⚡ 社區配電 即時模型

依據：數字背後的模型

模擬器使用的每一個關係式及其來源。標示為假設的常數是示意校準值。

居民用電需求遵循日負荷曲線並隨天氣變化；每輛電動車以 7.2 kW 充電直到充滿。

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]假設：負荷曲線、電動車數據、饋線阻抗、冷負荷參數和風扇容量均為一條通用郊區饋線的示意值，並非真實電網的數據。

頂層油溫升以指數規律趨近當前負荷對應的終值，時間常數為數小時。

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]

繞組熱點溫度高於油溫，並在幾分鐘內跟隨電流變化。

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]簡化：熱點溫升遵循單一指數（k21 = 1，時間常數 k22·τw）。IEC 60076-7 中雙項 f2(t) 在負荷突然階躍後出現的短暫過衝沒有建模，因此熱點讀數可能短時偏低幾開爾文。

冷卻檔位：風扇改變指數和負荷所參照的額定容量。

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]假設：負荷曲線、電動車數據、饋線阻抗、冷負荷參數和風扇容量均為一條通用郊區饋線的示意值，並非真實電網的數據。

絕緣老化速率，以 110 °C 為基準；大約每升高 6–7 K 就翻一倍。

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]

空載損耗加上隨電流平方增長的負載損耗。

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]

沿變壓器和饋線的近似電壓降。

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]假設：負荷曲線、電動車數據、饋線阻抗、冷負荷參數和風扇容量均為一條通用郊區饋線的示意值，並非真實電網的數據。

電壓標準規定的供電電壓範圍。

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]

保護：變壓器和相鄰饋線何時跳閘。

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]假設：30 分鐘過載整定、2.0 pu 瞬時元件和 140 °C 熱點跳閘均為示意整定值，依據 IEC 60076-7 對配電變壓器的限值（正常週期性負載 1.5 pu，短時應急 2.0 pu，熱點 140 °C）。真實保護使用熔斷器或繼電器曲線。

停電之後，恆溫類負荷會同時啓動；額外負荷按指數規律衰減。

M0 = 1 + 1.4·(1 − e^(−D/90 min)); CLPU(t) = 1 + (M0 − 1)·e^(−t/60 min)[8][1]假設：負荷曲線、電動車數據、饋線阻抗、冷負荷參數和風扇容量均為一條通用郊區饋線的示意值，並非真實電網的數據。

模型使用的其他常數。

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 scale假設：負荷曲線、電動車數據、饋線阻抗、冷負荷參數和風扇容量均為一條通用郊區饋線的示意值，並非真實電網的數據。

隨機性：帶種子的 mulberry32 產生器；所用分布包括均勻分布、指數分布（反 CDF）、常態分布（Box–Muller）及泊松分布（Knuth）。種子會顯示出來，並可分享。

來源

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