Transformer Diagram
Loading Gauge
Nameplate Data
Event Log
Efficiency vs Loading Curve
Loss Breakdown
Voltage Regulation vs Load (Lagging PF)
Low-Side Voltage vs Load
Optimal Loading Point
Temperature Rise vs Loading (Steady-State Est.)
Rough Insulation Life vs Hotspot Temperature
Cooling Performance
Thermal Reference Limits (IEEE C57.91-2011)
| Parameter | Normal | Planned (Beyond Nameplate) | Long-Time Emergency | Short-Time Emergency |
|---|---|---|---|---|
| Hotspot (absolute) | 120°C | 130°C | 140°C | 180°C |
| Top Oil (absolute) | 105°C | 110°C | 110°C | 110°C |
App Display Thresholds
| KPI | Good | Caution | Danger |
|---|---|---|---|
| Hotspot Temp | <120°C | 120–139°C | ≥140°C |
| Top Oil Temp | <105°C | 105–109°C | ≥110°C |
| Aging Factor (FAA) | <1.0 | 1.0–3.9 | ≥4.0 |
Inrush Current Waveform (Conceptual Only)
Fault Current vs Impedance (Low Side)
Fault Current & Withstand Details
Practice Scenarios
Transformer Knowledge Quiz
Power Transformer Fundamentals
A power transformer transfers electrical energy between circuits through electromagnetic induction. It consists of two or more windings linked by a common magnetic core.
- Line Voltage Ratio: V_HV / V_LV — the ratio of high-side to low-side line-to-line voltages.
- Winding Turns Ratio: The physical turns ratio depends on connection. For delta-wye, the winding (phase) voltages differ from line voltages by √3.
- kVA Rating: Apparent power capacity, determined by insulation class and cooling. May be specified as base ONAN rating or active cooling-stage rating.
- Impedance (Z%): Percentage of rated voltage required to circulate rated current through the short-circuited winding. Limits fault current but causes voltage drop under load.
Impedance, Resistance & Reactance
The transformer nameplate impedance Z% combines winding resistance and leakage reactance. This simulator derives the per-unit resistance from the full-load (copper) loss:
X_pu = √(Z_pu² − R_pu²)
X/R = X_pu / R_pu
If the full-load loss implies R_pu ≥ Z_pu, the data is physically inconsistent.
Voltage Regulation
Voltage regulation is the change in low-side voltage from no-load to full-load. This simulator uses a simplified series-impedance phasor approximation:
VR% = (E_pu − 1) × 100
Forward: V_loaded = V_noLoad / E_pu (voltage drops under load)
Reverse: V_gen = V_noLoad × E_pu (voltage rises at generator terminals)
For reverse (generation) power flow, the generator at the LV side must develop a higher terminal voltage to push current through the transformer impedance. The displayed "voltage rise" is a simplified educational mirror of the forward regulation model.
Losses & Efficiency
- No-Load (Core) Losses: Hysteresis + eddy current losses. Constant regardless of load.
- Load (Copper) Losses: I²R losses in windings. Vary with the square of load current.
- Maximum Efficiency: Occurs when core loss = copper loss, typically at 50–70% of rated load.
Optimal load = √(P_core / P_copper_FL) × 100%
Thermal Performance
This simulator uses a steady-state educational model inspired by IEEE C57.91 concepts:
θ_topOil = θ_rated × ((K²·R + 1)/(R + 1))^n
θ_hotspot = θ_HS,rated × K^(2m)
where K = load pu (adjusted for cooling stage), n = oil exponent, m = winding exponent
At no load, top-oil rise is non-zero because core losses still generate heat. Transient behavior is not modeled.
Insulation Aging
- Thermally Upgraded Paper (110°C ref): FAA = exp(15000/383 − 15000/(θ_HS + 273)). FAA = 1.0 at 110°C.
- Non-Thermally Upgraded (98°C ref): FAA = 2^((θ_HS − 98)/6). FAA = 1.0 at 98°C.
"Rough equivalent life" = baseLifeHours / FAA / 8760. This is a rough educational estimate at constant hotspot temperature, not a prediction.
The 180,000 h base life used here is the IEEE C57.91-2011 normal insulation life for thermally upgraded paper at 110°C. Applying the same base life to non-upgraded paper (98°C reference) is an educational simplification — the classic non-upgraded loading guides use a different basis.
Connections & Vector Groups
- Dyn11: Most common distribution connection. Primary delta, secondary wye grounded. +30° phase shift (LV leads HV).
- Dyn1: Same winding arrangement as Dyn11 but −30° phase shift (LV lags HV).
- YNyn0: Both windings wye grounded. No phase shift. Can have third-harmonic issues.
- Dd0: Both delta. No neutral available. Good for industrial loads.
- Yd11: Primary wye, secondary delta. Used for step-up applications. 30° phase shift.
Fault Current
With source: Z_total = Z_xfmr + Z_source, where Z_source = xfmrBaseMVA / sourceSCmva
This gives symmetrical RMS fault current. Asymmetric (DC offset) and motor contribution are not modeled.
Approximation note: Z_source and Z_xfmr are added here as scalar magnitudes, which is exact only when both impedances have the same X/R angle. Both are typically predominantly reactive, so the error is small (usually <2%), but exact short-circuit analysis adds them as complex quantities — the scalar sum slightly under-states fault current.
Magnetizing Inrush
On initial energization, the transformer can draw 8–12× rated current. The inrush is highly asymmetric. "Sinusoidal-equivalent peak" = RMS estimate × √2 — this is a mathematical conversion, not an actual peak prediction. Actual inrush depends on point-on-wave, residual flux, source impedance, core material, and winding connection.