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The Self-Excitation Process in Electrical Rotating Machines Operating in Pulsed Power Regime

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The Self-Excitation Process in Electrical Rotating Machines Operating in Pulsed Power Regime 1 The Self-excitation Process in Electrical Rotating Machines Operating in Pulsed Power Regime M.D. Driga The University of Texas Department of Electrical and Computer Engineering S.B. Pratap, A.W. Walls, and J.R. Kitzmiller The Center for Electromechanics at The University of Texas at Austin simultaneously the voltage and current would rise so Abstract-- The self-excitation process in pulsed air-core excessively that the machine would burn out...” rotating generators is fundamental in assuring record values of This statement is incomplete, since the machine does not power density and compactness. This paper will analyze the burn out if the excessive currents are flowing during a conditions for the self-excitation process in pulsed electrical relatively short pulse - intensity and duration being in machines used as power supplies for electromagnetic launchers, competition - but involuntarily suggests the use of self- using the analogy and methods of the positive feedback in control excitation in pulsed rotating, electric generators for EML systems. technologies in which the pulse duration is measured in In the classical "ferromagnetic" electrical machines in the milliseconds. Of course, even in EML pulsed rotating power self-excitation process, the machine output is used in order to supplies, the runaway self-excitation may be stopped by fault gradually excite the generator until the steady-state voltage is conditions such as mechanical failure from excess braking finally reached. The end of the process and, consequently, the force, increased ohmic losses from heating and even depletion stability and repeatability, is assured by the intersection of the (or insufficient) rotational kinetic energy stored (quantified by strongly nonlinear magnetization characteristic and the ω=ω excitation straight line. the critical c ). In the air-core, pulsed power machines such as homopolar This paper tries to show that the self-excitation is one of generators and compulsators, the two characteristics are the fundamental ways of increasing the power densities for apparently linear and both the end and the initiation of the such generators, thus drastically reducing their weight and process must be forced. The paper shows that the pattern of the volume. As an illustration, Fig. 1 presents a picture of the self-excitation process is very similar in all the EML power Cannon Caliber Electromagnetic Gun (CCEMG ) generator - supplies (homopolar, compulsators, asynchronous) and the a self-excited compulsator of high power density and initially unstable process reaches stability in a very controlled compactness capable of delivering 1.2 MJ to a railgun for way. three five-round salvos at a short repetition rate of 5 Hz. The The paper also shows how the self-excitation can create a new self-excited compulsator stores 40 MJ at 12,000 rpm and EML power supply with an original use, from a classical weighs only 2,045 kg, its compactness being shown by a electrical machine. graphic comparison [2, 3]. I. INTRODUCTION HE invention of the self-excitation process in electrical Tmachines credited to Werner von Siemens almost a century and a half ago, looked (and still does) somewhat a miracle. For an electric generator considered as a power amplifier with a power gain equal to the ratio of the output to the excitation power, the self-excitation starts with an extremely small input (the remnant magnetism, for example) and reaches the full output power, increasing manifold the one-stage power gain. The amplification is obviously achieved on the account of the energy supplied by the prime mover. In [1] as in a majority of classical treatments of electrical machines is stated the general idea that “any self- excitation is inconceivable without the magnetic saturation, since no stability of voltage and current in the machine would be attained. Without saturation... the magnetic flux and Manuscript received April 21, 1999. Fig. 1. Cannon caliber self-excited compulsator 2 This paper also points out that the self-excitation is a closed loop process which, unlike in classical control theory, employs a positive feedback: the energy of the electric II. THE ROLE OF SELF-EXCITATION IN generator is brought back to the excitation stage using the INCREASING POWER DENSITY positive feedback network in order to achieve the desired In order to quantify the role of self-excitation in the terminal voltage and other output parameters in conditions of increase of power density, we will refer to Figure 2, showing a relatively high amplification factor. the reversibility principle in electromechanical energy Also, while self-excitation can be applied to all types and conversion for a unit volume of active conductor (or by topologies of electrical machines (homopolar and heteropolar, multiplication by the volume element dv , for an elementary synchronous and asynchronous, steady-state and pulsed volume of active conductor). This diagram makes the point operation), it has become evident lately that it offers that an electromechanical structure represents a pulsed incredible benefits, especially to the pulsed rotating generator or an accelerator, depending on the direction of the generation used in electromagnetic launch technology. Such power flow. In Fig. 2, P , P , P are the densities for benefits are two-fold: not only does it achieve, almost kin conv el 3 exponentially (due to the positive feedback connection), high kinetic, converted, and electrical power (in wm ), while values of the excitation flux densities, but such values are P and J 2 σ represent the mechanical and electrical maintained, only for the short duration of the machine mech 3 discharge time, limiting the excitation losses to reasonable (joule) losses (also expressed in wm ). In spite of the values. appearance of being incomplete and simplistic, the diagram The basic topologies and types of electrical machines will describes the local power density for the converter. Such local be considered and discussed, showing that in principle (or power density in the condition of lossless electromechanical rather in spirit), all their self-excitation processes are similar: power conversion per unit volume of active conductor of the their point of departure is a small magnetic field (a seed) generator is given by the mixed vector product: such as remnant magnetism, a discharging capacitor, etc., −(JB ×) •= u( uB ×) • J (1) leading to an unstable (positive feedback!) initial 2 exponential increase of the output. However, nearing the where J is the current density ( Am ), B is the magnetic final state, a limiting mechanism occurs, either due to a drop flux density (T), and u is the local velocity. in the angular velocity below the critical value ( ωc ) as in the When the two sides of expression (1) are multiplied by the case of homopolar generators, as a result of a massive elementary volume dv , we obtain the true definition of conversion of kinetic energy into magnetic energy, or by a instantaneous conversion. The "active conductor" is the seat skillful commutation as in the compulsators case, or by a of the power conversion and by the principle of equality of stable exponential approach to the steady-state enforced by action and reaction, is equally felt in both the stator and rotor saturation in iron core dc generators. of the electromechanical converter. Finally, a new generator or, conversely, a new beginning The flux density B in expression (2) is the vectorial sum for an electrical machine with almost no applications outside of the impressed excitation field Bimp and the induced field of the area of pulsed EML is proposed as an ideal power supply for industrial/civilian applications. by the armature reaction, Ba, ind (invoking the Lenz rule) such that: Fig. 2. The principle of reversibility in EML electromechanical conversion 3 characteristic equation of the self-excited rotating electrical −×−•=×−•JBB( imp a,, ind ) uuBB( imp a ind ) J (2) generator modeled in Fig. 3 is: A pulsed electrical machine exploits the manner in which the two B vectors add (or rather subtract) in different 10+=AB( s) (3)Equation (3) leads to several relations moments of discharge. By partially eliminating the direct axis for the analysis and design for the generator, since it implies shield, one can achieve a first self-excitation scheme without two conditions related to magnitude and phase angle: unreasonably increasing the losses by eddy currents, especially if a separate exciter winding is used in order to AB( s) =1; < AB( s) =(2 k +π 1) (4) "protect" the optimality of the main armature winding. The rules for root locus construction, well known from the The mixed vector product in expressions (1) and (2) points control system theory, cannot be used here because of out that increasing the excitation field B by self-excitation is positive feedback, which leads to instability. one of the three fundamental directions of drastically For the self-excited electrical machines, the rules will be reducing the weight and volume of the rotation power modified such that: (a) the gain K is varied from 0 to +∞ supplies used in electromagnetic launch technology: (a) the (instead of taking negative values as in the case of regular, increase in the velocity u , by employing the most advanced negative feedback); (b) root loci occur on a segment of real composite structural materials for the rotor; (b) the increase in axis, only if there are an even number (as opposed to an odd the current density J by improvements in the machine number for negative feedback) or poles and zeros of the open cooling; and (c) the increase in B by self-excitation up to the loop transfer function lying to the right of that segment; (c) limit allowed by the losses in the short excitation time. finally, (21k +π) is replaced in construction by 2kπ . Formula (2) cautions us that the impressed excitation field B will give an optimistic evaluation of the power density; imp IV.
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