Reformulation of the LCC Savings in Terms of A and B Values

DOE Distribution Transformer Negotiating Subcommittee Memo November 28, 2011

The LCC equation serves as the basis for both the LCC analysis and the LCC spreadsheet model. The LCC equation reflects both the first cost of a transformer and the present value of the operating costs throughout the service life of that transformer. The LCC equation is:

LCC = FC + ∑ � OC n (

1+ Drate )

n � Lifetime

n=0 .

Where:

FC = the first cost ($);

n = the index for the year of operation (n=0 is the standard year); Lifetime = the service life of the transformer;

OC

n = the operating cost in year n , including the value of the lo sses and maintenance costs ( $/yr); and

Drate = the discount rate applied to the calculation (%).

The first cost is the sum of three components:

FC = MFR_Price (1 + Markup ) + Inst_Cost

Where:
MFR_Price = the manufacturer price as given in the engineering design table ($) ; Markup = the distributor markup (%);
Inst_Cost = the cost of installation ($) ;

The quantity of interest is the change in LCC (Δ LCC ) u nder a change in efficiency. A change in efficiency leads to both a change in first cost (ΔFC) and a change in operating cost ( Δ OC

n ). The change in operating cost depends on the following parameters:

PEgy NL = the price of energy for the no -load losses ($/kWh); PCap NL = the annualized price of capacity for the no -load losses ($/kW- yr) ; PEgy LL = the price of energy for the load losses ($/kWh); PCap LL = the annualized price of capacit y for the load losses ($/kW- yr) ;
EPT

n = the electricity price trend factor for year n (n=0 is the standard year)

LG

n = the load growth factor for year n (n=0 is the standard year)

RMS = the annual average RMS load divided by the transformer capacity

PRF = the peak responsibility factor

Δ NL = the change in the no- load loss rate defined by the engineering data (W)

ΔLL = the change in the load loss rate defined by the engineering d ata (W)The economic parameters, transformer lifetime, and parameters defining the loading characteristics are not affected by a change in efficiency. Only the first cost and the magnitude of the losses change when the transformer efficiency changes.

The equatio n for the change in LCC can be reformulated using two parameters , A LCC and B LCC , that represent the total economic value of the no-load and load- losses calculated over the life of the transformer. This definition is conceptually the same as that used to define A and B parameters in the Total Ownership Cost estimates used in evaluating transformer losses. The practical difference is that, in the LCC, the values of A LCC and B LCC are calculated a posteriori using the economic parameters, lifetime and loading characteristics that have been chosen from

the statistical models used in the simulation. The equation for the change in the LCC is:

ΔLCC = ΔFC + A LCC * ΔNL + B LCC * ΔLL

The value of one watt reduction to the no-load losses is

A

LCC = ( 1/ 1000 ) � ( 8760 ∗ PEgy NL + PCap NL ) Lifeti me

n=0 � EPT n (

1+ Drate )

n �

The value of one watt reduction to the load losses is

B

LCC = ( 1/ 1000 ) � ( 8760 ∗ RMS 2 ∗ PEgy LL + PRF ∗ PCap LL ) Lifetime

n=0 � LG
n ∗ EPT n (

1 + Drate ) n �

The figures below show values of A LCC and B LCC for 1000 transformer simulations for Design Line 1 (liquid- immersed, 50kVa). The values of A LCC are distributed primarily between 10 and 30 $/Watt, while the values of B LCC fall primarily between 1 and 10 $/Watt. The value of A LCC vs. B LCC for each transf ormer installation is shown in the scatter plot of Figure 3. All of the inputs to the LCC equation are discussed in detail in Chapter 8 of the draft TSD.

The equation for A LCC can also be written in the form:

A

LCC = [ ( 8760 ∗ PEgy NL + PCap NL )/ 1000 ] � � EPT n (

1+ Drate )

n � Lifetime

n=0

The quantity in square brackets is the value of losses over one year, and the sum is a present
value factor that incorporates both the discounting and the electricity price trend over the life of
the transformer. The A values currently specified by transformer purchasers tend to be much

smaller than the A LCC values calculated here. This will be the case if the purchaser requires a
short payback period, which is mathematically equivalent to using a large discount rate in the

pr esent value factor. This implies that, for the purchaser, the energy losses have no value afterthe end of the payback period. The Department’s perspective is that the losses have value over

the entire life of the unit, and so the value of A LCC is higher. The same argument holds for B LCC

.

Figure 1 Distribution of A LCC

Figure 2 Distribution of B LCC

Figure 3 Scatter plot of A LCC vs. B LCC