Review of Optimal Design Strategies for Hybrid Electric

Review of optimal design strategies for hybrid electric vehicles

Citation for published version (APA):Silvas, E., Hofman, T., & Steinbuch, M. (2012). Review of optimal design strategies for hybrid electric vehicles.In Proceedings of the IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling (E-CoSM'12), 23-25 October 2012, Rueil-Malmaison, France (pp. 77-84). Pergamon.

Document status and date:Published: 01/01/2012

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Review of Optimal Design Strategies for HybridElectric Vehicles

Emilia Silvas∗, Theo Hofman∗, Maarten Steinbuch ∗

∗Department of Mechanical Engineering, Technische Universiteit EindhovenEindhoven, The Netherlands (e-mail: [email protected]).

Abstract: In this last decade, the industry headed in multiple transportation sectors towards hybridiza-tion and electrification of powertrains. This trend can be particularly observed in the automotive industry(passenger vehicles, commercial and construction vehicles), as well as, in water and air transportationsystems. This change was a clear result of multiple environmental or market driven objectives as high fueleconomy, pollution or limited resources. The electrification of transportation has brought an increase inthe design complexity of the powertrain; and, in the same time a challenge for the research institutes andoriginal equipment manufactures (OEMs). Multiple hybrid electric architectures have been developedunder a continuous struggle to find the best solution with respect to various objectives and constraints.To find the optimal design of, for example, a hybrid electric vehicle (HEV), is a complex optimizationproblem that can be addressed through various methods. Prior to the choice of a suitable algorithm forthe optimization of this design problem, there is a need of in-depth understanding of the current state ofknowledge in architecture choices and optimization algorithms. This paper presents an overview of theexisting approaches and algorithms used for optimal design of hybrid electric vehicles (HEV). It alsoincludes an introduction in various hybrid topologies and examples from different transportation sectors.

Keywords: optimal design, hybrid configurations, powertrain simulation, topology and sizeoptimization, integrated framework, hybrid electric vehicles(HEV), hybrid electric submarines (HES),hybrid electric boats (HEB).

1. INTRODUCTION

In recent years, when the future of automotive power trainsis discussed, the emphasis on reducing the CO2 emissions issignificant. This is enabled by the usage of other energy sourcesand leads directly to reduced air pollution. After Toyota Priuswas lunched for the Japanese market in 1997, Audi was the firstEuropean car manufacturer that released a hybrid passengerscar. Nowadays hybrids are offered or planned by Ford, GeneralMotors, Honda, Nissan, GM, Daimler Chrysler, PSA PeugeotCitron, Mercedes-Benz, Hyundai and others. As they haveproven their beneficial aspects, hybrid concepts have enteredother markets as well. We can find now, hybrid commercialvehicles (as for example buses, Trigui et al. (2009), or trucks,Kadri et al. (2006)), hybrid construction machineries (as fork-lifts, Minav et al. (2010)), hybrid boats (see for applicationsexamples Bolognani et al. (2008), Pizzo et al. (2010), Tang et al.(2006)), hybrid submarines, Skinner et al. (2009), or hybridaircrafts, Rajashekara et al. (2008).

When a hybrid system is designed particular choices need tobe done for each component of the drive line, and each ofthese choices are influencing the performance of the vehicle,e.g., fuel consumption, emissions, drivability or others. Findingthe optimal design of a power train implies that the optimalsolution for each design parameter has been found such thatthe propulsion is conducted at the optimal overall efficiency.Due to the complexity of the problem this has not been solvedso far in an integrated way. In Guzzella and Sciarretta (2007),three different existing layers of optimization have been definedas: (i) structural optimization, where the objective is definedin terms of the powertrain structure (topology), (ii) parametric

optimization, where the objective is defined in terms of theparameters of the fixed structure (size and type of components)and, (iii) control system optimization, where the objective isto find the best energy management system (EMS). Variousmethods address these optimization problems, yet until nowthere is no systematic optimization methodology that simulta-neously considers all these layers. The broad design space tobe searched and the multiple possible cases makes this problemnon-trivial. As a follow-up of these complex requirements theHEV design needs to be addressed with a strongly interdis-ciplinary approach, Moore (1997). The papers that have ad-dressed this (or, part of) problem for power train optimal designanalysis are considered in the following sections.

Hybrid vehicles are characterized by two, or more powersources to produce, store and deliver power, and this usuallyrefers to an engine and an electric motor (EM). This configura-tion for hybrid electric (HE) systems, engine and an EM, willalso be considered here as default unless stated otherwise. Thishybridization brings along a wide variety of possible topologies(architectures) when building the powertrain, yet, more gener-ally, all these topologies can be split into three categories: se-ries, parallel and series-parallel topologies, Ehsani et al. (2007).

Since, series drive trains, as depicted in Figure 1, perform bestin stop-and-go driving, they are primarily being considered forbuses and other urban work vehicles, Emadi et al. (2005). Ifthe series hybrid topology is not used in city driving, then highpowers need to be transmitted to the wheels from the EM,hence large electrical machines are required for high vehiclesspeeds. The features of the traction motor are deducted from thevehicle dynamic required performance, therefore the remaining

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variables that can be optimized with respect to size are thebattery pack size and the generating group (engine/generator)power. While in series topologies there is more flexibility inpositioning the components, in parallel topologies, as depictedin Figure 1, the energy losses are smaller due to the mechanicalconnection.

The larger battery and motor, along with the generator in aseries configurations makes these more expensive than the par-allel hybrids. When compared with other topologies a disad-vantage of the series topology is at high vehicle loads relativelylow transmission efficiencies are achieved, Hofman (2007).

Engine

Electric motor

Transmission

Generator

Battery

Mechanical connection Electrical connection

EM1

EM2

Electric motor

Transmission

Battery

Engine

(a)

(b)

Fig. 1. Topologies for hybrid electric vehicles: (a) Series topol-ogy and (b) parallel topology

The third category of hybrid topologies, series-parallel combinethe benefits and drawbacks from both series and parallel archi-tectures. For a wide variety of applications, these can bring re-duced fuel consumption, Xiong and Yin (2009). The efficiencyof any hybrid topology varies according to the conditions underwhich they are driven and the design choice of one or anotherarchitecture depends on the mission of the vehicle and the trade-off between cost and performance.

Intensive research has been conducted on hybrid componentstechnologies and storage devices for different applications. Theparticular requirements of each application define the technol-ogy that is chosen for usage as well as the sizes. This paperprovides an overview of the state of the art of design algorithmsthat can include also topology, technology or size optimization.In this paper the problem of real time implementable EMS isnot addressed. Instead paper focuses on the overall design ofboth topology and EM in the design phase of the powertrain.Section 2 discusses the optimal design problem, it offers anoverview of existing algorithms used and their results in variousareas of transportation. An analysis on trade-offs and benefits isdone in this section, with the intention of helping the reader ina future choice of optimal design algorithms. Finally, Section 3presents the conclusions of this analysis.

2. OPTIMAL DESIGN METHODS

Research is done in automotive industry to formalize the de-velopment of the product such that multiple-objectives can beconsidered in one step, which is an important economical aspectfor OEMs. The user can define constraints on the technology,the size or the topology of the vehicle as well as on the controlperformance. The very general mathematic problem statementcan be build as follows:

minimize...

f (x) = { f uel consumption, emissions, costs, ...}

with respect to...

x = {engine size, motor position, battery size, motor size, ...}

sub ject to..

0−60 km/h time ≤ ...

(...),

(1)

where the desired objectives, parameters and constraints canbe defined by the user. All the parameters/choices of this opti-mization problem together with the desired targets/constraintsand the given application can be summarized as in Figure 2.One approach in solving this problem, target cascading, wasproposed in Kim et al. (2003) and used in Hofman and vanDruten (2004), where the objectives of reducing the fuel, emis-sions or the costs, can be cascaded down to subsystem leveland further on to component level, which shows the direct cou-pling between components, subsystems and design objectives(see Figure 2). The advantage with this approach is that theoriginal problem is split into hierarchical set of subproblems,and ”local” optimizations can be defined and solved for eachsubproblem.

•Transmission

•Engine

•Battery

•Plug-in

•3-way catalyst

•High-level system: Integrated EMS (thermal, emissions, fuel)

•Low-level subsystem control

•Parallel/Series/Series-Parallel

•Single-/Multimode Power split

•Storage (Flywheel, Battery)

•Conversion (Engine, Electric machine)

Size Topology

Control

Motorcycle

Vehicle

Truck

Crane

Ship

Airplane

Fuel

Emission

Performance

Comfort, Handling

Cost

Application Parameters Targets /

Constraints

(pre

dic

ted

) o

pe

rati

on

co

nd

itio

ns

Technology

Fig. 2. Vehicular Propulsion Design

For control purpose, both the energy management system(EMS) and component control, numerous algorithms have beenanalyzed, and these can be split into two general categories: (1)rule-based algorithms, and (2) optimization-based strategies.An overview of these methods can be found in Salmasi (2007)and in Ganji and Kouzani (2010) and their classification is gen-erally depicted in Figure 3 from Salmasi (2007). Advantagesand disadvantages of these algorithms are stated in terms of thecapacity of finding the global optimum solution (as for exam-ple dynamic programming (DP)), rapidity of computation, thepossibility of real time implementation, reusability, complexityand so on. A study on the EMS strategies for HEV with theemphasis on those that consider the look-ahead road situationand trajectory information can be found in Ganji and Kouzani(2010).

In this paper optimal design algorithms which have been usedfor topology/technology/size and control optimization are dis-cussed together with their results for various applications. Para-metric optimization, with emphasis on sizing, of powertraincomponents have proven to be beneficial with respect to fuel

2

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58

Optimization - Based

Rule-Based

Global - optimization

Real –time Optimization

Fuzzy RB Deterministic RB

Predictive Adaptive Conventional

State machine Power Follower Thermostat Control

EFC Minimization Robus Control Model Predictive Decoupling Control

Linear Programing Dynamic Programming Stocastic D.P. Game Theory Genetic Algorithms

Fig. 3. Classification of the hybrid power train control strate-gies

consumption, emissions, costs and dynamic performance of thetransportation system. Finding the optimal size of some pow-ertrain components can be found in Murgovski et al. (2011),Gao and Porandla (2005), Trigui et al. (2009), Sundstrom et al.(2010c), Sundstrom (2009), Rousseau et al. (2008), Hofmanet al. (2005), Gao et al. (2007), Pizzo et al. (2010), Skinneret al. (2009) and others. Variation in the type of technology forthe second storage device can be found in Williamson et al.(2005), and for the type of transmission and size in Hofmanet al. (2008). Variation of topologies can be found in Skinneret al. (2009) and Murgovski et al. (2011).

2.1 Parametric and structural design optimization examples

In recent years, beside control system optimization, paramet-ric and structural design optimization problems have been ad-dressed in multiple application areas. In Figure 4 a split of thereference papers, involved in optimal design of hybrid electric(HE) transport systems, is done between different applicationsand the types of topologies they analyzed. The fastest grow-ing automotive research area is represented by passenger cars,where multiple manufacturers are heading towards HEV/EV orPlug-in HEV(PHEV). Examples will start, as depicted in Figure4 with passenger cars and will continue with increasing in loadapplications, from trucks and busses to boats and submarines;furthermore, the algorithms used for optimal design are catego-rized and analyzed in the end of this section.

Optimal sizing is discussed for passenger vehicles with paral-lel topologies in Fellini et al. (1999), Rousseau et al. (2008),Sundstrom et al. (2010a), Gao and Porandla (2005), Hofmanet al. (2005) and Gao et al. (2007). The solution is to definethe application (given HEV and the driving cycle) and decidewhat are the parameters to be varied (e.g. internal combustionengine (ICE), battery (BAT) or EM size, minimum and max-imum allowed state of charge (SOC) of the BAT). Accord-ingly, the fuel consumption has been analyzed by comparingthe results of existing optimization algorithms (DIRECT, DP,Sequential Quadratic Programming (SQP), Genetic Algorithms(GA), Simulated Annealing (SA), Particle Swarm Optimiza-tion (PSO), Equivalent Consumption Minimization Strategy(ECMS)) or Rule Based (RB) algorithms on the defined optimaldesign problem.In Fellini et al. (1999), a parallel topology of a Chevrolet

Lumina MidSize Sedan was analyzed. The simulations studieswere done in ADVISOR where Turbo Diesel Engine Simula-tion (TDES) program was integrated. This integration is mo-tivated following the need of a more modular object orientedsoftware for vehicle simulation. The simulated model containsa 1.45 L diesel engine, a 55 kW EM and a 65 kW BAT, resultingin a fuel economy of 43.41 m.p.g. . 5 optimization algorithmsare discussed here (SQP, Trajectory, Complex, DIRECT andSequential Metamodel Optimization (SMO)) and from these,motivated by the presence of numerical noise, two derivative-free optimization algorithms, namely DIRECT and Complex,were chosen to solve the parametric optimization problem. Theresulted fuel economy of 12% was a consequence of a smallerengine, motor and battery obtained from the optimization algo-rithm. For the particular problem DIRECT algorithm was moreefficient then the Complex algorithm, both as fuel economyand as total number of function calls until convergence (here,whenever Complex algorithm got stuck in infeasible regions, are-starting of the simulation was required).

A second parametric optimization example for passaged carswith parallel topologies can be found in Gao and Porandla(2005). Here, a topology with a 33 kW EM, a 88 kW GasolineEngine, a 240 cells BAT with capacity 6.5 Ah and a 4 speedmanual gearbox with final drive ratio of 3.63 is used forsimulations. This configuration leads to a fuel consumption of35.1 mpg, which, using 3 different algorithm is improved with 5mpg. The drive cycle is composed out of a city driveway (FTP-75 cycle) and highway driving (HWFET cycle). DIRECT, SAand GA are used to optimize 6 design variables of the HEVgiven some bounds, were the resulting values are presentedin Table 1. A comparison of the initial values of the designparameters and the optimum design variables show that SAand DIRECT find almost the same optimum point, while GAwas assumed that it got stuck in a local minimum point. For afair comparison here all algorithms are restricted to the samemaximum number of evaluation functions. All three methods

Design Variable Initial Value DIRECT SA GAFuel converter powerrating

86 kW 83.1 kW 82.4 kW 53.8 kW

Motor controllerpower rating

10 kW 20.2 kW 21.9 kW 65.4 kW

Battery number ofcells

240 245 311 220

Min. allowed SOC 0 0.25 0.22 0.21Max. allowed SOC 1 0.84 0.78 0.83Final drive ration 3.63 3.9 4.0 3.49

Table 1. Final design variables values

lead to a decrees in the mass of the vehicle, reduced fuelconsumption and improved vehicle performance. Motivated bythe slow convergence of the DIRECT algorithm a new hybridoptimization algorithm results by combining DIRECT withSQP. The results of applying this algorithm to the Rosenbrook’sBanana function are compared with the results obtained withDIRECT and the hybrid algorithm manages to find the optimumfunction with a much smaller number of function evaluations.

A mid-sized to large family car, with a parallel topology, isanalyzed in Sundstrom et al. (2010b). The optimal sizing ofthe powertrain components (ICE, BAT and EM) is discussed.First the sizing is analyzed by using DP; and, then, a sizing rulefor the hybrid vehicle is developed that can find the optimalhybridization ratio with very little computational effort. Various

3


59

[12]

Passager cars Small/medium trucks

Construction equipament (forklifts, escavators, so on..)

Heavy trucks Ships /vessels/boats Buses Submarines

Series

Topology

Parallel

Series- parallel

Type of hybride transport mode

[6]

[1] Sundstrom et al. (2010a) [2] Rousseau et al. (2008) [3] Hofman et al. (2005) [4] Gao and Porandla (2005) [5] Trigui et al. (2009) [6] Murgovski et al. (2011) [7] Williamson,2005 [8] Dupriez-Robin et. al (2009) [9] Pizzo et al. (2010) [10] Kadri,2006 [11] Skinner,2009 [12] Williamson et al. (2006) [13] Xiong ,2009 [14] Jo and Kwak ( 2011) [15] Hofman, 2008 [16] Fellini et al.(1999) [17] Gao et al. (April 2007) [18] Bolognani et al. (2008) [19] van Leeuwen (2011)

[6]

[5] [4] [2]

[3]

[1]

[3]

[7]

[10] [9]

[8]

[11]

[11]

[12]

[13]

[14]

[14]

[14]

[15] [16]

[17]

[18]

[19]

Fig. 4. Overview of existing hybrid powertrains and the topologies they use (per citation)

parameters are varied and based on their influence on the designvariables rules are constructed. The proposed method for sizingthe vehicle finds the optimal point within 3.2% of the globaloptimum point for all 8 cycles. For most of the cycles, themethod performs with less then 1% error. The method is robustto different variations and it performs slightly worse in thehighway cycle because the SOC boundary is reached and theproposed algorithm needs to be modified, while DP can handleand overcome this problem. The advantage with this approachis the removed computational burden had by DP when solvingthe optimal control problem.

In Rousseau et al. (2008) a parallel gasoline Citroen vehicleis analyzed, which has the EM located near the wheels. Sizevariations for different powertrain components are discussedusing DP and using a real time approach, e Equivalent Con-sumption Minimization Strategy (ECMS). Using AMESim as asoftware tool for validation, Matlab/Simulink for optimizationand NEDC as input driving cycle, the optimal power split isfound with DP. Starting from the initial design, where the fuelconsumption of the HEV is 3.76 l/100 km (conventional ve-hicle 4.76 l/100 km), the following have been concluded: (i)by changing the BAT capacity (with the same weight), willcause the engine to change its operating point and it will notinfluence the fuel consumption as long as the SOC remains inits bounds without touching them; (ii) variation of BAT weightwill influence the fuel consumption since the weight of thevehicle will also vary; (iii) the variations of the maximum andminimum EM power may change the fuel consumption (but notsignificant), but it will also change the state of charge trajectory.The results with DP in AMESim are compared, and only a smalldifference can be observed.

Two models, Honda Civic and Toyota Prius, are discussed inHofman et al. (2005) and their parameters are varied to observethe influence on fuel economy. For this analysis 2 transmissiontypes are considered, the CVT from the IMA and the E-CVTfrom the Prius, 3 combustion cycles (Otto, Diesel and Atkinson)and 3 vehicles, the two initial ones and an average betweenthem. The influence of the transmission and different enginesare done in the conventional case, with the use of DP tocompute the optimal power split. The main conclusion withrespect to transmission and engine type, when a NEDC drivecycle is used, are: (i) the V-belt CVT results in a 4% higher fuel

consumption, (ii) downsizing the engine results in a better fuelconsumption and changing the combustion cycle from Otto toDiesel and from Otto to Atkinson saves about 13% and 16%respectively.

In Gao et al. (2007), the optimization of 6 design variables ofa parallel topology are used to compare 4 optimization algo-rithms using a composite driving cycle. The results, summa-rized in Figure 5, show that a significant improvement can beobserved in fuel economy, power rating of, especially, the EMand dynamic performance after optimization. Here the resultshave been normalized to 100% such that the difference betweenthe value before optimization and the values after optimizationis easily understandable. The mass of the vehicle increasesslightly for GA and PSO and descreses for DIRECT and SA.The load has a direct influence on the fuel consumption, henceGA and PSO have worse performance then DIRECT and SA,with SA offering the biggest fuel economy. We observe a sig-nificant decrees, approximately of 70% from the initial value,of the power rating of the motor for all algorithms, an increaseof the power rating of the ICE in case of GA with 11%

The results presented here from a limited number of papersshow the importance of optimization in design, and more, thedifficulty brought by the big dimensions of the search space.By widening the analysis to multiple transportation sectors, itcan be concluded that these research questions (in general ,the search of optimal design parameters) are acknowledged,but not yet addressed or developed properly in an integratedway, also see Chan et al. (2010). When looking at heaviertransport applications, trucks, boats, submarines or airplanes,the dependency of the powertrain design on the particular typeof applications is maintained. Some work can be found forcity hybrid electric busses, hybrid electric submarines (HES)or hybrid electric boats (HEB). Environmental, energy andcost issues have driven also the construction equipment in-dustry to develop more energy-saving and efficient machines.The potential of hybridization of machines as forklifts trucks,loaders, excavators is discussed in Jo and Kwak (2011). Herethe emphasis is done on the uniqueness of each equipment’spowertrain and the challenges that this brings when the designstep is done, see for example the hybrid topology of an exca-vator in Figure 6. By capturing kinetic energy from the swingbody and potential energy from its boom, the energy storage

4


60

0%

20%

40%

60%

80%

100%

120%

Fuel Economy Vehicle Weight Power rating of the EM

Power rating of the ICE

0-60 mph 40-60 mph 0-85 mph Bat. No of cells

Perc

en

t C

han

ge

Before Opt. DIRECT Simulated Annealing (SA) Genetic Algorithms (GA) Particle Swarm Optimization (PSO)

Fig. 5. Performance assessment and final design variables values after optimization of a parallel HEV - 4 different algorithms, seealso [Gao et al.(April 2007)]

system can be recharged for later usage. By hybridization, indifferent commercial available applications can reduce fuel asmuch as about 20% without any degradation of performance ofdrivability.

Engine Motor Transmission Generator

Battery

Arm cylinder

Ultracapacitor

Motor Transmission Bucker cylinder

Motor/ Generator

Transmission Boom

cylinder

Motor/ Generator

Swing reduction

Gear

Fig. 6. Series topology of a hybrid excavator

In Williamson et al. (2006), a structural analysis is done fora heavy-duty diesel electric city transit bus. Here the paralleltopology with an integrated starter-alternator is concluded to bemore suitable for typical stop and go type diesel HEV transitbusses. This, when compared with a series and a parallel topol-ogy. From various analysis, the series topology has resultedas being the less desired for the analyzed kind of application.The main disadvantage of series architecture is that the over-all vehicle weight is with 1 ton greater then in the other twocases, leading inherently to bigger fuel consumption and higheremissions. Worth here to mention is that the overall efficiencyof the series topology reduces radically with time making thiscase not suitable for long drive distances.

In Murgovski et al. (2011), the optimization of componentsizing is discussed for a PHEV city bus. The battery and thepower generation unit sizes are discussed and results from con-vex optimization are compared with results from DP for twocases: a parallel and a series topology. Taking into considerationsome assumptions, as the gear and the engine on/off state whichare determined prior to the optimization, and making someapproximations, the original problem is translated into a con-vex optimization problem. These approximations are necessarybecause some components yield inequality constraints whichare not convex and equality constraints which are not affine,making the problem not solvable trough convex optimization.The optimization, subject to both time dependent and timeinvariant variables, is solved both with convex optimization ap-proach and with DP. The results show that the vehicle with theparallel powertrain consumes 19.27 l/100 km while the seriesconsumes 16.88 l/ 100km. This is strongly connected with the

bigger size of the BAT resulted for the parallel powertrain, 489cells compared with 394 cells resulted for the series powertrainconfiguration. When the results from convex optimization arecompared with the results from dynamic programming it isconcluded that the error due to the approximations used forconvexifying is small while the improvement in computationtime and the number of variables used is significant.

The optimal sizing for the battery and the combustion engineis analyzed in Trigui et al. (2009) for a PHEV city microbus.The vehicle has a series topology and a predefined bus lineto follow, a loop of 5.7 km long with nearly 3 stops per km,repeated 21 times per day. First DP is used to find the optimalSOC trajectory for the EMS, and next, the sizing process forthe BAT pack and the engine. The most favorable case is whenthe largest battery is used at the highest depth of discharge. Forthe European average the CO2 reduction is less then 15% in thebest case. A trade off must be made between the cost of thevehicle and the CO2 emissions.

The flexibility that a series topology gives to the designer hasmade this topology to be more used in boats and ships sector,where space and positioning flexibility is important, for exam-ples see Pizzo et al. (2010), Bolognani et al. (2008). Similar tothe automotive design challenges for HEV, in a hybrid subma-rine the mechanical propulsion can be used for high propul-sive loads and electric propulsion for low propulsive loads,improving the efficiency points at which the power suppliers arefunctioning. In Skinner et al. (2009) three topologies of a next-generation SSN (nuclear powered attack submarine) subma-rine, as in Figure 8, are analyzed (direct electric drive, geared-electric drive and hybrid electrical/mechanical drive) and com-pared with the conventional mechanical drive using 4 drivingcycles. The design optimization approach used in Guzzellaand Sciarretta (2007), where multiple devices are consideredsimultaneous for the optimization is used here to show whichtopology and which sizes will find the best combination of cost,risk and mission effectiveness. An evolutionary multiobjectiveoptimization (EMOO) approach, namely a multiobjective ge-netic algorithm (MOGA) as described in Konaka et al. (2006),is used to optimize 9 design variables (EM size, propellerdiameter, number of EM, EM gear ratio, steam turbine ratedload-propulsion, steam turbine rated load-electrical, power splitratio, number of AC generator pole pair and AC scaling factor).5 objective functions are defined and each of these objective

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functions are evaluated for each of the 4 scenarios resulting in20 objective function in total. Each evaluation is performed inMatlab/Simulink and SQP is used to select the optimal powersplit method. From this analysis, it is concluded that the hybridconfiguration brings the best results by resulting, in average, inan improvement of 8% in the energy consumption.

Electric Motor

Electric Motor

Electric Motor

Gearbox

Steam Turbine

Electric Motor

Gearbox

(a) (b) (c)

Fig. 7. (a) Direct electric drive architecture, (b)Hybrid elec-trical/mechanical drive architecture ,(c) Geared-electricdrive architecture

Size optimization for a series hybrid boat is addressed in Pizzoet al. (2010) and for a series-parallel one in Dupriez-Robin et al.(2009). The HEB, with the topology depicted in Figure 8 is aconvectional bus boat used by the Venetian Transport Consor-tium Company, with 23 m length and 4.22 m width, propelledby a single 140 kW ICE that is able to develop all the powerrequired in each operating conditions. Two cases are discussed:(1) when the engine is at fixed speed and power (around 80% ofits maximum power, where ICE usually have their maximum)and (2) when the engine is functioning at variable speed andpower, both in a series drive train framework. Case 1 leads toan increased ICE but a good efficiency functional point. Case 2leads to a lower overall efficiency but also a reduced weight forthe storage system. From a cost point of view this representsa clear benefit. Given a particular driving cycle, based on thepower requirements of the system, the authors of this paper areanalyzing (manually) different sizes. In the second paper where

Engine

Electric motor

Reduction Gearbox

Generator

Battery

Mechanical connection Electrical connection

EM1

EM2

Fig. 8. Power train system architecture in hybrid series boats

a parallel HEB is analyzed, Dupriez-Robin et al. (2009), theimportance of the ”driving cycle” defined for the boat is em-phasized since defining this can be more difficult then for HEV.In all designed cases the fuel consumption changes with thecapacity of the battery, and it is not significant if regenerativebraking is not allowed.

2.2 Trends in optimal design strategies

A decade ago the realization of HEV was acknowledged aspossible and analyzed as functionality, see Chan (2002). Thisarea has emerged and, as a subsequent effect, the control al-gorithms for HEV have been developed to improve fuel con-sumption and performance and decrease emissions and costs,Chan (2007). Nowadays the challenge has changed towardshow can we extract the best result given the real functionalityand requirements of the transportation mean.

From these analyzed cases it can be concluded that finding theoptimal design is a complex problem, where multiple param-eters and cases need to be analyzed. Trade-offs between per-formance, cost, fuel consumption, computation time exist andthey depend strongly on the application. From Figures 4 and9, which summarizes found topologies for various applications,it can be concluded that there is no best, predefined, topologyfor any application. Hence, in future research the choice oftopology has to be addressed and integrated with the choicesof sizes, technologies and control.

Depending on the usage of the transportation system and theloads that this has to carry we can observe a trend in usingdifferent types of topologies as depicted in Figure 9. All trans-portation systems that are possible to drive on a ”highway type”of cycle will, most likely, not have a series topology, whiletransportation systems that will work in a stop and go mannerwill most likely not have a parallel topology.

Weight [tons]

Topology

Hyb

rid

ap

plic

atio

n

1 2 3 10 15 30 50 100

Topology type

Weight range

Passager cars

Small trucks

Medium trucks

Heavy-duty trucks

series parallel Series-parallel

Airplanes

Submarines

Ships

Construction Equipament

Boats

Busses

400

Fig. 9. Hybrid powertrains usage depending on application

The importance of the assumptions and the approximations thatare made during the optimization and their influence on thefinal result needs to be stressed here. For example, many ofthe optimization algorithms assume that the battery SOC willnot hit the bounds, which in practice can become a problem(as for example in plug-in HEV) if not explicitly treated by theenergy management system. In plug-in HEV the objective is todischarge the battery as much as possible before plugging thevehicle in the electric grid, Serrao et al. (2011). The questions toanswer is if these algorithms can cope with this, how and whatis the effect on the objective of the optimization when thesebounds are reached or violated.

Regardless on the topology, it is noted that the efficiency im-provement is fairly dependent on the overall efficiency of theenergy storage system, which is usually limited by the overallweight of the supplementary drive train components. The re-quirements that energy storage systems need to meet for heavy-duty applications is different then for light duty applications. Acomparison of different energy storage devices is presented inEhsani et al. (2007) and the trends towards combined chemicalbatteries and ultracapacitors is mentioned as being the mostpromising way to meet the energy power demands within fu-ture compact and lightweight structures. In Williamson et al.(2005) the secondary storage device for heavy-duty hybridvehicles is analyzed. The performances of lead-acid (PBA),lithium-ion (LiIon), nickel-cadmium (Ni-Cd), nickel-metal hy-dride (Ni-MH), and nickel-zinc (Ni-Zn) batteries, as well asultra-capacitors (UC) are investigated over city and highway

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driving schedules for a heavy-duty diesel-parallel hybrid transitbus application. Pros and cons for all these are presented andrecommendations are given towards their possible use withinHEV. Not addressed here but with a clear contribution on theresult are the simulation software environments. These need tobe sufficiently sophisticated such that accurate analysis can bemade. Gao et al. (2007) presents an overview of these tools,their applicability depending on the application and examples.

Another important factor when implementing these algorithmsis their complexity and the computation time required whenimplemented. As stated (and used) in Fellini et al. (1999), thecomputational time can be substantially decreased if the sim-ulation is performed on distributed workstations. For the algo-rithms used in this paper the advantage was the non-dependencyon computing the gradient. Nevertheless, a disadvantage is thatthe global convergence comes at the expense of a large andexhaustive search over the domain, hence an increase of thesimulation time. Figure 10 classifies the algorithms found inSection 2.1 for optimal vehicle design. This classification isdone to create a clear picture of the reasons of why one oranother algorithm has been used. As stated in the introductionof this paper here, the real time implementable optimization itis not included, since it is outside of the scope of this paper.

Global Deterministic

Derivative free

Dynamic Programing

DIRECT

Genetic algorithms

Multi-objective Genetic

Algorithms

Particle Swarm Optimization

Simulated Aanealing

Sequential Quadratic

Programing

Convex optimization (subgradient)

Convex optimization

(gradient)

Fig. 10. Different classifications for design optimization algo-rithms

Global optimization algorithms are often classified as eitherdeterministic, as DP in Figure 10, or stochastic. Hence, withinthe category ”global” only dynamic programming guarantiesglobal optimum while the other algorithms rely purely onheuristics. Here a trade-off is found between the amount ofcomputation and the type of guarantee of optimality. However,in large problems a heuristic based algorithm will rarely findthe best solution, and the designer needs to be satisfied with aprobabilistic estimate of the global optimum. Researchers aretrying to compare multiple algorithms from different categoriesand conclude upon the result which one is better. As seen inGao and Porandla (2005) a comparison was made between3 global algorithms, where DIRECT is a deterministic algo-rithm whereas Simulated Annealing and Genetic Algorithmsare based on stochastic. The authors show, through simulations,that DIRECT has good results, and they combine this withfmincom routine in Matlab to overcome the disadvantage ofcomputation time.

It is strongly desired to add more then one optimization ob-jective to the design problem, and here, again a separationscan be made between algorithms that can and cant do this.

For example, this challenge is solved in Skinner et al. (2009)with the use of a multiple-objective genetic algorithm, but formost of the algorithms found here there exist versions wherethis is possible (which come with an increase of computationtime). From the analysis done here it can be observed thatalgorithms which can search the global solution are preferred.This is often the case since when stuck into a local minimum,the optimization fails to reach the OEMs desire, i.e. the ”best”solution. For this reason, DP is a widely used algorithm, butits long computation time represents an important drawbackwhen more then two variables are used in the optimizationproblem. Sometimes, see Sundstrom et al. (2010c), DP is usedin prior studies and rule-based algorithms are developed basedon this analysis. So-called, ”hybrid” algorithms are proposed toto overcome drawbacks, offer faster computations and (near, or)global optimum solutions to the design optimization problem.SA and DIRECT offer in several papers good results. Moreextensive steps towards the vehicle design problem have beenmade in the work of Sundstrom (2009) and Murgovski (2012),where the focus is made on the sizing and control layers. So farthere is no automated method to be found in literature to solveall the optimization layers within the design problem at once.

3. CONCLUSIONS

This paper presents an overview, examples and trends that canbe found in solving the optimal design of a hybrid powertrainproblem, with specific emphasis on size, technology and topol-ogy optimization. From given examples the spread of hybridtechnologies can be observed in all transportation areas, and inall of them the optimum power train design solution is desiredfor fuel consumption minimization, emissions and dynamicperformance. Future work of this research involves the analysisand development of a tool that can offer integrated optimaldesign for commercial vehicles under given work conditions.

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