Resonant and repetitive controllers are well suited for single-phase grid-connected inverters due to their optimum tracking and harmonic rejection capability. In particular, in this paper, their application for single-phase photovoltaic systems is considered. The effects of nonlinear inductance on the performance of current controllers designed to track periodic signals and/or to compensate periodic disturbances are investigated. When the inductance has a nonlinear behavior, a distorted current waveform is produced. Two different nonlinearities have been considered: saturation for high currents and a light nonlinearity, which occurs in the first portion of the magnetization curve, for low currents. A current-dependent model of the nonlinear inductance has been developed. It is mathematically based on the Volterra-series expansion, and it allows us to prove how the harmonic compensation provided by resonant and repetitive controllers can also mitigate the effects of the inductance saturation. This result is the main contribution of this paper, and it is also substantiated with experimental evidence. Moreover, the repetitive controller is able to comply with the harmonic limits reported in IEEE 1547 and IEC 61727, even in very hard saturation conditions.

Study of the Effects of Inductor Nonlinear Behavior on the Performance of Current Controllers for Single-Phase PV Grid Converters

The powder-core-based inductor has a wide inductance variation due to the soft-saturation nature when subjected to varying load current. Under such a condition, the current ripple is influenced, and the conventional inductor design principle may be inaccurate. Besides, the voltage of the inductor is distorted. Also, the bandwidth of the controller is hard to determine. In this paper, the current ripple under the condition of wide inductance variation is analyzed, and its change rule is revealed; then, a new inductance design principle is proposed. The harmonic components for the three-phase converter with the powder core inductor are investigated, and the harmonic characteristic of the input current is analyzed. According to the current harmonic characteristic, the resonance controllers are introduced to eliminate harmonics, and the quality of the current is improved. Besides, the bandwidth of the controller is found to vary with the output power. Then, a compensation method is proposed to eliminate the influence of inductance variation on the bandwidth. The experimental results verify the analysis.

Current Ripple Analysis and Controller Design for Grid-Connected Converters Considering the Soft-Saturation Nature of the Powder Cores

The stability analysis of grid-connected converters have attracted increasing attentions, due to the oscillations arising in wind power plants, micro-grids, and other emerging power electronics based power systems. The modeling tool of converters thus becomes essential to faithfully reveal oscillations without any hidden regions. This paper presents a detailed comparison of two linearized modeling methods, which are, respectively, developed in the Linear Time-Invariant (LTI) and the Linear Time-Periodic (LTP) frameworks. The LTP model can consider the effect of frequency-coupling dynamics, which are occurred by the time-varying behavior, while the conventional LTI model can not capture this behavior. The advantages and limits of two models are then illustrated with examples. The compared results are verified in the frequency domain and time domain as well.

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Comparison of LTI and LTP models for stability analysis of grid converters

Recently, maintenance applications around power lines have been actively studied. These applications usually supply power through magnetic energy harvesting(MEH) to devices around the power line. A major challenge for practical MEH is to overcome magnetic saturation, which can cause degradation of power density under a wide current range in the power line. In this paper, we propose a design methodology to harvest maximized output power by considering the saturation effect. To consider magnetic saturation, the output power model and the saturable magnetizing inductance model based on magnetizing current were comprehensively analyzed. Additionally, the critical point of saturation for the maximum harvested power was analyzed by considering different primary side current conditions. With the proposed design methodology, the accuracy and efficiency of the output model were verified with experimental results compared to the conventional model. To consider the real environment, a 150 kW class of AC resistor load bank was implemented to control the primary current from 0 to 100 A with power frequency of 60 Hz. Experimental results show that the proposed method can harvest an average power of 14.32 W on 70 A power line, which is an increase of 39.8 % compared with the conventional design method.

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The Magnetic Energy Harvester With Improved Power Density Using Saturable Magnetizing Inductance Model for Maintenance Applications Near High Voltage Power Line

In dynamic wireless charging applications, segmented transmitter coils transfer power to a moving receiver coil. This article proposes a method in which the field strength in coupled transmitter coils automatically adjusts based on the position of the receiver. Specifically, a saturable inductor is applied to provide a high uncompensated inductive reactance in the uncoupled condition. By exploiting the reflected reactance as the system approaches the maximum coupled condition, the inductor saturates and the field strength in the coupled transmitter coils automatically increases. The field strength is at its peak when the transmitting and receiving coils reach their maximum coupling and sharply decreases when the receiver is decoupled from the transmitter. Consequently, the difference between the coupled and uncoupled currents in the transmitter coil is maximized, resulting in a near six-fold improvement in field containment performance compared to previously reported findings. This allows for system-level efficient power transfer and compliance with electromagnetic emission standards without complex shielding circuits and auxiliary active position detection approaches. We present the analysis, design criteria of the compensation network, and experimental validation for the proposed method.

Dynamic Wireless Charging: Reflexive Field Containment Using Saturable Inductors

Passive filter design is traditionally considered to be very important for many power electronic circuits and power systems. It is is very critical in the design of these power electronic circuits and power systems to know how to obtain accurate corner frequencies. It is known that when the load is large, the inductance of an inductor is known to always change. This phenomenon is due to the fact that when the current load is high, the inductance always suffers from saturation or hysteresis. It is extremely difficult to estimate the actual value for the nonlinear inductance in large currents because the inductance is nonlinear. The paper investigates the saturation phenomenon for a nonlinear inductance. The describing function method can be used to linearise the nonlinear inductor and then estimate the inductance in large current situations. Hence, the corner frequency for the lowpass filter can also be calculated accurately. It is shown that, when the current is very large, the corner frequency drifts to a larger value in the low-pass filter. The drift value of the corner frequency can be easily calculated by the describing function. Simulation and experimental results verify this phenomenon. However, it should be stressed that the method used in the paper is restricted to low frequencies. The higher frequency effects are neglected throughout the paper.

S.C. Chung

Papers

Applications of describing functions to estimate the performance of nonlinear inductance