Balance Fault Analysis, Symmetrical Components

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ECE 476POWER SYSTEM ANALYSIS

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

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Announcements

• Be reading Chapter 8
• HW 8 is 7.6, 7.13, 7.19, 7.28 due Nov 3 in
  class.
• Start working on Design Project. Tentatively due
  Nov 17 in class.

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In the News

• Earlier this week the Illinois House and Senate
  overrode the Governors veto of the Smart Grid
  Bill it is now law
• On Tuesday Quinn called it a smart greed plan
• Law authorizes a ten year, 3 billion project to
  modernization the electric grid in Illinois
• All ComEd customers and most of Ameren will get
  smart meters
• Effort will be paid for through rate increases
  over the period ComEd estimated the average
  increase of 36 per year would be offset by
  electricity savings

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Network Fault Analysis Simplifications

• To simplify analysis of fault currents in
  networks we'll make several simplifications
• Transmission lines are represented by their
  series reactance
• Transformers are represented by their leakage
  reactances
• Synchronous machines are modeled as a constant
  voltage behind direct-axis subtransient reactance
• Induction motors are ignored or treated as
  synchronous machines
• Other (nonspinning) loads are ignored

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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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Extension to Larger Systems
However to use this approach we need to first
determine If
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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 does not come into play during
  balanced system analysis (since net current to
  ground would be zero).
• Becomes important in the study of unbalanced
  systems, such as during most faults.

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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.
• Typical substation grounding resistance is
  between 0.1 and 1 ohm fence is also grounded,
  usually by connecting it to the substation ground
  grid.

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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