Modeling and Stability Analysis of Parallel Connected Inverters in Micro-grid Systems

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In the future grid, more distributed generation resources will replace traditional synchronous generators. As a result, smaller, localized generation units are integrated near the consumption sites, resulting in the use of inverter-based generation to meet voltage and frequency requirements. It is important to note that, despite the many advantages of inverters, they are vulnerable to stability and resonance problems in many applications, including rooftop solar inverters, MW-scale solar inverters, electric traction systems, offshore wind farms, and high-voltage direct current transmission lines. For these reasons, modeling of power electronic converters, particularly inverters, has become an increasingly important part of analyzing the potential impact of their widespread adoption on future power grids. Furthermore, in order to establish a resilient and reliable grid infrastructure, it is crucial that investigations are conducted in advance, focusing on resonance and stability phenomena. In response to these challenges, this thesis proposes small signal DC impedance models for a grid-tied converter operating in an open loop, closed loop dq current control, and DCLV (DC link voltage control) control loop with consideration of PLL dynamics. It is noticed that both the magnitude and phase plots of DCIMs show surges and dips around the PLL bandwidth. Because of this, when DCIMs interact with DCNIs close to the PLL bandwidth, they cause oscillations in the DCLV, which results in unstable operation of the converter. The research presented in this thesis is further extended by proposing impedance models (i.e., observing from the DC side) for grid-forming converters' open-loop and closed-loop load voltage control. DC link voltage stability analysis has been investigated using the proposed DC impedance models. Based on the impedance stability analysis, it can be concluded that the variations in the parameters of the outer loop controller are responsible for the unstable operation of the grid-forming converter. In addition, it is evident that the changes in DCNI (Equivalent impedance of converters connected at the DC network terminals) result in the instability of the overall system. This thesis also proposes a comprehensive state space modeling and Eigenvalue-based stability analysis of islanded microgrids that incorporate all control loops and parameters of the networks to ensure equal and proportional reactive power sharing. Also, the proposed modeling and analysis accurately predict the effect of various control loop parameters on the stability of an islanded AC microgrid. Additionally, the limiting values of different control parameters are presented, facilitating the design of effective control strategies. The proposed modeling and analysis are validated using Typhoon Hardware in-the-loop testbed, and the results are presented. Finally, this thesis developed and presented detailed small-signal state-space models specially designed for islanded microgrids with IMC. Time-domain simulations have validated these models to ensure their fidelity and applicability. The proposed state-space models were tested for robustness by performing a load change test. Furthermore, a control strategy that combines line impedance compensation with virtual impedance control has been introduced to achieve equal active and reactive power sharing among converters, particularly in the presence of differing cable impedances.

Impedance-based Stability Analysis, Internal Model Controller, Parallel Operation of Inverters, and Grid Forming Inverters
Portions of this document appear in: Gaddala, R.K.; Majumder, M.G.; Rajashekara, K. DC-Link Voltage Stability Analysis of Grid-Tied Converters Using DC Impedance Models. Energies 2022, 15,6247.