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Virtual synchronous generator of PV generation without energy storage for frequency support in autonomous microgrid

Cheng Zhong, Huayi Li, Yang Zhou, Yueming Lv, Jikai Chen, Yang Li

arXiv:2107.01560v1eess.SYcs.SYeess.SP

TL;DR

Autonomous microgrids with high PV penetration face frequency-regulation challenges because converter-interfaced generation lacks inertia. The paper proposes a VSG that reserves PV power and applies droop and swing-equation control through the DC–DC converter. Simulations indicate frequency support across irradiance conditions and improved frequency-response performance as PV penetration increases.

  • Problem

    Autonomous microgrids with high distributed-generation penetration have low inertia and limited frequency regulation, while conventional VSG control does not adapt to two-stage PV systems without storage.

    Source: §1 · pp. 1–2

  • Method

    The proposed PV VSG reserves active power using a pre-defined power-versus-voltage curve and applies emulated droop and swing-equation control to the DC–DC converter.

    Source: §1 · p. 2, §6 · p. 25

  • Results

    Simulations indicate that the proposed VSG supports frequency under different irradiance conditions and that frequency nadir and steady frequency perform better as PV penetration increases.

    Source: §6 · p. 25

  • Takeaways & Limitations

    In the studied island-microgrid simulations, PV generation without storage can provide frequency support using the proposed VSG strategy.

    Source: §6 · p. 25

    PLL measurement delay and error, noise sensitivity in dωg/dt, and power-tracking-based inertial support may reduce control stability or frequency-regulation performance and differ from a synchronous generator’s natural inertial response.

    Source: §5.1 · p. 14

Abstract

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In autonomous microgrids frequency regulation (FR) is a critical issue, especially with a high level of penetration of the photovoltaic (PV) generation. In this study, a novel virtual synchronous generator (VSG) control for PV generation was introduced to provide frequency support without energy storage. PV generation reserve a part of the active power in accordance with the pre-defined power versus voltage curve. Based on the similarities of the synchronous generator power-angle characteristic curve and the PV array characteristic curve, PV voltage Vpv can be analogized to the power angle {\delta}. An emulated governor (droop control) and the swing equation control is designed and applied to the DC-DC converter. PV voltage deviation is subsequently generated and the pre-defined power versus voltage curve is modified to provide the primary frequency and inertia support. A simulation model of an autonomous microgrid with PV, storage, and diesel generator was built. The feasibility and effectiveness of the proposed VSG strategy are examined under different operating conditions.

1. Introduction

Autonomous microgrids with high distributed-generation penetration have low inertia and limited frequency regulation, while conventional VSG control does not fit two-stage PV systems without storage. The paper proposes a PV VSG using power reserve control and droop and swing-equation control on a DC–DC converter.

1. Introduction

  • High distributed-generation penetration leaves microgrids with low inertia and limited frequency regulation, especially in autonomous operation.Converter-interfaced PV and wind generation lack inherent inertia and frequency-regulation ability, and storage or diesel capacity is costly.Source: §1 · p. 1
  • Droop control offers communication-free, plug-and-play operation, while VSG control adds virtual inertia that conventional droop-based DGs lack.The introduction presents VSG as inheriting droop’s advantages while supporting system inertia.Source: §1 · p. 1
  • Conventional VSG control is unsuitable for two-stage PV without storage because PV output is environmentally limited and its DC-link voltage loop occupies the inverter’s active-power control loop.The paper therefore targets an improved VSG for PV without energy storage.Source: §1 · p. 2
  • The proposed VSG combines power reserve control with governor droop and emulated swing-equation control on the PV system’s DC–DC converter.Its pre-defined power-versus-voltage curve reserves active power without irradiance measurement.Source: §1 · p. 2

2. FR strategies for PV system

PV frequency-regulation strategies either draw reserve from energy storage or reserve power within the PV system itself. The section reviews reserve-control methods, prior PV VSG approaches, and the study’s exclusion of partial shading.

2. FR strategies for PV system

  • PV frequency-regulation strategies either obtain reserve from energy storage or use power-reserve control within the PV system.Storage-based strategies can handle frequency disturbances, while PV de-loading methods operate below maximum power.Source: §2 · p. 2
  • PV reserve-control approaches include tracking and modeling methods, with trade-offs such as costly irradiance sensing, multistring mismatch constraints, or offline model parameters.The review also notes methods based on measured irradiance and temperature, voltage or current, and single-sample estimation.Source: §2 · pp. 2–3
  • Prior PV VSG strategies without storage add frequency-responsive active power to reserved PV power, but do not mimic the synchronous-generator swing equation.The cited approaches use maximum-power estimation or reserve methods for peer-to-peer and master-slave PV systems.Source: §2 · pp. 3–4
  • Table 1 summarizes the main features of the reviewed PV frequency-regulation strategies.Its caption identifies it as a comparison of PV FR strategies.Source: Table 1 · p. 3, §2 · p. 4
  • The study neglects partial shading because it considers a small-capacity PV system, although partial shading can produce multiple peaks in the PV power-voltage curve.The section notes that prior partial-shading approaches include curve fitting and reference-point scanning.Source: §2 · p. 4

3. PV-diesel-storage island microgrid modeling

The paper models an islanded PV–diesel–storage microgrid based on Yongxing Island and specifies diesel, battery, and two-stage PV subsystems. The model frames why typical VSG control is not adapted to two-stage PV generation.

3. PV-diesel-storage island microgrid modeling

  • The Yongxing Island microgrid operates independently of the utility grid and includes a diesel unit, three two-stage PV generators, battery storage, and distributed loads.Its frequency regulation depends on the diesel unit and battery, while PV operates in MPPT and does not participate in frequency regulation.Source: §3 · pp. 4–5

3.1 Diesel unit

  • The diesel-unit model comprises a diesel unit, valve actuator, synchronous generator, and exciter, with mechanical power and terminal voltage entering the generator.Generator speed and electrical output power are the model outputs.Source: §3.1 · p. 5

3.2 Battery storage

  • The battery is modeled as an ideal voltage source with internal resistance Rs and uses typical VSG control for its DC/AC converter.The VSG swing equation and droop emulate inertia, damping, and governor response, allowing the battery to adjust active power and support primary frequency regulation.Source: §3.2 · pp. 5–6

3.3 PV System

  • Two-stage PV uses a boost converter and grid-connected inverter; conventional control regulates DC-link voltage while PV tracks MPPT rather than providing frequency regulation.The authors identify the inverter active-power loop's DC-link regulation role as a constraint on typical VSG control and motivate an improved strategy for two-stage PV.Source: §3.3 · pp. 6–7

4. The proposed virtual synchronization control of PV generation

The section builds a PV power-reserve curve and maps PV voltage to synchronous-generator power angle to provide frequency support without energy storage. It also estimates maximum-power voltage from PV measurements, with small modeled voltage errors.

4.1. PV array model

  • The study uses a single-diode equivalent PV-array model, whose accuracy the authors consider sufficient for their purpose.The selected array is SunPower's SPR-305E-WHT-D, configured with 5 series and 66 parallel modules.Source: §4.1 · p. 7

4.2. Power reserve control for the PV system

  • A de-loaded power-voltage curve reserves part of PV power, and tracking moves the operating point toward its intersection with that curve from either side.The proposed tracking process is described as automatic regardless of irradiance conditions.Source: §4.2 · pp. 7–8

4.3 The principle of the proposed VSG strategy

  • The PV curve and synchronous-generator power-angle curve share a rising segment with a decreasing rate of change, motivating an analogy between Vpv and δ despite different curve shapes.The analogy is intended to make PV voltage vary with grid-frequency changes and produce similar natural inertial behavior.Source: §4.3 · p. 9

4.4 The proposed VSG strategy

  • Droop control supplies virtual mechanical torque, while swing-equation frequency deviation generates a PV voltage step that shifts the de-loaded curve and target operating point.A voltage limiter keeps operation on the uphill PV-curve segment; at zero grid-frequency deviation, the swing-equation block is disabled and reserve control remains active.Source: §4.4 · pp. 10–12

4.5. Maximum power voltage Vmpp estimation method

  • Measured PV power and voltage define an oblique line that intersects a piecewise-linear maximum-power-voltage curve to estimate Vmpp.The start-up segment is ignored because its PV output power is very small.Source: §4.5 · p. 12
  • PV array modeling reports deviations of 0.4069 V, 0.1653 V, and 0.0058 V between intersections C1–D1, C2–D2, and C3–D3, respectively; D1, D2, and D3 are actual MPPs, and the errors are considered negligible.Source: §4.5 · p. 12

5. Time-domain simulation results

Simulations in an island PV–diesel–storage microgrid compared the proposed VSG with PRC-VSG and PV without frequency regulation across load, irradiance, and PV-penetration conditions. The proposed strategy supported frequency regulation through PV power adjustments and improved frequency response in the reported tests.

5.1 Comparison with the existing VSG method

  • The proposed controller uses a mimic swing equation without dωg/dt and substitutes PV voltage Vpv for power angle δ, while PRC-VSG relies on PLL-derived dωg/dt that is sensitive to delay, error, and noise.The proposed strategy’s self-generated synchronous-generator speed weakens the effect of PLL input.Source: §5.1 · p. 14

5.2 Sudden change in load under standard conditions

  • 49.77 Hz was the proposed VSG frequency nadir after a 10 kW load increase, 0.03 Hz higher than PRC-VSG; PV, diesel unit, and battery peak powers were 14.56, 39.68, and 6.16 kW.The proposed strategy’s power and frequency showed a smooth dynamic process.Source: §5.2 · p. 16, Figure 13 · p. 16
  • 50.23 Hz was the proposed VSG frequency peak after a 10 kW load decrease, 0.03 Hz below PRC-VSG; PRC-VSG’s peak was 50.26 Hz, versus 50.5 Hz without VSG.The proposed strategy reduced PV active power more during the transient; the steady state matched PRC-VSG.Source: §5.2 · p. 17, Figure 15 · p. 18

5.3 Load step change under change in irradiance

  • With changing irradiance, the PV strategies adjusted output around the de-loaded power; when irradiance increased as load fell, the proposed VSG peak was 50.23 Hz, 0.02 Hz below PRC-VSG.At 60 s, both strategies had a system frequency of 50.18 Hz.Source: §5.3 · pp. 20, 22, Figure 19 · p. 22
  • 0.12 Hz maximum frequency deviation, 50.0304 Hz RMS, and 0.0689 Hz RMSE were reported with the proposed VSG under actual load and irradiance, versus 0.16 Hz, 50.0392 Hz, and 0.0886 Hz with PRC-VSG.The figure reports smaller frequency fluctuations with VSG than without it.Source: Figure 21 · p. 23, §5.3 · p. 23

5.4 Effects of PV power penetration level

  • At 30%, 50%, and 70% PV penetration, frequency nadirs with VSG were 49.7, 49.77, and 49.81 Hz; without VSG, nadirs were nearly the same across penetration levels.The paper reports that nadir and steady frequency improve as PV penetration increases when PV participates in frequency regulation.Source: §5.4 · p. 24, Figure 22 · p. 24

6. Conclusion

Simulations in a real island microgrid model indicate that the proposed VSG strategy supports frequency regulation under different irradiance conditions. The reported frequency performance is better as PV penetration increases.

6. Conclusion

  • The strategy reserves part of PV active power using a de-loaded power-voltage curve, then uses PV voltage as an analogue of the synchronous generator power angle to apply swing-equation and droop-governor control.Additional active power is generated and added to the de-loaded power for frequency support.Source: §6 · p. 25
  • The proposed VSG strategy effectively provides PV frequency support under different irradiance conditions in the simulated island microgrid.The study also investigated different PV-PLLs.Source: §6 · p. 25
  • With increased PV penetration, the reported FN and steady frequency show better performance.Source: §6 · p. 25

Appendix

The appendix lists parameter tables for the diesel generator, PV array, fitted equations, and PV generation.

Appendix

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