How transformer loss of life is calculated
Paper insulation ages faster as the winding hot spot gets hotter. The hot spot is calculated every 10 minutes from the measured top oil temperature and load current (IEC 60076-7):
θh = θtop + H × gr × Ky
K is the load factor (highest phase current ÷ rated current), H = 1.3 is the hot-spot factor, gr = 26 K is the rated winding-to-oil gradient and y = 1.3 is the winding exponent. The ageing rate V for thermally upgraded paper then compares the insulation ageing with rated conditions (V = 1 at 110 °C):
V = exp(15000 ÷ 383 − 15000 ÷ (θh + 273))
Loss of life (h) = Σ V × Δt, with Δt = 10 min
Heat is not the only thing that ages paper. Water and oxygen in the insulation speed it up several times, which the temperature formula alone does not capture. The ageing rate is therefore multiplied by an environment factor:
fenv = 2.0 (oxygen, free-breathing conservator) × (1 + 0.1 × (moisture in oil − 10 ppm)), at least 2.0
Loss of life (h) = Σ V × fenv × Δt
Loss of life is added up over the selected period (24 h, 7 days or 30 days). Life consumed since commissioning = years in service × 8,760 h × the 30-day average of V × fenv × 0.85, where 0.85 allows for lighter loading in earlier years.
Remaining life = the smaller of: (180,000 h − life consumed) ÷ (8,760 × V × fenv), and 50 years − years in service
At the light loading typical of distribution transformers, insulation ageing alone gives very long lives, so the 50-year design life usually governs. A furan analysis or degree-of-polymerisation (DP) result from an oil or paper sample gives the actual paper condition and should replace this estimate when available.
Ageing rate by hot spot
| Hot spot | V | Life used per day |
|---|
| 80 °C | 0.036 | 0.86 h |
| 90 °C | 0.116 | 2.77 h |
| 98 °C | 0.282 | 6.76 h |
| 104 °C | 0.536 | 12.87 h |
| 110 °C | 1.000 | 24.00 h |
| 116 °C | 1.830 | 43.91 h |
| 120 °C | 2.709 | 65.01 h |
| 130 °C | 6.984 | 167.62 h |
| 140 °C | 17.199 | 412.79 h |
Status
Normal ageing average V up to 1
Accelerated ageing average V above 1 up to 2
High ageing average V above 2
Worked example
How contact life is calculated
Every tap change wears the diverter switch contacts. Wear rises with the current being switched, but even a change at low current causes some arcing and mechanical wear. Wear is added up for each of the six contacts (main and transition contacts on phases R, Y and B):
Wear per operation = ktype × kphase × (0.2 + 0.8 × (Isw / Ir)1.5)
Isw is the load current at the moment of the tap change and Ir the rated current, so a change at rated current counts as 1. The fixed part (0.2) is the minimum wear of any operation. ktype is 1.0 for transition contacts and 0.55 for main contacts, which carry less arcing duty. kphase is (phase current ÷ average current)², so the more heavily loaded phase wears faster.
Contact life used (%) = Σ wear ÷ 300,000 × 100
300,000 is the rated electrical life in operations at rated current. Operations before the monitoring record are estimated with the average wear per operation of the recorded operations.
Remaining operations = the smaller of: contact life left ÷ wear per operation, and 800,000 − total operations
800,000 is the mechanical life of the tap changer. At light loading the mechanical life, not contact wear, is usually the limit. Remaining operations are also shown as years at the 30-day average operation rate; above 40 years the dashboard states that the service interval governs.
How tap-changer service planning is calculated
Service is due at 60,000 operations or 7 years after the last service, whichever comes first:
Due by operations = today + (60,000 − operations since service) ÷ operations per day
Due by time = last service date + 7 years
Operations per day is the average over the selected period (24 h, 7 days or 30 days), so the forecast date moves with the period you choose. Status turns caution within 90 days of the due date and alarm once service is overdue.
Contact life status
Healthy below 75% used
Plan replacement 75 to 89%
Replace 90% or more
Same limits apply to mechanical life used.
The 50-year design life, the environment factor (2.0 and 0.1 per ppm) and the 0.85 history factor are placeholders; set them from MEA asset policy and DP or furan results. Rated contact and mechanical life, the minimum wear (0.2), the exponent (1.5), wear factors and the service interval are placeholders for design review. Replace them with values from the tap-changer manufacturer for each OLTC model.