Analysis, Dimensioning and Robust Control of Shunt Active Filter for Harmonic Currents Compensation in Electrical Mains

Abstract

In this chapter some results related to Shunt Active Filters (SAFs) and obtained by the authors and some coauthors are reported. SAFs are complex power electronics equipments adopted to compensate for current harmonic pollution in electric mains, due to nonlinear loads. By using a proper "floating" capacitor as energy reservoir, the SAF purpose is to inject in the line grid currents canceling the polluting harmonics. Control algorithms play a key role for such devices and, in general, in many power electronics applications. Moreover, systems theory is crucial, since it is the mathematical tool that enables a deep understanding of the involved dynamics of such systems, allowing a correct dimensioning, beside an effective control. As a matter of facts, current injection objective can be straightforwardly formulated as an output tracking control problem. In this fashion, the structural and insidious marginally-stable internal/zero dynamics of SAFs can be immediately highlighted and characterized in terms of sizing and control issues. For what concerns the control design strictly, time-scale separation among output and internal dynamics can be effectively exploited to split the control design in different stages that can be later aggregated, by using singular perturbation analysis. In addition, for robust asymptotic output tracking the Internal Model Principle is adopted.In authors' opinion, SAF case is an illustrative example of common issues in dimensioning and control of complex power electronics equipments, hence the proposed design approach can be generalized for such class of systems (e.g. large-power electric drives; generators and converters, particularly for renewable energies; Uninterruptible Power Supplies, UPS, and power supplies for special applications as particle accelerators). Remarkable the role of "system theory approach" in enlightening crucial sizing issues, this fact strongly testifies how relevant the "control viewpoint" is in all the fields of engineering, particularly when complex dynamic behavior is requested.The presented chapter has been invited for possible publication (after a review process) in the book "Robust Control / Book 1", by INTECH (www.intechweb.org).

Control of Shunt Active Filters With Actuation and Current Limits

“…Finally,ū = [ū dūq ] T is the control input vector, which can be mapped to the inverter command vector u 1 by suitable two-phase to three-phase transformation and PWM technique (see [4] for details). The nonlinear load current vector i l can be approximated by the sum of a finite number of harmonics [20].…”

“…According to [20], in the synchronous reference frame, each current vector is split into its real or active part (the d-component) and virtual or reactive part (the q-component). This allows a natural formulation of the control problem (details are reported in [4] and [10], and here just the main points are sketched). The main objective for SAFs is to steer their currents to cancel out the undesired load harmonics at the line side.…”

“…The system control inputs are the converter legs voltages that directly affect the filter current dynamics, while the dc-link voltage can be shown to be a nonminimum phase zero dynamic with respect to the filter current outputs. Hence, additional active current drained from the mains is usually exploited to stabilize the capacitor voltage, in a back-stepping fashion [4]. Several control strategies have been proposed in the literature.…”

“…Regarding current control, nonlinear [5], adaptive [6], as well as hysteresis [7] and predictive [8], [9] controllers have been proposed. In [4] and [10], the internal model principle (IMP) is exploited to achieve robust tracking. Indirect compensation has also been performed, controlling the mains currents [11].…”

“…All of these solutions are technically sound and have been successfully implemented in state-of-the-art SAFs. Nevertheless, relying on suitable sizing procedures [4], [15], they do not explicitly account for the device physical constraints, namely, the control input saturation, the converter current limits, and the maximum dc-link capacitor voltage. Anyway, in industrial applications, SAFs often face off-nominal conditions, leading to control input saturation and/or dangerous values of the SAF internal state.…”