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**SYMMETRICAL COMPONENETS OF POWER SYSTEM**

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**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

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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.

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**An organization of power system analysis problem**

Source (Reference #1)

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**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.

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**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.

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**Normal types of fault are:**

Fault due to lightning Tree limbs falling on the line Wind damage Insulation deterioration Vandalism

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

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**Sources of Asymmetrical fault are: (Reference#2)**

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**Sources of Asymmetrical fault are (cont.)**

One phase open circuit Unbalanced in load mainly the arc loads

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**Sources of Asymmetrical fault are (cont.)**

One phase open circuit

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**Sources of Asymmetrical fault are (cont.)**

SLG fault

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**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.

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**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

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**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

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**The phasor notation of a-operator**

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

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Phasor a or a-operator

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Phasor a or a-operator

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**Equation in matrix form**

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**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.

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**Symmetrical components for three Phase system (cont)**

The phasor representation of three phase system (source reference#2)

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**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.

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**Symmetrical components for three Phase system (cont)**

Relations of voltage components in matrix form

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**Symmetrical components of generator**

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**Symmetrical components of generator**

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**Symmetrical components of transformer (zero)**

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**Fault analysis using symmetrical components**

The most common type of fault is the single line to ground fault:

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**Fault analysis using symmetrical components (cont)**

The sequence component connection for the single line to ground fault:

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**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.

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**Fault analysis using symmetrical components (cont)**

LL fault:

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**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.

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**Fault analysis using symmetrical components (cont)**

LLG fault:

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**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.

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**Software available for carrying fault analysis**

The most commonly used soft ware are: MATLAB EDSA ETAP CYME

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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.

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**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

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