An evaluation framework for second-life EV/PHEV battery application in power systems

Energy storage is essential for balancing the generation and load in power systems. Building a battery energy storage system (BESS) with retired battery packs from electric vehicles (EVs) or plug-in hybrid electric vehicles (PHEVs) is one possible way to subsidize the price of EV/PHEV batteries, and at the same time mitigating forecast error introduced by load and renewable energy sources in power systems. This paper proposes a detailed framework to evaluate end-of-life (EOL) EV/PHEV batteries in BESS application. The framework consists of three parts. A generalized model for battery degradation is first introduced. It is followed by modeling the battery retirement process in its first life. Two vehicle types—EV and PHEV—as well as two retirement modes—nominal and realistic modes—are considered. Finally, the application of the second-life BESS in power systems is modeled in a detailed economic dispatch (ED) problem. This is how second-life BESS’s performance translates into cost savings on power generation. An optimization problem is formulated to maximize total cost savings in power generation over the battery’s second life. This is done by striking a balance between short-term benefit (daily cost savings) and long-term benefit (cost savings through service years). Numerical results validate the effectiveness of the proposed framework/models. They show that battery usage and retirement criterion in its first life directly affect the performance in its second life application. In our case study, EV battery packs possess larger EOL energy capacities and consequently generate more cost savings in the second life. However, the BESS built from retired PHEV batteries has higher cost savings per MWh. It is because, with the proposed degradation model, battery health is better preserved in PHEV applications. Compared to nominal retirement mode, realistic retirement mode results in extra cost savings due to the reduced first-life service years.


I. INTRODUCTION
Energy storage is essential for balancing the generation and load. With the proliferation of renewable energy sources (RES) worldwide, the need for storage increases remarkedly in recent years. Despite the increasing market foothold of electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs) in recent years, the price remains the most significant hurdle against EVs' popularization. Bringing down the costs is essential to have long-term commercial viability [1]. On the other hand, end-of-life (EOL) battery disposal becomes an emerging issue. Repurposing retired EV/PHEV battery provides a potential way to reduce the cost hurdle while alleviating environmental concerns over EOL battery disposal [2]. In power systems, battery energy storage systems (BESS) can be built from EOL batteries and provide services. It is due to the fact that EOL batteries can still meet the requirement for the less-demanding grid services [3]. Building a BESS with second-life EV/PHEV batteries is especially appealing as the increasing RES capacity in power systems calls for more spinning reserves [4].

A. LITERATURE REVIEW
Economic and technical aspects of EOL EV/PHEV battery and its second-life applications have been studied over the last two decades [1]- [3], [5]- [16]. Among the existing literature, potential economic benefits and business models for post-vehicle battery applications are discussed extensively. Comprehensive studies on the feasibility of applying used EV batteries in stationary applications are given by Sandia National Laboratories [10] and National Renewable Energy Laboratory [11], [13]. Application considered spans from transmission support, area regulation, and spinning reserve to renewable firming load leveling. Williams and Lipman [12], [17] explore repurposing battery packs for stationary use as a way to reduce battery-lease payment. Potential business models of second-life EV batteries are reported in [2] and [7]. In [15], the economic viability is assessed based on electricity tariffs across three countries. In [11], the initial purchase price of second-life EV/PHEV batteries is calculated based on net present value. Simplified economic analysis for frequency regulation service is carried out in [1], where various scenarios are studied regarding the state of health (SOH) and rates for regulation service. Recently, thorough reviews are given by Martinez-Laserna et al. on second-life applications of lithium-ion batteries [3], [9].
For specific applications, modeling both battery and second-life applications are required. Several works of literature provide insights in this regard. Li et al. [6] design a real-life test framework for second-life EV batteries in a residential application. For the same application, a MATLAB-Simulink model is proposed in [5]. Alimisis and Hatziargyriou [14] study the case in the island of Crete (non-interconnected), where used EV batteries are deployed to complement wind power. In [18], various ways for modeling Li-ion batteries considering battery SOH in grid-scale applications are reviewed. Experimental tests on used EV batteries are reported in [8], [19]. Economic analyses on second-life EV batteries in applications such as renewable smoothing are presented in [20], [21] and [22].
A general framework for second-life battery application is given in Figure 1. The modeling work involved is threefold: 1. Battery degradation model, 2. Battery retirement model and 3. Modeling of the second-life application. As outlined in the figure, Part 1 decides how battery performance degrades over time. Part 2 determines at what stage the battery is retired and repurposed. Finally, a technical/economic assessment for the second-life application is carried out in Part 3. Depending on the specific scope of work, the complexity of the model in each part can vary.
In prevailing studies, the focus is business models and economic viability across different second-life applications (i.e., Part 3 in Figure 1). For those studies, the battery degradation process (i.e., Part 1) is often not elaborated. Instead, fixed life expectancy is assumed. In modelling battery retirement process (i.e., Part 2), simple criterion for first-life retirement are applied, such as fixed energy capacity [7], [12], [14], [23], [24]. For second-life application (i.e., Part 3), economic feasibility is assessed with given tariff structures. This is suitable for scenarios in which the stakeholder of repurposed batteries is the price taker. However, storage systems' operation has a direct impact on power generation's planning and operation. It is especially true in systems where intermittent generation sources' share is higher, and storage is required to lower the level of risk resulting from the intermittency [25], [26]. Consequently, the cost of power generation is heavily affected by both generators and storage systems in such systems and needs to be considered. To summarize, the existing literature focuses only on one or two parts of the three-part framework, leaving the remaining as simple assumptions.

A. CONTRIBUTION OF THIS WORK
In this paper, a comprehensive evaluation framework is proposed for EV/PHEV batteries' second-life application in power systems. In this framework, all three parts (in Figure  1) are taken into considered and modeled. It answers the question of how battery degradation and retirement in the vehicle can affect its second-life BESS application and subsequently translate into cost savings on the power generation side.
With the rising share of intermittent RES and increasing load in power systems, it gets challenging to get accurate predictions for their power output and demand [27]- [29]. This paper is the first to envision BESS made from EOL batteries to be used to absorb forecast error of wind power and load (i.e., Part 3 in Figure 1). The operation of the second-life battery is integrated into a detailed generation scheduling (economic dispatch) problem. Maximum cost savings throughout the second life is achieved by balancing charging/discharging depth and service years in the second life. The battery degradation process is modeled (i.e., Part 1), accounting for performance deterioration. In modeling battery retirement (i.e., Part 2), first-life usage patterns as well as retirement criteria are considered for both PHEV and EV types. Two battery retirement modes are considered: nominal and realistic modes. Normally, battery packs are retired upon they fail to meet certain technical criteria [30]. However, it is usual that in practicing vehicle retirement or change of ownership can take place earlier [31]. If collected at this stage, the repurposed battery will exhibit different EOL performances.
The organization of this paper is as follows. A simplified model for measuring battery performance degradation is introduced in Section II (corresponding to Part 1 in Figure 1), followed by retirement models for EV and PHEV battery packs in Section III (i.e., Part 2 in Figure 1). Based on these models, the status of battery packs at the commencement of their second-life application can be determined. The operating strategy of the BESS is proposed in Section IV (i.e., Part 3 in Figure 3). An economic dispatch (ED) problem is then formulated. In Section V, numerical testing is studied. Section VI concludes the paper.

II. MODELING BATTERY PERFORMANCE DEGRADATION
Given the myriad types of cathodes and electrolytes and requirements for model complexities, currently, there is no single presiding degradation model for lithium batteries [11], [32]- [36]. However, general degradation patterns can be extracted with simplification assumptions. In this paper, a simplified model for battery performance degradation are generalized from [33]- [35], [37].

A. CAPACITY FADE
Field tests and research works have revealed that the energy capacity fade of modern batteries strongly depends on the number of cycles, depth of discharge (DoD), C-rate, and ambient temperature [33]- [35], [38]. Among these variables, the temperature is often regarded as a given condition under which the cycle life tests are carried out [35][34] [33]. For EV/PHEV batteries, typical C-rate profiles reflecting driving patterns are also provided [33]- [35], [39]. Consequently, the remaining energy capacity of the batteries in per-unit value, i.e., relative capacity, can be simplified as a function of cycle As the number of cycles accumulates monotonously and serves as a type of "timestamp" in batteries' life, in the remainder of this paper " " is represented by superscript instead. i.e.

( ) = ( , )
Without loss of generality, superscripts in this paper are reserved for chronological variables such as cycle number , hour , and day count .
General degradation trend and boundary conditions are given by (2)-(6), when the ambient temperature is around 35°C [33]- [35], [38]: 0% DoD results in zero degradation, (2), either does 0 cycle number, (3). Monotonicity in performance degradation is depicted by (4) and (5) with regard to the number of cycles and DoD, respectively. Battery capacity either reduces or stays at the same level with any given , i.e. (4), and , i.e. (5). The other general observation is that capacity fade normally speeds up over time, as provided in (4). As the number of cycles accumulates, capacity loss between cycles also increases.
A linear relationship can be found between DoD ( ) and the logarithm of cycle number (log( )), [35]. Using the techniques of curve and surface fitting [40], [41], relative capacity can be represented by a function of cycle number and DoD as: where , and are designated constants. (7) is consistent with condition (2)- (6). Its proof is presented in Appendix-A.

B. EFFICIENCY DECAY
Approximate linear relationships can be observed between internal loss and cycle number and between internal loss and DoD [33]- [35]. Also, the slope of the linear relationship between internal loss and cycle number increases with DoD. As external circuits have much greater resistance than the internal, the percent increase in internal loss is assumed to equate to percent efficiency decay. The efficiency function is given by: and 1 -3 and 1 -3 are designated constants; 1 3 ⁄ should be equal to ( 3 − 100%) 2 ⁄ . With (8)-(10), the above efficiency decay trend can be met. Its proof is detailed in Appendix-B.
It should be noted that although a generalized degradation model for lithium-ion batteries is used in this paper, our proposed framework can adopt any degradation model by replacing the above (1)-(10) if battery type or requirements for model complexity change. The whole evaluation process for second-life battery in this paper holds as long as battery capacity fade and efficiency decay can be estimated.

III. BATTERY RETIREMENT MODES IN EV/PHEV
EOL battery status is heavily dependent upon the usage pattern and the service duration in its vehicle application. However, currently, it is not certain at what stage EV/PHEV batteries are retired and repurposed. In this paper, two vehicle retirement modes-nominal and realistic modes-are considered alongside the vehicle types. Nominal retirement mode describes the situation where batteries are recycled when they reach their technical EOL conditions. Realistic retirement mode considers the fact that vehicles are often retired before they are technically retired.

A. NOMINAL RETIREMENT MODE -EOL FOR PHEV BATTERY PACK
Technical EOL are defined by consortiums such as USABC [30]. For example, it is compulsory for a PHEV battery pack to last for 5,000 cycles in charge depleting (CD) mode and 300,000 cycles in charging sustaining (CS) mode [30]. The initial battery status for its second-life application is then the EOL condition in PHEV. EOL capacity and efficiency are given in (11) and (12), respectively. In this paper, subscripts "1st" and "2nd" are used to indicate first and second-life applications of battery, respectively.
where ∆ CD and ∆ CS are required energy for CD and CS modes, respectively. For example, ∆ CD is 11.6 kWh for a 20.7 kWh PHEV battery pack and ∆ CS is 0.5 kWh [30]. Total cycle numbers and DoD that are nominally required for CD and CS modes are first applied to degradation model (1)- (10). The EOL status is then determined by either CD or CS mode, whichever results in lower values, thus min{} in (11) and (12). When calculating the EOL, one thing worth noticing is the DoD definition. DoD is usually given in percentage value. In some test results, the denominator of DoD is the rated energy capacity of the battery, which is a constant. In some other test results, the DoD value is based on actual energy capacity, which is a variable that decreases along with the cycle test. If the latter DoD definition is used when modeling battery degradation, cycle-to-cycle iterations should be carried out to calculate relative capacity and efficiency. In each cycle, the DoD base needs to be updated.

B. NOMINAL RETIREMENT MODE -EOL FOR EV BATTERY PACK
EOL relative capacity and efficiency for EV battery pack are given by (13) and (14), respectively. 2nd, where ∆ is energy requirement incurred by daily travel mileage and is given by (18), assuming daily mileage for each EV are constant.
Different from PHEV, battery is the only energy source for EV propulsion. As a result, the battery would be retired when its energy capacity is no longer able to deliver the daily travel mileage requirement, i.e., violation of (15), assuming the consumption rate of EV is 0.20 kWh/mile, Besides, it could also be retired once EV's nominal EOL mileage T is reached, i.e., violation of (16): Substituting (13) and (14) into (15), the maximum cycle number max is determined by the comparison between the above two conditions (15) and (16): where ∆ can be calculated with given , assuming each EV completes 1 cycle every day:

C. REALISTIC RETIREMENT MODE
In the real world, it is usual that vehicle retirement or change of ownership takes place before it is technically retired. The length of vehicle ownership in the United States averages 11.6 years while 6.6 years for new vehicle ownership [31]. After the first ownership ends, EV/PHEV can be repurposed at a low cost. For PHEV application, it can be regarded charge depleting and charge sustaining cycles are deployed with a same frequency over its life span. The number of cycles used in CD or CD mode is thus proportional to the actual life in the vehicle application.

IV. COST-SAVING EVALUATION FOR BESS MITIGATING FORECAST ERROR
Battery can be used for many applications in power systems [26], [42]- [45], from regulation service [46]- [48] to load balancing [49]. Among them, applications requiring frequent charging and discharging such as regulation service can wear second-life BESS down quickly as recycled battery packs may already be in unhealthy conditions. Applications with long duration and large energy discharge such as peak shaving are not acceptable as well since deep DoDs can also make the battery deteriorate seriously.
For second-life battery, two main applications are residential demand response and power smoothing renewable integration [9], [21], [22]. In this paper, the latter is considered. With wind power penetration escalating nowadays, the unavoidable errors caused by wind power forecasts and load forecast can significantly affect the system operation. The second-life BESS can mitigate the effects of such errors while maintaining its battery performance by properly choosing the time window and energy capacity for operation.

A. OPERATING STRATEGY OF THE BESS
In this paper, BESS operation is integrated into daily EDs with an hourly time window. With BESS absorbing forecast error of wind power and load, the total cost for power generation is reduced. The more energy is used for each charge/discharge cycle, the more cost savings will incur. However, deeper DoD might also accelerate the degradation, hence reduce the total savings over its service life.
Here, a decision variable called daily operating energy capacity for BESS (∆ BESS ) is introduced. ∆ BESS specifies the total daily amount of energy charged into or discharged from the second-life BESS for the purpose of forecast error mitigation. For illustration, Figure. 2(a) shows a typical distribution of forecast error. As the distribution has the mean of zero [29], the chances of battery charging and discharging are even in the long run. An error-duration curve can be  Figure. 2(b). ∆ BESS thus designates a fixed area in the power-time plane. Since it directly links to the forecast errors to be mitigated during the day as well as the DoD, ∆ BESS represents the trade-off between daily cost savings and service life of the BESS. The generation scheduling problem is formulated to determine the optimal ∆ BESS , with which maximum cost savings can be achieved.

B. PROBLEM FORMULATION
The total cost savings made by second-life BESS lies in the balance between daily cost savings and service life. The total cost savings is the sum of the daily cost savings throughout the service life of the BESS. It is a function of ∆ BESS , as charging/discharging affects ED scheduling. Determining ∆ BESS poses a decision problem. For instance, higher ∆ BESS could mean higher daily cost savings, but BESS's service life may shorten; lower ∆ BESS , on the other hand, does not necessarily interpret into lower total cost savings since service life can be extended.
BESS operation is to maximize the total cost savings. Relative capacities and efficiencies of battery packs can be regarded as constant during the day and degradation takes place between days. So, battery status is updated on a daily basis, same as ED. The optimization problem is formulated as follows: Maximize: subject to: The cost savings (22) designates the difference between the results of daily EDs with and without the operation of the BESS. Emission cost [50] is considered in (23). Power balance at each time should be maintained, as given in (24), where the WTGs have the power curve: The total forecast error FE is comprised of errors from forecast wind power and load demand. Both the errors can be regarded as uncorrelated normal distributions with mean values of zero [51] [4]. Therefore FE follows a normal distribution with a standard deviation, i.e., FE~( 0, 2 ), where, The total daily capacity ∆ BESS is capped by the total initial capacity of the BESS (25). It is fixed for charging and discharging, (26) and (27), as explained in Section IV-A.
BESS, < 0 represents battery charging. The generator output is altered as load demand is changed by the operation of BESS, (28) and (29). To preserve relative capacity, battery packs with higher relative capacities should contribute more. Therefore, the energy contribution of battery packs for each time period is proportional to their remaining capacities, i.e., relative capacity at the beginning of the day (30). The average energy contribution ∆ 2nd, , which is the numerator of the DOD used for calculating the daily degradation, is obtained by (31). The daily cycle number required by (31) can be easily counted with the proposed operating strategy. As all battery packs in the BESS are utilized in each charge and discharge operation ((30)), the cycle number for each battery pack is identical throughout as long as it is not retired from the BESS.
The operating condition for battery packs and the BESS are given by (32) and (33), respectively. Set (32) is given to check whether a battery pack should be excluded from the BESS. A single battery pack is retired if its relative capacity, efficiency or total service life reaches certain criteria. During the service life of BESS, perceivably, the number of battery packs ( V ) keeps decreasing. The BESS retires when it is unable to provide operating capacity or maximum service life is reached, (33). Criteria given in (32) and (33), such as minimum relative capacity, round trip efficiency and service life are subject to revision in case of different requirements and considerations.
Similar to the calculation of the degradation process mentioned in Section III, iterative procedures should be carried out as well for updating 2nd, (.) and 2nd, (.), if DoD used in battery degradation formulas is defined with the variable denominator (i.e., the actual energy capacity).

C. SOLUTION
The procedure for solving the problem in (22)-(33) is as follows: Step 1: Read system data and parameters, including EOL battery packs and wind power penetration.
Step 3: Randomly sample WTG and FE .
Step 4: Schedule ED for day without the operation of BESS.
Step 5: Reform load by applying charging and discharging of BESS by (26)- (29) and share the energy contribution among battery packs using (31); Step 6: Re-schedule ED with updated load by BESS operation and calculate cost savings for that day using (23).
Step 7: = + 1; Accumulate daily saving to total cost savings. Update S Batt , retire a battery pack upon violation of (32); Update S BESS , retire the BESS upon infringement of (33).
Step 9: Store total cost savings for this configuration (∆ BESS ) upon the retirement of the BESS.
Step 10: Cease searching if optimal ∆ BESS are found; otherwise, go to Step 2. Given the nonlinearity and non-differentiability of the above problem, evolution algorithms (EAs) are suitable to avoid local optimum. In this paper, self-adaptive differential evolution (SaDE) [52] is used. To solve specific optimization problems using typical EAs, time-consuming trial-and-error searches are required for appropriate control parameters such as population NP, scaling factor , and crossover rate CR. Besides, strategies and parameters are fixed once chosen but may not be effective throughout the evolution as the population may move through different regions. SaDE eliminates these drawbacks by using self-adapted trial vector generation strategies and associated control parameter values [52]- [54]. Figure 3 gives the consolidated graphical paradigm for the proposed evaluation framework. It is composed of two parts: 1) Battery retirement in the first life, i.e., Section III, and 2) cost saving maximization in the second life, i.e., Section IV. In the first-life application, four scenarios are ensued from the consideration of vehicle types and retirement modes-PHEV with nominal retirement mode, EV with nominal retirement mode, PHEV with realistic retirement mode, and EV with realistic retirement mode. The outcome of the firstlife modelling, i.e., battery EOL performance, is the input of the calculation of the second life. It can be seen from the figure that the battery degradation model (Section II) is applied throughout the two parts.

V. CASE STUDY
The proposed framework is illustrated in a case study, where a 3,000 fleet (i.e., 3,000 battery packs) is recycled into a 3generator system. Battery capacity is rated at 20.5 kWh for PHEV application and 40 kWh for the EV application. The case study is implemented in MATLAB environment.

A. FIRST LIFE: EOL PERFORMANCE
Parameters for EOL are given as follows. For PHEV in nominal retirement mode (Section III-A), ∆ CD and ∆ CS are 11.6 kWh and 0.5 kWh, respectively, [30]. Minimum 5,000 CD and 300,000 CS cycles are required prior to nominal retirement (i.e CD and CS in Section III-A), [30]. For EV's nominal retirement mode (Section III-B), daily travel mileages are randomly sampled from [55]. For realistic retirement mode (Section III-C), a probability distribution of vehicle ownership length is used [31], as is given in Appendix-C.
M G Z y s 3 P z C / n F w t L y y u q a u b 5 R U 2 E s K a v S U I S y 4 R L F B A 9 Y F T g I 1 o g k I 7 4 r W N 3 t n 2 X 1 + j W T i o f B F Q w i 5 v i k G 3 C P U w L a a p v b L Z 9 A z / W S y 7 T 9 g 6 c E I G 2 b R a t k D Y W n w R 5 D s Z M G Z y s 3 P z C / n F w t L y y u q a u b 5 R U 2 E s K a v S U I S y 4 R L F B A 9 Y F T g I 1 o g k I 7 4 r W N 3 t n 2 X 1 + j W T i o f B F Q w i 5 v i k G 3 C P U w L a a p v b L Z 9 A z / W S y 7 T 9 g 6 c E I G 2 b R a t k D Y W n w R 5 D s Z By calculating performance degradation under the two retirement modes for both vehicle types, mean values of relative capacities and efficiencies of EOL battery packs are plotted in Figure. 4. Box plot is used to illustrate variances across 3,000 vehicles. It is most obvious to find that usage and retirement mode in the transportation sector have direct effects on EOL battery performance.
Vehicle type-wise, Figure. 4 shows that in either retirement mode EV application leads to more serious capacity fade and efficiency decay. Although battery packs for EV application are double the capacity of PHEVs', the fact that battery is the sole energy source powering EV implies deeper DoD exerted. Meanwhile, batteries in PHEV take up a supportive role, where only standard CD/CS cycles are required, (11) and (12). The EOL variance of EV battery packs can be observed in both battery retirement modes. It is because each EV's daily mileage varies, as does its ∆ , (18).
Not only the vehicle types but their retirement modes also affect the EOL performance. On average, battery packs in realistic retirement mode are better preserved than the in nominal modes. It is because vehicles could be retired before reaching its technical EOL in reality (Section III-C and Appendix-C). Besides, EOL performance in realistic retirement modes is more widely distributed for both vehicle types. Overall, battery packs retired from PHEVs in nominal mode represent the most uniform situation whereas battery packs retired from EVs in realistic mode are most randomly distributed due to variances in both served years in vehicles and daily mileages. For degradation model used in this paper, capacity fade is more sensitive to vehicle usage than battery efficiency decay.

B. SECOND LIFE: COST SAVINGS
Parameters of generators in the power system are provided in Table I. Coal price is $2.50 MMBtu and CO2 price is $4.76 MMBtu. Forecast load profile is from RTS-96 [56]. Peak load is set at 855 MW. 50 MW wind power penetration is first assumed. The wind speed follows a Weibull distribution with a shape factor of 1.72 and a scale factor of 8. The cutin, rated and cut-out speeds of the WTGs are 3.6, 13 and 25 m/s, respectively. LE is 0.02 per MW and WE is 2.21 per MW installed capacity. By fitting test results from [33]- [35], [38], constants in degradation formula (7) and (8)  To have a grasp on the relationship between daily operating energy capacity (∆ BESS ) and total cost savings. The total cost savings is first calculated with ∆ BESS increased step by step. PHEV battery and nominal retirement mode is chosen. Results and trend are plotted in Figure. 5.
As shown in the figure, the trend is that the total cost savings ascend with increased ∆ BESS until it reaches its peak value. According to (22), the total cost savings is affected by two factors: the difference between power outputs of committed generators with and without BESS ( and ′ ) and length of service life of BESS ( S BESS ). The larger the ∆ BESS is the more is the forecast error that can be eliminated by BESS ( (28) and (29)), which indicates increased daily savings. However, a higher ∆ BESS leads to a higher value of ∆ BESS, , which means deeper DoD for daily operation (30). Charging and discharging with deeper DoD generally make battery performance degrade sooner, (31).    Thus the BESS ends its service earlier, (32). If being operated with extremely high DoD values, e.g. when ∆ BESS ≥ 39 MWh in PHEV-nominal scenario, the BESS retires in a short period with hardly any cost savings. In sum, the optimal daily operating energy capacity of the second-life BESS is a compromise between daily cost savings and service life takes place. For current penetration level of wind power, i.e. 5.85%, the maximum total cost savings appears when ∆ BESS is around 21 MWh. Following the calculation process in Section IV-C, optimal ∆ BESS values can be found for each combination of vehicle type and retirement mode. Table II lists maximal total cost savings for the four scenarios as well as their total EOL energy capacity, total cost savings per EOL capacity and their optimal ∆ BESS . It can be seen from the table that different EOL status of EV/PHEV batteries (Section V-A) go on affect their economic performance in second-life application. For same vehicle types, realistic retirement modes result in higher cost savings of the BESS than the nominal ones. In terms of total cost savings, BESS built from EV battery packs in realistic mode trumps other scenarios. However, it should be noted that an EV battery pack possesses double the energy capacity of a PHEV battery pack. The total EOL capacity is the largest, 72.58 MWh, in the EV-Realistic scenario.
To have a meaningful comparison across the four scenarios, total cost savings per EOL capacity for the second-life application are listed in Table II. In terms of cost savings per MWh, PHEV battery in realistic mode outperforms other scenarios. The second-life BESS in the PHEV-Realistic scenario can save 0.034 $M per MWh of EOL capacity compared with 0.030 $M/MWh in the EV-Realistic scenario. Despite larger total cost savings gained, battery packs in EVrealistic scenario have inferior EOL status than in PHEVrealistic scenario. That makes EV battery packs retire sooner thus the lower cost savings per MWh. Comparing between PHEV-nominal and EV-nominal scenarios, the larger EOL EV battery capacity can interpret into more total cost savings, whereas EOL PHEV battery is better preserved. The two factors even out-resulting in the same cost savings per EOL capacity, 0.025 $M/MWh, (the first and third rows in the table).

C. SENSITIVITY STUDY
Finally, PHEV-realistic scenario is chosen to study the impact of WTG penetration levels on total cost savings. Total cost savings is re-calculated with varying WTG capacity. The amount of forecast error arises with increased wind power penetration, (37). As can be shown in Figure. 6, when the penetration level is below 10%, the total cost savings remains at a low level and insensitive to the level of penetration. When the penetration level increases from 10% to 30%, i.e., wind power accounts for more error, the total cost savings becomes sensitive to and increases with the penetration level. After penetration level reaches 30%, the cost savings still increases but the slope becomes flatter. This is because although the amount of forecast error grows with increase of penetration level, the limited energy capacity of the BESS confines further improvement of total cost savings.

D. COMPARISON OF OPTIMIZATION ALGORITHMS
To find out the effectiveness of SaDE used in solving the optimization problem in the second-life application, classic evaluation algorithms such genetic algorithm (GA) ('ga' command in MATLAB environment), particle swarm optimization (PSO) ('particleswarm'), and differential evolution (DE) [57] are used as comparison. The same PHEV-realistic scenario is used. Wind penetration is set to the original 50 MW. The comparison results are given in Table III. In terms of computing time, SaDE outperforms the other three. As mentioned in Section IV-C, SaDE's adaptiveness contributes to the faster convergence. On the other hand, the default parameter setting for GA, PSO and DE might not be in favor of this specific problem. The tuning of the parameters is timeconsuming. In terms of the solution, however, all the algorithms can find optimum consistently.

VI. CONCLUSION
In this paper, a comprehensive framework evaluating second-life EV/PHEV battery in BESS application is proposed. The framework comprises of three modules: 1) Battery performance degradation model; 2) EV/PHEV battery retirement modes; and 3) evaluation for BESS application in power systems. The second-life BESS is proposed to mitigate load and wind power forecast errors. Daily operating energy capacity is optimized to maximize total cost savings of economic dispatch across the second life span of batteries.
The case study shows that the proposed framework determines the best operating strategy for the second-life BESS. The battery degradation and various first-life EOL statuses  are considered. Results shows that the performance of EOL application is strongly correlated with usage and retirement mode prior to EOL. Reduced service years in vehicle application can help second-life BESS gain extra cost savings. Although EV battery packs possess larger EOL energy capacities and consequently generate more cost savings, the BESS built from retired PHEV batteries has higher cost savings per MWh. It is because in the proposed degradation model battery capacity and efficiency are better preserved in PHEV applications. Given EOL battery packs, the best second-life performance of the BESS can be obtained when a balance between short-term benefit (daily cost saving) and service years is achieved. The proposed three-part framework can be adopted to second-life BESS applications on the generation side in the power systems. The operating strategy proposed (Section IV-A) can be used as long as there are forecast errors to be absorbed. The single decision variable (∆ BESS ) in the optimization problem simplifies the operational process in real systems. Other degradation models for batteries [20]- [22] can also be used (in Section II) to reflect the actual battery wear and tear in specific cases.