Battery Switching Station System

There three important components for BSS; swapping machine, chargers, and battery inventory.

Based on these important components, two critical performance measurements need to be considered for building BSS system; the number of batteries to be kept in the stations and waiting time for the electric vehicles to get a fully charged battery.

2.2.1. Waiting Time

Waiting time for the electric vehicle to get fully charged battery is an important issue to be considered. The electric truck should not wait too long to get a battery or else it will hinder the advantage of BSS that allows an electric vehicle to get fully charged battery fast. Moreover, for the delivery truck, the time schedule can be very strict. For understanding how to calculate waiting time, the BSS system should be analysed first.

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Figure 5. Battery Swapping Station with Ample System

To make analysis simpler, BSS can be seen to have two connected systems. Those are battery charging system that focuses on the charging battery activity, and swapping battery system that focuses on the swapping battery activity to make the electric vehicle get a used battery out and get a fully charged battery. For battery charging system, similar to the research that has been done by Avci, Girotra, and Netessine (2015) and Mak, Rong, and Shen (2013), battery Switching Station will have multi-echelon inventory system for repairable items (METRIC) by considering the charging time as repairing service time and used battery as failed item needs to be repaired.

In the METRIC system, the repair process usually happens in the depot, for BSS case, the repair process happens in charging machine and the front area that needs to meet customer demands is usually called as Base in METRIC, for BSS case, this front area is at swapping machine.

The rules used in BSS for managing battery and rules in METRIC are same, both of them use FIFO rule and one-for-one replenishment system. One-for One replenishment system means that each time customer comes bringing a failed item to the base, the base will give customer failed item, sends the failed item to the depot and will ask depot immediately for the new non-failed item.

Based on the METRIC theory, the queue in charging machines with charging type-1 is M/G/∞ as it is assumed that there are no limitation numbers of charging machine type-1, which has to charge time of eight hours. It is because the requirement for charging type-1 system is the only socket as a plug for electricity. Therefore, for battery charging system, the used battery that needs to be charged does not need to wait in the queue to get charged. The only bottleneck for charging system to fulfil battery demand happens due to the long charging time. It is assumed that the electric trucks come to BSS have used the energy in the battery until it is almost finished.

Therefore the charging time will be around eight hours.

There is another queueing model in the BSS that happens in front of swapping machine. The model for the queue in swapping machine is M/D/1 since the demand is assumed to have Poisson

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distribution, the service time has Deterministic distribution, and the station has one swapping machine. Based on the M/D/1 model, since the demand arrival has passion distribution, the inter arrival variability is one, and the variability of swapping battery process is zero.

Based on this, the waiting time for an electric vehicle that comes to BSS should be the waiting time in front of a swapping machine, and there might be additional waiting time due to charging process to fulfil the demand. Nevertheless, because the truck is operated for 9.33 hours in a day and the charging time for used battery takes around eight hours, which is almost the same with working hours for the truck, BSS is designed to fulfil all of its demand through battery inventory.

The used battery will be charged and will only be used for the demand of following days.

Therefore, the waiting time that might happen due to charging process does not occur for this BSS system and the waiting time should only occur due to swapping battery process.

The waiting time for the electric truck to get a fully charged battery can be calculated based on M/D/1 model:

𝐶𝐶𝐶𝐶 = cycle time or total waiting time to get a fully charged battery at BSS that start from electric truck enter BSS until get battery swapped done

𝐶𝐶𝐶𝐶𝐹𝐹 = waiting time in queue until get swapped battery process

𝐷𝐷 = effective swapping process time needed to swap used battery to a fully charged battery at electric truck, which is assumed to be five minute or 0.08 hours.

The swapping process time at BSS is three minutes for the private electric vehicle (Liu, 2012).

For this project, the effective swapping time is made almost twice of the swapping time process stated by Liu (2012) to be safe. This is because there is no information of swapping process time for an electric truck that might be different from swapping process time for the private electric vehicle.

Since at BSS there will be one swapping machine, the 𝐶𝐶𝐶𝐶_𝐹𝐹 is:

𝐶𝐶𝐶𝐶_𝐹𝐹 = ^{(𝐷𝐷𝑡𝑡2+𝐷𝐷𝑒𝑒}₂ ²⁾ ._1−𝑚𝑚^𝑚𝑚 . 𝐷𝐷 (8) 𝐷𝐷𝐷𝐷 = coefficient of variation for arrival of vehicle

𝐷𝐷𝐷𝐷 = coefficient of variation for processing time or swapping service time 𝑜𝑜 = utilization

𝑤𝑤𝐷𝐷 = arrival rate of electric truck to BSS

𝑤𝑤𝐷𝐷 = rate of effective battery swapping processing time 𝐶𝐶𝐶𝐶 can be calculated as:

18 𝐶𝐶𝐶𝐶 = (0.5)

�∑^𝐼𝐼_𝑖𝑖=0𝛼𝛼. 𝑉𝑉_{𝑖𝑖𝑖𝑖2}. 𝐷𝐷. 𝑓𝑓_𝑖𝑖

𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤 ℎ𝑤𝑤𝑜𝑜𝑤𝑤𝑜𝑜 𝑀𝑀 𝐵𝐵𝑖𝑖

� �

�𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤 ℎ𝑤𝑤𝑜𝑜𝑤𝑤𝑜𝑜 𝑀𝑀 𝐵𝐵𝑖𝑖− ∑𝐼𝐼 𝛼𝛼. 𝑉𝑉𝑖𝑖𝑖𝑖2. 𝐷𝐷. 𝑓𝑓𝑖𝑖

𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤 ℎ𝑤𝑤𝑜𝑜𝑤𝑤𝑜𝑜 𝑀𝑀 𝐵𝐵𝑖𝑖=0 _𝑖𝑖 �

. 𝐷𝐷 + 𝐷𝐷

𝐶𝐶𝐶𝐶 = (0.5).𝑤𝑤𝑡𝑡𝑤𝑤𝑖𝑖𝑖𝑖𝑤𝑤𝑤𝑤 ℎ𝑡𝑡𝑚𝑚𝑤𝑤𝑜𝑜 𝑚𝑚 𝐵𝐵^{∑𝐼𝐼𝑚𝑚=0𝛼𝛼.𝑉𝑉}𝑗𝑗^{𝑚𝑚𝑗𝑗2}−∑^.𝑜𝑜𝐼𝐼^𝑗𝑗 𝛼𝛼.𝑉𝑉𝑚𝑚𝑗𝑗2.𝑡𝑡.𝑜𝑜𝑗𝑗

𝑚𝑚=0 . 𝐷𝐷²+ 𝐷𝐷 (9)

With

𝑉𝑉_{𝑖𝑖𝑖𝑖2} = numbers of vehicle electric vehicle, which is described with k=2, with age-i, at year-j

𝐵𝐵𝑖𝑖 = numbers of battery switching stations at year j

In addition to waiting time, there are other important things needs to be considered to ensure that the waiting time in front of swapping machine will not be too high. That important thing is the maximum capacity of BSS which needs to be set by the company that wants to build BSS.

To calculate the maximum capacity at BSS, the waiting time in the swapping machine until EV get battery swapped is assumed to be limited to 10 minutes (0.16 hours), while the effective swapping time for the battery is 5 minutes (0.08 hours). It means the maximum waiting time is 2𝐷𝐷.This limitation of waiting time is made to ensure that electric trucks do not wait spent time much at BSS and can continue its delivery operation soon. This short waiting time is used to make sure that BSS can perform like normal gas station. Based on this assumption the maximum utilization in swapping machine is:

𝐶𝐶𝐶𝐶 = 𝐶𝐶𝐶𝐶𝐹𝐹 + 𝐷𝐷 2𝐷𝐷 = 𝐶𝐶𝐶𝐶_𝐹𝐹 + 𝐷𝐷 𝐶𝐶𝐶𝐶_𝐹𝐹 = 𝐷𝐷

𝐶𝐶𝐶𝐶_𝐹𝐹 = ^{(𝐷𝐷𝑡𝑡2+𝐷𝐷𝑒𝑒}₂ ²⁾ ._1−𝑚𝑚^𝑚𝑚 . 𝐷𝐷 𝐷𝐷 = ⁽¹⁺⁰₂²⁾ ._1−𝑚𝑚^𝑚𝑚 . 𝐷𝐷

𝑜𝑜𝑚𝑚𝑡𝑡𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 = 0.67 (10)

The maximum arrival rate at BSS and maximum number of EVs can be serviced by a BSS (BSS’s capacity) can be found out based on the maximum utilization:

𝑜𝑜𝑚𝑚𝑡𝑡𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 = 0.67 𝑤𝑤𝐷𝐷

𝑤𝑤𝐷𝐷 = 0.67

𝑀𝑀𝐷𝐷𝑀𝑀𝐷𝐷𝑀𝑀𝑜𝑜𝑀𝑀 𝐶𝐶𝐷𝐷𝑠𝑠𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷 𝐵𝐵𝐵𝐵𝐵𝐵 𝐵𝐵𝐵𝐵𝐵𝐵 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤 ℎ𝑤𝑤𝑜𝑜𝑤𝑤𝑜𝑜

1𝐷𝐷

= 0.67

𝑀𝑀𝐷𝐷𝑀𝑀𝐷𝐷𝑀𝑀𝑜𝑜𝑀𝑀 𝐶𝐶𝐷𝐷𝑠𝑠𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷 𝐵𝐵𝐵𝐵𝐵𝐵 =(0.67). 𝐵𝐵𝐵𝐵𝐵𝐵 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤 ℎ𝑤𝑤𝑜𝑜𝑤𝑤𝑜𝑜 𝐷𝐷

𝑀𝑀𝐷𝐷𝑀𝑀𝐷𝐷𝑀𝑀𝑜𝑜𝑀𝑀 𝐶𝐶𝐷𝐷𝑠𝑠𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷 𝐵𝐵𝐵𝐵𝐵𝐵 =(0.67) . (9.33) ℎ𝑤𝑤𝑜𝑜𝑤𝑤𝑜𝑜 0.083 ℎ𝑤𝑤𝑜𝑜𝑤𝑤

𝑀𝑀𝐷𝐷𝑀𝑀𝐷𝐷𝑀𝑀𝑜𝑜𝑀𝑀 𝐶𝐶𝐷𝐷𝑠𝑠𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷 𝐵𝐵𝐵𝐵𝐵𝐵 = 75 (11)

For this system, the maximum capacity of BSS in one day is 75 electric vehicles.

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2.2.2. Minimum Numbers of Battery in The Inventory of BSS

It is assumed that BSS has 95% of service level (𝛼𝛼), which means that minimum 95% of demand should be fulfilled. This service level affect the minimum number of batteries in the inventory of BSS. The minimum number of batteries is calculated as:

𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤 𝑤𝑤𝑓𝑓 𝑃𝑃𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑤𝑤𝐷𝐷 𝐷𝐷𝑤𝑤 𝐷𝐷ℎ𝐷𝐷 𝐷𝐷𝑤𝑤𝑎𝑎𝐷𝐷𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤𝐷𝐷

= 𝑀𝑀𝐷𝐷𝑤𝑤𝑀𝑀𝑜𝑜𝑀𝑀 𝐷𝐷𝑀𝑀𝑠𝑠𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑑𝑑 𝐷𝐷𝑤𝑤𝑤𝑤𝐷𝐷𝑎𝑎𝐷𝐷𝐷𝐷 𝑤𝑤𝑓𝑓 𝐸𝐸𝑉𝑉 𝐷𝐷ℎ𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷𝑤𝑤 𝑃𝑃𝐷𝐷 𝑜𝑜𝐷𝐷𝑤𝑤𝑎𝑎𝐷𝐷𝑑𝑑 𝑃𝑃𝐷𝐷𝑜𝑜𝐷𝐷𝑑𝑑 𝑤𝑤𝑤𝑤 𝑜𝑜𝐷𝐷𝑤𝑤𝑎𝑎𝐷𝐷𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷𝑎𝑎𝐷𝐷𝐷𝐷 + 𝑜𝑜𝐷𝐷𝑓𝑓𝐷𝐷𝐷𝐷𝐷𝐷 𝑜𝑜𝐷𝐷𝑤𝑤𝐷𝐷𝑤𝑤 𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤 𝑤𝑤𝑓𝑓 𝑃𝑃𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑤𝑤𝐷𝐷 𝐷𝐷𝑤𝑤 𝐷𝐷ℎ𝐷𝐷 𝐷𝐷𝑤𝑤𝑎𝑎𝐷𝐷𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤𝐷𝐷 = 𝛼𝛼 𝑀𝑀 𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤𝑜𝑜 𝑤𝑤𝑓𝑓 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑤𝑤𝐷𝐷𝐷𝐷 𝑎𝑎𝐷𝐷ℎ𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 + 𝑜𝑜𝐷𝐷𝑓𝑓𝐷𝐷𝐷𝐷𝐷𝐷 𝑜𝑜𝐷𝐷𝑤𝑤𝐷𝐷𝑤𝑤 (12) Since the demand is assumed to have a normal distribution, the estimation of safety stock of battery in the BSS can be calculated based on square root formula. The square root formula predicts the safety stock based on the number of the warehouse of BSS in the system. Maister (1976) explains the square root formulas as:

𝑜𝑜𝐷𝐷𝑓𝑓𝐷𝐷𝐷𝐷𝐷𝐷 𝑜𝑜𝐷𝐷𝑤𝑤𝐷𝐷𝑤𝑤 = 𝑍𝑍(𝛼𝛼). 𝜎𝜎. √𝐿𝐿𝐷𝐷𝐷𝐷𝑑𝑑 𝐷𝐷𝐷𝐷𝑀𝑀𝐷𝐷. �𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤 𝑤𝑤𝑓𝑓 𝑤𝑤𝐷𝐷𝑤𝑤𝐷𝐷ℎ𝑤𝑤𝑜𝑜𝑜𝑜𝐷𝐷 (13) with

𝑍𝑍(𝛼𝛼) = Z-value from service level, which is 1.65

Therefore, the number of battery in the all of BSS’s inventory with Poisson arrival distribution and lead time of one day :

𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤 𝑤𝑤𝑓𝑓 𝑃𝑃𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑤𝑤𝐷𝐷 𝐷𝐷𝑤𝑤 𝐷𝐷ℎ𝐷𝐷 𝐷𝐷𝑤𝑤𝑎𝑎𝐷𝐷𝑤𝑤𝐷𝐷𝑤𝑤𝑤𝑤𝐷𝐷 = 𝛼𝛼 𝑀𝑀 𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤𝑜𝑜 𝑤𝑤𝑓𝑓 𝐸𝐸𝑉𝑉 + �𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤 𝑤𝑤𝑓𝑓 𝐵𝐵𝐵𝐵𝐵𝐵. 𝑍𝑍(𝛼𝛼). �𝑤𝑤𝑜𝑜𝑀𝑀𝑃𝑃𝐷𝐷𝑤𝑤 𝑤𝑤𝑓𝑓 𝐸𝐸𝑉𝑉 (14)