📘 Transformer Efficiency – Complete Theory & Numericals
Efficiency of transformer is the ratio of output power to input power. Since transformers are static devices, efficiency is very high (95–99%).
🔹 1. Definition
Efficiency (η) = Output Power / Input Power
Or,η = Output / (Output + Losses)
🔹 2. Transformer Losses
Total losses =- Core Loss (constant)
- Copper Loss (variable)
Copper Loss = I²R
🔹 3. Efficiency at Given Load
If load fraction = x, Copper loss at that load:P_cu = x² × (Full load copper loss)
Efficiency:η = (x S cosφ) / (x S cosφ + P_core + x² P_cu_full)
Where: S = rated kVA🔹 4. Maximum Efficiency Condition
Maximum efficiency occurs when:Copper Loss = Core Loss
Very important result.🔹 5. Example 1
Given: Core loss = 500 W Full load copper loss = 800 W Rated = 10 kVA Power factor = 0.8 Find load at maximum efficiency. Condition:x² × 800 = 500
x² = 500 / 800 = 0.625 x = 0.79 Maximum efficiency at 79% load.🔹 6. Example 2 – Efficiency Calculation
At 0.8 load: Copper loss:= (0.8)² × 800 = 512 W
Output:= 0.8 × 10,000 × 0.8 = 6400 W
Total losses:= 500 + 512 = 1012 W
Efficiency:η = 6400 / (6400 + 1012) η = 86.35%
🔹 7. All-Day Efficiency
Used for distribution transformers.All-day efficiency = Energy output / Energy input (24 hours)
Very important conceptual question.🎯 GATE Important Points
- Maximum efficiency when copper loss = core loss
- Copper loss varies with square of load
- All-day efficiency for distribution transformers
- Transformer efficiency very high (above 95%)
Maximum Efficiency Condition = Most Repeated GATE Concept
.png)
No comments:
Post a Comment