A Hybrid Current Control for a Controlled Rectifier Alberto Soto Lock*
Edison R. da Silva*
Student
Fellow
Malik E. Elbuluk**
Darlan A. Fernandes
Senior Member
Member
* Universidade Federal de Campina Grande - LEIAM Av. Aprígio Veloso, 882 Bloco CH, Campina Grande, Paraíba - 48429 Brazil ** University of Akron, Ohio, USA *** Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte, Campus Natal Central e-mail address:
[email protected],
[email protected],
[email protected],
[email protected] Abstract - A current controller must satisfy the contradictory requirements of having a fast dynamic response in transient and a low harmonic content in steady state, characteristics that are found in linear and hysteresis controllers, respectively. Predictive current controllers partly satisfy these requirements but at expenses of complexity. The present work proposes an alternative approach for modifying the linear controller in order to have a faster response. This consists of the One Cycle Control (OCC) current controller modified by the use of a lead-lag compensator. An additional feature of this controller is that it can be implemented with DSP. Besides mathematical analysis, simulation and experimental results are presented to validate the proposed controller. Index Terms - AC-DC power conversion, Reactive power, Pulse width modulation.
I.
INTRODUCTION
In conventional control strategies used for controlled rectifiers, the rectifier performance strongly depends on the current controller dynamic response [1]. Current controllers can be divided into three main categories [2]: Linear, Predictive, and Hysteresis controllers. Linear controllers [2][4] are based on PWM modulators. Although they have a well defined harmonic spectrum and a fixed frequency operation, their dynamic response is considered as inadequate [3], [4]. Hysteresis current control (HCC) is an instantaneous feedback system which maintains the current inside an assigned band [2], [3]. It gives fast response, good accuracy and a kind of load parameters independence; however, its very-wide operation-frequency and phase-switching interference random behavior are its two main drawbacks [5], [6]. On the other hand, Predictive Current Control is a digital sampled technique which predicts the current or voltage of next modulation cycle, on the basis of the actual error and system parameters (i.e. grid voltage, dc link voltage, input current and so forth). They can work with linear or hysteresis
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controllers [7] and are commonly implemented by Digital Signal Processors (DSP) [8]. These current controllers partly satisfy the contradictory requirements of a fast dynamic response and a low harmonic content [3], [8], [9], but at expenses of complexity. Besides that, the One-Cycle Control (OCC) technique [10] provides power factor control, very low distortion, while regulating the output voltage, with a simple circuit. To generate driving pulses for the converter switches, OCC compares input currents to variable amplitude carrier [11], [12]. In order to vary the input current proportionally with the grid input voltage, the impedance seen from the utility voltage emulates a resistance. Although this controller has fast response, integrators or Low-PassFilters (LPF) used to reproduce the average input currents introduce delays to the process. This paper proposes a current control technique that achieves fast dynamic response and a low harmonic content by using OCC technique. Similarly to conventional OCC, it presents control simplicity and fixed frequency, while using a lead-lag compensator so that some dynamics is added to the control system to maintain the delay under control. A multiplier is employed to manage the variable amplitude triangle-carrier. Simulation and experimental results are used to validate the proposed technique. II.
MODEL SYSTEM CONFIGURATION
Consider the two-level controlled rectifier shown in Fig. 1, in which VO=VC1+VC2 and VC1=VC2=VO/2. Its representation per phase is given in Fig. 2(a), where Ig is the phase current, Vg=Em cosωt (for g=a ,b, c) is the input voltage, and VgN (for g=A, B, C) is the pole voltage. From Fig. 2(a), rI g + L
d I g = Vg 0 − VGN dt
(1)
It is assumed that compensated phase current Igs and phase current Ig are proportional according to
920
where Hbs and Hbi are the inferior and superior bands of the compensated current in Fig.2. In order to have unity power factor, the phase current must follow input voltage. This can be expressed as Km E cos ω t Re
I g* ( t ) = Fig.1. Two level controlled rectifier
(5)
where Re is the input resistance and Km is a constant. On the other hand, assuming I*g(nT)≈I*g(n+d)T), from (4) and (5), and assuming that sin ( n ω T ) ≈ sin(( n + d )ω T ) it can be shown that C10 =
dTE cos( nωT ) L
C20 =
dTE E (2n + d )ωT cos(nωT ) − 0 2L L
and (6)
Also, from Fig. 2(d), tgβ1 =
I g* H bs YT
tgβ 2 =
=
I g* H bi
I g* H bs PY
and
VX
=
I g* H bi
(7)
XP
leading to Fig.2(a) Per phase equivalent circuit of controlled rectifier; (b) Compensated current and comparison ramp. (c) Firing pulses. (d) Compensated current detailed view.
Igs=k Ig/Z= k1 Em cos(ωt+2mπ /3+2nπ)
I g* H bs VP 2
(2)
where m=0, 1, 2 refers to the phase currents and the integer number n corresponds to the delay introduced in the process and
Z = r 2 + (ωL ) . Note that (2) involves the unity 2
power factor condition. Other assumptions are: (i) Carrier frequency is much greater than line frequency; (ii) Phase current Ig flows in the circuit, while the compensated phase current Igs is utilized for modulation purposes, (iii) The voltage between neutral grid point 0 and middle point N can be neglected For r
