cont analysis

8/2/2019 Cont Analysis

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Contingency Analysis


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AbstractIn this presentation the development of a simple and fast method to calculate a new

set of distribution factors using the sensitivity property of Newton Raphson load flow

of jacobian at a base operating point has been shown.

The accuracy of post outage results using these distribution factors has beenestablished with respect to full AC load flow results on IEEE14-bus system by using

Newton raphson method.


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Proposed Distribution Factors

In the voltage security or reactive power security studies, the effect of line/transformer or

generator outages on the system voltage profile and reactive power output of sources are

required to be computed.

Two groups of distribution factors have been suggested they are

The vo ltage distribution factors which can be used to compute the post-outage voltage profilein the system .

The reactive power distribution factors which can be used to compute the post-outage output ofthe reactive power sources.

For a line/transformer outage, these factors have been termed as Line outage voltagedistribution factors (LO VDFs) and Line outage reactive power d istribution factors (LOQ DFs),respectively.

In the case of a generator outage, they have been termed as theGenerator outage voltagedistribution factors (GO VDFs) and the Generator outage reactive power distribution factors(GOQDFs),respectively.


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Consider the outage of a line or a transformer-l carrying an average real power PlTand

reactive power QlTdefined as


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Line ou tage distribution factors

i) Line outage voltage distribution factors

ii) Line outage Reactive power distribution factors


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Generator outage distribution factors

i) Generator outage voltage distribution factors

ii) Generator outage reactive power distribution factors

i=1,,N & g=1,.,Ng

j=1,,Nq& g=1,.,Ng


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Post contingency voltage profile and reactive power output of the system

For line outage

For generator outage


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Calculation of distribution factors


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i) Line outage voltage distribution factors


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ii) Generator outage voltage distribution factors

iii) Line outage Reactive power distribution factors

iv) Generator outage reactive power distribution factors


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Results and discussion

The accuracy of post outage results using these distribution factors has been

established with respect to full AC load flow results on IEEE14-bus system by

using Newton raphson method.

LINE FLOWS

LINE FROM BUS TO BUS REAL REACTIVE

1.0000 1.0000 2.0000 1.5705 -0.1713

2.0000 1.0000 5.0000 0.7495 0.07073.0000 2.0000 3.0000 0.7588 -0.1556

4.0000 2.0000 4.0000 0.5544 0.0063

5.0000 2.0000 5.0000 0.4125 0.0399

6.0000 3.0000 4.0000 -0.2099 0.2754

7.0000 4.0000 5.0000 -0.5894 0.1669

8.0000 4.0000 7.0000 0.2734 0.0477

9.0000 4.0000 9.0000 0.1571 0.0672

10.0000 5.0000 6.0000 0.4536 0.1966

11.0000 6.0000 11.0000 0.0799 0.0739

12.0000 6.0000 12.0000 0.0799 0.030013.0000 6.0000 13.0000 0.1818 0.0924

14.0000 7.0000 8.0000 0.0000 -0.1109

15.0000 7.0000 9.0000 0.2734 0.1429

16.0000 9.0000 10.0000 0.0466 0.0055

17.0000 9.0000 14.0000 0.0889 0.0128

18.0000 10.0000 11.0000 -0.0434 -0.0527

19.0000 12.0000 13.0000 0.0181 0.0122

20.0000 13.0000 14.0000 0.0621 0.0414

1.0000 2.0000 1.0000 -1.5259 0.2511

2.0000 5.0000 1.0000 -0.7210 -0.0037

3.0000 3.0000 2.0000 -0.7321 0.22194.0000 4.0000 2.0000 -0.5373 0.0076

5.0000 5.0000 2.0000 -0.4031 -0.0456

6.0000 4.0000 3.0000 0.2182 -0.2894

7.0000 5.0000 4.0000 0.5945 -0.1633

8.0000 7.0000 4.0000 -0.2734 -0.0320

9.0000 9.0000 4.0000 -0.1571 -0.0517

10.0000 6.0000 5.0000 -0.4536 -0.1423

11.0000 11.0000 6.0000 -0.0788 -0.0716

12.0000 12.0000 6.0000 -0.0791 -0.0282

13.0000 13.0000 6.0000 -0.1792 -0.087214.0000 8.0000 7.0000 -0.0000 0.1130

15.0000 9.0000 7.0000 -0.2734 -0.1326

16.0000 10.0000 9.0000 -0.0466 -0.0053

17.0000 14.0000 9.0000 -0.0878 -0.0106

18.0000 11.0000 10.0000 0.0438 0.0536

19.0000 13.0000 12.0000 -0.0180 -0.0121

20.0000 14.0000 13.0000 -0.0612 -0.0394


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Considering the outage of heavily loaded line 3 connecting busses 2 and 3

Program Output :

CONTINGENCY ANALYSIS

Press 1 for line outage

Press 0 for generator outage

1

enter the line number where outage has occurred 3

ap =

-0.0022

0

0.0385

-0.0095

-0.0079

-0.0094

-0.0103

-0.0103

-0.0106

-0.0105

-0.0101

-0.0096

-0.0098

-0.0105

aq =

-0.0021

0

0.1099

-0.0145

-0.0106

-0.0136

-0.0150

-0.0150

-0.0150

-0.0149

-0.0143

-0.0140

-0.0141

-0.0150

v_profile =

1.0356

1.0230

0.9930

0.9391

0.9503

0.9446

0.9287

0.9287

0.9137

0.9106

0.9233

0.9265

0.9199

0.8956

c_p =

0.2008

0.2204

0.1471

0.4289

0.3069

0.00700.1913

0.0000

0.1173

0.0153

0.0123

0.0244

0.0567

0.0509

c_q =

0.2003

0.2247

0.1508

0.4349

0.3076

0.0070

0.1928

0.0000

0.1184

0.0155

0.0124

0.0246

0.0571

0.0513

post_reac =

0.1946

0.3418

0.3336

0.4174

0.3138

0.0818

0.1859

0.0000

0.2801

0.0729

0.0300

0.0397

0.1131

0.0994


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Average real power PlTand reactive power Ql

T are Computed from base load flow equations

Hence LOVDFS are calculated.

Using the new computed values of voltage magnitudes and angles, the reactive power output at

the source buses and hence, the change in their reactive power outputs from pre-outage to post-

outage condition can be computed. The change in reactive power output of the source-g due to

only real power and only reactive power outage of the line can be written as

Note that

Hence LOQDFs are calculated.


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Similarly for GOVDFs and GOQDFs are calculated by calculating appropriate power

mismatches and multiplying with sensitivity matrix.

In this presentation results are to be shown for outage of Generator at bus 1 which hasthe maximum generating capacity from base load flow.

GENERATION LOAD

BUS VOLTS ANGLE REAL REACTIVE REAL REACTIVE

1.0000 1.0400 5.1602 2.3200 -0.1006 0 0

2.0000 1.0230 0 0.4168 0.2687 0.2170 0.1270

3.0000 1.0253 -8.5783 0.0000 0.6874 0.9420 0.1900

4.0000 0.9915 -5.4450 0 0 0.4780 0.0000

5.0000 0.9925 -3.8653 0 0 0.0760 0.0160

6.0000 1.0240 -9.8830 0.0000 0.1289 0.1120 0.0750

7.0000 1.0056 -8.6601 0 0 -0.0000 -0.0000

8.0000 1.0250 -8.6601 -0.0000 0.1130 0 0

9.0000 0.9904 -10.3908 0 0 0.2950 0.1660

10.0000 0.9884 -10.6112 0 0 0.0900 0.0580

11.0000 1.0023 -10.3787 0 0 0.0350 0.018012.0000 1.0070 -10.8140 0 0 0.0610 0.0160

13.0000 1.0006 -10.8655 0 0 0.1350 0.0580

14.0000 0.9758 -11.7193 0 0 0.1490 0.0500


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Considering the outage of Generator at bus 1 which has the maximum generating

capacity from base load flow.

Program Output :

CONTINGENCY ANALYSIS

Press 1 for line outage

Press 0 for generator outage

0

enter the line number where outage has occurred 1

bgp =

-0.0123

-0.0099

-0.0010

-0.0021

-0.0025

-0.0028

-0.0023

-0.0023

-0.0023

-0.0024

-0.0026

-0.0028

-0.0028

-0.0026

bgq =

0

0

0

0

0

0

0

0

0

0

0

0

0

0

dgp =

0.0891

0.1031

0.0619

0.1851

0.1297

0.0029

0.0828

0.0000

0.0509

0.0066

0.0053

0.0105

0.0244

0.0220

dgq =

0

0

0

0

0

0

0

00

0

0

0

0

0

v_profile =

1.0090

1.0000

0.9356

0.9448

0.9529

0.9483

0.9346

0.9346

0.9197

0.9163

0.9281

0.9304

0.9241

0.9009

post_reac =

0.2068

0.3661

0.3336

0.4294

0.3169

0.0818

0.1922

0.00000.2840

0.0734

0.0303

0.0404

0.1147

0.1010


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LOVDFS & LOQDFS are calculated for line outage and they are used to calculate post

contingency voltage profile and reactive power outputs.

GOVDFS & GOQDFS are calculated and are used to calculate post contingency voltage

profile and reactive power outputs.

All the above calculations were carried out and they are to be compared with NR method in

terms of speed and accuracy.


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cont analysis

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