Variable Hysteresis Current Control Applied in a Shunt Active Filter with Constant Switching Frequency
Abstract
Hani Vahedi
Abdolreza Sheikholeslami
Department of Electrical Engineering Babol University of Technology Babol, Iran
Department of Electrical Engineering Babol University of Technology Babol, Iran
[email protected]
[email protected]
- Presence of harmonics in
power networks makes it
inevitable to use power filters. Shunt active power filters (APF) are widely used in power systems to eliminate the current harmonics
and to
compensate
reactive
power due to
their
accurate and fast operation. In this paper the instantaneous power theory is used to extract the harmonic components of
VSII(t) 'V vsdt)
frequency
'V vslt)
disadvantages, the adaptive hysteresis current control (AHCC) is
'V
system current. Then fixed-band hysteresis current control is explained.
Because
of
fixed-band
variable
i,Jt)
h,(t)
LII
isb(t)
ilb(t)
Lb
isb(t)
illt)
Le
introduced that leads to fix the switching frequency and reduce the high frequency components in source current waveform. Some simulations are done in Matlab/Simulink. The Fourier Transform and THD results of source and load currents are discussed to prove the validity of this method.
Index Terms - Power System Harmonics, Shunt Active Power Filter, Instantaneous Power Theory, Adaptive Hysteresis Current Control. 1. INTRODUCTION
Due to power electronics technology and switching devices, the waveform of source current in power network will change. These power switches tum on and off repeatedly and make alternative transient mode in current waveform called power network harmonics. These current harmonics increase the power losses and causes the voltage source generates reactive power which is not desirable [1]. Some equipment have been employed to eliminate voltage and current harmonics in power networks like passive, active, series, shunt and hybrid filters. Among these devices, shunt active power filters (APF) have been widely developed and have been used in electric systems to eliminate current harmonics and compensate reactive power because of their fast response and accurate operation [1-3]. Fig. 1 shows a 3-phase power system includes voltage source, nonlinear load and a 3-phase APF which has been connected to it through interface inductors. APFs are based on voltage source inverters (VSI) and include two other important sections. One section is its controller and the other is a power switching pulse producer. In controller section, the required current for eliminating harmonics is calculated called reference current. At the other section, switching pulses are made according to the reference current waveform. These pulses will be sent to VSI power switches, so the generated current is injected to power network results in compensating the harmonic current of the load, thus the source current only compose of main component [3].
Fig. 1 Power System Diagram with APF
Different switching methods are used to produce switching pulse leads to generate reference current. Switching approaches are classified into two general sections: voltage control, and current control. Current control methods are faster and more accurate than voltage control ones. Hysteresis current control (HCC) has been noticed more than other current control techniques, due to simplicity and quicker dynamic response. In this method, two bands are assumed around the reference current and the filter current goes into this band. If the filter current touch the upper or lower band, the off or on command will be sent to the inverter switches, so the output voltage of inverter varies in order to reference current waveform and the filter current will be made subsequently [4]. In this method, if a fix value used for band width, the hysteresis block can be made by a simple comparator relay which results in more simplicity and faster operation but. Beside these advantages, high variation of switching frequency is one of fixed-band HCC disadvantages which cause audio noises. Further more different frequency components in current waveform will be appeared due to
different switching frequencies that make it difficult to design appropriate filters to eliminate these components. To overcome this problem, an adaptive hysteresis current control (AHCC) has been introduced in this paper. Using this method, variable hysteresis bandwidth is calculated instantaneously, leads to reduce the switching frequency variation, thus the fixed-band HCC issues will be amended. In this paper, in section II, the instantaneous power theory has been explained to extract the harmonics components of current waveform. Then in section III, the fixed-band HCC has been clarified. Proposed AHCC has been introduced in section IV. Finally, some simulations have been done with Matlab/Simulink and the results consist of switching frequency diagrams and current THD in high frequency range have been discussed in section V. By comparing the results of simulations, advantages of proposed AHCC in fixing switching frequency and modifYing above mentioned problems, especially reducing the high frequency components in source current waveform have been proved. II.
INSTANTANEOUS POWER THEORY
The initial step in eliminating the load current harmonics and imbalance is extraction of the compensation reference currents. Then, the derived reference signals should be produced by employing precise switching modulation of voltage source inverter. Eventually, through connecting inductances or other low-pass passive filters, the generated filtering currents should be injected in the grid to compensate efficiently the harmonics and imbalance. One of the popular compensation reference current extraction methods is the instantaneous reactive power theory (p-q theory). Although there are some problems with this theory, it is well-established and simple in implementation. The p-q theory could be briefly reviewed as follow [5]: Assume a three-phase load with the instantaneous voltages as v(t)=[va(t) Vb(t) vc(t)r and the instantaneous currents as iICt)=[ila(t) ilb(t) ilc(t)]i (Fig. 1). Using (1), vet) and i](t) can be converted to o-a-p coordination where C is the matrix (2): [vo(t) vu(t) vp(t)]t C [va(t) V b(t) vc(t)F (1) [ilO(t) i1u(t) i1p(t)]t C [ila(t) i1b(t) ilc(t)]t =
=
C
=
fi �3
l� � � o
2
2
,/3
-,/3
2
(2)
2
Let's assume that the zero sequence current (ilO(t) is null. Thus, the instantaneous active (P(t» and reactive (q(t» powers can be calculated as: Vp(t) iIU(t) pet) = vu(t) (3) v -vp q(t) (t) u(t) iIP(t) pet) and q(t) can be decomposed to the average parts (p(t), (j(t) and the oscillating parts (p(t), (j(t). It is notable that pet) is produced by the fundamental harmonic of the positive sequence component of the load current. Therefore, in
[ ]
l
j[ ]
order to compensate the harmonics and the instantaneous reactive power, compensation reference currents can be extracted as follow: vu(t) i u(t) Vp(t) -1 -pet) (4) -vp(t) vu(t) -q(t) itp(t) [ija(t) ijb(t) ijc(t)F C-1[0 iju(t) ijp(t)Y (5)
l� j l
j [ ]
=
=
III.
FIXED-BAND HYSTERESIS CURRENT CONTROL
Hysteresis current control is used for generating the switching pulses. Among the various current control techniques, HCC is the most extensively used technique because of the noncomplex implementation, outstanding stability, absence of any tracking error, very fast transient response, inherent limited maximum current, and intrinsic robustness to load parameters variations. As indicated in [4, 6] a review of used current control techniques for PWM converters reveals that HCC shows certain superiority for active power filter applications. HCC provides a better low order harmonic suppression than PWM control, which is the main target of the active power filter. It is easier to realize with high accuracy and fast response. However, as a disadvantage its switching frequency might fluctuate. In the HCC technique the error function is centered in a preset hysteresis band. When the error exceeds the upper or lower hysteresis limit the hysteretic controller makes an appropriate switching decision to control the error within the preset band and send these pulses to VSI to produce the reference current as shown in Fig. 2.
ift)
If
Switching Pulses
Hysteresis Block
Fig. 2 fixed-band hysteresis current control loop.
i./ is a vector of the desired compensation current reference signals. if is a vector of the feedback actual voltage source inverter output currents. ij and it signals are each demultiplexed to 3 signals phase A, B and C reference current signals and phase A, B, and C actual feedback current signals. Reference and actual signals are compared and fed into a hysteresis block and the output of the hysteresis block is the firing pulse. For explaining the technique it is best to consider only phase A. When ij is greater than if, the resultant difference signal e, is positive. If the magnitude of e is bigger than the upper boundary of the specified hysteresis band, the hysteresis block output goes high, firing the upper bridge device of the leg and making the leg current increase. When if becomes greater than ij, e becomes negative. If the magnitude of e is smaller than the lower boundary of the hysteresis band, the hysteresis block goes low, firing the lower bridge device of the leg and making the leg current decrease. If e is within the limits of upper and lower boundaries of hysteresis band, hysteresis block keeps its current state.
The outputs of the hysteresis blocks are directly fed as the firing pulse of upper bridge device of each leg of the inverter and NOT of that signal is fed as the firing pulse of lower bridge device of each leg. This is necessary for operation and avoiding the conduction of same leg switches simultaneously. In fixed-band HCC, the hysteresis bandwidth (HB) has been taken as a small portion related to system current and in many researches it has been taken as 5% of main current which will be HB=0.6A, here. IV.
PROPOSED ADAPTIVE HYSTERESIS CURRENT CONTROL
(AHCC) As above-mentioned, the crucial concern with the fixed band hysteresis current control is producing a varying modulation frequency of the power converter which, in tum, results in increasing the switching losses. To avoid this situation, adaptive hysteresis current controller methods with the variable hysteresis band have been recommended in literature [7, 8]. Hence, a variable hysteresis band is defined for each phase so that the switching frequency remains almost constant.
/
J
Fig. 3 Single- phase diagram of a power system with APF.
The variable hysteresis band (HB) formula can be calculated based on Fig. 1. For the sake of simplicity, consider Fig. 3 as the single-phase diagram of the system in Fig. 1. According to Fig. 3, the following KVL equation can be easily achieved:
t eVf - vs(t)) Where Vf is the
{ V dC
inverter-side voltage and can be
upper switch is ON Vf - V C the the lower switch is ON - d
(7)
i/(� -,,, - ,i-�--;;;ii(t) ;-(1)
(8)
_
(9)
are the rising current and the falling current, respectively. Furthermore, the following relations can be extracted:
{
difa (t) dija (t) 2 -d-t tl - -d-t tl - HB di'ja (t) dija (t) = -d-t 1 t2 - -d-t t2 - 2HB 1= _ tl +_t2 Where t1 and t2 are switching
-
-
*
_
*
(10)
*
*
(11)
intervals and 1 is the switching frequency. By substituting (8), (9) and (11) in (10), the hysteresis band (HB) can be achieved as follow:
HB
=
Vde 4fLt
_
)
(
--.!.:.L vs(t) + dij(t) 2 Lt dt 4fVde
(12)
The adaptive HB should be derived instantaneously during each sample time to keep the switching frequency constant. SIMULATION RESULTS
To verify validity of the proposed method some simulations are done using MATLAB/Simulink. The nonlinear load consists of a three-phase diode rectifier with a DC-side resistive load. It should be mentioned that the nonlinear load is connected to the grid via inductances (L.r=5mH). Besides, the load voltages have an rms value of 220V-50Hz. Fig. 5 shows the source voltage which is remained sinusoidal and does not contain any harmonics. Fig. 6 shows comparative diagrams of load current, filter current and source current respectively for Fixed-band HCC and AHCC methods simulation. These diagrams show a good filtering leads to eliminate the source current harmonics, so the source current contains just the main component. TABLE 1 APF SIMULATION PARAMETERS
(6)
elaborated as below: _
difa (t) = � (V vs(t)) dt Lt f di'ja(t) = � + (V vs(t)) Lt f dt Where ij(t) and ii(t)
V.
�n iit) ] 1
di�;t) =
Having paid attention to Fig. 4, the below relations can be obtained:
Supply Phase Voltage
220 V
Grid Frequency
50 Hz
Load Resistanc RI
25 0
Inverter Side Inductance Lf
5 mH
Rectifier Side Inductance LI
2 mH
APF dc-link Voltage "''''
750 V
Fixed Hysteresis Bandwidth
O.6 A
I
" "
/
Fig. 4 The upper and lower bands of the reference compensation current.
!
, J
.
.
·6. -100
-260
0.05
Time (Sec)
Fig. 5 The source voltage for phase (a)
:;-20
Fixed Band Hysteresis Simulation
:;-20
'"
'"
'"
'"
..,...
� 0
� 0
..,... �
�·20
Variable Band Hysteresis Simulation
0.062
0.07
·20
0.078
0.062
is obvious that the switching frequency in fixed-band HCC varies in vast range (in this case it changed from 12 KHz to 22 KHz) and cause audio noises and inject high frequency components in source current that makes it difficult to design appropriate filters for eliminating them. Fig. 9 proves that many high frequency components have been injected to the source current due to variable switching frequency, but in Fig. 8, the AHCC results prove the fact that this method has worked properly results in fixing switching frequency (12 KHz to 15 KHz). This result influences the source current THO especially in high frequency range. Since the variation range of switching frequency has been limited to small domain, the high frequency components of source current have been reduced to a narrow range which is apparent in Fig. 10. As the variable switching frequency cause audio noises, the AHCC fixes this problem by constant switching frequency, too.
0.07
30,---.-----,
�
�
'"
'"
;:·10
0.062
0.07
;:·10
0.078
0.062
0.07
0.062
0.07 Time (Sec)
0.078
'" '"
�
0
'"
..
u
"' 20 L-
�
0.062
�� �� �� o.� �� Time (Sec) Fig. 7 Instantaneous switching frequency for fixed band HCC
u
0.07 Time (Sec)
�20
0.078
Fig. 6. The Currents for phase (a)
30,---.-----,
Table 2 and table 3 show the RMS and THO% values of the source and load currents respectively. The RMS values show that there were negligible losses that the load and source current values are close to each other. The THO results show that AHCC method works properly to track the reference current and there was a good filtering process. But the following figures show the difference between fixed-band and AHCC. The AHCC distinction will be proved by figures 7, 8, 9 and 10.
0.035
0.045 0.055 0.065 Time (Sec) Fig. 8 Instantaneous switching frequency for AHCC
TABLE 2 THE RMS VALUE OF LOAD AND SOURCE CURRENTS (A) Source Current RMS
I I
I
I
Load Current RMS
Phase a
Phase b
Phase c
Phase a
Phase b
Phase c
Fixed-band
12.27
12.27
12.28
12.66
12.66
12.66
AHCC
12.28
12.28
12.29
12.66
12.66
12.66
Fixed-band AHCC
0.075
TABLE 3 THD% VALUE OF LOAD AND SOURCE CURRENTS Source Current THD% Load Current THD% Phase c Phase b Phase c Phase a Phase b Phase a 2.59 22.37 22.28 2.15 2.83 2244 22.37 3.81 22.44 22.28 3.02 3.03
Figures 7 and 8 show the instantaneous switching frequency for the fixed-band HCC and AHCC respectively. It
Fundamental
2
f.. §
= 17.65 THO= 2.1
1.5
·
.. ! .. ·
·
:IIi
0.5 0
0
5
10 15 20 Frequency (KHz) Fig. 9 FFT analysis of the source current in fixed band method
25
m�
m--
= 17.68
Fundamental
--
THO= 3.02%
I § ..
t o
i
..
o
0
5
10
__
15
Erequency (KI-:fz),
20
25
_______
Fig. 10 FFT analysis of the source current in AHCC
IV. CONCLUSION Shunt active power filters are widely used in power networks to eliminate the current harmonics and compensate the reactive power. In this kind of filters, the harmonic component of the current are extracted at first. Instantaneous power theory is one of effective methods which has been explained in this paper. Afterwards, the hysteresis current control has been clarified and the AHCC method has been introduced to fix the frequency switching leads to modifY the fixed-band disadvantages like audio noises and high frequency harmonic components. The simulation results proved that AHCC technique made the switching frequency to be constant, so reduced the high frequency components of source current and the switching losses. The THD was desirable, too.
REFERENCES [I] E.L. Owen, "A History of Hannonics in Power Systems", IEEE Industry Application Magazine, January/February 1998, pp. 6-12 [2] M. Tavakoli Bina, E. Pashajavid, "An efficient procedure to design passive LCL-filters for active power filters", Elsevier Journal Electric Power Systems Research, 2009, Vol. 79, Iss. 4, pp. 606-614. [3] Ali Emadi, Abdolhossein Nasiri, Stoyan B. Bekarov, "Uninterruptable Power Supplies and Active Filters", Illinoise Institute of Technology, 2005 [4] Marian P Kazmierkowski, Ramu Krishnan, Frede Blaabjerg,"Control in power electronics", Academic Press, 2001. [5] Wenjin Dai, Yongtao DaiTingjian Zhong, "A New Method for Hannonic and Reactive Power Compensation", IEEE Int. Conf on Industrial Technology, ICIT, 2008, pp.I-5 [6] M. P. Kazmierkowski and L. Malesani, "Current control techniques for three-phase voltage source PWM converters: a survey", IEEE Trans. Industrial Electronics, vol. 45(5), pp. 691-703, 1998. [7] B.K.Bose, "An Adaptive Hysteresis Band Current Control Technique of a Voltage Feed PWM Inverter for Machine Drive System", IEEE Trans. On Ind. Elec., 1990, pp. 402-406 [8] Wenjin Dai, Baofu Wang, Hua Yang, "A Hysteretic Current Controller for Active Power Filter with Constant Frequency", IEEE Int. Conf. on Computational Intelligence for Measurement Systems and Applications, CIMSA, 2009, pp.86·90
