Integrated energy management for electrified vehicles

Integrated energy management for electrified vehicles

2

Electrified vehicles incorporate a plethora of new challenges and implementation issues that are not always transparent to designers and customers. When focusing on hybrid electric vehicles, the complexity of full electric and conventional vehicles is multiplied. On the one hand, conventional vehicle developers are forced to adapt engine calibration to the new powertrain characteristics, the vehicle transmission becomes more complex, new expertise in electric components and power electronics becomes necessary and more complex control strategies need to be developed. On the other hand, the end customer is unaware of the level of complexity achieved in hybrid electric vehicles and generally receives limited information about the strategy followed to reduce fuel consumption. In order to properly understand electrified vehicle control, it is necessary to analyse in detail the powertrain’s characteristics, layout possibilities and consequent capabilities from low-level components to a high-level controller’s perspective. This chapter briefly reviews the basics of electrified vehicles with special attention on the transition from conventional to full electric powertrains, highlighting their key characteristics and providing a comprehensive review of the main energy management strategies used for electrified vehicle control. The advantages and disadvantages of existing controllers are analysed and future solutions for vehicle control are proposed within the context of the current infrastructure capabilities and the forecasted development directions of the automotive industry. The chapter is closed with the proposal of a new framework able to serve as an immediate solution to achieve close-to-optimal real-time control of electrified vehicle consumption and a future merger with more sophisticated connectivity features under development.

2.1

Vehicle electrification levels

Conventional vehicles have dominated the road networks with undoubted supremacy for decades. Nonetheless, in recent years their leadership is being threatened by electrified powertrain solutions. Within conventional vehicles, with 0% electrification level, and battery electric vehicles (BEVs), with 100% electrification level, there is a large electrification range and a wide variety of hybrid powertrains. Although several alternative classifications can be found in the literature, the generally accepted arrangement agrees with a lower to higher electrification level that includes micro-hybrids, mild-hybrids, full-hybrids, plug-in hybrids and range-extended [1]. The first electrification step is taken with the micro-hybrids, which are a controversial class as they consist of vehicles that only integrate a starter generator able iHorizon-Enabled Energy Management for Electrified Vehicles. https://doi.org/10.1016/B978-0-12-815010-8.00002-8 © 2019 Elsevier Inc. All rights reserved.

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iHorizon-Enabled Energy Management for Electrified Vehicles

to perform the Start-Stop feature and do not have the capability of providing torque assist in the vehicle propulsion. Micro-hybrid powertrains can considerably reduce idling time and therefore fuel consumption, but since the electric motor does not assist the internal combustion engine, they are not considered to be ‘proper’ hybrids by many authors. The next electrification step includes mild-hybrids, which integrate a low power electric motor able to assist the internal combustion engine so as to absorb transients and improve the overall efficiency. Unfortunately, neither the electric motor power limits nor the battery capacity allow for electric-only mode; that is, the electric motor is not able to be used alone to propel the vehicle. In contrast, full hybrid electric vehicles (HEVs) integrate electric components sufficiently powerful to allow for electric drive and perform vehicle modes associated with full electric vehicles. That is the case of the electric launch available in the Toyota Prius. By incorporating the plug-in feature, the vehicles can incorporate larger and more powerful electric components, which implies wider margin for fuel displacement and emissions reduction. Besides, the grid support allows for depleting the battery charge completely and therefore replaces the equivalent fuel consumption with electricity. Finally, range-extended vehicles are a particular type of plug-in hybrid electric vehicle (PHEV) in series configuration, where the engine is not mechanically connected to the wheels but is used instead as a generator to produce electricity to recharge the battery when necessary. Range-extended vehicles are in essence plug-in electric vehicles provided with an additional on-board source of power that produces electricity from electric sources. Range-extended vehicles can only be fully understood by taking into account the possible configurations of both electric motor or motors and the internal combustion engine. Various hybrid architectures with different capabilities can be developed by modifying the connection of the power sources. This connection can be either mechanical or electrical, when the machines are mechanically linked to the wheels and through power transmitted through cables, respectively. These connections allow differentiating between series, parallel and power-split. The first are fully propelled using the electric motor exclusively, whilst the internal combustion engine is electrically connected and used to produce electricity to extend the vehicle range. In this configuration, the internal combustion engine is detached from the driver power demands and operates instead in steady-state, high-efficiency conditions. Due to the fact that series hybrids are exclusively propelled by the electric motor or motors, these require the installation of powerful enough electric machines able to satisfy the driver demand alone. In addition, extra losses are added to the battery charging and discharging operations through the internal combustion engine. That is, the energy produced in the combustion is not directly used to propel the vehicle but is transformed into electricity, accumulated and discharged as a result of the charging and discharging operation. The series configuration is implemented in the Opel Ampera and in the range-extended version of the i3. In contrast, in parallel vehicles both electric motor and internal combustion engine are mechanically connected and cooperate together in the vehicle propulsion. Finally, power-split configurations, also known as series–parallel, incorporate both series and parallel architectures. Usually they integrate two electric machines: one is calibrated as generator and used to produce electricity through engine recharging mode or

Integrated energy management for electrified vehicles

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regenerative braking, whilst the second is calibrated to assist in the propulsion. Both parallel and power-split configurations require a torque split device able to couple the machine’s torque mechanically. Figs 2.1–2.3 illustrate series, parallel and power-split vehicle configurations, respectively. Notice that wide line connections mean mechanical link and thin lines electrical link [1]. These hybrid architectures also imply important differences in terms of control and support the necessity of this book. Whilst conventional vehicles and battery electric vehicles have a single source of torque, hybrid electric vehicles have at least two sources that have to be coordinated; that is, there is at least one degree of freedom that needs to be supplied by a controller. Both series and parallel configurations incorporate one degree of freedom, whilst power-split powertrains have two, assuming both series and parallel vehicles implement only one electric motor and the power-split integrates two. The energy management strategy is the module that fills the degree

ICE

Generator Power link

EM

GB

Vehicle

Battery

Fig. 2.1 Series configuration of a hybrid electric vehicle. The electric motor is used alone to propel the vehicle, whilst the internal combustion engine is connected to a generator and therefore electrically to the powertrain so as to produce extra electricity.

ICE

Battery

Power link

EM

Torque coupler

Vehicle

Fig. 2.2 Parallel configuration of a hybrid electric vehicle. Both the electric motor and internal combustion engine are coupled and cooperate in the vehicle propulsion.

ICE

Battery

Generator

Power split device

Power link

EM

GB

Fig. 2.3 Power-split configuration of a hybrid electric vehicle.

Vehicle

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iHorizon-Enabled Energy Management for Electrified Vehicles

or degrees of freedom and provides guidelines for the low-level controller of the components [1]. Nevertheless, these degrees of freedom are not equally complex in mildHEVs, full-HEVs and PHEVs. The low margin for battery use and vehicle modes allowed in mild-HEVs does not require the development of sophisticated controllers, whilst the co-leadership of electric motor and internal combustion engine in PHEVs is a complex control task.

2.2

HEV vs PHEV control complexity

Electrified vehicles have been present on public roads for a few years, registering a substantial increase in the recent past. The hybrid electric vehicle has been the most popular version but is giving way gradually to PHEVs and BEVs in response to even more challenging emissions legislation. Mild and limited full hybrid electric vehicles are well-proven technologies due to experience with them over the past few years and their simpler technology in terms of electric components and power electronics, in comparison to higher electrification levels. Nevertheless, current plug-in hybrid electric vehicle energy management is far from exploiting the full capability of this technology. On the one hand, hybrid vehicles incorporate reduced-size batteries and operate within a small range of charge windows, on the order of 20% [1], which can be effectively managed with suboptimal controllers and which do not provide any major benefits when implementing more sophisticated optimised strategies. On the other hand, plug-in hybrid electric vehicles use larger batteries in a similar fashion to battery electric vehicles, within 50% or even 70% state of charge margins, which improve considerably with optimisation-based control. Hybrid electric vehicles generally implement charge-sustaining (CS) controllers, which encourage charging and discharging cycles of small amplitude due to the limited capacity of hybrid electric vehicles to charge the battery, either through regenerative braking or an engine recharging mode. The CS immediate extension to PHEV consists of the charge depleting–charge sustaining (CD–CS) strategy. The energy stored in the battery at the beginning of the drive cycle is used to maximise the electricity used and minimise fuel requirements until the battery state of charge reaches a safety limit during the charge-depleting mode. Then, the controller switches into the charge-sustaining mode as in an ordinary HEV, therefore losing all PHEV margin for improvement [2, 3]. CD–CS features simplicity and ease of implementation, but does not achieve efficient results either in real-life scenarios [4] or a simulation environment, as proven in Refs. [5, 6]. Ideally, plug-in hybrid electric vehicles’ batteries should be depleted along the drive cycle so that both the internal combustion engine and the electric motor cooperate during the whole trip, and full battery depletion should not be reached until the very end. This is the so-called blended mode control, as claimed in Refs. [7–10]. However, blended mode strategies are considerably more complex and require trip information in advance, which strongly complicates their implementation in-vehicle [6, 11, 12]. Provided that the required information is available, blended mode yields considerable improvements in fuel consumption and fully exploits plug-in hybrid electric vehicle capabilities [13]. Fig. 2.4 includes a

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Fig. 2.4 Comparison between CD–CS developed by a rule-based strategy and blended mode using optimisation-based control in a given drive cycle in simulation environment.

comparison between the CD–CS strategy, developed using a set of rules, and the blended mode strategy using optimisation-based control obtained with a dynamic programming algorithm. The rule-based strategy results in a deep depletion during the first 3 to 4 minutes, whilst blended mode suggests a gradual depletion until the end point of the drive cycles is achieved. Generally, charge-depleting, charge-sustaining mode is associated with the so-called rule-based strategies, whilst blended mode is implemented through optimisation-based algorithms. This classification is used in the following to elaborate energy management strategies applied to electrified powertrains in Section 2.3, on rule-based control, and Section 2.4, on optimisation-based control [14–16]. Fig. 2.5 summarises a classification of the main energy management strategies applied to regular hybrid electric vehicles and plug-in hybrid electric vehicles, including some of the approaches that will be elaborated in the following sections.

2.3

Experience transformed into rules

The most popular strategies implemented for hybrid electric vehicle control are the so-called rule-based strategies and fuzzy logic. Essentially these are described by a set of predefined thresholds applied over the control variables, which are obtained either based on experience or inspired on optimal control policies computed in selected drive cycles [2, 9]. These thresholds define the vehicle operating modes [3, 17], are generally easy to interpret and implement and their performance in a low level of electrification is satisfactory. These are the main reasons for their

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Deterministic-based

Rule-based (vector- and map-based), fuzzy logic

Static methods

EMS

Optimisation-based

Dynamic methods

Derivative-free: Simplex method, complex method, DIRECT, metaheuristic Gradient-based: Sequential QP Indirect methods: DP, PMP, ECMS Direct methods

Other methods

Game theory, machine learning, model predictive control, stochastic optimization control, nonlinear optimal control

Fig. 2.5 Energy management strategies classification according to their characteristics into rule-based and optimisation-based. The classification includes some of the approaches elaborated on in this chapter.

popularity when implemented in industry in first-generation hybrid electric vehicles [18]. Such characteristics have encouraged the extension of rule-based and fuzzy logic from HEV into PHEV control, despite their suboptimal performance in real-life applications [7, 19, 20]. Compared to rule-based strategies, fuzzy logic includes the thresholds in map format and provides a higher level of abstraction, allowing for a wider margin of improvement. In fuzzy logic, the variables are categorised using linguistic classification, interpretable by the programmer, and membership functions, which rate how well a variable fulfils a specific category. Consequently, instead of implementing hard thresholds, fuzzy logic allows for using soft classification, so that a variable value can belong to more than one classification simultaneously. Despite presenting better performance than rule-based, fuzzy logic strategies still yield suboptimal solutions [15, 21]. Fig. 2.6 illustrates an example of two variables modelled using fuzzy logic. The membership functions indicate the degree of membership of each variable and assign a linguistic term: low, high, medium, etc. These linguistic categories serve the designers in developing the strategy and can be translated into mathematical values during implementation. Recent examples of fuzzy logic applications for automotive control are still numerous, particularly in battery management [22–24]. Furthermore, many authors have combined fuzzy logic with other strategies more sophisticated to improve fuzzy logic performance but still take advantage of its real-time implementation properties [21, 25–27]. Albeit these strategies are suitable for low electrification levels, they are

Degree of membership

Integrated energy management for electrified vehicles

1

Low Med-low

Medium

Med-high

21

High

0.8 0.6 0.4 0.2 0

20

40

60

80

100

(%)

Fig. 2.6 Examples of fuzzy logic membership functions. The graphs allow interpreting the variables in linguistic terms whilst expressing the membership of the variables in a specific classification with fuzzy limits as opposed to hard thresholds used in rule-based strategies.

Degree of membership

State of charge 1

Low

Medium

High

0.8 0.6 0.4 0.2 0

10.9

11.4

11.9

12.4

12.9

13.4

13.9

Voltage (V)

not sufficient for plug-in hybrid electric vehicle control, where optimisation-based controllers become a necessity. Nonetheless, this improvement is overshadowed by major associated implementation issues, such as complexity, robustness, computational burden, and sensitivity to the drive cycle characteristics. These are the main issues that hinder the integration of optimal strategies in industry.

2.4

Optimisation-based control

Optimisation is an important paradigm with a vast range of application areas that include industry and engineering. It consists of finding the minimum/maximum of a specific function called the objective function and defined in a particular space. A general optimisation problem can be expressed as [28–31]: 9 minimise f ðxÞ > = subject to gi ðxÞ  bi , i ¼ 1, …, m where : f : ℝn ! ℝ; gi : ℝn ! ℝ and hj : ℝn ! ℝ > ; hj ðxÞ ¼ ci , j ¼ 1, …, p

(2.1)

where x ¼ (x1, …,xn), f, gi, hj, bi and cj are, respectively, variables to optimise, objective function, inequality constraint functions, equality constraint functions and

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iHorizon-Enabled Energy Management for Electrified Vehicles

constants that represent the limits to bound each inequality and equality constraints, respectively. The optimal solution for x is the one that has the smallest possible objective value and satisfies the constraints. When all functions are linear, then the optimisation problem is referred to as linear programming. Otherwise, the problem consists of nonlinear optimisation [28–31]. Apart from various equality and inequality constraints, optimisation problems can involve one or more objectives. Automotive applications can involve at the same time the optimisation of fuel consumption, emissions reduction and battery state of health. These objectives are generally conflicting, which implies that they cannot be improved simultaneously and consequently the optimisation process consists of achieving a trade-off between them. Multiobjective optimisation problems can be more complex to solve, depending on the strategy used to include the objectives. The possible approaches for multiobjective optimisation can be summarised into Pareto-optimal problems, soft constraints optimisation or hard constraints. On the one hand, Pareto-optimal problems consider more than one objective simultaneously, which requires the implementation of an algorithm able to develop parallel computation and therefore conditions the whole optimisation process [32–34]. Although these algorithms can deal with several objectives, their characteristics might not be the most convenient for vehicle control and may condition the accuracy of the results. On the other hand, the most simplified strategy consists of optimising one objective and limiting the rest of the objectives to a ‘desired’ range of values using extra hard constraints [35]. The alternative and probably the most-used approach is the soft constraints approach, which combines the objectives weighted in a single objective function. That is, all objectives are combined in the same objective function and their importance is rated through specifically selected weights. Despite the fact that this approach easily allows for including many objectives, the quality of the solution strongly depends on the weights selection [32]. A general optimisation problem is difficult to solve, even when the objective function and constraints have a ‘smooth’ shape, and it generally requires a large amount of computational time. Furthermore, problems of large dimension can be intractable and require unmanageable computational effort. Nonetheless, a compromise on the solution computation can be found in local optimisation, which consists of looking for an optimal solution in a specific region formed by the points close to a specific target value. That is, although the optimal solution is not known, it is assumed to be contained in a limited area. These methods only require differentiability of the objective and constraints functions in the mentioned area, as opposed to all the possible states. In addition, these can be faster than global optimisation algorithms, whose search is limited to a considerably smaller area, and therefore can handle larger-scale problems. Nevertheless, the solution quality of this approach relies on an initial guess of the solution and the area delimitation. If the initial solution proposed is closed to a local optimum, the final solution might not be able to converge into the global optimal. Similarly, the optima point will not be achieved if it lies out of the search area. Also, the approaches discussed here are very sensitive to the algorithm parameters that determine the convergence criteria [28].

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Apart from the previous analysis, the suitable algorithm or algorithms able to tackle a specific optimisation problem depend on the nature of the problem and the requirements over the desired solution: accuracy, computational resources, computational time allowed, real-time application, etc. [29].

2.4.1 Dynamic programming Life can only be understood going backwards, but it must be lived going forwards. Søren Aabye Kierkegaard

Energy management of electrified vehicles can be expressed as a discrete optimisation problem and solved by any optimisation algorithm. There are many methods for solving the optimisation of discrete problems. These are generally referred to as mathematical programming, although they implement different strategies that are associated with advantages and disadvantages, which makes them suitable for specific applications. It is consequently of interest to determine in every case which algorithm is superior to use to solve the problem at hand [1]. In particular, dynamic programming can find the global optimal solution that minimises a certain cost function, whilst handling multiple complex constraints applied to both states and control inputs. This can be achieved with relatively low computational burden when compared to other algorithms of similar characteristics [1]. Dynamic programming focuses on problems where a sequence of decisions must be taken and obtains the optimal set with respect to a function of the decisions to take. This function represents the so-called cost function and is cumulative in time as a result of the decision taking [36–38]. Furthermore, it can be applied to finite horizons and to any problem including nonlinear and integer variables expressed as a general state function in a discrete time horizon [37]. The general discrete problem that can be solved with dynamic programming is expressed as: xk + 1 ¼ fk ðxk , uk , wk Þ k ¼ 0, 1,…, N  1

(2.2)

where the state of the system, xk+1, at a specific discrete time, k, is described by any function, fk, time dependent, and from the previous state xk, control input uk, disturbances wk in N discrete stages in a finite time horizon [1, 37, 38]. The power of dynamic programming resides in dividing the decision process into subproblems whose solution is also optimal for the original problem. Dynamic programming optimality is supported by Bellman’s Principle of Optimality, which can be summarised as: “optimal policies have optimal subpolicies” [36, 38, 39]. That is to say that the global optimal solution is constituted by optimal subsolutions of the subproblems that form the global one. Consequently, dynamic programming computational efficiency can improve considerably when the problem of interest has common subproblems, which need to be calculated only once and can be reused. Likewise, when two alternative solution candidates converge into the same subproblem, the one associated with a higher cost can be eliminated to reduce the number of solution

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iHorizon-Enabled Energy Management for Electrified Vehicles

candidates and therefore the computational effort [36]. These situations are usual in vehicle control where similar case scenarios will occur along the drive cycle and most likely alternative strategies might converge into the same point, which makes dynamic programming suitable to tackle energy management in electrified vehicles efficiently. Fig. 2.7 illustrates an example of a discrete cost minimisation problem solved using a dynamic programming formulation. The optimisation problem starts at the end conditions, xf. The first iteration does not achieve any common state and therefore all possible strategies are maintained in the following step. At the second iteration, Step 2, three alternative strategies converge in state 6 and therefore the one associated with the minimum cost is preserved whilst the rest are eliminated. Consequently, at the next step the eliminated strategies do not need to be taken into account, releasing computational effort and memory resources. Similarly, in Step 3 two strategies converge in state 4 and therefore the one associated with the higher cost can be deleted. Eventually, all three possible final strategies converge to the initial conditions and the one associated with the minimum cost can be declared as optimal. The resolution methodology followed allowed the final computations to be reduced to only three strategies,

Fig. 2.7 Example of dynamic programming resolution in a discrete minimisation problem. The problem optimisation can be solved in 5 steps. In steps 2 and 3, some of the possible strategies converge into common states, a situation that allows solution candidates to be deleted, therefore releasing computational effort, time and memory requirements.

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compared to the six possible ones, relaxing significantly the required resolution time, computational effort and memory resources. Nevertheless, the main drawback of dynamic programming is that either all disturbances have to be known at the outset, when implementing deterministic dynamic programming (DDP), or their stochastic properties must be known, when using stochastic dynamic programming (SDP). This is the main reason why dynamic programming cannot be used directly for real-time vehicle control, where uncertainties are never fully known. Nonetheless, dynamic programming is still useful as a solution benchmark to aid in the design of real-time controllers and assess their quality [1], the main reason why its use is widespread in the research community.

2.4.1.1 Dynamic programming implementation To understand dynamic programming implementation, the dynamic programming premise that decisions cannot be evaluated separately must be acknowledged, but it must be considered taking into account present and future costs that are implied. That is, a decision must be taken considering the present consequences and future costs in subsequent stages that will be incurred as a result of it [1, 37]. Therefore, the optimisation is performed by minimising (or maximising) the cost function additive in time. When the disturbances are known along the entire time horizon, DDP is expressed with the following cost function [1, 37, 38]: J 0 ¼ gN ð xN Þ +

N 1 X

g k ð x k , uk , w k Þ

(2.3)

k¼0

where the first term represents the terminal cost incurred as a consequence of the end conditions, imposed by the problem definition, and the second term accumulates the cost of any decision and future cost incurred as a result of all decisions taken. In cases where the disturbances are not known, but instead their statistic formulation is, the cost function can be expressed by a random variable using SDP [1, 37, 38]: ( J 0 ¼ E gN ð x N Þ + (

N 1 X

) g k ð x k , uk , w k Þ

k¼0

J 0 ¼ Ew k g N ð x N Þ +

N 1 X

) g k ð x k , uk , w k Þ

(2.4) with k ¼ 0,1, …, N  1

k¼0

The control signal that minimises (or maximises) the cost function is the global optimal solution. The optimisation process starts at the end conditions cost, which is known and does not depend on any variable, and the cost function is then minimised backwards, transiting from N to N  1 stage [1, 37, 38]. JN1 ¼ gN ðxN Þ + gN1 ðxN1 , uN1 , wN1 Þ

(2.5)

By minimising the previous, the optimal uN1 can be obtained. At the next step, JN2 is calculated to obtain uN2 that optimises the cost function and successively.

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iHorizon-Enabled Energy Management for Electrified Vehicles

Dynamic programming is therefore solved backwards in time, from end conditions towards initial conditions.

2.4.1.2 Curse of dimensionality and numerical issues When the models cannot be expressed or simplified so that there is an analytical solution for the minimisation problem, the cost function has to be solved numerically. Unfortunately, numerical solution computation times are proportional to the possible state values [1]. In general, the computational burden of all DDP algorithms scales linearly with the problem timeline, N, and with exponential complexity with the number of states n and control inputs m: Ο ð N  p n  qm Þ

(2.6)

where p represents all possible states, q is all possible control inputs [1, 36]. Apart from the dynamic programming curse of dimensionality, dynamic programming is associated with other implementation issues such as grid selection and solution interpolation. The first alludes to the selection of discrete states and control inputs suitable to model the process with appropriate accuracy and the second is a result of the previous discretisation, which limits the possible solutions [1]. On the one hand, the continuous inputs and states have to be approximated to discrete values selecting a suitable step, p and q, which is generally not obvious and strongly conditions the quality of the solution. Again, the curse of dimensionality needs to be taken into account, given the fact that large p and q would result in accurate solutions, but would require high computational burden, and vice versa [1]. On the other hand, when a new state is calculated and does not match any of the discrete finite possible states, it has to be approximated. This can be chosen either as the closest possible value or by interpolating it according to the grid points. The first is simpler and has higher computational speed but relatively poor accuracy, whilst the second is associated with higher computational burden and better accuracy [1]. Furthermore, infeasible states or inputs are commonly handled by assigning an infinite cost to such states and inputs. However, if an infinite cost is used together with an interpolation scheme, the interpolated value becomes infinity as well. If this problem is not handled correctly, the number of infeasible states is artificially increased during the calculations, reducing the solution space artificially. One solution to this problem is using relatively large real constants instead of infinity to penalise infeasible states and inputs, greater than the cost-to-go for any of the states in the solution. These constants are sometimes obtained iteratively, due to the fact that the maximum cost-to-go is not known in advance [1].

2.4.1.3 Practical examples in electrified vehicles As previously stated, dynamic programming and particularly DDP are widely utilised in offline analysis to benchmark other energy management strategies. It serves to design rule-based strategies based on optimal solutions, tune control parameters

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and produce training data to develop machine learning algorithms, among others [1, 40, 41]. Other automotive applications include gear shifting optimisation and travel time reduction [40, 42]. Furthermore, dynamic programming has been widely used to conduct deep analysis of hybrid electric vehicles and plug-in hybrid electric vehicle operational modes, configuration and design. Yang et al. proposed the use of dynamic programming to explore the potential of two configurations of the same hybrid electric vehicle, P1 and P2, in terms of fuel savings with focus on the velocity coupling to assist the engine [43]. Xie et al. presented a holistic analysis of a series–parallel hybrid electric bus considering both fuel and electricity cost to account for market price fluctuations and five control variables: engine torque, torque split, engine speed, clutch state and brake torque split. The study focused on the effect of the drive cycle length, battery capacity and control variables [44]. EMS optimisation using dynamic programming solutions was performed by Cubito et al., who used DDP to inspire a set of rules for vehicle control considering the availability of specific trip information, such as travelled time, in urban scenarios [45]. Similarly, Peng et al. developed an optimisation-based, rule-based strategy able to better adapt to different drive cycles based on offline optimal results produced with DDP [46]. Examples of DDP optimal results used as training material for neural network–based energy management strategies can be found in Ref. [8] using predefined drive cycles and in Ref. [47] using speed profile prediction with a combination of auto-regressive and moving averages algorithms. Likewise, DDP was used by Lin et al. to obtain implementable rules for energy management and gearshift optimisation in a hybrid truck in Refs. [48, 49] and Sundstr€om et al. optimised a dualclutch six-speed transmission in Ref. [50]. An investigation of the optimal energy management strategy for a fuel-cell hybrid provided by a dual storage system consisting of an ultracapacitor and a battery was provided in Ref. [51]. The previous examples either utilise dynamic programming solutions to design new strategies or simplify them, to implement them directly in-vehicle or simply ease the associated computational burden. Some other authors opted for dynamic programming adaptation in order to allow for online control, such as Larsson et al., who derived an analytic solution of the optimal torque split by locally approximating the cost-to-go at each point in the gridded values using a polynomial [52]. Similarly, Kum et al. reduced the DDP computational burden by linearising the model functions for offline cold-start analysis [53]. Alternatively, Zhang et al. proposed a simplified model and integrated a cycle preview so as to tackle both trip uncertainty and computational burden. The authors compared rule-based, equivalent consumption minimisation strategy (ECMS) and dynamic programming with and without preview capabilities [40]. The future cycle uncertainty can be tackled using SDP instead of DDP, as suggested by Lin et al. who claimed in Ref. [54] an implementable energy management strategy using infinite-horizon SDP. The authors modelled the driver demand using a Markov model obtained from several drive cycles and developed a timeinvariant control strategy for charge sustaining in a hybrid electric vehicle. Vagg et al. also proposed SDP as an attractive alternative to DDP for direct real-world application, although recognising difficulties in implementation [55]. Similarly, Opila et al.

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iHorizon-Enabled Energy Management for Electrified Vehicles

proposed a shortest path SDP algorithm with real-time application potential as claimed by the authors. This was achieved by reducing the computational burden by extensive offline computations stored in tables and through the stochastic implementation in Ref. [56] and later in Ref. [57].

2.4.2 Equivalent consumption minimisation strategy The implementation and numerical problems associated with dynamic programming has encouraged the use of alternative algorithms able to ease the computational burden. One of the most extended ones is Pontryagin’s minimum principle (PMP), which is intrinsically equivalent to the so-called equivalent consumption minimisation strategy (ECMS), also very well-known in the research community [38, 58]. Whilst PMP is yielded mathematically, ECMS is based on an engineering interpretation of the cost function, which also returns a local optimisation version of the original problem. Hereby both methods are introduced and their similarities highlighted to explain their extended popularity in vehicle control and effectiveness [38].

2.4.2.1 Mathematical derivation. Pontryagin’s minimum principle PMP consists of a set of necessary conditions of optimality and therefore not sufficient to yield global optimal solutions. Nonetheless, these conditions permit redefining the global optimisation problem in terms of local conditions and, in the event of numerous solutions, the global optimal can be identified for being associated with the lowest total cost. PMP can be applied to a general dynamic system expressed in state equations continuous in time [38]: x_ ðtÞ ¼ f ðxðtÞ, uðtÞ, tÞ where xðtÞ 2 ℝn ; uðtÞ 2 ℝn

(2.7)

where similarly to the notation used in dynamic programming, x, u, t and f represent respectively the system states, control inputs, time variable and the dynamic function that describes the states derivative in time. The Hamiltonian function for the previous problem is defined as [38]: H ðxðtÞ, uðtÞ, λðtÞ, tÞ ¼ LðxðtÞ, uðtÞ, tÞ + λðtÞT  f ðxðtÞ, uðtÞ, tÞ

(2.8)

where f is the system dynamic equation previously introduced and L is the instantaneous cost as described by the cost function continuous in time as in [38]: ðN J ¼ gN ðxN Þ +

Lðxt , ut , tÞdt

(2.9)

0

Finally, λ is a vector of the same dimension as x that contains the optimisation variables usually known as ‘adjoint states’ or ‘co-states’ of the system. According to the

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PMP, the optimal control law, u∗(t) is achieved when the following conditions are satisfied by the state and co-state [38]: x_ ∗ ðtÞ ¼

 ∂H ¼ f ðx∗ ðtÞ, u∗ ðtÞ, tÞ ∂λ u∗ ðtÞ

 ∂H  ¼ hðx∗ ðtÞ, u∗ ðtÞ, λ∗ ðtÞ, tÞ λ_ ∗ ðtÞ ¼  ∂x u∗ ðtÞ  T ∂L ∂f ∗ ¼  ðx∗ ðtÞ, u∗ ðtÞ, tÞ  λ∗ ðtÞ  ðx ðtÞ, u∗ ðtÞ, tÞ ∂x ∂x

(2.10)

(2.11)

x∗ ðt0 Þ ¼ x0

(2.12)

x∗ ðtN Þ ¼ xN

(2.13)

Provided that the previous conditions are met, the optimal control strategy that minimises the Hamiltonian for the finite horizon such that [38]: H ðuðtÞ, x∗ ðtÞ, λ∗ ðtÞ, tÞ  H ðu∗ðtÞ, x∗ ðtÞ, λ∗ ðtÞ, tÞ, 8u∗ ðtÞ 2 U ðtÞ, 8t 2 t0 , tf

(2.14)

which implies that the optimal control policy should be the one that minimises the Hamiltonian [38]: u∗ ðtÞ ¼ arg min ðH ðuðtÞ, xðtÞ, λðtÞ, tÞÞ uðtÞ2U ðtÞ

(2.15)

where U is the set of admissible control policies.

2.4.2.2 Engineering derivation. Equivalent consumption minimisation strategy Equivalent consumption minimisation strategy (ECMS) is a heuristic method intrinsically equivalent to PMP. It was developed by Paganelli et al. in 1999 [59] and was originally designed for hybrid electric vehicles operating in CS mode. Charge sustaining assumes equal initial and final state of charge, which implies that the battery actuates as an auxiliary reversible fuel tank and, consequently, any energy discharged must be replenished through either internal combustion engine recharging mode or regenerative braking. In ECMS there are two case scenarios for battery use [4, 38, 60–62]: (1) Discharge case: energy used from the battery has to be replenished in the future, an operation that will cause additional fuel consumption dependent on the internal combustion engine operating conditions during recharging and on the amount of energy recovered during braking. Fig. 2.8 illustrates the process of present battery discharge (right hand side— present) and future consequences in terms of fuel consumption (left hand side—future).

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iHorizon-Enabled Energy Management for Electrified Vehicles

Fig. 2.8 Discharge use case allows using instantaneously (Present) the energy in the battery to reduce the internal combustion engine load. Nevertheless, the charge reduction implies the necessity of future battery charge through the engine (Future) in the event that regenerative braking cannot produce a sufficient amount of charge.

Fuel tank ICE

ICE Vehicle

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EM Battery

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Vehicle

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Battery Future Present Battery recharge through brakes

Battery Future Present Battery recharge through ICE

Fig. 2.9 Recharge use case can happen either through regenerative braking (left image) or through engine recharging mode (right picture). It implies instantaneous fuel consumption (Present), but future fuel savings when both internal combustion engine and electric motor contribute to the vehicle propulsion. (2) Charge case: the extra energy stored can be used in future fuel savings when both the internal combustion engine and electric motor cooperate on the vehicle propulsion, which again depends on the engine future operating conditions. Fig. 2.9 illustrates the process of battery recharge and future consequences for fuel consumption reduction either using regenerative braking (left) or engine recharging mode (right).

ECMS interprets the electrical energy stored as an equivalent quantity of fuel, m_ ress ðtÞ, that can be summed with the actual fuel consumption, m_ f ðtÞ, so as to obtain the instantaneous equivalent fuel consumption, m_ f , eqv ðtÞ [38, 61, 62]: m_ f ,eqv ðtÞ ¼ m_ f ðtÞ + m_ ress ðtÞ

(2.16)

This virtual fuel associated with the energy in the battery can be expressed as: m_ ress ðtÞ ¼ sfceq ðtÞ  Pbatt ðtÞ

(2.17)

Integrated energy management for electrified vehicles

31

where sfceq and Pbatt represent respectively the virtual specific fuel consumption and the power used from the battery. The virtual specific fuel consumption is proportional to the equivalence factor, s, and the fuel lower heating value, Qlhv [38, 61, 62]: sfceq ðtÞ ¼ sðtÞ=Qlhv

(2.18)

The equivalence factor can adopt two values to account for charge and discharge scenarios and essentially represents the chain of efficiency associated with the transformation of electricity into tractive power and vice versa. Nonetheless, this equivalent amount is a priori unknown because it depends on the driving conditions in each cycle. Albeit the equivalent factor is strongly linked to the cycle characteristics, ECMS usually describes it as a constant or set of constants, which average the overall efficiency of the electric path. This constant value changes for each driving cycle, represents the past, present and future efficiency of the engine and the electrical source and its value affects the charge sustainability and therefore the energy management strategy (EMS) [38, 61]. The equivalence factor use implies the global optimisation problem reduction into local minimisation. Nevertheless, provided that the constant equivalence factors are properly chosen for a specific drive cycle, ECMS results can be comparable to the ones obtained with dynamic programming. Unfortunately, ECMS still relies on information about the future drive cycle to approach to the global optimal solution [38].

2.4.2.3 Similarities between ECMS and PMP ECMS is based on engineering derivation of the equivalent fuel consumption concept, but it can be yielded analytically using PMP [38, 58, 61]. In the power-based formulation, ECMS and Hamiltonian can be expressed as: Peqv ðtÞ ¼ Pfuel ðtÞ + sðtÞ  Pbatt ðtÞ

(2.19)

H ¼ Pfuel ðtÞ + λðtÞ  Pech ðtÞ

(2.20)

where Pfuel, Pbatt and Pech are respectively fuel power, electrical power and electromechanical power correlated to the effective state of charge variation in each case. Electrical and electromechanical power are related by the charge and discharge efficiency, ηbatt, and therefore λ can be interpreted as the weighting factor that performs the conversion from battery power to fuel power. Assuming [38]:  Pech ðSoCðtÞ, Pbatt ðtÞÞ ¼

Pbatt ðtÞ=ηbatt ðSoC, Pbatt Þ if Pbatt ðtÞ  0 ðdischargeÞ Pbatt ðtÞ  ηbatt ðSoC, Pbatt Þ if Pbatt ðtÞ < 0 ðchargeÞ (2.21)

the relationship between the co-state and the equivalence factor can be stated as [38]:

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iHorizon-Enabled Energy Management for Electrified Vehicles

schg ðtÞ ¼ λðtÞηbatt

(2.22)

sdis ðtÞ ¼ λðtÞ=ηbatt

(2.23)

and therefore, the relation between charge and discharge equivalence factors hold [38]: schg ðtÞ ¼ η2batt sdis ðtÞ

(2.24)

which allows using a single equivalence factor when the efficiency conditions are assumed to be constant along the operating conditions [38].

2.4.2.4 Automotive applications of ECMS and PMP Investigations in equivalence factor offline calibration are presented by Stockar et al. in Ref. [63], who presented an analysis on its influence in CD–CS and blended mode [63]. Apart from prior knowledge about the future cycle, ECMS still requires an optimisation process that is time consuming. In order to reduce computational effort for online applications, the solutions of the Hamiltonian need to be solved in advance and stored in maps. This increases the memory requirements, but reduces the computational time for real-time applications [7]. ECMS real-time implementation is addressed by Stockar et al. in Ref. [61], who proposed the offline Hamiltonian resolution and its map-based implementation. Similarly, the potential of ECMS against traditionally used heuristic strategies in real-time control was evidenced in a simulation environment by Sciarreta et al. [7]. Triboli et al. used instead PMP results in offline computations so as to inspire the design of a rule-based strategy. The authors use PMP in a similar fashion to dynamic programming results presented in the previous section [9]. Apart from fuel consumption reduction, Serrao et al. implemented PMP taking into account battery ageing during drive cycles reproduced in a simulation environment to analyse the trade-off between vehicle performance and battery life [64]. Further simplifications for online control included exploring regular patterns in the solution to allow for PMP approximation using piecewise linear equations as in Ref. [10]. As opposed to the previous, some authors proposed adaptive ECMS implementation to online tuning the equivalence factor instead of using a constant value. Musardo et al. presented an automatic modification of the parameter based on the available trip information with periodical updates along the route [65]. A similar approach was introduced by Tianheng et al., who proposed a neural network-based prediction of the future drive cycle, route preview, to implement an adaptive ECMS [66] and by Kermani et al., who implemented the Hamiltonian optimisation in a model predictive control framework [67]. An analysis of ECMS, co-state and equivalence factor calculations with diverse knowledge about past, present and future conditions was provided by Sciarreta and Guzzella in Ref. [68]. More advanced approaches assumed vehicle-to-vehicle and vehicle-toinfrastructure communication to develop a high-level velocity prediction used in a

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lower level controller for optimal hybrid electric vehicle operation using ECMS in an adaptive manner [69]. Finally, a recent publication exploited the benefits of PMP and combined it with dynamic programming to develop an online implementable energy management strategy globally optimal within the battery state of charge limits [70].

2.4.3 Model predictive control The energy management strategies previously introduced evidence the trip information importance for effective vehicle control. Before continuing with alternative control methods, it is worth paying attention to the model predictive control (MPC) framework. MPC is not a strategy on its own, but a predictive scheme that can be incorporated in a range of control methodologies that make use of a model of the system to obtain the control policy that minimises a cost function. The main difference when using MPC, as opposed to the already introduced methods, is the use of a receding horizon. That is, every time step the fixed horizon of finite number of steps is translated towards the future. In MPC the forecast and control polity are computed every step along the entire horizon, whilst only the first step is eventually implemented. In a general dynamic process, MPC implies the problem resolution along the entire horizon whilst only the current step is used every time, discarding the rest of the calculations and updating the state. MPC can be explained in the flow chart included in Fig. 2.10. As illustrated, the first step consists of calculating the prediction from the current instant in time up to N steps. Secondly, the control policy is calculated in the predicted horizon, but only the current instant is applied in step 3, discarding all other computations in step 4. Consequently, every time increment a total of N steps in time are computed, but only one is applied, eliminating the rest to update the measurements at the current instant and proceed again with the receding horizon until the final time is achieved [71]. An intuitive analogy of MPC can be found in the control strategy of a driver following a route. The driver knows the reference trajectory to follow and the car response and can anticipate the future driving conditions based on the current surrounding circumstances. Nevertheless, the vehicle is operated decision by decision

Prediction in N time steps

Control policy from t to t + N

Apply control policy in t

No

Update measurements at t and discard previous results

t = tf ?

Yes

END

Fig. 2.10 Flow diagram that represents the steps that describe the MPC framework in a receding horizon.

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iHorizon-Enabled Energy Management for Electrified Vehicles

as the driver updates the surrounding conditions and modifies the strategy accordingly [71]. MPC is fully defined by three main elements: prediction model, objective function and control law computation. The objective function is formulated so that the process follows the desired behaviour as happened in previously introduced optimisation methods, but both prediction model and control law need to comply with MPC framework characteristics. On the one hand, the process model is of utmost importance to meet the desired prediction accuracy [72]. On the other hand, the optimiser needs to be selected so that the processor can handle the computational burden [18, 72]. This is crucial due to the characteristics of the receding horizon, which requires every time step the computation of N steps in time. The selection of the optimiser and the horizon length is strongly linked to the size of the problem and the processor computational capacity. That is, large complex problems and a complex optimiser would require more computational time and therefore would limit to shorter horizons, and vice versa [72]. Optimisation algorithms would benefit from an MPC framework that can effectively reduce the uncertainties of the future horizon at least in a finite number of steps. For instance, ECMS could benefit from MPC to compute an adaptive equivalence factor in prevision to future driver demand and therefore develop a strategy less sensitive to the characteristics of the drive cycle. Ideally, long and accurate prediction horizons could allow DDP implementation, assuming full cycle information can be obtained. Zhang et al. proposed the use of MPC in a plug-in hybrid electric vehicle with a dual electric source formed by a battery and ultracapacitor. MPC was used to improve the implemented rule-based strategy with a combination of rule-based and optimisationbased approaches using the advantage of future information provided by the framework [73]. Nevertheless, real-time implementation requires the use of algorithms less computationally intensive such as ECMS and other approaches that will be introduced in the remainder of this chapter. For instance, Borhan et al. used quadratic programming to ease the optimisation computational cost and facilitate its potential real-time implementation [18]. The same authors used PMP in a later publication to reduce the computational effort [74]. Similarly, Kermani et al. employed PMP, referred to by the authors as Lagrange formalisms in referring to the Hamiltonian partial derivatives, in a predictive framework so as to find the values of the co-state with the best accuracy possible [67]. An example of use of a predictive framework enhanced with specific traffic information was presented by Sun et al., who detailed a long-term, short-term forecast scenario. The authors used different approaches of models and data-driven algorithms to perform the prediction along with a study of the effect of the horizon length on the accuracy of the results [5]. Ripaccioli et al. described the implementation of stochastic MPC assuming the driver demand can be described by a Markov process. The algorithms received the driver power demand and predicted the future distribution with a Markov model [75]. A different application was proposed by Wang et al., who implemented MPC to control a hybrid electric tracked bulldozer. The authors defended the complexity of the working environment with sudden changes in the working conditions as opposed to the ordinary hybrid electric vehicles. Dynamic programming

Integrated energy management for electrified vehicles

35

was used as a benchmark solution in three scenarios and the MPC solution with QP implementation was analysed, modifying algorithm parameters such as horizon length and disturbances. The results were compared with rule-based and dynamic programming solutions showing a fuel improvement of 6% over rule-based and 98% optimality [76]. Furthermore, some authors have attempted to enhance the prediction accuracy using additional information provided that the vehicle can connect to systems such as global positioning systems or intelligent transportation systems [68].

2.4.4 Derivative free algorithms Methods using derivatives can be very efficient, but can also be associated with numerical issues and require strict conditions on the cost function such as continuity. Furthermore, derivatives can trap the optimisation engines in local minima [29]. Due to these limits and the characteristics of the energy management control of electrified vehicles, derivative-free methods have been also applied for vehicle control. Within derivative-free algorithms, metaheuristic methods are widely used as optimisation tools. These are usually inspired in nature and have some advantages when compared to conventional optimisation algorithms for specific applications. Their efficiency relies on the imitation of the best processes happening in nature and biological systems that have evolved naturally [29]. The main derivative-free algorithms applied to vehicle control are DIRECT, genetic algorithm, particle swarm optimisation and simulated annealing. DIRECT is a deterministic method, whilst the rest are stochastic and metaheuristic. These algorithms do not require derivative computation, but use instead alternative population methods to harness the solution, a reason why they perform well under noisy and discontinuous objective functions. Furthermore, they often sample the complete allowed solution area, encouraging a global optimal solution search [20, 77]. Nevertheless, the solution derivation still depends on certain design parameters to direct the search from global to local minima during convergence, which must be properly chosen [78]. These parameters balance their two main characteristics, intensification and diversification, which can be associated to local and global optimisation. The main task in the design of these algorithms is the proper balance between both, so that the global optimal solution is achieved with acceptable accuracy [29].

2.4.4.1 Direct DIRECT, DIviding RECTangles method, is a sampling global optimisation method. It was developed by Donald R. Jones in 2001 [79] as a modification of the standard formulation of Shubert’s Lipschitz algorithm, where the Lipschitz constant is replaced by a balanced search for local and global optimal. DIRECT consists of a partitioning algorithm that increases the finesse of the searching area where the cost is lower or complies with a predefined criterion. The global and local search are coordinated by selecting the hyperrectangles of interest, search areas, and calculating the cost value at the centre. Typically, the optimisation is ended when the expected minimum cost is reached, albeit there are other criteria such as number of iterations.

Step 1

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iHorizon-Enabled Energy Management for Electrified Vehicles

1

2

3 2

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4 5 6 10

7 89

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12

1

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5 6

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Potential optimal

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Fig. 2.11 Three iterations in a two-dimensional problem solved with the DIRECT method. In step 1 the area is divided into three parts and their costs are evaluated in the centre. Step 2 identifies the potential optimal area and divides it again. In Step 3, both areas 4 and 1 are divided, as area 1 still complies with the potential optimality criteria.

A hyperrectangle is considered potentially optimal when its cost value is below a minimum cost threshold or is situated below the ones measured in previous areas [20, 29, 77]. Fig. 2.11 illustrates three iterations of the DIRECT method applied to a twodimensional problem. Initially the entire area is divided by the longest dimension and the cost is evaluated in the centre of the new rectangles as measured in the draft on the right. Area 3 is identified as the best candidate and therefore is divided in the second step. The new evaluation identifies area 4 as the best candidate but also recovers area 1 as a possible solution to support the global minima search and proceeds with new area division in step 3. The criteria for potentially optimal areas search identifies the minimum cost location, but also allows a return to other areas that comply with predefined conditions so that a global optimal search is encouraged and the algorithm does not get trapped in local minima [29, 77]. DIRECT can be a very efficient algorithm when dealing with small problems, but those of higher dimension might require an exhaustive number of evaluations, causing cumbersome computational effort [20, 29, 77]. When compared to other derivative-free methods, DIRECT is relatively simple, it does not require tuning parameters, it is robust to disturbances and can handle equality and inequality constraints [20, 77]. In particular, DIRECT has been applied to hybrid electric vehicles control in several occasions in the literature. Gao et al. implemented various derivative-free methods and compared them in a simulation environment in terms of vehicle performance, fuel consumption and components design [77]. Rousseau et al. used the DIRECT method to optimise the parameters of a predefined controller for a set of drive cycles and identify their influence on the strategy and relationship with the characteristics of the drive cycle. Although DIRECT is not used for online control, it was able to identify the parameter sensitivity to the drive cycle and find the best compromise for fuel consumption [20]. Similarly, DIRECT was used by Hao et al. to optimise seven parameters defining an existing rule-based control

Integrated energy management for electrified vehicles

37

strategy affecting torque, battery power, throttle pedal operation and speed. The authors claimed a 7% reduction in fuel consumption every 100 km [80]. Whitefoot et al. implemented DIRECT in Matlab to develop a robust controller of a hybrid electric vehicle in offline investigation. The main reason for this selection was the reduced number of computations required by this algorithm, which were controlled by a stopping criterion. In particular, optimality was assumed to be achieved if the function evaluation did not change after 100 iterations. The authors used this inexpensive method to introduce performance constraints in terms of acceleration time, maximum speed, etc. [81]. Market et al. also claimed the effectiveness of the DIRECT method in finding global solutions for electrified vehicle control, but also highlighted issues in convergence time, which can be intolerable for real-time implementation. The authors performed an offline analysis of eight variables in a fuel cell hybrid vehicle, including four sizing parameters and four control signals. DIRECT allowed for a holistic analysis with relatively low computational effort and yielded important insights of the vehicle operation and performance [82].

2.4.4.2 Genetic algorithm A genetic algorithm is a metaheuristic algorithm based on Darwin’s evolution of biological systems, which belongs to a larger class of evolutionary algorithms. It was developed by Holland in 1975 [83] and implements the operators of crossover and recombination, mutation and selection mathematically. A genetic algorithm accepts complex problems, including discontinuities and nonlinear formulations, and allows for parallel computation, which permits computing Pareto solutions. Furthermore, it only stores the results of the last population, reducing the memory resources required for its implementation. The algorithm encodes the solution in strings, in imitation of chromosomes, and is initialised with a random population of solutions. Then the genetic algorithm initiates a sequence of operations divided into three main steps [29, 77]: (1) Crossover (stochastic): part of two solutions ‘is swapped’ to produce new ones. (2) Mutation (stochastic): part of a new solution ‘is flipped’ to generate a new one and prevent it from converging into local optima. (3) Selection: the new solutions are evaluated according to the objective function and the best candidates are selected.

In some cases, the elitism operator is also implemented to ensure that the best solutions are passed to the next generation unaltered, therefore guaranteeing that the best candidates remain in the solution set. The sequence continues until terminating conditions or a predefined number of generations is achieved [29, 77]. Fig. 2.12 illustrates crossover and mutation operations using binary chromosomes as examples. Nevertheless, the genetic algorithm does not allow for direct applications of constraints, which can be taken into account through penalty functions, P, which combined with the objective function, J, create the fitness function, F. The penalty functions penalise for infeasible solutions so that these are never reached during the optimisation process, as in [35, 84]:

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iHorizon-Enabled Energy Management for Electrified Vehicles

Crossover

Mutation

1

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Fig. 2.12 Examples of crossover and mutation operations over binary chromosomes. On the right, information from two chromosomes is swapped to generate the children chromosomes. On the left, two members of the same chromosome are flipped to encourage the solution candidates’ variability.

FðxÞ ¼

nconstraints X 1 α i  Pi ð x Þ + J ðxÞ i¼1

(2.25)

where αi is a penalty factor, a positive constant that determines the degree of penalisation of each constraint. Provided that unlimited time is allowed, the process will eventually converge into the optimal solution, ‘best fit’, taking into account objective function and constraints. Nevertheless, the optimality of the solution cannot be guaranteed in either a specific number of iterations or computation time and the convergence depends on the setting parameters [29, 35]. Real-time control requires fast and robust algorithms, the main reason why threshold-based, rule-based and fuzzy logic strategies dominate industry approaches. The genetic algorithm’s simple implementation and powerful search engine have been used by many authors to optimise the threshold selection in such deterministic controllers. Chen et al. implemented a genetic algorithm to optimise the internal combustion engine in a power-split plug-in hybrid electric vehicle by generating the new engine-on power threshold based on the current working conditions. Then, the battery command was calculated using QP and the fuel consumption was obtained. The authors claimed the algorithm convergence in limited time because they used only one variable during optimisation [85]. Montazeri-Gh et al. also applied a genetic algorithm for hybrid electric vehicle control, this time in a parallel configuration. The authors targeted both fuel consumption and emissions reduction and considered vehicle performance as part of the constraints. The genetic algorithm was implemented as part of an electric assist control strategy further simplified into five variables to reduce the number of decisions to take and was compared with the existing strategy available in ADVISOR [35]. The same authors proposed a fuzzy logic–based controller for a PHEV optimised for specific driving conditions using a genetic algorithm for the case scenarios congested, urban, urban extra (arterial roads) and highway [86]. Similarly, Zhou et al. implemented a genetic algorithm to optimise the parameters selection in a fuzzy logic strategy for a fuel cell hybrid electric vehicle. The algorithm was applied in a multiparametric optimisation that included state of charge, power demand and characteristics of the fuel cell. The genetic algorithm was selected due to its capability of handling multiparameter optimisation [87]. Another real-time automotive application was presented by Yu et al., where a genetic algorithm was used to optimise the

Integrated energy management for electrified vehicles

39

parameters of a fuzzy controller. The authors proposed an online strategy for fast charging of an electric bus with a hybrid energy storage system [88]. Panday et al. took a step forward using a genetic algorithm to optimise the parameters required to develop a PMP-based energy management strategy for a hybrid electric vehicle. A genetic algorithm was used to determine the speed threshold, engine off time threshold and engine on state of charge level [89]. A more sophisticated approach was taken by Bashash et al., who described the use of a nondominated sorting genetic algorithm. The authors benefitted from the algorithm parallel computation capability to tackle two conflicting objectives, energy consumption reduction and battery health preservation, and obtained the Pareto optimal charging patterns [90]. A similar approach was taken by Qi et al. to optimise a plug-in hybrid electric vehicle in real time using such an evolutionary algorithm to avoid using gradient methods and due to its flexibility to multiobjective problems [91]. A genetic algorithm often appears as a combination with other algorithms to compensate for their deficiencies and yield better results. That was the case of Li et al., who presented the energy management strategy of a plug-in hybrid electric bus using a genetic algorithm in conjunction with the enhanced ant colony algorithm. The main idea of the authors was to take advantage of the rapid convergence of the genetic algorithm at early iterations and, at latter stages, to use the combined algorithm with adaptive crossover operator to accelerate convergence and prevent local optimisation [92]. Similarly, Hui et al. used simulated annealing to accelerate the algorithm convergence at final stages for adaptive control of a hydraulic hybrid vehicle [93].

2.4.4.3 Particle swarm optimisation Particle swarm optimisation was developed in 1995 by the authors Kennedy and Eberhart [94], inspired by the behaviour of social organisms in groups, such as bird and fish schooling or ant colonies. This algorithm emulates the interaction between members to share information. Particle swarm optimisation has been applied to numerous areas in optimisation and in combination with other existing algorithms. This method performs the search of the optimal solution through agents, referred to as particles, whose trajectories are adjusted by a stochastic and a deterministic component. Each particle is influenced by its ‘best’ achieved position and the group ‘best’ position, but tends to move randomly. A particle i is defined by its position vector, xi, and its velocity vector, vi [29]. Every iteration, each particle changes its position according to the new velocity as in Refs. [29, 77, 95]:   vti + 1 ¼ ωvti + c1 r1 xBestti  xti + c2 r2 gBestti  xti

(2.26)

xti + 1 ¼ xti + vti  t

(2.27)

where xBest and gBest denote the best particle position and best group position and the parameters ω, c1, c2, r1 and r2 are respectively inertia weight, two positive constants and two random parameters within [0, 1]. In the baseline particle swarm optimisation algorithm ω is selected as unit, but an improvement of the algorithm is found in its

40

iHorizon-Enabled Energy Management for Electrified Vehicles

inertial implementation using ω  [0.5 0.9]. Usually maximum and minimum velocity values are also defined and initially the particles are distributed randomly to encourage the search in all possible locations. One of the advantages of particle swarm optimisation over other derivative-free methods is the reduced number of parameters to tune and constraints acceptance [29, 77, 95, 96]. Fig. 2.13 illustrates a two-dimensional representation of one particle, ‘i’, movement between two positions. It can be observed how the particle best position, Pbest, and the group best position, Gbest, influence the velocity of the particle at the next iteration. Nevertheless, the stochastic properties of the algorithm allow for solution variability to guarantee the solution space exploitation. Gao et al. presented a holistic analysis of various derivative-free algorithms for hybrid electric vehicle optimisation in a simulation environment. The authors implemented GA, SA, DIRECT and particle swarm optimisation with interest in fuel consumption reduction, performance and design. The study highlighted simulated annealing and particle swarm optimisation as the best compromise, where particle swarm optimisation presented a slightly better solution [77]. Particle swarm optimisation was also implemented by Chen et al. to simultaneously optimise design and energy management of a parallel hybrid electric vehicle with interest in both fuel consumption and emissions reduction. The authors claimed a substantial reduction in fuel and exhaust emissions by combining design and control with particle swarm optimisation [95]. N€uesch et al. proposed the combination of DDP and particle swarm optimisation to optimise fuel consumption and powertrain cost. The optimal fuel consumption for a predefined cycle was obtained with DDP, whilst particle swarm optimisation was used to optimise the powertrain cost, based on the obtained results from DDP [97]. Similarly, Chen et al. implemented particle swarm optimisation for vehicle control, claiming its simple implementation and fast convergence, thanks to its efficient search engine. Nevertheless, the authors recognised the algorithm risk to fall in local minima and combined it with simulated annealing to compensate for this deficiency and reduce the dependency on the initial solution [98]. Furthermore, the baseline particle

+1 +1

Fig. 2.13 Movement of the particle ‘i’ in the solution space during iterations k and k + 1. The evolution of the particle movement is influenced by the particle best position, Pbest, and the group best position, Gbest.

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swarm optimisation algorithm can be time consuming and prevent real-time vehicle control, as claimed by Lin et al., who used offline particle swarm optimisation results to train a neural network real-time implementable with near-optimal performance and satisfactory results in a simulation environment [99]. Chen et al. proposed a control strategy for online control of a PHEV using the combination of particle swarm optimisation and rule-based implementation. The implemented rule-based strategy introduced four threshold parameters correlated to the control signal that were optimised offline using particle swarm optimisation. Consequently, the strategy could perform real-time with close-to-optimal results as a consequence of the offline optimisation with different drive cycles [100]. A step further was taken by the same authors in a later publication, where they proposed the use of a fuzzy logic algorithm to recognise the driving conditions and select the suitable set of parameters obtained offline using particle swarm optimisation and therefore adapt the rule-based strategy to the drive cycle [101]. Particle swarm optimisation has also been applied to other automotive related optimisation areas, such as vehicle routing. Nevertheless, in problems of such a largescale, a particle swarm optimisation searching engine might be inefficient, a reason why Marinakis et al. proposed a hybrid implementation of particle swarm optimisation to optimise vehicle routing at a ‘very large-scale’ as stated by the authors [102].

2.4.4.4 Simulated annealing Simulated annealing was developed in 1983 by Kirkpatrick et al. [103] and is one of the first metaheuristic algorithms inspired on the physical phenomena happening in the solidification of fluids, such as metals. As happens in other derivative-free methods, simulated annealing prevents being trapped in local minima using a random search engine expressed in terms of a Markov chain. Simulated annealing introduces changes in the solution to improve the objective function, but also keeps solutions that, despite underperforming the best ones, comply with certain criteria. In a minimisation problem, any better modifications that decrease the objective function, J, are accepted; nevertheless, candidates that increase J are also included in the solution set with a probability p, called transition probability [29, 104]: p ¼ exp ½ΔE=kB T 

(2.28)

where kB is Boltzmann’s constant, T is the control parameter, temperature of the annealing process, and ΔE is the energy level, which is linked to the change of the objective function through a real constant, γ [29, 104]: ΔE ¼ γ  ΔJ

(2.29)

Whether a change in the solution is accepted or not is decided by a random threshold, r, so that p > r. Along the optimisation process, T decreases and the system cools down as defined by the cooling factor, α [29, 104]: T ðtÞ ¼ T0  αt , with t ¼ 1,2, …, tf and α 2 ½0, 1

(2.30)

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iHorizon-Enabled Energy Management for Electrified Vehicles

where tf is the number of iterations. As a consequence of the simulated annealing formulation, the selection of the initial T0 strongly influences the solution. Very large T values would cause the acceptance of all solutions, whilst very low values would not accept any diversity, as happens in hill-climbing methods. Consequently, large T implies high-energy systems and difficulties to reach minima and low T implies low-energy systems that can be trapped in local minima. A proper T selection should be able to initially search the space for global minima and later, as the system cools down, converge on a solution with proper accuracy [29, 77, 104]. The stopping criteria is included in tf, which restricts the number of iterations, or in terms of the improvement of the objective function [77, 104]. Fig. 2.14 illustrates an example of simulated annealing convergence in seven iterations. Initially the energy of the system is large due to large T values and the solution variability is large, searching over the entire space in iterations 1–3. As the system ‘cools down’ the solution search reduces the variability of the candidates as in 3–5 and finally, low temperature values allow for converging accurately into a solution, presumably after iteration 7. The benefits of simulated annealing are its easy implementation and its possibility of finding a global optimal even after finding a local minimum, as it accepts solutions that are worse than the best candidate. Furthermore, it can provide satisfactory results with a relatively low number of iterations, which makes it suitable for real-time control [78, 104]. Trova˜o et al. proposed online energy management of a battery electric vehicle provided by a hybrid electric power source able to obtain in real time the share of the power between electric sources. The strategy was formed by a rule-based, long-term controller based on experience and a short-term power management that implemented simulated annealing to obtain the optimised control signals used as reference for the

Cost – J (t)

1 3 2 5

4 6 7

Fig. 2.14 Seven iterations of simulated annealing algorithm convergence from large values of T in iterations 1–3 for global optimal exploration to low T values in iterations 5–6 for accurate minima computation.

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controller [78, 104]. Similarly, Wang et al. used simulated annealing to obtain the value of the parameters for a rule-based energy management strategy for a series hybrid electric vehicle real-time control for engine turn on/off and efficient operation. The authors claimed the suitability of simulated annealing for hybrid electric vehicle control and compared the results with similar methods, such as DIRECT and baseline strategy prior to optimisation [105]. Other applications in the literature tend to combine simulated annealing with other optimisation tools to compensate for their deficiencies. Chen et al. proposed the energy management strategy of a power-split plug-in hybrid electric vehicle using a combination of PMP and simulated annealing. The authors approximated the fuel rate with a quadratic function, defined the battery current as input and implemented PMP to find the current command and simulated annealing to compute the engine-on power and the battery maximum current coefficient. An extended version of the algorithm was also introduced to account for the battery state of health (SoH). The authors claimed the algorithm could provide an effective fuel consumption reduction with fast computational speed [106]. Another algorithm combination was proposed by Hui et al., who combined simulated annealing with a genetic algorithm in a multiobjective adaptive control strategy for a hydraulic hybrid vehicle to optimise the key components for fuel consumption, performance and cost. The authors compensated the genetic algorithm slow convergence with simulated annealing and modified the algorithm to favour an adaptive implementation for premature convergence [93]. Alternatively, Chen et al. implemented an energy management strategy to reduce the emissions and fuel consumption of a hybrid electric vehicles by combining particle swarm optimisation and simulated annealing. The authors made use of the simple implementation and fast convergence of particle swarm optimisation, and efficient search engine superior to genetic algorithm. The risk of falling in local minima was compensated for using simulated annealing, which favoured the solution variability [98]. Another simulated annealing automotive application that has recently been commonly used is the vehicle routing problem, which has been solved with successful results in Refs. [107, 108].

2.4.5 Neural networks Neural networks along with artificial intelligence have become a topic of utmost interest in recent years. Despite being a well-proved ‘old’ technology, the rise in popularity of these algorithms owes its development to computers that are ever more powerful. The possibility of applying more complex structures has opened new areas of applications in real-time control.

2.4.5.1 Neural networks description Neural networks emerged from the analysis of structure and signal processing of natural biological systems. In the human brain a large number of ‘standard units’, known as neurons, are interconnected in a complicated fashion. During learning, new

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connections are created and previous ones either strengthen or weaken. Artificial neural networks (NN) are extremely simplified models from natural networks, given the high complexity of natural systems [109–112]. Neural networks process input signals and produce outputs as ‘black models’: that is, their users do not necessarily need to understand the process taking place in the network. The neural network parameters are computed using a training algorithm that allows the system to ‘learn’ to behave in a specific way [109]. Neural networks have a wide range of applications, usually related to pattern recognition, and they can be used to identify, evaluate, monitor, optimise, recognise, classify and filter patterns [109, 112]. Some of the areas where neural networks have been applied include aerospace, automotive, banking, defence, electronics, financial, medical, manufacturing, robotics, speech, security, telecommunications and transportation [110]. The key characteristics of neural networks include their parallel computation capability and their capacity for generalisation; that is, their capacity to yield a reasonable output when encountering an input never experienced before (during the training phase). These properties allow for the approximation of very complex functions and even intractable problems. Useful neural network capabilities include nonlinear operation, input to output mapping, adaptability, confidence in the response, contextual information, fault tolerance, numerical implementation and uniformity in its form of design [111]. As formerly described, neural networks are formed of basic units called neurons. Each neuron performs an affine transformation and a nonlinear operation of its input by applying the neuron activation function. When expressed in the frequency domain, the neuron transformations are described by transfer functions. A typical neuron output, y, can be obtained with a function of the form of [110–113]: y¼

1 with η ¼ w1 x1 + … + wn xn + γ 1 + exp ðη=T Þ

(2.31)

where T defines the characteristics of the function and η is the transformed input of the neuron, the weighted summation, wi, of the input-signals, x, and γ is a bias constant. Usually, the general formulation includes the bias into the input signals by defining x0 ¼ + 1 and w0 ¼ γ. With the previous definition, the input to the neurons can be summarised as [110–113]: η ¼ w 0 x 0 + w1 x 1 + … + w n x n ¼

n X

wi xi

(2.32)

i¼0

Fig. 2.15 illustrates a hypothetical neuron i that receives m inputs and performs a weighted-biased summation of the signals (affine transformation), η, before applying its inner function to produce a nonlinear response, y. This simplified model of a neuron simulates a very simplified information processing in a biological neuron, but it is not able to take into account the relationship between inputs and outputs in time or accumulate the effect of specific signals [112].

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These characteristics are modelled when forming the neural networks. A neural network is formed by the combination of multiple neurons organised in layers interconnected with each other [113]. The neural network structure can become more complex when adding new layers and interconnections between them. These are either feedforward when layers are connected only in one direction, towards the output, or feedback, also known as layer recurrent, when layers recur to themselves or to previous layers. Layer recurrent structures include dynamics of the process modelled through the neural network by recirculating signals with a specific delay [110–112]. Furthermore, the function used in the neurons can be varied and can include: hard limit also known as a threshold function, linear saturated, log-sigmoid, hyperbolic tangent, etc. [110, 111]. Fig. 2.16 illustrates two neural network

x1

W1i NEURONi

xn

+

Wni

hi = åwjixji + gi

yi

gi

Fig. 2.15 Neuron, basic unit of a neural network, numerated as ‘i’. Neurons in a network receive the inputs from the previous layer, x; these inputs are multiplied by the respective neuron weights and summed to produce the neuron input, ηi. Then the neural network performs a nonlinear operation such as (1 + exp( ηi/T))1 to produce the neuron output, yi.

Context layer

Hidden layer 1

Hidden layer p

Output layer

Input layer

Output layer

x1

y1

x1

y1

x2

y2

x2

y2

xn

yn

xn

yn

Input layer

w1, input

wp, ...,1

woutput, p

w1, input

wp, ...,1 Hidden layer

woutput, p

Fig. 2.16 Neural network structures. On the left, a multiple-layer neural network with p hidden layers in a feed-forward connection. On the right, a layer recurrent neural network with one hidden layer and one context layer causing a signal delay and nonlinear transformation.

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iHorizon-Enabled Energy Management for Electrified Vehicles

architectures. On the right is a feed-forward neural network with p hidden layers and on the left is a feedback or layer recurrent neural network with one hidden layer and a context layer that includes the network dynamics and active delay. The capability of neural networks to emulate processes as surrogate models depends on their architecture design and parameter tuning [113]: (1) Architecture selection: input signals required to emulate the process, number of layers and neurons per layer, interconnection between layers and activation function. (2) Network training: weights computation (neural network coefficients) to emulate the process of interest. The network parameters are usually obtained using the error backpropagation algorithm and sufficient quantity of training data of required accuracy and variability to model the process of interest in a specific region of the possible input signals space.

A sufficiently complex neural network can approximate any general set of functions [113]. The process followed to modify the neural network parameters, weights, is generally known as the training algorithm or learning rule. Herewith only supervised learning is considered for application to energy management in electrified vehicles, which is essentially based on error-correction learning. This assumption implies that the training data is labelled, the desired output to a training input set is known and feeds into the training algorithm to compute the value of the parameters to emulate the desired behaviour [110, 111]. One of the most popular training algorithms is the so-called back-propagation, which consists of the use of the output error to correct the network weights. It is a gradient descent method and uses the steepest way to modify the parameters, and therefore speed the convergence, using a first-order Taylor series expansion [109, 110, 112]. This method uses the direction of maximum decrease of the error function, multiplied by a parameter known as the learning rate, α, to update the weights. Large values of the learning rate imply larger changes in the weights update, and vice versa. Ideally, the learning rate should be large at the beginning of the training for faster convergence and should be low at the last stages to guarantee that accurate results are achieved. Furthermore, relatively large learning rates would generate unstable learning that would never achieve convergence, whilst relatively low learning rates might prevent the algorithm’s convergence in a realistic amount of time [110]. Despite the popularity of the back-propagation algorithm, there are numerous alternative training algorithms that have been engineered to yield more accurate solutions in a fewer number of steps. One example is Newton’s method, which implements a second-order Taylor series through a quadratic approximation of the error function. This method is particularly convenient when the function is quadratic or has a similar form, a situation in which it converges in one step. Newton’s method generally presents faster convergence, but its behaviour is considerably more complex when compared to steepest descent and requires the computation of second-order derivatives, Hessian matrix. Furthermore, whilst a steepest descent is guaranteed to converge with a relatively low learning rate, Newton’s method can oscillate or even diverge [110]. Besides, when facing problems of large scale, the Hessian calculation and storage can be too expensive and prevent a Newton’s method implementation. Ideally, the

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requirement should be for an algorithm that requires only first-derivative computation but that still yields quadratic convergence behaviour. The conjugate gradient follows the previous description and is essentially able to obtain the conjugate vectors, eigenvectors of the Hessian, without having to calculate them using a computation constrained by the Hessian conjugacy conditions [110].

2.4.5.2 Antecedents in neural networks application in automotive control Among the wide range of neural networks applications, the latest advances in the automotive sector have shown increasing interest in artificial intelligence. Neural networks applications in hybrid vehicle control is supported in the statement of Boyali et al. included in Ref. [47], where the authors affirmed: “The algorithms that require iterations are not convenient for hybrid vehicle power distribution problems”. This statement refers to the constringent computational requirements of real-time control and supports neural networks as good candidates with online implementation potential. Preliminary applications of neural networks in vehicle control take advantage of their adaptability property. Khayyam et al. proposed an adaptive neurofuzzy inference, which provided a fuzzy logic controller with learning capabilities. The authors developed a controller able to adapt to a wider application range by automatically tuning the strategy thresholds. Information requirements were analysed in terms of road characteristics, environmental conditions and driver behaviour so as to find a trade-off between the algorithm performance and information requirements [21]. Chen et al., who claimed the need of intelligent controllers as a trade-off between computational effort and robustness, took a step forward by implementing a neural network–based controller. In this case, the neural network was trained using dynamic programming optimal data to minimise fuel consumption in a PHEV. The authors simulated a wide range of driving conditions to generate comprehensive training data and therefore improve the generalisation properties of the developed controller. The strategy consisted of two neural network modules applicable to different case scenarios dependent on the information about the future trip. On the one hand, N1 was used when the trip information was available to maximise the battery used, and N2 was applied otherwise [8]. A similar approach was proposed by Prokhorov et al. to control in realtime a power-split hybrid electric vehicle Toyota Prius considering route data information [114] and by Boyali et al. who again developed a neural network–based controller for a hybrid electric vehicle using training data from dynamic programming optimisation [47]. Likewise, Suzuki et al. presented fuel consumption improvement of a hybrid electric vehicle truck by implementing a neural network–based energy management strategy [115] and Murphey et al. proposed in two consecutive publications [116, 117] an energy management strategy for a power-split hybrid electric vehicle based on neural networks and dynamic programming expert data. The trained controllers were claimed to operate in real time and exhibited parallel computation as validated in a simulation environment.

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Despite the high quality of the solutions produced with dynamic programming algorithms, in applications where either a large number of variables or a large quantity of data is required, alternative optimisation methods might be recommended. That is the case of Lin et al., who employed particle swarm optimisation instead of dynamic programming to generate training data and synthesised a neural network–based energy management strategy [99]. Further applications of neural networks to the automotive field can be found in the literature so as to exploit their forecast capabilities. Sun et al. included neural networks in an MPC framework for short-term prediction horizons. The neural network–based model was able to release computational effort for MPC implementation [5]. In a later publication the same authors presented a future speed prediction algorithm based on machine learning. This time the neural network forecasting capabilities were compared to those of Markov chains and alternative models for speed prediction. The authors claimed to obtain up to 92% fuel optimality in a simulation environment by using the neural network–based predictor when compared to the benchmark solution calculated with dynamic programming [118].

2.4.6 Game theory Game theory consists of a range of analytical tools where decision makers with selfobjectives, certain knowledge and expectations interact reasonably. The models in game theory could be interpreted as abstractions of real-life situations expressed mathematically, where the competition and cooperation between parties is studied. A game is understood as the description of available strategies, constraints over the possible actions and consequences of these actions. As if in an ordinary game, it describes the ‘rules’, but not the actual strategy that the players eventually take. Hereby a player is a basic entity that takes rational decisions, meaning that it is aware of its alternatives, has preferences, has expectations about the uncertainties and chooses actions deliberatively. When players act with individual interest, the game is called noncooperative, as opposed to the case when players act with common interest and the game is understood as cooperative [119–121]. Further game classifications can be found in Ref. [119]. Assuming absence of uncertainty, a set of possible actions A has associated with it a set of consequences of form C. Given any set of possible actions B for a particular case scenario, a rational player chooses a specific action, a, that is possible and optimal in terms of the associated consequences, usually referred to as payoff or utility. The players solve the optimisation problem of maximising the benefit or minimising the cost based on the consequences of the possible actions [119, 120]. Table 2.1 includes the payoff that Player 2 can achieve according to its own actions and in conjunction with Player 1 actions in the rock-paper-scissors game. Both players play without information about the other player’s strategy and receive a benefit/cost depending on the other’s action. The respective Player 1’s payoff matrix would be the opposite. The solution of the game is usually achieved using the Nash equilibrium, which consists of a steady-state situation where all players decide not to take further actions as their benefit cannot be improved by any of the possible actions. Unfortunately, the

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Table 2.1 Example of payoff matrix associated with the consequences of Player 2 actions with respect to the actions taken by Player 1 Consequences of Player 2 actions with respect to Player 1 Player 1 Player 2

Rock

Paper

Scissors

Rock Paper Scissors

0 1 1

1 0 1

1 1 0

Nash equilibrium does not necessarily always exist and it might not be unique; that is, achieving a steady-state scenario does not imply that it is ‘fair’ to all players or that it is the best solution that could be computed [119, 120]. Despite the popularity of Nash equilibrium in noncooperative games of two or more players, game theory can implement several types of equilibriums, such as Stackelberg and Bayesian equilibrium [122]. When applied to the automotive field, both cooperative and noncooperative games have potential applications. An example of a cooperative game of two players could be the internal combustion engine and electric motor in a hybrid electric vehicle, where both operate so as to minimise a common objective, fuel consumption. Alternatively, the game between the vehicle powertrain and the driver can be modelled as noncooperative due to the conflicting objectives of fuel consumption minimisation and vehicle performance, respectively. When applied to energy management in electrified vehicles, the two players noncooperative game implementation is preferred. Dextreit et al. implemented a driver-powertrain noncooperative game to optimise the energy management strategy of a Jaguar Land Rover Freelander 2 hybrid electric vehicle. The conflicting objectives consisted of vehicle performance against efficient operating conditions for fuel consumption minimisation. Game theory allowed for introducing the driver directly into the control strategy, known to be an important asset in fuel consumption through driving style. The strategy developed was compared to similar dynamic programming and MPC approaches in a simulation environment to benchmark and showcase a game theory robust approach. Likewise, the authors highlighted the elevated computational burden of game theory comparable to that of dynamic programming, which hindered its online implementation for real-time control. In this respect, Dextreit et al. proposed strategy simplification through map- and vectorbased implementation, so as to develop a time- and cycle-independent controller [123, 124]. A comparable application was presented by Gielniak et al., who introduced a game theory–based energy management strategy of a fuel cell hybrid electric vehicle, where again the conflicting objectives of performance vs powertrain efficiency were considered. Further insights about the strategy recognised game theory as a complex algorithm that requires deep knowledge of the system of study and no extrapolation to either different vehicle platforms or components [125]. A different

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application was presented by Yin et al. in Ref. [122], where the authors tackled the problem of hybrid energy system control formed by engine-generator, battery and ultracapacitor and conflicting objectives of fuel consumption minimisation, battery life preservation and performance [122]. Despite the previous approaches in electrified vehicle control, game theory’s main application is generally the offline investigation in a similar fashion to dynamic programming. In this respect, a preferred application of game theory deals with electrified grid management for hybrid, full electric and autonomous vehicles. Many examples of its application in this area can be found in the literature, including both cooperative and noncooperative implementation with the interaction of varied entities [126–128].

2.4.7 Sliding mode controller Sliding mode control (SMC) consists of an algorithm inherently robust to changes in the parameters, nonlinear models, external disturbances and uncertainty. It is used when the robustness requirement is of utmost importance in vehicle applications and in the presence of strong uncertainties [129]. Sliding mode control is based on variable structure systems composed with independent structures of different properties and a switching logic between them. When the system moves on a sliding line or surface, it is said the system slides. Then a sliding mode takes place close to a switching surface when the system state vector is directed to it, ‘attracted’. By definition, a surface s(x) ¼ 0 is attractive when either trajectories starting in the surface remain in it, or trajectories starting outside the surface tend to it. The sliding motion occurs when the motion of the state trajectory x is towards the surface of either side of it, creating a discontinuity on the differential system [129, 130]: lim s_ < 0 and lim s_ > 0

s!0 +

s!0

(2.33)

Assuming a general case when the system differential equations are discontinuous, the SMC differential equations can be solved using the Filippov method. Given a dynamical system defined by the state equations x_ ¼ f ðx, uÞ, with f representing a system of equations, and sliding along the switching surface s(x) ¼ 0, let us define the velocity vectors [129, 130]: f  ¼ f ðx, u Þ and f + ¼ f ðx, u + Þ

(2.34)

where the control signal is defined as:  ui ðtÞ ¼

ui+ for si ðxÞ > 0 with i ¼ 1, 2, …, m and ui+ ðtÞ 6¼ u i ðtÞ u i for si ðxÞ < 0

(2.35)

Then the resulting velocity vector f 0 can be obtained as: f 0 ¼ αf  + ð1  αÞf + where α 2 ½0, 1

(2.36)

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Based on the previous formulation, the complexity of the strategy relies on the design of the sliding surface, whose mathematics can be relatively complicated as compared to the formerly introduced control strategies [129]. Some examples of SMC automotive applications are found in the literature. Gokasan et al. developed a sliding mode controller–based energy management strategy for a series hybrid electric vehicle. The suitability of SMC for the specific application was claimed based on the time-varying parameters and nonlinear characteristics of the system. The authors designed two controllers for engine speed and engine and generator combined torque control to explore SMC robustness properties against the model itself and component parameter uncertainties. The performance of the new controller was compared with an existing controller registering improved performance and overall efficiency with emissions and fuel consumption reduction in a simulation environment [131, 132]. An adaptive sliding mode controller was designed by Wang et al. to control a hybrid storage system in Ref. [133]. The authors combined battery and supercapacitor to extend the battery life, and applied SMC to palliate the risk of overcurrent shock during mode switching, due to its robustness to the system uncertainties, given the unpredictable perturbations that can occur during modes switching and external load disturbances. Furthermore, SMC was combined with hysteresis control to stabilise the current status under different operating modes [133]. A similar approach was followed by Snoussi et al., who also implemented SMC in a battery ultracapacitor hybrid system [134]. Likewise, Song et al. presented a sliding mode–based controller of a hybrid storage system in Ref. [135]. The authors controlled the supercapacitor current using a Lyapunov function–based controller to regulate the voltage in the direct current bus and an SMC to control both battery and supercapacitor current [135]. Apart from electrified vehicle applications, SMC has been found useful for diesel engine control in many publications in the past decades, with that being that its main application [136–139].

2.4.8 Convex programming The previously introduced algorithms incurred various numerical drawbacks, including: numerical issues, high computational burden, convergence not guaranteed in a given time, local minima computation, etc. Herewith, strategies that guarantee global minima convergence with efficient computational engines are presented and discussed, including linear programming, quadratic programming and convex programming. When expressed in the previous terms, optimisation problems become amenable to powerful solvers able to operate in real time and produce robust solutions for online implementation. Nevertheless, these solvers require the models’ implementation in convex terms, which can be challenging and not suitable to control any system [28].

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2.4.8.1 Convex programming in mathematical terms An optimisation problem is classified as convex when the equality constraints are affine and both objective and inequality constraints functions are convex, satisfying [28, 140]: fi ðαx + βyÞ  αfi ðxÞ + βfi ðyÞ; 8x, y 2 ℝn

(2.37)

where α and β are real constants and comply with α  0, β  0 and α + β ¼ 1. The previous equation holds as an equality for linear functions, which implies that any linear problem is convex and therefore convex optimisation can be considered as a generalisation of linear programming. The convexity rule implies that any segment joining two points contained in the convex set lies within the convex set; that is, every point in the convex set can be ‘seen’ by the other points. Furthermore, a function is affine when satisfying [28, 140]: θx1 + ð1  θÞx2 2 C; for C  ℝn ; x1 , x2 2 C and θ 2 ℝ

(2.38)

That is, the set C contains any linear combinations of two points contained in C provided that the coefficients in the linear combination sum to 1. The previous condition is more strict than the convexity one, which means that affinity implies convexity but convexity does not imply affinity [28, 140]. Fig. 2.17 illustrates an example of convex function shape in three dimensions to evidence the benefits of convex problem formulation in finding the global optimal solution. Given the convex formulation, the shape of the process modelled is of the same characteristics as Fig. 2.7, where local minima are simultaneously global minima. This property is key to finding the optimal solution allowing considerably simplified search strategies. General optimisation problems are well-known for being extremely difficult to solve. Nevertheless, there are some exceptions that count with powerful rules that can solve the convex problem, which include linear programming and least-squares. In contrast to least-squares and linear programming exceptions, the general convex programming solution does not have an analytical formula, but counts with effective Fig. 2.17 Three-dimensional example of the shape of a convex optimisation problem. As illustrated, local minima become global minima when the problem is formulated in convex terms, which considerably simplifies the solution search.

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solvers, such as interior-point methods, whose number of iterations and computational effort can be controlled and which accept a large number of variables and constraints [28, 140]. As formerly mentioned, convex programming imposes strict requirements over the optimisation functions, which might imply strong simplifications of the model equations. Consequently, even when the global optimal solution is achieved, the solution quality can be strongly influenced by the model simplifications and lack usefulness. Nevertheless, convex optimisation can play an important role in nonconvex problem solution by providing an initial guess for the optimisation solvers [28, 140].

2.4.8.2 Convex programming in automotive applications When convex programming is applied to automotive uses, this might imply strong simplifications over the powertrain model, including: (1) eliminating integer decisions such as engine on/off state and gear shifting; (2) relaxing nonaffine equality constraints to inequality constraints; (3) replacing variables to preserve convexity, such as state of charge by battery energy; and (4) discretising the problem formulation [141]. Nevertheless, provided that the previous conditions are met, convex programming presents a powerful optimisation engine that allows increasing the number of variables to optimise. Convex programming has been found to be particularly beneficial in tackling the combined problem of energy management and electrified powertrain design, known to be strongly coupled, but to involve simultaneously a burdensome number of variables. Egardt et al. proposed a combined design and energy management optimisation based on convex programming to provide an overview to the coupled problem. The model required reformulation to comply with convex terms and express the powertrain as a function of the component size, but provided a holistic analysis of the design trade-offs [141]. Hu et al. proposed a holistic analysis of the vehicle carbon footprint including influencing factors such as charging protocol, timing, energy management, battery size and emissions. The authors implemented the study in convex terms to allow for efficient calculation of the optimal control variables [142]. Simultaneous energy management and component sizing optimisation was also tackled with similar approaches in Refs. [143–146]. String vehicle control was proposed by Hu et al., who analysed fuel consumption and recuperation efficiency of a series plug-in electric bus with two alternative strategies, namely CD–CS and blended mode developed using convex optimisation and benchmarked against dynamic programming results. Convex programming offered a solution with considerably lower computational requirements and allowed performing a holistic analysis of the effect of the battery size over fuel consumption and recuperation efficiency [147]. Another publication on the same line of research implemented convex optimisation to simultaneously optimise vehicle component sizing and energy management in a fuel cell hybrid electric vehicle for drive cycles of different characteristics. The strategy allowed the incorporation of various control variables and understanding of the effect of the component size over fuel consumption and fuel cell health in Refs. [148, 149]. Convex simplification requirements are

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reduced when the electrified powertrain includes a continuous variable transmission as presented by Murgovski et al. in Ref. [6].

2.4.8.3 Analytical solutions for automotive control As an alternative to model simplification incurred when implementing convex programming, some researchers prefer the simplification of the searching engine in particular applications to yield an analytical solution. That is the case of Zhang et al., who developed an analytical solution for optimal control of plug-in hybrid electric vehicles in real-world applications considering powertrain components, cycle characteristics and the battery depletion target. The study required the model simplification into quadratic equations, but was able to capture the essential characteristics of the system with <3% error in a simulation environment and provide insights into the controller of both PHEVs and HEVs [6]. Beck et al. also presented a publication with a main focus on real-time implementation of optimal control, by rejecting sophisticated solvers and focusing on the simplification of the problem and vehicle model. The simplified model was implemented in an adaptive ECMS and in a mixed integer with quadratic constraints and linear programming, which can be efficiently solved. Both strategies were benchmarked against dynamic programming results and evaluated for real-time implementation. The simulation results showed satisfactory scores of the mixed integer implementation with considerably faster computation time (2.5 times) [150]. Similarly, Koot et al. proposed vehicle model simplification to reduce dynamic programming computational burden and allow for real-time control in-vehicle implementable. The authors expressed the vehicle model in quadratic terms and proposed a first strategy depending on future drive cycle information and a second approach based on present and past drive cycle data [151]. Despite the fact that plug-in hybrid electric vehicles require a real-time controller that can be achieved with convex programming, variables such as gear shift and engine state cannot be simplified in the vehicle model. Hou et al. proposed an approximation of a PMP solution through piecewise linear fit, reducing considerably the computational effort for online implementation [10]. A linear interpolation of the Hamiltonian was also proposed by Delprat et al., who achieved a reduction of the baseline PMP computation time of 17 times [152]. Similarly, Zhao et al. proposed a vehicle model based on line and quadratic functions to facilitate an analytic solution for the Hamiltonian equation. The authors assessed the algorithm optimisation of the component sizing in a ‘reasonable’ computation time and applied the algorithm for simultaneous optimisation of vehicle control and sizing [153].

2.5

The role of the driver

So far, energy management has been focused on the optimisation of the vehicle component operation to minimise fuel consumption, but the driver influence has only been mentioned when elaborating game theory examples in vehicle control. Nevertheless, apart from vehicle characteristics, road type and traffic, a key factor that strongly

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conditions fuel consumption and the overall powertrain efficiency is the driving style [154–157], which has been however generally ignored in energy management studies and has not been addressed with sufficient depth [158]. Furthermore, driving style can be of vital importance to calculate the remaining range for PHEV and BEV, which can diverge widely between drivers in the same route. Proof of the influence of driving style on fuel consumption can be found in the related literature. Bolovinou et al. combined route, gradient profile, traffic information and driving style to compute the remaining range available in a battery electric vehicle [159]. Besides, recent studies have evidenced the margin of potential improvement in fuel consumption in a simulation environment, reaching a 20%–40% reduction in [160, 161] and 5%–40% improvement in [162]. The reason for this variable margin is the road characteristics. For instance, Mudgal et al. registered a 33% fuel consumption reduction in highway roads, but only a 5% improvement in urban environments [163]. These figures have incentivised strategies to monitor and ‘correct’ driving style to encourage more fuel-efficient driver behaviour as presented by Reichart et al. [164] and Syed et al., who have conducted intense research in driving style, driving style correction and its influence on fuel consumption using machine learning and driver-adaptive corrective strategies [165]. For the particular case of HEVs and PHEVs, different driving styles can trigger different mode transitions, due to the various instantaneous power demands, and consequently affect considerably the optimal strategy to follow and engine triggering points. Furthermore, this affects full electric vehicles, regular hybrid electric vehicles and plug-in hybrid electric vehicles differently, depending on their architecture and component characteristics [166].

2.6

Energy management interaction with the infrastructure

As previously reiterated, in optimisation-based energy management, information about the future trip is of utmost interest, vital to effectively displace fuel consumption and improve the overall efficiency [167]. In the present situation, where automated vehicles and sensor fusion have become the agreed-upon future direction to develop the automotive sector, vehicle-to-vehicle and vehicle-to-infrastructure communication is gradually becoming a reality, a scenario particularly supported by the increasing popularity of smartphones with global positioning systems and internet connection. This reality makes possible the use of applications able to incorporate additional information, such as real-time traffic as provided by Google service. Nevertheless, researchers have also put effort into predictive frameworks applicable in the event of the absence of vehicle-to-vehicle and vehicle-to-infrastructure information. Such is the case of Huang et al., who proposed a predictive algorithm based on machine learning that provides a prediction of 50 s of future vehicle speed based on the past 150 s registered [168]. Nonetheless, despite an evident relationship between past and future vehicle speed, real-life drive cycles have a high level of randomness and disturbances provoked by traffic conditions, pedestrians and the

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environment. The reduction of such uncertainty requires research on energy management strategies with available trip information [169] and that are robust to different levels of trip knowledge. Zhang et al. proposed a four-level trip information system: (1) full distance, speed and road profile; (2) distance and road profile with estimated speed; (3) distance and; (4) no information [12]. Global positioning systems and smartphone support can provide external information, which was combined in a MPC framework by Sun et al. to develop a two-level controller for a power-split plug-in hybrid electric vehicle. The authors assumed the availability of real-time traffic information for long-term planning of a supervisor strategy so as to optimise the battery depletion. This cycle-length prediction was used as a guideline for lower level controllers, again using an MPC framework to optimise engine torque and speed in the short term using neural network prediction [5]. Other approaches to energy management strategies optimisation using route information, global positioning systems and geographical information systems can be found in Refs. [15, 167]. Despite the previous efforts towards vehicle control with limited trip information, the evolving infrastructure and important attention on intelligent mobility have supported approaches with further levels of connectivity. Gong et al. underscored the benefits of the combination of intelligent transportation systems, geographical information systems, global positioning systems and traffic flow modelling [170], and later provided an extensive analysis of the impact of intelligent transportation systems on fuel consumption reduction in plug-in hybrid electric vehicles [11, 171]. The authors investigated the relationship between speed profile and vehicle performance using a statistical analysis of the drive cycle [11, 171] and the fusion of real-time information with historical data to optimise energy management strategies [170]. Furthermore, the possibility of infrastructure connection allowed not only the access to information but also the use of cloud-computing; Ozatay et al. targeted cloud-based future speed optimisation to coordinate a group of vehicles using three servers able to provide ‘unlimited’ resources for its computation in Ref. [172]. This strategy assumed full traffic and road information availability, used to compute optimal strategies based on dynamic programming that were transmitted to the vehicles in the controlled fleet for optimal coordinated control. The authors claimed 14.1% and 7.4% of fuel consumption reduction in highway and urban roads, respectively, when the advised strategies were followed [172]. Fig. 2.18 illustrates the cloud-computing control strategy where a fleet of vehicles is monitored using a supercomputer with ‘unlimited’ computational capacity and information about the vehicle route and traffic conditions. The optimal policies that optimise the vehicle individually and the entire fleet simultaneously are computed in the cloud to reduce overall fuel consumption, idle time, and trip duration and to avoid traffic congestion. Apart from extra information, cloud computing can relax the computational effort required on-board, simplifying the vehicle design, and can provide even better strategies that seek not only a single vehicle energy control optimisation, but optimisation of an entire fleet for further fuel displacement, trip time reduction, congestion elimination and a long list of benefits. An ‘unlimited’ computation capacity also allows for using more accurate models, considering more optimisation variables such as weather conditions and including drivers as additional players. A comprehensive analysis of the

Integrated energy management for electrified vehicles

57

Fig. 2.18 Cloud computing allows managing of various vehicles with unlimited computational capacity and additional real-life traffic information, traffic light states, vehicle routes, etc.

factors with major impact on fuel consumption was provided by Marano et al. in Ref. [173], where the authors pay particular attention to weather conditions, including temperature and wind direction influence over aerodynamic and rolling resistances, and traffic conditions [173]. The latest research approaches also include group-based optimisation of higher scale through cloud computing and intelligent transportation systems [167, 172] and introduce game theory in the cloud to manage the tasks more effectively [174]. One of the latest approaches found in the literature is the plug-in hybrid electric bus control using cloud computing presented by Yang et al. The strategy was divided into offline and online parts and machine learning was used in combinations with stochastic methods in a receding horizon for fuel consumption reduction and traffic flow improvement [175]. HomChaudhuri et al. developed a two-level controller to control a fleet of hybrid electric vehicles, including a high-level controller provided by traffic lights, vehicle-to-infrastructure and vehicle-to-vehicle information, and a lower-level controller communicating to the previous that uses an MPC framework to optimise the velocity profile using an adaptive ECMS [69, 176]. Vehicle-to-infrastructure connectivity not only can benefit real-time energy management strategies for vehicle control, but also the overall energy fluctuation of the electric grid, the so-called Smart Grids able to manage energy more effectively and efficiently. In order to manage peaks in demand and fluctuating renewable energy generation in current and future electric grids, storage is indispensable. In this respect,

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iHorizon-Enabled Energy Management for Electrified Vehicles

BEV and PHEV can serve as temporal energy storage devices, which, managed in the connected grid, can be of great benefit for the electric network, absorbing peaks, balancing energy prices and introducing the new concept of vehicle-to-grid and smart charging [177, 178]. Furthermore, batteries of no use for electrified vehicles can be reutilised to develop large storage modules, enlarging their useful life and facilitating additional storage of low cost and larger flexibility than vehicles still in use. These technologies are of low impact today, but the forecasted integration of a larger number of electrified powertrains will definitely change the concept of energy in cities towards the so-called smart cities [178]. More analysis on the impact of plug-in electric vehicles and battery electric vehicles in the electric grid can be found in Refs. [179–182].

2.7

Future trends

The future of the automotive sector in the oncoming decades will be strongly influenced by the legislative exercises of global government on the country scale and local incentives to improve metropolitan air quality. Furthermore, strong investment in ADAS and autonomous vehicles will have future outcomes in vehicle and infrastructure technology, which is apparently evolving parallel to electrified vehicles, but which will eventually cause a heavy impulse in the definite integration and consolidation of electrified powertrains. Cloud computing, intelligent transportation systems, geographical information systems, smart grid, smart cities and other cyberphysical systems will lead to vehicle electrification development.

2.7.1 The future electrified vehicle concept As previously stated, a wealth of efforts on electrified vehicle energy management strategies have been exerted by the research community. Nevertheless, the variety of algorithms is not evident in industry due to the difficulties that these innovative approaches incur in terms of implementation. New strategies need to be developed to guarantee electrified vehicle market penetration and public acceptance and to enhance the performance and fuel displacement. Table 2.2 summarises the advantages and disadvantages of diverse control approaches; it seems clear that none of them is individually able to respond to all requirements, which is the main reason why there is no consensus in vehicle control. Therefore, future trends will most likely opt for the combination of two or more algorithms to compensate for their deficiencies. Examples of hybrid controllers have already been mentioned in this chapter and include the Elbert et al. approach to combine convex programming with PMP that allows for engine on/off control [184]; the N€ uesch et al. combined dynamic programming and convex programming, again for mixed-integer variables introduction [57]; and the Panday et al. combined genetic algorithm and PMP [89]. Apart from algorithm combinations, new applications of optimisation-based mathematical methods might be extended to vehicle control as

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Table 2.2 Summary of optimisation-based energy management strategies applied to electrified vehicles, including main advantages and disadvantages in terms of vehicle control [183] Strategy

Main advantages

Maid disadvantages

Dynamic programming

-

Global optimality (benchmark)

-

Curse of dimensionality Full cycle information (not in SDP)

ECMS

-

Fuel and electricity as single objective—equivalence factor Possible online implementation Stochastic solution generation (metaheuristic) to escape local optima Few tuneable parameters Control over terminal conditions Fast computation (online control) Learning and adaptive capability

-

Cycle sensitivity Local optima for deficient tuning

-

Accuracy/optimality not guaranteed in limited number of iterations

-

Strongly depended on quality and quantity of training data Uncertain behaviour out of the training space

Comprehensive trade-off of conflicting objectives Driver introduction in EMS

-

Curse of dimensionality Nonunique solutions (local minima)

Robust to uncertainties Robust to parameters change Fast computation—online and high number of control variables

-

Complex mathematics: s(x)

-

Strong model simplification: solution validity

Derivative free

-

Neural network

-

Game theory

-

SMC Convex programming

-

-

new mathematical algorithms emerge, such as pseudo-spectral algorithms [185]. Furthermore, the development of infrastructure, sensor installation and data management are provoking a rapidly growing area in machine learning, with algorithms such as neural networks, support vector machine, Bayesian inference and reinforcement learning [186]. These algorithms possess attractive characteristics for vehicle control and fit into the data era where vehicle automation is leading future research [187]. In addition, vehicle control finds two main hindering issues: trip information and computational resources. Imperfect information about the future and limited computation time support the implementation of simplified models that fail to incorporate all influencing factors and do not include the component dynamics, such as engine transients [173], battery polarisation [188] and battery power fading [106, 149]. Additionally, the important characteristics of grid support that differentiate PHEVs and HEVs

60

iHorizon-Enabled Energy Management for Electrified Vehicles

have not been sufficiently addressed by the research community, which prevents full exploitation of this technology despite its higher cost due to high power electric components. Battery models need to reproduce more realistic behaviour [189] and powertrain response to external and internal temperature conditions [190]. New algorithms, combinations of methodologies and accurate models require computational power, this being the concomitant challenge reiterated in most algorithm approaches. More complex models will also allow representation of a larger number of influencing factors which inevitably will increase the number of conflicting objectives to consider during optimisation. Fuel consumption reduction of interest for customers does not happen simultaneously with emissions decrease, which can be critical in plug-in hybrid electric vehicles where the engine off state can be maintained during larger periods and cause several cold starts [5, 10, 53, 191, 192]. Furthermore, fuel minimisation translates into extra stress on the battery, the most expensive component, affecting its useful life [64, 90] and fuel consumption reduction does not imply the same for CO2, as the electricity used depends on the percentage of clean technologies used for energy production. Besides, extra criteria affecting high power vehicles might require a drivability or comfort objective to satisfy the customers’ expectations for such products [35, 77]. Multiobjectives approaches increase the computational effort required for problem resolution either through Pareto capable algorithms [35] or using a single objective weighted function, whose optimality depend on the weights selection [32]. Nevertheless, even when applying alternative algorithms, all optimisation-based controllers require trip information to yield and guarantee satisfactory solutions. This has been attempted using commuting trip information, preestablished routess such as the ones used in buses, and predictive algorithms, using MPC and machine learning. These approaches intend to develop adaptive controllers such as adaptive-ECMS in Refs. [66, 150, 193], but strict optimal strategies can only be computed when the optimisation is performed over the entire drive cycle, instead of a limited receding horizon in MPC. Longer horizons not only optimise the cycle itself, but can also serve to coordinate vehicle recharging for efficient grid management and weighting time reduction of users and therefore increase of customer acceptance. Both trip information and additional computational resources can be guaranteed provided that vehicle-to-infrastructure communication channels are available and are robust to guarantee vehicle control. Cloud computing can be a solution to ease vehicle computational effort and find global optimal policies to coordinate individual vehicles in the entire fleet. In terms of recharging, several assessments have been provided in Refs. [194, 195] for energy management combined with recharging management. Further development of the infrastructure, vehicle-to-vehicle and vehicle-toinfrastructure communication will allow for better traffic coordination to increase both road capacity and overall efficiency. One favoured solution is vehicle platooning, already implemented for heavy-duty vehicles sharing the same route. This system allows reducing the intervehicle distance to minimise aerodynamic resistance and decrease the required manoeuvring to avoid traffic flow disruption [196, 197]. The extension to light-duty vehicles is possible within the so-called vehicular ad-hoc network, the wireless environment within intelligent transportation systems where the

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data is exchanged [198, 199]. Smart traffic lights, vehicle-to-vehicle and vehicle-toinfrastructure have been used in a simulation environment to test the benefits of shared information in Refs. [69, 200]. This technology can be used to introduce multiagent cooperative energy management strategies, cooperative look-ahead energy management strategies, distributed MPC-based control and advanced networks for energy management strategies. Finally, further improvement on vehicle connectivity will support the introduction of increasing levels of automation and autonomous features such as lane change [201] and T-intersection control [202].

2.7.2 Electronic horizon Among the latest developments in environment perception and trip planning is the so-called electronic horizon (eHorizon) which, along with the development of standardised software for its implementation, represents a watershed. eHorizon implements vehicle location within digital precise maps enhanced with topographical data. It can also influence internal combustion engine management to adapt to the road slope and it has prediction capability to anticipate the host vehicle’s most probable path to regulate the engine transitions [203–206]. This allows the driver to ‘see’ further ahead in the road, even beyond the driver vision line and around corners [207], and has various applications including electrified vehicle energy management improvement [207–210] and enhancement of ADAS and autonomous features [204, 207, 211–214]. Nevertheless, eHorizon implementation requires standardised protocols to guarantee its compatibility along vehicle platforms and manufacturers. With this purpose, the Advanced Driver Assistance Interface Specification (ADASIS) was developed [205, 215], an industry platform that was created in 2002 as a standardised interface for: (1) ADAS horizon development and implementation; (2) increasing ADAS capabilities; and (3) accelerating the market integration. ADASIS is the result of the cooperation of ADAS suppliers, vehicle manufacturers, map and data providers and navigation system suppliers to define open standardised protocols [207]. This technology is supplied by providers such as Bosch [206], Continental AG [216–218] and HERE [214]. In addition, dSpaces provides a block set accessible from Simulink that implements the eHorizon through ADASIS protocols, and other companies involved are Elektrobit, IPG Automotive GmbH, and TomTom [219]. Nonetheless, eHorizon fails to solve two key issues that might prevent it from fully exploiting the information processed. On the one hand, the path predictive is static and does not consider the driving style, albeit it can incorporate real-time traffic information. The speed profile dynamics are crucial to anticipate the driver power demand and therefore fuel consumption and optimal mode transitions in electrified powertrains. Consequently, eHorizon might not be able to integrate the distinctive dynamics of real-life drive cycles and their influence over speed and acceleration for fuel consumption reduction [161]. On the other hand, eHorizon implements comprehensive high-level information requiring a consequently large and robust communication bandwidth not necessarily available in ordinary vehicle platforms nowadays. As understood by the authors, the eHorizon static approach and information requirements

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iHorizon-Enabled Energy Management for Electrified Vehicles

neither provides dynamic information required to achieve efficient energy management and implement full autonomy, nor fully exploits the capabilities of the current technology. Hereby these deficiencies are considered and an alternative approach is proposed to improve eHorizon within a platform that can be readily implemented in vehicles with limited communication capabilities and can be merged to complement eHorizon.

2.8

Intelligent horizon

Intelligent Horizon (iHorizon) is designed to compensate for the issues of eHorizon, facilitate its immediate implementation in current ordinary vehicles and improve its prediction capability. iHorizon combines limited information readily available through intelligent transportation systems, geographical information systems or global positioning systems, which aligns with eHorizon data sources and therefore is compatible with its platform. Nevertheless, iHorizon assumes the availability of scarce data, which is enhanced using machine learning algorithms. This novel framework ensures full benefits can be obtained from the existing information and introduces dynamics into the speed and acceleration profile prediction. The iHorizon framework is formed by three main modules as in real-life drive cycles (Fig. 2.19): (1) driving style recognition algorithm; (2) short-term speed

Fig. 2.19 iHorizon framework formed by three main modules: (1) driving style recognition algorithm; (2) short-term speed prediction module; and (3) long-term cycle-length speed prediction module.

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prediction; and (3) long-term speed prediction. Driving style recognition is developed using real-life data through unsupervised learning algorithms in a semisupervised implementation approach. Speed prediction is completed in short receding horizons of 10 s and in long-term covering the complete cycle length for local correction of the energy management along with cycle-length global optimal control. The speed predictors are developed using real-life data and Markov chains particularly designed to incorporate real speed and acceleration profile dynamics for realistic power demand prediction. iHorizon benefits from machine learning algorithms with enhanced learning capabilities, exhaustive statistical analysis and pattern recognition. Despite the limited information handled, iHorizon still provides a holistic driver adaptive framework to extend the use of such predictive frameworks to all vehicle users by all means possible and provide close-to-optimal and safer vehicle control within the current infrastructure. In the following chapters, iHorizon modules are elaborated.

2.9

Conclusion

Electrified vehicle control has been presented as a complex task with strong requirements in terms of computational effort, mathematical complexity and connectivity capabilities. The variety of component architectures and characteristics, along with the complexity of the problem in hand and implementation requirements, have prevented reaching an agreed-upon solution involving the research community and industry. Nevertheless, the answer for this paradigm might not be in the direction of the current research towards more sophisticated controllers and mathematical algorithms, but might be found in the holistic analysis of the current state and future of the automotive industry. The future vehicle will be provided by vehicle-to-vehicle and vehicle-to-infrastructure connectivity, will transit smart roads and smart cities and will be provided with ADAS features and autonomous capabilities. The future development of electrified vehicles needs to comply with the future vehicle concept, adapt to the new framework and take full advantage of their benefits.

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