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October 6, 2011 

Members of the NEMA/ DOE Rulemaking Group 

I would like to share some thoughts that I hope will provoke us all into our making more good decisions as 

we move forward with this project. 

From what I am reading there seems to be a need to have a little better understanding of what the “A” 

and “B” factors can really do for our analysis. 

As we examine these factors, we must remember that they are developed for the sole purpose to indicate 

the additional revenues that are needed by the electric utility companies to fund the components in their 

respective fixed charge rates. As we all know, the “A” and “B” factors are important parts of the TOC 

calculation, as they represent the additional revenue coefficients that are applied to the losses of the 

transformers purchased by the electric utilities. 

We need to remember that for, say a 20% annual fixed charge rate (FCR), the components comprising 

this rate include: sinking fund factor depreciation, property taxes, the utility’s weighted cost of 

capital, and a few other smaller items. 

Suppose the utility is buying a transformer for $ 1000 that has no losses (0 watts of NL and LL losses). 

Annually this transformer must generate revenue of $ 200 (@ a 20% annual FCR). The equivalent first 

cost of the transformer is $ 1000 but the present worth of the annual revenue requirement over 30 years 

at a 7% annual discount rate is $ 200 X 12.4 = $ 2481.80, where 12.4 is the present worth factor of a 

uniform annual cost (at year’s end) over 30 years. 

Below is a table that shows the relationship of equivalent first cost, annual cost from a FCR, and 

present worth. 

. 

Conversion Factors FOR                                     

Uniform Annual Cost                                        

Equivalent First Cost                                        

Present Worth

        

GIVEN    DESIRED    MULTIPLY GIVEN

BY

UNIFORM ANNUAL

COST

EQUIVALENT FIRST

COST

1/(FCR)

UNIFORM ANNUAL

COST

PRESENT WORTH (PWF)

EQUIVALENT FIRST

COST

UNIFORM ANNUAL

COST

(FCR)

EQUIVALENT FIRST

COST

PRESENT WORTH (FCR) (PWF)

PRESENT WORTH UNIFORM ANNUAL

COST

1/(PWF)

PRESENT WORTH EQUIVALENT FIRST

COST

1/((PWF)(FCR))

FCR = ANNUAL FIXED CHARGE RATE                                         

PWF=PRESENT WORTH FACTOR                 
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Now let’s suppose this $ 1000 transformer has some NL losses and Load losses. To the annual revenue 

requirement to recover the $ 1000 investment the cost of losses must be added. In most cases that 

amount on an equivalent first cost basis will be equal to or greater than the selling price of the 

transformer. This is the TOC approach for evaluating transformers. 

My basic point is that the TOC is not a life cycle cost for the transformer. It is the revenue requirement

to cover the transformer price and its associated cost of losses. 

We could claim the TOC a life cycle cost but that claim would apply on for only electric utility customers. 

For the Institutional, Commercial, and Industrial customers (ICI customers) TOC and “A” and “B” 

factors should not be applied, because these types of businesses don’t have what is known as an annual 

fixed charge rate (FCR). This is the reason that ICI types of customers employ the concept of a payback 

period for a quantitative input on investment decisions. Most ICI customers will not make incremental 

investments that have payback periods in excess of 3 years due to risk and uncertainty factors. 

From the discussions and communications I’ve seen on this most recent endeavor to ascertain the proper 

transformer efficiencies, it appears that we just accept “A” and “B” as given values that are absolutely 

accurate and correct for a particular utility. This may not be so. 

The Value of “A” = [1/FCR] * [PLANT$ * FCR + 8760 *($/kw-hr)] * [Core Loss in KW] 

The Value of “B” = [1/FCR] * [ K2

] * [PLANT$ * FCR * RsFAC + 8760 * ($/kw-hr) * Loss Factor)] * (Cond Loss in KW) 

Looking at the core loss expression for “A” we must remember that not only is the utility’s cost per kw-hr 

involved; but also their investment in generating plants plus transmission & distribution systems 

(PLANT$) must be considered. So far in our communications about the ICI customers we’ve included 

only the cost of energy but ignored the demand charge (representing equipment investment by the utility) 

in our PW valuations of the cost of losses. 

Note in the expression for “B”: K2, is the PW of the peak loads in p.u. of NP, the responsibility factor is 

the portion of the time that the peak load on the transformer coincides with the utility’s system peak, and 

the loss factor is the portion of time during the year that the actual peak load on the transformer would 

have to be present to equal the total load losses that were actually incurred. If each of these special 

factors were equal to 1.00, “B” would be equal to “A”. But these parameters are not equal to 1.00 usually. 

For Low Voltage Dry and Medium Voltage transformers we’ve considered K2

 to be equal to either (.35)2 

or (.5)2 . And these K2 values may be much lower based on some excellent input by Mr. Tom Patzner of 

Schneider. Typically responsibility factors will range from 0.7 to 0.9, and loss factors will be somewhere 

in the 0.5 range. So we can say we’re right to show the values of “B” to be less than “A”. 

But what we can’t say without a lot more research is what the order of magnitude should be for “A” and 

“B”. For instance if the system cost is $4000/kw and the energy cost is 10¢ per kw-hr,, with a FCR of 

20%, “A” would be equal $ 8380/KW or $ 8.38/watt. 

I suspect the system cost is more nearly in the range of $ 2000/KW and from Mr. Phil Hopkinson’s 

excellent paper the utility energy cost is $0.045/kWH. With these values “A” becomes equal to $ 

3871/KW or $ 3.71/watt. 

Having caused the readers to grit your teeth through all of this boring and mundane analysis ,in which I 

have tried to emphasize how the TOC arithmetic should be understood and mention all of the complex 

judgments that go into the choosing of the correct factors and costs, may I suggest the following: 

1. For the Liquids: We select an efficiency level that causes the utility customer to pay no more 

than 70¢ for each Total Owning Cost $ saved with a higher efficiency (TSL) than the present 

DOE 2010 efficiencies 

2. For the Drys: (LV and MV): We select an efficiency level (TSL) that allows the end user to 

experience a payback period of no longer than 5 years. 
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Unless we are presented better information for the electricity cost values, for the recommendations in 

numbers 1 and 2 above I propose that we should use the values presented in Phil Hopkinson’s 9/24/11 

report sent to the negotiating committee. 

Thank you for consideration of this recommendation and I welcome comments and corrections to this 

letter. 

Very truly yours, 

Bob Smith, Negotiating Committee Alternate 

Product Manager 

Federal Pacific