Battery powered energy systems such as electric vehicles utilize power electronics for controlling energy flows between the battery and the load or generation, respectively. Therefore, the battery is under high frequency stress due to fast switching power electronic devices. However, most battery models throughout the literature are not able to cope with high frequency excitation. This paper proposes an easy to implement equivalent circuit model that covers aforementioned frequency regions with a series of inductors that are each connected in parallel with an ohmic resistance. This circuit is parameterized by electrochemical impedance spectroscopy (EIS) up to 100 kHz. For further regions that reach regions of megahertz a skin effect model is investigated and compared to the RL-model. It is shown that such semi-empirical models can be motivated by geometrical considerations that can be found in the literature. Moreover, the proposed model is validated by simulating the voltage response from an input current that originates from an actual back-to-back half bridge DC/DC converter. The promising results indicate that such models might be implemented in future battery energy systems to improve insights on how batteries react to perturbations such as EMI noise or high frequency current ripple.

Introduction

It is commonly accepted that lithium-ion batteries are going to be a crucial factor for the energy transition from fossil fuels towards renewable energies regarding either the necessity to buffer fluctuating feed-ins from solar and wind power plants, improving grid quality and grid stability or as one feasible energy storage for electric mobility [1,2]. Given that distributed generation is an immanent feature of renewable energies, a paradigm shift towards new forms of electrical energy networks such as microgrids [3] has been initiated and batteries are commonly seen as a self-evident part of such smaller scaled networks to guarantee uninterrupted service or increase the degree of utilization of renewable power plants [4]. One example is to equip electric cars with back-to-back battery chargers [5] instead of the nowadays widely used unidirectional vehicle battery chargers [6] so that the car’s traction battery can be used as a backup storage which is known as the concept “vehicle to grid” (V2G) [7,8]. Regardless of all the aforementioned ideas being future concepts or already commercially available, they have one vital similarity: The design of energy systems cannot be done without taking power electronics into account. In principle, power electronic devices convert a mostly arbitrary current or voltage signal into another with power switches such as field-effect transistors (FET) or insulated gate bipolar transistors (IGBT) that are turned on and off periodically, e.g. controlled by pulse-width modulation (PWM) [9]. The switching frequency is within the magnitude of several kilohertz and therefore induces highfrequency noise and current ripple as shown for a half bridge based DC/ DC converter in Fig. 1. Thus, batteries that are connected to power electronics face highfrequency excitation. Therefore, a novel model that is able to represent a battery’s high-frequency behavior with a satisfactory explanation for its elements needs to be developed. In order to achieve a model that is easy to parameterize and is potentially simple enough to be implemented in online battery monitoring systems without inducing too much computational burden [10], two well established methods for modeling and parameterizing batteries, respectively, have been chosen.