This paper proposes an improved maximum power point tracking (MPPT) method for the photovoltaic (PV) system using a modified particle swarm optimization (PSO) algorithm. The main advantage of the method is the reduction of the steady- state oscillation (to practically zero) once the maximum power point (MPP) is located. Furthermore, the proposed method has the ability to track the MPP for the extreme environmental condition, e.g., large fluctuations of insolation and partial shading condition. The algorithm is simple and can be computed very rapidly; thus, its implementation using a low-cost microcontroller is possible. To evaluate the effectiveness of the proposed method, MATLAB simulations are carried out under very challenging conditions, namely step changes in irradiance, step changes in load, and partial shading of the PV array. Its performance is compared with the conventional Hill Climbing (HC) method. Finally, an experimental rig that comprises of a buck-boost converter fed by a custom-designed solar array simulator is set up to emulate the simulation. The soft- ware development is carried out in the Dspace 1104 environment using a TMS320F240 digital signal processor. The superiority of the proposed method over the HC in terms of tracking speed and steady-state oscillations is highlighted by simulation and experimental results.

An Improved Particle Swarm Optimization (PSO)–Based MPPT for PV With Reduced Steady-State Oscillation

This paper addresses the harmonic stability caused by the interactions among the wideband control of power converters and passive components in an ac power-electronics-based power system. The impedance-based analytical approach is employed and expanded to a meshed and balanced three-phase network which is dominated by multiple current- and voltage-controlled inverters with LCL- and LC-filters. A method of deriving the impedance ratios for the different inverters is proposed by means of the nodal admittance matrix. Thus, the contribution of each inverter to the harmonic stability of the power system can be readily predicted through Nyquist diagrams. Time-domain simulations and experimental tests on a three-inverter-based power system are presented. The results validate the effectiveness of the theoretical approach.

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Modeling and Analysis of Harmonic Stability in an AC Power-Electronics-Based Power System

This paper investigates the capacitor-current-feedback active damping for the digitally controlled LCL-type grid-connected inverter. It turns out that proportional feedback of the capacitor current is equivalent to virtual impedance connected in parallel with the filter capacitor due to the computation and pulse width modulation (PWM) delays. The LCL-filter resonance frequency is changed by this virtual impedance. If the actual resonance frequency is higher than one-sixth of the sampling frequency (fs/6), where the virtual impedance contains a negative resistor component, a pair of open-loop unstable poles will be generated. As a result, the LCL-type grid-connected inverter becomes much easier to be unstable if the resonance frequency is moved closer to fs/6 due to the variation of grid impedance. To address this issue, this paper proposes a capacitor-current-feedback active damping with reduced computation delay, which is achieved by shifting the capacitor current sampling instant towards the PWM reference update instant. With this method, the virtual impedance exhibits more like a resistor in a wider frequency range, and the open-loop unstable poles are removed; thus, high robustness against the grid-impedance variation is acquired. Experimental results from a 6-kW prototype confirm the theoretical expectations.

Capacitor-Current-Feedback Active Damping With Reduced Computation Delay for Improving Robustness of LCL-Type Grid-Connected Inverter

This paper addresses the resonance problem in a parallel-inverter-based grid-interactive microgrid. Unlike the single grid-connected inverter system where the resonance frequency is mainly fixed by the inverter output LCL filter parameters, the parallel-inverter-based grid-interactive microgrid system presents a more challenging picture where inverter interactions will excite complex resonances at various frequencies. As a result, line currents of inverters can be severely distorted even when the control schemes and filter circuits are properly designed based on the single-inverter model. This paper first develops a microgrid model using discrete time-domain closed-loop Norton's equivalent circuit. Multiple resonances can then be evaluated with the developed model. To improve the microgrid power quality, this paper also designs a virtual-harmonic-resistance-based active damping method. The proposed damping method can be seamlessly incorporated into the conventional deadbeat control scheme through the direct control reference modification. Therefore, the active damping method is able to address both the transient and steady-state resonances within the deadbeat current control bandwidth. Simulation and experimental results are provided to validate the correctness of the developed resonance modeling and active damping methods.

Investigation and Active Damping of Multiple Resonances in a Parallel-Inverter-Based Microgrid

The current-controlled grid-connected inverter with LCL filter is widely used in the distributed generation system (DGS), due to its fast dynamic response and better power quality features. However, with the increase of power injected into the grid, control performances of the inverter will be significantly influenced by the nonideal grid conditions. Specifically, the possible wide variation of the grid impedance challenges the system stability. Meanwhile, background harmonics of the grid can greatly distort the injected current. Therefore, the control of the inverter should be designed with strong stability-robustness and high harmonic-rejection-ability, both of which correlate closely with the inverter output impedance. However, it is difficult to shape the output impedance into the one with a desirable characteristic simply by adjusting the current loop gain. In this paper, an impedance shaping method is proposed with virtual impedances, and the current control loop can be designed independently. The implementation and parameter design of the virtual impedances are studied under the practical considerations. With this proposed method, the grid-connected inverter can work stably over a wide range of the typical inductive-resistive grid impedance and exhibit strong rejection ability of grid-voltage harmonics. Experimental results from a 6-kW single-phase grid-connected inverter confirm the effectiveness of the proposed method.

Impedance Shaping of the Grid-Connected Inverter with LCL Filter to Improve Its Adaptability to the Weak Grid Condition

Designing adequate control laws for grid-connected inverters with LCL filters is complicated. The power quality standards and the system resonances burden the task. In order to deal with resonances, system damping has to be implemented. Active damping is preferred to passive damping so as to improve the efficiency of the conversion. In addition, paralleled grid-connected inverters in photovoltaic (PV) plants are coupled due to grid impedance. Generally, this coupling is not taken into account when designing the control laws. In consequence, depending on the number of paralleled grid-connected inverters and the grid impedance, the inverters installed in PV plants do not behave as expected. In this paper, the inverters of a PV plant are modeled as a multivariable system. The analysis carried out enables to obtain an equivalent inverter that describes the totality of inverters of a PV plant. The study is validated through simulation and field experiments. The coupling effect is described and the control law design of paralleled grid-connected inverters with LCL filters in PV plants is clarified.

M Borrega

Papers

Modeling and Control of $N$ -Paralleled Grid-Connected Inverters With LCL Filter Coupled Due to Grid Impedance in PV Plants