Power Systems Analysis

  1. Power Flow Analysis
    1. The Power Flow Problem
      1. Objectives of Power Flow Analysis
        1. Planning and Operation
          1. System Planning Studies
            1. Operational Planning
            2. Voltage Profile Assessment
              1. Voltage Magnitude Analysis
                1. Voltage Angle Analysis
                2. Loss Minimization
                  1. System Loss Calculation
                    1. Loss Optimization
                  2. Formulation of Power Flow Equations
                    1. Nodal Power Balance Equations
                      1. Real Power Balance
                        1. Reactive Power Balance
                        2. Nonlinear Nature of Equations
                          1. Voltage Magnitude Dependencies
                            1. Trigonometric Functions
                        3. Bus Admittance Matrix
                          1. Definition and Properties
                            1. Matrix Structure
                              1. Sparsity Characteristics
                                1. Symmetry Properties
                                2. Formation by Inspection
                                  1. Rule-Based Construction
                                    1. Diagonal Elements
                                      1. Off-Diagonal Elements
                                    2. Algorithmic Formation
                                      1. Computer Implementation
                                        1. Data Structure Requirements
                                          1. Algorithm Steps
                                          2. Handling Shunt Elements
                                            1. Shunt Admittance Addition
                                              1. Transformer Tap Effects
                                          3. Bus Classifications
                                            1. Slack Bus
                                              1. Role and Selection Criteria
                                                1. Reference Bus Function
                                                  1. Selection Guidelines
                                                  2. Specified and Unknown Quantities
                                                  3. Load Bus
                                                    1. Specified Quantities
                                                      1. Real Power Specification
                                                        1. Reactive Power Specification
                                                        2. Unknown Quantities
                                                        3. Generator Bus
                                                          1. Specified Quantities
                                                            1. Real Power Specification
                                                              1. Voltage Magnitude Specification
                                                              2. Reactive Power Limits
                                                                1. Maximum Reactive Power
                                                                  1. Minimum Reactive Power
                                                                    1. Limit Violation Handling
                                                                2. Numerical Solution Methods
                                                                  1. Gauss-Seidel Method
                                                                    1. Iterative Algorithm
                                                                      1. Algorithm Steps
                                                                        1. Convergence Criteria
                                                                        2. Acceleration Techniques
                                                                          1. Acceleration Factor
                                                                            1. Optimal Acceleration
                                                                            2. Convergence Characteristics
                                                                              1. Convergence Rate
                                                                                1. Convergence Problems
                                                                              2. Newton-Raphson Method
                                                                                1. Jacobian Matrix Formulation
                                                                                  1. Partial Derivative Calculations
                                                                                    1. Matrix Structure
                                                                                    2. Iterative Algorithm
                                                                                      1. Algorithm Steps
                                                                                        1. Matrix Inversion Requirements
                                                                                        2. Convergence Characteristics
                                                                                          1. Quadratic Convergence
                                                                                            1. Initial Guess Sensitivity
                                                                                            2. Handling PV and PQ Buses
                                                                                              1. Variable Switching
                                                                                                1. Reactive Power Limit Handling
                                                                                              2. Fast Decoupled Load Flow Method
                                                                                                1. P-θ and Q-V Decoupling
                                                                                                  1. Decoupling Assumptions
                                                                                                    1. Simplified Jacobian Matrices
                                                                                                    2. Assumptions and Advantages
                                                                                                      1. Computational Efficiency
                                                                                                        1. Memory Requirements
                                                                                                        2. Limitations
                                                                                                          1. Convergence Issues
                                                                                                            1. Applicability Constraints
                                                                                                        3. Analysis of Results
                                                                                                          1. Bus Voltage Magnitudes and Angles
                                                                                                            1. Voltage Profile Analysis
                                                                                                              1. Voltage Limit Violations
                                                                                                              2. Real and Reactive Power Flows in Lines
                                                                                                                1. Line Loading Analysis
                                                                                                                  1. Thermal Limit Violations
                                                                                                                  2. System Losses
                                                                                                                    1. Calculation of Line and System Losses
                                                                                                                      1. Line Loss Formulas
                                                                                                                        1. Total System Losses
                                                                                                                      2. Control of Voltage and Power Flow
                                                                                                                        1. Tap Changer Operation
                                                                                                                          1. Voltage Control Methods
                                                                                                                            1. Tap Position Optimization
                                                                                                                            2. Reactive Power Compensation
                                                                                                                              1. Capacitor Bank Control
                                                                                                                                1. Reactor Control

                                                                                                                          Previous

                                                                                                                          2. Foundational Concepts and Modeling

                                                                                                                          Go to top

                                                                                                                          Next

                                                                                                                          4. Symmetrical Fault Analysis