You operate the 500 kVA transformer and low-voltage feeder that supply 150 homes and their electric vehicles. Overload heats the insulation and ages it fast; a long feeder lets the voltage sag at the far end. One step is 5 minutes.
Fans raise the cooling rating by about a third; the oil runs cooler for the same load.
Managed modes apply only to drivers enrolled in the programme; the rest charge on arrival.
Closes the tie switch for part of the feeder. The neighbour has its own limit (120 %) and the long tie drops voltage.
150 kvar of reactive support: raises the far-end voltage and trims the current a little.
Each step raises every voltage by 1.25 % — at light load it can push the near end above +5 %.
Direct load control of water heaters and air-conditioners: one block of −15 % of household load for 60 min, then a 2-hour lockout while they recover. Half of the shed energy comes back afterwards.
| Top-oil temperature | 53 °C |
|---|---|
| Outdoor temperature | 30.8 °C |
| Insulation life used (equivalent hours) | 0.0 h |
| Transformer load | 202 kW |
| EV charging power | 0 kW |
| Voltage at the transformer | 100.9 % |
| Voltage at the feeder end | 100.0 % |
| Losses | 3.1 kW |
| Energy not supplied | 0 kWh |
| Load shed by control | 0 kWh |
| EV energy still missing | 0 % |
| Neighbouring transformer loading | 42 % |
| Cold-load pickup factor | 1.00 × |
A heatwave afternoon: air-conditioners are running in every home and 100 electric vehicles will plug in between 17:00 and 20:00 — on top of the evening household peak. Only 70 % of drivers are enrolled in managed charging. Get through to 07:00 without overheating or tripping the transformer, and without leaning on load shedding.
At 17:00 the neighbouring transformer fails. Half of its homes are switched onto the far end of your feeder through the long tie cable. The extra current flows the whole length of your line: keep every home within ±5 % of nominal voltage (ANSI C84.1 Range A) and avoid overloading your own transformer.
A six-hour outage on a freezing evening ends at 18:00. Every heater has been off and every EV is waiting to charge. When the crew closes the switch, the load comes back far above normal — lose diversity and the transformer trips again. Restore without a second outage, keep the voltage in range and the curtailment small.
Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.
P_homes = 150 × 2.0 kW × shape(h) × [1 + 0.025·max(0, θa−24) + 0.02·max(0, 15−θa)] × CLPU(t); P_EV = Σ 7.2 kW while plugged and not full[9]Assumption: the load profile, EV numbers, feeder impedances, cold-load parameters and fan rating are illustrative values for a generic suburban feeder, not data from a real network.Δθ_TO,U = 55 K · [(K²R+1)/(R+1)]ⁿ; Δθ_TO ← Δθ_TO,U + (Δθ_TO − Δθ_TO,U)·e^(−Δt/τ_TO), τ_TO = 180 min (ONAN) / 150 min (ONAF); R = P_k/P₀ at the rating K is referred to: 5 (ONAN), 5 × 1.33² ≈ 8.8 (ONAF)[1][2]Δθ_H,U = 25 K · K^(2m); Δθ_H ← Δθ_H,U + (Δθ_H − Δθ_H,U)·e^(−Δt/(k22·τw)), k22·τw = 8 min; θ_H = θ_A + Δθ_TO + Δθ_H[1][2]Simplification: the hot-spot rise follows one exponential (k21 = 1, time constant k22·τw). The short overshoot of the IEC 60076-7 two-term f2(t) after a sudden load step is not modelled, so the hot spot can briefly read a few kelvin low.ONAN n = 0.8, m = 0.8; ONAF n = 0.9, m = 0.8 (IEEE C57.91), with K and R referred to the ONAF rating (1.33 × ONAN, R ≈ 8.8)[1][3]Assumption: the load profile, EV numbers, feeder impedances, cold-load parameters and fan rating are illustrative values for a generic suburban feeder, not data from a real network.F_AA = exp(15000/383 − 15000/(θ_H + 273)); aged hours = Σ F_AA·Δt; F_EQA = Σ F_AA·Δt / Σ Δt; normal life 180 000 h[1][3][2]P_loss = P₀ + P_k·K² + r_f·S_b·(|s_d|²/3 + Re(s_d·s_p*) + |s_p|²) + r_tie·S_b·|s_tie|², s_d = distributed load, s_p = far-end block (incl. capacitor); P₀ = 1 kW, P_k = 5 kW[7][2]ΔV ≈ p·r + q·x (pu); distributed load drops ½ of the lumped value; capacitor Q_c raises V by Q_c·x; V_src = 1.02 + 0.02·(0.5 − shape) + tap × 1.25 %[7]Assumption: the load profile, EV numbers, feeder impedances, cold-load parameters and fan rating are illustrative values for a generic suburban feeder, not data from a real network.target |V − 1| ≤ 5 % (ANSI C84.1 Range A); Range B −8.3 % / +5.8 %; EN 50160: ±10 % for 95 % of 10-min means[4][5][6]trip if K ≥ 1.5 for 30 min (accumulated), K ≥ 2.0 at once, or θ_H ≥ 140 °C; neighbour trips if K_B ≥ 1.2 for 30 min; re-energised after 60 min[2]Assumption: the 30-minute overload setting, the 2.0 pu instantaneous element and the 140 °C hot-spot trip are illustrative settings built on the IEC 60076-7 limits for distribution transformers (1.5 pu normal cyclic, 2.0 pu short-time emergency, 140 °C hot spot). Real protection uses fuse or relay curves.M0 = 1 + 1.4·(1 − e^(−D/90 min)); CLPU(t) = 1 + (M0 − 1)·e^(−t/60 min)[8][1]Assumption: the load profile, EV numbers, feeder impedances, cold-load parameters and fan rating are illustrative values for a generic suburban feeder, not data from a real network.500 kVA transformer, 30 °C rated ambient (55 K oil + 25 K gradient → 110 °C) · 60 EVs, 6–20 kWh need, arrival ≈ N(18:30, 1 h), depart 07:00 · curtailed charging 3.6 kW · transformer r = 1 %, x = 4 %; feeder r = 4 %, x = 2 %; tie r = 10 %, x = 4 % (500 kVA base) · neighbour 400 kVA, 120 homes, transfer ≤ 40 % · capacitor 150 kvar · tap ±4 × 1.25 % · shedding one 15 % block for 60 min, 120 min lockout, 50 % payback · fans 0.4 kW · ±3 % load noise, ±5 % daily scaleAssumption: the load profile, EV numbers, feeder impedances, cold-load parameters and fan rating are illustrative values for a generic suburban feeder, not data from a real network.Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.
Educational model — not for operational decisions. Real sites calibrate every constant to their own equipment and data.