Phasor-I1 Grid Following Voltage Source Converter
Context
The Phasor-\(I_1\) Grid Following Voltage Source Converter (VSC) model [1] is derived from the Full-Phasor.
Model use, assumptions, validity domain and limitations
The model can be used to fasten the simulations for low-frequency phenomena studies. If the simulation step size is desired to be close to the dynamics of the current control loop (around \(10^3\) \(\mu s\)), the Phasor-\(I_1\) model performs better than the Full-Phasor model, which will have an important increase of the error (or even divergence) when using these step sizes.
The assumptions made starting from the Full-Phasor model are the following:
- The current loop is substituted by a first-order transfer function with a given time constant.
The model shows a performance close to more accurate models during for slow dynamics such as setpoint tracking or voltage/frequency deviation. It can solve high frequency phenomena with clear limitations, as the results do not capture correctly the dynamics of phenomena like asymmetrical faults.
Although it allows a bigger time step than the Full-Phasor model, it eventually will diverge if it is increased too much, as it still retains some dynamics in an approximate way. The Phasor-\(I_0\) model is more suitable as it completely removes the current loop dynamics.
Model description
The diagram of the complete model is shown in the following figure.
Figure 1: Phasor-I1 Model Block Diagram [1]
The following subsections will describe the changes with respect to the Full-Phasor model.
Current loop
The differential equations that modelled the behavior of the current loop are substituted by a first-order transfer function with a given time constant:
\[ \frac{i_c^{qd*}}{i^{qd*}} = \frac{1}{1 + \tau_c s} \]
where \(\tau_c = \frac{1}{w_c}\) is the time constant of the current loop, being \(w_c\) the frequency that is set to match the bandwidth of the original current loop.
Outer loop
No changes are made directly to this outer-loop, although the time constant \(\tau_c\) will act as a low-pass filter of the current setpoint provided by the outer loop.
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