A State-Space Model of an Inverter-Based Microgrid for Multivariable Feedback Control Analysis and Design

Abstract

In this work, a synchronous model for grid-connected and islanded microgrids is presented. The grid-connected model is based on the premise that the reference frame is synchronized with the AC bus. The quadrature component of the AC bus voltage can be cancelled, which allows to express output power as a linear equation for nominal values in the AC bus amplitude voltage. The model for the islanded microgrid is developed by integrating all the inverter dynamics using a state-space model for the load currents. This model is presented in a comprehensive way such that it could be scalable to any number of inverter-based generators using inductor–capacitor–inductor (LCL) output filters. The use of these models allows designers to assess microgrid stability and robustness using modern control methods such as eigenvalue analysis and singular value diagrams. Both models were tested and validated in an experimental setup to demonstrate their accuracy in describing microgrid dynamics. In addition, three scenarios are presented: non-controlled model, Linear-Quadratic Integrator (LQI) power control, and Power-Voltage (PQ/Vdq) droop–boost controller. Experimental results demonstrate the effectiveness of the control strategies and the accuracy of the models to describe microgrid dynamics.

A Linear Quadratic Regulator With Optimal Reference Tracking for Three-Phase Inverter-Based Islanded Microgrids

“…The complete microgrid model is used to assess stability and robustness in islanded mode. Other applications regarding stability and robustness analysis of this model have been presented in [31]. The circuit considered for the islanded microgrid model is shown in Fig.…”

“…Also, robustness of the entire microgrid is assessed by using robustness analysis techniques such as robustness margins estimations under frequency and load and variations. Other applications regarding stability and robustness analysis of this model are presented in [31].…”

Review of Dynamic and Transient Modeling of Power Electronic Converters for Converter Dominated Power Systems

“…A methodology to develop a small-signal model of a CDPS in grid-forming mode for any number of PECs in the dq0 frame was developed in [80]. The resulting model was able to describe the interaction between all the PECs with regards to the voltage, current, and shared power.…”

Design of a Hybrid Energy System with Energy Storage for Standalone DC Microgrid Application

“…The DC-DC Boost Converter regulates the DC bus voltage through MPPT control and PI control algorithms, discussed in the previous subsections. The MPPT control output is shown by (21), while the one from the PI is shown by (22). One should note that the reference r[k] of ( 22) is replaced by V dc,re f [k] and the measured output y[k] is replaced by the measured DC bus voltage V dc [k].…”

“…There have been active studies on stability of microgrids connected to the main grid [18][19][20] with some promise of good performance. The model for the islanded microgrid is developed by integrating all the inverter dynamics using a state-space model for the load currents [21]. However, these studies are not focused on voltage control of DC microgrids for rural areas.…”