Unified Virtual Oscillator Control for Grid-Forming and Grid-Following Converters

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.Source: §I · p. 1
• 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.Source: §I · p. 1, §II · p. 2, A. Grid Following (GFL) Operation · p. 3

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.Source: §II · p. 2, Figure 1 · p. 2
• 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.Source: §II · p. 2, Figure 2 · p. 2

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.Source: A. Grid Following (GFL) Operation · p. 2
• 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.Source: A. Grid Following (GFL) Operation · p. 3, Figure 3 · p. 3

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.Source: B. Grid Forming Operation · p. 3
• 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.Source: B. Grid Forming Operation · p. 3
• 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.Source: B. Grid Forming Operation · p. 4
• 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.Source: Figure 4 · p. 3, B. Grid Forming Operation · p. 4

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.Source: §III · p. 4
• 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.Source: §III · p. 4, Figure 6 · p. 4
• 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.Source: §III · p. 4

A. SVO Parameter Selection

• η and µ are selected from desired steady-state responses, with GFL η selection following the same process as GFM.Source: A. SVO Parameter Selection · p. 4
• 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.Source: A. SVO Parameter Selection · p. 5, Figure 7 · p. 5
• EVI increases converter output impedance at harmonic frequencies to suppress current distortion from switching nonidealities or distorted grid voltage.Source: B. Emulated Virtual Impedance (EVI) · p. 5
• Rvir supplies proportional damping because the oscillator control laws are integral, while its bandwidth is limited to preserve SVO dynamic stability.Source: B. Emulated Virtual Impedance (EVI) · p. 5

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.Source: C. Single Phase Operation · p. 5
• Small-signal analysis supports selecting Rvir and designing the DC-bus voltage regulator.Source: §IV · p. 6
• Rvir appears between the oscillator and switch network, helping ensure SVO stability despite electromagnetic-line dynamics and grid-impedance variation.Source: A. Normal Operation · p. 6
• 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.Source: A. Normal Operation · p. 6

B. Fault Ride-Through Operation

• Fault operation uses a circular limiter that saturates the current reference and current error.Source: B. Fault Ride-Through Operation · p. 6
• 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.Source: B. Fault Ride-Through Operation · pp. 6–7
• The virtual resistance, DC-bus regulator, and pre-synchronization filter are designed to achieve the desired dynamic response.Source: §V · p. 7

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.Source: A. Selection of Virtual Resistance · p. 7, Table III · p. 7
• 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.Source: B. DC Bus Voltage Regulation (GFL… · p. 7
• 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.Source: C. Pre-Synchronization · p. 7
• For GFM startup, the filter estimates current before STS closure; for GFL startup, it enables synchronization before DC-voltage control and switching begin.Source: 1) STS Closing for GFM Converters… · p. 7, 2) Start-Up in GFL Converters · p. 7

• The analytical and measured DC-bus voltage-regulation frequency responses are compared for the active-rectifier model.Source: A. Small Signal Model Validation · p. 8, Figure 9 · p. 8
• 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.Source: B. GFL Operation with Weak Grid · p. 8, Figure 11 · p. 8, Figure 10 · p. 8
• 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.Source: C. Fault Ride-Through · p. 8, Figure 12 · p. 8, Figure 13 · p. 8
• A band-limited virtual inductance can limit initial current overshoot at fault occurrence and clearance in relatively strong grids.Source: C. Fault Ride-Through · pp. 8–9

D. Validation of Droop Response

• Simulated and analytical GFM droop responses are compared while varying grid frequency and voltage.Source: D. Validation of Droop Response · p. 9, Figure 14 · p. 9

A. GFL Operation

• The GFL converter stabilizes its DC bus during startup and accurately tracks ±500 VAR reactive-power commands with minimal transient.Source: A. DC Bus Voltage Regulation (GFL… · p. 9, Figure 15 · p. 9, Figure 16 · p. 9
• 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.Source: A. DC Bus Voltage Regulation (GFL… · pp. 9–10, Figure 18 · p. 10

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.Source: B. Fault Ride-Through · p. 10, Figure 19 · p. 10
• 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.Source: B. Fault Ride-Through · p. 10, Figure 20 · p. 10, Figure 21 · p. 10

• The hybrid AC-DC microgrid uses two interlinking converters and static transfer switches to connect or island the AC and DC systems.Source: C. GFM Operation · p. 10, Figure 22 · p. 11
• Pre-synchronization aligns ILC1 with the grid before STS1 closes, enabling grid connection after synchronization is achieved.Source: 1) Islanded Operation · p. 11, Figure 24 · p. 11, Figure 25 · p. 11
• When the system islands unintentionally by opening STSg, the AC load current experiences no noticeable disturbance.Source: 2) Grid-Connected Operation · p. 11, Figure 27 · p. 12
• 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.Source: 2) Grid-Connected Operation · pp. 11–12, §VIII · p. 12, Table IV · p. 12

• The general GFM dynamics are obtained by resolving oscillator behavior along the d and q axes for arbitrary φ.Source: Appendix A · p. 12, Appendix B · p. 13
• The operating voltage and frequency follow from the oscillator dynamics after imposing the steady-state voltage condition.Source: §2 · p. 12
• For φ=π/2, real power is related to instantaneous frequency while reactive power is related to voltage-vector magnitude.Source: Appendix B · p. 12
• Controller parameters η and µ are selected from rated-power, allowable-frequency-deviation, voltage-range, and reactive-power constraints.Source: Appendix B · p. 12
• For φ=0, the appendix derives the complementary P−V and Q−ω droop relationship.Source: Appendix B · pp. 12–13

• The uVOC-based VSC dynamics are organized using equations (17)–(20).Source: Appendix C · p. 13
• The linearized model uses state vector xc = [∆Id ∆Iq ∆V ∆θs ∆vdc]T and input vector u = [∆P0 ∆Q0]T.Source: Appendix C · p. 13
• 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).Source: Appendix C · p. 13