# 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 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 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