Equipment ageing & decay
Transformer thermal ageing (hot-spot temperature and daily loss of life), the IEC 60909 short-circuit decay curve (κ, τ, ip, i_dc) and the device thermal/dynamic withstand check.
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Transformer thermal ageing is estimated by per-interval integration to IEC 60076-7: the hot-spot temperature of each interval θ_h,i = ambient temperature + temperature rise (the rise reuses the engine single source engines/params.js tempRiseAt: Δθ_oil = 55×((1+R·K²)/(1+R))^0.8 with R = Pk/P0 and a 55 K rated top-oil rise, Δθ_hs = Δθ_oil + 25×K^1.6 for the 80 K rated hot-spot rise); relative ageing rate V_i = 2^((θ_h,i−98)/6) (the classic IEC 60076-7 expression with a 98 °C reference hot-spot and a 6 K exponent); ageing rate = Σ(V_i·Δt_i)/Σ(Δt_i) (interval-weighted equivalent) and daily equivalent loss of life = Σ(V_i·Δt_i)/24 h × 100% — integrated interval by interval, not a single value times the total duration
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κ and τ from the R/X ratio, the DC component envelope over time and the curve exported point by point.
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Per-device I²t and peak short-time check against the rated values, with the rating source stated.
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About Transformer ageing & device withstand
Three engine studies plus the moved ageing card drive this page. study.transformerAgeing (P2-03) applies the IEC 60076-7 exponential ONAN simplification - oil rise 55 x ((1 + R x K2)/(1 + R))^0.8, hot-spot rise = oil rise + 25 x K^1.6, hot-spot temperature = ambient + hot-spot rise - to the loading sequence of the time-series study and returns a relative ageing rate and the daily life loss for every transformer, with P0 and Pk from the user or from GB 20052 typical values. study.scDecay (P0-06) builds the fault-current decay curve: peak factor kappa = 1.02 + 0.98 x exp(-3 x R/X), DC component time constant tau = (X/R)/(2 x pi x f), peak current ip = kappa x sqrt2 x I-k, all from the IEC 60909-0 and GB/T 15544.1 formulas, taking I-k and R/X from the existing short-circuit result instead of recomputing them. study.deviceShortTime (P0-07) checks every device in bulk: thermal I-k2 x t_k against Icw2 x t_rated and peak withstand against ip, with the clearing time built from the protection trip time, the breaker opening time (0.06 s default) and a margin, per GB 50060-2008 and IEC 60865-1:2011. study.thermal returns the cable minimum section for the fault duty.
Two failures cost the owner the most money: a transformer that quietly loses its insulation life because it runs hot, and equipment that survives the steady state but is destroyed by the first fault. Ageing is the argument for a larger or better-cooled transformer (and for the price you pay for it), while the withstand checks are what an inspector opens the file for - so both verdicts should come from the same fault current and the same load profile.
Input = topology plus the ageing switch, the ambient temperature and the load profile. Chain: the time-series engine produces a loading sequence per branch (quasi-steady load-flow slices, optionally built here with the same solver when the time-series switch is off), the loading factor K drives the oil-rise and hot-spot formulas above, the instantaneous ageing rate is integrated over the periods to give the relative ageing rate and the daily life loss. In parallel the short-circuit result feeds the decay study (kappa and tau from R/X, ip = kappa x sqrt2 x I-k with the DC component curve and the peak withstand verdict per device) and the bulk withstand study (thermal duty from the fault current and the clearing time, dynamic duty from ip). Output = study.transformerAgeing[] with its basis disclosure, the scDecay curve and per-device table, the deviceShortTime pass/fail/unknown counts and table, and the cable thermal section. Linkage: transformer capacity changes the loading factor and therefore the ageing rate, the losses and the purchase price on the same page set; the protection settings change the clearing time and therefore the thermal duty; cable section changes both the thermal result and the losses.
Ageing, decay and the device short-time check are three lazy cards. The decay card is what the protection page used to render inline — it now lives here.