# 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

Minimum 17%

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

Minimum 1

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 shape0 100 200 300 400 500 600 700

2 13 25 37 49 59Frequency 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

- 1500kVA0 100 200 300 400 500 600 700

2 13 25 37 49 59Frequency 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 2050Price 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 2035Real 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 180Load 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 180Load 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 180Load 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