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Energy-Optimal Control of Plug-in Hybrid Electric Vehicles for Real-World Driving Cycles Stephanie Stockar, Vincenzo Marano, Marcello Canova, Giorgio Rizzoni, Fellow, IEEE, and Lino Guzzella, Fellow, IEEE

Abstract—Plug-In Hybrid Electric Vehicles (PHEVs) are today recognized as a promising solution for reducing fuel consumption and emissions, due to the ability of storing energy through direct connection to the electric grid. Such benefits can be achieved only with a supervisory energy management strategy that optimizes the energy utilization of the vehicle. This control problem is particularly challenging for PHEVs, due to the possibility of depleting the battery during usage and the vehicle-to-grid interaction during recharge. This paper proposes a model-based control approach for PHEV energy management that is based on minimizing the overall CO2 emissions produced - directly and indirectly from the vehicle utilization. A supervisory energy manager is formulated as a global optimal control problem and then cast into a local problem by applying the Pontryagin’s Minimum Principle. The proposed controller is implemented in an energybased simulator of a prototype PHEV, validated on experimental data. A simulation study is conducted to calibrate the control parameters and to investigate the influence of vehicle usage conditions, environmental factors and geographic scenarios on the PHEV performance, using a large database of regulatory and ”real-world” driving profiles.

NOMENCLATURE Cnom E f H Ibatt J K L m˙ CO2 m˙ equiv

Battery Nominal Capacity Energy Torque Split Factor Hamiltonian Battery Current Cost Functional Final State Penalty Term Lagrangian CO2 Mass Flow Rate Equivalent Mass Flow Rate

S. Stockar (Corresponding Author), V. Marano, M. Canova and G. Rizzoni are with the Ohio State University Center for Automotive Research, Columbus, OH 43212, USA. Email: [email protected]. L. Guzzella is with the Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland.

m˙ f QLHV Pbatt R s S t T u Vbatt Voc x

Fuel Mass Flow Rate Fuel Lower Heating Value Battery Power Battery Internal Resistance Equivalency Factor Target Set for the Final State Time Torque Control Law Battery Voltage Open Circuit Voltage State Variable

η ηch λ λi κ µl τCS ω Ωx

Efficiency Battery Charger Efficiency Lagrange Multiplier Initial Condition for the Lagrange Multiplier Specific CO2 content Scalar Lagrange Multiplier Fraction of Driving Cycle in CS Mode Angular Velocity Feasible Set for the State

AER BSA CS CD ECMS EM HEV ICE PHEV SDP SoC SoE

All Electric Range Belted Starter Alternator Charge Sustaining Charge Depleeting Equivalent Consumption Minimization Strategy Electric Motor Hybrid Electric Vehicle Internal Combustion Engine Plug-in Hybrid Electric Vehicle Stochastic Dynamic Programming State of Charge State of Energy

off-line and tabulate the results in the actual implementation. I. INTRODUCTION The Equivalent Consumption Minimization Strategy (ECMS) is a well-known approach for on-line energy management of HEVs that has recently been adapted to the supervisory control of PHEVs [15], [16], [17], [18], [19], [20]. The proposed approach is based on assuming that the energy expended by the vehicle can be converted into an equivalent consumption of fuel.

Plug-in Hybrid Electric Vehicles (PHEVs) are today considered a solution to reduce fuel consumption and CO2 emissions in the transportation sector. Compared to conventional hybrid vehicles, the high-capacity energy storage system of PHEVs and the ability to recharge the battery through connection to the electric grid provide the opportunity to control the battery depletion during vehicle utilization, ultimately improving the fuel economy. Various studies have shown that the performance of PHEVs depend on several factors, many of which have little or no influence on charge-sustaining hybrids and conventional vehicles [1], [2], [3], [4], [5], [6], [7]. To name a few, the length of the driving path, the contribution of the electricity on the overall energy consumption of the vehicle, the cost of the electric energy and its specific CO2 content have been recognized as predominant factors in the assessment of fuel economy and emissions for PHEVs. A subject of strong interest on the part of the automotive industry is to understand the implications of different energy management strategies on fuel consumption, CO2 emissions, battery life, range and performance. To this extent, one of the critical challenges for control design is to properly account for the grid energy in the vehicle energy optimization problem. Some methods have been so far proposed to design supervisory controllers for PHEVs, including the minimization of an equivalent fuel consumption, or the vehicle operating costs or the cumulative CO2 emissions [2], [3], [4], [8], [9]. Due to the complexity of the control problem, heuristic methods have been often considered [8], [10], [11], [12]. Although rule-based methods are often successfully employed in industry, it is generally found that the controller design process is cumbersome, time-consuming and its results are limited to a specific vehicle design and usage conditions. For this reason, model-based approaches can improve on all of these drawbacks and yield more cost-effective solutions. Stochastic Dynamic Programming (SDP) appears more indicated, especially when a small number of reference driving profiles can be found as statistically representative of the vehicle utilization [13]. Recent results show improvements in fuel economy, operation costs and emissions [8], [14]. The SDP approach however requires significant amount of data to provide a statistically relevant validation framework. Further, the policy evaluation typically requires large computation time, partially overcome by estimating the control policy

The results presented lead to the conclusion that nearoptimal fuel economy can be achieved if the control algorithm depletes the battery proportionally to the driving distance. However, this implies that the vehicle velocity profile must be known a priori. Such condition prevents the ECMS to be generalized, requiring calibration of the equivalency factor for each driving profile. Furthermore, the assumption of converting the battery energy into an equivalent fuel mass flow rate, is not formally applicable to PHEVs, since the electric energy stored from the grid depends on the energy generation mix. This paper presents a novel supervisory energy management strategy for charge-depleting hybrid vehicles that accounts for the vehicle primary energy consumption, including the fuel energy and the electric energy from the grid. The structure of the proposed algorithm is general and adaptable to different vehicle architectures (series, parallel, series-parallel) and to any number of power splits. The proposed approach is based on the formulation of a global optimal control problem that minimizes the global CO2 emissions produced (directly and indirectly) by the vehicle use. The Pontryagin’s Minimum Principle is then applied to obtain a local minimization problem. The control strategy is applied to a forward-oriented simulator of a series-parallel PHEV and used to conduct vehicle performance analysis, evaluating the impact of the control parameters for a variety of vehicle utilization and environmental scenarios. The paper is organized as follows: after an overview of the hybrid vehicle configuration and the model adopted for the control study, a description of the energy management strategy and its implementation into a control algorithm are given. Simulation results are presented to evaluate the sensitivity of the proposed control strategy to the vehicle usage conditions, environmental and geographic scenarios, also providing an assessment of vehicle performance, fuel consumption and CO2 emissions. 2

II. DESCRIPTION OF THE VEHICLE AND OF THE SIMULATOR

block computes the tractive force, which is the input to a vehicle longitudinal dynamics model that predicts the vehicle velocity.

The vehicle considered in this study is a series-parallel prototype PHEV, built on a mid-size SUV platform [21], [22]. As shown in Figure 1, the vehicle drivetrain includes a downsized Diesel engine coupled to a Belted Starter Alternator (BSA) and a 6 speed automatic transmission on the front axle, and an Electric Motor (EM) with on the rear axle. Table I describes the main vehicle components. The configuration chosen for this vehicle allows for a variety of operating modes such as pure electric drive, electric launch, engine load shifting, motor torque assist, and regenerative braking [22].

Fig. 1.

Fig. 2. Information flows in the forward-oriented vehicle simulator

The drivetrain components included in the vehicle powertrain are detailed in Figure 3. The energy-based (quasi-static) modeling approach is adopted to predict the overall vehicle fuel consumption over a driving cycle, neglecting high-frequency dynamic effects [25]. The engine model is based on its steady-state fuel consumption map, implemented in the simulator as a function of the engine speed and input torque. Similarly, the electric machines are modeled as static elements, wherein the efficiency is mapped as a function of their speed and input torque. The combined engine and BSA torque is transmitted through a torque converter and a 6-speed automatic transaxle, while the EM is coupled to the rear axle through a fixed gearbox. Losses in the transmission components are accounted for through the definition of efficiency terms. The gear shifting strategy is determined by a simple scheduling controller based on the engine speed and accelerator command.

Diagram of the prototype PHEV drivetrain.

TABLE I D ESCRIPTION OF THE VEHICLE DRIVETRAIN COMPONENTS . Component Chassis Engine

Type Mid-size SUV Diesel

Starter/ Alternator Energy Storage

Permanent Magnet Li-Ion

Transmission

6 Speed Auto AC Induction

Electric Motor

Specifications 2005 Chevrolet Equinox 1.9l, Inline 4, 103kW @ 4000rpm, 305Nm @ 2000rpm 10.6kW Nominal, 80Nm Peak Torque, 4150r/min Max Speed 3.2V, 2.3Ah (nominal) per cell; 90 cells in series, 15 modules in parallel; 10kWh pack energy 450Nm torque capacity 32kW Nominal, 185 Nm Peak Torque

A forward-oriented, energy-based simulator was developed and validated using a combination of driving tests and laboratory test data [21], [22], [23], [24]. Figure 2 describes the information flows within the vehicle simulator [25], [26], [27]. The accelerator and brake pedal position commands from the driver are input to the controller, which determines the torque commands to the engine, electric motor and BSA. The powertrain

Fig. 3.

Block diagram of the drivetrain power flows.

A. Energy-Based Model of the Battery As shown in Table I, the vehicle includes a 10kWh LiIon battery pack, which enables for an All Electric Range (AER) of 25km [1]. A simplified model of the battery 3

was built according to the equivalent circuit analogy [24], [28], [26]. In particular, a zero-order model is here considered to describe the battery voltage output:

calculated over the entire mission of the vehicle. A constraint on the battery state of charge at the end of the mission is also included to ensure nominally charge sustaining operations:

Vbatt (t) = Voc (SoC (t)) − R (SoC (t)) · Ibatt (t)

SoC(tb ) = SoC(ta )

(1)

The open circuit voltage Voc and internal resistance R are polynomial functions of the battery SoC [28]. The state of charge of the battery is defined as: SoC (t) = SoC0 −

The control sequence u(t) that satisfies the above state constraint is the solution of the optimal control problem [30], [31], [32], [25], [33], [34]. By applying the Pontryagin’s Minimum Principle [35], [36], the constrained global optimization problem presented above is cast into a local minimization problem given by a Hamiltonian function defined by the vehicle equivalent fuel consumption [25], [37]:

Z t

1

Ibatt (t) dt (2) Cnom 0 where Cnom represents the nominal battery capacity, indicated in Table I. Although the above model represents a strong approximation of the real battery behavior, it is consistent with the energy-based formulation, which limits the analysis to the steady-state and low-frequency behavior of the system. More complex and accurate battery models, for example including the high-frequency dynamics and the effects of temperature, can be included in the same vehicle simulator, for example to study the effects of driving conditions and energy management control on battery aging [29]. The battery model is here utilized to formulate the energy management control problem. In this case, the battery dynamics is described by the state equation: Ibatt (t) d SoC (t) = −η dt Cnom

m˙ equiv (t) = m˙ f (t) + s (t) ·

ηbatt (SoC(t),t) =

Vbatt (t) Voc (SoC (t))

(3)

(4)

(5)

For the zero-order model described by Equation 1, the battery efficiency can be explicitly calculated:

ηbatt (SoC(t),t) = 1 −

R (SoC (t)) Ibatt (t) Voc (SoC (t))

(6)

In order to define a supervisory energy management strategy for PHEVs, an optimal control problem for charge-depleting systems is here formulated. Compared to the energy management problem formulation presented above, the constraint on the final SoC defined in Equation (8) must be eliminated to enable charge-depleting operations. Further, the equivalence between the battery energy usage and the fuel mass flow rate shown in Equation (9) is formally incorrect for PHEVs, where the battery energy is mostly provided by the grid, hence decoupled

For a charge sustaining HEV, the supervisory controller formulates a control law u (t) that minimizes a cost function over a period of time [ta ,tb ]. Commonly, the cost function is the vehicle fuel consumption: Z tb ta

m˙ f (t) dt

(9)

IV. OPTIMAL CONTROL PROBLEM FORMULATION FOR PHEV ENERGY MANAGEMENT

III. OVERVIEW OF THE ENERGY MANAGEMENT PROBLEM FOR CHARGE-SUSTAINING HYBRID VEHICLES

JHEV (u) = m f =

Pbatt (t) QLHV

where s(t) is a fuel energy equivalency factor (nondimensional), Pbatt is the net power drawn from the battery and QLHV is the fuel lower heating value. The cost functional defined by Equation (9) is minimized at each time step. This allows one to find a solution to the optimal control problem that can be implemented on a vehicle. Note that the approximation of converting an electrical energy utilization into a fuel mass flow rate introduces the equivalency factor s(t). This calibration parameter has a considerable impact on the battery SoC during a driving path. For this reason, the equivalency factor must be optimized or adapted based on the specific vehicle driving profile considered, in order to achieve optimal fuel economy and charge sustaining operations [27], [37]. Experimental results however show that the ECMS performs close to the global optimum with modest calibration effort, with the advantage of being implementable on-line [31], [21].

and

 ηbatt if Ibatt (t) ≤ 0 η= 1  if Ibatt (t) > 0 ηbatt where the battery efficiency is defined as:

(8)

(7) 4

from the fuel energy. This implies that the cost function must be redefined for PHEVs. In this study, the cost function is defined to account for the primary energy consumed by the vehicle during a driving path. The most representative indicator of the well-to-wheel energy utilization of a PHEV is given by the cumulative CO2 emissions produced by the vehicle utilization: JPHEV (u) =

Z tb ta

m˙ CO2 , f (t) + m˙ CO2 ,e (t)dt

Based on the state equation above, the control variable u(t) for the energy management problem can be defined as the vector:   PEM,el (t) (15) u (t) = Pbatt (t) ; Pbatt (t) where the second element represents the power split between the rear EM and the BSA electric power outputs. Since the mechanical power demand to the drivetrain is known, the electric EM and BSA power can be obtained from the efficiency maps of the two components and simple energy balances, according to the power flow diagram in Figure 3. In order to respect the physical limitations imposed by the drivetrain components, the control and state variables are subject to constraints. In particular, the battery SoE and power must be limited to prevent abuse and agingrelated issues [40]:

(10)

where mCO2 , f represents the mass CO2 produced by the consumption of the fuel (when the engine is utilized) and mCO2 ,e results from the consumption of the electric energy stored on-board. In order to apply the optimal control theory to the PHEV energy management, the variables mCO2 , f and mCO2 ,e must be related to vehicle system variables as follows: m˙ CO2 , f (t) = κ1 · Pf uel (t) (11) Pbatt (t) m˙ CO2 ,e (t) = κ2 · ηch

SoEmin ≤SoE (t) ≤ SoEmax Pbatt,min ≤Pbatt (t) ≤ Pbatt,max

where, usually SoEmin = 0.25 and SoEmax = 0.95. Further constraints stem from the power limits of the drivetrain components:

where, according to Figure 3, Pf uel is the power associated to the fuel utilization and is determined as follows, assuming a lower heating value (QLHV = 43MJ/kg): Pf uel (t) = m˙ f (t) · QLHV

PEM,min ≤PEM (t) ≤ PEM,max PBSA,min ≤PBSA (t) ≤ PBSA,max

(12)

Ebatt (t) Enom

V. SOLUTION OF THE PHEV ENERGY MANAGEMENT PROBLEM The optimization problem defined above is tackled using Pontryagin Minimum Principle [35], [36], which, in principle, allows one to obtain closed-form expressions for locally optimal control signals. In the general case, an explicit control signal can only be found solving a two-point boundary value problem. For the specific problem at hand, an optimal solution can be found adopting the reasonable simplifications shown below. The starting point is a description of the system dynamics:

(13)

where Enom = Cnom · Voc is the nominal battery energy (kW h). Considering the SoE as the new state variable instead of the SoC, the state equation of the system becomes: d Pbatt (t) SoE (t) = −η (SoC (t)) dt Enom

(17)

where the power limits are functions of the EM and BSA speed.

The term ηch = 0.86 in Equation (11) represents the battery charger efficiency (when the vehicle is connected to the grid) [38], and κ1 and κ2 are defined as the specific CO2 content in the fuel and electricity per kW h. Note that κ1 corresponds to the engine Brake Specific CO2 (BSCO2 ), which can be readily calculated from fuel consumption data. The term κ2 can be reasonably estimated based on the average CO2 content of the electricity generation mix for a specific geographic region [39]. To account for the energy stored in the battery, the State of Energy (SoE) is introduced: SoE (t) =

(16)

dx (t) = f (x (t) , u (t) ,t) dt with the cost functional: J (u) =

(14)

Z tb ta

L (x (t) , u (t) ,t) dt + K (xb ,tb )

(18)

(19)

The theorem introduces the Hamiltonian function:

where η is defined according to Equation (5), and Pbatt is the battery power, defined positive if discharging. Note that, if Vbatt (t) = Voc , then SoE = SoC.

H(x(t), u(t), λ (t),t) = L(x(t), u(t),t)+ λ (t)· f (x(t), u(t),t) (20) 5

which has to be minimized at each time t to provide the optimal control policy. If uo (t) is the optimal control policy, then the following necessary conditions must be satisfied:

lower boundary are limited in occurrence, the value for µl0 is determined here by a trial and error procedure [35]. The necessary condition for the co-state λ o (t) is:    ∂ κ2 · Pbatt (t) d λ o (t) ∂ o = −∇x H|o = − + κ1 Pf uel (t) − dx (t) dt ∂x ∂x ηch = ∇λ H|o = f (xo (t) , uo (t) ,t) i)   dt ∂ Pbatt (t) · η (SoC(t)) d λ o (t) + · (λ o (t) + µ (t)) ii) = −∇x H|o ∂x Enom dt (23) iii) xo (ta ) = xa with the initial condition λ o (t = ta ) = λi . Since no iv) xo (tb ) ∈ S ⊆ Rn explicit condition is given for λi , this parameter needs o o o o o v) H (x (t) , u (t) , λ (t) ,t) ≤ H (x (t) , u (t) , λ (t) ,t) to be calibrated. The ODE for the co-state λ o (t) can be further simIf the state x (t) is bounded, namely: plified since Pf uel (t) and Pbatt (t) do not depend on the battery SoE (or SoC). However, the above assumption is vi) xo (t) ∈ Ωx (t)∀t ∈ [ta ,tb ] , not valid for the battery efficiency. In fact, the battery Ωx (t) = {x ∈ Rn |G (x,t) ≤ 0; G : Rn x [ta ,tb ] → R} power is P (t) = I (t) ·V (t), while the maximum batt batt batt battery power during discharging is Pmax (t) = Ibatt (t) · where G (x,t) defines the inequality constraints, an addiV (SoC(t),t). This will further penalize any operation oc tional term is introduced in the Hamiltonian function in at low SoE, when the battery efficiency is lower. order to account for this limitation. The corresponding Inserting this expression in Equation (23), the co-state Lagrange multiplier is a scalar denoted by µl and subject equation can be rewritten as follows: to the Kuhn-Tucker condition:  Pbatt (t) · (λ o (t) + µ (t)) ∂ ηbatt  vii) µlo ≥ 0   · if Pbatt (t) < 0; o d λ (t) Enom ∂x = o For the PHEV control problem, an extended HamilPbatt (t) · (λ (t) + µ (t)) ∂ ηbatt  dt  − if Pbatt (t) ≥ 0; · tonian function is defined, based on the cost functional Enom · ηbatt (SoC(t),t)2 ∂x (24) in Equation (10) and the state constraints on the battery SoE: According to the minimum principle, the control policy denoted by uo (t) is optimal if H(xo (t), u(t), λ o (t),t) H(x(t), u(t), λ (t), µ (t),t) = κ1 · Pf uel (t)+   presents a global minimum with respect to uo (t). κ2 λ (t) · η (SoC(t)) µ (t) · η (SoC(t)) As a final remark, a proof of equivalence between +Pbatt (t) − − ηch Enom Enom the ECMS and the solution of the optimal control (21) problem through the Pontryagin Minimum Principle was with:  obtained for the charge-sustaining HEV case in [31],  if SoE(t) ≥ SoEmax µl [27]. This proof is here extended to the charge-depleting µ (t) = −µl if SoE(t) ≤ SoEmin (22) PHEV case. In fact, the ECMS formulation presented in   0 else Equation (9) can be made equivalent to the Hamiltonian function defined by Equation (21) if the equivalency where Pf uel can be calculated from the engine fuel factor s(t) is defined as: consumption maps, as in Figure 3 and µl is the scalar Lagrange multiplier for the inequality constraints on the κ2 η (SoC(t),t) − · (λ (t) + µ (t)) s(t) = (25) SoE. κ1 · ηch Enom · κ1 The extended Hamiltonian function allows one to include the state constraints within the same optimal VI. IMPLEMENTATION OF THE ENERGY control problem. Note that Equation (21) provides necesMANAGEMENT STRATEGY sary conditions for optimality according to the previously The solution of the optimal control problem defined by mentioned conditions. Such formulation, however, can lead to sub-optimal results if the state constraints are Equation (21) can be applied to forward-oriented models active. When this occurs, the optimal value for the or to a vehicle control system. Figure 4 illustrates a parameter µl is unknown and should be determined procedure for the implementation of the solution into by applying conditions i)-vii). Since the time intervals a control algorithm. Note that, although the vehicle during which the state is sliding along of the upper or drivetrain includes three propulsion systems (namely an 6

engine and two electric motors), the proposed implementation allows for the optimal torque split between an arbitrary number of power generation elements.

The torque delivered by each component is then limited according to Equation (17). Note that the torque variables defined are considered as mechanical, hence calculated at the shaft of each component. The electrical power provided by the battery and the the power associated to the engine fuel utilization are then computed to evaluate the Hamiltonian function in Equation (21). Specifically Pf uel is determined from the engine fuel consumption, according to Equation (12), while the the power of the electric machines is computed from the efficiency maps for the BSA and EM: PEM,el (t) = TEM (t) · ωEM (t) · ηEM,el PBSA,el (t) = TBSA (t) · ωICE (t) · ηBSA,el

(28)

where, for the rear electric motor, ηEM,el = 1/ηEM if the machine is working as a motor, and ηEM,el = ηEM if as a generator. For each torque split combination that satisfies the above constraints, the Hamiltonian function is defined batt based on Equation (21). In doing so, the expression ∂∂ηSoE in Equation (24) is explicitly calculated, according to Equation (5): Ibatt (t) d ηbatt (SoC(t)) = · dSoE Voc (SoC(t)) − R(SoC(t)) · Ibatt (t)   ∂ R(SoC(t)) R(SoC(t)) ∂ Voc (SoC(t)) · − ∂ SoC(t) Voc (SoC(t)) ∂ SoC(t) (29) Note that, since the parameters Voc and R are continuous piecewise polynomial functions [28], they can be differentiated in the entire SoC range. o o At any time step, the combination fICE and fBSA that minimizes the Hamiltonian function matrix is chosen as the solution of the optimization problem. It is worth observing that the proposed algorithm, although suitable for implementation into forward-oriented simulators or hardware-in-the-loop systems for control development and testing, can not be directly applied to real-time control due to the required computation and numerical optimization of the Hamiltonian function at each time step. However, the computation effort can be significantly decreased by pre-computing the Hamiltonian function and importing the results as maps in the vehicle control system. A similar approach was adopted for the implementation of an ECMS to a charge-sustaining HEV [33], [21], [37].

Fig. 4. Flow chart describing the implementation of the energy management algorithm.

According to Figure 4, the variables fICE and fBSA define the fraction of the torque demand to the drivetrain (Treq ) that is commanded to the engine and to the BSA, respectively. By conducting an energy balance on the system in Figure 3, three matrices containing all the possible torque combinations that satisfy the drivetrain demand are generated: TICE (t) = fICE · Treq (t)

∈ Rnxm

TBSA (t) = fBSA · (1 − fICE ) · Treq (t)

∈ Rnxm

TEM (t) = (1 − fBSA ) · (1 − fICE ) · Treq (t)

∈R

(26) nxm

where the dimensions m and n are related to the chosen resolution for the factors fICE and fBSA . The torque request at the driveshaft, Treq is evaluated using the driver accelerator and brake commands α and β as follows: + − Treq (t) = α (t) · Tmax + β (t) · Tmax

(27) VII. RESULTS AND ANALYSIS

+ is the maximum positive torque that the where Tmax powertrain can generate combining ICE, BSA and EM, − is the maximum negative torque that can while Tmax be absorbed by the electric machines (BSA and EM), accounting for battery power limitations.

The energy management algorithm was applied to the forward-oriented PHEV simulator to conduct an evaluation of the vehicle performance for a variety of usage conditions. 7

The focus of the study conducted is on the effects of the control parameters on the vehicle fuel economy and CO2 emissions, and the influence of driving conditions and energy generation scenarios.

Switzerland (κ2 = 142 [g/kWh]) 4% 1%

20%

44%

51%

50%

Coal Hydro Nuclear Gas Other Renewable

A. Vehicle Driving Scenarios The characteristics of the driving profile have a strong impact on the calibration of the PHEV control algorithm [10], [11], [15], [41]. In this study, a rich set of driving profiles was adopted as a validation framework for the energy management control algorithm, analyzing scenarios consistent with the driving behavior of customers and improving the generality of the results. The simulations were conducted on a set of regulatory and real-world driving profiles extracted from a database of fleet studies data to statistically represent typical usage conditions of a PHEV, including urban, extra-urban and highway segments with variable driving length [42]. Table V in the Appendix lists the main characteristics (velocity and energy demand at the wheel) of all the the driving cycles considered in this study. The cycles are all characterized by a driving distance greater than the vehicle all electric range. This allows for the possibility of depleting the battery, depending on the calibration of the energy management strategy.

Germany (κ2 = 646 [g/kWh])

19% 8%

France (κ2 = 75 [g/kWh])

9%

5% 1% 4% 12%

11%

48%

27% 4%

79%

Fig. 6. Summary of electricity generation mix for four countries (Sources: [43] [44] [45] [46] [47]).

For simplicity, it will be assumed that the grid energy consumed by the PHEV has the same specific CO2 content as the generation mix. Note that this must be considered an approximation for the European countries, where the open energy market may cause differences between the CO2 content of the electricity produced by each country and that consumed by the vehicle.

150 Velocity [km/h]

United States (κ2 = 567 [g/kWh]) 3%

100

C. Definition of Controller Parameters and Performance Metrics

50 0 0

10

20

Based on the optimal control problem in Equation (21), the parameters requiring calibration are the initial condition for the Lagrange multiplier λi and the scalar Lagrange multiplier µl (which varies the penalty on the battery SoE constraints). The impact of the above parameters will be evaluated through three different metrics. First, the evolution of the battery SoE during the driving pattern and its final value SoE f inal (λi , µl ), will be considered. Then, the overall CO2 mass calculated with Equations (10-11) will be evaluated:

30

Time [min]

Fig. 5. Example of velocity profile for the controller validation (indicated as Path 3 in Table V).

Figure 5 shows the velocity profile of one of the nonregulatory cycles considered. This pattern is representative of mixed-mode driving conditions, alternating urban driving and a highway segment. B. Electricity Generation Scenarios

mCO2 = κ1 m f QLHV + κ2

The impact of the electricity generation mix on the PHEV utilization was evaluated by varying the specific CO2 emission coefficient κ2 to encompass different energy generation scenarios, including electricity production from both fossil fuel and renewable sources. Four of the values considered for κ2 are representative of the energy generation mix for USA, Switzerland, France and Germany, as summarized in Figure 6.

1 Enom ∆SoE ηch

(30)

where QLHV is the fuel lower heating value, ∆SoE is the difference between initial and final SoE. Another variable is introduced to indicate whether the vehicle is operating in Charge Depleting (CD) or Charge Sustaining (CS) mode, hence identifying how fast the control strategy depletes the battery. The variable τCS 8

defines the fraction of the driving cycle where the vehicle operates in CS mode at its lower SoE bound: tCS τCS = (31) tcyc

energy than the one allowed. In the second case, the controller requires the engine to produce more power to further charge the battery. If any of the above cases occurs, the corresponding solution is not part of the feasible domain and cannot be considered for the control problem. For this reason, the points violating the state constraints will be removed from the following results. Figures 8(a) and 8(b) show the contribution from the fuel energy and the electric energy to the total vehicle CO2 emissions. Comparing with Figure 7, a final SoE close to its upper bound implies that most of the energy consumed by the vehicle was supplied by the ICE, leading to high fuel consumption and engine CO2 contribution. Conversely, a low final SoE results in lower engine CO2 emissions. Combining the CO2 from fuel energy and battery energy, it is possible to obtain the overall CO2 emissions for the PHEV, as shown in Figure 8(c). The response to the control parameters is almost flat, indicating rather limited benefits on the vehicle CO2 emissions. This behavior can be explained by the high specific CO2 content of the electricity in the scenario considered [43] [44]. In fact, the production of energy from coal (a carbon-rich fuel) and the low well-to-tank efficiency of the electricity generation ultimately offset the higher tank-to-wheel efficiency of the electric traction, to the point where the CO2 produced from the battery energy use is comparable to the fuel energy utilization. Figure 9 shows the PHEV fuel consumption over the sample cycle. Since the factor κ1 is constant, the fuel consumption is directly related to the CO2 contribution from the fuel energy. This implies a simplification in the study, since the brake specific CO2 of the engine varies based on the engine operating condition. However, for a PHEV such differences would be minimal, as the engine operating range is limited compared to a conventional vehicle. Comparing Figure 9 with Figure 8(c), it is evident that best engine fuel consumption is achieved whenever the battery is completely depleted at the end of the cycle. However, the optimal value of the parameter λi is determined by minimizing the cumulative CO2 emissions, which does not necessarily correspond to best fuel economy. On the other hand, if the specific CO2 content of the grid, κ2 , tends to zero, the minimum of the CO2 and the best fuel economy would be coincident. This corresponds to an ideal case where the electric energy is produced entirely from renewable sources. Figure 10 shows the fraction of cycle duration where the vehicle operates in CS mode at its lower SoE bound

Specifically, tCS is calculated considering the time during which the vehicle operates within a ±5% window around SoE = SoEmin . In the following results, the battery is assumed at SoE = SoEmax = 95% at the beginning of each cycle. Knowledge of the fraction of the driving cycle in CS mode is not only relevant for energy optimization, but also for reliability, safety and aging issues [48]. D. Analysis of Simulation Results for One Driving Cycle and One Energy Scenario In order to illustrate the results, one case study will be analyzed in detail, with reference to the driving cycle shown in Figure 5 and the U.S. energy generation scenario. Simulations were conducted to evaluate the vehicle CO2 emissions, fuel economy and the utilization of the battery energy in relation with the control parameters. Figure 7 reports the the values of the final battery SoE obtained by varying the parameters λi and µl . Note that an undesired complete depletion of the battery is possible for certain combinations of the control strategy parameters.

1 0.9

Final State of Energy [−]

0.8 0.7 0.6 0.5 0.4 0.3 0.2

Constraints on SOE violated

0.1 0 20

15

10

5

0

−5

Parameter λi

−10

−15

−20

0

4

8

12

16

20

Parameter µ

l

Fig. 7. Final value of the battery SoE as function of λi and µl for the case study (Cycle Path 3, U.S. scenario).

It is evident that µl affects the ability of the controller to respect the state constraints. In particular, the SoE exceeds its boundaries when µl is below a threshold (for the considered scenario, µl < 10). The parameter λi determines whether the lower or the upper SoE bound is violated. In the first case, the vehicle uses more battery 9

350

2

CO from Fuel Energy [g/km]

300 250 200 150 100 50 0 25

20

15

10

5

0

4

0

−5 −10 −15 −20

12

8

16

20

Parameter µl

Parameter λ

i

Fig. 9. Fuel economy of the PHEV as function of λi and µl for the case study (Cycle Path 3, U.S. scenario).

(a) Contribution from fuel energy.

as a function of the control parameters. For high values of λi , the vehicle is operated in CD-CS mode and the SoE reaches the lower bound before the end of the driving path. For the driving cycle considered, τCS is slightly below 40%, meaning that approximately 60% of the energy requested to the drivetrain can be satisfied with the battery.

350

2

CO from Grid Energy [g/km]

300 250 200 150 100 50 0 20

15

10

5

0

−5

−10

Parameter λi

−15

−20

0

4

8

12

16

20

Parameter µ

l

50 Fraction of Driving in CS Mode [%]

(b) Contribution from electric energy.

2

Overall Vehicle CO [g/km]

350

300

40

30

20

10 20 16 0

12 −20 20

250

15

8 10

5

0 Parameter λ

i

4 −5 −10 −15 −20

0

Parameter µ

l

200

150

Fig. 10. Percentage of the cycle in charge sustaining mode at the low SoE bound as function of λi and µl for the case study (Cycle Path 3, U.S. scenario).

20 100 20

16 12 15

10

8 5

0

−5

Parameter λ

i

4 −10

−15

−20

0

Parameter µ

l

For λi > 10 the control strategy forces the vehicle to deplete the battery and, when the lower SoE bound is reached, switches to CS mode. Conversely, as λi decreases, τCS decreases steeply to zero and, when λi ≤ 0, the control strategy is no longer able to deplete the battery. At this condition, the final SoE is near the same value as the initial one, hence the control strategy tends

(c) Combined. Fig. 8. Overall vehicle CO2 emissions as function of λi and µl for the case study (Cycle Path 3, U.S. scenario).

10

to operate the system in CS mode at the higher SoE bound.

12

Optimal Value for λi

1 304 gCO2/km State of Energy [−]

λi,fit= − 0.0027*x [MJ] + 5.8

10

0.8

8 6 4 2

296 gCO2/km

0.6

λi = +6

0.2

λi = +10 0

5

40

278 gCO2/km

λi = +4

0.4

0

0 30

λi = −10

15

20

60 70 80 Energy Demand at the Wheel [MJ]

90

100

Fig. 12. Optimal value of the initial condition λi as function of the vehicle energy demand for different driving cycles (U.S. scenario).

289 gCO2/km 10

50

25

Time [min]

Fig. 11. Battery SoE profile during the driving cycle for µl = 18 varying λi (Cycle Path 3, U.S. scenario).

This is confirmed in Figure 11, where the evolution of the battery SoE during the driving cycle is represented for four different values of λi , while µl is set constant. Intermediate solutions are observed for values of λi included within the two bounds. In particular, a value λi = 6 allows the battery to be gradually depleted during the cycle, reaching the lower SoE bound only at the end of the driving pattern and avoiding any charge sustaining operations. This operation, known as Blended Mode, allows for achieving the minimum vehicle fuel consumption along a prescribed driving cycle [17].

Driving Cycle

λiopt

Min. Energy (93) Max. Energy (6) Min. λiopt (94) Max. λiopt (63) Max. λiopt (81)

6 5 3.75 7.75 7.75

J opt (gCO2 /km) 260 289 296 293 276

Var. λi ±1 ±1 ±1 ±1 ±1

Dev. (%) 2.0/1.9 0.4/0.3 0.8/1.9 0.5/0.1 1.4/0.1

TABLE II S ENSITIVITY ANALYSIS OF THE COST FUNCTIONAL J(u) TO THE PARAMETER λi (U.S. SCENARIO ).

Table summarizes the sensitivity results to variations in λi around the optimal value corresponding to each of the five driving cycles considered. In all cases, the sensitivity of the vehicle CO2 emissions is very limited. The results confirm that, for the energy generation scenario considered, the control strategy is relatively insensitive to the characteristics of the driving pattern [26]. The behavior can be justified by considering that the parameter λi is the initial condition of the co-state ODE of the optimal control problem. Therefore, its influence on the optimal solution decreases progressively with the duration of the driving cycle, as λ (t) converges. In summary, the simulation results show that the vehicle CO2 emissions are relatively insensitive to the Lagrange multiplier λi , for the considered energy generation scenario. Furthermore, the optimal value of the control parameter, which allows the vehicle to operate in Blended Mode with minimum energy consumption, is nearly independent from the driving cycle duration and vehicle energy demand. Conversely, the parameter µl has no impact on the vehicle performance, but ensures satisfaction of the constraints on the battery SoE bounds. Specifically, a threshold value can be identified for µl so that the state constraints are always respected, allowing one to reduce the controller calibration problem to the sole parameter λi . This presents advantages for parameters tuning, as

E. Effects of Driving Cycle Characteristics For all the vehicle driving profiles listed in Table V and the U.S. energy generation scenario, a full factorial design of experiments was generated, varying the control parameters λi and µl of the supervisory controller. Then, the optimal combination (λi , µl )opt was determined by minimizing the CO2 emissions produced by the PHEV. Figure 12 summarizes the results of the simulations, representing the optimal value of the Lagrange multiplier λi against the vehicle energy demand at the wheel calculated for the driving cycles considered in the study. The parameter µl was set to a constant value so as to ensure the constraints on the battery SoE are always respected. As Figure 12 shows, the results tend to cluster within a limited range of values for the parameter λi and are almost independent on the energy demand at the wheel. A sensitivity study was conducted to evaluate the influence on the cost functional J(u) of errors in the optimal value of the control parameter λi . The analysis was conducted with reference to five specific driving patterns, representing the limit scenarios for Figure 12. 11

Optimal value for the parameter λi

near-optimal results can be achieved with minimal calibration effort, in particular without the need of information such as the driving length. F. Effects of Energy Generation Scenarios In order to extend the validation framework, different scenarios were considered to evaluate the sensitivity of the control parameter λi to different values of the energy generation mix. As an example, this analysis was initially limited to the sample driving cycle shown in Figure 5. Figure 13 represents the vehicle CO2 emissions and engine fuel consumption against the parameter λi for the four different energy generation scenarios shown in Figure 6. κ Decreasing 2

Germany USA

France Switzerland

0 15 Germany USA

0 Switzerland

−2 −4

0

Switzerland

5

100 200 300 400 500 600 Specific CO content in the grid energy κ [g CO /kWh] 2

700

2

2 λi,fit = − 0.026*x [MJ] − 0.39

France

0 i

0 −20

Germany

France

2

−15

−10

−5

0 Parameter λ

5

10

15

Optimal Value for λ

Fuel economy [l/100km]

4

Figure 15 summarizes the optimal value of the Lagrange multiplier λi against the vehicle energy demand at the wheel for all the driving cycles considered. The low specific CO2 content of the electric energy generation in Switzerland causes a different behavior, compared to the the one observed in Figure 12 for the U.S. scenario. Although the results are still clustered in a limited range of λi , a slightly increase dependence of the optimal parameter value with the driving cycle energy demand can be observed.

200

10

USA

Fig. 14. Influence of the energy generation mix parameter κ2 on the optimal value of the parameter λi (Cycle Path 3).

300

100

opt

λi (κ2)=0.014*κ2−2.4

6

2

2

Overall CO [g/km]

400

8

20

i

Fig. 13. Impact of the energy generation mix on the CO2 and fuel consumption against the parameter λi for different energy generation scenarios (Cycle Path 3).

−2 −4 −6 −8 −10 30

The U.S. and German energy production scenarios are relatively similar, with the high specific CO2 content of the electric generation mix causing a relatively flat response of the vehicle overall emissions to the control parameter λi . Conversely, the case of Switzerland and France is rather different, as the energy generation is predominantly composed by renewable or low CO2 primary sources. These two scenarios offer promising opportunities for a large PHEV penetration. Here, a higher sensitivity in the vehicle CO2 emissions can be observed with respect to the control strategy parameter. Figure 14 illustrates the influence of the specific CO2 content of the grid energy on the optimal value of the Lagrange multiplier λi , with reference to the sample driving cycle, indicating a linear correlation between κ2 and λi . This suggests that the calibration of the PHEV supervisory controller could be done when the battery is connected to the grid, based on the specific CO2 content of the electricity generation during the charging operation.

40

50

60 70 80 Energy Demand at the Wheel [MJ]

90

100

Fig. 15. Optimal value of the initial condition λi as function of the vehicle energy demand for different driving cycles (Swiss scenario).

Driving Cycle

λiopt

Min. Energy (93) Max. Energy (6) Min. λiopt (25) Max. λiopt (51) Max. λiopt (92)

-1 -2 -5 0 0

J opt (gCO2 /km) 137 227 220 117 229

Var. λi ±1 ±1 ±1 ±1 ±1

Dev. (%) 13.5/23.8 6.0/1.2 10.0/30.0 30.6/11.2 2.8/0.1

TABLE III S ENSITIVITY ANALYSIS OF THE COST FUNCTIONAL J(u) TO THE PARAMETER λi (S WISS SCENARIO ).

This behavior indicates that the optimality of the control strategy (and, consequently, the PHEV fuel consumption and CO2 emissions) is more affected by the driving cycle characteristics as the electric energy is predominantly generated from renewable sources. 12

Similar to the U.S. scenario, a sensitivity study was conducted on the cost functional J(u) varying the parameter λi for different driving patterns. It is possible to notice here the increased sensitivity of the vehicle CO2 emissions to errors in the optimal value of the control parameter. On the other hand, a considerably large error must be given to λi in order to detect sufficiently high variations in the cost functional J(u). This indicates the presence of a relatively large region around the ”sweet-spot” where the CO2 emissions and the vehicle performance vary only marginally.

Furthermore, the sensitivity to the vehicle usage conditions and the tradeoff between fuel and electrical power consumption are dependent on the specific CO2 emissions associated to the electricity generation. In particular, a higher sensitivity was observed for the energy generation scenarios characterized by a low CO2 content. While the present paper does not specifically address real-time control developments, its insights are valuable in developing energy management strategies that can lead to more readily tunable algorithms that can address different objectives. In particular, the analysis presented in this paper can assist in addressing differences in electricity generations between different regions and countries, allowing for the development of energy management strategies that can achieve, for example, minimum CO2 emissions in the face of a different mix of electric power generation feedstocks. Given the increasing use of geographical information systems and navigation systems, which can lead to some degree of a-priori knowledge of the vehicle trajectory, the results presented in this paper represent a step forward in understanding of the potential of formal optimization methods in guiding the design of real-time energy management strategies.

VIII. CONCLUSION The paper presents a novel approach to the supervisory energy management of Plug-in Hybrid Electric Vehicles. The paper addresses the fuel consumption and CO2 emissions associated to the PHEV use through a wellto-wheel energy balance that explicitly accounts for the fuel energy and grid energy utilization. An optimal control problem was formulated by defining a cost functional based on the cumulative CO2 produced - directly and indirectly - by the vehicle. The Pontryagin’s Minimum Principle was then applied to reduce a global optimization problem to a local minimization, allowing for the control problem to be solved and implemented in an algorithm. The control algorithm was then implemented on a validated energy-based PHEV simulator. Simulations were conducted to evaluate the sensitivity of the supervisory controller to different vehicle utilization and energy generation scenarios. A large database of driving profiles, including regulatory cycles and ”real-world” vehicle velocity profiles extracted from fleet studies data, were considered to provide a validation framework. Based on the analysis conducted, the proposed energy management strategy presents a relatively low sensitivity to the driving profile characteristics (i.e., the energy demand at the wheel or the driving distance). This result was achieved because of the definition of a cost functional that formally accounts for the different mix of primary energy forms utilized by the PHEV, representing an improvement over the conventional control approaches that approximate the energy utilization with an equivalent fuel consumption metric. In particular, the vehicle CO2 emissions show a presence of an optimal condition varying the control strategy parameter λi , but also a relatively large ”sweetspot” where only marginal variations from the optimal condition occur. Conversely, a higher sensitivity to the control parameter λi was observed on the battery SoE profile and, ultimately, the vehicle operating mode.

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A PPENDIX A brief description of the driving cycles characteristics considered in the validation study is here reported. A combination of regulatory and real-world driving cycles was used to validate the proposed supervisory energy management strategy. For each cycle, information on the distribution of vehicle velocity, the driving distance and the energy demand at the wheel are provided. The energy demand at the wheel is computed based on the road load equation [25]:  Z te  Z te Z te dV 1 V Ewheel = M V 3 dt +Cr Mg dt + ρaCx A f V dt dt 2 ti ti ti (32) where V is the vehicle velocity, M is the vehicle mass, ρa the air density, Cx the aerodynamic friction coefficient, A f the vehicle frontal area, Cr the tire rolling resistance coefficient and g the acceleration of gravity. The above equation neglects the effects of the road grade. The vehicle parameters are listed in Table IV. Parameter M ρa Cx Af Cr

Value 2130 1.29 0.417 2.86 0.015

Units kg kgm−3 m2

TABLE IV V EHICLE PARAMETERS U SED IN E QUATION 32.

Table V summarizes the most relevant metrics of the driving cycles. In particular, the distribution of the distance was chosen so as to ensure a driving length greater than the vehicle all electric range, but also a maximum distance that is representative of typical daily commuting trips.

15

Cycle 2FTP 3FTP 4FTP Path 3 Path 4 Path 5 Path 6 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

Velocity [m/s] Vmean Vmax 23.98 8.82 35.97 8.82 47.96 8.82 28.24 18.48 30.10 12.16 29.93 23.03 29.88 8.08 40.20 14.44 65.66 9.94 77.73 18.03 45.67 9.09 82.94 13.93 88.98 16.22 80.43 18.58 44.43 9.82 39.88 18.92 80.20 10.90 48.35 11.76 80.39 13.98 49.82 13.73 74.69 12.58 47.51 9.79 85.32 9.87 78.79 7.59 36.42 10.47

Length [km] 25.35 25.35 25.35 30.60 35.00 34.17 21.67 33.06 32.50 33.06 28.89 33.06 33.06 33.06 32.50 33.06 33.06 33.06 33.06 33.06 33.06 33.06 33.06 30.56 31.39

Energy [MJ] Pos Neg 18.67 -6.54 28.00 -9.80 37.34 -13.07 28.77 -4.10 29.96 -7.18 31.17 -1.59 26.36 -11.06 40.32 -6.85 61.52 -17.48 82.71 -8.98 41.11 -13.17 83.17 -14.55 95.40 -10.64 90.20 -8.84 39.25 -12.38 40.72 -3.53 80.50 -18.04 52.31 -8.25 82.33 -11.68 49.77 -7.70 76.84 -16.08 48.45 -11.76 85.06 -21.50 70.47 -29.88 34.82 -9.38

Cycle 20 21 22 23 24 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

Velocity [m/s] 38.28 17.50 73.50 10.84 38.90 14.28 75.73 14.52 52.42 10.93 96.50 8.40 87.16 10.59 36.35 5.95 39.74 11.17 90.67 9.03 90.42 14.82 60.24 10.84 54.18 9.06 90.10 11.79 58.33 7.65 59.74 9.62 57.13 9.77 48.40 8.62 36.42 10.27 71.03 16.89 47.29 15.61 93.51 10.63 72.14 6.81 67.29 14.88 64.57 9.77 61.68 22.66 66.52 21.91 34.54 8.00 64.02 8.70 47.90 17.95 34.17 7.60 84.52 9.35 76.66 13.46 72.65 10.44 83.42 12.88 92.75 13.57 86.49 8.59 36.55 9.05 56.08 8.17 69.41 14.45 81.96 16.25 61.35 9.10 75.80 10.03 88.98 16.86 90.30 15.66 60.76 13.32 33.75 9.57 50.49 7.86 70.17 10.41 57.02 12.05 88.86 9.68 44.92 7.69 81.41 11.99 66.17 12.41 53.77 8.89 66.96 8.61 80.65 9.90 65.76 14.96 96.29 10.23 80.12 16.37 53.08 10.66

Length 33.06 33.06 33.06 33.06 33.06 33.06 33.06 25.56 33.06 33.06 33.06 30.83 33.06 31.39 27.50 33.06 33.06 33.06 33.06 33.06 33.06 33.06 29.44 33.06 33.06 33.06 33.06 30.00 33.06 33.06 30.56 33.06 33.06 33.06 33.06 33.06 33.06 29.44 33.06 33.06 33.06 33.06 33.06 33.06 33.06 33.06 32.50 27.50 33.06 33.06 33.06 33.06 33.06 33.06 30.56 31.39 33.06 33.06 33.06 33.06 33.06

Energy [MJ] 41.66 -4.86 69.30 -18.73 41.92 -6.53 81.07 -11.29 49.31 -12.74 90.06 -33.11 81.83 -19.78 33.73 -17.33 42.49 -7.93 89.17 -25.48 93.59 -14.00 54.82 -15.03 52.79 -16.94 82.59 -20.54 52.53 -23.14 62.59 -15.98 55.80 -14.50 46.88 -16.25 38.11 -8.92 79.37 -7.95 50.86 -6.84 85.27 -23.82 66.84 -31.30 69.12 -9.56 63.74 -17.74 69.42 -3.47 69.79 -5.02 31.47 -13.31 62.39 -20.75 55.20 -4.76 30.98 -11.70 76.85 -24.38 79.60 -13.71 71.80 -18.17 79.66 -17.91 94.89 -14.95 81.56 -29.63 33.62 -9.28 53.82 -18.46 74.58 -10.70 86.55 -12.69 59.80 -18.38 68.92 -21.76 89.12 -10.26 94.40 -12.29 60.03 -10.40 33.61 -9.23 45.21 -18.46 67.44 -19.28 56.38 -11.89 83.63 -24.64 42.87 -16.68 79.99 -17.80 68.00 -12.61 48.16 -16.64 61.72 -21.97 74.50 -21.46 71.55 -8.98 89.61 -27.05 83.87 -12.51 50.07 -12.62

Cycle 90 91 92 93 94 95

Velocity [m/s] Vmean Vmax 43.69 10.54 84.58 23.12 89.62 22.18 34.35 12.53 43.36 12.69 42.07 8.09

Length [km] 33.06 33.06 33.06 30.00 33.06 33.06

Energy [MJ] Pos Neg 43.60 -8.78 95.08 -4.55 95.39 -6.43 30.96 -8.51 44.43 -9.00 39.57 -13.89

TABLE V S UMMARY OF METRICS FOR THE DRIVING CYCLES CONSIDERED IN THE STUDY.

16