A New Current Differential Protection Scheme for DC Multi-Infeed Systems

Abstract

To meet the demands of deep grid integration of renewable energy and long-distance power transmission, this paper presents a hybrid multi-infeed DC system architecture that includes an AC power source (AC), a voltage source converter (VSC), and a modular multilevel converter (MMC). Addressing the limitations of traditional differential protection—such as insufficient sensitivity under high-resistance grounding and susceptibility to false operations under out-of-zone disturbances—this paper introduces an enhanced current differential criterion based on dynamic phasor analysis. By effectively decoupling DC bias and load current components and optimizing the calculation of action and braking quantities, the proposed method enables the rapid and accurate identification of typical faults, including high-resistance grounding, three-phase short circuits, and out-of-zone faults. A multi-scenario simulation platform is built using MATLAB to thoroughly validate the improved criterion. Simulation results demonstrate that the proposed method offers excellent sensitivity, selectivity, and resistance to false operations in multi-infeed complex systems. It achieves fast fault detection (~2.0 ms), strong sensitivity to high-resistance internal faults, and low false tripping under a variety of test scenarios, providing robust support for next-generation DC protection systems.

1. Introduction

In recent years, with the large-scale access to renewable energy and the cross-regional optimization of power resources, high-voltage direct current (HVDC) technology has developed rapidly around the world, strongly supporting the efficient consumption and cross-regional transmission of clean energy [1]. Among them, the flexible direct current transmission technology, voltage-source-converter-high-voltage direct current (VSC-HVDC) based on VSC, can flexibly realize independent regulation of active and reactive power by virtue of the fully controlled devices constituting the converter. It is mainly used in scenarios such as asynchronous interconnection of power grids, island power supply, renewable energy transmission, and urban power grid expansion. At the same time, the modular multilevel converter (MMC), as an important implementation form of flexible direct current technology, has better waveform quality and scalability. Because of its significant advantages in reducing energy loss, voltage support, and power regulation, it has been applied in actual engineering projects in many countries and regions [2,3]. In the early hybrid direct current system, there was a hybrid topology that used LCC (thyristor converter) with VSC and MMC to improve transmission capacity and operation flexibility, but it also introduced new protection challenges. Especially under fault conditions, the differences in the structure and control strategies of different converters lead to the system showing characteristics such as multi-source dynamic injection, strong coupling of electrical quantities, and complex transient processes [4,5], which increases the difficulty of differential protection. However, with the maturity of flexible DC technology, the mainstream new multi-input DC systems in current engineering applications are mainly VSC and MMC.

In current engineering practice, early hybrid systems mostly use the VSC-HVDC framework, and their main protection generally adopts a non-unit strategy based on the traveling wave principle [6], relying on the high-frequency transient characteristics of the initial fault to achieve millisecond-level rapid action. However, this type of method is not adaptable enough to high fault resistance [4] and multi-terminal systems [7]: the traveling wave signal is easily distorted due to line attenuation or impedance coupling, resulting in protection failure or misclassification [6,7]. For this reason, current differential protection is usually configured as a backup in engineering (such as the frequency modulation surge impedance scheme in reference [4]), but its action delay and communication synchronization requirements limit the rapid fault isolation capability of complex systems [6], and it is urgent to develop new protection algorithms to compensate for this.

In the current mainstream VSC-MMC multi-infeed DC system, traditional current differential protection also faces severe challenges. Studies have shown that the strong electromagnetic coupling effect caused by the installation of AC and DC lines in the same corridor can induce a power-frequency voltage on the DC line, leading to circulating current problems and aggravating the complexity of the transient fault process. At the same time, there are essential differences in the fault response mechanisms of VSC and MMC converters: MMC injects high-frequency pulse current into the line due to the rapid discharge of submodule capacitors and PWM control switching at the moment of fault [8]; VSC relies on current limiting and control strategies, and its dynamic response characteristics are different from those of MMC. When the two types of converters are connected to the same protection area, the superposition of dissimilar dynamic responses will cause short-term asymmetric fluctuations in the differential current, weakening the reliability of traditional judgment criteria [9,10].

In order to improve the adaptability of differential protection in VSC-MMC multi-terminal systems, domestic and foreign scholars have conducted studies to improve differential protection criteria. They can be mainly divided into the following two categories: one is the improved current criterion, and the other is the non-current auxiliary quantity criterion.

In terms of improved current criteria, reference [11] constructs the differential current using a frequency-dependent distributed parameter model and introduces a fast time-domain convolution algorithm to achieve high-sensitivity fault detection within 3 ms; however, it requires complex modeling and calculations, resulting in high deployment costs. Reference [12] enhances differential protection by applying amplitude and phase angle correction factors, combined with abnormal data and CT saturation detection, which improves adaptability and robustness under high-resistance and rectification conditions; however, the algorithm is highly complex and sensitive to parameter settings. Reference [13] uses a sigmoid function to optimize the braking characteristic and enhance sensitivity in scenarios where the phase angle approaches 90°, but the setting process is complicated and prone to disturbance saturation. Reference [14] employs the current direction at the characteristic frequency of the DC filter to distinguish between internal and external faults, reducing dependence on high sampling rates; however, it relies heavily on filter parameters, making it difficult to handle complex operating conditions. Reference [15] introduces the MMC negative-sequence current differential as an auxiliary judgment criterion to improve asymmetric fault identification; however, the negative-sequence component is vulnerable to interference under multi-infeed or system fluctuation conditions, posing a risk of misjudgment.

In terms of non-current auxiliary quantity criteria, reference [16] designs primary and backup protection based on the transient voltage ratio (ROTV) of the inductance at both ends of the DC line, which can quickly distinguish DC faults from external disturbances, operates independently of communication, and is adaptable to high-resistance faults. However, it places high demands on the parameters of the sensing elements and the accuracy of high-frequency measurements, making implementation complex. Reference [17] similarly employs a transient voltage ratio protection scheme to improve selectivity and robustness in multi-terminal VSC-HVDC systems, but it is highly dependent on high-frequency components and is sensitive to sampling frequency and signal-to-noise ratio. Reference [18] uses the characteristic frequency current of the DC filter to build protection, addressing the low sensitivity of the traveling wave and voltage derivative methods under high-resistance faults, without requiring high-frequency sampling or synchronization; however, it relies on the resonance characteristics of the filter, limiting its applicability. Reference [19] develops guided protection based on the U–Q characteristic curve of the LCC-MMC system, which provides strong fault identification capability but involves complex parameter settings and is sensitive to operating conditions and power flow variations. Reference [20] integrates AC/DC transient information, using the RMS ratio of the transient voltage across the current-limiting reactor and the zero-sequence voltage difference on the AC side to quickly locate the fault pole, thereby enhancing local protection capability in MMC-HVDC systems. However, it has stringent requirements for high-frequency modeling and converter dynamic response, and its robustness still needs further validation.

In summary, although existing studies have proposed various innovative solutions for differential protection and auxiliary criteria—such as the introduction of frequency-dependent models, transient voltage ratios, characteristic frequency currents, and AC/DC coupling information—which effectively enhance sensitivity and selectivity in specific scenarios, several bottlenecks remain in practical VSC-MMC multi-infeed systems with complex topologies: (1) the nonlinear and heterogeneous dynamic behaviors of multiple converters lead to more complex short-term fluctuations in electrical quantities, making traditional judgments based solely on current measurements prone to failure; (2) some approaches that depend on high-frequency transients, inductor voltage ratios, or U–Q characteristics impose high demands on hardware, synchronization, and system modeling, making them difficult to implement on a large scale in engineering practice; (3) most studies focus on a single physical quantity or feature, lacking the integration and identification of multi-source information and multi-modal characteristics, resulting in insufficient robustness and generalization when confronted with complex disturbances [21,22].

To address the above shortcomings, this paper develops a multi-scenario simulation model based on a typical VSC-MMC multi-infeed DC system and proposes a protection scheme using an improved differential current criterion. The approach focuses on converter characteristics, current response behaviors, and the impact of DC offset within the multi-infeed system and achieves fast and reliable identification of typical operating conditions—including high-resistance grounding, three-phase short circuits, and out-of-zone disturbances—through dynamic compensation and criterion optimization.

The main work of this paper is as follows:

(1) A multi-infeed hybrid DC system model, incorporating an AC power system, a variable-speed constant-frequency converter based on VSC, and an MMC modular multilevel converter, was developed. The model fully accounts for the dynamic characteristics of the converters and the current response behavior under a multi-source power supply, providing a simulation platform for subsequent protection strategy design.

(2) To address the insufficient adaptability of traditional differential protection in multi-infeed systems under conditions such as high-resistance grounding, symmetrical short circuits, and out-of-zone disturbances [23,24], an improved differential current criterion was proposed. Using dynamic phasor analysis, the DC component was separated, the calculation methods for the action quantity and braking quantity were optimized, and the fault identification capability was enhanced.

(3) A multi-scenario simulation was implemented in MATLAB R2022b, covering typical conditions such as metallic grounding, high-resistance grounding, three-phase short circuits, and out-of-zone faults. The differential current, criterion curves, and action times were generated. The proposed method’s sensitivity, selectivity, and resistance to false operations were systematically evaluated, and its applicability under different feed-in architectures was analyzed.

2. Line Model and Parameter Decoupling of the Multi-Infeed System

2.1. System Structure

In the system, the M side connects to an AC system, a VSC, and an MMC, while the N side is connected to both an AC system and an MMC converter. E_M and E_N represent the grid-equivalent sources at both ends. Specifically, the VSC, built with fully controlled devices, can flexibly regulate active and reactive power, while the MMC adopts a modular multilevel topology and delivers output to the AC side through multiple sub-modules, providing excellent waveform quality and scalability.

Under multi-source power supply or fault disturbance conditions, the feed-in currents on both sides of M and N can produce complex coupling in the time domain and frequency domain, causing asymmetric components, non-power frequency harmonics, and DC bias in the MN segment. Especially when VSC control fails or MMC is locked, strong DC and high-frequency components can be introduced into the system, causing great interference to the fault judgment of differential protection.

Therefore, to ensure protection performance, it is necessary to design a protection strategy that incorporates DC compensation, high-frequency suppression, and improved current criterion to enhance sensitivity and reliability. Differential protection measurement points are installed on the M-side and N-side buses, respectively. The corresponding system model and parameters are shown in Figure 1, with detailed data provided in

Table 1. Model parameters.

Parameters	Value
Terminal voltage EM, EN	230 kV
MN line length	50 km
M-side AC source equivalent impedance	0.01 + j0.15 Ω
N-side AC source equivalent impedance	0.012 + j0.18 Ω
VSC converter station’s DC rated voltage	500 kV
MMC converter station’s DC rated voltage	500 kV

.

2.2. Selection of Line Models and Parameter Decoupling Calculations

The transmission line adopts a distributed parameter model, where the line’s characteristic impedance is much greater than its resistance, as shown in Figure 2. In this model, the resistance of the line segment between the MN busbars in Figure 1 is concentrated at both ends and the midpoint, effectively representing the MN line as two sections of lossless transmission lines, k₁m₁ and k₂m₂.

It should be noted that the simplified line model in Figure 2, where resistance is concentrated at the ends and midpoint, is used primarily to facilitate the segmentation and parameter decoupling of the transmission line for differential protection analysis. The line’s distributed electrical properties—including inductance (L) and capacitance (C)—are fully preserved and explicitly incorporated in the subsequent differential Equation (1).

In Figure 2, R is the line resistance, l is the line length, and taking the left half of the transmission line k₁m₁ as an example, its differential equation is as follows:

$$\left\{\begin{array}{c}(\partial U/\partial s)=-L(\partial I/\partial t)\\ (\partial I/\partial s)=-C(\partial U/\partial t)\end{array}\right.$$

(1)

In Equation (1), U is the voltage along the line (kV); s is the distance from the end k₁ of the lossless transmission line to any point along the line; I is the current along the line (kA); L is the line inductance (H); t is the time (s); C is the line capacitance (F).

The relationship between the voltage and current distribution along the line is as follows:

$$\begin{array}{l}(U, \mathrm{t}) = (I, \mathrm{t})/\mathrm{Z}\\ =[U_k(t+s/v)-I_k(t+s/v)\cdot Z]/2+U_k(t-s/v)-I_k(t-s/v)\cdot Z]/2\end{array}$$

(2)

In Equation (2), Z is wave impedance (Ω); v is wave velocity (m/s).

Based on the differential equation, the time-domain circuit model of the lossless transmission line k₁m₁ can be derived, as shown in Figure 3. By applying the distributed parameter model, the two sections of lossless transmission lines, k₁m₁ and k₂m₂, in Figure 2 are replaced with the equivalent circuit from Figure 3, resulting in the time-domain equivalent circuit of the MN line, as shown in Figure 4.

Under multi-input conditions, especially when an asymmetric fault occurs in the line (such as single-phase grounding or a two-phase short circuit), the three-phase electrical quantities will show unbalanced characteristics such as inconsistent amplitudes and obvious phase differences. At this time, in order to accurately extract the differential quantity and realize fault component isolation, it is necessary to perform phase decoupling processing on the line-end voltage and current signals. This paper adopts the Wedpohl phase mode transformation method [25] to perform modal decoupling on the measured electrical quantities, and the transformation matrix is shown as follows:

$$S=\left[\begin{array}{ccc}1& 1& 1\\ 1& 0& -2\\ 1& -1& 1\end{array}\right],S^{-1}={\displaystyle \frac{1}{6}}\left[\begin{array}{ccc}2& 2& 2\\ 3& 0& -3\\ 1& -2& 1\end{array}\right]$$

(3)

After transforming the three-phase voltage (or current) signals [S_A, S_B, S_C]^T at points M and N of the line, the corresponding zero-sequence, positive-sequence, and negative-sequence components [S⁽⁰⁾, S⁽¹⁾, S⁽²⁾] can be obtained. The expressions are as follows:

$$\left[\begin{array}{l}{S}_{\mathrm{m}}^{(0)}\hfill \\ S_{\mathrm{m}}^{(1)}\hfill \\ S_{\mathrm{m}}^{(2)}\hfill \end{array}\right]=\left[\begin{array}{lll}2\hfill & 2\hfill & 2\hfill \\ 3\hfill & 0\hfill & -3\hfill \\ 1\hfill & -2\hfill & 1\hfill \end{array}\right]\left[\begin{array}{l}{S}_{\mathrm{A}}\hfill \\ S_{\mathrm{B}}\hfill \\ S_{\mathrm{c}}\hfill \end{array}\right]=\left[\begin{array}{l}2S_{\mathrm{A}}+2S_{\mathrm{B}}+2S_{\mathrm{C}}\hfill \\ 3S_{\mathrm{A}}-3S_{\mathrm{C}}\hfill \\ S_{\mathrm{A}}-2S_{\mathrm{B}}+S_{\mathrm{C}}\hfill \end{array}\right]$$

(4)

In Equation (4), $S_{\mathrm{m}}^{(0)}$, $S_{\mathrm{m}}^{(1)}$, and $S_{\mathrm{m}}^{(2)}$ are zero-sequence, positive-sequence, and negative-sequence voltages or currents, respectively; S_A, S_B, and S_C are voltages or currents on both sides.

The mode current is synthesized into the line current through inverse transformation. The inverse transformation process is as follows:

$$\left[\begin{array}{c}{S}_{\mathrm{A}}^{\prime }\\ S_{\mathrm{B}}^{\prime }\\ S_{\mathrm{C}}^{\prime }\end{array}\right] = \left[\begin{array}{ccc}1& 1& 1\\ 1& 0& -2\\ 1& -1& 1\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{m}}^{(1)}\\ S_{\mathrm{m}}^{(2)}\\ S_{\mathrm{m}}^{(0)}\end{array}\right] = \left[\begin{array}{c}{S}_{\mathrm{m}}^{(0)}+S_{\mathrm{m}}^{(1)}+S_{\mathrm{m}}^{(2)}\\ S_{\mathrm{m}}^{(1)}-2S_{\mathrm{m}}^{(0)}\\ S_{\mathrm{m}}^{(1)}-S_{\mathrm{m}}^{(2)}+S_{\mathrm{m}}^{(0)}\end{array}\right]$$

(5)

In Equation (5), $S_{\mathrm{A}}^{\prime }$, $S_{\mathrm{B}}^{\prime }$, and $S_{\mathrm{C}}^{\prime }$ are the three-phase AC currents after decoupling.

This method can effectively decouple three-phase electrical quantities into independent modal channels, making it particularly suitable for current extraction and criterion reconstruction in differential protection under asymmetric conditions. Figure 5 shows a comparison between the original phase A current (blue solid line) on the M side during a three-phase short-circuit fault and the decoupled positive-sequence current (red dotted line) waveform. It can be observed that the decoupled positive-sequence current exhibits a smoother and more periodic pattern, effectively suppressing the high-frequency disturbances and stray components present in the original current and highlighting the main fault components. In weak fault scenarios, such as high-resistance grounding, the original current waveform is heavily influenced by system noise and dynamic disturbances, whereas the positive-sequence component more clearly reveals the current variations caused by the fault.

In summary, this chapter constructs a multi-input system line model that can reflect the disturbance characteristics of heterogeneous converters and realizes the pre-processing of differential quantity extraction through modal decoupling, providing a solid foundation for the subsequent construction and simulation verification of the differential criterion.

3. Analysis of Differential Protection Performance in Multi-Infeed VSC-MMC System

Current differential protection typically employs the ratio restraint action criterion [10], which compares the differential current with the restraint current to determine the appropriate protection action. As shown in Equations (6) and (7), I_M and I_N are the currents at both ends of line MN; I_d and I_r represent the differential current and restraint current, respectively; I_d/I_r defines the full-current protection criterion; and K is the full-current protection restraint coefficient.

$$I_d=I_M+I_N , I_r={\displaystyle \frac{\left|I_M\right|+\left|I_N\right|}{2}}$$

(6)

$${\displaystyle \frac{I_d}{I_r}}>K$$

(7)

3.1. Analysis on the Adaptability of Traditional AC Differential Protection in Multi-Infeed Systems

To study the adaptability of AC differential protection in multi-infeed systems, the number of different types of DC converter stations and AC lines can be controlled in the model to compare the DC feed-in characteristics of different intensities and combinations. As shown in Figure 1, the system topology includes AC busbars on the M and N sides, with VSC converter stations (L₁) and MMC converter stations (L₂ and L₃) connected to the M side, and MMC converter stations (L₄ and L₅) connected to the N side. The AC rated voltage on both sides of M and N is 230 kV, and the total length of the line is 50 km.

The hybrid DC multi-infeed system shown in Figure 1 has three cases:

• When only AC (AC source E_M, E_N) is connected to both the M side and the N side, that is, L₁, L₂, L₃ on the M side and L₄, L₅ on the N side are not put into the converter station, the model is a pure AC system without DC feed-in.
• When AC + VSC (L₁) is put into the M side and AC + MMC (L₄, L₅) is put into the N side, it is an AC system with VSC-MMC hybrid DC feed-in, recorded as multi-feed system 1.
• When VSC + MMC (L₁, L₂, L₃) is put into the M side and MMC (L₄, L₅) is put into the N side, it is an AC system with VSC-MMC hybrid DC feed-in, recorded as multi-feed system 2.

Through these different scenarios, the adaptability of AC differential protection in the face of high-frequency harmonics, current imbalance, and DC bias introduced by hybrid multi-feed and converter station access can be systematically analyzed.

To comprehensively evaluate the adaptability of traditional AC differential protection in multi-infeed DC systems, this paper establishes multiple groups of representative fault scenarios based on the developed VSC-MMC hybrid DC system model. The analysis focuses on internal fault identification capability, the risk of false operation under external faults, and the risk of failure under high-resistance grounding faults. The fault types considered include three-phase short circuits, single-phase grounding, high-resistance grounding, and other conditions, aiming to verify the robustness of the differential criterion in multi-infeed systems.

Table 2. Pure AC system protection action.

Protection Criteria	Single-Phase Ground Fault		Three-Phase Short-Circuit Fault	External Fault
	Metallic Grounding	High-Resistance Grounding
Id/Ir action	>K trip	>K trip	>K trip	<K no trip

,

Table 3. Protection action of multi-infeed AC system 1.

Protection Criteria	Single-Phase Ground Fault		Three-Phase Short-Circuit Fault	External Fault
	Metallic Grounding	High-Resistance Grounding
Id/Ir action	>K trip	<K failure to operate	>K trip	<K no trip

and

Table 4. Protection action of multi-infeed AC system 2.

Protection Criteria	Single-Phase Ground Fault		Three-Phase Short-Circuit Fault	External Fault
	Metallic Grounding	High-Resistance Grounding
Id/Ir action	>K trip	<K failure to operate	>K trip	>K maloperation

present the performance of the three AC system configurations under various fault conditions.

From the analysis of Table 2, Table 3 and Table 4, it can be observed that the applicability of the traditional differential protection criterion I_d/I_r changes significantly across different feed-in scenarios. For the pure AC system (Table 2), the protection criterion operates accurately under metallic grounding, high-resistance grounding, phase-to-phase short circuits, and other faults, and consistently refrains from operating under out-of-zone faults, demonstrating good reliability.

In multi-feed system 1 (Table 3, including VSC-MMC hybrid feed-in), the protection’s ability to operate under high-resistance grounding faults declines, leading to instances of failure to operate, as shown in Figure 6. However, it remains reliable for other in-zone faults and does not operate for out-of-zone faults.

In multi-feed system 2 (Table 4, with more converter stations connected on the VSC-MMC side), system complexity increases further, and DC-side disturbances become more pronounced. Under these conditions, the traditional criterion not only fails to operate for high-resistance grounding faults but may also misidentify out-of-zone faults as in-zone faults due to false differential currents, resulting in false operations, as shown in Figure 7.

Overall, as the feed-in structure evolves from a pure AC system to a complex multi-feed system, the applicability of traditional protection criteria gradually diminishes, highlighting the urgent need to enhance the criteria or supplement them with diversified approaches.

3.2. Analysis of Reasons for Decreased Adaptability

Since the rectifier side of the hybrid multi-infeed DC system adopts constant current control, and the inverter side voltage is determined by the receiving end AC bus, the hybrid DC transmission system can be equivalent to a voltage-controlled current source controlled by the receiving end, as shown in Figure 8. In Figure 8, Z₁ and Z₂ are the equivalent system impedances on both sides of the AC line; Z_M and Z_N are the line impedances on both sides of the fault point; ΔI_dc,MMC1 and ΔI_dc,MMC2 are the equivalent fault component current of the MMC hybrid DC system; ΔI_dc,VSC is the equivalent fault component current of the VSC hybrid DC system; ΔI_dcf, ΔI_dcM, and ΔI_dcN are the DC feed-in fault components at the fault point and the line MN end; and ΔI_dcM = ΔI_dcN + ΔI_dcf can be obtained.

When a high-resistance grounding fault occurs in the area, the full current differential protection is affected by the hybrid DC feed-in, and its sensitivity is reduced. This is similar to the refusal to operate when a high-resistance grounding fault occurs in a pure AC system. The fault wiring diagram of the pure AC system is shown in Figure 9. In Figure 9, E_M and E_N are equivalent power sources on both sides of the AC system, R_g is the system transition resistance, Z₁ and Z₂ are equivalent system impedances on both sides of the AC line, and Z_M and Z_N are line impedances on both sides of the fault point. Let I_cy be the load current transmitted from the M terminal to the N terminal under normal operating conditions, ΔI_M be the changing current on the M side, ΔI_N be the changing current on the N side, and the capacitive current be ignored. The currents at both ends of M and N can be set as Equation (8):

$$\left\{\begin{array}{l}{\stackrel{·}{I}}_{\mathrm{M}}=(\Delta {\stackrel{·}{I}}_{\mathrm{M}}+{\stackrel{·}{I}}_{\mathrm{cy}})\hfill \\ {\stackrel{·}{I}}_{\mathrm{N}}=(\Delta {\stackrel{·}{I}}_{\mathrm{N}}-{\stackrel{·}{I}}_{\mathrm{cy}})\hfill \end{array}\right.$$

(8)

Taking the load current into account, the action amount I_d1 and the braking amount I_r1 of the traditional full current differential protection can be expressed as follows:

$$I_{\mathrm{d}1}=|{\stackrel{·}{I}}_{\mathrm{M}}+{\stackrel{·}{I}}_{\mathrm{N}}|=|\Delta {\stackrel{·}{I}}_{\mathrm{M}}+\Delta {\stackrel{·}{I}}_{\mathrm{N}}|$$

(9)

$$I_{\mathrm{r}1}=|{\stackrel{·}{I}}_{\mathrm{M}}-{\stackrel{·}{I}}_{\mathrm{N}}|=|\Delta {\stackrel{·}{I}}_{\mathrm{M}}-\Delta {\stackrel{·}{I}}_{\mathrm{N}}+2{\stackrel{·}{I}}_{\mathrm{cy}}|$$

(10)

From Equations (9) and (10), it can be obtained that in the full current criterion, the action amount I_d1 is not affected by the load current, while the braking amount I_r1 increases with the increase of the load current, and the protection sensitivity decreases accordingly.

Figure 10 shows the high-resistance ground fault wiring model in the hybrid VSC-MMC multi-feed scenario.

I_dcMMC and I_dcVSC are the equivalent DC currents injected by the converter, I_dc.M is the total DC feed-in at the M end, I_dc.N is the total DC feed-in at the N end, and I_dc.M = I_dc.N + I_dc.f. The currents at both ends of the line after DC feeding can be calculated by the following:

$${\stackrel{·}{I}}_{\mathrm{M}1}=(\Delta {\stackrel{·}{I}}_{\mathrm{M}}+{\stackrel{·}{I}}_{\mathrm{cy}1}+{\stackrel{·}{I}}_{\mathrm{de}.\mathrm{M}})$$

(11)

$${\stackrel{·}{I}}_{\mathrm{N}1}=(\Delta {\stackrel{·}{I}}_{\mathrm{N}}-{\stackrel{·}{I}}_{\mathrm{cy}1}-{\stackrel{·}{I}}_{\mathrm{de}.\mathrm{N}})$$

(12)

In Equations (11) and (12), I_cy1 is the load current after DC feeding; I_M1, I_N1 are the currents at both ends of the line after DC feeding.

Combining Equations (9) and (10), the action amount and braking amount after multiple inputs are as follows:

$$I_{\mathrm{d}2}=|\left.{\stackrel{·}{I}}_{\mathrm{M}1}+{\stackrel{·}{I}}_{\mathrm{N}1}\right|=|\Delta {\stackrel{·}{I}}_{\mathrm{M}}+\Delta {\stackrel{·}{I}}_{\mathrm{N}}+{\stackrel{·}{I}}_{\mathrm{dcf}}|$$

(13)

$$I_{\mathrm{r}2}=|\left.{\stackrel{·}{I}}_{\mathrm{M}1}-{\stackrel{·}{I}}_{\mathrm{N}1}\right|=|\Delta {\stackrel{·}{I}}_{\mathrm{M}}-\Delta {\stackrel{·}{I}}_{\mathrm{N}}+2{\stackrel{·}{I}}_{\mathrm{cy}1}+{\stackrel{·}{I}}_{\mathrm{dc}\mathrm{M}}+{\stackrel{·}{I}}_{\mathrm{dc}\mathrm{N}}|$$

(14)

I_d2 and I_r2 are the current action and current braking after the hybrid DC multi-feed, respectively. From Equation (14), it can be seen that in full-current protection, as the transition resistance increases, the influence of the system load current becomes greater than that of the DC feed component. Under normal operating conditions, the load current increases with the DC feed, so in a high transition resistance state, the load current remains the primary factor contributing to the increase in the restraining quantity and the decrease in protection sensitivity.

4. Improved Current Criterion Differential Protection Method

In order to alleviate the problem of decreased sensitivity of differential protection criteria under high-resistance grounding faults and easy misoperation or failure to operate, this paper proposes an improved current criterion protection strategy. Based on the equivalent separation of DC feed-in components and load currents, this strategy constructs improved action and braking quantities with better fault resolution capabilities, thereby improving the sensitivity and selectivity of differential protection under complex injection conditions. This improved current criterion mechanism can take into account the sensitivity and selectivity of protection under complex injection conditions. The specific method and implementation are described as follows.

According to the analysis in Section 3, the inadaptability of traditional protection criteria is mainly due to the DC feed-in and load current, so the DC feed-in and load current are calculated and analyzed first.

The traditional steady-state modeling method assumes that the system is in a linear periodic condition, which makes it difficult to characterize the above-mentioned non-power frequency dynamic characteristics. In order to achieve accurate equivalence and quantification of the feed-in components, this paper introduces the dynamic phasor method to model and extract them.

The dynamic phasor method projects the time-domain signal into the complex exponential basis space to obtain its frequency-domain “slow-varying component,” that is, the average frequency response characteristics in a short time window. This method is particularly suitable for system modeling problems containing high-order control, non-periodic disturbances, and frequency offset components. Its basic idea can be expressed as Equation (15):

$${〈x(t)〉}_p={\displaystyle \frac{1}{T}}{\displaystyle {\int }_0^{T}x}(t)e^{-jp{\omega }_{0}t}dt$$

(15)

In Equation (15), ω₀ is the fundamental angular frequency (power frequency), p is the extracted harmonic order, and T is the observation window width.

The converter control trigger action in the hybrid system can be represented by the switching function S_ip(t), and the inverter side feed current is represented by I_dc. After the two are processed as dynamic phasors, the equivalent expression of the DC feed component can be obtained according to Equation (15):

$$I_{dc.eq\left(p\right)}={\displaystyle \sum _q{〈I_{dc}〉}_{p-q}}\cdot {〈S_{ip}〉}_q$$

(16)

where I_dc.eq(p) is the DC feed-in equivalent component at the pth frequency, 〈I_dc〉_p-q is the (p-q)_th order dynamic phasor of the inverter current signal, and 〈S_ip〉_q is the qth order dynamic phasor of the switching function. Equation (16) reflects a convolution structure, that is, the feed-in current is composed of the spectrum reconstruction of the inverter injection current multiplied by its switching behavior.

When the analysis target is concentrated on the power frequency component (i.e., p = q = 1), Equation (16) can be simplified to Equation (17).

$$I_{dc.eq}={\langle I_{dc}\rangle }_{(0)}\cdot {\langle S_{ip}\rangle }_{(1)}$$

(17)

where 〈I_dc〉₍₀₎ is the DC (0th order) component of the DC current. 〈S_ip〉₍₁₎ is the modulation coefficient of the switching behavior to the power frequency, defined as Equations (18) and (19):

$${〈S_{ip}〉}_{(1)}={\displaystyle \frac{1}{T}}{\displaystyle {\int }_0^T{S}_{ip}}(t)e^{-j{\omega }_{0}t}dt$$

(18)

$${\stackrel{·}{I}}_{\mathrm{dc}.\mathrm{eq}}=<I_{\mathrm{dc}}{>}_{(0)}<S_{i\phi }{>}_{(1)}$$

(19)

In Equations (18) and (19), T is the switching period (s); ω is the angular frequency (rad/s); at this time, the phase of the DC input component is determined by S_iφ, and the amplitude is determined by S_iφ and I_dc.

Equation (19) essentially converts the nonlinear switching action into a modulation function, which is then multiplied by the DC current base value to form an equivalent AC injection model of the feed channel.

The full-current protection action is not directly affected by the load current but can be improved by incorporating the load current into the restraining quantity. Since the load current cannot be measured directly, it must be calculated based on the electrical quantities at both terminals and the line impedance parameters. Assume that the voltages at the two ends of the line are U_M and U_N, and the line impedance is Z = Z_M + Z_N. Equations (20)–(22) can be derived as follows:

$${\stackrel{·}{U}}_{ \mathrm{M}}=Z_{ \mathrm{M}}{\stackrel{·}{I}}_{ \mathrm{M}1}+({\stackrel{·}{I}}_{ \mathrm{M}1}+{\stackrel{·}{I}}_{ \mathrm{N}1})R_{\mathrm{g}}$$

(20)

$${\stackrel{·}{U}}_{ \mathrm{N}}=Z_{ \mathrm{N}}{\stackrel{·}{I}}_{ \mathrm{N}1}+({\stackrel{·}{I}}_{ \mathrm{M}1}+{\stackrel{·}{I}}_{ \mathrm{N}1})R_{\mathrm{g}}$$

(21)

$$R_{\mathrm{g}}={\displaystyle \frac{({\stackrel{·}{U}}_{\mathrm{M}}{\stackrel{·}{I}}_{\mathrm{M}1}+{\stackrel{·}{U}}_{\mathrm{N}}{\stackrel{·}{I}}_{\mathrm{N}1}-Z{\stackrel{·}{I}}_{\mathrm{M}1}{\stackrel{·}{I}}_{\mathrm{N}1})}{{({\stackrel{·}{I}}_{\mathrm{M}1}+{\stackrel{·}{I}}_{\mathrm{N}1})}^2}}$$

(22)

After deriving Equations (20)–(22), the Y-type impedance network of the line section in Figure 5 is equivalently transformed into a △-type impedance network, as shown in Figure 11. Through this impedance transformation, the coupling relationship between the load current path and the feed-in current is clarified.

According to impedance transformation, Equations (23) and (24) can be derived as follows:

$$Z_{\mathrm{MN}}=Z_{\mathrm{M}}+Z_{\mathrm{N}}+Z_{\mathrm{M}}{Z}_{\mathrm{N}}/R_{\mathrm{g}}$$

(23)

$${\stackrel{·}{I}}_{\mathrm{cy}1}=({\stackrel{·}{U}}_{\mathrm{M}}-{\stackrel{·}{U}}_{\mathrm{N}})/Z_{\mathrm{MN}}$$

(24)

From Equations (20)–(24), Equation (25) can be obtained.

$${\stackrel{·}{I}}_{\mathrm{cy}1}={\displaystyle \frac{({\stackrel{·}{U}}_{\mathrm{M}}-{\stackrel{·}{U}}_{\mathrm{N}})({\stackrel{·}{U}}_{\mathrm{M}}{\stackrel{·}{I}}_{\mathrm{M}1}+{\stackrel{·}{U}}_{\mathrm{N}}{\stackrel{·}{I}}_{\mathrm{N}1}-Z{\stackrel{·}{I}}_{\mathrm{M}1}{\stackrel{·}{I}}_{\mathrm{N}1})}{{\stackrel{·}{U}}_{\mathrm{M}}{\stackrel{·}{I}}_{\mathrm{M}1}Z+{\stackrel{·}{U}}_{\mathrm{N}}{\stackrel{·}{I}}_{\mathrm{N}1}Z-{({\stackrel{·}{U}}_{\mathrm{M}}-{\stackrel{·}{U}}_{\mathrm{N}})}^2}}$$

(25)

To suppress the interference of DC feed on the differential quantity and eliminate the masking effect of the load current in the braking quantity, this paper adopts the following strategy: remove the MMC injection current I_dc.M on the M side, add the DC system fault component I_dc.N on the N side, and subtract the post-DC-feed load current I_cy1 when constructing the new braking quantity. The modified action quantity, braking quantity, and protection criterion are presented in Equations (26) and (27):

$$\left\{\begin{array}{l}{I}_{\mathrm{d}3}=|({\stackrel{·}{I}}_{\mathrm{M}1}-{\stackrel{·}{I}}_{\mathrm{dc}.\mathrm{M}})+({\stackrel{·}{I}}_{\mathrm{N}1}+{\stackrel{·}{I}}_{\mathrm{dc}.\mathrm{N}})|=\left|{\stackrel{·}{I}}_{\mathrm{f}}\right|\\ I_{\mathrm{r}3}=|({\stackrel{·}{I}}_{\mathrm{M}1}-{\stackrel{·}{I}}_{\mathrm{de}.\mathrm{M}})-({\stackrel{·}{I}}_{\mathrm{N}1}+{\stackrel{·}{I}}_{\mathrm{de}.\mathrm{N}})-{\stackrel{·}{I}}_{\mathrm{cy}1}|=\left|k{\stackrel{·}{I}}_{\mathrm{f}}\right|\end{array}\right.$$

(26)

$$I_{\mathrm{d}3}>K{I}_{\mathrm{r}3}$$

(27)

where K is the braking coefficient, which is taken as 1.0 in this paper, and the improved I_d3 and I_r3 are applied in the main criterion. This value was selected based on extensive simulation trials to balance sensitivity and security. It ensures reliable operation for various fault resistances and fault locations while minimizing the risk of misoperation under external disturbances. While K is a fixed threshold in this work, it can be adapted in practical applications according to system conditions or online learning-based adjustments.

In summary, the differential current required on the M side is (I_M − I_dc.M); that is, the differential current required on the N side is (I_N + I_dc.N).

The overall decision-making logic of the proposed protection scheme is illustrated in Figure 12. The algorithm starts by sampling current signals from both ends, followed by dynamic decoupling processing. The calculated differential current I_d3 and restraining current I_r3 are then used to evaluate the criterion I_d3 > KI_r3. Based on the result, the scheme distinguishes internal and external faults and initiates a trip command if necessary.

5. Simulation Verification and Performance Evaluation of the Differential Protection Current Improvement Criterion Strategy

To verify the effectiveness and robustness of the proposed improved current-criterion differential protection strategy in complex power systems, this paper develops a simulation model of a multi-scenario hybrid multi-infeed system on MATLAB, covering various feed-in architectures such as AC, VSC, and MMC. By setting typical operating conditions—including phase A metallic grounding, high-resistance grounding, three-phase short circuits, and out-of-zone faults—the performance of the main and auxiliary criteria is systematically evaluated in terms of fault identification, false operation suppression, parameter sensitivity, and other aspects. Figure 12 and Figure 13 present the main simulation waveforms and criterion responses under different system scenarios.

5.1. Hybrid Multi-Infeed AC System 1

In the hybrid multi-infeed AC system 1 (M-side infeed: AC + VSC; N-side infeed: AC + MMC), the simulation verifies the adaptability of the proposed improved current-criterion differential protection strategy under typical internal and external fault conditions. Figure 13 presents the current waveforms and criterion responses for phase A metallic grounding, high-resistance grounding, three-phase short circuits, and external faults.

For the metal ground fault of phase A (Figure 13a), the simulation results show that under the condition of mixed feeding of AC, VSC, and MMC, the differential current can rise rapidly after the fault occurs, the braking current does not cause significant interference, and the action ratio stably crosses the judgment threshold, achieving fast and effective fault detection. In the high-resistance ground fault scenario (Figure 13b), although the fault current amplitude is weakened due to the large transition resistance, the proposed strategy can still maintain stable action characteristics and meet the sensitivity requirements by dynamically adjusting parameters and multi-feature discrimination.

For the three-phase short-circuit condition (Figure 13c), the differential current curves of each phase show high synchronization, and the action ratio curve does not show obvious phase-to-phase deviation, which verifies the multi-phase consistency of the strategy under symmetrical faults. In the out-of-zone fault scenario (Figure 13d), the feeding characteristics of the M and N sides in the simulation bring different current responses, but the braking current effectively suppresses the differential action ratio throughout the process, and no false operation occurs. This shows that the proposed criterion has good stability and selectivity under the AC + VSC and AC + MMC hybrid structures.

Overall, the simulation results for multi-infeed system 1 demonstrate that the improved full-current criterion strategy achieves fast and reliable fault detection as well as strong anti-false-operation capability in a typical AC–power electronics hybrid system, verifying the effectiveness of the proposed method.

5.2. Hybrid Multi-Infeed AC System 2

In the hybrid multi-infeed AC system 2 (M-side infeed: AC + VSC + MMC; N-side infeed: AC + MMC), the system exhibits more complex multi-infeed characteristics. Figure 14 presents the current waveforms and criterion responses under phase A metallic grounding, high-resistance grounding, three-phase short-circuit, and external faults.

In the A-phase metal grounding fault scenario (Figure 14a), since the M side contains AC, VSC, and MMC feeds at the same time, the system injects multiple frequency components and DC offsets. The simulation shows that the proposed criterion can effectively extract the main fault features under complex signal conditions and maintain stable fault detection capabilities. For high-resistance grounding faults (Figure 14b), although the large transition resistance causes the fault current amplitude to weaken, the criterion combines the dynamic adjustment mechanism with multi-feature discrimination and can maintain the action response under weak signal conditions, meeting the sensitivity requirements.

Under the three-phase short-circuit condition (Figure 14c), the differential current and action ratio curves maintain a high degree of synchronization as a whole, and each phase does not show significant deviation, which verifies the adaptability of the strategy under multi-phase fault conditions. In the out-of-zone fault scenario (Figure 14d), the current disturbance caused by the difference in the feed structure on the M and N sides did not cause the differential action ratio to exceed the limit, and the braking current played an effective inhibitory role, ensuring the ability of the criterion to resist false operation under complex topologies.

In summary, the simulation results for multi-infeed system 2 demonstrate that the proposed improved current-criterion differential protection strategy operates stably in complex, multivariate power electronic systems and exhibits strong adaptability to multi-frequency characteristics and asymmetric disturbances.

Through the simulation analysis of two types of hybrid multi-feed systems, it can be seen that the proposed improved current criterion differential protection strategy shows good action response, sensitivity, and selectivity under typical fault conditions. In the multi-electron power system containing VSC and MMC, the strategy can effectively extract the main fault characteristics, adapt to complex signal environments, and maintain action capabilities in weak signal scenarios such as high-resistance grounding. At the same time, under out-of-zone faults and high-power disturbances, the braking link can effectively suppress the differential ratio and avoid false operation.

5.3. Performance Comparison with Existing Methods

To provide a functional-level assessment of the proposed protection method, a comparison is made with representative schemes from the literature based on three key protection performance metrics: response time, sensitivity to high-resistance faults, and false tripping rate.

While each method is originally designed for different system configurations (e.g., bipolar DC, hybrid LCC-VSC, or MMC-based systems), this comparison focuses solely on their core protection capabilities under similar fault detection objectives. The aim is not to evaluate topological compatibility, but to highlight general advantages in terms of speed, sensitivity, and security for fault discrimination.

As shown in

Table 5. Functional performance comparison of DC protection methods.

Protection Method	Response Time (ms)	Sensitivity to High-Resistance Faults	False Tripping Rate
Proposed Method	~2.0	High	Low
Reference [7]	2.5–3.0	Low	Medium
Reference [9]	~1.8	Medium–High	Low
Reference [20]	2.5–3.0	Medium	Low

, the proposed method provides a favorable trade-off among speed, sensitivity, and security. It demonstrates fast operation, reliable performance under high-resistance fault conditions, and a low risk of false tripping, making it particularly well-suited for protection in DC multi-infeed systems.

Although this study is simulation-based, the proposed method is designed for engineering feasibility. It relies only on line-end current measurements and avoids high-frequency components or converter-side variables, making it suitable for implementation with existing protection hardware. Potential challenges such as measurement noise and communication delay can be mitigated through modal decomposition and appropriate filtering. The algorithm’s moderate computational complexity also allows for real-time embedding in practical relay platforms.

6. Conclusions

In this paper, an improved current differential protection strategy based on dynamic phasor analysis is proposed to solve the problem of insufficient adaptability of traditional AC differential protection in typical working conditions such as high-resistance grounding, symmetrical short circuits, and out-of-zone disturbances in hybrid multi-infeed systems, including AC power systems, VSCs, and MMCs. The main conclusions are as follows:

(1)

A simulation model covering multiple infeed architectures was developed, and the effects of converter dynamic characteristics, DC bias, and high-frequency harmonics on differential protection in a multi-infeed system were systematically analyzed.

(2)

An improved current differential criterion was proposed. By equivalently separating the DC injection and load current components and optimizing the calculation of the action and restraining quantities, the sensitivity and selectivity of differential protection under complex operating conditions were effectively enhanced.

(3)

Compared with existing schemes in [7,9], and [20], the proposed method introduces a fundamentally different approach by leveraging modal decomposition and current differential features. It achieves improved selectivity and robustness in multi-infeed topologies and high-resistance faults, with less reliance on high-frequency data or grounding mode assumptions. Simulation results indicate that the method responds within approximately 2.0 ms, maintains high sensitivity for high-resistance faults, and demonstrates a low false tripping rate across various external disturbance scenarios.

(4)

Simulation results show that the proposed strategy can quickly and accurately identify faults in typical scenarios such as high-resistance grounding, three-phase short circuits, and external faults, and exhibits strong robustness under complex injection conditions, outperforming the traditional current-criterion scheme.