Exercises of course ELEC0029

Power flow computation and sensitivity analysisin a simple system

T. Van Cutsem

February 2018

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System data

Lines data

UN (kV) X (/km) X/R C/2 (S/km) SN (MVA) km

380 0.3 10 1.5 1350 50150 0.4 5 1.2 300 50

Transformers data

orig extr R (pu) X (pu) B (pu) SN (MVA) n (extr side)

A B 0 0.14 0 500 1.08F B 0 0.14 0 250 1.08D B 0 0.14 0 300 1.00E C 0 0.14 0 600 1.00

2 / 27

Operating point data

I generators:I voltage at bus A: 15 kVI voltage at bus F: 15 kVI production of F: 150 MW

I loads:I at bus E: 400 MW / 120 MvarI at bus D: 100 MW / 30 Mvar

3 / 27

I Specify the data at all buses and run a power flow computation todetermine the electrical state of the system. In this computationassume that transformers D-B and E-C are of Yd11 type, and takeinto account the phase angle of their transformer ratios.

The data are available in the file 6bus.dat, while the results can bedisplayed on the one-line diagram by using the file 6bus.svg

I Detail the active and reactive power balances of the system.

I Check that line D-E and transformer C-E operate below theirthermal ratings.

4 / 27

Transformers D-B et E-C of type Yd11; complex ratios

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

0.9912

1.0000

106

14

53

14

54

352

163

348

128347

137

154

56

1.0363

1.0134

1.0194

347

5.9 7.8

20.2

0.0

100

30

1.0000

150

79

0.9

400

120

17.6

5 / 27

I Simulate the misuse of a transformer E-C of type Yy0, whiletransformer D-B is of type Yd11. Show that the resulting electricalstate is unacceptable.

6 / 27

Transformer D-B of type Yd11 and E-C of type Yy0

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

0.9205

1.0000

207

87

310

20

332

372

296

90

20690

221

432

147

0.9967

0.9495

0.9732

90

6.5 6.9

11.2

0.0

100

30

1.0000

150

145

1.3

400

120

8.3

7 / 27

I Getting back to the correct configuration of the transformers,perform a new power flow computation in which the phase angles ofthe transformer ratios are set to zero. Comment on the resultsobtained.

Unless otherwise specified, the phase angles are neglected in thesequel.

8 / 27

Phase angles of transformer ratios neglected

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

12.4

0.9912

1.0000

106

14

53

14

54

352

163

348

128347

137

154

56

1.0363

1.0134

1.0194

347

5.9 7.8

9.8

0.0

100

30

1.0000

150

79

0.9

400

120

9 / 27

I Assuming that transformer D-B is equipped with a phase shiftingdevice allowing to vary progressively the phase angle of itstransformer ratio, study the impact of this phase angle on branchpower flows and bus voltage magnitudes.

10 / 27

Varying the phase angle of the ratio of transformer D-B

10 for E-C and 1 for D-B. Example for = 10.

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

10.6

0.9815

1.0000

132

12

153

7

157

355

179

248

136247

151

257

68

1.0315

1.0073

1.0145

247

6.0 7.3

2.6

0.0

100

30

1.0000

150

87

0.9

400

120

11 / 27

Variation of

-100

0

100

200

300

400

500

600

-15 -10 -5 0 5 10 15

phi (deg)

P B-C (MW)P D-E (MW)P B-D (MW)

0

20

40

60

80

100

120

140

160

-15 -10 -5 0 5 10 15

phi (deg)

Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

1.015

1.02

-15 -10 -5 0 5 10 15

phi (deg)

V C (pu)V D (pu)V E (pu)

12 / 27

I Assuming that transformer D-B is equipped with a tap changerallowing to vary progressively (the magnitude of) its transformerratio, study the impact of this ratio on branch power flows and busvoltage magnitudes.

I Same question for an identical variation of the ratios of bothtransformers D-B an E-C.

13 / 27

Varying the (magnitude) of the ratio of transformer D-B

10 for E-C and n0 for D-B. Example for n = 0.95.

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

12.2

1.0029

1.0000

74

46

61

48

62

352

162

340

91339

102

162

91

1.0364

1.0541

1.0232

339

5.9 7.8

9.7

0.0

100

30

1.0000

150

79

0.9

400

120

14 / 27

Variation of n

0

50

100

150

200

250

300

350

400

90 95 100 105 110

n (pu)

P B-C (MW)P D-E (MW)P B-D (MW)

-50

0

50

100

150

200

90 95 100 105 110

n (pu)

Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

90 95 100 105 110

n (pu)

V C (pu)V D (pu)V E (pu)

15 / 27

Same variation of the ratios of transformers D-B et E-C

n0 for both transformers. Example for n = 0.95.

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

11.8

1.0487

1.0000

105

15

55

15

56

352

159

346

123345

133

156

55

1.0374

1.0705

1.0210

345

5.9 7.8

9.5

0.0

100

30

1.0000

150

77

0.9

400

120

16 / 27

Same variation of n in both transformers

50

100

150

200

250

300

350

400

90 95 100 105 110

n (pu)

P B-C (MW)P D-E (MW)P B-D (MW)

0

20

40

60

80

100

120

140

90 95 100 105 110

n (pu)

Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)

0.85

0.9

0.95

1

1.05

1.1

1.15

90 95 100 105 110

n (pu)

V C (pu)V D (pu)V E (pu)

17 / 27

I Let ARTERE (the power flow computation software) adjustautomatically the ratios of both transformers D-B and E-C so as tobring the voltages at buses D and E in the dead-band [1.02 1.04] pu

18 / 27

Automatic adjustment of the ratios of both transformersto bring the voltages at buses D and E in [1.02 1.04] pu

iter max mismatches : MW Mvar phi(MVA)

1 395.2 407.1 605.1

2 27.4 62.4 78.0

3 1.0 1.2 2.0

4 0.1 0.1 0.1

in-phase trfo taps : 2 down 0 up

4 4.4 58.8 90.6

5 0.2 0.8 1.0

6 0.0 0.1 0.1

in-phase trfo taps : 1 down 0 up

6 4.5 61.1 83.7

7 0.1 0.7 0.7

8 0.0 0.0 0.0

in-phase trfo taps : 1 down 0 up

8 4.5 63.5 86.9

9 0.1 0.7 0.7

10 0.0 0.0 0.0

transfo ctld bus volt set-pt tol ratio tap max

E-C E 1.0275 1.0300 0.0100 0.963 14 25

D-B D 1.0350 1.0300 0.0100 0.988 16 2519 / 27

Situation after the transformers have been adjusted

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

12.1

1.0275

1.0000

121

1

51

2

51

352

161

351

143349

151

151

38

1.0368

1.0350

1.0184

349

5.9 7.8

9.6

0.0

100

30

1.0000

150

78

0.9

400

120

20 / 27

I Study the effect of varying the voltage of generator F on thereactive power productions of both generators, on the branch powerflows and on the bus voltage magnitudes.

I Same question for an identical variation of the voltages of bothgenerators A and F.

21 / 27

Varying the voltage of generator F

Example: VF = 0.98 pu

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

12.5

0.9828

1.0000

106

14

53

14

54

352

189

348

129347

137

154

56

1.0283

1.0052

1.0112

347

5.9 7.9

9.9

0.0

100

30

0.9800

150

55

0.8

400

120

22 / 27

Variation of VF

0

50

100

150

200

250

0.96 0.98 1 1.02 1.04

V F (pu)

Q Gen A (MVar)Q Gen F (MVar)

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

0.96 0.98 1 1.02 1.04

V F (pu)

V C (pu)V D (pu)V E (pu)

23 / 27

Variation of VF

50

100

150

200

250

300

350

0.96 0.98 1 1.02 1.04

V F (pu)

P B-C (MW)P D-E (MW)P B-D (MW)

0

20

40

60

80

100

120

140

0.96 0.98 1 1.02 1.04

V F (pu)

Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)

24 / 27

Same variation of voltages of generators A and F

Example: VF = VA = 0.98 pu

150 kV

380 kVpuissances ractives (Mvar)

puissances actives (MW)

D E

A

B

C

modules tensions (pu)15 kV phases tensions (deg)

F

13.0

0.9658

0.9800

106

14

53

15

54

352

168

348

131347

139

154

57

1.0124

0.9888

0.9949

347

6.2 8.1

10.3

0.0

100

30

0.9800

150

81

0.9

400

120

25 / 27

Variation of VF = VA

60

80

100

120

140

160

180

0.96 0.98 1 1.02 1.04

V Gen (pu)

Q Gen A (MVar)Q Gen F (MVar)

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

0.96 0.98 1 1.02 1.04

V Gen (pu)

V C (pu)V D (pu)V E (pu)V B (pu)

26 / 27

Variation of VF = VA

50

100

150

200

250

300

350

0.96 0.98 1 1.02 1.04

V Gen (pu)

P B-C (MW)P D-E (MW)P B-D (MW)

0

20

40

60

80

100

120

140

0.96 0.98 1 1.02 1.04

V Gen (pu)

Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)

27 / 27