Voltage-Current Curve-Based Line Protection for Renewable Energy Systems with Grid-Forming Inverters

1. Introduction

The rapid integration of renewable energy resources is changing power systems from synchronous-generator-dominated networks to networks with high shares of inverter-based resources [1,2,3]. During faults, these resources exhibit nonlinear and time-varying voltage, current, and impedance characteristics that differ from those of synchronous machines [4,5,6,7]. Grid-forming converters are especially important because they can provide fast power support, flexible regulation, and stronger support for weak grids. However, their fault response is governed by power-electronic hardware and control strategies. Current limiting, nonlinear transients, and weakened fault-current contribution make conventional relay protection less dependable and impose stricter requirements on protection speed, reliability, and selectivity.

Existing studies have addressed the reduced adaptability of transmission-line protection in grid-forming-resource systems from several perspectives. One approach is to design protection criteria from source-side fault-response features. Reference [8] combined an IIRES current-control strategy with distance protection to improve line protection for asymmetric faults in renewable-energy integration scenarios. Reference [9] analyzed protection behavior using the dynamic characteristics of fault current-limiting control and showed that control strategies strongly affect current output during faults. Reference [10] proposed an iterative short-circuit current calculation method that accounts for the voltage-controlled current-source characteristics of renewable energy resources. Reference [11] analyzed current phase characteristics on both sides of a photovoltaic transmission line and proposed a longitudinal protection method based on the Dice similarity coefficient. These methods improve fault discrimination by exploiting renewable-energy fault responses, but their performance remains closely tied to control strategies, current-limiting methods, and fault ride-through behavior. When the source operating mode or control parameters change, their adaptability still requires further validation.

A second research direction is to enhance fault detectability through active signal injection. Reference [12] identified fault zones in DC grids by injecting sinusoidal test signals of different frequencies through converters and analyzing the resulting response differences. Reference [13] proposed an impedance-phase-based active-injection method for radial VSC-HVDC grids, in which frequency-specific post-fault signals are used to determine whether the fault is inside or outside the protected zone. Although active-injection methods can create new discriminative features, they usually require additional signal sources or supplementary control loops. This increases hardware cost and complicates coordinated control-protection design. A third class of methods seeks criteria that are less sensitive to source characteristics. Reference [14] used line-parameter identification and fault-component information to reduce the impact of source-side fault variations. Reference [15] proposed a distance backup protection scheme based on a steady-state DC line model, and Reference [16] used early-fault information for parameter-identification-based distance protection of AC transmission lines. These methods reduce dependence on source-side fault output, but they often require accurate circuit models, high-quality sampling data, iterative solutions, differential calculations, or simplified line models. These requirements can slow the response and make engineering implementation more complex.

Although parameter-identification methods are relatively robust to source-side variations, iterative computation and simplified line modeling can still limit protection speed and reliability. To overcome these limitations, this paper proposes a three-dimensional voltage-current coupling characteristic curve (UIC) representation constructed from voltage and current measurements at both line terminals. The UIC shape features reflect changes in line topology and parameters. An ellipsoidal feature space is then established for normal operation and external faults using sample statistics, and internal faults are identified by comparing the measured UIC feature vector with this feature space. The proposed scheme is verified through PSCAD simulations. Because the criterion is based on line topology and terminal coupling features, it does not depend on the fault output characteristics of grid-forming resources and avoids complex iterative computation.

2. The Impact of Grid-Forming Power Sources on Traditional Protection Systems

2.1. Fault Control Strategies for Grid-Forming Power Sources

The objective of grid-forming control is to make the converter behave as a voltage source during grid-connected operation, in a manner similar to a synchronous machine. The converter can autonomously establish terminal-voltage magnitude and phase instead of relying on the external grid voltage for lock-in synchronization. A typical grid-forming controller contains an outer loop and an inner loop. The outer loop generates voltage-magnitude, frequency, or phase references, while the inner loop regulates voltage and current according to these references and produces drive signals through the PWM stage [17]. Figure 1 shows the basic structure of a grid-forming power source. Point P denotes the equivalent grid-connection point, θ is the voltage phase reference, $U_m^{*}$ is the reference voltage amplitude, and $U_{abc}^{*}$ is the three-phase voltage modulation waveform.

Grid-forming power sources commonly use droop control, virtual synchronous generator control, or synchronous power control to establish the outer-loop dynamics. Droop control emulates primary frequency and voltage regulation through active-power-frequency and reactive-power-voltage characteristics. Virtual synchronous generator control adds inertia and damping to improve dynamic support under disturbances. The power loop generates a frequency or phase reference, which is integrated to obtain θ. At the same time, the voltage loop produces the voltage reference $U_m^{*}$. Together with the inner voltage and current loops, this reference regulates the common-coupling-point voltage. As a result, the grid-forming source exhibits the external behavior of a voltage source with controlled impedance during steady-state operation.

2.2. Impact of Grid-Forming Power Sources on Traditional Protection Methods

Grid-forming power sources establish terminal voltages actively through control methods such as droop control and virtual synchronous generator control. Their output can therefore be represented equivalently as a controlled voltage source in series with a virtual impedance. Unlike conventional synchronous sources, grid-forming sources usually apply current-limiting and voltage-support control during faults. The amplitude, phase, and transient evolution of the output current therefore depend strongly on the controller. Protection criteria derived from the short-circuit behavior of synchronous sources may consequently be unsuitable for grid-forming-source scenarios [18].

In terms of output characteristics, a grid-forming power source can be modeled as a controlled voltage source in series with an equivalent impedance, as shown in Figure 2. The port voltage can be approximated as:

$${\dot{U}}_{\mathrm{s}}=E-Z_{\mathrm{G}}\dot{I}$$

(1)

In this equation, E is the voltage reference, Z_G is the virtual impedance, and $\dot{I}$ is the output current. When a system fault occurs, the fault current is constrained by the current-limiting element and satisfies Equation (2).

$$\left|{\dot{I}}_f\right|\le I_{\max }$$

(2)

During a fault, the voltage and current at both line terminals are limited. This changes the protection features available to conventional criteria and weakens the stable relationship between fault characteristics and operating thresholds. This effect is analyzed below using distance protection and differential protection as examples.

Distance protection typically relies on measured impedance to identify the faulted section, as shown in Equation (3).

$$Z_{\mathrm{m}}={\displaystyle \frac{{\dot{U}}_{\mathrm{m}}}{{\dot{I}}_{\mathrm{m}}}}$$

(3)

In traditional power grids, the measured impedance generally decreases as the fault approaches the relay, and its trajectory is relatively stable. After grid-forming power sources are integrated, voltage support, virtual impedance, and current-limiting control jointly affect the magnitude and phase of voltage and current. As a result, Z_m may deviate from the conventional setting trajectory and cause misoperation.

For current differential protection, one classic method is the percentage differential protection criterion based on braking characteristics [19], whose basic criterion can be expressed as:

$$\left\{\begin{array}{l}{I}_{\mathrm{dif}}=\left|{\dot{I}}_1+{\dot{I}}_2\right|\\ I_{\mathrm{res}}={\displaystyle \frac{\left|{\dot{I}}_1\right|+\left|{\dot{I}}_2\right|}{2}}\end{array}\right.$$

(4)

In this equation, ${\dot{I}}_1$ and ${\dot{I}}_2$ denote the currents at the two line terminals. During faults involving grid-forming power sources, current-limiting behavior changes the amplitude and phase relationship between the terminal currents. The ratio between the differential quantity and the restraining quantity can therefore deviate from conventional setting assumptions, reducing the sensitivity and selectivity of differential protection.

In summary, grid-forming power sources change the evolution of line voltage, current, and impedance during faults through voltage-source control, virtual impedance, and current-limiting control. This reduces the applicability of traditional distance and differential protection criteria designed around synchronous-source fault characteristics. Because the fault behavior of grid-forming sources is difficult to characterize generically, protection criteria should rely less on source-side short-circuit output and more on intrinsic line parameters and terminal coupling relationships. This consideration motivates the method proposed in this paper.

3. Fault Characteristic Analysis Based on UICs

3.1. Proposed Voltage-Current Characteristic Curves

Figure 3 shows simplified transmission-line diagrams of a large-scale power system under normal operation and under an internal fault. Taking line MN as an example, the voltages and currents at the two terminals are coupled through relationships determined by the line parameters. Let the instantaneous voltages and currents at terminals M and N be denoted by u_m, u_n, i_m, and i_n, respectively. Under normal operating conditions, these quantities satisfy:

$$\Delta u=u_{\mathrm{m}}-u_{\mathrm{n}}=f\left(i_{\mathrm{m}},i_{\mathrm{n}}\right)$$

(5)

The function f(.) is associated with line parameters such as line-to-ground capacitance. It describes the numerical relationship among u_m ̶ u_n, i_m, and i_n during normal operation and external faults. Because it is determined by line parameters, it is independent of source-side fault characteristics.

When a fault occurs within the dashed region in Figure 3, the fault branch changes the line structure and alters the coupling relationship among the electrical quantities. The terminal quantities then satisfy:

$$\Delta u=u_{\mathrm{m}}-u_{\mathrm{n}}=g\left(i_{\mathrm{m}},i_{\mathrm{n}},i_f\right)$$

(6)

Here, if denotes the fault current, and g(.) depends on the line-to-ground capacitance, transition resistance, and fault location. Under this condition, the electrical quantities at the two line terminals no longer satisfy Equation (5).

In principle, a fault can be identified by testing whether the terminal electrical quantities satisfy Equation (5). However, obtaining f(.) requires equivalent line modeling, and fault identification based on f(.) requires iterative solution. These steps reduce protection speed and reliability. To avoid this difficulty, this paper constructs a three-dimensional curve from the voltages and currents at both line terminals. The problem of verifying Equation (5) is thereby transformed into a curve-shape matching problem for internal-fault identification.

Figure 4 shows representative UICs and their projections under normal operation, internal faults, external faults, and external faults with CT saturation. When an internal fault occurs, the line topology changes abruptly and fault current is injected, producing substantial variations in the terminal voltages and currents. The resulting three-dimensional voltage-current curve has an elliptical distribution with a large enclosed area. By contrast, the curves under normal operation, external faults, and external faults with CT saturation remain ellipse-like but have much smaller enclosed areas.

3.2. Curve Characteristic Analysis

The three-dimensional voltage-current ellipses associated with different operating and fault states differ substantially in geometric shape and spatial distribution. These states can therefore be distinguished using the ellipse area and its distribution in the three-dimensional coordinate system.

During normal operation, the voltages and currents at the two line terminals remain within the rated operating range, and i_m and i_n have similar magnitudes and nearly identical phases. During external faults, the currents on the two sides of the line also remain similar in magnitude and phase. The three-dimensional voltage-current curve constructed from these quantities therefore forms a small ellipse-like distribution concentrated near the y = x plane. CT saturation is usually limited under normal operating conditions [20]. When saturation occurs during an external fault, existing CT-saturation detection and correction methods are used to correct the UIC so that the curve retains the characteristics of an external fault [21].

During an internal fault, the fault branch changes the original line topology and introduces a large fault-current component. This produces a pronounced voltage sag on the line side and a clear difference between i_m and i_n. The area enclosed by the three-dimensional voltage-current ellipse increases significantly, and its spatial distribution deviates from the y = x plane.

The proposed three-dimensional voltage-current curve features therefore capture the variation patterns of terminal electrical quantities under different operating conditions. They support discrimination among internal faults, external faults, and normal operation while retaining clear physical meaning. Because the features are based on line-side voltage-current coupling, they are independent of source-side fault characteristics and provide a basis for the protection criterion developed below.

4. Protection Principle Based on UIC Features

4.1. Fault Feature Extraction

To transform the elliptical UIC features into quantitative metrics for fault identification, three core features are extracted from the three-dimensional voltage-current ellipse. The definitions and calculation formulas are derived from sampling data over a half cycle after fault inception. Let the total post-fault sampling sequence length be N. Using the valid half-cycle data, the number of samples is n = N/2.

• Trajectory divergence

Trajectory divergence characterizes the overall dispersion of the three-dimensional voltage-current trajectory and reflects the spatial distribution of fault components. It is calculated as follows:

$$\left\{\begin{array}{l}S=\sqrt{{\sigma }_{i_{\mathrm{m}}}^2+{\sigma }_{i_{\mathrm{n}}}^2+{\sigma }_{\Delta u}^2}\\ {\sigma }_x=\sqrt{{\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{k=1}^n{\left(x_k-\overline{x}\right)}^2}}\end{array}\right.$$

(7)

In Equation (7), σ_im, σ_in, and σ_Δu denote the standard deviations of the current and voltage difference sequences at terminals M and N, respectively. The arithmetic mean of sequence x_k is used in the standard deviation calculation. This feature has inherent disturbance resistance and requires no additional processing. For internal faults, the fault branch causes strong spatial dispersion and severe component fluctuations, so S is large. For external faults and normal operation, the terminal currents and voltages are more balanced, the fault-component fluctuations are milder, and the spatial distribution is concentrated, so S is small.

2.

Average distance from the sampling points to the plane y = x

The average distance from the sampling points to the plane y = x characterizes the perpendicular distance from the current vector to the symmetry plane i_m = i_n. It therefore reflects the degree of asymmetry between the terminal currents. To improve disturbance immunity, the two largest outliers are discarded before averaging. The instantaneous distance and the disturbance-resistant average distance are calculated as follows:

$$\left\{\begin{array}{l}{d}_{x=y,k}={\displaystyle \frac{\left|i_{\mathrm{m},k}-i_{\mathrm{n},k}\right|}{\sqrt{2}}}\\ D_{x=y}={\displaystyle \frac{1}{n-2}}{\displaystyle \sum _{k=1}^{n-2}sort\left(d_{x=y,k}\right)}\end{array}\right.$$

(8)

In Equation (8), sort d_x=y,k denotes the instantaneous distance sequence sorted in ascending order. The two largest outliers are removed, and the arithmetic mean is calculated from the remaining n ̶ 2 samples. During an internal fault, the amplitudes and phases of the terminal currents differ markedly. The sampling points move away from the i_m = i_n symmetry plane, giving a large D_x=y value. During external faults and normal operation, the terminal currents remain highly similar and the sampling points stay close to the i_m = i_n plane, so D_x=y is small.

3.

Average spatial distance

The average spatial distance is defined as the mean Euclidean distance from the three-dimensional voltage-current vectors to the origin. It reflects the overall magnitude of the fault components. The same robustness treatment, removing the two largest outliers, is applied. The instantaneous spatial distance and the robust average distance are calculated as follows:

$$\left\{\begin{array}{l}{d}_k=\sqrt{i_{\mathrm{m},k}^2+i_{\mathrm{n},k}^2+\Delta u_k^2}\\ D_{avg}={\displaystyle \frac{1}{n-2}}{\displaystyle \sum _{k=1}^{n-2}sort\left(d_k\right)}\end{array}\right.$$

(9)

In Equation (9), sort d_k denotes the instantaneous spatial distance sequence sorted in ascending order. The two largest outliers are removed, and the arithmetic mean is calculated from the remaining n ̶ 2 samples. For internal faults, the fault current and differential voltage generated at the fault point have large amplitudes, so the three-dimensional vector is generally far from the origin. For external faults, the fault-component amplitudes are smaller, and the vector remains closer to the origin. This feature therefore distinguishes the strength of fault components intuitively.

The three features are fused to construct the fault feature vector F = [S, D_x=y, D_avg]^T. This vector describes the difference between internal and external faults in terms of spatial dispersion, current similarity, and fault-component magnitude. Although CT-saturation correction is applied to the terminal currents to reduce waveform distortion, residual correction errors may remain. The complementarity of the three features improves the adaptability and robustness of the method under abnormal operating conditions.

4.2. Protection Criterion

After the three feature quantities are fused into F = [S, D_x=y, D_avg]^T, an ellipsoidal envelope based on second-order sample statistics is used to construct the feature space [21,22]. This feature space converts the quantitative UIC features into a criterion space for fault diagnosis. It is established from the statistical distributions of normal operation and external faults, whose feature patterns are stable. Internal faults are identified by calculating the distance between the online feature vector F and the ellipsoidal feature space.

• Offline feature-space construction

Eigenvalue decomposition of the covariance matrix is used to determine the principal directions of the ellipsoid. The second-order sample statistics, represented by the covariance, characterize the variability of the data along different directions. Let the sample points used for feature-space construction be p_i (i = 1,...,N). The covariance distance from the sample center μ can then be calculated using Equation (10), and the ellipsoidal feature-space center can be determined.

$$\left\{\begin{array}{l}\mu ={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{p}_i}\\ \Sigma ={\displaystyle \frac{1}{N-1}}{\displaystyle \sum _{i=1}^N\left(p_i-\mu \right){\left(p_i-\mu \right)}^T}\end{array}\right.$$

(10)

The sample points are projected onto the principal-axis coordinate system so that the data extension can be represented by axial scales in the local coordinate system. The transformed sample point ${p^{\prime }}_i$ is expressed as:

$$\left\{\begin{array}{l}{p^{\prime }}_i=R^T\left(p_i-\mu \right)\\ \Sigma =R\Lambda R^T\end{array}\right.$$

(11)

In this equation, R is an orthogonal matrix whose columns are the eigenvectors of Σ. It defines the rotation from the original coordinate system to the principal-axis coordinate system.

A rotating ellipsoid is then constructed in the principal-axis coordinate system. Equal radii a and b are assigned to the first and second principal axes, and radius c is assigned to the third principal axis. The analytical form of the ellipsoid in the local coordinate system is given by Equation (12).

$${\displaystyle \frac{{x^{\prime }}^2+{y^{\prime }}^2}{a^2}}+{\displaystyle \frac{{z^{\prime }}^2}{c^2}}\le 1$$

(12)

Here, x', y', and z' are the components of p'. To include the samples, a, b, and c are solved using Equation (13). For points that still lie outside the ellipsoid, the corresponding semi-axis is scaled proportionally until all points are enclosed. This process yields the major and minor axes that define the ellipsoidal feature space.

$$\left\{\begin{array}{l}a=b=\max \sqrt{x_i^{\text{'}2}+y_i^{\text{'}2}}\\ c=\max \left|z_i^{\text{'}2}\right|\end{array}\right.$$

(13)

Thus, the feature space of normal operation and external faults is described by the ellipsoid center and by the major and minor axes calculated from Equations (10)-(13).

2.

Online fault detection criterion

In online applications, the UIC feature vector is calculated from the voltage and current data collected at both line terminals using Equations (7)-(9). The values of S, D_x=y, and D_avg in F are then substituted into x', y', and z' in Equation (14) to calculate dF.

The value dF is the normalized distance from F to the ellipsoidal feature space. Equation (15) determines whether the sample lies inside or outside the ellipsoid. When dF > 1.0, the point lies outside the ellipsoid and is theoretically classified as an internal fault. When dF < 1.0, the point lies inside the ellipsoid and is classified as an external fault or normal operation. To account for transient effects during feature extraction, a reliability threshold of 1.1 is used in practical applications. If dF > 1.1, the condition is judged as an internal fault and the protection trips. Otherwise, it is judged as an external fault or normal operation, and line protection is blocked.

$$dF={\displaystyle \frac{x^{\prime 2}+y^{\prime 2}}{a^2}}+{\displaystyle \frac{z^{\prime 2}}{c^2}}$$

(14)

$$dF={\displaystyle \frac{x^{\prime 2}+y^{\prime 2}}{a^2}}+{\displaystyle \frac{{z^{\prime }}^2}{c^2}}\ge d_{\mathrm{set}}$$

(15)

The features of external faults on system-fed lines differ from those under normal operation. The discrepancy in electrical parameters becomes more pronounced as transition resistance increases and the fault location approaches the protected line. Therefore, low-resistance near-zone faults and selected far-zone faults are simulated to characterize the external-fault feature space. If normal-operation and external-fault samples are used to construct two separate subspaces, their sample distributions become more compact, which can further improve discrimination.

4.3. Protection Scheme

To satisfy the speed and reliability requirements of line protection, a startup criterion based on transient local voltage variations is established. This criterion uses only locally measured voltage data and identifies the initial fault disturbance by comparing changes in the fault-voltage component. The startup condition is expressed as:

$$\Delta u\left(t\right)=\left|u\left(t\right)-u\left(t-T\right)\right|$$

(16)

Here, T denotes one power-frequency cycle, and u denotes the voltage at terminal M or N. When Δu(t) at either terminal exceeds the activation threshold Δu_set, a line fault is suspected. A high-frequency signal is then sent to activate protection at the local and remote terminals, and the fault feature vector is extracted from the UIC.

After line protection is activated, the terminal currents are checked for CT saturation. If saturation is detected, the measured currents are corrected [23].

Finally, Equation (15) is used to determine the position of the fault feature vector relative to the ellipsoid. When the internal-fault criterion is satisfied, a trip signal is issued.

The complete algorithmic flow of the proposed protection scheme is shown in Figure 5.

5. Results

To verify the preceding analysis and the proposed protection principle, a PSCAD simulation model was developed for a grid-forming inverter power source connected to the grid through a 110 kV transmission line, as shown in Figure 6 [24]. The photovoltaic source has a total capacity of 100 MW. The 0.38 kV/35 kV step-up transformer has a capacity of 120 MVA and a leakage reactance of 0.0676 pu. The busbar length is 200 m, with positive-sequence impedance Z₁ = 0.33 + j0.41 Ω/km, positive-sequence capacitive reactance to ground X_C1 = -j4.5473 × 10⁵ Ω·km, zero-sequence impedance Z₀ = 1.04 + j1.25 Ω/km, and zero-sequence capacitive reactance to ground X₀ = -j7.9577 × 10⁵ Ω·km. The local load consumes 15 MW active power and 1.5 Mvar reactive power. The 35 kV/110 kV step-up transformer has a capacity of 150 MVA, and its positive-sequence leakage reactance is 0.1 pu. The ab interconnection line is 20 km long, with positive-sequence impedance Z₁ = 0.01 + j0.41 Ω/km, positive-sequence capacitance-to-ground reactance X'_C1 = -j3.5886 × 10⁸ Ω·km, zero-sequence impedance Z₀ = 0.33 + j1.32 Ω/km, and zero-sequence capacitance-to-ground reactance X'_C0 = -j5.1175 × 10⁸ Ω·km. The grid-side equivalent impedance is Z_g = 0.020 + j14.137 Ω, and the grid source is modeled as an ideal 110 kV voltage source.

In the simulation model, a line fault is applied at 1 s. After fault inception, voltage and current data are collected from both line terminals, and the proposed criterion is used to protect line ab.

5.1. Feature-Space Modeling

Because feature variations are relatively stable under normal operation and external faults, and because the fault features show strong clustering, a feature space can be constructed from normal-operation and external-fault samples. This space provides the basis for discriminating internal and external faults. Using the three-dimensional feature vector F = [S, D_x=y, D_avg]^T, the simulation samples are statistically analyzed and represented by an ellipsoidal envelope in three-dimensional feature space.

The sample set includes several external-fault conditions: single-phase-to-ground faults, phase-to-phase faults, phase-to-phase-to-ground faults, three-phase-to-ground faults, and three-phase faults. The transition resistance is varied from 50 Ω to 200 Ω, and 30 dB noise is superimposed to improve the adaptability of the feature-space construction to complex operating environments. The PCA-based rotating ellipsoid method described above is then used to determine the center, principal-axis directions, and semi-axis lengths of the feature space. The resulting ellipsoidal feature space for external faults and normal operation is shown in Figure 7.

The ellipsoid center is μ = [10.3175, 0.0094, 9.9857], with semi-axes a = b = 0.7267 and c = 15.1697. The normal operation and external-fault samples are mainly distributed within or near this ellipsoidal feature space, indicating that the constructed space captures the statistical distribution of external operating conditions.

This feature space defines the discrimination criterion. If the feature vector of a test sample lies within the ellipsoidal space, namely dF < 1.1, the condition is classified as an external fault or normal operation. If the feature vector exceeds the feature-space boundary, namely dF > 1.1, the condition is classified as an internal fault.

5.2. Performance of the Protection Criterion

Using the ellipsoidal feature space, internal-fault samples under different fault locations, transition resistances, fault types, noise levels, and CT-saturation conditions were tested to evaluate the effectiveness and robustness of the proposed method.

• Effect of fault location

Single-phase-to-ground faults at different locations were simulated and compared. Figure 8 shows the UICs and current waveforms at both line terminals for a single-phase-to-ground fault inside the protected zone with a transition resistance of 50 Ω. The fault is located 2 km from end a and 2 km from end b, respectively. In both cases, the change in line topology causes the fault components to be affected by the fault branch. The components fluctuate substantially, and the currents at ends a and b differ markedly from those observed during external faults and normal operation.

Table 1 lists the identification results for single-phase-to-ground faults at different locations along the 20 km line (2, 5, 10, and 18 km from the measurement point a), confirming the effectiveness of the proposed method.

2.

Effect of transition resistance

For ground faults, transition resistance is typically between 10 Ω and 300 Ω. Table 2 lists the identification results for single-phase-to-ground faults at the midpoint of line ab with transition resistances of 50, 100, 150, and 200 Ω. Even at high transition resistance, the current difference between the two line terminals remains substantial for faults inside the protected zone, and the proposed line protection method remains effective.

3.

Effect of fault type

Although single-phase-to-ground faults are the most common transmission-line fault type, other fault types must also be considered. Table 3 lists the identification results for single-phase-to-ground, phase-to-phase, three-phase, phase-to-phase-to-ground, and three-phase-to-ground faults at the midpoint of line ab, with a transition resistance of 50 Ω. Across these fault types, the voltage-current characteristic curves of the faulted phase at both line terminals retain the internal-fault features, and the proposed protection method remains effective.

4.

Noise disturbance

To evaluate robustness under practical operating conditions, a single-phase-to-ground fault at the midpoint of line ab was simulated with a transition resistance of 50 Ω and noise levels of 20 and 30 dB. Figure 9 shows the corresponding voltage and current response curves, and Table 4 lists the identification results. The proposed protection scheme operates correctly under noisy conditions and shows good noise immunity.

5.

CT saturation

To evaluate performance under CT saturation, an external single-phase-to-ground fault with a transition resistance of 50 Ω was simulated outside the protected zone. Figure 10 shows the voltage-current curve when slight CT saturation occurs on the a-side current transformer before correction. Table 5 lists the identification results under several CT-saturation conditions. Even with CT saturation, the proposed protection scheme operates correctly and shows good adaptability.

5.3. Method Comparison

The conventional distance protection of line ab was tested using the simulation model in Figure 6 and standard distance-protection setting principles. Four simulation cases were selected: the fourth fault condition in Table 1, the seventh fault condition in Table 2, and the third and fifth fault conditions in Table 3. The results are shown in Figure 11. In all four cases, the measured impedance did not enter the setting range, so conventional distance protection failed to operate. This failure is caused by the low fault current and weak current-transfer characteristics of inverter-based power sources, together with the influence of control strategies.

By contrast, the proposed method rapidly identifies all four internal-fault scenarios. It is therefore more suitable than conventional distance protection for grid-connection scenarios involving grid-forming inverters.

6. Conclusions

This paper proposes a transmission-line protection criterion based on voltage-current coupling features at both line terminals to address the reduced adaptability of conventional protection in systems with grid-forming renewable energy sources. The method constructs feature quantities from intrinsic line-side coupling relationships and uses multi-feature fusion to distinguish internal faults from external faults. PSCAD simulations show that the proposed scheme maintains reliable operation under different fault locations, transition resistances, fault types, noise levels, and CT-saturation conditions. These results indicate that UIC-based protection can reduce dependence on source-side short-circuit characteristics and improve protection adaptability in renewable energy systems with grid-forming inverters. Future work will optimize the criterion for systems containing multiple types of grid-forming sources and will evaluate the method in larger and more complex grid scenarios.