The recently introduced proportional-resonant (PR) controllers and filters, and their suitability for current/voltage control of grid-connected converters, are described. Using the PR controllers, the converter reference tracking performance can be enhanced and previously known shortcomings associated with conventional PI controllers can be alleviated. These shortcomings include steady-state errors in single-phase systems and the need for synchronous d-q transformation in three-phase systems. Based on similar control theory, PR filters can also be used for generating the harmonic command reference precisely in an active power filter, especially for single-phase systems, where d-q transformation theory is not directly applicable. Another advantage associated with the PR controllers and filters is the possibility of implementing selective harmonic compensation without requiring excessive computational resources. Given these advantages and the belief that PR control will find wide-ranging applications in grid-interfaced converters, PR control theory is revised in detail with a number of practical cases that have been implemented previously, described clearly to give a comprehensive reference on PR control and filtering.

Proportional-resonant controllers and filters for grid-connected voltage-source converters

Synchronization with the utility networks is crucial for operating three-phase grid-interfaced converters. A challenge of synchronization is how to fast and precisely extract the fundamental positive and negative sequences under the distorted and unbalanced conditions. Many phase-locked loop (PLL) and synchronization techniques have been presented in the past decades. Most of them make a tradeoff between the accuracy and dynamic response under severe distorted and unbalanced conditions. In this paper, a multiple-complex coefficient-filter-based PLL is presented, and its unique feature lies in the accurate and rapid extraction of the positive and negative sequence components from the polluted grid voltage, and the harmonic components can also be estimated precisely, which has the potential use for selective compensation in active filter applications. Another advantage of the proposed method is its flexibility for simplifying its structure in some specified conditions. Results of continuous-domain simulations in MATLAB and discrete-domain experiments based on a 32-b fixed-point TMS320F2812 DSP are in good agreement, which confirm the effectiveness of the proposed method.

Multiple-Complex Coefficient-Filter-Based Phase-Locked Loop and Synchronization Technique for Three-Phase Grid-Interfaced Converters in Distributed Utility Networks

This paper proposes a unified mathematical model of a voltage-sourced converter (VSC) based on positive and negative synchronously rotating frames under both unbalanced grid supply and imbalanced input impedances. Based on the developed model, a new definition of instantaneous reactive power is introduced, and an accurate mathematical model of the instantaneous active and reactive powers at different locations of the VSC is derived. To avoid the use of band-trap filter for decomposing the positive- and negative-sequence dq components of current and voltage, a new control scheme with multifrequency proportional-resonant controller in the stationary alphabeta frame is employed to improve the steady state and dynamic response under generalized unbalanced operation conditions. Simulation and experimental studies with various factors were conducted and compared under different types of unbalanced conditions. The simulated and experimental results demonstrate that the proposed control scheme in the stationary alphabeta frame provides sufficiently steady-state tracking capability for ac input current, and a better transient response in compensation for wide-range generalized unbalanced operation conditions.

Modeling and Control of Grid-Connected Voltage-Sourced Converters Under Generalized Unbalanced Operation Conditions

Harmonic reference generators for active filter systems are commonly implemented in the synchronous reference frame, so that simple low- or high-pass filter functions can be used depending on the requirements of a particular application. High-pass filters in particular are used when the reference generator is required to produce an "everything but the fundamental" target waveform. This paper presents a stationary frame notch filter equivalent to a high-pass synchronous frame harmonic reference generator for such systems. The use of the stationary frame allows for quicker calculation of the reference generation in a discrete digital implementation, and also allows classical control techniques to be used to analyze the active filter system without requiring synchronous frame transformations of the outside system model. Both simulation (continuous and discrete) and experimental results showing the equivalency of the stationary and synchronous frame reference generation process are presented using both shift and delta-operator-based infinite-impulse response digital filters.

Stationary frame harmonic reference generation for active filter systems

https://research.aalto.fi/files/33039704/1_s2.0_S1053811919301958_main_1.pdf

On-scalp MEG system utilizing an actively shielded array of optically-pumped magnetometers.

The use of the delta operator in the realizations of digital filters has recently gained interest due to its good finite-word-length performance under fast sampling. We studied efficient direct form structures, and show that only some of them can be used in delta configurations, while others are evidently unstable. In this paper, we focus on the roundoff noise analysis. Of all the direct-form structures, the direct form II transposed (DFIIt) delta structure has the lowest quantization noise level at its output. This structure outperforms both the conventional direct-form (delay) structures, as well as the state-space structures for narrow-band low-pass filters with respect to output roundoff noise. Excellent roundoff noise performance is achieved at the cost of only a minor additional implementation complexity when compared with the corresponding delay realization. Complexity of a signal processor implementation of the DFIIt delta structure, which was found to be the most suitable delta structure for signal processors, is compared with those of the direct form and state-space delay structures. In addition, some hardware implementation aspects are discussed, including the minimization of the internal word length.

/pdf/delta-operator-realizations-of-direct-form-iir-filters-18ehfqff2n.pdf

Delta operator realizations of direct-form IIR filters

Delta operator realizations of IIR filters have received a lot of interest due to their good finite-wordlength properties. We present a detailed analysis of the computationally efficient transposed direct form II delta structure, which is also known to have excellent roundoff noise performance under fast sampling. The focus is on the roundoff noise minimization in fixed-point implementations. The free /spl Delta/ parameter in the delta operator is optimized with respect to the output roundoff noise within the scaling constraints. Moreover, the required internal wordlength to obtain a prespecified noise performance is derived.

Roundoff noise minimization in a direct form delta operator structure

The roundoff noise and coefficient sensitivity performance of the delta operator realized recursive digital filters have been shown to be good under fast sampling. Recently it has been found out that in fixed point delta operator implementations limit cycles may occur. We have proposed a small but important modification into the delta operator which enables us to eliminate zero-input limit cycles completely if magnitude truncation quantization is used. In this paper, we study in detail the scaling and roundoff noise in the modified delta operator direct form structure when magnitude truncation is used.

J. Kauraniemi

Papers

Delta operator realizations of direct-form IIR filters

Delta operator realizations of direct-form IIR filters

Roundoff noise minimization in a direct form delta operator structure

Roundoff noise analysis of modified delta operator direct form structures

Delta Operator Realizations of Recursive Digital Direct Form Filters