1. SYMMETRICAL COMPONENETS OF POWER SYSTEM

2. OUTLINE OF THE PRESENTATION
INTRODUCTION
NEED FOR THE SYMMETRICAL COMPONENET METHOD
TECHINQUES USED TO ANALYSIS SYMMETRICAL
SYMMETRICAL METHODS USED TO STUDY POWER SYSTEM FAULTS
CONCLUSION
REFERENCES

3. INTRODUCTION
The normal operating conditions of an electric power system are occasionally disrupted because of faults.
Analysis of power systems usually implies the computation of network voltages and currents under a given set of conditions.
Under many circumstances we tend to ignore the unbalanced operation in the system and unbalanced operation is always present.

4. An organization of power system analysis problem
Source (Reference #1)

5. Effects of faults on power system
Flow of excessive current
Abnormal voltages
Voltage elevation of system neutral
Induce over voltages on neighbouring equipments .
Hazards to human, equipment and animals.

6. Need for fault analysis
Design of protection system requires the knowledge of fault current.
The information obtained from the fault studies are used:
to select the sizes of circuit breaker,
fuse and characteristic,
setting of relay.

7. Normal types of fault are:
Fault due to lightning
Tree limbs falling on the line
Wind damage
Insulation deterioration
Vandalism

8. Types of fault
Symmetrical fault :
Usually three phase to ground fault
Unsymmetrical fault
The fault is unbalanced in nature

9. Sources of Asymmetrical fault are: (Reference#2)

10. Sources of Asymmetrical fault are (cont.)
One phase open circuit
Unbalanced in load mainly the arc loads

11. Sources of Asymmetrical fault are (cont.)
One phase open circuit

12. Sources of Asymmetrical fault are (cont.)
SLG fault

13. Need for the symmetrical component analysis
Negative sequence relay in generator has helped in protecting the generator from over heating in the event of unbalanced loads.
The positive sequence segregating network is used to supply the sensing voltage to generator voltage regulators
Certain connections of CT and PT develop zero sequence components that are used in protective ground relaying scheme.

14. Method of adopted for symmetrical component analysis (cont)
Mathematically:
Va= Va1+ Va2+ Va Van
Vb= Vb1+ Vb2+ Vb Vbn
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Vn= Vn1+ Vn2+ Vn Vnn
Where:
Va, Vb……. Vn are unbalanced set of phosors
Va1, Vb1…… Vn1 first set of n balanced phasors with an angle 2pi/n
between components a,b,…..n

15. Method of adopted for symmetrical component analysis (cont)
Mathematically:
Va2, Vb2…… Vn2 second set of n balanced phasors with an angle 4pi/n between components a, b………,…..n
……………………………………………………….
Va(n-1), Vb(n-1)…… Vn(n-1)are (n-1)th set of n balanced phasors with an angle 2pi(n-1)/n between components a, b………,…..n

16. The phasor notation of a-operator
Phasor a or a-operator
The phasor notation of a-operator

17. Phasor a or a-operator

18. Phasor a or a-operator

19. Equation in matrix form

20. Symmetrical components for three Phase system
The n-phase system presented above is of academic interest only and only the practical three phase system will be emphasised.
Power is generated, transmitted and consumed mostly in three phase only.

21. Symmetrical components for three Phase system (cont)
The phasor representation of three phase system (source reference#2)

22. Symmetrical components for three Phase system (cont)
The positive sequence set consisting of three components of equal magnitude, displaced by 120 & 240o respectively and having the phase sequence of abca.
The negative sequence set consisting of three components of equal magnitude displaced by 240 & 120o respectively, having phase sequence of acba.
The zero sequence set of the component of which being equal both in magnitude and and phase.

23. Symmetrical components for three Phase system (cont)
Relations of voltage components in matrix form

24. Symmetrical components of generator

25. Symmetrical components of generator

26. Symmetrical components of transformer (zero)

27. Fault analysis using symmetrical components
The most common type of fault is the single line to ground fault:

28. Fault analysis using symmetrical components (cont)
The sequence component connection for the single line to ground fault:

29. Fault analysis using symmetrical components (cont)
The sequence component connection for the single line to ground fault:
The sequence components are connected in series.
The three currents in the case of SLG fault are equal.

30. Fault analysis using symmetrical components (cont)
LL fault:

31. Fault analysis using symmetrical components (cont)
LL fault:
There is no zero sequence component due to absence of ground return path.
The positive and negative sequence components are connected in parallel.

32. Fault analysis using symmetrical components (cont)
LLG fault:

33. Fault analysis using symmetrical components (cont)
LLG fault:
For the zero sequence component it requires to add an external impedance of Zf+3Zg
The networks are connected in parallel.

34. Software available for carrying fault analysis
The most commonly used soft ware are:
MATLAB
EDSA
ETAP
CYME

35. Conclusion
Power system analysis using symmetrical component is very helpful in improving the reliability of the power system.
The principle adopted for the analysis of unbalanced fault system is symmetrical component method.
By knowing the principle, the results obtained from the computer can be analysed.

36. References: 1. Paul M. Anderson, Analysis of Faulted Power Systems.
2. W.D. Stevenson, Elements of Power System Analysis.
3. A.P.S Meliopoulos, Power System Grounding and Transients.
4. Olle. I. Elgerd, Electric Energy Systems Theory.
5. IEEE Transactions