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Transformer Loss Evaluation Formula Development

Modelling Optimal Designs for Distribution Transformers
Project objective
A large provincial power utility wished to determine the optimal designs of distribution transformers that they should purchase to ensure the minimal lifetime cost when the transformers were applied in various applications on their system. To acquire a method to convey the no-load and load loss design parameters of these transformers to manufacturers, the utility contracted Kinectrics to create transformer loss evaluation formulae.


Scope of work

Kinectrics was requested to develop a method to evaluate the transformer “cost-of-losses”, which could be used in assessing the Total Ownership Cost (TOC) of transformers purchased. The cost-of-losses formula was to determine the operating cost of the transformer over its lifetime, and when summed with the transformer capital cost, would yield a Net Present Value for the lifetime cost of the transformer.
The TOC of alternative transformer designs could then be compared so taht the utility could select those designs offering the lowest TOC. This allowed the utility to assess whether or not there was economic benefit in paying a higher capital cost to obtain transformers with reduced losses and lower operating costs. The utility required formulae to be developed for transfomrers applied in urban, rural, and commercial applications. .
Work performed.

Development of the formulae to compute the lifetime costs of the inherent energy losses of the transformers required quantifying and modelling the time-varying loads and losses for the transformer, and the associated costs of the losses at time-varying rates.
The formulae were derived utilizing transformer load profile projections and predicted economic factors from the year 2016 forward. Of significant difference from previous cost-of-losses formulae, the 2016 formulae consider on-peak, mid-peak and off-peak energy costs, applied to 5 daily time-periods, as well as different rate allocations for summer and winter periods.
Actual measured residential load profiles were used to develop and validate the theoretical load profiles used in the computations. An example of the derived load profile is shown at the beginning of this document. Load factors and loss factors were determined from the load profiles. Utilization factors and responsibility factors were applied to further quantify the time-varying load.
Kinectrics developed the three cost-of-losses formulae, shown in the Table below; for transformers to be applied in rural, urban and commercial environments.  By inputting the measured load and no-load loss values of the transformer design into the formulae, the lifetime cost of that design can be determined.
Cost of-Losses Formulae for Distribution Transformers in Rural, Urban and Commercial Applicaitons (for proprietary reasons the acutal values are not provided).
Transformer Cost-of Losses Formulae
Transformers for Rural Application
TOC =CAPCOST + $18*NLL  +  $3* LL
Transformers for Urban Application
TOC =CAPCOST + $18*NLL  +  $5* LL
Transformers for Commercial Application
TOC =CAPCOST + $16*NLL  +  $5* LL
TOC = Total Ownership Cost (net present value in $)
CAPCOST = Capital cost of the transformer
NLL = No-load losses in Watts
LL = Load losses in Watts
Selection of the optimal transformer using the formulae, as opposed to choosing an inappropriate design, can make a difference of approximately $1000.00 per transformer  over a 30-year lifetime.
For a utility with over half a million installed distribution transformers, proper ongoing application of the formulae developed by Kinectrics can have substantial positive economic impact. The client utility expressed their appreciation to Kinectrics for the thorough and timely execution of this project.