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### 2 B. References: 1. FERC Form 1 Data 2. Electric Utility Total Owning Cost history 3. NEMA TP-1 from 2002 and from 1996 4. Distribution Transformer Size Optimizati on by Forecasting Customer Load by Jerrod Luze, Black Hills Power, Rapid City, South Dakota. 5. DOE Chapter 6 Energy Use and End Use Load Characterization. 6. ABB Total Ownership Cost (TOC) Calculator 7. Loading Study of a Manufacturing Plant by Philip J Hopkinson, PE (1995 and 2005) 8. Boston NEMA TP-1 Background (1995) 9. Optimizing Energy Efficiency Standards for Low Voltage Distribution Transformers a thesis by Ken Harden of Schneider Electric at Purdue University 10. NEETRAC Distribution Transformer Ther mal Test Procedure from May 29, 2002 11. My experience as a distribution tran sformer design engineer from 1966-2011 C. Scope 1. Medium Voltage Liquid Filled Distribution Transformers 2. Medium Voltage Dry Type Distribution Transformers 3. Low Voltage Dry Type Transformers. D. Assumptions 1. Transformers always remain energized and core loss (no load loss) is always occurring. 2. Transformer winding losses along with stra ys and eddies vary with the square of load current. 3. Historical no load and load loss relationships may be a significant indication for future decisions. 4. For all load considerations, peak transfor mer efficiency always occurs at the point where no load losses equal load losses. 5. Highest transformer losses occur at the highest permissible load. Hence differences in alternative transformer efficiencies at the highest load have greater impact on total watt losses. 6. Electric Utility Total Owning Cost (A and B factors) is representative of both the value of a watt saved and of their loading models. 7. Load cycles vary by regions of the country, by seasons of the year and by time of day. 8. RMS equivalent load is most representative of the watt losses that are being dissipated in the transformer in service. 9. Routine tests at a manufacturer’s produc tion facility should be converted to expected RMS equivalent load to verify the efficiency t hat will be most representative of the inservice condition. 10. The DOE measurement point for effici ency will normally o ccur at the most representative RMS equivalent load, which may or may not be equal to the point of peak efficiency where core loss equals load loss. However the transformer is usually most optimally designed for lowest cost wh en the measurement point occurs at the point of peak efficiency. E. A look at the 25 kVA single phase pole type transformer 1. The 25 kVA pole type transformer has been the most representative kVA rating for pole type transformers for many decades of time.

### 3 2. Many of the relationships for the 25 kVA transformer apply broadly to other medium voltage transformers, such as Total Owning Cost relationships and loss ratios. 3. During the 1960’s the 25 kVA transformer normally had 100 watts of core loss and 300 watts of load loss. 4. During the 1970’s Total Owning Cost relati onships were introduced with two factors, called A and B. The A factor was the present worth of a watt saved and was measured in $ / watt. The B factor was app lied to adjust full load winding loss to the value of load loss that is most representative of the normal expected operating condition, or the RMS equivalent load in se rvice. Mathematically, the following is a good way to visualize B: B= (PU Load)^2 * A (1) Where PU load is the per unit load of the transformer. Here, if PU Load is 0.5 then B becomes: B at 0.5 load = 0.5^2 * A = 0.25 * A (2) 5. In practice, the B factor is usually sli ghtly greater than the square of per unit load times A to recognize the value associated with peak demand. By increasing B slightly, the transformer will have suffici ently low load losses as to maintain a relatively flat efficiency over wide changes in load. This is im portant because loading can vary significantly and even exceed trans former rated kVA. If the transformer efficiency deteriorates excessively at high load then the peak demand may result in higher net cost to serve the load. 6. Total Owning cost formulas initially focused on an A factor of $3/watt and a B factor of $1/watt and remained in that range fr om the 1970’s to the mid 1980’s. 7. During the 1980’s and 1990’s wide variations of loss evaluations occurred with A factors varying from a low of under a dollar to as high as $10/watt. Interestingly the B factors remained mostly in a range of 0.2-0.3 * A. 8. In 1996, NEMA introduced TP-1, but derived from the relationship of a B factor = 0.25 A. Many manufacturers were solicited to supply design data that became the basis for the published efficiencies. 9. In 2007, the DOE published new mandatory efficiency values that became effective in 2010 that assumed an RMS equivalent load of 50% of nameplate. Manufacturers report that the same efficiencies may be reached by using TOC methods with an A factor of $4/watt and a B factor of $1/watt. 10. In 2011, many Utilities purchase transfor mers that just meet the DOE published efficiencies however some Utilities purchase tr ansformers to a TOC owning cost formula that reaches beyond the DOE requirements. The most common TOC formula for premium efficiencies is: a. A = $5.91/watt b. B = $1.81/watt 11. For any TOC relationship the RMS equivalent load is simply: RMS equivalent load = (B/A)^0.5 (3)
12. Recall that in the 1960’s the 25 kVA no load watts were 100 and the load watts were 300. Hence the assumed per unit load was: PU load in the 1960’s = (100/300)^0.5 = 0.58 (4) 13. From the 1970’s to the mid 1980’s t he assumed per unit load remained unchanged 14. During the 1980’s to 2000, some owning cost formulas had a B that was 0.25 A hence: PU load in the 2000-2011 period has ranged from 0.5-0.58 for all popular owning cost formulas.F

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