Dynamic model of a lead acid battery for use in a domestic fuel cell system

doi:10.1016/j.jpowsour.2005.12.075

Journal of Power Sources

Volume 161, Issue 2, 27 October 2006, Pages 1400-1411

https://doi.org/10.1016/j.jpowsour.2005.12.075 Get rights and content

Abstract

This paper presents a review of existing dynamic electrical battery models and subsequently describes a new mathematical model of a lead acid battery, using a non-linear function for the maximum available energy related to the battery discharge rate. The battery state of charge (SOC) is expressed in a look-up table relative to the battery open circuit voltage (VOC). This look-up table has been developed through low discharge experiments of the battery modelled. Further, both the internal resistance and self-discharge resistance of the battery are subsequently expressed as functions of the open circuit voltage. By using an electrical model with these characteristics and a temperature compensation element to model different rates of charge and discharge, a relatively simple and accurate battery model has been developed.

The new model takes into account battery storage capacity, internal resistance, self-discharge resistance, the electric losses and the temperature dependence of a lead acid battery. It is shown in this paper how the necessary parameters for the model were found. The battery modelled was a Hawker Genesis 42 Ah rated gelled lead acid battery.

The simulation results of the new model are compared with test data recorded from battery discharge tests, which validate the accuracy of the new model.

Introduction

This paper forms the first part of a series of papers describing, modelling and testing a complete domestic scale fuel cell (FC) combined heat and power (CHP) system. This FC CHP system, built at the University of Strathclyde, has been described in detail in [1]. The motivation to develop a new battery model within the Matlab/Simulink environment lies in the study of a domestic scale fuel cell system, in which a lead acid battery bank is used as an energy storage/buffer device. To simulate and study the overall FC system the behaviour of each element, in this first case the lead acid battery, has to be fully understood and models short term discharge performance before going on in a separate paper to investigate long term cycling effects.

Most of the commercial research in stationary FC technology is concentrated in the development of grid-connected systems, which typically do not have integrated thermal and electric buffer/storage systems [2]. This is mainly due to cost reasons, as the control system will be less complicated and therefore less expensive, the costs for the buffer devices will be avoided and operation and maintenance costs (O&M costs) will be reduced. Any additional electrical power, e.g. for fast or peak load changes, will be drawn from the electrical grid for such a system. That kind of system configuration is primarily suitable for integration in infrastructures with an existing electrical grid connection, hence, mainly in urban areas. The FC system is electric power controlled, which makes it necessary to match electrical supply and demand powers at all times. Due to cost concerns it is more economic to use a hybrid FC/battery system than purely a FC only system.

The advantages of a hybrid FC/battery system for a grid independent system can be easily understood by analysing a typical domestic load profile (Fig. 1).

A domestic electric load profile of a typical single household in the UK (summer period) gives an average power demand of 0.5 kW_e, but a peak power demand of greater than 7 kW_e. This profile is assumed constant throughout the year, as thermal demand is anticipated to be met through an existing central heating system. With FC prices currently between £1500 kW_e⁻¹ and £5000 kW_e⁻¹, FC stacks remain far more expensive than battery systems (£70–300 kWh⁻¹); hence, it makes economic sense to use a FC with a rating of approximately the average power demand to allow a relatively high running time of the FC [4], [5], [6]. The additional power is provided by a backup system (e.g. batteries).

The FC system developed at Strathclyde University uses an alkaline fuel cell (AFC) that has a current increase limitation of 10 A s⁻¹, which makes it necessary to provide additional power for sudden load demands from batteries.

Mainly for cost reasons (e.g. see Fig. 4) the FC/battery hybrid system will use lead acid batteries and in particular gel-filled Hawker Genesis 12 V dc 42 Ah types to minimise the safety risk of acid leakage within an fuel cell system environment. Nonetheless, the model described here can be used for other battery types by changing the energy–voltage characteristic and the internal model parameters as introduced later. In the following sections, the experimental tests used to determine these parameters with a simple battery test station are described followed by a detailed presentation of the battery model developed.

Lead acid batteries are still the most common devices to store and deliver electricity in the range from 5 V to 24 V dc [7]. A low price, high availability and ease of manufacture account for the wide use of the lead acid battery in many designs, sizes, and system voltages. The lead acid battery is almost always the least expensive storage battery for any application, while still providing reasonable performance and life characteristics. Fig. 2 gives a comparison of main characteristics for commonly used types of secondary batteries. The numbers 1–5 give a rating from 1—excellent to 5—poor performance.

During the mid 1970s the design of the lead acid battery has been improved by the development of the maintenance-free lead acid battery that could operate in any position. The liquid electrolyte was transformed into moistened separators and the enclosure was sealed. Safety valves were added to allow venting of gas during charge and discharge. Driven by different market needs, two lead acid systems emerged: the sealed lead acid (SLA), also known under the brand name of Gelcell, and the valve-regulated lead acid (VRLA).

Section snippets

Battery models

As mentioned before, it is very difficult to develop a truly generic model, which takes all factors of a battery into account. Depending on the use of the model different approaches have been made.

In the following section some of the most common electrical circuit battery models are introduced and their main features are explained.

A new approach to a dynamic battery computer model

Recognising that many factors influence battery behaviour and that there are difficulties in describing them accurately and simply in a dynamic, non-linear model, a new approach to battery modelling is presented. Based on the non-linear battery model in Section 2.4 the author's model uses a new approach to determine the open circuit voltage during a dynamic simulation. In the new model, the open circuit voltage VOC depends on the actual discharge current I_B, the energy drawn from the battery E_cd

Discharge tests

To verify the simulation results it was necessary to carry out a range of tests using a 42 Ah Hawker Genesis battery. For this purpose a test station was built, consisting of an electronic load (model: Emerson Electronic load EL-300), measurement equipment for voltage, current and temperature and a computer data acquisition system. Furthermore an environmental chamber (model: Thermotron SM32-C Environmental Chamber) was used to undertake tests over a range of different temperatures. Fig. 22

Discussion of the results and conclusions to the battery model

The mathematical model developed during this work accurately describes the behaviour of a lead acid battery under typical discharge conditions.

By developing and modelling a look-up table to describe the battery state of charge vs. voltage characteristic a simple but accurate method has been developed to model a typically highly non-linear lead acid battery.

The non-linear elements of the battery, such as the internal resistance and the self-discharge resistance have been expressed by functions

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