A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL Estimation Methods for Second-Life Batteries

*Simon Montoya-Bedoya, Laura A. Sabogal-Moncada, Esteban Garcia-Tamayo and Hader V. Martínez-Tejada*

## **Abstract**

Humanity is facing a gloomy scenario due to global warming, which is increasing at unprecedented rates. Energy generation with renewable sources and electric mobility (EM) are considered two of the main strategies to cut down emissions of greenhouse gasses. These paradigm shifts will only be possible with efficient energy storage systems such as Li-ion batteries (LIBs). However, among other factors, some raw materials used on LIB production, such as cobalt and lithium, have geopolitical and environmental issues. Thus, in a context of a circular economy, the reuse of LIBs from EM for other applications (i.e., second-life batteries, SLBs) could be a way to overcome this problem, considering that they reach their end of life (EoL) when they get to a state of health (SOH) of 70–80% and still have energy storage capabilities that could last several years. The aim of this chapter is to make a review of the estimation methods employed in the diagnosis of LIB, such as SOH and remaining useful life (RUL). The correct characterization of these variables is crucial for the reassembly of SLBs and to extend the LIBs operational lifetime.

**Keywords:** second-life batteries, RUL/SOH estimation, circular economy, energy storage, Li-ion battery

## **1. Introduction**

The Sustainable Development Goals (SDGs) are a call to action against global issues in the twenty-first century [1] such as climate change, geopolitical topics, overgrowing population, increasing energy demand, and resource scarcity, among others [2]. According to the International Energy Agency (IEA) statistics, the electricity and heat producers and transport sector are the largest greenhouse gas emitters, with at least 90% of the total CO2 emissions [3, 4]. In 2018, above 26% of electric energy was generated from renewable sources (RSs) [5]. However, this percentage is still low in order to maintain global warming below the 2°C increment threshold stated in the 2015 Paris Agreement [6]. Taking this into account, its clear

that humanity must implement disruptive strategies to tackle these challenges. In this regard, electricity generation with RSs and electric mobility (EM) have become two of the main mechanisms for the decarbonization of the power and mobility sectors. In this context, electrochemical energy storage (EES) is a fundamental technology to realize these energy transitions by coupling both sectors in this time in history and transforming RSs from an alternative to a reliable source.

ions to flow from the cathode to anode. This process is performed to convert

In general, commercial LIBs have highly pure graphite as active material for anode and different transition metal oxide lithium compounds as active material for cathode, such as LiNi0.33Mn0.33Co0.33O2 (NMC 111), LiFePO4 (LFP), and LiCoO2 (LCO), among others. All these cathode materials are found in commercial batteries and are referred to in the literature as battery or cathode chemistries. However, it

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL…*

Despite the positive attributes previously described for LIB systems, there are also a set of critical characteristics that affect the battery behavior with time and as a result of their usage. The sum of these effects is a process commonly referred in literature as battery degradation or aging, which affects the cells' ability to store energy and meet power demands and, ultimately, leads to their end of life (EoL). LIBs are sensitive to the way they are charged and discharged, especially in extreme conditions such as overcharge and deep discharge as they increase the aging effect. Thus, it is of outmost importance for any device powered by LIBs to be informed of the amount of energy that can be stored and the power that can be provided by the battery at any point in time. However, the rates at which these variables degrade over time cannot be directly measured in real applications, so they must be inferred indirectly using methods and models that use input data that can be measured

Degradation in Li-ion cells is caused by a large number of physical and chemical mechanisms, such as active material particle cracking during Li-ion insertion and de-insertion, formation of a passivating layer on the anode/electrolyte interphase during the first cycles (solid electrolyte interphase, SEI), SEI decomposition and precipitation in the electrolyte, lithium plating and dendrite formation that could cause internal short circuit, and dissolution of transition metals from the cathode in the electrolyte, among multiple others. Multiple reviews can be found in the litera-

Fabrication of LIBs uses key and critical raw materials, whose exploitation and market are associated to unequal distribution of the mineral resources in the world [14]. Although lithium is a key ingredient in LIBs, manufacturers commonly use lithium carbonate or lithium hydroxide in batteries rather than pure metallic lithium. They also include other metals, such as cobalt, graphite, manganese, and nickel. Among them, cobalt and lithium are the most constrained materials [15], and nickel is important in recycling and is highly toxic to the environment. According to the US Geological Survey, worldwide lithium supply had an increase of around 23% from 2017 to 2018, coming in at 85,000 metric tons (MT) of lithium content [16]. Harper et al. estimated that the 1 million EVs that were sold in 2017 together account for nearly 250,000 MT of batteries [17]. BloombergNEF recently reported that 2 million EVs were sold in 2018, from just a few thousand in 2010, and there is no sign of slowing down. Annual passenger EV sales are forecasted to rise

In a rough approximation, if a full electric vehicle with a 33-kWh battery pack requires ≈ 5.3 kg of Li, just the EVs sold in 2018 may have required ≈10,600 MT of lithium content. If battery capacities will have an increase of at least 1.8 times by 2025 (i.e., in 6 years the capacity for the Ford Focus EV raised from 23 kWh in 2012 to 33.5 kWh in 2018, while the Renault Zoe changed from 22 kWh in 2012 to 51 kWh in 2019), the EV market will require ≈93,000 MT of lithium content (assuming the design or battery chemistries will not change over time), exceeding current world production. Therefore, there is still not a clear way to use less metal

ture summarizing and describing in detail these aging mechanisms [11–13].

to 10 million in 2025, 28 million in 2030, and 56 million by 2040 [18].

without compromising life span or energy storage capacity.

**69**

electrical energy back to chemical energy.

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

during charge or discharge operations.

is important to clarify that all of them are LIB technologies.

The most familiar EES devices are batteries. Compared to other energy storage mechanisms, the energy capacity of batteries is relatively low, but its efficiency is high (>95%) [7]. This makes batteries an ideal energy storage system for small- and largescale applications [8]. According to Garcia-Tamayo [9], the convenience of batteries lies in the wide range of sizes in which they may be manufactured or assembled into packs, their ability to supply electrical power instantly, their portability (for smaller sizes), and the option of single-use or multiple-use units. The World Economic Forum reported that batteries could enable 30% of the required CO2 reductions in the transport and power sectors, provide access to electricity for 600 million people who currently lacking access, and create 10 million safe and sustainable jobs around the world [10]. Also, since the use of internal combustion engine (ICE) vehicles accounts for a large portion of the daily energy consumption, a continuous increase of batteries through electric vehicle (EV) adoption might lead to improve grid stabilization.

Li-ion batteries (LIBs) are the most common batteries available at present and are found in almost all commercial EVs today. The battery packs inside a vehicle are composed of modules connected in series or parallel to reach the energy output and power required. Each module, on its turn, is also composed of Li-ion cells connected in series or parallel. Thus, a Li-ion cell acts as a fundamental brick of today's battery systems. A schematic illustration can be found in **Figure 1**. When an electrical load (i.e., electric vehicle, solar panel/electrical grid) is plugged and the circuit closed, during discharge, electrons (green circles) flow from the anode to cathode creating an electronic current. Likewise, Li-ions (yellow circles) are flowing in the same direction (from anode to cathode), thus converting chemical energy into electrical energy. Ions move between the electrodes by means of an electrolyte which has the property to be a good electronic insulator and good ionic conductor. As a liquid electrolyte is used in most of the cases, a separator is placed in the middle in order to maintain an even spacing between both electrodes. This separator must provide blocking of electronic current and permeation of its ionic analogue. The process shown in the schematic occurs during cell discharge. During charge, an external voltage is applied to the circuit, forcing electrons and

**Figure 1.** *Schematic of a Li-ion cell during discharge.*

### *A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

ions to flow from the cathode to anode. This process is performed to convert electrical energy back to chemical energy.

In general, commercial LIBs have highly pure graphite as active material for anode and different transition metal oxide lithium compounds as active material for cathode, such as LiNi0.33Mn0.33Co0.33O2 (NMC 111), LiFePO4 (LFP), and LiCoO2 (LCO), among others. All these cathode materials are found in commercial batteries and are referred to in the literature as battery or cathode chemistries. However, it is important to clarify that all of them are LIB technologies.

Despite the positive attributes previously described for LIB systems, there are also a set of critical characteristics that affect the battery behavior with time and as a result of their usage. The sum of these effects is a process commonly referred in literature as battery degradation or aging, which affects the cells' ability to store energy and meet power demands and, ultimately, leads to their end of life (EoL). LIBs are sensitive to the way they are charged and discharged, especially in extreme conditions such as overcharge and deep discharge as they increase the aging effect. Thus, it is of outmost importance for any device powered by LIBs to be informed of the amount of energy that can be stored and the power that can be provided by the battery at any point in time. However, the rates at which these variables degrade over time cannot be directly measured in real applications, so they must be inferred indirectly using methods and models that use input data that can be measured during charge or discharge operations.

Degradation in Li-ion cells is caused by a large number of physical and chemical mechanisms, such as active material particle cracking during Li-ion insertion and de-insertion, formation of a passivating layer on the anode/electrolyte interphase during the first cycles (solid electrolyte interphase, SEI), SEI decomposition and precipitation in the electrolyte, lithium plating and dendrite formation that could cause internal short circuit, and dissolution of transition metals from the cathode in the electrolyte, among multiple others. Multiple reviews can be found in the literature summarizing and describing in detail these aging mechanisms [11–13].

Fabrication of LIBs uses key and critical raw materials, whose exploitation and market are associated to unequal distribution of the mineral resources in the world [14]. Although lithium is a key ingredient in LIBs, manufacturers commonly use lithium carbonate or lithium hydroxide in batteries rather than pure metallic lithium. They also include other metals, such as cobalt, graphite, manganese, and nickel. Among them, cobalt and lithium are the most constrained materials [15], and nickel is important in recycling and is highly toxic to the environment. According to the US Geological Survey, worldwide lithium supply had an increase of around 23% from 2017 to 2018, coming in at 85,000 metric tons (MT) of lithium content [16]. Harper et al. estimated that the 1 million EVs that were sold in 2017 together account for nearly 250,000 MT of batteries [17]. BloombergNEF recently reported that 2 million EVs were sold in 2018, from just a few thousand in 2010, and there is no sign of slowing down. Annual passenger EV sales are forecasted to rise to 10 million in 2025, 28 million in 2030, and 56 million by 2040 [18].

In a rough approximation, if a full electric vehicle with a 33-kWh battery pack requires ≈ 5.3 kg of Li, just the EVs sold in 2018 may have required ≈10,600 MT of lithium content. If battery capacities will have an increase of at least 1.8 times by 2025 (i.e., in 6 years the capacity for the Ford Focus EV raised from 23 kWh in 2012 to 33.5 kWh in 2018, while the Renault Zoe changed from 22 kWh in 2012 to 51 kWh in 2019), the EV market will require ≈93,000 MT of lithium content (assuming the design or battery chemistries will not change over time), exceeding current world production. Therefore, there is still not a clear way to use less metal without compromising life span or energy storage capacity.

that humanity must implement disruptive strategies to tackle these challenges. In this regard, electricity generation with RSs and electric mobility (EM) have become two of the main mechanisms for the decarbonization of the power and mobility sectors. In this context, electrochemical energy storage (EES) is a fundamental technology to realize these energy transitions by coupling both sectors in this time

The most familiar EES devices are batteries. Compared to other energy storage mechanisms, the energy capacity of batteries is relatively low, but its efficiency is high (>95%) [7]. This makes batteries an ideal energy storage system for small- and largescale applications [8]. According to Garcia-Tamayo [9], the convenience of batteries lies in the wide range of sizes in which they may be manufactured or assembled into packs, their ability to supply electrical power instantly, their portability (for smaller sizes), and the option of single-use or multiple-use units. The World Economic Forum reported that batteries could enable 30% of the required CO2 reductions in the transport and power sectors, provide access to electricity for 600 million people who currently lacking access, and create 10 million safe and sustainable jobs around the world [10]. Also, since the use of internal combustion engine (ICE) vehicles accounts for a large portion of the daily energy consumption, a continuous increase of batteries through electric vehicle (EV) adoption might lead to improve grid stabilization. Li-ion batteries (LIBs) are the most common batteries available at present and are found in almost all commercial EVs today. The battery packs inside a vehicle are composed of modules connected in series or parallel to reach the energy output and power required. Each module, on its turn, is also composed of Li-ion cells connected in series or parallel. Thus, a Li-ion cell acts as a fundamental brick of today's battery systems. A schematic illustration can be found in **Figure 1**. When an electrical load (i.e., electric vehicle, solar panel/electrical grid) is plugged and the circuit closed, during discharge, electrons (green circles) flow from the anode to cathode creating an electronic current. Likewise, Li-ions (yellow

circles) are flowing in the same direction (from anode to cathode), thus converting chemical energy into electrical energy. Ions move between the electrodes by means of an electrolyte which has the property to be a good electronic insulator and good ionic conductor. As a liquid electrolyte is used in most of the cases, a separator is placed in the middle in order to maintain an even spacing between both electrodes. This separator must provide blocking of electronic current and permeation of its ionic analogue. The process shown in the schematic occurs during cell discharge. During charge, an external voltage is applied to the circuit, forcing electrons and

**Figure 1.**

**68**

*Schematic of a Li-ion cell during discharge.*

in history and transforming RSs from an alternative to a reliable source.

*Green Energy and Environment*

At present, EV batteries, most of them based on Li-ion technology, have a useful lifetime (defined by the loss of capacity due to degradation until they reach 80% of their nominal capacity) of around 300–15,000 cycles, depending on the conditions in which the battery is charged and discharged [19]. However, it is likely that they will be changed before they reach the 80% threshold not because they do not work properly but because there are other battery technologies and chemistries that will get better in the near future. For example, a recent study by Professor Jeff Dahn's group at Dalhousie University and Tesla Canada presented a LIB testing benchmark where they included a battery with a lifetime of around 4600 cycles (1.600,000 km driving range), at extreme discharging conditions (i.e., bringing the battery to a full discharge in each cycle), which could also be employed in energy storage for 20 years after reaching its EV end of life [20]. Still, even if novel batteries will get more cost-effective and safer, the battery manufacturing processes remain energyintensive [21].

When EV batteries reach their end of life, i.e., when they reach the 80% threshold, they can still store enough energy and can operate perfectly in other uses, opening the possibility to extend their operational lifetime into a second one. Such use has been recently termed as second-life batteries (SLBs). SLB management and their possible applications are receiving a lot of attention because they could serve as a tool against the issue of 'waste' batteries being stored before repurposing or final disposal and could also save many tasks related with the managing, chemical and mechanical dismantling, and separation processes that recycling entails. To put it in perspective, the future 10 million EVs that will be sold in 2025 [18] account for nearly ≈2,200,000 MT of batteries [22], which, in the absence of a second life, would otherwise end up as waste. Moreover, in the waste management hierarchy, reuse is considered preferable to recycling [17].

state of health, and the remaining useful life (RUL), which are key variables that will provide the inputs needed to define possibilities for SLB applications.

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL…*

A systematic review methodology was employed as a screening method to select the information. Scopus was used as scientific database, using the following keywords as query string: Li-ion-batteries AND soh OR rul AND estimation methods AND electrochemical model OR second-life batteries. These keywords were chosen to narrow the scope of this review chapter to those focusing only on estimation methods that could be extended from SOH percentages below the 70–80% electric mobility threshold to scenarios for stationary energy storage applications that use SOH percentages that can go as low as 40%. This screening method resulted in 152 articles. A further selection was done after analyzing the title, abstract, keywords, and paper content. We identified and analyzed 15 papers which included journals and conference proceedings. The selected 15 references were studied in detail to extract useful information such as type of estimation method, estimated variables (SOH/RUL), experimental conditions, minimum SOH reached, and reported error.

Before reviewing and establishing a classification of the estimation methods, it is

important to provide definitions of the main variables found in the literature. *State of health* is a percentage that measures the remaining capacity of an aged

battery compared to the capacity when it was fresh. It is defined by Eq. (1).

*SOH* <sup>¼</sup> *<sup>Q</sup> actual*

*Q nominal*

where *Q actual* and *Q nominal* represent the actual capacity and the nominal

� 100% (1)

**2. Review methodology**

*Li-ion battery circular economy framework diagram.*

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

**Figure 2.**

**3. Estimation methods**

capacity, respectively.

**71**

According to the Advanced Battery Consortium (USABC), and in most literature related to electric mobility [23], the end of life for an EV battery is defined as a 20% drop of cell capacity from the nominal value or a 20% drop from the rated power density at 80% depth of discharge (DoD, defined as the fraction or percentage of the capacity which has been removed from the fully charged battery). Nonetheless, among other factors, from an electrical and electrochemical standpoint, in order to classify the delivery of SLBs as a capable and efficient energy storage system, its remaining capacity, power, and functionality must be properly identified.

A circular economy framework diagram for LIBs is shown in **Figure 2**: (i) Used batteries from EVs that have reached their end of first life are collected. Usually their state of health (SOH) is unknown but should be around 80%. (ii) SOH testing of the battery pack/module/cell is needed to characterize its remaining capacity as compared to its initial capacity. (iii.a) The battery is depleted if the SOH is less than 40%, (iii.b) It is still usable if SOH is greater than 40%. (iv) The battery is sent for repurposing. If needed it might be broken down into its fundamental parts (cells) to connect it in series or parallel to obtain the desired energy output power for each specific application. (v) At this point, the repurposed system becomes a second-life battery and is placed on the market as a new product to serve in a second-life application. (vi) The SLB is collected after reaching its end of second life, and step (ii) is repeated to check if a third-life application is possible. (vii) If not, the battery is sent for recycling where the raw materials will be recovered and restored. Finally, the recovered materials are sent for the remanufacture of new products such as the production of new Li-ion batteries (where the whole cycle would start over).

It is important to remark that step (ii), i.e., SOH testing, is crucial to determine if the battery is depleted and immediately goes to recycling or if it may be used as a SLB for other applications. In this chapter, we will review the diagnostic and prognostic methods needed to estimate the battery current storage capacity, the

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

**Figure 2.** *Li-ion battery circular economy framework diagram.*

state of health, and the remaining useful life (RUL), which are key variables that will provide the inputs needed to define possibilities for SLB applications.

### **2. Review methodology**

At present, EV batteries, most of them based on Li-ion technology, have a useful lifetime (defined by the loss of capacity due to degradation until they reach 80% of their nominal capacity) of around 300–15,000 cycles, depending on the conditions in which the battery is charged and discharged [19]. However, it is likely that they will be changed before they reach the 80% threshold not because they do not work properly but because there are other battery technologies and chemistries that will get better in the near future. For example, a recent study by Professor Jeff Dahn's group at Dalhousie University and Tesla Canada presented a LIB testing benchmark where they included a battery with a lifetime of around 4600 cycles (1.600,000 km driving range), at extreme discharging conditions (i.e., bringing the battery to a full discharge in each cycle), which could also be employed in energy storage for 20 years after reaching its EV end of life [20]. Still, even if novel batteries will get more cost-effective and safer, the battery manufacturing processes remain energy-

When EV batteries reach their end of life, i.e., when they reach the 80% thresh-

According to the Advanced Battery Consortium (USABC), and in most literature related to electric mobility [23], the end of life for an EV battery is defined as a 20% drop of cell capacity from the nominal value or a 20% drop from the rated power density at 80% depth of discharge (DoD, defined as the fraction or percentage of the capacity which has been removed from the fully charged battery). Nonetheless, among other factors, from an electrical and electrochemical standpoint, in order to classify the delivery of SLBs as a capable and efficient energy storage system, its remaining capacity, power, and functionality must be properly identified.

A circular economy framework diagram for LIBs is shown in **Figure 2**: (i) Used batteries from EVs that have reached their end of first life are collected. Usually their state of health (SOH) is unknown but should be around 80%. (ii) SOH testing of the battery pack/module/cell is needed to characterize its remaining capacity as compared to its initial capacity. (iii.a) The battery is depleted if the SOH is less than 40%, (iii.b) It is still usable if SOH is greater than 40%. (iv) The battery is sent for repurposing. If needed it might be broken down into its fundamental parts (cells) to connect it in series or parallel to obtain the desired energy output power for each specific application. (v) At this point, the repurposed system becomes a second-life battery and is placed on the market as a new product to serve in a second-life application. (vi) The SLB is collected after reaching its end of second life, and step (ii) is repeated to check if a third-life application is possible. (vii) If not, the battery is sent for recycling where the raw materials will be recovered and restored. Finally, the recovered materials are sent for the remanufacture of new products such as the production of new Li-ion batteries (where the whole cycle would start over).

It is important to remark that step (ii), i.e., SOH testing, is crucial to determine if the battery is depleted and immediately goes to recycling or if it may be used as a SLB for other applications. In this chapter, we will review the diagnostic and prognostic methods needed to estimate the battery current storage capacity, the

old, they can still store enough energy and can operate perfectly in other uses, opening the possibility to extend their operational lifetime into a second one. Such use has been recently termed as second-life batteries (SLBs). SLB management and their possible applications are receiving a lot of attention because they could serve as a tool against the issue of 'waste' batteries being stored before repurposing or final disposal and could also save many tasks related with the managing, chemical and mechanical dismantling, and separation processes that recycling entails. To put it in perspective, the future 10 million EVs that will be sold in 2025 [18] account for nearly ≈2,200,000 MT of batteries [22], which, in the absence of a second life, would otherwise end up as waste. Moreover, in the waste management hierarchy,

reuse is considered preferable to recycling [17].

intensive [21].

*Green Energy and Environment*

**70**

A systematic review methodology was employed as a screening method to select the information. Scopus was used as scientific database, using the following keywords as query string: Li-ion-batteries AND soh OR rul AND estimation methods AND electrochemical model OR second-life batteries. These keywords were chosen to narrow the scope of this review chapter to those focusing only on estimation methods that could be extended from SOH percentages below the 70–80% electric mobility threshold to scenarios for stationary energy storage applications that use SOH percentages that can go as low as 40%. This screening method resulted in 152 articles. A further selection was done after analyzing the title, abstract, keywords, and paper content. We identified and analyzed 15 papers which included journals and conference proceedings. The selected 15 references were studied in detail to extract useful information such as type of estimation method, estimated variables (SOH/RUL), experimental conditions, minimum SOH reached, and reported error.

### **3. Estimation methods**

Before reviewing and establishing a classification of the estimation methods, it is important to provide definitions of the main variables found in the literature.

*State of health* is a percentage that measures the remaining capacity of an aged battery compared to the capacity when it was fresh. It is defined by Eq. (1).

$$\text{LSOH} = \frac{\text{Q}\_{\text{actual}}}{\text{Q}\_{\text{nominal}}} \times \mathbf{100\%} \tag{1}$$

where *Q actual* and *Q nominal* represent the actual capacity and the nominal capacity, respectively.

*Remaining useful life* is an estimation of the remaining time or number of cycles until the SOH of a battery reaches a specific threshold usually defined by an application. For example, in electric mobility, it is calculated until the SOH reaches 80%. Although in the literature some authors define the RUL as the time in which the SOH of the batteries reaches 0% [24], there are few articles in which the SOH is estimated below the 80% threshold.

fade using three key parameters: (i) the volume fraction of accessible material in the anode, (ii) ionic and electronic resistance of the solid electrolyte interphase and deposited layers on the electrode surfaces, and (iii) diffusion coefficient of the electrolyte. These parameters must be estimated through experimental tests and validated by characterization techniques such as scanning electron microscopy, X-ray diffraction, or X-ray photoelectron spectroscopy for each battery chemistry. This model exemplifies two of the main disadvantages of white-box methods: the need to estimate a lot of parameters and the solution of complex PDE systems. Most of the times, white-box methods derive results that are not cost-

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL…*

Similarly, Gao et al. [38] proposed an electrochemical aging model that estimates the capacity fade considering the change of the open-circuit voltage (OCV) over the life span of a Li-ion battery. They reported a maximum error of about 2% for different batteries charged and discharged at different current rates (C-rates), namely, 1C, 2C, and 3C. However, this error tends to increase at the final phase of the cycling test. Likewise, with the purpose of reducing the complexity of electrochemical models, there are other methods such as single-particle models (SPMs), which assume each electrode as a single particle in order to obtain an ordinary differential equation system that models the Li-ion battery behavior [39–41]. SPMs have been integrated with a capacity degradation model coupled to a chemical/ mechanical degradation mechanism that allows the prediction of the capacity fade as a function of battery temperature and cycling. The root mean squared errors

**<sup>10</sup>***:***<sup>3</sup> <sup>10</sup><sup>3</sup>** for LiFePO4 (cathode)/graphite (anode) batteries tested at 15, 45, and

On the other hand, white-box methods have not been used for RUL estimation due to the reasons mentioned above, i.e., because of the complexity of the models and the fact that cycles are not explicit on most of this type of methods. Thus, it is difficult to obtain parameters for SLBs' RUL because the information of the batteries on their fresh state is normally unknown [43]. However, some authors have used empirical approximations, such as Arrhenius equation (takes temperature as an accelerated aging factor) and power law (takes mechanical/electrical stress as an accelerated aging factor), to model capacity loss on batteries as a function of

As a result, the implementation of these methods on SLBs has been relegated since most of them do not consider the C-rate as an explicit parameter on their aging models. SOH and RUL estimation for SLBs should consider the load profile of each future application in terms of the current (amperes) needed [26, 45]. These methods have been developed for automotive applications where batteries reach their EoL when they get to a state of health of 70–80% [46] and where the capacity degradation is approximately linear until this SOH threshold, as shown in **Figure 4**.

Black-box methods take advantage of data-driven models that establish relationships between unknown intrinsic electrochemical mechanisms and external measurable variables of a Li-ion battery (e.g., voltage, current, temperature, capacity) [23]. These methods extract relevant aging features and construct degradation models based on mathematical and stochastic equations to estimate the SOH and thus predict the RUL [49]. Indeed, aging feature extraction is crucial to obtain

After this point, the aging behavior changes and nonlinearities start to

, **<sup>7</sup>***:***<sup>43</sup> <sup>10</sup><sup>3</sup>**

, and

(RMSEs) in these estimation methods were **<sup>7</sup>***:***<sup>21</sup> <sup>10</sup><sup>3</sup>**

effective [33, 37].

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

60°C, respectively [42].

cycle number [30, 44].

appear [47, 48].

**73**

**3.2 Black-box methods**

One of the main aspects for RUL estimation is to have an accurate knowledge of the current battery state of health [25]. In the case of RUL for SLBs, it is crucial to know the minimum SOH requirements for each application in order to estimate the number of cycles or the remaining time that the batteries will last [26, 27].

In general, estimation methods for SOH and RUL are described separately in the literature [28–30]. Some authors have classified battery models for SOH diagnosis as *electrochemical*, *electrical*, and *mathematical models* [31], while others have grouped them as *direct measurements*, *model-based*, and *adaptive techniques* [32]. Similar categorizations can be found in the literature for RUL estimation methods and have been organized as *adaptive filter*, *intelligent*, and *stochastic techniques* [28]. Particularly, the classifications made by Saidani et al*.* [33] and Liao et al. [34] are interesting as they introduce a comprehensible way to group both SOH and RUL estimation methods in three categories, based on system theory concepts: *white-box*, *black-box*, and *gray-box* methods (see **Figure 3**). In general, these concepts refer to the level of theoretical or experimental knowledge needed to describe or model a process. Each set will be discussed in detail, but in summary white-box methods try to elucidate what happens inside a battery in terms of aging and degradation, while black-box methods employ mathematical and stochastic equations to establish correlations between intrinsic electrochemical mechanisms and external variables that can be easily measured. Gray-box methods are hybrid prognostics between whiteand black-box methods where both internal mechanisms of batteries and datadriven models are integrated.

### **3.1 White-box methods**

White-box models refer to methods that consider internal reactions and aging mechanisms of the batteries, which include physicochemical, electrochemical, and thermodynamic theories [35]. For instance, Fu et al. [36] developed a degradation model based on partial differential equations (PDEs) that estimate the capacity

**Figure 3.** *Classification of SOH and RUL estimation methods.*

### *A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

fade using three key parameters: (i) the volume fraction of accessible material in the anode, (ii) ionic and electronic resistance of the solid electrolyte interphase and deposited layers on the electrode surfaces, and (iii) diffusion coefficient of the electrolyte. These parameters must be estimated through experimental tests and validated by characterization techniques such as scanning electron microscopy, X-ray diffraction, or X-ray photoelectron spectroscopy for each battery chemistry. This model exemplifies two of the main disadvantages of white-box methods: the need to estimate a lot of parameters and the solution of complex PDE systems. Most of the times, white-box methods derive results that are not costeffective [33, 37].

Similarly, Gao et al. [38] proposed an electrochemical aging model that estimates the capacity fade considering the change of the open-circuit voltage (OCV) over the life span of a Li-ion battery. They reported a maximum error of about 2% for different batteries charged and discharged at different current rates (C-rates), namely, 1C, 2C, and 3C. However, this error tends to increase at the final phase of the cycling test. Likewise, with the purpose of reducing the complexity of electrochemical models, there are other methods such as single-particle models (SPMs), which assume each electrode as a single particle in order to obtain an ordinary differential equation system that models the Li-ion battery behavior [39–41]. SPMs have been integrated with a capacity degradation model coupled to a chemical/ mechanical degradation mechanism that allows the prediction of the capacity fade as a function of battery temperature and cycling. The root mean squared errors (RMSEs) in these estimation methods were **<sup>7</sup>***:***<sup>21</sup> <sup>10</sup><sup>3</sup>** , **<sup>7</sup>***:***<sup>43</sup> <sup>10</sup><sup>3</sup>** , and **<sup>10</sup>***:***<sup>3</sup> <sup>10</sup><sup>3</sup>** for LiFePO4 (cathode)/graphite (anode) batteries tested at 15, 45, and 60°C, respectively [42].

On the other hand, white-box methods have not been used for RUL estimation due to the reasons mentioned above, i.e., because of the complexity of the models and the fact that cycles are not explicit on most of this type of methods. Thus, it is difficult to obtain parameters for SLBs' RUL because the information of the batteries on their fresh state is normally unknown [43]. However, some authors have used empirical approximations, such as Arrhenius equation (takes temperature as an accelerated aging factor) and power law (takes mechanical/electrical stress as an accelerated aging factor), to model capacity loss on batteries as a function of cycle number [30, 44].

As a result, the implementation of these methods on SLBs has been relegated since most of them do not consider the C-rate as an explicit parameter on their aging models. SOH and RUL estimation for SLBs should consider the load profile of each future application in terms of the current (amperes) needed [26, 45]. These methods have been developed for automotive applications where batteries reach their EoL when they get to a state of health of 70–80% [46] and where the capacity degradation is approximately linear until this SOH threshold, as shown in **Figure 4**. After this point, the aging behavior changes and nonlinearities start to appear [47, 48].

### **3.2 Black-box methods**

Black-box methods take advantage of data-driven models that establish relationships between unknown intrinsic electrochemical mechanisms and external measurable variables of a Li-ion battery (e.g., voltage, current, temperature, capacity) [23]. These methods extract relevant aging features and construct degradation models based on mathematical and stochastic equations to estimate the SOH and thus predict the RUL [49]. Indeed, aging feature extraction is crucial to obtain

*Remaining useful life* is an estimation of the remaining time or number of cycles until the SOH of a battery reaches a specific threshold usually defined by an application. For example, in electric mobility, it is calculated until the SOH reaches 80%. Although in the literature some authors define the RUL as the time in which the SOH of the batteries reaches 0% [24], there are few articles in which the SOH is

One of the main aspects for RUL estimation is to have an accurate knowledge of the current battery state of health [25]. In the case of RUL for SLBs, it is crucial to know the minimum SOH requirements for each application in order to estimate the

In general, estimation methods for SOH and RUL are described separately in the literature [28–30]. Some authors have classified battery models for SOH diagnosis as *electrochemical*, *electrical*, and *mathematical models* [31], while others have grouped them as *direct measurements*, *model-based*, and *adaptive techniques* [32]. Similar categorizations can be found in the literature for RUL estimation methods and have been organized as *adaptive filter*, *intelligent*, and *stochastic techniques* [28]. Particularly, the classifications made by Saidani et al*.* [33] and Liao et al. [34] are interesting as they introduce a comprehensible way to group both SOH and RUL estimation methods in three categories, based on system theory concepts: *white-box*, *black-box*, and *gray-box* methods (see **Figure 3**). In general, these concepts refer to the level of theoretical or experimental knowledge needed to describe or model a process. Each set will be discussed in detail, but in summary white-box methods try to elucidate what happens inside a battery in terms of aging and degradation, while black-box methods employ mathematical and stochastic equations to establish correlations between intrinsic electrochemical mechanisms and external variables that can be easily measured. Gray-box methods are hybrid prognostics between whiteand black-box methods where both internal mechanisms of batteries and data-

White-box models refer to methods that consider internal reactions and aging mechanisms of the batteries, which include physicochemical, electrochemical, and thermodynamic theories [35]. For instance, Fu et al. [36] developed a degradation model based on partial differential equations (PDEs) that estimate the capacity

number of cycles or the remaining time that the batteries will last [26, 27].

estimated below the 80% threshold.

*Green Energy and Environment*

driven models are integrated.

**3.1 White-box methods**

**Figure 3.**

**72**

*Classification of SOH and RUL estimation methods.*

**Figure 4.** *Illustrative capacity degradation curve for a common Li-ion battery at its first and second life.*

accuracy estimations with these kinds of methods [50]. Jiang et al. [51] tested six LiFePO4 batteries, scrapped from a retired battery pack of an EV, with different load profiles simulating frequency regulation and peak shaving applications. They used the incremental capacity analysis (ICA) obtained from a curve of voltage (V) vs. charge/discharge capacity (Q) using Eq. (2), to develop a linear regression, constructed with the ordinary least squares (OLS) method, that could correlate features from the IC curve and the battery SOH. They obtained a mean absolute error and maximum error within 2%. Similarly, Quinard et al. [52] concluded that the ICA technique, used for SOH estimation in SLBs, has a high dependence on the C-rate (i.e., an inverse relationship between C-rate and accuracy). They reported a maximum absolute error of 5%.

$$IC = \frac{dQ}{dV} \tag{2}$$

Another strategy that has been used to address the issues for these data-driven methods was proposed by Tang et al. [62]. They developed a model migrationbased algorithm to predict the battery aging trajectory and the RUL with a notable reduction of experimental tests. This approach generates a well-known base model with enough data that is then employed in an analogous process with less available data. In this case, the base model takes advantage of accelerated aging tests, while the analogous process uses normal aging tests. As a highlight, they reached a RMSE

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL…*

of about 2% in RUL prediction making use of 15% of the aging data.

**3.3 Gray-box methods**

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

aging cycles.

first-order RC ECM.

**3.4 Estimation method summary**

methods for SLB estimation.

**75**

tion of ohmic internal resistance (Ro) and SOH.

It is important to mention that some data-driven models extract multiple features from LIBs that do not necessarily enhance the prediction due to an emergence of redundant information [63], whereby a sliding window-based feature extraction [63] and false nearest neighbor [64] algorithms have been implemented.

Gray-box methods are hybrid prognostics between white and black methods. In other words, this category integrates both internal mechanisms of batteries and data-driven models. Liao et al. [65] stipulated that including general aging progression (white-box methods) improves the prediction accuracy of black-box methods. Equivalent circuit models (ECM) have been commonly used to simulate internal parameters such as electrochemical systems in battery management systems (BMS) [45, 66]. For instance, Wei et al. [61] modeled the capacity and impedance degradation parameters using SVR and ECM, respectively. Also, they employed particle filter (PF) to improve the SVR simulation. Tracking these aging characteristics, they estimated SOH and RUL with a high accuracy compared to an artificial neural network-based model. Likewise, references [67, 68] developed a promising modified PF algorithm that avoids particle degradation. For example, Shi et al. [68] demonstrated that improved unscented PF (IUPF) had better accuracy than unscented Kalman filter (UKF) and unscented particle filter (UPF) model predic-

In the same way, Tian et al. [69] tested three commercial LiNi0.33Mn0.33Co0.33O2 (NMC) batteries, considering the effect of temperature and discharge rate on aging cycle, to develop an on-board SOH estimation. Their model consisted in a fractional order model (FOM) using Thevenin ECM with the forgetting factor recursive expanded least square (FFRELS) method to estimate the open-circuit voltage which was then correlated to the SOH using the ICA method. Their proposed method obtained a capacity fade with an error of less than 3.1%, independent of the C-rate

Similarly, Guo et al. [70] used an EDKF-based model and second-order RC circuit model to estimate the SOH, obtaining a maximum error below 4%. Hu et al. [71] achieved accurate results for SOH estimation with a relative error within 3%, using a modified moving horizon estimation (mMHE) method integrated to

A comparative summary of the SOH and RUL estimation methods mentioned above, which are included in the 15 references that resulted from the screening method described in the review methodology, can be seen in **Table 1**. For each method, it compares the employed aging feature and the reported error. Finally, there is a column for the minimum SOH reached in order to identify promising

Likewise, machine learning algorithms have been widely used in battery prognostics as these techniques can extract patterns from battery datasets, such as those from NASA [53] and University of Oxford [54], where batteries were tested at different aging conditions (C-rates and temperature). Support vector machines (SVM) [55], artificial neural networks [56, 57], and fuzzy logic [58] are some of the strategies used for SOH estimation. Nevertheless, to guarantee low-error predictions and robustness against noise, machine learning algorithms need an amount of cycling data corresponding to at least 25% of the whole battery life span [59], which could take months or years to be generated.

Taking this into account, Cai et al. [60] developed a novel method based on a combination of SVM for regression (SVR) and a genetic algorithm that employs short-term features extracted from the voltage response under a current pulse test that lasts just 18 seconds. Therefore, this process can be implemented in real SLB applications. As a result, they obtained a minor RMSE of **19.12** � **<sup>10</sup>**�**<sup>3</sup>** for a battery with a LiFePO4 chemistry compared to a RMSE of **24.8** � **<sup>10</sup>**�**<sup>3</sup>** obtained by a traditional SVR-based model for a LiCoO2 chemistry [61].

### *A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

Another strategy that has been used to address the issues for these data-driven methods was proposed by Tang et al. [62]. They developed a model migrationbased algorithm to predict the battery aging trajectory and the RUL with a notable reduction of experimental tests. This approach generates a well-known base model with enough data that is then employed in an analogous process with less available data. In this case, the base model takes advantage of accelerated aging tests, while the analogous process uses normal aging tests. As a highlight, they reached a RMSE of about 2% in RUL prediction making use of 15% of the aging data.

It is important to mention that some data-driven models extract multiple features from LIBs that do not necessarily enhance the prediction due to an emergence of redundant information [63], whereby a sliding window-based feature extraction [63] and false nearest neighbor [64] algorithms have been implemented.

### **3.3 Gray-box methods**

accuracy estimations with these kinds of methods [50]. Jiang et al. [51] tested six LiFePO4 batteries, scrapped from a retired battery pack of an EV, with different load profiles simulating frequency regulation and peak shaving applications. They used the incremental capacity analysis (ICA) obtained from a curve of voltage (V) vs. charge/discharge capacity (Q) using Eq. (2), to develop a linear regression, constructed with the ordinary least squares (OLS) method, that could correlate features from the IC curve and the battery SOH. They obtained a mean absolute error and maximum error within 2%. Similarly, Quinard et al. [52] concluded that the ICA technique, used for SOH estimation in SLBs, has a high dependence on the C-rate (i.e., an inverse relationship between C-rate and accuracy). They

*Illustrative capacity degradation curve for a common Li-ion battery at its first and second life.*

*IC* <sup>¼</sup> *dQ*

Likewise, machine learning algorithms have been widely used in battery prognostics as these techniques can extract patterns from battery datasets, such as those from NASA [53] and University of Oxford [54], where batteries were tested at different aging conditions (C-rates and temperature). Support vector machines (SVM) [55], artificial neural networks [56, 57], and fuzzy logic [58] are some of the strategies used for SOH estimation. Nevertheless, to guarantee low-error predictions and robustness against noise, machine learning algorithms need an amount of cycling data corresponding to at least 25% of the whole battery life span [59], which

Taking this into account, Cai et al. [60] developed a novel method based on a combination of SVM for regression (SVR) and a genetic algorithm that employs short-term features extracted from the voltage response under a current pulse test that lasts just 18 seconds. Therefore, this process can be implemented in real SLB applications. As a result, they obtained a minor RMSE of **19.12** � **<sup>10</sup>**�**<sup>3</sup>** for a battery with a LiFePO4 chemistry compared to a RMSE of **24.8** � **<sup>10</sup>**�**<sup>3</sup>** obtained by a

*dV* (2)

reported a maximum absolute error of 5%.

**Figure 4.**

*Green Energy and Environment*

**74**

could take months or years to be generated.

traditional SVR-based model for a LiCoO2 chemistry [61].

Gray-box methods are hybrid prognostics between white and black methods. In other words, this category integrates both internal mechanisms of batteries and data-driven models. Liao et al. [65] stipulated that including general aging progression (white-box methods) improves the prediction accuracy of black-box methods. Equivalent circuit models (ECM) have been commonly used to simulate internal parameters such as electrochemical systems in battery management systems (BMS) [45, 66]. For instance, Wei et al. [61] modeled the capacity and impedance degradation parameters using SVR and ECM, respectively. Also, they employed particle filter (PF) to improve the SVR simulation. Tracking these aging characteristics, they estimated SOH and RUL with a high accuracy compared to an artificial neural network-based model. Likewise, references [67, 68] developed a promising modified PF algorithm that avoids particle degradation. For example, Shi et al. [68] demonstrated that improved unscented PF (IUPF) had better accuracy than unscented Kalman filter (UKF) and unscented particle filter (UPF) model prediction of ohmic internal resistance (Ro) and SOH.

In the same way, Tian et al. [69] tested three commercial LiNi0.33Mn0.33Co0.33O2 (NMC) batteries, considering the effect of temperature and discharge rate on aging cycle, to develop an on-board SOH estimation. Their model consisted in a fractional order model (FOM) using Thevenin ECM with the forgetting factor recursive expanded least square (FFRELS) method to estimate the open-circuit voltage which was then correlated to the SOH using the ICA method. Their proposed method obtained a capacity fade with an error of less than 3.1%, independent of the C-rate aging cycles.

Similarly, Guo et al. [70] used an EDKF-based model and second-order RC circuit model to estimate the SOH, obtaining a maximum error below 4%. Hu et al. [71] achieved accurate results for SOH estimation with a relative error within 3%, using a modified moving horizon estimation (mMHE) method integrated to first-order RC ECM.

### **3.4 Estimation method summary**

A comparative summary of the SOH and RUL estimation methods mentioned above, which are included in the 15 references that resulted from the screening method described in the review methodology, can be seen in **Table 1**. For each method, it compares the employed aging feature and the reported error. Finally, there is a column for the minimum SOH reached in order to identify promising methods for SLB estimation.


**Authors**

**77**

 **Estimation**

 **method**

**Estimated**

**Experimental**

 **conditions\***

**Aging features employed for**

**Minimum SOH**

**Reported error\*\***

**reached**

**estimation**

**variables**

•

Internal resistance measure under (100 A, 200 A, and

300 A) pulsed current tests

Zhou

Simple linear regression

SOH

•

• Ch: 0.5C (CCCV protocol)

• Dch: 1C (CC)

> SOH

• LFP (3.3. V/2.5 Ah)

• Load profile of primary

frequency regulation

> •

Ambient

temperature:

 25°C Evolution of normalized

the incremental

 capacity curve

 peaks of

≈65%

Average errors for OLS

regression:

MAE (%):0.609

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL*

ME (%):1.226

RMSE: 0.589

Chemistry:

 LCO (1.1 Ah)

Integral from voltage series

≈75%

Average R2: 0.97

Average RMSE: 0.01

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

between 3.85 and 4.3 time on CC

charging phase Keen points in the voltage

≈84%

RMSE for Cell 1: 19.12 103

Cell 2: 13.14 103

> response under current pulse test

**BLACK BOX**

et al. [75]

Cai et al.

Support vector regression and

[60]

genetic algorithm

**BLACK BOX**

Jiang

Incremental

 capacity analysis

SOH

• LFP (60 Ah) obtained from a

retired battery pack

Load profiles of:

•

Frequency regulation

application

• Peak shaving application

•

> Wu et al.

> Neural network model with a

RUL

•

• Ch: CCCV protocol

• Dch: 1C (CC)

• NASA dataset LiCoO2 (2.1 Ah)

Test (1) for periods of 5 min:

• Ch: Series of random current

• Dch: CC Test (2) 2A

test after about 5 days

Quinard

Partial coulometric

 counter

SOH

•

• Full CC discharge at 1C forerun

by a wake-up cycle (partial

charge)

LMO-LNO

 (3.75 V/65 Ah)

Partial capacity from a partial

≈45%

For partial counter:

R2: 0.69 Average AE: 1.6

*…*

charge

et al. [52]

**BLACK BOX**

charging/discharging

CALCE dataset: LCO (1.1 Ah)

[76]

bat-based particle filter

algorithm

**BLACK BOX**

Ambient

temperature:

 25°C Cycle number or cycle time

 80% (CALCE defined

• R2 > 0.98 RMSE<0.04

Capacity degradation

 fit:

> threshold: 602 cycles)

(NAS2 defined

threshold:

• RUL predictions:

• For CALCE: AE: 2 cycles (at 500 cycles)

• For NASA: AE: 2.19 days (at

100.02 days)

146.83 days)

et al. [51]

with multiple linear regression

model and OLS estimation

**BLACK BOX**


*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

**Authors**

**76**

Bartlett

Reduced-order

electrochemical

SOH

•

• The cells were cycled using the

charge-depleting

profile defined by the US

Advanced Battery Consortium

 (CD) current

Chemistry:

 LMO-NMC

 (15 Ah)

Loss of cyclable Li-ion that causes

a shift of the normalized

concentration

the electrodes

 operation ranges of

et al. [72]

model for a composite electrode

battery with solid particle and

liquid sub-models

**WHITE BOX**

> Li et al.

Single

particle-based

 degradation

SOH

• •

Conditions

 shown in [73, 74]

Chemistry:

 LFP (2.2 Ah)

• Cycle number

≈76%

> •

Temperature

[42]

model

**WHITE BOX**

> Gao et al.

Order-reduced

 side reactions

electrochemical

SOH

•

• Ch: 1C (CCCV) protocol

•

• Dch: 1C (CC)

•

Ambient

temperature:

 25°C

Followed by a 30 min rest

Chemistry:

 NMC (26 Ah)

Capacity fade with the help of

60%

equilibrium

 electrode potential

[38]

model considering

**WHITE BOX**

> Lin et al.

Fuzzy logic

identification

 based

SOH

•

Chemistry:

2.37 Ah)

• Ch: 0.5 C (CCCV protocol)

• Dch: 0.2, 0.4, 0.6, 0.8, and 1C

(CC)

• Temp: 0–45°C

 LCO (3.7 V/

•

• OCV difference between fully charged battery and with

a load

> •

Voltage difference between

fully discharge and after

resting for 1 mi**n**

Capacity degradation

80% (defined

RUL prediction difference at:

Cycle 110: 26 cycles

Cycle 140: 1 cycle Cycle 150: 0 cycle Cycle 190: 1 cycle

threshold: 211 cycles)

Battery charging time

≈70%

Average error of good

diagnosis: 1.46%

[58]

on the closest normal

distribution

**BLACK BOX**

Long

Autoregressive

 model and the

RUL

•

• Ch: 0.5C (CCCV protocol)

• Dch: 0.5C (CC)

•

Ambient temperature

CALCE dataset: LCO (1.1 Ah)

> et al. [74]

improved particle swarm

optimization

**BLACK BOX**

Zhang

Three-layer

artificial neural network model

**BLACK BOX**

 back propagation

SOH

•

Batteries from Beijing Olympic

Internal resistance

Not reported. But

•

Average absolute error

0.899 Ah

> •

Capacity estimation error

within 2.5%

they reach the 80%

SOH from its use on

second life

EV bus

et al. [56]

 algorithm

 **Estimation**

 **method**

**Estimated**

**Experimental**

 **conditions\***

**Aging features employed for**

**Minimum SOH**

**Reported error\*\***

**reached**

≈85%

SOH estimation was performed on five different

automotive

different conditions

Mean estimate error: below

0.48 Ah

Error for predicted battery

capacity fade RMSE:

10.3 � 10�3

For cycles at 1C, 2C, and 3C

Maximum error is mostly

<2%

 cells tested at

*Green Energy and Environment*

**estimation**

**variables**


**Table 1.**

*Comparative summary of SOH and RUL estimation methods.*

**3.5 Brief discussion on the adaptability of EV estimation methods to SLBs**

*' results).*

*SOH estimation results for battery #5 from NASA dataset [53]. Model constructed using data before battery*

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL*

voltage curve, which was obtained using the constant current-constant voltage (CCCV) charging protocol as an aging feature. **Figure 5** shows the SOH estimation

0.2140 was obtained. Therefore, the authors believe that SOH and RUL estimation methods commonly employed for electric vehicle applications could be extended to estimate these variables in SLBs. However, to guarantee a better accuracy, different battery degradation behaviors must be considered depending on the load profile for

Electrochemical energy storage in the form of Li-ion batteries is proving to be a fundamental technology to catalyze an energy transition towards renewables and electric mobility. The EV worldwide fleet, and thus the amount of batteries, is expected to grow considerably in the following years. When EV batteries reach

<sup>2</sup> chemistry until SOH values as low as 65%. An RMSE of

As it has been discussed throughout this chapter, there is a lack of literature for SOH and RUL estimation methods validated for SLBs. In contrast, SOH and RUL variables have been extensively studied for first-life applications for EVs. Although some published works have developed approaches for diagnosis and prognostics of SLBs applied to real second-life scenarios, such as [26, 51, 52, 56, 77], we wanted to check if a SOH estimation method developed for EV application, designed for a SOH value of 80%, could be extended to SOH values below this threshold. Hence, the black-box method proposed by Zhou et al. [75] was used for this purpose. This method calculates the integral under the constant current section of a current

–

*…*

**estimation methods**

*reach the 80% of its nominal capacity (authors*

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

**Figure 5.**

for a battery with LiCoO

**4. Conclusions and final remarks**

each future use.

**79**

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

**Figure 5.**

*SOH estimation results for battery #5 from NASA dataset [53]. Model constructed using data before battery reach the 80% of its nominal capacity (authors' results).*

### **3.5 Brief discussion on the adaptability of EV estimation methods to SLBs estimation methods**

As it has been discussed throughout this chapter, there is a lack of literature for SOH and RUL estimation methods validated for SLBs. In contrast, SOH and RUL variables have been extensively studied for first-life applications for EVs. Although some published works have developed approaches for diagnosis and prognostics of SLBs applied to real second-life scenarios, such as [26, 51, 52, 56, 77], we wanted to check if a SOH estimation method developed for EV application, designed for a SOH value of 80%, could be extended to SOH values below this threshold. Hence, the black-box method proposed by Zhou et al. [75] was used for this purpose. This method calculates the integral under the constant current section of a current– voltage curve, which was obtained using the constant current-constant voltage (CCCV) charging protocol as an aging feature. **Figure 5** shows the SOH estimation for a battery with LiCoO2 chemistry until SOH values as low as 65%. An RMSE of 0.2140 was obtained. Therefore, the authors believe that SOH and RUL estimation methods commonly employed for electric vehicle applications could be extended to estimate these variables in SLBs. However, to guarantee a better accuracy, different battery degradation behaviors must be considered depending on the load profile for each future use.

## **4. Conclusions and final remarks**

Electrochemical energy storage in the form of Li-ion batteries is proving to be a fundamental technology to catalyze an energy transition towards renewables and electric mobility. The EV worldwide fleet, and thus the amount of batteries, is expected to grow considerably in the following years. When EV batteries reach

**Authors**

**78**

Casals

Aging model based on an

> et al. [77]

equivalent electric circuit that

simulates the battery's behavior

**GRAY BOX**

> Wei et al.

Support vector

regression-based

RUL/SOH • Gen 218,650-size

• Ch CCCV: 1.5 A CC until 4.2 V

and CV continue until 20 mA

• Dch CCCV: 2 A CC until 2.7

 LIBs

Aging features extracted from CV

≈65%

protocol

[61]

state-space

circuit, and particle filter

**GRAY BOX**

> Tian et al.

> Online OCV estimation based on

SOH

 Commercial

T: 10, 25, and 40°C

• Ch: 1C

• Dch: 1C, 2C, and 3C

 NMC

ICA peaks

60%

[69]

FOM and FFRELS

**GRAY BOX**

> Hu et al.

mMHE integrated to first-order

SOH

 Panasonic NCR18650B

at 25°C with maximum voltage

and current 5 V and 100 A,

respectively

*current-constant*

 *voltage charging protocol.*

 (3.35 Ah)

ECM parameters

Not reported

 Relative error of capacity

within 3%

[71]

RC ECM **GRAY BOX**

*\*Conditions:*

*\*\*Errors: AE: absolute error; MAE: mean absolute error; ME: maximum error; RMSE: root mean squared error.*

**Table 1.** *Comparative*

 *summary of SOH and RUL estimation*

 *methods.*

 *Ch: charge conditions; Dch: discharge conditions; CCCV: constant* 

 model, equivalent

 **Estimation**

 **method**

**Estimated**

**Experimental**

 **conditions\***

**Aging features employed for**

**Minimum SOH**

**Reported error\*\***

Maximum AE: 5.1 Estimated test time: 300 s

**reached**

**estimation**

**variables**

• •

SOH/RUL

 Real demand area regulation profile from the Spanish operator

"Red turbine power plant

Eléctrica"given

 to a gas

Ambient

temperature:

 25°C

Current (load profile) and

Considering

applications

providing area

regulation service:

Application

Application

 2: ≈46%

 1: ≈51%

 on

 two SLB

Considering

applications

area regulation service:

Application

7.35%

Application

8.1%

RMSE SOH SVR-PF [m (5.1) #6 (8.7) #7(6.6) #18

(5.7)

RUL prediction difference

below 4 cycles

Capacity fade error less than

3.1%

Ω] #5

 2: deviation of

 1: deviation of

 on providing

 two SLB

*Green Energy and Environment*

temperature

Sampling frequency: 10 Hz

their end of life (SOH ≈ 80%), they can still store enough energy and can be used in other applications as second-life batteries. Otherwise, they would end up as waste. It is in this context, under a circular economy scenario, that retired EVs are regarded as a primary source of SLBs. In order to do this, an accurate estimation of the state of health and remaining useful life is crucial to determine if the battery is depleted and goes to recycling or if it may be used as a SLB. Thus, sophisticated SOH and RUL estimation methods are needed to guarantee the correct performance of SLBs in different applications.

In this review chapter, we classified these methods in three categories, namely, white-box, black-box, and gray-box, which refer to the level of theoretical or experimental knowledge needed to describe the aging process in batteries. Each category has its advantages and disadvantages, and its implementation will ultimately depend on the context it will be applied. White-box methods, which are usually employed in laboratory environments, are important because they elucidate what happens inside a battery in terms of aging/degradation, and, usually, the estimation errors are lower. However, they imply the use of complex physicochemical and mathematical models and require a higher computational cost. Black-box methods, commonly employed in commercial battery management systems, make use of mathematical and stochastic equations to establish correlations between intrinsic electrochemical mechanisms and external variables that can be easily measured. Although their computational cost is usually low, they need a high amount of data to establish these correlations. Finally, gray-box methods, which are hybrid prognostics between white- and black-box methods, are considered as a promising alternative for more accurate SOH/RUL estimation as they take into account both internal mechanisms of batteries and data-driven models.

In conclusion, although there is a lack of literature for SOH and RUL estimation methods for SLBs, extensive diagnostic and prognostic approaches have been developed for EV applications. The authors believe that some of these methods could be extended to estimate these variables in SLBs. However, to guarantee a better accuracy, different battery degradation behaviors must be considered depending on the energy loads of each future use. Nevertheless, batteries intended to be repurposed in second-life applications will have to compete, at the end of their first life, with improved battery technologies and chemistries that will be likely produced at lower costs in the near future.

**Author details**

Simon Montoya-Bedoya<sup>1</sup>

and Hader V. Martínez-Tejada2,3,4

Engineering, UPB University, Medellín, Colombia

Mechanical Engineering, UPB University, Medellín, Colombia

Mechanical Engineering, UPB University, Medellín, Colombia

\*Address all correspondence to: laura.sabogal@upb.edu.co

provided the original work is properly cited.

**81**

, Laura A. Sabogal-Moncada<sup>1</sup>

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL…*

*DOI: http://dx.doi.org/10.5772/intechopen.91257*

2 Research Laboratory in Materials for Energy (LIMAE), Department of Mechanical

3 Grupo de Investigación sobre Nuevos Materiales (GINUMA), Department of

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

4 Grupo de Investigación Energía y Termodinámica (GET), Department of

1 Research Laboratory in Materials for Energy (LIMAE), Department of Nanotechnology Engineering, UPB University, Medellín, Colombia

\*, Esteban Garcia-Tamayo1,3,4

### **Acknowledgements**

This work was supported by Universidad Pontificia Bolivariana (UPB) in Colombia. Special acknowledgement goes to Seeding Labs and their Instrumental Access initiative which partially supported the foundation of the LIMAE research laboratory in UPB.

*A Circular Economy of Electrochemical Energy Storage Systems: Critical Review of SOH/RUL… DOI: http://dx.doi.org/10.5772/intechopen.91257*

## **Author details**

their end of life (SOH ≈ 80%), they can still store enough energy and can be used in other applications as second-life batteries. Otherwise, they would end up as waste. It is in this context, under a circular economy scenario, that retired EVs are

regarded as a primary source of SLBs. In order to do this, an accurate estimation of the state of health and remaining useful life is crucial to determine if the battery is depleted and goes to recycling or if it may be used as a SLB. Thus, sophisticated SOH and RUL estimation methods are needed to guarantee the correct performance

In this review chapter, we classified these methods in three categories, namely,

In conclusion, although there is a lack of literature for SOH and RUL estimation

methods for SLBs, extensive diagnostic and prognostic approaches have been developed for EV applications. The authors believe that some of these methods could be extended to estimate these variables in SLBs. However, to guarantee a better accuracy, different battery degradation behaviors must be considered depending on the energy loads of each future use. Nevertheless, batteries intended to be repurposed in second-life applications will have to compete, at the end of their first life, with improved battery technologies and chemistries that will be likely

This work was supported by Universidad Pontificia Bolivariana (UPB) in Colombia. Special acknowledgement goes to Seeding Labs and their Instrumental Access initiative which partially supported the foundation of the LIMAE research

white-box, black-box, and gray-box, which refer to the level of theoretical or experimental knowledge needed to describe the aging process in batteries. Each category has its advantages and disadvantages, and its implementation will ultimately depend on the context it will be applied. White-box methods, which are usually employed in laboratory environments, are important because they elucidate what happens inside a battery in terms of aging/degradation, and, usually, the estimation errors are lower. However, they imply the use of complex physicochemical and mathematical models and require a higher computational cost. Black-box methods, commonly employed in commercial battery management systems, make use of mathematical and stochastic equations to establish correlations between intrinsic electrochemical mechanisms and external variables that can be easily measured. Although their computational cost is usually low, they need a high amount of data to establish these correlations. Finally, gray-box methods, which are hybrid prognostics between white- and black-box methods, are considered as a promising alternative for more accurate SOH/RUL estimation as they take into account both

internal mechanisms of batteries and data-driven models.

produced at lower costs in the near future.

**Acknowledgements**

laboratory in UPB.

**80**

of SLBs in different applications.

*Green Energy and Environment*

Simon Montoya-Bedoya<sup>1</sup> , Laura A. Sabogal-Moncada<sup>1</sup> \*, Esteban Garcia-Tamayo1,3,4 and Hader V. Martínez-Tejada2,3,4

1 Research Laboratory in Materials for Energy (LIMAE), Department of Nanotechnology Engineering, UPB University, Medellín, Colombia

2 Research Laboratory in Materials for Energy (LIMAE), Department of Mechanical Engineering, UPB University, Medellín, Colombia

3 Grupo de Investigación sobre Nuevos Materiales (GINUMA), Department of Mechanical Engineering, UPB University, Medellín, Colombia

4 Grupo de Investigación Energía y Termodinámica (GET), Department of Mechanical Engineering, UPB University, Medellín, Colombia

\*Address all correspondence to: laura.sabogal@upb.edu.co

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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**Chapter 5**

**Abstract**

**1. Introduction**

**89**

Leveraging Integrated

Environment

biomethane, and synthetic gas production.

synthesis, performance targeting, and economics

**1.1 Bioenergy as a source of sustainable energy**

Model-Based Approaches to

Unlock Bioenergy Potentials in

*Fabrice Abunde Neba, Prince Agyemang, Yahaya D. Ndam,*

In the quest for a green economy, bioenergy has become a central component due to its ability to minimize depletion of natural energy resources and enhance environmental sustainability. However, the integration of bioenergy for a green economy has often led to policy resistance, the tendency for solutions to cause disastrous side effects on other aspects of the system that were not envisaged. The use of integrated model-based approaches for selection, design, and analysis of technological alternatives for bioenergy production would significantly enhance the systems'sustainability

by optimizing design and operation, improving growth and profitability, and enabling a more synergistic interaction between the engineering and the macroeconomic aspects of bioenergy production systems. This chapter is designed to develop model-based methodological frameworks that will support sustainable decision making by all stakeholders involved in the design, operation, and commercialization of bioenergy production systems. Practical case studies are presented for bioethanol,

**Keywords:** system thinking, model identification and analysis, bioreactor

Increasing concerns about depletion of natural resources, precarious nature of waste management and sanitation challenges, as well as environmental deterioration and climate change, have led to a growing interest by many countries to switch to renewable energy technologies. Consequently, the last two decades have seen a rapid implementation of new renewable energy systems, followed by integration of renewable energy into plants where fossil fuels exist. Amongst the existing renewable energy technologies, bioenergy systems are of special significance, because in addition to

Enhancing Green Energy and

*Endene Emmanuel, Eyong G. Ndip and Razak Seidu*

## **Chapter 5**
