GATE Electrical Engineering - Complete Master Library

 

📘 Power Systems – Advanced Numerical Marathon (Page 21)

Very Hard Multi-Step GATE + PSU Problems

---

🔹 Problem 1 – Per Unit + Fault + Actual Conversion

A 100 MVA, 13.8 kV generator has X = 0.2 pu. A 3-phase fault occurs at terminals. Step 1: Fault current in pu

I_f = 1 / 0.2 = 5 pu

Step 2: Base Current

I_base = S / (√3 V) = 100 / (1.732 × 13.8) = 4.18 kA

Step 3: Actual Fault Current

I_actual = 5 × 4.18 = 20.9 kA

---

🔹 Problem 2 – Stability Margin

E = 1.1 pu V = 1 pu X = 0.6 pu Pm = 1 pu Step 1: Pmax

Pmax = EV/X = 1.1/0.6 = 1.83 pu

Step 2: Initial angle

1 = 1.83 sinδ sinδ = 0.546 δ = 33°

Step 3: Stability Margin Maximum power limit = 1.83 Operating = 1 Margin ≈ 45%

---

🔹 Problem 3 – Economic Dispatch With Loss

Loss = 0.0004P1² C1 = 0.02P1² + 4P1 C2 = 0.025P2² + 5P2 Load = 250 MW Penalty factor method required (iterative solution). Advanced numerical – typically solved using lambda iteration.

---

🔹 Problem 4 – Load Flow Insight

Given 3-bus system, NR method preferred because:

• Faster convergence
• Better for large systems
• Less iteration required

---

🔹 Problem 5 – Multi-Source Fault Comparison

If X1 = 0.2 pu X2 = 0.25 pu X_line = 0.3 pu Parallel Xg = 0.111 pu Total Z = 0.411 pu I_fault = 2.43 pu If fault occurs closer to generator → current increases.

---

🔹 Quick Concept Check

• Reducing X increases stability margin
• Reducing impedance increases fault level
• Economic dispatch equalizes incremental cost
• HVDC improves long distance transfer

---

Page 21 – Advanced Numerical Marathon Completed