SELF-EXCITATION CONDITIONS OF CAPACITOR INDUCTION GENERATORS

Abstract

For low-power electricity consumers, it is more practical to use asynchronous generators (AG) as power supply sources, since they best meet the requirements of users: high output voltage quality, low weight, relatively low cost, high reliability, and simplicity of design and maintenance. An asynchronous generator with capacitive self-excitation (SEIG) is characterized by the fact that its windings are not connected to external power sources. Therefore, the steady- state operation of such a generator is described by a system of homogeneous algebraic equations in coordinate axes oriented along the flux linkage vector in the air gap of the asynchronous machine (AM). The mathematical expression of the electromagnetic self-oscillations in the stator of the SEIG is the existence of nontrivial solutions to the system of homogeneous equations of the generator’s steady-state model, which is possible only when the main determinant of the system equals zero. By expanding this determinant and setting it to zero, taking into account the dependence of the reactive impedances of the SEIG equivalent circuit on the stator current frequency, an algebraic equation is obtained with respect to the angular frequency of the generator field rotation. By solving this equation, one can determine the relationship between the angular frequency of self-oscillations of current and voltage in the SEIG and the capacitance of the excitation capacitors. The determinant, being a complex number, is set to zero, and from the condition that both its real and imaginary parts equal zero, a mathematical expression is derived for the condition of negative slip of the SEIG during the delivery of active power to the load. Using the described approach, the frequency of electromagnetic oscillations in the SEIG stator is also determined relative to the base angular frequency of the power network. From the condition of negative slip, the minimum capacitance of excitation capacitors per phase is obtained–below this value, the self-oscillating mode cannot be achieved, and the roots of the stator circuit characteristic equation become complex conjugates shifted into the left half-plane of the complex root plane.