The control block diagram of the grid-connected IBRs is shown in Fig. 3. Considering that most inverters adopt a negative-sequence current suppression strategy during faults, in this paper the positive-sequence current references are reset to align the angle of the current I˙mN with that of the fault-point current I˙f. As shown in Fig. 3, the positive-sequence current references for the improved inverter control strategy are mainly calculated by monitoring the voltage at bus N and the current I˙′mN on the high-voltage side of the transformer.

As the line studied in this paper is the distance protection on the IBRs side of a dedicated IBRs-connected outgoing line, no intermediate taps, load branches or other power sources are connected between the high-voltage side of the grid-connected inverter transformer and bus N. Also, for the 110 kV medium and short-distance line, the distributed capacitive current is extremely small at power frequency, and its influence on the currents at both sides is negligible. Therefore, current continuity is maintained in the line section, and the current amplitude and phase remain consistent. Thus, it is considered that I˙mN′ is approximately equal to I˙mN. However, the aforementioned assumption may deviate if loads or distributed power sources are connected in the line, or if the line is of extra-high voltage and extra-long distance. Such deviations will be verified by subsequent simulations. The phase angle of the inverter output current is directly determined by the positive-sequence current references, i.e., arg⁡(I˙mN)=θv+−arctan⁡(iqref+idref+), where θv+ is the angle of the positive-sequence voltage at the grid-connected bus. To ensure that the angle of I˙mN is aligned with that of I˙f, the relationship between the fault-point current angle and the positive-sequence current reference is further obtained as follows. (2)arg⁡(I˙f)=θv++arctan⁡(iqref+idref+)

Further considering the overcurrent capacity limits of IBR inverters (idref+)2+(iqref+)2≤Imax, the expression for the positive-sequence current reference is derived as follows. (3){idref+=Imax|cos⁡(arg⁡(I˙f)−θv+)|iqref+=idref+×tan⁡(arg⁡(I˙f)−θv+)where Imax is the maximum allowable current of the inverter. From (3), the accurate calculation of the reference value requires the fault current. However, the current angle at the fault point is difficult to obtain from the viewpoint of inverter control. Whereas the bus voltage and the transformer high-voltage-side current can be obtained through monitoring. To accurately calculate the current reference, it is necessary to analyze the relationship between the fault-point current, the bus voltage, and the transformer high-voltage-side current. However, the relationship varies under different fault types. The following mainly discusses the calculation method of the current reference under different fault types.

Considering that the fault-point current I˙f exists only under fault conditions, the relationship between the fault-point current, the bus voltage, and the transformer high-voltage-side current is derived by establishing the fault-component equivalent network. The derivation of the fault-point current angle relies on the assumption that the grid-side positive-sequence equivalent impedance is much smaller than the IBR-side impedance (including the transformer and the line), i.e., |Zs1|<<|ZIBR1+ZMN1|. This assumption is justified by the inherent characteristics of the two sources. On the IBR side, the fault current is strictly limited by the inverter’s overcurrent capability (typically 1.2–1.5 p.u.), which, from an equivalent circuit perspective, manifests as a large internal impedance. Additionally, the step-up transformer contributes a significant short-circuit impedance, with a typical short-circuit voltage of 10%–15%, further increasing ZIBR1. On the grid side, transmission-level IBRs are commonly connected to strong grids, where the short-circuit ratio (SCR) exceeds 3, implying a relatively small Zs1. Consequently, the assumption holds for the typical scenarios considered in this study. (1)

Three-Phase Fault

A three-phase fault is a symmetrical fault, and thus only positive-sequence components are considered. Fig. 4 shows the fault-component equivalent network under a three-phase fault.

According to Fig. 4, the fault-point current I˙f is the sum of the grid-side and IBR-side fault current components, i.e., I˙f=ΔI˙mM1+ΔI˙mN1. Considering the limited fault current injection capability of IBRs, the fault current provided by the strong grid is considerably larger than that from the IBR side. Consequently, the impedance relationship |Zs1|<<|ZIBR1+ZMN1| introduced at the beginning of this section is applicable. proposed earlier in this section is reasonably adopted. On the basis of the current division principle, the ratio between ΔI˙mN1 and I˙f in Fig. 4 is derived as (4)ΔImN1I˙f=Zs1+(1−d)ZMN1Zs1+ZMN1+ZIBR1=Zs1+(1−d)ZMN1ZMN1+ZIBR1where Zs1 is the positive-sequence equivalent impedance of the grid; ZIBR1 is the positive-sequence equivalent impedance of the IBRs-side (including the transformer); d is the ratio of the actual faulted impedance to the total impedance of the line MN.

It is assumed that both the grid-side positive-sequence equivalent impedance and the line impedance satisfy Zs1=ksZMN1 (ks is constant), The fault-point current angle can be derived from (4) as (5)arg⁡(I˙f)=arg⁡(ΔI˙mN1×ZMN1+ZIBR1(1+ks−d)ZMN1)=arg⁡(ΔI˙mN1×ZMN1−ΔU˙mN1)−φsetwhere ΔU˙mN1=−ΔI˙mN1⋅ZIBR1 is the fault component of the voltage at the IBRs-side relay B₂. φset is the impedance angle of the protected line. According to (5), the fault-point current angle can be calculated from ΔI˙mN1 and ΔU˙mN1. Meanwhile, both ΔI˙mN1 and ΔU˙mN1 are electrical quantities on the IBRs-side, which makes it possible to improve inverter control. (2)

Phase to Phase Fault

A phase-to-phase fault is an unsymmetrical fault, and thus the positive-sequence and negative-sequence components should be considered. Fig. 5 shows the fault-component equivalent network under the phase-B-to-phase-C fault.

According to Fig. 5, the fault-point current under the phase-B-to-phase-C fault can be expressed as (6)I˙f=I˙B1f+I˙B2f=I˙A1fe−j120∘+I˙A2fej120∘=I˙A1f(e−j120∘−ej120∘)=I˙A1f(−j3)where I˙B1f and I˙B2f are the phase-B currents at the fault point provided by the positive-sequence and negative-sequence networks. I˙A1f and I˙A2f are the healthy phase-A currents at the fault point provided by the positive-sequence and negative-sequence networks. As shown in (6), I˙f is related to the phase-A current I˙A1f of the fault point provided by the positive-sequence network. In fact, the variation characteristics of I˙A1f under a phase-to-phase fault is consistent with those of the fault-point current under symmetrical faults. Therefore, combining with (5), the expression for the angle of the fault-point current can be obtained as follows. (7)arg⁡(I˙f)=arg⁡(ΔI˙mN1×ZMN1−ΔU˙mN1)−φset−90∘

From (7), the fault-point current angle can also be calculated based on the electrical quantities ΔI˙mN1 and ΔU˙mN1 on the IBRs-side. (3)

Phase-to-Phase Ground Fault

A double-phase-to-ground fault is an unsymmetrical fault, and thus the positive-sequence, negative-sequence and zero-sequence components are considered. Fig. 6 shows the fault-component equivalent network under the phase B-to-phase C ground fault.

As shown in Fig. 6, the fault-point current under the phase-B-to-phase-C-to-ground fault can be expressed as (8)I˙f=−3I˙A1f

In (8), I˙f is also related to I˙A1f. By combining (5), the expression for the phase angle of the fault-point current can be obtained as follows. (9)arg⁡(I˙f)=arg⁡(ΔI˙mN1×ZMN1−ΔU˙mN1)−φset−180∘ (4)

Single-Phase-to-Ground Fault

A single-phase ground fault is an unsymmetrical fault, and thus the positive-sequence, negative-sequence and zero-sequence components should be considered. Fig. 7 shows the fault-component equivalent network under a phase-A ground fault. Combined with Fig. 7, I˙f and I˙A1f satisfy I˙f=3I˙A1f. Following the above analysis, the expression for the fault-point current can be derived as (10)arg⁡(I˙f)=arg⁡(ΔI˙mN1×ZMN1−ΔU˙mN1)−φset

From the preceding derivations, the fault-point current angles under different fault types can be calculated based on ΔI˙mN1 and ΔU˙mN1. The expressions for the current reference values can be obtained, as listed in Table 1.

As shown in Table 1, the current references for IBRs inverter control can be obtained using the locally measured ΔI˙mN1 and ΔU˙mN1. Under the proposed control strategy, the angle of I˙mN is always aligned with that of I˙f, thereby the additional impedance angle is always zero. If the angle is zero, the reactance component of the measured impedance becomes independent of both the fault resistance and the inverter control strategy.

It is worth emphasizing that the derivations above strictly rely on the assumption |Zs1|<<|ZIBR1+ZMN1|, which accurately characterizes the fault current distribution when the IBR is connected to a strong grid. However, under weak grid conditions or scenarios with extremely high penetration of inverter-based resources, the grid-side impedance Zs1 may no longer be negligible. In such cases, the calculation of the fault-point current angle via (5), (7), (9), and (10) may introduce errors, potentially affecting the angle tracking accuracy of the control strategy and the reliability of the protection criterion.

To evaluate the applicability of the proposed method under these challenging conditions, the simulation studies in Section 5 will further investigate the angle tracking performance and protection behavior under weak grid and high IBR penetration scenarios, thereby demonstrating the robustness and limitations of the proposed strategy.

Under the mentioned control strategy, the current angle provided by the IBRs is dynamically altered in order to align the angle of I˙mN with I˙f. As a result, the additional impedance angle becomes zero. The measured impedance expression of relay B₂ shown in Fig. 3 is given as follows. (11)ZmN=ZNk+Rf=(RNk+|I˙fI˙mN|Rf)+jXNkwhere R_Nk is the resistive component of the faulted line’s actual impedance; XNk is the reactive component of the measured impedance, and is equal to the reactive component of the faulted line’s actual impedance.

Fig. 8 shows the measured impedance characteristics under internal and external faults. As shown in Fig. 8, the measured impedance variation depends on the fault resistance R_f and the current amplitude ratio of I˙f to I˙mN.

Under internal faults, the measured impedance increases with rising R_f and the ratio. Its core characteristic is that the resistance component increases while the reactance component of the measured impedance remains constant, which corresponds to the actual reactance of the faulted line’s actual impedance. Under external faults, the measured impedance shows a similar trend to that under internal faults. However, the reactance component of the measured impedance under external faults differs significantly from that under internal faults. Specifically, the reactance component maintains a smaller constant under internal faults and a larger constant under external faults. The reactance component of the measured impedance directly corresponds to the reactance component of the faulted line’s actual impedance and can effectively characterize the actual fault distance. Therefore, based on the difference in the reactance component of the measured impedance between internal and external faults, a single-ended protection principle immune to the additional impedance is developed as follows. (12)0≤Im(ZmN)≤Im(Zset)where Im(Zset) is the reactance component of the setting impedance, typically chosen as 80%–90% of the protected line’s full impedance. The protection operating principle is defined as follows:

Forward internal fault (0≤Im(ZmN)≤Im(Zset)): A fault is determined to be within the protection zone. The device issues an instantaneous trip command.

Reverse fault (Im(ZmN)<0): The device is blocked reliably to prevent maloperation.

Forward external fault (Im(ZmN)>Im(Zset)): The fault is considered to be beyond the Zone I reach. No instantaneous trip is issued; it is left for time-delayed backup zones.

Although the proposed reactance principle accurately locates faults and mitigates the additional impedance interference, the performance can be adversely affected by boundary conditions, IBR fluctuations and system oscillations. To overcome these shortcomings, two auxiliary criteria are proposed to improve protection performance as follows.

Auxiliary Criterion 1: To mitigate the risks of maloperation for the main protection criterion under IBRs output current fluctuations and transient disturbances, A starting criterion using abrupt current changes on the high-voltage side of the transformer and the voltage at grid-connected bus N is proposed in Section 4.2. If the criterion is satisfied, the main protection and identification strategy is activated; otherwise, the protection is blocked.

Auxiliary Criterion 2: To solve the maloperation and poor selectivity of the pure reactance criterion at the protection zone boundary, under high-resistance faults and control-protection coordination failure, a simple resistance threshold criterion is proposed, which can be expressed as:(13)Rm∗=XmN⋅KR+ΔRmaxwhere KR is the ratio of the positive-sequence resistance to the positive-sequence reactance per unit length of the protected line; ΔRmax=10−30 Ω is set considering additional resistances from fault transition, IBRs integration and so on. When the measured reactance lies outside the operating region at the end of the protection range, the measured resistance acts to reliably block the main criterion and prevent maloperation, so as to improve the security and selectivity of the protection.

The proposed control-protection coordination strategy is implemented through the process illustrated in the Fig. 9. This strategy comprises four main stages: start-up criterion fault phase selection, control strategy switching, fault current calculation, and protection criterion. The detailed analysis is provided as follows.

(1)

Evaluate Starting Criteria

To ensure reliable activation of the proposed control-protection coordination scheme while maintaining sensitivity for both metallic and high-resistance faults, a composite starting criterion based on local electrical quantities is developed. The criterion employs an “OR” logic between the undervoltage and overcurrent conditions, as expressed in (14):(14)(Upcc≤0.9p.u.)∪(|ΔI˙mN|≥|ΔI˙set|)where the voltage threshold is set at 0.9 p.u. in accordance with typical low-voltage ride-through standards. The current variation threshold |ΔI˙set| is set above the maximum load fluctuation during normal operation to avoid nuisance trips caused by load switching or other non-fault transients.

The proposed protection starting criterion employs the OR logic of undervoltage and overcurrent criteria, which are complementary under various fault conditions. For high-resistance faults with weak voltage drops, the overcurrent criterion can effectively improve the starting sensitivity. In contrast, under weak grid conditions and high IBR penetration scenarios where the fault current is relatively low, the undervoltage criterion guarantees reliable starting. Furthermore, the criterion is identified using electrical data within only 1–2 fundamental frequency cycles, which can not only achieve fast response but also avoid misjudgment caused by normal system disturbances. The combined logic thus ensures high sensitivity and reliability under diverse operating conditions.

Once the starting criterion is satisfied, the adaptive phase control strategy described in Section 3 is immediately activated, and the distance protection element is triggered to enter the fault identification process. Simulation results in Section 5 will verify the effectiveness and reliability of the proposed starting criterion under disturbance scenarios. (2)

Identify Faulted Phase

Rapid and accurate identification of the fault type is the foundation for all subsequent analysis and control. Traditional phase selection elements are predominantly based on the principle of phase current difference variation, whose effectiveness relies on a significant difference in current variation between the faulted phases and the healthy phases. However, constrained by the internal control strategies of inverters, the short-circuit current exhibits characteristics such as limited magnitude and controlled phase. This results in a small magnitude and gradual change in the short-circuit current contributed from the PV side, which severely reduces the sensitivity or even causes the failure of traditional phase selection methods based on current variation.

To address this issue, this paper proposes a novel fault phase selection method based on the local phase-to-phase voltage difference variation combined with zero-sequence voltage at the protection installation point. The system voltage is primarily dominated by the strong system-side source and is relatively less affected by the weak-infeed PV plant. During fault transients, it can exhibit clearer and more robust asymmetry characteristics, thus providing a new criterion basis for reliable phase selection. The method is logically straightforward and is detailed as follows.

First, the presence of a ground fault is distinguished by detecting the magnitude of the zero-sequence voltage |ΔU˙0| exceeds the setting threshold ε0 (set to avoid the maximum unbalance voltage during normal operation), a ground fault is determined; otherwise, it is a non-ground fault. If a ground fault is identified, the specific faulted phase(s) are further identified based on the relative magnitude relationships among the three phase-to-phase voltage difference variations |ΔU˙AB|, |ΔU˙BC| and |ΔU˙CA|. The criteria are: (a)

If (m1|ΔU˙BC|≤|ΔU˙AB|) and (m1|ΔU˙BC|≤|ΔU˙CA|), it is identified as an A-phase-to-ground fault (AG).

If none of the above conditions are met, a double-phase-to-ground fault is determined. Then, based on the maximum value among the three phase-to-phase voltage difference variations: (d)

If (|ΔU˙A|≥|ΔU˙C|) and (|ΔU˙B|≥|ΔU˙C|) is the maximum, it is identified as an AB-phase-to-ground fault (ABG).

For a non-ground fault, the phase-to-phase short-circuit type is identified according to the following rules: (g)

If (m2|ΔU˙C|≤|ΔU˙A|) and (m2|ΔU˙C|≤|ΔU˙B|), it is identified as an AB phase-to-phase fault (AB).

In the above criteria, the setting coefficients m₁ and m₂ are set to 1.5 and 4, respectively. This method relies solely on local voltage quantities, effectively overcoming the influence of PV-side current weak-infeed characteristics, and provides adaptive and reliable fault type information for subsequent protection and control stages.

The robustness of the proposed phase selection method based on voltage variations is systematically analyzed from three aspects: measurement noise interference, the grid disturbances, and operating conditions with different transition resistances.

In the presence of measurement noise, the criterion for single-phase-to-ground faults is applied to select fault phases through amplitude comparison between voltage variations of sound phases and voltage differences of sound-faulty phase pairs. Small and irregular random voltage fluctuations are produced by noise in each phase. The core voltage characteristics are not changed, and the relative amplitude relationship is not damaged either. The criterion for phase-to-phase faults is adopted to identify faults through amplitude comparison between the voltage variation of the sound phase and those of the two faulty phases. Fault characteristics that voltage variations of faulty phases are much larger than those of the sound phase are not fabricated by noise. Only small and irregular disturbances are introduced, and the amplitude comparison logic of the criteria is not affected. Misjudgments caused by noise are avoided for both criteria, and favorable robustness is obtained.

Under the grid disturbances, synchronous small-amplitude fluctuations of three-phase voltages are caused. The phase-to-phase voltage difference characteristics required by single-phase-to-ground fault criteria are not formed, so the operation conditions of the criterion are not satisfied. The characteristic that voltage variations of faulty phases are obviously larger than those of the sound phase required by phase-to-phase fault criteria is not presented, so the criterion is not activated. Thus, misoperation caused by grid disturbances is effectively avoided for both phase selection criteria.

Under conditions with different transition resistances, the voltage of the faulty phase drops greatly in single-phase-to-ground faults with low transition resistance, and the corresponding phase-to-phase voltage difference is quite distinct. The amplitude of voltage variations is reduced in faults with high transition resistance, but the relative phase-to-phase voltage difference is still identified effectively. The sensitivity of the criterion is reduced only in faults with extremely high transition resistance due to the loss of voltage characteristics. In phase-to-phase faults with low transition resistance, the voltage of faulty phases drops significantly, and the gap of voltage variations between faulty phases and the sound phase is clearly distinguished. The amplitude gap is narrowed in faults with high transition resistance but still meets the requirement of identification. The criterion fails only in faults with extremely high transition resistance because of indistinct voltage characteristics. Such a limitation is shared by all phase selection methods based on voltage characteristics.

Simulation studies in Section 5 will verify the effectiveness and robustness of the proposed phase selection approach under the typical grid disturbance of load switching and high transition resistance. (3)

Activate the Enhanced IBR Control Strategy

Following protection startup and fault phase selection, the enhanced IBR control strategy described in Section 3 is activated. First, the protection device captures the voltage and current data at the point of common coupling before and after the fault, extracting the positive-sequence fault components ΔU˙mN1 and ΔI˙mN1. Subsequently, based on local system parameters and the fault type identified in the previous step, the corresponding analytical model is invoked to calculate the real-time phase angle of the fault current, arg⁡(I˙f).

The switching process follows the conventional low-voltage ride-through control framework: the outer-loop controllers (e.g., DC voltage control and reactive power control) are first blocked, and the positive-sequence current references for the inner current loop are switched to idref+ and iqref+, calculated from the expressions in Table 1. Using the calculated fault current angle together with the voltage angle θv+ obtained from the local phase-locked loop, the d-axis and q-axis reference values are computed online. The inverter then dynamically adjusts its output current angle arg⁡(I˙mN) to actively track arg⁡(I˙f), thereby forcing the additional impedance angle αad to zero.

To ensure a smooth control mode transition and maintain inverter stability during the fault transient, a gradual reference transition scheme is employed. Specifically, the calculated current references are passed through a first-order low-pass filter before being fed into the current inner loop, thereby mitigating current surges and oscillations that may arise from abrupt reference changes. The filter time constant is selected as 1–2 ms, which provides sufficient dynamic response while effectively attenuating high-frequency noise. In addition, the PI controllers in the current loop are equipped with anti-windup protection to prevent overshoot and oscillations caused by integrator saturation during reference variations. Furthermore, all current references are strictly limited to the inverter’s maximum allowable current Imax to ensure the safe operation of power devices.

It is worth noting that the control structure remains unchanged before and after the switching process—both are based on vector control in the synchronous reference frame—and only the reference calculation method is altered. Consequently, the stability of the control loop is inherently maintained. The entire switching process is completed within 2–3 power frequency cycles, which is compatible with the fault discrimination timeframe of the protection element and does not compromise its speed. The above mechanism ensures a smooth and fast switching process, and its dynamic response characteristics, as well as control stability under various fault scenarios, will be demonstrated in the subsequent simulation analysis. (4)

Apply Protection Criterion

With αad≈0∘ achieved, the additional impedance introduced by the transition resistance is constrained to be purely resistive, and its interference with the measured impedance is confined solely to the resistance axis. Under this condition, the measured reactance XmN accurately represents the actual line reactance from the protection installation point to the fault location. The process then transitions to the final protection decision stage: the protection device continuously calculates the updated XmN and compares it with the setting value XNset. If 0≤Im(ZmN)≤Im(Zset) is satisfied, a zone I internal fault is determined, and an instantaneous trip command is issued; otherwise, the logic for external or reverse faults is executed, either by reliably blocking the protection or handing over to backup protection. This completes the closed-loop workflow encompassing fault detection, real-time computation, active control, and reliable protection operation.

The core of the proposed strategy is to enable arg⁡(I˙mN) track arg⁡(I˙f) in real-time through IBRs’ inverter control, thereby eliminating the reactance component in the additional impedance. To verify this effect, faults including AG single-phase-to-ground, BCG double-phase-to-ground, BC phase-to-phase, and ABC three-phase short-circuit faults are simulated at a location 10 km forward from bus N at t = 2 s, with a duration of 1 s. The IBRs capacity is 15 MW. Figs. 10 and 11 respectively show the angle waveforms of I˙mN and I˙f under the conventional control strategy and the proposed strategy for different fault types.

As illustrated in Fig. 10, a pronounced angle difference between I˙mN and I˙f is observed under the conventional control strategy under all fault conditions. The difference peaks at more than 60° for the BC fault, and reaches approximately 40° and 35° for the AG and BCG faults, respectively, which agrees well with the theoretical analysis in Section 1. Such a severe angle misalignment introduces a considerable inductive component into the additional impedance in Eq. (1), which is verified as the root cause of the measured impedance error.

In contrast, Fig. 11 illustrates that the angle waveforms of I˙mN and I˙f are nearly coincident under all fault types, the angle difference between I˙mN and I˙f approaches zero. Consequently, the proposed strategy significantly mitigates this phase difference under fault conditions.

To verify the performance of the proposed distance protection scheme, it is compared with the control-protection coordination method in Ref. [27] and the adaptive distance protection method in Ref. [28]. The PV capacity is set to 15 MW unless otherwise stated. Three fault types are employed: AG, BC, and BCG. The simulation scenarios are configured as follows:

Weak-grid condition: The grid-side equivalent impedance is 160 Ω, representing low short-circuit capacity. A fault is placed 45 km from bus N with fault resistance.

High fault-resistance condition: A fault resistance is set at 45 km from bus N to test performance under high-resistance faults.

The protection operation results and analysis are listed in Table 9.

From Table 9, under the weak grid scenario, the operational performance of the three methods shows significant differences: the proposed method achieves 100% reliable operation for three typical faults (AG, BC, and BCG), with tripping times concentrated in 2.02–2.03 s; Ref. [27] operates reliably only for AG and BCG faults but fails to operate for BC phase-to-phase faults, with tripping times of 2.05–2.07 s. The core reason for its failure in BC faults is its reliance on dynamic phase synchronization between the IBR-side and grid-side currents. In weak grids, the fault current amplitude attenuates, and BC phase-to-phase faults lack zero-sequence components to enhance signal characteristics, leading to the loss of phase synchronization accuracy and the additional impedance being unable to maintain a pure resistive characteristic; Ref. [28] operates normally only for AG and BC faults but fails to operate for BCG double-phase-to-ground faults, with tripping times of 2.03–2.07 s. The core reason for its failure in BCG faults is its dependence on negative-sequence components to calculate the additional impedance angle. In weak grids, the grid-side negative-sequence components attenuate significantly, and BCG faults involve the superimposed interference of positive-sequence, negative-sequence and zero-sequence components, resulting in decreased separation accuracy of sequence components and calculation errors exceeding the fault tolerance threshold of the protection criterion. From the perspective of operating speed characteristics, the proposed method has the fastest operating speed and the smallest fluctuation range (only 0.01 s), which is 0.02–0.05 s faster than Ref. [27] and 0.01–0.04 s faster than Ref. [28], fully demonstrating its superior operating sensitivity and rapidity.

Under the high fault resistance scenario, the operational performance of the three methods also shows significant differences: the proposed method achieves 100% reliable operation for three typical faults (AG, BC, and BCG), with tripping times concentrated in 2.03–2.04 s; Ref. [27] operates reliably only for BC and BCG faults but fails to operate for AG faults, with tripping times of 2.09–2.11 s. The core reason for its failure in AG faults is its reliance on dynamic phase synchronization between the IBR-side and grid-side currents. In high fault resistance conditions, the transition resistance greatly suppresses the fault current and results in a sharp attenuation of the fault current amplitude. Meanwhile, the zero-sequence components for AG faults are further weakened, leading to insufficient signal characteristics for phase synchronization and a serious decline in synchronization accuracy. Therefore, the additional impedance cannot maintain a pure resistive characteristic, which results in protection failure; Ref. [28] operates normally only for AG and BC faults but fails to operate for BCG faults, with tripping times of 2.03–2.07 s. The core reason for its failure in BCG faults is its dependence on negative-sequence components to calculate the additional impedance angle. In high fault resistance conditions, the grid-side negative-sequence components attenuate further, and BCG faults involve the superimposed interference of positive-sequence, negative-sequence and zero-sequence components, leading to a significant decrease in the separation accuracy of sequence components and calculation errors exceeding the fault tolerance threshold of the protection criterion. From the perspective of operating speed characteristics, the proposed method has the fastest operating speed and the smallest fluctuation range (only 0.01 s), which is 0.05–0.08 s faster than Ref. [27] and 0.01–0.04 s faster than Ref. [28], fully demonstrating its superior operating sensitivity and rapidity. Meanwhile, reliable operation under all fault types indirectly reflects its superiority in error margin control.

In summary, the proposed method eliminates the inherent reliance of traditional schemes on phase synchronization and negative-sequence component extraction in principle. It realizes the innovative reconstruction of the protection mechanism, effectively overcomes the failure-to-operate bottleneck of the compared methods under specific fault conditions, and greatly extends the applicable range of relay protection strategies. Its tripping time is stably controlled within 2.02–2.04 s, with fast response and extremely low timing fluctuation, demonstrating superior operating rapidity and stability. In terms of fault identification, the proposed method operates reliably under all fault types, provides higher discrimination accuracy and protection sensitivity, and ensures excellent operating selectivity. Meanwhile, it maintains stable performance under extreme conditions such as weak grid and high-impedance faults, is rarely affected by changes in grid operating states and fault characteristics, and fully presents outstanding multi-scenario adaptability and robustness.