EE 369 POWER SYSTEM ANALYSIS

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EE 369POWER SYSTEM ANALYSIS

• Lecture 14Power Flow
• Tom Overbye and Ross Baldick

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Announcements

• Read Chapter 12, concentrating on sections 12.4
  and 12.5.
• Homework 12 is 6.43, 6.48, 6.59, 6.61, 12.19,
  12.22, 12.20, 12.24, 12.26, 12.28, 12.29 due
  Tuesday Nov. 25.

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The N-R Power Flow 5-bus Example
Single-line diagram
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The N-R Power Flow 5-bus Example
Bus Type V per unit ? degrees PG per unit QG per unit PL per unit QL per unit QGmax per unit QGmin per unit
1 Slack 1.0 0 ? ? 0 0 ? ?
2 Load ? ? 0 0 8.0 2.8 ? ?
3 Constant voltage 1.05 ? 5.2 ? 0.8 0.4 4.0 -2.8
4 Load ? ? 0 0 0 0 ? ?
5 Load ? ? 0 0 0 0 ? ?
Table 1. Bus input data
Bus-to-Bus R per unit X per unit G per unit B per unit Maximum MVA per unit
2-4 0.0090 0.100 0 1.72 12.0
2-5 0.0045 0.050 0 0.88 12.0
4-5 0.00225 0.025 0 0.44 12.0
Table 2. Line input data
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The N-R Power Flow 5-bus Example
Bus-to-Bus R per unit X per unit Gc per unit Bm per unit Maximum MVA per unit Maximum TAP Setting per unit
1-5 0.00150 0.02 0 0 6.0
3-4 0.00075 0.01 0 0 10.0
Table 3. Transformer input data
Bus Input Data Unknowns
1 V1 1.0, ?1 0 P1, Q1
2 P2 PG2-PL2 -8 Q2 QG2-QL2 -2.8 V2, ?2
3 V3 1.05 P3 PG3-PL3 4.4 Q3, ?3
4 P4 0, Q4 0 V4, ?4
5 P5 0, Q5 0 V5, ?5
Table 4. Input data and unknowns
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Let the Computer Do the Calculations! (Ybus Shown)
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Ybus Details
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Here are the Initial Bus Mismatches
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And the Initial Power Flow Jacobian
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Five Bus Power System Solved
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37 Bus Example Design Case
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Good Power System Operation

• Good power system operation requires that there
  be no reliability violations (needing to shed
  load, have cascading outages, or other
  unacceptable conditions) for either the current
  condition or in the event of statistically likely
  contingencies
• Reliability requires as a minimum that there be
  no transmission line/transformer limit violations
  and that bus voltages be within acceptable limits
  (perhaps 0.95 to 1.08)
• Example contingencies are the loss of any single
  device. This is known as n-1 reliability.

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Good Power System Operation

• North American Electric Reliability Corporation
  now has legal authority to enforce reliability
  standards (and there are now lots of them).
• See http//www.nerc.com for details (click on
  Standards)

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Looking at the Impact of Line Outages
Opening one line (Tim69- Hannah69) causes
overloads. This would not be Allowed.
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Contingency Analysis
Contingencyanalysis providesan automaticway of
lookingat all the statisticallylikely
contingencies. Inthis example thecontingency
set is all the single line/transformeroutages
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Power Flow And Design

• One common usage of the power flow is to
  determine how the system should be modified to
  remove contingencies problems or serve new load
• In an operational context this requires working
  with the existing electric grid, typically
  involving re-dispatch of generation.
• In a planning context additions to the grid can
  be considered as well as re-dispatch.
• In the next example we look at how to remove the
  existing contingency violations while serving new
  load.

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An Unreliable Solutionsome line outages result
in overloads
Case now has nine separate contingencies
having reliability violations (overloads in
post-contingency system).
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A Reliable Solutionno line outages result in
overloads
Previous case was augmented with the addition
of a 138 kV Transmission Line
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Generation Changes and The Slack Bus

• The power flow is a steady-state analysis tool,
  so the assumption is total load plus losses is
  always equal to total generation
• Generation mismatch is made up at the slack bus
• When doing generation change power flow studies
  one always needs to be cognizant of where the
  generation is being made up
• Common options include distributed slack, where
  the mismatch is distributed across multiple
  generators by participation factors or by
  economics.

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Generation Change Example 1
Display shows Difference Flows between
original 37 bus case, and case with a BLT138
generation outage note all the power change
is picked up at the slack
Slack bus
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Generation Change Example 2
Display repeats previous case except now the
change in generation is picked up by other
generators using a participation factor
(change is shared amongst generators) approach.
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Voltage Regulation Example 37 Buses
Automatic voltage regulation system controls
voltages.
Display shows voltage contour of the power system
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Real-sized Power Flow Cases

• Real power flow studies are usually done with
  cases with many thousands of buses
• Outside of ERCOT, buses are usually grouped into
  various balancing authority areas, with each area
  doing its own interchange control.
• Cases also model a variety of different automatic
  control devices, such as generator reactive power
  limits, load tap changing transformers, phase
  shifting transformers, switched capacitors, HVDC
  transmission lines, and (potentially) FACTS
  devices.

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Sparse Matrices and Large Systems

• Since for realistic power systems the model sizes
  are quite large, this means the Ybus and Jacobian
  matrices are also large.
• However, most elements in these matrices are
  zero, therefore special techniques, sparse
  matrix/vector methods, are used to store the
  values and solve the power flow
• Without these techniques large systems would be
  essentially unsolvable.

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Eastern Interconnect Example
Example, which models the Eastern
Interconnectcontains about 43,000 buses.
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Solution Log for 1200 MW Outage
In this example thelosss of a 1200 MWgenerator
in NorthernIllinois was simulated. This caused
a generation imbalancein the associated
balancing authorityarea, which wascorrected by
a redispatch of localgeneration.
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Interconnected Operation

• Power systems are interconnected across large
  distances.
• For example most of North America east of the
  Rockies is one system, most of North America west
  of the Rockies is another.
• Most of Texas and Quebec are each interconnected
  systems.

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Balancing Authority Areas

• A balancing authority area (previously called a
  control area) has traditionally represented the
  portion of the interconnected electric grid
  operated by a single utility or transmission
  entity.
• Transmission lines that join two areas are known
  as tie-lines.
• The net power out of an area is the sum of the
  flow on its tie-lines.
• The flow out of an area is equal to total gen -
  total load - total losses tie-line flow

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Area Control Error (ACE)

• The area control error is a combination of
• the deviation of frequency from nominal, and
• the difference between the actual flow out of an
  area and the scheduled (agreed) flow.
• That is, the area control error (ACE) is the
  difference between the actual flow out of an area
  minus the scheduled flow, plus a frequency
  deviation component
• ACE provides a measure of whether an area is
  producing more or less than it should to satisfy
  schedules and to contribute to controlling
  frequency.

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Area Control Error (ACE)

• The ideal is for ACE to be zero.
• Because the load is constantly changing, each
  area must constantly change its generation to
  drive the ACE towards zero.
• For ERCOT, the historical ten control areas were
  amalgamated into one in 2001, so the actual and
  scheduled interchange are essentially the same
  (both small compared to total demand in ERCOT).
• In ERCOT, ACE is predominantly due to frequency
  deviations from nominal since there is very
  little scheduled flow to or from other areas.

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Automatic Generation Control

• Most systems use automatic generation control
  (AGC) to automatically change generation to keep
  their ACE close to zero.
• Usually the control center (either ISO or
  utility) calculates ACE based upon tie-line flows
  and frequency then the AGC module sends control
  signals out to the generators every four seconds
  or so.

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Power Transactions

• Power transactions are contracts between
  generators and (representatives of) loads.
• Contracts can be for any amount of time at any
  price for any amount of power.
• Scheduled power transactions between balancing
  areas are called interchange and implemented by
  setting the value of Psched used in the ACE
  calculation
• ACE Pactual tie-line flow Psched 10ß ?f
• and then controlling the generation to bring ACE
  towards zero.

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Physical power Transactions

• For ERCOT, interchange is only relevant over
  asynchronous connections between ERCOT and
  Eastern Interconnection or Mexico.
• In Eastern and Western Interconnection,
  interchange occurs between areas connected by AC
  lines.

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Three Bus Case on AGCno interchange.
Generation is automatically changed to
match change in load
Net tie-line flow is close to zero
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100 MW Transaction between areas in Eastern or
Western
Scheduled 100 MW Transaction from Left to Right
Net tie-line flow is now 100 MW
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PTDFs

• Power transfer distribution factors (PTDFs) show
  the linearized impact of a transfer of power.
• PTDFs calculated using the fast decoupled power
  flow B matrix

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Nine Bus PTDF Example
Figure shows initial flows for a nine bus power
system
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Nine Bus PTDF Example, cont'd
Figure now shows percentage PTDF flows for a
change in transaction from A to I
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Nine Bus PTDF Example, cont'd
Figure now shows percentage PTDF flows for a
change in transaction from G to F
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WE to TVA PTDFs
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Line Outage Distribution Factors (LODFs)

• LODFs are used to approximate the change in the
  flow on one line caused by the outage of a second
  line
• typically they are only used to determine the
  change in the MW flow compared to the
  pre-contingency flow if a contingency were to
  occur,
• LODFs are used extensively in real-time
  operations,
• LODFs are approximately independent of flows but
  do depend on the assumed network topology.

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Line Outage Distribution Factors (LODFs)
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Line Outage Distribution Factors (LODFs)
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Flowgates

• The real-time loading of the power grid can be
  assessed via flowgates.
• A flowgate flow is the real power flow on one
  or more transmission elements for either base
  case conditions or a single contingency
• Flows in the event of a contingency are
  approximated in terms of pre-contingency flows
  using LODFs.
• Elements are chosen so that total flow has a
  relation to an underlying physical limit.

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Flowgates

• Limits due to voltage or stability limits are
  often represented by effective flowgate limits,
  which are acting as proxies for these other
  types of limits.
• Flowgate limits are also often used to represent
  thermal constraints on corridors of multiple
  lines between zones or areas.
• The inter-zonal constraints that were used in
  ERCOT until December 2010 are flowgates that
  represent inter-zonal corridors of lines.