Abstract:
A variable speed wind turbine is provided. The wind turbine comprises a generator, a power converter for converting at least a portion of electrical power generated by the generator wherein the power converter comprises a generator side converter, a grid side converter and a DC (direct current) link therebetween, a power dissipating unit operatively coupled to the DC link and a controller. The controller is adapted to determine a DC link voltage error signal, the DC link voltage error signal being the difference between a function of an actual DC link voltage and a function of a predefined reference DC link voltage, determine a DC link error power based on the DC link voltage error signal, determine a feed forward power and generate a duty ratio for operating the power dissipating unit based on the DC link error power and the feed forward power.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 12/976,292, filed Dec. 22, 2010, which claims priority to Danish Patent Application No. PA 2010 70004 filed on Jan. 4, 2010 and claims the benefit of U.S. Provisional Application No. 61/292,995 filed on Jan. 7, 2010, the content of each is incorporated by reference herein in its entirety for all purposes. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to a wind turbine, and in particular, to a method for operating a power dissipating unit in a wind turbine. 
     BACKGROUND OF THE INVENTION 
     A wind turbine is an energy conversion system which converts kinetic wind energy into electrical energy for utility power grids. Specifically, wind is applied to wind turbine blades of the wind turbine to rotate a rotor. The mechanical energy of the rotating rotor in turn is converted into electrical energy by an electrical generator. Because wind speed fluctuates, the force applied to the wind blades and hence the rotational speed of the rotor can vary. Power grids however require a constant frequency electrical power to be provided by the wind turbine. 
     One type of wind turbine that provides constant frequency electrical power is a fixed-speed wind turbine. This type of wind turbine requires a generator rotor that rotates at a constant speed. A disadvantage of such fixed-speed wind turbine is that it does not harness all of the wind&#39;s energy at high speeds and must be disabled at low wind speeds. Another type of wind turbine is a variable speed wind turbine. This type of wind turbine allows the generator to rotate at variable speeds to accommodate for fluctuating wind speeds. By varying the rotating speed of the generator rotor, energy conversion can be optimized over a broader range of wind speeds. 
     A variable speed wind turbine usually includes a power converter having a generator side converter coupled to a grid side converter via a direct current (DC) link. The generator side converter regulates the power of the generator. This power passes through the DC-link, and is eventually fed to the grid through the grid side converter. The same is true for the Doubly Fed Induction Generator (DFIG) systems where only a portion of the power from the generator passes through the power converter. 
     Under normal conditions, the electrical power or energy from the generator is supplied to the grid through the power converter. In other words, the energy captured from the wind by the wind turbine is passed to the grid. Therefore, it can be said that there is power balance during normal conditions. However, when there is a sudden wind gust and/or grid fault, this power balance may be disrupted, resulting in more power being generated than power being supplied to the grid. Such power imbalance might lead to undesired tower oscillations, drive train damage or turbine tripping. 
     Specifically, the power output of the generator in response to a sudden wind gust can be approximated as ramp input to the power system in the wind turbine with a steep slope. Such load ramping is one of the most difficult load behaviors for a control system in the wind turbine. A wind turbine normally handles wind gust by pitching the blades to reduce the speed of rotor as disclosed, for example, in US 2009/0224542 and EP 2107236. However, due to the dynamics of a pitch controller, the pitching of the blade may not be fast enough to respond to the sudden wind gust. Hence this results in the sudden increase in the power generated by the generator, leading to the undesired tower oscillations, etc as mentioned above. 
     When there is a grid fault, for example a low voltage event, there is a sudden drop in demand for active power from the grid. Since the pitching of the blades is not able to respond fast enough to reduce power generation, there is an imbalance of power in the wind turbine. U.S. Pat. No. 7,411,309 discloses the use of a crowbar circuit during low voltage events at the grid. The crowbar circuit is coupled to the DC link between the generator side converter and the grid side converter. When the DC link voltage exceeds a predetermined value (due to grid fault), the crowbar circuit is activated to drain the excess generator power, hence lowering the DC link voltage. 
     The use of a crowbar circuit or a dump load circuit may provide a good way of dissipating excess power during a power imbalance event. The dump load circuit is activated by detecting an abnormal increase in the DC link voltage or a sudden drop in grid voltage. However, it may not be the most effective method to handle power imbalance events such as wind gust, or in extreme conditions when wind gust and grid fault happen at the same time. Moreover in this method, the resistor bank in the dump load circuit is excessively stressed. 
     It is thus an object of the invention to provide an improved way of managing excess power generated in the wind turbine in power imbalance event. 
     SUMMARY OF THE INVENTION 
     According to a first aspect of the invention, a variable speed wind turbine is provided. The wind turbine comprises a generator, a power converter for converting at least a portion of electrical power generated by the generator, a power dissipating unit operatively coupled to a DC (direct current) link of the power converter and a controller. The controller is adapted to determine a DC link voltage error signal, the DC link voltage error signal being the difference between a function of an actual DC link voltage and a function of a predefined reference DC link voltage, determine a DC link error power based on the DC link voltage error signal, determine a feed forward power and generate a duty ratio for operating the power dissipating unit based on the DC link error power and the feed forward power. 
     The power converter includes a generator-side converter for converting at least a portion of AC power from the generator into DC power, a grid-side converter for converting the DC power into AC power having fixed frequency and a DC link between the generator-side converter and the grid-side converter. 
     The generator is an electromechanical machine capable of converting mechanical energy into electrical energy. The generator used in the wind turbine could be any type of generator including but not limited to, a permanent magnet generator, doubly-fed induction generator and squirrel cage induction generator. The electrical power from the generator has a variable frequency due to the variable rotational speed of the rotor. A portion or all of the electrical energy or power generated by the generator is converted by the power converter into a fixed frequency electrical power suitable to be supplied to a power grid or a load. 
     The load may be a DC or an AC (alternating current) load. For supply of power to the grid, the power converter converts the electrical power with variable frequency into electrical power having a fixed frequency required by the grid. When supplying power to a load, for example a DC load, the power converter converts the electrical power with variable frequency into a DC power. 
     The power dissipating unit is coupled to the DC link of the power converter. The power dissipating unit is adapted to dissipate any excess power generated by the generator which can not be given to the grid. The power dissipating unit may be a resistor bank and may also be known as a chopper resistor. 
     The controller is adapted to determine the DC link voltage error signal. The DC link voltage error signal is the difference between a function of the actual DC link voltage and a function of the predefined reference DC link voltage. The function of the actual DC link voltage and the function of the predefined reference DC link voltage refer to any mathematical expression of the DC link voltage. Examples of the function include: 
     ƒ(X)=aX+b; where a and b are constants, and 
     ƒ(X)=X 2 , or any form of a polynomial expression, 
     where X is the actual DC link voltage. The DC link voltage error signal can be expressed as ƒ 1 (X)−ƒ 2 (Y), where Y is the predefined reference DC link voltage. The functions ƒ 1  and ƒ 2  may denote the same or different functions. The DC link error power is derived from the DC link voltage error signal. Based on the DC link error power and the feed forward power, the duty ratio for operating the power dissipating unit is determined. 
     The duty ratio refers to the percentage of time period the power dissipating unit is activated or turned on in one cycle. The duty ratio has a value from 0 to 1. When the duty ratio is 0, the power dissipating unit is turned off completely, and when the duty ratio is 1, the power dissipating unit is turned on for the whole duty cycle. When the duty ratio is 0.7, the power dissipating unit is turned on for 70% of the duty cycle (it is off for 30% of the remaining duty cycle). The advantage of using a duty ratio to control the operation of the power dissipating unit is that only the amount of excess power in the wind turbine is dissipated. An effect of dissipating only the amount of excess power using such a duty ratio control according to the embodiment is that maximum power is still supplied to the grid. This is in contrast to the prior art where the power dissipating unit is turned on and off based only on DC link voltage when the DC link voltage rises above a predetermined level. As the method according to the prior art does not know how much power to dissipate (as controlled by the duty ratio) and is only concerned with maintaining the DC link voltage within the predetermined level, it tends to dissipate most of the power in the power dissipating unit. This results in very low or no power being supplied to the grid and other turbine utilities. The dissipation of most of the power in the power dissipating unit also stresses the resistor banks in the power dissipating unit. 
     Additionally, the inclusion of the feed forward power in determining the duty ratio results in a fast response in activating the power dissipating unit when there is power imbalance in the wind turbine. 
     According to an embodiment, the power dissipating unit comprises at least a switch and one resistor. The power dissipating unit is turned on by closing the switch. The switch may be a power semiconductor device such as an Integrated Gate Bipolar Transistor (IGBT) which can be turned on or off by a suitable voltage through a gate driver. In alternative embodiments, the power dissipating unit may include at least a switch and at least one of a resistor, an inductor or a capacitor. 
     According to an embodiment, the DC link voltage error signal is the difference between the squares of the actual DC link voltage and the predefined reference DC link voltage. Specifically, the DC link voltage error signal can be expressed as X 2 −Y 2 , where X is the actual DC link voltage and Y is the predefined reference DC link voltage. As described earlier, the DC link error signal can be the difference between other functions of the actual DC link voltage and the predefined reference DC link voltage in other embodiments, such as X−Y, (X 2 +1)−(Y 2 +1), etc. 
     According to an embodiment, the controller further comprises a PI (Proportional Integral) controller for determining the DC link error power based on the DC link voltage error signal. The advantage of using a PI controller for determining the DC link error power is its simplicity of implementation. In other embodiments, a P (Proportional) controller or a PID (Proportional Integral Derivative) controller may be used to determine the DC link error power. 
     According to an embodiment, the controller is further adapted to determine the feed forward power based on the difference between the power supplied to the generator side converter and the power transferred by the grid side converter. Under normal conditions, the power supplied to the generator side converter from the generator and the power transferred by the grid side converter is approximately the same. Therefore, the feed forward power is approximately zero, assuming zero power losses. However when there is wind gust and/or grid faults, the power supplied to the generator side converter exceeds the power transferred by the grid side converter. Hence, the feed forward power becomes non-zero. This non-zero feed forward power in the event of power imbalance in the wind turbine leads to faster activation of the power dissipating unit. It is also possible to determine the feed forward power based on other factors such as power captured from the wind in an alternative embodiment. 
     According to an embodiment, the controller is adapted to estimate the power supplied to the generator side converter based on the difference between the power extracted from the wind and power losses in the generator and in a drive train of the wind turbine. This has the advantage that the power supplied to the generator side converter from the generator can be obtained well in advance. In other embodiments, the power supplied to the generator side converter is obtained from the phase voltages and currents at the terminals between the generator and the generator side converter. 
     According to an embodiment, the controller is adapted to generate the duty ratio by determining power to be dissipated by the power dissipating unit, determining a maximum power that can be dissipated by the power dissipating unit, and determining the ratio of the power to be dissipated and the maximum power, thereby obtaining the duty ratio. The power to be dissipated by the power dissipating unit includes the DC link error power and the feed forward power. If the power to be dissipated exceeds the maximum amount of power that can be dissipated by the power dissipating unit, the duty ratio will be 1. In a further embodiment, the power dissipating unit is designed such that the maximum amount of power that can be dissipated by the power dissipating unit is always larger than the power that needs to be dissipated. 
     According to an embodiment, the controller is adapted to determine power extracted from the wind, power supplied by the wind turbine and power loss in the power dissipating unit, determine the difference between the power extracted from the wind and the sum of the power supplied by the wind turbine and power loss in the power dissipating unit, and activate the power dissipating unit when the difference in the power exceeds a predefined power difference threshold. 
     The power supplied by the wind turbine to the grid may also take into account power losses by various components in the turbine. When the difference between the power extracted from the wind and the sum of the power supplied by the wind turbine and power loss in the power dissipating unit exceeds the predefined power difference threshold, the power dissipating unit is turned on completely for the full time period. In other words, the duty ratio is set to 1. This has the advantage that it leads to an even faster response of the power dissipating unit under extreme conditions such as severe wind gust/turbulence and/or extreme grid faults, thus avoiding drive train damage, tower oscillations and turbine tripping. It should be noted that the power loss in the power dissipating unit is only non-zero when the power dissipating unit has been activated or turned on. In other words, when the power dissipating unit is turned off, the power loss in the power dissipating unit is zero. 
     According to a second aspect of the invention, a variable speed wind turbine is provided. The wind turbine comprises a generator, a power converter for converting at least a portion of electrical power generated by the generator wherein the power converter comprises a generator side converter, a grid side converter and a DC link therebetween, a power dissipating unit operatively coupled to the DC link and a controller. The controller is adapted to determine power extracted from the wind, power supplied by the wind turbine and power loss in the power dissipating unit, determine the difference between the power extracted from the wind and the sum of the power supplied by the wind turbine and power loss in the power dissipating unit, and activate the power dissipating unit when the power difference exceeds a predefined power difference threshold. 
     According to an embodiment, the controller is further adapted to set a duty ratio for operating the power dissipating unit to a non-zero value when the predefined power difference threshold is exceeded, thereby activating the power dissipating unit. 
     According to a third aspect of the invention, a method for operating a power dissipating unit in a wind turbine is provided. The wind turbine comprises a power converter for converting at least a portion of electrical power generated by a generator. The power converter comprises a generator side converter, a grid side converter and a DC link therebetween. The power dissipating unit is operatively coupled to the DC link. The method comprises obtaining a DC link voltage error signal, the DC link voltage error signal being the difference between a function of an actual DC link voltage and a function of a predefined reference DC link voltage, determining a DC link error power and a feed forward power, the DC link error power is determined based on the DC link voltage error signal, and generating a duty ratio for operating the power dissipating unit based on the DC link error power and the feed forward power. 
     It should be noted that a person skilled in the art would readily recognize that any feature described in combination with the first aspect of the invention could also be combined with the third aspect of the invention, and vice versa. 
     According to a fourth aspect of the invention, a method for operating a power dissipating unit in a wind turbine is provided. The wind turbine comprises a power converter for converting at least a portion of electrical power generated by a generator. The power converter comprises a generator side converter, a grid side converter and a DC link therebetween. The power dissipating unit is operatively coupled to the DC link. The method comprises determining power extracted from the wind, power supplied by the wind turbine and power loss in the power dissipating unit, determining the difference between the power extracted from the wind and the sum of the power supplied by the wind turbine and power loss in the power dissipating unit, and activating the power dissipating unit when the difference between the power exceeds a predefined difference threshold. 
     It should be noted that a person skilled in the art would readily recognize that any feature described in combination with the second aspect of the invention could also be combined with the fourth aspect of the invention, and vice versa. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be better understood with reference to the detailed description when considered in conjunction with the non-limiting examples and the accompanying drawings. 
         FIG. 1  shows a general structure of a wind turbine. 
         FIG. 2  shows an electrical system layout of the wind turbine with a chopper or power dissipating unit circuit. 
         FIG. 3  shows a control algorithm for operating the chopper circuit when there is power imbalance in the wind turbine according to an embodiment. 
         FIG. 4  shows a control algorithm for operating the chopper circuit when there is extreme power imbalance in the wind turbine according to an embodiment. 
         FIG. 5  shows an overall control algorithm for operating the chopper circuit. according to an embodiment. 
         FIG. 6  shows a flow-chart of a method for operating the chopper circuit in the wind turbine according to an embodiment. 
         FIG. 7  shows a flow-chart of a method for operating the chopper circuit in the wind turbine when there is extreme power imbalance in the wind turbine according to an embodiment. 
         FIG. 8  shows a flow-chart of a method for operating the chopper circuit in the wind turbine according to a further embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows a general setup of a wind turbine  1 . The wind turbine  1  includes a tower  2  having a number of tower sections, a nacelle  3  positioned on top of the tower  2 , and a rotor  4  extending from the nacelle  3 . The tower  2  is erected on a foundation  7  built in the ground. The rotor  4  is rotatable with respect to the nacelle  3 , and includes a hub  5  and one or more blades  6 . Wind incident on the blades  6  causes the rotor  4  to rotate with respect to the nacelle  3 . The mechanical energy from the rotation of the rotor  4  is converted into electrical energy by a generator (not shown) in the nacelle  3 . The electrical energy is subsequently converted into a fixed frequency electrical power by a power converter to be supplied to a power grid. The wind turbine may also form part of a wind farm or a wind power plant comprising a plurality of wind turbines. All the electrical power generated by the individual wind turbines in the wind farm are consolidated and supplied to the power grid via a Point of Common Coupling (PCC). 
     Although the wind turbine  1  shown in  FIG. 1  has three blades  6 , it should be noted that a wind turbine may have different number of blades. It is common to find wind turbines having two to four blades. The wind turbine  1  shown in  FIG. 1  is a Horizontal Axis Wind Turbine (HAWT) as the rotor  4  rotates about a horizontal axis. It should be noted that the rotor  4  may rotate about a vertical axis. Such a wind turbine having its rotor rotates about the vertical axis is known as a Vertical Axis Wind Turbine (VAWT). The embodiments described henceforth are not limited to HAWT having 3 blades. They may be implemented in both HAWT and VAWT, and having any number of blades  6  in the rotor  4 . 
       FIG. 2  shows an electrical system of the wind turbine having a power dissipating unit or a chopper circuit  105  according to an embodiment. The electrical system includes a generator  101 , a power converter  102  and a main transformer  103 . The electrical system is connected to a power grid  107 . The power converter  102  includes a generator-side converter  110  and a grid-side converter  111  connected via a direct current (DC) link  112 . The DC link  112  includes a DC link capacitor  113 . The chopper circuit  105  is connected to the DC link  112 , and includes a switch SW 1  and a resistor  114 . 
     The generator  101  converts mechanical energy or power to electrical energy or power having AC (alternating current) voltage and current (collectively referred to as “AC signals”), and provides the generated AC signals to the generator-side converter  110 . The AC signals from the generator have a variable frequency, due to varying wind. The generator-side converter  110  converts or rectifies the AC signals to a DC (direct current) voltage and a DC current (collectively know as “DC signals”) which are placed on the DC link  112 . The grid-side converter  111  converts the DC signals on the DC link  112  into fixed frequency AC signals for the power grid  107 . The power comprising the fixed frequency AC signals at the output of the grid-side converter  111  is stepped up by the main transformer  103  into a level suitable to be received and transmitted by the power grid  107 . 
     The operation of the generator-side converter  110  is controlled by a generator controller  121 , and the operation of the grid-side converter  111  is controlled by a grid controller  122 . The generator controller  121  and the grid controller  122  form part of a converter controller  120 . A wind turbine controller  123  provides an overall control of the operation of the wind turbine. For example, the wind turbine controller  123  may receive information (e.g. wind speed) from external sensors (e.g. anemometer) and provides control signal to a pitch control (not shown) for pitching the blades in order to obtain a desired rotor speed. The wind turbine controller  123  may also provide control signals to the converter controller  120  for controlling the converters  110  and  111 . 
     During normal operation of the wind turbine, the electrical power generated by the generator is converted by the power converter  102  into power having fixed frequency AC signals to be supplied to the power grid  107 . The switch SW 1  is open, and hence no power is dissipated in the resistor  114 . In other words, assuming no losses, almost all the power generated by the generator is supplied to the power grid  107 , and there is “power balance” in the wind turbine. When there is a voltage dip in the power grid  107  (low voltage event) resulting in decreased active power transferred by the grid-side converter to be supplied to the grid and/or when there is a sudden wind gust causing a sudden increase in the rotational speed of the blades of the wind turbine (wind gust event), the power generated by the generator exceeds the power supplied to the power grid  107 . In other words, there is “power imbalance” in the wind turbine. As mentioned earlier, such power imbalance in the wind turbine leads to undesired effects such as tower oscillations, drive train damage or turbine tripping. 
     When there is power imbalance in the wind turbine, any excess power that is not supplied to the grid  107  is dissipated by the resistor  114  in the chopper circuit  105  by closing the switch SW 1 . According to an embodiment, the operation (opening and closing) of the switch SW 1  is controlled so that the resistor  114  in the chopper circuit  105  only dissipates the excess power in the wind turbine. In other words, the chopper circuit  105  is only activated when there is power imbalance in the wind turbine, and only for a period just enough to dissipate the excess power. The control of the operation of the switch SW 1 , and hence the operation of the chopper circuit  105 , shall be described later with reference to  FIG. 3 . 
     It should be noted that the electrical system described with reference to  FIG. 2  is only an example of the electrical configuration of the wind turbine and only the main components are shown to illustrate the embodiments. The present invention should not be limited to the exact electrical system configuration shown in  FIG. 2 . Other electrical configurations are possible. For example, a Doubly Fed Induction Generator (DFIG) configuration may be used in other embodiments. Also, many components in the electrical system of the wind turbine are not shown in  FIG. 2 . For example, the electrical system may include filters between the generator  101  and the power converter  102 , and between the power converter  102  and the main transformer  103 . Also, there may be switches arranged at various locations for connecting or disconnecting certain components of the turbine. The resistor  114  in the chopper circuit  105  may include a single resistor or a bank of resistors. 
     The electrical system shown in  FIG. 2  need not be connected to the power grid  107 . It can be connected to an AC or a DC load. If it is connected to a DC load, the grid-side converter  111  and the transformer  103  may be omitted, and the DC link  112  can be connected directly to the DC load. Alternatively, a DC-to-DC converter may be arranged between the DC link  112  and the DC load to step up or step down the DC voltage at the DC link  112  to a suitable DC voltage for the DC load. 
       FIG. 3  shows a control algorithm for operating the chopper circuit when there is power imbalance in the wind turbine according to an embodiment. The voltage at the DC link  210  is used as one of the factors to decide whether the chopper circuit should be activated. This is because any electrical power from the generator if not transferred to the grid or load leads to an increase in the DC-link voltage. Therefore in this control algorithm, there is no need to detect any power imbalance separately as the chopper circuit is activated automatically in the event of power imbalance as will be evident from the description below. 
     In the control algorithm of  FIG. 3 , a function of the predefined reference DC link voltage  202  and a function of an actual DC link voltage  203  are obtained. As mentioned earlier, the function ƒ(X) of the actual DC link voltage (and also the function of the predefined reference DC link voltage) may be any mathematical expression of the DC link voltage, such as ƒ(X)=X, ƒ(X)=aX+b, or ƒ(X)=X 2 , or any polynomial relationship, where a and b are constants and X is the actual DC link voltage. In this embodiment, the function of the actual DC link voltage is X 2 . The function of the predefined reference DC link voltage also uses the same function in this embodiment. 
     The difference between the squares of the actual DC link voltage  203  and the predefined reference DC link voltage  202  is obtained as a DC link error voltage  205 . A PI (Proportional Integral) controller  201  receives the DC link error voltage  205  as input and outputs a DC link error power  206 . According to an embodiment, the control algorithm further includes determining a feed forward power. The feed forward power is the difference between the power supplied to the generator side converter  207  and the power transferred by the grid side converter  208 . 
     Under normal conditions when there is power balance in the wind turbine, the feed forward power is approximately zero, assuming no power loss. However when there is wind gust and/or grid fault leading to power imbalance, the feed forward power becomes non-zero. The addition of the feed forward power to the DC link error power  206  leads to a fast activation of the chopper circuit. 
     The power supplied to the generator side converter  207  can be expressed as:
 
 P   M   =V   am   I   am   +V   bm   I   bm   +V   cm   I   cm   (1)
 
where P M  is the power supplied to the generator side converter from the generator, V am , V bm  and V cm  are the phase voltages at the generator terminals, and I am , I bm  and I cm  are the currents through the generator terminals. The currents I am , I bm , I cm  can be measured between the power converter and the generator. The voltages V am , V bm , V cm  can be measured at the generator terminals directly. If it is not possible to measure the voltages V am , V bm , V cm  at the generator terminals, reference voltages at the converter terminals may be used. Using the reference voltages at the converter terminals and measured currents at the generator terminals, the power from the generator in αβ co-ordinate system can be given as:
 
 P   Mαβ =1.5( v   α   i   α   +v   β   i   β )  (2)
 
where P Mαβ  is P M  in the αβ co-ordinate system, v α ,v β  and i α ,i β  are voltages and currents in the α and β co-ordinates, respectively.
 
     In an alternative embodiment, the power supplied to the generator side converter from the generator P M  is estimated using the following expression:
 
 P   M   =P   Wind   −P   L,Drivetrain   −P   L,Generator   (3)
 
where P wind  is power extracted from the wind, P L,Drivetrain  are the losses in the drive train and P L,Generator  are the losses in the generator. For a given speed and torque, P L,Drivetrain  and P L,Generator  can be obtained using a lookup table for a given gearbox and generator. The advantage of estimating P M  using equation (3) is that the P M  can be obtained faster as compared to using equation (1).
 
     The power transferred by the grid side converter  208  can be expressed as:
 
 P   G   =V   ag   I   ag   +V   bg   I   bg   +V   cg   I   cg   (4)
 
where P G  is the power transferred by grid side converter, V ag , V bg  and V cg  are the voltages at the converter terminals, and I ag , I bg  and I cg  are the currents through the converter terminals. If the voltages at the converter terminals V ag , V bg , V cg  cannot be obtained, for example due to converter switching, reference voltages for the converter may be used instead. Using the reference voltages for the converter and measured currents at the converter terminals, the power transferred by the grid side converter in αβ co-ordinate system can be given as:
 
 P   Gαβ =1.5( v   α   i   α   +v   β   i   β )  (6)
 
where P Gαβ  is P G  in the αβ co-ordinate system, v α ,v β  and i α ,i β  are voltages and currents in the α and β co-ordinates, respectively.
 
     The total power P total  to be dissipated  209  is the sum of the DC link error power  206  and the feed forward power (P M −P G ). The maximum power that can be dissipated by the chopper circuit can be determined as follows: 
                     P   max     =       V   dc   2       R   chopper               (   7   )               
where P max  is the maximum power that can be dissipated by the resistor or resistor bank in the chopper circuit, V dc  is the actual DC link voltage, and R chopper  is the resistance of the resistor in the chopper circuit. The resistance value R chopper  of the resistor is normally selected such that the P max  is larger than an anticipated maximum power that may need to be dissipated in a wind gust and/or grid fault event. In an embodiment, the value of R chopper  is chosen such that P max  is about 10-20% larger than the nominal power rating of the turbine.
 
     The duty ratio for operating the chopper circuit is determined as the ratio between the total power to be dissipated P total  and the maximum power P max , that is: 
                     DR   1     =       P   total       P   max               (   8   )               
where DR 1  is the duty ratio. Since the total power P total  is always less than the maximum power P max , the duty ratio has a value from 0 to 1.
 
     Under normal conditions when there is no power imbalance in the wind turbine, the voltage at the DC link is regulated by a DC link controller to a preset DC link voltage. The preset DC link voltage is the voltage level which is maintained at the DC link under normal conditions. The reference DC link voltage V dc     —     ref  is predefined or set to a value which is higher than this preset DC link voltage. Therefore under normal conditions, the DC link error power  206  is negative as the DC link voltage (which is regulated to the preset DC link voltage) has a value lower than the reference DC link voltage. The feed forward power (P M −P G ) will be approximately zero, and hence P total , is negative. Accordingly, the duty ratio is zero. The switch SW 1  is not turned on, and chopper circuit is not activated. 
     When there is power imbalance, both the DC link error power  206  and feed forward power (P M −P G ) become non-zero. This results in the total power to become non-zero. Therefore, the duty ratio will now have a non-zero value from 0 to 1. When the duty ratio has a value of 0.5, the chopper circuit is only activated or turned on for 50% of the time in one duty cycle. Similarly when the duty ratio has a value of 0.3, the chopper circuit is only activated for 30% of the time in one duty cycle. 
     Accordingly, the chopper circuit is not activated all the time when there is power imbalance to dissipate power, but only for an appropriate period of time depending on the extent of the power imbalance in the wind turbine as controlled by the duty ratio. Therefore, the efficiency and effectiveness of the chopper circuit is ensured as only power that is not supplied to the grid is dissipated. The use of feed forward power also ensures fast activation of the chopper circuit in the event of power imbalance in the wind turbine. Thus oscillation of the wind turbine tower due to sudden wind gust and/or grid fault can be avoided as the chopper circuit can now be activated quickly. 
     The control algorithm of  FIG. 3  has been described with reference to the full scale converter based turbine shown in  FIG. 2 . It should be noted that the control algorithm described with reference to  FIG. 3  is also applicable in a DFIG system. In the full scale converter based turbine shown in  FIG. 2 , the power transferred by the grid side converter  111  is approximately the same as the power supplied to the grid  107  if any power losses between the output of the grid side converter  111  and the grid  107  is assumed to be negligible. Similarly, the power supplied to the generator side converter  110  is approximately the same as the power generated from the generator  101 , assuming negligible power losses between the output of the generator  101  and the generator side converter  110 . 
     In a DFIG system, the power supplied to the grid is the sum of the power transferred by the grid side converter  111  and the power transferred through the stator windings. The power generated from the generator  101  is the sum of the power supplied to the generator side converter  110  and the power transferred through the stator windings. 
       FIG. 4  shows a control algorithm for operating the chopper circuit when there is extreme and sudden power imbalance in the wind turbine according to an embodiment. The power extracted from the wind P wind , the power supplied to the grid or load P Grid  and the power loss in the chopper circuit P L,chopper  are obtained. The power difference P diff  between the power extracted from the wind P wind , and the power supplied to the grid P Grid  and the power loss in chopper circuit P L,chopper  is determined. Specifically, the power difference is determined using the following expression:
 
 P   diff   =P   wind   −P   Grid   −P   L,chopper   (9)
 
     The power difference P diff  is compared to a predefined power difference threshold P threshold . If the power difference P diff  exceeds the predefined difference threshold P threshold , the chopper circuit is turned on, i.e. the duty ratio DR 2  for operating the chopper circuit is set to 1. Otherwise, DR 2  is set to 0. The threshold P threshold  is set to a value such that it is only exceeded when the difference P diff  is large, for example during extreme wind gust and/or extreme fault conditions. P threshold  can be stored in a lookup table for various wind gust and/or extreme fault conditions. 
     The power from the wind can be determined using the following expression: 
               P   wind     =       1   2     ⁢   ρ   ⁢           ⁢     AV   wind   3     ⁢       C   p     ⁡     (     θ   ,   λ     )               
where ρ is the air density, A is the rotor area, V wind  is the wind speed, C p  is rotor power coefficient, θ is the pitch angle and λ is the tip speed ratio. Assuming constant rotor area A and air density ρ, the power from the wind P wind  is proportional to V wind   3 C p (θ, λ). The direct use of wind velocity V wind  provides a very fast method of determining whether there is a wind gust event.
 
     As mentioned earlier, in the full scale converter based wind turbine system, the power supplied to the grid P Grid  is approximately the same as the power transferred by the grid side converter  111 . Therefore, the power supplied to the grid can be determined using equation (4) as discussed above. In the DFIG system, the power supplied to the grid P Grid  is the sum of the power transferred by the grid side converter  111  and the power transferred through the stator windings as the stator is directly coupled to the grid. 
     The power loss in the chopper circuit P L,chopper  is:
 
 P   L,chopper   =V   dc   2   /R   chopper   ×DR   (11)
 
where V dc  is the DC link voltage and DR is the duty ratio of the chopper. It should be noted that DR may be the same as the duty ratio DR 2  in the embodiment where only the control algorithm in  FIG. 4  is used or is obtained by taking a maximum (MAX) of DR 1  and DR 2  in an embodiment where both the control algorithms in  FIG. 3  and  FIG. 4  are used (see  FIG. 5 ). When the chopper circuit is not activated, the power loss in the chopper circuit P L,chopper  is zero since the DR is zero.
 
     When there is no wind gust or grid fault, the power supplied to the grid P Grid  is approximately the same as the power extracted from the wind P wind , assuming negligible losses in the drive train. The power loss in the chopper circuit P L,chopper  is zero if the chopper circuit is not activated. At any given time, it can be assumed that the sum of the power supplied to the grid P Grid  and the power loss in the chopper circuit P L,chopper  is the total power consumption in the wind turbine (assuming no other losses in the wind turbine drive train). When there is extreme wind gust and/or grid fault, the power difference P diff  between the P wind  and the total power consumed P Grid  and P L,chopper  can become significantly large. This may lead to over speeding of the generator, tower vibration and/or turbine tripping. The power difference P diff  is compared to the difference threshold P threshold . This difference threshold P threshold  can be tabulated in a lookup table, and is the limit at which problems such as tower vibration and turbine tripping starts to occur. When the difference threshold P diff  exceeds the difference threshold P threshold , the chopper circuit is activated to reduce the power difference P diff . 
     Accordingly, the use of the control algorithm in  FIG. 4  to control the operation of the chopper circuit provides a fast and effective way of activating the chopper circuit in the event of extreme and sudden wind gust and/or grid fault conditions. 
     In an embodiment, the control algorithm in  FIG. 4  is used in conjunction with the control algorithm shown in  FIG. 3  for operating the chopper circuit in event of power imbalance in the wind turbine. When there is wind gust and/or grid fault, the operation of the chopper circuit is controlled by the duty ratio obtained using the control algorithm of  FIG. 3 . Under extreme and sudden wind gust or fault conditions, the control algorithm of  FIG. 4  is used to activate the chopper circuit. Such arrangement where both the control algorithms are used is shown in  FIG. 5 . 
     In  FIG. 5 , the control algorithm described with reference to  FIG. 3  is represented as block  300  and the control algorithm described with reference to  FIG. 4  is represented as block  301 . The outputs of both block  300  and block  301  are provided as inputs to a MAX function block  302 . The output of the MAX function block  302  is provided as the control signal for controlling the operation of the chopper circuit. Specifically, the output  303  of the MAX function block  302  is the duty ratio from the control algorithm of  FIG. 3  when there is power imbalance in the wind turbine. Under extreme power imbalance, the duty ratio at the output  303  of the MAX function block  302  gives a value of 1 due to the output of block  301  being 1. In other words, as long as one of the control algorithms gives a non-zero duty ratio, the chopper circuit is activated. 
     It should be noted that the configuration in  FIG. 5  is merely an illustrative example on how the control algorithms shown in  FIG. 3  and  FIG. 4  can be used in conjunction with each other. Other types of configurations, for example taking an OR of the outputs of blocks  300  and  301 , are possible in other embodiments. The control algorithms described above with reference to  FIG. 3  and  FIG. 4  may be implemented in the converter controller  120  and/or the wind turbine controller  123  of  FIG. 2 . It is also possible to implement the control algorithms using an independent and/or separate controller (not shown in  FIG. 2 ). It should also be noted that it is possible to use only one of the control algorithms described with reference to  FIG. 3  or  FIG. 4  to control the chopper circuit in other embodiments. 
       FIG. 6  shows a flow-chart of a method for operating the power dissipating unit in the wind turbine according to an embodiment. Step  400  includes obtaining a DC link voltage error signal. The DC link voltage error signal is the difference between a function of the actual DC link voltage and a function of the predefined reference DC link voltage. As mentioned earlier, the function of the actual and predefined reference DC link voltage may include any mathematical expression relating to the DC link voltage. In an embodiment, the function is the squares of the actual DC link voltage and the predefined reference DC link voltage. 
     Step  410  includes determining the DC link error power and the feed forward power. The DC link error power is determined based on the DC link voltage error signal. As mentioned earlier, the DC link error power may be determined using the PI controller with the DC link voltage error signal as an input. In an embodiment, the feed forward power includes the difference between the power supplied to the generator side converter and the power transferred by the grid side converter. Step  420  includes generating the duty ratio for operating the power dissipating unit. In an embodiment, the duty ratio is used to operate the power dissipating unit. The chopper circuit as described with reference to  FIG. 2  earlier is an example of the power dissipating unit. The duty ratio is generated based on the DC link error power and the feed forward power. In an embodiment, the duty ratio is the ratio between the power to be dissipated by the power dissipating unit and the maximum power the power dissipating unit can dissipate. The power to be dissipated is the sum of the DC link error power and the feed forward power in an embodiment. Steps  400  to  420  are then repeated, so that the duty ratio is constantly being updated. 
       FIG. 7  shows a flow-chart of a method for operating the chopper circuit in the wind turbine when there is extreme power imbalance in the wind turbine according to an embodiment. Step  500  includes determining the power extracted from the wind, the power supplied by the wind turbine and the power loss in the power dissipating unit. The power dissipating unit may be a chopper circuit in an embodiment. As described earlier, the power from the wind can be determined using equation (10) in an embodiment. The power loss in the power dissipating unit may be determined using equation (11). The power loss in the power dissipating unit is zero if the chopper circuit is not activated. 
     Step  510  includes determining whether the power difference between the power extracted from the wind, and the sum of the power supplied to the grid and the power loss from chopper circuit exceeds the power difference threshold. If the power difference exceeds the power difference threshold, the duty ratio is set to 1 at step  520 . Otherwise, the duty ratio is set to 0 (also at step  520 ). Steps  500  to  520  are then repeated, so that the duty ratio is constantly being updated. 
       FIG. 8  shows a flow-chart of a method for operating the power dissipating unit in the wind turbine according to a further embodiment. In this embodiment, the methods as defined in steps  400  to  420  and steps  500  to  520  are concurrently used for controlling the operation of the power dissipating unit. Steps  400  to  420  have already been described with reference to  FIG. 6  and steps  500  to  520  have already been described with reference to  FIG. 7 . Steps  400  to  420  and steps  500  to  520  are repeated to constantly update the duty ratio. 
     Step  540  includes determining a maximum of the duty ratios from step  420  and step  520 , and activating the power dissipating unit in step  550  based on the maximum of the two duty ratios. It should be noted that the power dissipating unit is only activated when the maximum of the duty ratios has a non-zero value. 
     It should be emphasized that the embodiments described above are possible examples of implementations which are merely set forth for a clear understanding of the principles of the invention. The person skilled in the art may make many variations and modifications to the embodiment(s) described above, said variations and modifications are intended to be included herein within the scope of the following claims.