Power Systems Analysis

  1. Foundational Concepts and Modeling
    1. Review of AC Circuit Theory
      1. Sinusoidal Waveforms and Parameters
        1. Amplitude and Peak Values
          1. Frequency and Period
            1. Phase Angle
              1. RMS Values
              2. Phasor Representation
                1. Complex Numbers in Power Systems
                  1. Rectangular Form
                    1. Polar Form
                      1. Euler's Formula
                      2. Phasor Diagrams
                        1. Construction Principles
                          1. Interpretation Methods
                        2. Complex Power
                          1. Real Power
                            1. Definition and Units
                              1. Physical Significance
                              2. Reactive Power
                                1. Definition and Units
                                  1. Physical Significance
                                  2. Apparent Power
                                    1. Definition and Units
                                      1. Relationship to Real and Reactive Power
                                      2. Power Factor
                                        1. Definition and Calculation
                                          1. Leading and Lagging Power Factor
                                          2. Power Triangle
                                            1. Geometric Representation
                                              1. Power Triangle Applications
                                            2. Three-Phase Systems
                                              1. Generation of Three-Phase Voltages
                                                1. Balanced Three-Phase Generation
                                                  1. Phase Sequence
                                                  2. Balanced Systems
                                                    1. Balanced Voltage Sources
                                                      1. Balanced Loads
                                                        1. Symmetry Properties
                                                        2. Unbalanced Systems
                                                          1. Unbalanced Voltage Sources
                                                            1. Unbalanced Loads
                                                              1. Analysis Methods
                                                              2. Wye Connection
                                                                1. Wye-Connected Sources
                                                                  1. Wye-Connected Loads
                                                                    1. Neutral Point
                                                                    2. Delta Connection
                                                                      1. Delta-Connected Sources
                                                                        1. Delta-Connected Loads
                                                                          1. Circulating Currents
                                                                          2. Phase and Line Quantities
                                                                            1. Phase Voltages and Currents
                                                                              1. Line Voltages and Currents
                                                                                1. Relationships in Wye Systems
                                                                                  1. Relationships in Delta Systems
                                                                                  2. Star-Delta and Delta-Star Transformations
                                                                                    1. Transformation Formulas
                                                                                      1. Applications in Circuit Analysis
                                                                                  3. The Per-Unit System
                                                                                    1. Definition of Base Quantities
                                                                                      1. Base Power Selection
                                                                                        1. Base Voltage Selection
                                                                                          1. Base Current Calculation
                                                                                            1. Base Impedance Calculation
                                                                                            2. Conversion to and from Per-Unit Values
                                                                                              1. Per-Unit Calculations for Different Quantities
                                                                                                1. Voltage Per-Unit Values
                                                                                                  1. Current Per-Unit Values
                                                                                                    1. Power Per-Unit Values
                                                                                                      1. Impedance Per-Unit Values
                                                                                                    2. Advantages of the Per-Unit System
                                                                                                      1. Simplification of Calculations
                                                                                                        1. Elimination of √3 Factors
                                                                                                          1. Simplified Transformer Calculations
                                                                                                          2. Comparison Across Voltage Levels
                                                                                                            1. Normalized Comparisons
                                                                                                              1. Equipment Rating Comparisons
                                                                                                            2. Changing the Base of Per-Unit Quantities
                                                                                                              1. Base Conversion Formulas
                                                                                                                1. Voltage Base Changes
                                                                                                                  1. Power Base Changes
                                                                                                                  2. Application in Multi-Voltage Systems
                                                                                                                    1. Multi-Level System Analysis
                                                                                                                      1. Transformer Base Changes
                                                                                                                  3. Modeling of Power System Components
                                                                                                                    1. Synchronous Machine Model
                                                                                                                      1. Equivalent Circuit Representation
                                                                                                                        1. Steady-State Equivalent Circuit
                                                                                                                          1. Phasor Diagram
                                                                                                                          2. Steady-State Model
                                                                                                                            1. Synchronous Reactance
                                                                                                                              1. Armature Resistance
                                                                                                                                1. Generated EMF
                                                                                                                                2. Transient and Subtransient Reactances
                                                                                                                                  1. Transient Reactance Definition
                                                                                                                                    1. Subtransient Reactance Definition
                                                                                                                                      1. Time Constants
                                                                                                                                      2. Saturation Effects
                                                                                                                                        1. Saturation Curve
                                                                                                                                          1. Unsaturated vs Saturated Values
                                                                                                                                        2. Transformer Model
                                                                                                                                          1. Single-Phase Transformer Equivalent Circuit
                                                                                                                                            1. Ideal Transformer Model
                                                                                                                                              1. Practical Transformer Model
                                                                                                                                                1. Referred Quantities
                                                                                                                                                2. Magnetizing and Leakage Reactance
                                                                                                                                                  1. Magnetizing Reactance
                                                                                                                                                    1. Leakage Reactance
                                                                                                                                                      1. Core Loss Resistance
                                                                                                                                                      2. Three-Phase Transformer Connections
                                                                                                                                                        1. Y-Y Connection
                                                                                                                                                          1. Voltage and Current Relations
                                                                                                                                                            1. Neutral Point Considerations
                                                                                                                                                            2. Δ-Δ Connection
                                                                                                                                                              1. Voltage and Current Relations
                                                                                                                                                                1. Circulating Current Effects
                                                                                                                                                                2. Y-Δ Connection
                                                                                                                                                                  1. Phase Shift Considerations
                                                                                                                                                                    1. Voltage and Current Relations
                                                                                                                                                                    2. Δ-Y Connection
                                                                                                                                                                      1. Phase Shift Considerations
                                                                                                                                                                        1. Voltage and Current Relations
                                                                                                                                                                      2. Off-Nominal and Tap-Changing Transformers
                                                                                                                                                                        1. Off-Nominal Tap Ratios
                                                                                                                                                                          1. Tap-Changing Transformer Models
                                                                                                                                                                            1. Voltage Regulation Effects
                                                                                                                                                                            2. Autotransformers
                                                                                                                                                                              1. Autotransformer Principles
                                                                                                                                                                                1. Equivalent Circuit
                                                                                                                                                                                  1. Advantages and Disadvantages
                                                                                                                                                                                2. Transmission Line Model
                                                                                                                                                                                  1. Line Parameters
                                                                                                                                                                                    1. Resistance Calculation
                                                                                                                                                                                      1. DC Resistance
                                                                                                                                                                                        1. AC Resistance
                                                                                                                                                                                          1. Temperature Effects
                                                                                                                                                                                          2. Inductance Calculation
                                                                                                                                                                                            1. Internal Inductance
                                                                                                                                                                                              1. External Inductance
                                                                                                                                                                                                1. Mutual Inductance
                                                                                                                                                                                                2. Capacitance Calculation
                                                                                                                                                                                                  1. Line-to-Ground Capacitance
                                                                                                                                                                                                    1. Line-to-Line Capacitance
                                                                                                                                                                                                    2. Conductance Effects
                                                                                                                                                                                                      1. Leakage Conductance
                                                                                                                                                                                                        1. Corona Loss Conductance
                                                                                                                                                                                                      2. Short Line Model
                                                                                                                                                                                                        1. Assumptions and Limitations
                                                                                                                                                                                                          1. Series Impedance Model
                                                                                                                                                                                                            1. Voltage and Current Relations
                                                                                                                                                                                                            2. Medium Line Model
                                                                                                                                                                                                              1. Nominal-π Model
                                                                                                                                                                                                                1. Circuit Configuration
                                                                                                                                                                                                                  1. Parameter Calculations
                                                                                                                                                                                                                  2. Nominal-T Model
                                                                                                                                                                                                                    1. Circuit Configuration
                                                                                                                                                                                                                      1. Parameter Calculations
                                                                                                                                                                                                                    2. Long Line Model
                                                                                                                                                                                                                      1. Distributed Parameter Representation
                                                                                                                                                                                                                        1. Differential Equations
                                                                                                                                                                                                                          1. Hyperbolic Functions
                                                                                                                                                                                                                          2. Surge Impedance and Propagation Constant
                                                                                                                                                                                                                            1. Characteristic Impedance
                                                                                                                                                                                                                              1. Propagation Constant
                                                                                                                                                                                                                              2. Ferranti Effect
                                                                                                                                                                                                                                1. Voltage Rise Phenomenon
                                                                                                                                                                                                                                  1. Capacitive Loading Effects
                                                                                                                                                                                                                              3. Load Modeling
                                                                                                                                                                                                                                1. Constant Impedance Loads
                                                                                                                                                                                                                                  1. Model Characteristics
                                                                                                                                                                                                                                    1. Voltage Dependency
                                                                                                                                                                                                                                    2. Constant Current Loads
                                                                                                                                                                                                                                      1. Model Characteristics
                                                                                                                                                                                                                                        1. Voltage Dependency
                                                                                                                                                                                                                                        2. Constant Power Loads
                                                                                                                                                                                                                                          1. Model Characteristics
                                                                                                                                                                                                                                            1. Voltage Dependency
                                                                                                                                                                                                                                            2. Composite Load Models
                                                                                                                                                                                                                                              1. ZIP Load Model
                                                                                                                                                                                                                                                1. Polynomial Load Model
                                                                                                                                                                                                                                                2. Dynamic Load Characteristics
                                                                                                                                                                                                                                                  1. Motor Load Dynamics
                                                                                                                                                                                                                                                    1. Load Recovery Effects

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                                                                                                                                                                                                                                              1. Introduction to Power Systems

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                                                                                                                                                                                                                                              3. Power Flow Analysis