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Unified Virtual Oscillator Control for Grid-Forming and Grid-Following Converters
M A Awal, Iqbal Husain
TL;DR
The paper addresses limited fault handling in oscillator-based GFM control and PLL-related synchronization issues in weak-grid GFL operation. It proposes uVOC as a unified oscillator-based framework with low-voltage synchronization, fast over-current limiting, and unified GFM/GFL analysis and design. Experiments demonstrate weak- and strong-grid synchronization, DC-bus regulation, and fault-management behavior.
Problem
Oscillator-based GFM controllers lack effective fault handling, while PLL-based synchronization can cause issues in weak-grid GFL operation.
Method
The paper develops uVOC, an oscillator-based framework using an SVO, virtual impedance, fault management, small-signal models, and systematic controller-design guidelines for GFM and GFL converters.
Results
Hardware experiments show uVOC supports synchronization with strong and weak grids, DC-bus voltage regulation, and fault ride-through with current limiting.
Takeaways & Limitations
uVOC provides a unified PLL-free control approach for GFM and GFL converters across grid-connected, islanded, weak-grid, and fault conditions.
Abstract
from arXiv · showhide
A unified virtual oscillator controller (uVOC) is proposed, which enables a unified analysis, design, and implementation framework for both grid-forming (GFM) and grid-following (GFL) voltage source converters (VSCs). Oscillator based GFM controllers, such as dispatchable virtual oscillator control (dVOC), offer rigorous analytical framework with enhanced synchronization, but lack effective fault handling capability which severely limits practical application. The proposed uVOC facilitates synchronization with an arbitrarily low grid voltage and fast over-current limiting; this enables effective fault ride-through unlike existing GFM controllers which typically switch to a back-up controller during fault. GFM operation with uVOC is achieved in both grid connected and islanded modes with seamless transition between the two. In GFL converters, bidirectional power flow control and DC bus voltage regulation is achieved with uVOC. No phase-locked-loop (PLL) is required for either GFL or GFM operation circumventing the synchronization issues associated with PLLs in weak grid applications. Detail small signal models for GFM and GFL operation have been developed and systematic design guidelines for controller parameters are provided. The proposed controller is validated through hardware experiments in a hybrid AC-DC microgrid.
I. INTRODUCTION
The paper proposes uVOC as a unified oscillator-based framework for GFM and GFL converters, addressing fault ride-through, weak-grid synchronization, and controller design. It develops the SVO formulation and explains how parameter choices shape power-tracking and droop behavior in GFL operation.
- I. INTRODUCTION: Oscillator-based GFM controllers provide rigorous synchronization analysis but lack compatible fault ride-through strategies, limiting practical application.The paper identifies synchronization under arbitrarily low grid voltage and fast over-current limiting as the two required capabilities.
- I. INTRODUCTION: uVOC unifies GFM and GFL control by enabling low-voltage synchronization, fast over-current limiting, and PLL-free operation without switching to a backup controller.The framework targets both grid-connected and islanded operation, including bidirectional power flow and DC-bus regulation for GFL converters.
- II. SPACE VECTOR OSCILLATOR (SVO): The SVO determines a converter voltage-vector control law that supports synchronization in both grid-following and grid-forming converters.The development uses a simplified VSC connected to an infinite bus through an equivalent impedance and represents three-phase voltage with stationary-frame space vectors.
- II. SPACE VECTOR OSCILLATOR (SVO): The voltage-vector derivative separates magnitude and frequency dynamics, with its real and imaginary components acting along the d and q axes, respectively.This decomposition provides the geometric basis for interpreting the oscillator's synchronization and power-control actions.
- A. Grid Following (GFL) Operation: The oscillator's harmonic component produces nominal-frequency rotation, while synchronization feedback realigns the voltage vector and adjusts its magnitude to track power references.The current-error vector decomposes into real-power and reactive-power tracking components, whose effects are rotated by the design parameter φ.
- A. Grid Following (GFL) Operation: In GFL operation, φ selects which power reference is tracked accurately, while the other power quantity exhibits a droop relation unless integral compensation is added.For φ = 0, real-power reference tracking is accurate regardless of grid conditions, while reactive power follows instantaneous frequency through droop.
B. Grid Forming Operation
uVOC GFM operation combines magnitude correction, harmonic-oscillator, and synchronization-feedback terms to produce self-synchronizing voltage control with configurable droop behavior.
- B. Grid Forming Operation: uVOC's GFM control law combines magnitude correction, harmonic-oscillator, and synchronization-feedback terms acting on the converter voltage vector.The magnitude correction restores nominal voltage magnitude, while the harmonic oscillator and synchronization feedback shape frequency and power behavior.
- B. Grid Forming Operation: The voltage magnitude exhibits a nonlinear droop because the magnitude correction term prevents freely adjusting the voltage vector magnitude during GFM operation.Near nominal operating conditions, the droop response can be approximated as linear.
- B. Grid Forming Operation: The time-domain implementation naturally produces droop behavior without explicitly regulating voltage amplitude and frequency from calculated output power.Along the q-axis, it yields the same P−ω droop relation described earlier.
- B. Grid Forming Operation: For φ = 0, uVOC produces P−V and Q−ω droop responses, while φ ∈ (0, π/2) enables coupled droop relations among P, Q, ω, and V.The preferred angle for faster synchronization depends on network impedance: φ = 0 for dominantly resistive networks and φ = π/2 for inductive networks.
III. IMPLEMENTATION OF UVOC
The uVOC implementation uses stationary-frame space-vector control with optional current-feedback locations, pre-synchronization, virtual impedance, fault management, and circular current limiting.
- III. IMPLEMENTATION OF UVOC: The controller implements GFL and GFM control in the stationary αβ frame and supports either converter-side or grid-side current feedback.The PWM duty ratio is generated from the uVOC output voltage using scaling based on the DC bus voltage measurement.
- III. IMPLEMENTATION OF UVOC: Pre-synchronization provides soft start-up and transition from islanded to grid-tied operation, while emulated virtual impedance is used in every operating mode.The pre-synchronization components are marked in green in the implementation diagram.
- III. IMPLEMENTATION OF UVOC: During faults, the circular limiter radially limits the current-reference vector when its magnitude exceeds the maximum allowable current, preserving its angle for synchronization.Under normal conditions the limiter is transparent; fault management generates signals that enable fault ride-through.
A. SVO Parameter Selection
The paper selects SVO parameters to constrain GFM power outputs across the full allowable PoC voltage and frequency range, while using emulated virtual impedance for harmonic compensation and stabilization.
- A. SVO Parameter Selection: η and µ are selected from desired steady-state responses, with GFL η selection following the same process as GFM.
- A. SVO Parameter Selection: Power outputs remain within rated real and reactive limits across the full allowable PoC voltage and frequency variation.The design guidelines account for the difference between switch-network pole behavior and PoC behavior caused by the LCL filter.
- A. SVO Parameter Selection: EVI increases converter output impedance at harmonic frequencies to suppress current distortion from switching nonidealities or distorted grid voltage.
- A. SVO Parameter Selection: Rvir supplies proportional damping because the oscillator control laws are integral, while its bandwidth is limited to preserve SVO dynamic stability.
C. Single Phase Operation
The single-phase implementation uses the full αβ uVOC vector controller while requiring virtual-impedance emulation only on the α axis. Small-signal modeling supports parameter selection and DC-bus regulator design.
- C. Single Phase Operation: The single-phase implementation uses the full vector controller, with iβ generated by delaying iα by one-quarter nominal period.Virtual impedance is emulated only on the α axis, and PWM uses the resulting v_cα signal.
- C. Single Phase Operation: Small-signal analysis supports selecting Rvir and designing the DC-bus voltage regulator.
- C. Single Phase Operation: Rvir appears between the oscillator and switch network, helping ensure SVO stability despite electromagnetic-line dynamics and grid-impedance variation.
- C. Single Phase Operation: The small-signal model represents perturbations in output currents, voltage magnitude, and oscillator angle around an operating point.The state is x = [∆I_d ∆I_q ∆V ∆θ_s]^T, with system matrices supplied for the linearized dynamics.
B. Fault Ride-Through Operation
During faults, uVOC modifies oscillator and current dynamics to limit over-current while enabling a modeled transition back to normal operation.
- B. Fault Ride-Through Operation: Fault operation uses a circular limiter that saturates the current reference and current error.
- B. Fault Ride-Through Operation: The fault-mode small-signal model is obtained by substituting compensated power references into the modified SVO dynamics.The effective resistance becomes R_e = R_vir + R_0, with an added R_0 i_0,sat term in the current dynamics.
- B. Fault Ride-Through Operation: The virtual resistance, DC-bus regulator, and pre-synchronization filter are designed to achieve the desired dynamic response.
A. Selection of Virtual Resistance
Virtual resistance is selected from small-signal pole locations, while separate regulator and pre-synchronization designs support DC-bus control and low-transient startup or reconnection.
- A. Selection of Virtual Resistance: Rvir = 0.5% is unstable, 1.15% is stable but lightly damped, and 4.9% produces a well-damped response for the analyzed GFM case.The same pole-based procedure can select Rvir for GFL operation using the corresponding model.
- A. Selection of Virtual Resistance: The DC-bus regulator dynamically generates P0 from voltage error using a lead-lag filter and PI compensator.Filter zero and pole placement provides phase boost, while the integral time constant is chosen for sufficient DC gain.
- A. Selection of Virtual Resistance: The pre-synchronization filter uses a virtual RL branch with Lps ≈ L_a + L_g and Rps ≈ Rvir.Exact LCL-filter parameter knowledge is not required for selecting these parameters.
- A. Selection of Virtual Resistance: For GFM startup, the filter estimates current before STS closure; for GFL startup, it enables synchronization before DC-voltage control and switching begin.
VI. SIMULATION RESULTS
Simulations validate uVOC models and demonstrate GFL DC-bus regulation under weak-grid conditions alongside GFM fault-response behavior across grid strengths.
- The analytical and measured DC-bus voltage-regulation frequency responses are compared for the active-rectifier model.
- Under SCR=1.9, GFL DC-bus voltage is quickly restored after both no-load-to-full-load and full-load-to-no-load transitions.
- During a 0.3 p.u. symmetrical AC fault, GFM operation clamps converter current at 1 p.u. and resumes normal operation after voltage recovery.
- A band-limited virtual inductance can limit initial current overshoot at fault occurrence and clearance in relatively strong grids.
D. Validation of Droop Response
Experiments validate uVOC droop behavior, GFL regulation and power dispatch, weak-grid operation, and GFM fault ride-through using laboratory converters.
- D. Validation of Droop Response: Simulated and analytical GFM droop responses are compared while varying grid frequency and voltage.
- A. GFL Operation: The GFL converter stabilizes its DC bus during startup and accurately tracks ±500 VAR reactive-power commands with minimal transient.
- A. GFL Operation: At SCR≈1.9, a 0-to-≈1.4 kW load step produces a damped DC-bus response settling within ≈250 ms, consistent with the ≈227 ms estimate.
- B. Fault Ride-Through: During a local-load short circuit, the GFM converter uses its full current capability for voltage support and quickly resumes normal operation after fault removal.
- B. Fault Ride-Through: For a dead-short at the converter terminal, output current is clamped at its rated value and prefault load-supplying operation quickly returns after clearance.
C. GFM Operation
Hardware experiments validate uVOC GFM operation in a hybrid AC-DC microgrid, including islanding, pre-synchronization, harmonic compensation, and uninterrupted load service.
- The hybrid AC-DC microgrid uses two interlinking converters and static transfer switches to connect or island the AC and DC systems.
- Pre-synchronization aligns ILC1 with the grid before STS1 closes, enabling grid connection after synchronization is achieved.
- When the system islands unintentionally by opening STSg, the AC load current experiences no noticeable disturbance.
- The experiments support uVOC operation with real-system nonidealities and demonstrate grid-tied GFL/GFM operation and effective fault ride-through without controller backup switching.
APPENDIX A DROOP RESPONSE OF OSCILLATOR
The appendix derives oscillator droop behavior for arbitrary rotation angle φ and identifies how φ selects the coupling between active/reactive power and frequency/voltage.
- The general GFM dynamics are obtained by resolving oscillator behavior along the d and q axes for arbitrary φ.
- The operating voltage and frequency follow from the oscillator dynamics after imposing the steady-state voltage condition.
- For φ=π/2, real power is related to instantaneous frequency while reactive power is related to voltage-vector magnitude.
- Controller parameters η and µ are selected from rated-power, allowable-frequency-deviation, voltage-range, and reactive-power constraints.
- For φ=0, the appendix derives the complementary P−V and Q−ω droop relationship.
APPENDIX C SMALL SIGNAL MODEL OF UVOC BASED VSC
This appendix organizes the uVOC-based VSC dynamics and derives a linearized small-signal representation. It partitions the state vector and system matrices to support analysis of different controller forms.
- The uVOC-based VSC dynamics are organized using equations (17)–(20).
- The linearized model uses state vector xc = [∆Id ∆Iq ∆V ∆θs ∆vdc]T and input vector u = [∆P0 ∆Q0]T.
- For analyzing different controller forms, xc is partitioned as [xT vdc]T, while matrices A and B are partitioned accordingly in equation (21).The detailed matrix forms are provided in equation (42).