A Circuit-Equivalent Battery Model Accounting for the Dependency on Load Frequency Yukai Chen Politecnico di Torino Email: yukai.chen@polito.it Enrico Macii Politecnico di Torino Email: enrico.macii@polito.it Massimo Poncino Politecnico di Torino Email: massimo.poncino@polito.it Abstract—Circuit-equivalent battery models are considered de- facto standard for modeling and simulation of digital systems due to many practical advantages. In spite of the many variants of models proposed in the literature, none of them accounts for one important feature of the battery dynamics, namely, the dependency on the frequency of current load profile. For a given average current value, current loads with different spectral distributions may have quite different impacts on the battery discharge. This is a very well-know issue in the design of hybrid energy storage systems, where different types of storages devices are used, each with different storage efficiency for different load frequency ranges. We propose a basic modification to a state-of-the-art model that incorporates this load frequency dependency, as well as a methodology to identify the frequency-sensitive parameters of the model from publicly available data (e.g., datasheets). The results show that frequency-agnostic models can significantly overestimate the battery state-of-charge, and that this effect is far from being negligible. I. I NTRODUCTION The ubiquity of battery-power devices has made models of bat- teries an essential component of electronic system simulators; the humongous variety of models available in the literature is driven by different needs by designers belonging to different application domains and with different backgrounds [1]. In the context of electronic design, users typically need basic feedback about a battery, e.g., the discharge time and/or its state-of-charge (SOC) for a given load profile. Although these effects can be tracked by different types of models, electronic designers tend to favor models in which the battery dynamics is mimicked by an equivalent electrical circuit [2]–[4], for their easy integration within existing EDA environment. State-of-the-art circuit equivalent models are reasonably accu- rate for providing such high-level information, and are able to track the most relevant battery non-idealities. However, these models tend to priviledge accurate tracking of the dynamics of the output voltage rather than the effect of these non-idealities on battery SOC. The main reason for this is that the most basic information in co-simulating a battery and a device is the lifetime of the battery, defined as the time in which the output voltage reaches a specific value (the cutoff voltage). However, in many applications, it is important also to accu- rately track the battery SOC, for example to drive custom battery management policies. The model of [3], which has become quite popular if not a standard in the domain of low- power digital design, does not model the effect that current load dynamics have on the battery SOC. By current dynamics we mean in particular (i) the variance (i.e., variation across the average value), and (ii) the frequency (i.e., the spectral characteristics) of the load frequency. In practice, [3] yields the same SOC profile for any load current waveform with a given average value. Due to the (non-linear) dependency of battery voltage on SOC, this is equivalent to say that the discharge time is not affected by the current dynamics. While the former issue (the variance) is taken into account in other similar models (e.g., [5]), the issue of load frequency has never been considered so far in battery models. However, this is a very well-know issue to be considered when designing hybrid energy storage systems, where different types of energy storages devices (ESDs) are used. Hybridization is introduced precisely because different ESDs have different “response” to current loads with different frequencies. To address this issue, we propose a basic modification to the model of [3] that incorporates this sensitivity to load frequency. Besides the model itself, one important contribution also includes as a methodology to identify the frequency- sensitive parameters of the model from publicly available data (e.g., datasheets). Results show that frequency-agnostic models such as [3] can significantly overestimate the battery state-of-charge, and that this effect is far from being negligible. II. BACKGROUND AND RELATED WORK A. Background In this work we focus only on the effects of load current dy- namics on the battery discharge. Other important, yet second- order, effects such as battery capacity loss and/or temperature- related effects are out of the scope of this work. A well-known non-ideality of a battery is the rated capacity effect [4], i.e., the fact that the usable capacity of a battery depends on the magnitude of the discharge current: at larger currents, a battery is less efficient in converting its chemically stored energy into electrical energy. Rated capacity effect normally refers to constant discharge currents, since datasheets usually report discharge curves for different current values. Nevertheless, usable capacity is also affected by the variance