Letter to the Editor Re “Fractional Modeling and SOC Estimation of Lithium-ion Battery”

Presents letters to the editor for this issue of the publication

Comments on “State of Charge-Dependent Polynomial Equivalent Circuit Modeling for Electrochemical Impedance Spectroscopy of Lithium-Ion Batteries”

A recent paper by Wang et al proposes a state of charge-dependent polynomial equivalent circuit model for lithium batteries. The model consists of an inductor, a Warburg element, a constant phase element (CPE) and two resistors [1]. Figure 1 shows the equivalent circuit model reproduced from [1

Application of Swingler's Method for Analysis of Multicomponent Exponentials with Special Attention to Non-equispaced Data

Swingler enhanced the work of Gardner to provide an elegant deconvolution method by which multiple summed exponential components might be resolved within time-domain data. Nevertheless, the application of the method remains limited owing to subtle complications that discourage many users. We present a tutorial and extend the approach to handle nonequispaced data. Finally the method’s limits are identified in the case of closely-spaced exponential components with added input noise

Fractional behaviour of rechargeable batteries

For decades authors have preferred to model batteries with either Thevenin-style models using RLC, or Randlesstyle by adding a Warburg element. These are claimed to model accurately. We present convincing empirical evidence suggesting that a fractional-derivative (constant-phase element) model is required. Our data shows that existing state-of-the-art models may be overly complicated, requiring numerical rather than physical considerations to find parameters

Extending randles’s battery model to predict impedance, charge-voltage, and runtime characteristics

The impedance of a battery can be modelled with an elegant fractional-capacitor or “constant phase element” (CPE) equivalent circuit and a series resistor. In this manuscript, we present new evidence that suggests that a linear model similar to Randles’ comprised solely of this impedance network is able to predict both the charge-voltage relationship epitomised by the familiar hysteresis curve of voltage as a function of charge as a battery charges and discharges through its linear region, and the recovery or “equilibration” transient that results from a step change in load current. The proposed model is unique in that it does not contain a source, either voltage or current, nor any purely reactive elements. There are important potential advantages of a passive battery model

New results for battery impedance at very low frequencies

In search of an equivalent circuit model for rechargeable batteries, many authors start with a measurement of battery impedance, spanning what is presumed to be the frequency range of interest. Various networks have been suggested in the literature to account for the measured impedance characteristic. Most incorporate two or more resistors, at least one capacitor, some include at least one Warburg element, and more recently “constant phase elements”(CPE), otherwise identified as fractional-derivative capacitors. Networks that are more successful at reproducing the measured impedance have from five up to tens of degrees of freedom. The frequency range upon which most models are based extends only to 1mHz. This is surprising since many batteries see a daily or longer usage cycle, corresponding to a frequency of ≈ 11.6 μHz or lower. We show in this manuscript that the most-cited impedance measurement instrument, and one of the few that can operate below 1mHz, can be unreliable at and below this boundary. We present a novel impedance measurement algorithm robust against the issues present while measuring the impedance of electrochemical systems to as low as 1 μHz. Next, we present reliable impedance data extending to a lower frequency limit of 10 μHz. A remarkable characteristic appears at the lower frequencies, suggesting a surprisingly simple and elegant equivalent circuit consisting of a single fractional capacitor. A new model is proposed, which requires only four parameters to predict the measured impedance as a function of frequency

Party rules, party resources, and the politics of parliamentary democracies: how parties organize in the 21st Century

This article introduces the first findings of the Political Party Database (PPDB) project, a major survey of party organizations in parliamentary and semi-presidential democracies. The project’s first round of data covers 122 parties in 19 countries. In this paper we describe the scope of the database, then investigate what it tells us about contemporary party organization in these countries, focussing on parties’ resources, structures and internal decision-making. We examine organizational patterns by country and party family, and where possible we make temporal comparisons with older datasets. Our analyses suggest a remarkable coexistence of uniformity and diversity. In terms of the major organizational resources on which parties can draw, such as members, staff and finance, the new evidence largely confirms the continuation of trends identified in previous research: i.e., declining membership, but enhanced financial resources and more paid staff. We also find remarkable uniformity regarding the core architecture of party organizations. At the same time, however, we find substantial variation between countries and party families in terms of their internal processes, with particular regard to how internally democratic they are, and in the forms that this democratization takes

Measuring and Comparing Party Ideology and Heterogeneity

Estimates of party ideological positions in Western Democracies yield useful party-level information, but lack the ability to provide insight into intraparty politics. In this paper, we generate comparable measures of latent individual policy positions from elite survey data which enable analysis of elite-level party ideology and heterogeneity. This approach has advantages over both expert surveys and approaches based on behavioral data, such as roll call voting and is directly relevant to the study of party cohesion. We generate a measure of elite positions for several European countries using a common space scaling approach and demonstrate its validity as a measure of party ideology. We then apply these data to determine the sources of party heterogeneity, focusing on the role of intraparty competition in electoral systems, nomination rules, and party goals. We find that policy-seeking parties and centralized party nomination rules reduce party heterogeneity. While intraparty competition has no effect, the presence of these electoral rules conditions the effect of district magnitude