Phasor-I0 Grid Following Voltage Source Converter

Authors: Carlos Alegre (eRoots)

Reviewers: Eduardo Prieto Araujo (UPC), Josep Fanals Batllori (eRoots)

Context

The Phasor-$I_0$ Grid Following Voltage Source Converter (VSC) model is derived from the Full-Phasor.

Model use, assumptions, validity domain and limitations

The model has uses similar to the $I_1$ model, with some improvement in the simulation speed while the precision is slightly reduced.

The assumptions made starting from the Full-Phasor model are the following:

The current loop is completely removed from the model. The current obtained from the outer loop is directly considered to be provided by the VSC.
Since there are no current dynamics, the outer loop is modified to maintain the closed-loop from the Full-Phasor model.

The model is valid for low-frequency phenomena studies, similarly to the Phasor-I1 model, but it allows for bigger time-steps (around 2 or 3 times greater time-step size). The medium to high-frequency events ($>100$ Hz) are not captured as well as in the Full-Phasor model for instance.

Model description

The diagram of the complete model is shown in the following figure.

Figure 1: Phasor-I0 Model Block Diagram [1]

The following subsections will describe the changes with respect to the Full-Phasor model.

Current loop

The block is completely removed, which means $i^{qd*} = i^{qd*}_c$.

Outer loop

The outer loop, or power loop, has to be adapted since it had the dynamics of the current loop included in its transfer function. The closed-loop transfer function of the outer loop is:

$$ C_{pq}(s) = \frac{G_{pq}(s)}{1 + G_{pq}(s)} = \frac{1}{1+\tau_{pq}s} $$

where $\tau_{pq} = \frac{1}{\omega_{pq}}$ is the time constant of the original outer loop. The new open-loop transfer function, which does not include the current loop dynamics, is:

$$ G_{pq}(s) = K_{pq}(s)\frac{3}{2}v_g^{q} $$

where $v_g^{q}$ can be considered to be $V_peak$. The controller is then:

$$ K_{pq}(s) = \frac{2}{3V_{peak}} \frac{1}{\tau_{pq}s} $$

Open-source implementations

No open-source implementations have been found.

Table of references

[1] Lacerda, V. A.; Prieto-Araujo, E.; Cheah, M.; Gomis-Bellmunt, O. “Phasor Modeling Approaches and Simulation Guidelines of Voltage-Source Converters in Grid-Integration Studies”, May 2022, IEEE Access, DOI: 10.1109/ACCESS.2022.3174958

[2] Lacerda, V. A.; Prieto-Araujo, E.; Cheah, M.; Gomis-Bellmunt, O. “Phasor and EMT models of grid-following and grid-forming converters for short-circuit simulations.”, October 2023, vol. 223, núm. 109662. DOI: 10.1016/j.epsr.2023.109662

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