**Electrified Powertrains for a Sustainable Mobility: Topologies, Design and Integrated Energy Management Strategies**

Editors

**Laura Tribioli Manfredi Villani**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editors* Laura Tribioli Universita degli Studi ` Niccolo' Cusano Italy

Manfredi Villani The Ohio State University USA

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Energies* (ISSN 1996-1073) (available at: https://www.mdpi.com/journal/energies/special issues/ electrified powertrains sustainable mobility).

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## **Contents**

## *Editorial* **Electrified Powertrains for a Sustainable Mobility: Topologies, Design and Integrated Energy Management Strategies**

**Laura Tribioli 1,\* and Manfredi Villani 2**

The Special Issue "Electrified Powertrains for a Sustainable Mobility: Topologies, Design and Integrated Energy Management Strategies" has been proposed with the main objective of contributing to the sustainable mobility agenda through enhanced scientific and multi-disciplinary topics, aimed at addressing concerns and real possibilities in the achievement of a greener mobility. It was therefore conceived to provide an interesting overview on new needs and investigation topics required for future developments.

In total, five articles, of which four research papers, and one review, have been submitted to the Special Issue covering a wide variety of topics within the proposed subject.

T. Donateo and A. Ficarella [1] have addressed the topic of urban air mobility with particular reference to air-taxi service. They propose a methodology for the design and energy analysis of conventional, hybrid-electric, and full-electric power systems for such application. The novelty of the paper with respect to the state of the art lies in the detailed modeling approach of the powertrains, the evaluation of CO2 emissions with a well-to-wing approach as a function of the electricity emission intensity factor and the comparison with road vehicles performing the same route in different driving conditions. The results demonstrate the advantages of an all-electric air-taxi with respect to a hybrid electric road taxi.

S. Lombardi et al [2] have tried to tackle the problem of reducing the energy consumption of the cooling circuit for the propulsion system of an all-electric road vehicle through two different approaches: optimization of the control strategy and improvement of the powertrain efficiency. In the first approach, a control strategy to reduce the auxiliary loads of the fan and the pump has been developed and compared with the conventional approach, where the pump and the fan are controlled with a thermostat, while in the second approach a single-motor powertrain has been replaced by smaller traction modules whose powers sum up to the total power of the original powertrain. The study has shown that increasing the powertrain efficiency leads up to a 54% reduction of energy consumption (but only if the cooling circuit is stressed enough and the fan is activated during the vehicle operation). While the optimization of the control strategy can lead up to a 27% energy consumption reduction if normally the cooling circuit is capable of lowering the coolant temperature without the intervention of the fan.

I. Komorska et al. [3] have proposed an algorithm which, by means of the segmentation and iterative synthesis procedures of Markov chains, returns an adaptive energy-efficient driving cycle for a road vehicle under a given route. Moreover, a Gaussian process regression is employed to monitor energy consumption during driving, so as to correct adaptively speed and acceleration in order to maintain the planned energy consumption. An autopilot driving cycle was verified in the study, and results showed that the energy consumption was reduced by approximately 15%, at the cost of increasing travel time by approximately 10%.

Q. Bi et al. [4] worked on a similar topic, but applied to cable shovels for robotic excavation. In particular, a two-phase multi-objective genetic algorithm was established for optimal digging trajectory planning for achieving effective and energy-saving operation.

**Citation:** Tribioli, L.; Villani, M. Electrified Powertrains for a Sustainable Mobility: Topologies, Design and Integrated Energy Management Strategies. *Energies* **2022**, *15*, 3095. https://doi.org/ 10.3390/en15093095

Received: 13 April 2022 Accepted: 19 April 2022 Published: 23 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The results of the optimization under different digging conditions indicated that the digging time could be decreased from an average of 20 s to 10 s, and the energy consumption per payload could be reduced by 13.28%.

Finally, D. Beltrami et al. [5] have proposed a detailed overview on the state of the art and future trends in the electrification of compact off-highway vehicles, which can be an excellent application for boosting the electrification process, mainly because they are usually more suited for zero-emission tasks, while development costs can be more easily minimized. The paper has allowed for the highlighting of the key differences between on-highway and off-highway vehicles and provides a comprehensive summary of information on the multiple solutions investigated by researchers and currently implemented by manufacturers.

Even if the theme of sustainable mobility is very wide and still entails a lot of work, we believe that this Special Issue can give a small and yet important contribution to stimulate the debate between industry and academic researchers, thanks to the variegated topics of the received articles that cover important aspects related to the full spectrum of sustainable mobility, spanning from air mobility to off-road vehicles.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **A Methodology for the Comparative Analysis of Hybrid Electric and All-Electric Power Systems for Urban Air Mobility**

**Teresa Donateo \* and Antonio Ficarella**

Department of Engineering for Innovation, The University of Salento, via per Monteroni, 73100 Lecce, Italy<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** The present investigation addresses the topic of Urban Air Mobility with particular reference to the air-taxi service with electrified power systems. A new and detailed methodology is proposed for the simplified design and energy analysis of conventional, hybrid-electric, and fullelectric power systems for this application. The original contributions to the scientific literature on UAM are the detailed modeling approach, the evaluation of CO2 emissions with a Well-to-Wing approach as a function of the electricity Emission Intensity factor, and the comparison with road vehicles performing the same route in different driving conditions. The comparison demonstrates the advantages of a full electric air-taxi with today's technology versus a hybrid-electric road taxi, especially in cases involving low emission intensity and unfavorable driving conditions (congested traffic, aggressive driving style, and high circuity factor values). In the case of 2035 technology, the comparison with a referenced fully electric road vehicle is detrimental to the air taxi but the values of Well-to-Wheel/Wing CO2 with the expected Emission Intensity of 90 g/kWe for the European Union are still quite low (67 g/km). The investigation also quantifies the negative effect of battery aging on the consumption of the air taxi and on the number of consecutive flights that can be performed without fully charging the battery.

**Keywords:** urban air mobility; WTW emissions; hybrid electric vehicles; battery aging

#### **1. Introduction**

According to Angel et al. [1], the number of people living in cities keeps growing and is expected to double from 2011 to 2054. This increase in the mobility requirement is leading to the need for faster, cheaper, safer, and cleaner forms of transportation [2], not only to avoid the depletion of fossil energy sources but above all to preserve the environment. Transportation accounts for around one-fifth of today's global carbon dioxide (CO2) emissions [3]. Road travel accounts for three-quarters of them, while the contribution of aviation to transport-associated emissions is 11.6%. Increasing the efficiency of the utilization of energy in transport systems, speeding up the deployment of sustainable energy sources, and enhancing zero-emission vehicles are the main actions that have been proposed to reduce the environmental impact of transportation [3] and fulfill future mobility requests.

In the last few years, many companies have developed delivery and taxi services conceived to work in the air. These new services are denoted as Urban Air Mobility (UAM) and Urban Air Delivery. This investigation focuses on Urban Air Mobility and, in particular, on the air-taxi service. In this field, several companies have developed electric vertical take-off and landing (eVTOL) aircraft over the past few years. However, there are still many open issues such as the lack of infrastructure, the need to ensure safety (in particular avoiding collisions during the mission), and the development of suitable air-traffic management systems [4–6].

UAM is an appealing application for electric power systems thanks to its short-range and limited speed requirements that make full electric powertrains possible, even with

3

**Citation:** Donateo, T.; Ficarella, A. A Methodology for the Comparative Analysis of Hybrid Electric and All-Electric Power Systems for Urban Air Mobility. *Energies* **2022**, *15*, 638. https://doi.org/10.3390/en15020638

Academic Editors: Laura Tribioli, Manfredi Villani and Tek Tjing Lie

Received: 10 December 2021 Accepted: 13 January 2022 Published: 17 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

today's batteries (i.e., despite their moderate values of energy density and power density, which are the major bottlenecks for larger aircraft). For longer distances, hybrid-electric concepts can be considered to provide the necessary range while guaranteeing silent and environmentally friendly transport systems. To ensure the success of electric and hybrid-electric air taxis, an extensive charging infrastructure powered by clean energy sources is needed as well as the availability of a large number of take-off and landing facilities [7]. Moreover, ad hoc flight mechanics analysis tools and design techniques need to be developed to tackle the challenge of sizing and management of hybrid and fully electric aircraft. In fact, the analysis of the energy request of this kind of vehicle and their environmental impact is a hot topic still in need of further research efforts, as proved by the limited works in this topic, such as the recent studies on Urban Air Delivery [8–10] and UAM [11–14].

Uber [11] performed a comparison between a traditional road vehicle and a VTOL one in terms of time spent, distance covered, and costs without considering the environmental impact. As pointed out in [12], the sustainability of air-taxi services is unclear because of the high energy requirement of this kind of vehicle, above all for take-off and climb. A comprehensive review of the research on UAM is presented in [15], where the development of more refined and high-fidelity models is suggested as one of the potential research directions in this field. This work also points out the importance of taking into account the largest safety allowed by the hybrid-electric power systems in rotorcraft thanks to the possibility of performing safe descents after an engine/motor failure.

The authors of [14], proposed a comparison of the Greenhouse Gas (GHG) emissions of a VTOL over a distance of 100 km versus ground-based passenger cars and, in particular, a conventional internal combustion engine vehicle and a battery-electric vehicle. However, this work performs a simplified analysis: the part-load efficiency of the powertrain and the large variability of energy consumption of a road vehicle due to the effect of the traffic conditions are not taken into account. The different effects of traffic conditions and weather on the travel time of road and aerial vehicles are addressed in [12] where it is also pointed out that the travel time of a VTOL is much more predictable than that of a road vehicle.

A similar but more detailed analysis is performed in [16], in which the authors developed a model to quantify trip emissions using UAM and compared them with automotivebased trips. The authors of this study consider gasoline and electric vehicles as automotive technology and calculate the emissions associated with electricity production using the emission factor of the metropolitan area of Chicago and Dallas. Moreover, this work proposes the detour ratio (defined as the distance saved or gained by using an aerial vehicle instead of a road vehicle driving the same route) as a metric to compare air and road transportation while the circuity factor (the ratio of the shortest road route to the Euclidian distance) is proposed in [12] to compare air and road vehicles.

The present work differs from [12,16] in the following aspects that constitute its novel contribution to the scientific literature on UAM:

A more complete analysis of the environmental impact of road and air vehicles should be performed at the cradle-to-grave emissions level [16], i.e., taking into account all processes from the extraction to the discarding of materials (thus including production, operation, and disposal phases). However, this is beyond the scope of this investigation.

After this first introductory section, the present paper is organized as follows. The second section depicts the simplified sizing of the aerial vehicles and their specification. The third part describes the proposed detailed methodology for the energy analysis of aerial vehicles. Then, the road vehicles used for the comparison are presented and the procedure for the evaluation of the environmental impact is explained in session 5. Finally, the results for today and 2035 technologies are discussed, and the conclusions are drawn.

#### **2. Simplified Sizing of the Air-Taxis**

A hypothetical four-passenger vertical take-off and landing (VTOL) rotorcraft with co-axial rotors is considered as air taxi architecture. This is in line with the works proposed in the literature; see, for example [12,17], in which electric VTOL vehicles with four to five occupants are considered for UAM.

In this work, three different power systems are proposed and compared: conventional (turboshaft-based powertrain), full electric (Lithium-ion battery and permanent magnet motors), and parallel hybrid electric (combining the previous technologies). The evaluation of the air-taxi mass in the three cases is not a trivial issue and depends on the present-day and future values for specific power and density of the main components [18–25]. The goal of the investigation is to propose a methodology for the energy analysis of a complex power system for UAM, not to analyze a particular technology. However, it is interesting to point out the strong expected improvement in the components of an electrified power system and to show how this affects the results of the proposed methodology. For this reason, the data retrieved in the scientific literature for today and future (2035) technologies (Table 1) were assumed for the turboshaft engines, the electric machines (and their inverter), and the battery. The potential different contribution of the gearbox to the weight of the proposed powertrains is neglected for simplicity.

**Table 1.** Current and future values of specific power and energy densities ([19,25]).

It is important to mention the relation between battery power density and energy density. The values of Table 1 are related to batteries optimized for energy density (this is the normal choice for a fully electric system), but the design of a Lithium-ion battery can be aimed at optimizing the power density at the expense of energy density or vice versa [26]. The power density of a battery mainly depends on its *Crate*, i.e., the maximum current at which the battery can be discharged, termed as a multiple of the battery nominal capacity [26]. In fact, the nominal continuous power (*Pbatt*,*nom*) of a Lithium-ion battery in discharge can be expressed as:

$$P\_{batt,nom} = \mathbb{C}\_{rate} \cdot \mathbb{C}\_{nom} \cdot \text{Ns} \cdot V\_{cell} \tag{1}$$

where *Cnom* is the nominal capacity (in Ah), *Vcell* is the nominal voltage of a Lithium-ion cell (3.6 V), and *Ns* is the number of cells in the series. Assuming a nominal voltage of 270 V for the battery pack (*Ns* · *Vcell*), as suggested by Bérubé et al. [20], it is easy to verify that the values in Table 1 refer to a battery with a continuous *Crate*, ranging between 3 and 4, but higher values of the *Crate* can be obtained even with today's technology [21] and without significantly penalizing the energy density. It should also be noted that, for a short interval of time compatible with the duration of the take-off (about 30 s), the battery can be operated at a current higher than *Crate* which is named burst *Crate* and is generally equal to 2*Crate* [24,26].

To obtain realistic specifications for the UAM powertrains, the following procedure is proposed here for fast preliminary sizing:

The iteration is terminated when the convergence on the empty mass is reached.

The take-off power is calculated as suggested in the literature [12,16] for VTOL vehicles by using the formula for the power request in hover:

$$P\_{hover} = \frac{M\mathcal{g}}{\eta\_P} \sqrt{\frac{\delta}{2\rho\_d}}\tag{2}$$

where *δ* is the disk loading and *ρa* is the sea-level air density (1.22 kg/m3), g is the gravity acceleration. For all the powertrains, a value of 0.85 was assumed for the propulsive efficiency [16] and the disk loading was set to 380 Nm−2 [16,27].

The results of the procedure are shown in Figure 1, Tables 2 and 3 in terms of final take-off mass and powertrain specifications.

**Figure 1.** Estimated take-off mass (in kg) of the proposed powertrain for the aerial taxi. (**a**) Today's technology; (**b**) 2035 technology.

**Table 2.** Specification of today's powertrains.

**Table 3.** Specification of the 2035 powertrains.

Regarding the take-off mass (Figure 1) the largest contribution of the powertrain to the take-off weight is associated with the battery, especially in the case of today's technology and fully electric aerial vehicles. It should also be noted that, at constant mass, the 2035 technology allows a designer to shift from conventional to hybrid (with about 1350 kg) and from hybrid to electric (accepting a take-off weight of about 1850 kg).

Regarding the installed power, in the conventional case, we considered a twin-engine configuration to allow safety in case of failure. The size of 295 kW (400 HP) was chosen according to the specification of the Hill GT500 engine [22]. Since it is difficult to scale down a turboshaft engine, the same nominal power was also considered for the 2035 technology. For the motors, we opted for modules of 120 kW since more powerful electric machines for aerospace applications are still under development [23]. The number of modules (*NEM*) was chosen so that the take-off could be performed with (*NEM* − 1) motors. The size of the battery was set equal to 35 and 140 kW for the hybrid and the full-electric case, respectively, based on the experience of the authors and with a trial-and-error procedure on the mission analysis described later in the paper.

For the hybrid electric taxi, take-off can be performed in thermal, electric, or power-assist modes. Since it is also necessary to guarantee that the battery can feed the motors in case of electric take-off, the minimum continuous *Crate* required for the battery in the different cases was estimated and entered in Tables 2 and 4. Based on the previous discussion about the typical continuous and burst *Crate* of today's battery, we can conclude that the battery is able to guarantee an electric take-off in all cases reported in Tables 2 and 3.

**Table 4.** Other specifications of the air taxis ([14,16]).

As a partial validation of the sizing procedure, it is possible to notice that the take-off mass obtained for the 2035 electric air taxis is very close to the value of 4000 lbs assumed in [11] for a UAV powered by a battery with 400 kWh/kg. However, the goal of this first step was not to propose a detailed sizing methodology but to obtain reasonable values for the take-off weights of the three powertrains to allow a fair comparison in terms of energy and power request.

#### **3. Proposed Methodology for the Air-Taxi**

Once the powertrain was defined, the energy and fuel consumptions were calculated with the procedure here explained and illustrated in Appendix A (Figure A1) for the hybrid propulsion system. Note that the fully electric and conventional powertrains can be considered as particular cases of this complex power system.

The simulations proposed in this investigation were performed with a quasi-static approach. Each mission was divided into intervals of time length *h* and, at any time step, the components of the power system were assumed to work in stationary conditions even if the working point was different at each time step. Such an approach is generally accepted in the minimization of fuel consumption in complex powertrains [26] because it allows the design of a supervisory controller to optimize the power flows in the propulsion system with a small computational effort. However, this approach requires the mission to be known a priori and is not able to handle feedback control problems or to take into account the dynamic response of the energy converters to a variable power request that affects the shaft dynamic in a rotorcraft or the dynamic behavior of the fuel valve [28]. A dynamic model of the whole power system, including the twin rotors, is currently being implemented by some of the authors of this investigation and preliminary results can be found in [29]. Note that a dynamic approach would be able to take into account other factors, such as the effect of temperature on each component of the power system, that are neglected in this investigation.

#### *3.1. The Route (Start and Final Points)*

The vehicles are supposed to perform the same hypothetical route which corresponds to a total straight-line or Euclidean distance of 70 km. When comparing air-taxi and groundbased transportation systems, it is necessary to take into account the circuity factor, i.e., the ratio between actual road travel distance and coordinate-calculated Euclidean distance. A circuity factor of 1.2 is considered in [30] for the comparison between air and road vehicles. However, this value is strongly variable from country to country, as pointed out in [18] where an average circuity factor of 1.46 is reported for Europe.

It is important to point out that the trip time of the road taxi is strongly affected by driving style, weather, and traffic conditions. Headwinds or tailwinds, on the other hand, do not change the true airspeed (TAS) of the aerial vehicle even if they affect the groundspeed. However, frequent back and forth along a given air-taxi route would likely balance these changes [12].

#### *3.2. Mission Profile and Flight Dynamics*

Based on the white paper of Uber [11], a typical mission was considered, consisting of take-off, climb, cruise, descent, and landing. The proposed mission was characterized by a cruise altitude of 458.6 m and a cruise speed of 67 m/s (150 mph); as suggested in [11,27] the *ROC* (Rate of Climb) and *ROD* (Rate of Descent) were assumed equal to 2.54 m/s (500 ft/min) in the present investigation.

The shaft power request vs. time was estimated using literature methods and data ([16,27]). For the vertical take-off and landing, the power request was calculated as in Equation (2).

At cruise conditions:

$$P\_{cruise} = \frac{M\mathcal{g}}{L/D} \frac{V}{\eta\_p} \tag{3}$$

For climb and descent:

$$P\_{climb} = \frac{M\text{g}}{\eta\_P} \left( R\text{OC} + \frac{V}{\frac{L}{D}} \right) \tag{4}$$

$$P\_{\text{descent}} = \frac{M\text{g}}{\eta\_p} \left( ROD + \frac{V}{\frac{L}{D}}\right) \tag{5}$$

In these equations, *M* is the take-off mass of the vehicle and *V* is the true airspeed. The values of the propulsive efficiency *ηp* used in this investigation are reported in Table 2. The powertrain efficiency is included in the denominator of these formulas in the approach proposed in [16], while in the present investigation, *ηp* in Equations (2)–(5) is only the propulsive efficiency (i.e., the efficiency of the rotor) while the powertrain efficiency is calculated with the detailed model explained below.

It is also necessary to point out that in the conventional and hybrid-electric powertrains, the mass of the vehicle decreases in time due to the consumption of fuel. Even if this effect can be easily implemented in the proposed procedure, it is not considered here because the amount of fuel consumed in the reference mission was much smaller than the take-off mass of the vehicle, as shown later. Note that the total power requirements for VTOL flight include the additional power drawn from auxiliary systems such as avionics or passenger comforts (heating/cooling, phone charging, radio, etc.). As suggested in [16], these contributions are neglected in this investigation.

The time histories of the shaft power request for the three powertrains (according to their different masses) are reported in Figure 2.

**Figure 2.** Power request of the three configurations with current and 2035 technology.

#### *3.3. Simulation of the Energy Flows*

The missions of Figure 2 were discretized with a time step of 1 s. At each time step, the required shaft power was used as input to the detailed model of the power system.

In the conventional case, the power shaft request is fulfilled by the engine. In the electric case, it is fully developed by the electric machines. For the hybrid electric powertrain, an appropriate energy management strategy must be defined because it can be operated in four different modes:

Note that the on-flight charge mode was not implemented in this work because it was found to be of little utility in the case of air vehicles [31]. All the other modes can be obtained with a specific value of the control parameter *u*, which is defined here as:

$$u(h) = \frac{P\_{EM}(h)}{P\_{EM, \text{now}}}, \text{with } 0 \le u \le 1 \tag{6}$$

where *PEM*,*nom* is the nominal power of the electric machine, and *PEM*(*h*) is the contribution of the electric machine at time step *h*. Therefore, the power to be delivered by the thermal engine, *Pice*(*h*), is:

$$P\_{ice}(h) = P\_{shaft}(h) - P\_{EM}(h) \tag{7}$$

Note that the denominator in the expression of the control variable *u*, Equation (6), should be the minimum between the nominal power of the electric motors and the available battery power. However, it has been already verified that the battery can satisfy the take-off power with reasonable values of the *Crate*. Similarly, *Pice*(*h*) should be compared with the maximum power of the engine at the flight altitude *z*(*h*) to ensure that the engine is able, at any moment, to satisfy the request. Since the engine is quite oversized (see Tables 2 and 4) and the other phases of the flight require much less power than take-off and landing (see Figure 2), this constraint is easily met.

In the authors' previous investigation [31], the ECMS (equivalent consumption minimization strategy) was proposed for a similar application to calculate the optimal *u*(*h*). The Equivalent Consumption Minimization Strategy [26] considers the battery as an auxiliary fuel tank and converts its electrical energy into virtual fuel consumption. The virtual and actual fuel flow rates are combined to obtain the instantaneous equivalent fuel consumption in the following way:

$$\min(\dot{m}\_{eq}) = \dot{m\_f}(h) + f\_{eq} \cdot P\_{batt}(h) \cdot f\_p(h) \tag{8}$$

where the equivalence factor *feq* converts the battery power to a virtual fuel flow rate. The virtual fuel flow rate can be either positive or negative according to the sign of the battery power (battery charged or discharged). Thus, the equivalent fuel consumption can be higher or lower than the actual fuel consumption in the ECMS original strategy. The penalty factor *fp* is a correction that accounts for the divergence of the current SOC from the (constant) desired value of the battery state of charge (*SOCref*). In this investigation, the penalty factor *fp* is calculated according to the deviation of SOC at timestep *h* from a reference curve *SOCref*(*h*):

$$\mathbf{x}(h) = \frac{\text{SOC}(h) - \text{SOC}\_{ref}(h)}{\text{SOC}\_{ref}(h)} \tag{9}$$

$$f\_p(h) = (1 + |\mathbf{x}|)^p \tag{10}$$

The optimal values of *feq* and *p* were obtained in a previous work [31].

According to the results of [31], we selected a reference SOC curve that decreases linearly over time, except in cruise where it is kept constant (the battery is not used).

During each simulation run with the proposed strategy, local optimization was performed at each time step *h* of the mission, by considering all the values of *u* ranging between 0 and 1 with a step of 0.1 and choosing the value of *u* corresponding to the minimum of . *meq*. In other words, an enumerative optimization technique was used. However, other

local search methods could have been used when the strategy was applied online in the UAM vehicle.

The ECMS has the main goal of minimizing fuel consumption during the mission. However other targets can be considered specifically for air-taxi operation. For this reason, we propose in this investigation a simple rule-based strategy aimed at reducing the environmental and acoustic impact of the hybrid-electric configuration during take-off and landing. To this scope, take-off and landing are performed in electric mode and cruise in thermal mode. The climb phase is performed in power assist mode (with *u* = 1) until the SOC reaches a threshold value (90%) to obtain the desired *SOCref* curve. The other phases of the flight are performed in thermal mode.

#### *3.4. Total Fuel Burn in the Mission* (*Mf)*

The total fuel burn is calculated starting from the *Pice*(*h*) of the turboshaft engine with a simple empirical model, developed in a previous investigation [31]. The specific fuel consumption *SFC*(*h*) at each time step is estimated as:

$$\frac{SFC(h)}{SFC\_0} = \left(\frac{Pice(h)}{Pice,nom}\right)^{b2} (z\_1 Z(h) + z\_0)(m\_2 M + m\_1 M + m\_0) + b1\tag{11}$$

where *Z* is the altitude (in meters) and *M* is the Mach number (note that this effect is negligible for this application). *Pice*, *nom*, and *SFC*0 are the shaft power and the specific fuel consumption of the engine at its design point, respectively. This equation contains seven parameters (*b*1, *b*2, *m*0, *m*1, *m*2, *z*0, *z*1) whose values were fitted in [31] by comparison with a detailed model of the engine.

The fuel flow rate is calculated as *mf* . (*h*) = *SFC*(*h*, *j*)·*Pice*(*h*). By numerically integrating *mf* . (*h*), the total fuel burn *Mf* is obtained for the conventional and hybrid electric power system.

#### *3.5. Electric Consumption of the Mission Etot*

The power contribution of the electric machines is used as input to calculate the electricity consumption. Each electric machine (inclusive of the driver) is modeled with a simple Willans line as proposed by [26] so that the battery current can be expressed as:

$$P\_{\rm hatt}(h) = \frac{P\_{\rm EM}(h) + P\_0}{e} \tag{12}$$

where *e* is the intrinsic efficiency of the electrical-to-mechanical energy conversion process and *P*0 accounts for the losses taking place after the energy conversion (friction, heat losses, etc.). In this investigation, we assumed *e* = 0.9 and *P*0 = 1.4 kW as reported in [26] for permanent magnet machines.

The battery is simulated with an electric equivalent circuit [26]. The Open-Circuit Voltage *OCV* is a function of the battery state of charge, while the internal resistance *R* is considered independent of the SOC but related to the specification of the battery and varying along with the battery life. Therefore, the battery current is calculated by solving the following equation:

$$P\_{batt}(h) = \left[ OCV(h) - R(t) \cdot I(h) \right] \cdot I(h) \tag{13}$$

By integrating the battery power, the total electric consumption of the mission *Etot* is obtained for the hybrid electric and full electric power systems.

The battery is also affected by the Peukert effect, i.e., the battery's actual capacity decreases when the discharge power is increased. To take into account this phenomenon, the effective current *Ieff* is calculated as:

$$I\_{eff}(h) = I(h) \cdot \left(\frac{I(h)}{I\_{\text{nom}}}\right)^{n-1} \tag{14}$$

where *n* is the Peukert coefficient, *Inom* is the current at which the nominal capacity of the battery is obtained.

Using the effective current, the state of charge is upgraded, at any time during the mission, as:

$$SOC(h) = SOC\_{in} - 100 \cdot \sum\_{1}^{N} \frac{I\_{eff}(t)}{\mathcal{C}} \tag{15}$$

where *SOCin* is the battery state of charge at the beginning of the mission. The Depth of Discharge (DOD) is calculated as the change between the initial and final SOC of the battery in each mission.

With this modeling approach, it is possible to take into account the increase in battery current at constant power due to the reduction in the SOC which, in turn, determines a reduction in the OCV. Another important characteristic of the proposed battery model is that the values of capacity, internal resistance, and Peukert coefficient are updated with the battery state of health. In particular, the values of these parameters at the beginning and the end of the battery life are shown in Table 5. For more details about the aging model, please refer to [32].

**Table 5.** Values assumed for the battery parameters.

The end of life for a vehicle drive battery is defined as the time when either the battery energy capacity or its available power (which is inversely proportional to the internal resistance) drop below a specified minimum, which is usually set equal to 80% of the initial value [33]. The time at which this condition is reached is the minimum between the cycle life (degradation due to repeated charge–discharge cycling) and the calendar life (degradation over time). Calendar and cycle life are affected by the battery operation, and in particular operating temperature, DOD, and charge/discharge current [34]. The dependence on DOD can be found in the datasheet provided by the battery manufacturer or estimated with the models proposed in the scientific literature (see for example [35,36]).

#### **4. Reference Road Vehicles**

The emissions of CO2 of the different powertrains for air taxi will be compared with those of a road vehicle performing the same mission. Recently, the European Commission revised the Regulation setting CO2 emission standards for cars and light commercial vehicles, reducing the target value by 37.5% in 2030 compared to the 2021 limit of 95 g CO2/km. However, this value refers to the whole fleet and only the Tank-to-Wheel emissions are considered. For a more detailed comparison, reference road vehicles are used in this investigation.

The vehicle used as an example of today's road technology is a well-known series/parallel hybrid electric vehicle, the Toyota Prius. The reason for the choice of this car is twofold: it is one of the most common vehicles used as a road taxi and is the most-studied hybrid electric vehicle (see, for example [37]). The Prius non-plug-in vehicle has a curb mass of 1470 kg and a declared fuel consumption of 4.8 L/km over the New European Driving Cycle. However, tests performed on the same vehicle [38] revealed that the fuel consumption (FC) of the Prius can range between 3 and 6 L/100 km on regulatory cycles (depending also on the version of the vehicle) while a still higher variability is obtained in real driving conditions [39] where the fuel consumption can be as high as 14.8 L/100 km in case of urban routes and aggressive driving styles. Note that the curb mass of the Toyota Prius is 1350 kg. By adding the same payload of the aerial vehicle (360 kg), a mass of

1710 kg is obtained, a value not much different than that of the hybrid electric air taxi with today's technology.

The fully electric Nissan Leaf was chosen as exemplative of 2035 road taxi because it is one of the most-studied electric vehicles and was also proposed for road-taxi services [40]. The Nissan Leaf has a range of 200 km and a nominal electric consumption of 0.17 kWh/km [41]. The expected improvement in technology for this kind of vehicle in 2035 is difficult to evaluate. For simplicity, we will assume that the expected increased energy density will allow the usage of a larger battery with the same mass. This will translate into a strong increase in range that will enhance the usage of vehicles as taxi service, but the energy consumption will be quite unchanged. Note that the electricity consumption must be corrected with the circuity factor, as in the case of the Toyota Prius, before performing the comparison with the aerial taxi. Moreover, the effects of traffic conditions and driving style are also to be considered [42]. For the Nissan Leaf, the study in [43] reports a value of 0.24 kWh/km in real driving conditions.

#### **5. Environmental Impact**

To compare the different vehicles from an environmental point of view, a Well-To-Wheel/Wing approach is considered, i.e., the greenhouse emissions are calculated considering the whole process from the primary energy source (e.g., crude oil) to the final energy to the wheels/wings. Moreover, they are normalized to the Euclidean distance between the initial and final places of the mission. To this scope, for gasoline and kerosene, it is possible to assume 3.15 kgCO2/kgfuel for the Tank-to-Wheel conversion, and 0.55 kgCO2/kgfuel for the WTT. In other words, the WTT emissions account for 15% of the WTW contribution [44]. The grams of CO2 per km of Euclidean distance (*ED*) of the aerial vehicle are calculated as:

$$\text{CO}\_{2\prime}\text{ thermal}, \text{axial} = \frac{\text{3.7M}\_f}{1000 \cdot ED} \tag{16}$$

where *Mf* is expressed in kg and *ED* in km.

To account for the circuity factor, the WTW emissions of CO2 of the Toyota Prius per km of Euclidean distance are calculated as:

$$\text{CO}\_2, \text{thermal}, \text{road} = 10 \cdot \text{FC} \cdot \text{p}\_{\text{gasoline}} \cdot \text{CF} \cdot 3.7 \tag{17}$$

where *FC* is the fuel consumption in l/100 km, ρgasoline = 0.755 kg/L, CF is the circuity factor, and 3.7 kgCO2/kgfuel is the WTW emission factor gasoline.

The contribution associated with the electricity for the aerial vehicles is linearly proportional to the amount of electricity released by the battery (*Etot*). To account for the losses in the grid and at the charging station, an overall efficiency *ηcharge* is introduced and its value is set to 80% [45]:

$$\text{CO}\_{2\prime}\text{ }\text{left, }\,\,aeral = EI \cdot \frac{E\_{\text{tot}}}{\eta\_{\text{charge}}ED} \,\,\,\,\tag{18}$$

where *EI* is the Emission Intensity factor in g/kWh for the production of electricity.

The Toyota Prius considered in this work is not a plug-in vehicle, therefore there was no electric consumption associated with the mission and the battery was continuously charged and discharged thanks to the presence of the engine (charge-sustaining strategy). For the Nissan Leaf, the electric consumption per km was corrected to take to account the circuity factor. The same values of *EI* and charge efficiency of the aerial vehicle are used in this case:

$$\text{CO}\_{2}, \text{ leec, } road = EI \cdot \text{CF} \cdot \frac{EC}{100 \cdot \eta\_{charge}} \tag{19}$$

where *EC* is the electric consumption expressed in kWh/100 km.

For the emission intensity factor *EI*, a sensitivity study was conducted. In fact, even if electricity generation from renewable sources has significantly increased in the last years, most of the electric energy is currently produced from fossil fuels [46,47].

According to the European Energy Agency (EEA [48]), the greenhouse Emission Intensity for EU in 2019 is, on average, 275.0 g CO2/kWh with a maximum of 891 g CO2/kWh for Estonia and a minimum of 8 g CO2/kWh for Sweden as shown in Figure 3a, where the value for Italy is also shown. However, the greenhouse emission intensity is expected to be reduced significantly in the next future. In this investigation, we will consider the average value of 90 g CO2eq/kWh as the projected value in 2035.

**Figure 3.** Past, present, and future emission intensity of European countries (elaboration of data from www.eea.europa.eu (accessed on 22 August 2021)). (**a**) Greenhouse Emission intensity in Europe (2019); (**b**) the trend of Greenhouse Emissions intensity vs. years (average value for EU 28 countries).

#### **6. Results**

The overall results of the proposed methodology are shown in Table 6 in terms of burn fuel *Mf* , electric consumption *Etot*, and battery DOD for the proposed configurations. Note that with today's technology, the overall energy consumption of the air taxi is very high for all the configurations but in particular for the full electric because of its very large mass.

**Table 6.** Burn fuel, electricity consumption, and battery DOD for the air taxi.

Starting from conventional powertrains, we can see that with current and 2035 technology the fuel consumption is 34.1 and 23.1 kg/100 km, respectively. Such levels of consumption are very high when compared with those typical of the Toyota Prius.

For the hybrid solution, the consumption strongly depends on the energy management strategy because of the different power distribution, as shown in Figure 4.

**Figure 4.** Power distribution, consumption, and efficiency time histories for the hybrid electric taxi with 2035 technology. (**a**) ECMS; (**b**) rule-based.

The ECMS strategy guarantees the best fuel economy because it allows the battery to be discharged up to the desired threshold of 60% at the end of the mission (for backup operation). With 2035 technology, the fuel consumption in the case of rule-based strategy is 38% higher than that obtained with the ECMS while the electric consumption is 46.6% lower. The higher fuel consumption obtained with the rule-based strategy is mainly associated with the lower usage of the battery. However, the rule-based strategy guarantees a reduction i emissions at the road level because take-off, landing, and part of the climb are performed in electric mode (see Figure 4). Moreover, the lower DOD obtained with this strategy is advantageous in terms of both battery life and charging time between two

consecutive flights. The bottom plots of Figure 4 show the efficiency curves of the motor and the engine in the two cases.

In the case of ECMS, engine efficiency is strongly dependent on the flight phases, like in a conventional aircraft. With the rule-based strategy, the engine is used only for cruise and part of the climb and is, therefore, quite oversized. This makes the engine work with an efficiency lower than 15% in the cruise phase. From a thermal efficiency point of view, it would be useful to choose a smaller engine or to select a different kind of thermal converter such as, for example, a piston engine. However, a smaller engine would not be able to perform take-off and landing in case of failure of the electric drive.

As for the electric powertrain, today's technology with the proposed size of the battery is not suitable for the mission considered in this study. In fact, the DOD is very high, and the electric consumption is 1.84 kWe/km. The very high DOD is not only detrimental to the battery life and charge time but also does not allow reserve hover time. Note that at the moment there is no official regulation from aviation authorities about the reserve energy of the battery [12].

In the case of 2035 technology the electric consumption is reduced to 0.58 kWe/km, which is still much higher than the value registered for the Nissan Leaf vehicle in the worst conditions (0.24 kWe/km). A smaller DOD could be obtained by choosing a larger battery. However, this would significantly increase the take-off weight of the fully electric vehicle according to the sizing procedure described in Section 2.

#### *6.1. WTW Analysis with Today Technology*

Figure 5 shows the WTW emissions of the air-taxi configurations with today's technology as a function of the Emission Intensity of electricity production. For simplicity, only the results with the rule-based strategy are reported for the hybrid electric vehicle. The best and worst cases related to the road taxi (Toyota Prius) were obtained with the following procedure.

**Figure 5.** Comparison of WTW emissions of CO2 per km of Euclidean distance with today technology.

The circuity factor was increased from 1.1–2.1 [30] and Equation (17) was applied with the two values of fuel consumption (3 and 14.8 L/100 km) representative of the best and worst conditions of traffic and driving style for the Toyota Prius to obtain the plot of Figure 6. In the same plot, it was demonstrated that the WTW emissions of CO2 per km of Euclidean distance ranged in the interval 92–868 g/kmED. These are the values reported in Figure 5 as best and worst cases for the road vehicle.

**Figure 6.** Equivalent WTW emissions of CO2 of the Prius as a function of circuity factor, traffic conditions, and driving style.

From the curve of Figure 5, we can notice that the air taxi with conventional or hybrid electric power systems generates levels of WTW emissions per km much higher than the road vehicles, even in the worst case. For the hybrid electric powertrain, the Emission Intensity of the electricity production has a weak effect on the overall values. The emissions of the full-electric air taxi are below those of the road vehicle under the best and worst driving conditions if the EI is below 40 and 360 g/kWe, respectively.

#### *6.2. WTW Analysis with 2035 Technology*

The final comparison with 2035 technology is shown in Figure 7. For the Nissan Leaf (road taxi) the best and worst cases were calculated with the following values: 24 kWh/100 km and a circuity factor of 2.1 as the worst case, 17 kWh/100 km and CF = 1.1 as the best case.

**Figure 7.** Comparison of WTW emissions of CO2 per km of Euclidean distance with 2035 technology.

Even in the worst conditions, the electric road taxi is advantageous over the air taxi in terms of overall WTW emissions of CO2 per kmED.

The WTW emissions with the expected Emission Intensity of 90 g/kWe for the European Union in 2035 are quite low (67 g/km) for the full electric air taxi. Moreover, if all road taxis would be replaced by aerial vehicles, there would be a significant improvement in the traffic level with positive effects on the consumption and emissions of the whole road fleet.

Note that the two electric vehicles (road and electric air taxi with 2035 technology) have about the same mass (curb + payload) but the power demand of the aerial vehicle is much higher because of the very high cruise speed (240 km/h). As a consequence, the flight time is about 20 min while the road taxi would take from 1 to 2.5 h according to the traffic conditions with a circuity factor of 1.28 [11,49].

To understand the corrective measures to be taken to reduce the unfavorability of aerial vs. road vehicles, it is sufficient to analyze the terms in Equation (3) since the cruise is the most relevant flight phase in terms of energy consumption. For the road vehicle, the power request at the wheel at constant speed V and no road grade can be calculated as:

$$P\_{\rm wheel} = \frac{1}{2} c\_d A\_f \rho\_a V^3 + c\_r M \mathcal{g} V \tag{20}$$

where *cd* is the aerodynamic coefficient, *Af* is the frontal area of the vehicle, *cr* is the rolling friction coefficient, and *ρa* is the ambient air density. Assuming the same mass of 1800 kg for each vehicle and suitable values of *cdAf* (0.7 m2) and *cr* (0.012) for a full-sized vehicle [26], the power request of the road vehicle is shown in Figure 8 and compared with those of the air taxi at the same speed (calculated from Equation (3)). Note that the road taxi power is lower than that of the aerial vehicle up to about 210 km/h, which is, however, too high a speed for a road vehicle. Moreover, improvement in *cdAf* and *cr* can be expected in the future for road vehicles that would further reduce the energy request of these vehicles.

**Figure 8.** Cruise power vs. travel speed for an air vehicle and a road taxi with the same mass.

For the aerial vehicle, the cruise power is equally influenced by *L*/*D* and propulsive efficiency so a strong improvement of one or more of these parameters would be needed to reduce the energy consumption at constant cruise speed.

#### *6.3. Effect of Battery Aging*

The results shown in the previous section were obtained with a battery at the start of its life. If the battery-aging phenomena were considered, the same trip would require more electricity to charge the battery (because the battery would be discharged faster) and the battery would not be able to sustain the selected mission (in particular in the case of the electric vehicle with today's technology).

To take into account the effect of battery aging, the energy consumption of the hybrid electric and electric power systems with 2035 technology was recalculated with the battery at the end of its life (equivalent to 400 full discharge–recharge cycles). The results are shown in Table 7. For the hybrid electric case, only the results with the rule-based strategy are shown in Figure 9. We noticed that the aging of the battery determined a slight increase in fuel consumption (+1.5%) because of the rules used during the climb. In fact, in this phase of the flight, the battery is used until its SOC reaches the value of 90%. In the case of the aged battery, this threshold is reached at the end of take-off so the climb is performed only in thermal mode. Because of the reduced capacity, increased internal resistance, and increased Peukert coefficient, the electric consumption is 12 and 27% higher for the hybridelectric and electric configuration, respectively. The DOD is also significantly increased in both cases with a reduction in the number of consecutive missions that the vehicle can perform before fully charging the battery. The DOD affects the charging time between two subsequent flights, which also depends on the charging current. Rapid charging introduces problems in terms of charging cost, reduces the battery life, and compromises the energy density (because there is a tradeoff between energy density and power density in the design of the batteries, as already explained).

**Table 7.** Effect of battery aging of consumption (with 2035 technology, rule-based strategy for the hybrid power system).

**Figure 9.** Effect of battery aging on the behavior of the hybrid electric air taxi (the hybrid electric taxi with 2035 technology). (**a**) new battery; (**b**) aged battery.

For a fully electric taxi, Uber [11] suggests that the vehicle should be operated continuously for at least 3 h without reaching the minimum reserve state of charge (30%) and with a 7 min recharge between each flight to partially recharge the battery. To do this, Uber suggests limiting the DOD in each mission and partially charging the battery between each mission. This approach was used here to estimate the number of consecutive missions with different levels of charging between them. This quantity was denoted as DOC (Depth of Charging) and varied between 0 (no charge) and 20%, meaning that the initial state of charge for a mission was set equal to the final SOC of the previous mission plus DOC. The simulation ended when the SOC reached the threshold of 20%. The procedure is illustrated in Figure 10 with specific reference to the electric air taxi with 2035 technology and the battery at the beginning of its life. The arrow in the Figure 10 explains the concept of DOC. The results obtained in the other cases are shown in Table 8. Note that the higher the DOC, the longer the charging time between two missions. The estimation of the charging time was not performed in this investigation because it is not relevant to the goal of this investigation.

**Figure 10.** Repeated flights with DOC = 20% for the electric air-taxi with 2035 technology and new battery. The arrow shows the increment of charge (DOC) between the end of flight 1 and the beginning of flight 2.

**Table 8.** Effect of battery aging on the number of consecutive flights.

In the case of a hybrid-electric vehicle with a DOD of 20% and a new battery, the vehicle can operate continuously because the DOD is almost equal to the DOC, while in the case of an aged battery it is possible to perform seven consecutive flights. For the fully electric vehicle, the continuous flight is obtained with DOC = 29.7% when the battery is at the beginning of its life.

The number of consecutive flights without full charge is very limited (two) in the case of DOC = zero, i.e., without intermediate partial charging for both the hybrid and the electric aerial taxis.

#### **7. Summary and Conclusions**

A new and detailed methodology was developed to analyze the performance of conventional, hybrid electric, and full-electric air taxis and to compare their environmental impact with road taxis performing the same route. The novel contribution to the state of the art is in the detailed modeling approach of the powertrains, the evaluation of CO2 emissions with a Well-to- Wing approach as a function of the electricity Emission Intensity factor, and the comparison with road vehicles performing the same route in different driving conditions.

In particular, the air taxis were designed according to current and 2035 technology and modeled with an in-house simulation tool. The proposed simulation approach computes the off-design efficiencies of the engine and motor during the mission and accounts for battery non-linear discharge effects (such as the Peukert dependence of capacity from discharge current) and aging phenomena. In the case of the hybrid-electric air taxi, two different energy management strategies were considered and compared.

Reference vehicles were selected for comparison with road taxis and literature values were assumed for the consumption of these vehicles in real driving conditions. The comparison demonstrated the advantages of the electrified air taxi with today's technology over a hybrid-electric road taxi, especially in the case of low emission intensity of the electricity production and penalizing boundary conditions (congested traffic, aggressive driving style, and high values of circuity factor). In the case of 2035 technology, the comparison with a fully electric road vehicle was unfavorable but the WTW emissions with the expected Emission Intensity of 90 g/kWe for the European Union in 2035 were quite low (67 g/km). Note that these results could be interpolated for a reasonable estimation of the energy consumption and CO2 emissions with short-term improvement (such as, for example, 2025 technologies).

The results of the simulation performed with the aged battery underlined the negative effect of this phenomenon on the consumption of the air taxi and on the number of consecutive flights that can be performed with fast intermediate charging of the battery. These results stress the importance of improving the battery technology not only in terms of power and energy density but also in terms of calendar and cycle life to enhance the usage of electrified propulsion systems as an air-taxi service. In future work, the authors will tackle the development of a dynamic model of the hybrid electric power system to account for the shaft dynamic of the rotorcraft and the transient behavior of the fuel system of the turboshaft engine.

**Author Contributions:** Conceptualization, T.D. and A.F.; methodology, T.D.; writing—original draft preparation, T.D.; writing—review and editing, T.D. and A.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

#### **Appendix A**

**Figure A1.** Flowchart of the proposed procedure.

#### **References**

## *Article* **Adaptive Driving Cycles of EVs for Reducing Energy Consumption**

**Iwona Komorska 1,\*, Andrzej Puchalski 1, Andrzej Niewczas 2, Marcin Sl ˛ ´ ezak 2 and Tomasz Szczepa ´nski 2**

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** A driving cycle is a time series of a vehicle's speed, reflecting its movement in real road conditions. In addition to certification and comparative research, driving cycles are used in the virtual design of drive systems and embedded control algorithms, traffic management and intelligent road transport (traffic engineering). This study aimed to develop an adaptive driving cycle for a known route to optimize the energy consumption of an electric vehicle and improve the driving range. A novel distance-based adaptive driving cycle method was developed. The proposed algorithm uses the segmentation and iterative synthesis procedures of Markov chains. Energy consumption during driving is monitored on an ongoing basis using Gaussian process regression, and speed and acceleration are corrected adaptively to maintain the planned energy consumption. This paper presents the results of studies of simulated driving cycles and the performance of the algorithm when applied to the real recorded driving cycles of an electric vehicle.

**Keywords:** electric vehicle; driving cycle; energy consumption; Markov chains; driving range

#### **1. Introduction**

The popularization of electric vehicles may decrease air pollution, particularly in cities. The more fossil-fuel-burning vehicles are replaced with electric vehicles, the less harmful substances (pollutants in particulate matter and gases, mainly nitrogen oxides and sulfur oxides) are released into the air. This is the most significant benefit of electromobility from the perspective of environmental impact. It will also reduce the emissions of greenhouse gases (particularly carbon dioxide and ozone). For vehicle owners, the primary advantage is significantly lower operating costs compared to those of conventional vehicles. An energy management system is critical for the development of electric vehicles because it directly affects their capacity to save energy. Power management aims to create the optimum policy for controlling power supplied to the vehicle. The applied driving cycle is required to optimize and assess power management in electric vehicles.

Predicting the driving cycle of a vehicle is becoming increasingly important in modern intelligent transport, particularly for controlling energy consumption in electric vehicles, planning the trajectory of autonomous terrestrial vehicles, energy management in hybrid electric vehicles, etc. In general, driving cycles illustrate changes in vehicle speed as a function of time. They are of fundamental importance to vehicle engineering. Originally, the primary application of driving cycles was to identify the performance characteristics of a vehicle, such as exhaust emissions and fuel consumption for cars with an internal combustion engine. Along with the development of HEVs, PHEVs and EVs, many studies have addressed the adaptation of driving cycles to these types of vehicles [1–6].

Driving cycles should reflect actual road conditions as well as local conditions in a particular country or region. Driving cycles with equivalent properties can be generated only using a dataset with recorded information about a vehicle or fleet operation as the

**Citation:** Komorska, I.; Puchalski, A.; Niewczas, A.; Sl ˛ ´ ezak, M.; Szczepa ´nski, T. Adaptive Driving Cycles of EVs for Reducing Energy Consumption. *Energies* **2021**, *14*, 2592. https://doi.org/10.3390/ en14092592

Academic Editor: Laura Tribioli

Received: 22 March 2021 Accepted: 27 April 2021 Published: 1 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

basis for generating time signals and final assessment of the quality of induced cycles. Many properties of the driving profile characterizing local driving cycles, such as the average, maximum and minimum values and standard deviations of speed, acceleration and delay, have been defined in the listed articles [1,3,7–12]. The impact of the velocity profile on energy consumption in EVs is analyzed in [13].

There are various methods for generating driving cycles, and they are still being developed. In general, however, three primary approaches can be identified: segmentation, Markov chain method and mixed method (a combination of the first two methods). Each method requires a sufficiently large dataset. The cycle is divided into microtrips in the segmentation method, defined as the speed trace between two successive stops [10] or as sections of the route grouped according to specific criteria, such as different road types, traffic conditions or speed limits. Segments are combined stochastically to generate new driving cycles.

The Markov chain method represents another mathematical approach to driving cycle generation. In the simplest algorithm, speeds are divided into classes, and the probability of transition from class to class is included in the TPM. Then, the TPM and speed probability distribution are used to generate new driving cycles. Their equivalence to the reference cycle is verified based on specific criteria [14–23].

The mixed method combines the two methods mentioned above so that the segment classes (e.g., cruising, idling, acceleration, deceleration or other defined classes) are selected according to the Markov chain algorithm [1,6,24,25]. The methods used for generating driving cycles in this study are discussed more specifically in Section 2.

Previous studies on driving cycles were used to synthesize the type of drive and the city region's test cycle characteristic. The new approach proposed in this article consists of modifying the driving cycle during its duration to the driving range extension based on well-known Markov process models. Here, energy consumption is estimated based on a statistical model (machine learning method), which is easily determined for each vehicle based on an exemplary driving profile. We go a step further by proposing a modification of the velocity profile during its duration using the new DBADC (distance-based adaptive driving cycle) method. The purpose of this study is to predict the driving cycle and correct it on an ongoing basis depending on road conditions and the vehicle energy consumption. Because of this purpose, driving cycles will be considered as distance-based velocity and not as time-based velocity, as is usually the case. The transition probability matrix (TPM) will be corrected on an ongoing basis during driving, not exceeding the energy-use boundary of a particular route. This method is dedicated to electric vehicles with autopilot feature and driven on specific routes, such as cars rented for a short time in the form of car-sharing and delivery vehicles, buses, etc.

#### **2. Methods**

This study uses the segmentation method and iterative Markov chains. Figure 1 shows an illustration of the method, referred to as distance-based adaptive driving cycle (DBADC), which consists of the following components: data collection and their synchronization based on distance, route segmentation and determination of the TPM for the segments, generation of a representative driving cycle and estimated energy consumption using Gaussian process regression (GPR; model-based energy calculation), and on-line correction of the current cycle (an adaptation of the current driving cycle).

**Figure 1.** Illustration of the DBADC method.

First, it is necessary to collect a dataset of driving cycles on routes in the particular region or on planned routes and associated instantaneous or average electricity consumption during these driving cycles.

#### *2.1. Cycle Segmentation*

A typical microtrip in a driving cycle is presented by Austin et al. [26] as the speed trace between two stops. The cycle begins with the idling phase, followed by the acceleration, cruise and deceleration phases. The entire driving cycle consists of such microtrips. The duration of the driving cycle varies depending on average speed and acceleration. Austin et al. suggest three methods for combining microtrips: random, best incremental (based on the Watson plot) and hybrid. The set of driving cycle candidates thus generated is used to select the driving cycle for which the probability distribution of acceleration and speed most closely resembles the actual driving dataset. Further versions of this method are based on improved methods for stochastically combining microtrips. Determination of the optimum combination of microtrips using a genetic algorithm (GA) is proposed in [10]. In this, segments with differing numbers of microtrips are combined until the desired driving cycle duration is reached. In [27], Nesamani et al. used microtrips based on road type to develop a driving cycle for PHEV city buses. A computer program was devised to select microtrips at random until the target distance was reached. The percentage of microtrips depending on road type and time spent on every road type was also calculated to further represent the observed data. In [6], kinematic segments were divided depending on the distance between successive bus stops, whereas the two-dimensional Monte Carlo Markov chain (MCMC) method was used to synthesize driving cycles between each interval of subsequent bus stops.

In the segmentation method, real driving cycles are divided into driving segments grouped according to similar average speed, road surface, traffic conditions or other criteria. The segments are connected stochastically. Lin and Niemeier [24] used the acceleration signal and the maximum likelihood estimation (MLE) method to divide the cycle into segments to associate the segment with specific modal operating conditions (e.g., cruise control, idling, acceleration or deceleration). Here, every class characterizes the driving style and, consequently, also represents a possible state in the Markov chain. Zähringer et al. [28] present the enhanced modal cycle construction (EMCC) method, which is a

modification of the method described in [24]. Here, the global driving state acceleration, deceleration and cruising are subdivided into substates. This enables development of a complete driving cycle using a first-order Markov chain with a constant transition matrix. The control segments to be combined are constructed parametrically based on characteristic values.

This paper proposes dividing a route into segments. Depending on the type of vehicle, segments range from one to several microtrips, which do not have to begin or end with the idling phase. For instance, for cars or delivery vehicles, the segment may include the route between intersections or longer, even though the idling phase may be absent when passing through an intersection. For a bus, the segments may include the route from one stop to another, with traffic lights on the way and a segment beginning and ending with the idling phase.

Figure 2 shows a sample segment of a driving cycle, recorded between traffic lights and covering a distance of approximately 700 m, frequently driven in heavy, congested traffic.

**Figure 2.** A sample segment (**a**) velocity vs. time, (**b**) velocity vs. distance, (**c**) acceleration vs. time, (**d**) acceleration vs. distance.

The two sample segments between traffic lights shown in Figure 2 have different maximum speeds, accelerations and travel times. This makes it difficult to compare them in the time domain (Figure 2a,c). However, cycles analyzed in the distance domain (Figure 2b,d) are more transparent. Because driving cycles are recorded at equal time intervals, it is necessary to use a cycle synchronization procedure based on travel distance.

The length of the segment is selected individually depending on the route and the type of vehicle. A single microtrip between traffic lights is shown in Figure 2. However, the segments should contain more microtrips, grouped according to road conditions such as driving on the ring road, route with heavy traffic (city center) and a built-up zone (residential). This allows for more effective cycle correction.

When the segments are analyzed in the distance domain, the idling phase is hidden. However, idling in electric vehicles affects only energy consumption unrelated to driving, used to power HVAC (heating, ventilation and air-conditioning) systems, radio or lights. Energy consumed during the idling phase can be statistically considered in each segment, if necessary. In this study, the idling phase was omitted from the development of the driving cycle. However, the energy consumption during this phase was statistically included.

When driving cycles are analyzed in the distance domain, known cycle lengths based on the planned route can be used to synthesize Markov chains.

#### *2.2. Markov Chain Method*

A Markov chain is the process wherein computation of the random variable future value is based on the current value, irrespective of the previous value. In mathematical terms, the random process *X* = {*X*1, *X*2, *X*3,...} in the discrete space of states *E* is the first-order Markov chain; if for each *j* ∈ *E* and *n* = 0, 1, 2, ... the conditional distribution *Xn*+1 is a function of the *Xn* variable only [15]:

$$\Pr\{X\_{n+1} = j | X\_0 = i\_0, \ X\_1 = i\_1, \dots, \ X\_n = i\_n\} = \Pr\{X\_{n+1} = j | X\_n = i\_n\},\tag{1}$$

for each set of states *i*0, *i*1,..., *in*.

Suppose a Markov chain is stationary, with probabilities not changing depending on time. In that case, the distribution of probabilities of transitions between particular *k*-states can be presented as a matrix called the transition probability matrix (TPM) *P* ∈ *Rkxk*. This is a stochastic matrix:

$$P = \begin{bmatrix} P\_{11} & \cdots & P\_{1k} \\ \vdots & \ddots & \vdots \\ P\_{k1} & \cdots & P\_{kk} \end{bmatrix} \tag{2}$$

The elements of the *P* matrix *Pij* can be calculated using the following equation:

$$P\_{ij} = \frac{N\_{ij}}{\sum\_{j} N\_{ij}} \tag{3}$$

where *Pij* is equal to the probability of transition from state *i* to state *j*, when *j* = *i* or remains in state i, when *j=i*. *Nij* is the number of transitions from state *i* and to state *j*. All entries of this matrix *Pij* ≥ 0, and the sum of the values of entries in each row, i.e., probabilities of remaining or leaving a given state, is equal to one.

Over the last decade, the Markov chain method has been used in an ongoing effort to improve driving cycles. Stochastic and statistical methods were combined by Lee and Filipi in [16]. They proposed a procedure for synthesizing real driving cycles to model naturalistic driving patterns for any distance. In [17], Gong et al. collected a large dataset of speed measurements for PHEV. The speed profiles were grouped into classes. Driving patterns were identified based on the grouping results, and the Markov chain model was used for the stochastic generation of speeds for different driving patterns. Souffran et al. [18] proposed a stochastic model of driving cycles based on a Markov matrix of three variables vehicle speed, acceleration and road slope—representing real driving conditions. In [6], Liu et al. considered speed, road slope and passenger load for a real bus route with a plug-in hybrid electric bus (PHEB). Kinematic segments were divided according to the distance between successive bus stops, whereas the two-dimensional MCMC method was used to synthesize the driving cycle between each interval of successive bus stops. A transition based on multidimensional Markov chains is presented by Silvas et al. in [19]. After the generation process, the result was verified according to the selected criteria. Moreover, this method can generate a driving cycle of the desired length by compressing the original driving cycle. Nyberg et al. [14] defined the mean tractive force (MTF) to verify equivalent driving cycles. When the individual components of MTF are used to generate driving cycles using Markov chains, equivalent driving cycles can be generated, sharing the same vehicle power usage based on real driving data. In [20], Zhao et al. synthesized a stochastic driving cycle based on their model. They combined the Markov chain process with the transition probability based on driving data input to determine the next possible state of the vehicle. In particular, speed and road slope were generated at the same time using a threedimensional Markov chain model. After the generation process, the result was verified according to selected criteria. Puchalski et al. [21] used a multifractal criterion to verify the

equivalence of driving cycles. Shi et al. [22] provided validation of the Markov property of the driving cycle. They used the theory of ergodicity to determine the relationship between speed and acceleration probability and the state transition matrix.

In the approach presented in this paper, the vehicle speed change process is regarded as a discrete Markov chain. During autonomous or partially autonomous driving, the driving cycle is determined step by step, as in a Markov chain. The next state v(i+1) depends on the previous state v(i) and disruption caused by road conditions.

Markov chains are efficient when the length is known in advance. Obviously, the longer the chain, the easier it is to achieve a given probability distribution. In the presented literature, Markov chains were used to represent a travel cycle with given duration. As the segment travel time is unknown and the distance is known, this article proposes a modification of the TPM. Transitions from one state to another take place in the distance domain, not the time domain.

#### *2.3. Data-Driven Model of Energy Calculation*

A mathematical model is needed to estimate electricity consumption. A backward model is generally used to compute the energy consumption of the vehicle from travel. Electric vehicle energy models are described in [10,13,29,30]. For this study, it was necessary to determine the relationship between the driving cycle parameters (speed and acceleration) and electric energy. We decided to use the statistical model developed with the machine learning method.

Regardless of the parameters of the vehicle, assuming a constant friction coefficient, it can be further assumed that instantaneous energy is a function of the kinematic variables of the vehicle and the slope of the road:

$$E = f\left[a(t), \ v(t), \ v(t)^2, \ a(t) \cdot v(t), slope\right] \tag{4}$$

where *v*(*t*) is velocity and *a*(*t*) is acceleration of the vehicle.

Machine learning methods were used to identify the function representing the kinematic variables of the vehicle.

Taking into account energy recovered from braking, energy consumption is integrated both in the tracking and braking phases:

$$E = \int\_{t} P\_{\overline{v}} dt \tag{5}$$

Average energy consumption *E* is defined as:

$$E = \frac{E}{s} \tag{6}$$

where *s* is the mileage.

There are many ways of modelling continuous signals using experimentally derived datasets. The most frequent method is linear regression, where the set of estimating functions is limited to linear forms, and the values of the parameters are inferred using the least-squares method. Other polynomial, logarithmic, exponential or logistic functions and other loss functions different from the sum of the squares of deviations of real values relative to the theoretical values are also used. An equally popular method is to estimate the signals' parameters by determining the maximum likelihood that a specific sample will occur (MLE). This method can be used to analyze nonlinear signals represented even by short time series, and the estimators thus obtained are asymptotically unbiased.

The Gaussian process regression (GPR) method was used in the study [31] to estimate the system's response, represented by current energy consumption, to input in the form of speed and acceleration measurement signals.

The vectors created from the signal input measurement and the signal output were adopted due to a random experiment, which means that the probability density function for their distribution includes complete information about their values.

When constructing a regression model, we assumed that the expected observed value y can be written as a specific monotonic linear transformation of a combination of independent variables corresponding to the model parameters θ = θ1, θ2, ... θk. This means that it is possible to determine the likelihood f(y|θ), which is a function of parameter θ.

In the maximum likelihood estimation method, the values of the estimated parameters are selected to maximize the likelihood function. In practice, this task requires solving the analytically equivalent problem of maximizing the logarithm lnf(y|θ). Using Bayesian inference in estimating the discussed regression model requires determining the posterior probability f(θ|y) of parameter θ under the condition of observation y. The posterior distribution density function of the parameters is obtained from the Bayesian formula:

$$f(\Theta/y) = \frac{f(y/\Theta)f(\Theta)}{f(y)}\tag{7}$$

where *f*(Θ) is the prior probability of the parameters, and *f*(*y*) is the factor normalizing the posterior probability—independent of Θ—the so-called global likelihood or evidence.

Maximum a posteriori estimation (MAP) can take into account both the past probability and earlier data concerning the event. The confidence intervals can also be interpreted more intuitively.

For a more accurate model, the cycles were divided into three parts: tractive phase, regenerative braking and idle phase. The energy consumption/recovery model in each phase was considered separately. The model identification result is expressed by one of the errors, e.g., RMSE (root mean squared error) or the R2 coefficient for the predicted response vs. true response dependence. The results of model identification using the GPR method for the real object, as well as the quality of this mapping, are discussed in Section 3.2.

#### *2.4. Adaptation of the Current Driving Cycle*

The dataset of driving cycles collected on the investigated route is used to determine representative driving cycles to estimate average electricity consumption. It is not the purpose of this study to develop driving cycles representative for the region; rather, the study aims to select adaptive driving cycles that can be used to optimize electricity consumption.

This entails the necessity of defining the values of typical driving cycles. Twenty-seven variables describing the driving cycle were summarized in [3]. The following parameters characterizing the segments of the cycle were selected for the purposes of this study (Table 1).

In the set of monitored parameters, va was introduced, which is the speed and acceleration product. It is one of the inputs in the data-driven energy calculation model and significantly impacts energy consumption. The main component of the tractive force is the inertial force of the vehicle (ma(t)), and the mechanical power is the product of force and speed. Therefore, the product of speed and acceleration (va) is a significant component of the model.

Boundary energy values are determined individually for each segment of the route. These parameters can be used to select energy-efficient cycles or cycles with average electricity consumption. They may be averaged values for a typical driving cycle on a particular route, values depending on the battery capacity, etc.

The boundary energy course is determined based on averaged energy consumption courses for a given vehicle and route. It means the total electricity consumption from the beginning of the segment to which the actual energy consumption of the car should aim. It consists of three phases: acceleration, cruising and braking. It is assumed that energy consumption increases linearly in the cruising phase, but in reality, this is not the case. Multiple microtrips can take place during this time. However, energy consumption should be around the assumed limit. In the last phase, braking, zero consumption is assumed, although energy is recovered. This makes it possible to make up for any energy losses in

the segment without additional cycle corrections. The limit of energy consumption may be additionally limited due to the driving range caused by the battery capacity, distance from the charging station, etc.

**Table 1.** The calculated parameters in driving cycles.

1 va is the product of vehicle velocity and acceleration.

The adaptive method involves the continuous monitoring of average energy consumption in each segment of the cycle, comparing this consumption with the boundary energy in a particular segment and appropriate correction of speed and acceleration. If energy consumption in a given segment exceeds the boundary energy, the vehicle speed is corrected. A 1000 m driving segment was simulated to illustrate the applied DBADC method. The algorithm plot is shown in Figure 3.

The red line in Figure 3b refers to the boundary energy, which triggers a correction of vehicle speed if it is exceeded. Due to road conditions during the cycle, the vehicle accelerated three times and braked three times, and it was only during the third acceleration that the boundary energy was exceeded. During speed correction, energy oscillated around the boundary energy, only to fall below the boundary energy at the end of the microtrip due to energy recovery during braking. If the correction had been insufficient, the next correction would have reduced the vehicle speed and acceleration.

#### **3. Results**

#### *3.1. Experiment Description*

Road tests were performed by the Motor Transport Institute in cooperation with Tesla Warsaw. The Tesla Model X vehicle with 90D drive was used for the tests presented in this article. The vehicle had three electric motors with a total 540 HP, driving both axles. The battery had a capacity of 90 kWh and a maximum power of 350 kW. The unladen mass of the vehicle was 2475 kg. The vehicle also had a second-generation autopilot, software version 9.0 (partially autonomous driving), which was used in the tests. The route included city traffic in the very center of Warsaw. The streets formed a closed loop with a shape resembling a square, with a total travel distance of approximately 6.5 km. The altitude was 137 m, varying within a range of +/− 6 m. Road slope did not exceed 1◦, which means that the area was relatively flat. A map with the travel route is shown in Figure 4.

**Figure 3.** Simulation of a sample driving cycle (**a**) and energy consumption (**b**) during a cycle with and without correction.

**Figure 4.** Travel route.

The tests were conducted in February on working days from 2:00 p.m. to 5:00 p.m., i.e., when traffic in the area was fairly heavy. The duration of a single cycle ranged from 15 to 22 min. The weather conditions during the test cycles varied only to a small extent because testing days were chosen to meet specific conditions, namely temperature between 8 and 13 ◦C, pressure between 970 and 995 hPa, humidity between 30 and 50%, wind speed of 10 km/h or less, no rain and dry pavement. Interior heating was on during the tests, with the temperature set at a constant 22 ◦C. Exterior lighting and the main screen, which was used to track the vehicle with a GPS and show messages from the onboard computer, were also turned on. The remaining devices were off. Battery charge status before each test was no less than 50% and no more than 80%. The vehicle was driven by two test drivers, each of whom represented two driving styles: calm and dynamic. The autopilot feature was used as well, and it drove the vehicle for at least 67% of the travel time. During the remaining

time, the test drivers controlled the vehicle themselves, driving calmly. The cycles during which the autopilot drove the vehicle were treated in the statistical calculations as if a third, independent driver was driving, although this driver was not able to change the driving style from calm to dynamic.

Figure 5a shows travel speeds as a function of time, and Figure 5b shows travel speeds as a function of travel distance. The figures show a comparison of cycles driven by the dynamic driver, the calm driver and the autopilot.

**Figure 5.** Recorded driving cycles (**a**) as a function of time, (**b**) as a function of travel distance for dynamic driving, eco-driving and autopilot.

Natural segments of the route separated by traffic lights can be easily distinguished in Figure 5b. It is possible to compare the speeds of the drivers in individual segments. Places with slower traffic are easy to identify.

Further analysis was carried out for speeds as a function of distance. The travel distance may differ in real segments by several or several dozen meters due to differences in lane lengths.

#### *3.2. Energy Consumption*

The recorded cycles were used to determine a statistical model of energy consumption using Gaussian process regression (GPR) depending on vehicle speed and acceleration. Figure 6 shows model verification results on the same route with a 95% prediction interval, a fragment of which has been magnified in Figure 6b, with the fit of the model shown in Figure 6c. The R2 coefficient for the predicted response vs. true response dependence (Figure 6c) was close to 1.

The energy consumption of the HVAC during the test was 1.074 kW.

The GPR model can be used to monitor electricity consumption during any driving cycle. To analyze the impact of speed and acceleration on electricity demand, four 1 km segments of driving cycles were simulated (Figure 7a). Figure 7b shows the energy consumption for the simulated cycles, which increased together with distance travelled.

The highest energy consumption corresponded to cycle 1 due to the highest vehicle speed. Cycle 3 showed a quick initial increase in energy consumption due to high acceleration, yet lower overall consumption in the microtrip because the average speed was lower than in cycle 1. Alternate braking and acceleration did not significantly impact the total energy used during the microtrip. During cycle 2, in which speed and accelerations were reduced to approximately 80% of those in cycle 1, energy consumption was approximately 73% of that in cycle 1. Cycle 4, which simulated driving in congested traffic, showed that such driving was very energy-efficient, although it excessively prolonged travel time.

**Figure 6.** Verification of the GPR model: (**a**) the predicted responses and 95% prediction intervals using the fitted model, (**b**) zoom, (**c**) predicted vs. true response.

**Figure 7.** Simulated segments of the driving cycle as a function of distance (**a**) and corresponding energy consumption (**b**).

#### *3.3. Representative Driving Cycle*

The characteristic parameters specified in Table 1 were determined for the cycles described in Section 3.1 and averaged for dynamic driving, calm driving and autopilot driving. The results are presented in Table 2. Due to the small number of recorded cycles, they cannot be regarded as representative of local driving and only illustrate the method.

**Table 2.** Driving cycle parameters.

#### Parameters 10–14 are shown in Figure 8a, and parameters 15–19 are shown in Figure 8b.

**Figure 8.** Comparison of driving cycle parameters for autopilot, eco-driving and dynamical driving: (**a**) percentage of time in speed ranges, (**b**) percentage of time in va ranges.

The driving profiles for autopilot and eco-driving were similar. However, the autopilot was found to have a slightly higher va, which resulted in higher energy consumption. Dynamic driving displayed a noticeable increase in the share of speeds over 50 km·h−1 and an increase of va >10 [m2·s−3], which resulted in a significant increase in average energy consumption. Interesting conclusions can be drawn from comparing average energy consumption and cruising time (Figure 9).

As noted above, the lowest consumption was recorded for eco-driving, slightly higher for autopilot and the highest for dynamic driving, which had the broadest distribution. Travel times for eco-driving and autopilot were comparable; they were shorter for dynamic driving, although they too were characterized by significant breadth of distribution.

The recorded cycles were used to determine the speed acceleration probability density (SAPD) for the entire route, taking into account only the eco-driving and autopilot phases (Figure 10).

**Figure 10.** SAPD for investigated driving cycle.

The average distributions of vehicle speeds (Figure 11) and TPM (Figure 12) were also recorded. The resolution of vehicle speeds was found to be 2.0875 km/h.

**Figure 11.** Average histogram of vehicle speeds on the tested route.

**Figure 12.** Average probability transition matrix for driving cycles on the route investigated.

After the route was divided into segments consisting of groups of microtrips or grouped according to traffic volume, speed limit etc., the TPM was determined for each segment and boundary energy.

#### *3.4. Simulation Results*

This method is dedicated to autonomous vehicles or vehicles with an autopilot feature (driving in semiautonomous mode). The test route was divided into four segments. The TPM was used to generate the next state that determines speed and acceleration. This state can be interrupted at any time by road conditions and traffic. Thus, the TPM is corrected on an ongoing basis, assuming that microtrips between traffic lights are driven at the speed limit and acceleration is additionally limited by energy consumption.

The division into segments was made to illustrate the functioning of the algorithm. For a longer route, a single segment could be used due to the road conditions. The application of the method for a sample driving cycle is shown in Figure 13. The energy boundary was determined based on average energy consumption during the driving cycles by the eco-driver. The corrected cycle was determined by simulation. Figure 13a shows the uncorrected distance-based driving cycle (blue dashed line) for driving with the autopilot and a cycle corrected by the algorithm (red line). In Figure 13b, the energy boundary for each of the four segments and energy consumption during driving (from the beginning of the segment) are added for the corrected and uncorrected cycle.

**Figure 13.** Illustration of the method using the investigated driving cycle: (**a**) distance-based driving cycle, (**b**) electricity consumption at successive route segments.

Figure 14 shows the corrected and uncorrected cycle as a function of time.

**Figure 14.** Time-based driving cycles for Figure 13a.

Table 3 shows average energy consumption during each driving segment and for the entire cycle. Reduced speed and acceleration results in approximately 15% reduction of energy consumption, albeit an 82 s (approximately 10%) extension of travel time (without idling).

Data from Table 3 are shown in the chart below (Figure 15).

Electricity consumption should oscillate around the boundary energy because braking at the end of each segment provides an opportunity to recover some of the energy expended. In the first segment, the vehicle speed is corrected, but if energy consumption at the end of the segment exceeds the boundary energy—as is the case in the first segment—the next (second) segment begins with a correction of speed and acceleration. The correction is made only with accelerations because decelerations result in energy recovery. The correction is implemented only until energy consumption drops below the boundary energy. In the fourth segment, speed is initially corrected; then, later in two microtrips, both speed and acceleration are corrected. The last microtrip does not require any correction.

**Table 3.** Comparison of average electricity consumption during driving in each segment in relation to the assumed boundary energy.

**Figure 15.** Comparison of electricity consumption in the uncorrected and corrected cycle in relation to the assumed boundary energy in each segment and in the overall cycle.

#### **4. Conclusions**

This article presents an adaptive method for optimizing the driving cycle with regard to energy consumption. Compared to methods used to develop representative driving cycles, the method described herein proposes distance-based driving cycles instead of time-based driving cycles. Driving cycles are segmented based on a driving cycle dataset. The next state, determined by speed and acceleration, is defined as the Markov chain next stage. However, this state can be disrupted by traffic conditions. Thus, TPM is updated on an ongoing basis and corrected where necessary if energy consumption is greater than assumed. Energy consumption during driving is monitored and compared with the assumed boundary energy. An autopilot driving cycle was verified in the study, with the cycle adapting to very restrictive limits on energy consumption. Speed or product of the speed and acceleration (va) were reduced when consumption was too high. Energy consumption was reduced by approximately 15%, although travel time was prolonged by approximately 10%.

The tests showed that driving was most energy-efficient at low speeds and accelerations (e.g., driving in congestion). However, many users would not regard this as the optimum driving cycle. It is also necessary to consider travel time, which is a significant aspect in the case of buses, and traffic flow, although this parameter cannot be measured directly. Further study should focus on the optimization criteria and the algorithm used to determine the energy boundary.

The study does not deal in detail with the energy consumption of HVAC systems. However, this energy has been statistically included in the design of the energy boundary. While the motor consumes no electricity during the idling phase, HVAC energy consumption is a real challenge in EV.

This paper is relevant to the topic of energy management in so-called intelligent public transport. Energy management is important for the transport of people (car-sharing, public bus transport) and goods (delivery vehicles).

**Author Contributions:** Conceptualization, I.K.; methodology, I.K. and A.P.; software, I.K.; validation, A.P. and A.N.; formal analysis, A.P.; investigation, M.S. and T.S.; resources, M. ´ S.; data curation, ´ T.S.; writing—original draft preparation, I.K.; writing—review and editing, I.K.; visualization, I.K.; supervision, A.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

#### **References**

## *Article* **Cooling System Energy Consumption Reduction through a Novel All-Electric Powertrain Traction Module and Control Optimization**

**Simone Lombardi \*, Manfredi Villani \*, Daniele Chiappini and Laura Tribioli**

Department of Industrial Engineering, University of Rome Niccolò Cusano, Via Don Carlo Gnocchi, 3, 00195 Rome, Italy<EMAIL_ADDRESS>(D.C<EMAIL_ADDRESS>(L.T.) **\*** Correspondence<EMAIL_ADDRESS>(S.L<EMAIL_ADDRESS>(M.V.)

**Abstract:** In this work, the problem of reducing the energy consumption of the cooling circuit for the propulsion system of an all-electric vehicle is approached with two different concepts: improvement of the powertrain efficiency and optimization of the control strategy. Improvement of the powertrain efficiency is obtained through a modular design, which consists of replacing the electric powertrain with several smaller traction modules whose powers sum up to the total power of the original powertrain. In this paper, it is shown how modularity, among other benefits, also allows reducing the energy consumption of the cooling system up to 54%. The energy consumption of the cooling system is associated with two components: the pump and the fan. They produce a so-called auxiliary load on the battery, reducing the maximum range of the vehicle. In conventional cooling systems, the pump and the fan are controlled with a thermostat, without taking into account the energy consumption. Conversely, in this work a control strategy to reduce the auxiliary loads is developed and compared with the conventional approach, showing that the energy consumption of the cooling system can be reduced up to 27%. To test the control strategy, numerical simulations have been carried out with a 1-D model of the cooling system. On the other hand, all the thermal loads of the components have been calculated with a vehicle simulator, which is able to predict the vehicle's behavior under different driving cycles.

**Keywords:** electric vehicle; propulsion cooling system; modularity; thermal management; control optimization

#### **1. Introduction**

One of the most limiting factors of all-electric vehicles is the limited range [1,2]. The most advanced electric rechargeable energy storage systems (RESS), such as Li-ion batteries, still suffer of low energy density when compared to fuels, meaning that large and heavy batteries would be required to meet the travel range of conventional vehicles. In addition, severe ambient conditions can dramatically reduce the range and reliability of battery powered vehicles [3]. Another important drawback of all-electric vehicles is that the battery is the only energy storage on-board and therefore it is also required to provide the energy for the operation of the auxiliary loads, such as the air conditioning compressor and the fan and pump of the propulsion cooling system. In all-electric vehicles, reducing these loads is of primary importance, as they drain energy form the battery and can further decrease the range of the vehicle.

Generally, studies on the impact of auxiliary loads on energy consumption are limited to weather and climatic conditions—i.e., Heating, Ventilation, Air Conditioning (HVAC) consumption and thermal comfort measures [4–7]—driver behavior and traffic conditions. Lalhou et al. [8] proposed a thermal comfort management approach that optimizes the thermal comfort while preserving the driving range during a trip is proposed. A large number of weather and traffic situations are simulated, and results show the efficiency

**Citation:** Lombardi, S.; Villani, M.; Chiappini, D.; Tribioli, L. Cooling System Energy Consumption Reduction through a Novel All-Electric Powertrain Traction Module and Control Optimization. *Energies* **2021**, *14*, 33. https://doi.org/10.3390/en14010033

Received: 15 November 2020 Accepted: 21 December 2020 Published: 23 December 2020

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).

of the proposed approach in minimizing energy consumption while maintaining a good comfort. Similarly, Desreveaux et al. [9], in order to plan the annual charging operation of an eco-campus, developed a simulation tool for an accurate determination of the consumption of an electric vehicle throughout the year. An overconsumption up to 33% in winter due to heating, and only 15% in summer due to air conditioning was found. Basciotti et al. [10] developed advanced simulation tools to improve the efficiency of climate control systems in order to accurately evaluate both the energy savings and thermal comfort.

On the other hand, very seldom the influence on energy consumption owe to cooling of powertrain components is included in the analysis. For example, the integrated thermal management of a pure electric vehicle is described in [11], including battery cooling/preheating, electric machines (EM) cooling and Air Conditioning (AC) or heat pump. Different approaches are proposed, but not modularity nor optimized control. Shojaei et al. [12] investigate the impact of the cooling power demands of the cabin and battery on the vehicle performance, focusing more on comfort levels and battery degradation. In [13], the National Renewable Energy Laboratory's modeling framework was used to explore control strategies for an electric vehicle combined loop system. The control approach included a mode selection algorithm and controllers for the compressor speed, cabin blower flow rate, coolant flow rate, and the front-end heat exchanger coolant bypass rate. The impact of these thermal systems on electric vehicle range during warmup was simulated showing up to a 10.9% improvement in range for the full system over the baseline during warmup from cold soak. The need to reduce the significant energy drain and resulting drive range loss due to auxiliary electrical loads is also addressed in [14].

As shown in the above literature review, in most of the research works, the problem of reducing the energy consumption of the auxiliary loads in an all-electric vehicle is translated into the effort of reducing the energy consumption of the AC system. On the other hand, in this work the energy consumption of the auxiliaries used in the propulsion cooling system is considered and two approaches are proposed to reduce it. To the author's knowledge, there are no contributions in the literature where the reduction of the energy consumption of the auxiliary loads from the propulsion cooling system is investigated. The first approach, at a design level, is modularity. The second approach, at a control level, is the optimization of the energy management.

The concept of modularity has been developed in DRIVEMODE, a project funded by the European Commission under the Horizon 2020 framework. The DRIVEMODE project stems from the idea of integrating a high-speed gearbox, a high-speed electric motor (e-motor) and a Si-C inverter to provide a highly efficient and compact integrated drivetrain module (IDM) to be used in cars of different classes, including mass produced battery and hybrid electric vehicles, low performance and high performance vehicles and different types of heavy-duty vehicles. Multiple IDM can be used in place of single larger electric machines and power electronic components. In the modules, the smaller electric machines, even though characterized by lower maximum efficiencies, will work in more efficient regions of the operating map, resulting in a lower thermal load to be rejected through the cooling system. In this paper, it is shown how modularity, among other benefits, also allows reducing the energy consumption of the cooling system.

The second approach consists of improving the energy management of the propulsion cooling system. Most of the works regarding the thermal management in electric vehicles are focused on either improving the battery cooling [15–17] or the e-motor cooling [18,19], without taking into account the cooling system energy consumption. Conventional control strategies are based on a feedback control on the radiator inlet temperature, with a thermostat valve. An interesting control approach to reduce the motor cooling system energy consumption is proposed in [20], but the considered vehicle is a hybrid electric. In this work a control strategy that reduces the energy consumption of the cooling system, namely of pump and fan, has been tuned for steady-state conditions and then tested with numerical simulation on different driving cycles. Even though the benefits of this control

strategy are smaller compared to those obtained with modularity, the implementation comes at no costs, since it does not require additional components or sensors.

This work relies on numerical simulation of experimentally validated models. Transient simulations of driving cycles have been carried out with a robust 1-D model of the vehicle cooling system built in GT-Suite [21]. On the other hand, all the thermal loads of the components of the drivetrain have been calculated with a vehicle simulator developed in Matlab/Simulink® [22].

The remainder of this paper is organized as follows: Section 2 presents the single e-motor and dual IDM configurations and modeling; Section 3 describes the cooling circuits for the two cases; finally, in Section 4 the simulations are presented, and the results are discussed; the conclusions are presented in Section 5.

#### **2. System Description and Modeling**

The vehicle considered in this study is an all-electric sedan-class car. The main parameters of the vehicle are listed in Table 1.

**Table 1.** Characteristics of the vehicle.

Two powertrain configurations are considered and further described in the next subsections: the single e-motor (with power electronics and transmission) and the dual Integrated Drivetrain Module (which incorporates e-motor, gearbox, and inverter). In both cases, the total power of the propulsion system must meet the speed and grade requirements indicated in Table 2.

**Table 2.** Performance requirements of the vehicle.

The general layout of the cooling system is composed of four integrated circuits (with a fifth separate loop for cooling charger and converters (400V-12V DC/DC and 800V-400V DC/DC)), as shown in Figure 1. The four loops are:

**Figure 1.** Cooling system circuits: AC refrigerant loop (blue), HVAC coolant loop (red), propulsion loop (purple), RESS loop (green).

The first loop provides air conditioning for cabin cooling through a compressed vapor cycle, whereas the second provides cabin heating. The third loop is responsible for the propulsion system cooling and the fourth loop ensures that the battery is maintained in the operating temperature range. These loops are all highly integrated, but this analysis is focused only on the propulsion coolant loop, which, however, is influenced by the HVAC refrigerant circuit through the condenser and by the RESS circuit through the RESS radiator: as shown on the left side of Figure 1, the same fan provides the air mass flow rate for the cooling of RESS, HVAC system (whose condenser is shown in blue) and propulsion module. The conditions of the air flow at the outlet of the RESS radiator and AC condenser are experimentally measured and used as an input to the simulations performed in this study.

#### *2.1. Single Electric Motor*

The conventional all-electric powertrain is composed of one single e-motor and one inverter. The e-motor is then connected through the transmission to the vehicle front wheels, as qualitatively shown in Figure 2.

**Figure 2.** Single e-motor propulsion system and cooling system.

The electric machine has a max peak power of 150 kW and max/min continuous torque of 266 N·m, with corner speed of 1500 RPM. Figure 2 also shows the layout of the propulsion cooling system. The main components of the circuit are:

As already mentioned, the fan is used to suck in the air and increase the air mass flow rate through the radiators of propulsion, condenser and RESS cooling loops. The coolant consists of water mixed with ethylene glycol (50% water + 50% glycol).

#### *2.2. Dual Integrated Drivetrain Module*

Introducing the concept of modularity [23], two smaller e-motors can be used instead of the larger single motor. Each of the smaller e-motors is integrated with gearbox and Si-C inverter to form a highly efficient and compact integrated drivetrain module (IDM). Two 75 kW IDMs are used in this study to replace the single motor, as qualitatively shown in Figure 3.

**Figure 3.** Dual IDM propulsion system and cooling system.

In particular, each module has a dedicated cooling circuit, with the coolant flowing through the IDM components in a series configuration. Eventually, the coolant streams coming from the two modules are sent to the same main radiator for heat rejection to the ambient. This configuration helps designing a single compact cooling circuit for the thermal management of all the propulsion components.

The benefits of modularity, i.e., using a larger number of smaller electric machines, are twofold: increased overall efficiency during the vehicle operation and reduced components heat rejection. The first benefit is explained considering that in a typical driving cycle the operating conditions will be mostly in the low-medium speeds and torques. This means that a larger EM will operate in the lower efficiency regions, while for a smaller EM most of the operating points will fall in the maximum efficiency region. Therefore, even though the larger EM could achieve greater maximum efficiency, during a driving cycle the overall efficiency of a modular propulsion system will be higher. The second benefit is strictly related to the first one, as a more efficient operation of the powertrain components will lead to less losses and heat rejection. This, in turn, will reduce the energy demand of the propulsion system cooling circuit, further improving the overall vehicle energy consumption.

#### *2.3. Electric Vehicle Model*

E-motor and inverter generate heat during their operation, especially at high power demands, because of ohmic losses. The cooling system is required to reject the generated thermal load to the ambient, keeping the temperatures within the operating range of the components. To evaluate the thermal load generated during the propulsion system operation, a quasi-static model of the electric vehicle has been developed in Matlab/Simulink®. The power losses in the inverter . *QINV*, which are equal to the heat generated, can be calculated as a function of the instantaneous inverter power *PINV*, with the following equation: .

$$Q\_{INV} = P\_{INV}(1 - \eta\_{INV}) \tag{1}$$

where for the inverter efficiency *ηINV* a constant average value equal to 97% has been used. This value results in being a bit conservative with respect to the first measurements at test bench.

On the other hand, the thermal load of the e-motor, . *QEM*, can be calculated as a function of the motor power, *PEM* , and efficiency, *ηEM*, using the following equation:

$$
\dot{Q}\_{EM} = P\_{EM}(1 - \eta\_{EM}) \tag{2}
$$

The efficiency of the single e-motor is evaluated from the map shown in Figure 4, which is obtained in [23] with the method proposed in [24].

**Figure 4.** Single e-motor efficiency map.

For the e-motors of the two IDMs, the Willans line model [25] has been used to scale down the single e-motor map. The result is shown in Figure 5, with the maximum peak power of the scaled motors being one half of the maximum power of the original e-motor. Thus, the two e-motors for the dual IDM configuration have the same total power as the single e-motor configuration.

**Figure 5.** IDM e-motor efficiency map.

The maps shown in Figures 4 and 5 have been implemented in the Matlab/Simulink® model to obtain a quasi-static forward-looking simulator of the entire vehicle. The power demand on the propulsion system components is evaluated by solving the longitudinal dynamics of the vehicle and using the following expression of the road load:

$$F\_{\rm load} = \frac{1}{2} \mathcal{C}\_{\rm d} \rho\_{\rm air} A\_{\rm f} v^2 + M\_{\rm g} \sin \theta + \mathcal{C}\_{\rm r} M\_{\rm g} \cos \theta \tag{3}$$

The first term on the right-hand side of Equation (3) is the aerodynamic drag force, with *C*d the drag coefficient, *ρ*air the air density, *A*f the frontal area of the vehicle and *v* the longitudinal speed of the vehicle. The second term is the force due to the road grade *θ*, where *g* is the gravity constant and *M* is the vehicle mass. Finally, the third term is the rolling resistance force, which is a function of grade, vehicle mass and tires rolling resistance coefficient *C*r. The values of these parameters have been previously reported in Table 1.

The simulator includes a driver's model based on a PID controller to track the desired speed profile (i.e., driving cycle) and a zero-th order equivalent circuit model for the battery. The main characteristics for the battery pack are listed in Table 3.

**Table 3.** Battery pack main characteristics.

The battery performance is obtained starting from the open circuit voltage (OCV) and internal resistance (R0) curves, shown in Figures 6 and 7, which have been derived from data available in [26] for a Li-Ion battery cell manufactured by A123 Systems, LCC (Livonia, MI, USA).

**Figure 6.** Battery cell open circuit voltage dependence on state of charge.

**Figure 7.** Battery cell internal resistance dependence on state of charge.

With the zero-th order equivalent circuit model the battery heat rejection, . *Qbatt*, can be calculated as: .

$$
\dot{Q}\_{httt} = I^2 \cdot R\_0(SoC) \tag{4}
$$

The battery current *I* is a function of the battery open circuit voltage, *VOC*, the power request, *Pbatt*, and the equivalent internal resistance *R*0(*SoC*), function of the state of charge (SoC):

$$I = \frac{V\_{OC} - \sqrt{V\_{OC}^2 - 4P\_{ultt}R\_0}}{2R\_0} \tag{5}$$

#### *2.4. Cooling Circuit Model*

The heat rejection profiles for each component, obtained with the Matlab/Simulink® model described above, are then used as input for the propulsion cooling circuit model developed in GT-Suite and shown in Figure 8. The other input to the GT-model is the vehicle speed, which is directly related to the air flow through the cooling system radiators. Two sides or two circuits are highlighted in the model:

**Figure 8.** Propulsion cooling system model in GT-Suite (dual e-motor configuration).

The main components of the circuit have been modeled as follows:

**Figure 9.** Cooling system pump map.

**Figure 10.** Cooling system fan map.

Additionally, the thermal load of the propulsion radiator is an output of the analysis rather than an input. All the data needed to model the heat transfer behavior of the radiator have been provided by the car manufacturer. The performance that the propulsion cooling system must meet are summarized in Table 4. In particular, the temperature must not exceed 65 ◦C. In the case of the dual IDM the constraint on the minimum volumetric flow rate imposes the usage of two pumps. This has been found to be consistent with the modularity requirement of the DRIVEMODE project, since each module comes with its own pump.

**Table 4.** Preliminary requirements for the cooling circuit.

#### **3. Cooling Circuit Control Strategy**

The second approach to reduce the energy consumption from the auxiliary loads related to the propulsion cooling system consists of optimizing the control strategy of fan and pump. The fan is responsible for increasing the air flow through the radiator, thus improving the heat rejection when the driving loads are high. The pump is used to ensure the desired flow of coolant through the propulsion system components and keep their temperature in the admissible range. In the following subsections, the conventional control strategy and the proposed optimized strategy are presented. Both strategies apply to either the single e-motor or the dual IDM configurations.

#### *3.1. Conventional Control*

The conventional control strategy acts on two control variables, which are the pump speed, and the input signal of the fan (on/off). The pump speed is initially set at 10 L/min and then it is linearly increased as the coolant temperature at the radiator inlet increases above 40 ◦C. The fan is off as long as this temperature is below 65 ◦C. For higher values, the fan is switched on at its maximum capacity (i.e., input signal equal to 90%) and is maintained on until the temperature drops down below 55 ◦C, performing a hysteresis

cycle. When the radiator inlet temperature reaches 65 ◦C and the fan is turned on, the pump flow rate is kept constant at its maximum value. The linear dependency of the pump speed (proportional to the pump flow rate) on the coolant temperature at the radiator inlet is shown in Figure 11. The minimum pump speed corresponds to 10 L/min, as per the constraint reported in Table 4, while the maximum volumetric flow rate is obtained for the maximum pump speed.

**Figure 11.** Pump conventional control strategy: linear dependence of mass flow rate on coolant temperature at radiator inlet.

#### *3.2. Optimized Control*

The optimized control strategy aims at reducing the energy consumption of pump and fan, ensuring the temperature constraints on the e-motor and inverter are met. In contrast with the conventional strategy, in this case the speed of the pumps is controlled based on the actual vehicle speed, actual heat rejection of the components and fan state. These signals are already available in the vehicle, as they are used for other tasks of the electronic control unit, so no additional sensors are required to implement the new control strategy.

The control strategy is built on the observation that for a given vehicle speed and thermal load on the cooling circuit, the pump speed corresponding to the minimum energy consumption is the lowest possible speed that avoids the fan to be switched on. Therefore, an optimization process has been carried out to evaluate the minimum pump speed required to reject different thermal loads at different vehicle speeds, without turning on the fan. A design of the experiment was performed with the Matlab/Simulink® simulator, varying vehicle speed and road grade to obtain the heat rejection of the components for different road load conditions. Those results were then used for steady-state simulations of the 1-D GT-Suite cooling circuit together with built in optimization algorithms from GT-Suite to create the control map shown in Figure 12. For the same vehicle speed, higher loads correspond to higher heat rejections and require higher mass flow rates (thus, pump speeds).

The map shows a step-shape because the pump speed has a low impact on the coolant temperature. Indeed, the most important variables for the heat transfer in the radiator are the air mass flow rate and the air temperature, which are influenced by vehicle speed and fan state. In other words, for the same level of required heat rejection, while the speed of the pumps can only produce a small change of the radiator inlet temperature, the fan state and vehicle speed can have a much greater impact. As a result, there is no advantage in maintaining high pump speeds during the fan operation, because the main contribution to lowering the temperature is from the fan, and the increasing fan operational time is negligible. Following this consideration, the optimal pump speed from the map is overwritten when the fan is turned on, setting the speed to its minimum value.

In the first step of the control strategy, the calculation of the pump speed is only based on the actual vehicle speed (i.e., air flow rate through the radiator) and heat rejection from the components, using the control map shown in Figure 12, which is embedded into a 2D lookup table. The actual optimal speed output signal from the 2D lookup table is time averaged to smooth speed variations. This is necessary to dampen the dynamics of the inputs to the lookup table, which is built from steady-state simulations.

In a second step, the actual coolant temperature at the radiator inlet is checked. If the temperature of the coolant exceeds 60 ◦C, then the fan is turned on and the minimum pump speed is imposed, overwriting the optimal speed output of the 2D lookup table. The fan performs the same hysteresis cycle between 60 ◦C and 55 ◦C as already described in the previous section.

To summarize, the control strategy is designed to optimize the speed of the pump(s) when the fan is off, and to set it to the minimum allowed value when the fan is on:

$$n\_{\text{pump}}\left(\mathbf{x}\_{\text{fan}}, \dot{Q}\_{\text{loss}}, v\_{\text{vehicle}}\right) = \begin{cases} \ \pi\_{\text{pump}}\left(\dot{Q}\_{\text{loss}}, v\_{\text{vehicle}}\right), & \mathbf{x}\_{\text{fan}} = 0\\\ n\_{\text{pump}} = 4250 \text{ rpm}, & \mathbf{x}\_{\text{fan}} = 1 \end{cases} \tag{6}$$

where *x*fan is the actual state of the fan, equal to 1 if the fan is on and equal to 0 if the fan is off; . *Q*loss represents the total heat rejection of the components that is a function of time; *v*vehicle is the actual vehicle speed; *n*pump is the speed of the pump and *n*pump is the time averaged value of *n*pump coming from the optimized control map. After a sensitivity analysis the averaging time of *n*pump has been set equal to 25 s for all the simulations.

#### **4. Simulations and Results**

To investigate the operation and performance of the cooling system, three different driving cycles (i.e., vehicle speed time profiles) have been selected: Aachen drive cycle, shown in Figure 13a; Federal Highway Driving Schedule (FHDS) drive cycle (repeated 10 times), shown in Figure 13b; World harmonized Light-duty vehicles Test Procedure (WLTC) drive cycle (repeated 3 times), shown in Figure 13c.

**Figure 13.** Test driving cycles: (**a**) Aachen; (**b**) FHDS × 10; (**c**) WLTC × 3.

The cycle repetitions are needed to obtain the same cooling circuit operating time and realistic trip length. Also, to add variability to the road power demand, each cycle repetition is characterized by a different road grade profile.

In the Matlab/Simulink® forward-looking model both the single motor and dual IDM configurations were simulated for the three driving cycles. The main outputs of these simulations are the heat rejection profile of the components and the effective vehicle speed. The operating average efficiency of the e-motors for the different driving cycles and the different powertrain architectures is reported in Table 5. It is clear that the modularity can improve the operating efficiency of the e-motors, thus reducing the heat generation that the cooling circuit will have to reject to the ambient.

**Table 5.** E-motor average efficiency.

The heat rejection profile and the vehicle speed are then used as inputs to the GT-Suite model, which solves the transient 1-D thermo-fluid dynamic problem and evaluates the performance of the cooling circuit. Both the conventional and the optimized control strategy for the pump(s) control are simulated.

The effectiveness of the control strategies has been tested under the following additional assumptions: constant gear box efficiency of 0.97; mass of the vehicle equal to the gross weight; no AC condenser heat rate; ambient temperature of 40 ◦C; coolant initial temperature of 40 ◦C. These extreme operating conditions have been chosen to stress the cooling system and trigger fan starting events. As an example, Figure 14 shows the heat rejections of the motor, inverter, and battery with respect to time for the WLTC × 3 cycle.

**Figure 14.** Outputs of the all-electric vehicle model: actual vehicle speed profile (top); motor, inverter and RESS heat rejections vs. time (bottom).

As one may note, there is a correlation between the velocity profile and the heat rejection, which is obviously affected by the road load. These plots are mostly provided to prove the soundness of the energy-based vehicle simulator. Those heat rejections have been calculated with the set of equations from (1) to (4).

#### *Results Discussion and Comparison*

To understand the impact of modularity and optimized control strategy on the energy consumption reduction, four cases have been analyzed for every driving cycle:

The different driving cycles highlight different aspects of the powertrain configurations and control strategies.

For the WLTC × 3 drive cycle, the speeds of pump and fan (which can be considered to be a measure of the energy consumption) are shown in Figures 15 and 16 for the single e-motor and the dual IDM configurations, respectively. The WLTC × 3 is the most power demanding driving cycle and in all the cases the fan must be activated to lower the coolant temperature. Moreover, comparing Figures 15 and 16, the single e-motor configuration requires one more fan start due to the higher heat rejection of the components in this powertrain.

**Figure 15.** Control strategy comparison for single e-motor on WLTC driving cycle: coolant pump speed (top); radiator fan speed (bottom).

**Figure 16.** Control strategy comparison for dual IDM on WLTC driving cycle: coolant pump speed (top); radiator fan speed (bottom).