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Dispatchable Virtual Oscillator Control for Decentralized Inverter-dominated Power Systems: Analysis and Experiments
Gab-Su Seo, Marcello Colombino, Irina Subotić, Brian Johnson, Dominic Groß, Florian Dörfler
TL;DR
Inverter-dominated grids need decentralized grid-forming control because conventional grid-following strategies depend on an already stable grid. This paper analyzes and experimentally validates dVOC, showing stable synchronization, programmable dispatch, and dynamic grid-support functions in a multi-inverter testbed.
Problem
Conventional grid-following control cannot maintain stability and synchronization in a purely inverter-based grid without synchronous generators.
Method
The paper analyzes dVOC’s droop characteristics and validates decentralized voltage regulation, synchronization, and dispatchability using inverter experiments with local measurements.
Results
dVOC inverters experimentally achieve dynamic synchronization, black start, load sharing, transient voltage regulation, and programmable power dispatch.
Takeaways & Limitations
dVOC combines grid-forming behavior with user-defined power set-points and local-information control for inverter-dominated power systems.
Abstract
from arXiv · showhide
This paper presents an analysis and experimental validation of dispatchable virtual oscillator control (dVOC) for inverter-dominated power systems. dVOC is a promising decentralized control strategy that requires only local measurements to induce grid-forming behavior with programmable droop characteristics. It is dispatchable i.e., the inverters can vary their power generation via user-defined power set-points and guarantees strong stability. To verify its feasibility, a testbed comprising multiple dVOC-programmed inverters with transmission line impedances is designed. With an embedded synchronization strategy, the dVOC inverters are capable of dynamic synchronization, black start operation, and transient grid voltage regulation with dynamic load sharing, and real-time-programmable droop characteristics for backward compatibility. All these features are experimentally verified.
I. INTRODUCTION
The paper addresses the need for decentralized grid-forming control in inverter-dominated systems and investigates dispatchable virtual oscillator control (dVOC) as a stable, programmable alternative. It analyzes dVOC droop behavior and experimentally validates synchronization, load sharing, and dispatchability.
- Inverter-based grids cannot rely on conventional grid-following control to maintain stability and synchronization without synchronous generators.
- Grid-forming inverters act as controlled voltage sources, while decentralized control based on local measurements supports plug-and-play operation.
- Conventional droop control is simple and backward-compatible, but its phasor models are well-defined only near synchronous steady state.
- dVOC provides user-specified inverter power set-points while inheriting virtual oscillator control’s favorable dynamical properties when set-points are absent.
- Under consistent set-points and technical assumptions, dVOC renders the inverter-based grid globally asymptotically stable with respect to the desired AC power-flow solution.
- The paper analyzes dVOC’s inherent droop characteristics and experimentally validates stability, load sharing, and droop properties in a two-inverter system.
II. DVOC FOR INVERTERS
dVOC is a decentralized grid-forming controller that regulates inverter terminal voltage using local current measurements and a virtual-oscillator control law. Its parameters encode power, reactive-power, voltage, and line-impedance-related design choices.
- dVOC achieves grid-forming synchronization while retaining control over each inverter’s power injections and voltage level.
- Each inverter monitors its output current and uses PWM to regulate its terminal voltage according to the dVOC control law.
- The dVOC law combines a harmonic-oscillator term, a phase-error term, and a magnitude-error term in the inverter-voltage dynamics.
- The controller parameters include active-power, reactive-power, and voltage-magnitude set-points, while κ adapts the controller to line parameters.
B. Interpretation of the dVOC Controller
dVOC can be interpreted as an oscillator with phase and magnitude error terms that regulate voltage and power toward inverter set-points. Under consistent AC power-flow set-points, it synchronizes the inverter grid and reaches the desired power flows.
- The dVOC controller combines a harmonic-oscillator term with phase-error and magnitude-error corrections.The magnitude error vanishes at the voltage-magnitude set-point, while the phase error vanishes when voltage levels and power injections match their set-points.
- The phase error vanishes when inverter voltage levels and power injections correspond to their set-points.
- With consistent AC power-flow set-points and stated technical assumptions, dVOC makes the inverter-based grid almost globally asymptotically stable.Regardless of initial conditions, the inverters synchronize and reach the desired set-points.
- When set-points are inconsistent with AC power-flow equations, dVOC exhibits droop-like characteristics that trade power imbalance and reactive power against frequency and voltage.
III. DROOP CHARACTERISTICS OF DVOC
dVOC extends decentralized droop control with nonlinear, parameter-dependent frequency–active-power and voltage–reactive-power relationships. It retains local droop behavior while providing convergence guarantees, and the paper examines this behavior using an inverter testbed configuration.
- Conventional droop determines inverter voltage frequency and magnitude from active- and reactive-power mismatches.Its decentralized implementation supports backward compatibility with generators and power sharing.
- In polar coordinates, dVOC produces nonlinear droop behavior whose form depends on the design parameter κ.
- κ = π/2 yields the dVOC (V − Q, ω − P) droop, whereas κ = 0 yields resistive (V − P, ω − Q) characteristics similar to VOC.
- The system is provably stable when κ = tan−1(ω0L/R) under a constant transmission-line inductance/resistance ratio, while simulations and experiments remain stable without that assumption.
- dVOC has a local droop characteristic while its inverter network almost globally converges to a predefined AC-power-flow solution.The intuitive droop derivation approximates ∥vi∥ ≈ v⋆i, assuming a small voltage-magnitude deviation.
- The experimental testbed can connect up to five inverters through configurable impedance emulation, while the reported experiments use two parallel inverters supplying a resistive load.
IV. IMPLEMENTATION OF DVOC AND EXPERIMENTAL VALIDATION
The experimental validation uses a configurable inverter testbed to examine dVOC under grid-connected and islanded conditions. The planned scenarios cover black start, synchronization and load sharing, load transients, and real-time dispatch.
- The hardware testbed emulates grid-connected and islanded conditions with different distribution and transmission-line impedances.It supports up to five 1-kVA inverters.
- The validation scenario examines collective grid regulation with multiple dVOC inverters.
- The experiments include black start from a dead grid under load, dynamic synchronization, and load sharing under loaded conditions.
- The experiments also evaluate load-transient performance with two active inverters and real-time set-point updates for dispatch.
A. Black Start
dVOC supports black starting an inverter-dominated grid under resistive and reactive loading. The oscillator establishes grid voltage, with synchronization designed to evolve faster than voltage magnitude.
- A dVOC inverter black-starts a dead grid under a 500-W resistive load, gradually establishing the grid voltage.
- With reactive components from two LCL filters, inverter #1 black-starts the grid under 500 W and 250 var loading.
- dVOC is designed so synchronization dynamics are much faster than voltage dynamics during black start.
- The black-start voltage evolution equation provides an indication of voltage rise-time and is compared with the experimental setup.
B. Synchronization of Multiple Inverters and Load Transients
Experiments show that dVOC supports dynamic synchronization when a second inverter is connected and enables rapid load sharing during transients.
- Black start: The black-start experiment uses inverter #1 under a 500 W load while dVOC establishes the grid voltage from the oscillator dynamics.The supplied figure passage identifies the black-start operating point as p⋆ = 500 W and q⋆ = −125 var.
- Black start: Figure 5 compares the theoretical and experimental voltage-magnitude curves during inverter #1’s black start under a 500 W load.
- Dynamic synchronization: The second inverter synchronizes with the grid within 150 ms (10 cycles) without significant over-current.Inverter #1 maintains the grid while inverter #2 is connected at t = 0 sec.
- Load transients: dVOC enables almost instantaneous dynamic load sharing during a 250 W to 750 W load transient with two inverters active.The response occurs without current overshoot or long settling time, unlike the described slow conventional droop response.
C. Set-point Updates
The experiments include updating a power set-point during dVOC operation, demonstrating real-time dispatch capability.
- Set-point dispatch: The set-point-update experiment demonstrates a power set-point change during dVOC operation.The supplied passage introduces dynamic set-point dispatch for real-time power-flow optimization in inverter-dominant grids.
V. CONCLUSION AND OUTLOOK
The paper verifies dVOC’s grid-forming behavior, synchronization, load sharing, nonlinear droop, and dispatchability through analysis and hardware experiments.
- Conclusion: dVOC inverters achieve almost instantaneous dynamic synchronization and load sharing using only local information.
- Conclusion: The analysis verifies dVOC’s embedded nonlinear droop law and programmable set-points for dispatching inverter power flows.
- Conclusion: The experimental results verify synchronization and dispatchability on a custom-built hardware setup.
- Outlook: The conclusion identifies dVOC as a promising candidate for future grid applications.
APPENDIX
The appendix derives equation (10) by solving the differential equation, exponentiating, and inverting the left-hand side on [0, 1].
- Derivation: The appendix shows that equation (10) solves the relevant differential equation.
- Derivation: The derivation then takes the exponent of both sides.
- Derivation: Finally, it inverts the left-hand side on [0, 1] and changes the variable back to ∥v_i∥ to obtain equation (10).