Output Filters for Grid-Tied Converters: Component Sizing, Controller Co-Design and Winding-Loss Analysis
There has been a high increase in demand for high-performance output filters for power converters, possessing high attenuation and high bandwidth. Many emerging applications require high bandwidth and low output distortion, e.g. controllable power sources and grid-tied converters. Moreover, at high switching frequency, the filter attenuation needs to comply with the electromagnetic interference (EMI) standard, which is more stringent than the conventional grid-harmonic standard. Designing an output filter to achieve both high attenuation and high bandwidth is extremely challenging. These new requirements stipulate research in new design tools and modeling approaches.
This thesis focuses on the various aspects of the design, modeling and validation of output filters, namely design of resonant-damping controller and component values, winding loss modeling, and winding loss measurement. The thesis aims to improve and facilitate these aspects by introducing a novel component-sizing and control co-design method, homogenization-based finite element (FE) method for winding-loss computation and a more accurate method of winding-resistance extraction.
The first part of the thesis presents a virtual circuit control (VCC) method to design a resonant-damping discrete-time controller for grid-tied voltage source converters with output filters. The method provides an intuitive way to specify the desired closed-loop behavior by means of a virtual reference circuit rather than abstract mathematical criteria such as closed-loop poles and weighting matrices. Therefore, the existing passive filter designs, which cannot be practically implemented due to excessive losses, and the well-established theory of filters can be exploited. The grid current and the common-mode capacitor voltage, which are the primary control objectives, inherit the main properties of their underlying virtual reference circuits, e.g. resonance damping and low-frequency behavior. Accordingly, the voltage/current controllers can be easily designed based on the low-frequency behavior of virtual circuits. The method can also be straightforwardly equipped with conventional controllers to enhance system performance, such as harmonic compensation. For validation, the simulation and experiment are performed to control a three-phase grid-tied VSC with an LCL filter. The results verify the effectiveness of the resonant damping and dynamic performance.
Subsequently, the VCC method is employed to formulate a novel co-design method of component sizing and control for actively-damped LC-ladder output filters of general order. This method executes the VCC method in reverse. The virtual circuit is firstly designed based on a singly-terminated ladder network. Starting from a desired closed-loop transfer function, the virtual circuit is synthesized to meet the physical requirements. The physical circuit is then realized by adopting the same components as the ones of the virtual circuit from the filter capacitor onward to the output. Therefore, it simultaneously tackles the design of the filter parameters and the resonant-damping control. The design example of LCL filters for a three-phase grid-tied voltage-source converter (VSC) is demonstrated and experimentally tested. The measured bandwidth of the small-signal reference tracking transfer function of the output current agrees with the theoretical model. At steady state, the output current shows excellent sinusoidal waveform as desired. Furthermore, the feasible extension to a design of 5th-order LCLCL filter by means of loss-volume Pareto multiobjective optimization has been demonstrated and compared with the 3rd-order LCL counterpart. The use of the former shows promising volume reduction for the applications requiring high bandwidth and/or high attenuation.
The third part of the thesis investigates a frequency-domain finite-element (FE) homogenization method for litz-wire bundles. The approach consists in adopting a frequency-dependent complex reluctivity in the litz-wire bundles and a frequency-dependent complex impedance in the electrical circuit, both in terms of dimensionless coefficients. They represent the skin and proximity effects, respectively. The litz-wire bundles become homogeneous conductors which are easy to integrate into an FE model. The homogenization method is validated by a 2-D transformer model and a 3-D axisymmetric inductor model of which the reference solutions are computed based on finely discretized litz-wire bundles. The results of the computed resistance and inductance agree well with the reference fine model with highly reduced computational cost.
Furthermore, the synthesis of an RL Cauer ladder network to homogenize the multi-turn winding in time-domain FE computations is examined. Two RL Cauer networks are synthesized to match the frequency-dependent complex impedance and reluctivity, with the accuracy depending on the order of the network to be appended. The proposed method yields an improved accuracy as compared to the previous study in which the topology of the ladder network was not well chosen. The results are validated by means of a 2-D axisymmetric inductor with a gapped nonlinear magnetic core.
The last part of the thesis deals with the winding-loss measurement through the extraction of the winding resistance. In general, the resistance value obtained from impedance measurements needs a compensation of undesirable effects, e.g. the core loss and the distributed winding capacitance. Herein, it is rigorously shown that the core loss (or core-loss resistance) measured with the two-winding method always includes the effect of the winding mutual resistance. At high frequencies, this effect becomes more prominent and can cause an overestimation of the measured core-loss resistance. As a result, the compensated winding resistances can be significantly underestimated. To mitigate this effect, the core-loss resistance should be measured on an auxiliary 1:1 transformer with single-turn windings. Subsequently, it is scaled to obtain the actual core loss. The proposed analysis and method are applicable to multi-winding components. For validation, we consider a gapped transformer with litz-wire winding for high-frequency operation. The experimental results are validated against the results from the 3-D FE model. The litz-wire winding is considered in the FE model by means of a homogenization approach (third part of this thesis). With the proposed measurement method, the experimentally extracted winding resistances are more accurate and in good agreement with the FE results.