Transient Voltage Support Strategy for Microgrids at the Distribution Network Edge Considering Cable Capacitance

Abstract

Microgrids are commonly connected through medium-voltage cables in coastal distribution networks and other microgrids. However, a faulted microgrid may increase the collapse risk if the supporting microgrids are disconnected due to voltage sags. Conventional voltage support methods, which primarily rely on the impedance characteristics of the transmission line, typically regulate the active-to-reactive current ratio (hereafter referred to as “current ratio”) to maximize positive sequence voltage while minimizing negative sequence voltage. Nevertheless, the distributed capacitance inherent in cables induces deviations in both the amplitude and phase of the transmitted current, while simultaneously intensifying the coupling between voltage and current. These effects complicate the voltage fluctuation behavior and impair the effectiveness of voltage support, thereby increasing the risk of disconnection and collapse for the faulted microgrid (hereafter referred to as “fault region”). To address this challenge, this study focuses on non-faulted microgrids (hereafter referred to as “microgrids”), proposing a method for active current correction and transient voltage support that considers the influence of cable distributed capacitance. By analyzing the voltage and current characteristics on both ends of the interconnecting cables, the method optimizes the current injection ratio. It mitigates deviation caused by cable capacitance effects, thereby enhancing the voltage support performance of the microgrid. Notably, the proposed method operates independently of real-time voltage and current measurements from the fault region, significantly reducing communication demands. Experimental results based on a practical microgrid validate the effectiveness of the proposed method, demonstrating a 27.9% improvement in voltage support performance compared to conventional methods.

1. Introduction

Modern distribution networks are undergoing a rapid transition driven by high penetration of distributed renewable energy and the increasing demand for resilient [1,2], flexible power supply architectures. As an offshore extension of the networks, microgrids rely mainly on local solar, wind, and marine resources, yet face challenges from harsh ocean environments and uneven resource distribution. Energy sharing and coordinated operation among neighboring islands therefore become essential to enhance efficiency and reliability. Cables, capable of continuous and dependable power transmission, enable such interconnections and are widely deployed on strategically important islands to support both civilian demand and critical operations [3,4].

While the interconnection structure of microgrids enhances the flexibility of energy deployment, it also allows the propagation of fault-induced disturbances from one microgrid to another through cables. Non-faulted microgrids (hereafter referred to as “microgrids”) are vulnerable to voltage sags and, in severe cases, may be forced to disconnect from the network. Concurrently, the faulted microgrid (hereafter referred to as “fault region”), which is deprived of external power support, increases the risk of collapse. Ensuring high-performance voltage support for microgrids is therefore essential to improving the reliability of the entire interconnected microgrid system [5,6].

However, the capacitive effect of cables presents a challenge to effective voltage support in microgrids. The charging current resulting from the cable’s distributed capacitance not only occupies part of the available transmission capacity for active current but also causes a portion of the injected current to be diverted into the capacitive branch during transmission [7,8]. This phenomenon leads to deviations in both current amplitude and phase. Although reactive power compensation is commonly implemented using static var generators or by increasing reactive current injection, these approaches function as limited-capacity reactive current sources [9,10]. And thus, they fall short in providing accurate compensation during fault conditions, particularly when rapid voltage fluctuation and surging current demands are present. Moreover, transient voltage fluctuations induce corresponding changes in capacitive current, thereby amplifying the deviations caused by capacitive effects. Under asymmetrical fault conditions, the capacitive voltage further intensifies the coupling between voltage and current, thereby complicating voltage regulation. The voltage support performance may deteriorate if the microgrid fails to inject current following the optimal active-to-reactive current ratio (hereafter referred to as the current ratio) [11,12,13,14]. Therefore, precise current injection and optimal voltage control are critical to enhancing voltage support performance in interconnected microgrids.

Due to the limited capacity of the microsources, the injected current can only be regulated within the maximum capacity constraint under severe fault conditions. Existing transient voltage support methods typically aim to optimize voltage by injecting coordinated positive and negative sequence currents tailored to the line parameters. These methods usually balance multiple objectives, including maximizing current injection, minimizing power oscillations, and enhancing power transfer efficiency [15,16,17,18]. For example, the method that dynamically adjusts the positive and negative sequence currents based on the depth of voltage sag can flexibly achieve objectives such as voltage support, current limitation, or power oscillation suppression [15]. To improve coordination among multiple parallel systems, the voltage recovery method calculates current references by considering the line impedance ratio and load composition [19]. Further advancements leverage the power balance characteristics of microgrids to formulate voltage support as a global optimization problem, facilitating the optimal allocation of current injections [20]. Based on this, some studies have modeled the voltage support task as a nonconvex optimization problem that can be solved in real time, thereby improving system responsiveness under complex fault scenarios [21,22]. In addition, several phase-voltage-based current injection methods have been proposed, which consider both phase voltage characteristics and fault types [23,24,25,26,27,28]. For example, by decomposing each phase current into active and reactive components, these methods enable precise adaptation to diverse voltage support requirements for different phases [29,30]. However, most of the methods mentioned above rely heavily on line impedance parameters. Although these methods can provide effective voltage support, they often neglect the influence of current deviations and voltage coupling effects introduced by the distributed capacitance of cables, resulting in suboptimal optimization performance.

To reduce reliance on line impedance information, some studies have proposed methods that allocate active and reactive currents by tracking the extremal points of microsource voltage and reactive current characteristics, without requiring data from the common connection point [31]. Other efforts have focused on mitigating overvoltage amplification by introducing an adaptive voltage sag coefficient, which can arise from delayed reactive current responses during abnormal voltage variations (e.g., from low to high voltage) [32]. Additionally, reactive current regulation factors based on voltage magnitude have been proposed, though their performance in different line impedance scenarios remains limited [33]. Further research has explored cooperative voltage support in parallel systems by constructing a system matrix and delineating feasible boundaries for positive and negative sequence reactive currents [34]. Despite these advancements, the core analytical frameworks of most methods remain fundamentally rooted in resistive–inductive line models, thereby constraining their support performance in systems with significant capacitive effects.

In summary, the existing transient voltage support methods are primarily designed for resistive, inductive, and resistive-inductive lines. However, the significant distributed capacitance of cables causes current deviation and intensifies the coupling between voltage and current, decreasing the voltage support performance of microgrids. To address this challenge, this paper proposes an active current correction and transient voltage support method for microgrids that considers the distribution capacitance effect of cables. The main contributions of this paper are as follows: (1) It reveals that under fault conditions, the voltage and current at both ends of a cable are influenced by voltage magnitude, active current, and reactive current, where reactive current losses and voltage phase shifts are identified as the principal causes of transmitted current deviation. (2) It constructs a local-port-based state estimation model that accurately calculates the voltage and current at the faulted microgrid terminal under non-communication conditions. (3) It introduces an active current correction strategy that relies solely on local measurements to eliminate current ratio deviations caused by cable capacitance, thereby ensuring the effectiveness of voltage support. (4) It proposes a transient voltage support method that achieves optimal voltage regulation, maximizing the utilization of the microgrid’s current capacity while minimizing the risk of disconnection under fault conditions.

2. Characterization of Microgrid Voltage and Current Coupling Under the Influence of Distributed Capacitance of Cable

To accurately describe voltage variations in microgrids interconnected via cables, this section employs two-port network theory to analyze the positive and negative sequence voltage characteristics under asymmetric fault conditions. By integrating the symmetrical component method with Park’s transformation, the analysis reveals the mechanisms through which current components and cable parameters affect the voltage amplitude of the microgrid.

2.1. Characterization of Positive-Sequence Voltage and Current Coupling of Microgrids

Based on the geographical resource distribution and engineering practices in the China Dawanshan Microgrid Demonstration Project, a representative topology of a microgrid interconnected via cables is illustrated in Figure 1, with the base voltage set to the rated line-to-line voltage of 10 kV and a rated apparent power of 15 MVA. The system comprises a variety of distributed energy sources, including photovoltaic arrays, wind turbines, and tidal energy devices—as well as diverse load categories such as seawater desalination systems, telecommunication base stations, and residential consumers. These renewable energy sources are typically located 2–4 km from the central control unit, while the interconnection cables span approximately 10–35 km. A communication system conforming to the IEC 61850 standard [35] is deployed to transmit fault-related information and dispatch control signals to the renewable energy units. The equivalent circuit model of the cable is also depicted in Figure 1, where Z_L and X_C represent the cable impedance and capacitive reactance, respectively; v₁ and v₂ represent the voltages of the microgrid and the fault region; and i₁ and i₂ represent the corresponding currents.

To establish a unified time-domain modeling framework compatible with converter-based control systems, the coupling relationship between voltage and current is derived by taking v₂ as the reference point and combining the symmetrical component method with Park’s transformation, as expressed in (1). The resulting dq-domain formulation enables direct integration with the inner current control loops and transient control strategies of power electronic converters, which is essential for the proposed transient voltage support strategy. In this formulation, $I_{2p}^{+}$ and $I_{2q}^{+}$ represent the positive-sequence active and reactive currents injected into the fault region, $I_{2p}^{-}$ and $I_{2q}^{-}$ represent the corresponding negative-sequence components, R_L, X_L, and Xc represent the resistance, inductive reactance, and capacitive reactance of the cable, respectively.

$$\left\{\begin{array}{l}{\dot{v}}_1^{+}=\left(1+{\displaystyle \frac{X_L}{X_C}}\right)v_2^{+}+R_L{I}_{2p}^{+}-X_L{I}_{2q}^{+}+j\left(-{\displaystyle \frac{R_L}{X_C}}{v}_2^{+}+X_L{I}_{2p}^{+}+R_L{I}_{2q}^{+}\right)\\ {\dot{v}}_1^{-}=\left(1+{\displaystyle \frac{X_L}{X_C}}\right)v_2^{-}-R_L{I}_{2p}^{-}-X_L{I}_{2q}^{-}-j\left(-{\displaystyle \frac{R_L}{X_C}}{v}_2^{-}-X_L{I}_{2p}^{-}+R_L{I}_{2q}^{-}\right)\end{array}\right.$$

(1)

Unlike resistive-inductive transmission lines, a voltage sag at the end of a cable induces not only a reduction in the longitudinal component of the sending-end voltage but also a variation in its transverse component. Existing transient voltage support strategies primarily focus on regulating the voltage amplitude. However, variations in the transverse component impose additional requirements on their implementation.

According to the monotonicity analysis, the relationship between voltage amplitude variation and current components can be quantitatively described by (2) to (7). As indicated by (2), the boundary value of $I_{2p}^{+}$ can be derived as shown in (4). When the amplitude of $I_{2p}^{+}$ exceeds this boundary, further increases in $I_{2p}^{+}$ will raise the positive-sequence voltage, with the enhancement becoming more pronounced as the deviation from the boundary grows. Conversely, when the amplitude falls below the boundary, the voltage support performance similarly intensifies with increasing deviation. This behavior also applies to $I_{2q}^{+}$, whose boundary value is shown in (5).

$${\displaystyle \frac{d{v}_1^{+}}{d{I}_{2p}^{+}}}={\displaystyle \frac{v_2^{+}+\left(R_L^2+X_L^2\right)I_{2p}^{+}}{\sqrt{{\left(\left(1+\frac{X_L}{X_C}\right)v_2^{+}+R_L{I}_{2p}^{+}-X_L{I}_{2q}^{+}\right)}^2+{\left(-\frac{R_L}{X_C}{v}_2^{+}+X_L{I}_{2p}^{+}+R_L{I}_{2q}^{+}\right)}^2}}}$$

(2)

$${\displaystyle \frac{d{v}_1^{+}}{d{I}_{2p}^{+}}}={\displaystyle \frac{-\left(X_L+\frac{X_L^2+R_L^2}{X_C}\right)v_2^{+}+\left(R_L^2+X_L^2\right)I_{2q}^{+}}{\sqrt{{\left(\left(1+\frac{X_L}{X_C}\right)v_2^{+}+R_L{I}_{2p}^{+}-X_L{I}_{2q}^{+}\right)}^2+{\left(-\frac{R_L}{X_C}{v}_2^{+}+X_L{I}_{2p}^{+}+R_L{I}_{2q}^{+}\right)}^2}}}$$

(3)

$${\mu }_{2p}^{+}=-{\displaystyle \frac{R_L}{R_L^2+X_L^2}}{v}_2^{+}$$

(4)

$${\mu }_{2q}^{+}=\left({\displaystyle \frac{1}{X_C}}+{\displaystyle \frac{X_L}{R_L^2+X_L^2}}\right)v_2^{+}$$

(5)

Notably, these two boundary values vary with both the voltage magnitude and the length of the cable, as described in (6) to (7) and illustrated in Figure 2, where d denotes the length of the cable, and r_c, x_Lc, and x_c represent its per-unit-length resistance, inductive reactance, and capacitive reactance, respectively. Under a fixed voltage condition, an increase in cable length leads to a gradual rise in the boundary value of the positive-sequence active current, whereas the boundary of the positive-sequence reactive current decreases.

$${\mu }_{2p}^{+}=-{\displaystyle \frac{1}{d}}{\displaystyle \frac{r_c}{r_c^2+x_{Lc}^2}}{v}_2^{+}$$

(6)

$${\mu }_{2q}^{+}=\left(d{\displaystyle \frac{1}{x_{Cc}}}+{\displaystyle \frac{1}{d}}{\displaystyle \frac{x_{Lc}}{r_c^2+x_{Lc}^2}}\right)v_2^{+}$$

(7)

2.2. Characterization of Negative-Sequence Coupling Island Voltage-Current in Microgrids

Like the positive-sequence current, the negative-sequence current also exhibits a boundary that varies with the magnitude of the negative-sequence voltage and the length of the cable, as described in (8) and illustrated in Figure 3. However, it should be noted that, unlike the enhancement of positive-sequence voltage, where significant deviation from the boundary improves support performance, the effective suppression of the negative-sequence voltage under fault conditions typically requires both the negative-sequence active and reactive currents to approach their respective boundary values.

$$\left\{\begin{array}{l}{\mu }_{2p}^{-}={\displaystyle \frac{1}{d}}{\displaystyle \frac{r_c}{r_c^2+x_{Lc}^2}}{v}_2^{-}\\ {\mu }_{2q}^{-}=\left(d{\displaystyle \frac{1}{x_{Cc}}}+{\displaystyle \frac{1}{d}}{\displaystyle \frac{x_{Lc}}{r_c^2+x_{Lc}^2}}\right)v_2^{-}\end{array}\right.$$

(8)

The above analysis indicates that, in cable-interconnected systems, voltage support methods in microgrids must be optimized not only based on line parameters but also with consideration of the phase shifts induced by voltage amplitude variations. During this process, both positive and negative sequence current injections are dynamically constrained by their corresponding boundary conditions. To achieve effective voltage amplitude regulation, positive sequence voltage support can be improved by injecting positive sequence currents that significantly deviate from their boundary values. In contrast, suppressing negative sequence voltage requires precise injection of negative sequence active and reactive currents that closely match their dynamic boundaries.

3. Voltage and Current Estimation Model of the Fault Region Under the Influence of Distributed Capacitance of the Cable

Accurate current injection is critical for the effective implementation of transient voltage support strategies. However, the significant distributed capacitance of cables introduces current deviation and amplifies the phase difference between the sending and receiving end voltages. Without real-time information from the fault region, microgrids may inject currents that diverge from the actual fault region inflow, thereby degrading voltage support performance. To address this challenge while minimizing communication requirements, this section conducts a comprehensive analysis of current variation characteristics at both ends of the cable. Based on this analysis, a voltage and current estimation model is developed to calculate the electrical state of the fault region using local port measurements from the non-faulted microgrid.

3.1. Characterization of the Variation in Injected Currents in the Microgrid

By applying the symmetrical component method and Park transformation, the current flowing into the fault region through the cable can be derived, as expressed in (9) and (10). The trend of the current deviation is illustrated in Figure 4, where the vertical axis represents the deviation across the cable, defined as ΔI₂ = I₂ − I₁, with I₁ and I₂ denoting the sending-end and receiving-end currents, respectively.

$$\left\{\begin{array}{l}{I}_{2p}^{+}={\displaystyle \frac{R_L}{X_C^2}}{v}_1^{+}+\left(1-{\displaystyle \frac{X_L}{X_C}}\right)I_{1p}^{+}-{\displaystyle \frac{R_L}{X_C}}{I}_{1q}^{+}\\ I_{2q}^{+}=-\left({\displaystyle \frac{2}{X_C}}-{\displaystyle \frac{X_L}{X_C^2}}\right)v_1^{+}-{\displaystyle \frac{R_L}{X_C}}{I}_{1p}^{+}+\left(1-{\displaystyle \frac{X_L}{X_C}}\right)I_{1q}^{+}\end{array}\right.$$

(9)

$$\left\{\begin{array}{l}{I}_{2p}^{-}=-{\displaystyle \frac{R_L}{X_C^2}}{v}_1^{-}+\left(1-{\displaystyle \frac{X_L}{X_C}}\right)I_{1p}^{-}+{\displaystyle \frac{R_L}{X_C}}{I}_{1q}^{-}\\ I_{2q}^{-}=-\left({\displaystyle \frac{2}{X_C}}-{\displaystyle \frac{X_L}{X_C^2}}\right)v_1^{-}+{\displaystyle \frac{R_L}{X_C}}{I}_{1p}^{-}+\left(1-{\displaystyle \frac{X_L}{X_C}}\right)I_{1q}^{-}\end{array}\right.$$

(10)

As shown in Figure 4, the distributed capacitance of the cable significantly affects the magnitude and phase of the current flowing into the fault region. Specifically, the current entering the fault region is influenced not only by the active and reactive components injected from the microgrid but also by voltage fluctuations along the cable. For example, in a 35 kV system using a cable with a distributed capacitance of 6 μF, the equivalent capacitive reactance X_C is approximately 0.53 × 10³ Ω. Under this condition, a voltage variation of 0.2 p.u. can induce a reactive current deviation of 26.3 A, which corresponds to approximately 16% of the rated current in a 10 MVA system. This deviation significantly impairs current transmission accuracy and compromises the effectiveness of transient voltage support methods. Therefore, accounting for the impact of distributed capacitance is essential for precise current regulation and high-performance voltage support during fault conditions.

3.2. Voltage and Current Estimation Model for Fault Region

The previous analysis reveals that the current flowing into the fault region is influenced by multiple factors. Furthermore, from the perspective of the fault region, the reference point of the inflow current shifts from v₁ (microgrid voltage) to v₂ (fault region voltage), resulting in a change in the ratio and phase of current.

By reapplying the symmetrical component method and Park transformation, the amplitude and phase of v₂ relative to the reference point v₁ can be derived as expressed in (11) and (12). The actual current flowing into the fault region can be calculated from (13) and (14), and the detailed derivation process is shown in Appendix A.

In summary, substantial discrepancies can arise between the sending-end and receiving-end currents of a cable due to distributed capacitance effects, especially under transient voltage disturbances. To address this challenge, this section develops voltage and current estimation models for the fault region using locally measured data from the microgrid. The proposed models, represented by Equations (11)–(14), enable real-time estimation of fault-region electrical states and serve as the theoretical foundation for the implementation of the subsequent current active correction and transient voltage support methods.

$$\left\{\begin{array}{l}{v}_2^{+}=\sqrt{{\left(\left(1-{\mu }_1\right)v_1^{+}-R_L{I}_{1p}^{+}+X_L{I}_{1q}^{+}\right)}^2+{\left({\mu }_2{v}_1^{+}-X_L{I}_{1p}^{+}-R_L{I}_{1q}^{+}\right)}^2}\\ v_2^{-}=\sqrt{{\left(\left(1-{\mu }_1\right)v_1^{-}+R_L{I}_{1p}^{-}+X_L{I}_{1q}^{-}\right)}^2+{\left({\mu }_2{v}_1^{-}+X_L{I}_{1p}^{-}-R_L{I}_{1q}^{-}\right)}^2}\end{array}\right.$$

(11)

$$\left\{\begin{array}{l}{\delta }_2^{+}=\arctan \left({\displaystyle \frac{{\mu }_2{v}_1^{+}-X_L{I}_{1p}^{+}-R_L{I}_{1q}^{+}}{\left(1-{\mu }_1\right)v_1^{+}-R_L{I}_{1p}^{+}+X_L{I}_{1q}^{+}}}\right)\\ {\delta }_2^{-}=\arctan \left(-{\displaystyle \frac{{\mu }_2{v}_1^{-}+X_L{I}_{1p}^{-}-R_L{I}_{1q}^{-}}{\left(1-{\mu }_1\right)v_1^{-}+R_L{I}_{1p}^{-}+X_L{I}_{1q}^{-}}}\right)\end{array}\right.$$

(12)

$$\left\{\begin{array}{l}{I}_{2p\_real}^{+}=\sqrt{{\left(I_{2p}^{+}\right)}^2+{\left(I_{2q}^{+}\right)}^2}\cos \left({\alpha }_{2\_real}^{+*}\right)\\ I_{2q\_real}^{+}=\sqrt{{\left(I_{2p}^{+}\right)}^2+{\left(I_{2q}^{+}\right)}^2}\sin \left({\alpha }_{2\_real}^{+*}\right)\end{array}\right.$$

(13)

Like the positive sequence current, the negative sequence current can be calculated by (14).

$$\left\{\begin{array}{l}{I}_{2p\_real}^{-}=\sqrt{{\left(I_{2p}^{-}\right)}^2+{\left(I_{2q}^{-}\right)}^2}\cos \left({\alpha }_{2\_real}^{-*}\right)\\ I_{2q\_real}^{-}=-\sqrt{{\left(I_{2p}^{-}\right)}^2+{\left(I_{2q}^{-}\right)}^2}\sin \left({\alpha }_{2\_real}^{-*}\right)\end{array}\right.$$

(14)

4. Transient Voltage Support Method for Microgrid Based on Current Correction Mechanism

To enable precise current regulation in microgrids, this section proposes a transient voltage support method that integrates a current active correction mechanism. The strategy is based on compensating for the deviation in the active-to-reactive current ratio caused by the distributed capacitance of cables. In parallel, the optimal current injection ratio for voltage regulation is derived to ensure the effective implementation of the voltage support.

4.1. Current Active Correction Strategy Based on Ratio Offset

As analyzed in the previous section, the distributed capacitance of cables causes a significant discrepancy between the current at the sending and receiving ends. To address this issue, the proposed correction strategy first defines reference values for the positive- and negative-sequence current ratios based on the commanded current. At the same time, the actual active and reactive components of the positive- and negative-sequence currents flowing into the fault region are estimated in real time using Equations (13) and (14). By comparing these estimated values with their respective references, deviations arising from both the capacitive effects and the shift in the current reference point, from v₁ to v₂, can be identified. These deviations are then fed back into the current control loop, enabling real-time correction of the injected current to the desired current ratio. The operating principle of the proposed current correction strategy is illustrated in Figure 5, where 1/S denotes the integration loop.

4.2. Positive and Negative Sequence Current Injection Strategies for Maximizing Voltage Support

Under fault conditions, the ideal transient voltage support strategy should aim to simultaneously enhance the positive sequence voltage and suppress the negative sequence voltage while remaining within the system’s maximum current capacity constraint. Achieving this objective requires coordinated allocation of both active and reactive current components. The corresponding optimization control objective is formulated in (15).

$$\left\{\begin{array}{l}\max v_1^{+}\left(I_{2p}^{+},I_{2q}^{+}\right)\& \min v_1^{-}\left(I_{2p}^{-},I_{2q}^{-}\right)\\ subject\hspace{0.33em}to:\max \left(I_{\mathrm{a}},I_{\mathrm{b}},I_{\mathrm{c}}\right)\le I_{\lim }\end{array}\right.$$

(15)

This problem constitutes a typical multivariable extremum optimization, which can be solved using the Lagrange multiplier method. The detailed derivation is provided in Appendix B. The ratio of positive-sequence current $k_{por2}^{+}$ for maximizing voltage support can be derived as:

$$k_{por2}^{+}=-{\displaystyle \frac{X_L\left(1+{\mu }_1\right)+R_L{\mu }_2}{\left(R_L\left(1+{\mu }_1\right)-X_L{\mu }_2\right)}}$$

(16)

Following a similar analytical procedure, the optimal injection ratio for the negative sequence current can also be derived as:

$$k_{por2}^{-}=-{\displaystyle \frac{\left(1+{\mu }_1\right)X_L+{\mu }_2{R}_L}{X_L{\mu }_2-\left(1+{\mu }_1\right)R_L}}$$

(17)

As indicated by (16) and (17), these optimal ratios differ from the conventional L/R ratios typically applied in inductive lines. The voltage support performance can be improved by integrating these optimal injection ratios with the current correction strategy proposed in the previous subsection. The control workflow, which combines current correction and optimal current injection, is illustrated in Figure 6.

4.3. Control Structure of Current Active Correction and Transient Voltage Support Method

Based on the above analysis, the control architecture of the proposed transient voltage support method based on current correction is illustrated in Figure 7. Upon detection of a fault in a neighboring microgrid, the reference values for the current injection ratio are calculated using (16) and (17), and voltage references are set along with the corresponding current ratio according to the positive and negative sequence voltage objectives outlined in [19]. Subsequently, using locally measured voltage and current data at the point of interconnection, the current flowing into the fault region is estimated in real time by (13) and (14). Any deviation between this estimated value and the predefined current ratio reference is then fed back into the current control loop, enabling real-time ratio correction of the injected current ratio. If a specific current demand is received from the fault region, the control strategy switches to the correction mode in which the microgrid adjusts its output to inject the commanded current accordingly. These current commands are then dispatched to the respective microsources for coordinated execution. It is important to note that the implementation of this method requires a fault location detection unit to be deployed at the interconnection point. This unit is activated exclusively when a fault is detected in a neighboring microgrid, thereby preventing erroneous operation in the event of faults occurring within the cable itself.

5. Case Study

To validate the effectiveness of the method proposed, a real-time simulation model is developed in RT-LAB to simulate the operating environment of the practical microgrid, as illustrated in Figure 8. The maximum allowable peak current is constrained to 1.0 p.u., and the system parameters are detailed in

Table 1. Parameters of the microgrid.

Symbol	Variable	Value
Vg	Rated voltage for microgrids	10.5 kV
SDG1	Rated Capacity of Tidal Energy	3 MVA
SDG2	Rated Capacity of Wind Turbine	8 MVA
SDG3	Rated Capacity of Photovoltaic	2 MVA
SDG4	Rated Capacity of Energy Storage	2 MVA
ZCab	Resistance of Cable	0.02 Ω/km
	Inductance of Cable	0.38 mH/km
	Capacitance of Cable	0.27 μF/km

.

5.1. Estimation of Fault Region Information and Validation of Current Active Correction Strategy

This subsection first verifies the accuracy of voltage and current estimation for the fault region, followed by the current ratio correction. Typical regression evaluation indexes, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE), are selected for estimation accuracy, as expressed in (18) to (20).

$$\mathrm{MSE}={\displaystyle \frac{1}{m}}{{\displaystyle \sum _{i=1}^m\left(y_i-{\widehat{y}}_i\right)}}^2$$

(18)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{m}}{{\displaystyle \sum _{i=1}^m\left(y_i-{\widehat{y}}_i\right)}}^2}$$

(19)

$$\mathrm{MAE}={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m\left|y_i-{\widehat{y}}_i\right|}$$

(20)

(1)

Verification of Voltage and Current Estimation Accuracy

For this validation, the injected currents are configured as follows: I_p⁺ = 0.1 p.u., I_q⁺ = −0.2 p.u., I_p⁻ = −0.1 p.u., I_q⁻ = −0.2 p.u. A single-phase grounding fault occurs in the fault region. The fault-region voltage and current are subsequently estimated and compared against direct measurements. Following the fault event, the voltage and current at the faulted microgrid terminal are estimated using (10) and (11) for voltage and (13) and (14) for current, respectively. The simulation results are shown in Figure 9 and Figure 10. The results confirm that both the magnitude and phase of the fault region voltage estimated by the proposed model exhibit a high degree of consistency with the measured values. Similarly, the current estimates closely match the waveform in the simulation, with statistical results shown in

Table 2. Evaluation of fault voltage and current calculation errors of the fault region.

Variant	MSE/10−3	RMSE	MAE
$V_2^{+}$/p.u.	0.67	0.02	0.01
$V_2^{-}$/p.u.	0.88	0.03	0.01
${\delta }_2^{+}$/rad	0.09	0.009	0.005
${\delta }_2^{-}$/rad	0.21	0.01	0.007
$I_{2\mathrm{p}}^{+}$/p.u.	2.90	0.05	0.03
$I_{2\mathrm{q}}^{+}$/p.u.	5.74	0.24	0.08
$I_{2\mathrm{p}}^{-}$/p.u.	1.90	0.04	0.03
$I_{2\mathrm{q}}^{+}$/p.u.	4.14	0.20	0.08

. These findings validate the accuracy of the proposed voltage and current estimation model, thereby establishing a robust foundation for the implementation of the current active correction strategy.

(2)

Validation of Current Active Correction Strategy

To further validate the effectiveness of the proposed current correction strategy, the test scenarios are configured as outlined in

Table 3. Active current correction test scenario setting.

Fault Conditions		Microgrid Injection Current
Parameters	Value	Parameters	Value	Current Ratio
$V_2^{+}$/p.u.	0.93	$I_{\mathrm{p}}^{+}$/p.u.	0.025	$k_{\mathrm{set}}^{+}=-10$
$V_2^{-}$/p.u.	0.06	$I_{\mathrm{q}}^{+}$/p.u.	−0.25
${\delta }_2^{+}$/°	0	$I_{\mathrm{p}}^{-}$/p.u.	−0.025	$k_{\mathrm{set}}^{-}=10$
${\delta }_2^{-}$/°	180	$I_{\mathrm{q}}^{-}$/p.u.	−0.25

, where $k_{\mathrm{set}}^{+}$ and $k_{\mathrm{set}}^{-}$ represent the desired current ratios of the fault region. The corresponding simulation results are shown in Figure 11, Figure 12 and Figure 13. Specifically, Figure 11 and Figure 12 demonstrate the currents of the microgrid injected and flowing into the fault region, while Figure 13 shows the variation in the current ratio flowing into the fault region.

As seen in Figure 11, following the activation of the current correction, the injected currents are adjusted to I_p⁺ = 0.214 p.u., I_q⁺ = −0.13 p.u., I_p⁻ = −0.06 p.u., I_q⁻ = −0.245 p.u. Figure 12 and Figure 13 further demonstrate that the current ratio k₁⁺ flowing into the fault region is successfully corrected from an initial value of −265 to a target value of −10, while k₁⁻ is adjusted from an initial value of 19.5 to 10. Notably, the initial deviation in the positive-sequence current ratio is more pronounced than that of the negative-sequence current, primarily due to the higher amplitude of the positive-sequence voltage. This observation is consistent with the theoretical predictions derived from (13) and (14).

Overall, these results confirm that the proposed current correction strategy effectively mitigates the current ratio deviations induced by the distributed capacitance of the cable. This capability provides a technical foundation for the reliable implementation of the subsequent transient voltage support method.

5.2. Validation of the Transient Voltage Support Method

To verify the effectiveness of the proposed transient voltage support method, this subsection examines its effectiveness under various fault scenarios and compares it with conventional voltage support methods. When the voltage drop at the contact port is monitored to be lower than 0.8 p.u. and the fault location unit identifies the fault within the neighboring microgrids, the microgrid activates the transient voltage support method. Three representative fault scenarios are considered: Case 1: a single-phase ground fault occurs in the faulty microgrid; Case 2: a two-phase ground fault occurs in the microsource of the faulty microgrid; and Case 3: a phase-to-phase short-circuit fault occurs in the fault region. Simulation results for the three cases are presented in Figure 14, Figure 15 and Figure 16.

(1)

Verification of Voltage Support Performance under Different Fault Conditions

(a)

Case 1: Single-phase ground fault occurs in the fault microgrid

In this scenario, the positive-sequence voltage of the microgrid drops to 0.649 p.u., while the negative-sequence voltage rises to 0.312 p.u. As shown in Figure 14, the proposed method adjusts the injected current components to I_p⁺ = 0.16 p.u., I_q⁺ = −0.46 p.u., I_p⁻ = −0.06 p.u., I_q⁻ = −0.48 p.u., aiming to enhance the positive-sequence voltage and suppress the negative-sequence component simultaneously. Following support, the positive sequence voltage increases to 0.704 p.u., while the negative sequence voltage is reduced to 0.260 p.u. And the positive and negative sequence current ratios are k₁⁺ = −2.8 and k₁⁻ = 8, respectively.

Whereas the theoretical values derived from (16) and (17) are $k_{\mathrm{opt}}^{+}$ = −5.9 and $k_{\mathrm{opt}}^{-}$ = 5.9. The deviation is attributed to the influence of voltage amplitude changes and the implementation of the current correction strategy, which adjusts the injected current based on local port measurements to ensure effective voltage support.

(b)

Case 2: Two-phase ground fault occurs in the fault microgrid

In Case 2, the positive sequence voltage of the microgrid drops to 0.333 p.u., while the negative sequence voltage increases to 0.321 p.u. As shown in Figure 15, the microgrid responds by injecting current components of I_p⁺ = 0.12 p.u., I_q⁺ = −0.48 p.u., I_p⁻ = −0.02 p.u., I_q⁻ = −0.49 p.u. This current injection elevates the positive-sequence voltage to 0.405 p.u. and suppresses the negative-sequence voltage to 0.271 p.u. The corresponding current ratios are k₁⁺ = −4 and k₁⁻ = 25, respectively, which again differ from theoretical values due to the voltage-dependent behavior of current deviation and the correction strategy applied. These results highlight the influence of fault characteristics on system response and correction behavior.

(c)

Case 3: Phase-to-phase short-circuit fault in the fault microgrids

In Case 3, the positive-sequence voltage of the microgrid drops to 0.531 p.u., while the negative-sequence voltage rises to 0.518 p.u. As shown in Figure 16, the injected current components are: I_p⁺ = 0.14 p.u., I_q⁺ = −0.48 p.u., I_p⁻ = −0.02 p.u., I_q⁻ = −0.49 p.u. Following current injection, the positive-sequence voltage recovers to 0.595 p.u., while the negative-sequence voltage decreases to 0.479 p.u. The resulting current ratios are k₁⁺ = −3.4 and k₁⁻ = 25, which again deviate from the theoretically calculated values, as well as the rest of the fault conditions.

These results collectively confirm the adaptability of the proposed transient voltage support method across diverse fault scenarios, validating its practical applicability in cable-interconnected microgrids.

(2)

Comparison with Other Methods

To further demonstrate the advantages of the proposed method, its performance is compared with several representative transient voltage support methods under a single-phase ground fault scenario, as summarized in

Table 4. Operating conditions of microgrids under different voltage support strategies.

Methods	Ip+ (p.u.)	Iq+ (p.u.)	Ip− (p.u.)	Iq− (p.u.)	V+ (p.u.)	V− (p.u.)
Fault State	0	0	0	0	0.649	0.312
GC	0	−0.50	0	0.50	0.681	0.279
OVS	0.08	−0.48	0.08	0.48	0.692	0.267
MOVS	0.08	−0.48	0.04	0.24	0.692	0.267
Proposed Method	0.16	−0.23	0.06	0.48	0.704	0.267

, including OVS [13], MOVS [19], and GC [29,30].

The GC method regulates positive and negative sequence currents based on voltage magnitude. However, it primarily relies on reactive current injection, without explicitly optimizing the active component. Under the constraint that the injected current does not exceed the maximum allowable value I_max, the GC method achieves a 0.032 p.u. improvement in positive sequence voltage and a suppression of 0.033 p.u. in negative sequence voltage.

In contrast, both OVS and MOVS strategies optimize the magnitude and distribution of sequence currents based on the impedance angle L/R ≈ 5.9. As shown in the third and fourth rows of Table IV, these methods achieve improved performance, with an increase of 0.043 p.u. in positive sequence voltage and a reduction of 0.044 p.u. in negative sequence voltage, while still within the current limit I_max.

The proposed method achieves further improvement in voltage support by explicitly incorporating the effect of the cable’s distributed capacitance in both the current correction and the optimization. Under the same current limit I_max, it achieves a positive sequence voltage rise of 0.055 p.u., representing a 27.9% improvement over existing methods. Meanwhile, the suppression of negative sequence voltage remains at 0.044 p.u., which is comparable to the other approaches. This slight discrepancy is attributed to the limited adjustment range of the negative-sequence current, which is constrained by system capacity and fault characteristics.

It is important to note that the microgrid simulated in this study has a rated capacity of 15 MW. In larger capacity systems, the improvement in voltage support will be more significant. According to international low-voltage ride-through standards, such as IEEE 1547-2018, Canadian C22.3 No.9 (R2015), German VDE-AR-N 4110, and Chinese GB/T 33593-2017 and GB/T 19963.1-2021 [36,37,38,39,40], a voltage lift of 0.06 p.u. can extend grid-connection retention by approximately 100 ms, offering substantial potential for practical engineering applications.

Moreover, microgrids are typically more vulnerable to voltage sags than frequency disturbances. While microsources equipped with fault ride-through capability can mitigate frequency deviations using integral control, their limited capacity restricts their ability to effectively restore fault voltage. Therefore, the interconnection capability of the microgrid discussed in this paper prioritizes voltage support characteristics over frequency regulation.

6. Conclusions

This paper addresses the challenge posed by the distributed capacitance of cables, which causes current deviation across the cable ends and intensifies the coupling between voltage and current. These effects significantly diminish the voltage support capability of microgrids during transient disturbances. To mitigate this issue, a transient voltage support method based on active current correction is proposed. This method corrects current ratio deviations and analyzes voltage-current coupling effects, thereby maximizing the effectiveness of voltage support.

Simulation results based on a realistic microgrid verify the robustness and effectiveness of the proposed method under various fault scenarios. The voltage support is improved by approximately 27.9% compared with conventional approaches. Importantly, the method does not rely on real-time fault region information, which significantly reduces the communication burden and enhances the autonomy and operational reliability of the microgrid. These features make the proposed approach well-suited for practical deployment in remote or communication-constrained marine energy systems.