ETAP - optimal power flow (OPF)

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)