Loss capitalisation: comparing transformer bids properly

Life-cycle cost (LCC) totals everything the owner pays: purchase price, transport and installation, the energy dissipated in the core and windings, maintenance, the expected cost of failure and lost output, and disposal at the end of life. Loss capitalisation is one of those terms — the losses — expressed in money and discounted to the date of award.

The distinction matters when a specification is written. LCC is a decision framework; loss capitalisation is a calculation with defined inputs that can be placed in a tender document and audited against a test certificate. It captures losses only. It says nothing about reliability, lead time or end-of-life risk, and a low capitalised-loss figure is not by itself evidence of a good transformer.

Loss capitalisation answers one question: what is an extra kilowatt of loss worth to this project today?

Take one kilowatt of no-load loss. A transformer that stays energised dissipates it for 8,760 hours a year, or 8,760 kWh. At an energy value of c per kWh, the annual cost is 8,760 x c. Discounted over a life of n years at a real rate r, the present value of that stream is:

A = c x 8,760 x [(1 - (1 + r)^-n) / r]

The bracketed term is the present-worth annuity factor, and A is the capitalisation coefficient for no-load loss, in currency per kilowatt. It depends only on the value of energy, the discount rate and the life, not on the transformer.

Load loss appears only when current flows, and varies approximately with the square of the current. Reduced to an equivalent per-unit current L — the constant current producing the same annual load-loss energy as the real duty cycle — the coefficient becomes:

B = A x L^2 x kT

kT corrects the guaranteed load loss from the bidder's reference temperature to the average winding temperature expected in service. IEC 60076-1 corrects winding resistance using 235 for copper and 225 for aluminium; 10 K above reference raises the resistive component by about 3 percent.

The evaluated price is then:

Evaluated price = bid price + A x P0 + B x Pk

where P0 and Pk are the bidder's guaranteed no-load and load losses in kilowatts at the stated reference conditions.

Neither coefficient is a constant of nature. Both are the buyer's own numbers, and should be derived from the project rather than copied from an earlier specification.

A is set by three inputs. The energy value c should be the real marginal cost of the energy the project does not sell, or the real price of the energy it buys — for a merchant plant, effectively the levelised offtake price. The discount rate r should be the owner's real weighted average cost of capital, not the equipment financing rate. The life n should be the project model's economic life. Because A scales linearly with c, a tender using 0.10 rather than 0.05 per kWh doubles the value of every loss.

B carries two further judgements. The equivalent load factor L is a property of the duty cycle, not of the transformer: a solar generator step-up unit is energised around the clock but carries current mainly during daylight, so its L sits well below 1, and assuming L = 1 overstates load-loss value by a factor of three or more. kT depends on the reference temperature the tender asks for, so two bids stating load loss at different reference temperatures cannot be compared without correction.

Publishing A, B and their derivation in the tender ends the later argument about whose numbers are right.

Losses are not a secondary cost. U4E/UNEP notes that transformers commonly remain in service for 30 years or more, and that the energy lost in them over that period can cost four times the purchase price. Where that ratio holds, an award rule based on purchase price optimises roughly a fifth of the cost and ignores the rest.

The mechanism is simple. Lower no-load loss means more core steel, higher-grade grain-oriented steel, or a lower flux density; lower load loss means more conductor cross-section. Both raise purchase price and weight. A bidder evaluated on price alone has a commercial incentive to take that material out, and the result is a transformer that is cheap on the day of award and expensive for 25 years.

Capitalisation changes the ranking, not merely the margin. Teams that have not run the calculation often assume the effect is small; on a 25-year life at a low real discount rate it usually is not.

Four items have to be in the document for the calculation to be enforceable.

1. The coefficients and their derivation. State A and B in currency per kilowatt, and state c, r, n and L. If a bidder disagrees with the discount rate, settle that before bids arrive, not after.

2. The measurement basis. Require no-load and load loss at the reference temperature defined in IEC 60076-1, measured to that standard and reported on the routine test certificate. Where the site has significant harmonic content, also require the harmonic loss factor treatment of IEEE C57.110, because eddy losses rise with harmonic order and a fundamental-only figure understates real load loss.

3. Guarantees and penalties. Ask for guaranteed maximum losses and set a liquidated-damages rate per kilowatt of measured excess, aligned with A and B. Capitalisation without enforcement is an accounting exercise: the bidder who loses on paper still wins if delivered losses are never measured.

4. Cooling auxiliary power. For units with forced cooling, fan and pump consumption runs for the same hours as load loss. Require it to be declared and capitalise it on the same basis.

State also that the loss evaluation is binding for award, and that the same A and B apply to any later re-rating or design change.

Assumptions, stated in full: a 40 MVA, 110 kV generator step-up transformer for a solar plant; economic life 25 years; real discount rate 7 percent; energy valued at 0.07 USD/kWh in real terms; no-load loss energised 8,760 hours per year; equivalent annual load factor L = 0.35; temperature correction kT = 1.03.

The present-worth annuity factor over 25 years at 7 percent is 11.654, so A = 0.07 x 8,760 x 11.654 = 7,146 USD per kW, and B = 7,146 x 0.35^2 x 1.03 = 902 USD per kW.

Bid B costs USD 60,000 more at purchase and USD 49,344 less over the life of the asset. On this tender's terms, Bid B is the lower-cost offer.

Errors that most often distort this comparison: using catalogue or typical losses instead of the bidder's guaranteed values; comparing load loss quoted at 75 C with load loss quoted at 85 C; applying a load factor of 1.0 to a plant whose current is intermittent; forgetting that no-load loss is paid for at night and in winter, when the plant is idle; mixing a nominal discount rate with a real energy price; omitting cooling auxiliary power; and issuing A and B without a measurement protocol or liquidated damages, so the calculation is never checked against the test certificate.