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Loss, temperature rise and core flux — engineering reference

Enter the nameplate data of one transformer and the fault data of one series reactor. The engine returns the winding temperature rise and hot-spot temperature with the daily ageing, the loss split between iron and copper, and the reactor fault-current waveform together with the core saturation characteristic. Every figure carries its basis and standard, and anything the engine does not return is shown as "—", never as zero.

Reference case inputs

These inputs build an in-memory reference case for this page only. Nothing is written to your saved schemes and nothing is read from them.

RequiredRecommendedLeft bar: blue = required, gold = recommended. Optional and advanced fields are collapsed by default.

One point per line as "current A, inductance mH". Leave empty to get the linear section only — the engine then reports no saturation point and no flux-linkage peak instead of inventing one.

Conclusionnot available

Not run yet. Press Compute reference case to get the figures from the engine.

Three key figures
Winding average rise
—K
Hot-spot temperature
—°C
Transformer loss at this load
—kW

Core flux-linkage peak λmax: — V·s— no manufacturer L–I curve

Computed charts
Losses
Iron loss P0
—kW
Copper loss
—kW
Total
—kW
P0 / Pk
— / —W
Loss-allocation cross-check (engine)
—kW
Loss versus loading — iron P0, copper Pk·(S/Sn)² and total, at 0 / 50 / 100 %
Chart not available — the engine returned no data for it.
Winding temperature rise and thermal ageing
Δθ_oil
—K
Δθ_hs
—K
θh
—°C
R = Pk/P0
—
Hot-spot temperature rise at 50 % / actual / 100 % load
Chart not available — the engine returned no data for it.
Hot-spot temperature over the 24 h load profile
Chart not available — the engine returned no data for it.
Equivalent relative ageing rate V_eq
—
Daily equivalent loss of life
—%
Maximum hot-spot over the profile
—°C
Limit
—°C
Core flux and saturation
Fault current peak (time domain)
—A
Linear-section peak (lower bound)
—A
Maximum rate of rise of current di/dt
—A/s
DC-component time constant τ
—ms
i_sat
—A
i_knee, L_knee
— / —A / mH
λ_max
—V·s
λ_min
—V·s
Reactor fault-current waveform i(t) — time-domain RL integration
Chart not available — the engine returned no data for it.
Core flux-linkage waveform λ(t) — time-domain integral of the fault-loop ODE
Chart not available — the engine returned no data for it.
Core saturation characteristic L–i and the saturation knee
Waiting for the manufacturer L–I saturation curve. With no curve the engine reports no saturation point and no flux-linkage peak — it does not extrapolate one.
L (mH) · lH(t)
Chart not available — the engine returned no data for it.
Basis and sources

Loss: P_loss = P0 + Pk·(S/Sn)² with S = P / cos φ; Q_loss = i0 %·Sn/100 + uk %·Sn/100·(S/Sn)². P0 and Pk are the values you entered, otherwise the GB 20052-2020 grade-1 typical values for that rating. Produced by the existing engine loss report — this page computes nothing of its own.

Temperature rise: Δθ_oil = 55·((1 + R·K²)/(1 + R))^0.8, Δθ_hs = Δθ_oil + 25·K^1.6, θh = θa + Δθ_hs with R = Pk/P0 and K = S/Sn — IEC 60076-7 oil-immersed ONAN exponential simplification. Relative ageing rate per the IEC 60076-7:2018 §7.3 equivalent ageing factor F_AA = exp(15000/383 − 15000/(θh + 273)); daily life loss = Σ(V_i·Δt_i) / 24 h × 100 %.

Core flux: the loop equation L·di/dt = Um·sin(ωt + θ) − R·i is integrated with fixed-step RK4 using the flux linkage λ over the manufacturer λ–i characteristic as the state variable (piecewise-linear interpolation; no hysteresis, no eddy currents, no remanence). Short-circuit basis IEC 60909-0:2016 (c = 1.1, Z_Q = Un²/Ssc, κ = 1.02 + 0.98·e^(−3R/X)); the saturation curve can only come from the manufacturer — IEC 60076-6 / GB/T 1094.6 provide no default one.

Reference case layout: one grid source, one two-winding transformer, one LV busbar and one static load, joined by three short cable sections of 10 m each (copper). The cable data does not drive the loss or temperature results - those come from P0/Pk and the loading only - but the sections must be present for the engine's load flow to run.

Modules reused unchanged: engines/reactor-transient.js · engines/trafo-ageing.js · engines/loss-allocation.js · engines/time-series.js · engines/params.js (tempRiseAt, resolveXfLoss). This page computes no engineering quantity of its own — it maps your inputs into the request and renders what the engine returns.

Definitions, units and why the number matters for selection and quotation. Searchable, grouped by topic, collapsed by default.

Every ? mark on this page opens the same explanation in place — no page change.

11 term(s) shown of 11

Short circuit & protection · 4
Ssc[MVA]Short circuit & protection

Short-circuit apparent power of the upstream network at the connection point, Ssc = √3·Un·I″k, or the equivalent source impedance behind it.

Why it matters: It is the single input that says how "stiff" the grid is. Without it no fault-current figure can be computed, so it must be requested from the utility (or taken from a stated assumption) before any switchgear can be quoted.

X/R[dimensionless]Short circuit & protection

Ratio of the equivalent reactance to the equivalent resistance seen from the fault point (IEC 60909-0).

Why it matters: It fixes two things at once: the peak factor κ (hence ip) and the decay rate of the DC component. A high X/R (inductive LV feeds, generator sources) gives both a higher peak and a longer DC transient, which the breaker must interrupt.

κ[dimensionless (1.0–2.0)]Short circuit & protection

Peak factor κ = ip / (√2·I″k): the ratio of the first peak to the rms value, calculated in IEC 60909-0 from the R/X ratio of the equivalent impedance.

Why it matters: It is what converts a short-circuit current into a mechanical force. An inductive network (LV cables, transformers) pushes κ towards 2.0 and raises the peak force, which is why ip cannot be derived from Ik alone.

ip[kA (peak)]Short circuit & protection

Peak short-circuit current ip = κ·√2·I″k (IEC 60909-0): the highest instantaneous value of the fault current, reached about half a cycle after inception.

Why it matters: It is the number that generates the electrodynamic force on busbars, cable cleats and device terminals. Compare it with the rated peak withstand Ipk — quoting only Ik leaves the mechanical strength of the switchboard unchecked.

Transformers & switchgear · 5
P0[kW (or W)]Transformers & switchgear

No-load loss of a transformer: the power absorbed at rated voltage and rated frequency with the secondary winding open (IEC 60076-1). It is essentially the core (hysteresis + eddy) loss.

Why it matters: It runs continuously — about 8 760 h a year — so it dominates the lifetime energy bill. Tenders commonly capitalise it at a $/W figure, which means a lower P0 can justify a higher purchase price.

Pk[kW]Transformers & switchgear

Load loss (short-circuit loss) of a transformer: the power absorbed at rated current with the secondary short-circuited, corrected to the reference temperature (IEC 60076-1). It includes the I²R loss plus stray and winding eddy losses.

Why it matters: It grows with the square of the load and is the basis of efficiency guarantees and of any loss-capitalisation clause. Pk and uk% come from the same test, so a datasheet giving one without the other is incomplete.

uk%[% (referred to rated current and the reference temperature)]Transformers & switchgear

Short-circuit impedance voltage of a transformer: the primary voltage, in percent of rated voltage, that drives rated current through the short-circuited secondary winding (IEC 60076-1).

Why it matters: It fixes the LV fault level (approximately I″k ≈ In / uk) and at the same time the voltage drop under load. This is a real quotation trade-off: a larger uk lowers the fault level (cheaper switchgear downstream) but increases voltage drop and losses. Always quote uk together with the transformer rating.

Um[kV (rms)]Transformers & switchgear

Highest voltage for equipment Um: the maximum rms line-to-line voltage at which the equipment may be operated (IEC 60071-1).

Why it matters: Um anchors the whole insulation-coordination table: it decides which lightning-impulse and power-frequency withstand values are required. Buying equipment with too low an Um is not a saving, it is a non-conforming offer.

LI[kV (peak)]Transformers & switchgear

Lightning impulse withstand voltage: the peak of the standard 1.2/50 µs impulse wave that the insulation must withstand without breakdown (IEC 60071-1).

Why it matters: It is a named specification and type-test item for switchgear, transformers and bushings. It is one of the first parameters a cheap offer silently reduces, so it must appear explicitly in the datasheet you compare.

Stability & storage · 1
λmax[multiplier (1.00 = present loading)]Stability & storage

Maximum loadability factor λmax of the continuation power flow: the multiplier applied to all loads at the nose point of the PV curve, the point where the voltage collapses.

Why it matters: It is the loading margin of the design: λmax = 1.35 means the network only collapses at 135 % of today load. Planners require a minimum margin (the number differs between grid codes — state the criterion used), and it decides whether a line reinforcement or more reactive compensation has to be quoted.

System & general · 1
Loading[%]System & general

Loading: the current (or power) carried by a branch expressed as a percentage of its rated capacity.

Why it matters: It is the acceptance number for cables and transformers. Above 100 % the element will trip or have to be derated, and the margin left at the design case is exactly what the customer is paying for — so it must be shown with the assumption (load factor, ambient temperature) that produced it.

Basis: transformer thermal model per IEC 60076-7 (oil-immersed ONAN exponential simplification — top-oil rise 55 K and hot-spot rise 80 K at rated load) driven by P0/Pk (your values first, otherwise the GB 20052-2020 grade-1 typical values for that rating); reactor transient per IEC 60909-0:2016 (c = 1.1, Z_Q = Un²/Ssc) with the core saturation curve taken only from manufacturer L–I data (IEC 60076-6 / GB/T 1094.6 give no default curve). Results are an engineering estimate for pre-selection: not a finite-element thermal simulation, not a system-level EMT study, and dry-type units, staged cooling and insulation moisture are outside this model.