A scheduling model may assign a cost to operating a transformer at elevated temperature. That can be useful for comparing otherwise feasible choices. The cost has two different ingredients: an insulation-ageing estimate and an economic conversion. Neither should be hidden inside a single unexplained currency value. [1] [2]
Describe the physical index before attaching a price
Specify the insulation system, thermal quantity, reference condition and ageing model used. A relative ageing factor describes a modeled rate compared with its reference. Integrating that rate over time gives a reference-equivalent exposure under the model. It does not observe every mechanism that may limit the installed transformer’s remaining life.
Thermal-state and parameter uncertainty affect the index. Evaluate the schedule across credible temperature estimates rather than assigning a precise life-consumption result to an uncertain hot spot. Do not apply a parameter set from one published transformer study to a different asset without a documented basis.
| Model layer | Required definition | Result should be labelled |
|---|---|---|
| Thermal state | Hot-spot estimate, inputs and uncertainty | Estimated temperature trajectory |
| Ageing relation | Material/model and reference condition | Relative modeled ageing rate |
| Time integration | Intervals and evaluation period | Reference-equivalent exposure |
| Economic conversion | Chosen valuation and accounting assumptions | Optimization penalty, not a measured invoice |
Make the conversion dimensionally visible
An illustrative penalty is Cₐ = cᵣ ΣfₖΔtₖ. Here fₖ is a dimensionless relative ageing factor, Δtₖ is in hours and cᵣ is an assumed currency cost per reference-equivalent hour. The result Cₐ is in currency units. The coefficient is an economic assumption; the equation does not make that assumption an actual replacement or repair cost.
State whether the valuation includes replacement, outage consequences or another defined objective. Avoid adding several values that represent the same consequence twice. Test whether reasonable changes in the valuation materially change the dispatch decision; if they do, the economic choice requires attention rather than more decimal places.
A penalty cannot replace an operating constraint
A finite ageing price may allow an optimizer to choose a thermally unacceptable point when another cost is high enough. Keep mandatory operating limits as explicit constraints. Use an ageing penalty to compare permissible trajectories, with the limits and penalty serving different purposes.
Assume ageing rates 2.0 for 1 h and 0.5 for 3 h: exposure is 3.5 reference-equivalent hours, versus 4.0 h at reference rate 1, a 12.5% reduction. Set a fictional valuation cᵣ = 20 currency units per equivalent hour: penalties are 70 and 80. If the modified schedule also incurs assumed additional service cost 15, its total is 85 versus 80; select the reference under this declared objective. Keep initial/operating/consequence cost boundaries consistent [3]. These valuations neither measure an invoice nor establish guaranteed asset-life savings; mandatory thermal constraints apply first.
Report the selected schedule, its estimated physical exposure and the economic assumptions separately. A lower modeled penalty is evidence about the comparison under those assumptions. It is not a guaranteed life extension, a field failure probability or a maintenance saving already earned.
References
- A. Jain and M. Karimi-Ghartemani, Mitigating Adverse Impacts of Increased Electric Vehicle Charging on Distribution Transformers, Energies 15, 9023, 2022. DOI: 10.3390/en15239023.
- IEC, IEC 60076-7:2018, Power transformers – Part 7: Loading guide for mineral-oil-immersed power transformers.
- J. Kneifel and D. Webb, NIST Handbook 135e2025, Life Cycle Costing Manual for the Federal Energy Management Program, August 2025, sections 4.2 and 8.3. DOI: 10.6028/NIST.HB.135e2025.