📘 Per Unit System – Theory & Numericals
Per Unit System simplifies power system calculations. It normalizes quantities using base values.
🔹 1️⃣ What is Per Unit?
Per Unit Value = Actual Value / Base Value
Example: If base voltage = 100 kV Actual voltage = 110 kV Per unit voltage = 110 / 100 = 1.1 pu🔹 2️⃣ Base Quantities
Choose two base quantities:- Base Power (S_base)
- Base Voltage (V_base)
Base Current = S_base / (√3 V_base)
Base Impedance = (V_base)² / S_base
These formulas are extremely important.🔹 3️⃣ Example 1 – Base Impedance
Given: S_base = 100 MVA V_base = 11 kV Z_base = V² / S = (11²) / 100 = 121 / 100Z_base = 1.21 Ω
🔹 4️⃣ Example 2 – Convert Impedance to PU
Actual impedance = 0.5 Ω Base impedance = 1.21 Ω Per unit impedance: = 0.5 / 1.21Z_pu ≈ 0.413 pu
🔹 5️⃣ Change of Base Formula
Very important for GATE.Z_pu(new) = Z_pu(old) × (S_new / S_old) × (V_old² / V_new²)
Memorize this formula.🔹 6️⃣ Example – Change of Base
Given: Z_old = 0.2 pu S_old = 50 MVA S_new = 100 MVA Voltage same. Z_new = 0.2 × (100/50) = 0.2 × 2Z_new = 0.4 pu
🔹 7️⃣ Advantages of Per Unit
- Transformer ratios eliminated
- Simplifies fault calculations
- Similar range of values
- Easy comparison of equipment
🎯 GATE Focus
- Base impedance formula
- Change of base formula
- Convert actual → per unit
- Convert per unit → actual
Per Unit System = Backbone of Power System Analysis
.png)
No comments:
Post a Comment