Alejandro G. Yepes

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.

Analysis and Design of Resonant Current Controllers for Voltage-Source Converters by Means of Nyquist Diagrams and Sensitivity Function

The following two types of resonant controllers are mainly employed to obtain high performance in voltage-source converters: 1) proportional + resonant (PR) and 2) vector proportional + integral (VPI). The analysis and design of PR controllers is usually performed by Bode diagrams and phase-margin criterion. However, this approach presents some limitations when resonant frequencies are higher than the crossover frequency defined by the proportional gain. This condition occurs in selective harmonic control and applications with high reference frequency with respect to the switching frequency, e.g., high-power converters with a low switching frequency. In such cases, additional 0-dB crossings (phase margins) appear; therefore, the usual methods for simple systems are no longer valid. In addition, VPI controllers always present multiple 0-dB crossings in their frequency response. In this paper, the proximity to the instability of PR and VPI controllers is evaluated and optimized through Nyquist diagrams. A systematic method is proposed to obtain the highest stability and avoidance of closed-loop anomalous peaks: it is achieved by the minimization of the inverse of the Nyquist trajectory distance to the critical point, i.e., the sensitivity function. Finally, several experimental tests, including an active power filter that operates at a low switching frequency and compensates harmonics up to the Nyquist frequency, validate the theoretical approach.

High-Performance Digital Resonant Controllers Implemented With Two Integrators

Resonant controllers are one of the highest performance alternatives for ac current/voltage control. The implementations based on two integrators are widely employed to achieve frequency adaptation without substantial computational burden. However, the discretization of these schemes causes a significant error both in the resonant frequency and in the phase lead provided by the delay compensation. Therefore, perfect tracking is not assured, and stability may be compromised. This paper proposes solutions for both problems without adding a significant resource consumption by correction of the roots placement. A simple expression to calculate the target leading angle, in delay compensation schemes, is also proposed to improve stability margins by means of a better accuracy than previous approaches. Experimental results obtained with a laboratory prototype corroborate the theoretical analysis and the improvement achieved by the proposed discrete-time implementations.

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.

Passivity-Based Controller Design of Grid-Connected VSCs for Prevention of Electrical Resonance Instability

The time delay in the current control loop of a grid-connected voltage-source converter (VSC) may cause destabilization of electrical resonances in the grid or in the VSCs input filter. Instability is prevented if the input admittance of the VSC can be made passive. This paper presents an analytical controller design method for obtaining passivity. The method is equally applicable to single- and three-phase systems, i.e., in the latter case, for both stationary- and synchronous-frame control. Simulations and experiments verify the theoretical results.

Three-Phase PLLs With Fast Postfault Retracking and Steady-State Rejection of Voltage Unbalance and Harmonics by Means of Lead Compensation

This paper proposes an advanced controller suitable for three-phase phase-locked loops (PLLs), which are employed in grid-connected power converters. This controller is formed of one or more lead compensators cascaded to the main proportional integral regulator. The proposed lead compensators are second order with pure imaginary roots: they have both a notch peak and a resonant peak (the notch frequency is lower than the resonant frequency). Hence, their phase versus frequency response exhibits phase wraps of ± 180°. Consequently, the parameters of each lead compensator are tuned with two objectives: to eliminate a specific frequency in the synchronous reference frame (SRF) and to enhance stability by a phase lead (phase boost). Through this technique, three-phase PLLs achieve both high bandwidth (fast transient response) and selective cancellation (filtering of unbalance and harmonics ripple in the SRF). The proposed controllers are suitable for simpler three-phase PLL schemes, such as the SRF-PLL. Therefore, big improvement is achieved without adding extra blocks and signals to basic PLL structures. Simulation and real-time implementation (dSpace DS1103) tests, emulating very demanding realistic conditions, have been performed. Key figures from these tests are shown, which prove the high performance and robustness of the proposal.

Parameter Identification of Multiphase Induction Machines With Distributed Windings—Part 1: Sinusoidal Excitation Methods

Multiphase induction machines (IMs) are gaining increasing interest in industry due to their numerous advantages over the conventional three-phase ones. A lot of different parameter estimation methods have been developed for three-phase IMs, but the existing literature regarding specific identification techniques for multiphase IMs is almost nonexistent at this point. This paper proposes simple offline methods to estimate the stator resistance and stator leakage inductance of multiphase IMs with distributed windings, under different conditions, utilizing the machines degrees of freedom associated with the nonflux/torque producing current components. Once these parameters are identified, the rotor ones can be easily calculated by combination with the total values obtained from locked-rotor tests. The procedure enables segregation of the stator and rotor parameters in a simple manner, something that is very difficult to achieve in three-phase IMs where, usually, equality of leakage inductances and a constant stator resistance are assumed. In this manner, the magnetizing inductance can be then also more accurately assessed from no-load tests, because the error in its estimation that would be caused by assuming both leakage inductances to be equal is avoided. The proposed methods are experimentally tested on two different five-phase IMs.

Passivity-Based Stability Assessment of Grid-Connected VSCs—An Overview

The interconnection stability of a grid-connected voltage-source converter (VSC) can be assessed by the passivity properties of the VSC input admittance. If critical grid resonances fall within regions where the input admittance acts passively, i.e., has nonnegative real part, then their destabilization is generally prevented. This paper presents an overview of passivity-based stability assessment, including techniques for space-vector modeling of VSCs whereby expressions for the input admittance can be derived. Design recommendations for minimizing the negative-real-part region are given as well.

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.