📘 Power Circle Diagram – Receiving & Sending End
Power Circle Diagram is a graphical representation of real and reactive power for a transmission line using ABCD parameters.
🔹 1️⃣ Basic ABCD Relation
Vs = A Vr + B Ir
Let: A = |A|∠α B = |B|∠β From this, power equations are derived.🔹 2️⃣ Receiving End Power Equation
Receiving end complex power:S_r = P_r + jQ_r
Power circle equation becomes:(P_r - P0)² + (Q_r - Q0)² = R²
This represents a circle in P–Q plane.🔹 3️⃣ Sending End Power Circle
Similarly:(P_s - P1)² + (Q_s - Q1)² = R²
Two circles are formed: ✔ Receiving End Circle ✔ Sending End Circle🔹 4️⃣ Important Concepts
- Center depends on |A| and |B|
- Radius depends on voltage magnitudes
- Power transfer limited by circle boundary
- Stability related to maximum real power
🔹 5️⃣ Maximum Power Transfer
For simple lossless line:P_max = (Vs Vr) / X
Occurs when: δ = 90° This connects to power angle equation.🔹 6️⃣ Example Problem
Given: Vs = 220 kV Vr = 220 kV X = 100 Ω Maximum power: P_max = (Vs Vr)/X = (220 × 10³ × 220 × 10³)/100 = (48.4 × 10¹⁰)/100 = 4.84 × 10⁹ WP_max ≈ 4840 MW
🔹 7️⃣ GATE Concept Questions
✔ Maximum power occurs at δ = 90° ✔ Circle shows power limit ✔ Stability depends on operating point🎯 GATE Focus Areas
- Power angle equation
- Maximum power condition
- Interpretation of P–Q circle
- Connection to stability
Power Circle Diagram = Graphical View of Power Transfer Limit
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