Cable Input Data

To better illustrate the cable impedance calculation, we will proceed, in the following examples, to the data entry and the calculation of each cable type supported by this PSAF module.

The following is covered in this section:

• Data entry and calculation of a three-conductor cable, below • Data entry and calculation of a 3 single-conductor cables, page 173 • Data entry and calculation of an unshielded cable, page 175

4.4.3.1 Data entry and calculation of a three-conductor cable

Let’s find the 60-Hz impedance of a 750-MCM three-conductor belted cable having 0.1563 inches of conductor insulation and 0.133 inches of lead sheath. The overall cable diameter is 2.833 inches and the conductors are sector-shaped with a sector depth of 0.78 inches, a resistance of 0.091/mile and a GMR of 0.366 inches. The diameter of an equivalent round conductor with the same cross-sectional area is 0.998 inches.

When you click on the Compute button as explained above, the following dialog box is displayed:

This Cable Impedance Calculation dialog has three tabs: the first is designed for shielded cables, the second for unshielded cables and the last one for the multi-wire

concentric neutral cables.

For this example, we should select the Shielded Cables tab and enter the required parameters based on the given data.

• Enter study parameters such as choice of units, earth resistivity (typical value 100 Ohm-m), and fundamental frequency of the system. These parameters are used for the calculation of the zero-sequence electrical parameters. In

• Specify, in the Phase conductor characteristics group box, the conductor data i.e.; external radius, GMR and DC resistance. A typical conductor can be selected in the combo box displaying all conductors are already entered in the current study database. To create a new conductor database or modify an existing one, click the Access DB button to access the Conductor

Database dialog box, as shown below, for the 750 MCM conductor.

Recall that the 750 MCM conductor used in this example is not round but sector- shaped; so the external radius to enter here is approximately 84% of the External

Diameter of an equivalent round conductor with same cross-sectional area which

diameter is 0.998 inches.

If the center axis of a conductor is made of dielectric materials or is hollow, then the radius of the dielectric-axis is Internal Radius, but for 750-MCM in this example, all cross-section is made of conductor material and it doesn’t have dielectric axis so “Internal Diameter= 0.0 “.

Therefore, from this assumption and the given data, we are able to type the required data in this (above) dialog as follows:

External Diameter = 0.84*0.998 = 0.83832 inches Internal Diameter = 0.0 inches

DC Resistance (25°C) = 0.0910 ohms/mile DC Resistance (50°C) ≈ 0.1 ohms/mile

Click OK to update the “Phase conductor characteristics” values.

• Identify the cable construction (3-core cable or 3 single-core cables) in the

Cable type section of the dialog box. Here, we select 3-core cable as stated

in the example. A bitmap illustrating the cable with the required data was displayed above.

• In the “Sheath radius” section of the dialog box, enter the inner sheath radius (ri) and the outer sheath radius (ro) as illustrated in the cable bitmap. Since the overall diameter of the cable is 2.833 inches, so the outer sheath radius is half of this diameter i.e. ro = 2.833/2 = 1.417 inches.

• Since lead sheath thickness is 0.133 inches so the inner sheath radius is the outer sheath radius minus this value: ri = 1.417 – 0.133 = 1.284 inches. • Select the insulation of the cable from the registered materials and the

dielectric constant of this insulation will be displayed in the adjacent field. If the cable insulation is not in the registered list, select “Other insulation” and type in the value of the dielectric constant. The assumption made here is

that the belted insulation is of the same type as the core insulation.

• Enter the distances between phases a, b and c. These distances Da-b, Db- c, Da-c are illustrated also in the bitmap. In fact, in this example, these distances are equal to the equivalent distance between the sectors, which can be taken as the sector depth (0.78 inches), plus twice the conductor insulation (0.156 inches). Therefore,

Da-b = Db-c = Da-c = 0.78 + 2*0.156 = 1.090 inches

• Finally, once the required data are entered, click Compute to perform the calculation. If the input data are correct, the 60-Hz impedance parameters i.e. R1, X1, B1, R0, X0 and B0 are calculated and displayed in the window next to the Compute button. Clicking OK will update the main cable database with the calculated parameters expressed in the selected units.

4.4.3.2 Data entry and calculation of a 3 single-conductor cables

Let’s determine the 60-Hz impedance of 3-1 MCM single-conductor cables that have been drawn into fiber conduits in the same horizontal plane (4.125 inches) between adjacent conductors. The conductor insulation is 0.469 inches and the lead sheath is 0.125 inches thick.

Since we are dealing with a shielded cable, we stay in the same tab Shielded

Cables as the previous example.

• The study parameters i.e. system of units, earth resistivity and fundamental frequency of the system remain the same as in the first example.

• From the PSAF conductors’ database, we select the conductor 1MCM, which is the phase conductor of this cable. The parameters of this conductor i.e. its external radius, its GMR and its DC resistance are displayed.

bonding” section in the dialog. It is specified here that the term “sheath

losses”, signifies the sheath circulating losses due to currents flowing driven by the sheath-induced voltages. The option “Single-point (open)”

means that the sheath losses are neglected since no circulating currents can flow. Instead, the option “Two point (shorted)” means that they are taken into account. In this example, we will neglect the sheath losses.

• The conductor radius of 0.576 inches plus the insulation thickness of 0.469 inches makes the inner sheath radius (ri) = 1.045 inches. This ri plus the sheath thickness 0.125 inches makes the outer sheath radius (ro) = 1.170 inches.

• The 3 single-core cables are in the same horizontal plane and distant 4.125 inches to each other, therefore:

Da-b = Db-c = 4.125 inches and Da-c = 2*4.125 = 8.250 inches

• Finally, once all the required data are entered, click Compute to perform the calculation. If the input data are correct, the 60-Hz impedance parameters (i.e. R1, X1, B1, R0, X0 and B0) are calculated and displayed in the window next to the Compute button.

4.4.3.3 Data entry and calculation of an unshielded cable

Now, let’s calculate the 60-Hz impedance of an unshielded 3-phase 120/208 Volt cable which is an assembly of three 500 MCM phase conductors arranged triangularly and a 0000 AWG neutral conductor interposed between phases B and C. The insulation thickness of the 500 MCM conductor is 0.156 inches and the one for the 0000 AWG conductor is 0.078 inches.

For this cable type, the appropriate tab is Unshielded Cables from the Cable

Impedance Calculation dialog box.

As you can see in the following figures, up to three different arrangements for the multiple conductors cables are supported:

• Three-conductor triangular grouping • Three-conductor cradled grouping • Six-conductor bunched grouping

Concerning the 3 single-core cables, a generic arrangement with up to three neutral conductors is supported.

Any random configuration of the phase and neutral conductors are allowed as long as they are realistic.

• As usual, the study parameters i.e. system of units, earth resistivity and fundamental frequency of the system should be specified.

• From the PSAF conductors’ database, we select the phase conductor 500MCM. The parameters of this conductor (i.e. its external radius), its internal radius and its DC resistance are displayed. The same process is repeated for the neutral conductor, namely the 0000 AWG conductor.

• As for the cable arrangement, this example dictates us to select “Three- conductor triangular grouping” with one neutral conductor. A bitmap just aside will display the selected cable configuration - giving the user a broad picture to enter the coordinates of the conductors based on the reference axis (X,Y).

• The spreadsheet table requires the coordinates of each cable conductors to be identified by its name: A, B, C or N (for example). The bitmap clearly identifies theses names and the user has only to enter the correct coordinates. The external radius of phase and neutral conductors, as well as their insulation thickness, allow us to calculate the entered coordinates as shown in the spreadsheet table.

• Finally, once all the required data are entered, click Compute to perform the calculation. If the input data are correct, the 60-Hz impedance parameters i.e. R1, L1, B1, R0, L0 and B0 are calculated and displayed in the window next to the “Compute” button. Clicking OK will update the main cable database with the calculated parameters expressed in the selected units.

Note: The capacitance of single core unshielded cables is not normally of interest. From the calculation point of view the capacitance is really not determinable, since no metallic sheaths are present. What the program calculates therefore is simply the capacitance with respect to the ground level (as if calculating the transmission line capacitances).

4.4.3.4 Data entry and calculation of a multi-wire concentric neutral cable

The following example calculation demonstrates the calculation of the sequence self-impedances of a three-phase circuit with multi-wire concentric neutral. Consider a 15 kV class circuit made from cables with 1000 MCM aluminum phase conductor and 20 #10 copper neutral wires.

The three-phase conductors A, B and C have a flat spacing with Da-b, Db-c and Da-c equal to 8, 8 and 16 inches respectively. The diameter over the phase conductor insulation is 1.729 inches.

By following the same steps as the previous examples, all the required data are entered in the Multi-wire Concentric Neutral Cables tab of the Cable Impedance

Calculation dialog box as indicated below.

The new data to be considered are:

• The number of the concentric neutral wires around a phase conductor: 20. • The diameter over the phase conductor insulation that is 1.729 inches (in this

displayed in the window next to the “Compute” button. Clicking OK will update the cable database with the calculated parameters expressed in the selected units.

4.4.3.5 Notes

The conductor radius, GMR (Geometric Mean Radius) and the resistance may be found in published tables, such as the ones in the ABB T&D Reference Book. You have the choice between Imperial units (inches) and SI units (cm.).

If the middle core axis of a conductor is made from dielectric materials, or is hollow, then the radius of the middle core is Internal Radius for conductor.

The GMR is defined as “the radius of a tubular conductor with an infinitesimally thin wall that has the same external flux out to a radius of one foot (30.5 cm.) as the internal and external flux of a solid conductor out to a radius of one foot”. (ABB T&D Book, p.36.) It is calculated as the N2 root of the product of the N2 distances between the N subconductors (strands) of the conductor.

N

Example: A conductor made up of 7 identical copper strands, each of radius R. (From Elements of Power System Analysis by W.D. Stevenson)

• Distances between conductors = measured center-to-center

• Inner and outer radii of the sheath: Losses in the sheath are represented by a small additional resistance computed using these values. A lead sheath is assumed.

• Geometric factor: It is applicable to the calculation of shunt susceptance. It is determined from the ratio of the sheath inner radius, ri, to the conductor

radius, r. (It can also be expressed in terms of the conductor diameter d and

insulation thickness T.)

The shunt susceptance B =0.3483 f k

( )( )

G

µ

where f is the frequency in Hz and k is the dielectric constant of the insulation.

Frequency is defined in the Study parameters (e.g. Study Parameters for Load Flow , in the CYMFLOW, CYM-Motor-Start & CYM-AC Contingency, Users’ Guide and Reference Manual.).

• Dielectric constant

Hint: k = 3.0 for EPR, 2.5 for XLPE, 4.0 for Butyl Rubber, 8.0 for PVC.

Note: The calculation is valid for single-conductor cables and three- conductor shielded cables. For three-conductor belted non-shielded cables, reduce the calculated B1 by 20% to 40% and reduce B0 by 50%. (Pages 68 and 77 of ABB T&D Book.)