International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 6

Number 4

December 2012

1 INTRODUCTION

Hybrid vehicles are now well established on land as

a viable mode of greener transportation. The use of

multiple energy sources and converters permits their

individual benefits to be better utilized, by

exploiting the inherent disparity between peak and

average power demands (Schofield et al. 2005).

At sea, powertrain hybridization would equally

permit the power demand to be met more effectively

than by a single source. Yet marine hybrids are still

not as popular as on land. ‘Conventional’ hybrids on

marine vessels include diesel-electric systems,

popular on passenger vessels, as well as CODLAG

systems found on naval vessels. Such configurations

of parallel electric and mechanical propulsors permit

better efficiencies at part-loading and low speeds,

due to the different sources being better suited for

different loadings (Woud & Stapersma 2002). These

hybrids however, differ from automotive ones in that

they lack an Energy Storage System (ESS), typically

in the form of chemical batteries.

The inclusion of an ESS would permit the loading

of the prime movers to be optimized for greater

periods of time, by using the ESS as a load bank

during periods of low propulsion demand. Compared

with automotive vehicles however, propulsive power

demands for marine vessels are significantly larger;

hence, by proportional scaling, the corresponding

ESS would be excessively large, with an associated

cost and weight factor.

The major shortcoming for marine hybrids stems

from a lack of significant regenerative capability. A

significant proportion of the energy efficiency for

automotive hybrids comes from regenerative braking

(Lukic et al. 2008). This permits energy which

would otherwise be dissipated as heat at the brakes

to be recovered to recharge the ESS. However, the

lack of stop signs and traffic lights at sea much

reduces the scope for energy recovery from

deceleration. This is most apparent when comparing

typical demand profiles between the New European

Driving Cycle (a European standardized profile)

representing a typical automotive suburban

commute, and a typical day cruise for a marine

vessel (Figure 1).

Optimization of Hybrid Propulsion Systems

E. Sciberras & A. Grech

MI-SE@MALTA, MARSEC-XL Foundation, Senglea, Malta

ABSTRACT: Powertrain hybridization permits the benefits of more than one power source to be integrated

and exploited for a beneficial effect on an objective, such as reduction of fuel consumption or emissions. Due

to their operating profiles however, marine hybrid vessels do not exhibit much opportunity for free energy re-

cuperation. Fuel savings can be realized by bettering component operating points, yet this requires correct siz-

ing matched to the expected usage. In this paper, a multi-objective genetic algorithm is used to optimally size

propulsion components in order to minimize fuel consumption as well as installation weight for a hybrid mo-

toryacht operating on a day cruise scenario.

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Figure 1. Comparison of automotive (top) and marine vessel

(bottom) propulsion timelines (Barabino et al. 2009).

Fuel savings in the case of a marine hybrid are

hence possible through correct sizing of

components, such that overall operating points are

improved over a particular scenario. Defining the

fuel consumption for a scenario therefore requires a

model for the hybrid system, which takes the

scenario power demand as its input.

2 MODELLING

The optimal sizing of the hybrid system is simply

the tip of the iceberg in the hybrid design process.

Essential for the correct sizing is the demand profile,

on whose realism the accuracy of the sizing will

depend.

The power demand timeline for a marine hybrid

consists of two parts, namely the propulsion demand

and the hotel load demand. Also differing from

automotive hybrids is a more significant hotel load,

since motoryachts generally need to support onboard

users for longer periods.

In determining the fuel consumption,

consideration must be given to the interaction

between prime mover, ESS and power demands.

This requires a complete model of the hybrid system

which considers all the power flows between the

various components.

This model was built in Simulink, since no

simulation tool was readily available for marine

vessels. A sixty foot motoryacht was considered, for

which trials data was available. A parallel hybrid

configuration was proposed for this existing boat, by

the addition of a battery bank and an electric

motor/generator coupled to each diesel engine by a

gearbox. The separate diesel generator could then be

omitted by supplying the hotel load from the main

battery bank and main engines.

From the trials data, the propulsive power

demands were input as a Look-Up Table (LUT),

returning the demanded power for the demanded

speed. This converts the speed demand timeline to a

power timeline. The diesel engine is modeled

similarly, by converting the engine’s performance

chart into a two-dimensional LUT, taking engine

speed and power as inputs, and returning the

instantaneous specific fuel consumption (SFC). The

cumulative fuel consumption is then the integral of

the SFC values. The electric machine is modeled by

its performance characteristic, with the power

splitting and sharing being determined by a central

control logic.

This steady-state modeling is valid since the

quantities of interest (power flows and operating

points) are required over a long period of time.

Hence, transient response is not of particular interest

for scenario fuel consumption determination. The

batteries are modeled using Simulink’s built-in

battery model. This provides a model for Lithium-

ion, Lead-acid and Nickel Metal Hydride batteries.

Figure 2. Complete Simulink model of parallel hybrid setup.

The central control logic controls the power

demanded from the electrical machine and/or diesel

engine, depending on the propulsion and hotel

loadings, as well as the current operating point of the

components. Critical above all is the batteries’ state

of charge, which is to be maintained within certain

limits.

3 OPTIMIZATION

Hybrid vehicle design is generally approached from

a satisfaction of specification. In a parallel

automotive hybrid, an internal combustion engine

(ICE) is sized to cater for the cruising speed

demand, such that maximum speed on top gear is

capable of being maintained. The low-speed side of

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the demand in turn influences the electric motor

sizing. Together with the transmission system in use,

this determines the acceleration capabilities of the

vehicle. As a first-order design, the ICE can be

assumed to cater for the steady-state rolling and air

resistances, such that the electric drive is sized to

completely meet the acceleration specification. The

size of this motor can then be lowered by examining

the power demanded for acceleration taking also into

account the power provided by the ICE at low

speeds (Ehsani et al. 2010).

For the ESS, the power requirement is selected to

be greater than the motor’s power rating to take into

account conversion inefficiencies. The energy

requirement is then dependent on the driving pattern

to be catered for, and hence its regeneration

potential. Taking into account the inefficiencies

associated with the process and the desired initial

and end capacities, then the stored energy

requirement can be calculated. This design is then

followed by simulation, when values such as fuel

consumption can be calculated. Iterative design can

then be performed in order to improve any aspect of

the system (Ehsani et al. 2010).

Yet with such a design for satisfaction of

specification, attributes such as fuel consumption,

emissions and system weight are secondary values

over which the designer has no direct control.

Intuitive design, and experience help to direct the

design and improve these parameters, however, the

design does not address these parameters as an

objective.

Optimization is a process whereby an objective is

addressed directly and an extreme value (either

maximum or minimum) located. This permits

objectives to be aimed for and designed for, rather

than following as a secondary consequence from

design.

Classical optimization techniques would involve

the use of mathematical tools such as the Newton-

Raphson or steepest descent methods. These

however require a mathematical equation for the

problem description, something which can’t be done

to quantify the fuel consumption over a scenario.

Furthermore, these methods all consider continuous

and linear functions. When considering discrete

component availability, classical optimization

techniques fail for this problem.

Genetic algorithms take a cue from nature as the

ultimate optimizer. Without requiring in depth

knowledge of the problem at hand, genetic

algorithms operate directly on a descriptor of the

problem, treating the underlying function as a black

box, requiring only the returned value. This robust

approach based on simulation is therefore highly

adept at optimizing hybrid vehicles, evidenced by

works such as (Desai & Williamson 2009), (Jain et

al. 2009) and (Hasanzadeh et al. 2005).

All the possible combinations of components

making a hybrid setup represent the search space,

from which the optimal configuration is chosen. In

keeping with the genetic analogy, the descriptor for

the component configuration is termed a

chromosome. Corresponding to each chromosome in

the search space is a solution in the objective space.

This maps the chromosome to the objective value of

interest such as fuel consumption.

The mapping from search to objective space is

performed by the fitness function. Optimization is

therefore performed on the solutions in the objective

space, returning the fittest chromosome as the

implementation to be selected.

Compared to classical methods, genetic

algorithms are global routines, capable of locating

population optima, rather than local ones. This is

done without knowledge of any auxiliary parameters

such as derivatives of the function, enabling genetic

algorithms to be a robust method of global

optimization.

Operating solely on the chromosome

representation, the search for optima revolves

around three operators. Considering a population of

chromosomes, the selection operator identifies the

fitter chromosomes to be used to generate the next

generation. The next generation comes about by

reproduction, whereby the previously selected

chromosomes are used to form a new chromosome,

termed the offspring. This represents the search

through the search space and is responsible for

locating the global optimum. Finally, the mutation

operator provides an insurance against premature

convergence by introducing a random variation to

offspring to ensure that the search does not become

stuck at a local optimum.

Figure 3. Three non-dominated ranks for bi-objective problem.

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3.1 Multi-objective optimization

Despite the apparent straight-forwardness of

optimization using genetic algorithms, optimization

for a single objective does not reflect real-world

practicalities. Locating an optimum with respect to a

single objective would give an optimized solution,

yet one which inherently ignores any other aspect of

the problem. Referring to the problem of a hybrid

motoryacht, optimizing for fuel consumption would

result in a large battery capacity (to minimize engine

operation and hence fuel consumption), yet come in

at a large weight and cost.

Such a solution would be impractical from an

application point of view, so a compromise must be

found between locating an optimized solution from

the consumption perspective, as well as the weight

or installation point of view. Compromise should not

imply substandard performance, but rather an

addressing of differences.

A multi-objective optimization problem can

trivially be converted to a single-objective one by

means of a weighting vector, where multiple

objectives are added up after being weighted to form

a single metric. This however requires a priori

knowledge of the demanded weighting. Results can

therefore be biased since this decision is taken

without any indication of results.

Basing the weighting after obtaining a set of

results is possible by using the concept of non-

domination and Pareto-ranking of solutions. Instead

of delivering a single final solution, a set of

optimized, compromise solutions is obtained, from

which the final solution is chosen by the user using

higher-level information. This higher-level

information is experience-based and generally

reflects non-technical influences, such as preference

for particular components, or an inclination towards

individual objectives. Though in effect this

represents the use of a virtual weighting vector, the

weighting values are applied to a set of results, thus

the selection is based on actual solutions without

postulating and introducing blind biases (Deb 2001).

Figure 4. Proposed parallel hybrid implementation for hybrid

motoryacht.

A very popular and efficient algorithm

implementing a Pareto-based approach is the

NSGA-II developed in (Deb 2002). The population

is quickly sorted into ranks using the concept of non-

domination, whereby a solution is said to be non-

dominated with respect to another, if in going from

one to the other, a certain sacrifice is demanded in

one objective for a gain in the other, clearly

illustrated as Figure 3. This shows a number of

ranks, with R1 being the fittest rank. There is no

benefit in choosing a solution from the lower ranks,

but they can be used to search for new solutions,

possibly giving better results.

Solutions in the first rank are the fittest, and this

ranking value is used for selection purposes, as

opposed to an explicit fitness value. This permits the

comparison of solutions with multiple objectives. In

order to further prioritize solutions for selection, a

crowding metric is used to identify solutions lying in

more isolated locations. This emphasizes a search in

zones still unpopulated to enhance the global nature

of the search.

4 IMPLEMENTATION

The model of the proposed parallel hybrid (Figure 4)

was built in Simulink as outlined previously, with

the genetic algorithm coded in Matlab.

The aim was to minimize both fuel consumption

as well as installation weight, in order to determine

the best compromise solution. The demand timelines

are given as Figure 5 for both the propulsion as well

as the hotel loads. The components to be optimized

are the diesel engine, the electric motor/generator,

the gearbox ratio and battery capacity as well as

type. Optimization is also performed on the

controller itself. This allows an even broader search

space and permits the exploration of different

control strategies.

Figure 5. Propulsion (top) and hotel load demand timelines for

sixty-foot motoryacht for day cruise scenario

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4.1 The controller

The control strategy determines the points at which

the vessel changes operating modes. For a parallel

hybrid, four basic modes are identifiable, namely:

− Electric-only mode – all loads are supplied by the

electric system from the batteries.

− Conventional mode – the diesel engines provide

propulsion while the hotel load is supplied via in-

verter from the batteries.

− Assist mode – the electric motor connected to the

batteries is used to assist the diesel engine during

acceleration or high power demands, with their

power added up at the gearbox.

− Charging mode – the diesel engine is run to pro-

vide propulsion and also supply the electric gen-

erator to recharge the batteries. Hotel load is sup-

plied off the electric generator.

A speed and/or power level can be defined to

control the changeover of modes, depending on the

battery state of charge. Charging mode is enabled

whenever the battery is discharged, while the other

propulsion modes are only possible if the charge

level is sufficient.

Operating the diesel engine at low power levels

will result in high SFC values, in addition to

suboptimal performance in terms of combustion,

leading to higher wear and maintenance

requirements. Thus, using electric propulsion for

low demands is an obvious candidate for improving

fuel consumption. However, raising the point to

which electric propulsion is maintained necessitates

increasing the battery size. Hence, the correct

balance must be found. Likewise, the point at which

assist mode is demanded can permit engine

downsizing, but can lead to significantly longer

charging times.

Figure 6. Power flows, with component set points decided by

controller

The point at which assist is performed is a

function of the diesel engine’s loading, and hence

the level of parallel operation demanded between

motor and engine. Varying this level therefore

allows the assist point to be optimized in order to

determine the best load sharing. The changeover

from electric-only to conventional mode is defined

mainly by the electric motor’s power and speed

ratings, since electric operation is permitted only in

this window.

Figure 6 illustrates the relation between the

controller and the other simulated components.

Based on the power demands and each components’

current operating point, the controller outputs the

desired setpoints for each component depending on

its control strategy.

4.2 Chromosome representation

Based on these variables for optimization, the

chromosome for searching through the search space

was defined as consisting of the following elements:

− Diesel engine index

− Battery type

− Number of parallel batteries

− Electric motor rating

− Gearbox ratio

− Engine power sharing point

− Electric-only launch power

These all represent a particular hybrid setup from

a database of components taken from manufacturer

brochures. Thus every solution actually represents

implementable setups. Real number representation is

used, since this permits infinite database growth

(without requiring chromosome modification as with

binary coding) as well as avoiding Hamming cliffs

which present an artificial hindrance to a gradual

search (Deb 2001).

Using real numbers requires some modification to

the standard algorithm, namely that a blending

operator is used instead of explicit crossover. BLX-α

was implemented with an α-parameter of 0.5 to give

the best balance between exploration and

exploitation (Herrera et al. 1998).

4.3 Crowding-distance metric

The aims of multi-objective optimization are to

identify the fittest possible set of compromise

solutions, as well as explore the search space for a

broader scope to this set. Deb proposes a crowded

distance metric which identifies the biggest

rectangle which can be fitted around a solution in the

objective space (Deb et al. 2002). Yet this was found

to give unsatisfactory results in this implementation,

with limited final solution diversity. This is

explained as being due to solutions having different

543

chromosome makeup, yet giving similar solution

values, thus decreasing an objective space metric’s

effectiveness.

This was further noted by Desai in (Desai &

Williamson 2009) for a similar application. Desai’s

approach in the search space involved calculation of

the Euclidean distance for between each point. This

however is quite computationally intensive. The

authors propose a novel uniqueness counter which

counts the number of repetitions for each element

for each chromosome in a population. Figure 7

illustrates the functioning of this uniqueness counter

on a sample population. This serves as an indicator

as to how unique a solution actually is. Thus, during

selection, in case of a tie between two solutions of

equal rank, a more unique solution is preferred to

ensure future diversity.

5 RESULTS

The algorithm was run for 100 generations in order

to iterate towards the optimal rank of solutions. The

equipment data was loaded from the component

database, while the scenario hotel and propulsion

timelines were obtained from previous work carried

out within MI-SE@MALTA for a day cruise

scenario for the 60-foot motoryacht under

consideration (Grech 2009).

Figure 7. Uniqueness counter on sample population

Figure 8. Solutions in objective space over 100 generations.

Note convergence towards left hand side of space

A population of size 200 was used, together with

a mutation constant equal to the reciprocal of the

chromosome length (Deb 2001). This gives a

mutation rate proportional to the number of variables

involved. A constraint of 10 tons is also introduced.

This serves to focus the search below a total weight

of 10 tons, representing a realistic figure which

would otherwise involve a significant performance

loss due to the added installation weight. It must be

noted that as a first order model, the demand power

is considered to be independent of loading, though in

actual fact increased loading would increase power

demand and correspondingly the fuel consumption.

The progression of the genetic algorithm is seen

in Figure 8, where starting off from a random

distribution in the objective (solution) space, the

solutions increase in fitness by gradually migrating

towards the left hand side of the objective space.

Figure 9 illustrates the final rank of optimized

solutions. These are all rank 1, expected since an

overall fitness improvement is demanded. Infeasible

solutions (greater than 10 tons) are not illustrated in

this figure. It is from this plot that the final solution

is chosen by the user, coupled with further

information obtained from examination of the

solution chromosomes themselves.

A sample of the solution chromosomes is listed in

Table 1. These chromosomes correspond to the

solutions observed in Figure 9 in the objective space.

All solutions utilize the same diesel engine as the

conventional system (895kW rated power). This is

understandable since the top speed requirement is

not reduced, which demands around 800kW of

propulsion power. Though electrical assistance is

possible, the energy capacity required from the

batteries would be excessive, resulting in a very

heavy solution, and hence these solutions are

dominated and discounted in early generations.

Figure 9. Final rank of optimized solutions

Also universally chosen was the option of having

no gearbox connected to the electrical machine.

Previous work (Sciberras & Norman 2010) without

controller optimization had indicated a trend towards

high speed machines coupled to a reduction gearbox.

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Figure 10. Component timelines for day cruise scenario. Chosen solution returns fuel consumption of 560.19 kg at a total weight of

5380kg.

Table 1. Selection of solution chromosomes after 100 generations. Repeated solutions have been omitted for clarity

545

The controller optimization however now allows

the motor’s operating point to be variable and hence

the additional weight of a gearbox can be avoided by

locating a different launching power value.

The results clearly indicated the trend towards an

energy dense solution. This involved Lithium-ion

batteries and permanent magnet machines. Lithium-

ion batteries offer the best specific energy capacity,

essential for a marine hybrid where energy

recuperation is largely absent. Though these involve

significant cost compared to traditional lead

batteries, their performance is highly superior (Lukic

et al. 2008).

Likewise, permanent magnet machines offer

greater power densities compared to conventional

machines. This is due to the field excitation being

provided by permanent magnets, removing the need

for external excitation, and therefore greater

efficiencies. This in turn implies a greater proportion

of stored energy being converted to usable power.

Permanent magnet machines are therefore more

compact and lighter compared to their conventional

cousins and are nowadays available off the shelf

from several manufacturers. Permanent magnet

machines also provide for more efficient generation

capability.

The final setup choice is made by the user based

on Figure 9 (visualizing the objective space) and

Table 1 (illustrating the search space). Engineering

experience and intuition now come into play, as well

as reflecting preferences towards objectives. Aiding

in the decision making, the user can visualize and

examine the power flows for the selected solutions,

such as Figure 10, by simulating a particular

solution’s behavior.

6 CONCLUSIONS

Objective design by simulation permits optimization

of hybrid vehicles such that attributes such as fuel

consumption can be aimed for and achieved by

correct design. Classical optimization techniques are

not able to successfully operate on complex models

such as hybrid vehicles, hence genetic algorithms

present a very powerful and robust way of arriving

at optima by mimicking natural evolution.

A model was developed to calculate the fuel

consumption of a hybrid motoryacht based on

steady-state parameters. In turn, an optimization

algorithm was developed to choose the best hybrid

components as well as optimal controller values.

This allows a hybrid vehicle to be virtually ‘bred’

from a computer.

Optimization is essential in marine hybrids, since

the absence of regeneration implies that any savings

must come about by improved component operating

points. Intuitive design satisfies performance

requirements, but does not guarantee fuel savings.

This is emphasized by design by simulation, coupled

with a robust optimization routine.

ACKNOWLEDGEMENTS

The work disclosed in this publication is based on

work carried out at the Marine Institute for Software

Engineering at Malta (MI-SE@MALTA) within the

MARSEC-XL Foundation based in Senglea, Malta.

The research work disclosed in this publication is

partially funded by the Strategic Educational

Pathways Scholarship Scheme (Malta). The

scholarship is part-financed by the European Union -

European Social Fund.

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