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.

The rapid growth of the distributed generators (DGs) integration into the distribution systems (DSs) creates new technical issues; conventional relay settings need to be updated depending on the network topology and operational mode as fault protection a major challenge. This emphasizes the need for new fault protection methods to ensure secure protection and prevent undesirable tripping. Total harmonic distortion (THD) is an important indicator for assessing the quality of the grid. Here, a new protection system based on the THD of the grid voltages is proposed to address fault events in the electrical distribution network. The proposed protection system combines the THD with the estimates of the amplitude voltages and the zero-sequence component for defining an algorithm based on a finite state machine (FSM) for the detection, identification, and isolation of faults in the grid. The algorithm employs communication lines between all the protective devices (PDs) of the system to transmit tripping signals, allowing PDs to be coordinated. A second order generalized integrator (SOGI) and multiple SOGI (MSOGI) are used to obtain the THDs, estimated amplitude voltages, and zero-sequence component, which allows for fast detection with a low computational burden. The protection algorithm performance is evaluated through simulations in MATLAB/Simulink and a comparative study is developed between the proposed protection method and a differential relay (DR) protection system. The proposed method shows its capability to detect and isolate faults during different fault types with different fault resistances in different locations in the proposed network. In all the tested scenarios, the detection time of the faults has been between 7–10 ms. Moreover, this method gave the best solution as it has a higher accuracy and faster response than the conventional DR protection system.

The dynamic performance of the local control of single-phase voltage source inverters (VSIs) can be degraded when supplying to nonlinear loads (NLLs) in microgrids. When this control is based on the droop principles, a proper calculation of the active and reactive averaged powers (P–Q) is essential for a proficient dynamic response against abrupt NLL changes. In this work, a VSI supplying to an NLL was studied, focusing the attention on the P–Q calculation stage. This stage first generated the direct and in-quadrature signals from the measured load current through a second-order generalized integrator (SOGI). Then, the instantaneous power quantities were obtained by multiplying each filtered current by the output voltage, and filtered later by utilizing a SOGI to acquire the averaged P–Q parameters. The proposed algorithm was compared with previous proposals, while keeping the active power steady-state ripple constant, which resulted in a faster calculation of the averaged active power. In this case, the steady-state averaged reactive power presented less ripple than the best proposal to which it was compared. When reducing the velocity of the proposed algorithm for the active power, it also showed a reduction in its steady-state ripple. Simulations, hardware-in-the-loop, and experimental tests were carried out to verify the effectiveness of the proposal.

The average active and reactive powers, P and Q, are crucial parameters that have to be calculated when sharing common loads between parallelized droop-operated single-phase inverters. However, the droop method algorithm should employ low-pass filters (LPF) with very low cutoff frequency to minimize the distortion impact in the provide droop amplitude and frequency references. This situation forces the droop control to operate at a very low dynamic velocity, degrading the stability of the parallelized system. For this reason, different solutions had been proposed in literature to increase the droop velocity, but the issues derived from the sharing of nonlinear loads had not been properly considered. This work proposes a novel method to calculate P and Q based on the fundamental components of the inverter's output voltage and current and using the measured phase angle between the output voltage and current. The method is used under normal and highly distorting conditions due to the sharing non-linear loads. The fundamental components are obtained by means of the highly filtering capability provided by norder cascaded second order generalized integrators (nSOGI). The proposed method leads to faster and more accurate P and Q calculations that enhances the droop-method dynamic performance. Simulations are provided to validate the proposal.

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