Method for computer-implemented determination of control parameters of a turbine

The invention relates to a method and a system for computer- implemented determination of control parameters of a turbine.

The operation of wind turbines is based on nominal character istic values of the wind turbine which characterize the wind turbines in terms of power output in dependency of wind speed. Using nominal parameters enables the manufacturer of the wind turbine to guarantee specific annual energy produc tion (AEP) to customers as the wind turbines are treated as having identical performance at its contractual rated point.

The nominal parameters therefore are used as a basis to de rive turbine control parameters (short: control parameters) with regard to a specific power output at a specific ambient condition, in particular wind speed. It is known that many components in a wind turbine are sensitive to temperature. As an example, the performance of permanent magnets in Direct Drive (DD) wind turbines, in terms of remanence and coercivi- ty, reversibly reduces as temperature increases, which reduc es torque and power and reduces the margins provided for de magnetization withstand under fault conditions. The operating temperature is a function of both the ambient air temperature and losses (e.g. copper loss, iron loss, self-heating due to magnet eddy currents). As a further example, the lifetime of insulations may be affected by temperature.

It is therefore essential to monitor the temperatures of sen sitive components during operation. However, it is extremely costly and complex and sometimes even not possible to fully instrument the critical components. Monitoring of the rotor and magnet temperatures is challenging as most sensors would require either an electrical connection via slip-rings there by affecting reliability and challenging on a large diameter and shaftless machine like a wind turbine, or wireless telem etry which increases complexity and cost and may also be challenging due to an electrically noisy environment (e.g. pulse-width-modulation fed windings).

As certain temperatures such as rotor magnet temperature are not readily available, the wind turbine is operated with suitable safety margins resulting in a loss of annual energy production (AEP). Alternatively, the wind turbine can be over engineered, i.e. a higher temperature grade of magnet may need to be used due to uncertainty of magnet temperatures. This alternative results in higher costs.

The same problems arise in other industrial processes, such as the operation of gas turbines.

It is therefore an object of the present invention to provide a computer-implemented method and a system which allow an op eration of a turbine with high power production while being protected at the same time. It is a further object of the present invention to provide a computer program product.

These objects are solved by a method according to the fea tures of claim 1, a computer program product according to claim 12 and a system according to the features of claim 13. Preferred embodiments are set out in the dependent claims.

According to a first aspect of the present invention, a meth od for computer-implemented determination of control parame ters of a turbine is suggested. The turbine may be a single wind turbine. The turbine may be a wind turbine of a wind park. In case the turbine is a wind turbine it comprises a generator. Alternatively, the turbine may be a gas turbine having a generator.

The method comprises the step of receiving, by an interface, one or more measurement values of turbine sensors. According to the number of turbine sensors spread over the turbine, a corresponding number of measurement values are provided. It is to be understood that the number of turbine sensors is ac quiring measurement values in predefined time intervals, re sulting in a data stream of measurement values received by the interface.

The method comprises as a further step, determining, by a processing unit, at components or turbine places being equipped or not with turbine sensors, one or more virtual pa rameters and/or temperatures by a simulation of the operation of the turbine, the simulation being made with a given tur bine model in which the one or more measurement values and one and more characteristic values of the turbine are used as input parameters.

The method comprises as a last step, deriving, by the pro cessing unit, the control parameters for the turbine from the one or more virtual parameters and/or temperatures.

Virtual parameters in the context of the present invention may be, for example, at least one of temperature, noise, vi brations, component stress and component strain.

By using a turbine model, which is a validated physical model coupled with nominal and/or measured manufacturing parame ters, in conjunction with a (small) number of measured per formance parameters in form of easier to measure measurement values, other parameters and/or temperatures can be predicted and/or estimated. This can be used, for example, to determine parameters of rotating components (e.g. magnets in a rotor of a motor or generator). The use of a (small) number of sensors can then be employed to confidently estimate the parameters and/or temperatures throughout the turbine with a high fidel ity which is determined by the turbine model fidelity rather than the number of sensors. This knowledge is used to operate the turbine closer to its potential thermal limits and there fore maintain high levels of AEP even if carrying certain faults, e.g. a cooling fan out of operation. Use of a turbine model which is bespoke to each turbine by using nominal and/or manufacturing data along with a number of readily measurable parameters, in particular temperatures, is used to predict a parameter and/or temperature of hard to reach/instrument components, thereby avoiding complex and costly sensors, such as slip-rings to carry signals from ro tating components to a static frame or telemetry or Wi-Fi. As a result, the suggested procedure enables decreasing the num ber of sensors to be installed at the turbine.

Considering suitable characteristic values for the turbine enables forming a tailored turbine "DNA" which can be regard ed as a unique map of characterizing turbine parameters. Hav ing knowledge about manufacturing tolerances of the turbine, a given turbine model can be fed with the characteristic val ues to determine whether the turbine is able to still produce power without getting damaged. In case of a wind turbine, the determination how much power can be generated according to the predicted and/or estimated parameters and/or temperatures can be derived from an associated power versus wind speed map which can be derived from the output of the given turbine model and which processes the one or more characteristic val ues of the wind turbine as input parameters in addition to the measurement values.

Hence, the characteristic values are considered in a turbine model to derive actual and turbine specific control parame ters. This mechanism on power maximization by using the given turbine model does not have negative impact to the existing turbine structure, such as generator, power converter and blades, etc. as their operation is considering nominal and/or actual characteristic values and functionality of turbine components .

According to a preferred embodiment, the turbine model is a physical model which is based on a number of equations found by simulations and/or validated test data and/or look-up ta- bles. The turbine model may, in addition, consider a number of measured performance parameters, such as temperatures, current load profile, etc. to determine, in case of a wind turbine, the power versus wind speed map for a specific wind turbine .

The one or more characteristic values may be retrieved and received, by the interface, from a database. The interface and the processing unit are part of a computer system. The computer system may be part of a controlling instance of the wind turbine. Alternatively, the computer system may be part of an external controlling system. The database may be stored on that computer system or may be an external database con nected to the computer system. The one or more characteristic values consist nominal parameters of the characteristic val ues (i.e. nominal characteristic values) and/or achieved or actual values of within manufacturing tolerance bands of the characteristic values (i.e. actual characteristic values) ob tained by measurement during the manufacturing process and collated, for a plurality of turbines, in the database.

The one or more characteristic values include one or more of: an airgap (between a rotor and a stator), a magnet perfor mance, a magnet dimension, a thermal conductivity and a coil resistance. In addition to the characteristic values, further characteristic values may be considered as well, such as var iations of stator segments and so on.

According to a further preferred embodiment, the one or more measurement values consist of a coil temperature and/or an ambient temperature and/or a current load profile. From these easy to measure values other parameters and/or temperatures can be predicted and/or estimated. The turbine model may con sider time constants for considering a thermal spread from the place of one or more temperature sensors to the component or turbine components for which the virtual temperature is to be determined. In addition the turbine model may be based on a heuristic approach due to various time constants of the components to be monitored. Due to that time based calcula tion the turbine model may be continually updated. This ena bles the consideration of reaction times which sometimes can be very long depending on materials and/or form of the compo nents, e.g. large thermal mass.

According to a further preferred embodiment, as further input parameters of the turbine model historical turbine sensor da ta and/or historical operating conditions may be processed for determining, by the processing unit, for the turbine, the virtual parameters and/or temperatures. Considering histori cal sensor data captured by physical and/or virtual sensors enables to receive information about the behavior of compo nents with respect to current power output and lifetime con siderations. Historical sensor data to be considered may con sist of component temperatures, ambient temperatures, wind speed, among others. The historical data may be compared with real-time sensor data during the past operation of the tur bine. The parameters and/or temperatures predicted by the model at locations that are equipped with sensors can also be compared with the actual measured values to act as a health monitor and indicate potential issues within the genera tor/turbine/sensors. A comparison of measured lifetime data with those resulting from the turbine model allows for a flexible exploitation of generous manufacturing margins to maximize, in case of a wind turbine, AEP according to a cur rent operation situation.

According to a further preferred embodiment, the turbine mod el considers a drive train consisting of a rotor hub, a gen erator and a converter, of the wind turbine. In case of a gas turbine, the turbine model considers a drive train consisting of a rotor hub, a generator and a converter. In addition or alternatively, the turbine model may consider blades and/or gearbox and/or nacelle and/or tower and/or cable and/or a transformer of the wind turbine. While the method described above can preferably be used to determine virtual parameters and/or temperatures of an elec trical drive train of the wind turbine, the method may also be used to monitor components of a converter of the wind tur bine to predict and/or estimate semiconductor temperatures based on heat sink coolant temperature inputs, semiconductor manufacturing data and electrical signals.

According to a second aspect of the present invention, a com puter program product directly loadable into the internal memory of a digital computer is suggested, comprising soft ware code portions for performing the steps of the method de scribed herein when said product is run on a computer. The computer program product may be in the form of a storage me dium, such as a CD-ROM, DVD, USB-stick or a memory card. The computer program product may also be in the form of a signal which is transferable via a wired or wireless communication line.

According to a third aspect, a system for computer-implemen ted determination of control parameters of a turbine is sug gested. The turbine may be a single wind turbine or a wind turbine of a wind park having a generator or a gas turbine having a generator. The system comprises an interface which is adapted to receive one or more measurement values of tur bine sensors, and a processing unit which is adapted to de termine at components or turbine places being equipped or not with turbine sensors, one or more virtual parameters and/or temperatures by a simulation of the operation of the wind turbine, the simulation being made with a given turbine model in which the one or more measurement values and one or more characteristic values of the wind turbine are used as input parameters and to derive the control parameters for the wind turbine from the one or more virtual temperatures.

The invention will be explained in more detail by reference to the accompanying figures. Fig. 1 shows a flow chart illustrating the steps of the method according to the present invention.

Fig. 2 shows a schematic diagram illustrating the steps for carrying out the method for determination of control parameters of a wind turbine.

Fig. 3 illustrates a schematic diagram illustrating a tur bine model which is used to determine improved con trol parameters of a wind turbine.

Fig. 4 illustrates exemplary temperature-time sequences of measured and determined temperatures.

In the following section, an example of the invention will be described by referring to a wind turbine. As will be under stood by the skilled person, the method can be used in other industrial applications as well, in particular in the field of gas turbines.

It is known that many components in a wind turbine are sensi tive to temperature, either with respect to power output or lifetime. For example, the performance of permanent magnets reversibly reduces as temperature increases, which reduces torque and power and reduces the margins provided for demag netization withstand under fault conditions. The operating temperature of a wind turbine is a function of both the ambi ent air temperature and losses (e.g. copper loss, iron loss, self-heating due to magnet eddy currents). As a further exam ple, the lifetime of insulations may be affected by tempera ture.

It is therefore essential to monitor the temperatures of sen sitive components during operation. To avoid costs and com plexity to fully instrument the critical components, it is suggested to monitor them by means of virtual temperatures which are predicted and/or estimated with a validated physi cal model in conjunction with a limited number of measured performance parameters of easier to measure coil tempera tures, ambient temperatures and current load profile.

The below described method enables a computer system to find a trade-off between minimizing the risk of damaging the wind turbine due to its thermal load and maximizing AEP.

Referring to Fig. 1, in step SI one or more measurement val ues of turbine sensors are received by an interface IF of a processing unit PU (Fig. 2). According to the number of tur bine sensors spread over the wind turbine, a corresponding number of measurement values is provided. As mentioned above, measurement values may be, for example, coil temperatures, ambient temperatures and current load profile. It is to be understood that the number of turbine sensors is acquiring measurement values in predefined time intervals, resulting in a data stream of the measurement values received by the in terface IF.

In step S2, the processing unit PU identifies, at components or turbine places being equipped or not with turbine sensors, one or more virtual parameters and/or temperatures by a simu lation of the operation of the wind turbine, the simulation being made with a given turbine model in which the one or more measurement values and one or more characteristic values of the wind turbine are used as input parameters. The simula tion is made with a given turbine model in which spread of temperature based on the measurement values is modelled. In addition, one or more manufacturing tolerances of character istic values for the wind turbine are used as input parame ter.

In step S3, control parameters CP for the wind turbine are derived from the one or more virtual parameters and/or tem peratures.

The turbine model may use a heuristic approach due to various time constants of the components and so the turbine model may be continually updated. In addition, the turbine model allows for error checking against measured parameters.

The possibility to use a small number of sensors (which might be low cost sensors) only enables to confidently estimate the parameters and/or temperatures throughout the wind turbine and its generator, respectively, with a high fidelity (deter mined by the model fidelity rather than the number of sen sors). The parameters and/or temperatures found by the tur bine model will be used to operate the wind turbine closer to potential thermal limits and therefore maintain high levels of AEP even if carrying certain faults, such as an operation with a cooling fan out of operation.

Although above described procedure has been described by a determination of temperatures of the wind turbine it is to be understood, that other parameters can be predicted and/or es timated using the turbine model alternatively or additional ly. Examples for such parameters are noise and vibrations as well as component stress and/or strain.

Although the description is related to a wind turbine in gen eral, the described method can be used to model, in particu lar, the behavior of its generator. Other applications might include the use of a component level model of the converter, which can estimate semiconductor temperatures based on heat sink coolant temperature inputs, semiconductor manufacturing data and electrical signals.

The method and the turbine model, respectively, preferably consider the impact of individual turbine manufacturing tol erances on the turbine performance, thereby allowing the pre diction and/or estimation of parameters and/or temperatures of the wind turbine. Due to the consideration of individual turbine manufacturing tolerances, the wind turbine can be op erated in an optimized manner resulting in a maximized AEP. However, it is to be understood the turbine model can be fed with nominal characteristic values as well. In a further im- plementation, both nominal characteristic values and actual characteristic values considering the manufacturing toleranc es may be used as input information in the turbine model.

Referring to Fig. 2, in a first or preparing step, measure ment of manufacturing data MMV is executed. Manufacturing tolerances having an impact on the turbine performance are, for example, an airgap AG, a magnet performance MP (as a re sult of the magnet material and/or dimensions MDM and/or man ufacturing processes), thermal conductivity TC, and coil re sistance CR. Each of these manufacturing tolerances are char acteristic values which are individual for each turbine to be considered. The manufacturing tolerances of these character istic values AG, MP, MDM, TC, CR do have an immediate impact on the turbine performance, both in normal operation without any issues and during operation when an issue has occurred.

The manufacturing tolerances, typically different for every turbine (turbine DNA), of the characteristic values AG, MP, MDM, TC, CR are collated and stored in a database DB. For each turbine Tl, ..., Tn (where n corresponds to the number of wind turbines in a wind park WP with n ³ 1), a manufacturing dataset MD _Ti , ...,MD _Tn may be stored containing the characteris tic values AG, MP, MDM, TC, CR. The manufacturing dataset MD _Ti , ...,MD _Tn may be regarded as DNA of each individual wind turbine Tl, ...,Tn. It is to be understood that storing of man ufacturing data consisting of the manufacturing tolerances of characteristic values AG, MP, MDM, TC, CR may be made in any way, such as a lookup-table, associated maps, etc.

The manufacturing tolerances of the characteristic values AG, MP, MDM, TC, CR are received at the interface IF of a comput er or computer system. The computer or computer system com prises the processing unit PU. The database DB may be stored in a memory of the computer (system) or an external storage of the computer (system). The database DB may be cloud based in another implementation. The processing unit PU is adapted to determine, for each of the number of wind turbines Tl, ..., Tn, a power versus wind speed map M _Ti , ..., M _Tn . The power ver sus wind speed map M _Ti , ..., M _Tn is calculated from the above mentioned given turbine model TM with the actual characteris tic values AG, MP, MDM, TC, CR considering manufacturing tol erances of the respective wind turbines Tl, ..., Tn and/or ac tual characteristic values AG, MP, MDM, TC, CR and the one or more measurement values MVi of turbine sensors (where i cor responds to the number of turbine sensors), as input parame ters.

For each type of wind turbine, a specific turbine model may be provided. In an alternative embodiment, a specific turbine model may be used for a respective wind turbine of the wind park. In a further alternative embodiment, a common turbine model may be used for all wind turbines of the wind park.

The turbine model is a physical model which is based on a number of equations found by simulations and/or validated test data. The turbine model can be regarded as a "digital twin" for each individual wind turbine. The power versus wind speed maps M _Ti , ..., M _Tn of each individual wind turbine Tl, ..., Tn are unique maps resulting from the turbine model and the nominal and/or characteristic values AG, MP, MDM, TC, CR as well as the one or more measurement values MVi of turbine sensors. They are created for the turbines having no malfunc tions. In addition, additional maps for each turbine may be created for all possible malfunctions. These maps may be cre ated in advance, i.e. before a respective issue is deter mined. Alternatively, these maps may be created upon receiv ing the information ML in indicating a component malfunction.

Fig. 3 illustrates an embodiment of the turbine model used to model an individual wind turbine. In this embodiment, the turbine model TM considers an electrical drive train of the wind turbines consisting of a rotor hub ROT, a generator GEN, a converter CON, cables CAB and auxiliary/ancillary compo nents AUX, and a transformer TRF. However, the turbine model TM can also consider further components of the wind turbine, such as blades, nacelle, tower, sub-stations, gearbox (for geared-drive turbine) and so on.

The turbine model TM calculates the losses of components within the drive train to account for the loss in pow er/energy between the turbine blade input and the output to grid during the electromechanical energy conversion and an cillary or supporting systems. As the loss mechanisms are temperature dependent and themselves generate heat, the tur bine model TM is coupled or includes a thermal model for the generator GEN (generator thermal model GTM) and/or a thermal model for the converter CON (converter thermal model CTM) and is solved iteratively. The generator thermal model GTM and the converter thermal model CTM are coupled to components af fecting the cooling of the drive train, such as cooling sys tem COOLS (e.g. cooling fans), heat exchanger HX, and nacelle ambient NAAMB.

The turbine model TM calculates the available power P _out at the (grid) output based on the input ambient conditions of wind speed WS and temperature ATMP. The turbine model TM can be used to assess the potential AEP for a given wind turbine and site by inputting historical and/or predicted wind condi tions over a given period of time. The use of the thermal models GTM, CTM allows for any control features such as high temperature curtailment to be accounted for accurately. Al ternatively, the turbine model TM can be employed in real time to assess the potential output and/or impact of control decisions on a specific generator operating point. Further more, it may be used as reference against the actual turbine comparing actual and predicted operation in response to the operating conditions to act as a health monitor.

The turbine model TM can be implemented in a number of dif ferent environments/programming codes. Typically, it may be based on iterative solver routines to handle both thermal coupling and control algorithms. Where possible, reduced or der models, look-up tables or functions (equations) are used to represent complex behaviors using suitable approximations and/or assumptions to ensure short computation times whilst maintaining a suitable level of accuracy.

The turbine model TM, as shown in Fig. 3, may be extended to include blade models or structural models of the turbine.

Such a model can be used to represent any electrical drive/generator system beyond the wind turbine.

More detailed the turbine model TM includes the following sub-models :

A rotor model for modelling the rotor ROT by converting wind speed WS into a rotor/blade rotational speed RS and mechani cal power P _{mech (} i.e. input torque M).

An optional bearing model for modelling the bearing by ac counting for non-ideal main bearings and hence power loss.

A generator model for modelling the generator GEN by consid ering the main mechanical to electrical energy conversion ac counting for the torque capability, voltage production and losses incurred in conversion: This may be implemented by a numerical computation of the electromagnetic performance (e.g. Finite Element Analysis), an analytical model, or a hy brid of these which uses a Reduced Order Model (ROM) in which the generator performance is derived through a-priori numeri cal modelling and distilled into simpler functions or look-up tables. The generator model is also adapted to calculate losses incurred in the conversion such as winding copper losses and stator electrical steel iron losses. It accounts for control decisions.

A converter model for modelling the converter CON: In a di rect dive permanent magnet generator the variable frequency output of the generator is interfaced with the fixed frequen cy grid via a power electronic converter (active rectifier - DC link - inverter) which allows for control of the generator operating conditions. The load dependent switching and con duction losses in the converter are accounted for.

A cable loss model for modelling the cables CAB by considera tion of Ohmic losses in connections cables.

An auxiliary/ancillary loss model for modelling auxilia ry/ancillary components AUX by accounting for power consumed by supporting services such as cooling fans, pumps and hy draulic control systems as these losses detract from the available power at the grid.

A transformer loss model for modelling the transformer TRF by accounting for Ohmic winding losses and core losses which are dependent on load conditions.

Thermal models of the generator GEN and the converter CON:

The performance and losses of the above components are tem perature dependent. For example, the resistance and hence copper losses produced by the stator electrical windings in crease due to the copper resistivity dependence on tempera ture and the flux produced by a permanent magnet (the field source in the generator) varies due to changes in the materi al remanence with temperature. As the losses themselves in crease component temperature the above loss models are calcu lated iteratively with the respective thermal model GTM, CTM. As with the generator model, this may be implemented by a Re duced Order model using parameters derived from numerical modelling e.g. CFD and Thermal FEA to create an equivalent circuit or lumped parameter network.

A number of maps M _R , M _Ti and M _T3 resulting from the turbine model TM is illustrated in the P-WS-diagram (power versus wind speed map PWM) of Fig. 2. In this diagram, a map M _R of a wind turbine which is calculated based on nominal parameters and two maps M _Ti and M _T3 for turbines Tl, T3 which are based on a bespoke turbine model and measurement values MVi of tur bine sensors are illustrated. By way of example only, the maps M _TI and M _T3 of the turbines Tl, T3 show that (at least some of) the manufacturing tolerances of the characteristic values AG, MP, MDM, TC, CR are different from that of the nominal turbine resulting in an additional power P for a giv en speed WS and/or the temperatures are lower than those of the wind turbine with nominal parameters.

Based on their associated power versus wind speed maps con trol parameters CP can be derived for each individual turbine (either with or without a malfunction) which are used for controlling the wind turbines.

Fig. 4 illustrates two exemplary temperature-time sequences (TMP-t sequences) of a generator of a wind turbine. In the upper diagram of Fig. 4, a measured coil temperature is de noted with TMP _RcT and virtual magnet temperatures determined by the turbine model are denoted with TMP _V , _MT - AS can be seen the temporal development of the temperatures corresponds with each other, thereby having an offset due to different places in the generator.

In the lower diagram of Fig. 4, a measured temperature of a component, e.g. of the coil, is denoted with TMP _R and the virtual magnet temperature of the component determined by the turbine model is denoted with TMP _V . As long as no problem arises, the temperatures correspond to each other. OCC de notes a problem which can be determined by a significant de viation of the two temperatures TMP _R and TMP _V . Comparing measured and determined temperatures can be used for health monitoring and would provide an alarm/report that a potential problem/issue has occurred and corrective/preventative action can be taken.

The temperatures TMP _R and TMP _VR , _CT represent measurement values MVi of turbine sensors, as described above.

The method described above may be used for wind turbines of a wind park which consists of a number n of turbines. It is to be understood, that the number of wind turbines may be arbi trary. The number of wind turbines may be one (1), i.e. the wind park corresponds to a single wind turbine. If the number of wind turbines is greater than one, the wind turbines pref erably are arranged in proximity to each other, to supply the total produced power at a single point to an energy grid.

By using a turbine-specific model and evaluating parameters and/or temperatures, the decision can be made as to what pow er level the turbine can be safely operated at. Thus maximum power can be produced from the turbine within safety limits found in the turbine model. For example, if at one turbine one of the fans has stopped working, the thermal performance of the turbine model for that particular turbine can be mod elled with one less fan. This will provide the new reference power requirements whilst remaining within the generator lim itations and whilst also accounting for any specific charac teristics of that turbine.

If this turbine would be operated at reduced power, however, without the above evaluation, the revised operating point could be underestimated so losing AEP or overestimated lead ing to extra faults, thermal overload (reducing the turbines overall lifetime) or damage.

Consideration of the impact of individual turbine manufactur ing tolerances and virtual parameters and/or temperatures on the turbine performance and using them in a turbine model for each individual turbine allows for maximizing of an AEP through a wind park optimization by operating the turbines in an optimized manner, even in case of a component malfunction, at each location based on its individual turbine performance.

Comparing measured lifetime data in the form of historical data AD which are received from the processing unit in addi tion to the manufacturing data allows for a flexible exploi tation of generous manufacturing margins to maximize AEP. In addition, the processing unit PU is able to incorporate health monitoring features through a comparison of measured parameters, such as component temperatures against those which may be predicted by the turbine model TM. The comparison of physical turbine data can be made with the associated turbine model TM to monitor situations where the turbine may be underperforming as well as providing possible insight into reasons of an underperforming. The comparison can flag potential issues and call for servicing as well as providing learning for future turbine development.

The invention encompasses the use of a turbine specific model in order to model certain scenarios, in particular within the turbine drive train, to extract power according to tolerable parameter and/or temperature limits. The turbine model intro duces a level of model fidelity that allows these different scenarios to be modelled. This will increase wind park avail ability and allow strict availability minimum limits to be met.