without directly affecting the AC system. Hence, it is both logical and sufficient to classify the converter stations based on the intrinsic characteristics of their grid-connected converter.

2.1. Vθ-Type MMC Model

The Vθ grid-forming control corresponds to an MMC that uses V/f control. The control structure of a typical grid-forming MMC based on a Voltage Source Converter (VSC) is shown in Figure 2; some variables were already introduced earlier.

The control structure of a grid-forming MMC consists of a three-loop controller, which is composed of a reference generator, an AC voltage controller, and an inner loop controller, in that order of signal transmission. The remaining part is the modulation loop. In fact, both grid-forming and grid-following MMCs can use the same structure for the inner loop controller and modulation loop, with the difference being in how the input variables are obtained. Therefore, the following sections will focus on the reference generator and the AC voltage controller.

For a MMC-fed receiving-end grid, a grid-following MMC must control the valve-side voltage phasor ${\overline{U}}_{\mathrm{V}}$ based on the reference generator. Thus, the output of the reference generator should include both U_sref and the reference phase angle θ_ref of the voltage.

Specifically, for a grid-forming Vθ MMC, which is typically unique within the entire power system, two prerequisites must be met to make the control feasible: first, when the active power output to the AC system varies significantly, the external circuit must maintain a constant U_dc. Second, the reference frequency of the AC grid must be determined and maintained by the grid-forming Vθ MMC. This way, for a grid-forming Vθ MMC, θ_ref undergoes periodic rotation on the coordinate plane, with the rotational frequency being f_ref.

It is worth pointing out that if the system is PV, the DC voltage reference signal is typically generated based on the maximum power point tracking (MPPT) and then provided to the grid-following inverter, which maintains a constant DC voltage. If the inverter adopts grid-forming control, it loses the ability to regulate the DC voltage, requiring an integrated battery energy storage system (BESS) to maintain the DC voltage.

2.2. Grid-Forming PV Type MMC Model

The basic control structure of the grid-forming HVDC converter was introduced earlier. The following mainly focuses on the characteristics of the grid-forming PV HVDC converter model. The grid-forming PV HVDC converter has a limited ability to regulate active power. This means that the output and input active power of the grid-forming PV HVDC converter should not have a linear relationship; otherwise, the capability to control the phase of the source will be weak. In other words, for a grid-forming PV HVDC converter, nonlinear control methods are more suitable for phase adjustment. For example, an improved power synchronization loop (PSL) can be used as part of the reference generator, as shown in Figure 3.

In Figure 3, ω_ref1 is the angular frequency obtained by the PSL through simulating the rotor motion of a synchronous machine, P_sref represents the mechanical power, P_s is the electromagnetic power, H is the virtual inertia time constant, D is the virtual damping coefficient, P_sHLimit is the hard limit of the active power reference, ω_Limit is the relative value limit of ω_ref1, ω_ref0 is the angular frequency calculated based on f_ref, and ω_ref is the final angular frequency used to calculate θ_ref. Additionally, the meanings of other variables remain as described earlier.

Considering that the generalized active power control is achieved by the reference generator, the AC voltage controller should take on the generalized reactive power control. A validated strategy is to make the d-axis component u_sd of the system-side voltage vector follow U_sref while keeping the q-axis component u_sq equal to zero. In this way, the AC voltage controller can obtain i_vdref and i_vqref based on the deviation between the system-side commanded voltage vector and the measured voltage vector. Specifically, since grid-forming HVDC converters have traditionally been studied as isolated entities, it is believed that i_vdref is more closely related to U_sref, and its control form is shown in Figure 4a. However, if the interaction between the grid-forming HVDC converter and other power sources and converters is stronger, it is recommended to swap the control on the d-axis and q-axis, as shown in Figure 4b.

In Figure 4, u_sdref and u_sqref give the reference values for u_sd and u_sq, while k_pud, k_idd, and u_sdSLimit are the proportional coefficient, integral coefficient, and soft limit of the controller on the d-axis, respectively. k_puq, k_iuq, and u_sqSLimit are the proportional coefficient, integral coefficient, and soft limit of the controller on the q-axis, respectively. Additionally, i_vdHLimit and i_vqHLimit are the hard limits for i_vdref and i_vqref.

2.3. Grid-Following PV Type MMC Model

The typical control structure for the grid-following HVDC converter based on the Voltage Source Converter (VSC) is shown in Figure 5. In this structure, a Phase-Locked Loop (PLL) is used to sample the phase of the AC voltage at the Point of Common Coupling (PCC) to obtain the coordinate transformation angle θ_PLL. Other control functions to be implemented include

• Obtaining the outermost reference values: In practice, the reference generator implements this function based on global control objectives and system operating conditions. For the grid-following PV HVDC converter, the required values are P_sref and the reference value of the AC voltage U_sref;
• Obtaining the valve-side current reference values: The outer loop controller divides the valve-side current into two components, i_vd and i_vq, on the rotating d-axis and q-axis, respectively, and then calculates their reference values, i_vdref and i_vqref, based on the outermost reference values to perform the function;
• Obtaining the valve-side voltage reference values: The inner loop controller can complete the calculation based on the output of the outer loop controller. The valve-side voltage is divided into two components, u_vd and u_vq, on the d-axis and q-axis, and their reference values are named u_vdref and u_vqref, respectively;
• Generating modulation signals: The modulation loop generates modulation signals to control the switching of self-rectifying power electronic devices, performing coordinate transformation based on θ_PLL to ensure that u_vd and u_vq follow the reference values. Thus, i_vd and i_vq can also track their reference values, and the final result is the fulfillment of global control objectives.

Similar to the control structure of the grid-forming HVDC converter shown in Figure 2, in this entire control structure, the reference generator, outer loop controller, and inner loop controller sequentially convert the control objectives into reference values for different variables, collectively referred to as the three-loop controller of the grid-following HVDC converter. Clearly, the three-loop controller has the same function as the well-known two-loop DC controller [21]. The three loops differ in that two reference generators are used to reflect whether the grid-following HVDC converter has the ability to control the AC voltage, as shown in Figure 6. The reference generator for the grid-following PV HVDC converter should output P_sref and U_sref, which are referred to as the P/V generator.

In Figure 6, the deviation between U_dc and its commanded value is converted into another command value for active power, Psref1, which may vary dynamically. U_dcref0, P_sref0, Q_sref0, and U_sref0 are the commanded values for the corresponding variables; P_sref, Q_sref, and U_sref are the output reference values; k_pUP, k_iUP, and P_sSLimit are the proportional coefficient, integral coefficient, and soft limit for DC voltage control, respectively.

3. Comparison of Transient Stability of MMCs Under Different Control Methods

3.1. Transient Stability Analysis Under Grid-Forming PV Control

The transient stability characteristics of a receiving-end grid fed by MMCs are studied using the electromagnetic transient simulation software PSCAD/EMTDC. Electromechanical transient simulation software typically ignores three-phase asymmetry, non-fundamental frequency conditions, and dynamic processes occurring on the electromagnetic response timescale. The response time of the PLL is usually within tens of milliseconds, making it difficult for electromechanical transient models to accurately capture the dynamic behavior of the PLL. Additionally, these models cannot reflect the impact of three-phase asymmetry and non-fundamental frequency components on phase-locked behavior. PSCAD/EMTDC can better reflect the above content.

First, the IEEE three-machine, nine-bus system, as shown in Figure 7, is set up. This system is used as an example to test the transient stability characteristics when MMCs employ grid-forming control.

In the three-machine, nine-bus system, the three power sources are replaced with MMCs under different control methods. The synchronous machine source G1 is set as a grid-forming PV controlled converter station, and G2 and G3 are set as converter stations with V/f control. The fault locations are chosen at buses 5, 6, and 8, and the fault types selected are single-phase ground fault (Phase A), two-phase ground fault (Phases AB), and three-phase ground fault. The simulation time is set to 20 s, with a fault occurring at 6 s. The waveforms of the power angle difference δ₁₃ between converter stations G1 and G3 are observed and recorded. The Critical Clearing Time (CCT) is measured, which is the maximum fault duration after which the system can return to stability.

The modeling and design of MMC are highly complex tasks. The modeling and design of MMC form the foundation of this study, and extensive research has been conducted in this area over the past few years. In this case study, the MMC uses the models provided in References [22,23,24]. The parameter tuning of PLL and PSL is a relatively complex task. Given that many scholars have conducted extensive research in this area, this study directly draws on relevant conclusions [1,2,25]. Meanwhile,

Table 2. Important simulation parameters.

Base Value		100 MVA, 50 Hz
G1	rated voltage of grid side	16.5 kV
	rated voltage of valve side	210 kV
	rated DC voltage	400 kV
	leakage reactance of transformer	0.1 pu
	reference active power (inverter)	0.175 pu
	reference reactive power (inverter)	0.062 pu
G2	rated voltage of grid side	220 kV
	rated voltage of valve side	210 kV
	rated DC voltage	400 kV
	leakage reactance of transformer	0.1 pu
	reference active power (inverter)	0.4065 pu
	reference reactive power (inverter)	0.0195 pu
G3	rated voltage of grid side	13.8 kV
	rated voltage of valve side	210 kV
	rated DC voltage	400 kV
	leakage reactance of transformer	0.1 pu
	reference active power (inverter)	0.4065 pu
	reference reactive power (inverter)	0.0195 pu
T1	winging 1 line to line voltage (RMS)	16.5 kV
	winging 2 line to line voltage (RMS)	230 kV
	positive sequence leakage reactance	0.0576 pu
T2	winging 1 line to line voltage (RMS)	220 kV
	winging 2 line to line voltage (RMS)	230 kV
	positive sequence leakage reactance	0.00675 pu
T3	winging 1 line to line voltage (RMS)	13.8 kV
	winging 2 line to line voltage (RMS)	230 kV
	positive sequence leakage reactance	0.0586 pu
PL1	Rated real power per phase	41.67 MW
	Rated reactive power (+inductive) per phase	16.67 MVAR
PL2	Rated real power per phase	30 MW
	Rated reactive power (+inductive) per phase	10 MVAR
PL3	Rated real power per phase	33.33 MW
	Rated reactive power (+inductive) per phase	11.67 MVAR

presents the key parameters of the relevant models.

To determine whether the receiving-end grid recovers stability, the method involves checking whether the power angle differences, δ₁₃ and δ₂₃, return to the stable state before the fault within a certain time period after the fault occurs. If the angles recover and the maximum power angle difference during this process does not exceed 180°, the transient stability of the system is considered good. Moreover, the larger the CCT for the same fault condition, the better the transient stability of the system. If the system recovers stability with the same fault duration under different operating conditions, the transient stability can be compared by the maximum value of δ₁₃ or δ₂₃ during the unstable period. The larger the maximum value, the weaker the system’s ability to resist the fault and the worse the transient stability.

Based on this judgment method, in this simulation, if the system recovers stability with a fault duration of 0.5 s, the maximum value of the power angle difference between G1 and G3 at this time is measured to compare the transient stability under different conditions. The experimental data are recorded in

Table 3. Simulation result of transient stability (PV-GFM, Scenario 1).

Fault Location	Fault Type	Maximum Power Angle Difference δ13 (rad)	Fault Critical Clearing Time tCCT (s)
BUS5	single phase ground fault	0.244	>0.5
	two phase ground fault	0.178	>0.5
	three phase ground fault	0.451	>0.5
BUS6	single phase ground fault	0.250	>0.5
	two phase ground fault	0.190	>0.5
	three phase ground fault	0.353	>0.5
BUS8	single phase ground fault	0.152	>0.5
	two phase ground fault	0.168	>0.5
	three phase ground fault	0.528	>0.5

.

In Table 3, the power angle difference δ₁₃ refers to the difference between the power synchronization loop (PSL) output phase angle of the grid-forming PV controlled converter station G1 and the phase angle output of the phase-locked loop (PLL) of the V/f controlled converter station G3.

Next, both synchronous machine sources G1 and G2 in the three-machine, nine-bus system are replaced with grid-forming PV controlled converter stations. The experimental data are recorded in

Table 4. Simulation result of transient stability (PV-GFM, Scenario 2).

Fault Location	Fault Type	Maximum Power Angle Difference δ13 (rad)	Fault Critical Clearing Time tCCT (s)
BUS5	single phase ground fault	0.114	>0.5
	two phase ground fault	0.299	>0.5
	three phase ground fault	0.658	>0.5
BUS6	single phase ground fault	0.077	>0.5
	two phase ground fault	0.238	>0.5
	three phase ground fault	0.643	>0.5
BUS8	single phase ground fault	0.032	>0.5
	two phase ground fault	0.198	>0.5
	three phase ground fault	/	0.33

.

In Table 4, the power angle difference δ₁₃ refers to the difference between the power synchronization loop (PSL) output phase angle of the grid-forming PV controlled converter station G1 and the phase-locked loop (PLL) output phase angle of the V/f controlled converter station G3. The δ₂₃ mentioned in this context refers to the difference between the PSL output phase angle of the grid-forming PV controlled converter station G2 and the PLL output phase angle of G3.

The following describes the method of obtaining the Critical Clearing Time (CCT) and analyzing the system’s transient stability based on the waveforms of δ₁₃ and δ₂₃ when the fault location is selected at BUS8 and the fault type is three-phase ground fault. In the case where the synchronous machine sources G1 and G2 are replaced with grid-forming PV-controlled MMCs, the waveforms of δ₁₃ and δ₂₃ at a fault duration of 0.33 s are shown in Figure 8. Upon observation, it was found that the power angle differences δ₁₃ and δ₂₃ recover to the stable state prior to the fault occurrence, indicating that the receiving-end grid is able to return to stability within a certain time, showing good transient stability.

If the fault duration is changed to 0.34 s, the waveforms of δ₁₃ and δ₂₃ are shown in Figure 9. Upon observation, it was found that the power angle differences δ₁₃ and δ₂₃ do not return to the stable state prior to the fault occurrence, indicating that the system cannot recover stability. This suggests poor transient stability of the receiving-end grid. Additionally, the waveform of δ₁₃ becomes unstable between 12 s and 13 s, which is due to the instability of the power angle of converter station G2 at that moment.

When the fault duration is 0.33 s, the system can eventually recover stability, while when the fault duration is 0.34 s, the system cannot recover stability. Therefore, the critical clearing time (CCT) for this condition can be determined as 0.33 s, as recorded in Table 4.

For the same fault location, the maximum power angle difference δ₁₃ is smallest during a single-phase fault and largest during a three-phase fault. This allows us to conclude that the transient stability of the receiving-end grid is weakest during a three-phase fault, followed by a two-phase fault. The grid maintains stronger transient stability during a single-phase fault.

For the same fault type, when the fault occurs at bus 6, the maximum power angle difference δ₁₃ is relatively small. The next smallest occurs at bus 5, and the largest δ₁₃ occurs at bus 8. This suggests that the transient stability of the receiving-end grid is strongest when the fault occurs at bus 6, weaker when the fault occurs at bus 5, and weakest when the fault occurs at bus 8.

3.2. Analysis of Transient Stability Under Grid-Following PV Control

Similarly, only the synchronous machine power source G1 in the three-machine, nine-node system was replaced by a grid-following PV-controlled converter, with its capacity and other relevant parameters remaining the same as in Section 1. The fault location and fault type selection method also remained unchanged. The experimental data are recorded in

Table 5. Simulation result of transient stability (PV-GFL, Scenario 1).

Fault Location	Fault Type	Maximum Power Angle Difference δ13 (rad)	Fault Critical Clearing Time tCCT (s)
BUS5	single phase ground fault	0.283	>0.5
	two phase ground fault	0.316	>0.5
	three phase ground fault	/	0.12
BUS6	single phase ground fault	0.280	>0.5
	two phase ground fault	0.319	>0.5
	three phase ground fault	/	0.12
BUS8	single phase ground fault	0.266	>0.5
	two phase ground fault	0.477	>0.5
	three phase ground fault	0.801	>0.5

.

In Table 5, the power angle difference δ₁₃ refers to the difference between the PLL output phase angle of the grid-following PV-controlled converter G1 and the PLL output phase angle of G3.

Next, both the synchronous machine power sources G1 and G2 in the three-machine nine-node system were replaced with grid-following PV-controlled converters. The experimental data are recorded in

Table 6. Simulation result of transient stability (PV-GFL, Scenario 2).

Fault Location	Fault Type	Maximum Power Angle Difference δ13 (rad)	Fault Critical Clearing Time tCCT (s)
BUS5	single phase ground fault	0.256	>0.5
	two phase ground fault	/	0.06
	three phase ground fault	/	0.03
BUS6	single phase ground fault	0.283	>0.5
	two phase ground fault	/	0.06
	three phase ground fault	/	0.02
BUS8	single phase ground fault	0.306	>0.5
	two phase ground fault	/	0.04
	three phase ground fault	/	0.01

.

In Table 6, the power angle difference δ₁₃ refers to the difference between the PLL output phase angle of the grid-following PV-controlled converter G1 and the PLL output phase angle of G3. Similarly, δ₂₃ refers to the difference between the PLL output phase angle of the grid-following PV-controlled converter G2 and the PLL output phase angle of G3.

When the fault location is the same, in the case of a single-phase fault, the system’s Critical Clearing Time (CCT) is greater than 0.5 s, meaning the system can still recover stability when the fault duration is 0.5 s. However, for the same fault duration, the system cannot recover stability in the case of two-phase and three-phase faults, and the CCT for the two-phase fault is greater than that for the three-phase fault. This leads to the same conclusion as in Section 1: the transient stability of the receiving end power grid is weakest during a three-phase fault, followed by a two-phase fault, while the system maintains relatively strong transient stability during a single-phase fault.

When the fault type is the same, a fault at bus 5 results in a relatively small maximum power angle difference δ₁₃ or a larger CCT, followed by faults at bus 6 and bus 8. Therefore, it can be concluded that the transient stability of the receiving end power grid is greatest during a fault at bus 5, weaker at bus 6, and weakest at bus 8.

3.3. Analysis of Transient Stability Under Hybrid PV Control

Under this configuration, the synchronous generator G1 in the three-machine, nine-bus system was replaced by a grid-following PV control converter station, and the synchronous generator G2 was replaced by a grid-forming PV control converter station. The parameters, such as the capacity of these HVDC converter stations, remained the same as in Section 2, and the selection criteria for fault locations and fault types also remained unchanged. The experimental data are recorded in

Table 7. Simulationresult of transient stability (mixed type).

Fault Location	Fault Type	Maximum Power Angle Difference δ13 (rad)	Fault Critical Clearing Time tCCT (s)
BUS5	single phase ground fault	0.137	>0.5
	two phase ground fault	0.354	>0.5
	three phase ground fault	/	0.09
BUS6	single phase ground fault	0.126	>0.5
	two phase ground fault	0.442	>0.5
	three phase ground fault	/	0.09
BUS8	single phase ground fault	0.129	>0.5
	two phase ground fault	0.285	>0.5
	three phase ground fault	/	0.22

.

In this scenario, the power angle difference δ₁₃ refers to the difference between the PLL output angle of the grid-following PV control converter station G1 and the PLL output angle of G3, while δ₂₃ refers to the difference between the PSL output angle of the grid-forming PV control converter station G2 and the PLL output angle of G3.

Using the same analysis method as in Section 1 and Section 2, it can be concluded that, for the same fault location, the transient stability of the receiving-end power grid decreases in the order of single-phase ground fault, two-phase ground fault, and three-phase ground fault. For the same fault type, the transient stability of the grid is significantly weaker when the fault occurs at buses 5 and 6 compared to when it occurs at bus 8.

3.4. Characteristics of MMC Under Fault Conditions

Considering the operability of the MMC during short circuits and voltage drops, it was necessary to conduct a detailed analysis of the transient processes of current and voltage in the MMC power circuit.

To analyze this mechanism through simulation, a small system with an MMC connected to an AC voltage source was selected. A system model, as shown in Figure 10, was built in the PSCAD/EMTDC electromagnetic simulation software. The system consists of two converter stations, whose DC sides are interconnected via overhead transmission lines.

The right-side MMC was fixed to constant DC voltage and constant reactive power control, while the simulation study focused on the left-side subsystem. The active power control mode of the left-side MMC was set to constant active power control, while its reactive power control mode was tested under three different conditions:

• Constant AC voltage control (AC voltage set to 1 pu);
• Constant reactive power control (reactive power set to 0);
• Constant reactive power control (reactive power set to 0.5 pu)

After 1 s of operation, a single-phase short-circuit fault was applied between the AC voltage source and the MMC. The fault was cleared after 0.5 s, and the AC-side voltage waveforms of the MMC under the three conditions were observed. The simulation waveforms of this process are shown in Figure 11, Figure 12 and Figure 13.

According to the simulation results, it is evident that the overvoltage level is relatively high under MMC constant AC voltage control (AC voltage set to 1 pu). Overvoltage also occurs under constant reactive power control with a reactive power setpoint of 0.5 pu. However, no overvoltage is observed when the MMC operates in constant reactive power control mode with a reactive power setpoint of 0.

To specifically investigate the transient stability of the MMC during a voltage sag, the third scenario mentioned above was taken as an example. The response curves of relevant variables during the voltage sag were provided, including the MMC grid-side voltage, valve-side voltage, capacitor voltage, dq components of the AC-side current, system active power, reactive power, and θ_PLL, as shown in Figure 14.

The simulation results show that, during a short-circuit fault in the power system, the MMC current reaches its limit. After the fault is cleared, the reactive current of the MMC cannot immediately decrease, resulting in system overvoltage.

Specifically, if the MMC operates in constant AC voltage control mode or constant reactive power control mode with a high reactive power setpoint, it will increase its reactive current during the fault to maintain AC voltage or reactive power. After fault clearance, the system is prone to overvoltage in the short term. Over time, as the MMC control adjusts and reduces the reactive current to a steady level, the overvoltage disappears.

If the MMC operates in constant reactive power control mode with a setpoint of zero, the reactive current remains at zero both during and after the fault, preventing overvoltage after fault clearance. Additionally, if the MMC can modify its LVRT strategy during a short-circuit fault by prioritizing active current, it will reduce its reactive current, regardless of whether it operates in constant AC voltage control or constant reactive power control, thereby avoiding overvoltage.

Meanwhile, it can be observed that, during the fault, the MMC exhibits the following transient characteristics:

• The asymmetry of the AC-side voltage leads to the appearance of zero-sequence and negative-sequence components at the MMC output, with significant voltage fluctuations on the grid side;
• Due to the sudden voltage drop caused by the fault, the current may experience spikes or severe fluctuations. In the dq reference frame, the current components change noticeably, especially with a possible sharp increase in the d-axis component;
• The capacitor voltages of MMC submodules are affected by unbalanced currents and energy exchange, resulting in significant charging and discharging fluctuations during the fault;
• The fault causes a sudden drop or fluctuation in active power, while the reactive power may increase rapidly to support voltage stability. These power variations reflect the system’s control response capability;
• Due to voltage distortion and frequency disturbance, the Phase-Locked Loop (PLL) may experience phase drift or unstable locking during the fault, affecting synchronization control.

In summary, the transient response of the MMC under short-circuit faults is complex. However, a control system with good dynamic performance and robustness can ensure stable system operation under disturbances.

3.5. Comparison and Analysis of Transient Stability

Using the same evaluation method as in the previous sections, a comparison of Table 3, Table 4, Table 5, Table 6 and Table 7, reveals that, under the same fault locations and fault types, the transient stability of the receiving power grid decreases in the following order: fully grid-forming control for the HVDC converter stations, hybrid control (a combination of grid-forming and grid-following control), and fully hybrid control. This is because when grid-forming control is used, the system’s CCT is generally greater than 0.5 s. In contrast, when hybrid control and grid-following control are used, the CCT significantly reduces. Furthermore, when other variables are held constant, the maximum power angle difference (δ₁₃) using hybrid control is noticeably smaller than that using grid-following control.

3.6. Results Summary

The results are summarized as follows:

• Influence of Converter Control Strategy on Transient Stability:

The control method employed in MMCs plays a critical role in determining transient stability. In the simulated three-machine, nine-bus system, a receiving-end grid equipped entirely with grid-forming PV-controlled converter stations demonstrates superior transient stability compared to one using only grid-following PV-controlled converter stations. When a hybrid approach—combining both grid-forming and grid-following PV control—is applied, the transient stability of the grid falls between these two configurations;

2.

Effect of Fault Type on Transient Stability:

The nature of the fault has a significant influence on the system’s transient stability. The grid exhibits its highest transient stability during single-phase faults, moderate stability during two-phase faults, and the lowest stability under three-phase faults. This trend indicates that the system tolerates asymmetrical faults considerably better than symmetrical three-phase faults;

3.

Role of Fault Location in Transient Stability:

The spatial position of a fault also exerts a noticeable impact on transient stability. Areas with a greater presence of grid-forming PV-controlled converter stations near the fault location result in stronger transient stability. Although having grid-following PV-controlled converter stations in the vicinity does contribute to stability improvements, grid-forming control offers a more pronounced enhancement.

4. Conclusions

The investigations carried out in this study demonstrate that the choice of control strategy for MMCs markedly influences the transient stability of the receiving-end grid. The simulation results consistently show that grid-forming control, by virtue of its self-synchronizing capability and inherent virtual inertia, delivers superior dynamic performance compared to grid-following control. Specifically, systems employing grid-forming control exhibit longer critical clearing times and reduced power angle deviations under fault conditions. A hybrid control approach, which combines elements of both strategies, achieves performance that lies between the two extremes, thereby offering a potential compromise when converter stations with different functionalities coexist within the same network.

In summary, the study emphasizes that proper control design is essential for managing the dynamic challenges posed by modern MTDC systems, especially as grids become increasingly decentralized and renewable-rich. Future research should further dissect the underlying physical mechanisms and extend the analysis to more diverse network topologies and operating conditions, ensuring that the most effective control techniques are identified for robust and resilient power system operation.