Newton_Raphson_Load_Flow_RajashekarK.pptx

Newton_Raphson_Load_Flow_

1. Newton–Raphson Method for Load Flow Studies Power System Analysis Presented by: Rajashekar K Rao Bahadur Y. Mahabaleshwarappa Engineering College, Ballari

2. Introduction - Load flow (power flow) studies determine bus voltages, power flows. - Used for system planning, operation & control. - Common methods: Gauss-Seidel, Newton–Raphson, Fast Decoupled Load Flow.

3. Objective of Load Flow Analysis - Determine steady-state operating condition of power system. - Obtain: voltage at each bus, real & reactive power flow, transmission losses. - Essential for planning and operation.

4. Types of Buses Slack Bus: Known V, δ; Unknown P, Q. PV (Generator) Bus: Known P, V; Unknown Q, δ. PQ (Load) Bus: Known P, Q; Unknown V, δ.

5. Newton–Raphson Method Overview - Iterative method based on Taylor Series expansion. - Linearizes nonlinear power flow equations. - High accuracy, fast convergence. - Approaches: Polar Form and Rectangular Form.

6. Load Flow Equations For each bus i: P_i = Σ V_i V_j (G_ij cosδ_ij + B_ij sinδ_ij) Q_i = Σ V_i V_j (G_ij sinδ_ij - B_ij cosδ_ij) Where G_ij and B_ij are from Y-bus matrix.

7. Newton–Raphson Formulation [ΔP ΔQ]^T = [J1 J2; J3 J4][Δδ ΔV]^T Jacobian matrix: J1 = ∂P/∂δ, J2 = ∂P/∂V, J3 = ∂Q/∂δ, J4 = ∂Q/∂V.

8. Iterative Solution Steps 1. Form Y-bus matrix. 2. Assume initial voltages (flat start). 3. Compute P and Q at each bus. 4. Calculate mismatches ΔP and ΔQ. 5. Form Jacobian matrix. 6. Solve [J][Δx] = [ΔP ΔQ]. 7. Update voltages and angles. 8. Repeat until convergence.

9. Advantages ✔ Fast convergence. ✔ Accurate results. ✔ Suitable for large systems. ✔ Handles polar and rectangular forms.

10. Disadvantages ✘ Requires more computation per iteration. ✘ Complex Jacobian formulation. ✘ Not ideal for manual computation.

11. Example (Conceptual) 3-Bus system example: - Given load and generation data. - Form Y-bus. - Use flat start. - Apply iterations until convergence.

12. Convergence Comparison Method | Speed | Accuracy | Complexity Gauss-Seidel | Slow | Moderate | Simple Newton–Raphson | Fast | High | Moderate Fast-Decoupled | Very Fast | Slightly lower | Simple

13. Applications - Power system operation & planning. - Fault analysis. - Economic dispatch. - Voltage stability studies. - Real-time system monitoring.

14. Conclusion - Most reliable and accurate load flow method. - Fewer iterations, faster convergence. - Widely used in modern power system software.

15. References 1. Hadi Saadat – Power System Analysis. 2. J. Grainger & W.D. Stevenson – Power System Analysis. 3. Nagrath & Kothari – Modern Power System Analysis.