© 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

200

400

600

800

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

200

400

600

800

1000

1200

1400

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

200

400

600

800

1000

1200

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)