Here, Comparative analysis of three phase, five phase and six phase symmetrical components is done. For MATLAB code, link is given at the of the PPT.

1. Comparative analysis of three phase,
five phase and
six phase symmetrical components
with MATLAB
Presented by,
Shridhar B. Kulkarni
RIT, Islampur

2. OUTINES
1. Introduction
2. Three phase Symmetrical components
3. Five phase Symmetrical components
4. Six phase Symmetrical components
5. MATLAB coding
6. Conclusion
7. References

3. 1. Introduction
 Multiphase systems are most applicable in case of transmission
lines and many electrical operations.
 The power system generally operates in normal and balanced
state with 3 ph. Sinusoidal waveforms.
 The disturbance occurs in system i.e. faults takes place in the
system ,which may be S.C. faults (viz. LG, LL, LLL, LLG) etc.
 Fortescue Theorem
 For analysis, provision by symmetrical components to solve
system problems is much simpler, due to which resulting equations
is linearly mutual independent if system in balance state.

4. 2.THREE PHASE SYMMETRICAL COMPONENTS
In the power system, three phase symmetrical components refers to +
ve, -ve and zero Sequence.
1. Positive sequence components consist of ‘abc’ phase sequence
which displaces with 120° from each other.
2. Negative sequence components consist of ‘acb’ phase sequence
which displaces with 120° from each other and which is opposite to
original phases.
3. Zero sequence components have three components of same
magnitudes with no angular displacement between all phases.
210 aaa VVVV 
21
2
0 aab yVVyVV 
2
2
10 aaC VyyVVV 
Vabc = [Y]* [V012]











2
2
1
1
111
yy
yyY

5. Continued..
Fig.2(a)
Positive Sequence
Fig.2(b)
Negative Sequence
Fig. 2(c)
Zero Sequence
Fig 2: Three phase symmetrical components

6. 3. FIVE PHASE SYMMETRICAL COMPONENTS
As per the Fortescue theorem, the set of unbalanced phasor quantity of six-phase
system can be broke up into balanced system of voltages and currents to number of
phases equal to number of components involved in analysis. The phase differences
between every two adjoining vectors are equivalent to 2π/n .
Adjacent Positive-sequence components: The phase sequence of this type of
component has same as the main unbalanced five phase system. The magnitude of
these components is same and they are displaced from each other by 72° apart.
Adjacent Negative-sequence components: This type of component has exactly
opposite phase sequence than that of original five phase system. The magnitude of
these components is same and they are displaced from each other by 72° apart.
Non-adjacent Positive-sequence components : These components are displaced
from each other by 72°with equal magnitude. These phasors rotate as the
nonadjacent original unbalanced five-phase system components rotates .

7. Continued…
Non-adjacent Negative-sequence components : This type of component has
exactly opposite phase sequence than that of non-adjacent original unbalanced five
phase system. The magnitude of these components is same and they are displaced
from each other by 72° apart.
Zero-sequence components : The magnitude of these components is same and they
are displaced from each other by 0° apart.
Equations are as follows:

8. .
Where, Vsc= symmetrical components of voltage. In matrix form five phase
symmetrical components can be represented as follows:
Where,

9. .
Fig. 3(a)
Adjacent Positive-sequence
Fig. 3(b)
Adjacent Negative-sequence
Fig. 3(c)
Zero Sequence
Fig. 3(d)
Non-adjacent Positive sequence
Fig.3(e)
Non-adjacent Negative-sequence
Fig 3: Five phase symmetrical components

10. 4. SIX PHASE SYMMETRICAL COMPONENTS
 As per the Fortescue theorem, the six-phase system can also be broke up into two
set of symmetrical components of voltages and currents which consisting of first
set of sequence components (a, b, c) and second set of sequence components
(a', b', c').
 The first set of components are consisting of first positive, first negative and first
zero sequence components where as the second set of components consist of
second zero, second positive and second negative sequence components.
 First zero sequence component: The first zero sequence components comprise
of three phasors whose magnitudes are equal and displaced from each other by
zero.
 First positive sequence component :The First positive sequence components
consisting three set of phasors in equal magnitude and they are displaced by 120
deg. apart. The phase sequence of these components is same as original phasors.

11. Continued…
 First negative sequence component :The first negative sequence components
consisting three set of phasors in equal magnitude and they are displaced by
120deg. apart. The phase sequence of these components is exactly
opposite to the original phasors.
 Second zero sequence component :The second zero sequence components
contain three phasors which are equal in magnitude and zero phase displacement
from each other.
 Second positive sequence component :The second positive sequence
components are comprised of three sets of phasors which are equal magnitude
and they are displaced by 120 degrees apart. The phase sequence of these
components is same as original phasors.
 Second negative sequence component :The second negative sequence
components consisting three set of phasors in equal magnitude and they are
displaced by 120 deg. apart. The phase sequence of these components is exactly
opposite to the original phasors.

12. .
 For consideration of six phase unbalanced voltages of the order [Vabcdef] by
using matrix transformation [Y] to obtain symmetrical components of order [Vsc]
can be represented is as follows:
Vabcdef = [Y]* [Vsc]
Where,
Here, y is the operator causes rotation of 60deg. in anti-clockwise direction.

13. Fig.4(a)
First Zero Sequence
Fig.4(b)
First Positive Sequence
Fig.4(c)
First Negative Sequence
Fig.4(d)
Second Zero Sequence
Fig.4(e)
Second Positive Sequence
Fig. 4(f)
Second Negative Sequence
Fig 4: Six phase symmetrical components

14. CONCLUSION
1. The unsymmetrical ‘N’ phasors can be solved in all ‘N’
symmetrical phasors by using linear complex transformation
2. In six phase system it is observed that two three phase
systems are formed in which each three phase system has
three symmetrical components where as in five phase system
one zero sequence component and two adjacent and two non
adjacent components are present.
3. The MATLAB coding is done to obtain three phase, five
phase and six phase symmetrical components

15. REFERENCES
[1]James E. Brittain, ‘Scanning the Past: Charles L. G. Fortescue and Method of
Symmetrical Components’, Proceedings of IEEE, Vol. 86(5), pp. 1020-1021, May
1998.
[2] Hadi Sadat, Power Systems Analysis, Tata McGraw Hill Edition, India, pp. 400-
406, 2002.
[3] Iranna Korachagaon “Five-Phase Unbalanced System and its Symmetrical
Components with MATLAB” IEEE conference on Electronic Systems, Signal
Processing and Computing Technologies (ICESC), pp.174-177, 2014
[4] Saifullah Payami Atif Iqbal “Analytical and Graphical Tool to Analyse Unbalanced
Five-Phase Supply System” International J. of Recent Trends in Engineering and
Technology ,Vol. 3, No. 3, May 2010.
[5] E. H. Badawy, M. K. El-Sherbiny, A. A. Ibrahim, M. S. Farghaly,
“A method of analyzing unsymmetrical faults on six phase power systems” IEEE
Transactions on Power Delivery, Vol. 6, Issue: 3, pp. 1139 – 1145, July 1991.

16. MATLAB Code: My IEEE paper, Click On link
given below
https://ieeexplore.ieee.org/document/8073507
Contact us:
Shreedhar.kulkarni65@gmail.com