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Transient Triggering Grid-Forming Synchronization Control Under Voltage and Frequency Dips

Dewan Mahnaaz Mahmud, Vinu Thomas, Bogdan Marinescu, Mickaël Hilairet

arXiv:2609.39719v1eess.SYcs.SY

TL;DR

Grid-forming inverters can lose synchronism during voltage or frequency dips, and few existing solutions address both disturbance types together. The paper proposes TTGFM control, which feeds terminal-voltage and power-difference signals into the power synchronization loop. EMT simulations report that TTGFM limits angle acceleration and resynchronizes after disturbances, unlike conventional droop control.

  • Problem

    Few state-of-the-art control solutions address synchronization stability during both voltage and frequency dips, despite this capability being required by grid operators.

    Source: §I · p. 1

  • Method

    TTGFM feeds terminal voltage and the difference between unsaturated and saturated power into the power synchronization loop as a transient virtual braking mechanism.

    Source: §I · p. 2

  • Results

    EMT simulations show conventional droop control losing synchronism during voltage and frequency dips, while TTGFM limits angle acceleration and resynchronizes after disturbance clearance.

    Source: §VII · p. 10

  • Takeaways & Limitations

    The paper reports that TTGFM and its grid-dynamics-aware analytical framework can be generalized beyond a single grid configuration to standard benchmark systems.

    Source: §I · p. 2

Abstract

from arXiv · show

Grid-forming (GFM) inverters are gaining attention as a promising alternative for conventional synchronous generators in the modern power systems. Unlike conventional synchronous generators, GFM inverters have limited overcurrent capability that makes them vulnerable during large disturbances. During disturbances i.e., voltage and frequency dips, GFM inverters are pushed into current-limited operation to protect the semiconductor switches. This causes the internal angle of the GFM inverters to accelerate and lose synchronism with the rest of the grid. To address this limitation, this article proposes a transient triggering grid-forming (TTGFM) synchronization control to enhance the synchronization stability performance under voltage and frequency dips. This method uses two feedback signals; terminal voltage and the difference between unsaturated and saturated power to adjust the internal angle which is generated by power synchronization loop (PSL) of the GFM inverters. These two signals manipulates the internal reference angle generation that act as a virtual braking mechanism. This mechanism limits the angle acceleration during voltage and frequency dips without requiring an extra supervisory signal or parameters to tune. The proposed method is benchmarked against two state-of-the-art synchronization enhancement schemes and validated through high-fidelity electromagnetic transient (EMT) simulations with a grid dynamic equivalent (GDE) model in MATLAB/Simulink\textsuperscript{\textregistered}. An analytical framework is developed to derive the synchronization instability mechanism and the critical limits of the stability margins. Generalization of the GDE model further shows that the TTGFM control is not restricted to a single configuration but is applicable to any standard benchmark system.

I. INTRODUCTION

The paper proposes TTGFM control to improve synchronization stability during voltage and frequency dips, addressing the limited coverage of prior approaches. It uses voltage and power feedback in the power synchronization loop and develops analysis and validation for the control.

I. INTRODUCTION

  • Current limiting during large disturbances can accelerate the inverter angle and lead to loss of synchronism with the grid.The current limiter protects semiconductor switches from overcurrent, but its activation is associated with internal-angle windup.Source: §I · p. 1
  • Prior approaches have often addressed voltage and frequency dips separately, while some combined-dip schemes require a PLL, virtual impedance, parameter tuning, or supervisory signals.The cited prior methods also have dip-specific limitations, including potentially ineffective responses to the other dip type.Source: §I · pp. 1–2
  • TTGFM control targets synchronization stability under both voltage and frequency dips, where few prior solutions address both requirements together.The paper also develops a grid-dynamics-aware analytical framework and benchmarks the method against two state-of-the-art schemes.Source: §I · pp. 1–2

II. TRANSIENT TRIGGERING GRID-FORMING CONTROL

  • The proposed control feeds terminal voltage and the unsaturated–saturated power difference into the PSL to act as a virtual brake on angle acceleration.The feedback acts during transient events and requires no extra tuning parameter, supervisory signal, or PLL.Source: §I · p. 2, §II · pp. 2–3
  • The voltage feedback uses three regions: unchanged power reference and droop above 0.9 p.u., proportional reduction for 0.5–0.9 p.u., and suppressed active-power injection at or below 0.5 p.u.These regions are selected based on grid connection standards.Source: §II · p. 2
  • The power-difference feedback is zero below the current limit and increases with saturation, compensating for the current-limiting effect in the PSL.When the limiter is active, frequency regulation uses unsaturated rather than saturated power.Source: §II · p. 2

III. SIMULATION-BASED CHARACTERIZATION

EMT simulations compare conventional droop control with TTGFM during voltage dips in a GFM inverter connected to a grid dynamic equivalent. Conventional control loses synchronism, while TTGFM limits angle deviation and restores the pre-fault state.

III. SIMULATION-BASED CHARACTERIZATION

  • The simulation evaluates a GFM inverter connected to a grid dynamic equivalent with a droop-based power synchronization loop and a circular current limiter.The model includes an LCL filter, cascaded voltage and current controllers, and equivalent grid inertia and damping.Source: §III · p. 3

A. Voltage Dips

  • With conventional control, a 0.3 pu, 100 ms voltage dip drives δ beyond 30 rad without settling to equilibrium.The current limiter activates at 1.2 pu, and the inverter loses synchronism.Source: A. Voltage Dips · pp. 3–4
  • The conventional-control instability also causes loss of synchronism for the whole system, unlike the behavior visible with an infinite-bus system.The section evaluates the inverter connected to a grid dynamic equivalent using full-order EMT simulation.Source: §III · p. 3, A. Voltage Dips · p. 4
  • TTGFM returns the angle difference δ to its pre-fault value after a voltage dip, whereas conventional control loses synchronism.The reported TTGFM deviation is less than −0.6 rad; the proposed-control simulation is shown in Fig. 3.Source: A. Voltage Dips · pp. 3–4, Figure 3 · p. 4

B. Frequency Dips

In frequency-dip simulations, conventional droop control loses synchronism while TTGFM settles to a new operating point. In benchmarking under voltage and load disturbances, only TTGFM maintains synchronism and restores stable operation after clearance.

B. Frequency Dips

  • During a 6% load increase, conventional control loses synchronism, whereas TTGFM limits δ deviation to less than 0.3 rad and settles within approximately 1 s.The inverter operates at 0.6 pu active-power reference; the load disturbance triggers the current limiter.Source: B. Frequency Dips · p. 4, Figure 5 · p. 4

IV. BENCHMARKING AGAINST STATE-OF-THE-ART ENHANCED SYNCHRONIZATION METHODS

  • Benchmark tests apply a 0.3 p.u. voltage dip and a 7.31% load disturbance for 250 ms at an active-power reference of 0.8 pu.The load disturbance corresponds to a rate of change of frequency of −4 Hz/s.Source: §IV · p. 5
  • For both benchmark disturbances, conventional control and Methods 1 and 2 lose synchronism, while TTGFM maintains synchronism and restores stable operation after clearance.Table II summarizes the outcomes; the authors report compatibility with connection requirement standards.Source: Table II · p. 5, §IV · p. 5

V. ANALYTICAL FRAMEWORK

The framework models the inverter and a dynamic grid equivalent, then derives angle dynamics for synchronization analysis. It includes current limiting and identifies figures comparing critical limits across controls for voltage and frequency dips.

V. ANALYTICAL FRAMEWORK

  • The GDE represents coupled voltage and frequency dynamics, with equivalent inertia and line impedance, and connects to the inverter through an LCL filter.The inverter uses cascaded voltage and current controllers and a droop-based power synchronization loop.Source: A. Preliminaries · p. 5
  • Figures 8 and 9 present critical-limit comparisons among conventional control, Method 1, Method 2, and TTGFM for voltage and frequency dips, respectively.The captions identify the cases but do not state their comparative outcomes.Source: Figure 8 · p. 6, Figure 9 · p. 7
  • The circular current limiter scales both current components by the same ratio above the rated threshold, preserving current phase angle.The limiter protects semiconductor switches when current exceeds Imax.Source: A. Preliminaries · p. 6
  • The power synchronization loop uses droop control with low-pass-filtered active-power measurement, and eliminating filtered power yields second-order angle dynamics.The loop parameters include the nominal frequency reference, active-power setpoint, droop gain, and filter time constant.Source: A. Preliminaries · p. 6
  • The analytical model collects the system state variables and current-limiter dynamics as the basis for synchronization-instability analysis.The grid-equivalent frequency evolves dynamically, and its angle is obtained by integrating that frequency.Source: A. Preliminaries · p. 6

B. Synchronization Instability Mechanism

The analysis examines second-order angle dynamics for the two disturbances discussed in Section III.

B. Synchronization Instability Mechanism

1) Voltage Dip:

During voltage dips, the framework links PCC-voltage reduction and active-power mismatch to accelerating angle dynamics and a critical clearing condition. Weaker grids are associated with faster acceleration and a smaller critical clearing time.

1) Voltage Dip:

  • The voltage-dip angle dynamics are derived by substituting the PCC-voltage expression and grid-frequency dynamics into the second-order angle equation.The voltage reduction depends on fault impedance and equivalent line impedance.Source: 1) Voltage Dip · p. 7
  • During a bolted fault, PCC voltage and inverter active power collapse while the grid power setpoint remains constant, leaving a mismatch that drives frequency dynamics.The fault simplifies the second-order angle-dynamics expression.Source: 1) Voltage Dip · p. 7
  • If the inverter angle passes the critical angle before the disturbance clears, the inverter loses synchronism because no stable equilibrium remains beyond that angle.The angle acceleration continues as the droop input remains positive while delivered power is zero.Source: 1) Voltage Dip · p. 7
  • A larger equivalent line impedance, corresponding to a weaker grid, produces a more severe voltage dip, faster angle acceleration, and smaller critical clearing time.The comparison is with a strong grid having smaller equivalent line impedance.Source: 1) Voltage Dip · p. 7

2) Frequency dip:

A load step creates a frequency dip and a restoring response that depends on current delivery. Once current limiting saturates that response, angle acceleration can persist and lead to loss of synchronism.

2) Frequency dip:

  • A positive load step creates a mismatch that accelerates grid-frequency dynamics, while the droop controller commands additional current to provide a restoring term.The restoring term is proportional to current deviation from its pre-step value.Source: 2) Frequency dip · p. 7
  • The full frequency-dip angle dynamics are obtained by substituting the power expression and grid-frequency dynamics into the second-order angle equation.The load-step magnitude is positive throughout the disturbance.Source: 2) Frequency dip · p. 7
  • When current limiting activates, the restoring term saturates and angle acceleration continues; crossing the critical angle before clearing leads to loss of synchronism.The restoring term depends on delivering the required current.Source: 2) Frequency dip · pp. 7–8

C. Angle Dynamics with TTGFM Control

The TTGFM control law modifies the PSL angle dynamics by adding virtual braking terms. Both terms are nonnegative, so the controlled angle cannot accelerate faster than under conventional droop.

C. Angle Dynamics with TTGFM Control

2) Voltage Dip:

TTGFM uses voltage- and current-limiter-related terms to brake angle acceleration during both voltage and frequency dips. Its frequency-dip dynamics include added braking terms beyond conventional droop dynamics.

2) Voltage Dip:

  • As voltage dips, f(V) reduces the effective power reference and droop input, while current limiting makes ϵ(I) positive and further slows angle acceleration.Source: 2) Voltage Dip · p. 8

3) Frequency Dip:

  • During a frequency dip, voltage reduction and current limiting activate braking terms that reduce angle acceleration and extend the synchronization stability margin.Source: 3) Frequency Dip · p. 8
  • The frequency-dip dynamics retain the first four terms of conventional angle dynamics and add terms arising from the piecewise functions.Source: 3) Frequency Dip · p. 8

D. Critical Limit

TTGFM has the highest reported critical limit among the compared controls, but it cannot prevent synchronization loss when a grid-frequency deviation persists long enough. The voltage-dip CCT comparison covers both the GDE and modified IEEE 9-bus systems.

D. Critical Limit

  • A persistent positive (ωg−ω*) term can keep driving δ toward δcr, so synchronization may still be lost despite TTGFM braking.Source: D. Critical Limit · p. 8
  • The voltage-dip CCT comparison shows GDE and modified IEEE 9-bus cases, with cases classified as within or beyond critical limits.Source: Figure 12 · p. 9
  • TTGFM achieves the highest critical limit against conventional droop control and Methods 1 and 2; exceeding the limit by 0.1% causes all compared methods to lose synchronism.Source: D. Critical Limit · p. 9, Figure 12 · p. 9

E. Effect of Critical Limit for Line Impedance Variation

Longer line impedance reduces the critical limit, although TTGFM retains a larger synchronization margin across the tested line lengths. The generalized GDE framework closely matches the modified IEEE 9-bus voltage-dip CCT when equivalent parameters are extracted.

E. Effect of Critical Limit for Line Impedance Variation

VI. GENERALIZATION OF TTGFM CONTROL TO BENCHMARK SYSTEMS

  • The GDE voltage-dip CCT closely matches the modified IEEE 9-bus result, supporting the equivalent model's replication of benchmark transient behavior.Source: §VI · p. 9
  • The framework extends to other benchmark or real systems if Heq and Zeq are correctly extracted; the study derives these equivalents for a modified IEEE 9-bus system.Source: §VI · pp. 9–10

VII. CONCLUSION

  • The conclusion reports larger synchronization margins than conventional control and benchmarked methods, while noting that sufficiently long grid-frequency deviation can still cause synchronism loss.Source: §VII · p. 10
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