On-ship Power Management and Voyage Planning Interaction825242/FULLTEXT01.pdf · On-ship Power Management and Voyage Planning Interaction by Mikael Frisk Voyage planning methods have

UPTEC F 15 033

Examensarbete 30 hpJuni 2015

On-ship Power Management and Voyage Planning Interaction

Mikael Frisk

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

On-ship Power Management and Voyage PlanningInteraction

Mikael Frisk

Voyage planning methods have advanced significantly in recent years to take advantage of the increasingly available computing power. With the aid of detailed weather predictions it is now possible to decide a route that is optimized with respect to some criterion. With the introduction of so called All Electric Ships; ships with diesel electric propulsion, varying the power production in order to adjust the propulsion has become easier. Incorporating a power management system with the voyage planning software on a ship allows for different techniques to reduce fuel consumption.In this thesis, three different approaches are developed, compared and combined. The first method handles the task of how to optimally share a load demand across a set of generators. The second is performing power production scheduling with respect to engine efficiencies, and finally in the third the potential in energy storage integration with the power management system is investigated. From the results, it is argued that the largest potential lies in the first approach where large fuel savings can be made without any large risk. The second approach shows potential for fuel reduction but this however is found to be heavily dependent on weather predictions and accuracy of the used models. Regarding energy storage it is found that while it is not economically feasible to increase the fuel efficiency, energy storage can be used to handle load transients and fulfil power redundancy requirements.

ISSN: 1401-5757, UPTEC F 15 033Examinator: Tomas NybergÄmnesgranskare: Kjartan HalvorsenHandledare: Mats Molander

Master Thesis

On-ship Power Management and VoyagePlanning Interaction

Author:

Mikael Frisk

Supervisor:

Mats Molander

A thesis submitted in fulfilment of the requirements

for the degree of Master of Science in Engineering

in the

Engineering Physics Program

Uppsala University

June 2015

Abstract

On-ship Power Management and Voyage Planning Interaction

by Mikael Frisk

Voyage planning methods have advanced significantly in recent years to take advan-

tage of the increasingly available computing power. With the aid of detailed weather

predictions it is now possible to decide a route that is optimized with respect to some

criterion. With the introduction of so called All Electric Ships; ships with diesel electric

propulsion, varying the power production in order to adjust the propulsion has become

easier. Incorporating a power management system with the voyage planning software

on a ship allows for di↵erent techniques to reduce fuel consumption.

In this thesis, three di↵erent approaches are developed, compared and combined.

The first method handles the task of how to optimally share a load demand across a

set of generators. The second is performing power production scheduling with respect

to engine e�ciencies, and finally in the third the potential in energy storage integration

with the power management system is investigated.

From the results, it is argued that the largest potential lies in the first approach where

large fuel savings can be made without any large risk. The second approach shows po-

tential for fuel reduction but this however is found to be heavily dependent on weather

predictions and accuracy of the used models. Regarding energy storage it is found that

while it is not economically feasible to increase the fuel e�ciency, energy storage can be

used to handle load transients and fulfil power redundancy requirements.

Acknowledgements

I would first of all like to express my great appreciation to my supervisor Mats Molander

in ABB Corporate Research for the many rewarding discussions and pieces of advice he

always had time for. Furthermore a big thanks to Rickard Lindkvist for his many words

of encouragement during the thesis.

I would also like to extend thanks to Kjartan Halvorsen for his proof-reading of my

report and for his positive outlook during my studies.

A very special thanks to my fellow thesis workers at ABB for our many dinners, game

nights and cheerful conversations at the co↵ee table that made these months pass by in

a flash.

ii

Contents

Abstract i

Acknowledgements ii

Contents iii

List of Figures v

Abbreviations vi

Symbols vii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Weather Routing 4

2.1 Methods of Weather Routing . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Isochrone Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.2 Isopone Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.3 Calculus of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.4 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Description of Chosen Method . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Optimal Loading of Diesel Generators 8

3.1 Engine Load Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1.1 Minimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.2 Identical Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.3 Non-identical Engines . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Example Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 Case 1: Four Identical Diesel Engines . . . . . . . . . . . . . . . . 11

3.2.2 Case 2: Two Pairs of Diesel Engines . . . . . . . . . . . . . . . . . 12

3.2.3 Case 3: Engines with Di↵erent Specific Fuel Consumption . . . . . 13

3.3 Engine Loading Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

iii

Contents iv

4 Method 17

4.1 Power Management In All-Electric Ships . . . . . . . . . . . . . . . . . . . 17

4.1.1 All-Electric Ship Power System Operation . . . . . . . . . . . . . . 17

4.1.2 Adjustment of Ship Power Consumption . . . . . . . . . . . . . . . 18

4.1.3 Power Generation Scheduling and Weather Routing . . . . . . . . 18

4.1.4 Hotel Load Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Energy Storage Management . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2.1 Load Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2.2 Energy Storage Load Shifting with Minimized Propulsion . . . . . 22

4.2.3 Energy Storage Bu↵er . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3 Load Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3.1 Propulsion Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3.2 Hotel Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.4.1 Water Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.4.2 Weather Forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5 Results 28

5.1 Engine E�ciency Optimization . . . . . . . . . . . . . . . . . . . . . . . . 28

5.1.1 Case Ship Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.2 Voyage Planning with a Power Management System . . . . . . . . . . . . 28

5.2.1 Weather Routing with Respect to Engine E�ciency . . . . . . . . 29

5.3 Schedulable Hotel Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.4 Energy Storage Bu↵er . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Discussion 35

6.1 Optimal Engine Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6.2 Power Management and Engine E�ciency . . . . . . . . . . . . . . . . . . 35

6.3 Integration of Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . 36

7 Conclusion 37

Bibliography 38

List of Figures

1.1 Diesel electric power system . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 3D-grid of journey stages . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 SFC of medium-speed diesel engine . . . . . . . . . . . . . . . . . . . . . . 9

3.2 SFC for varying generator loads . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Optimal engine loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4 SFC of power system with four generator . . . . . . . . . . . . . . . . . . 12

3.5 Optimal engine loading for di↵erent sized generators . . . . . . . . . . . . 13

3.6 Optimal SFC for a hybrid engine power system . . . . . . . . . . . . . . . 13

3.7 SFC of non-identical DG . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.8 Optimal engine loading for same sized DG with di↵erent SFC . . . . . . . 15

3.9 Optimal loading of case ship engines . . . . . . . . . . . . . . . . . . . . . 15

3.10 Engine Loading Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1 Ship Hotel Power Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Modelled ship hotel power . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.3 Water resistance model error . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 Weather forecast error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 Fuel consumption with optimal and nominal engine loading . . . . . . . . 29

5.2 Optimal engine loading fuel savings . . . . . . . . . . . . . . . . . . . . . . 29

5.3 Fuel consumption of di↵erent PMS strategies . . . . . . . . . . . . . . . . 30

5.4 Comparison of PMS strategies against sub-optimal engine loading . . . . 31

5.5 Comparison of optimal PMS strategies . . . . . . . . . . . . . . . . . . . . 31

5.6 SFC of route with minimized propulsion power . . . . . . . . . . . . . . . 32

5.7 SFC of route with minimized fuel consumption . . . . . . . . . . . . . . . 32

5.8 Payback period of energy storage integration . . . . . . . . . . . . . . . . 33

5.9 Schedulable hotel load fuel savings . . . . . . . . . . . . . . . . . . . . . . 33

5.10 Fuel savings from energy storage reserves . . . . . . . . . . . . . . . . . . 34

5.11 Payback period of energy storage reserves . . . . . . . . . . . . . . . . . . 34

v

Abbreviations

AES All Electric Ship

HFO Heavy Fuel Oil

DG Diesel Generator

PMS Power Management System

SFC Specific Fuel Consumption

SOC State Of Charge

vi

Symbols

P power W (Js�1)

Pprop

ship propulsion power W (Js�1)

Pprop,i

ship propulsion power during stage i W (Js�1)

Photel

ship hotel power W (Js�1)

Photel,i

ship hotel power during stage i W (Js�1)

Phf

fixed ship hotel power W (Js�1)

Phs

schedulable ship hotel power W (Js�1)

Pb

power charged or discharged from battery storage W (Js�1)

ToF total fuel consumption of a route tonnes

ToSF total saved fuel during a route tonnes

Fi

fuel consumption during stage i tonnes

SCj

start-up cost of generator j tonnes

Sij

start-up decision variable of generator j during stage i

�Ti

duration of stage i hours

�Tman,i

time spent in maneuver mode during stage i hours

Vi

ship speed during stage i knots

SOC battery state of charge %

⌘ e�ciency %

⌘sfc

specific fuel consumption g/kWh

⌘sfc,j

specific fuel consumption of generator j g/kWh

⌘sfc,tot

optimal specific fuel consumption for a set of generators g/kWh

vii

Dedicated to Albin, the bike guy

viii

Chapter 1

Introduction

1.1 Background

During the last couple of decades large-scale cruise ships have become increasingly com-

mon on the seas and only in the last five years the industry has grown with 20% [1].

The introduction of electric propulsion has led to a total electrification of ship power

systems with so called All-Electric Ships (AES) [2]. Compared to conventional ship

power systems, AES has quickly become an appealing technology with great potential

of fuel reductions [3]. In an AES, the main diesel propulsion is replaced by electric

motors, while the electrical power production is split between several diesel generators

(DG), allowing a high e�ciency throughout the whole range of operation with respect

to vessel speed. A typical configuration of an AES power system can be seen in figure

1.1, where four diesel engine-generator sets are connected to the AC-grid on a ship and

in extension the loads such as electric propulsion and various ship service loads. The

transition to AES is leading the way to new ships that are able to conform to modern

energy e�ciency directives [4], [5]. Two potential fuel saving technologies which are

possible to incorporate in an AES are power management systems (PMS), and energy

storage facilities [6].

Another area which is gaining more importance in the ship industry is weather routing,

that is the method of creating a voyage plan with route and vessel speed when taking

currents and weather forecasts into account. Scheduling a route in which storms and

large waves are avoided can have a large impact on fuel consumption. One opportunity

with AES is to incorporate a PMS, which is responsible for scheduling the on-board

electric loads, together with the weather routing system. Optimal operation of the

power system by managing the engine loading and the scheduling of electric loads, and

in particular the electric propulsion demand, can a↵ect the energy e�ciency on a ship.

1

Chapter 1. Introduction 2

If the e�ciency of the power production greatly varies with di↵erent loads, the potential

fuel savings can exceed 10%. One method of reducing the fuel consumption is to follow a

voyage plan optimized to minimize the required power of the propulsion. However, in the

case of large-scale cruise ships, they often have a power load that is heavily dependent

on every other system apart from propulsion, such as lighting, heating, ventilation and

fresh water generation. These auxiliary loads will in this thesis be collectively called hotel

load. When taking propulsion and hotel load demands into account, the total energy

generation might be done in a non-optimal way in regards to DG e�ciency. Integrating

the voyage plan with a power management system in such a way as to minimize the fuel

consumption with regards to the e�ciency of the power production, can be a way to

save additional fuel as opposed to only minimizing the power required for propulsion.

Figure 1.1: Typical configuration of an all-electric ship power system. Four dieselengine-generator sets are connected to the AC-grid on a ship and power ship loads suchas electric propulsion through a AC-AC converter and electric engine, and also various

ship service loads, called hotel load.

Chapter 1. Introduction 3

1.2 Objective

The main objective of this thesis is to investigate the fuel savings potential in di↵erent

strategies in which PMS and weather routing is integrated. To achieve this, the project

is divided into three major objectives. The first is to study the e�ciency of DGs and

how to achieve optimal loading of a set. Using the results from the first objective, the

second one is to study how more energy can be saved by taking engine e�ciency into

account in the weather routing. Lastly an investigation of how integrating energy storage

technology with the PMS can a↵ect fuel consumption.

1.3 Outline of Thesis

This thesis consists of the following chapters:

• Chapter 1 introduces the problem formulation and gives the reader a background

in the goals of the project.

• Chapter 2 presents the reader with a background in weather routing methodologies,

and includes a description of the selected algorithm.

• Chapter 3 acquaints the reader with the developed method in optimal handling of

DG sets.

• Chapter 4 presents the methods used for integrating weather routing with a PMS.

The chapter also describes the models used and contains analysis of model error

sensitivity of the methods.

• Chapter 5 presents the results obtained.

• Chapter 6 contains a discussion of the results in chapter 5.

• Chapter 7 contains the conclusions of the thesis.

Chapter 2

Weather Routing

2.1 Methods of Weather Routing

The art of creating a voyage plan for a ship, given weather conditions and a port of origin

and destination, is known as weather routing. In this chapter, the specific problem

addressed is that of finding an optimal route with respect to some cost function. A

given voyage plan is specified as the route and the corresponding speed profile. In the

following sections several methods are presented along with a description of the routine

used in this thesis.

2.1.1 Isochrone Method

One of the earlier methods used for weather routing is presented in James [7]. As the

name suggests, isochrones (time fronts) are calculated which are made up of points

that, given specified weather conditions and propeller speed, are reached at specific time

intervals. Hence, the fastest route is the one that goes through the fewest amounts

of isochrones. By adjusting the speed along this route in such a way that the arrival

time falls on the scheduled time of arrival, a voyage plan with approximate minimal fuel

consumption is found. One problem that arises when trying to go from one isochrone

to another along the normal of the current one is that it does not necessarily lead to

the next one. In Hagiwara [8] a modified version of the isochrone method is presented

which adjusts the solution to handle these cases.

4

Chapter 2. Weather Routing 5

2.1.2 Isopone Method

An extension of the isochrone method was developed by Klompstra [9]. It di↵ers in

the sense that each front is reached after a certain amount of fuel instead of time.

This property allows for direct optimization of fuel consumption, but needs the inverted

relationship between fuel consumption and speed.

2.1.3 Calculus of Variation

The route optimization problem can be set up as an optimal control problem [10] which

can be described by the following:

minu

J = �(x(tf

), tf

) +

t1Z

t0

L(x(t), u, t), dt (2.1)

dx

dt= f(x(t), u, t) (2.2)

where � is a penalty put on the arrival and L varies depending on the type of the

optimization problem. L is the fuel consumption rate if the minimization is done with

respect to fuel. In time minimization, L is simply the constant 1. To solve for a local

minimum in 2.2, it only exists if the following equations, called Euler-Lagrange equations,

are satisfied:

dx

dt= f(x(t), u, t) (2.3)

d�

dt= �

⇣�f�x

⌘T

�⇣�L�x

⌘T

(2.4)⇣�f�u

⌘T

�+⇣�L�u

⌘T

= 0 (2.5)

x(t0) = x0 (2.6)

�(tf

) =⇣ ��

�x(tf

)

⌘(2.7)

Several methods have been used to solve this problem. In Bleick and Faulkner [11] and

Haltiner [12] numerical methods are used to solve the problem directly, assuming that

the state-derivative function f is known.

In Bijlsma [13], the time minimization problem is solved by solving the Euler-Lagrange

equations using destination position as an input parameter. A family of time optimal


paths is created for a given arrival time, where all paths' end points make up isochrones

as in the isochrone method. The first path to reach the destination is the optimal

solution. The fuel minimization problem can be solved in a similar fashion [13].

2.1.4 Dynamic Programming

Dynamic programming has been implemented in several works in weather routing prob-

lems, where Zoppoli [14] was one of the first. To minimize the travel time, the possible

routes from a source to destination are chosen from a grid divided into discrete points

of possible positions. The routes are then associated with a certain cost, and thus the

total cost should be minimized. A summary of the concept can be seen in figure 2.1.

Using Bellman’s principle of optimality [15], the total cost can be minimized recursively

by demanding that each partial sum of the cost must be minimized for that specific part

of the voyage. Both a forward and a backwards recursive algorithm are possible to use,

but in the case of the backwards algorithm the times during each time step of the route

must be known in advance.

Figure 2.1: An example of dynamic programming

2.2 Description of Chosen Method

The weather routing method chosen in this thesis, is a slight variation of Hagiwara [8],

with the addition of land constraint handling from [16]. The journey is divided into

a number of stages, where each stage is defined by a number of possible locations. It

is not allowed to jump over a stage, or go between locations in a specific stage since

it is necessary to only go from one stage to the next in a sequential order. For each

possible location in each stage, a number of possible arrival times to the location are

defined which together creates a three-dimensional search grid as seen in figure 2.2, where


the final arrival time in the last node is fixed. If weather and water conditions (wind,

currents) are known, these conditions are assumed constant between stages, which makes

the heading and speed between two stages entirely defined by the departure and arrival

nodes. For a specific route through the grid, the total cost of a journey is calculated as

the sum of the costs between all the stages. Searching the grid after the cheapest way

is done with a graph-searching algorithm as described in Djikstra [17].

Figure 2.2: 3D search grid with two example routes. The x-y plane corresponds to thelongitude and latitude positions in space, and the z coordinate represents time.

Using a method such as Holtrop-Mennen [18], the water resistance in each node is

calculated. Since the resistance and speed is known in each node, the required propulsion

power will also be defined for each node pair. If the cost J is defined as

J = Pprop

�T (2.8)

where Pprop

is the propulsion power and �T is the time between the relevant stages,

then the final route will be one where the total propulsion power is minimized.

Chapter 3

Optimal Loading of Diesel

Generators

3.1 Engine Load Optimization

To reduce the amount of spent fuel in a power generation system, it should for every load

demand be operated in an optimal way with regards to fuel e�ciency. Diesel engines

have well defined e�ciency curves where the optimal extremum point of operation is

easily pin-pointed. The exact curve is di↵erent from engine to engine, but the shape is

typical for a medium-speed diesel engine, where the e�ciency increases for an increased

load up until a certain point after it descends again [19]. One typical example of such a

curve is seen in figure 3.1 where the specific fuel consumption (SFC) values taken from

a data sheet is marked. Engine data sheets typically specify SFC only at certain load

demands, thus requiring some method of interpolating the values in between. The given

points tend to have an uncertainty to them, and might also vary during the operation.

In that sense, a 2nd-order polynomial approximation could be good enough. However,

as seen in 3.1, the minimum of the 2nd-order polynomial is not at the correct load

demand. Using shape-preserving piecewise cubic Hermite interpolation allows the curve

to keep its minimum at the correct load demand. Presented in this chapter is a method

on how to find the optimal loading of a generator set for a fixed power demand. To allow

integration of the generators and the AC-grid, the frequency of the power production

must be held constant. Hence, by assuming that the generators are running at a fixed

speed, only the power outputs from each generator are used as the control variables.

8

Chapter 3. Optimal Loading of Diesel Generators 9

Power produced [pu]0 0.2 0.4 0.6 0.8 1

SFC

[g/k

Wh]

160

170

180

190

200

210

220

230

240

250

260Specific fuel consumption of a medium-speed diesel engine

2nd order polynomialShape-preserving interpolation

Figure 3.1: Specific fuel consumption of a typical medium speed diesel engine

3.1.1 Minimization Problem

With a power production system consisting of several DG with SFC curves that are

similar to figure 3.1, the optimal e�ciency is obtained when each generator is running

at its optimal load. However, this is not possible for every power demand and the

problem thus becomes to decide how many generators to use and how to distribute

the load demand between them. For many power demands, there are several possible

combinations of how many DG to use. The problem is thus to decide both how many

generators to run, and the load distribution between the active generators.

Given that the individual SFC curves for n generators in the system are known the prob-

lem of finding the optimal load sharing can be formulated as the following minimization

problem:

minPi

⌘sfc,tot

=

Pn

j=1 ⌘sfc,j(Pj

) · PjP

n

j=1 Pj

(3.1)

subject to:

nX

j=1

Pj

= Ptot

(3.2)

Pmin,j

Pj

Pmax,j

(3.3)


where n is the number of generators, ⌘sfc,tot

is the total specific fuel consumption, Ptot

is

the total power demand, ⌘sfc,j

is the specific fuel consumption for DG unit j and Pmin,j

and Pmax,j

are respectively the lower and upper bounds of the power production of DG

unit j. This problem can be solved using constrained convex optimization methods such

as sequential quadratic programming [20].

3.1.2 Identical Engines

Assuming that n diesel engines fulfil the following conditions:

⌘sfc,j

= ⌘sfc,j+1 8j (3.4)

Pmin,j

= Pmin,j+1 8j (3.5)

Pmax,j

= Pmax,j+1 8j (3.6)

(3.7)

the total SFC for the whole engine set can be written as:

⌘sfc,tot

=1

Ptot

nX

j=1

⌘sfc,j

(Pj

) · Pj

(3.8)

In figure 3.2, equation 3.8 is plotted for increasing values of Ptot

from 0.5 to 2Pmax

with P1 as a parameter for the case when there are two diesel engines. For clarity, the

2nd grade polynomial approximation in figure 3.1 is used. For low values of Ptot

the

SFC curves are concave while at higher values they turn convex instead. This results

in there being two minima for low demands and one for high demands. In turn, since

the engines are identical, the optimal loading of them is symmetrical loading for higher

power demands and asymmetrical for low demands.

3.1.3 Non-identical Engines

When the engines are non-identical, one or more of the SFC curves ⌘sfc,1, ⌘sfc,2, ...⌘sfc,n

are not equal to the others. This could, in a ship power system, mean that either the

system consists of two or more di↵erent sized generators, or that it consists of same

size generators where some are more or less e�cient than others. In the first case, the

loading of each identical pair will look the same as in section 3.1.2, and thus the main


Power Gen 1 [pu]0 0.2 0.4 0.6 0.8 1

SFC

[g/k

Wh]

175

180

185

190

195

Specific fuel consumption for varying loads

Figure 3.2: Total SFC for a generator set with two DG is plotted for varying generatorloading and total load demand. Load demand increases in arrow direction.

problem is to decide the loading between the di↵erent sized engines. In the second case,

the solution depends on how the shapes di↵er from curve to curve.

3.2 Example Scenarios

What follow in this section is three di↵erent scenarios with di↵erent sets of generators.

All three scenarios use four engines but of di↵erent types and sizing. The first two depict

ideal engines with specific fuel consumption as specified from data sheets while the third

scenario depicts data from a real cruise ship. The problem described in section 3.1.1 is

solved using constrained nonlinear sequential quadratic programming in Matlab.

3.2.1 Case 1: Four Identical Diesel Engines

The first scenario depicts a power system where four identical engines are used with the

constraints

0 < Pj

< 1 pu (3.9)

⌘sfc,j

= ⌘sfc

, 8j (3.10)

where the power quantities are in power units pu. The optimal load sharing as a function

of power demand is shown in figure 3.3 and the optimal specific fuel consumption in figure

3.4.


Power produced (pu)0 0.5 1 1.5 2 2.5 3 3.5 4

Engi

ne lo

ad (%

)

0

20

40

60

80

100Optimal engine loads

Engine 1Engine 2Engine 3Engine 4

Figure 3.3: Engine loads for optimal power distribution of four identical diesel gen-erators

Produced power [pu]0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

SFC

[g/k

Wh]

175

178

181

184

187

190

Optimal total specific fuel consumption for a4-generator power system with identical engines

Figure 3.4: Total specific fuel consumption for a set of four identical diesel engines

3.2.2 Case 2: Two Pairs of Diesel Engines

In the second scenario two pairs of engines are used where in each pair the DG are

identical. The first pair has the same power constraints as in 3.9, while the second pair

has the following constraints:

0 < Pi

< 1.6 pu (3.11)

⌘sfc,1 = ⌘

sfc,2 (3.12)


Figure 3.6 shows the optimal total specific fuel consumption for this scenario, while

figure 3.5 shows the optimal engine loading.

Produced power [pu]0 1.3 2.6 3.9 5.2

Engi

ne lo

ads [

%]

0

20

40

60

80

100

120

140

160

Optimal engine loads for power systemwith different sized generators


Figure 3.5: Engine loads for optimal power distribution of two pairs of identical dieselgenerators

Produced power [pu]0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2

SFC

[g/k

Wh]

172

176

180

184

188

Optimal total specific fuel consumption fora power system with different engines

Figure 3.6: Optimal total specific fuel consumption for two pairs of di↵erent dieselgenerators

3.2.3 Case 3: Engines with Di↵erent Specific Fuel Consumption

Scenario three depicts a system where all four engines have the same power constraints

as in 3.9, but their SFC curves are non-identical. Contrasting to scenario one and

two which depict ideal SFC taken from data sheets are the e�ciencies on a real ship

which tends to di↵er greatly from the theoretical values. In a practical application of


this method on a ship, it is of great importance to individually model the SFC of each

generator. Fuel consumption and power production data obtained from longer trips is

crucial when fitting these. Seen in figure 3.7 are four SFC curves corresponding to the

generators from a case cruise ship, modelled using fuel consumption data over a long

time span.

Age, usage, and rate of maintenance are factors which a↵ect the SFC of a unit, which

in this particular case can be observed where especially one generator has a much lower

SFC. In the resulting optimal total SFC curve shown in figure 3.9, observe that with an

increasing power demand, the SFC increases when new generators are switched on as a

direct result of turning on more e�cient generators first.

Produced power [pu]0 0.2 0.4 0.6 0.8 1

SFC

[g/k

Wh]

180

195

210

225

240

255

270

285

300

315SFC for four DG with different efficiencies

DG 1DG 2DG 3DG 4

Figure 3.7: SFC curves for the four engines on a case ship

With logged power production data from individual generators on a ship, the potential

fuel savings of optimal load distribution can be calculated by comparing the following

two formulas

ToFopt

=

TZ

0

Ptot

(t) · ⌘sfc,tot

(Ptot

(t)) dt (3.13)

ToF =

TZ

0

nX

j=1

Pj

(t) · ⌘sfc,j

(Pj

(t)) dt (3.14)


Produced power [pu]0 0.5 1 1.5 2 2.5 3 3.5 4

Engi

ne lo

ads [

%]

0

20

40

60

80

100

Optimal engine loads for generatorswith non-identical efficiencies


Figure 3.8: Engine loads for optimal power distribution of four generators with dif-ferent SFC curves

Power demand [pu]0 0.5 1 1.5 2 2.5 3 3.5 4

SFC

[g/k

Wh]

195

200

205

210

215

220Optimal Specific Fuel Consumption

Figure 3.9: Total SFC curves for a generator set with same sized engines but di↵erentSFC for the optimal loading strategy

with the constraintnX

j=1

Pj

(t) = Ptot

(t)

where ToF is the total fuel consumption of a route and Ptot

is the total power demand

at time t.

In equation 3.13 the loading is optimal. Depending on the load profiles Pj

and the SFC

curves ⌘sfc,j

for each DG, the total saved fuel ToSF = ToF �ToFopt

from using optimal

loading will vary.


3.3 Engine Loading Strategies

Optimal usage of engine loading as described in section 3.1.1 may not be possible or

practical on a real ship. There are usually safety criteria which specify when to start a

new generator before hitting the maximum level of the active ones. The stricter these

requirements are, the further away the resulting curve will be from the optimal one.

Typical loadings of the generators on cruise ships tend to be symmetrical, that is all

active generators have the total load split evenly between them. Without real ship

engine data, an initial assessment of the value of optimal engine loading can be done by

comparing the di↵erent total SFC curves for these strategies. As seen in figure 3.10, the

e�ciency is clearly dependent on the loading strategy.

Power demand [pu]0 0.5 1 1.5 2 2.5 3 3.5 4

SFC

[g/k

Wh]

170

180

190

200

210

220

230

Optimal vs symmetrical loadingat different engine switch criteria

Switch at 100%Switch at 75%Switch at 50%Optimal Loading4 DG Symmetric

Figure 3.10: Total specific fuel consumption for optimal engine loading and fourvariations of symmetric loading at di↵erent engine switch criteria

Chapter 4

Method

4.1 Power Management In All-Electric Ships

4.1.1 All-Electric Ship Power System Operation

In ships with electric propulsion and diesel generators as outlined in figure 1.1, the

balance between the production and consumption of power should be carefully handled.

While the typical power load demand varies from di↵erent type of ships, it can generally

be separated into electric propulsion and hotel load. The shapes of these are in more

detail described in section 4.3. In the following method, the total ship load in the ith

time interval is split into the average propulsion and hotel load as follows:

Ptot,i

= Pprop,i

+ Photel,i

(4.1)

Given a system with n generators with typical SFC curves ⌘sfc,j

as seen in figure 3.1,

the total variable fuel usage during the ith time interval �Ti

is:

Fi

=nX

j=1

(Pij

· ⌘sfc,j

(Pij

) ·�Ti

+ Sij

· SC) (4.2)

where SC is the start-up cost of a generator and Sij

is a decision variable which is 1 if

generator j is started at the beginning of time interval i. The total fuel ToF needed by

17

Chapter 4. Method 18

the power system of the ship for a route with m stages is calculated as:

ToF =nX

j=1

mX

i=1

(Pij

· ⌘sfc,j

(Pij

) ·�Ti

+ Sij

· SC) (4.3)

If optimal engine loading as seen in section 3.2 is used and an SFC curve ⌘sfc,tot

for the

whole power system has been calculated, equation 4.3 can be reduced to:

ToF =mX

i=1

(Pi

· ⌘sfc,tot

(Pi

) ·�Ti

+ Si

· SC) (4.4)

where Si

is the total number of generator start-ups at beginning of time interval i.

4.1.2 Adjustment of Ship Power Consumption

Intuitively it would be beneficial to as often as possible have a total ship load Ptot,i

that is

close to an optimal operation point. Assuming that a model of how the propulsion power

depends on ship speed and water and weather conditions is known, then by adjusting

the scheduled speed over ground to be lower or higher depending on the position on the

total SFC curve, the power system could at all times operate near peak e�ciency by

shifting the total load. If the ship is able to freely adjust speed during a larger part of

a journey, this could have a large impact on the total e�ciency of the power generation

system.

In typical cases, the electric propulsion constitutes the largest part of the total ship

load, but for very large cruise ships the hotel load could be a substantial part as well.

While the larger parts of the hotel load tend to be non-adjustable, such as HVAC and

lighting, there might depending on the type of ship be a fraction of the hotel load that

can be adjusted in a certain time window. One such example is fresh water production

which does not have to be done at a specific time of the day. Separating hotel load into

non-schedulable and schedulable parts gives more freedom to adjust the total power

load.

4.1.3 Power Generation Scheduling and Weather Routing

The solution to the problem of optimizing the electric power generation can be imple-

mented by incorporating equation 4.4 as the cost used in the weather routing method

described in section 2.2. How well it can perform is dependent on the accuracy with


which the propulsion and hotel power can be predicted (see section 4.4). For a route

with m stages, the optimization problem is formulated as:

Minimize:

ToF =mX

i=1

(Pi

· ⌘sfc,tot

(Pi

) ·�Ti

+ Si

· SC) (4.5)

Subject to:

1) Minimum and maximum generator power constraints

Pj,min

< Pij

< Pj,max

8i, j (4.6)

2) Hotel load power constraints

Pi

� Photel,i

8i, j (4.7)

3) Ship speed constraints

Vmin

< Vi

< Vmax

8i (4.8)

|Vi

� Vi�1| V

c,max

8i (4.9)

4) Initial and final arrival times

T1 = 0 (4.10)

Tm

= T (4.11)

where Pij

is the power produced by engine j at step i, Vi

is the vessel speed between

stage i and i+1, Vmin

is the minimum vessel speed, Vmax

is the maximum vessel speed,

Vc,max

is the maximum change of velocity between stages, Ti

is the arrival time at stage

i and T is the hard deadline on arriving at the final stage.

4.1.4 Hotel Load Scheduling

The part of the hotel load that is schedulable tends to be small and has been omitted

in the previous sections. However, with the large diversity of ships on the global market

there is still of interest to investigate what e↵ect a schedulable hotel load has on the fuel

optimization. A benefit of scheduling a certain amount of power over a given window


of time compared to scheduling propulsion where the speed is directly a↵ected is that

the only change done by rearranging the hotel load is a change in e�ciency while the

total energy produced will still be the same. Additionally, by only scheduling the hotel

load in the next certain window of time, it is less sensitive to future errors in weather

prediction. The method proposed is to optimize a route with respect to propulsion and

then schedule the hotel load to minimize the spent fuel. For each given window in the

schedule divided into k steps, the following problem is solved:

P = Pprop

+ Phf

+ Phs,tot

(4.12)

Photel

= Phf

+ Phs,tot

(4.13)

where Phf

is the fixed part of the hotel load, Phs,tot

is the total schedulable part of the

hotel load and Photel

is the total hotel load.

ToF =kX

i=1

((Pprop,i

+ Phf,i

+ Phs,i

) · ⌘sfc,tot

(Pprop,i

+ Phf,i

+ Phs,i

) ·�Ti

+ Si

· SC)

(4.14)

Subject to:

0 Phs,i

Ph,max

(4.15)

kX

i=1

Phs,i

= Phs,tot

(4.16)

where Ph,max

is the maximum power possible to use on the schedulable part of the

hotel load at any time step. Since Pprop,i

and Phf,i

are fixed for every time step i, the

optimization is done over only Phs,i

. Generally, a bigger value of Phs,tot

gives more

freedom to the optimization.

4.2 Energy Storage Management

This section presents three di↵erent methods of utilizing energy storage in an AES. The

first two directly incorporate energy storage with the energy system to shift the electric


loads, while the third presents a scenario where energy storage is used as an emergency

reserve.

4.2.1 Load Shifting

While the method presented in section 4.1.3 allows a route to be optimized with respect

to fuel usage, it does not necessarily mean that the engines are operating at peak e�-

ciency. Achieving higher e�ciency during a route without the need of spending more

fuel can be done with the addition of energy storage technologies to the AES power

system. With the possibility to store and discharge energy, the total load in each time

step can be shifted resulting in the following expression:

Ptotb,i

= Pprop,i

+ Photel,i

+ Pb,i

(4.17)

where Pb,i

is the power stored or withdrawn from the energy storage in each time step.

Adjusting the power flow from and to the energy storage in such a way as to minimize

⌘sfc,tot

(Ptotb,i

), could increase the total e�ciency of a route. For the purpose of inves-

tigating the maximum potential of integrating ES in this way, some assumptions are

made. The first assumption is that the energy storage is lossless both in the sense that

all energy can be utilized both when charging and discharging, and also that the SOC

is constant while Pb,i

is zero. Suitable in this case are batteries with high capacity and

medium power rate. One proposed technology with the required properties would be

sodium-sulphur batteries [21].

Solving the problem of adding energy storage to the power management system on an

AES can be done with the following modifications to the problem from section 4.1.3:

Minimize:

ToF =mX

i=1

(Ptot,i

· ⌘sfc,tot

(Ptotb,i

) ·�Ti

+ Si

· SC) (4.18)

With the additional constraints:

4) State of charge constraints

SOCmin

SOC SOCmax

(4.19)


5) Charge and discharge constraints

Pd

Pb,i

Pc

(4.20)

where SOCmin

and SOCmax

is the minimum and maximum state of charge allowed, Pb,i

is the power used by the battery, negative when discharging and positive when charging,

and Pd

and Pc

is correspondingly the maximum discharge and charge rate of the battery.

4.2.2 Energy Storage Load Shifting with Minimized Propulsion

As described earlier in this chapter, integrating a power management system with the

weather routing routine on a ship in order to optimize the engine e�ciency of a route is

heavily dependent on the accuracy of the prediction of hotel and propulsion loads. In the

presence of large uncertainties in those models and predictions, it might be beneficial

to ignore the benefit of the PMS and do weather routing with minimized propulsion

instead. A benefit of integrated energy storage in that scenario is that it does not need

to be scheduled ahead of time, but could instead in every step of a route be used to

adjust the total load in the most beneficial way with regards to engine e�ciency. Since

the problem

Minimize:

ToF = Ptot

·�T · ⌘sfc,tot

(Ptot

+ Pb

) (4.21)

Subject to:

SOCmin

SOC SOCmax

(4.22)

Pd

Pb

Pc

(4.23)

where the only control variable is Pb

, is solved independently for each time step, no grid

search needs to be done.

4.2.3 Energy Storage Bu↵er

With an increasing amount of ship tra�c in the world, the frequency of accidents follows

paving the way for new legislations focused on safety routines and accident prevention.

One such rule with regards to maneuvering redundancy was adopted in 2008 by the

International Marine Organization [22]. To ensure that a ship will not drift out of course


into hazards, it is required for a ship to have enough power available for maneuvering

in zones where such dangers are identified. One quantification of this rule specifies that

50% of total propulsion power should be guaranteed in the case of a single engine failure

[23]. Depending on the ship and the route this might require a ship to keep additional

generators active with a larger than required power production. Longer time spent in

maneuver zones will result in more fuel lost. Reducing this loss is possible if a ship

is fitted with energy storage capabilities large enough to compensate for the loss of a

generator during the time it takes to start up a new one. By doing this, no extra power

needs to be consumed unless an actual engine failure occurs. The total fuel ToSF that

can be saved from this can be calculated as:

ToSF =mX

i=1

Pi

·�Tman,i

· (⌘sfc,subopt

(Pi

)� ⌘sfc,opt

(Pi

)) (4.24)

where Pi

is the power used during stage i, �Tman,i

is the time spent in a maneuver zone

in stage i, ⌘sfc,subopt

(Pi

) is the suboptimal e�ciency when running an extra generator

at power demand Pi

and ⌘sfc,opt

(Pi

) is the optimal e�ciency at power demand Pi

.

Suitable for this purpose could be lead–acid energy storage with low capacity but high

power rating [21]. One limitation of this solution is that the energy storage cannot be

combined with the power management system as proposed in section 4.2.1. Partly since

in the case of a failure, the whole reserve needs to be available, and partly because the

suitable sizing and power rating of the energy storage is di↵erent in the two methods.

4.3 Load Modelling

A prerequisite for creating a voyage plan with respect to engine e�ciency is some sort

of model over the total electric ship load for the whole voyage. As described above,

this can be divided into propulsion and hotel load segments. This section describes the

simple models used in the simulations.

4.3.1 Propulsion Power

Propulsion power can be described as a function of ship speed and water resistance.

Obtaining the first of these is trivial but modelling the water resistance is a more complex

problem. As mentioned in section 2.2 the well-known Holtrop-Mennen method is used.

The method works by using a large amount of ship parameters such as length, width and


volume of several parts of a given ship, to produce calm water resistance as a function

of vessel speed. Using parameters obtained from a case ship, a decent model can be

constructed. Given that weather forecasts are available, wave resistance can also be

calculated and added together with the calm water resistance to give the total water

resistance.

4.3.2 Hotel Power

It has been shown that in the case of cruise ships on a well-known route, the hotel load

can be predicted with high accuracy using experience from previous trips [24]. Typical

behaviour includes heavy dependencies on water and air temperatures, and more general

time of day dependencies with additional energy consumed during certain intervals. In

figure 4.1 the load profile of a 48 hour trip where a sinusoid behaviour can be observed

with varying peak magnitude a↵ected by temperature. With the added simplification

that the temperature is constant, a reasonable model of the hotel load is that of a sinus

curve with a 12 hour period as seen in figure 4.2.

Time [days]0 0.5 1 1.5 2

Pow

er [k

W]

5400

5600

5800

6000

6200

6400

6600

6800Hotel load demand

Figure 4.1: Real hotel power consumption data during a two-day time span

4.4 Sensitivity Analysis

For results gained from the weather routing and e�ciency based power management

to have weight, the natural question of how sensitive the method is to modelling errors


Time [days]0 0.5 1 1.5 2

Pow

er [k

W]

5400

5600

5800

6000

6200

6400

6600Model of hotel load

Figure 4.2: Hotel power modelled as a sinusoid from cruise ship data

occurs. With respect to unknown and known errors alike, an approximation of how trust-

worthy the method is of great importance. In this section, the three most important

parameters in calculating the required power will be analysed in how they a↵ect the

fuel savings, for di↵erent model errors. Included in these are: weather forecast errors

and ship propulsion resistance errors. By taking a specific model profile as the true

representation of the ship and then varying the di↵erent error parameters one at a time,

a fuel profile can be created and compared to the true scenario. In doing this, an

assumption is made on the behaviour of the captain. It is assumed that the captain on

a ship will try to keep to a specific predetermined route in terms of speed and position,

even if the required power deviates from the simulations. Hence, for each time step, the

corresponding position and velocity of the ship will be the same, no matter what type

of model error is present.

4.4.1 Water Resistance

To judge the necessary propulsion power needed to propel a vessel at a certain speed,

a model for the water resistance of the vessel given speed is required. By estimating

this with a known method such as Holtrop-Mennen [18], approximation of the power

is possible. Since the propulsion power and by extension the e�ciency of the power

generation is dependent on the water resistance model, errors in the model will result in

a power scheduling that is not necessarily optimal with regards to fuel e�ciency.


A model that underestimates the true resistance will result in a lower propulsion power

prediction. The result would be that the corresponding SFC values in figure 3.4 will

be shifted to the left compared to the predicted case. In case of overestimation, a shift

to the right happens instead. As seen in figure 5.7, the produced power in a route

optimized with respect to engine e�ciency result in SFC values that tend to be around

the dips, which generally means that the true SFC will be higher when the power is

shifted in either direction. The same is typically not true for a route optimized with

minimized propulsion, since the power is not focused around the e�ciency peaks. For

50 di↵erent routes with 100 di↵erent arrival times, the mean and standard deviation of

the fuel savings of the minimized fuel route compared to the minimized propulsion route

when a↵ected by a varying model error can be observed in figure 4.3.

Error [%]-20 -10 0 10

Fuel

Sav

ed [%

]

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15Mean

Error [%]-20 -10 0 10

Fuel

Sav

ed [%

]

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22Std

Figure 4.3: The mean and standard deviation for fuel savings as function of waterresistance error over 50 routes with 100 respective arrival times

4.4.2 Weather Forecast

When creating a weather routing voyage plan, forecasts of the weather over the relevant

region is used. This allows prediction of wind and wave speed and directions, and also

wave height. The necessary propulsion power is, as described in section 2.2, calculated

using ship speed through water and the total water resistance. Part of the resistance

comes from added wave resistance which is dependent on the weather. An error in the

predicted weather will therefore result in an error in the water resistance. Depending on

the type of weather conditions that are wrongfully predicted, the resulting resistance er-

ror can fluctuate heavily. As described in section 4.4.1, the larger the di↵erence between


the erroneous and true resistance, the smaller the resulting fuel savings. The resulting

mean and standard deviation of the fuel savings can be observed in figure 4.4.

Forecast error [hours]-20 -10 0 10 20

Fuel

Sav

ed [%

]

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

Mean

Forecast error [hours]-20 -10 0 10 20

Fuel

Sav

ed [%

]

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

Std

Figure 4.4: The mean and standard deviation for fuel savings as function of weatherforecast error over 50 routes with 100 respective arrival times

Chapter 5

Results

5.1 Engine E�ciency Optimization

In this section the results from using optimized engine loading as described in chapter

3 are shown.

5.1.1 Case Ship Data

In order to study the potential in using optimal engine loading, the saved fuel from

optimised engine loading is investigated using the method in section 3.2.3, using logged

power production data from a case ship. Data has been obtained from the ABB EMMAr

system and is considered proprietary information. A simple summary of the ship power

system is presented in table 5.1. In figure 5.1 the fuel usage of a small section of the

data is shown both for the original usage of the diesel engines and also with optimal

distribution.

Presented in figure 5.2 is the relative di↵erence in fuel consumption between the plots

in figure 5.1. From figure 3.7 it is clear that one of the four generators in the system

has a much higher performance. Hence, the largest savings occur when the total fuel

consumption is low and the optimal loading makes sure to schedule the most e�cient

generator. Calculated over the whole set of data, the fuel savings amount to 2.1%.

5.2 Voyage Planning with a Power Management System

In this section, the results of route simulations using di↵erent fuel saving strategies are

presented. Unless otherwise specified, the simulations are done using the ship data in

28

Chapter 5. Results 29

Time [hours]0 1 2 3 4 5 6

Fuel

Con

sum

ptio

n [to

ns/h

our]

0.2

0.4

0.6

0.8

1

1.2

1.4Fuel consumption with normal and optimized engine loading

Sub-optimal engine loadingOptimized engine loading

Figure 5.1: Fuel consumption with optimal and nominal engine loading for a specificwindow of time of a route

Time [hours]0 1 2 3 4 5 6

Fuel

Sav

ings

[%]

0

2

4

6

8

10

12

14

16

18

20Fuel savings when using optimal engine loading

Figure 5.2: Fuel savings of optimal engine loading for a specific window of time of aroute

table 5.1 and with optimal engine loading with identical SFC curves. Heavy fuel oil is

used as fuel in all simulations.

5.2.1 Weather Routing with Respect to Engine E�ciency

In order to compare how di↵erent PMS strategies fare against each other in terms

of fuel usage, a specific route is chosen in which the di↵erent methods are applied.

With varying arrival time as a parameter to the routing routine, a comparison over


Table 5.1: Table describing the power and fuel capacities of the case ship diesel gen-erators

Gen 1 Gen 2 Gen 3 Gen 4

Nominal power (MW) 9 9 9 9Minimum power (MW) 2 2 2 2Start-up cost (ton fuel) 0.01 0.01 0.01 0.01

Ship Parameters

a large number of routes is shown. In figure 5.3, results from five di↵erent voyage

plans are shown. Including is routing with respect to minimized propulsion and routing

with respect to total ship load and engine e�ciency. Furthermore, included are also

two additional scenarios where energy storage load shifting is added to the mentioned

strategies. Added as a reference, is a route optimized with respect to propulsion but

without optimal loading of engines. Instead, the engine loading is done in such a way as

to emulate the behaviour of the case ship. This is chosen since it neither utilizes e�cient

PMS nor optimal loading of engines. Figure 5.4 displays the fuel savings compared to the

reference route. In order to compare the potential in optimizing a route with respect to

engine e�ciency, figure 5.5 displays only the savings of the routes with optimized engine

loading, with the route optimized with respect to minimized propulsion power taken as

the reference.

Arrival time [h]171 172 173 174 175

Fuel

spen

t [to

ns]

570

572

574

576

578

580

582

584

586

588Optimized Route Comparison

Min Propulsion w/o ESMin Propulsion with ESMin Fuel w/o ESMin Fuel with ESMin prop non-opt loading

Figure 5.3: Total fuel consumption of di↵erent PMS strategies for varying arrivaltimes

In a route with minimized propulsion power the SFC in each time step is not taken into

account which generally leads to SFC values spread out evenly over an interval during

the trip. This can be observed in figure 5.6 where each red marking symbolizes the SFC


Arrival Time [h]161 165 169 173 177 181 185

Fuel

save

d [%

]

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Fuel savings comparisons of different PMS strategies

Minimized propulsion with ESMinimized fuel without ESMinimized fuel with ESMinimized propulsion without ES

Figure 5.4: Total fuel savings of di↵erent PMS strategies for varying arrival times,compared against a minimized propulsion route with sub-optimal engine loading

Arrival Time [h]161 165 169 173 177 181 185

Fuel

save

d [%

]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Optimized Route Comparison

Minimized propulsion with ESMinimized fuel without ESMinimized fuel with ES

Figure 5.5: Total fuel savings with di↵erent PMS strategies for varying arrival timeswhen compared to a minimized propulsion route


of a specific time step during the route. In contrast to this, the SFC of every time step

in a minimized fuel consumption route can be seen in figure 5.7. There the produced

power tends to be such as to place the resulting SFC in the dips, hence resulting in a

lower average SFC over the whole trip.

Produced Power [kW] #104

0 0.6 1.2 1.8 2.4 3 3.6

SFC

[g/k

Wh]

170

175

180

185

190

195

200

Specific fuel consumption in each time stepfor route with minimized propulsion power

Figure 5.6: The total SFC for each time step of a route optimized with respect tominimized propulsion power

Produced Power [kW] #104

0 0.6 1.2 1.8 2.4 3 3.6

SFC

[g/k

Wh]

170

175

180

185

190

195

200

Specific fuel consumption in each time stepfor route with minimized fuel consumption

Figure 5.7: The total SFC for each time step of a route optimized with respect tominimized fuel consumption

In the case where energy storage has been integrated to increase the e�ciency, it is of

interest to see how the payback-time varies with the capacity of the energy storage.

The results are representative for a large scale cruise ship and modern prices of energy

storage and fuel [21] [25]. The results can be observed in figure 5.8.


Size of energy storage [MWh]0 2 4 6 8 10 12 14

Payb

ack

perio

d [y

ears

]

150

200

250

300

350

400

450

500

550Size dependent payback period of energy storage

Figure 5.8: Payback period for varying capacities of energy storage integrated with thePMS

5.3 Schedulable Hotel Load

In figure 5.9 the fuel savings from using PMS to schedule part of the hotel load are

shown.

Schedulable hotel load [%]0 3 6 9 12 15

Tota

l Sav

ed F

uel [

%]

0

0.03

0.06

0.09

0.12

0.15

Fuel savings as function of schedulable hotel load

Figure 5.9: Possible total fuel savings with varying size of schedulable hotel load

5.4 Energy Storage Bu↵er

By incrementally increasing the size of the maneuver zones along a route the total time

spent in these during a journey will increase. Creating a voyage plan for each case and

comparing the fuel usage with and without energy storage reserves result in an increased


amount of fuel savings as observed in figure 5.10. The payback period as seen in figure

5.11 is representative for a large scale cruise ship and modern prices of energy storage

and fuel [21] [25].

Time of route spent in maneuver mode [%]5 10 15 20

Fuel

savi

ngs [

%]

0.63

0.7

0.77

0.84

0.91

0.98

1.05Fuel savings from energy storage buffer

Figure 5.10: Fuel savings from using energy storage reserves instead of extra activediesel generators.

Time of route spent in maneuver mode [%]5 10 15 20

Payb

ack

perio

d [y

ears

]

2.1

2.4

2.7

3Payback period of energy storage buffer

Figure 5.11: Payback period of energy storage reserves investment.

Chapter 6

Discussion

6.1 Optimal Engine Loading

The problem presented in section 3.1.1 has been solved for various combinations of

generators. Comparisons of optimal engine loading to sub-optimal loading was made in

order to see if using PMS to distribute the electrical load demand could result in fuel

reductions. The trend that can be seen is that the more the individual e�ciency curves of

the generators di↵er from each other, the bigger the potential of fuel reduction. Typical

symmetric loading of engines in power systems is in the case of identical engines often

identical to the optimal case. Since maintenance and wear from usage continuously a↵ect

engine performance, regular identification of individual generator e�ciency is important.

However, an important limitation to take into account is the di↵erence between ideal

scenarios where engine switching can be done at maximum load, and ship power systems

where real maximum load limits have been set on each generator. Hence it is of great

interest to have a system where these limits are as non-strict as possible, resulting in a

total SFC curve closer to the optimal result. The reason behind the load limits is the

importance of delivering enough power in case of sudden power transients. Integration

of energy storage bu↵er as described in section 4.2.3 would be one way of negating this

limit.

6.2 Power Management and Engine E�ciency

A weather routing optimization with respect to total electric load and engine e�ciency

has been made and the results compared to routes optimized with respect to minimized

propulsion power, called the baseline. The results are in general positive, resulting in

routes where the e�ciency of the power generation is much higher than the baseline.

35

Chapter 6. Discussion 36

Exactly how much potential that lies in the method depends on several factors, where

most important is the behaviour of the diesel generators SFC. Larger di↵erences be-

tween the worst and best SFC of the generators in a ship power system will result in a

larger height di↵erence between the peaks and dips in the total SFC seen in figure 3.4.

Therefore, the importance of this method is closely tied to how well the total SFC curve

can be constructed as discussed in 6.1.

While the results show a potential of substantial additional fuel savings it is impor-

tant to look at the shortcomings from the method which mainly lies in its dependency

on accuracy in the electric load prediction. As pointed out in section 4.4, if the error is

large, the resulting route will be worse than a route with minimized propulsion power.

Hence, detailed models are a prerequisite for any superior engine e�ciency PMS.

6.3 Integration of Energy Storage

Two di↵erent usages of energy storage on an AES have been investigated. The first

further improve upon the e�ciency of the power production either with a minimized

propulsion route, or with a minimized fuel route. Results from both strategies show

that fuel consumption can be decreased by integrating energy storage with the PMS,

where the savings increase with the battery capacity. However, the saved energy is

of an order of magnitude smaller than savings achievable with the power management

discussed in section 6.2. Furthermore, when taking current prices of energy storage

technology into account, the payback period is too long for the method to be feasible.

These results apply to a cruise ship where the electric loads tend to follow the predicted

trend. A possible application could instead be to use energy storage for peak shaving

on ships with sudden large impulse loads such as ice breakers or war cruisers.

Secondly, a method where energy storage is not actively used, but instead kept as

an energy reserve in order to fulfil propulsion redundancy requirements. In the case of

large cruise ships with very large propulsion systems, if more than a small fraction of

a route is under these restrictions, fuel savings can be achieved. As the battery used

needs to handle the extra load in case of engine failure, the main di�culty lies in finding

storage with a high power rate to capacity ratio. If such storage can be utilized, it might

be economically feasible with a payback period shorter than 5 years.

Chapter 7

Conclusion

From the studies on the voyage planning and power management problems on all elec-

tric cruise ships, three main conclusions have been made. Before presenting these it

is important to note that these are based on data from one specific ship. Since some

results are heavily dependent on engine type and operational profile of the ship, they

might not be representative for any general cruise ship.

The first of these conclusions concerns the possibility for optimization of the loading

of generators. In this thesis it is found that the fuel consumption can be substantially

reduced up to 5% if the specific fuel consumption of the generators in a power generation

system is identified and optimal scheduling based on these is used.

The second conclusion is that using a power management system to schedule the

power production with respect to engine e�ciency has the potential to further decrease

the fuel consumption compared to an optimal route with minimized propulsion. How-

ever, this reduction is small compared to the benefit of optimal engine loading and to

guarantee any positive results at all, only small model errors below 8% are allowed.

The final major conclusion is that energy storage can be used in two scenarios on

board an AES which both results in fuel reductions. First of these is to continuously use

charge and discharge capabilities of energy storage for load shifting in order to increase

the e�ciency of the power production. This however, gives very small improvements and

is not feasible from an economical perspective. In the second scenario energy storage is

used as an energy bu↵er to prevent the need for additional active generators. This has

the potential to be economically feasible in scenarios where a ship often must be able to

guarantee power in case of unforeseen power demands.

37

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