ECE 476
Power System Analysis
Lecture 6: Power System Operations,
Transmission Line Parameters
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
overbye@illinois.edu
Announcements
• Please read Chapter 4
• Quiz today on HW 2
• HW 3 is 4.8, 4.10, 4.18, 4.23
•
•
•
It does not need to be turned in, but will be covered by an
in-class quiz on Sept 17
Positive sequence is same as per phase; it will be covered
in Chapter 8
Use Table A.4 values to determine the Geometric Mean
Radius of the wires (i.e., the ninth column).
Generator Costs
• There are many fixed and variable costs associated
with power system operation.
• The major variable cost is associated with
generation.
• Cost to generate a MWh can vary widely.
• For some types of units (such as hydro and nuclear)
it is difficult to quantify.
• For thermal units it is much easier. These costs
will be discussed later in the course.
2
Economic Dispatch
• Economic dispatch (ED) determines the least cost
dispatch of generation for an area.
• For a lossless system, the ED occurs when all the
generators have equal marginal costs.
IC1(PG,1) = IC2(PG,2) = … = ICm(PG,m)
3
Power Transactions
• Power transactions are contracts between areas to
do power transactions.
• Contracts can be for any amount of time at any
price for any amount of power.
• Scheduled power transactions are implemented by
modifying the area ACE:
ACE = Pactual,tie-flow - Psched
4
100 MW Transaction
Bus 2
8 MW
-2 MVR
-8 MW
2 MVR
Bus 1
1.00 PU
225 MW
113 MVR
1.00 PU
0 MW
32 MVR
150 MW AGC ON
138 MVR AVR ON
-92 MW
-84 MW
27 MVR
30 MVR
85 MW
-23 MVR
Home Area
93 MW
-25 MVR
Bus 3
Scheduled Transactions
100.0 MW
1.00 PU
113 MW
56 MVR
291 MW AGC ON
8 MVR AVR ON
100 MW
Net tie-line
flow is now
100 MW
Scheduled 100 MW
Transaction from Left to Right
5
Security Constrained ED
• Transmission constraints often limit system
economics.
• Such limits required a constrained dispatch
in order to maintain system security.
• In three bus case the generation at bus 3
must be constrained to avoid overloading the
line from bus 2 to bus 3.
6
Security Constrained Dispatch
Bus 2
-22 MW
4 MVR
22 MW
-4 MVR
Bus 1
1.00 PU
357 MW
179 MVR
1.00 PU
0 MW
37 MVR
100%
194 MW OFF AGC -142 MW
49 MVR
232 MVR AVR ON
145 MW 100%
-37 MVR
Home Area
Bus 3
Scheduled Transactions
100.0 MW
-122 MW
41 MVR
100 MW
124 MW
-33 MVR
1.00 PU
179 MW
89 MVR
448 MW AGC ON
19 MVR AVR ON
Dispatch is no longer optimal due to need to keep line
from bus 2 to bus 3 from overloading
7
Multi-Area Operation
• If Areas have direct interconnections, then they
may directly transact up to the capacity of their tielines.
• Actual power flows through the entire network
according to the impedance of the transmission
lines.
• Flow through other areas is known as “parallel
path” or “loop flows.”
8
Seven Bus Case: One-line
System has
three areas
44 MW
-42 MW
-31 MW
0.99 PU
3
1.05 PU
1
106 MW -37 MW
AGC ON
62 MW
79 MW
2
40 MW
20 MVR
Top Area Cost
8029 $/MWH
1.00 PU
-32 MW
Case Hourly Cost
16933 $/MWH
32 MW
80 MW
30 MVR
4
110 MW
40 MVR
38 MW
-61 MW
1.04 PU
31 MW
-77 MW
5
-39 MW
40 MW
94 MW
AGC ON
Area top
has five
buses
-14 MW
1.01 PU
130 MW
40 MVR
168 MW AGC ON
-40 MW
1.04 PU
6
20 MW
-20 MW
40 MW
1.04 PU
20 MW
200 MW
0 MVR Left Area Cost
4189 $/MWH
200 MW AGC ON
Area left has one bus
-20 MW
7
200 MW
Right Area Cost
0 MVR
4715 $/MWH
201 MW AGC ON
Area right has one bus
9
Seven Bus Case: Area View
Top
40.1 MW
0.0 MW
Area Losses
7.09 MW
-40.1 MW
0.0 MW
System has
40 MW of
“Loop Flow”
Left
Area Losses
0.33 MW
Right
40.1 MW
0.0 MW
Actual
flow
between
areas
Scheduled
flow
Area Losses
0.65 MW
Loop flow can result in higher losses
10
Seven Bus - Loop Flow?
Top
4.8 MW
0.0 MW
-4.8 MW
0.0 MW
Left
Area Losses
-0.00 MW
100 MW Transaction
between Left and Right
Area Losses
9.44 MW
Right
104.8 MW
100.0 MW
Note that
Top’s
Losses have
increased
from
7.09MW to
9.44 MW
Area Losses
4.34 MW
Transaction has
actually decreased
the loop flow
11
Pricing Electricity
• Cost to supply electricity to bus is called the
locational marginal price (LMP)
• Presently some electric makets post LMPs on the
web
• In an ideal electricity market with no transmission
limitations the LMPs are equal
• Transmission constraints can segment a market,
resulting in differing LMP
• Determination of LMPs requires the solution on an
Optimal Power Flow (OPF)
12
3 BUS LMPS - OVERLOAD IGNORED
Bus 2
Gen 2’s
cost
is $12
per
MWh
60 MW
60 MW
Bus 1
10.00 $/MWh
0 MW
10.00 $/MWh
120 MW
120%
180 MW
0 MW
Gen 1’s
cost
is $10
per
MWh
60 MW
Total Cost
1800 $/hr
120%
120 MW
60 MW
10.00 $/MWh
Bus 3
180 MW
0 MW
Line from Bus 1 to Bus 3 is over-loaded; all
buses have same marginal cost
13
LINE OVERLOAD ENFORCED
Bus 2
20 MW
20 MW
Bus 1
10.00 $/MWh
60 MW
12.00 $/MWh
100 MW
80%
100%
120 MW
0 MW
80 MW
Total Cost
1921 $/hr
80%
100%
100 MW
80 MW
14.01 $/MWh
Bus 3
180 MW
0 MW
Line from 1 to 3 is no longer overloaded, but now
the marginal cost of electricity at 3 is $14 / MWh
14
MISO LMPs 9/5/15 at 8:45 AM
https://www.misoenergy.org/LMPContourMap/MISO_All.html
Development of Line Models
•
Goals of this section are
1) develop a simple model for transmission lines
2) gain an intuitive feel for how the geometry of the
transmission line affects the model parameters
Primary Methods for Power Transfer
• The most common methods for transfer of electric
power are
–
–
–
–
–
Overhead ac
Underground ac
Overhead dc
Underground dc
other
345 kV+ Transmission Growth at a
Glance
18
345 kV+ Transmission Growth at a
Glance
19
345 kV+ Transmission Growth at a
Glance
20
345 kV+ Transmission Growth at a
Glance
21
345 kV+ Transmission Growth at a
Glance
22
Grid Weakness
Ameren Illinois Rivers 345 kV Project
• Ameren is in the process of building a number of 345
kV transmission lines across Central Illinois.
•
Locally this includes a line between Sidney and Rising
in Champaign County
http://www.ilriverstransmission.com/maps
Sidney to Bunsonville 345 kV
Sidney to Kansas (IL) 345
Sidney to Rising 345 kV
Sidney to Rising 345 kV
Champaign-Urbana Part of Grid
Line Conductors
• Typical transmission lines use multi-strand
conductors
• ACSR (aluminum conductor steel reinforced)
conductors are most common. A typical Al. to St.
ratio is about 4 to 1.