Utility Factor Curves for Plug-in Hybrid Electric Vehicles: Beyond the Standard Assumptions
Abstract
:1. Introduction
- The gap between standard and real UF values (Figure 1a) as well as the categories of reasons 1–3 (Figure 1b) were drawn in the “negative” direction (i.e., real UF being less than the standard UF). However, this is primarily for illustrative purposes. In reality, it is plausible for any of the three categories of reasons or the overall gap to be in either the positive (i.e., better UF than the standard rating) or negative directions.
- Each of the three main categories of reasons may include several sub-reasons; for example, category #1 (real-world attained AER) could be affected by the acceleration rate and speed driving style of vehicle owners, ambient temperature (which in turn affects both the efficiency of the electric powertrain as well as the heating/cooling power consumption for climate control of the passenger cabin), weight of passengers and cargo, gradient of the terrain (uphill/downhill), or towing load.
- It is also important to note that those three categories of reasons, while understood to be the main contributors to the UF gap, are not the only contributing reasons, nor is it necessarily true that they are linearly independent. For example, some PHEV designs may utilize electric power to warm up the battery during a cold climate, while others might utilize an alternative approach such as briefly turning on the engine, which in turn might affect the observable miles traveled in CD or EV mode.
- The (real-world) attained AER is not necessarily a static number like the nominal AER that is published by regulatory agencies such as the US EPA [14]. In fact, the attained AER can change from day to day depending on the vehicle usage conditions, and such daily variations in the attained AER can have interactions with the other two categories of reasons (charging frequency and distance traveled). Nonetheless, to avoid over-complicating the problem, secondary interactions between the reasons and “all other/unknown” reasons are often lumped with one of the three main categories of reasons.
2. Mathematical Model
2.1. Notations and Assumptions
2.2. Charging Frequency Less Than Once per Drive Day
2.2.1. Overview
2.2.2. Special Case: Binary Charging Behavior
2.2.3. Special Case: All Vehicles with the Same Charging Frequency
2.2.4. Generalized Upper and Lower Bounds
2.3. Charging Frequency: More Than Once per Drive Day
2.4. Summary of Modelled Cases
3. Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Case | Discussed | Description |
---|---|---|
λi ∈ {0, 1}, μ = 0 | Section 2.2.2 | No daytime charging. Overnight charging behavior is binary; some vehicles always charge, others never charge. |
All λi = λ, 0 ≤ λ ≤ 1, μ = 0 | Section 2.2.3 | No daytime charging. The overnight charging frequency is the same for all vehicles. |
0 ≤ λi ≤ 1, μ = 0 | Section 2.2.4 | No daytime charging. Generalized case for overnight charging, where some vehicles always charge, some never charge, others somewhere in-between. |
All λi = 1, 0 ≤ μi ≤ 1 | Section 2.3 | Vehicles always charge overnight. Some vehicles also gain one additional charging event during the day. |
0 ≤ λi ≤ 1, 0 ≤ μi | Section 3, future work | Fully generalized case where overnight charging frequency for each individual vehicle can be anywhere between always and never, while at the same time, each individual vehicle may have additional one or more charging events during the day |
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Hamza, K.; Laberteaux, K.P. Utility Factor Curves for Plug-in Hybrid Electric Vehicles: Beyond the Standard Assumptions. World Electr. Veh. J. 2023, 14, 301. https://doi.org/10.3390/wevj14110301
Hamza K, Laberteaux KP. Utility Factor Curves for Plug-in Hybrid Electric Vehicles: Beyond the Standard Assumptions. World Electric Vehicle Journal. 2023; 14(11):301. https://doi.org/10.3390/wevj14110301
Chicago/Turabian StyleHamza, Karim, and Kenneth P. Laberteaux. 2023. "Utility Factor Curves for Plug-in Hybrid Electric Vehicles: Beyond the Standard Assumptions" World Electric Vehicle Journal 14, no. 11: 301. https://doi.org/10.3390/wevj14110301