POWERWORLD SIMULATOR
University of Texas at Austin
By: Mohammad Majidi
Feb 2014
AGENDA
Contingency Analysis
 OPF
 SCOPF
 Examples

2
START CONTINGENCY ANALYSIS
Open case B7SCOPF from the Program
Files/PowerWorld/Simulator/Sample Cases
directory.
 Ensure Simulator is in Run Mode.
 Select Contingency Analysis from the Run
Mode ribbon group on the Tools ribbon tab.
Simulator opens the Contingency Analysis
Dialog.

CONTINGENCY ANALYSIS
DEFINING CONTINGENCIES
Different ways to define contingency:
Load Contingencies from a File
 Auto Insert Contingencies
 Use the local menu to

Insert contingencies
 Quick Insert of Single Element Contingency.

AUTO INSERT CONTINGENCIES
Select
Records>Auto Insert
Contingencies …
RUN CONTINGENCY ANALYSIS
OPTIMAL POWER FLOW OVERVIEW
The goal of an optimal power flow (OPF) is to
determine the “best” way to instantaneously
operate a power system.
 Usually “best” = minimizing operating cost.
 OPF considers the impact of the transmission
system
 We’ll introduce OPF initially ignoring the
transmission system

8
TWO BUS EXAMPLE
Total Hourly Cost :8459 $/hr
Area Lambda : 13.02
Bus A
Bus B
300.0 MW
199.6 MW
AGC ON
300.0 MW
400.4 MW
AGC ON
9
MARKET MARGINAL COST IS DETERMINED
FROM NET GEN COSTS
Below are some graphs associated with this two bus
system. The graph on left shows the marginal cost for each
of the generators. The graph on the right shows the
system supply curve, assuming the system is optimally
dispatched.
16.00
16.00
15.00
15.00
14.00
14.00
13.00
13.00
12.00
12.00
0
175
350
525
Generator Power (MW)
700
0
350
700
1050
Total Area Generation (MW)
Current generator operating point
1400
10
OPTIMAL POWER FLOW (OPF)
 Minimize
cost function, such as operating
cost, taking into account realistic equality
and inequality constraints
 Equality constraints

bus real and reactive power balance
 Inequality

constraints
generator MW limits
…
11
SOLVING THE LP OPF
All LP OPF commands are accessed from the LP OPF
menu item.
 Go to “Add Ons”
 and click on OPF Options and Results”

12
LP OPF OPTIONS: COMMON OPTIONS
13
LP OPF OPTIONS: COMMON OPTIONS
Check it if you want to ignore
transmission constraints.
It will convert OPF to ED
Cost of unenforceable line violations
14
UNENFORCEABLE CONSTRAINT COSTS

If a constraint can not be enforced due to
insufficient controls, the slack variable associated
with enforcing that constraint can not be
removed from the LP basis
marginal cost depends upon the assumed cost of the
slack variable
 this value is specified in the Maximum Violation Cost
field on the LP OPF, Options dialog.

15
MODELING GENERATOR COSTS

Generator costs are modeled with either a cubic
cost or piecewise linear cost function
Cost model is
specified on the
generator dialog
The LP OPF requires a piecewise linear model. Therefore any
existing cubic models are automatically converted to piecewise
16
linear before the solution, and then converted back afterward.
$ / MWh
COMPARISON OF CUBIC AND PIECEWISE LINEAR
MARGINAL COST CURVES
16.0
16.0
12.0
12.0
8.0
8.0
4.0
4.0
0.0
0.0
0
100
200
300
Generator Power (MW)
400
0
100
200
300
Generator Power (MW)
400
Continuous generator marginal Piecewise linear generator
cost curve
marginal cost curve with
five segments
This conversion may affect the final cost. Using more segments
17
better approximates the original curve, but may take longer to solve
OPF CASE INFORMATION DISPLAYS

Several Case Information Displays exist for use
with the OPF











OPF Areas
OPF Buses
OPF Lines and Transformers
OPF DC Lines
OPF Generators
OPF Phase Shifters
OPF Super Areas
OPF Interfaces
OPF Load Records
OPF Transactions
OPF Zones
18
OPF AREA RECORDS DISPLAY
AGC (automatic
generation control)
status must be set
to “OPF” to include
this are in the OPF
objective function
19
OPF AREA RECORDS DISPLAY

Controls Types that are available
XF Phase –specifies if phase‐shifters are available
 Load MW Dispatch –specifies if load can be moved
 DC Line MW -specifies if DC MW setpoint
can be moved


Constraint Types which should be enforced
Branch MVA –should branch limits be enforced
 Interface MW - should interface limits be enforced


Include Marg. Losses

Specifies if marginal losses are used in the OPF
20
OPF GEN RECORDS DISPLAY
21
OPF GEN RECORDS DISPLAY

Fast Start


OPF MW Control (YES, NO, or If Agcable)


The incremental cost of the generator used by the OPF (ma
ybe different than actual IC for cubic cost curve generators)
Initial MW, Cost


Should the generator be made available for OPF dispatch
IC for OPF


Should the generator be available for being turned on/off
by the OPF
The output and cost at the start of the OPF solution
Delta MW, Cost

The change in the output and cost for the last OPF solution
22
COST OF ENERGY, LOSSES AND CONGESTION
Some ISO documents refer to the cost components of energy,
losses, and congestion
 Open Bus7OPF case
 Go to the Add Ons ribbon tab and select OPF Case Info
>OPF Areas




Toggle Include Marg. Losses column of each area to YES
Choose OPF Case Info >Primal LP to resolve.
Now choose OPF Case Info >OPF Options and Results
Go to the Results Tab
 Go the the Bus MW Marginal Price Details subtab

Here you will find columns for the MW Marg Cost, Energy,
23
Congestion and Losses Congestion and Losses

COST OF ENERGY, LOSSES AND CONGESTION
The only value that is truly unique for an OPF so
lution is the total MW Marginal Cost
 The cost of Energy, Losses, and Congestion are
dependent on the reference for Energy and
Losses

24
SCOPF : SECURITY CONSTRAINT OPF
Click on Run Full
security constraint OPF
Make sure you have
already added
contingencies to your
model before running
SCOP.
25
EXAMPELS
26
TWO BUS EXAMPLE - NO CONSTRAINTS
With no
overloads the
OPF matches
the economic
Dispatch(ED)
Bus A
Total Hourly Cost : 8459 $/hr
Area Lambda : 13.01
13.01 $/MWh
Bus B
300.0 MW
197.0 MW
AGC ON
Transmission
line is not
overloaded
13.01 $/MWh
300.0 MW
403.0 MW
AGC ON
Marginal cost of supplying
power to each bus
(locational marginal costs)
27
TWO BUS EXAMPLE WITH CONSTRAINED
LINE
Total Hourly Cost : 9513 $/hr
Area Lambda : 13.26
Bus A
13.43 $/MWh
Bus B
380.0 MW
260.9 MW
AGC ON
13.08 $/MWh
300.0 MW
419.1 MW
AGC ON
With the line loaded to its limit, additional load at Bus A
must be supplied locally, causing the marginal costs to
diverge. (Load at Bus A is increased from 300MW to
380MW)
28
THREE BUS EXAMPLE
Consider a three bus case (bus 1 is system slack), with
all buses connected through 0.1 pu reactance lines,
each with a 100 MVA limit
 Let the generator marginal costs be

Bus 1: 10 $ / MWhr; Range = 0 to 400 MW
 Bus 2: 12 $ / MWhr; Range = 0 to 400 MW
 Bus 3: 20 $ / MWhr; Range = 0 to 400 MW


Assume a single 180 MW load at bus 2
29
B3 WITH LINE LIMITS NOT ENFORCED
Bus 2
60 MW
60 MW
Bus 1
10.00 $/MWh
0 MW
10.00 $/MWh
120 MW
120%
180 MW
0 MW
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 overloaded; all buses
have same
marginal cost30
B3 WITH LINE LIMITS ENFORCED
Bus 2
20 MW
20 MW
Bus 1
10.00 $/MWh
60 MW
12.00 $/MWh
100 MW
100%
80%
120 MW
0 MW
80 MW
80%
Total Cost
1921 $/hr
100%
100 MW
80 MW
14.01 $/MWh
Bus 3
180 MW
0 MW
LP OPF redispatches
to remove violation.
Bus marginal
costs are now
31
different.
WHY IS BUS 3 LMP = $14 /MWH

All lines have equal impedance. Power flow in a
simple network distributes inversely to
impedance of path.
For bus 1 to supply 1 MW to bus 3, 2/3 MW would
take direct path from 1 to 3, while 1/3 MW would
“loop around” from 1 to 2 to 3.
 Likewise, for bus 2 to supply 1 MW to bus 3, 2/3MW
would go from 2 to 3, while 1/3 MW would go from 2
to 1to 3.

32
WHY IS BUS 3 LMP = $ 14 / MWH?
With the line from 1 to 3 limited, no additional
power flows are allowed on it.
 To supply 1 more MW to bus 3 we need

Pg1 + Pg2 = 1 MW
2/3 Pg1 + 1/3 Pg2 = 0; (no more flow on 1-3)

Solving requires we up Pg2 by 2 MW and drop
Pg1 by 1 MW -- a net increase of $14.
33
THREE BUS CASE

View results using the LP OPF, OPF Areas, OPF
Buses, OPF Gens and OPF Line/Transformer
displays
on the OPF Line/Transformer display, toggle the
Enforce MVA field to enable/disable the enforcement
of individual lines.
 verify that the marginal cost of enforcing the line
overload is $ 6 / MVA/hr by changing the line limit
and resolving. Why is it $6?

34
BOTH LINES INTO BUS 3 CONGESTED
0 MW
Bus 2
0 MW
Bus 1
10.00 $/MWh
100 MW
12.00 $/MWh
100 MW
100%
100%
100 MW
0 MW
100 MW
Total Cost
3201 $/hr
100%
100%
100 MW
100 MW
20.00 $/MWh
Bus 3
250 MW
50 MW
For loads above 200
MW on bus 3, the load
must be supplied
locally.
Then what if the bus 3
generator opens?35
MARGINAL COST OF ENFORCING CONSTRAINTS
Similarly to the bus marginal cost, you can also
calculate the marginal cost of enforcing a line
constraint
 For a transmission line, this represents the
amount of system savings which could be
achieved if the MVA rating was increased by
1.0 MVA.

36
MVA MARGINAL COST
Choose OPF Case Info >OPF Lines and
Transformers to bring up the OPF Constraint
Records dialog
 Look at the column MVA Marginal Cost

37
WHY IS MVA MARGINAL COST $6/MVAHR
If we allow 1 more MVA to flow on the line from
1 to 3, then this allows us to redispatchas follows
Pg1 + Pg2 = 0 MW
2/3 Pg1 + 1/3 Pg2 = 1; (no more flow on 1‐3)
‐
 Solving requires we drop Pg2 by 3 MW and
increase Pg1 by 3 MW a net savings of $6

38
THREE BUS CASE
Increase the bus 3 load to 250 MW. Resolve with
line enforcement active. What are the new
LMPs? Why?
 Open the generator at bus 3 and then resolve.
Does this case have a solution? Why? Are the
LMPs valid?

39
CASE WITH G3 OPENED
UNENFORCEABLE CONSTRAINTS
Bus 2
53 MW
53 MW
Bus 1
10.00 $/MWh
47 MW
12.00 $/MWh
151 MW
152%
100%
203 MW
0 MW
99 MW
99%
Total Cost
2594 $/hr
151%
151 MW
99 MW
1040.55 $/MWh
Bus 3
250 MW
0 MW
Both constraints
can not be enforced.
One is unenforceable. Bus 3
marginal cost is
arbitrary
40
UNENFORCEABLE CONSTRAINT COSTS


Is this solution Valid? Not really.
If a constraint cannot be enforced due to insuffici
ent controls the slack variable
associated with enforcing that constraint cannot
be removed from the LP basis
marginal cost depends upon the arbitrary cost of the
slack variable the slack variable
 this value is specified in the Maximum ViolationCost
field on the LP OPF, Options dialog

41
SEVEN BUS CASE
Load the B7FlatLP case.
 What are the marginal costs of enforcing the line
constraints? How do the system costs change if
the line constraints are relaxed (i.e, not
enforced)? For example, try solving without
enforcing line 1 to 2.

42
SEVEN BUS CASE

Modify the cost model for the generator at bus
one.
How does changing from piece-wise linear to cubic
affect the final solution?
 How do the generation conversion parameters on the
option dialog affect the results?


Try resolving the case with different lines
removed from service.
43
PROFIT MAXIMIZATION
 If
the bus 7 generator has a marginal cost
equal 7$/MWh and were paid its bus LMP
* its output, its profit would be
Profit = LMP * MW - 7 * MW
 The
question then is what should they bid
to maximize their profit? This problem
can be solved using the OPF with
different assumed generator costs.
44
QUESTIONS?
45