Transformer Loading 

• Load Factor 

– Defined as the ratio of Average to Peak Load 

• RMS Load 

– Measure of Average Load 

• Loss Factor 

– Average of the square of the Load 

– Measure of Load Losses that are used in the LCC 

– Equal to the square of the RMS 
RMS Load for DL 1 – 50kVA 1P LI 

Forecast: RMS Loading 

Statistic Forecast values 

Trials 10,000 

Mean 34%

Median 34%

Mode '---

Standard Deviation 7%

Variance 0%

Skewness 0.2336 

Kurtosis 2.59 

Coeff. of Variability 0.2065 

Minimum17%

Maximum 56%

Mean Std. Error 0%
RMS Load for DL7 75kVA -LVDT 

0

100

200

300

400

500

600

4.2% 11.5% 18.8% 26.2% 33.5% 40.1%

Frequency

RMSLoading (annual) Forecast values

Trials 10,000

Mean 22.1%

Median 22.2%

Mode 27.6%

Standard Deviation 6.6%

Variance 0.4%

Skewness -0.0845

Kurtosis 2.65

Coeff. of Variability 0.2959

Minimum 2.8%

Maximum 41.9%

Range Width 39.1%

Mean Std. Error 0.1%
RMS Load for DL12 1500kva 

0

50

100

150

200

250

300

350

400

450

500

9.5% 20.3% 31.0% 41.7% 52.5% 62.1%

Frequency

RMSLoading (annual) Forecast values

Trials 10,000

Mean 36.3%

Median 36.7%

Mode 44.1%

Standard Deviation 9.8%

Variance 1.0%

Skewness -0.2511

Kurtosis 2.75

Coeff. of Variability 0.2688

Minimum 4.8%

Maximum 62.7%

Range Width 57.9%

Mean Std. Error 0.1%
Average Lifetime: DL 1 -50kVA 

Forecast: life 

Statistic Forecast values 

Trials 10,000 

Mean 32

Median 33

Mode 32

Standard Deviation 12

Variance 137

Skewness -0.3247 

Kurtosis 2.79 

Coeff. of Variability 0.3674 

Minimum1 

Maximum 60

Mean Std. Error 0 
Service Lifetime 

• Average transformer lifetime is 32 years 

– Reference: ORNL-6847 Determination Analysis of Energy Conservation 

Standards for Distribution Transformers 

• Each transformer in the LCC simulation has a unique lifetime 

• Failure rates: 

– 0.5% per year from the first year of installation, due to lightning and other 

random causes 

– Additional 0.5% per year due to corrosion, starting in year 15 

• The failure rates are used to create a survival function, assuming a 

standard Weibull shape
0

100

200

300

400

500

600

700

2 13 25 37 49 59

Frequency

life Forecast values

Trials 10,000

Mean 32

Median 33

Mode 35

Standard Deviation 12

Variance 138

Skewness -0.3293

Kurtosis 2.78

Coeff. of Variability 0.3686

Minimum 1

Maximum 60

Range Width 59

Mean Std. Error 0

Average Lifetime: DL 12 -1500kVA 
0

100

200

300

400

500

600

700

2 13 25 37 49 59

Frequency

life Forecast values

Trials 10,000

Mean 32

Median 33

Mode 35

Standard Deviation 12

Variance 138

Skewness -0.3293

Kurtosis 2.78

Coeff. of Variability 0.3686

Minimum 1

Maximum 60

Range Width 59

Mean Std. Error 0

Lifetime: DL 7 1500kVA 3P 125 kVA BIL 
Peak Load Factor 
Space Constrained Installations 

• The current analysis uses the same design lines 

identified in the 2007 notice of data availability: 

DLs 4, and 5. 

• The analysis models two scenarios: 

1. Where an existing vault is enlarged to accommodate 

a larger transformer in the standards case, thus 

incurring additional installation charges: $1840 

initial cost plus $28 per ft cubic foot 

2. Where vault enlargement is not an option, the new 

transformer in the standards case must be of equal 

or lower volume then the transformer in the 

basecase, resulting in a more expensive unit 

• Described in Chapter 11 LCC Subgroups Analysis 
Pole Replacement 

• Pole replacement is calculated for DL2 

• The current pole replacement algorithm determines if 

a pole should be replace based on transformer weight. 

– If a transformer in the standards case is greater than 

1000lbs, the pole replacement is warranted. 

– An additional $2000 cost is added to the transformer 

installation costs if pole replacement is warranted. 

– Does not account for additional costs of moving other 

equipment that may reside on the pole. 

• Transformer height and width are held constant in the 

engineering data across efficiency levels. 

• Details of this analysis can be found in TSD chapter 8. 
Rural Cooperatives 

• Rural cooperatives have been identified as 

groups of customers who may be 

disproportionately affected by any national 

energy-efficiency standard level. 

– The LCC model is modified by adjusting the load 

on the transformer to 75% of that of the national 

average. 

– Results in lower LCC Savings and Longer PBP 

– Details of this analysis can be found in TSD 

chapter 11 
Equipment Price Trends 

• Estimates the impacts of increasing or 

decreasing transformer prices at a national 

level over time. 

• These are calculated as sensitivities in the NIA 

– The default case assumes flat prices over time 

– The low price case is modeled on historical price 

index from 1967 to 2010. 

– The high price case is modeled on the historical 

price index from 1991 to 2010. 
Equipment Price Trends (cont.) 

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1960 1970 1980 1990 2000 2010 2020 2030 2040 2050

Price Factor Index (2010=1)

Year

Low Price Scenario: PPI Exponential Fit (1967 to 2010) Default Scenario: Constant Price Index

High Price Scenario: PPI Exponential Fit (1991 to 2010) Deflated PPI (2010=1)
Electricity Prices 

• Electricity prices were re-scaled using AEO 

Price Trends 

80%

85%

90%

95%

100%

105%

2005 2010 2015 2020 2025 2030 2035

Real Price Relative to 2008

Year

Reference Case High Growth Low Growth
Evaluation Rates 

• The Customer Choice Model used in the LCC 

to determine if purchaser of a new 

transformer uses A and B parameters to 

evaluate their purchase, or purchases based 

on first cost 

• The following evaluation rates are used. 

• Liquid-immersed: 50%

• Low-voltage Dry-Type: 2%

• Small Capacity Medium-Voltage Dry-Type: 10%

• Large Capacity Medium-Voltage Dry-Type: 20%
Limited Design Selection Due to a 

Fixed Efficiency 

• Fixed efficiency ratings only impact the 

selection of transformers with a diversity of A 

and B in the most extreme cases. 

• The following slides illustrate the designs 

selected in the LCC for DL7. 
NL vs LL for DL 1 at EL 1 

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

0 20 40 60 80 100 120 140 160 180

Load Losses (watts)

No Load Losses (watts)

Design Load Losses (LL) vs No-Load Losses (NL)

at rated load

Available Designs

Selected Designs, Base

Selected Designs, Standard
NL vs LL for DL 7 at EL 3 

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

0 20 40 60 80 100 120 140 160 180

Load Losses (watts)

No Load Losses (watts)

Design Load Losses (LL) vs No-Load Losses (NL)

at rated load

Available Designs

Selected Designs, Base

Selected Designs, Standard
NL vs LL for DL 7 at EL 6 (Max Tech) 

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

0 20 40 60 80 100 120 140 160 180

Load Losses (watts)

No Load Losses (watts)

Design Load Losses (LL) vs No-Load Losses (NL)

at rated load

Available Designs

Selected Designs, Base

Selected Designs, Standard
Refurbishments 

• There is currently not data available on 

refurbishment behavior. 

– If the committee can supply data on 

refurbishments it can be incorporated into the 

analysis. 
END MV