⚡ Stroomdistribúsje yn de buert Live model

Basis — it model efter de sifers

Elke relaasje dy't de simulator brûkt, mei de boarne. Konstanten dy't as oanname markearre binne, binne yllustrative kalibraasjes.

De húshâldlike fraach folget in deiprofyl en it waar; elke EV laadt mei 7,2 kW oant er fol is.

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]Oanname: it belêstingsprofyl, EV-getallen, feederimpedânsjes, kâldebelêstingsparameters en fanfermogen binne yllustrative wearden foar in generike foarstêdlike feeder, gjin gegevens fan in echt netwurk.

De boppeoaljestiging benaderet har einwearde foar de hjoeddeiske belêsting eksponinsjeel, mei in tiidkonstante fan oeren.

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]

It hjitte punt fan de wikkeling leit boppe de oalje en folget de stroom binnen minuten.

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]Ferienfâldiging: de stiging fan it hjitte punt folget ien eksponinsjele (k21 = 1, tiidkonstante k22·τw). De koarte oerskriuwing fan de twatermen f2(t) fan IEC 60076-7 nei in hommelse belêstingsstap is net modellearre, dus it hjitte punt kin koart in pear kelvin te leech lêze.

Koelstap: fans feroarje de eksponinten en it fermogen dêr't de belêsting op betrokken is.

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]Oanname: it belêstingsprofyl, EV-getallen, feederimpedânsjes, kâldebelêstingsparameters en fanfermogen binne yllustrative wearden foar in generike foarstêdlike feeder, gjin gegevens fan in echt netwurk.

Fergrizing fan de isolaasje relatyf oan de referinsje fan 110 °C; ferdûbelet sawat elke 6–7 K.

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]

Leechlêstferlies plus belêstingsferlies dat mei it kwadraat fan de stroom tanimt.

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]

Rûchwei de spanningsdaling lâns de transformator en feeder.

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]Oanname: it belêstingsprofyl, EV-getallen, feederimpedânsjes, kâldebelêstingsparameters en fanfermogen binne yllustrative wearden foar in generike foarstêdlike feeder, gjin gegevens fan in echt netwurk.

Tsjinstspanningsberiken út de spanningsnormen.

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]

Beskerming: wannear't de transformator en de buorman útskeakelje.

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]Oanname: de 30-minuten-oerbelêstingsynstelling, it daliks-elemint op 2,0 pu en de útskeakeling by 140 °C hjit punt binne yllustrative ynstellingen basearre op de IEC 60076-7-limiten foar distribúsjetransformators (1,5 pu normaal syklysk, 2,0 pu koarte-tiid needgefal, 140 °C hjit punt). Echte beskerming brûkt smeltfeiligens- of relêkurven.

Nei in útfal skeakelje alle thermostatyske lesten tagelyk oan; de ekstra belêsting nimt eksponinsjeel ôf.

M0 = 1 + 1.4·(1 − e^(−D/90 min)); CLPU(t) = 1 + (M0 − 1)·e^(−t/60 min)[8][1]Oanname: it belêstingsprofyl, EV-getallen, feederimpedânsjes, kâldebelêstingsparameters en fanfermogen binne yllustrative wearden foar in generike foarstêdlike feeder, gjin gegevens fan in echt netwurk.

Oare konstanten dy’t it model brûkt.

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 scaleOanname: it belêstingsprofyl, EV-getallen, feederimpedânsjes, kâldebelêstingsparameters en fanfermogen binne yllustrative wearden foar in generike foarstêdlike feeder, gjin gegevens fan in echt netwurk.

Willekeur: in seeded mulberry32-generator; brûkte ferdielingen — unifoarm, eksponinsjeel (omkearde CDF), normaal (Box–Muller), Poisson (Knuth). It seed wurdt toand en is te dielen.

Boarnen

1. IEEE Std C57.91-2011 — IEEE Guide for Loading Mineral-Oil-Immersed Transformers and Step-Voltage Regulators (clause 5 ageing, clause 7 temperature, Annex on cold-load pickup) — IEEE, 2011
2. IEC 60076-7:2018 — Power transformers, Part 7: Loading guide for mineral-oil-immersed power transformers — IEC, 2018
3. Comparison of Loading Guide Standards (IEEE C57.91 and IEC 60076-7): ageing equations, exponents n/m by cooling mode, 180 000 h normal life — IEEE PES Transformers Committee, C57.91 working group
4. ANSI C84.1 — Electric Power Systems and Equipment: Voltage Ratings (60 Hz); Range A service voltage ±5 % (114–126 V on 120 V), Range B 110–127 V — NEMA / ANSI (summarised in USDA Rural Utilities Service guidance), 2020
5. EN 50160:2022 — Voltage characteristics of electricity supplied by public electricity networks, clause 4 low-voltage supply characteristics (clause 4 is not in the free preview, which ends at the scope) — CENELEC, CLC/TC 8X (official preview of the English text via the Slovak national standards body ÚNMS SR, STN EN 50160:2023), 2022
6. A. Klajn, M. Bątkiewicz-Pantuła — Application Note: Standard EN 50160, Voltage characteristics of electricity supplied by public electricity networks (LV supply voltage variations: Un ± 10 % for 95 % of the 10-min mean rms values of each week) — European Copper Institute / Leonardo ENERGY, Publication No. Cu0147, 2013
7. W. H. Kersting — Distribution System Modeling and Analysis (approximate voltage drop, uniformly distributed load, line losses) — CRC Press, 2017
8. C. Hachmann et al. — Cold load pickup model parameters based on measurements in distribution systems (exponential decay model, CLPU factors ≈ 1.9–2.8) — IET Generation, Transmission & Distribution 13(23), 2019
9. SAE J1772 — Electric Vehicle and Plug-in Hybrid Electric Vehicle Conductive Charge Coupler (AC Level 2 charging, e.g. 32 A × 240 V ≈ 7.7 kW) — SAE International, 2017