The book deals with electrical machines, both direct and alternating, and the bulk of the material deals with methods of calculation and analysis of their characteristics in non-stationary operating modes. Stationary states are also covered to the extent necessary for the integrity of the text. The material is divided into fourteen chapters (576 pages), although in terms of the content of the book it could be divided into four parts: generalized theory, direct current machines, asynchronous machines and synchronous machines. The generalized theory of electrical machines, which is based on the theory of magnetically coupled circuits and on the principle of electromechanical energy conversion, is presented in the first four chapters of the book. In doing so, procedures based on matrix algebra with a special vector method are combined, which made it possible to exploit the advantages of both approaches in order to present the material as clearly as possible. In the second chapter, the so-called general model of an electric machine is defined and described, as an electromechanical structure with a two-phase symmetrical winding on the stator, which has salient poles, and on the rotor, which is cylindrical. Based on the equations of the general model, simple procedures are used to derive equations for the other two characteristic air gap configurations, i.e. for a two-phase machine with salient poles on the rotor and a two-phase machine with a constant air gap, which is discussed in Chapter 4. The transformation of coordinates (variables), which represents the core of the generalized theory and has a central place in the analysis of electrical machines, is discussed in a separate, third, chapter. This made it possible to do two important things. First, to derive a two-axis theory in Chapter 4 in a way that makes transparent the connection between the electromagnetic configuration of the machine and the transformation of variables to be applied. And, second, to establish, in a relatively simple way, the basic theory of individual types of electrical machines on the basis of the two-axis models for the three characteristic air gap configurations, in later chapters. In this respect, the DC machine is specific in that it was necessary to explain the function of the collector as a device by which the physical transformation of coordinates is achieved. Otherwise, for example, the equations of an independent DC and a two-phase asymmetric, or single-phase, asynchronous machine are derived on the basis of the same two-axis model. DC machines After explaining the function of the collector as a device by which the physical transformation of variables is achieved, the equations of the DC independently excited machine were obtained, in accordance with its structure, by appropriate simplification of the equations of the general model. The basic types of DC machines, their equations and stationary characteristics are considered. For an independently excited motor, an analysis of the dynamic characteristics during start-up and shock loading is given. A system of linearized equations is derived that describes the behavior of the motor in the environment of the operating point in accordance with the theory of small displacements, and assuming constant excitation, its transfer functions are defined. At the end of this, fifth chapter, a brief overview of the theory of amplidyne is given, which, when it does not have a compensation winding, is structurally identical to the general model with transformed variables. Asynchronous machines The next five chapters of the book deal with asynchronous machines. The theory of a three-phase symmetrical asynchronous machine is based on the equations of a two-axis model with a constant air gap. In the analysis of stationary characteristics, special attention is paid to the influence of the supply voltage frequency. The equations of a single-phase asynchronous motor, which theoretically represents an asymmetrically supplied two-phase asymmetrical asynchronous machine, are derived from the equations of the general model. Chapter 6 also discusses the theory of an asynchronous motor supplied from a current source, which is important for regulated electric motor drives. Chapter 7 deals with the modeling of squirrel-cage asynchronous machines with the influence of eddy currents in the rotor bars taken into account, without which a valid analysis of the dynamic characteristics of machines with higher powers is not possible. The basic theory of the cage winding is given and the procedure for reducing it to an equivalent three-phase or two-phase winding is defined. Different methods are discussed for setting up a surrogate scheme of the tall rod in the slot, which is the basis for modeling the eddy currents in the rotor rod using ordinary differential equations. Two different mathematical models of a cage asynchronous machine with tall rods in the rotor were set up, and one of these models also describes a machine with a two-cage rotor, or, theoretically speaking, a machine with an n-cage rotor. Using these models, characteristic dynamic regimes in which eddy currents in the rotor rods play an important role are simulated in later chapters. The material of the eighth, ninth and tenth chapters deals with the analysis of non-stationary states of three-phase asynchronous (coil and cage) machines. At the same time, they are combined neither analytical nor numerical procedures, so that the analysis of simulation results uses the knowledge obtained on the basis of simplified analytical solutions. For this purpose, non-stationary states, depending on the approach to the analysis, are divided into three characteristic groups: (1) transient phenomena at constant speed, (2) typical nonlinear dynamic regimes and (3) dynamic regimes in the environment of the operating point, i.e. in the regime of small displacements. In the analysis of non-stationary states from the first group, and partly from the third group, it is possible to apply analytical procedures, while the second group includes those regimes that can be successfully analyzed only by computer simulation. All simulations were performed assuming a sinusoidal voltage at the machine terminals, which significantly facilitated the analysis of the dynamic characteristics of the machine, on which time harmonics have a negligible effect anyway, except in some special cases. Transient phenomena in an asynchronous machine assuming a constant speed of rotation are discussed in Chapter 8. At a constant speed of rotation, a coil asynchronous machine is described by a system of four linear differential voltage equations. In vector form, due to the structural symmetry of the asynchronous machine, a system of two equations is obtained that is suitable for analytical solution. Based on the characteristic equation of the latter system, the general properties of the transient components in currents and chain currents are analyzed, i.e. time constants and natural frequencies at different speeds of rotation. Analytical solutions are given for two characteristic transient phenomena: connection of a stationary motor to the network and a short circuit at the terminals of an asynchronous machine. The results and insights from Chapter 8 are used in the interpretation of the results of the simulation of typical nonlinear dynamic regimes of an asynchronous motor in Chapter 9: start-up, sudden change in voltage at the terminals, reversing and reconnection. When analyzing the characteristics of an asynchronous motor in the starting mode, some phenomena that are characteristic of nonlinear dynamic regimes in electrical machines in general are explained, so this analysis is given in much more detail than in other cases. At the beginning of Chapter 9, the procedures for simulating an asynchronous machine on a digital computer are described. The tenth chapter of the book deals with the dynamic regimes of an asynchronous machine in the operating point environment. Linearized equations of an asynchronous machine without current suppression are presented, as well as linearized equations of a squirrel-cage machine that take into account the action of eddy currents in the rotor bars. Based on these systems of linear differential equations, eigenvalues are calculated and a corresponding analysis is made with regard to the influence of relevant parameters. Based on the theory of linear systems, a procedure for the formulation of the transfer functions of an asynchronous machine and for the calculation of their poles and zeros is defined, which is based on the application of standard software tools. The stability of an asynchronous motor is analyzed, starting from its structural symmetry, which allows the definition of general stability conditions for the low-frequency range of the supply voltage. At the end of the tenth chapter, an analysis of the dynamics of an induction motor is given, based on analytical solutions of linearized equations, neglecting stator resistance. The validity of the simplified analytical solutions is checked by comparing them with the results obtained by simulation using a complete nonlinear model, for dynamic regimes with a step change in load, alternating torque load, and a step change in voltage and frequency. Synchronous machines The theory of synchronous machines, which is presented in Chapter 11, is based on a two-axis model with salient poles on the rotor. First, the procedure for reducing a three-phase synchronous machine without a choke winding to a two-axis model is described, and then the configuration of a synchronous machine with a choke winding in the longitudinal and transverse axes, in the rotor coordinate system, is defined. The equations of a machine with classical excitation, from an electromagnet, and a machine with excitation from permanent magnets are set up in a form suitable for numerical integration. The armature winding operator impedances for the longitudinal and transverse axes are defined, based on which the reactance and time constants of the machine are analyzed. Equations describing stationary states are derived, based on which the influence of frequency reduction on the characteristics of the synchronous motor is analyzed. The procedure for calculating state variables at the stationary operating point is described. The approach to the analysis of non-stationary operating modes of synchronous machines is similar to that applied to asynchronous machines. Therefore, by nature, the emphasis is placed on the dynamic characteristics of synchronous generators. In Chapter 12, based on simplified analytical solutions, which were obtained assuming a constant speed of rotation, transient phenomena during three-pole and two-pole short circuits at the terminals of the synchronous generator are analyzed. First, a three-pole short circuit in a machine without a choke winding is analyzed, and then, using the obtained results, we move on to the more complicated case of a synchronous machine with a choke winding. This approach was used to better explain the role of the choke winding. In the case of a two-pole short circuit, two cases were considered that differ from each other, both in the approach to the analysis and in the behavior of the physical quantities of the machine during the transient phenomenon. These are a short circuit on open terminals and a short circuit in the network to which the machine is connected. The transient stability of the generator and the motor start-up are considered in Chapter 13, as typical nonlinear dynamic regimes in synchronous machines. In that chapter, the procedures for simulating a synchronous machine on a digital computer were previously described, including simulating the saturation of the main magnetic circuit. In the transient stability analysis, the results obtained by classical methods, which are based on an approximate transient torque characteristic and the application of the equal surface method, are compared with the results obtained by simulation using a complete mathematical model of the machine. The application of a lower-order mathematical model based on neglecting the inertia of the armature winding is also considered. In the case of synchronous motor starting, both important problems are addressed, asynchronous starting and synchronization, with special attention to the specifics that occur in permanent magnet motors. In addition to the simulation results, analytical expressions for the characteristics of quasi-stationary starting are also given, which are derived based on the machine equations for the stationary asynchronous operating mode. In Chapter 14, the synchronous machine is considered as a linearized dynamic system, using similar methods and procedures as in Chapter 10 for the asynchronous machine. Therefore, first, a linearized version of the mathematical model is derived in a form that is valid for operating modes with a variable stator voltage frequency. Then, an analysis of the eigenvalues in the generator and motor operating modes is given, a procedure for the formulation of transfer functions, and an analysis of the stability of the synchronous motor in the low frequency range of the supply voltage. Finally, the dynamics of the synchronous motor is considered based on a simplified linearized mathematical model, which was performed while neglecting the resistance of the armature and excitation winding.