Jano Malvar

Effects of Discretization Methods on the Performance of Resonant Controllers

Resonant controllers have gained significant importance in recent years in multiple applications. Because of their high selectivity, their performance is very dependent on the accuracy of the resonant frequency. An exhaustive study about different discrete-time implementations is contributed in this paper. Some methods, such as the popular ones based on two integrators, cause that the resonant peaks differ from expected. Such inaccuracies result in significant loss of performance, especially for tracking high-frequency signals, since infinite gain at the expected frequency is not achieved, and therefore, zero steady-state error is not assured. Other discretization techniques are demonstrated to be more reliable. The effect on zeros is also analyzed, establishing the influence of each method on the stability. Finally, the study is extended to the discretization of the schemes with delay compensation, which is also proved to be of great importance in relation with their performance. A single-phase active power filter laboratory prototype has been implemented and tested. Experimental results provide a real-time comparison among discretization strategies, which validate the theoretical analysis. The optimum discrete-time implementation alternatives are assessed and summarized.

Eliminating Ground Current in a Transformerless Photovoltaic Application

For low-power grid-connected applications, a single-phase converter can be used. In photovoltaic (PV) applications, it is possible to remove the transformer in the inverter to reduce losses, costs, and size. Galvanic connection of the grid and the dc sources in transformerless systems can introduce additional ground currents due to the ground parasitic capacitance. These currents increase conducted and radiated electromagnetic emissions, harmonics injected in the utility grid, and losses. Amplitude and spectrum of the ground current depend on the converter topology, the switching strategy, and the resonant circuit formed by the ground capacitance, the converter, the ac filter, and the grid. In this paper, the ground current in a 1.5-kW PV installation is measured under different conditions and used to build a simulation model. The installation includes a string of 16 PV panel, a full-bridge inverter, and an LCL filter. This model allows the study of the influence of the harmonics injected by the inverter on the ground current.

Assessment and Optimization of the Transient Response of Proportional-Resonant Current Controllers for Distributed Power Generation Systems

The increasing number of distributed power generation systems (DPGSs) is changing the traditional organization of the electrical network. An important part of these DPGSs is based on renewable energy sources. In order to guarantee an efficient integration of renewable-based generation units, grid codes must be fulfilled. Their most demanding requirements, such as low-voltage ride-through and grid support, need a really fast transient response of the power electronics devices. In this manner, the current controller speed is a key point. This paper proposes a methodology to assess and optimize the transient response of proportional-resonant current controllers. The proposed methodology is based on the study of the error signal transfer function roots by means of pole-zero plots. Optimal gains are set to achieve fast and nonoscillating transient responses, i.e., to optimize the settling time. It is proved that optimal gain selection results from a tradeoff between transients caused by reference changes and transients caused by changes at the point of common coupling. Experimental results obtained by means of a three-phase voltage source converter prototype validate the approach. Short transient times are achieved even when tests emulate very demanding realistic conditions: a +90° phase-angle jump in the current reference and a “type C” voltage sag at the point of common coupling.

Tuning Method Aimed at Optimized Settling Time and Overshoot for Synchronous Proportional-Integral Current Control in Electric Machines

Implementation of proportional-integral controllers in synchronous reference frame is a well-established current control solution for electric machines. Nevertheless, their gain selection is still regarded to be poorly reported, particularly in relation to the influence of the computation and modulation delay. To fill this gap, a design procedure to set the maximum gains for an acceptable damped response, with the delay being considered, has been recently proposed. In contrast, this paper presents a simple rule of thumb to achieve nearly the minimum settling time in combination with negligible overshoot for reference changes. This conclusion is theoretically demonstrated by the analysis of root locus diagrams and of overshoot versus settling time trajectories for sweeps of gain values. The design approaches aimed at gain maximization and the one developed here are compared, revealing that the latter provides shorter settling time and much lower overshoot in the command tracking response, while allowing greater stability margins. On the other hand, the proposed tuning method leads to a worse disturbance rejection, but by including an active resistance with enhanced pole/zero cancellation as a second degree of freedom, both design procedures attain comparable and optimized attenuation of disturbances. Matching simulation and experimental results validate the theoretical study.

Grid-synchronization methods for power converters

Grid synchronization is an important part in the control of grid-connected power electronic converters. The fundamental phase-angle at the point of common coupling should be tracked on-line in order to control energy transfers. Digital implementation allows to implement high performance algorithms, which are robust in the presence of power quality phenomena. However, different kinds of distortion cause a reduction of the effective bandwidth, and hence, affects to the transient response of the equipment. This paper reviews some of the highest performance algorithms for grid synchronization: phase locked loops (PLL), schemes based on synchronous reference frames (SRF) and digital filtering and finally, stochastic filtering based methods. The pros and cons of each one are assessed and some interesting techniques to enhance the dynamics are provided. The assessment in the presence of frequency deviations is analyzed in detail. The most significant techniques to provide a better frequency adaptation are enumerated and analyzed in the last section of this paper.

Tuning of Synchronous-Frame PI Current Controllers in Grid-Connected Converters Operating at a Low Sampling Rate by MIMO Root Locus

Current controller performance is key in grid-connected power converters for renewable energy applications. In this context, a challenging scenario is arising in multi-megawatt wind turbines, where sampling and switching frequencies tend to be lower and lower as power ratings increase. This strongly affects achievable control time constant. With this perspective, this paper presents a systematic procedure for accurate dynamics assessment and tuning of synchronous-frame proportional-integral current controllers, which is based on linear control for multiple-input-multiple-output (MIMO) systems. The dominant eigenvalues of the system are calculated with explicit consideration of time-delay and cross-coupling terms, two factors which clearly impair the system dynamics when considering a low sampling frequency. The proposed methodology is summarized as follows. First, the plant and controller matrices are modeled in state space. Subsequently, the characteristic polynomial of the closed-loop system is obtained and a computer-aided parametric analysis is performed to calculate the MIMO root locus as a function of the control gain. By its inspection, it is possible to identify the gain, which minimizes the current closed-loop time constant. This tuning is suitable for wind turbine applications, taking into consideration cascaded-control structures and grid-code requirements. The validity and accuracy of the analysis is fully supported by experimental verification.

Current Harmonics Compensation Based on Multiresonant Control in Synchronous Frames for Symmetrical

Low-order odd current harmonics arise in practical multiphase drives due to machine and converter nonlinear behavior (e.g., deadtime and flux saturation). If the windings are distributed, some harmonics cause torque ripple, whereas others produce losses. The latter is aggravated by the small impedance in the no-torque subspaces. Current harmonics can be compensated without steady-state error by proportional-integral controllers in multiple synchronous frames (SFs); however, a heavy computational load is required. In three-phase systems, the computational burden of this multiple SF (MSF) scheme is often avoided by implementing instead resonant controllers (RCs) tuned at the harmonics that are multiples of six in an SF rotating with the fundamental frequency. A similar structure has been proposed for nonlinearities compensation in asymmetrical six-phase machines. This paper extends this multiple RC (MRC) strategy to symmetrical machines of any phase number. The optimum frequencies for the RCs and for the SF in each plane, so that the number of RCs is minimized, are established. Then, the computational load of the resulting generic MRC scheme is assessed and compared with that of the MSF structure. The conditions in which the former is particularly preferable over the latter are identified. Experimental results are provided.

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Rigorous analysis and design of the current control loop in voltage source converters (VSCs) requires an accurate modeling. The loop behavior can be significantly influenced by the VSC working conditions. To consider such effect, converter losses should be included in the model, which can be done by means of an equivalent series resistance. This paper proposes a method to identify the VSC equivalent loss resistance for the proper tuning of the current control loop. It is based on analysis of the closed-loop transient response provided by a synchronous proportional-integral current controller, according to the internal model principle. The method gives a set of loss resistance values linked to working conditions, which can be used to improve the tuning of the current controllers, either by online adaptation of the controller gains or by open-loop adaptive adjustment of them according to prestored data. The developed identification procedure is tested in the laboratory at different specifications of power level and switching frequency.

-Phase Machines

Current control is crucial in active power filters. The current controller should provide perfect tracking of reference and total rejection of disturbance (grid voltage). The use of resonant controllers has been often proposed as one of the highest performance alternatives for alternating current and voltage control. In this work it is studied the effect of the discrete-time implementation of resonant controllers in their performance, specially when tracking high order components. It is proved that some methods cause a displacement of the resonant peaks, so infinite gain is not located at the desired frequencies. On the other hand, other options, such as impulse invariant, maintain the resonance at the design location, allowing for a superior performance. It is also studied the effect of zeros distribution on the behavior. A single-phase active power filter laboratory prototype has been built. The theoretical analysis is validated by experimental results, demonstrating the importance of the discrete-time implementation and the superiority of the impulse invariant method.

A Technique to Estimate the Equivalent Loss Resistance of Grid-Tied Converters for Current Control Analysis and Design

Precise knowledge of the plant time constant L/R is essential to perform a thorough analysis and design of the current control loop in voltage source converters (VSCs). From the perspective of the current controller dynamics in the low-frequency range, such plant time constant is also suitable for most cases in which an LCL filter is used. As the loop behavior can be significantly influenced by the VSC working conditions, the effects associated to converter losses should be included in the model, through an equivalent series resistance. In addition, the plant inductance may also present important uncertainties with respect to the value of the VSC L/LCL interface filter measured at rated conditions. Thus, in this paper, a method is presented to estimate both parameters of the plant time constant, i.e., the equivalent inductance and resistance in the plant model of current-controlled VSCs. The proposed technique is based on the evaluation of the closed-loop transient responses of both axes of the synchronous reference frame when a proportional-integral current controller is implemented. The method gives a set of resistance and inductance values that should be employed for a rigorous design of the current controllers. Experimental results validate the approach.