1 Introduction
2 Literature Review
2.1 Charging infrastructure planning models for high-level road networks
2.2 Modeling charging activity based on spatial and temporal traffic flow dynamics
2.3 Testing implementability of planned charging infrastructure
2.4 Progress beyond state of the art:
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With this study, we contribute to the currently scarce collection of studies dedicated to the stress-testing of charging infrastructure. The current study is the first one explicitly dedicated to the application of fast-charging infrastructure along highway networks in this context. Numerous proposed methods exist for planning and expanding charging infrastructure, and the growing share of BEVs necessitates their implementation. Therefore, the implementability of a planned charging infrastructure must be validated and tested to ensure that the installed charging stations and their sizing meet the charging demand while ensuring cost-effective allocation of infrastructure investment costs.
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We develop a charging model that determines the queuing and charging activities in a given fast-charging infrastructure. The model is formulated as a linear optimization program. Vehicle fleets are modeled as continuous, swarm-like entities in this model, resulting in a coarser granularity to the representation of traveling vehicles than in agent-based models. This allows the identification of infrastructural bottlenecks at geographically wider scale.
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The focus of this study is not only identifying missing or overestimated charging infrastructure capacities, but also on determining implications for improving the fast-charging infrastructure planning. The wide range of proposed modeling approaches used in the planning of highway charging infrastructure differ in the mathematical formulation, considered input parameters, and assumptions made in their design. Given this, the question arises as to what degree of limited input information, considering traffic flow, mobility patterns, and related assumptions, still leads to a sufficient allocation of charging capacity.
3 Methodology and Materials
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The spatio-temporal charging model forms the key component of this modeling framework. The model maps charging activity at charging stations in both time and space. This is accomplished by considering the spatial and temporal dimensions of traffic load along the highway network, including origin-destination flows and mapping charging demand bottom-up. The model is formulated as a linear optimization model, with continuous, swarm-like entities representing the traveling vehicle fleet along the highway network. The objective function describes the minimization of the number of waiting vehicles at all charging stations which directly minimizes the amount of time spent waiting at charging stations during all trips conducted on the given highway network.
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One part of the input data for the optimization model is the geography of the highway network along with information on the planned charging infrastructure for this network. The required descriptors of this input are, in particular, the locations of fast-charging stations and their respective sizing, that is, the planned capacities at each charging station. Furthermore, the number of traveling BEVs between specific origin and destination points, as well as the state of charge of the vehicles at the time of entry into the highway network are part of the traffic flow data. Both these parameters are determined randomly for each highway-entering vehicle fleet to include a representation of the variability of the vehicles’ state of charge.
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The most relevant output data of the optimization model used for further analysis are the load curves describing the operation of each charging station and time series reflecting the number of vehicles waiting in the queue to charge.
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To assess the implementability of the planned charging infrastructure, this study derived key performance indicators (KPIs) from the output data of the optimization model. At all planned charging stations, three KPIs are determined: The number of waiting vehicles in a queue corresponds to the number of vehicles whose charging demand is met with a delay rather than immediately upon arrival at a charging station. While queue length aids in the identification of bottlenecks in the charging infrastructure, two technical parameters, namely, the utility rate and the difference between planned capacities and the peak power at which a charging is operated, are also introduced as KPIs. These two KPIs are intended to provide insights into the business case of a fast-charging station along a highway, and reveal planned capacities that would be rarely or never used.
3.1 Spatio-temporal charging model
3.2 Description of Austrian case study
Model parameter | Value |
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Temporal resolution \(\Delta t\) | 0.25 h |
Driving speed \(v\) | 110 km\(/\)h |
BEV share \(\epsilon\) | 30% |
BEV battery capacity \(\text{Cap}^{\text{batt}}\) | 100 kWh |
BEV charging power \(\overline{P}^{\text{charge},\text{BEV}}\) | 250 kW |
BEV specific energy consumption at low temperatures \(\overline{d}^{\text{spec, winter}}\) | 0.2 kWh\(/\)km |
BEV specific energy consumption at high temperatures \(\overline{d}^{\text{spec, summer}}\) | 0.15 kWh\(/\)km |
3.2.1 Four representative days
Representative day | Description |
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Workday in winter | – Travels prominently for the purpose of commuting and business |
– Cold temperature | |
Workday in summer | – Travels prominently for the purpose of commuting and business |
– Warm temperature | |
Holiday in winter | – Travels prominently for the purpose of leisure, increased transit traffic |
– Increased amount of transit traffic | |
– Cold temperature | |
Holiday in summer | – Travels prominently for the purpose of leisure, increased transit traffic |
– Increased amount of transit traffic | |
– Warm temperature |
3.2.2 Origin-Destination flows
3.2.3 Input fast-charging infrastructure
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For charging station allocation, existing resting areas are considered potential sites, with an upper limit on installed capacity at each.
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Charging demand is defined at each rest stop and is assumed to be the result of the energy consumption of long-distance BEV drivers traveling along the highway network. Here, annual peaks in traffic load and increased energy consumption due to cold temperatures are taken into account. The algorithm determines where charging capacity should be allocated to meet this demand.
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This is done while considering the limited range of BEVs and the geographic distribution of traffic load along the highway network.
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The allocations of origin and destination points of BEVs traveling along the highway network are ignored.
3.3 Open-source programming environment and data availability
4 Results
4.1 Identification of bottlenecks and overcapacities in planned charging infrastructure
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The objective value equals 0 during all days, implying that no queuing occurs in all observed circumstances. Therefore, all battery electric vehicles (BEVs) recharge as soon as they arrive at a charging station, and the considered fast-charging infrastructure has no bottlenecks.
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During the workday in winter, all BEV’s total amount of charged energy is the highest which is also reflected by the highest, value of the average UR (0.52). This peak in energy demand is given by the high number of long-distance BEV trips and the increased energy consumption due to the low temperature during winter. The average value for \(\Delta\hat{P}\) is here also the lowest, indicating that, on average, a charging station has 2‑3 unused charging poles7.
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The state of charge of the vehicles at arrival is slightly higher during the summer workday and holiday than during the winter. This observation is most likely due to the lower energy consumption of BEVs during the summer.
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The distributions of the utility rates UR do not vary significantly between the representative days as the median and average values vary between 0.43 and 0.56.
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There are six charging stations where none of the observed traffic load and temperature, conditions cause all charging poles to be used. During a summer vacation, the number of charging stations that are not fully utilized increases to 12.
Representative Days | ||||
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Metric | Workday in winter | Workday in summer | Holiday in winter | Holiday in summer |
Total number of long-distance trips | 294,924 | 294,924 | 208,222 | 208,222 |
Total energy consumed (GWh) | 8.7 | 6.5 | 6.2 | 4.6 |
Total energy charged by all BEVs (GWh) | 3.3 | 2.8 | 2.7 | 2.3 |
Avg. state of charge at arrival (%) | 33% | 35% | 33% | 35% |
Avg. utility rate UR | 0.52 | 0.48 | 0.47 | 0.43 |
Avg. difference between peak power and installed capacity \(\Delta\hat{P}_{c}\) in kW (nb. of not used poles) | 874 (2–3) | 1579 (4–5) | 1672 (4–5) | 2687 (7–8) |
Objective value \(\sum_{t,f,c}n^{\text{queue},t}_{f,c}\) | 0.0 | 0.0 | 0.0 | 0.0 |
4.2 Insights into infrastructure utilization
Representative days | ||||
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Workday in winter | Workday in summer | Holiday in winter | Holiday in summer | |
Charging station A | ||||
UR | 0.29 | 0.24 | 0.22 | 0.16 |
\(\Delta\hat{P}\) (kW) | ||||
(nb. of not used poles) | 154 (0–1) | 299 (0–1) | 1456 (4–5) | 6212 (14–15) |
Charging station B | ||||
UR | 0.28 | 0.24 | 0.21 | 0.16 |
\(\Delta\hat{P}\) (kW) | ||||
(nb. of not used poles) | 67 (0–1) | 1143 (3–4) | 722 (2) | 3647 (10–11) |
4.3 Sensitivity analysis: capacity reduction
Before capacity reduction | After capacity reduction | |
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Total energy charged by all BEVs (MWh) | 3337 | 3307 |
Av. state of charge at arrival of all vehicles (%) | 32.52% | 32.47% |
Av. state of charge at arrival of vehicles traveling through charging station D(%) | 31.64% | 31.61% |
Avg. utility rate UR | 0.52 | 0.53 |
Objective value \(\sum_{t,f,c}n^{\text{queue},t}_{f,c}\) | 0.0 | 0.0 |