This paper demonstrates the design of robust proportional resonant (PR) controller using negative imaginary (NI) theorem for voltage control of three-phase islanded microgrid (MG) application. While operating MG as the islanded mode, different types of random and unknown load dynamics affect the MG. These loads eventually deteriorate the proper execution of MG-inducing disturbances in voltage and current. Therefore, to improve the performance of the three-phase MG, a simple, second-order controller is designed with the combination of NI theory and PR (NI-PR) controller. This controller is capable of providing higher level of damping as well as excellent stability properties. The stability and effectiveness of this controller are examined through imposing uncertainties, in terms of several load dynamics as well as different fault conditions. The comparison with respect to linear quadratic regulator and model predictive controller also ascertains the robustness of the designed controller. The NI-PR controller and the system are simulated in MATLAB/SIMULINK platform. Keywords Islanded microgrid • Negative imaginary theory • Second-order controller • Voltage control • Robust performance 1 Introduction Keeping the pace with progressive advanced facilities, demand for energy is rising lavishly. But due to the environmental protection, depletion of fossil fuel and sustainable development resulted in critical need for a cleaner energy technology (Bouchebbat and Gherbi 2017; Islam et al. 2020c). Hence, renewable energy sources are playing a vital role in today's power system applications. Some popular renewable energy sources are wind energy, photovoltaic (PV) system, biomass, wave energy, hydro-power, etc. (Coelho et al. 2018). Renewable energy sources-based distributed generators (DGs) are mainly small-scale power generation

The invention of doubly‐fed induction generator (DFIG) brings the wind energy one step ahead as renewable power generation. But the performance of the grid‐connected DFIGs are greatly affected by grid disturbances as their stator windings are interfaced to the grid directly. Different fault current limiters are capable of improving fault ride through capability during short circuit faults. Nonlinear controller based fault current limiters (FCLs) are superior to deal with the nonlinearity of the power systems. This paper proposes a nonlinear adaptive backstepping controller (ABSC) based capacitive bridge‐type FCL (CBFCL) to enhance the fault ride through capability of a DFIG‐based wind farm connected to a multi‐machine power system. At first, a complete modelling of the CBFCL is derived to understand its behaviour during the normal and fault period more accurately. Then, the ABSC is designed based on that dynamic model, along with the backstepping controller (BSC) and sliding mode controller (SMC) for comparison purpose. Finally, the performance of the ABSC to control the CBFCL has been analysed and verified by comparing with that of the BSC and the sliding mode controller. All the graphical and mathematical analyses favour the ABSC based CBFCL under symmetrical and asymmetrical fault (both temporary and permanent) scenarios.

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Growing application of distributed generation units at remote places has led to the evolution of microgrid (MG) technology. When an MG system functions independently, i.e., in autonomous mode, unpredictable loads and uncertainties emerge throughout the system. To obtain stable and flexible operation of an autonomous MG, a rigid control mechanism is needed. In this paper, a robust high-performance controller is introduced to improve the performance of voltage tracking of an MG system and to eliminate stability problems. A combination of a resonant controller and a lead-lag compensator in a positive position feedback path is designed, one which obeys the negative imaginary (NI) theorem, for both single-phase and three-phase autonomous MG systems. The controller has excellent tracking performance. This is investigated through considering various uncertainties with different load dynamics. The feasibility and effectiveness of the controller are also determined with a comparative analysis with some well-known controllers, such as linear quadratic regulator, model predictive and NI approached resonant controllers. This confirms the superiority of the designed controller.