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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
Available online at
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ISSN Print: 0976-6480 and ISSN Online: 0976-6499
© IAEME Publication
___________________________________________________________________________
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 & 5wire) 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.
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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.
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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.
Iao
Ibo
Ico
Ido
(a) Zero sequence system
Ia1
Id1
Ic1
Ib1
(b) First (positive sequence)system
(c) Second sequence system
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V. K. Tripathi and Prof. (Col.) G.Singh
(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
Ia
Ib
Ic
Id




I a1  I a 2
I b1  I b 2
I c1  I c 2
I d1  I d 2
 I a3  I a0 
 I b3  I b0 

 I c3  I c 0 
 I d 3  I d 0 
(1)
A. Four phase operator m
Now let the four phase complex operator m be defined as, exp j / 2  0  j1.0
m
m2
1
m3
Figure 3 phasor diagram and the various power of operator m.
Some of the properties of operator 'm' are summarized in equation. (2)
m  1900  0  J1.0 

m2  1 1800  1  J 0.0 

m3  12700  0  J1.0 

1  m  m2  m3  0

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(2)
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Load Balancing and Power Factor Correction for Multiphase Power Systems
B. Transformation
The symmetrical components of a four phase system may be represented in matrix
form by equation. (3)
 Ia  1 1
 Ib  1 m3
  
 Ic  1 m2
  
1
 Id  1 m
1
m2
1
m2
1   Ia0 
m1   Ia1 
m2   Ia2 
 
m3   Ia3 
(3)
The inverse relationship of equation (3) may be written as
1
1   Ia 
 Ia0 
1 1
 Ia 
1 m m2 m3   Ib 
 1  1 
 
(4)
4 1 m2 1 m2   Ic 
 Ia2 
 

 
3
2
1 m m m   Id 
 Ia3 
With the conventional rotation of current vectors in counter clockwise direction, the
instantaneous value of the currents can be expressed as follows.
1
1   Ia0 
 Ia  1 1
 Ib  1 m3 m2 m1   Ia 
 
  1
 Ic  1 m2 1 m2   Ia2 

  
1
2
3 
 Id  1 m m m   Ia3 
(5)
The vectors ia1 and ia3 are complex conjugate to each other and ia0 is a real quantity.
The neutral current -
in  ia  ib  ic  i d will be non zero if instantaneous current phasors are unbalanced and is
also equal to 4ia0.
The instantaneous symmetrical component va0,  a1, va2 and va3 of phase voltage va
can be written in term of va , vb , vc , vd as following equation (6)
 a 0 
1 1
v 

 a1   1 1 m
4 1 m 2
va 2 
 

3
1 m
 va 3 
1
m2
1
m2
1  va 
m3  vb 
m 2   vc 
 
m 2  vd 
(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,
isa  isb  isc  isd  0
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The balanced phase currents at desire power factor angle  can be translated with the
help of (5) and (6) into another equation (8)

i

 
 Vsa  mvsb  m2vsc  m3 vsd 
sa
 misb  m isc  m isd
2
3
(8)
The instantaneous power in a 4-phase 5-wire system is given by-
Vsa isa  Vsb isb Vsc isc  vsd isd  plavg
Solving (8), by taking m  e
We obtain -

(9)
J 2
2  ( A  B)
(10)
Where, A  Vsa  JVsb , B  isa  J isb taking tangent on both sides of (10) the
following relation is obtained.

Vsb isa  Vsa i sb
Vsa isa  Vsb i sb
(11)

Where   tan 

 2
Finally;
Vsa  Vsb 
2 Vsa2  Vsb2
V  Vsa 
 sb 2
2 Vsa  Vsb2
V  Vsb 
 sa 2
2 Vsa  Vsb2
V  Vsa 
 sb 2
2 Vsa  Vsb2
ica  ila 


icb  ilb


icc  ilc
icd  ild





Plavg 


Plavg 


Plavg 


Plavg 

(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
vsi i  a, b, c, d  and impedances Z i  a, b, c, d ) are given below-
vsi  320.25 sin( 100t  i * / 2)
respectively
(13) i   0,1, 2, 3 Corresponds to phase a, b, c, d
Z a  10  j12, Z b  10  j19
Z c  10  j18, Z d  05  j 04
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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 (isp  p  a, b, c, d )
and load currents ( ilp  p  a, b, c, d ) 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
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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 4phase 5-wire supply system
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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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