Multiconductor transmission lines wideband modeling : A delay-rational Green’s-function-based method

Abstract: The performance of variable-frequency drives (VFDs) commonly used in energy production plants can be severely affected by electromagnetic (EM) noise in the form of conducted disturbances.A VFD is composed of an inverter, a motor, and a connecting power cable. The insulated-gate bipolar transistor (IGBT) technology and the pulse-width modulation (PWM) technique, used in the inverter, amplified the role of the power cable, which experiences the so-called “high-frequency” or “transmission line” effects, such as reflections, crosstalk, and distortion. Therefore, a complete EM assessment of a VFD requires an accurate and computationally efficient mathematical model of the cable, which can be studied as a multiconductor transmission line (MTL). Accordingly, we developed the “delay-rational Green’s-function-based” (DeRaG) model that should overcome the main limitations of the existing methods in the literature. In the DeRaG model, the impedance (or admittance) matrix is the sum of a rational series and a so-called hyperbolic part realized by hyperbolic functions. The rational series consists of poles and residues and can be truncated to a suitable size by a delay extraction technique. The hyperbolic part retains the primary information of the high-frequency behaviors, such as attenuation and propagation delays, of a line; thus, the DeRaG model is a wideband model. The DeRaG model is independent of the terminations and sources of the line and enables a delayed state-space representation; it can also account for EM interference. Nevertheless, an EM assessment of a complex system can be performed only using a calculator and proper software. Most of the advanced models for MTLs have been adapted for SPICE-like transient solvers. However, power electronics applications are commonly simulated by using software packages such as Simulink that are optimized for system-level simulations. We thus proposed the implementation of the DeRaG model both in SPICE and in Simulink to embrace a larger group of users and applications. The Simulink implementation was notably proven to be extremely simple and easy to describe. In addition, we focused on the hyperbolic part to qualitatively assess the behavior of an MTL. Our investigation resulted in an outstanding outcome; namely, we provided the distortionless condition for MTLs, whereas the distortionless condition was previously defined only for single-conductor transmission lines as the well-known Heaviside condition. In conclusion, the DeRaG model is a wideband model for the EM analysis of generic transmission lines that is suitable for system-level simulations required in power electronics applications and offers new insights into the physics of the system.