Nonlinear Modeling of DC Constant Power Loads with Frequency Domain Volterra Kernels

Power system designers have more creative flexibility than ever before due to improvements in power electronics technology. The invention of the silicon (Si) insulated gate bipolar transistor (IGBT) in the 1980s was a major improvement over commonly used Si MOSFETs, for higher power applications, and thyristors, because they provided faster switching capabilities. New developments in silicon carbide (SiC) semiconductors are causing a similarly disruptive effect to the industry because of higher possible switching frequencies than Si IGBTs and the ability to create 10 kV devices with switching frequencies beyond 20 kHz. Higher breakdown voltage and faster switching enable converter designs with higher power densities (watts per cubic meter) that interface with higher voltage systems. These two factors along with decreasing costs of Si IGBTs and low voltage SiC MOSFETs make the increased use of power converters throughout a distributed power system possible. Power converters with a regulated output draw a constant input power from a distribution system. While constant power loads have a nonlinear relationship between input voltage and load current, linear systems theory historically dominated their analysis. The negative admittance model is often used with input filter parameters to create linear models of constant power loads suitable for small-signal stability analysis. However, systems with limited generation capacity and large constant power loads are susceptible to large-signal instability. Therefore, system stability analysis must include nonlinear models of system components to form an analytical, large-signal stability metric. We used the Volterra Series to model nonlinear responses of constant power loads through Volterra kernel measurement. A switch-mode power converter was designed to synthesize large-signal perturbations to measure frequency domain Volterra kernels of 380 VDC loads up to 5 kW. We measured the first and second order kernels of a 3 kW, 380 VDC constant power load from 0.1 Hz to 1000 Hz and verified significance of the second order kernel.