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Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) PDF Download

Symmetrical Components

A three-phase system is said to be symmetrical when the system viewed from any phase is similar. Thus, in a three-phase symmetrical system the self-impedance of all the three phases are equal and the mutual impedances, if any between the three phases are the same any three phase system having unbalanced phasor quantities can be represented in terms of three phase balanced phasor components as a combination of positive, negative and zero sequence component, which are as follows

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Positive Phase Sequence Components

It represents a set of balance phasors Va1, Vb1 & Vc1. These components have three phasors equal in magnitude displaced by 120o and having same phase sequence as original phasors.

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Negative Phase Sequence Components

These components have three phasors Va2, Vb2 & Vc2 equal in magnitude displaced by 120o but having phase sequence opposite to original phasors. It represents a set of balanced phasors 

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Zero Sequence Components

These phasors Vao, Vbo & Vco are equal in magnitude and having zero phase displacement.

α operator = e+/120°

= -0.5 + j 0.866

α2 = e240º= -0.5 - j 0.86

α3=1

α4

1 + α +α2 = 0

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

and

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

In matrix form

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Three Phase Power in Terms of Symmetrical Components

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

= sum of symmetrical components power

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Sequence Impedance

The positive sequence impedance of an equipment is the impedance offered by the equipment to the flow of positive sequence current. similarly, the negative sequence or zero sequence impedance of the equipment is the impedance offered by the equipment to the flow of corresponding sequence current.

Sequence Impedance of a Transmission Line

Positive sequence impedance Z1 = Zs - Zm

Negative sequence impedance Z2 = Zs - Zm

Zero sequence impedance Z0 = Zs – 2Zm + 3Zn

where, Zs = Self-impedance per phase

Zm = Mutual impedances between phases

Sequence Impedance of Synchronous Machine

  1. Positive Sequence, Impedance Z1 Depending on the time interval of interest one of the three reactances may be used.
    • For the subtransient interval, we use subtransient reactance Z1 = j Xd
    • For the transient interval, we use the transient reactance Z1 = j Xd'
    • If the steady state value is of interest we have Z1 = j Xd
  2. Negative Sequence Impedance
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
  3. Zero Sequence Impedance (Z0) Zero sequence current are all in phase and therefore, do not reproduce any rotating field. The zero sequence impedance Z0 depends upon the type of grounding and the zero sequence impedance per phase of the generator.

Sequence Networks Equations

Sequence Network of Unloaded Alternator

  1. Positive Sequence Network
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)Va = Ea = Z1I
  2. Negative Sequence Network
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
  3. Zero Sequence Network

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Sequence Impedance of Transformers

  • Switch A is closed when primary winding is star connected with neutral grounded.
  • Switch C is closed when primary winding is delta connected.
  • Switch B is closed when secondary winding is star connected with neutral grounded.
  • Switch D is closed when secondary winding is delta (∆) connected.
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
  • Keep both A and C open if when primary winding is star connected with natural isolated (not grounded).
  • Keep both B and D open if when secondary winding is star connected with natural isolated.

where Z0 = Zero sequence impedance of transformer.

Examples

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Fault may occur at different points in power system.

Faults that occur on a power system are broadly classified as follows

Transient on a Transmission Line

When a sudden change in voltage and current distribution takes place, a power energy distribution also changes. But energy distribution is called transient phenomenon in power system.

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

The current after short circuit I(t) has components i.e.,

I = Is + It

Where, Is = Steady state value of current

I= Transient current

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

3-ϕ Sudden Short Circuit of an Unloaded Alternator

Whenever a three-phase short circuit occurs at the terminals of an alternator, the armature current suddenly increases to a large value and voltage across its terminals drops.

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

  • Sub transient fault current
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
  • Transient fault current
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
  • Steady-state fault current
    Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Where Vt = RMS voltage from one terminal to neutral at no load

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) = Direct axis sub-transient reactance
Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)= Direct axis transient reactance
Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Xd = Direct axis synchronous reactance

Xd = XL + Xm

Where XL = Leakage reactance

Xm = Main winding reactance

Xt = Field winding reactance

Xd = Damper winding reactance

Note: Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Fault Analysis

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Three Phase Fault

Symmetrical short circuit on Synchronous Machine The selection of a circuit breaker for a power system depends not only upon the current the breaker is to carry under normal operating conditions but also upon the maximum current it may have to carry momentarily and the current it may have to interrupt at the voltage of the line in which it is placed.

In order to approach the problem of calculating the initial current, we need to study the behavior of a synchronous generator when it is short-circuited. When an ac voltage is applied suddenly across a series R-L circuit, the current which flows has two components 1.

a steady state sinusoidally varying component of constant amplitude and 2. a non-periodic and exponentially decaying with a time constant of L/R. (which is also referred as the dc component current). The initial value of the dc component of current depends on the magnitude of the ac voltage when the circuit is closed.

In such types of faults, all the three phases are short-circuited to each other and often to earth also. Such faults are balanced and symmetrical in the sense that the system remains balanced even after the fault.

Fault Level Calculations

In a power system, the maximum the fault current (or fault MVA) that can flow into a zero impedance fault is necessary to be known for switchgear solution. This can either be the balanced three phase value or the value at an asymmetrical condition.

The Fault Level defines the value for the symmetrical condition. The fault level is usually expressed in MVA (or corresponding per-unit value), with the maximum fault current value being converted using the nominal voltage rating.

The Short circuit capacity (SCC) of a busbar is the fault level of the busbar. The strength of a busbar (or the ability to maintain its voltage) is directly proportional to its SCC. An infinitely strong bus (or Infinite bus bar) has an infinite SCC, with a zero equivalent impedance and will maintain its voltage under all conditions.

MVAbase = √3. Nominal Voltage (kV). Ibase (kA)
MVAFault = √3. Nominal Voltage (kV). Isc (kA)

where

MVAFault  - Fault Level at a given point in MVA

Ibase - Rated or base line current

Isc - Short circuit line current flowing in to a fault

The per unit value of the fault Level may thus be written as   

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

The per unit value for nominal value of unity, so that

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Key Points

  • Positive sequence currents are present in all types of faults.
  • Negative sequence currents are present in all unsymmetrical faults.
  • Zero sequence currents are present when the natural of the system is grounded and the fault also involves the ground and the magnitude of the natural current (In) is equal to 3I.
  • Voltage of natural Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
  • Shunt faults are characterized by increase in current and fall in voltage and frequency whereas series faults are characterized by increase in voltage and frequency and fall in current in the faulted phases.
The document Symmetrical Component & Symmetrical Fault Analysis | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course GATE Notes & Videos for Electrical Engineering.
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FAQs on Symmetrical Component & Symmetrical Fault Analysis - GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

1. What is symmetrical component analysis in electrical engineering?
Symmetrical component analysis is a technique used in electrical engineering to analyze the behavior of unbalanced three-phase systems. It decomposes the unbalanced system into three symmetrical components: positive sequence, negative sequence, and zero sequence. This analysis is particularly useful in understanding the effects of unbalanced faults on power systems.
2. How does symmetrical component analysis help in fault analysis?
Symmetrical component analysis helps in fault analysis by simplifying the calculations and providing a clear understanding of the fault currents and voltages in an unbalanced system. By decomposing the unbalanced system into symmetrical components, fault analysis becomes more manageable and allows for the accurate determination of fault locations, fault currents, and fault voltages.
3. What are positive, negative, and zero sequence components in symmetrical component analysis?
In symmetrical component analysis, the unbalanced three-phase system is decomposed into three symmetrical components: - Positive sequence component: This component represents the balanced component of the system. It has the same magnitude and phase angle in all three phases and rotates in the same direction as the original system. - Negative sequence component: This component represents the unbalanced component with a phase shift of 180 degrees. It has the same magnitude as the positive sequence component but rotates in the opposite direction. - Zero sequence component: This component represents the unbalanced component that is in phase with all three phases. It has the same magnitude in all three phases but does not rotate.
4. How is symmetrical component analysis applied in power system protection?
Symmetrical component analysis is widely used in power system protection to analyze fault conditions. By calculating the symmetrical components of current and voltage during a fault, protection relays can determine the type of fault (symmetrical or unsymmetrical) and take appropriate actions to isolate the faulty section of the system. This analysis helps in detecting and clearing faults quickly, minimizing the impact on the power system.
5. What are the advantages of using symmetrical component analysis in electrical engineering?
Some advantages of using symmetrical component analysis in electrical engineering include: - Simplified fault analysis: Symmetrical component analysis simplifies the calculations involved in fault analysis, making it easier to determine fault currents and voltages accurately. - Clear understanding of unbalanced systems: By decomposing the unbalanced system into symmetrical components, engineers can gain a clear understanding of the behavior of unbalanced systems, helping in system design and fault mitigation. - Efficient power system protection: Symmetrical component analysis aids in designing effective protection schemes for power systems, enabling quick detection and isolation of faults, ensuring the reliability and stability of the system.
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