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A novel hysteresis voltage control of series active power filter
Fatiha Mekri (*), Nadia Ait Ahmed (**), Mohamed Machmoum (**), Benyounes Mazari (*)
(*) Université des Sciences et Technologies d’Oran, Algérie Faculté de Génie Electrique
BP 1505, 31000 Oran El M’naouar, Algéria E-mail : [email protected], [email protected]
(**) IREENA (Institut de Recherche en Electrotechnique et Electronique de Nantes Atlantique)
Bd. De l’Université, BP 406, 44602, Saint Nazaire Cedex, France E-mail: [email protected], [email protected]
Keywords «Series active power filter», «Robust PLL», «hysteresis voltage control», «adaptive band hysteresis control», «Sag», «Imbalance», «Harmonics»
Abstract In this paper a novel hysteresis voltage control for a series active power filter is proposed to improve the Power Quality (PQ), which is one of the most important issues of modern electrical distribution. The active filter controller is based on a new control strategy related to hysteresis band voltage control method, where the band is modulated with the system parameters to maintain the modulation frequency nearly constant. The new hystersis voltage control is presented and tested. This method has a good voltage tracking accuracy and a nearly constant switching frequency. Therefore, it is efficient and safe in operation. Simulation results show that this voltage control method improves the series active power filter performances noticeably. The determination of voltage references for series active power filter is based on a robust three-phase digital locked loop (PLL) system using RST regulator.
Introduction Active power filter is a very useful tool to improve the power quality of electrical distribution network. The main function of a series active power filter (SAPF) is the protection of sensitive loads from supply voltage sags. The active filter, connected in series with the network, is controlled like a source voltage and injects a voltage on the system in order to compensate any disturbance affecting the load voltage such as dips, imbalance and harmonic voltage. The load voltage quality can then be improved by adjusting voltage magnitude, wave-shape and phase shift of the injected voltages. The supply main voltages obtained after compensation are sinusoidal [1, 2, 3]. The general structure of the active power filter under study is presented in Fig. 1. Series active power filter is composed of 3-phase voltage source converter, LfCf filter to suppress switching ripples and series transformers which inject the compensating voltage to the line. Fig. 1. Global diagram of series active filter
LLooaadd
Supply Voltage
SSeerriieess AAccttiivvee FFiilltteerr
Vs Ls
Vc
is ich Vf
The SAPF performances will depend essentially on the dynamics of the modulation technique used to control the switches and on the method used to determine active filter voltage references. The control scheme of series active power filter is composed of two main blocks: the disturbance identification block and the voltage control. For identification of voltage references, a robust PLL system is used in this paper. Among various PWM techniques, hysteresis band current or voltage control PWM is popularly used because of its simplicity of implementation [4]. This known technique does not need any information about system parameters and has the disadvantage of uncontrolled frequency. As a result, the switching losses are increased and source currents or voltages contain excess ripples. The controller performances can be improved by using adaptive control system theory [5, 6]. This paper presents a new technique, based on the same concept of fixed hysteresis band, such as the band is modulated with the system parameters to maintain the modulation frequency to be nearly constant.
Disturbance identification There are various methods of the reference voltage identification; the method based on a three phase PLL is used [7, 8]. The PLL block allows to detect the amplitude and phase (Vs and dθ ) of fundamental positive sequence components of the utility voltages. The direct component voltages (Vsd1,2,3 ) will be subtracted from the instantaneous network voltages (Vs1,2,3 ) to determine disturbing homopolar and inverse components (Vdif1,2,3). The difference between the desired voltage amplitude (Vd-desired) and the direct voltage amplitude (Vs), provided by the PLL, gives, through Park inverse transformation, the regulated load voltages (Vr1,2,3). Finally, the reference voltages (Vref-1,2,3) are obtained by the sum of disturbing components (Vdif1,2,3) and regulated load voltages (Vr1,2,3) as show in Fig. 2 [7]. Fig. 2. Determination of the series active filter voltage references The detailed block diagram of the PLL, which can be completely implemented by software, is presented in Fig. 3. The PLL allows to control of an estimated phase angle ˆ
dθ with respect to the angle of mains voltage. Assuming that the measured voltages at the common coupling point are given by:
[ ]1 2 3
2 s in ( )2 = 2 s in ( )3
22 sin ( + )3
s s
s s s
s s
V
V V
V
θπθ
πθ
−
(1)
Measure of and Vs
PLL
P (- ) Transformation
2/3
Vs1(θ s) P (- ) Transformation
2/3
+ -
+ -
Vs1 Vs2 Vs3
Vref1
Vref2
Vref3
Vr1 Vr2 Vr3
Vd-desired
Vs
Vsd=0
Vsd1
Vsd2
Vsd3
cos( ) sin ( )
cos( ) dθ sin( ) dθ
dθ dθ
dθ
dθ dθ
+ -
++
++
++
- +Vs2(θ s) Vs3θ s)
Vdif3
Vdif1
Vdif2
They are converted in α, β coordinates and the d-q components are deduced by using Park’s rotation P(- ˆ
dθ ). The transformation angle results in an integration of the estimated supply voltage pulsation. Fig. 3. Detailed block Diagram of the PLL The d-q supply voltage components are given by:
ˆsin( ) sin( ) = 3 = 3
ˆ cos( )cos( )
sd s ds s
sq s d
VV V
Vθ θ θ
θθ θ
− ∆ − ∆− −
(2)
The PLL will be locked out of the supply voltages when the error between the phase of the supply voltage and the exit of PLL is null ( )ˆ
s dθ θ θ∆ = − . In this case Vsd = 0 and Vsq gives the amplitude of the fundamental component of the utility voltage.
0 , = - 3.sd sq sV V V= (3)
Thus, it is possible to control sθ by regulating Vsd to zero. In order to ensure a good quality of compensation of disturbance and to fulfill the desired requirements concerning the locking of the PLL, the control of Vsd must be carried out without variation and with a fast dynamic. The effectiveness of filtering of undesirable frequencies under unbalanced or distorted supply voltages conditions is achieved using an RST controller [7]. The RST controller is composed of three polynomials R(p), S(p) and T(p) defined so as to reach objectives of regulation. The functional diagram of the PLL with RST controller is presented in Fig. 4. This leads to the following closed loop relation:
*( ). ( )( ) . ( )
( ). ( ) ( ). ( )sd sdB p T pV p V p
A p S p B p R p=
+
(4)
3( )( )
sVB pA p p
= −
The control objectives are translated into constraints on polynomials R(p) and S(p) and into the choice of the closed loop poles. So R(p) and S(p) are split in two parts:
1 1( ) ( ). ( ); ( ) ( ). ( )c cR p R p R p S p S p S p= = (5)
+ -
Regulator
1/p
P(- dθ ) sin cos
T32t
T23t
dθ Vref
Vsd1 Vsd2 Vsd3
Vs3(θ s)
- 3 Vs Vsd Vsq
Vs2(θ s) Vs1(θ s)
The constraint part of S is taken as Sc(p)=p in order to insure a zero steady-state error. The dominant frequencies due to supply voltage imbalance and distortion (f1=100 Hz, f2=300 Hz) must be filtered by the regulator. To this end the constraint part Rc(p) is written as:
2 2 2 2 2 21 1 1 2 2 2( ) ( 2. (2 ) ).( 2. (2 ) )cR p p r p r f p r p r fπ π= + + + + + + (6)
r1 and r2 are fixed in order to have an attenuation at an approximate value of 50dB at the frequencies f1 and f 2 due respectively to unbalanced or distorted supply voltage.
Fig. 4. Functional diagram of the PLL with the RST regulator
The remaining polynomials R1(p) and S1(p) are calculated by solving the Diophantine equation (7):
( ) ( ). ( ) ( ). ( )F p A p S p B p R p= + (7) The roots of the closed loop characteristic polynomial F(p) are selected in order to ensure the robustness of control and to achieve the required goals.
Series Active filter output voltage regulation The series active filter is realized with a new control strategy related to hysteresis control method for the voltage inverter. The core of the SAPF is the control section that must be able to derive the reference voltage waveforms with matching ripples content in the line voltage. The equivalent diagram of the series active filter is given by Fig. 5. Fig. 5. Simplified model of series active filter
The system can be modeled by the following equations:
f ch
f
dV I Idt C
+= (8)
2
2 ( )f f cht f f f f f f f ch
dV dV dIV V L C R C L R Idt dt dt
= + + − + (9)
With: Vt : the output inverter voltage, Vf : the output voltage of the series active filter, Vc: the DC bus voltage, Ich: the load current witch can be considered as a disturbance.
Vsd(p) 3 sVp
− Vsd*(p)
R(p)
1/S(p)
T(p)
-
Vc
= ≈
Vt
Ich I
Vf
Lf ,Rf
Cf
New control of fixed hysteresis band To understand the principle of new control of fixed Hysteresis Band (HB), we will treat 3 cases as follows:
• Case1: The principal diagram of fixed hysteresis band control is shown in Fig.6. The hysteresis value band governs the inverter switching pattern in such a manner as to maintain the mean value of the control state at the required value. The instantaneous value of the output voltage is compared with the reference voltage, when the sensed output signal deviates from the reference by more than a prescribed value; the inverter is operated to reduce the deviation. This means that the switching occurs whenever the output voltage crosses the value of HB. The output voltage signal of the SAPF is given by:
Vf =Vref + HB in rising case. (10)
Vf =Vref – HB in decreasing case.
Fig. 6. Simplified model for fixed hysteresis-band voltage control
Thus the output wave is restricted to flow within a channel of width (HB) that follows the reference wave. The frequency of inverter depends of the width of the hysteresis band. The output voltage will contain significant ripples due to inductance trapped energy that prolongs the charging and discharging of the capacitor. To solve this problem, it is necessary to improve the hysteresis control.
• Case2: Understanding of the system helps us to find the effective ways to make the output ripple under control irrespective of (Lf-Cf) filter. Equation (8) shows that the rate of change of the output voltage gives a measure of inductance trapped energy at no load that charges the capacitor over. At loading case, this state gives a measure of the excess energy that prolongs the charging time outside the tolerance band. The state dVf /dt is an important signal that can be used to modify the control signal of the hysteresis controller. Hence, the control signal should be composed of the derivative term in addition to the proportional of the output voltage signal of the series active filter. This control signal is given by:
fcont f
dVV V
dt= + (11)
This signal with its reference determine the suitable switching instants so that the output remains in prescribed tolerance. The output voltage signal is given by:
ff ref
dVV V HB
dt= + − (12)
ff ref
dVV V HB
dt= − −
• Case 3:
In order, to improve establishment time and to better filter the output ripple especially in the case of a strong disturbance, the derivative term is replaced by a filter described by the following relation:
Ti
Vref T’i
Vf
-
+
1
2filter d
p wFT kp w
+=+
(13)
This filter can be assimilated to an advance phase:
With:2 1 2
1 2 2 1
11
1, , , 1,
advance phase
d
a pFT kp
a k k
ττ
ω ω ωτω ω ω ω
−+=
+
= = = ⟩ (14)
The pulsations 1ω and 2ω are chosen in order to have a good filtering of the ripple, improve the transient state, and to ensure stability of the system. In this case, the output voltage signal is given by:
filterf refV V HB FT= + − (15)
filterf refV V HB FT= + +
An adaptive hysteresis band The fixed hysteresis band is very simple and easy to implement, but it has the disadvantage of an uncontrollable high switching frequency. This high frequency produces a great stress for the power transistors and induces important switching losses. An adaptive hysteresis band method allows operating at nearly constant frequency and is usually performed by software using the system parameters. An adaptive hysteresis band voltage control PWM technique can be programmed as a function of reference voltage and the parameters of active filter to minimize the influence of voltage distortions on modulated waveform [5, 9, 10]. Based on equation (9) and by identification to adaptive band, the hysteresis voltage band can be written as:
2
22
0.125. ( ) ( )4( )(1 ( ) )c sl reff f
c f f c f f
V V t dV tR CHBf R C V R C dt
= − + (16)
with: 2
2 ( )ref chsl ref f f f f ch
dV dIV V L C L R Idt dt
= + − +
The output voltage signal is obtained using relations (15) and (16). The adaptive band is calculated by taking: Vc = 700V, Lf = 4*10-4H, Cf = 73 *10-4F , Rf =0,02Ω and fc = 8kHz
Simulation Results The system shown in Fig.1 is simulated using Matlab/ Simulink software. The series active power filter has been tested with different hysteresis bands voltage control. Figs. 7, 8 and 9 represent the case of control based on a fixed hysteresis band, and Fig. 10 represents the case of control using adaptive band. At t=0.06 a sudden load current impact (Ich = 777 A) is applied as a disturbance. Vf is the output voltage of the series active filter, Vref is the reference voltage and ‘e’ is the error between measured value and the reference (e= Vf -Vref.).
Fig. 7. Fixed hysteresis band control (case 1)
Fig. 8. Fixed hysteresis band control (case 2)
In Fig.7 the output voltage Vf presents significant ripple which depends on the value of the fixed bandwidth. This band influences the value of amplitude of the ripple and the average frequency of commutation, and the recovery time is very important. The ripple is minimized by using the derivative term (case 2), but this last can not compensate the transient, especially if the disturbance is important as show in Fig.8. To solve this problem, a filtered derivative term is used, as shown in Fig.9. The performances are thus improved, the magnitude ripple is not important and the recovery time is reduced compared to the previous cases. Fig.10 illustrates the results obtained with the adaptive band using the filtered derivative term. The transitory mode is compensated and the ripple is also reduced.
0 0.02 0.04 0.06 0.08 0.1 0.12-500
0
500
0 0.02 0.04 0.06 0.08 0.1 0.12-400
-200
0
200
Vref, Vf
e
t(s)
0 0.02 0.04 0.06 0.08 0.1 0.12-500
0
500
0 0.02 0.04 0.06 0.08 0.1 0.12
-200
-100
0
100
Vref, Vf
e
t(s)
Fig. 9. Fixed hysteresis band control (case 3) Fig.10. An adaptive hysteresis band control Simulation results of the SAPF obtained with adaptive band control method under unbalanced (V1=230V, V2=180V, V3=300V) and distorted supply voltages conditions are presented in Fig. 11. The supply voltages and consequently the output voltage references of the SAPF contain excessive harmonics (5, 7, 11 and 13 harmonics) with a THD equal to 27, 31%. At t=0.06 a sudden load current impact (Ich = 777 A) is again applied as a disturbance. Results show that the error is minimized, the load voltage is always sinusoidal and its harmonic distortion ratio THD decreases from 27, 31 % before compensation to less than to 0.1% . To compare hysteresis fixed band (case 3) and adaptive band control performances, two tests with a sudden load current impact (at t=0.06ms : Ich=200 A for test 1 and Ich =777 A for test 2) are realized. Results are summarized in table 1 where tr is the recovery time and PICmax is the maximum peak of error ‘e’ in the transitory mode. The performances of adaptive hysteresis band control are better than fixed hysteresis band control and the although those controls have the same dynamic. test1: V1=230V, V2=180V, V3=300V, THD=27.3%, Ich=200A, test2 : V1=230V, V2=180V, V3=300V,THD=27.3%, Ich=777A.
0 0.02 0.04 0.06 0.08 0.1 0.12-500
0
500
0 0.02 0.04 0.06 0.08 0.1 0.12-200
-150
-100
-50
0
50
Vref,Vf
e
t(s)
Vref , Vf
e
Fig. 11. Performances of the series active filter with an adaptive hysteresis band control
Table I: Simulation results under unbalanced and distorted supply voltages conditions
Test 1 (Ich = 200 A) Test 2 (Ich = 777 A) fixed Band
(case 3) adaptive Band fixed Band (case 3) adaptive band
e [V] 2,4 0,5 3 1 THD % 0,21 0,07 0,27 0.1 PICmax[V] 16,5 14 180 160 tr [s] 4.10-3 4.10-3 5.10-3 5.10-3 Fig.12 represents the SAPF behavior under nonlinear load conditions, in order to compensate single phase voltage sag (40%) during 40ms (from t=0.04s to t=0.08s). Vres, Ich Vref, HB and Vch are respectively the supply voltage, the non linear load current, the voltage reference, the adaptive hysteresis band and the load voltage. During the transient ( at t= 0.04s) the series active filter has a good dynamic and the load voltages are sinusoidal and balanced. Fig. 12. Performances of the series active filter with an adaptive hysteresis band control in the case of single phase sag voltage
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-500
0
500
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-200
0
200
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-200
-100
0
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
-500
0
500
Vref, Vf
Vres
e
Vch
t(s)
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-500
0
500
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-500
0
500
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1000
0
1000
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-100
0
100
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.115
20
Vres
Ich
Vref, Vf
HB
Vch
t(s)
Fig.13 presents the spectrum of the output filter voltage control and shows that the switching frequency is nearly constant and equal to 8 KHz.
Fig. 13. Spectrum of the output filter voltage control
Conclusion In this paper, the series active filter has shown the ability to compensate sag and unbalanced voltages based on a new hysteresis voltage control method. We have demonstrated that the modified control signal composed of the output voltage of the SAPF and its derivative makes the output ripple under control, and the band is modulated with the system parameters to maintain the modulation frequency nearly constant. This leads to improve the quality of the output signal and to more flexibility for filter design. In other hand, the control of the PLL has been done to extract fundamental positive sequence voltages system and to estimate the mains frequency under several supply voltages conditions. The associated RST regulator assures good reliability and a fast tracking performances.
References [1] M. Machmoum, N. Bruyant, M.A.E. Alali and S. Saadate, “Compensateur actif série d’harmoniques, de déséquilibre et de creux de tension des réseaux électriques”, Revue Internationale de Génie Electrique, vol. 4, no.3-4, pp 317-332, 2001. [2] H. Fujita, H. Akagi, “The unified power quality conditioner: the integration of series-and shunt-active filter”, IEEE Trans. on Power Electronics, vol. 13, no. 2, pp 315-322, March 1998. [3] J. Svensson, A. Sannino, “Active filtering of supply voltage with series-connected voltage source converter”, EPE Journal, Vol. 12, no. 1, February 2002, pp. 19-25. [4] M.A. Rahman, T.S. Radwan, A.M. Osheiba, A.E. Lashine, “Analysis of current controllers for voltage source inverter ”, IEEE Trans. on Ind. Electronics, vol. 44, no. 4, pp 477-485, August 1997. [5] B.K. Bose, “An adaptive hysteresis- band current control technique of a voltage fed PWM inverter for machine drive system”, IEEE Trans. on Ind. Electronics, vol. 37, no. 5, pp 402-408, October 1990. [6] K.M. Rahman, M.R. Khan, M.A. Choudhury, “Variable band hysteresis current controllers for PWM voltage source inverters”, IEEE Trans on Power Electronics , vol. 12, no. 6, November1997, pp. 964-970. [7] M. Machmoum, M. Shafiee Khoor,Y. Abdelli and J.C.Leclaire, “ Series active compensator for supply voltage disturbances”, EPE 2003, Toulouse, France. [8] Hilmy Award, Jan Svensson, Math Bollen, “Phase locked loop for static series compensator.” EPE 2003, Toulouse, France. [9] I. Fatouh “ A powerful and Efficient hysteresis PWM controlled inverter”, EPE Journal, Vol. 4, N°4, December 1994 [10] F. Mekri, B. Mazari, M. Machmoum, “Control and optimization of shunt active power filter parameters by fuzzy logic ’’, Canadian Journal of Electrical and Computer Engineering, Vo.31, N°3, Summer 2006, pp. 127-134.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
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Amplitu
de (V)
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