**3. Stationary and In-motion energy storage systems application-specific sizing**

#### **3.1 Electric vehicle storage application-specific sizing**

Due to widespread use of EVs, standards and regulations have been developed by various regulatory bodies [114]. These regulations include EPA certified driving patterns which permit the minimum permissible operational boundaries for an EV [115]. Four such EPA certified driving patterns are used as the criterion for EV storage sizing in this section. The Federal Test Procedure (FTP) version 75 defined by EPA as a test cycle for emission certification of light duty vehicles is a mandatory test procedure designed to identify the fuel economy performance of new vehicles. It consists of complex driving phases including a cold start phase until 505 seconds, a stabilized phase between 506 and 1375 seconds, and a hot start phase from 1376-1874 seconds. This test represents a transient driving cycle with an average speed of 9.47 meter/ second (21.2 miles/hour). The second profile, the Highway Fuel Economy Driving Schedule (HWFET) test cycle, defines certification and performance requirements for driving conditions on a highway. The average speed in this cycle is 21.59 meter/second (48.3 miles per hour). The third profile, the New York City Cycle (NYCC) test cycle, defines stop-and-go traffic driving constraints to assess the vehicle. The average speed in this cycle is 21.62 meter/second (48.37 miles per hour).

For EV certification applications, each of these tests assess vehicle performance, battery state, and energy consumption to simulate the vehicle model prior to production. The velocity versus time plots of each cycle (plotted in **Figure 2** and data for which is obtained from [116]) represent how a vehicle travels under different terrains and conditions, satisfying the minimum EPA requirements.

*Sizing and Lifecycle Assessment of Electrochemical Batteries for Electric Vehicles… DOI: http://dx.doi.org/10.5772/intechopen.110121*

**Figure 2.** *Standard EPA driving profile plots.*

**Table 3** shows a sizing case study listing applicable values for a 2000 Kg (4409 lbs) EV. The set of equations used for computing the minimum and maximum battery capacity for the EV are shown in Eq. (16).

$$E\_{\max\ (or\ min)} = P\_b \* \delta\_{\max\ (or\ min)},$$

$$P\_b = \frac{Power\ required\ by\ whhels}{\mathfrak{n}\_d \* \mathfrak{n}\_d} + \frac{P\_{acc}}{\mathfrak{n}\_d},$$

Power required by wheels ¼ 9*:*8 ∗*V rt* þ *rw* þ *rg* þ 1*:*1 ∗ *ra* ,

$$r\_l = \frac{w}{65} \ast \left(1 + 4.68 \ast 10^{-3} \ast V + 1.3 \ast 10^{-4} \ast V^2\right),\tag{16}$$

$$r\_w = \frac{\rho\_d}{g} \ast \frac{V^2}{2} \ast (C\_d \ast \lambda),$$

$$r\_\xi = w \ast \text{Sin}\theta,$$

$$r\_d = \frac{w}{g} \ast \frac{d(V)}{dt},$$

where, gravitational acceleration (*g*) = 9.8 *m/s*<sup>2</sup> , and air density (*ρa*) = 1.225 *Kg/m*<sup>3</sup> . Weight of the battery is generally ≤30% of vehicle weight. In this case, the velocity averages are identified from the above-mentioned standard driving cycles. The velocity differentials are calculated by building the linear trend-line equations for each of the driving cycles, as shown in Eq. (17). The parameters: *θ*, *Cd*, *λ*, *ηa*, *ηd*, *ηt*, and *Pacc* values are assumed averages from currently commercialized vehicles' testing


#### **Table 3.**

*Battery storage capacity range identification using driving cycles, for a 2000 kg (4409 lbs) vehicle.*

*Sizing and Lifecycle Assessment of Electrochemical Batteries for Electric Vehicles… DOI: http://dx.doi.org/10.5772/intechopen.110121*

specifications where variations in these values do not create a major change in the resulting battery capacity size. The key parameter is *w*, in which a minor change largely varies the battery capacity size range for the respective driving schedules.

$$\begin{aligned} \textbf{FTP} - \textbf{75} &: V = 0.0002t + 20.995, \\ \textbf{HWFET} &: V = 0.0166t + 42.052, \\ \textbf{NYCC} &: V = 0.0007t + 7.3611, \\ \textbf{USO6} &: V = -0.0069t + 50.594 \end{aligned} \tag{17}$$

The resulting average energy (battery capacity) is 105 kWh, that is the average of the lowest (1.83 kWh) and the highest (207.12 kWh) values. In terms of current commercially available and EPA certified vehicles, a 2020 Nissan Leaf (3946 lbs., 62 kWh), or a 2012 Tesla Model S (4,323 lbs., 100kWh) fall within this weight - battery capacity range combination.

### **3.2 Renewable energy storage application-specific sizing**

The electricity load profile analysis method termed as load summation method is used for computing the RES battery based on average and peak load calculations [117, 118]. In the average load calculation method, the average of the sum of hourly consumptions of the facility is taken into consideration which is mainly performed to define sizes for storage systems used for contingency planning or for operating limited-power (set of) equipment. The peak load calculation uses the peak of hourly consumptions of the facility to design a storage system which is capable of operating all the equipment for a defined period of time. In this case, hourly load profiles of a primary school and a hospital, both located in Miami, Florida for the year 2004 is obtained from [119, 120], corresponding plots for which are shown in **Figures 3** and **4** respectively.

The reason for the selection of the two datasets is the extremity in load profile variations and the frequency of variations. The sizing equations used for the analyses

**Figure 3.** *Load profile of a Hospital in Miami, Florida for the year 2004.*

**Figure 4.** *Load profile of a primary School in Miami, Florida for the year 2004.*

methods are shown in Eq. (18) for *Emax*(*or min*) (that is, the corresponding capacity range, in MWh) computation. Load factor is an energy consumption characteristic indicator comparing the actual energy used within a defined period with the energy usage if a peak demand occurs during the same period [121]. Here, the load factor is the ratio of the total yearly consumption and the yearly peak demand in the 365 days' time period for 24 hours/day.

The resulting load factor values for the primary school and hospital are 0.213 and 1.18 respectively. The de-rating factor is the expected deviation in battery parameters under defined conditions. There are no defined de-rating guidelines developed for interconnected batteries as the external controller (or a battery management system) provides the operational set points and limits [122]. Hence, it is assumed that the C-rate is fixed for the battery and the de-rating factor is not taken into consideration. Load growth factor is used to take into account the future facility expansion and corresponding growths in electrical loads that can be handled by the existing energy storage system size. Excess load growths beyond the storage system size addressing capability would need to be independent of the battery and be supplied by a separate feeder or a lateral. In this case, this factor is assumed to be 1, which means that the estimated load growth is twice the existing load.

$$E\_{\max(or\ min)} = P\_b \* Operating\ Hours,\tag{18}$$

$$\text{where}, P\_b = \frac{\text{Average or Peak Demand} \ (kW) \text{ of } (\text{Motor} + \text{Non} - \text{Motor Loads})}{\text{Load Factor} \ast \text{De} - \text{rating Factor} \ast \text{Load Growth Factor}},$$

$$\text{Load Factor} = \frac{\text{Total Consumption in a selected period} (kWh)}{\text{Peak Demand} (kWh) \* \text{Days in the selected period} \* \text{Hours} / \text{Days in the selected period}},$$

*Load Growth Factor* <sup>¼</sup> *Estimated Consumption kWh* ð Þ *in the following year* � *Current Yearly Consumption kWh* ð Þ *Current Yearly Consumption kWh* ð Þ

*Sizing and Lifecycle Assessment of Electrochemical Batteries for Electric Vehicles… DOI: http://dx.doi.org/10.5772/intechopen.110121*

The sizing is performed under the assumption that gas operated equipment is categorized as motor loads and electricity operated equipment are non-motor loads. This categorization eases the addition (or removal) of a load necessary (or redundant) for the required battery backup or an islanded (off-grid) operation. Additionally, no other renewable sources are taken into consideration, and it is assumed that the battery is connected to the load and the grid, for load demand responses and for battery-specific grid services respectively. The short and long duration grid service responses are taken into account for DOD identification in Section 4. The computed stepwise values and resulting *Emax* and *Emin* are tabulated in **Table 4**. The *Operating Hours* are chosen as 2 and 10 for the minimum (short duration) and maximum (long duration) capacity value computations, respectively. For the primary school, the resulting average energy is 25.735.

MWh, that is the average of the lowest (1.30 MWh) and the highest (50.17 MWh) values. For the hospital, the resulting average energy is 12.445 MWh, which is also the average of the lowest (2.19 MWh) and the highest (22.70 MWh) values. Although the load consumption peaks and frequency of load operations is higher in case of a hospital, the energy storage size requirement for it is comparatively lower than the primary school mainly because of the load factor. Higher is the load factor, lower is the energy storage size requirement, which also results in reduced average per kWh cost.

Further, comparing the load profiles in **Figures 3** and **4**, it can be seen that the peak consumptions take place at the same times of the year for both facilities. Apart from facility occupancy, the external weather plays a major role in this effect. Studies related to this work are out of scope of this chapter and the interested readers are advised to look into papers authored by Sarwat et al. [123, 124]. If the individual equipment current ratings are available, a duty cycle diagram can be built based on the operating periods of the equipment and the corresponding energy requirements can be evaluated [125]. The interconnection topology of the batteries to meet the required battery module size for both EV and RES applications is dependent on the battery management systems performance and application requirements [126].
