Overhead transmission lines

Typical data

The following table provides typical parameters of overhead lines for nominal voltage ranging from 230 kV to 1100 kV taken from [1]. The rated nominal frequency is 60 Hz. It is noted that bundled conductors are used for all lines listed below, except for the 230 kV line.

Nominal voltage	230 kV	345 kV	500 kV	765 kV	1100 kV
R (ohm/km)	0.050	0.037	0.028	0.012	0.005
X_L (ohm/km)	0.488	0.367	0.325	0.329	0.292
B_C (uS/km)	3.371	4.518	5.200	4.978	5.544
L (mH/km)	1.2945	0.9735	0.8621	0.8727	0.7746
C (uF/km)	0.0089	0.0120	0.0138	0.0132	0.0147
Zc (ohm)	380	285	250	257	230

The parameters from the previous table are per-phase values and can be taken as the inputs of the positive sequence data in the line models in HYPERSIM, for instance for PI Section, 3-ph and Constant Param, 3-ph models. The zero-sequence data can be calculated from the positive sequence data multiplying a ratio. A recommended practice is to assume a zero/positive sequence ratio based on the data of a known transmission line. The following section provides the electrical parameters of transmission lines used in a some EMTP application examples that can be taken as a reference.

Transmission line data from EMTP examples

The following data are taken from the application cases available in EMTP v4.1 [2].

This table shows typical data for a 735 kV continuously transposed transmission line.

Parameter	Zero sequence	Positive sequence	Zero/Positive sequence ratio
R (ohm/km)	0.2693	0.0154	17.49
X_L (ohm/km)	1.130	0.3356	3.37
B_C (uS/km)	3.037	4.909	0.62
L (mH/km)	2.9974	0.8902	3.37
C (uF/km)	0.008056	0.0130	0.62

The following table shows data for a 400 kV transmission line. Data taken from the BenchmarkT2WindHVDC EMTP benchmark.

Parameter	Zero sequence	Positive sequence	Zero/Positive sequence ratio
R (ohm/km)	0.3030	0.0209	14.5
X_L (ohm/km)	1.1892	0.3192	3.73
B_C (uS/km)	3.1743	5.1949	0.61
L (mH/km)	3.1544	0.8467	3.73
C (uF/km)	0.0084	0.0137	0.61

The following table shows data for a 345 kV transmission line. Data taken from the IEEE39 EMTP v3 example.

Parameter	Zero sequence	Positive sequence	Zero/Positive sequence ratio
R (ohm/km)	1.36245	0.0981	13.89
X_L (ohm/km)	0.718996	0.36058	1.99
B_C (uS/km)	2.74	4.49	0.61
L (mH/km)	1.9072	0.9565	1.99
C (uF/km)	0.00727	0.0119	0.61

The following table shows data for a 345 kV transmission line. Data taken from the IEEE39 EMTP v4 example.

Parameter	Zero sequence	Positive sequence	Zero/Positive sequence ratio
R (ohm/km)	0.1268	0.0315	4.03
X_L (ohm/km)	0.7917	0.3757	2.11
B_C (uS/km)	2.8045	4.3030	0.65
L (mH/km)	2.1000000	0.996640	2.11
C (uF/km)	0.0074393	0.011414	0.65

The following table shows data for a 230 kV continuously transposed transmission line. Data taken from the TRV EMTP example.

Parameter	Zero sequence	Positive sequence	Zero/Positive sequence ratio
R (ohm/km)	0.3167	0.0243	13.03
X_L (ohm/km)	1.2147	0.3477	3.49
B_C (uS/km)	2.9669	4.7500	0.62
L (mH/km)	3.222	0.9238	3.49
C (uF/km)	0.00787	0.0126	0.62

In the report from IEEE PSRC working group [3], it is mentioned that the zero-sequence inductance is typically between 2 and 3.5 times the positive sequence. Note that the data above satisfies the ratio suggested in [3].

Underground cables

Typical data

Underground cables exhibit a much lower series inductance and a much higher shunt capacitance. The series inductance of the cable circuit is lower than overhead lines because of the close spacing of cable conductors. The difference in the cable shunt capacitance is caused by the proximity of the cable conductor (surrounded by the cable grounded sheath) to ground potential, and the dielectric constant of the insulation, which is several times that of the air [3].

The following table shows typical data for two type of cables (taken from [1]), direct buried paper-insulated lead-covered (PILC) and high-pressure pipe type (PIPE), with nominal voltages of 115, 230 and 500 kV. Note that the characteristic impedance Zc of a cable is about one-tenth to one-fifth of that for an overhead line of the same voltage rating.

Nominal voltage	115 kV	115 kV	230 kV	230 kV	500 kV
Cable type	PILC	PIPE	PILC	PIPE	PILC
R (ohm/km)	0.0590	0.0379	0.0277	0.0434	0.0128
X_L (ohm/km)	0.3026	0.1312	0.3388	0.2052	0.2454
B_C (uS/km)	230.4	160.8	245.6	298.8	96.5
L (mH/km)	0.8027	0.3480	0.8987	0.5443	0.6510
C (uF/km)	0.6112	0.4265	0.6515	0.7926	0.2560
Zc (ohm)	36.2	24.5	37.1	26.2	50.4

This table is intended to be taken as a reference only, for cable modeling it is recommended to use the Cable Data module to calculate the electrical parameters of a cable based on the geometry of the cable. The produced data will be used by the Wideband Line/Cable Fitter, which creates the cable case for the Wideband Line/Cable model.

References

Data shown in this page is taken from the following references:

Kundur, P., Neal J. Balu, and Mark G. Lauby. Power System Stability and Control. New York: McGraw-Hill, 1994.
EMTPWorks 4.1 ApplicationCases examples.
PES Power System Relaying and Control Committee, “AC Transmission Line Model Parameter Validation”. PES technical report, 2014.

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