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International Journal of Advanced Research in Engineering and Technology

(IJARET) Volume 7, Issue 2, March-April 2016, pp. 91–100, Article ID: IJARET_07_02_009

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ISSN Print: 0976-6480 and ISSN Online: 0976-6499

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___________________________________________________________________________

LOAD BALANCING AND POWER FACTOR

CORRECTION FOR MULTIPHASE POWER

SYSTEMS

V. K. Tripathi

Department of Electrical Engineering

SHIATS, Allahabad, Uttar Pradesh

Prof. (Col.) G. Singh

CSED

SHIATS, Allahabad, Uttar Pradesh

ABSTRACT

In recent years the area of multi-phase (phase order more than three)

machines is popular. A multi-phase source may be derived from transformer

connection (3- phase to 4-phase) or by DC link 4-phase inverters. There are

problem of unbalance, harmonic distortion and poor power factor operation.

This paper proposes the supply side load balancing and power factor

correction .The proposed compensation scheme uses the shunt current source

compensation whose instantaneous values are determined by the

instantaneous symmetrical component theory. An ideal compensator in place

of physical realization of the compensator has been proposed in form of a

current controlled voltage source inverter. The compensation schemes

developed in the paper are tested for their validity on 4-phase (4-wire & 5-

wire) circuits through extensive simulations.

Index Terms: Multi-Phase, Power Factor Correction, Compensator, Load

Balancing

Cite this Article: V. K. Tripathi and Prof. (Col.) G.Singh. Load Balancing

and Power Factor Correction for Multiphase Power Systems. International

Journal of Advanced Research in Engineering and Technology, 7(2), 2016, pp.

91–100.

http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=7&IType=2

V. K. Tripathi and Prof. (Col.) G.Singh


1. INTRODUCTION

Multi-phase Power systems have several inherent benefits such as reduced torque

pulsation, harmonic content and current per phase without increasing the voltage per

phase, higher systems higher reliability and increased power in the same frame as

compared to their three-phase counterpart. So Multi-phase inverter fed induction

motor drives (especially 4-phase) are suitable for high power ratings and other

specialized applications. However the use of such multi drives and devices may be

effected by phase outages & unbalanced as well as nonlinear loading. Such conditions

may lead to many undesirable effects on the supply system such as additional losses

in connecting lines and interfacing devices, oscillatory torques in ac machines,

increased ripple in rectifiers, malfunctioning in sensitive equipments, harmonic and

excessive neutral currents etc. It is therefore desired to have the balanced power

system operation with minimum lower order harmonics. A number of methods have

been evolved for the compensation of harmonics and unbalances for the conventional

three phase systems. Generally These methods are based on the instantaneous reactive

power theory , theory of symmetrical components , and reference frame theory

Utilizing these theoretical concepts, techniques have been developed for load

balancing and power factor correction .This paper addresses the problem of balancing

of an unbalanced 4-phase (Multiphase) load and power factor correction on supply

side. The proposed compensation methods have been verified by simulation studies.

2. COMPENSATION SYSTEM

It is assumed that an ideal voltage source is connected to an arbitrary load ZL, drawing

unbalanced current from the source. In Order to make the source currents balanced, an

external controlled current source called compensator is proposed to be connected to

the load as shown in Fig.1.The point of connection of compensator to power system is

called point of common connection (PCC). The proposed compensation scheme can

be applied to both four-phase four-wire and four-phase five-wire power system. In

four-phase four-wire star connected load, the common point of the load ‘n’ is isolated

from ‘N’, the common point of source. On the other hand, in four-phase five-wire

system, the neutral point is formed by connecting the nodes ‘n’ and ‘N’ and is also

connected to the compensator at its common point n as shown in fig(1).This has the

advantage that the compensator currents ica, icb, icc & icd are currents in independent

circuits, and each phase of the compensator can supply currents independent of the

other three phases.

Figure 1 Compensation scheme for 4-phase star connected load.

Load Balancing and Power Factor Correction for Multiphase Power Systems


3. INSTANTANEOUS SYMMETRICAL COMPONENTS THEORY

Following the unbalanced four phasors of a four-phase system can be resolved into

the four component systems of balanced phasors known as:

The zero sequence system (zero phase differences);

First- (positive) sequence system (four phasors are displaced 90 deg. relative to each

other).

The second-sequence system (two phasors are displaced 180 deg. relative to each

other, each representing two phases, constituting two 2-phase zero sequences in

opposition);

Third-(negative) sequence systems (sequence in the opposite sense of rotation to that

of the first sequence system)

The positive sequence components of balanced four phase currents Ial, Ib1, Ic1, Id1

have original phase sequence like the original unbalanced four-phase currents. These

other three sets of components are shown in Fig. 2.below.

(a) Zero sequence system

(b) First (positive sequence)system

(c) Second sequence system

Iao

Ibo

Ico

Ido

Id1 Ia1

Ib1 Ic1



(d) Third (Negative sequence) system

Fig. 2 Symmetrical Components of Four-Phase System As the original

unbalanced four-phase phasors are resolved into four components, the components

when they are added yield the original phasors. Therefore

0321

0321

0321

0321

ddddd

ccccc

bbbbb

aaaaa

IIIII

IIIII

IIIII

IIIII

(1)

A. Four phase operator m

Now let the four phase complex operator m be defined as, 0.10exp 2/ jj

Figure 3 phasor diagram and the various power of operator m.

Some of the properties of operator 'm' are summarized in equation. (2)

01

0.102701

0.011801

0.10901

32

03

02

0

mmm

Jm

Jm

Jm

(2)

m2 1

m

m3



B. Transformation

The symmetrical components of a four phase system may be represented in matrix

form by equation. (3)

3

2

1

0

321

22

123

1

11

1

1111

Ia

Ia

Ia

Ia

mmm

mm

mmm

Id

Ic

Ib

Ia

(3)

The inverse relationship of equation (3) may be written as

Id

Ic

Ib

Ia

mmm

mm

mmm

Ia

Ia

Ia

Ia

23

22

32

3

2

1

0

1

11

1

1111

41 (4)

With the conventional rotation of current vectors in counter clockwise direction, the

instantaneous value of the currents can be expressed as follows.

3

2

1

0

321

22

123

1

11

1

1111

Ia

Ia

Ia

Ia

mmm

mm

mmm

Id

Ic

Ib

Ia

(5)

The vectors ia1 and ia3 are complex conjugate to each other and ia0 is a real quantity.

The neutral current -

dcban iiiii will be non zero if instantaneous current phasors are unbalanced and is

also equal to 4ia0.

The instantaneous symmetrical component ofvandvv aaaa 32,1,0 phase voltage av

can be written in term of dcba vvvv ,,, as following equation (6)

d

c

b

a

a

a

a

a

v

v

v

v

mmm

mm

mmm

v

v

v

223

22

32

3

2

1

0

1

11

1

1111

41

(6)

4. CALCULATION OF COMPENSATOR CURRENTS

The Compensator current is calculated on the basis of instantaneous symmetrical

component analysis of the load current. An explicit relation for the reference current

is derived in this section by applying multi-phase instantaneous power symmetrical

component transformation. A compensated source will have balanced supply currents

and therefore its zero sequence components will be zero. That is,

0 sdscsbsa iiii (7)



The balanced phase currents at desire power factor angle can be translated with the

help of (5) and (6) into another equation (8)

sdscsbsa

sdscsbsa

imimmii

vmvmmvV

32

32

(8)

The instantaneous power in a 4-phase 5-wire system is given by-

lavgsdsdscscsbsbsasa piviViViV (9)

Solving (8), by taking 2J

em

We obtain -

)(2

BA (10)

Where, sbsasbsa iJiBJVVA , taking tangent on both sides of (10) the

following relation is obtained.

sbsbsasa

sbsasasb

iViV

iViV

(11)

Where

2tan

Finally;

lavg

sbsa

sasbldcd

lavg

sbsa

sbsalccc

lavg

sbsa

sasblbcb

lavg

sbsa

sbsalaca

PVV

VVii

PVV

VVii

PVV

VVii

PVV

VVii

22

22

22

22

2

2

2

2

(12)

5. SIMULATION RESULTS

The proposed compensation scheme for four-phase system has been verified by

simulation. In this section, the simulation results will be presented and discussed.

A. Four-phase five wire system

The system shown in Fig.1 has the following specifications. The voltages

dcbaivsi ,,, and impedances ),,, dcbaZi are given below-

)13()2/*100sin(25.320 itvsi 3,2,1,0i Corresponds to phase a, b, c, d

respectively

0405,1810

1910,1210

jZjZ

jZjZ

dc

ba

(14)



In the simulation results, the system works with unbalanced load for one cycle

(0.03 sec) and runs for another five cycle (0.02 sec) with the proposed compensators.

It can be seen from Fig.4 (b) and Fig. 4 (c) that the source currents ),,,( dcbapisp

and load currents ( dcbapilp ,,, ) are equal and unbalanced When Compensator is

off currents (icp(p=a,b,c,d)) become unbalanced accordingly as shown in Fig.4(d).

Figure 4 4-phase 5-wire supply system with and without compensator

The instantaneous powers (source & load powers) and neutral currents (source &

load neutral currents) are plotted in Fig. 5. It can be seen from Fig. 5(a) that before

compensation, that is, when compensator is switched off, source power ( Ps) and load

power (Pl) are equal in magnitude and oscillating in nature due to unbalance in load

currents. But after compensation when compensator is turned on the oscillating

component of power in source attains a steady state value as can be seen from Fig. 5

(a) while load power is oscillating in nature as shown in Fig. 5 (a). The power

developed in the compensator (Pc) during its presence is also found unbalanced and

shown in Fig. 5(c).Moreover, the source neutral current ( isN) attains zero value when

the compensator is turned on and can be seen from Fig. 5(b) as it balances the source

currents. It can thus be inferred that the sum of the instantaneous compensator

currents is equal to load neutral current (i l n).

Figure 5 variation of power and neutral current for 4-phase 5- wire supply system

The variation of co-phasors-voltage and currents shows unity power factor

operation with compensator as it is evident from Fig. 6 It can be seen from (18) that

impedances are unbalanced and have reactive elements, but the currents are not only

balanced but also operate at unity power factor with compensator



Figure 6 (a)-(d) (1:10) scaled source voltage (solid line) source currents (dashed line) load

currents (hard solid line) 5- wire supply system.

B. Load compensation for phase outages

The multiphase loads like motor capability to operate with phase outages and it has

degraded performance source sees an unbalanced operation and therefore other loads

connected to such a source get affected. The proposed Compensator can be used for

load compensation for phase outages satisfactory. The results are shown in Fig.7 to

Fig.8

Figure 7 Variation of load currents, source currents and compensator currents when two

phase (a, b) are out (from load side) from 4-phase 5-wire system

Figure 8 Variation of power and neutral current for the phase outage (a ,b) of load for 4-

phase 5-wire supply system



It is found that from fig (7) and fig (8) that the source currents and power are

balanced When Compensator is on.

6. CONCLUSION

A method for load balancing and power factor correction on source side for 4-phase

(multiphase) load circuit is Proposed In this paper The proposed scheme has been

found to be suitable for unbalanced loading and phase outage source voltages, load

currents, source currents, neutral currents and compensator currents has been

observed during non-compensating and compensating period. The variations of the

load, source and compensator powers are analyzed.

It can be concluded that 4-phase (multi-phase) system equipped with multi-phase

compensator can work with phase outages and unbalanced loading.

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