Optimal Power Flow (OPF) - Optimal Power Flow.pdf · © 1996-2009 Operation Technology, Inc....
Transcript of Optimal Power Flow (OPF) - Optimal Power Flow.pdf · © 1996-2009 Operation Technology, Inc....
© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Optimal Power Flow
(OPF)
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
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
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
Slide 5© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Comparison of LF and OPF
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
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1000
1200
1400
0 5 10 15
X
Y
Solution Found
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
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0 5 10 15
X
Y
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
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1400
0 5 10 15
X
Y
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
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
• …
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)
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
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
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
VV2
,IndexSecurity Voltage
2
min,max,
,
ii
avgi
VVV
2
min,max, ii
i
VVdV
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
S2
IndexSecurity Flow Line
iSd
Slide 16© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
Other Constraints
• Bus Voltage Constraints
• Branch Flow Constraints
• Interface Flow Constraints
• …
Slide 17© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Objectives)
Slide 18© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Controls)
Slide 19© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Controls)
Slide 20© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Controls)
Slide 21© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Controls)
Slide 22© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Constraints)
Slide 23© 1996-2009 Operation Technology, Inc. – Workshop Notes: Optimal Power Flow
OPF Study Case Editor (Constraints)