ecen 615 methods of electric power systems analysis...
TRANSCRIPT
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Lecture 9: Advanced Power Flow, Gaussian
Elimination, Sparse Systems
ECEN 615Methods of Electric Power Systems Analysis
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
Texas A&M University
mailto:[email protected]
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Announcements
• Read Chapter 6
• Homework 2 is due on Sept 27
2
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Area Interchange Example: Seven Bus, Three Area System
3PowerWorld Case: B7Flat
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Example Large System Areas
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Each oval
corresponds to a
power flow area
with the size
proportional to
the area’s
generation
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Generator Volt/Reactive Control
• Simplest situation is a single generator at a bus
regulating its own terminal
• Either PV, modeled as a voltage magnitude constraint, or as a
PQ with reactive power fixed at a limit value. If PQ the
reactive power limits can vary with the generator MW output
• Next simplest is multiple generators at a bus. Obviously
they need to be regulating the bus to the same voltage
magnitude
• From a power flow solution perspective, it is similar to a single
generator, with limits being the total of the individual units
• Options for allocation of vars among generators; this can affect
the transient stability results
5
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Generator Volt/Reactive Control
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Case is Aggieland37_
Gen_VoltVar
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Generator Volt/Reactive Control
• Next complication is generators at a single bus
regulating a remote bus; usually this is the high side of
their generator step-up (GSU) transformer
• When multiple generators regulate a single point their exciters
need to have a dual input
• This can be implemented in the power flow for the generators
at bus j regulating the voltage at bus k by changing the bus j
voltage constraint equation to be
(however, this does create a zero on the diagonal of the
Jacobian)
• Helps with power system voltage stability 7
, 0k k setV V
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Generator Volt/Reactive Control
• The next complication is to have the generators at
multiple buses doing coordinated voltage control
• Controlled bus may or may not be one of the terminal buses
• There must be an a priori decision about how much
reactive power is supplied by each bus; example
allocations are a fixed percentage or placing all
generators at the same place in their regulation range
• Implemented by designating one bus as the master; this
bus models the voltage constraint
• All other buses are treated as PQ, with the equation
including a percent of the total reactive power output of
all the controlling bus generators 8
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Remote and Coordinated Var Control Example
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GIGEM69
KYLE69
KYLE138
WEB138
WEB69
BONFIRE69
FISH69
RING69
TREE69
CENTURY69
REVEILLE69MAROON69
SPIRIT69
YELL69
RELLIS69
WHITE138
RELLIS138
BUSH69
MSC69
RUDDER69
HULLABALOO138
REED69
REED138
AGGIE138 AGGIE345
16%A
MVA
33%A
MVA
78%A
MVA
78%A
MVA
18%A
MVA
55%A
MVA
14%A
MVA
54%A
MVA
60%A
MVA
16%A
MVA
49%A
MVA
49%A
MVA
45%A
MVA
50%A
MVA
49%A
MVA
49%A
MVA
35%A
MVA
A
MVA
57%A
MVA
45%A
MVA
A
MVA
72%A
MVA
75%A
MVA
33%A
MVA
68%A
MVA
33%A
MVA
39%A
MVA
68%A
MVA
68%A
MVA
22%A
MVA
A
MVA
19%A
MVA
52%A
MVA
57%A
MVA
39%A
MVA
63%A
MVA
70%A
MVA
70%A
MVA
0.97 pu
0.945 pu0.98 pu
0.96 pu
0.982 pu
0.97 pu
0.950 pu
0.972 pu0.97 pu
0.98 pu
1.000 pu
1.01 pu
0.993 pu
0.992 pu
0.975 pu0.98 pu
0.96 pu
0.96 pu 0.95 pu
0.981 pu
0.976 pu0.96 pu
1.01 pu1.03 pu
PLUM138
1.01 pu
14%A
MVA
0.97 pu
61%A
MVA
34 MW
0 Mvar
59 MW
17 Mvar
20 MW
8 Mvar
100 MW
30 Mvar
61 MW 17 Mvar
59 MW
6 Mvar
69 MW
0 Mvar
93 MW
58 Mvar
58 MW
17 Mvar
36 MW
24 Mvar
96 MW
20 Mvar
93 MW
65 Mvar 82 MW
27 Mvar
0.0 Mvar
35 MW
11 Mvar
25 MW
10 Mvar
38 MW 10 Mvar
22 MW
0 Mvar
0.0 Mvar
0.0 Mvar
0.0 Mvar
0.0 Mvar
0.0 Mvar
0.0 Mvar
31 MW
13 Mvar
49 MW
17 Mvar
deg 0
tap1.0875
tap1.0000
tap1.0213tap1.0213
3.4 Mvar
52.8 Mvar
pu 1.031
pu 0.993 10.0 Mvar
20.4 Mvar
39.2 Mvar
95%A
MVA
Each oval
corresponds to a
power flow area
with the size
proportional to
the area’s
generation
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Model Complexity Examples
• A recent 76,000 bus Eastern Interconnect (EI) power
flow model has voltage magnitudes controlled at about
19,000 buses (by Gens, LTCs, switched shunts) 94%
regulate their own terminals with about 1100 doing
remote regulation. Of this group 572 are regulated by
two or more devices, 277 by three or more, 12 by eight
or more, and three by 12 devices!
• It also has 27,622 transformers with 98 phase shifters
• Impedance correction tables are used for 351, including about
2/3 of the phase shifters; tables can change the impedance by
more than two times
10
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PV Bus Voltage Droop
• Traditionally the PV bus approach considered either 1)
on control at setpoint or 2) at a limit
• Increasingly this is no longer the case, particularly for
wind and solar. Rather regulation has a droop
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PV Bus Voltage Droop
• This actually allows for multiple generators to regulate
a single remote bus using different characteristics
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B2
RegBus
Generators are
all configured to
regulate the
RegBus
B3
B1
A2
A3
A1
“Arriving
Branches”
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PV Droop Implementation
• PowerWorld just implemented this using a voltage
droop control object
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B7Flat Example with PV Deadband
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Case is B7Flat_PVDroop
Research opportunity with the synthetic models to discuss
the impact of deadbands on, say, voltage stability
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Example of Hourly Voltage Variation Over Time
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Power Flow Topology Processing
• Commercial power flow software must have
algorithms to determine the number of asynchronous,
interconnected systems in the model
• These separate systems are known as Islands
• In large system models such as the Eastern Interconnect it is
common to have multiple islands in the base case (one recent
EI model had nine islands)
• Islands can also form unexpectedly as a result of
contingencies
• Power can be transferred between islands using dc lines
• Each island must have a slack bus
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Power Flow Topology Processing
• Anytime a status change occurs the power flow
must perform topology processing to determine
whether there are either 1) new islands or 2) islands
have merged
• Determination is needed to determine whether the
island is “viable.” That is, could it truly function as
an independent system, or should the buses just be
marked as dead
• A quite common occurrence is when a single load or
generator is isolated; in the case of a load it can be
immediately killed; generators are more tricky
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Topology Processing Algorithm
• Since topology processing is performed often, it must
be quick (order n ln(n))!
• Simple, yet quick topology processing algoritm
• Set all buses as being in their own island (equal to bus
number)
• Set ChangeInIslandStatus true
• While ChangeInIslandStatus Do
• Go through all the in-service lines, setting the islands for each of the
buses to be the smaller island number; if the island numbers are
different set ChangeInIslandStatus true
• Determine which islands are viable, assigning a slack bus as
necessary
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Example of Island Formation
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Top Area Cost
Left Area Cost Right Area Cost slack
1.00 pu
1.01 pu
1.04 pu1.04 pu
1.04 pu
0.99 pu1.05 pu
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
62 MW
61 MW
44 MW 42 MW 31 MW 31 MW
38 MW
37 MW
80 MW 78 MW
32 MW
33 MW
14 MW
38 MW
39 MW 20 MW 21 MW
42 MW
41 MW
A
MVA
21 MW 20 MW
8078 $/h
4652 $/h 4189 $/h
Case Hourly Cost 16919 $/h
Bus 1 Bus 3 Bus 4
Bus 2 Bus 5
Bus 6 Bus 7
MW106
MW171
MW200 MW198
110 MW
40 Mvar
80 MW 30 Mvar
130 MW 40 Mvar
40 MW
20 Mvar
MW 94
200 MW
0 Mvar200 MW
0 Mvar
AGC ON
AGC ON
AGC ON
AGC ON
AGC ON
80%A
MVA
Splitting large systems requires a careful consideration
of the flow on the island tie-lines as they are opened
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Bus Branch versus Node Breaker
• Due to a variety of issues during the 1970’s and 1980’s
the real-time operations and planning stages of power
systems adopted different modeling approaches
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PlanningUse simplified bus/branch model
PC approach
Use of files
Stand-alone applications
Real-Time OperationsUse detailed node/breaker model
EMS system as a set of integrated applications and processes
Real-time operating system
Real-time databases
Entire data sets and software tools developed around
these two distinct power system models
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Circuit Breakers and Disconnects
• Circuit breakers are devices that are designed to clear
fault current, which can be many times normal
operating current
• AC circuit breakers take advantage of the current going
through zero twice per cycle
• Transmission faults can usually be cleared in less than three
cycles
• Disconnects cannot clear fault current, and usually not
normal current. They provide a visual indication the
line is open. Can be manual or motorized.
• In the power flow they have essentially no impedance;
concept of a zero branch reactance (ZBR)21
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Google View of a 345 kV Substation
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Substation Configurations
• Several different substation breaker/disconnect
configurations are common:
• Single bus: simple but a fault
any where requires taking out the
entire substation; also doing breaker
or disconnect maintenance requires
taking out the associated line
23Source: http://www.skm-eleksys.com/2011/09/substation-bus-schemes.html
http://4.bp.blogspot.com/-9g6rjqRAD0I/ToXk6oQSRUI/AAAAAAAAApY/-4th5mJTvDY/s1600/SingleBus.png
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Substation Configurations, cont.
• Main and Transfer Bus:
Now the breakers can be taken
out for maintenance without
taking out a line, but protection
is more difficult, and a fault
on one line will take out at least two
• Double Bus Breaker:
Now each line is fully protected
when a breaker is out, so high
reliability, but more costly
24Source: http://www.skm-eleksys.com/2011/09/substation-bus-schemes.html
http://3.bp.blogspot.com/-yBG8xB2VDog/ToXlwGl-CbI/AAAAAAAAApc/4v4fTK9Ixbc/s1600/MainandTransferBus.pnghttp://3.bp.blogspot.com/-9Se44Ew3i_c/ToXmQZRcZzI/AAAAAAAAApg/al1E7kRV1L0/s1600/DoubleBusDoubleBreaker.png
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Ring Bus, Breaker and Half
• As the name implies with a ring
bus the breakers form a ring;
number of breakers is same as
number of devices; any breaker can
be removed for maintenance
• The breaker and half has two buses
and uses three breakers for two
devices; both breakers and buses
can be removed for maintenance
25Source: http://www.skm-eleksys.com/2011/09/substation-bus-schemes.html
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• EMS Model
– Used for real-time operations
– Called full topology model
– Has node-breaker detail
• Planning Model
– Used for off-line analysis
– Called consolidated model
by PowerWorld
– Has bus/branch detail
EMS and Planning Models
50 MW
20 Mvar
-30 MW
-18 Mvar
-40 MW
-10 Mvar
10 MW
3 Mvar10 MW
5 Mvar
-30 MW
-18 Mvar
-40 MW
-10 Mvar
10 MW
3 Mvar
10 MW
5 Mvar
26
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Node-Breaker Consolidation
• One approach to modeling systems with large numbers
of ZBRs (zero branch reactances, such as from circuit
breakers) is to just assume a small reactance and solve
– This results in lots of buses and branches, resulting in a much
larger problem
– This can cause numerical problems in the solution
• The alterative is to consolidate the nodes that are
connected by ZBRs into a smaller number of buses
– After solution all nodes have the same voltage; use logic to
determine the device flows
27
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Node-Breaker Example
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Case name is FT_11Node. PowerWorld consolidates
nodes (buses) into super buses; available in the Model
Explorer: Solution, Details, Superbuses
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Node-Breaker Example
Note there is ambiguity on how much power is flowing
in each device in the ring bus (assuming each device
really has essentially no impedance)29