# New model of multi-parallel distributed generator units based on virtual synchronous generator control strategy

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## Abstract

Virtual synchronous generator (VSG) control technique presents a promising alternative for controlling the inverter-based distributed generator (DG), due to its capability to improve the microgrid stability when the renewable energy has a high penetration level into the grid. The analyses and parameters design of the active and reactive power loop of DG are often based on a small-signal model, where a linear relationship between active and reactive powers versus control variables is obtained based on quasi-static method, in which the currents dynamic is neglected. This model gives qualitative results only in case of large conventional synchronous generators. However, for a small DG based on VSG controller with a small virtual inertia, fast power electronics devices and with coupling between active and reactive powers loops, this model does not give satisfactory results. To overcome the aforementioned problem, this paper proposes a new model of DG systems based on VSG operating in island microgrids. The proposed model incorporates the line impedance dynamic of the microgrid into the DG model. The accuracy of the proposed model has been investigated and compared with the conventional one using MATLAB/Simulink environment. Simulation obtained results prove that the new model is more precise compared to the conventional one in transit state reflecting by the way better the dynamics of the system and allowing as a consequence of a good analysis of the stability and behaviour of the global system.

## Keywords

Virtual synchronous generator (VSG) Microgrid Power electronics converter Renewable energy sources Distributed generator Grid stability## Abbreviations

- VSG
Virtual synchronous generator

- DG
Distributed generator

- SG
Synchronous generator

- PCC
Point of common coupling

- VSI
Voltage source inverter

- CSI
Current source inverter

## List of symbols

*L*_{F}Inductance of the inverter filter

*C*_{F}Capacitance of the inverter filter

*R*_{L}Line resistance

*X*_{L}Line reactance

*Z*_{L}Line impedance

*V*_{m}Inverter voltage magnitude

*V*_{g}Grid voltage magnitudes

*θ*_{m}Virtual mechanical phase

*θ*_{g}Grid voltage phase

*P*_{out}Injected active power

*Q*_{out}Injected reactive power

*V*_{gdq}Voltage at the PCC in dq reference frame

*I*_{gdq}Current at the PCC in dq reference frame

*D*Virtual damping coefficient

*J*Virtual inertia

*P*_{in}Input active power

*Q*_{out}Input reactive power

*ω*_{m}Virtual mechanical velocity

*ω*_{g}Grid angular velocity

*P*_{ref}Active power reference

*ω*_{0}No-load angular velocity

*K*_{p}Frequency droop regulator coefficient

*V*_{0}No-load voltage magnitude

*K*_{q}Reactive droop regulator coefficient

*K*_{i}Voltage regulator integral coefficient

*Q*_{ref}Reactive power reference

**δ**Load angle

- Δ
Small perturbations of the variable

## Subscripts

- 0
Equilibrium operating point

- out
Output

- in
Input

- dq
Direct and quadratic axis

- ref
Reference

- m
Mechanical

- g
Grid

- L
Line

- F
Filter

## Notes

### Acknowledgements

The Algerian Ministry of Higher Education and Scientific Research (Research PRFU Project A01L07UN190120180005) supported this research.

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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