This section presents the economical staging plan model. The proposed plan determines when the FCS units should be installed, along with their power capacities, in order to obtain the minimum overall cost of the FCS project. The proposed plan first estimates the public PEV charging demand by considering the traffic flow in the transportation network. The public PEV charging demand is distributed between the FCSs based on the traffic flow ratio. Then, the least-cost FCS units that satisfy the quality of service limits in terms of waiting and queueing times are selected to match the public PEV demand.
Start
K = 1 PN = 1 UT = 1
% Penetration Level (k)
Estimate Peak Demand
PEVs/ FCS Traffic Volume Data
FCSk (PN, UT) Satisfy Queuing Time Const. FCSk (PN, UT) K Kmax End K = K + 1 UT UTmax
Add Fast Charger PN = PN + 1 Change Charger Type
UT = UT + 1
Reset Chargers Type UT = 1 YES NO YES NO NO YES
Figure 6-1 Economical Staging Plan Model
It is assumed that a negative exponential distribution could model the PEV arrival times, and that the service time for FCSs follows a Poisson process [81]. Furthermore, there are several fast charging facilities in each FCS, and the PEVs are served based on a first-come first-served (FCFS) rule. Thus, the
staging plan problem for FCSs can be modeled as a nonlinear integer programming (NLIP) model according to the M/M/s queuing theory.
In order to obtain the minimum cost plan for an FCS network, the economical staging model involves several input parameters, as shown in the following.
6.2.1 Investment cost
There are currently various types and capacities of fast charging station units in the market. According to Aerovironment™ [82], there are four different standard FCS units, with capacities of 50, 100, 125, and 250 kW. Table 6.1 shows the FCS unit specifications and the best educated guesses for their cost figures.
Table 6-1 Fast charging station specifications and investment costs [82]
Parameters FCS50 FCS100 FCS125 FCS250
Lifetime (years) 10 10 10 10
Voltage Limit (V) 400 800 1,000 2,000
Amperage Limit (A) 125 125 125 125
Output Power (kW) 50 100 125 250
Charging duration of 20kWh Battery (min) 24 12 10 5
Max PEV/Day 60 120 144 288
Material Cost ($) 50,000 110,000 150,000 220,000
Installation Cost ($) 35,000 50,000 50,000 65,000
Distribution Transformer Cost ($) 10,000 15,000 17,500 35,000
Total Capital Cost ($) 95,000 175,000 217,500 320,000
Annual Operation Cost ($) 2,500 4,500 5,500 10,000
Total Operation Cost ($) 25,000 45,000 55,000 100,000
Total Investment Cost over 10 years ($) 120,000 220,000 272,500 420,000
Annual Levelized Cost (r = 6%) ($) 16,305 29,898 37,032 57,078
For the calculation of contribution margins, one must distinguish the total and levelized investment costs. While total cost refers to total capital cost and total operation cost, levelized investment cost distributes the total cost over the project’s lifetime. Equations (6.1 – 6.2) are utilized to calculate the annual levelized cost, with (r) being the interest rate and (k) the lifetime of the project.
𝐴𝑛𝑛𝑢𝑎𝑙 𝐿𝑒𝑣𝑒𝑙𝑖𝑧𝑒𝑑 𝐶𝑜𝑠𝑡 = 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝐶𝑜𝑠𝑡 × 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 (6.1)
𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 = (1+𝑟)𝑘× 𝑟
(1+𝑟)𝑘 −1 (6.2)
With interest fixed at 6% and a project lifetime of 10 years, an annuity factor of 0.1359 is obtained. This implies a yearly cost of 13.59% of total cost. A fast charging unit (50 kW) with a total cost of $120,000 would thus require a levelized cost of $16,305 per year.
Using high speed charging units will enhance the quality of service that an FCS can provide, especially at rush hour; however, for the same demand, when using faster charging units the utilization rate of the FCS will be impacted negatively due to the ability to serve more cars during the day. Thus, the profitability of an FCS has a positive correlation with the utilization of its units. Contrariwise, there is a negative relationship between FCS unit cost and service time, as shown in Fig. 6.2.
Figure 6-2 The relationship between the investment cost and the service time of FCS units based on a 20kWh charging event
Each charging unit has an hourly capability for serving PEVs. If the number of PEVs arriving at a charging station is greater than its capability, there will be PEVs waiting to be served, and therefore, if the actual queueing time is longer than the assumed queuing time, the system is not meeting requirements.
6.2.2 PEV market penetration
The number of PEVs is another parameter that should be considered when modeling an economical staging plan. FCS profit feasibility is associated with total PEV demand, which is proportional to the number of vehicles in the system. As discussed in Chapter 5, there are about 1.86 vehicles per household in North America according to National Household Travel Survey (NHTS) [53]. PEVs will be charged at public charging stations if the daily trip distances are longer than the PEVs’ driving ranges. The percentage of PEVs that require access to public charging stations (γ) to complete their daily trips can be estimated from the average daily travel distance data [53]. According to the discussion in Chapter 5, we assume that γ is equal to different values (0.1, 0.2, and 0.3) which represent different ratios of daily highway trips to all daily trips. As a result, the estimated number of PEVs requiring fast charging service can be obtained by equation (6.3):
0 5 10 15 20 25 30 FCS 50 FCS 100 FCS 125 FCS 250 0 100,000 200,000 300,000 400,000 500,000 SE R VI CE T IM E ( M IN .) IN VE ST M EN T CO ST ( $ )
Total Investment Cost and Charging Service Time for Different Charging Units
Cost Service Time
1680$/kW
2180$/kW 2200$/kW
PEV𝐹𝐶𝑆 = 𝛼𝑁𝑉 × 𝛾 × 𝑈𝑔,𝑡 ∑𝑇 ∑𝑁𝐹𝐶𝑆𝑔=1 𝑈𝑔,𝑡
𝑡=1
(6.3)
For the short run, the forecast model for PEVs presented in Chapter 3 is used to obtain (α); however, for the long run, The PEV penetration level is set to (5 – 30%) in predefined steps (stages) to cover the variety of PEV accommodation rates that will become available in the system in the future.
6.2.3 FCS average and peak demand
In order to choose the number and type of chargers for an FCS, the average daily number of PEVs serviced by the FCS as well as the peak number of PEVs arriving at the FCS has to be estimated. As discussed in Chapter 5, traffic volume data have to be involved in order to address FCS average and peak demands. The charging stations’ road assignments, the annual average daily trips (AADT) to each charging station, and the annual average trips conducted by PEVs at rush hour (λRH) to each charging
station are estimated using equations (5.1 – 5.2), as proposed in Chapter 5. The road assignment follows the shortest path technique, so each transportation node is assigned to the nearest charging station.
The λRH and AADT are key parameters for the economical staging plan for charging stations. On the one
hand, the traffic volume at rush hour is considered as the peak demand for the charging station, and λRH
plays the main role in selecting the number and type of fast chargers with regard to predefined waiting time thresholds. Hence, a higher number of PEVs served during rush hour influences the design and size of an FCS project, along with increasing its total investment cost. On the other hand, the average demand of PEVs is the main indicator for the profit feasibility of an FCS project. The project’s revenue is directly associated with the average number of PEVs served daily, so profit feasibility is increased with a higher number of PEVs served. The average number of PEVs served daily by an FCS (AADTFCS) can be
estimated using Equations (6.4 – 6.5):
𝑈(𝑔,𝑡) = ∑𝑟𝑑𝑎(𝑔,𝑟𝑑)× 𝛼 × 𝛾 × 𝐴𝐴𝐷𝑇(𝑟𝑑,𝑡) ∀ 𝑔, 𝑡 (6.4) 𝐴𝐴𝐷𝑇𝑔𝐹𝐶𝑆 = ∑24𝑡=1𝑈(𝑔,𝑡) ∀ 𝑔 (6.5)
6.2.4 Electricity prices and tariffs
FCS project owners should have clear foresight of electricity purchase prices from the electricity provider. The electricity purchase price is considered a main factor in the project running cost. The willingness of the customer to pay a markup for fast charging should be investigated, where the markup is considered as a margin over total electricity cost, including taxes and fees. Two different types of tariff are investigated: a) a flat rate; and b) a time-of-use rate (TOU). Local utilities have the option of charging different rates throughout the day, and these rates are divided into three separate bands, known as off-
peak, mid-peak and on-peak. These different bands and rates are set by local utilities that provide
electricity to FCS projects. If the local utility is not utilizing time-of-use billing, FCS projects are charged the same rate regardless of when they consume their electricity. The flat rate has two price tiers, and the price that FCS owners pay depends on how much electricity they use. In the summer, the higher price is used when they consume more than a given amount of kWh of electricity in a month. In the winter months, the higher electricity price is charged for consumption above a higher threshold of kWh. For example, Ontario’s Hydro One charges customers the following TOU rates: off – peak rate of 8.3 cents/kWh; mid – peak rate of 12.8 cents/kWh; and on – peak rate of 17.5 cents/kWh. However, Hydro One charges a flat rate in some places where the TOU is not applicable. The flat rate has two price tiers: 9.9 cents/kWh, and 11.6 cents/kWh. The price you pay depends on how much electricity you use. In the summer, the higher price is used when you consume more than 600kWh of electricity in a given month, and in the winter months, the higher electricity price is charged for consumption above 1,000 kWh.