A method and arrangement for controlling heating of a wind turbine blade

Abstract

A method for controlling at least one heating element of at least one wind turbine blade, the method comprising at least obtaining thermal properties relating to at least a first position on the at least one wind turbine blade and at least a second position on the at least one wind turbine blade, wherein said first position is associated with a first layer of a layer structure model representing the wind turbine blade and said second position is associated with a second layer of the layer structure model, obtaining a target temperature or a target temperature range for at least one target position on the at least one wind turbine blade, wherein said target position is associated with any layer of the layer structure model, obtaining one or more environmental parameters, and controlling at least one switching device provided in connection with the at least one heating element of the wind turbine blade to approach the target temperature or target temperature range at the target position based on the obtained environmental parameters and the obtained thermal properties and by utilizing a heat transfer model associated with the layer structure model.

Description

[0001]A METHOD AND ARRANGEMENT FOR CONTROLLING HEATING OF A WIND TURBINE BLADE TECHNICAL FIELD OF THE INVENTION The invention relates to wind turbines in general. More specifically, the invention relates to utilizing a heat transfer model associated with a layer structure model of the wind turbine blade to control at least one switching device provided in connection with at least one heating element of the wind turbine. BACKGROUND OF THE INVENTION Heating elements are widely used in connection with wind turbine blades to prevent or reduce formation of ice on the blades, which can significantly hinder their performance. Efficiently controlling heating of the blades with such heating elements may be difficult. The heating should be provided at a level that is sufficient to melt ice present on the blade and / or prevent the formation of ice on the blade, yet excess heating is not only a waste of energy but may also be degrading to the structure of the blade if the blade exceeds temperatures that are damaging to the blade materials. In many cases measuring or monitoring a real-time temperature of the wind turbine blade may be problematic. Temperature sensors that are used for this purpose are typically expensive, are subject to malfunction, are expensive to maintain, and complicate lightning protection of the blade. Sensors additionally only measure temperature highly locally, giving a temperature at a single point of the wind turbine blade. Wind turbine blades are large structures, and to efficiently monitor their temperatures, a large amount of temperature sensors should be utilized. Each additional temperature sensor may add to complexity of e.g., associated wiring arrangements. The weight of a wind a turbine blade is also highly relevant when considering efficiency, and each temperature sensor will add to the weight of the blade. Temperature sensors, their wiring, installation and maintenance work increase the cost of such blades and cost of energy. Thus, the number of sensors used should preferably be maintained as low as possible. Wireless sensors could provide benefits over wired sensors, but the sampling frequency, signal strength, and battery life of wireless sensors may not be high enough to be able to efficiently control heating of the wind turbine blade. Furthermore, rapidly changing environmental conditions may lead to temperature changes in the blade that cannot be detected with temperature sensors. Some prior art solutions present methods for estimating a temperature of the wind turbine blade and controlling heating of the blade based on the estimated temperature. These solutions, however, do not allow accurate evaluation of the blade temperature at differing positions on the wind turbine blade. It would be advantageous to devise a method for controlling a heating element of a wind turbine blade to provide an amount of heating power that is adequate for heating the blade to a desirable temperature, while avoiding excess power use. SUMMARY OF THE INVENTION An object of the invention is to alleviate at least some of the problems in the prior art. In accordance with one aspect of the present invention, a method for controlling at least one heating element of at least one wind turbine blade is provided, the method comprising at least obtaining thermal properties relating to at least a first position on the at least one wind turbine blade and at least a second position on the at least one wind turbine blade, wherein said first position is associated with a first layer of a layer structure model representing the wind turbine blade and said second position is associated with a second layer of the layer structure model, obtaining a target temperature or a target temperature range for at least one target position on the at least one wind turbine blade, wherein said target position is associated with any layer of the layer structure model, obtaining one or more environmental parameters, and controlling at least one switching device provided in connection with the at least one heating element of the wind turbine blade to approach the target temperature or target temperature range at the target position based on the obtained environmental parameters and the obtained thermal properties and by utilizing a heat transfer model associated with the layer structure model. An arrangement for controlling at least one wind turbine blade is also provided according to independent claim 19. According to further aspects of the invention, a computer program product is provided according to independent claim 20, a non-transitory carrier medium according to claim 21, and a system is provided according to independent claim 22. Through the present invention, heating of a wind turbine blade may be carried out efficiently, where the heating that is provided is adequate for preventing ice formation and / or melting ice formed on the wind turbine blade, while yet avoiding excessive power consumption. Compared to prior art solutions, the estimation of how temperatures of different positions on the wind turbine blade change over time can be determined more accurately due to the use of a heat transfer model associated with a layer structure model. Since the thermal properties of a plurality of different layers constituting the wind turbine blade in the layer structure model may be taken into consideration and a target position may be precisely determined or selected, it may be possible to accurately control the temperature at a selected position on the wind turbine blade. With the invention, the effects of a complex system and associated thermal phenomena may still be modeled simply enough to allow a processor to simulate the system in real time without detrimental loss of accuracy. Furthermore, any changes occurring in either environmental parameters or structural parameters of the wind turbine blade may be considered efficiently and in a timely manner. In some prior art solutions where simple models and calculations are used to estimate a temperature of a wind turbine blade, any change in structural parameters (such a change in a material of one or more layers of the wind turbine blade) necessitates the model to be constructed and validated. In the present solution, changes in structural parameters may be implemented by only obtaining new indications of such parameters and utilizing them directly in the model. The present invention may therefore be easily implemented in cases where parameters associated with one wind turbine blade change and / or in different cases where the parameters associated with different wind turbine blades differ. Any further parameters that may affect how heat is transferred in the layer structure of the wind turbine blade, such as a liquid water content of air flow, may also be considered without extensive changes to the layer structure model and / or the heat transfer model. The method may be carried out entirely without temperature measurement of the wind turbine blade or by using only a limited amount of temperature sensors which may only be required to be utilized more seldomly than in the prior art. For instance, if temperature sensors are used, one sensor per wind turbine may suffice. The method may comprise obtaining one or more structural parameters of the at least one wind turbine blade, optionally comprising a thickness and / or material of at least the first layer and / or the second layer, wherein obtaining thermal properties relating to the at least first position and the second position comprises determining thermal properties of the first layer and / or the second layer based on the obtained structural parameters. The method may comprise obtaining a maximum temperature for at least one of the first position and second position on the at least one wind turbine blade, wherein the controlling of the at least one switching device is carried out such that the maximum temperature(s) is essentially not exceeded or such that an average temperature of at least the first and / or second position during a selected time period essentially does not exceed the maximum temperature(s). Here, the integrity of all or at least selected material layers of the wind turbine blade may be ensured, as the temperature of any selected layer or associated position may be kept under a maximum temperature. A selected maximum temperature could momentarily even be exceeded, yet with the present invention, at least considering a certain time period, an average temperature of any selected position on the wind turbine blade may be maintained below a maximum temperature. In prior art solutions a general temperature of a surface of a wind turbine blade may be considered, but in these solutions it is possible that some portion of the wind turbine blade comprising e.g. different material than some other portion exceeds a temperature that the considered material can withstand, and thus the integrity and / or lifetime of the wind turbine blade may be compromised. The method may comprise determining at least one estimated temperature of at least one considered position on the at least one wind turbine blade, comprising at least determining an estimated temperature for the first position, second position, and target position, at a selected time, and / or the method may comprise determining at least one heating power reference for the target position for approaching or maintaining the target temperature or target temperature range, preferably by determining a thermal equilibrium state for the target temperature. The controlling of the at least one switching device may then comprise controlling the switching device based on the at least one estimated temperature or the determined heating power reference. The controlling of the at least one switching device may thus be determined based on determined estimated temperatures considering positions on the at least one wind turbine blade or the controlling of the at least one switching device may be determined without determining a temperature of any position of the wind turbine blade but based on required heating power reference for approaching the target temperature or target temperature range. Considering an embodiment where the method comprises controlling of the at least one switching device based on a determined temperature, the method may additionally comprise obtaining a starting temperature for at least the target position, preferably further obtaining a starting temperature for the first position and / or second position, the method further comprising iteratively determining, at predetermined time intervals, an estimated temperature of at least the target position, preferably further determining an estimated temperature of the first position and / or second position. The method may further comprise obtaining, at the start of each iteration, an indication of the state (currently activated or deactivated) of the at least one switching device. A starting temperature at each iteration may be an estimated temperature determined at the previous iteration or wherein the starting temperature is a measured temperature, or a starting temperature based on one or more environmental parameters. Controlling of the at least one switching device based on a determined temperature may comprise deactivating the at least one switching device at latest when the estimated temperature of the target position reaches or exceeds the target temperature or a maximum value of a target temperature range and / or activating the at least one switching device when the estimated temperature of the target position falls below the target temperature or falls below a minimum value of a target temperature range. The method may comprise obtaining an indication of a maximum temperature for at least one of the first position and second position on the at least one wind turbine blade, wherein the controlling of the switching device comprises deactivating the switching device before the estimated temperature of the target position reaches or exceeds the target temperature or a maximum value of a target temperature range if an estimated temperature of the first and / or second position exceeds the maximum temperature. A method where the controlling of the at least one switching device is based on a determined temperature may further comprise a resetting procedure, wherein the at least one switching device is deactivated until it is determined that a temperature of at least one considered position on the wind turbine blade is essentially equivalent to an ambient temperature, optionally wherein said resetting procedure is carried out after a predetermined time from a start of the method or after a predetermined time after a previous resetting procedure. An estimated temperature may contain some error, whereby during iterative determination of the temperature(s), errors in the temperature may accumulate. With the resetting procedure, errors in determined temperatures may be reduced. The layer structure model may comprise at least two layers, comprising at least one structural element layer and at least one heating element layer, preferably wherein the layer structure model comprises at least three layers, comprising at least one inner structural element layer, at least one heating element layer, and at least one outer structural element layer. Obtaining one or more environmental parameters may comprise obtaining of one or more of an ambient temperature, wind speed, wind direction, liquid water content of air flow, and relative humidity. The method may further comprise obtaining one or more operating parameters of the wind turbine blade, the operating parameters comprising one or more of: rotor speed, blade pitch angle, rotor azimuth angle, and wind turbine yaw direction. The obtained thermal properties may comprise at least a heat capacity and / or thermal conductivity. The method may further comprise obtaining further parameters relating to one or more boundary conditions to be utilized in the heat transfer model. The further parameters may comprise at least one of a convection heat transfer coefficient relating to a first surface of the outermost layer of the layer structure model, said first surface facing the environment, a convection heat transfer coefficient relating to a second surface of the innermost layer of the layer structure model, said second surface facing an inner hollow portion of the wind turbine blade, and a heating power of the heating element. Embodiments of the method where the method comprises determining a heating power reference for the target position for approaching or maintaining the target temperature or target temperature range, the method may further comprise determining a pulse width modulated (PWM) control for the switching device. A cycle on time and a cycle off time of a PWM control may have any duration, but in some embodiments, the cycle on time and cycle off time may last for at least about one second or more in some embodiments. With a cycle on time and cycle off time of the PWM control lasting for at least one second or more, the low switching frequency may allow e.g. use of a contactor or solid state relay as the switching device. Traditional PWM control employs higher frequencies, with cycle on time and cycle of time lasting for some seconds, for instance, in which case the use of e.g. contactors may not be possible, since these cannot withstand as many switching counts and high switching frequencies. Yet, if contactors could be used, the use of power converters that are more expensive, more complex, and generate more waste heat could be avoided. A PWM control may be determined by dividing the heating power reference by a total available heating power, wherein the total available heating power corresponds to a maximum heating power that is deliverable via the heating element. The heat transfer model utilized in a method may be a one-dimensional model, wherein the first position, second position, and target position reside essentially along a first normal of the surface of the wind turbine blade, said first normal residing at a first location on the surface of the wind turbine blade. Embodiments of the method may further comprise consideration of at least a second location on the surface of the wind turbine blade with respective second normal and respective at least first position, second position, and target position, wherein the controlling of the at least one switching device is carried out such that the target temperature or maximum value of a target temperature range of any considered target position is essentially not exceeded. The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific example embodiments when read in connection with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS Next the invention will be described in greater detail with reference to exemplary embodiments in accordance with the accompanying drawings, in which: Figure 1 shows at least a portion of one example of an arrangement for controlling at least one heating element of at least one wind turbine blade, Figure 2 illustrates one example of a system, Figure 3 shows at 3A a wind turbine blade and at 3B a cross-sectional view of the wind turbine blade illustrating an example of an associated layer structure model, Figure 4 shows a further example of a layer structure model, Figure 5 schematically illustrates a heat transfer model associated with a layer structure model, Figure 6 shows an example of determined temperatures in different positions with the heat transfer model associated with the layer structure model using temperature-based control, where 6A shows one location and 6B shows another location in a wind turbine blade, Figure 7 shows an example of temperatures when determining the reference power with the heat transfer model associated with the layer structure model using power-based control, where 7A shows one location and 7B shows another location in a wind turbine blade, and Figure 8 illustrates a flow chart of a method according to one embodiment of the invention. DETAILED DESCRIPTION Figure 1 schematically illustrates at least a portion of one example of an arrangement for controlling at least one heating element of at least one wind turbine blade. The arrangement comprises at least one processor 102. The processor 102 may be a microprocessor type controller device that may be integral with a wind turbine, such as implemented in connection with a general controller of the wind turbine that controls e.g. pitch angle of the blades or as a dedicated controller device that is integrated with the wind turbine, but separate from the general controller. The processor 102 may alternatively be part of a separate controller device such as a computer that resides at a distance from the at least one wind turbine. A processor 102 may also be arranged as a remote processor comprising one or more separate distributed units employing cloud computing platforms. The processor 102 may be configured to execute instructions embodied in a form of computer software stored in a memory, which may refer to one or more memory chips, for example, separate or integral with the processor 102. The processor 102 may comprise or be arranged to communicate with one or more databases 104, which may comprise data regarding e.g., layer structure model and / or heat transfer model parameters such as heat transfer coefficients, correlations, and / or material properties which will be discussed further below. At least one data interface 106 may be provided for providing communication capability to the arrangement to exchange data. Data may be exchanged with external systems and / or a UI (user interface) 103 may be provided and at least partially implemented by means of the interface 106. The arrangement may comprise or be arranged to be in communication with at least one switching device 108 which may be controlled by the processor and used to control an electric current being delivered to the heating element to activate or deactivate the heating element as determined by the processor 102. A switching device 108 may for example be an electromechanical switching device, such as contactor or relay, a semiconducting switching device such as solid-state relay, or a thyristor device. The switching device 108 may comprise or be in connection with a further control element which may be configured to control the switching device 108. A further control element may be a device configured to implement a pulse- width modulated (PWM) control and deliver a PWM signal to the at least one switching device 108 such as contactor or relay, a semiconducting switching device such as solid-state relay, or a thyristor device. The at least one processor 102 is configured to obtain thermal properties relating to at least a first position on the at least one wind turbine blade 112 and at least a second position on the at least one wind turbine blade 112. The first position is associated with a first layer of a layer structure model representing the wind turbine blade 112 and the second position is associated with a second layer of the layer structure model, as will be demonstrated further below. Thermal properties may include at least a heat capacity and / or thermal conductivity. The processor 102 may further be configured to obtain one or more structural parameters of the at least one wind turbine blade 112. The structural parameters may comprise at least a thickness and / or material of at least the first layer and / or the second layer. The structural parameters may be utilized to determine thermal properties of layers associated with considered positions of the wind turbine blade. Each layer of the layer structure model may be associated with a position, whereby each position may relate to one or more determined / obtained thermal properties. With obtained structural parameters, the lumped capacitance method may be used to determine thermal properties of the associated layer(s). Through use of the lumped capacitance method, modeling of heat transfer may be simplified such that heat transfer inside each separate layer is not modeled and heat transfer equations relating to the entire layer structure model are also simplified, leading to the present method being readily used in real time with relatively small computational capacity. Relating to parameters of the wind turbine, the processor 102 may additionally be configured to obtain operating parameters of the wind turbine blade, the operating parameters comprising one or more of: rotor speed, blade pitch angle, rotor azimuth angle, and wind turbine yaw direction. The processor 102 is also configured to obtain a target temperature or a target temperature range for at least one target position on the at least one wind turbine blade 112. The target position is also associated with a layer of the layer structure model. The target position may be one of the first or second positions, especially if the layer structure model comprises only two layers, or the target position may be associated with any layer of the layer structure model. The target temperature or targe temperature range may be obtained as input through data interface 106 or a target temperature may be predetermined and stored in database 104. The processor 102 is further configured to obtain an indication of one or more environmental parameters. Environmental parameters may comprise an ambient temperature, wind speed, wind direction, liquid water content of air flow, sun radiation, and / or relative humidity. The at least one processor 102 may be configured to obtain further parameters relating to one or more boundary conditions to be utilized in the heat transfer model. The further parameters may comprise at least a convection heat transfer coefficient relating to a first surface of the outermost layer of the layer structure model, said first surface facing the environment. The further parameters may additionally comprise a convection heat transfer coefficient relating to a second surface of the innermost layer of the layer structure model, said second surface facing an inner hollow portion of the wind turbine blade. One further parameter may be a heating power of the heating element 110. Further parameters such as radiation heat transfer may also be considered. The at least one processor 102 is then configured to control the at least one switching device 108 to approach the target temperature or target temperature range at the target position based on the obtained environmental parameters and the obtained thermal properties by utilizing a heat transfer model associated with the layer structure model. The heat transfer model may employ one or more boundary conditions. One or more operating parameters of the wind turbine blade may also be utilized. The controlling of the at least one switching device 108 may be implemented in different ways, as temperature-based controlling or power-based controlling. Temperature-based controlling may be based on determined estimated temperatures considering positions on the at least one wind turbine blade. Power-based controlling may be determined based on required heating power reference for approaching the target temperature or target temperature range. The controlling of the at least one switching device 108 may be carried out as open-loop control or closed-loop control. In the case of closed-loop control, one or more PID controllers or other control algorithms known by a skilled person may be employed. In closed-loop control, at least one determined or measured temperature may be utilized as a feedback parameter. In connection with temperature-based controlling, the at least one processor 102 may be configured to determine at least one estimated temperature of at least one considered position on the at least one wind turbine blade 112, comprising at least determining an estimated temperature for the first position, second position, and target position, at a selected time and using knowledge of a selected heating power being applied, such as a maximum heating power of the heating element 110. The selected heating power may also refer to a heating power of 0 W / m2, if it is determined that the heating element is deactivated. The selected time may be a current time or a future time. The processor 102 may additionally be configured to obtain a starting temperature(s) for at least the first position, the second position and the target position on the at least one wind turbine blade 112. The processor 102 may be configured to iteratively determine, at predetermined time intervals, an estimated temperature of at least the target position, preferably further determining an estimated temperature of the first position and / or second position. The determined temperature may be a temperature associated with a selected time, such as current time. The temperature may be determined for all positions considered associated with all layers in the layer structure model. At the start of each iteration, an indication of the state (currently activated or deactivated) of the at least one switching device 108 may be obtained by the processor 102. The state of the switching device may be used to determine the selected heating power to be used at the related iteration. A starting temperature at each iteration may be an estimated temperature determined at the previous iteration or the starting temperature may be a measured temperature or a starting temperature based on one or more environmental parameters, such as an ambient temperature. As may be appreciated by the skilled person, an ambient temperature may be used as a starting temperature for any position at the start of the method following the laws of thermodynamics. Controlling of the at least one switching device 108 based on a determined temperature may comprise deactivating the at least one switching device 108 at latest when the estimated temperature of the target position reaches or exceeds the target temperature or a maximum value of a target temperature range. The controlling of the at least one switching device 108 may further comprise activating the at least one switching device when the estimated temperature of the target position falls below the target temperature or falls below a minimum value of a target temperature range. The processor 102 may be configured to obtain an indication of a maximum temperature for at least one of the first position and second position on the at least one wind turbine blade 112. The controlling of the switching device 108 may then comprise deactivating the switching device 108 before the estimated temperature of the target position reaches or exceeds the target temperature or a maximum value of a target temperature range if an estimated temperature of the first and / or second position exceeds the maximum temperature. The maximum temperature(s) may be obtained as inputs e.g. from a user or the maximum temperatures may be predefined and could be based on the material of the layer in question. Any maximum temperatures may be stored in a database and retrieved upon need. The processor 102 may further be configured to initiate a resetting procedure, wherein the at least one switching device 108 is deactivated until it is determined that a temperature of at least one considered position on the wind turbine blade is essentially equivalent to an ambient temperature. The resetting procedure may be carried out after a predetermined time from a start of the method or after a predetermined time after a previous resetting procedure. If there is a temperature measurement available, this may be considered in the heat transfer model by adding a separate layer for the measuring sensor in its location. For example, the temperature of the outer / inner surface may be measured, and the measurement result is compared to the modeled temperature of the corresponding position and layer using a known statistical method. If the error between the modeled and measured temperature is low enough the resetting function may not be activated. Power-based controlling of the at least one switching device 108 may comprise determining at least one heating power reference for the target position for approaching or maintaining the target temperature or target temperature range by determining a thermal equilibrium state for the target temperature. The processor 102 may further be configured to determine a pulse width PWM control for the switching device. A PWM control may be determined by dividing the heating power reference by a total available heating power, wherein the total available heating power corresponds to a maximum heating power that is deliverable via the heating element 110. A cycle on time and a cycle off time of a PWM control may last for at least about one second or more in some embodiments. Inputs and data required by the processor, such as the obtained environmental and operational parameters, thermal properties, structural parameters, and / or boundary conditions to be utilized in the hat transfer model may be obtained via the one or more databases 104, data interfaces 106, sensor elements 114, while some may be provided on demand e.g., by a user of the arrangement. In one embodiment, an arrangement may comprise or be in communication with at least one sensor element 114. The at least one sensor element 114 may be a temperature sensor configured to detect an ambient temperature. Further sensor elements 114 may comprise one or more wind speed sensors, liquid water content sensors, ice sensors, and / or humidity condition sensors, for example. Environmental conditions data may additionally or alternatively be obtained by the processor 102 from external sources, such as weather providers through data interface 106. In one embodiment, at least one sensor element 114 may be configured to detect a temperature of at least one position on the wind turbine blade 112. A measured wind turbine blade temperature may be used to determine a starting temperature for a selected position and / or to correct a determined temperature value for a selected position. An arrangement may be provided integrated with a wind turbine or at least portions of the arrangement may be provided as separate entities. The connection or communication between entities of an arrangement or system as described below may be wired or wireless, depending on the embodiment. Figure 2 shows a schematical illustration of a system that may be provided. A system may comprise components described above in connection with an arrangement for controlling heating of at least one wind turbine blade, wherein the system additionally comprises at least one wind turbine 116 comprising at least one wind turbine blade 112 comprising at least one heating element 110. Any wind turbine blade 112 may comprise more than one heating element 110. As shown in Fig.2, one processor 102 or arrangement may be configured to control a plurality of switching devices 108 as required in connection with a plurality of wind turbine blades 112 and also a plurality of wind turbines 116. Also, one or more sensor elements 114 can be connected to or in communication with processor 102 to provide for example environmental parameters such as ambient temperature, wind speed, and / or icing. Switching devices 108, heating elements 110, and / or sensor elements 114 that are provided with separate wind turbine blades, for instance, are not depicted in Fig. 2 and such elements may be provided as integrated within the wind turbines 116. A system may alternatively comprise only one wind turbine 116, in connection with which a processor 102 is provided as an integrated element. In such a case, one processor 102 may be configured to serve the one or more heating elements provided on the wind turbine. Figure 3 shows at 3A a wind turbine blade 112. A coordinate system may be considered regarding any location on the blade surface such that a direction z is codirectional with a normal of the blade surface. Figure 3B shows a cross- section A-A of the wind turbine blade 112 of Fig.3A. The wind turbine blade 112 has a hollow portion 202 and a shell portion 204. The wind turbine blade 112 may also comprise a shear web portion (not depicted). The shell portion 204 may be represented by a layer structure model comprising at least two layers. The example of Fig.3B shows a layer structure comprising three layers, a first layer 206, a second layer 208, and a third layer 210. In the example of Fig.3, the first layer 206 may be an inner structural element layer, the second layer 208 may be a heating element layer, and the third layer 210 may be an outer structural element layer, such as protective layer of the heating element layer. If a shear web portion of a wind turbine blade 112 is to be accounted for in the method, the layer structure model may be adapted to include such layer. Fig.3B also shows examples of a first position 212, second position 214, and target position 216. A target position may also essentially correspond to a first or second position. The first position 212, second position 214, and target position 216 may essentially reside along the same line in the z direction and may constitute a one-dimensional model of a layer structure. The first position 212, second position 214, and target position 216 are utilized in the heat transfer model and be representative of positions on the wind turbine blade 112. Depending on an associated location with respect to a longitudinal axis or cross-sectional axis of the wind turbine blade 112 (referring to the axes x and y), an associated layer structure model may differ e.g. regarding thicknesses of the layers and / or a number of layers. A thickness of layer(s) may be thinner towards a tip of the wind turbine blade. A thickness of layer(s) and / or a number of layers may vary between different locations on the wind turbine blade 112 regarding either of the axes x or y. Regarding one wind turbine blade 112, a plurality of locations may be considered, each with respective first positions 212, second positions 214, and target positions 216, which may also be utilized in controlling at least one switching device 108, where the separate respective positions relate to different locations along a longitudinal and / or lateral axis of the wind turbine blade 112. In one embodiment, the plurality of locations (such as a root location and a tip location) and respective positions may be considered, and controlling of the switching device is based on parameters determined by using a heat transfer model associated with both locations to control the heating element such that a selected target temperature at a selected position is achieved or at least approached. Figure 4 shows a further example of layer a structure model that may be used to represent the shell portion 204 of a wind turbine blade 112. The example of Fig.4 comprises five layers, with a first layer 206, second layer 208, third layer 210, fourth layer 218, and fifth layer 220. A layer structure model may comprise any number of layers and may comprise e.g. a protective layer of the heating element 210, a paint or coating layer of the wind turbine blade, or a layer representing a sensor element, to name some further examples. A layer of the layer structure model may also comprise an ice or snow layer as an outer layer. This may be used especially in the case of a de-icing situation, where the arrangement may be used to determine a heating time and / or heating power for removing the layer of ice or snow. Each layer may be associated with a material, which may be a homogenous material such as paint, coating, adhesive, plastic, steel, or a layer may comprise composite material such as glass fiber material or carbon fiber material. Each layer and / or associated material may be assigned with respective material properties comprising at least the thermal properties comprising for instance heat capacity and / or thermal conductivity. Such parameters may for example be stored in the at least one database 104. A lumped capacitance method may be used for each layer, such that a thermal behaviour of the layer is assumed to be constant within the layer along the z direction. One layer in the layer structure model may also be used to represent several consecutive layers of the actual wind turbine blade 112. For example, an outermost layer of the layer structure may be representative of a paint layer and a protective glass fiber layer of the wind turbine blade 112, or structure under heating element consisting for example a glass fiber – balsa sandwich structure may be represented by a single layer in the layer mode. Figure 5 shows one more layer structure model and illustrates parameters that may be utilized with an associated heat transfer model. In general, a layer structure model may be considered to comprise n layers. The exemplary layer structure model comprises a first layer 206, a second layer 208, and a third layer 210, such that n=3. Each of the layers may be associated with at least a temperature T, a heat capacity C, and a thermal conductivity k. Regarding a model as shown in Fig. 5 with n=3 layers, it may considered that Tn=T3, Cn=C3, and kn=k3. The interfaces between the layer structure and the environment and hollow portion 202 of the wind turbine blade 112 are associated with convection heat transfer coefficients h. A first surface of the outermost layer of the layer structure model (here the third layer 210), where the first surface faces the environment, is associated with a first convection heat transfer coefficient h0. A second surface of the innermost layer of the layer structure model (here the first layer 206), said second surface facing an inner hollow portion of the wind turbine blade is associated with a second convection heat transfer coefficient hn+1. In the example of Fig.5 with n=3, it may be considered that hn+1=h4. Values for either of hn+1 or h0 may be obtained via a database or an external source as literature values, may be obtained as inputs by a user, or may be obtained through modeling. T0 refers to an environmental temperature and Tn+1 refers to a temperature of the hollow portion 202 of the wind turbine blade. Tn+1 may be measured or determined through modelling, or may be considered as equivalent to T0. In the example of Fig.5 with n=3, it may be considered that Tn+1=T4. In the example of Fig.5, the first layer 206 represents an inner structural layer comprising glass fiber composite, the second layer 208 represents a heating element layer comprising carbon fiber composite, and the third layer 210 represents an outer structural layer comprising paint and glass fiber composite. In the following, one example method of applying a heat transfer model with temperature-based controlling of the switching device 108 will be discussed. In the heat transfer model, for every layer transient heat is equivalent to the amount of heat that is delivered to said layer subtracted by the amount of heat that is carried out of said layer. Using the lumped capacitance method it is assumed that temperature difference inside each layer is negligible, thus each layer may be represented by one heat capacitance value. In an example associated with the layer structure model of Fig.5 with n=3 layers, the following set of equations may be applied: In equation set (1), P refers to a heating power applied by the heating element 110, dt refers to a time derivative, and dT refers to a temperature derivative. Using the Euler method (with the Euler method being used here as an example) where ^^ ^^ = ^^^^− ^^^^−1(2) ^^ ^^ = ∆ ^^ (3) it may be possible to obtain temperature estimates for each layer as: By solving the system of equations, a set of equations for temperature estimates (determined temperatures) for each position / layer may be obtained. The skilled person may readily solve such equations, which will not be demonstrated here due to complexity, but these equations will depend on constants and variables as follows: To demonstrate how the heat transfer model and layer structure model may be applied, below is one considered example with n=3 and selected values given for demonstrative purposes. Table 1 gives examples of values that may be used for thermal properties of layer structure model where n=3. Table 1: Exemplary thermal properties for layer structure model. Layer 1 Layer 2 Layer 3 C [J / K m2] 2000 1000 9000 k [W / m2K] 100 - 30 Further parameters that are obtained and used as boundary conditions in the heat transfer model may relate to the convection heat transfer coefficient h0 associated with the first surface and the second convection heat transfer coefficient h4 associated with the second surface. Such coefficients may e.g. obtained from a database or other source or as user input, but in this example they are calculated using at least an ambient temperature (assumed here to be -5 °C), wind speed 10 m / s, and wind turbine blade rotor speed 9 rpm. In this example, two selected locations are considered on the wind turbine blade, with each location being associated with three respective positions on the wind turbine blade, with the positions being associated with the different layers of the layer structure model. A first location is at the tip of the wind turbine blade and a second location is at the root of the wind turbine blade. Such locations are in this example located at positions x1=81.5 m and x2=28.5m along the x axis of the wind turbine blade. Air flow speed v at the selected locations may be calculated as: giving vtip=77.5 m / s and vroot=28.6 m / s. The convection heat transfer coefficients may be determined for selected locations using a nonlinear regression line derived from data regarding a large set of convective heat transfer coefficient simulations. The following equation may be utilized, where a, b, and c are constants: ℎ0= ^^ ∗ (1 − ^^− ^^∗ ^^) + ^^(9)With selected values for a, b, and c, one may obtain values of h0,tip = 223 W / m2K and h0,root = 53 W / m2K. From literature and experience, a value of h4 = 5 W / m2K may be utilized. In general, the effect of the liquid water content of air flow on convective heat transfer coefficients may be taken into account as being constant, as differing between a selected set of values based on freezing conditions that prevail, e.g. based on ice conditions measurement, or by determining a freezing condition by measuring an amount of liquid water using a sensor for detecting freezing intensity. As a further parameter to be used as a boundary condition, values of maximum heating power of the heating element may be used as P2,tip = 3000 W / m2and P2,root = 1000 W / m2. In a first iteration, a starting temperature of -5 °C (ambient temperature) may be used for all positions at both selected locations on the wind turbine blade. If heating is on, then the defined maximum heating power for each location is used but if heating is off, then value P2=0 is used instead. temperature values determined at each iteration may be used as starting values for the next iteration. The timestep ∆t is the selected time interval between iterations, which in this example is 1 second. A target location may be associated with the first layer. A target temperature in this example may be selected as 3 °C. The target temperature may be considered as having a hysteresis of 1 degree. Therefore, a target temperature range may be from 2 °C to 4 °C. A maximum temperature is also obtained in this example for the first and second layers. The maximum temperature for both layers is 20 °C. Thus, in this example the switching element is activated if the temperature of the target position is under 2 °C and the switching element is deactivated if the temperature of the target position exceeds 4 °C or if the temperature of either the first or second layer exceeds 20 °C. Additionally, a minimum cooling time between heating cycles of 3 seconds may be employed. Figure 6 shows determined temperatures as a function of time, with temperature for the first location (tip) in Fig. 6A and temperature for the second location (root) in Fig. 6B. An ambient / outside temperature is also depicted. As can be seen from Fig. 6, the heating is started immediately at the start of the simulation. The first heating cycle ends as the second position at the tip location exceeds the maximum temperature. The second heating cycle is started after a minimum cooling time between heating cycles because at the root location, the temperature of the first layer is below the smallest value of the target temperature range. The second heating cycle ends as the maximum temperature is exceeded at tip location. The third heating cycle starts when the temperature at the first position in the root location goes below the smallest value of the target temperature range. The third heating cycle ends as a maximum temperature is reached again at tip location. Until time t = 400s, the heating cycles start when the temperature at the first position goes below the smallest value of the target temperature range and the heating cycles end when a maximum temperature is reached. From t = 400s onwards, the heating cycles are not affected by maximum temperatures (i.e. the maximum temperatures are not exceeded) and the controlling of the switching device is based on temperature at the target position, which exceeds the largest value of the target temperature range or falls below the smallest value of the target temperature range. In some embodiments, it may be possible to estimate a deicing time after switching on of a heating element. The deicing time may be determined based on a time that e.g. the target position has been at the target temperature or target temperature range. Next, an example of power-based controlling of the switching device will be demonstrated. The example is given as an open-loop control, but power- based controlling may also be carried out as closed-loop control. In closed- loop control, temperature estimates at one or more positions could be used as feedback parameters. In the closed-loop control alternative, temperature estimates may be determined iteratively and then used to determine a duty cycle for PWM control of the heating which will lead to a target temperature being achieved. The heat transfer model may be based on a thermal equilibrium state, where temperature derivates dT are set to zero, thus the following set of equations may be used: In the above, P is a heating power reference, corresponding to a heating power required for achieving a target temperature and T is the target temperature. The above set of equations for a required power reference may be solved by eliminating two of the three target temperatures. The target temperature is here considered only for the first layer, and the target temperatures for the second and third layers may thus be left unconsidered. The power reference to be solved may then be obtained as: The values for parameters used in the example for temperature-based controlling will be applied also in this example. Upon using a target temperature of 3 °C for the first positions at both locations, the following power references may be obtained at the two selected locations: ൫ ^^0− ^^1, ^^൯ℎ0, ^^ ^^ ^^ℎ4^^1^ / (^^1∗ ^^3+ ℎ4∗ ^^1)= 1865 ^^ / ^^^2 (12) ൫ ^^0− ^^1, ^^൯ℎ0, ^^ ^^ ^^ ^^ℎ4^^1^ / (^^1∗ ^^3+ ℎ4∗ ^^1)= 472 ^^ / ^^^2 (13) The controlling of the at least one switching device may be carried out as PWM control. The duty cycles for the PWM control may be obtained as: If a total cycle time of 8 seconds is employed in this example, the following heating on and heating off times may be obtained: ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ∗ ^^ ^^^^ ^^ ^^= 5 ^^ (16) ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ − ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ∗ ^^ ^^^^ ^^ ^^= 3 ^^ (17) ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ∗ ^^ ^^^^ ^^ ^^ ^^= 3,8 ^^ (18) ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ − ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ∗ ^^ ^^^^ ^^ ^^ ^^= 4,2 ^^ (19) Figure 7 shows a result of a simulation for he above considered example. The obtained temperature at the target position is shown as a function of time. It should be noted that all used values are given here as examples and may vary with each use case. Ways of obtaining used parameters or determining the controlling of the switching device may also vary in different embodiments of the invention. Figure 8 shows a flow chart of a (computer-implemented) method according to an embodiment of the invention. The method comprises obtaining 802 thermal properties relating to at least a first position on the at least one wind turbine blade and at least a second position on the at least one wind turbine blade, wherein the first position is associated with a first layer of a layer structure model representing the wind turbine blade and the second position is associated with a second layer of the layer structure model. A target temperature or a target temperature range is also obtained 804 for at least one target position on the at least one wind turbine blade, wherein the target position is associated with a layer of the layer structure model. The method further comprises obtaining 806 one or more environmental parameters. Finally, at item 808, the method comprises controlling at least one switching device provided in connection with at least one heating element of the wind turbine blade to approach the target temperature or target temperature range at the target position based on the obtained environmental parameters and the obtained thermal properties and by utilizing a heat transfer model associated with the layer structure model.

Claims

CLAIMS 1. A method for controlling at least one heating element of at least one wind turbine blade, the method comprising at least - obtaining thermal properties relating to at least a first position on the at least one wind turbine blade and at least a second position on the at least one wind turbine blade, wherein said first position is associated with a first layer of a layer structure model representing the wind turbine blade and said second position is associated with a second layer of the layer structure model, - obtaining a target temperature or a target temperature range for at least one target position on the at least one wind turbine blade, wherein said target position is associated with any layer of the layer structure model, - obtaining one or more environmental parameters, and - controlling at least one switching device provided in connection with the at least one heating element of the wind turbine blade to approach the target temperature or target temperature range at the target position based on the obtained environmental parameters and the obtained thermal properties and by utilizing a heat transfer model associated with the layer structure model.

2. The method of claim 1, wherein the method comprises obtaining one or more structural parameters of the at least one wind turbine blade, optionally comprising a thickness and / or material of at least the first layer and / or the second layer, wherein obtaining thermal properties relating to the at least first position and the second position comprises determining thermal properties of the first layer and / or the second layer based on the obtained structural parameters.

3. The method of any of previous claim, the method comprising obtaining a maximum temperature for at least one of the first position and second position on the at least one wind turbine blade, wherein the controlling of the at least one switching device is carried out such that the maximum temperature(s) is essentially not exceeded or such that an average temperature of at least the first and / or second position during a selected time period essentially does not exceed the maximum temperature(s).

4. The method of any previous claim, wherein the method comprises: - determining at least one estimated temperature of at least one considered position on the at least one wind turbine blade, comprising at least determining an estimated temperature for the first position, second position, and target position, at a selected time, and / or - determining at least one heating power reference for the target position for approaching or maintaining the target temperature or target temperature range, preferably by determining a thermal equilibrium state for the target temperature, wherein the controlling of the at least one switching device comprises controlling the switching device based on the at least one estimated temperature or the determined heating power reference.

5. The method of claim 4, wherein the method comprises obtaining a starting temperature for at least the target position, preferably further obtaining a starting temperature for the first position and / or second position, the method further comprising iteratively determining, at predetermined time intervals, an estimated temperature of at least the target position, preferably further determining an estimated temperature of the at least first position and / or second position.

6. The method of claim 5, wherein controlling of the switching device comprises deactivating the at least one switching device at latest when the estimated temperature of the target position reaches or exceeds the target temperature or a maximum value of a target temperature range and / or activating the at least one switching device when the estimated temperature of the target position falls below the target temperature or falls below a minimum value of a target temperature range.

7. The method of claim 6, wherein the method additionally comprises obtaining an indication of a maximum temperature for at least one of the first position and second position on the at least one wind turbine blade, wherein the controlling of the switching device comprises deactivating the switching device before the estimated temperature of the target position reaches or exceeds the target temperature or a maximum value of a target temperature range if an estimatedtemperature of the first and / or second position exceeds the maximum temperature.

8. The method of any of claims 5-7, wherein the method comprises obtaining, at the start of each iteration, an indication of the state of the at least one switching device.

9. The method of any of claims 5-8, wherein a starting temperature at each iteration is an estimated temperature determined at the previous iteration or wherein the starting temperature is a measured temperature or a starting temperature based on one or more environmental parameters.

10. The method of any previous claim, wherein the method comprises a resetting procedure, wherein the at least one switching device is deactivated until it is determined that a temperature of at least one considered position on the wind turbine blade is essentially equivalent to an ambient temperature, optionally wherein said resetting procedure is carried out after a predetermined time from a start of the method or after a predetermined time after a previous resetting procedure.

11. The method of any of previous claim, wherein the layer structure model comprises at least two layers, comprising at least one structural element layer and at least one heating element layer, preferably wherein the layer structure model comprises at least three layers, comprising at least one inner structural element layer, at least one heating element layer, and at least one outer structural element layer.

12. The method of any previous claim, wherein obtaining of one or more environmental parameters comprises obtaining an indication of one or more of an ambient temperature, wind speed, wind direction, liquid water content of air flow, and relative humidity.

13. The method of any previous claim, further comprising obtaining one or more operating parameters of the wind turbine blade, the operating parameters comprising one or more of: rotor speed, blade pitch angle, rotor azimuth angle, and wind turbine yaw direction.

14. The method of any previous claim, wherein the thermal properties comprise at least a heat capacity and / or thermal conductivity.

15. The method of any previous claim, the method further comprising obtaining further parameters relating to one or more boundary conditions to be utilized in the heat transfer model, said further parameters comprising at least one of a convection heat transfer coefficient relating to a first surface of the outermost layer of the layer structure model, said first surface facing the environment, a convection heat transfer coefficient relating to a second surface of the innermost layer of the layer structure model, said second surface facing an inner hollow portion of the wind turbine blade, and a heating power of the heating element.

16. The method of any of claims 1-4 or 10-15, wherein the method comprises determining a heating power reference for the target position for approaching or maintaining the target temperature or target temperature range, and determining a pulse width modulated (PWM) control for the switching device, optionally wherein a cycle on time and a cycle off time of the PWM control lasts for at least about one second or more.

17. The method of claim 16, wherein the PWM control is determined by dividing the heating power reference by a total available heating power, wherein the total available heating power corresponds to a maximum heating power that is deliverable via the heating element.

18. The method of any previous claim, wherein the heat transfer model is a one-dimensional model, wherein the first position, second position, and target position reside essentially along a first normal of the surface of the wind turbine blade, said first normal residing at a first location on the surface of the wind turbine blade, wherein the method optionally further comprises consideration of at least a second location on the surface of the wind turbine blade with respective second normal and respective at least first position, second position, and target position, wherein the controlling of the at least one switching device is carried out such that the target temperature or maximum value of a target temperature range of any considered target position is essentially not exceeded.

19. An arrangement for controlling at least one heating element of at least one wind turbine blade, the arrangement comprising at least one processor configured to: - obtain thermal properties relating to at least a first position on the at least one wind turbine blade and at least a second position on the at least one wind turbine blade, wherein said first position is associated with a first layer of a layer structure model representing the wind turbine blade and said second position is associated with a second layer of the layer structure model, - obtain a target temperature or a target temperature range for at least one target position on the at least one wind turbine blade, wherein said target position is associated with any layer of the layer structure model, - obtain one or more environmental parameters, and - control at least one switching device provided in connection with the at least one heating element of the wind turbine blade to approach the target temperature or target temperature range at the target position based on the obtained environmental parameters and the obtained thermal properties and by utilizing a heat transfer model associated with the layer structure model.

20. A computer program product comprising program code means adapted to execute the method items of any of claims 1-18 when run on the processor of the arrangement of claim 19.

21. A non-transitory carrier medium comprising the computer program product of claim 20.

22. A system comprising at least one wind turbine, said wind turbine comprising at least one wind turbine blade comprising at least one heating element, wherein the system additionally comprises at least one arrangement according to claim 19.

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