*This article is excerpted from "Premium-Efficiency Motors and Transformers", a*CD-ROM is available from the Publications List.

## Introduction

Transformers typically can be expected to operate 20-30 years or more, so buying a unit based only on its initial cost is uneconomical and foolish. Transformer life-cycle cost (also called "total owning cost") takes into account not only the initial transformer cost but also the cost to operate and maintain the transformer over its life. This requires that the total owning cost (TOC) be calculated over the life span of the transformer. With this method, it is now possible to calculate the real economic choice between competing models. (This same method can be used to calculate the most economical total owning cost of any long-lived device and to compare competing models on the same basis.) The TOC method not only includes the value of purchase price and future losses but also allows the user to adjust for tax rates, cost of borrowing money, different energy rates, etc.

A basic version of the TOC formula would look like this:

Since the formula includes the cost of losses, which will occur in the future, it is necessary to discount these future costs to equate them to present-day dollars (your company comptroller may be of assistance here). The transformer manufacturer supplies the bid price. If the A and B values are known, then the manufacturers should base the bid prices on the same A and B factors in all cases.

The cost of no-load and load losses are calculated using the following formulas:

**Cost of No-load Losses = A x (No-load Losses) Cost of Load Losses = B x (Load Losses)**

## How to Calculate Transformer Life-Cycle Cost

The A and B factors as described in an article titled, "Introduction to Transformer Losses," (elsewhere on this CD-ROM) have been determined on the basis of equivalent first cost and need no further manipulation. This has the benefit of allowing the manufacturer to design the transformer to meet the A and B factors specified by the customer. No-load losses are constant for each transformer design, being dependent on the core steel characteristics and design. Load losses, on the other hand, are variable and directly proportional to the load on the transformer, typically being stated at the full-rated nameplate loading.

If the A and B values are not known, as is typical of smaller users, merely use the load loss and no-load loss in watts, multiplying each by the relevant hours and cost per kWh. (The case history of Herman Miller Company uses this method.)

## Benefits of Using Transformer Life-Cycle Cost (Total Owning Cost)

Life-cycle cost (or total owning cost) analysis is a method that encompasses not only the initial purchase price but also the comparative operating costs of competing models, equalized to present-day dollars. **Since the operating cost of a transformer over its life may be many times its initial price, the only fair comparison with competing models must take operating costs into account.**

Another benefit to owning a transformer with low life-cycle cost, results from the fact that it runs cooler. Loss in the form of heat reduces the life of a transformer by causing damage to the insulation over time. It can also cause transformers to fail. Consequently, a transformer with lower life-cycle cost wouild be expected to have a longer life and lower failure rate, as well as lower losses. A transformer with lower losses (both core and coil) reduces the amount of power generation needed to accommodate the losses. This in turn reduces the emission of greenhouse gases, *i.e.* carbon dioxide (CO^{2}), produced by fossil fuel generators.

## Why Is a Premium-Efficiency Transformer Worth the Cost?

A premium-efficiency transformer costs more initially, but saves sufficient money over time to more than pay back the extra purchase cost. Pay a little more up front for a premium transformer and save money over the life of the unit, or save a few dollars on a low-first-cost standard-efficiency transformer and continue to spend more money on wasted electric power for 20-30 years.

Premium-efficiency transformers have cores made of low-loss silicon steel with copper windings or amorphous steel with copper windings. Copper windings have lower resistance per cross-sectional area than aluminum windings. Thus, copper windings require smaller cores that produce lower no-load losses and offer greater reliability.

The transformer manufacturers have reduced the no-load losses of silicon steel transformers by over 60 percent in the last 30 years. They have accomplished this reduction in four ways: (1) they have improved the construction of the silicon steel, itself; (2) they have improved the cutting of the laminations; (3) they have improved the stacking or assembling of the laminations in the core of the transformer; (4) and finally, by using improved computer models of the no-load losses, they can better design the core to reduce no-load losses.

Premium-efficiency transformers with cores made of amorphous steel with copper windings have even lower no-load losses than silicon steel transformers. Transformers with amorphous steel in their cores lose 70-80 percent less energy in their core than silicon-core transformers.

Manufacturers also reduce core losses by using thinner laminations in the core and by using step-lapped joints. Rather than butting the laminations joints, they interleave laminations and increase the amount of steel that bridges the joint gap. This reduces the resistance between the laminations and thus reduces eddy current losses.

## Example 1: Life-Cycle Cost Comparison of Two 75-kVA Transformers Using A and B Values

An example of the TOC of a more efficient (copper-wound) 75 kVA transformer to less efficient (aluminum wound) 75 kVA at 100% loading provided by Olsun Electrics illustrates the lower TOC of the more-efficient copper-wound transformer: In this example, the A value is assumed to be $1.50 per watt, and the B value is $0.35 per kWh.

TOC = Initial cost of transformer + Cost of the No-load Losses + Cost of the Load Losses

**TOC of more efficient** = $2,064 + ($1.50/watt)(320 watts) + ($0.35)(1670 watts)

= $3,128.50

**TOC of less efficient**= $1,979 + ($1.50/watt)(350 watts) + ($0.35)(1874)

= $3,159.90

In this example, the more efficient transformer costs $85 more initially, but has 30 watts less core loss, and 204 watts lower coil loss, so the total owning cost of the more efficient unit is less than the cheaper first-cost unit.

## Example 2: Total Owning Cost of a 750 kVA Transformer Using No-load and Load Losses and Present Value of Money

If you do not have, or do not use A and B factors in your business (they are typically used at utilities, but frequently not at many commercial businesses), you should ask for the no-load and load losses in watts from the manufacturer. Having that data, two other types of economic calculation can be performed, total owning cost both with and without the present value of money factored in.

Let's consider a simplified comparison of two alternative transformers assuming we have the no-load and load loss. We will assume that electricity costs are $0.075 per kWh, and are steady for 15 years of estimated life, with no variation for time of day. The "discount" factor for relating future costs to present day dollars is assumed to be 10 per cent (consult your comptroller or accountant for the correct factor for you). By present value, we mean that in order to pay for $1 in losses one year from now, we need to have $0.91 today, which can be invested (after taxes) at 10% return. Our transformer will be loaded to 75% of nameplate rating for 6,000 hours per year, and zero load for 2,760 hours per year. Salvage value, rate changes, inflation and maintenance costs are omitted for simplification.

For one year, the present worth of a sum at 10% discount factor is:

PW= |
1(1 + i) ^{n} |

where: **i** = discount factor, **n** = number of years (in this case n= 1)

for one year, PW = 1 / (1 + 0.1)^{1}

PW = 1 / (1.1) = 0.909

For a series of equal payments (costs) over time, the present worth formula becomes:

PW = |
(1 + i)^{n} - 1 |

i(1 + i)^{n} |

Let's plug in some typical values for a 750 kVA transformer.

Standard Transformer | High-Efficiency Transformer |
---|---|

Purchase price - $10,194 No-load losses - 1647 W Load losses at 100% - 9507 W Load loss at 75% - 5348 W |
$10,845 1018 W 6769 W 3808 W |

**Total Owning Cost of Transformer #1 (standard efficiency):**

TOC = purchase price + present value of future no load losses + present value of future load losses

Purchase price = $10,194

No load losses per year = 1.647 kW x 8760 h/y x $0.075/kWh = $1,082.08

Present Value (P.V.) of no load losses for 15 yrs

= $1082.08 x ((1+0.1)15 -1) / (0.1) x (1+ 0.1)15

= $1,082.08 x ( 4.1772 -1) / 0.41772

= $8,229.74

Load losses per year = 5.348 kW x 6000 h/y x $0.075/kWh = $2,406.60

P.V. of load losses for 15 yrs. = $2,406.60 x (4.1772 - 1) / 0.41772

=$18,304.72

**Total Owning Cost of Standard-Efficiency**= $10,194.00 + $8,229.74 + $18,304.72 =

**$36,728.46**

**Total Owning Cost of transformer #2 (high efficiency):**

TOC = purchase price + present value of future no load losses + present value of future load losses

Purchase price = $10,845

No load losses per year = 1.018 kW x 8760 h/y x $0.075/kWh = $668.83

P.V. of no load losses for 15 yrs | = $668.83 x ((1+0.1)^{15} -1) / (0.1)(1+ 0.1)^{15} |

= 668.83 x (4.1772 -1) / 0.41772 | |

= $5,087.16 |

Load losses per year = 3.808 kW x 6000 h/y x $0,075/kWh = $1,713.60

P.V. of load losses for 15 yrs. | = $1,713.60 x (4.1772 - 1) / (.41772) |

= $13,033.73 |

**Total Owning Cost of Premium-Efficiency**= $10,845.00 + $5,087.16 + $13,033.73) =

**$28,965.89**

**Present Value of Savings with Energy Efficient transformer**= $36,728.46 - $28,965.89 =

**$7,762.57**

## Example 3: Simplified Total Owning Cost (without time value of money)

A third, and simpler method of calculating savings is to omit the present value of money entirely, and simply calculate the annual owning cost. Many purchasers use this method as a quick alternative to more complex methods, producing different numerical answers but the same *conclusions*. We will use the same purchase price and loss figures as Example 2, above.

Here are the purchase and loss values again:

Standard Transformer | High Efficiency Transformer |
---|---|

Purchase price - $10,194 No-load losses - 1647 W Load losses at 100% - 9507 W Load loss at 75% - 5348 W |
$10,845 |

Cost of Standard Transformer (over 15 years) = purchase price+ [(value of load loss) + (value of no load loss)] x 15

Purchase price = $10,194

Annual cost of load losses = 5.348 kW x 6000 h/y x $0.075/kWh = $2,406.60

Annual cost of no load losses = 1.647 kW x 8760 h/y x $0.075/kWh = $1,082.08

Annual cost of load losses and no load losses = $3,488.68

**TOC of Standard transformer**= $10,194 + ($2,406.60 x 15) + ($1,082.08 x 15) =

**$62,524.20**

Cost of Energy Efficient transformer (over 15 years):

Purchase price = $10,845

Annual cost of load losses = 3.808 kW x 6000 h/y x $0.075 = $1,713.60

Annual cost of no load losses = 1.018 kW x 8760 h/y x $0.075 = $668.83

Annual cost of load losses and no load losses = $2,382.43, *i.e*. saves $1,106.25 every year

**TOC of Efficient transformer**= $10,845 + (1713.60 x 15) + (668.83 x 15)

**=**

**$46,581.45**

**15-year savings with energy-efficient transformer**= $62,524.20 - $46,581.45 =

**$15,942.75**

The energy efficient transformer will **SAVE** almost **ONE AND ONE-HALF TIMES** its initial purchase price over the 15-year assumed ownership, compared to the less efficient model.

Whichever method you choose, the conclusion is the same. Even though the more- efficient transformer costs more initially, its lower operating cost saves money over its life.

## Example 4: Total Owning Cost of a 75 kVA Transformer

Olsun Electrics Corporation, a manufacturer of dry-type transformers, switch gear and reactors, provided a comparison of the no-load and load losses of 75-kVA dry-type transformers. In this example, the low-efficiency aluminum-wound transformer cost $1,336 and had no-load losses of 375 watts and full-load losses of 2,829 watts. The high-efficiency copper-wound unit cost $3,214 and had no-load losses of 190 watts and full-load losses of 993 watts (see **table**). It was assumed that the transformer would operate continuously throughout the year.

Here are the numbers:

Transformer rating: | 75 kVA |

Number of shifts loaded | 1 (8760 h/y) |

Energy cost: | $0.070/kWh |

The Total 15-Year Operating Cost is calculated: | |
---|---|

Operating Cost (in $) = |
[(NLL x 8760 x 0.070) + (FLL x 8760 x 0.070)] x 15 |

Where:

NLL = No load losses (kW)

FLL = Full load losses (kW)

Estimated full load hours per year = 8760

Total hours per year = 8760

NOTE: The simplified table below does not account for taxes, depreciation or the time value of money

Inserting the bidders' cost and operating data and the estimated duty cycle numbers into an total owning cost (TOC) analysis, the following table shows the TOC calculations for the low and high efficiency units based on the following formula:

**TOC = price + cost of the no-load losses + cost of the load losses**

Option | Purchase Price | No-Load Losses, watts | Full-Load Losses, watts | One-Year, Operating Cost | 15-Year Operating Cost | Total 15-Year Owning Cost |
---|---|---|---|---|---|---|

Low Efficiency |
$1,336 | 375 | 2,829 | $1,965 | $29,475 | $30,811 |

High Efficiency | $3,214 | 190 | 993 | $725 | $10,875 | $14,084 |

## Life-Cycle Cost Analysis

The savings associated with the high-efficiency copper-wound transformer, not taking into account depreciation, inflation or the time value of money, is $16,727 over a 15-year study period.

If the time value of money is taking into consideration, the TOC = price + A x (no-load losses) + B x (full load losses). Where,

A = | (System Capacity Cost) + (Energy Cost) x (8760) x 0.001 |
---|---|

(Carrying Charge Rate) | |

B = | (System Capacity Cost) + (Energy Cost) x (No. hrs operate in a yr.) x 0.001 |

(Carrying Charge Rate) |

Using the above formula and assuming there is no system capacity cost, that the carrying charge rate is 11 percent, and the transformer operates continuously throughout the year, the A and B factors equal $5.57/watt. This results in a TOC of $19,182 for the low-efficiency unit and $9,803 for the high-efficiency copper-wound unit, and a TOC savings of $9,379 for the high-efficiency copper-wound transformer.

## Conclusions

The lesson learned in this example is that the purchase of a higher-cost higher-efficiency, copper-wound unit instead of a lower-cost, low-efficiency aluminum-wound unit will result in significant savings over the life of the transformer. As for the environmental benefits, the high-efficiency copper-wound transformer will contribute to reducing greenhouse gas emissions by reducing the consumption of fossil fuel necessary to accommodate excessive transformer losses.