Grid-connected inverter with virtual synchronous machine

Introduction

VSG model

The VSG consists of an energy source, a converter, and a control mechanism. The VSG control block is based on the following the swing equations for SGs.

Swing Equation:

$\ddot{\theta }=\frac{1}{J}\left(T_e-T_m-D_p\dot{\theta }\right)$

Electromagnetic torque:

${\mathrm{T}}_{\mathrm{e}}=M_f{i}_f〈i,\widetilde{\sin \theta }〉$

Three-phase generated voltage:

$e=\dot{\theta }{M}_f{i}_f\widetilde{\sin \theta }$

Reactive power:

$Q=-\dot{\theta }{M}_f{i}_f〈i,\widetilde{\cos \theta }〉$

where:

$\widetilde{sin\theta } =\left[\begin{array}{c}\sin \theta \\ \sin (\theta -\frac{2\pi }{3})\\ \sin (\theta +\frac{2\pi }{3})\end{array}\right]$

$\widetilde{\cos \theta } =\left[\begin{array}{c}\cos \theta \\ \cos \theta -\frac{2\pi }{3}\\ \cos \theta +\frac{2\pi }{3}\end{array}\right]$

Virtual inertia is proportional to the nominal power of the VSG divided by the maximum allowable rate of frequency change.

Model description

The electrical part of the model is shown in Figure 1. It is a three-phase inverter model. For powering the DC link, the inverter uses an ideal DC source. The grid-side connection of the inverter is implemented using an LC filter. The suggested parameters of the filter for this model are C=20e-6 F and L=2.6e-3 H (the parameters are set in the model initialization panel). On the left side of the schematic there is the three-phase grid with an RL impedance. Components for the phase measurements of current and voltage are located between the grid and the inverter.

Figure 1: Three-phase grid-connected inverter

The control part consists of active- and reactive-power regulation loops which are shown in Figure 2. The reference for the frequency (wg) is set in the model initialization panel. The reference for the active power (Pref) is set in HIL SCADA by adjusting the slider to the desired value. The active power loop uses a mechanical friction coefficient (D) as a feedback gain. Further, this loop regulates the speed of the VSG and generates the phase angle theta. The reference for the reactive power (Qref) is set in HIL SCADA by adjusting the slider to the desired value. This loop generates the phase angle phi, which is further used in the torque calculation and in the generation of the converter reference signals.

Figure 2: Active and reactive power regulation loops

The electromagnetic torque calculation and reference signals for the inverter are shown in Figure 3. The electromagnetic torque (left of Figure 3) is calculated using the Swing Equations described in the VSG Model section. The PWM reference signals are generated and routed to the inverter via the voltage of the DC link (VDC, shown in Inverter Voltage References at the right of Figure 3), the phi angle from the reactive power regulation loop (previously calculated in Reactive Power Regulation at the bottom right of Figure 2), and sine transformations (calculated in Trigometric Functions in the middle of Figure 3).

Figure 3: Electromagnetic torque calculation and voltage reference signals

Simulation

This application comes with a pre-built SCADA panel (Figure 4). The panel offers most essential user interface elements (widgets) to monitor and interact with the simulation in runtime. You can customize it freely to fit your needs.

Figure 4: SCADA panel

Authors

The model featured in this application note was originally created by our academic partners. For domain-specific questions, the original authors of the application can be contacted directly:

• Prof. Felipe Bovolini Grigoletto ([email protected])
• Prof. Márcio Stefanello, ([email protected]), Federal University of Pampa, Brazil (UNIPAMPA).