1
A Comparative Study of Harmonic Current Identification for Active Power Filter
L. MERABET
1
, S. SAAD
2
, A. Omeiri
3
, D. Ould Abdeslam
4
,
1
Electrical department of Annaba University, Algeria, Email: lei_elt@yahoo.fr
2
Electromechanically department of Annaba University, Algeria, Email: saadsalah2006@yahoo.fr
3
Electrical department of Annaba University, Algeria,
Omeiriamar@univannaba.org
4
MIPS laboratoire, Université de Haute Alsace, 4 rue des frères lumière, 68093 Mulhouse, France, djaffar.ouldabdeslam@uha.fr
ABSTRACT
Active power filter requires accurate harmonic current identification to compensate harmonics in power system distribution. The purpose of this paper is to present a comparative study of two techniques for harmonics currents identification based on
PQ
theory and Adaline(ADAptiveLINear Element) neural networks. The harmonic current can be identified from powers or currents. The first method is based on the instantaneous powers taking advantage from relationship between load currents and power transferred from the supply source to the loads. The second method concerns the artificial neural networks based on the LMS (least mean square) algorithm. This approach adjusts the weights by iteration and provides more flexibility to perform the compensation. The developed architecture is validated by computer simulation proving its effectiveness, capability and robustness.
Key words
 Nonlinear load Active power filter Harmonics Fourier series – Adaline, neural network. 1.
I
NTRODUCTION
The switching action of the rectifying device produces non sinusoidal current in the a.c. supply. Therefore, the value of the supply impedance will differ for each harmonic frequency; hence the voltage in the point of common coupling will contains harmonic voltage components. If other loads or consumers are fed from this point the system react to each particular frequency. Furthermore, harmonic voltages and currents propagate into the supply system, increasing losses, causing measurement errors and interfering with other consumers. Currentlyactivepower filters have been widely used, studied and presented as a solution to mitigate harmonics from power network. These filters are classified into shunt active power filter, series active power filter, hybrid filters (parallel passive filters and series active power filter) and finally, Unified Power Quality Conditioner UPQC (series active power filter and shunt active power filter) [1], [2]. Actually, artificial neural networks (ANNs) have been successfully applied to power systems [3], [4], [5] especially for harmonic identification [6], [7], [8], [9]. The learning capacities of the ANNs allow on online adaptation to any change in electrical network parameters. These techniques are also applied to the control of active filter to improve its performances and replace the conventional PID controllers [5], [8], [10], [11], [12]. This paper presents a comparative study of two techniques for harmonics currents identification. The first technique is based on instantaneous power theory and the second is based on Adaline(ADAptiveLINearElement)neural network, [9]. The developed algorithms are simulated. The obtained resultsare compared, and discussed
2.
P
RINCIPLE OF
SHUNT
APF
The APF is a voltage source inverter connected to the threephase line through the inductor L Fig.1. This inverter injects an appropriate current into the system tocompensate harmonic current that is responsible for low power factor.
Figure 1. Principle of APF
Supply PCC
1
Lh
ii
+
L
d
L
Nonlinearload Inverter
s
i
h
i
−
C
d
R
2012 First International Conference on Renewable Energies and Vehicular Technology
9781467311700/12/$31.00 ©2012 IEEE 366
2
3. INSTANTANEOUS POWER THEORY (
pq
theory)
The instantaneous power theory [1], [2] is defined on the basis of the instantaneous values of voltage and current waveforms in a three phase system.
Figure 2.The instantaneous space vectors
Using the Clarke transformation, these threephase vectors are transformed to the orthogonal
o
,,
β α
coordinate system.
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎣⎡
−−−=
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡
sc sb sa
vvvvvv
232302121121212132
0
β α
(1)
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎣⎡
−−−=
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡
sc sb sa
iiiiii
232302121121212132
0
β α
(2) Since the load is balanced, and there is no neutral line, the system does not have a zerosequence,
0
v
and
0
i
are equal to zero and the system equations are simplified to:
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡
−−−=
⎥⎦⎤⎢⎣⎡
sc sb sa
vvvvv
232302121132
β α
(3)
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡
−−−=
⎥⎦⎤⎢⎣⎡
sc sb sa
iiiii
232302121132
β α
(4) The conventional instantaneous power in a three phase system
p
and
q
in [1], [2] was based on the following equation:
β β α α
iviv p
+=
(5)
β α α β
ivivq
+−=
(6) Equations (5) and (6) are written in matrix form as shown in equation (7).
⎥⎦⎤⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡
=
⎥⎦⎤⎢⎣⎡
β α α β β α
iivvvvq p
_
(7) The currents can be deduced by:
⎥⎦⎤⎢⎣⎡
=
⎥⎦⎤⎢⎣⎡
⎥⎥⎦⎤⎢⎢⎣⎡
−
−
q pii
vvvv
α β β α
β α
1
(8) The active and reactive powers as calculated from equation (7) and can be split into DC and AC components as illustrated below:
p p p
+=
~
(9)
qqq
+=
~
(10) Where
p
and
q
are the DC active and reactive power while
p
~
and
q
~
are the AC active and reactive power. Two lowpass filters are needed to extract
p
~
and
q
~
, [1]. If the system is designed to compensate harmonic and reactive power drawn by the load simultaneously, it has to eliminate the two components of instantaneous reactive power (
q
and
q
~
) as well as the AC component of the instantaneous real power (
p
~
). The
α
and
β
reference currents that are needed to achieve the required compensation are calculated by the following equations:
⎥⎦⎤⎢⎣⎡
+=
⎥⎥⎦⎤⎢⎢⎣⎡
⎥⎥⎦⎤⎢⎢⎣⎡
−
−
qq pii
vvvv
ref ref
~~
1
α β β α
β α
(11) The obtained threephase harmonics currents that the inverter has to inject into the supply are given by (12):
⎥⎥⎦⎤⎢⎢⎣⎡⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡
−=
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡
ref ref refcrefbrefa
iiiii
β α
3123210132
(12) If the system is unbalanced it is necessary to calculate the direct voltage components. This can be achieved by a conventional [11], [12] or a neuronal PLL [6], [9], [10].
4. DIPHASE CURRENTS NEURAL METHOD
Diphase currents neuronal method introduced in [13] is simple and provides more flexibility with a linear approach based on the Adaline Neural Networks and presents a less computations compared to the instantaneous power theory (IPT). This method works in the DQspace and can be easily implemented.
aa
iv
,
caxis aaxis
β
axis
α
axis
bb
iv
,
cc
iv
,
β β
iv
,
α α
iv
,
367
3
4.1. Adaline neural network algorithm
The Adaline neural network [4], [5], [13]is a linear combiner that uses the LMS algorithm for its operation. Fig. 3, shows the structure of Adaline where
x
is an input vector of dimension n. The output of Adaline can be calculated for any input
i
x
as follow:
Figure 3. Basic architecture of Adaline neural network
w xiwi x y
T ni
==
∑
=
0
)()(
(13)
4.2. Learning rules
Widrow proposed the LMS (least mean square) algorithm, which has been extensively applied in adaptive signal processing and adaptive control [3], [4], [9]. The
µ
LMS algorithm is structured as follows: 1: Initialise the weights and the learning rate µ 2: Present new inputs and desired output
d
of the neuron. 4: Calculate the error:
yd
−=
δ
(14) 5: Update the weights, at simpling time
k
according to the equation below:
)()()()1(
k x yd k W k W
k k
−+=+
µ
, (15) Where
d
the desired output, and µ (
10
≺≺
µ
) is the learning rate. The weights of the Adaline are enforced to converge to values which are representative of real harmonic content of power distribution network.
4.3. Diphase harmonics currents identification
The Diphase Current Method works in the DQspace and provides a good dynamic response for the identification online of fluctuating harmonics. If the system is imbalanced we must calculate the direct angle
θ
d
. This can be achieved by a conventional [10], [11] or a neural PLL method [3], [14]. According to the Fourier series, the threephase load currents can be expressed as:
∑
=+−−−−++−−−−=
⎥⎦⎤⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡⎥⎦⎤⎢⎣⎡
N nnt nnt nnt nnit t t i Lci Lbi Lai
232cos()32cos()cos(321cos()321cos()1cos(1
π α ω π α ω α ω π α ω π α ω α ω
(16) This load current can be written in the DQspace with
D
i
and
Q
i
by applying respectively the Clarke transformation and Park transformation. The Clarke transformation is applied to achieve the
αβ
components in the stationary reference frames:
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡
=
⎥⎦⎤⎢⎣⎡
dLcdLbdLat
iiiT ii
32
β α
(17) With :
⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡
−−−=
232302121132
32
t
T
In this approch, the zerosequence components in voltages and currents are neglected. Then, a modified Park transformation is applied to calculate the dq components in the synchronous reference frame from the
αβ
components.
⎥⎦⎤⎢⎣⎡
−=
⎥⎦⎤⎢⎣⎡
β α
ω
iit pii
Q D
)(
(18) With,
⎥⎦⎤⎢⎣⎡
−=−
)cos()sin(
)sin()cos(
)(
t t t t t p
ω ω ω ω ω
(19)
[ ]
[ ]
∑
= −−−−+−=
N n nt nnt nniiQi Di
2))1sin((
))1cos((
23)1sin()1cos(123
α ω α ω α α
(20) These currents can be decomposed into two components: 
The continuous components
⎥⎦⎤⎢⎣⎡
−=
⎥⎥⎦⎤⎢⎢⎣⎡
)sin()cos(23
111
α α
iii
Q D
(21) 
The alternative components
∑
=
⎥⎦⎤⎢⎣⎡
−−−−=
⎥⎥⎦⎤⎢⎢⎣⎡
N n nnnQ D
t nt niii
...13,11,7,5
))1sin((
))1cos((
23~~
α ω α ω
(22) Two Adalines are used to learn the two linear expression shown in equation (20) and to estimate the DC components,
D
i
and
Q
i
, of the instantaneous
DQ
currents. The resulting threephase harmonics currents are given by (23).
QQQ D D D
iiiiii
−=−=
~~
(23) This allows computing the reference currents that will be injected on opposite phase in the power system
0
w
∑
2
x
. . .
y
n
x
1
w
1
x
2
w
n
w
1
368
4
⎥⎥⎦⎤⎢⎢⎣⎡
=
⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡
Q Drefcrefbrefa
iit pT iii
~~)(
32
ω
(24) With space vector notation: )()(
t X W t i
DT D D
=
(25)
)()(
t X W t i
QT QQ
=
(26) And
⎥⎦⎤⎢⎣⎡
=
N N N N
T D
iiiiiW
α α α α α
sin23cos23...sin23.cos23cos23
555511
(27)
[ ]
t N t N t t X
T D
ω ω ω ω
)1sin()1cos()...4sin(.)4cos(1
−−=
(28)
⎥⎦⎤⎢⎣⎡
−=
N N N N
T Q
iiiiiW
α α α α α
sin23cos23....sin23cos23sin23
555511
(29)
[ ]
t N t N t t X
T Q
ω ω ω ω
)1cos()1sin(....)4cos()4sin(1
−−−−=
(30) Currents decomposition and learning are represented in Fig.4.
Figure 4. Diphase method current principle
5. COMPARATIVE RESULTS 5.1. Implementation consideration
In order to compare the
pq
theory method with the diphase currents method mentioned in sections 3 and 4, respectively different implementation aspects have to be considered. Table 2 gives an idea of the capabilities and the complexity associated to each method. It can be seen that the instantaneous power method needs two low pass filters, a PLL to compute the direct voltage component and requires current and voltage
αβ
space transformation. The diphase current method needs two Adalines for harmonics currents extraction and a Park’s current transformation. The objective can be harmonic current compensation, reactive power compensation and power factor correction.
5.2. Simulation results
Computer simulations with Matlab /Simulink are carried out to validate the performance of the new approach under industrial operating conditionusing the system parameters given in table 1. The system is supplied from a balanced threephase voltage sources feeding a threephase diode bridge rectifier with inductive load. The parallel APF has the structure of a three phase PWM power converter connected to the line by an inductance. The DC link storage component is a capacitor.The DC voltage controller is a proportionalintegral (PI) which receives as input the reference
*
dc
V
and the measured dc voltage
dc
V
, and outputs the reference active filter current.
Table.1. System parameter Utility source Voltage (line toneutral) 230V
rms
Frequency 50Hz Source resistance 0.25m
Ω
Source inductance 19.4µH Nonlinear load Load inductance 3mH Load resistance 6.7
Ω
Active Power filter APF inductance 3mH APF capacitance 400
μ
F Control bloc: Carrier signal magnitude and 10, 10KHz frequency
The reference current identified by the neuronal method called the diphase current as shown in the Fig.7 is similar to the current identified by the conventional
pq
theory method based on the instantaneous powers. The time response of reference current for IPT (20 ms) is greater than for neural method (10 ms) Fig.7. The harmonics currents considered on the inputs of the two Adalines for Diphase Current Method are the 5
th
, 7
th
, 11
th
, 13
th
, 17
th
and 19
th
. The THDI is reduced from 25.73% (Fig.5) to 1.53% (Fig.8.b) for instantaneous power identification and to 1.48% (Fig.9.b) for diphase currents method based on neural approach. Before compensation the phaseshift angle between the fundamental current and the voltage is (Fig.5.a). After compensation this angle is compensated. The resulting power factor is therefore close to unit (Fig. 10).
Q
i
~
D
i
~
α
i
~
est Qi
−

∑
∑
D
i
Q
i
1
w
))1sin((
t N
ω
−
))1cos((
t N
ω
−
)4cos(
kT
ω
)4sin(
kT
ω
e e
est Di
−
β
i
refc
i
refa
i
refb
i
)4cos(
kT
ω
Lc
i
)(
d p
θ
−
La
i
Lb
i
α
i
32
T
+
)(
d p
θ
32
t
T
D
i
Q
i
Q
i
β
i
~
3
w
1
−
n
w
n
w
1
)4sin(
kT
ω
1
))1cos((
t N
ω
−
))1sin((
t N
ω
−
. . . . . . . .
2
w
3
w
1
−
n
w
1
w
n
w
+ +    + 
369
5At time t=0.06s, the nonlinear current is modified to pass from 80A to 150A Fig.5.The neural method is efficient and fast for identifying online fluctuating harmonics than the IPT method under load fluctuation for learning rate (µ=0.01), Fig. 7. Fig.6 For 0.01 <µ<0.03, the proposed neural approach instantaneously follows the load variation, Fig.6. Then the learning rate must be tested for obtain the convergence of this technique. The Adaline neural method can estimate online the harmonic terms individually, and realize a selective compensation.
Table.2. COMPARATIVE METHODS IdentificationMethods Direct components required Time response Referential required Harmonics compensation Reactive power compensation Valid for tri /single phase system Harmonic extraction method PQ theory
d v
20ms
αβ
q p
~,~
q
Threephase Two LPF Diphase currents _ 10ms (µ=0.01) 20ms (µ=0.0005)
dq
Q D
ii
~,~
Q
i
Threephase Two Adalines
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.120015010050050100150200time (s)
L o a d c u r r e n t ( A )
0.020.0250.030.0350.040.0450.050.05510050050100Time (s)FFT window: 2 of 5 cycles of selected signal0510152005101520Harmonic orderFundamental (50Hz) = 86.85 , THD= 25.73%
M a g ( % o f F u n d a m e n t a l )
Figure 5. Load current (a) and its spectrum (b)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.180604020020406080t(s)
i r e f a ( A )
µ=0.03µ=0.02µ=0.001µ=0.01µ=0.0005
Figure 6.Harmonic components of load current estimated online by the Neuronal method with several rate learning. Figure 7.Harmonic components of load current estimated online by the Neuronal method (µ=0.01) and with IPT method.
0.030.0350.040.04510050050100Time (s)FFT window: 1 of 5 cycles of selected signal0510152000.10.20.30.40.50.60.7Harmonic orderFundamental (50Hz) = 89.46 , THD= 1.48%
M a g
Figure 8. Source current wave form (a) and its harmonic spectrum (b) with diphase current identification
0.040.0450.050.05510050050100Time (s)FFT window: 1 of 5 cycles of selected signal0510152000.10.20.30.40.50.60.7Harmonic orderFundamental (50Hz) = 89.52 , THD= 1.53%
M a g
Figure 9. Source current wave form (a) and its harmonic spectrum (b) with instantaneous powers identification
aab
b
a b
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110080604020020406080100Time sirefa(Neural methodIPT method
370