Modelling MultiMicrogrids: Comparative Studies on Modelling Details
Sidhaarth Venkatachari (NIT Trichy), Praanesh Raman, and J. C. H. Peng  Summer Project  Date: 2018
Proper modeling of inverterbased microgrids is essential for accurate assessment of grid stability. Recent research has shown that the stability region of droopcontrolled microgrids is significantly different from those known in conventional power systems. In particular, the network dynamics have a major influence on the stability of slower modes despite their fast decaying nature.
Microgrid models depend on a set of assumptions/simplifications. With respect to the stability analysis, the main point to ponder is whether a particular model reduction technique would give incorrect results – predicting instability when the system is actually stable. To this end, a detailed model has been developed considering all internal states of an inverter. While the detailed model is perhaps the most reliable option for stability assessment, it suffers from the following drawbacks:

Detailed models are computationally expensive, particularly with increase in the number of inverters.

Difficult to analyse the factors influencing the system stability since there are several interrelated parameters. In short, proper correlation between various parameters and their corresponding effects on the stability of the system is difficult.
Lessons Learnt:

It has been found that the obtained stability conditions are unique for microgrids, and similar behaviour has not been observed in largescale power system networks.

The conventional thirdorder model does not take into account the electromagnetic transients. The model could mislead the operator about the true stability of the network.

The influence of fast degrees of freedom on the system dynamics can be accurately quantified in the FifthOrder and High Fidelity ThirdOrder models. We could show that it is the network dynamics that play the key role in stability violation. As a result, neglecting the network dynamics could lead to incorrect prediction of the stability regions.
High Fidelity Model
Fig. 1. Polezero plot of high fidelity model for a single inverter
Electromagnetic FifthOrder Model
Fig. 2. Polezero plot of high fidelity model for a single inverter
The high fidelity thirdorder model accounts for the electromagnetic transients in the formation of its Ybus matrix. Laplace terms are added to each complex impedance to account for the electromagnetic transients.
One may assume that the fast electromagnetic transients  currents Id and Iq always remain close to their quasistationary values derived from Kirchhoff’s laws. Formally, this procedure is equivalent to neglecting the derivative terms in the line equations. Such approximation is universally accepted for small signal stability analysis in traditional power systems. The key to building a fifthorder statespace model is to represent the line parameters in terms of inverter parameters. It is here that the Ybus matrix could be put to use effectively.
Validation using RealTime Digital Simulator (RTDS)
A twoinverter system (with droop control) has been built using RSCAD software, and is complied to run on RTDS. Construction of the circuit and the corresponding results are shown in Fig. 3 and 4. The frequency droop coefficient is 0.2%, and the voltage droop coefficient is 5%. The timedomain waveforms agree with those found in the numerical simulations.
Fig. 3 Twoinverter system with droop control and equal load sharing.
Fig. 4 Schematic of the developed microgrid in RSCAD.
Fig. Voltage profile at each inverter point of common coupling (PCC). Note that grid frequency is around 50 Hz.