EP4039578A1

EP4039578A1 - Energy storage device equivalent fuel consumption

Info

Publication number: EP4039578A1
Application number: EP21155425.8A
Authority: EP
Inventors: Miltiadis Kalikatzarakis
Original assignee: Damen 40 BV
Current assignee: Damen 40 BV
Priority date: 2021-02-05
Filing date: 2021-02-05
Publication date: 2022-08-10

Abstract

Methods and systems are disclosed for determining a power distribution for a plurality of power sources of a hybrid power system. The plurality of power sources may comprise an energy storage device, preferably a battery. The energy storage device may be associated with a charge rate and/or a discharge rate, and with a state of charge. The plurality of power sources may further comprise one or more electric-power generators electrically coupled to the energy storage device. An electric-power generator may be associated with a maximum amount of provided power, P<sub>max</sub>, and may also be associated with a power-specific fuel consumption, sfc(P), defining a quantity of fuel consumed per quantity of energy provided as a function of provided power. The method may comprise determining a discharging equivalent specific fuel consumption based on the respective power-specific fuel consumptions of the respective one or more electric-power generators. The discharging equivalent specific fuel consumption may define an estimated amount of fuel that will be consumed by recharging the energy storage device. The method may, additionally or alternatively, comprise determining a charging equivalent specific fuel consumption obtainable by determining the amount of fuel consumed according to the discharging equivalent specific fuel consumption at a discharge rate that is equal to a given charge rate. The method may further comprise determining a power distribution based on at least the discharging equivalent fuel consumption and/or the charging equivalent fuel consumption.

Description

Field of the invention

The invention relates to an energy storage device equivalent fuel consumption; and, in particular, though not exclusively, to methods and systems for determining an energy storage device equivalent fuel consumption and a computer program product enabling a computer system to perform such methods.

Background of the invention

Hybrid power systems are system comprising different power sources, typically an energy storage device such as a battery and a combustion engine. Hybrid power systems have successfully been implemented in vehicles e.g. cars, vessels, and trains to reduce fuel consumption and local emissions (e.g. in heavily populated areas).
As the capacity of most energy storage devices is limited, the combustion engine may be used as an electric-power generator to (re)charge the energy storage device. Depending on the system, the combustion engine may be e.g. a dedicated electric-power generator, typically a Diesel generator, for providing electrical power; or a propulsion engine that is coupled to e.g. an asynchronous motor which may be used to charge the energy storage device. In order to determine which power source to use for propelling the vehicle in question and, in particular, when to discharge and charge the energy storage device, a hybrid power system may comprise a controller that selects one or more power sources based on at least the current power demand.
Conventionally, these controllers are rules-based. More advanced systems may use an optimisation algorithm, e.g. an Equivalent Consumption Minimisation Strategy, which may result in a higher fuel efficiency than a rules-based controller. However, in order to apply an optimisation algorithm, an equivalent fuel consumption must be associated with the battery in order to make a meaningful comparison with the fuel consumption of the electric-power generator. Conceptually, when the battery is discharged by a certain amount, the associated equivalent fuel consumption represents the fuel required by the electric-power generator to recharge the battery, at some future point in time, by the same amount; and when the battery is charged by a certain amount, the associated equivalent fuel consumption represent the fuel saved, i.e., not consumed by a combustion engine, at some future point in time, by discharging the battery the same amount.
However, the amount of fuel required to charge a battery (or saved by discharging a battery) is generally not known at the time the battery is discharged (respectively charged), as it depends on the load of the electric-power generator, the charge rate of the battery, the state of charge (SOC) of the battery, and so on, at the point in time when the battery is charged (respectively discharged). Various solutions to this problem are known in the art.
For example, R. Geertsma, Autonomous Control for Adaptive Ships with Hybrid Propulsion and Power Generation (2019), pages 183-214, discloses a constant equivalence model, where the battery equivalent fuel consumption depends on a nominal fuel consumption of the electric-power generator. This model only provides a solution close to the global optimum if the battery usage is limited to a relative narrow SOC range. The same document also discloses a battery equivalent fuel consumption based on a predicted propulsive load, which prediction is based on historical data. This model may give a more realistic estimate of the equivalent fuel consumption for charging or discharging the battery, especially for vessels with a fairly predictable load pattern, such as ferries. However, the method does not take the (potential) presence of a multitude of power generators that may charge the battery into account. Furthermore, the effect of the battery's state of charge is only taken into account close to the minimum and maximum allowed state of charge.
Therefore, there is a need in the art to provide a method for determining an energy strategy of a hybrid power system that further reduces fuel consumption, and in particular for a method for selecting a power source in a hybrid system based on an energy storage device equivalent fuel consumption.

Summary of the invention

It is an aim of the embodiments in this disclosure to eliminate, or at least reduce one or more of the drawbacks known in the art. It is furthermore an aim of the embodiments in this disclosure to provide a method to reduce fuel consumption of a hybrid power system.
In an aspect, the invention may relate to a method for determining a power distribution for a plurality of power sources of a hybrid power system. The plurality of power sources comprises an energy storage device, preferably a battery. The energy storage device may be associated with a charge rate and/or a discharge rate, and with a state of charge. The plurality of power sources further comprises one or more electric-power generators electrically coupled to the energy storage device. An electric-power generator may be associated with a maximum amount of provided power, P _max, and may also be associated with a power-specific fuel consumption, sfc(P), defining a quantity of fuel consumed per quantity of energy provided as a function of provided power. The method may comprise determining a discharging equivalent specific fuel consumption for the energy storage device based on the respective power-specific fuel consumptions of the respective one or more electric-power generators. The discharging equivalent specific fuel consumption may define an estimated amount of fuel that will be consumed by recharging the energy storage device as a function of the discharge rate of the energy storage device. Preferably, the discharging equivalent specific fuel consumption for a discharge rate is obtainable by performing the steps of:

a) determining a discharge power associated with the discharge rate;
b) selecting a first electric-power generator from the one or more electric-power generators, and;
c) IF the discharge power is smaller than the maximum amount of provided power associated with the selected electric-power generator,
THEN determining the equivalent estimated amount of fuel by determining an amount of fuel consumed by the selected electric-power generator when providing power equal to the maximum provided power of the selected electric-power generator minus the determined discharge power and, optionally, multiplying the determined amount of fuel with a predetermined proportionality factor larger than 0 and smaller than or equal to 1, to obtain the discharging equivalent specific fuel consumption;
ELSE updating the discharge power by subtracting the maximum amount of provided power associated with the selected electric-power generator from the previously determined discharge power, selecting a next power generator from the one or more electric-power generators, and repeating step c.

As used herein, an energy storage device may also refer to an energy storage system comprising a plurality of devices. The energy storage device is typically a device for storing electrical energy. The previously determined discharge power refers to the discharge power as it was before the updating step. A power distribution for a plurality of power sources may be understood to define, for each power source of the plurality of power sources, an amount of power provided by the power source in question.
The energy storage device being associated with a charge rate and/or a discharge rate may be understood as that the energy storage device is currently being charged at said charge rate and/or being discharged at said discharge rate. Similarly, the energy storage device being associated with a state of charge may be understood as that the energy storage device currently has that state of charge.
An electric-power generator being associated with a maximum amount of provided power may be understood as that that generator can at most provide said maximum amount of provided power.
It has been found that an energy management system selecting a power source based on this energy storage device equivalent fuel consumption defined in embodiments in this disclosure, is surprisingly more fuel efficient than one based on known methods such as a constant equivalence model. In general, this method guides the one or more electric-power generators towards running at or near their optimum power efficiency, while remaining flexible enough to adequately deal with varying circumstances.
It is a further advantage of this method that it only depends on known design parameters and momentaneous power demand, and does not depend on previously collected data. Thus, it can be used directly without having to spend a period collecting data. Moreover, the method may also be used for hybrid power systems with an irregular power demand.
In an embodiment, the proportionality factor may be based on the state of charge of the energy storage device. This way the system is guided to recharge the energy storage device when the state of charge is low, and to discharge the energy storage device when the state of charge is high, and vice versa.
In an embodiment, the method may further comprise controlling a power source to deliver power based on the determined power distribution.
In an embodiment, selecting a power source may comprise determining a minimum equivalent fuel consumption based on at least the respective power-specific fuel consumptions of the one or more electric-power generators, and the discharging equivalent fuel consumption and/or the charging equivalent fuel consumption. The method may further comprise selecting the power source or combination of power sources associated with the minimum equivalent fuel consumption.
The determined equivalent fuel consumption may be used in an optimisation algorithm, e.g. an Equivalent Consumption Minimisation Strategy, in order to minimise fuel consumption of a hybrid power system.
In an embodiment, the minimum equivalent fuel consumption may be determined using a Mesh Adaptive Direct Search algorithm. In other embodiments, different non-convex optimisation algorithms may be used.
In an embodiment, the hybrid power system may further comprise one or more main engines, preferably combustion engines, for providing mechanical power at a rotational speed. Each of the one or more combustion engines may be associated with a power-specific fuel consumption. Determining a minimum equivalent fuel consumption may further be based on the respective power-specific fuel consumptions associated with the one or more main engines, and, optionally, on the respective rotational speeds of the one or more main engines.
In a further aspect, embodiments of this disclosure may relate to a controller for a hybrid propulsion system comprising a plurality of power sources. The plurality of power sources may comprise an energy storage device, preferably a battery. The energy storage device may be associated with a charge rate and/or a discharge rate, and with a state of charge. The plurality of power sources may also comprise one or more electric-power generators electrically coupled to the energy storage device. Each electric-power generator may be associated with a maximum amount of provided power, and may be associated with a power-specific fuel consumption defining a quantity of fuel consumed per quantity of energy provided as a function of provided power. The controller may comprise a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium. Responsive to executing the computer readable program code, the processor may be configured to perform executable operations comprising: determining a discharging equivalent specific fuel consumption for the energy storage device based on the respective power-specific fuel consumptions of the respective one or more electric-power generators, the discharging equivalent specific fuel consumption defining an estimated amount of fuel that will be consumed by recharging the energy storage device as a function of the discharge rate of the energy storage device, preferably the discharging equivalent specific fuel consumption being obtainable by, for each of a plurality of discharge rates, performing the steps of:

a) determining a discharge power associated with the discharge rate in question;
b) selecting a first electric-power generator from the one or more electric-power generators, and;
c) IF the discharge power is smaller than the maximum amount of provided power associated with the selected electric-power generator,
THEN determining the equivalent estimated amount of fuel by determining an amount of fuel consumed by the selected electric-power generator when providing power equal to the maximum provided power of the selected electric-power generator minus the determined discharge power and, optionally, multiplying the determined amount of fuel with a predetermined proportionality factor larger than 0 and smaller than or equal to 1, ELSE updating the discharge power by subtracting the maximum amount of provided power associated with the selected electric-power generator from the previously determined discharge power, selecting a next power generator from the one or more electric-power generators, and repeating step c;

In further embodiments, the executable operations may comprise any of the process steps described above.
In a further aspect, embodiments of this disclosure may relate to a hybrid propulsion system comprising a plurality of power sources and a controller. The plurality of power sources may comprise an energy storage device, preferably a battery. The energy storage device may be associated with a charge rate and/or a discharge rate, and with a state of charge. The plurality of power sources may also comprise one or more electric-power generators electrically coupled to the energy storage device. Each electric-power generator may be associated with a maximum amount of provided power, and may be associated with a power-specific fuel consumption defining a quantity of fuel consumed per quantity of energy provided as a function of provided power. The controller may be a controller for the hybrid propulsion system, as described above.
In a further aspect, embodiments of this disclosure may relate to a vehicle, preferably a vessel, more preferably a marine vessel, comprising a hybrid propulsion system as described above.
In a further aspect, the invention may also relate to a computer program product comprising software code portions configured for, when run in the memory of a computer, executing the method steps according to any of the process steps described above.
As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system". Functions described in this disclosure may be implemented as an algorithm executed by a microprocessor of a computer. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied, e.g., stored, thereon.
Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non- exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fibre, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can comprise, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.
Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fibre, cable, RF, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including a functional or an object oriented programming language such as Java(TM), Scala, C++, Python or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer, server or virtualized server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).
Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor, in particular a microprocessor or central processing unit (CPU), or graphics processing unit (GPU), of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer, other programmable data processing apparatus, or other devices create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.
The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The invention will be further illustrated with reference to the attached drawings, which schematically will show embodiments according to the invention. It will be understood that the invention is not in any way restricted to these specific embodiments.

Brief description of the drawings

Fig. 1 depicts a schematic overview of a hybrid propulsion system according to an embodiment of the invention;
Fig. 2 depicts a graph representing a power-specific fuel consumption;
Fig. 3 depicts a power supply system according to an embodiment of the invention;
Fig. 4 depicts a flow chart of a method for determining a discharging equivalent specific fuel consumption according to an embodiment of the invention;
Fig. 5A and 5B depict an example of a determination of an equivalent power-specific fuel consumption according to an embodiment of the invention;
Fig. 6A-C depict an alternative description of a determination of an equivalent power-specific fuel consumption according to an embodiment of the invention;
Fig. 7 depicts a graph representing equivalent power-specific fuel consumption for charging and discharging an energy storage device;
Fig. 8 depicts an example of an energy optimisation routine according to an embodiment of the invention;
Fig. 9A and 9B depict graphs showing the effect of determining a power distribution according to an embodiment on, respectively, the state of charge of an energy storage device and an amount of consumed fuel; and
Fig. 10 is a block diagram illustrating an exemplary data processing system that may be used for executing methods and software products described in this disclosure.

Detailed description

In this disclosure embodiments are described for determining an charging and/or discharging equivalent power-specific fuel consumption of an energy storage device in a hybrid power system. Based on the equivalent power-specific fuel consumption, an efficient power distribution may be determined.
Fig. 1 depicts a schematic overview of a hybrid propulsion system according to an embodiment of the invention. The hybrid propulsion system 100 comprises a main engine 102, for example an internal combustion engine such as a Diesel engine or gas turbine, connected to a propeller 104 via a shaft 103. The main engine is arranged to power the propeller and may comprise or be connected to a gearbox (not shown). The propeller is preferably a screw propeller and may be a fixed pitch propeller or a variable pitch propeller. Other embodiments may use different propulsion systems, e.g. paddles or pump jets.
An asynchronous motor or induction motor 106 is also coupled to the propeller and typically acts on the shaft 103. The induction motor may be electrically connected to a switchboard 110 via one or more transformers and/or AC/DC converters 108_1-2. The switchboard may further electrically connect an energy storage device 112, e.g. a battery pack, one or more electric-power generators 116_1-2 , e.g. Diesel generators, and other electric loads, e.g. so-called hotel loads 118. Hotel loads may refer to any electrical loads not used for propulsion, e.g. for lighting, climate control, or communication. The energy storage device may be connected to the switchboard via an AC/DC converter 114.
Depending on the configuration, the one or more power generators may be arranged to provide hotel electric power, to charge the energy storage device, and/or to power the induction motor. In some embodiments, there may be no electric-power generators. In such and other embodiments, electric power for charging the energy storage device may (additionally) be provided by e.g. the main engine and absorbed by the induction engine coupled to the same shaft, and/or by absorbing breaking energy. In some embodiments, there may be no main engine, and the propeller may only be powered by the induction motor.
The hybrid propulsion system may comprise further mechanical and/or electrical components for further controlling the propulsion. In some embodiments, the hybrid propulsion system may also comprise one or more additional main engines and/or one or more additional propellers. In some embodiments, each propeller may be powered by a plurality of main engines.
A controller 120 is communicatively connected to one or more elements of the hybrid propulsion system to control one or more aspects of the propulsion system, such as a state, e.g. the rotational speed, of the main engine, the charging or discharging of the energy storage device, a state of the one or more electric-power generators, et cetera.
The controller may comprise a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium. Responsive to executing the computer readable program code, the processor may be configured to perform executable operations for predicting a load and/or determining a power distribution. The power distribution may define how much power one or more components of the power system (e.g. main engine, induction motor, energy storage device and electric-power generators) may provide and/or absorb.
Fig. 2 depicts a graph displaying a power-specific fuel consumption. The power-specific fuel consumption 202 defines the relation between the amount of fuel consumed per amount of energy provided, versus the amount of power (energy per unit time) provided. The depicted graph is typical for a Diesel generator, which has a very low efficiency at low loads, and a maximum efficiency at or close to maximum load, indicated by P _max. For relatively high loads, the change in efficiency for a change in provided power is much smaller than for relatively low loads. The power-specific fuel consumption is sometimes known as the brake-specific fuel consumption.
The power-specific fuel consumption of an engine is typically provided by the manufacturer and may be known, at least approximate, during design of a vehicle. In some cases, a manufacturer may provide a power-specific fuel consumption only for a limited set of delivered power values. Other values may then be obtained by function fitting or other interpolation and/or extrapolation methods. In other cases, the power-specific fuel consumption may have to be obtained in other ways, e.g. by doing measurements.
In the example depicted in Fig. 1 , such a power-specific fuel consumption might be provided or obtained for each of the main engine 102 and the one or more electric-power generators 116_1-2. If only the electric-power generators will be used to charge the energy storage device, it may be sufficient to only be provided or obtain the power-specific fuel consumptions of the electric-power generators.
Fig. 3 depicts a power supply system according to an embodiment of the invention. The power supply system comprises an energy storage device 312, e.g. a battery pack, associated with a maximum charge and a current charge, a maximum charge rate, a maximum discharge rate, and a current charge/discharge rate. For a typically energy storage device, the maximum charge rate is equal in magnitude to the maximum discharge rate. For example, the energy storage device may have a maximum charge of 2000 kWh and have a maximum discharge rate providing a maximum power P _max = 6000 kW.
In some embodiments, the maximum charge/discharge rate may be dependent on the current charge, but typically, the maximum charge/discharge rate is fairly constant over at least a large range of charge values.
The energy storage device may be arranged to be electrically coupled, for instance via a switchboard 310, to one or more electric-power generators 316_1-4. In the depicted example, there are four electric-power generators, but other embodiments may have more or less electric-power generators. It is typical that there is more than one electric-power generator.
Each of the electric-power generators may be associated with a maximum power P _max and an power-specific fuel consumption sfc(P) 322_1-4. In the depicted example, the power generators are all identical, and each electric-power generator is associated with a maximum amount of provided power P _max = 2500 kW, and is associated with an identical power-specific fuel consumption. In other embodiments, different numbers of electric power generators may be used. In some embodiments, some of the electric-power generators may be different from each other.
The one or more electric-power generators and the energy storage device are communicatively coupled to a controller 320. The controller may be configured to control the charge or discharge rate of the energy storage device. The controller may further be configured to control the power provided by each of the one or more electric-power generators. The controller may comprise a memory for storing software for determining an equivalent power-specific fuel consumption according to an embodiment of this disclosure. The memory may also store one or more parameters associated with the electric-power generators, such as the maximum provided power and the power-specific fuel consumption. Alternatively, the controller may be communicatively connected to an external system and may be configured to request such parameters from the external system as needed.
Fig. 4 depicts a flow chart of a method for determining a discharging equivalent specific fuel consumption according to an embodiment of the invention. The method may e.g. be executed by a controller as depicted in Fig. 1 or Fig. 3 for controlling a system comprising an energy storage device and one or more electric-power generators Gen' (i = 1, ..., n; n ≥ 1) electrically coupled to the energy storage device.
In a first step 404, an actual or potential discharge power of the energy storage device (P _dis) is determined, which may be referred to as a computational discharge power P ^c _dis (P ^c _dis = P _dis). The computational discharge power P ^c _dis may be based on a power demand, for example of a hybrid propulsion system, and/or on a discharge rate C _dis of the energy storage device
In a next step 406, a first (i = 1) electric-power generator Gen ⁱ is selected. If all electric-power generators are identical, any selection is mathematically equivalent. In an embodiment with different electric-power generators, the electric-power generator may be selected based on any suitabel selection method, e.g. based on cumulative run time (typically selecting the electric-power generator that has the lowest run time first), based on some quality metric (typically selecting the 'best' electric-power generator first), or even at random.
The maximum delivered power Pⁱ _max associated with the selected electric-power generator is then determined, typically via a look-up. Subsequently, the computational discharge power P ^c _dis is compared 408 with the maximum delivered power of the selected electric-power generator Pⁱ _max. If the computational discharge power P ^c _dis is larger than the maximum delivered power Pⁱ _max associated with the selected electric-power generator (P ^c _dis > Pⁱ _max), then the computational discharge power P ^c _dis is reduced with the maximum delivered power Pⁱ _max: ${P^{c}}_{dis} = {P^{c}}_{dis} - {P^{i}}_{\max}$
that is, a (new or updated) computational discharge power P ^c _dis is determined 410 by subtracting the maximum delivered power Pⁱ _max associated with the selected electric-power generator from the (current) computational discharge power.
If there are any unselected electric-power generators (i < n), then a next (i = i + 1) electric-power generator from the one or more electric-power generators is selected 412. The method then returns to the comparison step 408, comparing the (new) computational discharge power P ^c _dis with the maximum delivered power Pⁱ _max associated with the (newly) selected electric-power generator.
If the computational discharge power P ^c _dis is not larger than the maximum delivered power Pⁱ _max associated with the selected electric-power generator (P ^c _dis ≤ Pⁱ _max), then an (estimated) equivalent amount of fuel sfc_eq(C _dis) is determined 414 by multiplying a predetermined proportionality factor f _prop > 0 and the amount of fuel consumed sfc ⁱ (P) by the selected electric-power generator Gen ⁱ when providing power equal to the maximum provided power of the selected electric-power generator minus the determined discharge power: ${sfc}_{eq} (C_{dis}) = f_{prop} \times {sfc}^{i} ({P^{i}}_{\max} - {P^{c}}_{dis})$
In an embodiment, the proportionality factor may be based on the state of charge of the energy storage device, preferably the proportionality factor being larger if the state of charge of the energy storage device is larger. The proportionality factor is preferably chosen to obey 0 < f _prop ≤ 1. For example, the proportionality factor may be given by: $f_{prop} (SOC) = (1 - α) + α \times SOC$
where 0 ≤ α ≤ 1 and SOC denotes the relative state of charge of the energy storage device where 0 denotes a completely empty energy storage device and 1 denotes a completely charged energy storage device (so 0 ≤ SOC ≤ 1). This way the system is guided to recharge the energy storage device when the state of charge is low, and to discharge the energy storage device when the state of charge is high, and vice versa. Depending on the type of energy storage device, the relation between f _prop and SOC may be further adjusted to prevent the energy storage device from fully discharging and/or from fully charging.
In a typical embodiment, the total maximum delivered power of the electric-power generators together is larger than the maximum discharge power of the energy storage device, such that always i ≤ n. In other embodiments, the maximum discharge power may be larger than the total maximum power deliverable by the electric-power generators. In such embodiments, the equivalent power-specific fuel consumption may be based on a representative measure of the specific power consumption, preferably the median power-specific fuel consumption of the combined electric-power generators.
In an embodiment, the determined equivalent power-specific fuel consumption may be used to select a power source, based on the power-specific fuel consumptions of the one or more electric-power generators and the equivalent power-specific fuel consumption of the energy storage device, typically by minimizing an (equivalent) fuel consumption.
In order to further elucidate the method, Fig. 5A ,B depict an example of a determination of an equivalent power-specific fuel consumption according to an embodiment of the invention. In this example, a hybrid power system comprises at least a first and a second electric-power generator 516_1,2, each being associated with a respective maximum delivered power P ¹ _max = P ² _max = 2500 kW and with a respective power-specific fuel consumption sfc¹(P) 522₁ and sfc²(P) 522₂, as depicted. The hybrid power system further comprises an energy storage device 512 electrically connectable to the first and electric-power generators.
Fig. 5B depicts an enlarged version of the graph representing power-specific fuel consumption sfc²(P) associated with the second electric-power generator. According to the example, an equivalent power-specific fuel consumption for the energy storage device providing a power of P _dis = 4000 kW is to be determined. Thus, the initial computational discharge power is P ^c _dis = 4000 kW. The first electric-power generator is selected and the computational discharge power is compared to the maximum delivered power P ¹ _max associated with the first electric-power generator 516₁: $4000 kW > 2500 kW \to {P^{c}}_{dis} > {P^{1}}_{\max}$
As the computational discharge power is larger than the maximum delivered power P ¹ _max, the maximum delivered power P ¹ _max is subtracted from the computational discharge power P ^c _dis: ${P^{c}}_{dis} = {P^{c}}_{dis} - {P^{1}}_{\max} = 4000 kW - 2500 kW = 1500 kW$
Subsequently, the second electric-power generator is selected and the (newly determined) computational discharge power P ^c _dis is compared to the maximum delivered power P ² _max associated with the second electric-power generator 516₂: $1500 kW < 2500 kW \to {P^{c}}_{dis} < {P^{2}}_{\max}$
Therefore, the computational discharge power P ^c _dis is subtracted from the maximum delivered power P ² _max: ${P^{2}}_{\max} - {P^{c}}_{dis} = 2500 kW - 1500 kW = 1000 kW$
and the power-specific fuel consumption sfc²(P) associated with the second electric-power generator is obtained for the determined value and, optionally, multiplied with a proportionality constant f _prop to yield the desired equivalent power-specific fuel consumption: ${sfc}_{eq} (4000 kW) = f_{prop} \times {sfc}^{2} (1000 kW)$
The equivalent specific fuel consumption may be determined for a single point, e.g. a single discharge rate or single provided power amount, as in the previous example. A graph of the equivalent specific fuel consumption may be determined by evaluating the equivalent specific fuel consumption for a plurality, preferably a large number, of values for the discharge rate or amount of provided power.
Fig. 6A-C depict an alternative, equivalent description of the same computation as detailed above with reference to Fig. 5A ,B. Fig. 6A depicts a graph 602 representing a power-specific fuel sfc¹(P) associated with a first electric-power generator.
Fig. 6B depicts a 'reversed' graph 604, which is determined based on the graph representing sfc¹(P). The reversed graph may be obtained by 'mirroring' the original graph around P = ½ P ¹ _max. For P ≤ P ¹ _max, the equivalent fuel consumption may be proportional to the reversed power-specific fuel consumption of the first electric-power generator. This is mathematically equivalent to determining: ${sfc}_{eq} (P) \propto {sfc}_{reversed}^{1} (P) = {sfc}^{1} (P_{\max}^{} - P) .$
Here P ¹ _max denotes the maximum provided power associated with the first electric-power generator and P is a variable denoting provided power. Thus, the discharge equivalent power-specific fuel consumption is relatively low if the power delivered by the energy storage device is low, and increases as the delivered power approaches the maximum delivered power of the first electric-power generator.
As a consequence, battery discharging is seen by the optimization routine as inefficient around areas where the electric-power generators are efficient, and vice versa. This is advantageous, since any power supplied by the battery will reduce the load of the electric-power generators, essentially pushing them towards areas of less efficient operation. Instead, the equivalent power-specific fuel consumption is preferably defined such that the electric-power generators are operated at more efficient operating points, by either shutting down the batteries, or by recharging them if possible.
Fig. 6C depicts a 'concatenated' graph. The power-specific fuel consumptions for the other power generators are similarly reversed, and based on the reversed graphs a 'concatenated' graph 606 is determined. In this disclosure, concatenation of graphs or functions means that for two functions with a bounded domain, the second function is shifted such that a minimum value of the domain of the second function coincides with the maximum value of the first function. Thus, for a delivered power slightly larger than the maximum delivered power of a first electric-power generator, the equivalent power-specific fuel consumption is proportional to the power-specific fuel consumption of the second electric-power generator.
It may be noted that the order of reversing and concatenating is not important and provides the same result. However, the (reversed) concatenated power-specific fuel consumption of the first and second electric-power generators is different from the (reversed) combined power-specific fuel consumption of the first and second electric-power generators, that is, the amount of fuel consumed by the first and second electric-power generators together when together providing a certain power. For example, the combined power-specific fuel consumption of two identical electric-power generators providing more than the maximum power of a single electric-power generator is, in principle, twice the power-specific fuel consumption of a single electric-power generator providing half the power: $({sfc}^{1, 2}_{combined} (P) = {sfc}^{1} (P / 2) + {sfc}^{2} (P / 2) = 2 sfc (P / 2), {for P}_{\max} \leq P < 2 P_{\max}) .$
However, in the same situation, the concatenated power-specific fuel consumption is equal to the power-specific fuel consumption of the amount of power provided more than the maximum power of a single electric-power generator: $({sfc}^{1, 2}_{concatenated} (P) = {sfc}^{2} (P - P_{\max}), {for P}_{\max} \leq P < 2 P_{\max}) .$
The discharge equivalent power-specific fuel consumption may then be obtained by multiplying the concatenated mirrored power-specific fuel consumption with an optional proportionality factor f _prop, and may be described by: ${sfc}_{eq} (P) = f_{prop} \times {sfc}^{j} (\sum_{i = 1}^{j} P_{\max}^{i} - P)$
where j is determined such that: $\sum_{i = 1}^{j - 1} P_{\max}^{i} \leq P < \sum_{i = 1}^{j} P_{\max}^{i}$
So, in the example depicted in Fig. 5A ,B and 6A-C, for P = 4000 kW, one may find j = 2, as P ¹ _max = 2500, P ¹ _max + P ² _max = 2500 + 2500 = 5000 kW, and 2500 kW ≤ 4000 kW < 5000 kW, and therefore P ¹ _max ≤ P < P ¹ _max + P ² _max. The value may also be obtained directly by reading from the concatenated graph 606.
Fig. 6D depicts a graph 612 of an equivalent power-specific fuel consumption of a hybrid power system comprising two identical electric-power generators, each capable of providing up to 2500 kW of electric power. In this example, the discharge power of the energy storage may be larger than the total maximum power provided by the electric-power generators. A first part 614₁ of the graph represents a reversed power-specific fuel consumption of a first electric-power generator, and a second part 614₂ of the graph represents a reversed power-specific fuel consumption of a second electric-power generator. A third part 614₃ of the graph represents a statistically representative quantity of the power-specific fuel consumptions of the first and second electric-power generators, in this case the median.
In some embodiments, the discharge power of the energy storage may be larger than the total maximum power provided by the electric-power generators. In such embodiments, for a delivered power larger than the total maximum power, the equivalent power-specific fuel consumption may be based on a statistically representative quantity of the power-specific fuel consumptions of the electric-power generators, preferably based on a median value of the power-specific fuel consumptions. Thus, the equivalent power-specific fuel consumption may be given by: ${sfc}_{eq} (P) = f_{prop} \times med (sfc) (^{1 - n} (P)), for P > \sum_{i = 1}^{n} P_{\max}^{i}$
where med(.) denotes the median. In other embodiments, other quantities may be used, such as the average power-specific fuel consumption.
If the electric-power generators are identical, the median power-specific fuel consumption may be equal to the power-specific fuel consumption corresponding to a delivered power of half the maximum delivered power of one of the electric-power generators: $med (sfc) (^{1 - n} (P)) = {sfc}^{1} (P_{\max} / 2) .$
If the electric-power generators are identical, the selection which electric-power generator is the first and which one is the second, et cetera, has no effect on the determined equivalent power-specific fuel consumption. In other embodiments, however, the electric-power generators may be non-identical. In such embodiments, the order in which the electric-power generators are selected may be determined in various ways. For example, the electric-power generators may be selected in increasing order of running hours, the generators with the fewest running hours being selected first. This reflects the fact that it may be advantageous to balance use among all electric-power generators. The selection may also depend on further factors, e.g. an operation mode of a vessel which may have a 'travel mode' and a 'work mode', and which may affect which electric-power generators are predominantly used.
Fig. 7 depicts an equivalent power-specific fuel consumption for charging and discharging an energy storage device. In an embodiment, an equivalent power-specific fuel consumption may be determined for charging an energy storage device. The charging equivalent power-specific fuel consumption may be determined by determining the amount of fuel consumed according to the discharging equivalent specific fuel consumption at a discharging rate that is equal to a given charging rate. In other words: ${sfc}_{eq, charge} (P_{charge}) = {sfc}_{eq, discharge} (P_{discharge}) {for P}_{charge} = P_{discharge}$
where P _charge is the amount of power used to charge the energy storage device and P _discharge is the amount of power provided by discharging the energy storage device; or, alternatively: ${sfc}_{eq} (P) = {sfc}_{eq} (- P)$
where a power P > 0 denotes discharging the energy storage device and P < 0 denotes charging the energy storage device.
In principle, it is not necessary to determine a discharge equivalent power-specific fuel consumption in order to determine a charge equivalent power-specific fuel consumption. The charge equivalent power-specific fuel consumption may, for example, also be obtained by shifting a concatenated power-specific fuel consumption over the combined maximum provided power of all electric-power generators: ${sfc}_{shifted}^{1 - n} (P) = {sfc}_{concatenated}^{1 - n} (P + \sum_{i = 1}^{n} P_{\max}^{i})$
where n is the number of electric power generators and P < 0 denotes charging the energy storage device. The charge equivalent power-specific fuel consumption may then be obtained multiplying with the optional proportionality factor f _prop, and may be described by: ${sfc}_{eq} (P) = f_{prop} \times {sfc}^{j} (\sum_{i = 1}^{j} P_{\max}^{i} + P)$
where j is determined such that: $\sum_{i = 1}^{j - 1} P_{\max}^{i} \leq - P < \sum_{i = 1}^{j} P_{\max}^{i}$
Fig. 8 depicts an example of an energy optimisation routine according to an embodiment of the invention. An energy optimisation routine typically receives operator input data 802, such as parameters are set by a controller, e.g. a desired shaft speed n _set. The energy optimisation routine may further receive system input data 804, such as dynamically determined parameters representing a state of the power system, e.g. a state of charge of the energy storage device and an amount of electric power required by the hotel. These parameters may affect the desired output of the hybrid power system.
The energy optimisation routine may further have access to a data storage 806 comprising parameters and/or functions describing the hybrid power system, such as the number and types of engines, the power-specific fuel consumptions of the one or more main engines sfc ⁱ _ME(P, n) and the electric-power generators sfc ^j _DG(P), and the efficiency of the induction motor as a function of power and/or rotational speed. The data storage may further comprise a precomputed function or look-up table defining an equivalent power-specific fuel consumption of the energy storage device according to an embodiment of this enclosure, e.g. as described above with reference to Fig. 2-6 . Alternatively, the data storage may comprise the elements needed to construct an equivalent power-specific fuel consumption, e.g. the power-specific fuel consumptions of the electric-power generators, an optional proportionality factor, and relations defining equivalent power-specific fuel consumption of the energy storage device according to an embodiment of this enclosure, e.g. as described above with reference to Fig. 2-6 , allowing the equivalent power-specific fuel consumption to be constructed during runtime.
In some embodiments, the operator input data and/or the system input data may be pre-processed 808 by a pre-processor, which may provide derived input data 810 as output. For example, in a vessel with an adaptive pitch propeller, the pre-processor may determine a new propeller pitch which may affect the relation between required power and shaft speed, and thus the efficiency of the main engine. In some embodiments, the pre-processor may also determine a predicted power demand P _pred.
Based on the operator input data and/or the system input data and, optionally, the derived input data, as well as, optionally, on parameters or functions from the data storage, the optimiser may determine 812 one or more boundary conditions or constraints, limiting the solution space to ensure viable solutions and, preferably, decrease the computational burden. For example, the solutions may be limited such that the power provided by the main engine(s) and electric-power generator(s) does not exceed their respective maximum provided power. Thus, constraints may be used to prevent overloading, to ensure sufficient electric power for the hotel at a predetermined voltage and frequency, et cetera.
Based on the operator input data and/or the system input data and, optionally, the derived input data, as well as, optionally, on parameters or functions from the data storage, the optimiser may determine 814 a target function may be determined. Typically, the object of the optimiser is to minimise the (equivalent) fuel consumption of the hybrid power system while providing the desired power to satisfy the hotel needs and set shaft speed. In an embodiment, the object function may be formulated as: $\min ({\dot{m}}_{f} (t)) = \min (\sum_{i = 1}^{N_{ME}} {\dot{m}}_{f, {ME}_{i}} (t) + \sum_{j = 1}^{N_{DG}} {\dot{m}}_{f, {DG}_{j}} (t) + {\dot{m}}_{f, {BAT}_{j}} (t))$
where ṁ_f (t) is the total (equivalent) fuel consumption rate of the hybrid power system, which in a typical system is equal to the sum of fuel consumption rates of the main engines and the electric-power generators and the equivalent fuel consumption rate of the energy storage device. Here, ṁ_f,MEi (t) is the fuel consumption rate of the i ^th of the N_ME main engines, ṁ_f,DCj (t) is the fuel consumption rate of the j ^th of the N_DG electric-power generators, and ṁ _f,BAT(t) is the equivalent fuel consumption rate of the energy storage device, based on the equivalent power-specific fuel consumption defined above. In general, the fuel consumption rate is proportional to the delivered power multiplied with the power-specific fuel consumption. In the example depicted in Fig. 1 , N_ME = 1 and N_DG = 2. In other embodiments, there may be a plurality of energy storage devices, in which case the last term in equation (21) would be a summation over all such devices.
An optimisation algorithm may then optimise 816, for example minimise, the target function subject to the determined boundary conditions. In general, the optimiser may use any non-convex optimiser, for example an optimiser based on the Mesh Adaptive Direct Search algorithm. The Mesh Adaptive Direct Search algorithm is described in more detail in C. Audet & J. Dennis, 'Mesh adaptive direct search algorithms for constrained optimization', SIAM Journal on Optimization (2006) 188-217.
Based on the output of the optimiser, one or more power distributions 818 may be determined, for instance a propulsive power distribution defining a power split between the main engine(s) and the induction engine(s), and/or an electric power distribution defining a power split between the energy storage device and the electric-power generator(s). One or more power sources may then be selected based on at least one of the power distributions.
As was explained above, the (long-term) optimal power distribution can only be determined with hindsight, as it depends on future events. A common way in the art to determine the quality of an optimisation routine is to determine one or more sample trajectories and determine the optimal (typically, minimal) fuel consumption taking the entire trajectory into account. This may be achieved using a method named Dynamic Programming. Actual optimisation routines may have knowledge of current conditions and of past conditions, but lack knowledge of future power demands. The quality of a routine may then be determined by comparing the fuel consumption according to the routine to the optimal fuel consumption according to dynamic programming. Similarly, other quantities such as state of charge of the energy storage device may be plotted.
Fig. 9A depicts a graph comparing the state of charge of an energy storage device as determined according to an embodiment of this disclosure with dynamic programming and with a rules-based method according to the state of the art. The example is based on an actual power demand of a maritime vessel. The solid line 902 represents the state of charge according to an energy optimisation method implementing an equivalent power-specific fuel consumption for the energy storage device, as discussed above (Equivalent Consumption Minimisation Strategy, ECMS). The dotted line 904 represents the dynamic programming (optimal) solution, and the dashed 906 line represents the state-of-the-art rules-based solution. It can be clearly seen that the ECMS solution is much more similar to the optimal dynamic programming solution than the rules-based method, generally deciding to charge and discharge the energy storage device during the same parts of the trajectory as the dynamic programming solution, but often at a slightly more conservative rate.
Fig. 9B depicts the corresponding cumulative fuel consumption. Again, the solid line 912 represents the solution according to an embodiment of this disclosure (referred to as ECMS), the dotted line 914 represents the (optimal) dynamic programming solution, and the dashed 916 line represents the state-of-the-art rules-based solution. Although the amount of fuel saving of the EMCS method relative to the rules-based method varies over the trajectory, the ECMS method is generally more fuel-efficient than the rules-based method. Compared to the state-of-the-art solution, the ECMS method overall achieves an almost 5% reduction in fuel consumption.
Table 1 compares the amount of consumed fuel, the fuel savings, and the state of charge at the end of the simulated trajectory. Table 1. Comparison of the amount of consumed fuel, fuel savings, and final state of charge over a simulated trajectory

Dynamic Programming ECMS Rules-based

Fuel [kg] 1085 1163 1223

Fuel savings [%] 11,31% 4,91% 0 % (baseline)

Final SOC 0,2 0,36 0,75
Fig. 10 is a block diagram illustrating an exemplary data processing system that may be used in as described in this disclosure. Data processing system 1000 may include at least one processor 1002 coupled to memory elements 1004 through a system bus 1006. As such, the data processing system may store program code within memory elements 1004. Further, processor 1002 may execute the program code accessed from memory elements 1004 via system bus 1006. In one aspect, data processing system may be implemented as a computer that is suitable for storing and/or executing program code. It should be appreciated, however, that data processing system 1000 may be implemented in the form of any system including a processor and memory that is capable of performing the functions described within this specification.
Memory elements 1004 may include one or more physical memory devices such as, for example, local memory 1008 and one or more bulk storage devices 1010. Local memory may refer to random access memory or other non-persistent memory device(s) generally used during actual execution of the program code. A bulk storage device may be implemented as a hard drive or other persistent data storage device. The processing system 1000 may also include one or more cache memories (not shown) that provide temporary storage of at least some program code in order to reduce the number of times program code must be retrieved from bulk storage device 1010 during execution.
Input/output (I/O) devices depicted as input device 1012 and output device 1014 optionally can be coupled to the data processing system. Examples of input device may include, but are not limited to, for example, a keyboard, a pointing device such as a mouse, or the like. Examples of output device may include, but are not limited to, for example, a monitor or display, speakers, or the like. Input device and/or output device may be coupled to data processing system either directly or through intervening I/O controllers. A network adapter 1016 may also be coupled to data processing system to enable it to become coupled to other systems, computer systems, remote network devices, and/or remote storage devices through intervening private or public networks. The network adapter may comprise a data receiver for receiving data that is transmitted by said systems, devices and/or networks to said data and a data transmitter for transmitting data to said systems, devices and/or networks. Modems, cable modems, and Ethernet cards are examples of different types of network adapter that may be used with data processing system 1000.
As pictured in Fig. 10 , memory elements 1004 may store an application 1018. It should be appreciated that data processing system 1000 may further execute an operating system (not shown) that can facilitate execution of the application. Application, being implemented in the form of executable program code, can be executed by data processing system 1000, e.g., by processor 1002. Responsive to executing application, data processing system may be configured to perform one or more operations to be described herein in further detail.
In one aspect, for example, data processing system 1000 may represent a client data processing system. In that case, application 1018 may represent a client application that, when executed, configures data processing system 1000 to perform the various functions described herein with reference to a "client". Examples of a client can include, but are not limited to, a personal computer, a portable computer, a mobile phone, or the like.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.

Claims

A method for determining a power distribution for a plurality of power sources of a hybrid power system, the plurality of power sources comprising:
an energy storage device, preferably a battery, the energy storage device being associated with a charge rate and/or a discharge rate, and with a state of charge; and

one or more electric-power generators electrically coupled to the energy storage device, each electric-power generator being associated with a maximum amount of provided power, and associated with a power-specific fuel consumption defining a quantity of fuel consumed per quantity of energy provided as a function of provided power,

the method comprising:
determining a discharging equivalent specific fuel consumption for the energy storage device based on the respective power-specific fuel consumptions of the respective one or more electric-power generators, the discharging equivalent specific fuel consumption defining an estimated amount of fuel that will be consumed by recharging the energy storage device as a function of the discharge rate of the energy storage device, preferably the discharging equivalent specific fuel consumption being obtainable by performing, for each of a plurality of discharge rates, the steps of:
a) determining a discharge power associated with the discharge rate in question;

b) selecting a first electric-power generator from the one or more electric-power generators, and;

c) IF the discharge power is smaller than the maximum amount of provided power associated with the selected electric-power generator,
THEN determining the equivalent estimated amount of fuel by determining an amount of fuel consumed by the selected electric-power generator when providing power equal to the maximum provided power of the selected electric-power generator minus the determined discharge power and, optionally, multiplying the determined amount of fuel with a predetermined proportionality factor larger than 0 and smaller than or equal to 1, to obtain the discharging equivalent specific fuel consumption;
ELSE updating the discharge power by subtracting the maximum amount of provided power associated with the selected electric-power generator from the previously determined discharge power, selecting a next power generator from the one or more electric-power generators, and repeating step c;

and/or the method comprising determining a charging equivalent specific fuel consumption obtainable by determining the amount of fuel consumed according to the discharging equivalent specific fuel consumption at a discharge rate that is equal to a given charge rate; and

determining a power distribution based on at least the discharging equivalent fuel consumption and/or the charging equivalent fuel consumption.
The method as claimed in claim 1, wherein the proportionality factor is based on the state of charge of the energy storage device, preferably the proportionality being proportional to the state of charge.
The method as claimed in claim 1 or 2, further comprising controlling at least one power source to deliver power based on the determined power distribution.
The method as claimed in claim 3, wherein selecting a power source comprises:
determining a minimum equivalent fuel consumption based on at least the respective power-specific fuel consumptions of the one or more electric-power generators, and the discharging equivalent fuel consumption and/or the charging equivalent fuel consumption; and

selecting the power source or combination of power sources associated with the minimum equivalent fuel consumption.
The method as claimed in claim 4, wherein the minimum equivalent fuel consumption is determined using a non-convex optimisation algorithm, preferably a Mesh Adaptive Direct Search algorithm.
The method as claimed in claim 4 or 5,
wherein the hybrid power system further comprises one or more main engines, preferably combustion engines, for providing mechanical power at a rotational speed, each of the one or more combustion engines being associated with a power-specific fuel consumption; and
wherein determining a minimum equivalent fuel consumption is further based on the respective power-specific fuel consumptions associated with the one or more main engines, and, optionally, on the respective rotational speeds of the one or more main engines.
A controller for controlling a plurality of power sources of a hybrid power system, the plurality of power sources comprising:
an energy storage device, preferably a battery, the energy storage device being associated with a charge rate and/or a discharge rate, and with a state of charge; and

one or more electric-power generators electrically coupled to the energy storage device, each electric-power generator being associated with a maximum amount of provided power, and associated with a power-specific fuel consumption defining a quantity of fuel consumed per quantity of energy provided as a function of provided power;

the controller comprising a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium, wherein, responsive to executing the computer readable program code, the processor may be configured to perform executable operations comprising:
determining a discharging equivalent specific fuel consumption for the energy storage device based on the respective power-specific fuel consumptions of the respective one or more electric-power generators, the discharging equivalent specific fuel consumption defining an estimated amount of fuel that will be consumed by recharging the energy storage device as a function of the discharge rate of the energy storage device, preferably the discharging equivalent specific fuel consumption being obtainable by, for each of a plurality of discharge rates, performing the steps of:
a) determining a discharge power associated with the discharge rate in question;

b) selecting a first electric-power generator from the one or more electric-power generators, and;

c) IF the discharge power is smaller than the maximum amount of provided power associated with the selected electric-power generator,
THEN determining the equivalent estimated amount of fuel by determining an amount of fuel consumed by the selected electric-power generator when providing power equal to the maximum provided power of the selected electric-power generator minus the determined discharge power and, optionally, multiplying the determined amount of fuel with a predetermined proportionality factor larger than 0 and smaller than or equal to 1,
ELSE updating the discharge power by subtracting the maximum amount of provided power associated with the selected electric-power generator from the previously determined discharge power, selecting a next power generator from the one or more electric-power generators, and repeating step c;

and/or determining a charging equivalent specific fuel consumption by determining the amount of fuel consumed according to the discharging equivalent specific fuel consumption at a discharge rate that is equal to a given charge rate; and

determining a power distribution based on at least the discharging equivalent fuel consumption and/or the charging equivalent fuel consumption.
A hybrid propulsion system comprising a plurality of power sources and a controller, the plurality of power sources comprising:
an energy storage device, preferably a battery, the energy storage device being associated with a charge rate and/or a discharge rate, and with a state of charge; and

one or more electric-power generators electrically coupled to the energy storage device, each electric-power generator being associated with a maximum amount of provided power, and associated with a power-specific fuel consumption defining a quantity of fuel consumed per quantity of energy provided as a function of provided power;

the controller comprising a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium, wherein, responsive to executing the computer readable program code, the processor may be configured to perform executable operations comprising:
determining a discharging equivalent specific fuel consumption for the energy storage device based on the respective power-specific fuel consumptions of the respective one or more electric-power generators, the discharging equivalent specific fuel consumption defining an estimated amount of fuel that will be consumed by recharging the energy storage device as a function of the discharge rate of the energy storage device, preferably the discharging equivalent specific fuel consumption being obtainable by, for each of a plurality of discharge rates, performing the steps of:
a) determining a discharge power associated with the discharge rate in question;

b) selecting a first electric-power generator from the one or more electric-power generators, and;

c) IF the discharge power is smaller than the maximum amount of provided power associated with the selected electric-power generator,
THEN determining the equivalent estimated amount of fuel by determining an amount of fuel consumed by the selected electric-power generator when providing power equal to the maximum provided power of the selected electric-power generator minus the determined discharge power and, optionally, multiplying the determined amount of fuel with a predetermined proportionality factor larger than 0 and smaller than or equal to 1,
ELSE updating the discharge power by subtracting the maximum amount of provided power associated with the selected electric-power generator from the previously determined discharge power, selecting a next power generator from the one or more electric-power generators, and repeating step c;

and/or determining a charging equivalent specific fuel consumption by determining the amount of fuel consumed according to the discharging equivalent specific fuel consumption at a discharge rate that is equal to a given charge rate; and

determining a power distribution based on at least the discharging equivalent fuel consumption and/or the charging equivalent fuel consumption.
A vehicle, preferably a vessel, more preferably a marine vessel, comprising a hybrid propulsion system as claimed in claim 8.
Computer program product comprising software code portions configured for, when run in the memory of a computer, executing the method steps according to any of the claims 1-6.