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The active and reactive powers, P and Q, are crucial variables in the parallel operation of single-phase inverters using the droop method, introducing proportional droops in the inverter output frequency and voltage amplitude references. P and Q, or P-Q, are calculated as the product of the inverter output voltage and its orthogonal version with the output current, respectively. However, when sharing nonlinear loads these powers, Pav and Qav, should be averaged by low-pass filters (LPFs) with a very low cut-off frequency to avoid the high distortion induced by these loads. This forces the droop method to operate at a very low dynamic velocity and degrades the system stability. Then, different solutions have been proposed in literature to increase the system velocity, but only considering linear loads. Therefore, this work presents a method to calculate Pav and Qav using second-order generalized integrators (SOGI) to face this problem with nonlinear loads. A double SOGI (DSOGI) approach is applied to filter the nonlinear load current and provide its fundamental component to the inverter, leading to a faster dynamic velocity of the droop-based load sharing capability and improving the stability. The proposed method is shown to be faster than others in the literature when considering nonlinear loads, while smoothly driving the system with low distortion levels. Simulations, hardware-in-loop (HIL) and experimental results are provided to validate this proposal.

A novel passivity-based coordinated control strategy is proposed for an islanded AC microgrid including renewable energy source and energy storage system units. The main advantage is that the proposed coordinated control strategy manages the microgrid without using a phase-locked loop system. In the microgrid, the energy storage system supports the voltage of the microgrid, and the renewable energy sources inject their maximum power to the microgrid in the normal operation. For the energy storage system, we use a proportional-resonant controller, and for the renewable energy sources, we use a voltage modulated direct power control method, which has not only a good tracking performance but also a good steady-state behavior. Another advantage of the proposed method is that the asymptotical stability of the whole microgrid can be guaranteed by using the passivity principle when the heterogeneous renewable energy sources are integrated into the microgrid. To validate the proposed coordinated control law, we use a microgrid consisting of one energy storage system, one wind turbine, one photovoltaic and two controllable loads. Simulation results show that the plug-andplay capability of the wind turbine and photovoltaic in the microgrid is enhanced when comparing with the conventional vector current control method with a phase-locked loop system. Moreover, the voltage and frequency of the microgrid are recovered to its nominal value by the energy storage system with the proposed method as well. Finally, experimental verification of the proposed coordinated control algorithm is performed

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