Modelling Multi-Microgrids: Comparative Studies on Modelling Details

Sidhaarth Venkatachari (NIT Trichy), Praanesh Raman, and J. C. -H. Peng | Summer Project | Date: 2018

Proper modeling of inverter-based microgrids is essential for accurate assessment of grid stability. Recent research has shown that the stability region of droop-controlled 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:


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

  2. Difficult to analyse the factors influencing the system stability since there are several inter-related parameters. In short, proper correlation between various parameters and their corresponding effects on the stability of the system is difficult.

Lessons Learnt:

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

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

  3. The influence of fast degrees of freedom on the system dynamics can be accurately quantified in the Fifth-Order and High Fidelity Third-Order 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. Pole-zero plot of high fidelity model for a single inverter

Electromagnetic Fifth-Order Model

Fig. 2. Pole-zero plot of high fidelity model for a single inverter


The high fidelity third-order model accounts for the electromagnetic transients in the formation of its Y-bus 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 quasi-stationary 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 fifth-order state-space model is to represent the line parameters in terms of inverter parameters. It is here that the Y-bus matrix could be put to use effectively.

Validation using Real-Time Digital Simulator (RTDS)

A two-inverter 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 co-efficient is 0.2%, and the voltage droop co-efficient is 5%. The time-domain waveforms agree with those found in the numerical simulations.

Fig. 3 Two-inverter 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.

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