النمذجة الحرارية للمحول وحساب النقطة الساخنة في الملفات (IEC 60076-2 / IEC 60076-7)

الصياغة الرياضية لارتفاع حرارة أعلى الزيت، ومعامل النقطة الساخنة H، وثوابت الزمن الحراري للملفات، وحركية التقادم الحراري وفق أرهينيوس لمحولات القدرة.

1. Thermal Degradation of Cellulose Insulation

The operational lifespan of power transformers is determined by the rate of thermal deterioration of solid cellulose paper insulation at the highest temperature point: the Winding Hot-Spot Temperature (θ_h).

2. Thermal Limits and Temperature Rise Thresholds (IEC 60076-2)

Cooling Class	Max Ambient Temp (θ_a)	Max Top-Oil Rise (Δθ_to)	Max Average Winding Rise	Max Hot-Spot Temp (θ_h)
ONAN / ONAF	40°C (Peak) / 30°C (Annual avg)	60 K	65 K	118°C (Emergency: 140°C)
OFAF / ODAF	40°C	60 K	65 K	118°C
AN (Cast Resin Class F)	40°C	N/A (Dry)	100 K	145°C
AN (Cast Resin Class H)	40°C	N/A (Dry)	125 K	170°C

3. Mathematical Formulation of Hot-Spot Temperature

Per IEC 60076-7, steady-state hot-spot temperature is calculated as:

θ_h = θ_a + Δ θ_to + H · g_r · K^y

Parameter Definitions:

θ_a: Ambient temperature (°C).
Δ θ_to: Top-oil temperature rise over ambient under rated load (K).
H: Hot-spot factor (1.10 - 1.30 for distribution; 1.30 - 1.50 for large power units).
g_r: Average winding-to-average oil temperature gradient at rated load (K).
K: Load current ratio (I_load / I_rated).
y: Winding temperature exponent (1.6 for ONAN/ONAF, 2.0 for OFAF/ODAF).

4. Arrhenius Insulation Aging Acceleration Model

V = 2^{(θ_h - 110) / (6)}

Operating at θ_h = 116°C doubles the aging rate (V = 2), halving expected lifespan from 30 years to 15 years.

*Reference: IEC 60076-2:2011; IEC 60076-7:2018; IEEE Std C57.91-2021.*