TECHNICAL FIELD

The present disclosure relates to speed trajectory optimization to reduce the energy consumption and battery degradation of an electrical vehicle. BACKGROUND

In recent years, there has been a significantly growing trend of electrification of vehicles. Due to factors such as environmental friendliness and cheaper running costs of electrical vehicles compared to conventional vehicles, the number of electrical vehicles is expected to excel even more in the coming years. Meanwhile, there is also extensive research and development ongoing for autonomous vehicles. There is research and development ongoing for both fully autonomous vehicles as well as semi-autonomous vehicles. The implementation of autonomous vehicles is hoped to increase safety, eco-friendliness and reduce the error of the vehicles.

As a consequence, autonomous electrical vehicles are being developed by a majority of the vehicle manufacturers in the world. There exist certain challenges with this type of vehicles that the manufacturers have to address. A disadvantage with electrical vehicles is that the battery life of the vehicle is limited and that the battery of an electrical vehicle degrades over time. Thus, with the uprising of autonomous electrical vehicles, a challenge to address is how to reduce the energy consumption and battery degradation of the battery of an autonomous electrical vehicle.

Based on this, a major challenge of autonomous electrical vehicles is how to control the velocity of a vehicle from departure to destination in an eco-driving manner. Thus, there is a need to develop solutions to control factors such as acceleration, coasting, deceleration and braking of an autonomous or semi-autonomous electrical vehicle in an eco-driving way in order to reduce the energy consumption and battery degradation of the vehicle and meanwhile increase the safety of the vehicle on the road.

SUBSTITUTE SHEET (Rule 26) Accordingly, there is a need for improvements of the present art in order to overcome the abovementioned issues. It would be desirable to provide an electrical vehicle that fulfils requirements related to reducing the energy consumption and battery degradation of the vehicle.

SUMMARY

It is therefore an object of the present disclosure to provide a method to reduce energy consumption and battery degradation of an electrical vehicle, a computer readable storage medium and an electrical vehicle to mitigate, alleviate or eliminate one or more of the above- identified deficiencies and disadvantages.

This object is achieved by means of a method to reduce energy consumption and battery degradation of an electrical vehicle, a computer readable storage medium and an electrical vehicle as defined in the appended claims 1-10.

The present disclosure is at least partly based on the insight that by providing a method for speed trajectory optimization, a computer readable storage medium and a vehicle that is able to obtain an optimal speed trajectory of a vehicle for a predefined set of road segments, the energy consumption and battery degradation of an electrical vehicle is reduced.

The present disclosure provides a method for speed trajectory optimization to reduce the energy consumption and battery degradation of an electric vehicle, the method comprises the steps of obtaining traffic data of a predefined set of road segments associated with a trajectory of the vehicle. Further, the method determines the system dynamics of the vehicle by constructing state-space equations (or utilizing a state-space model) indicative of a correlation of vehicle velocity, state of charge, SOC and state of health, SOH of a battery of the vehicle. Further, an optimization module is deployed based on the system dynamics and the traffic data to obtain an optimal speed trajectory of the vehicle over the predefined set of road segments. Furthermore, based on the optimal speed trajectory, a control signal is transmitted to a control unit configured to adjust the velocity of the vehicle in a first segment of the predefined set of road segments.

SUBSTITUTE SHEET (Rule 26) A benefit of the method is the speed trajectory of a vehicle can be optimized so to reduce the energy consumption of the vehicle and the degradation of the battery of the vehicle. In other words, the optimization of the speed trajectory of the vehicle may result in that the energy consumption of the vehicle and the degradation of the battery of the vehicle is minimized over the pre-defined set of road segments. Thus, by determining system dynamics of the vehicle that depend on both state of charge and state of health of the battery of the vehicle, the speed trajectory is optimized so to both reduce/minimize the energy consumption of the battery in the short-term during its journey through the road segments, and to maintain the battery in the longer run in future use, resulting in that the battery of the vehicle will have a longer lifetime. Hence, the battery is efficiently utilized in both short and long terms. The method results in a vehicle that optimizes the speed trajectory of the vehicle to efficiently utilize a battery both in short-term and long-term. The term correlation may be beneficially replaced with "dependencies".

The optimization module may comprise an adaptive alternating method of multipliers (ADMM) algorithm, configured to determine, based on the system dynamics, the optimal velocity in real time subject to a total trip time of the trajectory for the predefined set of road segments and traffic data in order to minimize the energy consumption and degradation of the battery.

A benefit of this is that the algorithm allows for the vehicle to adjust its velocity in real-time subject to the total trip time constrains of the vehicle which comprises of a plurality of road segments. Thus, the velocity is adjusted in real-time to optimize a total trip resulting in that battery utilization is optimized.

The ADMM algorithm may further determine at least one of the cumulative SOC change and SOH change of the battery of the vehicle, allowing for the energy consumption and the health of the battery to be monitored.

A benefit of determining the cumulative SOC and SOH change of the battery of the vehicle is that the parameters may be monitored by the vehicle/driver, allowing a driver to note parts of a trip that are less advantageous for the vehicle such that the driver may choose a different route which is better for the health of the battery next time the driver is doing a similar trip

SUBSTITUTE SHEET (Rule 26) between two similar points on a map i.e. the parameters may be used to provide alternative routes for superior energy efficiency and battery health.

The optimal velocity subject to the total trip time constraint for the predefined set of road segments may be obtained by minimizing the total energy consumed and battery degradation determined as:

Wherein i is the predefined road segment number, x _i is the velocity at the beginning of road segment i, and x is the velocity vector consisting of x _i ;

, k is a vector consisting of k _i indicating at least four scenarios of driving profiles in a segment, wherein k _i = 1 - discharging only, k _i = 2 - charging only, k _i = 3 - changing from discharging to charging, k _i = 4 - changing from charging to discharging, wherein η and θ are functions of x and k;

J = [J ^ME ,J ^MD ] ^T , J ^ME indicates the consumed energy and J ^MD indicates the battery degradation.

A benefit of the minimizing function is that it indicates four scenarios of driving profiles in a segment. Thus, resulting in a precise determining of the optimal velocity subject to the total trip time constraint.

The optimization module may be a model predictive control, MPC framework comprising a cloud computing system. Thus, the optimal velocity may be shared between different vehicles to achieve overall efficiency at a fleet level.

The traffic data may comprise topography data, road curvature data, stop light data, speed limit data, road restriction data and surrounding traffic data. Thus, the traffic data takes into account all (or at least the most influential) factors that may affect a vehicle that drives in a trajectory of road segments.

SUBSTITUTE SHEET (Rule 26) The state-space equations may comprise a state transition function indicating vehicle velocity and an output function indicating SOC and SOH variations of the battery.

The SOC of the battery may be defined by a ratio of remaining available capacity and nominal capacity of the battery. There is also disclosed a computer-readable storage medium storing one or more programs configured to be executed by one or more processors of an electronic device, the one or more programs including instructions for performing the method as disclosed herein.

There is also disclosed an electrical vehicle comprising a battery, control circuitry and a control unit, wherein the control circuitry is configured to obtain traffic data of a predefined set of road segments associated with a trajectory of the vehicle. Further, determining system dynamics of the vehicle (or by constructing) by means of state-space equations indicative of a correlation of vehicle velocity and a state of charge, SOC and state of health, SOH of the battery of the vehicle. Further deploying an optimization module based on the system dynamics and the traffic data to obtain an optimal speed trajectory over the predefined set of road segments. Based on the optimal speed trajectory, a control signal is transmitted to the control unit in the vehicle configured to adjust the velocity of the vehicle in a first segment of the predefined set of road segments.

BRIEF DESCRIPTION OF THE DRAWINGS Further objects, features and advantages of embodiments of the disclosure will appear from the following detailed description, reference being made to the accompanying drawings, in which:

Figure 1 depicts a flow chart of a method for speed trajectory optimization to reduce the energy consumption and battery degradation of an electric vehicle of in accordance with an embodiment of the present disclosure.

Figure 2 depicts an MPC framework in accordance with an embodiment of the present disclosure.

SUBSTITUTE SHEET (Rule 26) Figure 3 schematically depicts a diagram over the velocity of a vehicle in n segments

Figure 4 schematically depicts a vehicle in accordance with an embodiment of the present disclosure.

Figure 5a depicts in a diagram the road altitude in-between two destinations Figure 5b depicts in a diagram the road slope in-between two destinations.

Figure 6 depicts the relative changes of energy consumption and trip time in-between two destinations.

Figure 7a depicts comparison of results between ADMM, DP, PIC and CC based on road slopes

Figure 7b comparison results of SOC reduction between ADMM, DP, PIC and CC based on the road slopes in Figure 7a

Figure 7c depicts comparison of results between ADMM, DP, PIC and CC based on road slopes

Figure 7d comparison results of SOC reduction between ADMM, DP, PIC and CC based on the road slopes in Figure 7c

Figures 8a-d depicts simulation results on flat roads with different preceding velocities and initial distances.

Figure 9a shows speed trajectories and road altitude corresponding to 7a.

Figure 9b shows SOC reductions in accordance with Figure 9a.

Figure 9c shows speed trajectories and road altitude corresponding to 7b.

Figure 9d shows SOC reductions in accordance with Figure 9c. Figure 10a shows the speed trajectories of the simulation results from Sodertalje to Norrköping under heavy traffic.

Figure 10b shows the SOC reduction results of the simulation in 10a.

SUBSTITUTE SHEET (Rule 26) Figure 10c shows the speed trajectories of the simulation results from Norrköping to Södertälje under light traffic.

Figure 10d shows the SOC reduction results of the simulation in 10c. DETAILED DESCRIPTION

In the following detailed description, some embodiments of the present disclosure will be described. However, it is to be understood that features of the different embodiments are exchangeable between the embodiments and may be combined in different ways, unless anything else is specifically indicated. Even though in the following description, numerous specific details are set forth to provide an understanding of the provided method and the vehicle, it will be apparent to one skilled in the art that the method and the vehicle may be realized without these details. In other instances, well known constructions or functions are not described in detail, so as not to obscure the present disclosure.

In the following description of example embodiments, the same reference numerals denote the same or similar components.

The term "vehicle" refers to cars, trucks, busses or any other suitable type of vehicle. The vehicle (e.g. see ref. 1 in Figure 4) as referred to herein may be an autonomous vehicle that operates at Level 1, Level 2, Level 3, Level 4, or Level 5 of SAE (Society of Automotive Engineers) International Standard J3016.

The term "electric vehicle" refers to a vehicle (e.g. see ref. 1 in Figure 4) that uses one or more electric motors or traction motors for propulsion. An electric vehicle may be powered by at least one battery, or electricity from off-vehicle sources, or may be self-contained to convert fuel to electricity.

The term "speed trajectory optimization" may refer to optimizing the velocity profile of a vehicle in a trip comprising of a plurality of road segments such that the velocity of the vehicle is adapted to benefit specific parameters of the vehicle such as the battery degradation or state of charge of the vehicle. Accordingly, this may comprise adjusting the vehicle operations such as the maximal acceleration, acceleration, coasting, deceleration, maximal deceleration

SUBSTITUTE SHEET (Rule 26) and braking in different traffic environments/scenarios in order to in best possible manner benefit specifics of the vehicle.

The term "optimization module" may refer to a module generating output for operating a control unit of a vehicle. The optimization module (see ref. 5 in Figure 4) may be implemented in the control circuitry (see ref. 3 in Figure 4) of the vehicle and be configured to communicate with the control unit of a vehicle. The control circuitry of the vehicle may be a sub-component of the control unit of the vehicle. According to some embodiments, the optimization module may be implemented in a cloud computing system i.e. sensor data may be sent to an external system performs all or parts of the steps of the method and transmits a control signal to the control unit of the vehicle.

The control circuitry (see ref. 3 in Figure 4) may comprise at least one memory, at least one sensor interface and/or at least one communication interface. Accordingly, the control circuitry may also be configured to receive traffic data of the surroundings of a vehicle. The data, according to some embodiments, may be received from an acquisition system of the vehicle communicating with the control circuitry. An acquisition system may be one responsible for acquiring raw sensor data from on-board sensors such as cameras, LIDARs and RADARs, ultrasonic sensors, and converting this raw data into scene understanding.

A communication interface (see ref. 7 in Figure 4) may be arranged to communicate with other control modules of the vehicle and may thus be seen as control interface also. Local communication within the vehicle may also be of a wireless type with protocols such as WiFi, LoRa, Zigbee, Bluetooth, or similar mid/short range technologies. However, the internal communication of the vehicle may be by the use of a local network setup, such as CAN bus, I2C, Ethernet, optical fibres, etc.

The term "non-transitory," as used herein, is intended to describe a computer-readable storage medium or memory (see memory in ref. 6 in Figure 4) excluding propagating electromagnetic signals, but are not intended to otherwise limit the type of physical computer-readable storage device that is encompassed by the phrase computer-readable medium or memory. For instance, the terms "non-transitory computer readable medium", "memory" or "tangible memory" are intended to encompass types of storage devices that do not necessarily store information permanently, including for example, random access memory

SUBSTITUTE SHEET (Rule 26) (RAM). Program instructions and data stored on a tangible computer-accessible storage medium in non-transitory form may further be transmitted by transmission media or signals such as electrical, electromagnetic, or digital signals, which may be conveyed via a communication medium such as a network and/or a wireless link. Thus, the term "non- transitory", as used herein, is a limitation of the medium itself (i.e., tangible, not a signal) as opposed to a limitation on data storage persistency (e.g., RAM vs. ROM).

Figure 1 discloses a method 100 for speed trajectory optimization to reduce the energy consumption and battery degradation of an electric vehicle. The method comprises the steps of obtaining 101 traffic data of a predefined set of road segments associated with a trajectory of the vehicle. Further, the method determines 102 system dynamics of the vehicle by constructing (or by means of) state-space equations indicative of a correlation of vehicle velocity, state of charge, SOC and state of health, SOH of a battery (see e.g. ref.2 in Figure 4) of the vehicle. Further, the method deploys 103 an optimization module based on the system dynamics and the traffic data to obtain an optimal speed trajectory of the vehicle over the predefined set of road segments. Accordingly, based on the optimal speed trajectory, a control signal is transmitted 103 to a control unit configured to adjust the velocity of the vehicle in a first segment of the predefined set of road segments. The term "deploy" may be interchanged with "utilized" or "use" or "launch". The step "by constructing state-space equations indicative of a correlation of vehicle velocity, state of charge, SOC and state of health, SOH of a battery of the vehicle, may in other words, be expressed as "by utilizing/means of a state-space model indicative of a correlation of vehicle velocity, state of charge, SOC and state of health, SOH of a battery of the vehicle".

Thus, the method 100 allows an electrical vehicle which is e.g. on a trip from e.g. point A to point B to divide the trip between A-B as a plurality of road segments. Further, traffic data from the plurality of road segments of the trip A-B are obtained. Thus, the method allows for reduction of energy consumption and degradation of the battery when the vehicle is transporting from point A to point B. The velocity may be adjusted in real-time by continuously deploying the optimization module during the trip of the vehicle to always be up to date with the most optimal speed trajectory of the vehicle. Each road segment may be within the range of 20-800m and wherein the predefined set of road segments may be within the range of 20-60 road segments.

SUBSTITUTE SHEET (Rule 26) The term "State of health" or "SOH" may refer the general condition of a battery and its ability to deliver the specified performance compared with a fresh battery. The general condition of the battery may be determined from factors as charge acceptance, internal resistance, voltage, and self-discharge which may give an indication of long term health of the battery and how much of the available "lifetime energy throughput" of the battery has been consumed, and how much is left.

The term "stage of charge" or SOC" may refer to the available capacity of the battery in the short-term i.e. the SOC may indicate the range of a battery before it e.g. has to be charged again. The optimization module may comprise an adaptive alternating method of multipliers (ADMM) algorithm, configured to determine, based on the system dynamics, the optimal velocity in real time subject to a total trip time of the trajectory (journey) of the vehicle for the predefined set of road segments and traffic data in order to minimize the energy consumption and degradation of the battery. Further, the ADMM algorithm may determine at least one of the cumulative SOC change and SOH of the battery (or batteries) of the vehicle. This allows for the energy consumption and the health of the battery to be monitored such that errors and less beneficial traffic conditions for the vehicle may be properly identified. The energy consumption and the health of the battery may be continuously monitored cumulatively from when the vehicle starts to move in a trajectory e.g. when the vehicle starts a journey from point A to point B, these factors are cumulatively determined.

The optimal velocity subject to the total trip time constraint for the predefined set of road segments is obtained by minimizing the total energy consumed and battery degradation, determined as: wherein i is the predefined road segment number, x _i is the velocity at the beginning of road segment i, and x is the velocity vector consisting of x _i ;

SUBSTITUTE SHEET (Rule 26) k is a vector consisting of k _i indicating at least four scenarios of driving profiles in a segment, wherein k _i = 1 - discharging only, k _i = 2 - charging only, k _i = 3 - changing from discharging to charging, k _i = 4 - changing from charging to discharging, wherein η and Θ are functions of x and k;

J = [J ^ME ,J ^MD ] ^T , J ^ME indicates the consumed energy and J ^MD indicates the battery degradation.

Figure 2 illustrates an MPC framework according to one aspect of the disclosure. Accordingly, the optimization module may be a model predictive control, MPC framework comprising a cloud computing system. The MPC framework may allow the real-time velocity of the vehicle in a first road segment to be optimized, while keeping future timeslots (i.e. future road segments) in account. This is achieved by optimizing over a plurality of road segments, but wherein implementation is performed real-time. Thus, there is an iterative optimization of road segments associated with the trajectory of the vehicle but only real-time implementation of the optimal velocity of the vehicle.

The traffic data may comprise topography data, road curvature data, stop light data, speed limit data, road restriction data and surrounding traffic data. The traffic data may also comprise environmental conditions such as e.g. rain. The state-space equations may comprise a state transition function indicating vehicle velocity and an output function indicating SOC and SOH variations of the battery. The vehicle velocity may be the vehicle velocity at the beginning of a segment of the plurality of road segments. Thus, the state space equations may define dependencies among vehicle velocity, state of charge and state of health of the battery (or batteries) of the vehicle.

According to some embodiments of the present disclosure the system dynamics may be determined as follows:

First, the trajectory of the vehicle is divided into N equally spaced segments of unit length, and segment i begins at t _i .

The definition of segment variables is listed in Table 1.

SUBSTITUTE SHEET (Rule 26) Table 1 Segment variables definition for segment i

Let x = (x ₁ , ..., x _N ), y = (y ₁ , ...,y _N ), a = (a ₁ , ..., a _N ), and T = (T ₁ , ...,T _N ) . This is further shown in the schematic diagram in Figure 3.

Given the acceleration of a _i in segment i , the state (velocity) x _i and output (SOC increment) y _i in segment i are given by x _i+1 = F _i (x _i ,a _i ),y _i = G _i (x _i ,a _i ) (1) where the state transition function F _i (·,·) and the output function G _i (·,·) are given by

(2) (3) where k _i = 1,2, 3, 4 indicates the number of the four possible cases within each road segment.

The parameters are given in Table 2.

Table 2 Value of vector parameter y _i

SUBSTITUTE SHEET (Rule 26)

Note that the above state-space model is highly nonlinear. However, the model simplifies considerably under the following idealizing conditions that may be sufficient in practice:

A1: the battery charging and discharging coefficients are identical and equal to 1;

A2: the segment length is sufficiently small that the track force does not change signs within each segment.

Under A1 and A2, the AET state-space model may be given by

(4) (5) where indicating that vector parameter y _i is independent of x _i and a _i . Although assumptions A1-A2 are restrictive, they lead to simple optimization algorithms.

According to some embodiments, the optimization may be based on:

The total energy consumed (E) may be given by the cumulative SOC change such as: (6) where parameters y _i ⁽⁰⁾ ,y _i ⁽¹⁾ ,y _i ⁽²⁾ are given with (5). x _i , a _i and T _i are related by

(A1) which gives

The state transition is then given by

(A2)

From Eqs. (A1) and (A2), we have

SUBSTITUTE SHEET (Rule 26) (7)

(8)

Substituting a _i in the total energy expression, the following is achieved:

(9) where

The minimum energy control is to minimize the energy consumption subject to a total triptime constraint τ: minimize

∈ R ^N

Subject to where are, respectively, the lower and upper speed limits. Note that involves two sets of variables including the speed x and the travel time T to be optimized.

Note that although the above optimization is nonconvex, optimizing x for fixed T is convex (quadratic) that can be solved easily. For fixed x, solving T that satisfies the constraints amounts to solving a linear equation. Thus, a method of alternately solving x and T can be

SUBSTITUTE SHEET (Rule 26) Derived easily. This method is referred to as an alternating direction method of multipliers (ADMM) method.

Energy minimization without assumptions A1 and A2: Similarly, the total energy consumed is given by the cumulative SOC change in this case as

(10) where as described before, k _i = 1,2,3,4 indicates the number of the four possible cases within each road segment, and the determination of k _i value depends on the vector (x _i , a _i ).

The parameters can be referred to in Table 2.According to (7), substituting a _i in the total energy expression, we have

(11)

10 where and

Still, the minimum energy control is to minimize the energy consumption subject to a total trip- time constraint τ:

Subject to

SUBSTITUTE SHEET (Rule 26)

Note that although the objective function is no longer convex, the optimization problem has a similar structure as that of , and thus, the structure of ADMM can still be used here.

The ADMM is a simple but powerful algorithm that is well suited to distributed optimization problems. It takes the form of a decomposition-coordination procedure, in which the solutions to small local subproblems are coordinated to find a solution to a large global problem. ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization.

As in the method of multipliers, we form the augmented Lagrangian by relaxing the constraints in where μ, λ, and p are the augmented Lagrangian coefficients, and · When the speed trajectory x is fixed, the driving case within each road segment indicated as k _i is determined, and η ₀ (x,k) and η _i (x,k) are obtained accordingly. The above equation can thus be expressed as a quadratic function of T with x being fixed:

(12) where is a matrix coefficient of the quadratic term, p ∈ R ^N is a vector coefficient of the first-order term, and q ∈ R is a constant.

The ADMM may be given by the iterations:

Step 1: Initialize μ,λ,ρ.

Step 2: Initialize the speed trajectory and the trip time T ^{(0 )} .

SUBSTITUTE SHEET (Rule 26) Step 3: Solve the primal variables

(13) where the Matlab algorithm fmincon(.) is used to solve (15). Further, k ⁽ⁿ⁺¹⁾ is updated according to x ⁽ⁿ⁺¹⁾ , and for each iteration within fminconQ ), the vector x is always firstly determined, followed by the calculation of the vector k and then the function value (14) where T ⁽ⁿ⁺¹⁾ is obtained by calculating the minimum value .Step 4: Update the multipliers

(15)

(16)

Step 5: Repeat Steps 3-4 until the solution difference between two iterations is small enough with and the constraints of the optimization problem are met with . Note that ε ₁ and ε ₂ are two predefined positive real numbers close to zero.

There is also provided a computer-readable storage medium storing one or more programs configured to be executed by one or more processors of an electronic device, the one or more programs including instructions for performing the method as disclosed herein.

As shown in Figure 4, there is further provided an electrical vehicle 1 comprising a battery 2, control circuitry 3 and a control unit 4, wherein the control circuitry 3 is configured to obtain traffic data of a predefined set of road segments associated with a trajectory of the vehicle 1 and further to determine system dynamics of the vehicle 1 by constructing state-space equations indicative of a correlation of vehicle velocity and a state of charge, SOC and state of health, SOH of the battery 2 of the vehicle. Also further, the control circuitry 3 is configured to deploy an optimization module based on the system dynamics and the traffic data to obtain an optimal speed trajectory over the predefined set of road segments. Based on the optimal

SUBSTITUTE SHEET (Rule 26) speed trajectory, the control circuitry 3 transmits a control signal to the control unit 4 in the vehicle configured to adjust the velocity of the vehicle in a first segment of the predefined set of road segments.

As further shown in Figure 4, the vehicle may comprise a communication interface 7, a memory 6 and an optimization module 5 may be implemented in the control circuitry.

Figures 5 - 10 discloses test results of the method and the vehicle as disclosed herein in accordance with an aspect of the disclosure. In other words, the test results are not in any manner limiting to the disclosure, and the disclosure is not limited to the embodiments shown in the test results, and may be varied within the present disclosure. The tests were performed on the slope data of highway E4 between the cities of SddertSlje and Norrköping in Sweden.

The road slope and altitude are shown in Figures 5a-5b. The electric truck modeled was a Tesla Semi tractor and trailer

There are some algorithm parameters to be initialized before simulation. The length of each road segment i was set to 50 m and the number of segments N was set to 30. Therefore, the prediction horizon was 1500 m. The speed lower bound was set to 0 km/h, while the speed upper bound was set to 90 km/h, which is the legal maximum permissible speed in the EU. The trip time τ was set by the user. In this study, τ was set equal to the trip time of that using a uniform speed of 85 km/h to travel through the same distance. Two comparative tests were conducted based on the road data between SddertSlje and Norrköping to compare the performance of the ADMM controller and the uniform speed cruise control (CC) controller. The CC speed was set at 85 km/h, and the relative changes of energy consumption and trip time between the two controllers are shown in Figure 6. A negative value indicates that the ADMM controller had a lower value than the CC does. The results show that, compared to the CC the ADMM controller saved 4.28% energy from Södertälje to Norrköping and 4.83% energy from the return, while the trip time between these two controllers were similar to each other in both directions.

SUBSTITUTE SHEET (Rule 26) Comparisons with energy efficient driving algorithms for traditional trucks are conducted where dynamic programming (DP) and proportional integral control (PIC) were proposed. All parameters that could affect the vehicle energy consumption. Figures 7a-d presents the comparison results between ADMM, DP, PIC and CC based on road slopes. The speed value of the CC was set to have the same trip time as that of PI. The relative changes in energy consumption and trip time (ΔSOC, ΔT) of ADMM to other methods are also presented in Figures 7a-d for each road scenario.

Since the charging/discharging efficiency of the vehicle is less than 1, the regenerative braking is only able to regenerate a part of the consumed energy. Besides, moving the truck forward also consumes energy to overcome different kinds of resistances, and this energy consumption further reduces the efficiency of the regenerative braking. Therefore, energy consumption can be reduced by avoiding any undesirable braking. Figure 7a shows that the AET kept constant speed based on ADMM except during downhill stretches, where the truck decelerated first, then accelerated, finally decelerated again to a constant speed. The ADMM-based energy consumption on the downhill in Figure 7b is zero, which indicates the truck moved forward in the most energy conserving fashion with no undesirable braking, whereas braking was observed in Figure 7b for all other methods including the DP, PIC, and CC. Note that the traditional truck needed to downshift (decelerate) to increase the driving force when going uphill (see DP and PIC-based speed trajectory in Figure 7a, which caused the undesirable acceleration and braking on the downhill (see DP and PIC-based energy consumption in Figure 7b to meet the trip time requirement. Because the ET powered by the motor was able to go uphill without decelerating and with a high speed, it left wider space for improving energy consumption when going downhill than the traditional truck did. In each case, the CC performed the worst since it used the most undesirable braking and thus consumed the most energy to keep a constant speed when going downhill. The energy consumption results in Figure 7b show that, with a similar trip time, the ADMM, respectively, consumed 1.72%, 1.78%, and 1.93% less energy than the DP, PIC and CC did.

Figure 7c shows the optimal speed trajectories on a road with a long downhill segment where braking was inevitable for the AET within the speed upper limit. In this case, the ADMM used less braking and thus consumed less energy than other methods. The energy consumption results show that the ADMM, respectively, consumed 2.22%, 2.99%, and 9.02% less energy than

SUBSTITUTE SHEET (Rule 26) the DP, PIC and CC while keeping a similar trip time. Figures 7a-7d discloses the speed optimization results and the road altitude data. The corresponding energy consumption, which is indicated by SOC reduction, is presented in Figures 7b and 7d.

Energy minimization of ET is only one of issues of AET eco-d riving control. Also relevant is the impact of driving algorithm on battery health. Limited to the current battery technology, the battery life is generally shorter than the EV life.

Battery aging includes cycling aging and calendar aging. For a long-haul ET, the most suitable operation mode would be shipping during the day and charging at night. This operation mode indicates that the ET battery pack will be cycled most of the day. In this case, the evaluation comprises the cycling aging of batteries for the ET.

The case study shows that generally, a long-haul ET should run more than 500 km each working day. Therefore, the road data from Sodertalj to Norrköping and the return (about 240 km long) was repeated to generate the road data profile with the wanted travel distance. Assuming the ET shipped during the day and got charging at night. A slow charging was preferred for extending the battery life and thus the charging rate was set at 0.1 C in the modeling. Note that the truck was expected to be used each working day and thus it would operate 260 days each year. Currently, the EV battery degradation limit is agreed upon 30% limit. Three cases where simulated for each case the truck drove a pre-determined distance, or the battery pack reached a pre-determined ending SOC each day. Case 1 : The truck traveled 800 km long each day, which distance is the Tesla claimed truck driving range with batteries fully charged. The battery DODs for the ADMM and CC benchmark are, respectively, 90.86% and 95.12% after the trip and the Ah throughputs of one battery pack are, respectively, 328.8 Ah and 400.3 Ah. It was observed that after speed control using ADMM, the charge delivered by the battery reduces 71.5 Ah, which accounts for 22.9% of the battery nominal capacity. As the capacity degradation is proportional to the Ah throughput, the ADMM controller was expected to extend the battery life by more than 20% compared to the CC policy. This high improvement showed that, when compared with the CC benchmark, the proposed eco-control algorithm not only minimized energy consumption but also extended battery life. The improvement of battery health came from the fact that the proposed minimum energy control avoided undesirable braking. Note that the battery delivered about twice the

SUBSTITUTE SHEET (Rule 26) regenerative charge by each undesirable braking comparing with the case when the undesirable braking is avoided.

In this case, the SOC cycling range for ADMM and CC benchmark were, respectively, [95.74%, 4.88%] and [100%, 4.88%]. The battery aging evaluation results are presented in Table 4. It was surprising to find that battery life based on ADMM was extended by 34.9% compared to CC. The ADMM controller led to lower battery DOD and thus smaller SOC _avg and SOC _dev than the CC controller did. This low battery DOD caused a reduction of 15.5% on the capacity fading rate δξ using ADMM compared to using CC. This is the reason why ADMM extended the battery life much higher than the afore-mentioned value of 20%. It was also found that the ET battery life was shorter than 5 years for both controllers, which indicated the necessity to extend battery life from the perspective of EV real-time operations.

Table 3 EV battery aging and life estimation results for case 1

Cases 2 and 3: Generally, an EV needs to be recharged when the battery SOC is lower than 10%- 20%. Therefore, in cases 2 and 3, the battery ending SOC was, respectively, setting to 10% and

20%, which corresponds to a truck travel distance of 760 km and 675 km each day. The battery aging results for the two cases are presented in Table 4. It was found that the battery life based on ADMM was extended by more than 30% compared to CC in both cases. With a higher ending SOC each day, the battery is expected to be used longer, while the travel distance each day is also shorter. In Case 3, the battery life was as long as 6.84 years based on ADMM. Note that the travel distances in cases 2 and 3 would shorten as the battery aged.

Table 4 EV battery aging and life estimation results for cases 2 and 3

SUBSTITUTE SHEET (Rule 26)

The performance of the method and the vehicle disclosed herein is also evaluated with surrounding traffic involved.

The energy consumption results for trucks following a preceding vehicle on a flat road (road slope = 0) are investigated herein. Further, there is investigated the truck energy consumption following a preceding vehicle on a road with changing slopes. Finally, the truck energy consumption results from Södertälje to Norrköping and the return are evaluated based on heavy and light traffics, respectively.

Figures 8a-d illustrates the simulation results on flat roads with different preceding velocities and initial distances. Figure 8a shows Speed trajectories based on ADMM and CC with a preceding vehicle velocity of 22 m/s and initial spacing of 90 m, and SOC reductions as the position are presented in Figure 8b. Figure 8c shows speed trajectories based on ADMM and CC with a preceding vehicle velocity of 20 m/s and initial spacing of 70 m, and SOC reductions as the position are presented in Figure 8d. Note that the CC speeds were obtained based on two rules: first, the CC travel time was the same as that based on ADMM, and second, the headway

SUBSTITUTE SHEET (Rule 26) for CC was also set to 1.2 s. It was observed that the ADMM controller saved more energy than the CC does in both cases, when the ADMM still braked less on flat roads. In case 1, the ADMM perfectly used resistances (air and frictional) to decelerate while the CC used additional braking which thus consumed more energy. In case 2, the ADMM braked for a little while at first then decelerated perfectly depending on resistances, while the CC braked until reaching the desired speed. Figure 8 indicates that the method still worked on saving energy for trucks following a preceding vehicle, and more energy was expected to be further saved with the road slopes involved.

Figures 9a-9d the simulation results with road slopes referred to in Figures 7a-d involved. Simulation results with both road slopes and traffics involved: Figure 9a shows speed trajectories and road altitude corresponding to Figure 7a. Figure 9b shows SOC reductions. Figure 9c shows speed trajectories and road altitude corresponding to Figure 7c. Figure 9d shows SOC reductions.

It was observed that the ADMM still braked as less as possible and thus made use of the energy more efficiently. Figure 7 (b) and (d) show the energy consumption based on ADMM was, respectively, reduced by 6.07% and 19.46% compared to that based on CC. These results indicate that the method still performed excellently on energy consumption improvement for trucks following a preceding vehicle on roads with changing slopes.

Figure 10 shows the simulation results from Södertälje to Norrköping under heavy traffic and the return under light traffic. Figures 10a and 10b present the speed trajectories and SOC reduction results under heavy traffic. Figures 10c and 10d present the speed trajectories and SOC reduction results under light traffic. The traffic stochastics was simulated based on the exponential distributions described herein. Figure 10a shows that most speeds based on the CC policy were less than the pre-determined speed (85km/h), which indicated there was a preceding vehicle ahead most of the traveling time. The speed trajectory of ADMM changed as both the speed of the preceding vehicle and the road altitude to minimize energy consumption, while the speed of CC changed as only the speed of the preceding vehicle. Figure 10b shows that the saved energy based on ADMM increased as the trip distance extended, and the energy consumption was reduced by 4.12% compared to using the CC policy. Figure 10c shows the scenario when there was no preceding vehicle most of the trip time and the energy

SUBSTITUTE SHEET (Rule 26) consumption based on ADMM in this case was reduced by 5.05% compared to using CC (see e.g. figure 8d). These energy saving results indicated that our method adjusted well to different traffic situations to minimize energy consumption.

The battery aging under traffic was also evaluated and the simulation results are listed in Table 6. In this case, both the road altitudes and traffics from from Södertälje to Norrköping and the return were repeated to generate the desired road and traffic profiles for simulation. The ending SOC each day was set to 15%, which energy consumption equivalents to running a truck of 725 km each day. The SOC cycling ranges based on ADMM and CC were thus, respectively, [96.14%, 15%] and [100%, 15%]. Table 5 shows that the ADMM controller extended the battery life of 3.96 years based on CC to more than 5 years, which life extension was as high as 32.81%.

Table 5: EV battery aging and life estimation results under traffic

The simulation results show that the developed method is able to exploit topographical conditions for improved energy management, both in terms of minimizing total battery discharge and prolong battery lifetime. It shows that the ADMM control consumes less energy under different scenarios than the dynamic programming (DP) control, proportional integral control (PIC) and uniform speed cruise control (CC). Generally, ADMM consumes 4%-5% less energy than CC does. It is thrilling to find the method and vehicle herein generally extends battery life by more than 30% than CC does. These results suggest the necessity to improve battery energy consumption and aging by optimizing truck speed trajectories. The battery energy and aging improvement values still hold when the traffic is introduced, which indicates that our method is also able to be used to suitable electric vehicles such as passenger vehicles, buses or trucks in urban driving.

SUBSTITUTE SHEET (Rule 26)