978-1-5090-0128-6/16/$31.00 ©2016 IEEE

ADALINE Based LMS Algorithm in a Three Phase

Four Wire Distribution System for Power Quality

Enhancement

Trilochan Penthia Anup Kumar Panda,

Senior Member, IEEE Sunil Kumar Sarangi Mrutyunjaya Mangaraj

Department of Electrical Engineering, National Institute of Technology, Rourkela-769008, India

Abstarct—This paper describes a new control approach called

Adaptive linear neuron (ADALINE) based Least mean square

(LMS) algorithm used in a three phase four wire (3P4W)

distribution system under single phase fault condition. Three

phase reference supply currents are generated by using the

proposed control technique thereafter they compared with the

corresponding sensed supply currents to produce switching

pulses for the IGBTs of a four leg voltage source converter (4-

leg VSC) based distribution static compensator (DSTATCOM).

In this paper, the DSTATCOM is used for voltage regulation,

power factor correction and elimination of

distorted/unbalanced source current & excessive neutral

current in the system. MATLAB/SimPowerSystem environment

is used to simulate the distribution system under both fault and

without fault conditions.

Keywords— ADALINE; Power Quality Improvement; Custom

power device; THD; LMS algorithm; 3P4W distribution system

1. INTRODUCTION

Various types of outages and service interruptions in a

distribution system can cause serious damages in sensitive

industrial as well as domestic loads and computer based

controllers etc.. Generally, those outages and interruptions in

a three phase distribution system are caused due to faults,

device failure or unbalanced loading and they are termed as

power quality (PQ) problems [1-2]. PQ problems in a system

can be related to the supply current or voltage. Different

topologies and controllers are choosen as per the quality

problems related to either current or voltage in a power

system. Presence of harmonics in a power system can cause

serious problems like produce unwanted disturbances,

increasing losses in rotating machines and inaccurate

operation of control systems, protective devices, measuring

& communication equipment etc. [2-4].

To handle such type of PQ problems, many custom power

devices with different control techniques have been

introduced to improve the PQ in a distribution systems.

Custom power devices such as active power filters (APFs),

distribution static compensator (DSTATCOM), dynamic

voltage restorer etc. and control algorithms such as artificial

neural network (ANN), synchronous reference frame (SRF)

theory, power balanced theory (PBT) etc. [1-10].

Alleviation of harmonics, excessive neutral current due to

unbalanced load and reactive power in a distribution system

has been a great challenge for power engineers. These

problems create low power factor, system instability,

overheating and increase losses in the system.

This paper describes advantages of ADALINE based

LMS algorithm for control of DSTATCOM device.

DSTATCOM is a FACTS device used in a distribution

system for mitigation of power quality issues. Mainly,

DSTATCOM is a shunt type compensator, thereby it is used

for compensation of current quality related problems. The

ADALINE is a simple structured and high speed of data

processing type adaptive controller that offers excellent

performance in estimation of the variations in amplitude and

phase angle of the harmonic components. It has highly

convergence speed in tracking the harmonic components in

the system. Furthermore, this technique can also be

utilized in several disciplines of electrical engineering

including recognition of transient and steady-state

disturbances in high voltage transmission lines, frequency

tracking, detection & determination of current and voltage

signals in a three-phase unbalanced system [5-7]. The

proposed algorithm is used to extract the refernce source

current to generate switching signals for VSC of the

DSTATCOM by receiving different signals from several

parts of the system [8-10].

2. SYSTEM TOPOLOGY

A distribution system consist of a four wire nonlinear load

supplied by a three phase four wire ac supply. A VSC based

DSTATCOM is connected at the point of common coupling

(PCC) through an interfacing impedance (𝑍𝑐), as shown in

Fig.1. Generally, series connected impedance (𝑍𝑐) is

inductive in nature with an optimum resistance to eliminate

ripple in the supply current. The four-leg VSC of the

DSTATCOM consists of eight IGBTs and a DC-link

capacitor (𝐶𝑑𝑐). As IGBT is an ideal choice for a small to

medium rating electrical networks. Switching pulses for the

IGBTs of VSC are generated by using ADALINE based

LMS control algorithm and the control algorithm is

explained in next section below.

a- ph

b-ph

c-ph

3-ph, 4-wire(3P4W)

Uncontrolled

Bridge rectifier

(Non-linear load)

ila

ilb

ilcisc

isb

isa

ica iccicb

Zs

Zc

Source

C

Vdc

i*

sci*sbi

*sa

vdc(ref)

vdc

Hysteresis current

controller

Eight Switching signals

isa

isb

isc

ila ilb ilc

N

VSC

S1S7 S5 S3

S8 S6 S4 S2

i*

n

in

iln

vs

Load

Compensator

va

vb

vc

PCC

in

Fault

Reference currents generation

by using Adaline based LMS

algorithm

Fig.1: Schematic diagram of the proposed system

3. CONTROL ALGORITHM

In this section, the proposed ADALINE based control

strategy for the DSTATCOM is discussed. ADALINE is a

version of ANN technique and it functions as an efficient

controller in the whole compensation process. ADALINE

based LMS algorithm needs sensed supply voltage, DC-link

voltage and load currents as input parameters for its

calculation, as shown in Fig.2. The control approach involves

two steps to produce switching pulses required for the IGBTs

of the VSC-DSTATCOM as follows [4-5]:

A. Estimation of weighting value using ADALINE

based LMS algorithm

Let us consider the supply voltage of the three phase

system is purely sinusoidal and it can be given as:

𝑣𝑠 = 𝑉𝑚𝑠𝑖𝑛𝑤𝑡 (1)

The non-linear load current is given as:

𝑖𝑙 = 𝐼1 sin(𝑤𝑡 + ∅1) + ∑ 𝐼𝑛sin (𝑛𝑤𝑡 + ∅𝑛)

∞

𝑛=2

(2)

It can also be represented as,

𝑖𝑙 = 𝑖𝑙𝑝+ + 𝑖𝑙𝑞

+ + 𝑖𝑙ℎ− (3)

Where, 𝑖𝑙𝑝+ , 𝑖𝑙𝑞

+ , and 𝑖𝑙ℎ− are positive sequence active load

current, positive sequence reactive load current and negative

sequence load current (harmonic components) respectively.

The active component of current for a single phase is

obtained as,

𝑖𝑝 = 𝑊𝑚𝑢𝑠 (4)

Where, 𝑢𝑠 is the unit current template, calculated by

phase lock loop (PLL) concept and 𝑊𝑚 is the calculated

weight from ADALINE based LMS control algorithm.

Normally, this iterated weight depends on the magnitude of

the phase voltage and the load current.

𝑊𝑚(𝑘+1) = 𝑊𝑚(𝑘) + 𝜇[𝑖𝑙𝑘 − 𝑊𝑚(𝑘)𝑢𝑠(𝑘)]𝑢𝑠(𝑘) (5)

𝜇, is the step size of the convergence or also called as

convergence coefficient (varies from 0.1 to 1.0).

The unbalanced current in the system can be removed by

averaging the weights as follows:

𝑊𝑚+ =

(𝑊𝑚𝑎+ + 𝑊𝑚𝑏

+ + 𝑊𝑚𝑐+ )

3 (6)

B. Generation of reference source currents

DC-link voltage error for nth sampling instant is given by,

𝑣𝑑𝑐(𝑛)∗ − 𝑣𝑑𝑐(𝑛) = ∆𝑣𝑑𝑐(𝑛) (7)

Then the voltage error is fed to a PI controller and output of

the PI controller at the nth sampling instant is given as:

𝐼𝑠𝑚(𝑛) = 𝐼𝑠𝑚(𝑛−1) + 𝐼𝑃𝐼 (8)

Where, 𝐼𝑃𝐼 = 𝑘𝑝𝑑𝑐[∆𝑣𝑑𝑐(𝑛) − ∆𝑣𝑑𝑐(𝑛−1)] + 𝑘𝑖𝑑𝑐∆𝑣𝑑𝑐(𝑛)

and 𝑘𝑝𝑑𝑐 & 𝑘𝑖𝑑𝑐 are the proportional gain & the integral

gain of the PI controller respectively.

Now, the three phase reference source currents can be

calculated as:

𝑖𝑠𝑎∗ = (𝑊𝑚

+ + 𝐼𝑠𝑚)𝑢𝑠𝑎 (9)

𝑖𝑠𝑏∗ = (𝑊𝑚

+ + 𝐼𝑠𝑚)𝑢𝑠𝑏 (10)

𝑖𝑠𝑐∗ = (𝑊𝑚

+ + 𝐼𝑠𝑚)𝑢𝑠𝑐 (11)

Where, (𝑊𝑚+ + 𝐼𝑠𝑚) is considered as the magnitude of the

reference source current and 𝑢𝑠𝑎, 𝑢𝑠𝑏 and 𝑢𝑠𝑐 are the three

phase unit current templates.

Similarly, reference neutral current can be calculated as

follows:

𝑖𝑛∗ = 𝑖𝑠𝑎

∗ + 𝑖𝑠𝑏∗ + 𝑖𝑠𝑐

∗ (12)

Finally, the sensed source currents (𝑖𝑠𝑎 , 𝑖𝑠𝑏 & 𝑖𝑠𝑐) are

subtracted from the reference source currents (𝑖𝑠𝑎∗ , 𝑖𝑠𝑎

∗ , & 𝑖𝑠𝑎∗ )

and then the individual source currents error (including

neutral current error) are fed to a hysteresis current controller

(HCC) each separately to generate the switching pulses

(𝑆1, 𝑆2, 𝑆3, 𝑆4, 𝑆5, 𝑆6, 𝑆7 & 𝑆8) for 4-leg VSC of the

compensator, as shown in Fig.2.

+ -i

*n= (i

*sa+ i

*sb+ i

*sc)

in

ADALINE

ila

usa

Wma+

PI Controller

vdc

vdc(ref)+

-

i*

sa+

-

+ -

+ -

i*

sb

i*

sc

isa

isb

isc

ila

usa

ila

usa

ADALINE

ADALINE

+ + +

Wmb+

Wmc+

1/3

+ + Wm

+

Ism

(Wm++ Ism)

S5

S6

S3

S4

HCC2

HCC3

S7

S8HCC4

S1

S2HCC1

Fig.2: ADALINE based LMS control technique

4. SIMULATION RESULTS AND DISCUSSION

Simulations of the distribution system are carried out

under both fault condition and without fault condition in

MATLAB/SimPowerSystem environment. A comparative

simulation results of different performance parameters of the

system under aforementioned conditions are shown in table-

I. The system parameters taken in the simulation are listed in

table-II (in appendix section) . A single phase type fault

condition is considered (occurred between 0.6 sec to 0.7 sec)

in the ditribution system to check the effectiveness of the

DSTATCOM. The details of the compensation process are

described as follows:

(i) Without fault condition

The simulation of the proposed distribution system has been

performed successfully without considering any fault

conditions. Waveform of the sensed source voltage (𝑣𝑠),

neutral current & source current (𝑖𝑠), load voltage (𝑣𝑙), load

current (𝑖𝑙), compensating voltage (𝑣𝑐), compensating current

(𝑖𝑐) and DC-link voltage (𝑣𝑑𝑐) during simulation are depicted

in Fig.3. A comparative waveform of a-phase source current,

load current and compensating current, from top to bottom,

are given in Fig.4. Total harmonic distortion (THD) of the

source current and load current are obtained 3.51% and

21.30% respectively, shown in Fig.5 and Fig.6.

Fig.3: Source voltage, source current, load voltage, load current,

compensating voltage, compemsating current and dc link voltage.

Fig.4: Source current, load current and compesating current

-5000

500

vs (

V)

-1000

100

i s (

A)

-5000

500

vl (V

)

-100

0

100

i l (A

)

-5000

500

vc (

V)

0.5 0.55 0.6 0.65 0.7 0.75 0.80

500

Time (Sec)

vdc (

V)

-50

0

50

i c (

A)

-50

0

50

i sa (

A)

-50

0

50

i la (

A)

0.5 0.55 0.6 0.65 0.7 0.75 0.8-20

0

20

Time (Sec)

i ca (

A)

Fig.5: Percentage of source current THD

Fig.6: Percentage of load current THD

(ii) Under single phase fault (a-phase fault) condition

After 0.6 seconds of the simulation, a single phase (1-L) fault

is introduced at a-phase of the distribution system. Duration

of the fault is 0.1 second i.e. fault occurred at 0.6 second of

the simulation and lasted upto 0.7 second. The simulation has

been performed successfully under a-phase fault condition.

Fig.7: Source voltage, source current, load voltage, load current,

compensating voltage, compemsating current and dc link voltage.

Fig.8: Shows a-phase Source current, load current and compesating current

Fig.9: Percentage of Source current THD

Fig.10: Percentage of Load current THD.

Waveform of the sensed source voltage (𝑣𝑠), neutral current

& source current (𝑖𝑠), load voltage (𝑣𝑙), load current (𝑖𝑙),

compensating voltage (𝑣𝑐), compensating current (𝑖𝑐) and

DC-link voltage (𝑣𝑑𝑐), from top to bottom, during simulation

are depicted in Fig.7. A comparative waveform of a-phase

source current, load current and compensating current are

given in Fig.8. THD of the source current and load current

are obtained 3.75% and 21.17% respectively, shown in Fig.9

and Fig.10.

From the above simulation studies, it has been seen that

the ADALINE based LMS algorithm is implemented

effectively for power quality enhancement in the proposed

system. Excessive neutral current and distorted & unbalance

source currents in the system are compensated effectively as

shown in the 2nd wave form, in Fig.7 (from top to bottom). In

spite of that, voltage regulation, system stabilization and

power factor improvement are achieved by applying the

control technique in the system.

0 200 400 600 800 10000

5

10

Frequency (Hz)

Fundamental (50Hz) = 53.89 , THD= 3.51%

Mag (

% o

f F

undam

enta

l)

0 200 400 600 800 10000

5

10

15

Frequency (Hz)

Fundamental (50Hz) = 52.54 , THD= 21.30%

Mag (

% o

f F

undam

enta

l)

-5000

500

vs (

V)

-100

0

100

i s (

A)

-100

0

100

i l (A

)

-5000

500

vc (

V)

-50

0

50

i c (

A)

0.5 0.55 0.6 0.65 0.7 0.75 0.80

500

Time (Sec)

vdc (

V)

-5000

500

vl (V

)

-50

0

50

i sa (

A)

-50

0

50

i la (

A)

0.5 0.55 0.6 0.65 0.7 0.75 0.8-50

0

50

Time (Sec)

i ca (

A)

0 200 400 600 800 10000

5

10

Frequency (Hz)

Fundamental (50Hz) = 54.63 , THD= 3.75%

Mag (

% o

f F

undam

enta

l)

0 200 400 600 800 10000

10

20

30

40

Frequency (Hz)

Fundamental (50Hz) = 52.01 , THD= 21.17%

Mag (

% o

f F

undam

enta

l)

Table-I: Comparison of different performance parameters

Performance parameter Without fault

condition Under single phase

(a-ph) fault condition

Source current (A) 53.89 54.63

THD of source current 3.51 % 3.75 %

Load current (A) 52.54 52.01

THD of load current 21.30 % 21.17 %

5. CONCLUSION

In this paper, the distorted supply current, excessive neutral

current and low input power factor due to presence of single

phase fault and nonlinear load in the system are compensated

successfully by using the DSTATCOM with a novel control

approach called ADALINE based LMS algorithm. The three

phase source current found from the simulation results are

balanced and its THD is below 5%, thereby satisfying the

IEEE-519 standard on harmonic limits. Also, voltage

regulation and reactive power compensation are achieved by

using the proposed control technique effectively.

Appendix

Table-II: System parameters for simulation studies

Source side

Source voltage, (𝑣𝑠)= 230V,50Hz

Source resistance, (𝑅𝑠)= 0.01 Ω

Source inductance, (𝐿𝑠)= 2 mH

Load side

3-phase diode rectifier with RL load

Resistance = 20 Ω

Inductance = 10mH

Compensator (DSTATCOM)

DC-link voltage, 𝑉𝑑𝑐(𝑟𝑒𝑓)= 700V

DC-link capacitor, 𝐶𝑑𝑐= 2050 μF

Compensating resistance, 𝑅𝑐= 0.10 Ω

Compensating inductor, 𝐿𝑐= 25 mH

PI gain: KP,= 10.45 , KI = 0.15

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