Transient Analysis of Electric Power Circuits Handbook

Chapter 1 Classical approach to transient analysis. Introduction. Appearance of transients in electrical circuits. Differential equations describing electrical circuits. Exponential solution of a simple differential equation. Natural and forced responses. Characteristic equation and methods of its determinations. Roots of the characteristic equation and different kinds of transient responses. First order characteristic equation. Second order characteristic equation. Independent and dependent initial conditions. Two switching laws (rules). Methods of finding independent initial conditions. Methods of finding dependent initial conditions. Generalized initial conditions. Methods of finding integration constants. Chapter 2 Transient response of basic circuits. Introduction. Five steps of solving problems in transients analysis. First order RL circuits. RL circuits under dc supply. RL circuits under ac supply. Applying a continuous flux linkage law to inductive circuits. First order RC circuits. Discharging and charging a capacitor. RC circuits under dc supply. RC circuits under ac supply. Applying a continuous charge law to capacitance circuits. The application of a unit-step forcing function. Superposition principle in transient analysis. Second order RLC circuits. RLC circuits under dc supply. RLC circuits under ac supply. Transients in RLC resonant circuits. Switching-off in RLC circuits. Chapter 3 Transients in complicated circuits and the Laplace transform. Introduction. The Laplace transform. Properties of the Laplace transform. Laplace transform of basic time functions. Initial-value and final-value theorems. Examples of finding circuit responses. Inverse transform and partial fraction expansion. Ohm and Kirchhoff's laws with the Laplace transform. Equivalent circuits with Laplace transform techniques. More examples of finding circuit responses. Using nodal analysis. Using mesh analysis. Mutually coupled circuits. Some techniques for simplifying the solution. Chapter 4 Transient analysis using the Fourier transform. Introduction. The inter-relation between the transient behavior of electrical circuits and their spectral properties. The Fourier transform. The definition of the Fourier transform. Relationship between a discreet and continuous spectra. Symmetry properties of the Fourier transform. Energy characteristics of continuous spectra. The comparison between Fourier and Laplace transforms. Some properties of the Fourier transform. Some important transform pairs. Input-impulse (delta) function. Unit-step function. Decreasing sinusoid. Saw-tooth pulse. A periodic time function. Convolution integral in the time domain and its Fourier transform. Circuit analysis with Fourier transform. Ohm and Kirchhoff's laws with the Fourier transform. Inversion of the Fourier transform using the residues of complex functions. Approximate transient analysis with the Fourier transform. Chapter 5 State variable analysis. Introduction. The concept of state variables. Order of complexity of a network. State equations and trajectory. Basic considerations in writing state equations. Fundamental cut-set and loop matrixes. 'Proper tree' method for writing state equations. A systematic method for writing the state equation based on circuit matrix representation. Complete solution of the matrix equation. The natural solution. Matrix exponential. The particular solution. Basic considerations in determining functions of a matrix. Evaluating the matrix exponential by the Laplace transform. Chapter 6 Transients in three-phase circuits. Introduction. Short circuit transients in power systems. Base quantities and per-unit conversion in three-phase circuits. Equivalent circuits and their simplification. Using the superposition principle. Short-circuiting in a simple circuit. Short-circuiting of a power transformer. Short-circuiting