UPTEC F 15 033 Examensarbete 30 hp Juni 2015 On-ship Power Management and Voyage Planning Interaction Mikael Frisk
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
Chapter 2. Weather Routing 6
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
Chapter 2. Weather Routing 7
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)
Chapter 3. Optimal Loading of Diesel Generators 10
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
Chapter 3. Optimal Loading of Diesel Generators 11
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.
Chapter 3. Optimal Loading of Diesel Generators 12
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)
Chapter 3. Optimal Loading of Diesel Generators 13
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
Engine 1Engine 2Engine 3Engine 4
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
Chapter 3. Optimal Loading of Diesel Generators 14
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)
Chapter 3. Optimal Loading of Diesel Generators 15
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
Engine 1Engine 2Engine 3Engine 4
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.
Chapter 3. Optimal Loading of Diesel Generators 16
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
Chapter 4. Method 19
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
Chapter 4. Method 20
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
Chapter 4. Method 21
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)
Chapter 4. Method 22
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
Chapter 4. Method 23
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
Chapter 4. Method 24
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
Chapter 4. Method 25
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.
Chapter 4. Method 26
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
Chapter 4. Method 27
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
Chapter 5. Results 30
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
Chapter 5. Results 31
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
Chapter 5. Results 32
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.
Chapter 5. Results 33
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
Chapter 5. Results 34
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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