maxImum dIVersIFIed demand

ln . ln .

.

. . ,

1 6182 1 07175 0 48130

0 06929 6 946 or 7 years

Therefore, if the 7500/9375 kVA-rated transformer is installed, it will be loaded to its fans-on rating in about 7 years.

2.3  maxImum dIVersIFIed demand

Arvidson [7] developed a method of estimating DT loads in residential areas by the diversified-demand method, which takes into account the diversity between similar loads and the noncoinci-dence of the peaks of different types of loads.

To take into account the noncoincidence of the peaks of different types of loads, Arvidson intro-duced the hourly variation factor. It is “the ratio of the demand of a particular type of load coinci-dent with the group maximum demand to the maximum demand of that particular type of load [2].”

Table 2.2 gives the hourly variation curves for various types of household appliances. Figure 2.13 shows a number of curves for various types of household appliances to determine the average maxi-mum diversified demand per customer in kilowatts per load. In Figure 2.13, each curve represents a 100% saturation level for a specific demand.

To apply Arvidson’s method to determine the maximum diversified demand for a given satura-tion level and appliance, the following steps are suggested [2]:

1. Determine the total number of appliances by multiplying the total number of customers by the per-unit saturation.

2. Read the corresponding diversified demand per customer from the curve, in Figure 2.13, for the given number of appliances.

3. Determine the maximum demand, multiplying the demand found in step 2 by the total number of appliances.

4. Finally, determine the contribution of that type load to the group maximum demand by multiplying the resultant value from step 3 by the corresponding hourly variation factor found from Table 2.2.

example 2.12

Assume a typical DT that serves six residential loads, that is, houses, through six service drops (SDs) and two spans of secondary line (SL). Suppose that there are a total of 150 DTs and 900 resi-dences supplied by this primary feeder. Use Figure 2.13 and Table 2.2. For the sake of illustration, assume that a typical residence contains a clothes dryer, a range, a refrigerator, and some lighting and miscellaneous appliances. Determine the following:

a. The 30 min maximum diversified demand on the DT.

b. The 30 min maximum diversified demand on the entire feeder.

c. Use the typical hourly variation factors given in Table 2.2 and calculate the small portion of the daily demand curve on the DT, that is, the total hourly diversified demands at 4, 5, and 6 PM, on the DT, in kilowatts.

table 2.2 hourly Variation Factors heat PumpaWater heaterb oPWhc hour

lighting and  miscellaneous  refrigeratorhome  Freezerrangeair-conditioningacooling  seasonheating  seasonhousea  heatingboth elements  restrictedonly bottom  elements restricteduncontrolledclothesd  dryer 12 AM0.320.930.920.020.400.420.340.110.410.610.510.03 10.120.890.900.010.390.350.490.070.330.460.370.02 20.100.800.870.010.360.350.510.090.250.340.300 30.090.760.850.010.350.280.540.080.170.240.220 40.080.790.820.010.350.280.570.130.130.190.150 50.100.720.840.020.330.260.630.150.130.190.140 60.190.750.850.050.300.260.740.170.170.240.160 70.410.750.850.300.410.351.000.760.270.370.460 80.350.790.860.470.530.490.911.000.470.650.700.08 90.310.790.860.280.620.580.830.970.630.871.000.20 100.310.790.870.220.720.700.740.680.670.931.000.65 110.300.850.900.220.740.730.600.570.670.930.991.00 12 noon0.280.850.920.330.800.840.570.550.670.930.980.98 10.260.870.960.250.860.880.490.510.610.850.860.70 20.290.900.980.160.890.950.460.490.550.760.820.65 30.300.900.990.170.961.000.400.480.490.680.810.63 40.320.901.000.240.971.000.430.440.330.460.790.38 50.700.901.000.800.991.000.430.7900.090.750.30 60.920.900.991.001.001.000.490.8800.130.750.22 71.000.950.980.300.910.880.510.7600.190.800.26 80.951.000.980.120.790.730.600.541.001.000.810.20 90.850.950.970.090.710.720.540.420.840.980.730.18 100.720.880.960.050.640.530.510.270.670.770.670.10 110.500.880.950.040.550.490.340.230.540.690.590.04 12 PM0.320.930.920.020.400.420.340.110.440.610.510.03 Source:From Sarikas, R.H. and Thacker, H.B., AIEE Trans., 31(pt. III), 564, August 1957. With permission. a Load cycle and maximum diversified demand are dependent on outside temperature, dwelling construction and insulation, among other factors. b Load cycle and maximum diversified demands are dependent on tank size, and heater element rating; values shown apply to 52 gal tank, 1500 and 1000 W elements. c Load cycle dependent on schedule of water heater restriction. d Hourly variation factor is dependent on living habits of individuals; in a particular area, values may be different from those shown.

1 2 3 4 5 6 7 8

Average maximum diversified demand (kW/load)

9 10 109

87 6 5 4 3

2

1.00.9 0.70.6 0.5 0.4 0.3

0.2

0.10 0.080.07 0.06 0.05 0.04 0.03

0.02

0.01 20 30 40 50 60 70 100

L

K

A

C B

D E F

G H I

J

Number of loads

FIgure 2.13  Maximum diversified 30 min demand characteristics of various residential loads: A, clothes dryer; B, off-peak water heater, “off-peak” load; C, water heater, uncontrolled, interlocked elements;

D,  range; E, lighting and miscellaneous appliances; F, 0.5-hp room coolers; G, off-peak water heater,

“on-peak” load, upper element uncontrolled; H, oil burner; I, home freezer; J, refrigerator; K, central air- conditioning, including heat-pump cooling, 5-hp heat pump (4-ton air conditioner); L, house heating, including heat- pump- heating-connected load of 15 kW unit-type resistance heating or 5 hp heat pump.

(From  Westinghouse Electric Corporation, Electric Utility Engineering Reference Book-Distribution Systems, Vol. 3, Westinghouse Electric Corporation, East Pittsburgh, PA, 1965.)

solution

a. To determine the 30 min maximum diversified demand on the DT, the average maximum diversified demand per customer is found from Figure 2.13. Therefore, when the number of loads is six, the average maximum diversified demands per customer are

Pav

1.6 kW/house for dryer 0.8 kW/house for range 0.066 kW

,max =

//house for refrigerator

0.61 kW/house for lighting and misc. appliances



(3.076 kW/house)(6 houses) = 18.5 kW

Thus, the contributions of the appliances to the 30 min maximum diversified demand on the DT is approximately 18.5 kW.

b. As in part (a), the average maximum diversified demand per customer is found from Figure 2.13. Therefore, when the number of loads is 900 (note that, due to the given curve characteristics, the answers would be the same as the ones for the number of loads of 100), then the average maximum diversified demands per customer are

Pav

1.2 kW/house for dryer 0.53 kW/house for range 0.044 k

,max=

W

W/house for refrigerator

0.52 kW/house for lighting and misceellaneous appliances



Therefore, the 30 min maximum diversified demand on the entire feeder is

( ) .

However, if the answer for the 30 min maximum diversified demand on one DT found in part (a) is multiplied by 150 to determine the 30 min maximum diversified demand on the entire feeder, the answer would be

150 × 18.5 ≅ 2775 kW

which is greater than the demand 2064.6 kW found previously. This discrepancy is due to the application of the appliance diversities.

c. From Table 2.2, the hourly variation factors can be found as 0.38, 0.24, 0.90, and 0.32 for dryer, range, refrigerator, and lighting and miscellaneous appliances. Therefore, the total hourly diversified demands on the DT can be calculated as given in the following table in which

(1.6 kW/house)(6 houses) = 9.6 kW (0.8 kW/house)(6 houses) = 4.8 kW (0.066 kW/house)(6 houses) = 0.4 kW (0.61 kW/house)(6 houses) = 3.7 kW

time

lighting and misc. total hourly dryers, kW ranges, kW refrigerators, kW appliances, kW diversified demand, kW

(1) (2) (3) (4) (5) (6)

4 PM 9.6 × 0.38 4.8 × 0.24 0.4 × 0.90 3.7 × 0.32 6.344

5 PM 9.6 × 0.30 4.8 × 0.80 0.4 × 0.90 3.7 × 0.70 9.670

6 PM 9.6 × 0.22 4.8 × 1.00 0.4 × 0.90 3.7 × 0.92 10.674

Note: The results given in column (6) are the sum of the contributions to demand given in columns (2)–(5).