WO2011075080A1

WO2011075080A1 - Method and system for estimating the lifetime of a battery of an energy backup system of a wind turbine

Info

Publication number: WO2011075080A1
Application number: PCT/SG2010/000458
Authority: WO
Inventors: Tie Ling Zhang; Kim Hui Too; Abdullah Zain
Original assignee: Vestas Wind Systems A/S
Priority date: 2009-12-17
Filing date: 2010-12-08
Publication date: 2011-06-23

Abstract

A method (300, 1600) and a system (400, 500, 600) for estimating the lifetime of a battery of an energy backup system (200) of a wind turbine (100) are provided. The method includes determining battery information characterizing a current battery state or at least one battery state of the past (302), and estimating the lifetime of the battery in dependence on the determined battery information (304).

Description

METHOD AND SYSTEM FOR ESTIMATING THE LIFETIME OF A BATTERY OF AN ENERGY BACKUP SYSTEM OF A WIND TURBINE

TECHNICAL FIELD

[0001] The present invention relates generally to a method and a system for estimating the lifetime of a battery of an energy backup system of a wind turbine.

BACKGROUND

[0002] Energy backup systems of wind turbines generally comprise a battery for providing power to the wind turbine if the normal energy supply of the wind turbine fails. In such a case, the power of the battery may for example be supplied to a wind turbine controller to complete all the commands and actions, e.g. commands and actions needed when the wind turbine is in a shutdown process due to safety or grid drop or other imminent issues in order to safely stop the wind turbine.

[0003] Battery failures of energy backup systems are one of the major factors that cause wind turbine failures and may result in a lot of unscheduled turbine maintenance services. Therefore, if the remaining lifetime of a battery can be accurately calculated or predicted, the battery can be replaced by a scheduled maintenance service before it fails. Thus, unscheduled maintenance services can be reduced.

[0004] Hence, it is desirable to estimate the lifetime of the batteries of the energy backup system of wind turbines. SUMMARY

[0005] According to one embodiment of the present invention, a method of estimating the lifetime of a battery of an energy backup system of a wind turbine is provided. The method includes determining battery information characterizing a current battery state or at least one battery state of the past, and estimating the lifetime of the battery in dependence on the determined battery information.

[0006] According to one embodiment of the present invention, the battery information includes predetermined battery parameter values of a battery parameter.

[0007] According to one embodiment of the present invention, the battery information includes current battery parameter values or battery parameter values which have been tracked during the operation of the energy backup system.

[0008] According to one embodiment of the present invention, the battery information includes predetermined relations between different battery parameters.

[0009] According to one embodiment of the present invention, the battery information includes information on the current temperature value of the battery or information on at least one tracked temperature value of the battery or information on at least one predetermined temperature value.

[0010] According to one embodiment of the present invention, the battery information includes information on the charging or discharging method.

[0011] According to one embodiment of the present invention, the battery information includes information on the current discharging depth value of the battery or information on at least one tracked discharging depth value of the battery or information on at least one predetermined discharging depth value.

[0012] According to one embodiment of the present invention, the battery information includes information on the current charging or discharging current value of the battery or information on at least one tracked charging or discharging current value of the battery or information on at least one predetermined charging or discharging current value.

[0013] According to one embodiment of the present invention, the battery information includes information on the current charging or discharging voltage value of the battery or information on at least one tracked charging or discharging voltage value of the battery or information on at least one predetermined charging or discharging voltage value.

[0014] According to one embodiment of the present invention, the battery information includes information on the current charging or discharging speed value of the battery or information on at least one tracked charging or discharging speed value of the battery or information on at least one predetermined charging or discharging speed value.

[0015] According to one embodiment of the present invention, the battery information includes information on the number of charging or discharging cycles of the battery carried out in the past.

[0016] According to one embodiment of the present invention, the battery information includes information on the period between discharging and charging of the battery. [0017] According to one embodiment of the present invention, the method further includes tracking battery parameter values of a battery parameter during operation of the battery, preparing a histogram of the tracked battery parameter values, wherein the histogram comprises a relation between a plurality of battery parameter values and battery operating hours in which, to each battery parameter value, a number of battery operating hours is assigned, converting, for each battery parameter value, the operating hours assigned to the battery parameter value into equivalent battery operating hours referring to a reference parameter value, wherein the converting process is carried out based on a predetermined relation between the battery parameter and the maximum battery operating time, summing up the equivalent battery operating hours to obtain a total equivalent operating time, and subtracting the total equivalent battery operating time from a maximum battery operating time obtained from the predetermined relation, thereby obtaining the remaining estimated battery operating hours.

[0018] According to one embodiment of the present invention, the predetermined relation is a linear relation when viewed on a logarithmic scale.

[0019] According to one embodiment of the present invention, for a given period of time of wind turbine operation, the equivalent operating hours assigned to a particular battery parameter value are calculated using the following formula:

L_ref + (x - ref)k) wherein x indicates different battery parameter values, At_x is the number of operating hours assigned to the battery parameter value x, ref is the battery parameter reference value, Lre is Log[battery lifetime if battery parameter is kept at parameter reference value ref], and k is the gradient of the linear relation. [0020] According to one embodiment of the present invention, the battery parameter is the battery temperature.

[0021] According to one embodiment of the present invention, summing up the equivalent battery operating hours to obtain the total equivalent battery operating time is carried out using the following formula:

wherein index x denotes the different possible temperature values, At_x is the number of operating hours assigned to the battery temperature value x, a is a lower limit of the battery operating temperature and b is an upper limit of the battery operating temperature.

[0022] According to one embodiment of the present invention, the method further includes tracking battery parameter values of a battery parameter during operation of the battery, preparing a histogram of the tracked battery parameter values, wherein the histogram comprises a relation between a plurality of battery parameter values and battery operating hours in which, to each battery parameter value, a number of battery operating hours is assigned, determining a weighted average battery parameter value based on the histogram, and determining an estimated lifetime of the battery based on the weighted average battery parameter value using a predetermined relation between the battery parameter and the lifetime of the battery.

[0023] According to one embodiment of the present invention, the determination of the weighted average battery parameter value is carried out using the following formula: '

wherein index / denotes the different possible battery parameter values, δ, denotes the battery operating hours at battery parameter value , a is a lower limit of possible battery parameter values and b is an upper limit of possible battery parameter values.

[0024] According to one embodiment of the present invention, the method further includes modelling an internal resistance of the battery, simulating a discharge process of the battery based on the modelled resistance, carrying out a discharge process of the battery, comparing the simulated discharge process with the discharge process carried out, and estimating the remaining lifetime of the battery based on a result of the comparison.

[0025] According to one embodiment of the present invention, the internal resistance is modelled as a function of battery temperature, battery discharge current level, state of discharge of the battery, and aging factor of the battery.

[0026] According to one embodiment of the present invention, the modelled internal resistance is the sum of a first resistance, a second resistance and a third resistance, and wherein the first resistance is a function of battery temperature, battery discharge current level and battery lifetime, wherein the second resistance is a function of state of discharge of the battery and battery temperature, and wherein the third resistance is a function of battery aging.

[0027] According to one embodiment of the present invention, determining the first resistance includes a) setting a battery discharge parameter to a first discharge parameter value, b) discharging the battery, c) determining the voltage drop at the beginning of the discharge process, d) determining a change of the first resistance reflected by the voltage drop, e) setting the battery discharge parameter to a second discharge parameter value being different from the first discharge parameter value, f) repeating steps a) to e) at least one time, g) carrying out steps a) to f) for each battery discharge parameter, h) determining the dependencies of the first resistance on each battery discharge parameter based on the determined changes of the first resistance, and i) determining the first resistance as a function of the determined dependencies on the battery discharge parameters based on the determined dependencies using a mathematical approximation method.

[0028] According to one embodiment of the present invention, the battery discharge parameters are battery temperature and battery discharge current level.

[0029] According to one embodiment of the present invention, determining the second resistance includes a) setting the battery temperature to a first temperature value, b) discharging the battery at the first temperature value, thereby obtaining a discharge curve indicating the relation between the battery voltage and the state of discharge, c) for each of several states of discharge values, determining the corresponding voltage drop between the discharge curve and a reference discharge curve, d) determining a change of the second resistance reflected by the voltage drop for each of the state of discharge values, e) determining the second resistance as a function of the temperature and the state of discharge based on the determined voltage drops using a mathematical approximation method, f) setting the battery temperature to a second temperature value being different from the first temperature value, and g) repeating steps b) to f).

[0030] According to one embodiment of the present invention, the discharge processes for determining the second resistance are carried out using a constant discharge current level. [0031] According to one embodiment of the present invention, determining the third resistance includes carrying out steps a) to i) for determining the first resistance and steps a) to g) for determining the second resistance respectively several times at different battery ages.

[0032] According to one embodiment of the present invention, a lifetime estimation system for estimating the lifetime of a battery of a wind turbine energy backup system is provided. The lifetime estimation system includes a battery information determining unit being adapted to determine battery information characterizing a current battery state or at least one battery state of the past, and an estimation unit being coupled to the battery information determining unit, the estimation unit being adapted to estimate the lifetime of the battery in dependence on the determined battery information.

[0033] According to one embodiment of the present invention, the lifetime estimation system further includes at least one database unit being coupled to the battery information determining unit for storing battery information determined by the battery information determining unit.

[0034] According to one embodiment of the present invention, the lifetime estimation system further includes a battery information tracking unit being coupled to the battery and to the battery information determining unit and being adapted to track battery parameter values of the battery during the operation of the energy backup system. The battery information tracking unit is further adapted to supply the tracked battery parameter values to the battery information determining unit.

[0035] According to one embodiment of the present invention, the lifetime estimation system further includes an input unit coupled to the battery information determining unit through which fixed battery parameter values provided by the battery supplier can be fed into the battery information determining unit.

[0036] According to one embodiment of the present invention, the battery information includes information regarding current battery temperature, current battery discharging depth, current battery charging or discharging voltage, current battery charging or discharging current, current battery charging or discharging cycles, current battery charging or discharging speed, the number of battery charging or discharging cycles, or at least one tracked value of at least one of the above battery parameters, or at least one fixed predetermined value of at least one of the above battery parameters.

[0037] According to one embodiment of the present invention, the lifetime estimation system is implemented as an online tool or a standalone tool.

[0038] According to one embodiment of the present invention, the lifetime estimation system further includes an output unit being coupled to the estimation unit and being adapted to output a lifetime distribution graph of a plurality of batteries.

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In the drawings, like reference characters generally refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the following description, various embodiments of the invention are described with reference to the following drawings, in which:

[0040] Figure 1 illustrates a common setup of a conventional wind turbine. [0041] Figures 2a and 2b show possible locations of batteries of an energy backup system of the wind turbine.

[0042] Figure 3 shows a flowchart of a process of estimating the lifetime of a battery of an energy backup system of a wind turbine according to one embodiment of the present invention.

[0043] Figure 4 shows a schematic diagram of a lifetime estimation system for estimating the lifetime of a battery of a wind turbine energy backup system according to one embodiment of the present invention.

[0044] Figure 5 shows a schematic diagram of another lifetime estimation system for estimating the lifetime of a battery of a wind turbine energy backup system according to one embodiment of the present invention.

[0045] Figure 6 shows a schematic diagram of still another lifetime estimation system for estimating the lifetime of a battery of a wind turbine energy backup system according to one embodiment of the present invention.

[0046] Figure 7 shows an exemplary user interface of a lifetime estimation system according to one embodiment of the present invention.

[0047] Figure 8 shows the exemplary user interface of Figure 7 in an extended interface mode according to one embodiment of the present invention.

[0048] Figure 9 shows an exemplary graph of service life of a battery plotted against a battery temperature usable within the method of lifetime estimation according to one embodiment of the present invention.

[0049] Figure 10 shows a table containing experimental battery data usable within the method of lifetime estimation according to one embodiment of the present invention. [0050] Figure 1 1 shows a histogram of historical records of nacelle controller temperatures (corresponding to the battery operating temperature) over a period of 1 year usable within the method of lifetime estimation according to one embodiment of the present invention.

[0051] Figure 12 shows a flowchart of a method of estimating a lifetime of a battery of an energy backup system of a wind turbine according to one embodiment of the present invention.

[0052] Figure 13 shows a flowchart of a method of estimating a lifetime of a battery of an energy backup system of a wind turbine according to one embodiment of the present invention.

[0053] Figure 14 shows a curve of battery lifetime plotted against battery temperature usable within the method of lifetime estimation according to one embodiment of the present invention.

[0054] Figure 15 shows a curve of battery lifetime plotted against battery temperature usable within the method of lifetime estimation according to one embodiment of the present invention.

[0055] Figure 16 shows a schematic diagram of an equivalent circuit representation of a battery usable within the method of lifetime estimation according to one embodiment of the present invention.

[0056] Figure 17 shows a flowchart of a method of estimating a lifetime of a battery of an energy backup system of a wind turbine according to one embodiment of the present invention. [0057] Figure 18 shows a flowchart of a method of determining a first resistance of the equivalent circuit of figure 16 according to one embodiment of the present invention.

[0058] Figure 19 shows a curve of a battery terminal voltage plotted against SOD under a constant discharge current condition usable within the method of lifetime estimation according to one embodiment of the present invention.

[0059] Figure 20 shows a flowchart of a method of determining a second resistance of the equivalent circuit of figure 16 usable within the method of lifetime estimation according to one embodiment of the present invention.

[0060] Figure 21 shows experimental data obtained at a common discharge current level usable within the method of lifetime estimation according to one embodiment of the present invention.

[0061] Figure 22 shows a curve of a second resistance of the equivalent circuit of figure 16 at -20°C plotted against SOD level usable within the method of lifetime estimation according to one embodiment of the present invention.

[0062] Figure 23a and 23b show experimental data obtained for different temperatures at a constant discharge current level of 12 A according to one embodiment of the present invention.

[0063] Figure 24a and 24b show experimental data obtained for different constant discharge current levels at a temperature of 25 °C usable within the method of lifetime estimation according to one embodiment of the present invention.

[0064] Figure 25 shows experimental data obtained at a battery service life of zero months usable within the method of lifetime estimation according to one embodiment of the present invention. [0065] Figure 26 shows experimental data obtained at a battery service life of 6 months usable within the method of lifetime estimation according to one embodiment of the present invention.

[0066] Figure 27 shows experimental data obtained at a battery service life of 12 months usable within the method of lifetime estimation according to one embodiment of the present invention.

DETAILED DESCRIPTION

[0067] Figure 1 illustrates a common setup of a conventional wind turbine 100. The wind turbine 100 is mounted on a base 102. The wind turbine 100 includes a tower 104 having a number of tower sections, such as tower rings. A wind turbine nacelle 106 is placed on top of the tower 104. The wind turbine rotor includes a hub 108 and at least one rotor blade 1 10, e.g. three rotor blades 110. The rotor blades 1 10 are connected to the hub 108 which in turn is connected to the nacelle 106 through a low speed shaft which extends out of the front of the nacelle 106.

[0068] Batteries are used in the wind turbine 100 as a source of back-up energy for various components and systems in the wind turbine 100 in case the power grid is down or is unstable. Figures 2a and 2b show possible locations of the batteries 200 in the wind turbine 100. The batteries 200 are located in the nacelle 106 and/or in the tower 104. The batteries 200 located in the tower 104 may be placed on the floor 202 of the tower 104. The types and locations of the batteries 200 used in the wind turbine 100 may vary for example according to the type of wind turbines. [0069] Since the batteries 200 serve as a source of back-up energy, it is desirable to ensure that the batteries 200 are in good working condition. One way of ensuring that batteries 200 are in good working condition is to estimate the lifetime or the remaining useful lifetime (RUL) of the batteries 200, and to replace or repair the batteries if their respective estimated lifetimes are insufficient to perform their functions.

[0070] Figure 3 shows a flowchart of a method of estimating the lifetime of a battery of an energy backup system of a wind turbine. At 302, battery information characterizing a current battery state or at least one battery state of the past is determined. At 304, the lifetime of the battery is estimated in dependence on the determined battery information.

[0071] The term "battery information" may for example include:

• current battery parameter values

• battery parameter values which have been tracked during the operation of the energy backup system (i.e. battery parameter values of the past).

• fixed battery parameter values which do not change over time (e.g. battery parameter values provided by the battery supplier or entered by a user).

The term "battery information" or "battery parameter" may for example include:

• information on the current temperature value of the battery or information on at least one tracked temperature value of the battery or information on at least one predetermined temperature value.

· information on the current discharging depth value of the battery or information on at least one tracked discharging depth value of the battery or information on at least one predetermined discharging depth value. • information on the current charging or discharging current value of the battery or information on at least one tracked charging or discharging current value of the battery or information on at least one predetermined charging or discharging current value.

• information on the current charging or discharging voltage value of the battery or information on at least one tracked charging or discharging voltage value of the battery or information on at least one predetermined charging or discharging voltage value.

• information on the current charging or discharging speed value of the battery or information on at least one tracked charging or discharging speed value of the battery or information on at least one predetermined charging or discharging speed value.

• information on the number of charging or discharging cycles of the battery carried out in the past.

• information on the charging or discharging method.

• information on the period between charging and discharging of the battery (i.e. the time period that elapses between the occurrences of power grid failure).

It is to be understood that other types of battery information/battery parameters may also be used. According to one embodiment of the present invention, the term "current battery state" may include information based on current battery measurements (i.e. current battery parameter values) or information based on predetermined battery information (e.g. fixed battery parameter values provided by a battery supplier or a user) or both types of information. According to one embodiment of the present invention, the term "battery state of the past" may include information based on previous battery measurements (i.e. previous battery parameter values) or information based on predetermined battery information (e.g. fixed battery parameter values provided by a battery supplier or a user) or both types of information.

[0072] Figure 4 shows a schematic diagram of one embodiment of a lifetime estimation system 400 for estimating the lifetime of a battery of a wind turbine energy backup system. The lifetime estimation system 400 includes a battery information determining unit 402 and an estimation unit 404 coupled to the battery information determining unit 402. A database unit 406 and a battery information tracking unit 408 are also coupled to the battery information determining unit 402. The battery information tracking unit 408 is also coupled to the battery 410 of the wind turbine energy backup system. An input unit 412 is coupled to the battery information determining unit 402.

[0073] Fixed battery parameter values which are provided by the battery supplier can be fed into the battery information determining unit 402 via the input unit 412. The input unit 412 may include but is not limited to a keyboard. The battery information tracking unit 408 is adapted to track battery parameter values of the battery 410 during the operation of the wind turbine energy backup system. The battery information tracking unit 408 is further adapted to supply the tracked battery parameter values to the battery information determining unit 402. The input unit 412 may also be used by a user to input battery parameter values of the battery 410 occurred during the operation of the wind turbine energy backup system in the past which have not been tracked by the battery information tracking unit 408. [0074] The battery information determining unit 402 is adapted to determine battery information characterizing a current battery state or at least one battery state of the past. The battery information determining unit 402 may determine battery information characterizing a current battery state or at least one battery state of the past based on the information received from the input unit 412 and the battery information tracking unit 408. The battery information determining unit 402 may send the determined battery information to the estimation unit 404 for further processing and to the database unit 406 for storage.

[0075] The estimation unit 404 is adapted to estimate the lifetime of the battery in dependence on the determined battery information. The database unit 406 may store battery information determined by the battery information determining unit 402.

[0076] The battery information determined by the battery information determining unit 402 may include but is not limited to information regarding current battery temperature, information on the charging or discharging method like current battery discharging depth, current battery charging or discharging voltage, current battery charging or discharging current, current battery charging or discharging cycles, current battery charging or discharging speed, the number of battery charging or discharging cycles, or at least one tracked value of at least one of the above battery parameters, or at least one fixed predetermined value of at least one of the above battery parameters. The battery information may also include information on the period between charging and discharging of the battery (i.e. the time period that elapses between the occurrences of power grid failure). Additional battery information characterizing a current battery state or at least one battery state of the past may be determined in different embodiments. All of the above battery parameters may be time-varying parameters. The period between discharging and charging of the battery, i.e. the duration of grid downtime, is a parameter which cannot be determined in advance.

[0077] Figure 5 shows a schematic diagram of another embodiment of a lifetime estimation system 500 for estimating the lifetime of a battery of a wind turbine energy backup system. In this embodiment, the lifetime estimation system 500 includes a battery lifetime calculation tool 502. The battery lifetime calculation tool 502 may include a database 504 for storing battery information collected from various battery information sources like the databases indicated by reference numerals 506, 508, and 510.

[0078] The lifetime estimation system 500 includes a turbine service database 506 which for example stores information on the battery commissioning date, and a parameter record database 508 which for example stores fixed parameter information on the wind turbine and varying parameter information like temperature data of the system within which the battery is used. The fixed parameter information on the wind turbine may include the wind turbine unit type, mark release of the wind turbine (i.e. wind turbine version), and the location of the wind turbine such as the region, the country and the wind park name at which the wind turbine is installed. The varying parameter information like temperature data may be collected in regular time intervals, e.g. every 10 minutes. The temperature data may include average ambient temperature, average hub temperature, average ground controller temperature, average top controller temperature and average nacelle temperature. The lifetime estimation system 500 may further include a turbine database 510 which stores wind turbine log data. It is to be understood that in other embodiments, depending on the application, at least one of the databases 506, 508, and 510 may be omitted.

[0079] The turbine service database 506, the parameter record database 508, and the turbine database 510 are coupled to the battery lifetime calculation tool 502. The information stored in the turbine service database 506, the parameter record database 508, and the turbine database 510 may be supplied to the battery lifetime calculation tool 502.

[0080] Information sources 512 on battery type such as brand and model of the battery, and information sources 514 on battery models such as battery lifetime models and battery performance models may feed respective information into the battery lifetime calculation tool 502 e.g. via an input unit (not shown). These information sources 512, 514 may for example be humans or databases.

[0081] The battery lifetime calculation tool 502 may estimate the lifetime of the battery based on the information received from the turbine service database 506, the record database 508, the turbine database 510 and the information sources 512, 514, and send the results to an output unit 516 coupled to the lifetime calculation tool 502. The results may include but are not limited to remaining lifetime of the battery, confidence interval for the remaining lifetime of the battery, a lifetime distribution for a plurality of batteries, and a report for suggestion of replacement of batteries.

[0082] The output unit 516 may receive the generated results from the battery lifetime calculation tool 502 and display the results. The output unit 516 may include but is not limited to be a computer monitor.

[0083] In this embodiment, at least some of the various units (e.g. the battery lifetime calculation tool 502 or the databases 506, 508, and 510) of the lifetime estimation system 500 used for calculation remaining lifetime of batteries and evaluating performance of the batteries may be software modules, e.g. written in C code.

[0084] Figure 6 shows a schematic diagram of another embodiment of a lifetime estimation system 600 for estimating the lifetime of a battery of a wind turbine energy backup system. The lifetime estimation system 600 includes a processor unit 602 and a database unit 604 coupled to the processor unit 602. The database unit 604 stores battery characteristics (relationships between service life and temperature) provided by the battery manufacturer or obtained from testing results. The database unit 604 also stores other battery information like brand, model number, turbine unit type, mark release and battery location.

[0085] The lifetime estimation system 600 also includes an "Input" user interface unit 606, a "New Battery information" user interface unit 608, and an "Output" user interface unit 610. The lifetime estimation system 600 also includes a server unit 612 coupled to the processor unit 602.

[0086] The "Input" user interface unit 606 allows a user of the lifetime estimation system 600 to input information on battery brand, battery model number, the wind turbine (Turbine Selection), a period of time during which the battery has been used (Period), and 10 minutes signals representing data tracked every 10 minutes, e.g. temperature data. The information on the wind turbine may include the wind turbine unit type, mark release of the wind turbine, and the location of the wind turbine such as the region, the country and the wind park name at which the wind turbine is installed. The information on the 10 minutes temperature data may include average temperature of nacelle, average temperature of nacelle (top) controller, average temperature of hub controller and average temperature of ground controller. The information on the battery brand and the battery model number is fed to the processor unit 602. The information on the wind turbine (Turbine Selection), the period of time during which the battery has been used (Period), and 10 minutes signals representing e.g. temperature data is fed into the server unit 612. The server unit 612 may then transmit information (e.g. turbine information for the respective selected wind turbines, the 10 minutes temperature data for the system where the battery is used over the selected period of time, and the date and time in which the 10 minutes temperature data were recorded) corresponding to the received information on the wind turbine (Turbine Selection), the period of time during which the battery has been used (Period), and 10 minutes temperature data for the system where the battery is used over the selected period of time, to the processor unit 602.

[0087] The processor unit 602 may choose the right battery characteristics stored in the database unit 604 based on the information (e.g. the battery brand and the battery model number) inputted by the user on the "Input" user interface unit 606. The processor unit 602 may process the information inputted by the user on the "Input" user interface unit 606 and the information received from the database unit 604 and the server unit 612. The processor unit 602 may then calculate the remaining useful lifetime and expected useful lifetime of each battery and generate a lifetime distribution of batteries based on the information inputted by the user on the "Input" user interface 606 and the information received from the database unit 604 and the data centre server 612.

[0088] According to one embodiment of the present invention, the term "remaining useful lifetime (RUL)" may refer to the remaining lifetime of a battery before the battery fails. The term "expected useful lifetime" may refer to the estimated total lifetime of a battery before the battery fails. The "service life" may refer to the total operating lifetime of the battery since the first day the battery was used.

[0089] The calculated remaining useful lifetime and expected useful lifetime of each battery and the generated lifetime distribution of batteries may be displayed on the "Output" user interface 610.

[0090] In addition, the "New Battery information" user interface unit 608 of the lifetime estimation system 600 allows the user to input information of a new battery. The information of the new battery may include information on battery brand, battery model number, the unit type of the wind turbine in which the battery is used, the mark release of the wind turbine and the battery location. The information of the new battery may also include parameters for relationship between service life and temperature of the battery which can be obtained from the battery supplier. The information of the new battery may be processed by the processor unit 602 and stored in the database unit 604.

[0091] Figure 7 shows an exemplary user interface 700 usable as part of a lifetime estimation system. The user interface 700 has an "Input" section 702 allowing a user to input battery information. The "Input" section 702 has a "Turbine Selection" subsection 704 allowing a user to input or select information characterizing a wind turbine. The user may input/select the turbine information using the following input/selection masks: "Turbine Unit Type" 706, "MK (Mark) Release" 708, "SBU" 710, "Country" 712 and "Park Name" 714. The "Input" section 702 further has a "Date Range" subsection 716 in which the user can input the period of time during which batteries have been used using the following input/selection masks: "Start Date" 718 and "End Date" 720. If a wrong time range is inputted, a warning message (e.g. "time input is wrong") may be displayed. [0092] The "Input" section 702 may also require the user to select one of a plurality of temperature sensors which is closest to (or most representative of) the location of the battery and which should serve as a basis for the lifetime calculation of the battery using the input/selection mask 722. The input/selection mask 722 may for example offer the following entries: average temperature of nacelle, average temperature of nacelle (top) controller, average temperature of hub controller and average temperature of ground controller. The user may select one of the above four entries. Additional entries may be used in different embodiments. The user may also be required to use the input/selection masks "Battery Brand" 724 and "Battery Model Number" 726 in the "Input" section 702 to input/select corresponding information.

[0093] It is not necessary to select/input all the information offered for selection/which may be inputted in the "Input" section 702 for results to be generated in the "Output" section 730. If, for example, only a broad searching pattern is used like information restricted to "Turbine Unit Type" 706, "Start Date" 718 and "End Date" 720, all information which matches the searching pattern can be obtained from the database. Hence, the output results can still be obtained. Other information may be inputted in the respective input/selection masks for narrowing down the number of selected turbines.

[0094] After all the required information is inputted and/or selected in the "Input" section 702, the "Calculate" button 728 can be clicked. Warning messages may be displayed if there is any wrong input. If all the inputs are correct, the lifetime of the batteries may be calculated and a lifetime distribution of the batteries may be generated after the "Calculate" button 728 is clicked. The output subsection 732 again summarizes the data on which the lifetime calculation has been based and the generated lifetime distribution 738 may be displayed in the output subsection 734 of the "Output" section 730.

[0095] The output subsection 732 summarizes the data of each selected battery on which the lifetime calculation has been based and calculated data of each selected battery on table 736 like turbine information (turbine ID, turbine unit type, mark release, SBU, country and park name), battery information (battery location, battery brand and battery model number), period of use, remaining useful lifetime (RUL) at a reference temperature (for example, 20°C) of each battery and expected useful life corresponding to the historical temperature profile of each battery. Other information may be shown by table 736 in different embodiments.

[0096] The lifetime distribution is shown as a graph 738, the probability density or the number of batteries being indicated by the y-axis, and the remaining useful lifetime (RUL) of battery with or without a given reference temperature (for example, 20°C) being indicated by the x-axis. The graph 738 may only be plotted if a plurality of batteries is selected. The graph 738 will not be plotted if only one battery is selected. The graph 738 may be calculated using e.g. the Weibull Parameter Estimation approach. In the "Output" section 730, the user can enter a particular period of time that the batteries will be used (in years) by using the input/selection mask 740 to find out the probability and number of batteries that can last for within the particular time period. For example, the user can enter a time period of e.g. 3 years by using the input/selection mask 740. The number of batteries that can last for further 3 years (or 3 years in total, depending on the application) will be calculated. In order to give more "defense" information, a probability value may be given specifying the reliability of the above indicated number of batteries. Information such as total number of batteries, battery brand and model number, turbine information, probability of the batteries that can last for within the selected time period, and number of the batteries that can last for within the selected time period may be displayed in the subsection 742 of the "Output" section 730. The information displayed in the subsection 742 of the "Output" section 730 may be information of a plurality of batteries having one or more common characteristics (e.g. having the same battery brand and model number).

[0097] The user interface 700 provides a "New Battery Information" section 744 enabling a user to enter information of new batteries. To enter the information of new batteries, the "Add to Database" button 746 can be clicked. A "New Battery Information" user interface unit 802 appears on the user interface 700 after the "Add to Database" button 746 is clicked, as shown in Figure 8. The user can enter the information of the new battery using the following input/selection masks: "Battery Brand" 804, "Battery Model Number" 806, "Turbine Unit Type" 808, "MK (Mark) Release" 810, "Battery Location" 812, "Tstart (Temperature at which degradation of service life of battery due to temperature starts)" 814, "T_end (Temperature at which degradation of service life of battery due to temperature ends)" 816, "YR_start (Service life at which degradation of service life of battery due to temperature starts)" 818, and "YRend (Service life at which degradation of service life of battery due to temperature ends)" 820. To save the inputted information in the database, the "Enter" button 822 is clicked. If the "Cancel" button 824 is clicked, the information may not be saved and the user interface 700 may revert back to that as shown in Figure 7. The lifetime of the new batteries may be evaluated after the information of the new batteries is saved in the database. [0098] The user interface 700 provides a "Help" button 748 as a help link. The "Help" button 748 can be clicked to get an explanation on how to use the lifetime estimation system.

[0099] The lifetime estimation systems 400, 500, 600 as described above can be implemented as an online tool which may allow the wind turbine service team to monitor the estimated lifetime of the battery remotely. The lifetime estimation systems 400, 500, 600 as described above can be implemented as a standalone tool. Therefore, the lifetime estimation systems 400, 500, 600 can be used for remote maintenance/controlling services. The remaining useful lifetime of the battery can be determined based on the wind turbine operational environment (e.g. ambient temperature, wind speed and turbine operation status) and historical data of the parameters measured for the past batteries of the same brand and model number. By using the lifetime estimation systems 400, 500, 600, the wind turbine service team can obtain the estimated remaining useful lifetime (RUL) and expected useful life of the battery as an indication whether the battery needs to be replaced before the battery fails. Therefore, the power production can be increased and the mean time between inspections (MTBI) can be improved due to a reduction of unscheduled maintenance services of wind turbines caused by battery failures.

[0100] Further, engineers can analyze the impact of the battery working conditions and environment (e.g. the ambient temperature, the temperature of the location at which the battery is located, the location of the battery, etc) on the battery lifetime from the data calculated by the lifetime estimation systems 400, 500, 600. This may help the engineers to design a battery control system for controlling the operation of the battery to optimize the battery lifetime. [0101] The engineers can also use the lifetime estimation systems 400, 500, 600 for evaluating a new battery. This may help to reduce the cost and time that need to be spent on real-testing when qualifying the new battery. The reason is that it usually takes a long time to determine the estimated battery lifetime in the field by real-testing. A few months of ALT (accelerated life testing) may be needed for testing selected battery samples such as 20 or 30 samples. During real-testing, the battery temperature may be determined based on the operating temperature of the wind turbine. However, by using the lifetime estimation systems 400, 500, 600, all the real-testing may not be needed. For example, only the information of the new battery, i.e. the relation between battery service lifetime versus the battery operating temperature, is required to be inputted into the lifetime estimation systems 400, 500, 600 to determine the estimated service lifetime of the new battery. Thus, using the lifetime estimation systems 400, 500, 600 may be easier, faster and more cost-efficient.

[0102] In addition, the engineers can use the lifetime estimation systems 400, 500, 600 to compare a lifetime distribution of a plurality of batteries of a new brand of batteries and a lifetime distribution of a plurality of currently used batteries of another brand. By comparing these two lifetime distributions, the engineers can compare the probability of failure of the two different brands of batteries over a particular period of time. A lower probability of failure may indicate that the particular brand of batteries is better. Hence, the lifetime estimation systems 400, 500, 600 can help in battery brand selection for a new design of energy backup system. [0103] One effect of the lifetime estimation systems 400, 500, 600 is that the lifetime estimation systems 400, 500, 600 are designed to be user-friendly and to be easy to use for the wind turbine service team, the engineers and any other relevant parties.

[0104] As mentioned above, the lifetime estimation systems 400, 500, 600 can calculate the remaining useful lifetime and expected useful life of the battery. Various methods can be used for calculating the remaining useful lifetime and expected useful life of the battery. Details of the methods are described in the following.

[0105] Methods - Introduction

Figure 9 shows a graph 900 of service life of a battery plotted against the battery temperature. In Figure 9, curve 902 indicates the upper lifetime limit, while curve 904 indicates the lower lifetime limit. According to one embodiment of the present invention, the term "upper lifetime limit" may refer to the longest period of time that the battery can operate under different temperatures. The term "lower lifetime limit" may refer to the shortest period of time that the battery can operate under different temperatures. Figure 9 illustrates how the battery temperature affects the service life of the battery. For example, as can be derived from curves 902 and 904 of Figure 9, the lifetime of the battery drops if the battery is operated above 20°C. If the battery operates below 20°C, the battery lifetime can be as long as 4 years. If the battery operates at 38°C, the battery lifetime can be as short as 1.3 years.

[0106] From Figure 9 which is provided by the battery supplier, some exemplary data values are shown in Figure 10 by tables 1000 and 1002. From the data shown in Figure 10, it can be derived that Log(Y) has a linear relation with the battery temperature, where Y is the battery service life. The linear relation of Log(Y) and the battery temperature can be represented by the following equation:

y = kx + b. (1)

where y = Log(Y), x is battery temperature, k is a gradient of the linear relation and b is a constant. The values of k which are shown in Figure 10 can be calculated based on the data shown in Figure 10 and the equation (1).

[0107] For calculation of the remaining useful lifetime and expected useful life of the battery, a reference battery operating temperature is required. For example, 25°C can be used as the reference battery operating temperature, and the reference battery service life at this reference temperature is about 3 years.

[0108] Historical records of the battery temperature (which may correspond to the nacelle controller temperature) may be obtained for calculation of the remaining useful lifetime of the battery. Any period (e.g. 1 month, 6 months, 1 year, 2 years, etc) of the historical records of the battery temperature may be selected. The historical records of a particular wind farm, several wind farms, a particular wind turbine or several wind turbines may be selected. A histogram can be derived based on the historical records of the nacelle controller temperature as the battery locates in the nacelle controller. Figure 11 shows for example a histogram 1100 of the historical records of the nacelle controller temperatures (i.e. the battery operating temperatures) for a period of 1 year.

[0109] Method 1

Figure 12 shows a flowchart 1200 of a method of estimating the lifetime of a battery of an energy backup system of a wind turbine based on method 1. At 1202, battery parameter values of a battery parameter during operation of the battery are tracked. At 1204, a histogram of the tracked battery parameter values is prepared. The histogram includes a relation between a plurality of battery parameter values and battery operating hours in which, to each battery parameter value, a number of battery operating hours is assigned. At 1206, for each battery parameter value, the operating hours assigned to the battery parameter value are converted into equivalent battery operating hours referring to a reference parameter value. The converting process is carried out based on a predetermined relation between the battery parameter and the maximum battery operating time. At 1208, the equivalent battery operating hours is summed up to obtain a total equivalent operating time. At 1210, the total equivalent battery operating time is subtracted from a maximum battery operating time obtained from the predetermined relation for the reference parameter value, thereby obtaining the remaining estimated battery operating hours. A possible, more detailed example of this method will be described in the following.

[0110] From Figure 11, it can be derived that the battery works under temperature 31°C for 1019.2 hours (battery operating hours) during the 1 year period. The equivalent battery operating hours corresponding to a reference temperature ref can be calculated as follows.

[0111] With reference to Figure 9, A_x is the battery service life (operating hours) under temperature x, and A_re/ is the battery service life (operating hours) under the reference temperature ref Let L_x = Log(A ) and L_ref = Log(A_re ), then the following equation can be obtained:

[0112] If the battery operates under temperature x for At_x hours during the 1 year period, the equivalent time (equivalent battery operating hours) that the battery operates at the reference temperature ref can be obtained using the following equation:

[0113] Using equation (3), the operating hours for each battery temperature can be converted into equivalent battery operating hours of the reference temperature ref. A total equivalent operating time based on the reference temperature ref can be obtained by summing up the equivalent battery operating hours of the reference temperature ref converted for each battery temperature for the whole of 1 year period.

[0114] The total equivalent time that the battery operates at the reference temperature ref can be obtained using the following equation:

where a is a lower limit of the battery operating temperature and b is an upper limit of the battery operating temperature. In one embodiment, the lower limit of the battery operating temperature (a) may be 20°C and the upper limit of the battery operating temperature (b) may be 60°C.

[0115] If the calculated value of _ref→equ is lower than the value of L_ref which can be obtained from Figure 9, it means the battery can have a service life which is longer than one year. The battery can be evaluated in a similar way to find out if the battery! can provide a longer service life of e.g. 2 or 3 years. In order to build a confidence level (i.e. in order to make sure that the battery temperature data are reasonable), the battery temperature data from different turbines can be obtained and compared. For example, data from 30 or 60 turbines for a given period of time of e.g. 1 year, 2 years or longer can be obtained. For each of the different turbines, the estimated remaining battery service life can be obtained by subtracting the calculated value of L_t from the value of L_re .

[0116] Method 2

Figure 13 shows a flowchart 1300 of a method of estimating the lifetime of a battery of an energy backup system of a wind turbine based on method 2. At 1302, battery parameter values of a battery parameter during operation of the battery are tracked. At 1304, a histogram of the tracked battery parameter values is prepared. The histogram includes a relation between a plurality of battery parameter values and battery operating hours in which, to each battery parameter value, a number of battery operating hours is assigned. At 1306, a weighted average battery parameter value is determined based on the histogram. At 1308, an estimated lifetime of the battery is determined based on the weighted average battery parameter value using a predetermined relation between the battery parameter and the lifetime of the battery. A possible, more detailed example of this method will be described in the following.

[0117] Referring to Figure 11 , it can be derived that the battery works under temperature 31°C for 1019.2 hours, works under temperature 32°C for 1083.83 hours, and works under temperature 33°C for 764.5 hours, etc. during the 1 year period. A weighted average temperature can be calculated using the following equation:

b

Avg-W Ϊ (5)

i where index / denotes the different possible battery parameter values (temperature values), δ, denotes the battery operating hours at battery parameter (temperature) value i, a is a lower limit of possible battery parameter values (temperature values) and b is an upper limit of possible battery parameter values (temperature values). In one embodiment, the lower limit of the possible battery parameter values (temperature values) (a) may be 20°C and the upper limit of the possible battery parameter values (temperature values) (b) may be 60°C.

[0118] The equivalent service life for the weighted average temperature T_Avg-w can be obtained from Figure 9. If the equivalent service life under the weighted average temperature TAvg-w is longer than the time period selected (i.e. the time period from which data was used for calculation of the weighted average temperature T_Avg-w) for estimating the lifetime of the battery under Method 2, it means that the battery can have an operational life more than the time period. For example, if the temperature file downloaded is one year's data, the battery may have a service life (operating hours) of more than one year. The battery can be evaluated in a similar way to find out if the battery can provide a longer service life of e.g. 2 or 3 years.

[0119] Method 3

Figure 14 shows a curve 1400 of the battery lifetime (months) plotted against the battery temperature (°C). Curve 1400 is a fitted line plot derived from lifetime calculation based on curve 904 (lower lifetime limit of the battery) of Figure 9. Curve 1400 can be approximated by the following equation:

Battery Lifetime = 165.8 - 8.466T + 0.1569T² - 0.001024T³ (6) The battery lifetime can be directly obtained from curve 1400 based on the battery temperature.

[0120] Alternatively, as shown in Figure 15, a curve 1500 of the battery lifetime (months) plotted against the battery temperature (°C) can be derived from lifetime calculation based on an average of curve 902 (upper lifetime limit of the battery) and curve 904 (lower lifetime limit of the battery) of Figure 9. The plot 1500 is approximated by the following equation:

Battery Lifetime = 197.1 - 9.648T + 0.1706T² - 0.001064T³ (7)

The battery lifetime can be directly obtained from curve 1500 based on the battery temperature.

[0121] Similar to Method 1, let A* be the battery service life under temperature x and let A,,,/ be the battery service life under the reference temperature ref. A_x and A_re/ can be directly obtained from equation (6) or equation (7). If the battery operates under temperature x for At_x hours during e.g. a one year period, the equivalent time that the battery operates at the reference temperature ref can be obtained using the following equation:

i_{x w/} - At_x - A_ref/A_x. (8)

[0122] Using equation (8), the operating hours for each battery temperature can be converted into equivalent battery operating hours of the reference temperature ref. A total equivalent operating time of the reference temperature ref for the whole of 1 year period can be obtained by summing up the equivalent battery operating hours of the reference temperature ref converted for each battery temperature. The total equivalent operating time of the reference temperature ref for the whole of 1 year period can be obtained using the following equation:

b

L rej→equ = Y / f →ref

x=a

=∑( At_x - A_ref/A_x) (9)

x-a where index x denotes the different possible battery parameter values (temperature values), a is the lower limit of the battery operating temperature and b is the upper limit of the battery operating temperature. In one embodiment, the lower limit of the battery operating temperature (a) may be 20°C and the upper limit of the battery operating temperature (b) may be 60°C.

[0123] If the calculated value of L_ref→egu is lower than the value of L_ref which can be obtained from Figure 9, it means the battery can have a service life which is longer than one year. The battery can be evaluated in a similar way to find out if the battery can provide a longer service life of e.g. 2 or 3 years. In order to build a confidence level (i.e. in order to make sure that the battery temperature data are reasonable), the battery temperature data from different turbines can be obtained and compared. For example, data from 30 or 60 turbines for a given period of time of e.g. 1 year, 2 years or longer can be obtained. For each of the different turbines, the estimated remaining battery service life can be obtained by subtracting the calculated value of L_ref→equ from the value of Z_ref-

[0124] Method 4

Figure 16 shows a schematic diagram of an equivalent circuit representation 1600 of a battery. The battery internal resistance Rint may be modelled as a function of battery temperature, battery discharge current level, state of discharge of the battery, and aging factor of the battery. The modelled internal resistance R^ may be the sum of a first resistance Rj, a second resistance R₂ and a third resistance R₃. The first resistance Ri may be a function of battery temperature, battery discharge current level and battery lifetime (e.g. number of charging and discharging cycles of the battery). The first resistance Ri may be defined as the internal resistance of the battery at a state of discharge (SOD) level of 0. The second resistance R₂ may be a function of state of discharge of the battery and battery temperature. The second resistance R₂ may account for the increase in the battery internal resistance Rjj,_t as SOD increases. The third resistance R₃ may be a function of battery aging. The third resistance R₃ may be dependent on time only. E represents an internal electromotive force (EMF) of the battery. V represents a terminal voltage of the battery.

[0125] In this embodiment, the estimation of the remaining battery lifetime of the battery may be carried out based on the internal resistance

of the battery. Figure 17 shows a flowchart 1700 of a method of estimating a lifetime of a battery of an energy backup system of a wind turbine based on method 4. At 1702, an internal resistance of the battery is modelled. At 1704, a discharge process of the battery based on the modelled resistance is simulated. At 1706, a discharge process of the battery is carried out. At 1708, the simulated discharge process is compared with the discharge process carried out. At 1710, the remaining lifetime of the battery is estimated based on a result of the comparison.

[0126] To obtain the internal resistance Rim, the first resistance Ri, the second resistance R₂ and the third resistance R₃ have to be determined, respectively. The details of determining the first resistance Rj, the second resistance R₂ and the third resistance R₃ are described in the following.

[0127] Determination of the first resistance R^

Figure 18 shows a flowchart 1800 of a method of determining the first resistance R_\. At 1802, a battery discharge parameter is set to a first discharge parameter value. At 1804, the battery is discharged. At 1806, the voltage drop at the beginning of the discharge process is determined. At 1808, a change of the first resistance reflected by the voltage drop is determined. At 1810, the battery discharge parameter is set to a second discharge parameter value being different from the first discharge parameter value. At 1812, it is determined if the processes from 1802 to 1810 have been repeated at least one time. If no, the process goes back to 1802. If yes, the process proceeds to 1814. At 1814, it is determined if the processes at 1802 to 1812 have been carried out at least one time for each battery discharge parameter. If no, the process goes back to 1802. If yes, the process proceeds to 1816. At 1816, the dependencies of the first resistance on each battery discharge parameter are determined based on the determined changes of the first resistance. At 1818, the first resistance is determined as a function of the determined dependencies on the battery discharge parameters based on the determined dependencies using a mathematical approximation method. The battery discharge parameters are battery temperature and battery discharge current level. In the following, a possible embodiment of the above mentioned determination method of the first resistance R] will be given.

[0128] Figure 19 shows a curve 1900 of a battery terminal voltage plotted against SOD under a constant discharge current condition. In this example, the discharge is carried out at a constant current of about 2 A and at a constant temperature of about 25°C. As shown in Figure 19, there is an initial and sudden voltage drop at the beginning of the discharge, i.e. when SOD = 0⁺. The first resistance R_\ can be calculated by dividing the initial voltage drop by the discharge current at SOD=0.

[0129] In the last paragraph, a way has been shown how to determine the first resistance R_\ assuming that the discharge current is 2 A, and that the battery temperature is 25°C. Assuming that the discharge current is different from 2 A, or that the battery temperature is different from 25°C, the determined values of the first resistance Ri would respectively be different. More generally, since the first resistance Ri may be a function of battery temperature, battery discharge current level and battery lifetime (e.g. number of charging and discharging cycles of the battery), the first resistance Ri can be represented as

R. =/(/, T, I) (10)

Taking derivative on both sides of equation (10) yields:

[0130] Thus, from a sample of battery discharge tests, n sets of measurement of the changes in the first resistance R_\ (voltage drop measurements as shown in figure 19) corresponding to different variations in battery discharge current level i, battery temperature T and battery lifecycle / (number of charging and discharging cycles) can be obtained. The changes in the first resistance R_\ can be expressed in a matrix form as follows:

The changes in the first resistance R], i.e. ··■ 8R " ]^T and the matrix

can be calculated from the experimental data. A least-square curve-fitting method may be one way to obtain the derivatives (or analytical functions) of — ,— and— . That is,

di dT dl

from the discrete voltage drop measurement results carried out as indicated in figure 19, respective analytical functions are derived by applying respective curve fitting methods.

[0131] Then the first resistance Ri can be represented as

where i_ref, T_ref, l_ref are the discharge current, temperature and lifecycle of a reference condition. R_{l ref} is the internal resistance under a reference condition when SOD=0. Based on the reference condition, the value of the first resistance R_\ under other discharge conditions can be obtained.

[0132] Determination of the second resistance R?

Figure 20 shows a flowchart 2000 of a method of determining the second resistance R₂. At 2002, the battery temperature is set to a first temperature value. At 2004, the battery is discharged at the first temperature value. A discharge curve indicating the relation between the battery voltage and the state of discharge can be obtained. At 2006, for each of several states of discharge values, the corresponding voltage drop between the discharge curve and a reference discharge curve is determined. At 2008, a change of the second resistance reflected by the voltage drop for each of the state of discharge values is determined. At 2010, the second resistance is determined as a function of the temperature and the state of discharge based on the determined voltage drops using a mathematical approximation method. At 2012, the battery temperature is set to a second temperature value being different from the first temperature value. At 2014, the processes from 2004 to 2012 are repeated for the second temperature value. The battery temperature may be set to different temperatures and the processes from 2004 to 2012 may be repeated for the respective temperatures. The discharge processes for determining the second resistance may be carried out using a constant discharge current level. In the following, a possible embodiment of the above mentioned determination method of the second resistance R₂ will be given.

[0133] The second resistance R₂ may be defined as the additional resistance included in the circuit model 1600 of Figure 16 which may vary in value when the battery temperature varies from a reference temperature, for example 25°C. Since it is assumed here that the second resistance R₂ is a function of state of discharge (SOD) of the battery and the battery temperature, the second resistance R₂ can be defined as a function of SOD and the battery temperature, as follows:

R₂ = g(r, SOD) (14) [0134] Figure 21 shows experimental data, namely discharge curves, obtained at a common discharge current level of 1 A, however at different temperatures. Curve 2102 is a measured reference discharge curve obtained at a discharge condition of a reference temperature (here: 25°C). Curve 2104 is a measured discharge curve obtained at a discharge condition of a temperature of -20°C. The two curves 2102 and 2104 can be used to determine a voltage difference between the different curves 2102 and 2104, wherein the voltage difference represents a difference in the second resistance R₂. Here, the voltage difference between the curves 2102 and 2104 represents a resistance R_2,-20 which reflects the difference of R₂ between the temperature of 25 °C and the temperature of -20°C. That is, it can be observed how the second resistance R₂ changes with temperature and SOD. The range of the second resistance R₂ may be studied within a predetermined SOD limit so that the voltage does not decrease beyond a pre-set value, for example the voltage of the battery.

[0135] For illustration purposes, the SOD level of 0.7 is selected. From Figure 21, it can be derived that the corresponding voltage drop at -20°C between curve 2104 and curve 2102 at the SOD level of 0.7 due to the second resistance R₂ is i*R_2)-2₀.

[0136] Figure 21 also shows a curve 2106 which is a measured discharge curve obtained at a discharge condition of a temperature of -30°C. From Figure 21, it can be derived that the corresponding voltage drop at -30°C between curve 2106 and curve 2102 at the SOD level of 0.7 due to the second resistance R₂ is i*R₂.₃o.

[0137] A correction term for the temperature of -30°C can be defined as a ratio of the voltage drop as follows: ct(30° C) = '_, * ^^{2 "30} = ^=^- (15)

Ϊ * R₂ _20 ^2,-20 The correction term as indicated in equation (15) allows scaling of the second resistance R₂ based on the second resistance R_2j.₂₀ at -20°C. The above procedures may be repeated for any other SOD levels and any other temperatures. The value of the second resistance R₂ at -20°C is compared with the value of the second resistance R₂ at 25°C. The value of the second resistance R₂ at 25°C is 0Ω . At a given SOD, since the curves were obtained at the same discharge level, the voltage drop indicated as i*R_2i-2o may be due to an increase of the second resistance R₂.

[0138] Figure 22 shows a curve 2200 of the second resistance R₂ plotted against SOD level assuming that the temperature where this resistance was obtained is -20°C. Curve 2200 can be approximated by a polynomial equation as follows:

where is coefficient of the k^th order term of the polynomial representation, SOD(i) is k th

function of current i, and SOD (i) refers to the k power to SOD(i) . can be determined based on e.g. a least-square curve fitting method.

[0139] With a known R_2>-20 and by applying the correction term a(T), the second resistance R₂ at any other temperature (7) can be calculated using the following equation:

R₂ = a(T) *∑r_k * SOD^k(i) (17)

[0140] Figures 23a and 23b show exemplary experimental data obtained for a battery for different temperatures at a constant discharge current level of 12 A. Figure 23a shows curves having battery voltage plotted against discharge time at different temperatures. Curve 2302 is a discharge curve obtained at a discharge condition of a temperature of - 30°C. Curve 2304 is a discharge curve obtained at a discharge condition of a temperature of 25°C. Curve 2306 is a discharge curve obtained at a discharge condition of a temperature of 40°C. Curve 2308 is a discharge curve obtained at a discharge condition of a temperature of 60°C.

[0141] Figure 23b shows curves having battery voltage plotted against SOD at different temperatures. Curve 2310 is a discharge curve obtained at a discharge condition of a temperature of -30°C. Curve 2312 is a discharge curve obtained at a discharge condition of a temperature of 25°C. Curve 2314 is a discharge curve obtained at a discharge condition of a temperature of 40°C. Curve 2316 is a discharge curve obtained at a discharge condition of a temperature of 60°C. The rates of discharge at a constant current level for different temperatures can be observed from Figures 23a and 23b. The second resistance R₂ and the correction term a can be derived from Figures 23a and 23b. Figure 23b shows the same information as Figure 23 a, just expressed differently (SOD can be expressed in time and vice versa).

[0142] Figures 24a and 24b show experimental data obtained for different constant discharge current levels at a temperature of 25°C. Figure 24a shows curves having battery voltage plotted against time at different constant discharge current levels. Curve 2402 is a discharge curve obtained at a discharge condition of a constant discharge current level of 1 A. Curve 2404 is a discharge curve obtained at a discharge condition of a constant discharge current level of 3 A. Curve 2406 is a discharge curve obtained at a discharge condition of a constant discharge current level of 5 A. Curve 2408 is a discharge curve obtained at a discharge condition of a constant discharge current level of 8 A. Curve 2410 is a discharge curve obtained at a discharge condition of a constant discharge current level of 12 A. Curve 2412 is a discharge curve obtained at a discharge condition of a constant discharge current level of 16 A.

[0143] Figure 24b shows curves having battery voltage plotted against SOD at different constant discharge current levels. Curve 2414 is a discharge curve obtained at a discharge condition of a constant discharge current level of 1 A. Curve 2416 is a discharge curve obtained at a discharge condition of a constant discharge current level of 3 A. Curve 2418 is a discharge curve obtained at a discharge condition of a constant discharge current level of 5 A. Curve 2420 is a discharge curve obtained at a discharge condition of a constant discharge current level of 8 A. Curve 2422 is a discharge curve obtained at a discharge condition of a constant discharge current level of 12 A. Curve 2424 is a discharge curve obtained at a discharge condition of a constant discharge current level of 16 A. The rates of discharge at a constant temperature for different constant discharge current levels can be observed from Figures 24a and 24b. Figure 24b shows the same information as figure 24a, just expressed differently (SOD and time are correlated with each other).

[0144] The methods to determine R_\ and R₂ as described by equations (10) to (17) are conventional, and they are of the basis to determine R₃. R₃ is the third resistance of the studied battery, which depends on the battery usage life.

[0145] Determination of the third resistance R₃

The third resistance R₃ may reflect the battery aging factor in the circuit model 1600 of Figure 16 so that the battery discharge voltage profile at any given temperature, battery age, SOD and discharge level conditions can be simulated. The third resistance R₃ may be determined by carrying out the process for determining the first resistance as described above and the process for determining the second resistance as described above respectively several times at different battery ages. The increase in battery internal resistance at a given service life longer than zero usage life is reflected by R₃.

[0146] For example, new sets of tests for a sample of batteries may be carried out at different age/lifetime of the sample of batteries. It is desirable that the sampled batteries are stored at the same ambient conditions, and discharged at the same current level and the same temperature condition.

[0147] Figure 25 shows experimental data obtained at a battery service life of zero months. Graph 2502 shows curves of voltage drop plotted against temperature for a battery life cycle (i.e. number of charge/discharge cycles) of zero. Graph 2504 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of zero. Graph 2506 shows curves of voltage drop plotted against temperature for a battery life cycle of 30. Graph 2508 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of 30. Graph 2510 shows curves of voltage drop plotted against temperature for a battery life cycle of 100. Graph 2512 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of 100.

[0148] Graphs 2502, 2506 and 2510 can be used to obtain the values of the first resistance R_\ at the battery service life of zero months for the respective battery life cycles of 0, 30 and 100. Graphs 2504, 2508 and 2512 can be used to obtain the values of the second resistance R₂ at the battery service life of zero months for the respective battery life cycles of 0, 30 and 100. In graphs 2502, 2506 and 2510, it is assumed that the discharge current is different for each discharge curve, and that the state of discharge is the same for all discharge curves. In graphs 2504, 2508 and 2512, it is assumed that the discharge temperature is different for each discharge curve, and that the discharge current is the same for all discharge curves.

[0149] Figure 26 shows experimental data obtained at a battery service life of 6 months. Graph 2602 shows curves of voltage drop plotted against temperature for a battery life cycle of zero. Graph 2604 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of zero. Graph 2606 shows curves of voltage drop plotted against temperature for a battery life cycle of 30. Graph 2608 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of 30. Graph 2610 shows curves of voltage drop plotted against temperature for a battery life cycle of 100. Graph 2612 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of 100.

[0150] Similarly, graphs 2602, 2606 and 2610 can be used to obtain the values of the battery internal resistance increase from at the battery service life of 6 months for the respective battery life cycles of 0, 30 and 100. Graphs 2604, 2608 and 2612 can be used to obtain the values of the battery internal resistance increase from R₂ at the battery service life of 6 months for the respective battery life cycles of 0, 30 and 100. In graphs 2602, 2606 and 2610, it is assumed that the discharge current is different for each discharge curve, and that the state of discharge is the same for all discharge curves. In graphs 2604, 2608 and 2612, it is assumed that the discharge temperature is different for each discharge curve, and that the discharge current is the same for all discharge curves.

[0151] Figure 27 shows experimental data obtained at a battery service life of 12 months. Graph 2702 shows curves of voltage drop plotted against temperature for battery life cycle of zero. Graph 2704 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of zero months. Graph 2706 shows curves of voltage drop plotted against temperature for a battery life cycle of 30. Graph 2708 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of 30. Graph 2710 shows curves of voltage drop plotted against temperature for a battery life cycle of 100. Graph 2712 shows curves of discharge voltage plotted against SOD for different temperatures for a battery life cycle of 100.

[0152] Similarly, graphs 2702, 2706 and 2710 can be used to obtain the values of the battery internal resistance increase from Rj at the battery service life of 12 months for the respective battery life cycles of 0, 30 and 100. Graphs 2704, 2708 and 2712 can be used to obtain the values of the battery internal resistance increase from R₂ at the battery service life of 12 months for the respective battery life cycles of 0, 30 and 100. In graphs 2702, 2706 and 2710, it is assumed that the discharge current is different for each discharge curve, and that the state of discharge is the same for all discharge curves. In graphs 2704, 2708 and 2712, it is assumed that the discharge temperature is different for each discharge curve, and that the discharge current is the same for all discharge curves.

[0153] The third resistance R₃ may be determined based on the experimental data obtained from Figures 25 to 27. In other embodiments, the same test procedure for obtaining values of the first resistance Ri and the second resistance R₂ may be carried out at different battery service lifetimes and for different battery life cycles to determine the value of the third resistance R₃.

[0154] Using the above described method 4, the parameters of the battery under any given discharge, SOD, temperature and lifetime conditions can be determined. The circuit model 1600 as shown in Figure 16 can be used to predict the voltage profile of the battery under any discharge condition. Based on the predicted voltage profile, it can be determined if the battery has reached its end-of-life in the following manner.

[0155] The basic circuit equation of the circuit 1600 can be represented by the following equation:

£ = + i x (R, + R₂ + R₃ ) (18)

The battery may be discharged at a constant power level for a fixed time (e.g. 30 minutes). The discharge process may be simulated at the stated constant power level for a stipulated period. If within the stated discharge period, the terminal voltage V is observed to be equal to a certain preset voltage limit level, it may be concluded that the battery has reached its end-of-life. Since the battery lifetime is dependent on the ambient temperature condition at which the battery discharges, it is desirable to calibrate the end-of-life of the battery against the battery operating temperature.

[0156] While embodiments of the invention have been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

What is claimed is: 1. A method of estimating the lifetime of a battery of an energy backup system of a wind turbine, the method comprising:

determining battery information characterizing a current battery state or at least one battery state of the past,

estimating the lifetime of the battery in dependence on the determined battery information.

2. The method according to claim 1,

further comprising:

modelling an internal resistance of the battery,

- simulating a discharge process of the battery based on the modelled resistance, carrying out a discharge process of the battery,

comparing the simulated discharge process with the discharge process carried out, estimating the remaining lifetime of the battery based on a result of the comparison.

3. The method according to claim 2,

wherein the internal resistance is modelled as a function of battery temperature, battery discharge current level, state of discharge of the battery, and aging factor of the battery.

4. The method according to claim 3,

wherein the modelled internal resistance is the sum of a first resistance, a second resistance and a third resistance, and wherein the first resistance is a function of battery temperature, battery discharge current level and battery lifetime, wherein the second resistance is a function of state of discharge of the battery and battery temperature, and wherein the third resistance is a function of battery aging.

5. The method according to claim 4,

wherein determining the first resistance comprises:

a) setting a battery discharge parameter to a first discharge parameter value, b) discharging the battery,

c) determining the voltage drop at the beginning of the discharge process, d) determining a change of the first resistance reflected by the voltage drop, e) setting the battery discharge parameter to a second discharge parameter value being different from the first discharge parameter value,

f) repeating steps a) to e) at least one time,

g) carrying out steps a) to f) for each battery discharge parameter,

h) determining the dependencies of the first resistance on each battery discharge parameter based on the determined changes of the first resistance,

i) determining the first resistance as a function of the determined dependencies on the battery discharge parameters based on the determined dependencies using a mathematical approximation method.

6. The method according to claim 5,

wherein the battery discharge parameters are battery temperature and battery discharge current level.

7. The method according to any one of the claims 4 to 6,

wherein determining the second resistance comprises:

a) setting the battery temperature to a first temperature value,

b) discharging the battery at the first temperature value, thereby obtaining a discharge curve indicating the relation between the battery voltage and the state of discharge,

c) for each of several states of discharge values, determining the corresponding voltage drop between the discharge curve and a reference discharge curve,

d) determining a change of the second resistance reflected by the voltage drop for each of the state of discharge values,

e) determining the second resistance as a function of the temperature and the state of discharge based on the determined voltage drops using a mathematical approximation method,

f) setting the battery temperature to a second temperature value being different from the first temperature value, and

g) repeating steps b) to f).

8. The method according to claim 7,

wherein the discharge processes for determining the second resistance are carried out using a constant discharge current level.

9. The method according to any one of the claims 5 to 8,

wherein determining the third resistance comprises carrying out steps a) to i) for determining the first resistance and steps a) to g) for determining the second resistance respectively several times at different battery ages.