ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and...

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ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana- Champaign [email protected]

description

Two Bus Newton-Raphson Example For the two bus power system shown below, use the Newton-Raphson power flow to determine the voltage magnitude and angle at bus two. Assume that bus one is the slack and S Base = 100 MVA. 2

Transcript of ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and...

Page 1: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

ECE 476 Power System Analysis

Lecture 13: Power Flow

Prof. Tom OverbyeDept. of Electrical and Computer Engineering

University of Illinois at [email protected]

Page 2: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Announcements

• Read Chapter 6• H6 is 6.19, 6.30, 6.31, 6.34, 6.38, 6.45. It does not

need to be turned in, but will be covered by an in-class quiz on Oct 15

• Power and Energy scholarships will be decided on Monday; application on website; apply to Prof. Sauer

• Grainger Awards due on Nov 1; application on website; apply to Prof. Sauer

• energy.ece.illinois.edu/

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Page 3: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Newton-Raphson Example

Line Z = 0.1j

One Two 1.000 pu 1.000 pu

200 MW 100 MVR

0 MW 0 MVR

For the two bus power system shown below, use the Newton-Raphson power flow to determine the voltage magnitude and angle at bus two. Assumethat bus one is the slack and SBase = 100 MVA.

2

2

10 1010 10busj j

V j j

x Y

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Page 4: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Example, cont’d

i1

i1

2 1 22

2 1 2 2

General power balance equations

P ( cos sin )

Q ( sin cos )

Bus two power balance equations(10sin ) 2.0 0

( 10cos ) (10) 1.0 0

n

i k ik ik ik ik Gi Dikn

i k ik ik ik ik Gi Dik

V V G B P P

V V G B Q Q

V V

V V V

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Page 5: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Example, cont’d

2 2 22

2 2 2 2

2 2

2 2

2 2

2 2

2 2 2

2 2 2 2

P ( ) (10sin ) 2.0 0

( ) ( 10cos ) (10) 1.0 0Now calculate the power flow Jacobian

P ( ) P ( )

( )Q ( ) Q ( )

10 cos 10sin10 sin 10cos 20

V

Q V V

VJ

V

VV V

x

x

x x

xx x

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Page 6: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Example, First Iteration

(0)

2 2(0)2

2 2 2

2 2 2(0)

2 2 2 2

(1)

0Set 0, guess

1Calculate

(10sin ) 2.0 2.0f( )

1.0( 10cos ) (10) 1.0

10 cos 10sin 10 0( )

10 sin 10cos 20 0 10

0 10 0Solve

1 0 10

v

V

V V

VV V

x

x

J x

x1 2.0 0.2

1.0 0.9

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Page 7: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Example, Next Iterations

(1)2

(1)

1(2)

0.9(10sin( 0.2)) 2.0 0.212f( )

0.2790.9( 10cos( 0.2)) 0.9 10 1.08.82 1.986

( )1.788 8.199

0.2 8.82 1.986 0.212 0.2330.9 1.788 8.199 0.279 0.8586

f(

x

J x

x

(2) (3)

(3)2

0.0145 0.236)

0.0190 0.85540.0000906

f( ) Done! V 0.8554 13.520.0001175

x x

x

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Page 8: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Solved Values

Line Z = 0.1j

One Two 1.000 pu 0.855 pu

200 MW 100 MVR

200.0 MW168.3 MVR

-13.522 Deg

200.0 MW 168.3 MVR

-200.0 MW-100.0 MVR

Once the voltage angle and magnitude at bus 2 are known we can calculate all the other system values,such as the line flows and the generator reactive power output

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Page 9: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Case Low Voltage Solution

(0)

2 2(0)2

2 2 2

This case actually has two solutions! The second "low voltage" is found by using a low initial guess.

0Set 0, guess

0.25Calculate

(10sin ) 2.0f( )

( 10cos ) (10) 1.0

v

V

V V

x

x

2 2 2(0)

2 2 2 2

20.875

10 cos 10sin 2.5 0( )

10 sin 10cos 20 0 5VV V

J x

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Page 10: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Low Voltage Solution, cont'd

1(1)

(2) (2) (3)

0 2.5 0 2 0.8Solve

0.25 0 5 0.875 0.0751.462 1.42 0.921

( )0.534 0.2336 0.220

x

f x x x

Line Z = 0.1j

One Two 1.000 pu 0.261 pu

200 MW 100 MVR

200.0 MW831.7 MVR

-49.914 Deg

200.0 MW 831.7 MVR

-200.0 MW-100.0 MVR

Low voltage solution

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Page 11: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Two Bus Region of Convergence

Slide shows the region of convergence for different initialguesses of bus 2 angle (x-axis) and magnitude (y-axis)

Red regionconvergesto the highvoltage solution,while the yellow regionconvergesto the lowvoltage solution

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Page 12: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

PV Buses

• Since the voltage magnitude at PV buses is fixed there is no need to explicitly include these voltages in x or write the reactive power balance equations– the reactive power output of the generator varies to

maintain the fixed terminal voltage (within limits)– optionally these variations/equations can be included by

just writing the explicit voltage constraint for the generator bus

|Vi | – Vi setpoint = 0

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Page 13: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Three Bus PV Case Example

Line Z = 0.1j

Line Z = 0.1j Line Z = 0.1j

One Two 1.000 pu 0.941 pu

200 MW 100 MVR

170.0 MW 68.2 MVR

-7.469 Deg

Three 1.000 pu

30 MW 63 MVR

2 2 2 2

3 3 3 3

2 2 2

For this three bus case we have( )

( ) ( ) 0V ( )

G D

G D

D

P P PP P PQ Q

xx f x x

x

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Page 14: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Generator Reactive Power Limits

• The reactive power output of generators varies to maintain the terminal voltage; on a real generator this is done by the exciter

• To maintain higher voltages requires more reactive power

• Generators have reactive power limits, which are dependent upon the generator's MW output

• These limits must be considered during the power flow solution

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Page 15: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Generator Reactive Limits, cont'd

• During power flow once a solution is obtained check to make generator reactive power output is within its limits

• If the reactive power is outside of the limits, fix Q at the max or min value, and resolve treating the generator as a PQ bus– this is know as "type-switching"– also need to check if a PQ generator can again regulate

• Rule of thumb: to raise system voltage we need to supply more vars

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Page 16: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

400 MVA15 kV

400 MVA15/345 kV

T1

T2800 MVA345/15 kV

800 MVA15 kV

520 MVA

80 MW40 Mvar

280 Mvar 800 MW

Line 3 345 kV

Line

2

Line

1345 kV 100 mi

345 kV 200 mi

50 mi

1 4 3

2

5

Single-line diagram

The N-R Power Flow: 5-bus Example

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Page 17: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Bus TypeV per unit

degrees

PG

perunit

QG

perunit

PL

perunit

QL

perunit

QGmax

perunit

QGmin

perunit

1 Swing 1.0 0 0 0

2 Load 0 0 8.0 2.8

3 Constant voltage

1.05 5.2 0.8 0.4 4.0 -2.8

4 Load 0 0 0 0

5 Load 0 0 0 0

Table 1. Bus input data

Bus-to-Bus

R’ per unit

X’per unit

G’per unit

B’per unit

MaximumMVA

per unit

2-4 0.0090 0.100 0 1.72 12.0

2-5 0.0045 0.050 0 0.88 12.0

4-5 0.00225 0.025 0 0.44 12.0

Table 2. Line input data

The N-R Power Flow: 5-bus Example

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Page 18: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Bus-to-Bus

R perunit

Xperunit

Gc

perunit

Bm

perunit

MaximumMVA

per unit

MaximumTAP

Settingper unit

1-5 0.00150 0.02 0 0 6.0 —

3-4 0.00075 0.01 0 0 10.0 —

Table 3. Transformer input data

Bus Input Data Unknowns

1 V1 = 1.0, 1 = 0 P1, Q1

2 P2 = PG2-PL2 = -8Q2 = QG2-QL2 = -2.8

V2, 2

3 V3 = 1.05P3 = PG3-PL3 = 4.4

Q3, 3

4 P4 = 0, Q4 = 0 V4, 4

5 P5 = 0, Q5 = 0 V5, 5

Table 4. Input data and unknowns

The N-R Power Flow: 5-bus Example

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Page 19: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Time to Close the Hood: Let the Computer Do the Math! (Ybus Shown)

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Page 20: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Ybus Details

02321 YY

24 ' '24 24

1 1 0.89276 9.919640.009 0.1

Y j per unitR jX j

unitperjjjXR

Y 83932.1978552.105.00045.0

11'25

'25

25

2211 '

25'24

'25

'25

'24

'24

22BjBj

jXRjXRY

288.0

272.1)83932.1978552.1()91964.989276.0( jjjj

unitperj 624.845847.284590.2867828.2

Elements of Ybus connected to bus 2

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Page 21: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Here are the Initial Bus Mismatches

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Page 22: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

And the Initial Power Flow Jacobian

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Page 23: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

])0()0(cos[){0()()0( 211212122222 VYVPxPPP])0()0(cos[]cos[ 233232322222 VYVY

])0()0(cos[ 2442424 VY]})0()0(cos[ 2552525 VY

)624.84cos()0.1(5847.28{0.10.8 )143.95cos()0.1(95972.9 )}143.95cos()0.1(9159.19

unitper99972.7)1089.2(0.8 4

])0()0(sin[)0()0()0(1 2442424224 VYVJ

]143.95sin[)0.1)(95972.9)(0.1( unitper91964.9

And the Hand Calculation Details!

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Page 24: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Five Bus Power System Solved

slack

One

Two

ThreeFourFiveA

MVA

A

MVA

A

MVA

A

MVA

A

MVA

1.000 pu 0.974 pu

0.834 pu

1.019 pu

1.050 pu 0.000 Deg -4.548 Deg

-22.406 Deg

-2.834 Deg

-0.597 Deg

395 MW 114 Mvar

520 MW 337 Mvar

800 MW 280 Mvar

80 MW 40 Mvar

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Page 25: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

37 Bus Example Design Case

slack

Metropolis Light and Power Electric Design Case 2SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69

HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

1.03 pu

1.02 pu

1.03 pu

1.03 pu

1.01 pu

1.00 pu1.01 pu

1.00 pu1.02 pu

1.01 pu

1.00 pu

1.01 pu1.01 pu

1.01 pu1.01 pu

1.02 pu

1.00 pu

1.00 pu

1.02 pu

0.99 pu

0.99 pu

1.00 pu

1.02 pu

1.00 pu1.01 pu

1.01 pu

1.00 pu 1.00 pu

1.01 pu

1.02 pu 1.02 pu

1.02 pu 1.03 pu

A

MVA

1.02 pu

A

MVA

A

MVA

LYNN138

A

MVA

1.02 pu

A

MVA

1.00 pu

A

MVA

System Losses: 10.70 MW 220 MW 52 Mvar

12 MW 3 Mvar

20 MW 12 Mvar

124 MW 45 Mvar

37 MW 13 Mvar

12 MW 5 Mvar

150 MW 0 Mvar

56 MW 13 Mvar

15 MW 5 Mvar

14 MW 2 Mvar

38 MW 3 Mvar

45 MW 0 Mvar

25 MW 36 Mvar

36 MW 10 Mvar

10 MW 5 Mvar

22 MW 15 Mvar

60 MW 12 Mvar

20 MW 28 Mvar

23 MW 7 Mvar

33 MW 13 Mvar 15.9 Mvar 18 MW

5 Mvar

58 MW 40 Mvar

60 MW 19 Mvar

14.2 Mvar

25 MW 10 Mvar

20 MW 3 Mvar

23 MW 6 Mvar 14 MW

3 Mvar

4.9 Mvar

7.3 Mvar

12.8 Mvar

28.9 Mvar

7.4 Mvar

0.0 Mvar

55 MW 25 Mvar

39 MW 13 Mvar

150 MW 0 Mvar

17 MW 3 Mvar

16 MW -14 Mvar

14 MW 4 Mvar

KYLE69A

MVA

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Page 26: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Good Power System Operation

• Good power system operation requires that there be no reliability violations for either the current condition or in the event of statistically likely contingencies• Reliability requires as a minimum that there be no

transmission line/transformer limit violations and that bus voltages be within acceptable limits (perhaps 0.95 to 1.08)

• Example contingencies are the loss of any single device. This is known as n-1 reliability.

• North American Electric Reliability Corporation now has legal authority to enforce reliability standards (and there are now lots of them). See http://www.nerc.com for details (click on Standards)

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http://www.nerc.com/
Page 27: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Looking at the Impact of Line Outages

slack

Metropolis Light and Power Electric Design Case 2SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69

HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

1.03 pu

1.02 pu

1.03 pu

1.03 pu

1.01 pu

1.00 pu1.01 pu

1.00 pu1.02 pu

1.01 pu

1.00 pu

1.01 pu1.01 pu

1.01 pu1.01 pu

1.02 pu

1.01 pu

1.00 pu

1.02 pu

0.90 pu

0.90 pu

0.94 pu

1.01 pu

0.99 pu1.00 pu

1.00 pu

1.00 pu 1.00 pu

1.01 pu

1.01 pu 1.02 pu

1.02 pu 1.03 pu

A

MVA

1.02 pu

A

MVA

A

MVA

LYNN138

A

MVA

1.02 pu

A

MVA

1.00 pu

A

MVA

System Losses: 17.61 MW 227 MW 43 Mvar

12 MW 3 Mvar

20 MW 12 Mvar

124 MW 45 Mvar

37 MW 13 Mvar

12 MW 5 Mvar

150 MW 4 Mvar

56 MW 13 Mvar

15 MW 5 Mvar

14 MW 2 Mvar

38 MW 9 Mvar

45 MW 0 Mvar

25 MW 36 Mvar

36 MW 10 Mvar

10 MW 5 Mvar

22 MW 15 Mvar

60 MW 12 Mvar

20 MW 40 Mvar

23 MW 7 Mvar

33 MW 13 Mvar 16.0 Mvar 18 MW

5 Mvar

58 MW 40 Mvar

60 MW 19 Mvar

11.6 Mvar

25 MW 10 Mvar

20 MW 3 Mvar

23 MW 6 Mvar 14 MW

3 Mvar

4.9 Mvar

7.2 Mvar

12.8 Mvar

28.9 Mvar

7.3 Mvar

0.0 Mvar

55 MW 32 Mvar

39 MW 13 Mvar

150 MW 4 Mvar

17 MW 3 Mvar

16 MW -14 Mvar

14 MW 4 Mvar

KYLE69A

MVA

80%A

MVA

135%A

MVA

110%A

MVA

Opening one line (Tim69-Hannah69) causes an overload. This would not be allowed 27

Page 28: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Contingency Analysis

Contingencyanalysis providesan automaticway of lookingat all the statisticallylikely contingencies. Inthis example thecontingency setIs all the single line/transformeroutages

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Page 29: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Power Flow And Design

• One common usage of the power flow is to determine how the system should be modified to remove contingencies problems or serve new load• In an operational context this requires working with the

existing electric grid• In a planning context additions to the grid can be considered

• In the next example we look at how to remove the existing contingency violations while serving new load.

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Page 30: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

An Unreliable Solution

slack

Metropolis Light and Power Electric Design Case 2SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

1.02 pu

1.01 pu

1.02 pu

1.03 pu

1.01 pu

1.00 pu1.01 pu

1.00 pu1.02 pu

1.01 pu

1.00 pu

1.01 pu1.01 pu

1.01 pu1.01 pu

1.02 pu

0.99 pu

1.00 pu

1.02 pu

0.97 pu

0.97 pu

0.99 pu

1.02 pu

1.00 pu1.01 pu

1.01 pu

1.00 pu 1.00 pu

1.01 pu

1.02 pu 1.02 pu

1.02 pu 1.03 pu

A

MVA

1.02 pu

A

MVA

A

MVA

LYNN138

A

MVA

1.02 pu

A

MVA

1.00 pu

A

MVA

System Losses: 14.49 MW 269 MW 67 Mvar

12 MW 3 Mvar

20 MW 12 Mvar

124 MW 45 Mvar

37 MW 13 Mvar

12 MW 5 Mvar

150 MW 1 Mvar

56 MW 13 Mvar

15 MW 5 Mvar

14 MW 2 Mvar

38 MW 4 Mvar

45 MW 0 Mvar

25 MW 36 Mvar

36 MW 10 Mvar

10 MW 5 Mvar

22 MW 15 Mvar

60 MW 12 Mvar

20 MW 40 Mvar

23 MW 7 Mvar

33 MW 13 Mvar 15.9 Mvar 18 MW

5 Mvar

58 MW 40 Mvar

60 MW 19 Mvar

13.6 Mvar

25 MW 10 Mvar

20 MW 3 Mvar

23 MW 6 Mvar 14 MW

3 Mvar

4.9 Mvar

7.3 Mvar

12.8 Mvar

28.9 Mvar

7.4 Mvar

0.0 Mvar

55 MW 28 Mvar

39 MW 13 Mvar

150 MW 1 Mvar

17 MW 3 Mvar

16 MW -14 Mvar

14 MW 4 Mvar

KYLE69A

MVA

96%A

MVA

Case now has nine separate contingencies with reliability violations 30

Page 31: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

A Reliable Solution

slack

Metropolis Light and Power Electric Design Case 2SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

1.03 pu

1.01 pu

1.02 pu

1.03 pu

1.01 pu

1.00 pu1.01 pu

1.00 pu1.02 pu

1.01 pu

1.00 pu

1.01 pu1.01 pu

1.01 pu1.01 pu

1.02 pu

1.00 pu

0.99 pu

1.02 pu

0.99 pu

0.99 pu

1.00 pu

1.02 pu

1.00 pu1.01 pu

1.01 pu

1.00 pu 1.00 pu

1.01 pu

1.02 pu 1.02 pu

1.02 pu 1.03 pu

A

MVA

1.02 pu

A

MVA

A

MVA

LYNN138

A

MVA

1.02 pu

A

MVA

A

MVA

System Losses: 11.66 MW 266 MW 59 Mvar

12 MW 3 Mvar

20 MW 12 Mvar

124 MW 45 Mvar

37 MW 13 Mvar

12 MW 5 Mvar

150 MW 1 Mvar

56 MW 13 Mvar

15 MW 5 Mvar

14 MW 2 Mvar

38 MW 4 Mvar

45 MW 0 Mvar

25 MW 36 Mvar

36 MW 10 Mvar

10 MW 5 Mvar

22 MW 15 Mvar

60 MW 12 Mvar

20 MW 38 Mvar

23 MW 7 Mvar

33 MW 13 Mvar 15.8 Mvar 18 MW

5 Mvar

58 MW 40 Mvar

60 MW 19 Mvar

14.1 Mvar

25 MW 10 Mvar

20 MW 3 Mvar

23 MW 6 Mvar 14 MW

3 Mvar

4.9 Mvar

7.3 Mvar

12.8 Mvar

28.9 Mvar

7.4 Mvar

0.0 Mvar

55 MW 29 Mvar

39 MW 13 Mvar

150 MW 1 Mvar

17 MW 3 Mvar

16 MW -14 Mvar

14 MW 4 Mvar

KYLE69A

MVA

Kyle138A

MVA

Previous case was augmented with the addition of a 138 kV Transmission Line 31

Page 32: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Generation Changes and The Slack Bus

• The power flow is a steady-state analysis tool, so the assumption is total load plus losses is always equal to total generation• Generation mismatch is made up at the slack bus

• When doing generation change power flow studies one always needs to be cognizant of where the generation is being made up• Common options include system slack, distributed across

multiple generators by participation factors or by economics

32

Page 33: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Generation Change Example 1

slack

SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69

A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69

HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69

HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

0.00 pu

-0.01 pu

0.00 pu

0.00 pu

0.00 pu

-0.03 pu-0.01 pu

0.00 pu0.00 pu

0.00 pu

-0.03 pu

-0.01 pu0.00 pu

0.00 pu0.00 pu

0.00 pu

0.00 pu

0.00 pu

0.00 pu

-0.002 pu0.00 pu

0.00 pu

0.00 pu

0.00 pu0.00 pu

0.00 pu

0.00 pu 0.00 pu

0.00 pu

0.00 pu 0.00 pu

0.00 pu 0.00 pu

A

MVA

-0.01 pu

A

MVA

A

MVA

LYNN138

A

MVA

0.00 pu

A

MVA

0.00 pu

A

MVA

162 MW 35 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

-157 MW -45 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 2 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW

0 Mvar

0 MW 3 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 4 Mvar

0 MW 0 Mvar

0 MW 0 Mvar -0.1 Mvar 0 MW

0 Mvar

0 MW 0 Mvar 0 MW

0 Mvar

-0.1 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar 0 MW

0 Mvar

-0.1 Mvar

0.0 Mvar

-0.1 Mvar

-0.2 Mvar

0.0 Mvar

0.0 Mvar

0 MW 51 Mvar

0 MW 0 Mvar

0 MW 2 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

Display shows “Difference Flows” between original 37 bus case, and case with a BLT138 generation outage; note all the power change is picked up at the slack 33

Page 34: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Generation Change Example 2

slack

SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69

A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69

HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69

HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

0.00 pu

-0.01 pu

0.00 pu

0.00 pu

0.00 pu

-0.03 pu0.00 pu

0.00 pu0.00 pu

0.00 pu

-0.03 pu

-0.01 pu-0.01 pu

0.00 pu0.00 pu

0.00 pu

0.00 pu

0.00 pu

0.00 pu

-0.003 pu0.00 pu

0.00 pu

0.00 pu

0.00 pu0.00 pu

0.00 pu

0.00 pu 0.00 pu

0.00 pu

0.00 pu 0.00 pu

0.00 pu 0.00 pu

A

MVA

0.00 pu

A

MVA

A

MVA

LYNN138

A

MVA

0.00 pu

A

MVA

0.00 pu

A

MVA

0 MW 37 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

-157 MW -45 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW

0 Mvar

42 MW -14 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

99 MW -20 Mvar

0 MW 0 Mvar

0 MW 0 Mvar -0.1 Mvar 0 MW

0 Mvar

0 MW 0 Mvar 0 MW

0 Mvar

-0.1 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar 0 MW

0 Mvar

0.0 Mvar

0.0 Mvar

-0.1 Mvar

-0.2 Mvar

-0.1 Mvar

0.0 Mvar

19 MW 51 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

0 MW 0 Mvar

Display repeats previous case except now the change in generation is picked up by other generators using a participation factor approach 34

Page 35: ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.

Voltage Regulation Example: 37 Buses

Display shows voltage contour of the power system, demo will show the impact of generator voltage set point, reactive power limits, and switched capacitors

slack

SLACK345

SLACK138

RAY345

RAY138

RAY69

FERNA69

A

MVA

DEMAR69

BLT69

BLT138

BOB138

BOB69

WOLEN69

SHI MKO69

ROGER69

UI UC69

PETE69

HI SKY69

TI M69

TI M138

TI M345

PAI 69

GROSS69

HANNAH69

AMANDA69HOMER69

LAUF69

MORO138

LAUF138

HALE69

PATTEN69

WEBER69

BUCKY138SAVOY69

SAVOY138

J O138 J O345

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVAA

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

1.03 pu

1.01 pu

1.02 pu

1.03 pu

1.01 pu

1.00 pu1.00 pu

0.99 pu1.02 pu

1.01 pu

1.00 pu

1.01 pu1.01 pu

1.01 pu1.01 pu

1.02 pu

1.00 pu

1.00 pu

1.02 pu

0.997 pu0.99 pu

1.00 pu

1.02 pu

1.00 pu1.01 pu

1.00 pu

1.00 pu 1.00 pu

1.01 pu

1.02 pu 1.02 pu

1.02 pu 1.03 pu

A

MVA

1.02 pu

A

MVA

A

MVA

LYNN138

A

MVA

1.02 pu

A

MVA

1.00 pu

A

MVA

219 MW 52 Mvar

21 MW 7 Mvar

45 MW 12 Mvar

157 MW 45 Mvar

37 MW 13 Mvar

12 MW 5 Mvar

150 MW 0 Mvar

56 MW 13 Mvar

15 MW 5 Mvar

14 MW 2 Mvar

38 MW 3 Mvar

45 MW 0 Mvar

58 MW 36 Mvar

36 MW 10 Mvar

0 MW 0 Mvar

22 MW 15 Mvar

60 MW 12 Mvar

20 MW 9 Mvar

23 MW 7 Mvar

33 MW 13 Mvar 15.9 Mvar 18 MW

5 Mvar

58 MW 40 Mvar 51 MW

15 Mvar

14.3 Mvar

33 MW 10 Mvar

15 MW 3 Mvar

23 MW 6 Mvar 14 MW

3 Mvar

4.8 Mvar

7.2 Mvar

12.8 Mvar

29.0 Mvar

7.4 Mvar

20.8 Mvar

92 MW 10 Mvar

20 MW 8 Mvar

150 MW 0 Mvar

17 MW 3 Mvar

0 MW 0 Mvar

14 MW 4 Mvar

1.010 pu 0.0 Mvar

System Losses: 11.51 MW

35


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