primary distribution lines when calculating loss factors.
The cost per peak kilowatt for line losses for the sample cooperative is then determined as follows:
The resulting expense per kilowatt of loss can be used to quickly estimate the savings that will result from using UD designs that operate at lower losses. The loss savings can be compared with the annual carrying charges on the extra in- vestment costs required to achieve lower losses. This type of economic comparison is discussed in detail in the Distribution System Loss Manage-
ment Manual.
CABLE SYSTEM LOSSES
An essential step in the economic evaluation of losses is calculating the expected electrical losses for alternative designs. For a primary UD cable, losses occur in the conductor, sheath, and di- electric, and as a result of cable charging current.
Primary Cable Conductor Losses
The losses resulting from load current interact- ing with the conductor resistance (I2R losses) are by far the most significant losses in primary UD cables. For a run of three-phase cable, these
Annual Demand Cost per kW of Peak Losses $10/kW/month × 12 months = $120/kW
Annual Energy Cost per kW of Non-Load-Dependent Peak Losses 8,760 hours × $0.03/kWh = $263/kW
Annual Energy Cost per kW of Load-Dependent Peak Losses 0.3 × 860 hours × $0.03/kWh = $79/kW
Total Annual Cost per kW of Non-Load-Dependent Peak Losses
$120/kW + $263/kW = $383/kW
Total Annual Cost per kW of Load-Dependent Peak Losses $120/kW + $79/kW = $199/kW
Equation 1.1
WR=3 I2R L
where: WR= Total loss, in watts I = Load current, in amperes R = Phase conductor resistance, in
ohms per kilofoot (kft) L = Circuit length, in kft
losses are calculated by the formula shown in Equation 1.1.
Primary Cable Sheath Losses
The normal UD practice is to ground cable sheaths at both ends. When this is done on three-phase cable runs, a small amount of circu- lating current will be induced in the cable sheaths. The flow of this current produces a small loss in the sheaths, calculated as shown in Equation 1.2.
XM is determined using Equation 1.3.
Equation 1.2
where: WS= Total sheath loss, in watts I = Load current, in amperes RS = Sheath resistance, in ohms per kft L = Circuit length, in kft
XM= Sheath reactance, in ohms per kft WS= 3 I2R SL X2M R2 S+ X2M Equation 1.3
where: XM= Sheath reactance, in ohms per kft S = Center-to-center spacing, in mils,
for equilaterally spaced cables rM = Mean radius, in mils, to the sheath
for each cable XM= 0.05292 log10
S rM
Primary Cable Dielectric Losses
Voltage stress on cable insulation produces a slight heating effect that leads to power losses. These dielectric losses can be calculated using Equation 1.4.
The formula in Equation 1.4 shows that di- electric losses are directly proportional to the product ofεtand cosφ. Cable engineers refer to
the productεtcosφ as the cable loss factor. This
use of the term loss factor is completely different from the use of loss factor earlier in this section. Dielectric losses are a consequence of the cable being energized and are, therefore, continuous; whereas the more common use of the term loss
factor deals with losses due to the resistance of
the conductor and, therefore, vary with the mag- nitude of the load being carried by the cable.
Primary Cable Charging-Current Losses
The capacitance of an underground cable draws charging current that interacts with the conduc- tor resistance to produce a small loss. If the cable is delivering current to low power factor load, the charging current will be beneficial be- cause its leading nature will cancel out some of the lagging load current. Therefore, charging- current losses are of concern for only unloaded cables or those carrying unity power factor loads.
The procedure for calculating charging-cur- rent losses begins with determining the cable capacitance per phase with Equation 1.5.
Equation 1.4
where: WD = Total three-phase dielectric loss, in watts
E = Line-to-ground operating voltage, in kV
L = Circuit length, in kft
εt = Dielectric constant of the insulation cosφ = Insulation power factor, per unit T = Insulation thickness, in mils D = Conductor diameter, in mils
WD= 8.28 E2Lε tcosφ log10 2T+D D Equation 1.5
where: C = Cable capacitance, in nanoFarads (nF) per kft
εt = Dielectric constant of the insulation T = Insulation thickness, in mils D = Conductor diameter, in mils
2T+D D C = 7.354εt log10 Equation 1.6 IC= 0.000377 C E
where: IC = Charging current, in amperes per kft C = Cable capacitance, in nF per kft E = Line-to-ground operating voltage,
in kV
Equation 1.7
WC= R I2CL3
where: WC= Total three-phase charging current loss, in watts
R = Phase conductor resistance, in ohms per kft
IC = Charging current, in amperes per kft L = Circuit length, in kft
Data for Cable Loss Calculations
Many items of technical data are needed on the cables involved to calculate losses from the above formulas. Physical measurements such as diameter and insulation thickness are usually shown on manufacturers’ catalog sheets. Basic electrical data such as voltage, amperes, and resistance are known from the system or can
Next, charging current per kilofoot of cable length is calculated with Equation 1.6.
Finally, the charging-current loss is calculated as shown in Equation 1.7.
easily be found from catalog sheets or standard references.
The insulation dielectric constant,εt, and power factor, cosφ, are sometimes difficult to determine. Manufacturers’ data sheets often do not give these parameters. For pure materials such as TR-XLPE, the information may be ob- tained from standard references. However, most modern insulation types contain additives that affect dielectric constant and power factor. To
be sure that the correct values are known, it is usually necessary to contact engineering special- ists on the staff of the manufacturer of each spe- cific cable type. There are often large differences in values for dielectric constant and power fac- tor among various cable types. The spread in values is especially pronounced for the power factor. In addition, the cable power factor often varies substantially with cable temperature. It is recommended that, if comparisons are being
EXAMPLE 1.1: Cable Loss Calculations.
This example contains typical data; however, don’t use the sample data in actual-case calculations. For actual situations, consult the cable manufacturer to get accurate data on the cable being used. Table 1.19 shows data and loss calculation results for a typical three-phase cable run. Three insulation types are represented at two different temperatures.
@ 25° C @ 50° C
Low-Loss High-Loss Low-Loss High-Loss
Insulation Type Sample Data TR-XLPE EPR EPR TR-XLPE EPR EPR
(E) Line-to-Ground Operating Voltage in kV 7.2 7.2 7.2 7.2 7.2 7.2
Conductor Size 1/0 A1 1/0 A1 1/0 A1 1/0 A1 1/0 A1 1/0 A1
(D) Diameter in mils 373 373 373 373 373 373
(T) Thickness in mils 220 220 220 220 220 220
(rM) Mean Radius in mils 430 430 430 430 430 430
(S) Center-to-Center Spacing in mils 1,180 1,180 1,180 1,180 1,180 1,180
(R) Resistance inΩ/kft 0.20 0.20 0.20 0.20 0.20 0.20
(RS) Sheath Resistance inΩ/kft 0.60 0.60 0.60 0.60 0.60 0.60
(εt) Dielectric Constant of the Insulation 2.35 2.9 3.27 2.35 2.9 3.27
(cosφ pu) Insulation Power Factor per Unit 0.06 0.25 2.0 0.06 0.30 3.25
(L) Circuit Length in kft 4.0 4.0 4.0 4.0 4.0 4.0
(I) Load Current in Amperes 60 60 60 60 60 60
Conductor Loss, Watts 8,640 8,640 8,640 8,640 8,640 8,640
Concentric Neutral Loss, Watts 38.7 38.7 38.7 38.7 38.7 38.7
Dielectric Loss, Watts 715 3,679 33,184 715 4,414 53,924
Charging Loss, Watts 0.3 0.4 0.5 0.3 0.4 0.5
TOTAL LOSS, Watts 9,394 12,358 41,863 9,394 13,093 62,603
*Insulation Data Courtesy of the Okonite Company
made among cable types, the engineer should use only written data obtained from the manu- facturer of that cable type. An excellent source of this data is the cable manufacturer’s Insulated Cable Engineers Association (ICEA) Qualification Report for the particular cable construction. Once the figures are obtained, compare the data from different sources to confirm the reasonableness of the information for a particular cable type.
When requesting data from cable manufactur- ers, be as specific as possible about the data being requested. Ask the manufacturer for the data from ICEA qualification tests. Losses should be quoted for a specific temperature, such as 40°C.
The loss figures in Table 1.19 show that sheath, dielectric, and charging-current losses are negligi- ble compared with conductor load-current losses, except in the case of high-loss EPR. However, under light-load or other unusual conditions, the relative values of the three types of losses may become more significant. Charging-current loss- es, for example, may become significant for ex- tremely long cable runs because these losses in- crease with the cube of the circuit length.
Another important consideration is that small loss differences among alternative cable types can accumulate to a significant expense if an extremely large amount of cable is placed in ser-
vice. The dielectric loss differential between nor- mal EPR cable and TR-XLPE cable is approxi- mately 0.22 kW per circuit mile from the results shown on the table. Because this loss is non- load-dependent, the annual loss expense per mile as calculated above is typically $84 per mile (0.22 kW/mile × $383/kW). For 100 circuit miles of installed cable, this expense comes to $8,400 per year, which no longer seems insignif- icant. However, in a total economic evaluation, the cost of additional dielectric losses ($84 per mile) must be compared with any additional life expectancy that might be available from the higher loss insulation system. Appendix D of NRECA CRN Project 90-8 provides a method for evaluating cable losses and life expectancy in the purchasing process.
Secondary Cable Losses
For secondary UD cables, losses other than load-current-related conductor I2R losses are truly insignificant. Loss control methods for ap- plication to secondary designs are the same as described in the NRECA Distribution System Loss
Management Manual for either overhead or un-
derground situations. Appendix B to that manual gives annual kilowatt-hour losses for a selection of conductor sizes and loading levels.
This example illustrates how the losses on secondary cables are calculated. Sample data are shown in Table 1.20.
The conductor resistance is obtained from standard ref- erences. A conductor temperature of 25°C is assumed for underground secondary cables that are not heavily
loaded. In this case, a resistance of 0.167 ohms per kft is given by reference tables.
Load on the neutral is assumed to be negligible. There- fore, the conductor distance is 300 feet, and the total resistance is 0.05 ohms.
Losses at peak load are calculated as follows:
Annual energy losses are determined by using the loss factor:
EXAMPLE 1.2: Calculating Losses on Secondary Cables.
Voltage of Circuit 120/240-V, single-phase
Circuit Length 150 feet
Conductor No. 1/0 AWG, aluminum
Peak Load 85 amperes
Loss Factor 20%
TABLE 1.20: Sample Secondary Cable Data.
WR= I2R = 852× 0.05 = 361 watts
Energy Losses = 0.2 × 8,760 hours × 361 watts = 632,472 watt-hours = 632 kWh
PAD-MOUNTED TRANSFORMER LOSSES
The losses on pad-mounted transformers used on UD systems are a significant expense. Close attention to the management
of losses on any type of trans- former is essential to a loss control program.
As with all types of trans- formers, losses on pad- mounted transformers are of two distinct types. The first category, core losses, is not
load dependent and represents a continuous ex- pense whenever the transformer is energized. The second category, winding losses, comprises load-dependent losses that become especially expensive during peak loads.
Higher efficiency transformers with losses
Consider a 50-kVA pad-mounted transformer having 140 watts of core losses and 490 watts of winding losses at nameplate load. If this unit is loaded to 60 kVA at peak load, the winding losses will be as follows:
With the annual cost figures given for losses at the beginning of this subsection, the annual costs associated with each type of loss can be calculated as follows:
The total annual cost of the losses associated with operating this transformer is $194.
EXAMPLE 1.3: Typical Costs Associated with Transformer Losses.
Winding Losses = (60 ÷ 50)2× 490 watts = 706 watts
Core Loss Cost = $383/kW × 0.140 kW = $54 Winding Loss Cost = $199/kW × 0.706 kW = $140
approximately 20 percent less than this example are available from manufacturers. Use of the higher efficiency transformer will save about $40
annually, which is enough to amortize about $300 in initial investment cost at a 12 percent carrying charge rate over a 20- year period. Thus, if the higher efficiency transformer can be purchased for less than a $300 price premium over the sam- ple transformer, then it is a better economic choice in the long run.
The Distribution System Loss Management
Manual provides thorough coverage of the issue
of transformer losses and the means to control the associated expenses to the extent feasible.
DEFERMENT OF TRANSFORMER ENERGIZATION
New housing developments often require the construction of the electric UD system well be- fore most living units are built and occupied. When energized transformers are installed be- fore there are consumers to serve, the non-load- dependent or no-load losses on the transformers represent an expense that is uncompensated by revenue. This expense can be avoided by keep- ing the transformers de-energized until they are needed. Service to street lights can be concen- trated in a small number of transformers to allow the de-energization of most of the units in areas not yet occupied.
Installing a de-energized transformer requires the use of a feed-through stand-off bushing which, in most cases, costs about $150. Because this bushing can be reused elsewhere after the transformer is placed in service, the special bushing cost is equivalent to $20 annually at a 12 percent carrying charge rate over a 20-year period. Despite this expense, the avoidance of core losses represents a net savings, as shown by Table 1.21.
If hundreds of units are involved, the savings associated with deferred energization could ex- ceed $8,000 annually.
For 50- and 100-kVA installations, larger sav- ings can be achieved by deferring the installation of each transformer not needed for immediate service by placing a pedestal containing a feed-