This document discusses optimal power flow (OPF) analysis, which determines optimal settings for control variables like generator outputs and transformer taps to minimize objectives like power losses while satisfying operating constraints. The key aspects covered include: the differences between standard load flow and OPF; examples of optimization problems; common objective functions and control variables used in OPF; and the use of an OPF study case editor to set up optimization problems.

1. © 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Optimal Power Flow
(OPF)

2. Slide 2© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Table of Contents
• Review of Load Flow Solution
• Optimal Power Flow Approach
• Comparison of LF and OPF
• Optimization Examples
• Power Balance Equation
• Control Variables
• Objective Functions
• Other Constraints
• OPF Study Case Editor

3. Slide 3© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Review of Load Flow
Solution
• Given generation, loading and control
settings (Mwgen, Vgen, LTC, Capacitor
Bank, …)
• Solve bus voltages and branch flows
• Check over/under voltage, device
overloading conditions
• Reset controls and run Load Flow again
• Iterative process

4. Slide 4© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Optimal Power Flow
Approach
• Given control setting ranges
• Specify bus voltage and branch loading
constraints
• Select optimization objectives (Min. P
Losses, Min. Q Losses, …)
• Solve bus voltages, branch flows and control
settings
• Direct solution

5. Slide 5© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Comparison of LF and OPF

6. Slide 6© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Optimization Example 1
• Objective function: Min. y(x) = 20x2 –80x–10
• Control variable x range: 0 x 10
Non-constrained
-200
0
200
400
600
800
1000
1200
1400
0 5 10 15
X
Y
Solution Found

7. Slide 7© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Optimization Example 2
• Objective function: Min. y(x) = 20x2 –80x–10
• Control variable x range: 0 x 10
• Balance equation y = 60x – 100
Solution Found
Constrained (Solution Found)
-200
0
200
400
600
800
1000
1200
1400
0 5 10 15
X
Y

8. Slide 8© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Optimization Example 3
• Objective function: Min. y(x) = 20x2 –80x–10
• Control variable x range: 0 x 10
• Balance equation y = 20x – 300
Solution not
found!
(Infeasible)
Constrained (No Solution)
-400
-200
0
200
400
600
800
1000
1200
1400
0 5 10 15
X
Y

9. Slide 9© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Pgen – Pload – Ploss = 0
Qgen – Qload – Qloss = 0
P = 0 and Q = 0
Power Balance Equation
Load Flow Solves
Power Balance Equation Only

10. Slide 10© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Control Variables
• Load Tap Changer (LTC) Settings
• Generator AVR Settings
• Generator MW Generation
• Series or Shunt VAR Compensator Settings
• Phase Shift Transformer Tap Positions
• Switched Capacitor Settings
• Load Shedding
• DC Line Flow
• …

11. Slide 11© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Objective Functions
• Minimize Real Power Losses
- To minimize real power losses in the system
• Minimize Reactive Power Losses
- To minimize reactive power losses in the system
• Minimize Swing Bus Power
- To minimize real power generation at the swing
bus(s)

12. Slide 12© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Objective Functions
• Minimize Shunt var Devices
- To minimize var generation from available shunt
var control devices
• Minimize Fuel Cost
- To minimize total generation fuel cost
• Minimize Series Compensation
- To minimize var generation from available
series var control devices

13. Slide 13© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Objective Functions
• Minimize Load Shedding
- To minimize load to be shed from the available
bus load shed schedule
• Minimize Control Movement
- To minimize total number of controls
• Minimize Control Adjustment
- To minimize overall adjustment from all controls

14. Slide 14© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Objective Functions
• Maximize Voltage Security Index
Where,
AllBuses
i
n
i
avgii
dV
VV
2
,
IndexSecurityVoltage
2
min,max,
,
ii
avgi
VV
V
2
min,max, ii
i
VV
dV

15. Slide 15© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
• Maximize Line Flow Security Index
Where, is the line rating
• Flat Voltage Profile
- Voltage Magnitude difference between all
buses is minimum
Objective Functions
sAllBranche
i
n
i
i
S
S
2
IndexSecurityFlowLine
iSd

16. Slide 16© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Other Constraints
• Bus Voltage Constraints
• Branch Flow Constraints
• Interface Flow Constraints
• …

17. Slide 17© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Objectives)

18. Slide 18© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Controls)

19. Slide 19© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Controls)

20. Slide 20© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Controls)

21. Slide 21© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Controls)

22. Slide 22© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Constraints)

23. Slide 23© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor
(Constraints)