CN104675629A - Maximum wind energy capturing method of variable-speed wind generating sets - Google Patents

Abstract

The invention relates to a maximum wind energy capturing method of variable-speed wind generating sets. The method includes that current optimum rotary speed of a plurality of wind generators is estimated by capturing conditions of wind energy through the wind generators within previous control periods and is taken as the input of a controller, errors are reduced through proportional control on the basis of an indirect speed control algorithm, the optimum rotary speed in tracking the wind generators is realized, and the maximum output power is acquired. With the method, precise modeling of the wind generators is not needed, nor is measuring of wind velocity; simpleness in structure is achieved, parameters are easy to adjust, production energy is higher than that by a maximum wind energy capturing method and a speed velocity indirect control method which are commonly used in industry, influence of environment factors and structural changes of the wind generators on energy generation can be weakened, a control objective that most of the wind generators are lower than rated wind velocity sections can be met, and great application values are achieved.

Description

A kind of maximal wind-energy capture method of Variable Speed Wind Power Generator

Technical field

The present invention relates to control technology on wind electricity generation unit field, particularly the maximal wind-energy capture of the low wind speed section of wind-driven generator controls.

Background technique

Wind energy is a kind of green non-pollution, reproducible new energy, and therefore, catching of wind energy has great importance for solution environmental pollution and energy crisis.In the last few years, wind-powered electricity generation switch technology worldwide obtained and developed fast.Adopt the Power Electronic Technique of variable speed constant frequency, the variable pitch and variable speed wind generating machine obtained progressively is improved on the basis of original fixed pitch Fixed Speed Wind Turbine Generator group, become the mainstream type of wind-powered electricity generation installation.The operation generating state of variable pitch and variable speed wind generating unit roughly can be divided into two stages, the maximal wind-energy capture stage of low wind speed section and the output-constant operation stage of high wind speed section.But, wind power generating set itself due to wind energy power is the Great inertia system of nonlinear time-varying, meanwhile, brings the wind speed of strong disturbance, there is the inaccurate and disabled engineering present situation of measured value, the uncertain factor that grid-connected and outdoor operation brings simultaneously is again another difficult problem of wind-power electricity generation control.Therefore, high performance control technique improves the key technology of wind-power electricity generation level, has conclusive effect for raising Wind energy extraction and reliability of generating electricity by way of merging two or more grid systems.

Wind-driven generator when low wind speed section is run, to obtain power as much as possible for control objectives.Wherein, wind power utilization coefficient Cp determines the wind energy that wind energy conversion system obtains to a great extent, in β mono-timing for the wind-driven generator of separate unit, also exists one and correspond to best power coefficient C _pmaxoptimum tip-speed ratio λ _opt, now wind-driven generator conversion efficiency is the highest, obtains wind energy maximum.Also just mean, for a certain specific wind speed v, wind-driven generator only operates in a specific rotational speed omega _roptjust have the highest wind energy conversion efficiency down.

Because the wind speed recorded in reality is single-point wind speed, and in formula, use the spatial averaging of the wind speed be evenly distributed on wind power generator oar blade, so during industrial design low wind speed section control algorithm, generally do not use wind speed as the input of controller, the indirect rotational speed governor design of industrial general use is as follows:

First, for wind-driven generator modeling:

$J_r{\stackrel{\·}{\mathrm{\ω}}}_r=T_a-K_r{\mathrm{\ω}}_r-T_{\mathrm{ls}}$

$J_g{\stackrel{\·}{\mathrm{\ω}}}_g=T_{\mathrm{hs}}-K_g{\mathrm{\ω}}_g-T_{\mathrm{gm}}$

In model, impeller torque T _a(unit Nm) drives, by low speed torque T _ls(unit Nm) slows down.For generator, it is with ω _gthe angular velocity of (unit rad/s) rotates, by high speed torque T _hs(unit Nm) drives, by electromagnetic torque T _em(unit Nm), J _r, J _gthe rotary inertia of impeller and generator, unit K gm ², K _r, K _gthe out-damping of impeller and generator, unit Nm/ (rads).

Comprehensive above formula, can obtain transmission system Expression formula below:

$J_t{\stackrel{\·}{\mathrm{\ω}}}_r=T_a-K_t{\mathrm{\ω}}_r-T_g$

In formula,

$\left\{\begin{array}{c}{J}_t=J_r+n_g^2{J}_g\\ K_t=K_r+n_g^2{K}_g\\ T_g=n_g{T}_{\mathrm{em}}\end{array}\right.$

$n_g=\frac{{\mathrm{\ω}}_g}{{\mathrm{\ω}}_r}=\frac{T_{\mathrm{ls}}}{T_{\mathrm{hs}}}$

When the indirect rotating speed control algorithm of industrial design thinks that wind-driven generator reaches stable state, T _a≈ T _gand λ=λ _opt, C _p(λ)=C _pmax, simultaneously according to aerodynamics, so last controller:

$T_g=K_{\mathrm{opt}}{\mathrm{\ω}}_r^2,$ Wherein $K_{\mathrm{opt}}=\frac{1}{2}\mathrm{\π\ρ}{R}^5\frac{C_{p\max }}{{\mathrm{\λ}}_{\mathrm{opt}}^3}$

Whether " the indirect rotating speed control " of industrial use or not the measured value of wind speed, and control algorithm is fairly simple, and the operational capability for controller is less demanding.But it also exists some shortcomings: first, this controlling method is poor for the tracking performance of optimized rotating speed.Because wind speed exists fluctuation always, can not be stabilized to a certain determined value, this makes the most of the time, and under this kind of method, actual speed change slowly, and optimized rotating speed has obvious deviation, and be larger departing from.In this case Wind energy extraction effect is not very well, causes wind energy utilization lower.In addition, need to obtain K accurately in this controlling method _optvalue, but this value is different for different wind-driven generator, and be difficult to know exactly, especially along with the operation of wind-driven generator and the change of environment, K _optvalue also can change, maximum change may reach 20%-50%, and control effects is deteriorated.

Summary of the invention

Poor in order to overcome the indirect rotating speed control algorithm tracking performance that industrial tradition uses, being subject to wind-driven generator self structure and environmental change affects larger shortcoming, the present invention proposes a kind of maximal wind-energy capture method of Variable Speed Wind Power Generator, as follows:

First the model of wind turbine power generation power is provided, be in low wind speed section with wind-driven generator and run the maximum generated output of acquisition for control objectives, when wind speed the unknown, according to the situation of the power of several periodic wind power generators acquisition before, wind-driven generator optimized rotating speed to be estimated and as the input of controller, described controller is based on indirect rotational speed governor, with the deviation of the current rotating speed of proportional controller correction and optimized rotating speed, thus realize the tracking of wheel speed to optimized rotating speed of wind-driven generator, to realize maximal wind-energy capture.

Step 1: get 2n control cycle, generator torque T in this 2n control cycle _gremain unchanged, then compare the energy-producing summation of a front n control cycle and a rear n control cycle in 2n control cycle, if rear n control cycle produce power is large compared with front n control cycle, then the optimized rotating speed of estimation is added a Δ ω, otherwise deduct Δ ω, be formulated as:

$\left\{\begin{array}{c}\widehat{\mathrm{\ω}}\left(m\right)=\widehat{\mathrm{\ω}}(m-1)+\mathrm{sgn}\left(P_e\right)\mathrm{\Δ\ω}\\ P_e=\underset{k=n+1}{\overset{2n}{\mathrm{\Σ}}}{P}_k-\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k\end{array}\right.$

Step 2: due to the difference of wind speed amplitude of variation, cause the extent of produce power also different, so, the knots modification Δ ω of corresponding optimized rotating speed also should change to some extent, according to the difference of the produce power of a front n control cycle and a rear n control cycle in 2n control cycle, by intelligent fuzzy algorithm, determine different Δ ω, operating process is as follows:

(2-1) determine the Fuzzy Distribution of amount inputting, export, triangular membership chosen to the fuzzy subset of the difference Δ W of produce power:

1), selected 7 fuzzy subsets, negative large (NB) respectively, in negative (NM), negative little (NM), zero (ZO), just little (PS), center (PM), honest (PB) is for containing the domain [-6000,6000] of input quantity Δ W;

2), selected 7 fuzzy subsets are negative large (NB) respectively, in negative (NM), and negative little (NM), zero (ZO), just little (PS), center (PM), honest (PB) contains the domain {-0.06 of output quantity Δ ω,-0.05 ,-0.04 ,-0.03,-0.02 ,-0.01,0,0.01,0.02,0.03,0.04,0.05,0.06}.

(2-2) fuzzy rule is set up

According to relevant experience, set up following 7 fuzzy rules, rule is as follows:

R ₁:IfΔW is NB,thenΔωis NB；

R ₂:IfΔW is NM,thenΔωis NM；

R ₃:IfΔW is NS,thenΔωis NS；

R ₄:IfΔW is ZO,thenΔωis ZO；

R ₅:IfΔW is PS,thenΔωis PS；

R ₆:IfΔW is PM,thenΔωis PM；

R ₇:IfΔW is PB,thenΔωis PB.

Rule list is as follows:

Produce power difference Δ W

NB

NM

NS

ZO

PS

PM

PB

Adjustment step delta ω

NB

NM

NS

ZO

PS

PM

PB

(2-3) approximate resoning is carried out

For inputting Δ W arbitrarily ^*, adopt parallel method to carry out reasoning, that is:

$\begin{array}{c}{\mathrm{\Δ\ω}}_1^{*}={\mathrm{\ΔW}}^{*}o{R}_1\\ .\\ .\\ .\\ {\mathrm{\Δ\ω}}_7^{*}={\mathrm{\ΔW}}^{*}{\mathrm{oR}}_7\end{array}$

Final output is ${\mathrm{\Δ\ω}}^{*}={\mathrm{\Δ\ω}}_1^{*}\∪{\mathrm{\Δ\ω}}_2^{*}\∪{\mathrm{\Δ\ω}}_3^{*}\∪{\mathrm{\Δ\ω}}_4^{*}\∪{\mathrm{\Δ\ω}}_5^{*}\∪{\mathrm{\Δ\ω}}_6^{*}\∪{\mathrm{\Δ\ω}}_7^{*}$

(2-4) ambiguity solution is carried out

The Δ ω finally will obtained ^*use weighted mean method ambiguity solution, obtain the knots modification Δ ω of final optimized rotating speed and the estimated value of optimized rotating speed.

Step 3: the rotational speed omega obtaining current wind generator impeller _m, with step 1, the optimized rotating speed estimated value obtained in 2 is poor, producing a deviation e, in order to accelerate speed of response, have employed proportional control, will the part exported as controller, and add industrial conventional indirect rotational speed governor, it is as follows that the final controller obtained exports representation:

$T_g=k_{\mathrm{opt}}{\mathrm{\ω}}_m^2+k(\widehat{\mathrm{\ω}}\left(m\right)-{\mathrm{\ω}}_m)$

The present invention is by such design, do not use the measured value of wind speed, avoid the counter productive that measuring wind speed value is inaccurate brought, and based on indirect rotating speed control algorithm, add the estimation item for optimized rotating speed, for the estimation of optimized rotating speed based on the change of the output power of wind-driven generator, namely be the actual value that the value that estimation is obtained can not represent optimized rotating speed completely, also current rotating speed is provided to need the direction of adjustment, simultaneously, by the difference changed for produce power, change the knots modification Δ ω of optimized rotating speed, reflect the amplitude that current rotating speed needs adjustment better.Due to the existence of one, and k _optω _m ²knots modification can be from item is compensated, and makes K _optalong with the change of wind-driven generator mechanical structure and environment and the change produced the impact of Wind energy extraction effect is improved.The method that the present invention designs can accelerate the speed of following the tracks of optimized rotating speed, thus produces better Wind energy extraction effect.

Accompanying drawing explanation

Fig. 1 is the roughly operation phase figure of variable pitch and variable speed wind generating unit.

Fig. 2 is the actual dynamic model of wind power generating set.

Fig. 3 is the maximal wind-energy capture method flow diagram of Variable Speed Wind Power Generator.

Fig. 4 is trigonometric form membership function figure corresponding to fuzzy subset.

Fig. 5 is wind speed curve figure.

Fig. 6 is K _optwind power generating set generated output plotted curve when not changing.

Fig. 7 is K _optwind turbine power generation power when increasing 50%.

Fig. 8 is K _optwind turbine power generation power when reducing 50%.

Embodiment

Below in conjunction with accompanying drawing, enforcement of the present invention is done as detailed below:

The present embodiment does control analysis to certain rated power 1.5MW Large-scale Wind Turbines that certain wind-powered electricity generation limited company produces.

Accompanying drawing 1 is the roughly operation working area of wind power generating set, can be divided into two sections, low wind speed section is maximal wind-energy capture working area, mainly keeps propeller pitch angle constant, by controlling generating torque, maintaining optimum tip speed ratio and reaching the target improving wind energy utilization; And high wind speed section adopts power limitation control, namely maintain generated output steady, high quality generating is beneficial to grid-connected, reduces the impact to electrical network.The present invention carries out Controller gain variations mainly for low wind speed section.

Accompanying drawing 2 is actual dynamic models of this wind power generating set, and in a particular embodiment, what wind-driven generator adopted is rated power 1.5MW tri-leaf horizontal axis windward type speed-changing wind power generator, wind wheel rotary inertia J _r=4456761Kgm ², wind wheel out-damping K _r=45.52Nm/ (rads), generator rotation inertia J _g=123Kgm ², generator external damping K _g=0.4Nm/ (rads), J _tand K _tpress with calculate.

The basic parameter of this wind-driven generator unit is as follows:

Wind power generating set basic parameter	Number range
		Rated power	1500KW
Power factor	-0.95～+0.95
		Incision wind speed	3m/s
Rated wind speed	11m/s
		Cut-out wind speed	25m/s
Rotor diameter	77m
		Swept area	4654㎡
The number of blade	3
		Gear box ratio	104.494

High speed shaft inertia	12Kg·m
		Generator inertia	123Kg·m

Generator type	Wound-rotor type double-fed asynchronous generator
		Rated power	1500KW
Voltage rating	690V
		Mains frequency	50Hz 60Hz
Rated speed	1800rpm≈188.4rad/s

Accompanying drawing 3 is the maximal wind-energy capture method flow diagrams for Variable Speed Wind Power Generator, in actual emulation, gets n=3, i.e. generator torque T in these 6 control cycles _gremain unchanged, then the energy-producing summation of front 3 control cycles and rear 3 control cycles in 6 control cycles is compared, if rear 3 control cycle produce powers are large compared with front 3 control cycles, then the optimized rotating speed of estimation added a Δ ω, otherwise deduct Δ ω.

Be formulated as:

$\left\{\begin{array}{c}\widehat{\mathrm{\ω}}\left(m\right)=\widehat{\mathrm{\ω}}(m-1)+\mathrm{sgn}\left(P_e\right)\mathrm{\Δ\ω}\\ P_e=\underset{k=n+1}{\overset{2n}{\mathrm{\Σ}}}{P}_k-\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k\end{array}\right.$

Secondly, adopt intelligent fuzzy algorithm to obtain the knots modification Δ ω of corresponding optimized rotating speed according to energy-producing difference, step is as follows:

(1) determine the Fuzzy Distribution of amount inputting, export, triangular membership (this membership function is shown in accompanying drawing 4) chosen to the fuzzy subset of the difference Δ W of produce power:

I. selected 7 fuzzy subsets, negative large (NB) respectively, in negative (NM), negative little (NM), zero (ZO), just little (PS), center (PM), honest (PB) is for containing the domain [-6000,6000] of input quantity Δ W;

Ii. selected 7 fuzzy subsets are negative large (NB) respectively, in negative (NM), negative little (NM), zero (ZO), just little (PS), center (PM), honest (PB) contains the domain {-0.06 of output quantity Δ ω,-0.05 ,-0.04 ,-0.03,-0.02 ,-0.01,0,0.01,0.02,0.03,0.04,0.05,0.06};

(2) fuzzy rule is set up

According to relevant experience, set up following 7 fuzzy rules, rule is as follows:

R ₁:IfΔW is NB,thenΔωis NB；

R ₂:IfΔW is NM,thenΔωis NM；

R ₃:IfΔW is NS,thenΔωis NS；

R ₄:IfΔW is ZO,thenΔωis ZO；

R ₅:IfΔW is PS,thenΔωis PS；

R ₆:IfΔW is PM,thenΔωis PM；

R ₇:IfΔW is PB,thenΔωis PB；

Rule list is as follows:

Produce power difference Δ W

NB

NM

NS

ZO

PS

PM

PB

Adjustment step delta ω

NB

NM

NS

ZO

PS

PM

PB

(3) approximate resoning is carried out

For inputting Δ W arbitrarily ^*, adopt parallel method to carry out reasoning, that is:

$\begin{array}{c}{\mathrm{\Δ\ω}}_1^{*}={\mathrm{\ΔW}}^{*}o{R}_1\\ .\\ .\\ .\\ {\mathrm{\Δ\ω}}_7^{*}={\mathrm{\ΔW}}^{*}{\mathrm{oR}}_7\end{array}$

Final output is ${\mathrm{\Δ\ω}}^{*}={\mathrm{\Δ\ω}}_1^{*}\∪{\mathrm{\Δ\ω}}_2^{*}\∪{\mathrm{\Δ\ω}}_3^{*}\∪{\mathrm{\Δ\ω}}_4^{*}\∪{\mathrm{\Δ\ω}}_5^{*}\∪{\mathrm{\Δ\ω}}_6^{*}\∪{\mathrm{\Δ\ω}}_7^{*}$

(4) ambiguity solution is carried out

By the Δ ω obtained ^*use weighted mean method ambiguity solution, obtain final Δ ω and the estimated value of optimized rotating speed.

Finally, with indirect rotating speed control rate (k _optω _m ²) based on, add part of this reflection optimized rotating speed estimated value change just constitute our design for maximal wind-energy capture method, shown in following formula:

$\left\{\begin{array}{c}{T}_g=k_{\mathrm{opt}}{\mathrm{\ω}}_m^2+k(\widehat{\mathrm{\ω}}\left(m\right)-{\mathrm{\ω}}_m)\\ \widehat{\mathrm{\ω}}\left(m\right)=\widehat{\mathrm{\ω}}(m-1)+\mathrm{sgn}\left(P_e\right)\mathrm{\Δ\ω}\\ P_e=\underset{k=n+1}{\overset{2n}{\mathrm{\Σ}}}{P}_k-\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k\end{array}\right.$

In said method, the concrete parameter used is K _opt=1175, k=350, n=3.Use commercial wind-driven generator simulation software GH Bladed, do simulating, verifying to the low wind speed paragraph controller adopted, during emulation, sampling period and the control cycle of employing are all 0.04s, and simulation time is 400s, and the anemobiagraph that emulation adopts is shown in accompanying drawing 5.

In the simulation result finally obtained, accompanying drawing 6 is at wind-driven generator self K _optwhen not changing, (label 1 curve is control algorithm of the present invention to use algorithm of the present invention and conventional indirect rotational speed governor to obtain the comparison diagram of power, label 2 curve is conventional indirect rotating speed control algorithm), final statistical result showed, algorithm of the present invention produce power in 400s has exceeded 0.51%.

Accompanying drawing 7 is wind-driven generator self K _optafter increasing 50% (can be realized by the parameter of model in amendment Bladed), algorithm of the present invention and conventional indirect rotational speed governor is used to obtain the comparison diagram of power, final statistical result showed, algorithm of the present invention has exceeded 0.78% in produce power in 400s.

Accompanying drawing 8 is wind-driven generator self K _optafter reducing 50% (can be realized by the parameter of model in amendment Bladed), algorithm of the present invention and conventional indirect rotational speed governor is used to obtain the comparison diagram of power, final statistical result showed, algorithm of the present invention has exceeded 6.1% in produce power in 400s.

The technical program has carried out repeatedly verifying at this rated power 1.5MW large-scale wind driven generator, as can be seen from accompanying drawing 6,7 and 8, and no matter K _optwhether change; algorithm used in the present invention is all better than algorithm conventional on general industry in produce power effect; and especially for the K caused by the change of environment residing for wind-driven generator and the change (wind power generator oar blade being such as in area, plateau often can freeze, and when raining, on blade, subsidiary rainwater also can affect the air dynamic characteristic of wind-driven generator) of self structure _optsituation about changing, algorithm of the present invention significantly can improve the situation of the power drop that these reasons are brought.Obtain peak output in wind-driven generator actual motion, increase economic efficiency and there is larger meaning and using value.

Claims (4)

1. the maximal wind-energy capture method of a Variable Speed Wind Power Generator, it is characterized in that, first the model of wind turbine power generation power is provided, be in low wind speed section with wind-driven generator and run the maximum generated output of acquisition for control objectives, when wind speed the unknown, according to the situation of the power of several periodic wind power generators acquisition before, wind-driven generator optimized rotating speed to be estimated and as the input of controller, described controller is based on indirect rotational speed governor, with the deviation of the current rotating speed of proportional controller correction and optimized rotating speed, thus realize the tracking of wheel speed to optimized rotating speed of wind-driven generator, to realize maximal wind-energy capture.

2. method according to claim 1, is characterized in that, gets 2n control cycle, the torque T of wind-driven generator in this 2n control cycle _gremain unchanged, then compare the energy-producing summation of a front n control cycle and a rear n control cycle in 2n control cycle, then optimized rotating speed is estimated.

3. method according to claim 2, is characterized in that, adopt intelligent fuzzy algorithm to obtain the knots modification Δ ω of corresponding optimized rotating speed according to energy-producing difference, step is as follows:

(1) determine the Fuzzy Distribution of amount inputting, export, triangular membership chosen to the fuzzy subset of the difference Δ W of produce power:

I. selected 7 fuzzy subsets, negative large (NB) respectively, in negative (NM), negative little (NM), zero (ZO), just little (PS), center (PM), honest (PB) is for containing the domain [-6000,6000] of input quantity Δ W;

Ii. selected 7 fuzzy subsets are negative large (NB) respectively, in negative (NM), negative little (NM), zero (ZO), just little (PS), center (PM), honest (PB) contains the domain {-0.06 of output quantity Δ ω,-0.05 ,-0.04 ,-0.03,-0.02 ,-0.01,0,0.01,0.02,0.03,0.04,0.05,0.06};

(2) fuzzy rule is set up

According to relevant experience, set up following 7 fuzzy rules, rule is as follows:

R ₁:If ΔW is NB,then Δω is NB；

R ₂:If ΔW is NM,then Δω is NM；

R ₃:If ΔW is NS,then Δω is NS；

R ₄:If ΔW is ZO,then Δω is ZO；

R ₅:If ΔW is PS,then Δω is PS；

R ₆:If ΔW is PM,then Δω is PM；

R ₇:If ΔW is PB,then Δω is PB；

Rule list is as follows:

Produce power difference Δ W NB NM NS ZO PS PM PB Adjustment step delta ω NB NM NS ZO PS PM PB

(3) approximate resoning is carried out

For inputting Δ W arbitrarily ^*, adopt parallel method to carry out reasoning, that is:

$\begin{array}{c}{\mathrm{\Δ\ω}}_1^{*}=\mathrm{\Δ}{W}^{*}o{R}_1\\ .\\ .\\ .\\ \mathrm{\Δ}{\mathrm{\ω}}_7^{*}={\mathrm{\ΔW}}^{*}o{R}_7\end{array}$

Final output is ${\mathrm{\Δ\ω}}^{*}={\mathrm{\Δ\ω}}_1^{*}\∪\mathrm{\Δ}{\mathrm{\ω}}_2^{*}\∪{\mathrm{\Δ\ω}}_3^{*}\∪{\mathrm{\Δ\ω}}_4^{*}\∪\mathrm{\Δ}{\mathrm{\ω}}_5^{*}\∪\mathrm{\Δ}{\mathrm{\ω}}_6^{*}\∪{\mathrm{\Δ\ω}}_7^{*}$

(4) ambiguity solution is carried out

The Δ ω finally will obtained ^*use weighted mean method ambiguity solution, obtain final Δ ω and the estimated value of optimized rotating speed.

4. according to the method in claim 1-3 described in any one, it is characterized in that, with indirect rotating speed control rate (k _optω _m ²) based on, add part of this reflection optimized rotating speed estimated value change just constitute our design for maximal wind-energy capture method, shown in following formula:

$\left\{\begin{array}{c}{T}_g=k_{\mathrm{opt}}{\mathrm{\ω}}_m^2+k(\widehat{\mathrm{\ω}}\left(m\right)-{\mathrm{\ω}}_m)\\ \widehat{\mathrm{\ω}}\left(m\right)=\widehat{\mathrm{\ω}}(m-1)+\mathrm{sgn}\left(P_e\right)\mathrm{\Δ\ω}\\ P_e=\underset{k=n+1}{\overset{2n}{\mathrm{\Σ}}}{P}_k-\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k\end{array}\right.$

So far, the torque T obtained by this formula _g, be exactly the output of the maximal wind-energy capture method of the Variable Speed Wind Power Generator that this is estimated based on optimized rotating speed.