CN103291548B - Electromechanical coordination suppression device for vertical axis wind turbine rotating spindle vibration - Google Patents

Abstract

The invention discloses an electromechanical coordination suppression device for vertical axis wind turbine rotating spindle vibration. The electromechanical coordination suppression device comprises a two-shaft tilt angle sensor, a revolution speed sensor, an air velocity transducer, a wind driven generator, an electromagnetic rear axes brake mechanism, a revolving speed inner ring controller and an electromechanical coordination outer ring controller. The electromechanical coordination suppression device can measure and calculate current vibration intensity of a spindle in real time, suppresses vibration of the spindle, and enables a wind turbine to maintain mechanical stabilization and meanwhile obtain the highest wind energy capture efficiency as far as possible.

Description

Electromechanical Coordination Suppression Device for Vibration of Rotating Main Shaft of Vertical Axis Wind Turbine

This application is a divisional application with application number: 201210049193.0, application date: 2012.2.29, titled "Mechatronic Coordination Suppression Method and Device for Vibration of Rotating Main Shaft of Vertical-axis Wind Turbine".

technical field

The invention relates to the field of mechatronics control of a wind power generating set, in particular to an electromechanical coordination intelligent suppression method and device for the vibration of the rotating main shaft of a vertical axis wind power machine.

Background technique

Except for the establishment of experimental wind farms in a few areas of the world, vertical axis wind turbines have not yet been widely promoted, but their superior aerodynamic performance has attracted more and more attention from researchers in various countries.

Structurally speaking, the vertical rotating main shaft structure of the vertical axis wind turbine belongs to the mast structure in the towering structure. Since the main characteristics of towering structures are higher height and softer stiffness in the horizontal direction, horizontal loads cause large structural responses. In addition, in order to further improve the wind energy utilization rate of the vertical axis wind turbine, a wind collecting hood that can rotate with the wind direction is often installed on the outside of the vertical axis wind turbine, that is, a wind collecting plate is installed on the windward side, and a navigation panel is installed on the downwind side. Empennage, such as the "vertical axis wind turbine" proposed by Lin Yanshan in patent CN2086318U, the "wind gathering device for vertical axis wind generators with self-navigation" proposed by Wu Guoqing and others in patent CN101649809, and the shore waves and others in patent JP The "direct-current windmill" proposed in JP-A 2007-16661A further improves the flexibility of the vertical axis wind turbine.

Therefore, under the joint effect of high flexibility of mechanical structure and randomness of wind load, the main shaft of vertical axis wind turbine is particularly sensitive to the effect of wind, and the wind effects often formed include: the vibration response of the structure in the downwind direction, the vortex induced vibration of the structure in the cross wind direction , self-excited vibration, parametric vibration and other forms. The complexity of the structure of the whole machine and the installation environment makes it extremely difficult to accurately measure the natural frequencies of these wind effects.

On the other hand, from a mechanical point of view, the vertically rotating main shaft belongs to the rotor system, and its rotational speed is related to the aerodynamic characteristics of the electrical load power of the wind turbine and the wind energy absorbed by the wind turbine. In engineering applications, in order to obtain the maximum wind energy absorption efficiency of wind turbines, wind turbines often adopt closed-loop speed control, and adjust the generator speed in real time according to the current wind speed, so that the impeller speed driven by the vertical rotation of the main shaft of the wind turbine is the same as the theoretical maximum The wind captures the RPM to match.

For this reason, using the basic method that "the wind turbine speed closed-loop controller can effectively adjust the speed of the vertically rotating main shaft", some scholars have proposed a simple method of "reducing the wind force The control strategy to suppress the phenomenon by means of the speed of the machine, such as the "wind power tower resonance active suppression device" proposed by Donglei et al. in patent CN201661421U, and the "wind force Power generating equipment and method of controlling the same", etc.

However, the existing method of "suppressing the free vibration of the tower by reducing the speed of the wind turbine" is too conservative. Maximum wind capture speed. Theoretical analysis and wind tunnel experiments show that when a certain wind speed excites the natural vibration of the vertical rotating shaft, increasing or decreasing the speed of the wind turbine can suppress the natural vibration of the vertical rotating shaft.

In addition, different from the natural vibration suppression principle of the tower of the horizontal axis wind turbine, the reasons for the vibration of the rotating shaft of the vertical axis wind turbine are more diverse, not only the natural frequency natural vibration, but also other reasons such as wind effect and mechanical shaft eccentricity. Therefore, it is necessary to study and design a vibration suppression method for the rotating shaft of a vertical axis wind turbine, using the active and fast adjustment method of the wind turbine speed, including rapidly increasing or decreasing the wind turbine speed, to improve the performance of this type of wind power generation system. stability and efficiency.

Contents of the invention

The purpose of the present invention is to provide an electromechanical device that can measure and calculate the current vibration intensity of the main shaft in real time, suppress the vibration of the main shaft, and make the wind turbine obtain the highest vibration of the rotating main shaft of the vertical axis wind turbine as much as possible while maintaining mechanical stability. Coordinate suppression devices.

Technical solution of the present invention is:

An electromechanical coordination suppression method for the vibration of the rotating main shaft of a vertical axis wind turbine, which is characterized in that it includes the following steps:

(1) Obtain the vertical inclination angle of the rotating main shaft in real time, the vertical inclination angle includes the inclination angle values αx and αy in two orthogonal directions in the horizontal section of the main shaft;

(2) Calculate the flutter intensity K _v of the rotating spindle, which is defined as, $K_v=\sqrt{{{\mathrm{\α}}_x}^2+{{\mathrm{\α}}_{\mathrm{the\; y}}}^2}+\sqrt{{{\stackrel{\&Center\; Dot;}{\mathrm{\α}}}_x}^2+{{\stackrel{\&Center\; Dot;}{\mathrm{\α}}}_{\mathrm{the\; y}}}^2}+\sqrt{{{\stackrel{\&Center\; Dot;\&Center\; Dot;}{\mathrm{\α}}}_x}^2+{{\stackrel{\&Center\; Dot;\&Center\; Dot;}{\mathrm{\α}}}_{\mathrm{the\; y}}}^2};$

(3) According to the current wind speed, calculate the optimal speed ω _op under the maximum power tracking target of the wind turbine;

(4) According to the vibration intensity of the rotating main shaft, analyze and determine the expected speed ω _g of the wind turbine:

a) Obtain the current speed ω _c of the wind turbine;

b) Judging whether the vibration intensity of the rotating spindle exceeds the preset critical control threshold Kt,

If yes, go to step d);

If not, go to step c);

c) Determine the optimal speed ω _op as the expected speed ω _g of the wind turbine;

d) Compare the current speed ω _c with the optimal speed ω _op ,

If |ω _c -ω _op |>ε, then determine the optimal speed ω _op as the desired speed ω _g of the wind turbine;

If |ω _c -ω _op |≤ε, then set the desired speed ω _g of the wind turbine to be lower than the optimal speed ω _op ;

In the formula, ε is a positive real number, which is a numerical quantity representing the difference between the current speed ω _c and the optimal speed ω _op ;

(5) The speed of the wind turbine is driven by the speed inner loop controller to quickly reach the desired speed ω _g ;

(6) Determine whether the vibration intensity of the rotating spindle exceeds the preset maximum safety control threshold Ks,

If yes, go to step (7);

If not, return to step (1);

(7) The reverse electric braking function of the wind turbine generator in the inner loop controller of the starting speed, and the electromagnetic brake mechanism of the rotating main shaft, so that the speed of the wind turbine generator drops rapidly;

(8) Send a fault stop signal, and wait for the reset restart command.

In the step 10), the vertical inclination angle values αx and αy are obtained by installing a two-axis inclination sensor on the stationary part at the top of the rotating spindle.

The wind generator is a switched reluctance wind generator.

The fast speed adjustment method of the speed inner loop controller in step (5) is the generator speed-up method that directly cuts off the excitation of part of the phase windings or the generator speed-down method that releases the current chopping limit.

A special device for the electromechanical coordination suppression method of vibration of the rotating main shaft of a vertical axis wind turbine, which is characterized in that it at least includes:

The two-axis inclination sensor is installed on the stationary part at the top of the rotating main shaft, and is used to obtain the inclination angle values αx and αy in two orthogonal directions in the horizontal section of the rotating main shaft;

The rotational speed sensor is installed on the fuselage of the wind-driven generator to obtain the current rotational speed ω _c of the wind-driven generator;

The wind speed sensor is installed on the working site of the vertical axis wind turbine to obtain the wind speed on site;

The wind generator is installed coaxially with the rotating shaft of the vertical axis wind turbine, and is used for electromechanical energy conversion and adjustment of the speed of the vertical axis wind turbine;

The electromagnetic brake mechanism is installed coaxially with the rotating shaft of the vertical axis wind turbine to prevent the rotation of the vertical axis wind turbine;

The speed inner loop controller is used to control the speed of the wind turbine. According to the expected speed ω _g given by the outer loop controller and the current speed ω _c detected by the speed sensor, the application includes power generation control, reverse electric braking The speed closed-loop control algorithm including technology makes the speed of the wind turbine quickly reach the desired speed ω _g ;

The electromechanical coordinated outer loop controller is used to receive the signals of the two-axis inclination sensor, wind speed sensor, and rotational speed sensor in real time, and thus calculate the vibration intensity of the rotating main shaft, the optimal rotational speed ω _op under the maximum power tracking target, and judge the rotational speed of the main shaft The strength of the flutter intensity relative to the critical control threshold and the maximum safety control threshold determines the expected speed ω _g of the wind turbine, the reverse electric braking command, the electromagnetic brake command, and the shutdown and reset signals.

The wind generator is a switched reluctance wind generator.

Compared with the prior art, the present invention has the following advantages:

(1) The two-axis inclination sensor is used as the detection element to measure and calculate the vibration intensity of the main shaft in real time, so: (a) It is not necessary to know the precise natural frequency value of the rotating shaft of the vertical axis wind turbine in advance, only through the current vibration intensity value It can be judged whether the main shaft is in the state of natural vibration, that is, the detection of the state of main shaft natural vibration is accurate, reliable, and self-adaptive; (b) the vibration intensity value can not only reflect whether the main shaft has natural vibration, but also It reflects whether there are other wind effects on the spindle, mechanical rotation eccentricity, excessive deviation of the verticality of the spindle and other spindle instability states, that is, the discrimination of the spindle vibration source is diverse and accurate.

(2) According to the vibration intensity of the vertically rotating main shaft, the optimal speed under the maximum power tracking target of the wind turbine, and the current speed of the wind turbine, determine the expected speed of the wind turbine to suppress the vibration of the main shaft. The expected speed value is formulated scientifically and reasonably so that the wind turbine can obtain the highest wind energy capture efficiency as much as possible while maintaining mechanical stability.

(3) Adopt electromechanical coordinated speed control method, including generator reverse electric braking and electromagnetic brake, to adjust the wind turbine speed. It has the advantages of fast adjustment speed, high work efficiency and good real-time performance. In particular, the reverse electric braking method using switched reluctance wind turbines, the generation of positive/negative torque is only related to the rise/fall interval of the phase inductance to which the conduction angle belongs, and the adjustment of the torque is only related to the phase current Therefore, the reverse electric braking torque is smooth and easy to control.

Description of drawings

The present invention will be further described below in conjunction with drawings and embodiments.

Fig. 1 is a flow chart of an embodiment of an electromechanical coordination suppression method for vibration of a rotating main shaft of a vertical axis wind turbine according to the present invention.

Fig. 2 is an example flow chart of analyzing and determining the expected rotational speed of the wind power generator in Fig. 1 .

Fig. 3 is a structural schematic diagram of an electromechanical coordination suppressing device for vibration of a rotating main shaft of a vertical axis wind turbine according to the present invention.

Fig. 4 is a control block diagram of the electromechanical coordination suppressing device for vibration of the rotating main shaft of the vertical axis wind turbine according to the present invention.

Detailed ways

Referring to FIG. 1 , this figure is a flow chart of an embodiment of the electromechanical coordination suppression method for vibration of the rotating main shaft of a vertical axis wind turbine according to the present invention. This embodiment comprises the following steps:

S100, start.

S110. Obtain the vertical inclination of the rotating main shaft in real time.

The vertical inclination angle includes inclination angle values α _x and α _y in two orthogonal directions in the horizontal section of the main shaft. The inclination angle value can be obtained by installing a two-axis inclination sensor on the stationary part at the top of the rotating spindle.

S120. Calculate the vibration intensity K _v of the rotating main shaft.

The tremor intensity is defined as, $K_v=\sqrt{{{\mathrm{\α}}_x}^2+{{\mathrm{\α}}_{\mathrm{the\; y}}}^2}+\sqrt{{{\stackrel{\·}{\mathrm{\α}}}_x}^2+{{\stackrel{\·}{\mathrm{\α}}}_{\mathrm{the\; y}}}^2}+\sqrt{{{\stackrel{\&Center\; Dot;\·}{\mathrm{\α}}}_x}^2+{{\stackrel{\&Center\; Dot;\·}{\mathrm{\α}}}_{\mathrm{the\; y}}}^2}$

It can be seen from the above calculation formula that the value of the flutter intensity K _v includes the amount of inclination of the main axis of rotation in the horizontal section (the square root of the square sum of the inclination angle values αx and αy, ), tilt velocity (the quadratic root of the sum of the squares of the first derivatives of the tilt angle values αx and αy, ) and tilt acceleration (the quadratic root of the sum of the squares of the second derivatives of the tilt angle values αx and αy, ) and other information, which can reflect the real-time static and dynamic working characteristics of the rotating spindle, including whether the spindle has natural vibration, downwind vibration, crosswind vortex induced vibration, degree of eccentricity of rotation, degree of static deviation of verticality, etc.

S130. According to the current wind speed, calculate the optimal rotational speed ω _op under the maximum power tracking target of the wind turbine;

According to the characteristic parameter C _p (λ, β) of the wind turbine, according to the current wind speed, the optimal speed tracking power P _max -ω _op of the wind turbine can be calculated online (including table look-up interpolation method, etc.). Running at the optimal speed ω _op can absorb wind energy to the greatest extent.

S140. Analyzing and determining the expected rotational speed ω _g of the wind turbine according to the vibration intensity of the rotating main shaft;

S150. Drive the speed of the wind generator to quickly reach the desired speed ω _g by the speed inner loop controller;

The speed regulation algorithm of the speed inner loop controller needs to be designed according to the type of wind turbine. The present invention selects the switched reluctance wind-driven generator, therefore, it can be seen from the control principle of the switched reluctance wind-driven generator that the speed inner loop controller can adopt the APC control of adjusting the excitation switch angle, the CCC control of adjusting the excitation current limit, and the adjustment of the excitation intensity Conventional methods such as voltage PWM control to drive the speed of the wind turbine to the desired speed ω _g ; especially, in order to adjust the speed of the multi-phase switched reluctance wind generator more quickly, the present invention designs a method that directly cuts off part of the phase windings Excitation generator speed-up method (after the phase winding is cut off, the corresponding phase has no excitation current, that is, no negative torque can be generated, and mechanical energy cannot be converted into electrical energy, so the generator will speed up rapidly driven by the wind turbine) and release current Generator deceleration method with chopper limit (after the current chopper limit is released, the excitation current increases sharply, the negative torque also increases squarely, and a large amount of mechanical energy is converted into electrical energy. Therefore, the generator drives the wind turbine to decelerate rapidly) , these two unconventional speed regulation methods.

S160, judging whether the vibration intensity of the rotating spindle exceeds the preset maximum safety control threshold Ks,

If yes, go to step S170;

If not, return to step S110;

S170, the reverse electric braking function of the wind turbine generator in the inner loop controller of the starting speed, and the electromagnetic brake mechanism of the rotating main shaft, so that the speed of the wind turbine generator drops rapidly.

The purpose of this step is to reduce the speed quickly to ensure the mechanical stability of the vertical wind turbine. In consideration of efficiency and reliability, the present invention adopts the electromechanical coordinated speed control method: mechanically, the electromagnetic brake mechanism has a large output and reliable operation. It is also convenient to adjust the negative resistance torque of the brake through the voltage PWM control method; in terms of electricity, the reverse electric braking state of the switched reluctance wind turbine can effectively and quickly generate negative resistance torque, and through such as APC Control, CCC control and voltage PWM control methods enable flexible adjustment of negative resistance torque.

In particular, it can be seen from the basic operating principle of switched reluctance motors that the switched reluctance wind turbine is in the electrodynamic state or generating state, only related to the rise or fall of the phase winding conduction angle interval in the phase inductance interval, it can be in different Under the conditions of changing the power converter and the control circuit, it is convenient to operate in the power generation state or the reverse electrodynamic state (generate negative torque) through the adjustment of the control algorithm, and the adjustment of the negative torque is only in accordance with the phase given by the controller. Therefore, the reverse electric braking torque adjustment process of the switched reluctance wind turbine is smooth and easy to control, which has obvious advantages in function and regulation compared with other types of wind turbines.

S180. Send a fault shutdown signal, and wait for a reset and restart instruction.

The fault shutdown signal represents the occurrence of an event that the vibration intensity of the rotating spindle exceeds a preset maximum safety regulation threshold. The reset and restart command can be given by external manual operation, or it can be automatically restarted after the system delays for a period of time and confirms that the main shaft of the wind turbine is in a stable state.

In this embodiment, the expected speed ω _g of the wind generator is determined according to the vibration intensity of the vertically rotating main shaft, the optimal speed ω _op under the maximum power tracking target of the wind power generator, and the current speed ω _c of the wind power generator. Its purpose is to suppress the vibration of the main shaft by controlling the speed of the wind turbine, so that the wind turbine can obtain the highest wind energy capture efficiency as much as possible while maintaining mechanical stability. The details are as follows.

Referring to FIG. 2 , this figure is an example flow chart of analyzing and determining the expected rotational speed ω _g of the wind turbine in FIG. 1 . It includes the following steps:

S141. Obtain the current rotational speed ω _c of the wind turbine;

The current speed _ωc can be detected by a speed sensor installed on the rotor shaft of the wind turbine.

S142. Judging whether the vibration intensity of the rotating spindle exceeds a preset critical control threshold Kt,

If yes, enter step S143;

If not, enter step S144;

S144. Set the desired rotational speed ω _g of the wind turbine to the optimal rotational speed ω _op , that is, ω _g ←ω _op .

S143. Comparing the current speed ω _c with the optimal speed ω _op ,

If |ω _c -ω _op |>ε, it indicates that the difference between the current speed ω _c and the optimal speed ω _op is relatively large, then the optimal speed ω _op is determined as the expected speed ω _g of the wind turbine, that is, ω _g ←ω _op ;

If |ω _c -ω _op |≤ε, it indicates that the current speed ω _c is not much different from the optimal speed ω _op and close to equal, then the expected speed ω _g of the wind turbine is set to be lower than the optimal speed ω _op , That is, ω _g < ω _op ;

In the formula, ε is a positive real number, which is a numerical quantity representing the difference between the current speed ω _c and the optimal speed ω _op .

Through the above intelligent online analysis and decision-making process, the expected speed ω _g value of the wind turbine at the moment can be determined under the current state (the ω _g value can be greater than, equal to or smaller than the current speed ω _c value). Then introduce the expected speed ω _g value to the given input end of the speed inner loop controller to achieve the purpose of suppressing the vibration of the main shaft by changing the speed of the wind turbine.

The electromechanical coordination intelligent suppression device for vibration of the rotating main shaft of a vertical axis wind turbine according to the present invention will be described below.

Referring to Fig. 3 and Fig. 4, the electromechanical coordination suppression device for the vibration of the rotating main shaft of the vertical axis wind turbine includes: two-axis inclination sensors 1 and 2, installed on the stationary part 11 at the top of the rotating main shaft 3, used to obtain the horizontal section of the rotating main shaft The tilt angle values αx and αy in the two orthogonal directions; the rotational speed sensor 7 is installed on the fuselage of the wind-driven generator 6 to obtain the current rotational speed ω _c of the wind-driven generator 6; the wind speed sensor 10 is installed on The working site of the vertical axis wind turbine is used to obtain the on-site wind speed; the wind generator 6 is installed coaxially with the rotating main shaft 3 of the vertical axis wind turbine 4, and is used to adjust the speed of the vertical axis wind turbine 4; the electromagnetic brake mechanism 5 is connected with the The rotating main shaft 3 of the vertical axis wind turbine 4 is coaxially installed to prevent the rotation of the vertical axis wind turbine 4;

The speed inner loop controller 8 is used to control the speed of the wind turbine 6. According to the expected speed ω _g given by the outer loop controller 8 and the current speed ω _c detected by the speed sensor 7, the power generation control (through Regulate the electric power sent by the generator to control its speed), and the speed closed-loop control algorithm including the reverse electric braking technology, so that the speed of the wind turbine 6 quickly reaches the desired speed ω _g ;

The electromechanical coordinated outer loop controller 9 is used to receive the signals of the two-axis inclination sensors 1 and 2, the wind speed sensor 10, and the rotation speed sensor 7 in real time, and thus calculate the vibration intensity of the rotating main shaft 3 and the optimal power tracking target under the maximum power. Rotating speed ω _op , judging the strength of the vibration intensity of the rotating main shaft 3 relative to the critical control threshold and the maximum safety control threshold, determining the expected speed ω _g of the wind turbine, the reverse electric braking command, the electromagnetic brake command, and Stop, reset signal;

The wind power generator 6 is a switched reluctance wind power generator. In this embodiment, due to the mechanical motion relationship between the rotating main shaft 3 and the stationary part 11, the switched reluctance wind generator 6 is an outer rotor type, that is, the outer rotor of the generator 6 is connected to the rotating main shaft 3 to rotate synchronously, and the inner stator is connected to the stationary part 11. Components 11 are connected and stationary;

The speed inner loop controller 8 and the electromechanical coordination outer loop controller 9 also store parameters related to control.

Pre-set critical control threshold K _t : an amount representing the intensity of the vibration of the rotating shaft. When the vibration intensity of the rotating shaft is less than the critical control threshold K _t , it means that the vibration of the rotating shaft is weak and in a good mechanically stable working state , without external intervention.

Pre-set maximum safety control threshold K _s : an amount representing the intensity of the vibration of the rotating shaft, K _s >K _t , when the vibration intensity of the rotating shaft is greater than the maximum safety control threshold K _s , it means that the vibration of the rotating shaft is severe , is about to reach a very dangerous mechanically unstable working state, if a stronger direct and rapid deceleration method is not adopted for regulation, accidents may result.

Claims (1)

1. an electromechanical coordination suppression device for vertical-shaft wind machine rotating main chatter, is characterized in that: at least comprise:

Diaxon dip sensor, is installed on the static part on rotary main shaft top, for obtaining the inclination drift angle value α in both direction orthogonal in rotary main shaft horizontal section _xand α _y;

Speed probe, is installed on the fuselage of wind-driven generator, for obtaining the current rotational speed omega of wind-driven generator _c;

Air velocity transducer, is installed on the working site of vertical axis wind electric unit, for obtaining on-the-spot wind speed;

Wind-driven generator, coaxially installs with vertical-shaft wind machine rotating main, for energy converting between mechanical and the rotating speed regulating vertical axis windmill;

Electromagnetism brake holding mechanism, coaxially installs with vertical-shaft wind machine rotating main, for stoping the rotation of vertical axis windmill;

Ring controller in rotating speed, for controlling the rotating speed of wind-driven generator, according to the expectation rotational speed omega that outer ring controller provides _g, and speed probe detects the current rotational speed omega obtained _c, use the speed closed loop control algorithm comprising generated output control and reverse electrodynamic braking technology, make the rotating speed of wind-driven generator arrive expectation rotational speed omega fast _g; In rotating speed, the quick rotational speed regulation mode of ring controller is the generator raising speed method of direct cutout portion phase winding excitation or the generator deceleration method of relieving current chopping limit;

The outer ring controller of electromechanical coordination, for real-time reception diaxon dip sensor, air velocity transducer and signals of rotational speed sensor, and thus, calculates the optimized rotating speed ω under the chatter earthquake intensity of rotary main shaft, maximal power tracing target _op, judge that the chatter earthquake intensity of rotary main shaft regulates and controls the degree of strength of threshold value relative to critical adjustment and control threshold value and maximum safety, determine the expectation rotational speed omega of wind-driven generator _g, oppositely electrodynamic braking instruction, electromagnetism brake holding instruction and shut down, reset signal;

Described chatter earthquake intensity is defined as, $K_v=\sqrt{{{\mathrm{\&alpha;}}_x}^2+{{\mathrm{\&alpha;}}_y}^2}+\sqrt{{{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_x}^2+{{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_y}^2}+\sqrt{{{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_x}^2+{{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_y}^2};$

Described wind-driven generator is switching magnetic-resistance wind-driven generator.