Synchronous Reference Frame Based Controllers Applied to Shunt Active Power Filters in ThreePhase Four-Wire Systems Sergio A. Oliveira da Silva 1 Angelo Feracin Neto 1 Silvia G. S. Cervantes 2 Alessandro Goedtel 1 Claudionor F. Nascimento 3 Federal Technological University of Paraná – UTFPR 1 State University of Londrina – UEL 2 Federal University of ABC – UFABC 3 Av. Alberto Carazzai, 1640, CEP. 86.000-300 1 Cornélio Procópio – PR, Brazil
[email protected] [email protected] [email protected] [email protected] [email protected]
Abstract- This work presents compensation algorithm schemes used for shunt active power filters applied to three-phase fourwire systems, allowing harmonic current suppression and reactive power compensation, which results in an effective power factor correction. The strategies used to extract the threephase reference currents are based on the synchronous reference frame method. Although this method is based on balanced three-phase loads, it can also be used for single-phase loads, allowing independent control of all three phases. Accordingly, a fictitious quadrature current needs to be generated through software implementation, and be orthogonal to the measured load current. This creates the fictitious balanced currents in the two-phase stationary reference frame system, allowing the choice of an adequate compensation strategy which will result in either balanced or unbalanced sinusoidal source currents. Three shunt APF topologies are evaluated under unbalanced load conditions: Split-Capacitor (SC), Four-Leg (F-L) and Three Full-Bridge (3F-B). The proposed algorithms applied to the three APF topologies are evaluated and discussed. Mathematical analyses of the SRF-based algorithms are presented and simulation results are performed to validate the theoretical development and confirm the performance of the shunt APFs.
I.
INTRODUCTION
Harmonic pollution of the power supply system has risen significantly in recent years due primarily to an increase of non-linear loads connected to the utility through residential, commercial and industrial customers. Power supply voltages become distorted due to the high level of undesired harmonic current drawn from the utility. Additionally, drops in fundamental voltage are caused by the interaction between the reactive current and network impedances. To solve or minimize some power quality problems, hybrid, shunt and series active power filters (APFs) have been developed [1-14)]. While the series APFs are normally used to compensate utility voltage disturbances such as sags, swells, unbalances and harmonic voltages, shunt APFs have commonly been used to compensate reactive power, suppression of harmonic currents in three-phase three-wire and four-wire systems, and load unbalanced currents and neutral current in three-phase four-wire systems [1-12].
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When the three-phase four-wire systems are used to feed three-phase unbalanced loads, negative and zero sequence components of the source currents will appear, helping degrade the performance of equipments such as transformers, electrical machines and others. For non-linear loads, therefore, the source currents will contain unbalanced fundamental and harmonic components. In this case, even with perfectly balanced single-phase non-linear loads, a third harmonic component and its multiples will flow through the neutral wire. Moreover, an excessive zero sequence current can help cause damage in the neutral conductor [6-7, 16]. For three-phase four-wire systems, depending on the adopted control strategy, the chosen controller can be used to control each phase independently [9]. In this case, the balance of the sinusoidal compensated source currents is not performed, i.e., the compensation of the fundamental negative sequence components is not taken into account. If the based controller used is phase dependent it will result in sinusoidal and balanced source currents, i.e., the negative and zero sequence components will be compensated [15]. In this paper the compensation algorithms used to extract the three-phase reference currents are based on the synchronous reference frame (SRF) method [13-14]. Although the SRF method is based on the balanced threephase loads, it can also be used for single-phase loads, allowing independent control of all three phases. The flexibility to choose the SRF-based controller strategy will determine if the negative, zero or both sequence current components will be compensated. The SRF-based algorithms will be evaluated under unbalanced load conditions and will be applied to three shunt APF topologies: split-capacitor, four-leg and three F-Bridge. Mathematical analyses of the SRF-based algorithms are presented and simulation results are performed to validate the theoretical development and confirm the performance of the shunt APFs. II. SHUNT APF TOPOLOGIES The three shunt APF topologies applied to three-phase four-wire systems are shown in Fig. 1. The split-capacitor (SC), four-leg (F-L) and three Full-Bridge topologies (3F-B) are shown in Figs. 1 (a), (b) and (c), respectively.
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The main circuit of the shunt APF shown in Fig. 1(a) is implemented using the three-leg split-capacitor topology [14]. It uses three independent controllers acting on a halfbridge pulse width modulation (PWM) VSI converter. A common capacitor is coupled to a dc-bus with the midpoint connected to the neutral wire, while the ac side is connected to the power supply system using three coupling inductors, which act as low pass filters (LPF). This topology requires a control strategy to balance the dc-bus capacitor voltages. The circuit shown in Fig. 1 (b) is implemented using the four-leg full-bridge VSI topology [5-8]. The neutral wire current is controlled via an additional leg, requiring an additional coupling inductor. Despite needing an additional leg, smaller capacitors than those of the S-C topology are required, and balancing the dc-bus capacitor voltage is not necessary. Fig. 1 (c) shows the shunt APF implemented using three single-phase full-bridge VSI converters, as well as an increasing number of switching devices. However, the 3F-B topology allows independent control of the three phases [9],
When the load unbalance compensation is implemented the source currents become balanced and sinusoidal. However, when the phases are individually controlled the source currents will be sinusoidal but unbalanced. As the SRF-based algorithm is based on balanced three-phase loads, some modification must be done to apply it to a three-phase system, where each phase is treated as a single-phase system.
while the dc-bus voltage drops by a factor of 3 when compared with the F-L topology, and by factor of 2 when compared with the S-C topology [7]. As shown in Fig. 1 (c), three single-phase isolation transformers are necessary.
(a)
III. STATE FEEDBACK CURRENT CONTROLLER The block diagram of the single-phase current controller model is shown in Fig. 2, and the algorithm used to generate the compensation reference currents ( ic∗a ,b ,c ) is shown in Fig. 3. The closed loop transfer function of the shunt APF ica ,b ,c ( S ) / ic∗a ,b ,c ( S ) is given by (1), and the dynamic
stiffness transfer function is given by (2). Equation (2) is defined as the magnitude of the variations of the input voltages ( vsa ,b ,c ) that cause a unit deviation in the respective compensation currents ( ica ,b ,c ). These
(b)
variations are treated as a disturbance. ica ,b ,c ( S ) ic∗a ,b ,c ( S
)
vs a ,b ,c ( S ) ica ,b ,c ( S )
=
K Pp S + K Ip 2
L fp S + ( K Pp + RL fp )S + K Ip
=−
L fp S 2 + ( K Pp + RL fp )S + K Ip S
(1)
(2)
A. SRF-Based Algorithm The SRF-based algorithms will generate the compensation ∗ ) for all topologies and, reference currents ( ic∗a , ic∗b , icc ∗ ) when the F-L specifically, the neutral reference current ( icn APF topology is used. The SRF-based algorithms can be used to perform load unbalance compensation or to independently compensate each of the three phases.
(c) Fig. 1. Three-phase four-wire shunt APFs: (a) Split-capacitor; (b) Four-leg; and (c) Three F-Bridge.
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ic∗ = ih cosθ − iq sinθ
C. SRF-Based Algorithm Applied to shunt APF Fig. 4 shows the complete algorithm that will be used to implement the compensation strategies for the shunt APF topologies, which can provide independent phase control compensation and load unbalance compensation. For independent phase control the reference compensation
Fig. 2. APF converters: single-phase current controller.
B. SRF-Based Algorithm Applied to Single-Phase Loads The SRF-based algorithm applied to single-phase loads is shown in Fig. 3. Measuring the load current of any phase ( iL ) provides the two-phase stationary reference frame αβ quantities ( iα , iβ ). Using software, the acquired load current
is thus treated as the α coordinate of the fictitious two-phase stationary reference frame (αβ). Subsequently, iα has a π 2 radian phase delay, producing the fictitious β coordinate ( iβ ). Therefore, a new two-phase system, represented by (3), can be studied in the αβ axes. The dq value ( id , iq ) of the SRF is obtained by (4), where
∗ currents ( ic∗a , ic∗b , icc ) can be used in all topologies (S-C, F∗ L and 3F-B). The neutral reference current ( icn ) is used only
for F-L topology, which is calculated by (7). ∗ ∗ ∗ ∗ icn = ica + icb + icc
( is∗a , is∗b , is∗c ) in (8), the strategy for which is shown in Fig. 4, ⎡ ⎢ 1 ⎡i*s ⎤ ⎢ ⎢ a⎥ 2⎢ 1 ⎢i*sb ⎥ = − 3 ⎢ 2 ⎢* ⎥ ⎢ 1 ⎢⎣isc ⎥⎦ ⎢− ⎣ 2
id dc and adding the result to idc , which is obtained from the
dc link controller. The single-phase reference current ic∗ can be achieved directly from the synchronous rotating dq reference frame given by (6), which includes the compensation of the reactive and harmonic components of the load current.
⎡id ⎤ ⎡ cos θ ⎢ ⎥=⎢ ⎣iq ⎦ ⎣− sinθ
sin θ ⎤ ⎡iα ⎤ ⎢ ⎥ cosθ ⎥⎦ ⎣iβ ⎦
ih = id − id dc + idc
⎤ 0 ⎥ ⎥ 3 ⎥ ⎡iα T ⎤ ⎥ ⎢ 2 ⎥ ⎣⎢iβT ⎦⎥ ⎥ 3 − ⎥ 2 ⎦
respectively.
id Tdc =
(4)
iα T = id Tdc cos( ωt )
(9)
iβT = id Tdc sin( ωt )
(10)
3 ⎛⎜ idTdc a + idTdcb + idTdcc 2 ⎜⎝ 3
⎞ ⎟ ⎟ ⎠
(11)
The three-phase APF compensation reference currents are thus found as ∗ ∗ ica = iLa − is∗a , icb = iLb − is∗b and ∗ icc = iLc − is∗c .
Fig. 3. Block diagram of the current SRF-based algorithm for 1-phase load.
(8)
where iαT , iβT and id Tdc are given by (9), (10) and (11),
(3)
(5)
(7)
For unbalanced load compensation new reference currents must be obtained by generating the source reference currents
the phase-angle θ is obtained from a PLL system [18-20], which will be identical to the utility phase-angle. The dc component of id ( id dc ) can be found by using a Low-Pass Filter (LPF). The harmonic current component of id ( ih ), given by (5), is obtained by subtracting id from
⎡iα ⎤ ⎡ i L ( ωt ) ⎤ ⎢i ⎥ = ⎢ ⎥ ⎣ β ⎦ ⎣i L ( ωt − π 2 )⎦
(6)
(12)
Fig. 4 shows the PI (Proportional-Integral) controller used to control the dc-bus voltage at a constant level and to compensate the losses related to the inductances and switching devices. The PI output signal idcT represents the total active current required to maintain a constant dc-bus voltage level. To design suitable PI controller gains, a simplified second order dc-bus controller model was adopted [17].
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Fig. 5. Scheme of the single-phase PLL control system.
The nominal utility rms phase-voltage is equal to 127 V and the unbalanced R-L loads are: Ra = 4.5 Ω, Rb = 6.5 Ω, Rc = 12.5 Ω and La = Lb = Lc = 50 mH. The control model used to implement the PWM converters is shown in the block diagram in Fig. 2, while the simulation parameters are shown in Table I. TABLE I SIMULATION PARAMETERS APF Topologies
dc-Link Voltage Vdc (V)
Capacitor value C (F)
Inductor values (per-phase) L fp (H)
Inductor value (neutral) L fp (H)
Split-Capacitor
250 + 250
3m+3m
1m
-
Four-Leg
500
3m
1m
1m
Three F-Bridge
250
3m
1m
-
n
Table II shows the controller parameters used in the current and dc-bus controllers. TABLE II CONTROLLER PARAMETERS
Fig. 4. Block diagram of the complete current SRF-based algorithm.
D. Single-Phase PLL System
Given that the reference currents ic∗a ,b ,c are achieved directly from the synchronous rotating reference frame as given by (6) or (8), the phase-angle θ, which will be identical to the utility phase-angle, must be obtained from any single or three-phase PLL (Phase-Locked Loop) structure. In this experiment three single-phase PLL system were implemented, adopting the scheme shown in Fig. 5 [18], in which, using software, and knowing only one phase-angle among the three phases of the utility, all coordinates of the unit vector ( sin θ a ,b ,c and cos θ a ,b ,c ) for the three singlephase current SRF-based algorithms can be obtained (Fig. 4).
Current Controller Integral gain ( K Pp ) ( K Ip )
APF Topologies
Proportional gain
Split-Capacitor Four-Leg Three F-Bridge
31.42 62.83 31.42
1570 1570 1570
dc-bus Controller Integral gain ( K Pdc ) ( K Idc )
Proportional gain
0.4018 1.2053 0.4018
18.35 82.55 18.35
The compensated source currents isa , isb and isc plus neutral current isn for the S-C, F-L and 3F-B APF topologies are shown in Figs. 7, 8 and 9, respectively. The SRF-based algorithm was implemented by compensating reactive power and harmonic suppression. This strategy, which employs independent phase control, will result in sinusoidal but unbalanced source currents.
IV. SIMULATION RESULTS To verify the application of the SRF-based controllers presented, the three, three-phase four-wire APF topologies were simulated with the simulation tool PSIM version 7.0. The three-phase four leg parallel PWM converter operates at 20 kHz switching frequency while the unbalanced non-linear loads are composed of three single-phase diode bridge rectifiers, followed by R-L loads as shown in Fig. 6.
Fig. 6. Three-phase four-wire shunt APF topologies.
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Fig. 10 shows the neutral currents iLn , icn and isn for the Four-Leg shunt APF topology (Fig; 1 (b)). Using the load unbalanced compensation algorithm shown in Fig. 4, the source currents will became sinusoidal and balanced, as shown in Figs. 11, 12 and 13. In this case, the negative and zero sequence components were compensated. Fig. 14 shows the neutral currents iLn , icn and isn for the FL topology, and that isn is equal to zero.
Fig. 15 shows the S-C APF behavior when load transient occurs for independent phase control. The dc-bus voltages ( vdc1 , vdc2 ) and phase ‘a’ load current, plus compensation current and source current are shown in Figs. 15 (a), (b), (c), (d) and (e), respectively. In Fig. 16, the S-C APF behavior is shown for load unbalanced compensation. The dc-bus voltage oscillation is increased due to fundamental negative sequence component compensation.
Fig. 7. S-C APF source currents: (a) isa ; (b) isb ; (c) isc ; (d) isn
.
Fig. 11. S-C APF source currents: (a) isa ; (b) isb ; (c) isc ; (d) isn .
Fig. 8. F-L APF source currents: (a) isa ; (b) isb ; (c) isc ; (d) isn
.
Fig.12. F-L APF source currents: (a) isa ; (b) isb ; (c) isc ; (d) isn .
Fig. 9. 3F-B APF source currents: (a) isa ; (b) isb ; (c) isc ; (d) isn .
Fig. 13. 3F-B APF source currents: (a) isa ; (b) isb ; (c) isc ; (d) isn .
Fig. 10. F-L APF neutral currents: (a) i Ln ; (b) icn ; (c) isn
Fig. 14. F-L APF neutral currents: (a) i Ln ; (b) icn ; (c) isn
.
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.
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[2] [3] [4] Fig. 15. Phase ‘a’ S-C APF for independent control: (a) v dc1 ; (b) v dc2 ; (c) i La ; (d) ica ; (e) isa .
[5]
[6]
[7]
[8]
[9] Fig. 16. Phase ‘a’ S-C APF for load unbalanced compensation: (a) v dc1 ; (b) v dc2 ; (c) i La ; (d) ica ; (e) isa . [10]
V. CONCLUSIONS This paper presented compensation strategies, based on SRF controllers, which can be used in shunt APF topologies, when applied to three-phase four-wire systems, which allow harmonic current suppression, reactive and neutral current compensations to be conducted. The SRF-based controllers were used in three shunt APF topologies, and performed effectively. The algorithms allow the compensation of both load unbalances to generate sinusoidal and balanced source currents, and control each of the three phases independently. In this case the source currents will be sinusoidal but unbalanced. Although the 3F-B topology uses additional switches and isolation transformers when compared with Split-Capacitor and Four-Leg topologies, it also requires lower dc-bus voltage, which can be an attractive factor when high power applications are required. Compared to S-C topology, the F-L topology requires both lower voltage and current ratings in the dc-bus capacitor. In addition, F-L and 3F-B topologies need only one dc-bus voltage to be controlled. The simulation results closely approximated the theoretically predicted results.
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ACKNOWLEDGMENT The authors gratefully acknowledge the financial support received from CNPq under grant 474290/2008-5 and 471825/2009-3.
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