Transmission line theory for cable modeling: a delay-rational model based on Green's functions

Abstract: At present, induction motors are controlled via the so-called variable-frequency drives (VFD) that allow to control the speed for the motors. The purpose of this PhD thesis is to improve electromagnetic modeling techniques for the study of conducted electromagnetic emissions in variable-frequency drives, with the aim of enhancing their reliability in energy production plants. Pulse-width-modulated voltage converters are used to feed an AC motor, and they are considered to be the primary reason for high-frequency effects in both the motor and the supply grid. In particular, high-frequency currents, known as common mode currents, flow between all energized components and the ground and travel via low-resistance and low-inductance interconnects such as the power cable between the inverter and the motor. Electrically long power cables are commonly used in VFD installations, and require particular attention. Accurate models can be obtained using the theory of multiconductor transmission lines. In the case of nonlinear terminations, such as an inverter, only time-domain analysis is possible. In recent years, several techniques have been proposed. Some of these techniques include the lumped-element equivalent circuit method, the method of characteristics (MoC) and its generalizations, and the Pad´e approach. In this context, a modeling technique based on Green’s functions has been proposed. The input/output impedance matrix is expressed as a rational series, whose poles and their residues are identified by solving algebraic equations. The primary disadvantage of this method lies in the large number of poles that is typically necessary to model the dynamics of the system, especially when electrically long interconnects are considered. To overcome this limitation, we have proposed the Delay-Rational Green’s-Function-based Method, abbreviated as DeRaG. In this method, the line delay is extracted and, by virtue of suitable mathematical manipulation of the rational series, is incorporated through hyperbolic functions. The delay extraction enables the use of a reduced number of poles and improves the accuracy of the model in general, avoiding any ringing effects in the time-domain response. The primary advantage of the proposed method compared with other well-known techniques lies in the delayed state-space representation. The obtained model can be computed regardless of the terminations and/or sources, and the terminal conditions can be immediately and essentially incorporated. The next step will be to simulate the entire inverter-cable-motor system. The partial element equivalent circuit (PEEC) technique will be used to model the interconnects as well as the discontinuities in the power cable that can be caused, for example, by switch disconnectors. The theoretical results will be verified against experimental measurements. The final objective is to provide new techniques for modeling the electrodynamics of variable-frequency drives to allow their complete EMC assessment as early as the design stage and to enable the planning of corrective actions in advance.