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.

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 In such cases, additional 0-dB crossings (phase margins) appear; therefore, the usual methods for simple systems are no longer valid.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.

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.

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.

In the last few years, interest in multiphase converter technology has increased due to the benefits of using more than three phases in drive applications. Besides, multilevel converter technology permits the achievement of high power ratings with voltage limited devices. Multilevel multiphase technology combines the benefits of both technologies, but new modulation techniques must be developed in order to take advantage of multilevel multiphase converters. In this paper, a novel space vector pulsewidth modulation (SVPWM) algorithm for multilevel multiphase voltage source converters is presented. This algorithm is the result of the two main contributions of this paper: the demonstration that a multilevel multiphase modulator can be realized from a two-level multiphase modulator, and the development of a new two-level multiphase SVPWM algorithm. The multiphase SVPWM algorithm presented in this paper can be applied to most multilevel topologies; it has low computational complexity and it is suitable for hardware implementations. Finally, the algorithm was implemented in a low-cost field-programmable gate array and it was tested in a laboratory with a real prototype using a five-level five-phase inverter.

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.