Elsevier

Applied Energy

Volume 248, 15 August 2019, Pages 512-525
Applied Energy

Development of a degradation-conscious physics-based lithium-ion battery model for use in power system planning studies

https://doi.org/10.1016/j.apenergy.2019.04.143Get rights and content

Highlights

  • A physics-based Li-ion battery model is developed for power system planning studies.

  • Side reactions of the negative electrode are considered in an equivalent circuit model.

  • Parametric values of the circuit components are automatically updated.

  • Short- and long-term performance is predicted based on power flow at battery terminal.

  • Stored energy, degradation, and constraints are available for optimization of design.

Abstract

A computationally-efficient and reliable method is developed to permit the simultaneous assessment of both the short- and long-term performance of lithium-ion battery in power system planning studies. Toward this end, a physics-based equivalent circuit model of the lithium-ion battery is derived in which side reaction-induced degradation of the battery is included. Whence a computational procedure is developed to enable the parametric values of the circuit elements in the equivalent circuit model to be automatically updated as the battery operates. The resulting model allows the increase in the internal resistance and the decrease in the energy storage capacity of the battery to be determined, based solely on the information of the power flows at the battery terminals. Dynamic simulation results obtained using the developed equivalent circuit model are shown to be in close agreement with those obtained from well-established electrochemical models, but at a much reduced computational burden.

Introduction

Battery energy storage is increasingly being recognized as essential for modern electric power systems which contain significant amount of renewable generation. Of the various types of battery, lithium-ion (Li-ion) battery has become the most prominent candidate in such application [1], [2]. A case in point is the 100-MW/129-MWh Li-ion battery energy storage system (BESS) which operates in conjunction with the 315-MW Hornsdale wind farm in South Australia [3]. Renewable generations, such as that based on wind and sunlight, tends to be uncertain and can seriously compromise the security and reliability of power supply as a result [4]. The role of the BESS is to alleviate such undesirable impacts on the power systems, and the BESS have to be judiciously designed at the planning stage so as to comply with stipulated technical and economic requirements [5].

System-level design of the BESS usually involves two aspects. First, operational planning is the strategization of the short-term (from several hours up to several days) power flows at the BESS plant terminals and the design of charging/discharging pattern of the BESS. Various approaches to BESS design have been developed aiming to achieve such short-term control objectives as power smoothing, peak shaving, and/or dispatch scheduling. In [6], a BESS control strategy and the real-time power allocation method have been developed for photovoltaic and wind generation by modifying the smoothing target according to the monitored BESS state of charge. To enable the renewable generators to emulate the ability of the traditional thermal units in providing reliable power dispatch, operational strategies based on feedback control [7], model predictive control [8], and rule-based control [9] have been proposed, the purpose of which is to minimize the generation schedule tracking error. The short-term dispatch schedule for a dual-BESS scheme has been studied in [10] for a wind farm, with the objective to minimize the number of the switch-over between the two battery banks. In these works, the storage capacity and power rating of the BESS have been assumed known a priori. On the other hand, the aspect of battery sizing is to determine suitable BESS energy storage capacity and power rating during the design and planning stage of the BESS. The aim of the study is to ensure the long-term (say, several years) technical and economic requirements imposed on the BESS can be met. As the design objective for short-term operation affects the results of battery sizing study, the above-mentioned two aspects of the BESS design have to be considered simultaneously. Toward this end, the BESS design can always be formulated as a system-level optimization problem, with some form of cost-benefit analysis. For example: the dispatch strategy and BESS capacity are determined by maximizing a defined service lifetime/cost index, so that the short-term dispatchability of a wind farm is achieved [11]. On the other hand, by treating the BESS as a power smoothing device or as an energy buffer to be utilized to reduce the degradation on the quality of electricity supply due to the uncertain renewable sources, the optimal BESS capacity can be determined using a cost-benefit analysis, as has been done in [12]. A variable-interval reference signal optimization approach and a fuzzy control charging/discharging scheme are proposed in [13] for BESS to smoothen the generated wind power, and the optimal BESS capacity is determined by minimization of the BESS annualized cost. In [14], the optimal planning of distributed BESS in active distribution networks has been investigated with the consideration of reactive power support and short-term network reconfiguration, the optimal power/energy capacities and location has been obtained using mixed-integer second-order-cone programming. The optimal placement, capacity and operation of BESS in conjunction with high penetration of photovoltaic in distribution network has been studied in [15] to effectively limit the voltage rise. A method to maximize the profit of wind farm is presented in [16] to incorporate BESS, and the optimal BESS design is obtained using dynamic programming. A statistical approach to determine the capacity and the charging/discharging strategy for battery-supercapacitor hybrid storage system is discussed in [17], with the aim to achieve a dispatchable wind farm. Operational planning for a wind-battery system is carried out in [18] using a modified min-max dispatch method. A coordinated operational dispatch and capacity determination scheme for a BESS-wind farm is proposed in [19], with the view to mitigate the fluctuation and stochastic nature of the wind resources through changing the wind farm output power reference value between the optimistic and pessimistic forecast scenarios. Based on Sequential Monte Carlo simulation technique, a wind farm incorporated with BESS is designed in [20] to track the generation schedule while the optimal BESS capacity and control strategy is studied by considering the real-time pricing of electricity in [21]. In all these works [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], precise prediction of the lifetime of the battery has been considered an important long-term factor for the economic evaluation. One common concern pertaining to the aforementioned works is that empirical measurements of battery lifetime, such as that based on maximum cycle number or Ah-throughput, have been used to predict the BESS end-of-life (EOL). Unfortunately, these relatively simple battery lifetime determination methods have not been proven to be entirely reliable for Li-ion based batteries. This is because the degradation of the batteries are known to be dependent of the potential, current direction, current magnitude, depth of discharge, temperature, amongst other factors [22], [23].

Furthermore, the optimization procedure referred to in the planning studies requires BESS model which is able to accurately predict both the short- and long-term battery performance, but at acceptable computational burden. As befitting the short-term role of energy buffer, the amount of the energy stored in the BESS is often evaluated, subjected to hard constraints such as the BESS energy capacity and power rating [20]. In this connection, the BESS dynamic behavior can be studied using battery equivalent circuit models (ECMs), as has been done in [6], [7], [8], [9], [10]. The main reasons for using this type of empirical models are that ECMs are intuitive to the researchers in the field of electrical engineering, while the short-term battery performance can be readily analyzed using well-established circuit theory. Additional constraints such as applied current and terminal voltage limits can be readily included, as part of the optimization design procedure. Unfortunately, as the capability of Li-ion battery to efficiently store or release energy reduces with battery usage, the degradation of BESS performance has to be included. Although for online control purpose, the parametric values of the circuit components in the ECMs could be adjusted to fit the observed battery performance, this approach requires complex set of data to be extracted from laboratory experiments or staged tests [24]. The suitability of such an approach to battery modeling at the planning study stage of the BESS is doubtful because the experimental or staged test conditions can be significantly different from that encountered in the field [25].

In contrast to the ECM and based on electrochemical and thermodynamic principles, various physics-based Li-ion battery models have been developed in recent years for the purpose of battery cell design [26]. These models do consider the internal behavior and the major causes of battery aging, such as that due to side reactions and mechanical stresses, and are indeed capable of predicting accurately both the short- and long-term performance of the battery cell [27]. Also, intensive investigations have identified the side reactions in the negative electrode are the major cause of Li-ion cell degradation [28]. Various phenomena due to the side reactions, such as the loss of active material and the increase of the depletion layer, can be readily incorporated into these physics-based models [29]. The physics-based models have been further simplified in the attempt to balance between model accuracy and computational efficiency, so that they can be incorporated into advanced battery management systems for online prediction of battery cell performance and lifetime [30], [31]. Notwithstanding these developments however, these simplified first-principle models are still too complex and are incompatible for use in the planning and capacity determination studies of the BESS.

In consideration of [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], the aim of the present work is to develop a reliable and practical method to predict Li-ion BESS performance for system-level BESS design and planning studies. Toward this end, a physics-based ECM of the Li-ion battery is derived from an electrochemical model such that the quantitative links between the electrochemical process of the Li-ion battery and the circuit dynamics are established. The long-term impacts of side reactions on battery storage capacity and internal resistance are included in the ECM. Whence a numerical procedure that is compatible with system-level optimization procedure is developed to automatically update the parametric values of the physics-based ECM circuit parameters as the battery cell degradation progresses. The resulting model allows accurate and rapid prediction of the behavior of Li-ion battery, thanks to the recent research outcomes in battery electrochemistry and circuit theory. To the best knowledge of the authors, the present investigation is the first reported work to incorporate physics-based Li-ion model in the design and planning of grid-connected BESS.

Accordingly, the remaining contents are organized as follows: Section 2 presents the modeling considerations of grid-connected BESS and the essence of an electrochemical model of Li-ion battery, from which Section 3 develops a physics-based ECM with the incorporation of the major degradation mechanism. A reduced-order ECM suitable for system-level studies is also derived. Several indices are then developed in Section 4 to provide quantitative measures of the energy storage and power delivery capabilities of the battery which can be directly used for BESS design. Section 5 includes a comparison of reported experimental data, simulation results obtained using well-established electrochemical battery models with those from the developed ECMs. Examples of the application of the developed models are also given. Main findings are included in Section 6.

Section snippets

Some preliminary considerations

In order to develop the Li-ion battery model which shall be computationally efficient and yet sufficiently accurate for use in power system planning studies, the following assumptions have been made.

Low C-rate: It is well recognized BESS is suitable for use to support intra- and inter-day energy management of power grids [32]. For such an application, the maximum C-rate of the BESS is often limited to a much lower level compared to that used in mobile applications, such as in electric vehicles

Derivation of a physics-based equivalent circuit model for Li-ion battery

It is intuitive and convenient to use equivalent circuits in the field of electrical engineering for system design and indeed, using ECM is a popular pathway toward studying the behavior of BESS. However, conventional empirically-derived ECMs do not provide information on the various battery internal states which can affect battery long-term performance. In view of this shortcoming, a degradation-conscious physics-based ECM will now be derived from (1a), (1b), (2a), (2b), (2c), (3), (4), (5),

Impact of degradation on circuit parameters

Fig. 6(a) shows the relationship between the OCV and Q1+(t), i.e. z, of the particular type of Li-ion battery considered in [26], [28], [40]. The curves correspond to the battery at BOL (k = 0), at an arbitrary state of degradation k, and at such a degraded state that the battery is considered to have reach its EOL. Also, define herewith the end-of-charge (EOC) state as when the battery OCVk reaches the pre-specified maximum voltage level VEOC, and the corresponding Q1+ is Q1+EOC,k. Similarly

Model validation

In this sub-section, the developed RO-ECM is to be validated using the experimental data obtained in [43] where it reports that a LiCoO2 battery with 1.8-Ah rated capacity is tested under certain cyclic conditions. In each cycle, firstly, the battery is charged from a given initial stoichiometry. The charging current is constant at 1 A until the battery terminal voltage reaches VEOC of 4.2 V. Then, the terminal voltage is kept constant by reducing the charging current until the current falls

Conclusions

A physics-based equivalent circuit models which can be used to assess the long-term performance and to predict the lifetime of grid-connected lithium-ion battery energy storage system have been developed. By taking into account the side reactions into the modelling process, it is shown that the derived battery models yield results which are in good agreement with those obtained from reported test measurements, as well as with those simulation results obtained using the well-established

Acknowledgments

This work was supported by the Australian Research Council Discovery Grant [grant numbers: DP160101325] and Queensland University of Technology.

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