Complex Controllers Applied to Space Vectors: A Survey on Characteristics and Advantages
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Complex Controllers Applied to Space Vectors: A Survey on Characteristics and Advantages Rafael C. Neto1 · Francisco A. S. Neves1
· Helber E. P. de Souza2
Received: 17 May 2019 / Revised: 8 May 2020 / Accepted: 10 June 2020 © Brazilian Society for Automatics–SBA 2020
Abstract This work presents the characteristics and advantages of using complex controllers applied to space vectors. A mathematical background is presented to show that the harmonic spectrum of a space vector indicates the phase-sequence of each harmonic that composes this vector. As consequence, a reference space vector can be used for applications in which the control system has three-phase reference signals. This approach allows the implementation of complex controllers that present lower order, require less memory elements and have better dynamic response than real controllers. A literature review is made to enable a structural comparison (in terms of computational cost) between several real and complex control schemes based on the internal model principle. Two experimental applications are used to evaluate the performance of complex controllers. Keywords Control systems · Complex controller · Space vector · Harmonic compensation
1 Introduction Due to the increasing demand for renewable energy sources, such as solar and wind energies, a significant increase in the number of three-phase grid-connected inverters has been observed in recent decades. Most applications of these inverters have a structure that includes an internal current control loop. Therefore, the performance of these systems depends heavily on the current control strategy applied (Kazmierkowski and Malesani 1998). Several control strategies have been proposed in the literature with the objective of regulating the output currents in three-phase inverters, even though these signals have high harmonic content. In general, these solutions are control structures that have infinite gain in a set of frequencies selected by the designer, being applicable to systems in which
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Francisco A. S. Neves [email protected] Rafael C. Neto [email protected] Helber E. P. de Souza [email protected]
1
Universidade Federal de Pernambuco, Recife, Brazil
2
Instituto Federal de Educação Ciência e Tecnologia de Pernambuco, Recife, Brazil
it is desired to compensate currents with harmonic components of known orders. The first modern control strategies for three-phase motor drives required sinusoidal balanced phase currents to be imposed to the machine stator. Due to the widespread use of PI (proportional–integral) controllers, synchronous reference frame (SRF) can be used to transform sinusoidal phase signals into dc quantities, to which PI controllers become adequate (PI-SRF) (Bhattacharya et al. 1996). PI-SRF has been also applied for three-phase grid-connected inverters. Alternatively, the satisfactory results are obtained in stationary reference frame by using the second-order generalized integrator (SOGI) (Zmood and Holmes 2003), also known as resonant controller. For
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