Commutation Failure Immunity Mechanism and State-Aware Coordinated Protection Strategy for SLCC-HVDC in Weak Receiving-End Grids

Abstract

In weak receiving-end grids, the active support of the valve-side static var compensator and filter (SVF) extends the commutation failure (CF) boundary of LCC-HVDC. However, SVF control state transitions reshape valve-side voltage and harmonic characteristics, causing conventional fixed threshold protection to exhibit concurrent misblocking and failure to operate risks, while SVF zone internal faults are prone to excessive pole-level escalation. This paper proposes a state-aware coordinated protection strategy for symmetric single-pole SLCC-HVDC systems. A normalized commutation margin index, derived from the commutation voltage time integral, characterizes the nonlinear CF boundary under SVF support. SVF control mode, health status, and reactive power margin serve as conditioning variables for adaptive threshold and time window modification. A three-level escalation strategy—local isolation, derated ride-through, and pole-level action—is further designed for SVF zone faults. Validation via RTDS sequence of events records and EMT–protection logic replay co-simulation shows that the proposed index achieves a 100% CF risk prediction rate across five fault scenarios, versus 40% for conventional indices. The method maintains zero failure to operate with a misblocking rate ≤ 10.1% at SNR ≥ 30 dB. The staged response correctly escalates all four SVF zone fault types to the required level, compared with two of four for the fixed threshold baseline. These results confirm effective enhancement of protection robustness, fault ride-through capability, and operational continuity for SLCC-HVDC in weak receiving-end grids.

1. Introduction

Driven by carbon neutrality targets and the high penetration of renewable energy, the voltage stability support capability of cross-regional transmission corridors and receiving-end grids has become a critical factor in enhancing energy system security and resilience. Due to its large capacity, low losses, and favorable economics, thyristor-based line-commutated converter HVDC (LCC-HVDC) remains widely used for long-distance bulk power transmission. However, in multi-infeed and weak receiving-end scenarios, AC-DC coupling is significantly enhanced. Existing studies have shown that commutation failure (CF) risk is closely correlated with system strength [1,2], and that fault types and receiving-end voltage stability levels can significantly alter the CF triggering boundary [3,4]. CF not only causes DC power dips and recovery delays but may also affect adjacent AC and secondary systems through measurement errors, feature distortion, and protection coordination actions, further reducing transmission corridor availability and power supply continuity [5]. Therefore, enhancing the CF immunity and recovery resilience of LCC-HVDC under weak receiving-end fault conditions, without violating equipment protection constraints, has become a research problem of both theoretical significance and engineering urgency.

To suppress CF risk, existing research can broadly be divided into two categories. The first focuses on improving system strength and commutation voltage conditions. For example, synchronous condensers and series voltage regulation have been used to enhance voltage support during faults [6,7], sending-end voltage fluctuation suppression helps improve the commutation environment and mitigate adverse post-fault effects [8]. In addition, synchronized phasor measurement has been used to improve risk identification in multi-infeed scenarios [9]. The second category focuses on control and protection. Existing work has reduced the occurrence and propagation of subsequent commutation failures through DC current prediction and suppression control [10,11], adaptive current control [12], and chain reaction suppression [13]. Notably, the mechanism of sending-end voltage fluctuation and its suppression methods have been further extended in recent studies [14]. Meanwhile, CF prediction, detection, and identification methods continue to evolve. Prediction methods for asymmetric faults and predictive detection methods considering voltage harmonics have been reported [15,16], detection methods based on the energy change rate and high-accuracy identification algorithms have further improved fault identification capability [17,18], improved prediction methods for subsequent commutation failures are also being refined [19]. These studies provide an important foundation for CF risk assessment and control, but most still focus on system enhancement or event identification, with insufficient discussion of how protection input features are reshaped after active reactive power support intervention and how protection logic should be adaptively adjusted based on device states.

In recent years, with the development of power electronic auxiliary commutation, hybrid DC topologies, and intelligent protection technologies, HVDC protection research has been shifting from single quantity criteria toward multi-feature fusion and state-awareness. Regarding auxiliary commutation and topology innovation, some studies have pointed out that active support devices may introduce new coupling paths and side effects under specific fault types or control configurations [20]. Other work has shown that certain active commutation support devices or topological innovations can significantly mitigate or even eliminate CF risk [21,22]. In addition, recovery and suppression strategies after active support have provided new ideas for subsequent CF mitigation [23]. However, these works mainly focus on improving commutation performance itself, with limited discussion of how active support reshapes protection criteria.

In HVDC line protection, Xiao et al. proposed a disturbance blocking criterion for differential protection of LCC-HVDC lines [24]. Liu et al. proposed a non-unit protection method suitable for long-distance LCC-HVDC lines based on voltage traveling-wave waveform characteristics [25]. S. Deb et al. proposed an improved protection algorithm based on the transient energy signum function to enhance fault detection and classification for monopolar HVDC lines [26]. Lei et al. proposed a single-end line protection method based on boundary characteristic frequency band energy ratio for hybrid HVDC systems [27]. These works reflect the trend of HVDC protection transitioning from traditional amplitude-based criteria toward multi-feature combined criteria that integrate boundary characteristics, transient energy, and frequency band information. However, they primarily focus on line fault discrimination or transient feature extraction, which addresses a different problem dimension from the converter station protection mismatch under SVF active support studied in this paper.

In the data-driven direction, Liang et al. proposed a hybrid HVDC fault identification method based on wavelet packet energy spectra and convolutional neural networks (CNN), demonstrating that data-driven methods have good feature extraction capability under complex boundary conditions [28]. Such methods expand the feature space but likewise do not address the coordination between device state and protection thresholds.

In summary, the above studies have not yet systematically answered the following questions: when SVF active support causes valve-side voltage amplitude, phase, and harmonic characteristics to change simultaneously, why does conventional fixed threshold protection exhibit the concurrent mismatch of misblocking and failure to operate; and when SVF zone internal faults can be locally isolated, how should protection logic avoid unnecessary pole-level escalation?

From an engineering perspective, at least three research gaps exist in SVF active support scenarios. First, existing commutation risk criteria mostly rely on conventional quantities such as voltage magnitude or extinction angle and cannot directly characterize the nonlinear compensation mechanism of SVF fast reactive power injection on the commutation voltage time integral. Second, existing protection methods generally assume stable statistical properties of input features and rarely incorporate control mode, health status, and reactive power margin explicitly into protection threshold and time window tuning. Third, for SVF zone local faults, existing research lacks a unified coordination framework that jointly addresses local isolation priority, derated ride-through, and pole-level action escalation conditions. These shortcomings indicate that the protection problem for weak receiving-end SLCC-HVDC is no longer simply a discrimination problem of whether CF occurs but a comprehensive problem of how commutation physics, device state, and protection action logic work together.

To address the above issues, this paper takes the symmetric single-pole LCC-HVDC system with valve-side SVF under weak receiving-end conditions as the research subject and studies the commutation boundary changes, protection criteria mismatch, and local fault escalation under SVF active support. Unlike existing research that mainly focuses on system strength enhancement, CF detection and identification, or line fault discrimination, this paper aims to establish a unified coordinated protection framework integrating commutation physical quantities, device state quantities, and protection decision logic. Specifically, the main contributions of this paper are as follows:

(1)

A normalized commutation margin index is proposed based on the commutation voltage time integral to characterize the nonlinear extension of the CF boundary under SVF active support, and its intrinsic relationship with and essential differences from conventional voltage magnitude and extinction angle indices are clarified from a physical mechanism perspective.

(2)

A state-conditioned threshold modification method is proposed, incorporating SVF control mode, health status, and reactive power margin as explicit conditioning variables to achieve adaptive adjustment of protection thresholds and time windows, thereby reducing the risk of misblocking and failure to operate of fixed threshold protection during state transitions.

(3)

A local isolation derated ride-through–pole-level action staged response strategy is proposed for SVF zone internal faults to limit the fault impact range and improve system operational continuity.

The remainder of this paper is organized as follows. Section 2 analyzes the commutation boundary extension mechanism under SVF active support and explains the distinction between the normalized commutation margin index and conventional indices. Section 3 presents the state-conditioned threshold modification method and the staged response strategy. Section 4 validates the effectiveness and robustness of the proposed method through engineering SoE records and EMT–protection logic co-simulation replay. Section 5 provides conclusions and directions for future work.

2. Commutation Failure Boundary Analysis and Protection Mismatch Mechanism Under SVF Active Support

2.1. SVF Active Support, Commutation Boundary, and Normalized Margin Index

A symmetric single-pole SLCC-HVDC system comprises an LCC converter and a valve-side parallel SVF, which provides both reactive power support and filtering. During fault ride-through, the SVF modifies the valve-side voltage waveform and harmonic characteristics, influencing both the physical commutation process and the observable inputs to the protection system. Figure 1 illustrates the configuration of the studied symmetric monopole HVDC system with a single-side SLCC retrofit.

Commutation theory traditionally describes the commutation margin and CF risk using the overlap and extinction angles. Successful commutation fundamentally depends on whether the commutation voltage time integral (or commutation voltage time area) within the commutation window is sufficient to complete the DC current transfer. The commutation voltage time integral is defined as:

$$J_c\left(t\right)={\int }_t^{t+T_w}{u}_c\left(\tau \right)d\tau$$

(1)

where u_c(t) is the commutation voltage and T_w is the commutation evaluation window. The normalized commutation margin is further defined as:

$${\eta }_c\left(t\right)={\displaystyle \frac{J_c\left(t\right)}{L_c{I}_{dc}\left(t\right)+ϵ}}$$

(2)

where L_c is the equivalent commutation reactance, I_dc(t) is the DC current, and ε is a small regularization constant (typically 10⁻⁶) to prevent division by zero during fault transients. When ηc(t) approaches or falls below 1, the commutation voltage time integral is insufficient, and CF risk increases. This quantity can be extracted directly from electromagnetic transient waveforms and is suitable as a quantifiable index linking waveform observation and commutation physics.

In SLCC, the SVF’s fast reactive power injection reshapes the valve-side voltage waveform:

$$u_V\left(t\right)=u_{\mathrm{grid}}\left(t\right)+\Delta u_{\mathrm{SVF}}\left(t\right)$$

(3)

where u_v(t) is the valve-side bus voltage and Δu_SVF(t) is the voltage component injected by SVF. Under quasi-steady-state (QSS) conditions, the voltage boost from SVF reactive power injection can be approximated as follows:

$$\mathit{\Delta }{u}_{\mathrm{SVF}}(t)\approx {\displaystyle \frac{Q_{\mathrm{SVF}}\left(t\right)\cdot X_{eq}}{U_V(t)}}$$

(4)

where Q_SVF(t) is the reactive power injected by SVF, X_eq is the equivalent system reactance seen from the SVF connection point, and U_v(t) denotes the RMS value of the valve-side bus voltage. The SVF simultaneously changes the amplitude, phase, and distortion characteristics of the valve-side voltage, thereby altering J_c(t) and η_c(t), and nonlinearly extending the CF boundary toward weak receiving-end conditions.

Remark 1

(Applicable Scope of the QSS Approximation). The QSS approximation in Equations (3) and (4) is primarily intended to analyze the influence of SVF active support on the commutation boundary and threshold modification trends, rather than for precise real-time margin calculation under extreme transients. Under severe voltage sags, strong harmonic distortion, or significant phase jumps, rapid voltage variations and harmonic reconstruction may reduce the numerical accuracy of the approximation. However, as long as it correctly captures the boundary trend (sufficient–critical–insufficient), its theoretical value for protection criteria design remains valid. Accordingly, this paper employs the QSS model only for deriving protection threshold boundaries and analyzing parameter influence mechanisms. The real-time protection quantity η_c is computed directly from sampled commutation voltage and DC current via time-domain integration, ensuring that approximation errors do not enter the online protection action chain. A detailed analysis of QSS approximation error sources and protection decision consistency is provided in Appendix B.

The minimum margin over the fault interval [t_f, t_c] is defined as:

$${\eta }_{c,\mathrm{m}\mathrm{i}\mathrm{n}}={\mathrm{m}\mathrm{i}\mathrm{n}}_{t \in [t_f,t_c]}{\eta }_c(t)$$

(5)

The CF boundary is correspondingly defined on the parameter plane as:

$${\eta }_{c,\mathrm{m}\mathrm{i}\mathrm{n}}=1$$

(6)

Compared with conventional extinction angle or voltage magnitude indices, the proposed normalized commutation margin emphasizes the physical consistency among the commutation voltage time integral, DC current, and system reactance. It provides a stable nonlinear characterization of commutation capability under SVF active support.

Comparison with Conventional Indices

The normalized commutation margin index η_c is inherently consistent with conventional extinction angle and commutation voltage magnitude indices, as all three attempt to characterize the converter’s ability to complete current commutation. However, their physical focus differs. The voltage magnitude index is an amplitude-type indicator reflecting voltage support strength. The extinction angle index is an angle-type indicator reflecting the safety margin during thyristor turn-off. In contrast, η_c is a time area indicator that integrates the effects of commutation voltage, current, and reactance. It focuses on whether a sufficient voltage time integral has accumulated within the commutation window, aligning more directly with the physical constraints of the commutation process.

Under SVF active support, these differences are amplified. SVF reactive power injection alters the amplitude, phase, and harmonic characteristics of the valve-side voltage; its effect manifests through changes in the effective voltage time integral. When the SVF enters current limiting, saturation, withdrawal, or bypass states, the effective voltage time integral may decrease significantly even if the voltage magnitude remains relatively stable. Since η_c is constructed directly from the commutation voltage time integral, it more naturally captures this nonlinear compensation effect. Conversely, the conventional voltage magnitude index is susceptible to sliding-window smoothing, and its response to rapid state transitions often lags behind the true commutation process. The extinction angle index may be maintained near its setpoint by the controller, weakening its sensitivity to intermediate risk regions. Thus, η_c is better suited for characterizing the nonlinear deviation between voltage magnitude and commutation capability, as summarized in

Table 1. Conceptual comparison of the normalized commutation margin and conventional indices.

Index	Physical Basis	Type	Key Limitation/Feature Under SVF Active Support
ηc	Ratio of commutation voltage time integral to current transfer requirement	Time area	Reflects changes in effective voltage time integral; characterizes nonlinear compensation effects
Ucomm	Sliding-window RMS amplitude of commutation or valve-side voltage	Amplitude	Susceptible to smoothing; response to rapid state transitions is relatively lagged
γest	Natural extinction angle estimated from commutation equations	Angle	Affected by controller regulation; insufficient sensitivity to intermediate risk and gradual margin erosion

.

2.2. Mismatch Mechanism of Traditional Protection Criteria

Traditional LCC-HVDC protection assumes a stable positive correlation between voltage dip depth, DC disturbance, harmonic characteristics, and commutation margin. SVF active support breaks this statistical consistency in three respects.

First, voltage magnitude and commutation margin become decoupled. The SVF can rapidly raise measurable voltage during a fault, but due to phase jumps and waveform distortion, the time integral within the commutation window may still be insufficient. Thus, a voltage increase does not necessarily correspond to a synchronous enhancement of commutation capability.

Second, SVF state transitions cause feature non-stationarity. Current limiting, blocking, and control loop withdrawal alter u_v(t), THD, and Q(t) at the millisecond level. Fixed threshold criteria cannot distinguish between fault-induced distortion and control loop mutations, leading to misblocking or failure to operate. The most affected elements are the commutation failure protection (CFP), low-voltage blocking criteria, and auxiliary criteria relying on harmonic or voltage features.

Third, local faults may be excessively escalated. SVF zone internal faults can generally be managed through local isolation or bypass. However, if protection logic cannot distinguish the fault impact range, these faults may be escalated to pole blocking or isolation, causing unintended outages.

In summary, voltage magnitude/commutation-margin decoupling, feature non-stationarity due to SVF state transitions, and excessive local fault escalation collectively constitute the starting point for the method design in this paper. Section 3 will propose state-conditioned threshold modification and staged response methods to address these issues.

3. State-Aware Coordinated Protection Method

This paper addresses the aforementioned mismatch from three dimensions: the normalized commutation margin provides a physics-level verification quantity; state-conditioned threshold modification handles feature non-stationarity; and staged response addresses excessive local fault escalation.

3.1. State-Conditioned Threshold Modification

Under SVF active support, protection input features vary with state transitions. The SVF operating state must therefore be explicitly incorporated into protection criteria to enable dynamic adaptation of thresholds and time windows.

3.1.1. State Vector Definition

The SVF protection-related state vector is defined as: S_svf(t) = {S_health, Q_margin}, where S_health characterizes the status of key control loop switching and limiting functions—typical states include normal, current limiting, withdrawal, and bypass; Q_margin represents the available reactive power margin, defined as:

$$Q_{\mathrm{margin}}(t)={\displaystyle \frac{Q_{\mathrm{m}\mathrm{a}\mathrm{x}}-Q_{\mathrm{cmd}}\left(t\right)}{Q_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(7)

where Q_max is the SVF reactive power output limit and Q_cmd(t) is the current reactive power command. Q_margin reflects the remaining headroom in reactive power output.

These two state components characterize SVF support capability in terms of operational constraints and support headroom. To distinguish genuine degradation from measurement errors, a redundant consistency check mechanism is integrated into the state-sensing logic. This mechanism cross-validates S_health with the measured Q_margin: if S_health indicates degradation (level ≥ 2) but the reported Q_margin exceeds the rated capacity (a physical inconsistency), a suspicious-measurement flag is triggered, and the protection falls back to a conservative threshold.

Table 2. Redundant consistency check validation.

Scenario	SVF Health Status	Qmargin	Suspicious Flag
Healthy	-	Nominal	No
Measurement deviation	Healthy (0)	>Nominal	No
State conflict	Degraded (2)	>>Nominal	Yes
Genuine degradation	Degraded (2)	Below nominal	No
Bypass degradation	Bypass (3)	0	No

presents the check results for five scenarios.

All five scenarios are correctly classified, confirming that the check logic effectively distinguishes genuine degradation, measurement deviation, and state conflict. When the suspicious flag is active, the protection automatically adopts a more conservative threshold to ensure safety, while logging the inconsistency for maintenance review.

3.1.2. Threshold Modification Rules

The core principle of state-conditioned threshold modification is to increase protection sensitivity (lower thresholds and shorter time windows) when SVF support capability decreases or feature stability deteriorates, thereby reducing missed-detection risk. Conversely, when the SVF is in a normal state with sufficient margin, protection criteria are moderately relaxed to suppress misoperation.

Specifically, threshold modification coefficient k_θ and time window modification coefficient k_T are defined. The modified threshold and time window are:

$${\theta }^{\prime }\left(t\right)=k_{\prime }\left(S_{\mathrm{SVF}}\right(t\left)\right)\cdot {\theta }_0,T^{\prime }\left(t\right)=k_T\left(S_{\mathrm{SVF}}\right(t\left)\right)\cdot T_0$$

(8)

where θ₀ and T₀ are the nominal threshold and time window, and k_θ, k_T ∈ (0,1] are state-dependent modification coefficients.

Table 3. State-conditioned threshold modification rules (example).

State Condition	kθ	kT	Description
Shealth = Normal, Qmargin > 0.3	1.0	1.0	Nominal state
Shealth = Normal, Qmargin ≤ 0.3	0.9	0.8	Reduced support margin
Shealth = Current limiting	0.8	0.6	Reactive power output limited
Shealth = Loop exit	0.7	0.5	Harmonic characteristics may mutate
Shealth = Bypass	0.6	0.4	No active support
ηc ≤ 1 − δ (superimposed)	×0.8	—	Forced tightening

provides an example of the state-conditioned threshold modification rules.

3.1.3. Characteristics of State-Conditioned Threshold Modification

State-conditioned threshold modification offers three key advantages. First, it reduces misblocking risk: when the SVF is in a normal state with sufficient commutation margin, transient feature variations due to control state transitions do not trigger excessive protection responses. Second, it reduces failure to operate risk: as SVF support capability decreases, thresholds tighten accordingly, ensuring that the protection responds promptly to commutation risk even if the voltage magnitude briefly rises. Third, the method is implemented via a state-threshold mapping table, providing high interpretability, auditability, and ease of engineering configuration.

3.2. Staged Response Decision

Conventional protection logic may excessively escalate SVF zone internal faults to pole-level actions. To address this, a staged response strategy with verifiable escalation conditions is designed.

In SLCC configurations, SVF zone internal faults—such as starting resistor faults or valve group connection line faults—can generally be managed through local isolation or bypass procedures. This allows the SVF to exit active support mode without affecting LCC valve zone operation. Escalation to pole-level actions is considered only when commutation constraints cannot be satisfied after local handling. Thus, the protection response must incorporate staged characteristics and a verifiable escalation mechanism.

3.2.1. Response Level Classification

Based on the preceding analysis, three response levels are defined:

• Level I Response (Local Handling): SVF zone internal faults are identified by local protection, and isolation or bypass actions are executed. The impact is limited to the SVF zone, with no effect on the LCC valve zone.
• Level II Response (Derated Ride-Through): After local handling, the SVF exits active support, and the system enters a derated ride-through state. The commutation margin is then evaluated to determine whether operational constraints are satisfied without SVF support.
• Level III Response (Pole-Level Action): Pole blocking or isolation is executed only when derated ride-through fails to satisfy commutation constraints.

The three-level response classification adheres to the local priority principle: prioritizing the containment of fault impact range and expanding the action scope only when necessary.

3.2.2. Escalation Criteria and T_ver Tuning Framework

Escalation from Level II to Level III requires satisfying verifiable escalation conditions. These conditions must balance premature escalation, which compromises system availability, and delayed escalation, which jeopardizes equipment safety.

This paper employs a condition persistence and time verification escalation mechanism: escalation conditions must be persistently met for a verification duration T_ver before triggering a Level III response. Tuning T_ver is a constrained problem where the lower bound is determined by the dynamic recovery process and the upper bound by equipment thermal capacity. A general tuning method is adopted:

Step 1: Determine the dynamic lower bound T_ver,min. This bound must cover the transient recovery process after fault clearance, SVF control state switching, and measurement/communication latency:

Specific escalation conditions can be formalized as:

$$T_{\mathrm{v}\mathrm{e}\mathrm{r},\mathrm{m}\mathrm{i}\mathrm{n}}=\max \left(T_{\mathrm{f}\mathrm{a}\mathrm{u}\mathrm{l}\mathrm{t},\mathrm{m}\mathrm{a}\mathrm{x}}+∆T_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}},k_{\mathrm{s}\mathrm{c}\mathrm{r}}{T}_{\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{t}\mathrm{l}\mathrm{e}}\right)$$

(9)

where T_fault,max is the typical fault clearance time, ΔT_meas is the measurement and communication margin, T_settle is the transient time constant for key quantities (η_c, Q_margin, and valve-side voltage) to recover near steady state, and k_scr is a correction factor reflecting system strength. A lower receiving-end SCR implies slower recovery and longer post-switching oscillations, necessitating a larger k_scr and T_ver,min.

Step 2: Determine the thermal stability upper bound T_ver,max. This bound ensures that thermal and electrical stresses on relevant equipment remain within allowable limits during worst-case faults and derated ride-through:

$$T_{\mathrm{v}\mathrm{e}\mathrm{r},\mathrm{m}\mathrm{a}\mathrm{x}}=T_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}\left(I_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}},S_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}}\right)-∆T_{\mathrm{a}\mathrm{c}\mathrm{t}}$$

(10)

where T_thermal is the thermal stability limit of relevant equipment under allowable overload conditions, and ΔT_act is the reserved time for protection execution and circuit breaker operation. S_proj denotes the rated engineering capacity. For the same equipment design platform, higher rated capacity and current generally reduce the permissible thermal withstand time, thereby tightening the upper bound of T_ver.

Step 3: Select the setting value between the bounds:

$$T_{\mathrm{v}\mathrm{e}\mathrm{r},\mathrm{m}\mathrm{i}\mathrm{n}}\le T_{\mathrm{v}\mathrm{e}\mathrm{r}}\le T_{\mathrm{v}\mathrm{e}\mathrm{r},\mathrm{m}\mathrm{a}\mathrm{x}}$$

(11)

In practice, the minimum feasible value satisfying this constraint is preferred to balance suppressing transient false escalation and avoiding excessive delays in pole-level action. For weak systems (low receiving-end SCR) or high measurement latency, T_ver should be increased. Conversely, when equipment thermal stability margin is small or rated capacity is large, T_ver should be reduced. The range 100–500 ms is a typical empirical range for weak receiving-end HVDC projects; the specific value must be determined by the general constraint relationship above.

The formal escalation condition is:

$${[{\eta }_c\left(t\right)<1-\delta ]}_{\ge {\mathrm{T}}_{\mathrm{v}\mathrm{e}\mathrm{r}}}\vee {[Q_{margin}\left(t\right)<Q_{min}]}_{\ge {\mathrm{T}}_{\mathrm{v}\mathrm{e}\mathrm{r}}}\vee {\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}}$$

(12)

where [·]_≥T denotes that the condition is persistently satisfied for a duration exceeding T, and F_mandatory denotes mandatory action conditions from differential or converter protection. Level III escalation is triggered when η_c(t) < 1 − δ or Q_margin < Q_min persists beyond T_ver, or when a mandatory action condition is met.

3.2.3. No De-Escalation Constraint

For safety, de-escalation from Level III is prohibited when differential protection remains active, converter protection blocking has not been released, or valve-zone equipment faults have not been isolated. This ensures that once pole-level actions are triggered, the system can only recover after the fault is fully resolved.

3.2.4. Characteristics of the Staged Response Strategy

The staged response strategy enhances operational continuity and recovery readiness while ensuring compliance with equipment protection constraints. For locally isolable SVF zone internal faults, the system can resume operation without pole-level actions. For severe faults requiring pole-level intervention, verifiable conditions guarantee both timely response and auditability.

3.3. Overall Coordinated Protection Flow

Integrating the two methods, the overall flow of the state-aware coordinated protection is as follows: the protection system periodically samples u_v(t), u_c(t), I_dc(t), and S_SVF(t). In each computational cycle, η_c(t) is calculated and classified. Threshold modification coefficients are then derived based on the SVF state and η_c(t) classification. CFP, low-voltage, and other protection conditions are evaluated using the modified thresholds. Finally, the response level is determined according to the staged response criteria, and corresponding actions are executed.

The three mechanisms are synergistic: the commutation margin index η_c(t) provides the physics-level input for both state-conditioned threshold modification and staged response; threshold modification improves criteria accuracy, reducing misjudgments in the staged response; and the local-priority principle and verifiable escalation mechanism in the staged response ensure a balance between safety and availability. The overall flow of state-aware coordinated protection is illustrated in Figure 2.

4. Verification Framework and Results

4.1. Simulation Platform and Verification Logic

This study employs a verification framework that integrates engineering sequence of events (SoE) data with electromagnetic transient (EMT) simulation. The verification process consists of two stages. First, actual RTDS closed-loop SoE records are analyzed to identify three types of mismatch phenomena in conventional fixed threshold protection under SVF active support, namely lagging protection function switching, non-stationary observable features caused by control loop state transitions, and excessive escalation of SVF zone local faults. Second, an EMT and protection logic replay co-simulation platform is established to evaluate the effectiveness and robustness of the proposed state-aware coordinated protection strategy against conventional baseline methods. This hardware-in-the-loop and real-time EMT co-simulation approach has been shown to provide high engineering validity in multi-station HVDC studies [29].

The engineering case is based on the Yangzhou–Zhenjiang HVDC Phase II project, a symmetric single-pole point-to-point scheme with metallic return grounding. Both the sending and receiving stations are equipped with 12-pulse LCC converters, while the receiving station is additionally configured with an SVF for voltage stability enhancement. AC filters (ACFs) and DC filters (DCFs) are installed to suppress harmonics and improve power quality. In the RTDS closed-loop simulation, key electrical quantities, including AC voltage, positive and negative pole DC voltages and currents, and converter firing angles, are monitored in real time. The simulation model reproduces the multi-layered DC line protection chain used in engineering practice, including traveling-wave protection, line di/dt protection, line under-voltage protection, and line differential protection. The main circuit configuration of the Yangzhou–Zhenjiang HVDC Phase II project is shown in Figure 3.

The test program includes two categories. The first comprises AC-side transient fault tests covering power-forward and power-reverse operating conditions, rectifier-side and inverter-side fault locations, and single-phase, phase-to-phase, two-phase-to-ground, and three-phase fault types, all with a fault duration of 100 ms. Different receiving-end short-circuit ratio (SCR) conditions are constructed by adjusting the AC equivalent impedance to emulate weak receiving-end scenarios. The main observed quantities include the timestamps and durations of protection blocked/released events in the SoE records, harmonic control loop exit and re-entry statistics, and the duration of pole isolation commands under fault scenarios.

4.2. AC Fault Ride-Through Verification

4.2.1. Representative Case and Low-Voltage Protection Function Switching

A representative case is selected: a power-forward, full-voltage operation, rectifier-side single-phase-to-ground AC fault with a duration of 100 ms. Upon fault inception, the AC voltage dip causes transient disturbances in the DC-side voltage and current, and the DC line low-voltage protection function enters a blocked state. After fault clearance, the electrical quantities recover gradually, whereas the release of the protection function is delayed relative to the waveform recovery.

Figure 4 presents representative transient waveforms of the AC voltage, DC voltage, and DC current for this case, compiled from engineering RTDS closed-loop recordings. During the fault interval, the AC voltage exhibits a pronounced dip accompanied by waveform distortion, while the DC voltage and DC current show clear transient deviations and subsequent recovery. The waveforms indicate that the main electrical quantities return close to their steady-state levels shortly after fault clearance, whereas the associated protection function is not restored immediately.

The SoE records provide direct evidence of this delayed restoration. In a representative injection under the above condition, the DC line low-voltage protection function is blocked during the fault window and released only afterward, yielding a blocking duration of approximately 0.397 s, which is significantly longer than the 100 ms fault duration. According to the SoE records, the blocking event appears at 18:59:57.070, and the corresponding release event appears at 18:59:57.467. In addition, the interval between the disappearance of the “low AC voltage switching system state” and the appearance of the “low-voltage protection function released” event is approximately 0.28 s, indicating a clear recovery delay in protection function restoration. Figure 5 illustrates the SoE timeline of these key events.

This observation has an important engineering implication. After fault clearance, the electrical quantities may have essentially recovered while the protection function remains in the blocked state. If other protection or control logic uses “low-voltage protection function restored” as an input condition, misjudgment may occur. Therefore, protection function states and their recovery delays should be incorporated as explicit conditioning variables in coordinated protection criteria. This directly supports the state-conditioned threshold modification method proposed in Section 3.1.

4.2.2. Statistical Analysis of Protection Blocking and Low-Voltage Switching Durations

Batch parsing of the SoE records from all 48 AC transient fault test cases yields the statistical results shown in

Table 4. DC line low-voltage protection function blocking duration statistics (n = 108).

Statistic	Value (s)
Minimum	0.396
Median	0.608
Mean	0.608
Maximum	0.815

and

Table 5. Low AC voltage switching system state duration statistics (n = 202).

Statistic	Value (s)
Minimum	0.005
Median	0.130
Mean	0.261
Maximum	0.495

.

Table 4 and Table 5 show that the mean and median blocking duration are both approximately 0.608 s, with a maximum of 0.815 s, which significantly exceeds the 100 ms fault duration. This is not an isolated artifact but a recurring statistical pattern across 48 test scenarios and 108 blocking/release event pairs, demonstrating that protection function switching is prevalent under weak receiving-end AC fault ride-through conditions. Table 5 further indicates that the duration of the low AC voltage switching state spans a wide range, reflecting the significant influence of fault severity and system strength on the monitoring-state duration.

4.2.3. Harmonic Control Loop State Transitions

During weak receiving-end fault ride-through, the SoE records contain a large number of harmonic control loop exit and re-entry events. The statistical results are summarized in

Table 6. Harmonic control loop exit event statistics.

Statistic	Value
Total exit events	3189
Maximum concurrent exits at same timestamp	30

.

Figure 6 illustrates the SoE evidence of concurrent harmonic control loop exit and re-entry events around a representative timestamp. At the same instant, 30 control loops exit simultaneously; approximately 0.176 s later, a cluster of re-entry events occurs. This pattern reveals that the filtering control loops undergo sub-second concentrated exit–re-entry switching during the fault ride-through window. The exit–re-entry transient causes abrupt changes in the valve-side voltage harmonic spectrum: upon loop exit, previously suppressed harmonic components reappear; upon loop re-entry, the harmonic characteristics shift again. If protection criteria use voltage harmonics as inputs with fixed thresholds, they face a high risk of false triggering within this window.

The above evidence supports the design rationale of Section 3.1: the SVF health status S_health (including harmonic control loop exit/re-entry flags, current limiting/blocking flags, etc.) should be incorporated as an explicit conditioning variable for protection criteria, enabling thresholds and time windows to adapt to the SVF operating state rather than remaining fixed during control loop state transitions.

4.2.4. Fixed Threshold Criteria Mismatch Analysis

Synthesizing the engineering evidence from Section 4.2.1, Section 4.2.2 and Section 4.2.3, two types of mismatch risks inherent to fixed threshold criteria under SVF active support scenarios can be identified:

• Risk 1: Misblocking: During fault ride-through, transient feature mutations caused by concentrated harmonic control loop exits may be misinterpreted by fixed threshold criteria as persistent commutation failure signals, thereby triggering unnecessary blocking or prolonging the blocking duration.
• Risk 2: Failure to operate: In the early stage of a fault, the SVF rapidly injects reactive power and briefly raises the voltage magnitude, causing voltage-based criteria to perceive system recovery. However, due to phase jumps and waveform distortion, the commutation voltage time integral may still be insufficient, and the commutation margin η_c may remain below unity. Under these conditions, fixed threshold criteria may release the protection prematurely and miss the commutation failure risk window.

The root cause of both risks is that SVF active support breaks the implicit assumption underlying traditional LCC protection, namely, that voltage magnitude is monotonically and positively correlated with commutation margin. Under SVF support, the same voltage magnitude may correspond to different commutation risks depending on the SVF operating state. The state-conditioned threshold modification proposed in Section 3.1 is designed specifically to address this mismatch mechanism.

4.3. SVF Zone Internal Fault Verification

The second test category comprises SVF protection zone internal fault tests, including the starting resistor fault (F101), valve group connection line fault (F102), valve group internal fault (F103), and reactor connection fault (F104). As shown in Figure 7, the SVF protection zone extends from the converter transformer valve-side CT to the SVF reactor-side CT. These faults belong to the local isolation priority category of the staged response strategy. Local protection can isolate the fault and trigger the SVF to exit active support without directly initiating pole-level actions.

4.3.1. Representative Case Analysis

Under full-voltage, 1.0 p.u. power level, and inverter-side reactive power U-control conditions, RTDS injections were performed for F101 and F102.

• F101: SoE records show that the pole isolation command appears at 17:43:44.068 and disappears at 17:43:46.912, a duration of approximately 2.844 s. This indicates that under an SVF zone local fault, existing engineering protection triggers a pole-level action lasting several seconds. In a staged response, the starting resistor fault could be handled via local isolation, followed by a derated ride-through attempt after the SVF exits active support. However, existing logic did not distinguish the fault scope and escalated directly to pole isolation, causing a full-pole outage.
• F102: The pole isolation command duration is approximately 0.088 s (88 ms). Compared with F101, the durations for these two SVF zone internal faults differ by a factor of 32, exhibiting a cross-order-of-magnitude distribution.

4.3.2. Statistical Analysis of Pole Isolation Command Duration

The pole isolation command duration is statistically analyzed for all SVF zone internal fault scenarios in the SoE records (n = 70), with results shown in

Table 7. Pole isolation command duration statistics (n = 70).

Statistic	Value (s)
Minimum	0.002
Median	0.033
Mean	0.102
Maximum	2.844

.

The pole isolation command duration spans from 2 ms to 2.844 s, covering three orders of magnitude. The median is only 33 ms, whereas the maximum approaches 3 s. This distribution exhibits a pronounced heavy-tail characteristic, indicating that most SVF zone faults result in short-duration pole isolation commands, while a few scenarios (e.g., F101 starting resistor fault) trigger prolonged pole-level actions.

4.3.3. Necessity Analysis for Staged Response

The evidence confirms the necessity of the proposed staged response strategy for three reasons. First, locally isolable SVF zone faults should prioritize local handling to avoid unnecessary pole-level actions. Second, after the SVF exits active support, the commutation margin must be evaluated to determine whether derated ride-through is feasible. Third, pole-level action should be triggered only when commutation constraints persistently fail, ensuring equipment safety.

4.4. Protection Logic Replay and Robustness Verification

To further validate the proposed method, the proposed logic and two conventional baselines are compared on an EMT and protection logic replay co-simulation platform. Baseline-A emulates conventional low-voltage protection without SVF awareness, using a fixed threshold θ_lv = 0.85 p.u. Baseline-B also uses fixed thresholds but selects them from a pre-computed lookup table according to SVF health status; it does not employ continuous tracking of the normalized commutation margin η_c. Representative fault waveforms from EMT runs are replayed through a discrete-time protection model so that all methods are evaluated under identical transients.

Robustness to measurement noise is assessed via SNR scans, and sensitivity is analyzed for key threshold coefficients, the verification time window, and dead-band settings. Throughout this section, the misblocking rate R_ob is the proportion of incorrect blocking commands, and the failure to operate rate R_mt is the proportion of missed responses.

Figure 8 presents a representative time-domain comparison for a moderate inverter-side fault (single-phase-to-ground, Rf = 30 Ω) under four protection methods. The top panel in Figure 8 shows the normalized commutation margin η_c; the middle panel shows the staged response level; and the bottom panel shows the threshold modification coefficient k_θ.

As shown in Figure 8, when the SVF operates normally, the proposed method and Baseline-B exhibit nearly identical η_c trajectories and both triggers only a brief Level I response, confirming that the state-aware logic does not impose additional operational burden under normal conditions. Baseline-A, using the most conservative fixed threshold, does not respond to this fault. In contrast, when the SVF is unavailable, the proposed method reduces k_θ from 1.0 to approximately 0.4 and escalates to Level III promptly, reflecting the automatic tightening of the protection criterion in response to degraded support capability.

4.4.1. SNR Robustness and Noise Tolerance Boundary

An SNR scan was performed at five noise levels (Inf, 40, 30, 20, and 10 dB) for two representative scenarios. For each SNR level, 10 noise realizations were tested, and the results are summarized in

Table 8. SNR robustness scan results.

SNR (dB)	ηc,min (Moderate)	Rob (Moderate)	σ(ηc) (Moderate)	ηc,min (Severe)	Rob (Severe)
Inf	0.631	0.100	0.014	0.0006	0.101
40	0.642	0.100	0.015	0.0035	0.101
30	0.661	0.100	0.023	0.0112	0.101
20	0.627	0.200	0.061	0.0196	0.101
10	0.309	0.998	0.187	0.0217	0.998

.

Protection performance is reliable at SNR ≥ 30 dB (R_ob and R_mt stable). Figure 9 further compares the mean values and error bars of the minimum η_c, misblocking rate, and η_c standard deviation under different SNR conditions across the 10 noise realizations.

As shown in Figure 9, both representative scenarios remain comparatively stable when SNR is not lower than 30 dB: the mean η_c minimum value changes only slightly, R_ob stays near its nominal level, and the error bars remain narrow. Once the SNR decreases to 20 dB, the moderate fault case begins to show visible dispersion and an increase in false blocking, indicating that noise starts to interfere with threshold discrimination. At 10 dB, the moderate fault response deteriorates sharply, and the misblocking rate approaches 1.0, which identifies the practical noise tolerance boundary of the method for the tested conditions.

4.4.2. Combined Effects of SNR and Parameter Variations

The joint effect of parameters and noise was examined over 27 combinations (3 SNR levels × 3δ values × 3T_ver values). Nominal parameters δ = 0.05 and T_ver = 100 ms were selected based on the tuning constraints in Section 3.2.2. For these settings, R_ob = 0.050 at SNR = 30 dB and R_ob = 0.100 at SNR = 20 dB. Figure 10 visualizes this parameter noise interaction.

Figure 10 shows that the parameter region around δ = 0.05 and T_ver = 100 ms remains comparatively stable under noise, whereas the smaller dead-band setting δ = 0.02 exhibits clear sensitivity amplification. When T_ver is fixed at 100 ms, increasing δ from 0.05 to 0.10 produces only limited additional reduction in R_ob, which means the main benefit of avoiding too small a δ is robustness rather than further performance gain. Conversely, when δ = 0.05 is fixed, increasing T_ver enhances verification conservatism but also prolongs blocking duration and action latency. Therefore, δ = 0.05 and T_ver = 100 ms provide the best overall compromise for the present case study.

4.4.3. SVF Zone Internal Fault Staged Response Verification

Staged response verification was conducted for SVF zone internal faults, and the comparison between the baseline and proposed methods is summarized in

Table 9. SVF zone internal fault staged response comparison.

Fault Type	Method	Highest Response Level	Escalation Successful	Escalation Delay (ms)
F101 (Starting resistor)	Baseline-B	I	No	—
F101	Proposed	III	Yes	0
F102 (Valve group connection line)	Baseline-B	III	Yes	0.3
F102	Proposed	III	Yes	0
F103 (Valve group internal)	Baseline-B	II	No	—
F103	Proposed	III	Yes	0
F104 (Reactor connection)	Baseline-B	III	Yes	0.3
F104	Proposed	III	Yes	0

.

The proposed method achieves Level III escalation with zero delay across all four fault types. Baseline-B reaches Level III only for F102 and F104 with a 0.3 ms delay and remains at lower levels for F101 and F103.

4.4.4. Overall Performance Comparison

Taken together, the replay results show that the proposed state-aware coordinated protection method offers three practical advantages over the conventional baseline. First, it maintains zero failure to operate in the tested weak receiving-end ride-through scenarios while suppressing misblocking under SVF degradation and noisy measurements. Second, for SVF zone internal faults, it limits unnecessary escalation by correctly matching the response level to the fault scope and achieving Level III escalation for all four tested fault types. Third, by combining adaptive threshold modification with state-consistency checks, the method remains effective across different support states and reactive power margins without relying on a single fixed threshold. These results confirm the coordinated benefit of the proposed method in balancing ride-through capability, operational continuity, and equipment protection constraints.

4.5. Discussion

4.5.1. Interpretation of Results

The proposed method’s advantage over fixed threshold baselines is most evident in two scenario types. (1) SVF degradation and state transition scenarios: as the SVF degrades from healthy to bypass, the adaptive threshold tightens proactively, with R_ob increasing by 0.06–0.16. This reflects a protection philosophy of limited conservatism in exchange for zero failure to operate. Fixed threshold methods, lacking state information, are essentially insensitive to deteriorating support capability. (2) SVF zone internal fault scenarios: the proposed method achieves Level III escalation in all four fault types, while the baseline achieves this for only two of four. Under normal SVF operation in conventional fault scenarios, the proposed method and Baseline-B perform similarly (R_ob ≈ 0.10), confirming that the state-sensing logic does not impose additional action burden under normal conditions.

Compared with existing research, the key advantage is the unification of three previously disconnected problems: η_c describes the commutation physics boundary under SVF active support, addressing the inability of conventional voltage/extinction angle indices to characterize nonlinear compensation effects; SVF health status and reactive power margin are explicitly incorporated into threshold tuning, addressing the insensitivity of fixed threshold methods to state transitions; and local fault isolation, derated ride-through, and pole-level action are integrated into a single staged response framework. This enables the method to not only identify risk but also constrain the action scope. The proposed method is therefore complementary to existing work on system strength enhancement, CF prediction/identification, and HVDC line fault detection.

4.5.2. Parameter Sensitivity

Sensitivity analysis of key parameters δ, T_ver, and the state-conditioned threshold coefficient k_θ reveals a trade-off between low misblocking and fast response. In the sensitivity scan, the tabulated k_θ values in Table 3 are uniformly scaled to examine the effect of globally tighter or looser threshold settings. δ = 0.02 produces an overly tight threshold and amplifies noise sensitivity; T_ver > 300 ms may cause thermal limit violations under low thermal stability margins. For this case study, T_ver = 100 ms balances false escalation suppression, noise robustness, and action speed. From a broader engineering perspective, δ can be maintained within [0.05, 0.10], with T_ver determined by equipment thermal stability margin and weak receiving-end recovery time. Figure 11 shows the sensitivity heatmaps of R_ob and R_mt over the δ–T_ver parameter plane, with k_θ scaling and L_c scaling fixed at their nominal values.

Figure 11a reveals a sharp contrast between δ = 0.02 and larger dead-band settings: the former produces high R_ob across all T_ver values, while δ > 0.04 maintains R_ob below 0.15 throughout the tested range, confirming that δ = 0.02 should be avoided in practice. Figure 12b shows that R_mt remains near zero across the entire parameter space, indicating that the method preserves its failure to operate performance regardless of the specific δ and T_ver combination.

When the k_θ values are uniformly scaled over [0.7, 1.2], R_ob plateaus once the scaling reaches approximately 1.15, identifying the recommended reference range. Figure 12 presents a representative scan result.

Figure 12 indicates that uniformly tightening the tabulated k_θ values can reduce unnecessary blocking in the loose threshold region, but the benefit gradually saturates as the scaling factor approaches about 1.15. Beyond this point, the reduction in R_ob becomes limited, while the associated changes in blocking duration and effective threshold level suggest diminishing returns. In contrast, excessive relaxation of k_θ weakens the protection criterion and increases the risk of undesired actions. The figure therefore supports using the plateau region near the nominal setting as the practical tuning interval.

4.5.3. Engineering Implementation Feasibility

The results confirm that SVF active support does not equate to “voltage recovery = commutation recovery.” The core issue is that voltage magnitude, phase, harmonics, and protection inputs do not share a simple monotonic mapping; they are strongly influenced by the control state. The key contribution of this paper is unifying device state, commutation physics, and protection logic into a single coordinated framework.

From an engineering deployment perspective, the proposed method has strong practical potential. The η_c calculation requires only three-phase voltage sampling and DC current measurement, completed via sliding-window integration. Its computational load is comparable to conventional RMS-type protection relays and is well within the capability of modern digital protection hardware. SVF health status and reactive power margin are already accessible in the DCS of existing SLCC-HVDC projects; only a communication channel from the DCS to the protection device is needed. The protection logic can be implemented as IEC 61850 standard [30] logic nodes embedded in existing protection devices or station control layer applications, without modifying the power system topology or primary equipment. For existing engineering systems, the method is better suited as an enhancement module for online threshold adjustment and protection coordination, rather than a complete replacement of existing protection chains.

5. Conclusions

This paper proposes a state-aware coordinated protection method for LCC-HVDC systems with SVF active support in weak receiving-end grids. The primary findings are as follows:

• The normalized commutation margin index η_c constructed from the commutation voltage time integral, characterizes the nonlinear extension of the CF boundary under SVF support. Engineering SoE evidence confirms that voltage magnitude recovery alone does not guarantee a sufficient commutation margin, making η_c-based consistency verification necessary.
• By explicitly incorporating the SVF state into threshold modification and combining it with a staged response strategy, the proposed method addresses both the non-stationary features that arise during fault ride-through and the excessive escalation of SVF zone internal faults. EMT and protection logic replay results show that the method exhibits good robustness and adaptability in the tested scenarios, maintains zero failure to operate at SNR ≥ 30 dB, and effectively suppresses misblocking during SVF degradation.
• The proposed method is compatible with existing engineering action matrix architectures and can be deployed as an enhancement module within existing protection and dispatch software frameworks without changing the primary system topology or adding hardware, thereby providing support for protection tuning, logic optimization, and improved operational continuity in weak receiving-end LCC-HVDC systems.

The present study mainly verifies the consistency between the QSS model and protection decisions under conventional scenarios, while further discussion is still needed regarding the errors that may arise under more extreme transient conditions. In addition, the current validation is based on a single engineering parameter set and a representative fault set, and has not yet been extended to different capacity ratings, multi-terminal DC systems, or more complex control strategies. Moreover, the noise tolerance and engineering generality of the proposed method still warrant further assessment through higher-noise disturbance tests and field closed-loop validation. Future research may, therefore, focus on online EMT-assisted calibration, broader engineering scenarios, and field-oriented validation to further improve the applicability of the method under complex operating conditions.