Accelerated Simulation of High-Fidelity Models of Supercapacitors Using Waveform Relaxation Techniques

The waveform relaxation (WR) technique is used to accelerate the time-domain simulation of high-fidelity models of supercapacitors. Because of their high power density, supercapacitors are suitable energy storage options in electrified transportation fleets and renewable energy systems. Given their fast charging/discharging profile, high-fidelity models, such as transmission-line models or multistage ladder structures, are conventionally adopted for design and simulation purposes. High-fidelity models, that include fast dynamic modes, can slow down the simulation process. This is problematic, in particular, since supercapacitors are parts of a larger, more complex system, e.g., a power train, with a wide dynamic range. In this paper, frequency-domain characterization of a supercapacitor is conducted by the electrochemical impedance spectroscopy. Then, the equivalent multistage ladder model of the supercapacitor is extracted and parameterized. The high-fidelity model is verified by considering the measured charging profile of the supercapacitor. The WR technique, including circuit partitioning and time windowing, is considered for the resulting high-fidelity model. WR results in an order-of-magnitude improvement in simulation speed while maintaining an excellent agreement with the hardware measurement and conventional simulations.