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• Alonso Martí Portella

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14 Bus System DIgSILENT PowerFactory ∗

Abstract This paper describes the 14 Bus System in PowerFactory . The parameters of the individual elements like generators, loads, shunts, transformers and lines are explained. Results for the load flow calculation are presented.

1

The nominal frequency of the 14 Bus System is 60 Hz. In [1] the network parameters are given in per unit values based on 100 MVA. Loads and generation are given in MW and Mvar. The following subsections describe the network data used for symmetrical load flow calculation.

General Description 2.1

The 14 Bus System consists of 14 buses (nodes), 5 generators, 11 loads, 16 lines, 5 transformers and one shunt. 3 of these 5 transformers are used to represent one single 3-winding transformer. Figure 1 shows the single line diagram. It is a simplified model of the transmission system in the Midwest United States.

2

Loads

The loads are not voltage-dependent, but have constant active and reactive power demand. Please note that this is achieved by disabling the load option “Consider Voltage Dependency of Loads” in the PowerFactory load flow calculation command. Load data (active power P and reactive power Q) have been taken from [1] and are listed in Table 1.

Model Parameters

Data have been taken from [1] and have been completed by assuming the following typical values as nominal voltages: • Bus 1 - Bus 5: 132 kV • Bus 6, Bus 9 - Bus 14: 33 kV • Bus 7: 1 kV • Bus 8: 11 kV ∗ DIgSILENT GmbH, Heinrich-Hertz-Str. 9, 72810 Gomaringen, Germany, www.digsilent.de

DIgSILENT PowerFactory, r1339

2.2

Generators

Generator “Gen 0001” is the slack generator, therefore voltage magnitude and voltage angle are given (1.060 p.u., 0.0 degrees). The other generators are configured to control the active power injection and voltage magnitudes at the connected buses. Therefore the active power dispatch and controlled voltage magnitudes at their terminals are given. The data have been taken from [1] and are listed in Table 2 and 3. The machines at the buses 3, 6 and 8 are synchronous condensers.

1

DIgSILENT

14 Bus System

Load_0013

Load_0014

Bus_0013 Load_0012

Li TypLne_001 ne 00 3_00 13 14 to 00 14

3 3 01 01 _0 0 12 to 00 12 e_ 00 Lin Lne p Ty

TypLine_ Ln 00 e 0 06_ 00 00 6 to 12 00 12

Load_0010

Shnt_0009

Bus_0009

SG ~

Trf_0004_0009 TypTr2 0004 to 0009

~ SG

Trf_0005_0006 TypTr2 0005 to 0006

Bus_0007

Bus_0005

Ty Lin Ty Lin pL e_ pL e_ ne 00 ne 00 00 01_ 00 01_ 01 00 01 00 to 02 to 02 00 /1 00 /2 02 02

Trf_0007_0008 TypTr2 0007 to 0008

Trf_0004_0007 TypTr2 0004 to 0007

Line_0 001 TypLne 0001 _0005 to 000 5

Load_0005

Gen_0006 TypSym_0006

Bus_0006

Gen_0008 TypSym_0008

Line_000 9_00 TypLne 0009 to 10 0010

Bus_0008

Load_0006

Line_001 0_00 TypLne 0010 to 11 0011

Load_0009

Bus_0010

11 6_00 0011 _000 06 to Linene 00 TypL

~ SG

Bus_0001

Lin TypL e_00 ne 00 09_0 09 to 014 0014

Bus_0011

Trf_0007_0009 TypTr2 0007 to 0009

Gen_0001 TypSym_0001

Bus_0014

Load_0011

Line_0006_0013 TypLne 0006 to 0013

Bus_0012

Bus_0004

Load_0004

5 Line_0004_000 to 0005 TypLne 0004

004 Line_0002_0 to 0004 TypLne 0002

Line_0003_0004 TypLne 0003 to 0004

_0005 Line_0002 to 0005 0002 TypLne

Load_0002

Bus_0002

SG ~ Gen_0002 TypSym_0002

Line TypLne_0002_0003 0002 to 0003

Load_0003

Bus_0003

SG ~ Gen_0003 TypSym_0003

Inactive Out of Calculation De-energized

Voltage Levels 132, kV 33, kV 11, kV 1, kV

DIgSILENT GmbH

14 Bus System 01 - Load Flow Case Original Grid

PowerFactory 15.1.4

Project: Graphic: 14 Bus System Date: 5/23/2014 Annex:

Figure 1: Single line diagram of the 14 Bus System 2.2.1

Transmission Lines

Line data are given in per unit (p.u.) based on the base power Sb = 100 MVA as represented in Table 5, without information about the line length [1]. The susceptance b in p.u. is twice the given line charging qc/2 in p.u., which is given as one-half of the total charging of lines [1] (Eq. (3)).

Un2 [kV2 ] Sb [MVA] U 2 [kV2 ] = x [p.u.] · n Sb [MVA]

R [Ω] = r [p.u.] ·

(1)

X [Ω]

(2)

Qc [Mvar]

= 2 · qc/2 [p.u.] · Sb [MVA](3)

B [µS] =

Qc [Mvar] · 10−6 (4) 2 2 Un [kV ] S [MVA] b [p.u.] · b · 10−6 Un2 [kV2 ]

For the PowerFactory model input data are required in Ω/km and µS/km (or µF/km) respectively. Line data have been recalculated for the network model with a nominal voltage Un given in Table 4 using Equations (1) – (4).

2.2.2

As there is no line length given in [1], the length of each line in the PowerFactory model has been set to 1 km. Line data of the PowerFactory model are represented in Table 4. The rated current of each line is not known and therefore assumed to be 1 kA.

Transformer data are given in per unit (p.u.) as represented in Table 6 based on the base power Sb = 100 MVA [1]. The rated power of each transformer is assumed as Sr = 100 MVA.

The line between bus 1 and bus 2 is a double circuit, and has therefore been modelled as two parallel lines with adapted parameters in the PowerFactory model.

Transformer parameters of the PowerFactory model are given in Table 6. In addition tap changers are modelled in order to achieve the transformer taps as given in Table 6.

DIgSILENT PowerFactory, r1339

=

Transformers

2

14 Bus System The three 2-winding transformers connected to Bus 0007 represent a 3-winding transformer [1]. The 3-winding transformer model of PowerFactory can be used instead of three 2-winding transformers. This is done in the Study Case “02 - Load Flow Case 3Winding Trf”, which activates the Variation “3-Winding Transformer”. The input parameters for the impedances (short-circuit voltages uk ) of the 3-winding transformer model have been calculated with Equations (5), (6) and (6). Figure 2 shows the corresponding simplified electrical circuit of the 3-winding transformer.

uk,HV−MV = (5) uk,HV · Sr,HV + uk,MV · Sr,MV min(Sr,HV , Sr,MV ) uk,MV−LV = (6) uk,MV · Sr,MV + uk,LV · Sr,LV min(Sr,MV , Sr,LV )

at bus 9, which has a susceptance b of 0.19 p.u. based on the base power Sb = 100 MVA. PowerFactory uses either the susceptance B in µS (Eq. 8) or the rated reactive power Q in Mvar (Eq. 9) of the shunt.

S [MVA] · 10−6 (8) B [µS] = b [p.u.] · b Un2 [kV2 ] Q [Mvar] = b [p.u.] · Sb [MVA] (9)

3

Load Flow Results

The steady-state load flow is examined by executing the load flow calculation ( ). The study cases contain pre-defined bar diagrams which display the results for busbar voltage magnitudes (see Figure 3) and power injection of generators active and reactive power (see Figure 4). The results of the PowerFactory load flow calculation are also given in Appendix B.

References uk,LV−HV = (7) uk,LV · Sr,LV + uk,HV · Sr,HV min(Sr,LV , Sr,HV )

[1] L. L. Freris, A. M. Sasson: “Investigation of the load-flow problem”, PROC. IEE, Vol. 115, No. 10, October 1968, pp. 1459-1470

HV

uk,HV

uk,LV

uk,MV

LV

MV

Figure 2: Simplified electrical circuit of a 3winding transfomer (positive sequence)

2.3

Shunt

Shunt data are given in per unit (p.u.). The 14 Bus System possesses one capacitor

DIgSILENT PowerFactory, r1339

3

DIgSILENT

14 Bus System

1,12

1,09

1,06

1,03

1,00

Bu s_ 00

14

13 Bu s_ 00

12 Bu s_ 00

11 Bu s_ 00

09

10 Bu s_ 00

Bu s_ 00

Bu s_ 00

08

07 Bu s_ 00

06 Bu s_ 00

Bu s_ 00

05

04 Bu s_ 00

03 Bu s_ 00

02 Bu s_ 00

Bu s_ 00

01

0,97

Voltage, Magnitude in p.u.

DIgSILENT

Figure 3: Voltage magnitudes (load flow case with original grid)

250,00 200,00 150,00 100,00 50,00

Ge n

8 _0 00 Ge n

_0 00

6

3 _0 00 Ge n

Ge n

Ge n

_0 00

_0 00

2

1

0,00

Active Power in MW 80,00 60,00 40,00 20,00 0,0000

8 _0 00 Ge n

Ge n

_0 00

6

3 _0 00 Ge n

Ge n

Ge n

_0 00

_0 00

2

1

-20,00

Reactive Power in Mvar

Figure 4: Active and reactive power of generators

DIgSILENT PowerFactory, r1339

4

14 Bus System

A

Tables with Input Data

DIgSILENT PowerFactory, r1339

5

14 Bus System Table 1: Load demand Load Load 0002 Load 0003 Load 0004 Load 0005 Load 0006 Load 0009 Load 0010 Load 0011 Load 0012 Load 0013 Load 0014

Bus Bus 0002 Bus 0003 Bus 0004 Bus 0005 Bus 0006 Bus 0009 Bus 0010 Bus 0011 Bus 0012 Bus 0013 Bus 0014

P in MW 21.7 94.2 47.8 7.6 11.2 29.5 9.0 3.5 6.1 13.5 14.9

Q in Mvar 12.7 19.0 -3.9 1.6 7.5 16.6 5.8 1.8 1.6 5.8 5.0

Table 2: Generator dispatch Generator Gen 0001 Gen 0002 Gen 0003 Gen 0006 Gen 0008

Bus Bus 0001 Bus 0002 Bus 0003 Bus 0006 Bus 0008

P in MW N.A. 40.0 0.0 0.0 0.0

Q in Mvar N.A. N.A. N.A. N.A. N.A.

Table 3: Generator controller settings Generator Gen Gen Gen Gen Gen

0001 0002 0003 0006 0008

Bus Type

Voltage in p.u.

Slack PV PV PV PV

Minimum capability in MVA

1.060 1.045 1.010 1.070 1.090

Maximum capability in MVA

N.A. -40.0 0.0 -6.0 -6.0

N.A. 50.0 40.0 24.0 24.0

Table 4: Data of lines given in [1] based on 100 MVA From Bus

To Bus

r in p.u.

x in p.u.

qc/2 in p.u.

b in p.u.

1 1 2 2 2 3 4 6 6 6 9 9 10 12 13

2 5 3 4 5 4 5 11 12 13 10 14 11 13 14

0.01938 0.05403 0.04699 0.05811 0.05695 0.06701 0.01335 0.09498 0.12291 0.06615 0.03181 0.12711 0.08205 0.22092 0.17093

0.05917 0.22304 0.19797 0.17632 0.17388 0.17103 0.04211 0.19890 0.25581 0.13027 0.08450 0.27038 0.19207 0.19988 0.34802

0.0264 0.0246 0.0219 0.0187 0.0170 0.0173 0.0064 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0528 0.0492 0.0438 0.0374 0.0340 0.0346 0.0128 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

DIgSILENT PowerFactory, r1339

6

14 Bus System

Table 5: Data of lines in the PowerFactory model

Line Line Line Line Line Line Line Line Line Line Line Line Line Line Line Line

Line 0001 0002/1 0001 0002/2 0001 0005 0002 0003 0002 0004 0002 0005 0003 0004 0004 0005 0006 0011 0006 0012 0006 0013 0009 0010 0009 0014 0010 0011 0012 0013 0013 0014

From Bus 1 1 1 2 2 2 3 4 6 6 6 9 9 10 12 13

To Bus 2 2 5 3 4 5 4 5 11 12 13 10 14 11 13 14

Un in kV 132.0 132.0 132.0 132.0 132.0 132.0 132.0 132.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0

R in Ω 6.753542 6.753542 9.414187 8.187537 10.125090 9.922968 11.675820 2.326104 1.034332 1.338490 0.720374 0.346411 1.384228 0.893524 2.405819 1.861428

X in Ω 20.619560 20.619560 38.862490 34.494280 30.722000 30.296850 29.800270 7.337246 2.166021 2.785771 1.418640 0.920205 2.944439 2.091643 2.176693 3.789938

B in µS 151.5152 151.5152 282.3691 251.3774 214.6465 195.1331 198.5767 73.4619 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 6: Data of transformers given in [1] based on 100 MVA, with rated voltages added in the PowerFactory model

Trf Trf Trf Trf Trf

Transformer 0004 0007 0004 0009 0005 0006 0007 0008 0007 0009

From Bus 4 4 5 7 7

To Bus 7 9 6 8 9

DIgSILENT PowerFactory, r1339

Ur HV in kV 132.0 132.0 132.0 11.0 33.0

Ur LV in kV 1.0 33.0 33.0 1.0 1.0

r in p.u. 0.0 0.0 0.0 0.0 0.0

x in p.u. 0.20912 0.55618 0.25202 0.17615 0.11001

Transformer final turns ratio 0.978 0.969 0.932 0.000 0.000

7

14 Bus System

B

Tables with Results of the Symmetric Load Flow Calculation

DIgSILENT PowerFactory, r1339

8

14 Bus System

Table 7: Results of buses Name Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus

0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014

Ul, Magnitude in kV 139.92 137.94 133.32 134.46 134.67 35.31 1.06 11.99 34.86 34.69 34.88 34.82 34.66 34.18

u, Magnitude in p.u. 1.060 1.045 1.010 1.019 1.020 1.070 1.062 1.090 1.056 1.051 1.057 1.055 1.050 1.036

U, Angle in deg 0.00 -4.98 -12.72 -10.32 -8.78 -14.22 -13.37 -13.37 -14.95 -15.10 -14.80 -15.08 -15.16 -16.04

Table 8: Results of generators Name Gen Gen Gen Gen Gen

0001 0002 0003 0006 0008

Active Power in MW 232.39 40.00 0.00 0.00 0.00

Reactive Power in Mvar -16.89 42.40 23.39 12.24 17.36

Table 9: Results of lines Name Line 0001 0002/1 Line 0001 0002/2 Line 0001 0005 Line 0002 0003 Line 0002 0004 Line 0002 0005 Line 0003 0004 Line 0004 0005 Line 0006 0011 Line 0006 0012 Line 0006 0013 Line 0009 0010 Line 0009 0014 Line 0010 0011 Line 0012 0013 Line 0013 0014

Losses in MW 2.1474 2.1474 2.7638 2.3202 1.6770 0.9023 0.3714 0.5165 0.0547 0.0717 0.2115 0.0131 0.1168 0.0123 0.0062 0.0536

DIgSILENT PowerFactory, r1339

Reactive Losses in Mvar 3.6318 3.6318 6.0843 5.1494 1.1062 -0.8712 -2.6120 0.2990 0.1146 0.1492 0.4166 0.0348 0.2484 0.0288 0.0057 0.1091

Capacitive Loading in Mvar 2.9246 2.9246 5.3248 4.6256 3.9824 3.6260 3.5598 1.3303 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Current in kA 0.3263 0.3263 0.3121 0.3067 0.2352 0.1738 0.1018 0.2727 0.1328 0.1336 0.3129 0.1123 0.1677 0.0678 0.0294 0.0980

9