Neural Network based p-q-r Theory for Harmonic Reduction and Neutral Current Mitigation

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 8, No. 2, April 2018, pp. 825~836
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i2.pp825-836  825
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Neural Network based p-q-r Theory for Harmonic Reduction
and Neutral Current Mitigation
S. Malathi, J. Jayachandran
Departement of Electrical and Electronics Engineering, SASTRA University, India
Article Info ABSTRACT
Article history:
Received May 28, 2017
Revised Nov 3, 2017
Accepted Nov 10, 2017
The power quality compensator chosen in this paper is a DSTATCOM which
integrates a three phase four leg Voltage Source Converter (VSC) with a DC
capacitor. The major role of the DSTATCOM is to mitigate the components
of harmonic/reactive current present in the line current thereby shapes the
grid current to be sinusoidal and improves the power factor nearly unity
under varying conditions. In addition DSATATCOM mitigates neutral
current (Isn) and balances the load currents under unbalanced conditions in
three phase four wire (3P4W) distribution system. The control strategy
proposed for the DSTATCOM is a Neural Network (NN) based p-q-r theory
with two Artificial Neural Network (ANN) controllers for a 3P4W
distribution system. The reference signal for 3P3W Shunt Active Power
Filter (SAPF) is calculated by implementing an ANN controller. The
alleviation of Isn under unbalanced condition is achieved by another ANN
controller which produces reference signal for the 1Φ APF. The performance
of the proposed DSTATCOM is analysed for various conditions through
simulations in MATLAB SIMULINK and the simulation results justify the
effectiveness of the propounded NN based control algorithm for
DSTATCOM.
Keyword:
DSTATCOM
Neural network
Neutral current mitigation
Total harmonic distortion
Unbalanced and/or distorted
source
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
S. Malathi,
Departement of Electrical and Electronics Engineering,
SASTRA University,
Thirumalaisamudram, Thanjavur, Tamil Nadu 613401, India.
Email: jj_chandru@eee.sastra.edu
1. INTRODUCTION
In earlier days, equipment were robust and insensitive to minor variations in supply voltage. The
loads on the earlier electric distribution networks were of non-polluting nature. A major concern in such
electric power systems was reactive power support. The development of modern power electronic switching
devices has completely changed the load characteristics [1], [2]. Switched Mode Power Supplies (SMPS), arc
welding machines, DC and AC drives, Uninterrupted Power Supplies (UPS) etc., are some out of the vast
applications of power electronic devices. The operation of these equipment/loads introduces harmonics and
contaminate the modern distribution system. These equipment are often insensitive to voltage disturbances;
however, they draw currents which are highly distorted in nature. Studies show that such equipment produce
distortion in supply voltages [3], [4]. The harmonics and unbalanced currents result in distorted and
unbalanced voltages. The pollution on the distribution network is increasing to such an extent that the utility
providers can no longer support them. Therefore, the utility imposed strict standards on the industrial and
domestic consumers to restrict the harmonic currents that a load may inject into the network. To comply with
power quality standards, customers have to introduce mitigation techniques to reduce the extent of pollution
caused by their loads and avoid heavy penalties imposed by the utility. There is a necessity to install
mitigating equipment that help both the utility and the customer. In such environments, the objective is to
protect sensitive equipment from voltage disturbances and at the same time reduce the distortion injected into

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 8, No. 2, April 2018 : 825 – 836
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the network. Quality of electrical power can be improved using the following two methodologies. a) Load
conditioning and b) Installation of power line conditioners. The former counteracts voltage and current
disturbances and the latter limits the circulation of harmonic currents in power distribution system. They are
usually custom designed for a particular application [5], [6].
In industries, residential and commercial buildings, the electric power delivered to 1P/3P loads is
mainly by 3P4W distribution system. Even well balanced 1P non-linear loads on a 3P4W system can produce
considerable Isn. Non-linear loads draw non-sinusoidal phase currents. The phasor sum of balanced non-
sinusoidal 3Φ currents can produce current in the neutral conductor [7]. The problem due to high neutral
current are: a) Wiring failure b) Common mode noise c) Flat-topping of voltage waveform and
d) Overloading of distribution feeders and transformers. Surplus neutral currents can be eliminated by
incorporating neutral current compensation techniques. The use of 3P4W APF is one of the active solutions
which is recommended for the mitigation of neutral current [8], [9].
In this paper, the role of power quality compensator is accomplished through a NN based p-q-r
control strategy for 3P4W DSTATCOM. The topology of a DSTATCOM constitutes four leg VSC and a DC
capacitor. A separate NN controller is implemented for the fourth leg of VSC to mitigate the neutral current.
The main functions of the proposed control strategy are a) To maintain unity power factor and draw
sinusoidal current from the source side under any load and source conditions b) To compensate reactive
power c) To reduce the % Total Harmonic Distortion (THD) of source current (Is) and iv) To alleviate neutral
current under varying conditions.
2. PROPOSED NN BASED CONTROL ALGORITHM FOR SAPF
The Figure 1 represents the schematic diagram of 3P4W DSTATCOM. The NN based p-q-r theory
satisfies power conservation theory in the calculation of instantaneous power and the three power
components can be controlled independently [10]. The proposed NN based p-q-r theory proves to be superior
to all other control strategies for 3P4W system both in definition and compensation aspects. The proposed
control strategy employs NN blocks which adjust the control variables to satisfy the requirement with
advantages of high accuracy and faster response. The control technique implemented has two major functions
accomplished by two ANN controllers. (a) ANN controller NN1 is employed for estimating the reference
current. It extracts the load real power ( p ) and thereby enforces the utility to deliver the real part of the
fundamental current. (b) Another ANN controller NN2 is employed for the alleviation of Isn under
unbalanced loads.
Figure 1. Schematic representation of SAPF
The block diagram of the proposed system is depicted in Figure 2. The p-q-r theory can have smooth
control over the supply currents even when the supply voltages are unbalanced and/or distorted and under
unbalanced load conditions. The source voltages are sensed and transformed into α-β-0 coordinates using
Equation (1).

Int J Elec & Comp Eng ISSN: 2088-8708 
Neural Network based p-q-r Theory for Harmonic Reduction and Neutral Current Mitigation (S. Malathi)
827
[ ] √ ⁄
[
√ √ √
√ √
]
[ ] (1)
The α-β-0 coordinates of load currents are calculated from Equation (2).
Figure 2. Block diagram of the proposed system
[ ] √ ⁄
[
√ √ √
√ √
]
[ ] (2)
The α-β-0 coordinates of load currents are converted to p-q-r coordinates as given in Equation (3).
[ ]
[ ]
[ ] (3)
Where
√ (4)
√ . (5)
To achieve sinusoidal source currents and balanced condition even under non-linear loads, the compensation
reference currents are calculated using Equation (6), Equation (7) and Equation (8).
̃ (6)
̃ (7)
(8)

 ISSN: 2088-8708
828
Current ̃ has both DC and AC components. The DC component of current is
extracted using an ANN filter unlike the low pass filter in conventional technique. The terms ̃ & ̃
contribute for the harmonic power and the term contribute for the reactive power demanded by the loads.
The reference zero sequence current contributes to zero-sequence power [11]. The SAPF supplies the
compensation reference currents to shape Is. The reference compensation currents in p-q-r coordinates are
transformed into α-β-0 coordinates using Equation (9).
[ ]
[ ]
[ ] (9)
The reference compensation currents in a-b-c coordinates are determined from Equation (10).
[ ] √ ⁄
[
√
√
√
√
√
]
[ ] (10)
Hysteresis current controller (HCC) produces the switching signals for the SAPF by comparing i *Ca, i *Cb,
i *Cc and ishabc.
3. PROPOSED NN BASED ALLEVIATION OF Isn
The schematic of NN based Isn alleviation is depicted in Figure 3. The vector sum of the unbalanced
load currents gives the neutral current. Thus the load currents of all the phases are measured and added
incorporating a summer. The isn value is compared with the reference value i*Sn which is considered as zero.
The output from the summer is applied to the ANN controller and thus the controller calculates the neutral
current (i*Cn). The HCC produces gate pulses for 1- φ APF using i*Cn. Thus the proposed control strategy
mitigates neutral current for an unbalanced load condition.
Figure 3. Schematic of NN based Isn alleviation
4. ANN ARCHITECTURE
Back Propagation architecture is proposed in this paper for the NN controllers. The architecture
constitutes input, hidden and output layers [12], [13]. The input and output layers are decided based on the
problem formulation and it is 1 for both input and output layers of NN controllers. The optimum hidden layer
neurons are chosen by analyzing the performance error and training period for each value. The optimum
number of neurons in the hidden layer are 12 & 10 for the NN controllers. „Purelin‟ a linear activation
function is adopted in the neurons of the output layer and to manage the non-linearity tangsigmoid activation
function „tansig‟ is adopted in neurons of hidden layer and output layer. The biases and weigths of the
network function are varied by implementing „Dotprod‟ function. The weights and biases are further fine-
tuned by adopting „Adaptwb‟ function. Levenberg-Marquardt (LM) back propagation training algorithm
“trainlm” is identified to be more suitable for the stated problem. The number of training data considered are
500 and 200 for NN1 and NN2 and the number of testing data are 100 and 40 respectively. The performance
goal is chosen as 1e-3
. The leaning rate and testing accuracy are 0.05, 98.9% for NN1 and 0.04, 99.2% for

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NN2. Figure 4 depicts the performance curve of NN controllers and it is clear from the performance curve
that error reaches to 0.00109 and 0.00118 after 210 and 225 epochs to attain the goal.
Figure 4. Performance curve of NN based p-q-r control strategy, (a) NN1, (b) NN2
5. DISCUSSION ON SIMULATION RESULTS
To model the SAPF, computer aided simulation is performed using MATLAB/SIMULINK. The
performance of proposed NN based control algorithm in terms of THD reduction, reactive power
compensation, and alleviation of neutral current is validated for varying conditions. The APF performance is
also analysed for conventional controller. The performance of the APF with proposed and conventional
controllers are compared. The simulation of the APF with proposed control algorithm is performed for four
different source conditions as shown in Table 1. To adhere with the limitations in the number of pages
simulation results are presented only for source cases II, III and IV and with one load condition. The load
condition considered includes 3-ϕ converter ( RL load) + three 1-ϕ converters (RL load) + linear
unbalanced load + three 1-ϕ converters (RC load). To highlight the dynamic performance of the APF, the
loads are changed in a sequential manner 3φ -2φ -1φ -2φ, 3φ. System parameter values are given in
Appendix-A. The performance of SAPF with proposed control algorithm is analysed for the above mentioned
supply voltage conditions with the specified load condition and the traces of (a) supply voltage (Vsabc)
(b) supply currents (Isabc) (c) load currents (ILabc) (d) compensator current of 3P3W APF (Ishabc) and
(e) DC bus voltage of APF (Vdc) are depicted to demonstrate its superior performance when compared to
conventional controller in percentage THD reduction.
Table 1. Details of various source voltage conditions
Case Source voltage condition Description
I Ideal 415V, 50 Hz & (0°,-120°, +120°)
II Unbalanced a)415V, 50 Hz & phase unbalance (20°,-120°, +120°)
b) 20% sag for the duration ( t = 0.2 s - 0.3 s)
III Balanced & Distorted a)415V, 50 Hz & (0°,-120°, +120°)
b) 20% of 3rd
& 5th
order harmonics (t = 0.25 s - 0.4 s)
IV Unbalanced & Distorted a)415V, 50 Hz & phase unbalance (20°,-120°, +120°)
b) 20% sag for the duration (t = 0.2 s - 0.3 s)
c) 20% of 3rd
& 5th
order harmonics (t = 0.25 s - 0.4 s)
5.1. Mitigation of harmonic currents
5.1.1. Performance of SAPF under Case: II
Dynamic performance of the NN p-q-r control strategy based shunt APF under case: II is depicted in
Figure 5. The proposed NN control strategy alleviates the % THD of the Is in phases a, b, c to 1.22%, 1.55%
and 1.73%. The THD of the Is comply with IEEE-519 standard. The measured values of % THD of source
currents without APF are 22.87%, 24.21%, and 25.97% for phases a, b, c which do not satisfy IEEE-519
recommendation. The performance of the APF is also analysed with conventional control strategy which
reduces the % THD of the source currents to 7.35%, 6.52% and 5.90% for phases a, b, c.

 ISSN: 2088-8708
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Figure 5. Performance of NN based p-q-r control theory under case: II
5.1.2. Performance of SAPF under Case: III
Dynamic performance of the NN p-q-r control strategy based shunt APF under case: III is depicted
in Figure 6. The proposed NN control strategy alleviates the % THD of the Is in phases a, b, c to 2.37%,
1.77% and 1.48%. The THD of the Is comply with IEEE-519 standard. The measured values of % THD of
source currents without APF are 23.61%, 25.01%, and 26.14% for phases a, b, c which do not satisfy IEEE-
519 recommendation. The performance of the APF is also analysed with conventional control strategy which
alleviates the % THD of the Is in phases a, b, c to 6.27%, 7.35% and 8.23%.

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Figure 6. Performance of NN based p-q-r control theory under case: III
5.1.3. Performance of SAPF under Case: IV
Dynamic performance of the NN p-q-r control strategy based shunt APF under case: IV is depicted
in Figure 7. The proposed NN control strategy alleviates the % THD of the Is in phases a, b, c to 2.23%,
1.62% and 2.03%. The THD of the Is comply with IEEE-519 standard. The measured values of % THD of
source currents without APF are 22.37%, 24.91%, and 27.32% for phases a, b, c which do not satisfy IEEE-
519 recommendation. The performance of the APF is also analysed with conventional control strategy which
alleviates the % THD of the Is in phases a, b, c to 7.28%, 8.41% and 7.73%.

 ISSN: 2088-8708
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Figure 7. Performance of NN based p-q-r control theory under case: IV
Table 2. Performance comparison of SAPF
Source
Conditions
% THD Proposed Controller Conventional Controller
ILa ILb ILc % THD Vdc
(V)
% THD Vdc
(V)ISa ISb ISc ISa ISb ISc
Case I 20.63 23.53 24.97 0.95 0.85 1.33 680 5.8 6.1 5.7 679
Case II 22.87 24.21 25.97 1.22 1.55 1.73 680 7.35 6.52 5.90 679
Case III 23.61 25.01 26.14 2.37 1.77 1.48 680 6.27 7.35 8.23 679
Case IV 22.37 24.91 27.32 2.23 1.62 2.03 680 7.28 8.41 7.73 679

833
Figure 8. Comparison of %THD of supply current under various voltage source conditions
The efficacy of the NN based proposed control algorithm for SAPF, is jusitfied from the following
observations made through the simulation results. (a) The source currents are balanced, sinusoidal and the
power factor is maintained close to unity even for varying conditions. (b) After the compensation of
harmonic currents the THD of source currents are less than 5% satisfying the limits suggested by power
quality standards. (c) The Vdc is regulated tightly at 680V. d) The performance of the NN controller is
superior to that of conventional controller in improving the power quality of the utility. Figure 8 and Table 2
highlight the performance of the NN based proposed control strategy for various cases of voltage source. To
prove the enhanced performance of proposed system, its simulation results are compared with those of the
conventional controller.
5.2. Alleviation of neutral current
The traces of (a) Source neutral current (Isn) (b) Load neutral current (ILn) and (c) Compensation
neutral current (Icn) are depicted for supply voltage cases II, III and IV to demonstrate the performance of
proposed control strategy in alleviating the neutral current.
5.2.1. Performance of SAPF under Case: II
Figure 9. Performance of NN based 3P4W four leg topology under case: II

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5.2.2. Performance of SAPF under Case: III
Figure 10. Performance of NN based 3P4W four leg topology under case: III
5.2.3. Performance of SAPF under Case: IV
It is evident from Figure 9 to Figure 11, that the NN based 3P4W APF alleviates the Isn to nearly
zero. The compensation neutral current Icn is in phase opposition with the load neutral current ILn, which
verifies proper neutral current compensation.
Figure 11. Performance of NN based 3P4W four leg topology under case: IV

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6. CONCLUSION
A NN based p-q-r control theory has been proposed for the SAPF in 3P4W distribution system. The
proposed system has good compensating characteristics which includes the advantages of both cross vector
and conventional p-q theory. In addition the control strategy satisfies power conservation theory and also the
mathematical expression is simple and systematic. The performance of shunt APF with proposed control
algorithm is evaluated under varying conditions using MATLAB/Simulink. The simulation results of SAPF
with proposed and conventional controllers are compared. The traces obtained from the simulation results
and tabulation prove that the proposed system is better than conventional system. The efficacy of the NN
based proposed control algorithm for SAPF, is validated from the following observations made through the
simulation results. a) The source currents are balanced, sinusoidal and the power factor is maintained close to
unity even under varying source conditions. b) After the compensation of harmonic currents the THD of
source currents are less than 5% satisfying the limits suggested by power quality standards. c) The Vdc is
regulated tightly at 680V. d) The performance of the NN controller is superior to that of conventional
controller in improving the power quality of the utility.
REFERENCES
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[3] Stuti Shukla, et al., “Implementation of Empirical Mode Decomposition Based Algorithm for Shunt Active Filter,”
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APPENDIX A
Vs = 415 V, 50Hz, Rs = 0.02 Ω, Ls=1.6 mH, C = 3000 µF, Linear load = 30.5 kVA, 25.2 kVA,
34.7 kVA, Non-linear load R = 2 Ω, L = 5 mH, C = 9µF, interfacing inductor = 2.5mH/phase.

 ISSN: 2088-8708
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BIOGRAPHIES OF AUTHORS
S. Malathi was born in India. She received the B.E. degree in Electrical and Electronics
Engineering from Bharathidasan University, Tamilnadu in 2000 and M.Tech. degree in Power
Electronics and Drives from SASTRA University, Thanjavur Tamilnadu in 2004. Presently
Pursuing Ph.D. in the area of Power Electronics at SASTRA University, Thanjavur, India. Her
area of interest are Power Converters and power quality.
J. Jayachandran was born in India. He received the B.E. degree in Electrrical and Electronics
Engineering from Kongu Engineering college, Tamilnadu in 1999 and M.E. degree in Power
Electronics and drives from Bharathidasan University, Thanjavur Tamilnadu in 2000. Presently
Pursuing Ph.D. in the area of Power Electronics at SASTRA University, Thanjavur, India. His
area of interest are Power Quality, Power Converters and Renewable Energy Sources.

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