Fault Analysis, Grounding, Symmetrical Components

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ECE 476POWER SYSTEM ANALYSIS

• Lecture 19
• Fault Analysis, Grounding, Symmetrical
  Components
• Professor Tom Overbye
• Department of Electrical andComputer Engineering

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Announcements

• Homework 8 is 7.1, 7.17, 7.20, 7.24, 7.27
• Should be done before second exam not turned in
• Be reading Chapter 7
• Design Project has firm due date of Dec 4.
• Exam 2 is Thursday Nov 13 in class.
• Closed book, closed notes, except you can bring
  one new note sheet as well as your first exam
  note sheet.

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Network Fault Example
For the following network assume a fault on the
terminal of the generator all data is per
unit except for the transmission line reactance
generator has 1.05 terminal voltage supplies
100 MVA with 0.95 lag pf
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Network Fault Example, cont'd
Faulted network per unit diagram
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Network Fault Example, cont'd
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Fault Analysis Solution Techniques

• Circuit models used during the fault allow the
  network to be represented as a linear circuit
• There are two main methods for solving for fault
  currents
• Direct method Use prefault conditions to solve
  for the internal machine voltages then apply
  fault and solve directly
• Superposition Fault is represented by two
  opposing voltage sources solve system by
  superposition
• first voltage just represents the prefault
  operating point
• second system only has a single voltage source

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Superposition Approach
Faulted Condition
Exact Equivalent to Faulted Condition
Fault is represented by two equal and opposite
voltage sources, each with a magnitude equal to
the pre-fault voltage
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Superposition Approach, contd
Since this is now a linear network, the faulted
voltages and currents are just the sum of the
pre-fault conditions the (1) component and the
conditions with just a single voltage source at
the fault location the (2) component
Pre-fault (1) component equal to the pre-fault
power flow solution
Obvious the pre-fault fault current is zero!
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Superposition Approach, contd
Fault (1) component due to a single voltage
source at the fault location, with a magnitude
equal to the negative of the pre-fault voltage at
the fault location.
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Two Bus Superposition Solution
This matches what we calculated earlier
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Determination of Fault Current
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Determination of Fault Current
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Three Gen System Fault Example
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Three Gen Example, contd
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Three Gen Example, contd
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Three Gen Example, contd
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PowerWorld Example 7.5 Bus 2 Fault
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Problem 7.28
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Grounding

• When studying unbalanced system operation how a
  system is grounded can have a major impact on the
  fault flows
• Ground current only impacts zero sequence system
• In previous example if load was ungrounded the
  zero sequence network is (with Zn equal infinity)

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Grounding, contd

• Voltages are always defined as a voltage
  difference. The ground is used to establish the
  zero voltage reference point
• ground need not be the actual ground (e.g., an
  airplane)
• During balanced system operation we can ignore
  the ground since there is no neutral current
• There are two primary reasons for grounding
  electrical systems
• safety
• protect equipment

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How good a conductor is dirt?

• There is nothing magical about an earth ground.
  All the electrical laws, such as Ohms law, still
  apply.
• Therefore to determine the resistance of the
  ground we can treat it like any other resistive
  material

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How good a conductor is dirt?
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How good a conductor is dirt?
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Calculation of grounding resistance

• Because of its large cross sectional area the
  earth is actually a pretty good conductor.
• Devices are physically grounded by having a
  conductor in physical contact with the ground
  having a fairly large area of contact is
  important.
• Most of the resistance associated with
  establishing an earth ground comes within a short
  distance of the grounding point.

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Calculation of grounding R, contd

• Example Calculate the resistance from a
  grounding rod out to a radial distance x from the
  rod, assuming the rod has a radius of r

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Calculation of grounding R, contd
The actual values will be substantially less
since weve assumed no current flowing downward
into the ground
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Analysis of Unsymmetric Systems

• Except for the balanced three-phase fault, faults
  result in an unbalanced system.
• The most common types of faults are single
  line-ground (SLG) and line-line (LL). Other
  types are double line-ground (DLG), open
  conductor, and balanced three phase.
• System is only unbalanced at point of fault!
• The easiest method to analyze unbalanced system
  operation due to faults is through the use of
  symmetrical components

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Symmetric Components

• The key idea of symmetrical component analysis is
  to decompose the system into three sequence
  networks. The networks are then coupled only at
  the point of the unbalance (i.e., the fault)
• The three sequence networks are known as the
• positive sequence (this is the one weve been
  using)
• negative sequence
• zero sequence

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Positive Sequence Sets

• The positive sequence sets have three phase
  currents/voltages with equal magnitude, with
  phase b lagging phase a by 120, and phase c
  lagging phase b by 120.
• Weve been studying positive sequence sets

Positive sequence sets have zero neutral current
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Negative Sequence Sets

• The negative sequence sets have three phase
  currents/voltages with equal magnitude, with
  phase b leading phase a by 120, and phase c
  leading phase b by 120.
• Negative sequence sets are similar to positive
  sequence, except the phase order is reversed

Negative sequence sets have zero neutral current
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Zero Sequence Sets

• Zero sequence sets have three values with equal
  magnitude and angle.
• Zero sequence sets have neutral current

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Sequence Set Representation

• Any arbitrary set of three phasors, say Ia, Ib,
  Ic can be represented as a sum of the three
  sequence sets

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Conversion from Sequence to Phase
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Conversion Sequence to Phase
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Conversion Phase to Sequence
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Symmetrical Component Example 1
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Symmetrical Component Example 2
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Symmetrical Component Example 3
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Use of Symmetrical Components

• Consider the following wye-connected load

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Use of Symmetrical Components
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Networks are Now Decoupled