CN107273647B - Low-speed gear box doubly-fed wind turbine generator optimization design method based on direct-current power transmission - Google Patents

Low-speed gear box doubly-fed wind turbine generator optimization design method based on direct-current power transmission Download PDF

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CN107273647B
CN107273647B CN201710665913.9A CN201710665913A CN107273647B CN 107273647 B CN107273647 B CN 107273647B CN 201710665913 A CN201710665913 A CN 201710665913A CN 107273647 B CN107273647 B CN 107273647B
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闫绍敏
蔡彬
褚晓广
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Qufu Normal University
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Abstract

The invention relates to a low-speed gear box doubly-fed wind turbine generator optimization design method based on direct-current power transmission, and belongs to the field of wind power. The method adopts a topological structure of a double-fed wind power generation system to optimally design and control a double-fed wind power generation set comprising a gear box, a double-fed generator (DFIG) and a direct current converter; firstly, a stator magnetic flux vector directional control strategy is adopted to optimize the ratio of the stator current and the rotor current of the DFIG before and after optimization to the total current of the direct current converter; secondly, the total cost C of the double-fed wind turbine generator set after optimization is solveds2(ii) a And finally, solving the optimal design parameters of the wind turbine generator: according to Cs2Formula, drawing Cs2Lambda curve, lambda being the ratio of the step-up ratios of the gearboxes before and after optimization, to find Cs2And the optimal value of lambda, thereby obtaining the optimized gearbox step-up ratio and the stator-rotor current, synchronous rotating speed and stator rated frequency of the DFIG. The invention reduces the speed increasing ratio of the gear box, can reduce the failure rate and cost, and improves the operation reliability of the system.

Description

Low-speed gear box doubly-fed wind turbine generator optimization design method based on direct-current power transmission
Technical Field
The invention relates to an optimal design method, in particular to an optimal design method of a low-speed gear box double-fed wind turbine generator based on direct-current power transmission, and belongs to the technical field of wind power generation.
Background
The double-fed wind power generation system mainly comprises a wind turbine, a gear box, a double-fed wind power generator (DFIG), a converter and the like. The DFIG is a high-speed and small-size generator, and because a wind turbine runs at a low rotating speed, a speed-increasing gearbox with a high speed-increasing ratio is usually adopted to increase the rotating speed of the wind turbine to a high-speed rotor rotating speed. The higher the speed increasing ratio of the gearbox is, the smaller the volume and the cost of the DFIG are; however, the larger the speed increasing ratio of the gear box is, the higher the volume and the cost of the gear box are, the larger the energy loss and the fault rate are, and the worse the reliability of the whole system is. The main losses of doubly fed wind power systems originate from the gearbox and converter system, wherein approximately 65% or so of the system losses originate from the gearbox each year. Therefore, it is necessary to research a gearbox with a low step-up ratio to reduce the cost and loss of the system and improve the reliability of the system operation. However, the conventional DFIG stator is usually directly connected to an ac power grid, and the DFIG must adopt a constant voltage and constant frequency operation mechanism to ensure that the frequency of the stator is consistent with the grid frequency, so that a gear box with a low speed increasing ratio cannot be adopted.
The existing direct current transmission technology is deeply concerned due to the advantages of reliable operation, long distance, low cost, small loss and the like, becomes an ideal technology for connecting a long-distance large-scale wind power plant and a power grid, and is widely applied to a wind power generation and transmission system. The utility model patent ZL201420171452.1 discloses a double-fed type wind turbine generator system converter topological structure for flexible direct current transmission system, this converter includes stator side converter, the machine side converter, net side DC-DC converter, can be directly with double-fed type aerogenerator output access direct current electric wire netting, wherein stator side converter is connected with DFIG's stator, realize the rectification, that is to say DFIG's stator is not connected with alternating current electric wire netting, therefore the output voltage and the frequency of stator need not the constant voltage constant frequency, stator frequency and stator voltage can be adjusted in a flexible way to the converter, this makes the frequency of stator can be less than the electric wire netting frequency (like 50Hz), consequently the synchronous revolution of generator can reduce, thereby can adopt the gear box of low step-up ratio. However, the increase ratio of the gear box is reduced, the synchronous rotating speed is reduced, the currents of a stator and a rotor of the DFIG are increased, the size and the cost of the gear box are increased, and therefore the problems of the whole system optimization design and control caused by the increase ratio and the synchronous rotating speed are solved.
Disclosure of Invention
The main purposes of the invention are as follows: aiming at the defects and blanks in the prior art, according to the characteristics of a flexible direct current transmission system, an optimal design method for a double-fed wind turbine generator set through selecting an optimal gear box speed change ratio is provided, so that the speed increasing ratio of the gear box is reduced, the cost of the double-fed wind turbine generator set is reduced, and the reliability of the system is improved.
In order to achieve the above purpose, the invention provides a low-speed gear box double-fed wind turbine generator optimization design method based on direct-current transmission, which adopts a double-fed wind turbine generator system topology structure based on direct-current transmission to optimize and control a double-fed wind turbine generator, wherein the double-fed wind turbine generator system comprises a wind turbine, a gear box, a double-fed wind turbine generator, a direct-current converter and a direct-current bus, the direct-current converter comprises a stator-side converter and a rotor-side converter, and the double-fed wind turbine generator comprises the gear box, the double-fed wind turbine generator and the direct-current converter, and is characterized by comprising the following steps:
step 1, assuming that the power of the wind turbine is unchanged before and after optimization, the pole pair number of the doubly-fed wind generator, the inductive reactance of a stator of the doubly-fed wind generator, the inductive reactance of a rotor of the doubly-fed wind generator and the mutual inductance between the stator and the rotor of the doubly-fed wind generator are kept unchanged, and the magnetic flux of the stator is kept unchanged, so that:
λ＝M/N (1)
wherein N, M is the speed increasing ratio of the gearbox before and after optimization, respectively, and M < N, λ is the ratio of the speed increasing ratio of the gearbox after and before optimization;
by adopting a stator magnetic flux vector directional control strategy, the ratio of the stator current, the rotor current, the total current and the total current of the direct current converter of the doubly-fed wind generator before and after optimization is obtained, and the calculation formulas are respectively as follows:
Figure BDA0001371766770000021
Figure BDA0001371766770000022
Figure BDA0001371766770000023
Figure BDA0001371766770000024
in the formula Is1、Isd1、Isq1、Ir1、It1Before optimization, the stator current d-axis component, the stator current q-axis component, the rotor current and the total current I of the doubly-fed wind generator are respectivelyc1The total current of the direct current converter before optimization; i iss2、Isd2、Isq2、Ir2、It2The stator current, the d-axis component of the stator current, the q-axis component of the stator current, the rotor current and the total current I of the doubly-fed wind driven generator are respectively optimizedc2β is the stator self-inductance L of the doubly-fed wind generatorsMutual inductance L with stator and rotormI.e. β -Ls/Lm；α＝Ird1/Isq1。
Step 2, establishing an optimized calculation model of the total cost of the doubly-fed wind turbine generator; the calculation model is as follows:
Figure BDA0001371766770000025
in the formula, Cs2To optimize the total cost of the doubly-fed wind turbine, Ct1、Cg1、Cc1Before optimization, the cost of the doubly-fed wind generator, the cost of the gearbox, the cost of the DC converter, k0、k1、k2、k3Respectively, fitting coefficients of a cost curve of the gearbox.
Step 3, solving the optimal design parameters of the doubly-fed wind turbine generator according to the calculation model in the step 2, and specifically comprising the following steps:
1) and (3) drawing a curve according to the formula (6) by taking lambda as an abscissa and the cost as an ordinate to obtain the total cost C of the doubly-fed wind turbine generators2Minimum value of (C)s2minI.e. the optimized optimal cost of the double-fed wind turbine generator, and the corresponding lambda is the ratio lambda of the speed increasing ratio of the optimal gearboxopt；
2) Changing λ to λoptSubstituting the formula (1), and obtaining the speed increasing ratio M ═ lambda of the gearbox after optimizationoptN；
3) Changing λ to λoptRespectively substituting the formula (2) and the formula (3), and obtaining the optimized stator current I of the doubly-fed wind generators2And rotor current Ir2Respectively as follows:
Figure BDA0001371766770000031
Figure BDA0001371766770000032
4) according to the ratio of the synchronous rotating speeds of the double-fed wind driven generator after optimization to the synchronous rotating speeds of the double-fed wind driven generator before optimization:
Figure BDA0001371766770000033
in the formula, n1N、n1MBefore and after optimization respectively, the synchronous rotating speed omega of the doubly-fed wind generatorm1、ωm2Before and after optimization, the rotor speed n of the doubly-fed wind generatorwThe rotating speed of the wind turbine;
changing λ to λoptSubstituting into formula (9), and obtaining the optimized synchronous rotating speed n of the doubly-fed wind generator1M＝λoptn1N；
5) According to
Figure BDA0001371766770000034
In the formula, n1Synchronous speed, f, obtained for said doubly-fed wind generator1For the stator nominal frequency, n, of said doubly-fed wind generatorpThe number of pole pairs of the doubly-fed wind generator is;
n is to be1＝n1M＝λoptn1NSubstituting into formula (10), and obtaining the stator rated frequency f of the doubly-fed wind generator after optimization1N＝npλoptn1N/60。
The invention has the beneficial effects that: along with the reduction of the speed increasing ratio of the gear box, the size of the gear box is reduced, the cost is reduced, the failure rate is reduced, the cost of the whole system is reduced, and the reliability of the system operation is improved.
Drawings
Fig. 1 is a schematic view of a topology structure of a doubly-fed wind power generation system adopted in the present invention.
FIG. 2 is a graph of the optimized cost versus ratio λ of the gear box step-up ratio.
Wherein, 1-a wind turbine; 2-a gearbox; 3-double-fed wind power generator; 31-stator of doubly-fed wind generator; 32-rotor of doubly-fed wind generator; 4-a direct current converter; 41-stator side converter; 42-rotor side converter; 5-DC bus
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the double-fed wind power generation system adopted by the invention comprises a wind turbine 1, a gear box 2, a double-fed wind power generator 3, a direct current converter 4 and a direct current bus 5; the dc converter 4 includes a stator-side converter 41 and a rotor-side converter 42; the gear box 2, the doubly-fed wind generator 3 and the direct current converter 4 are collectively referred to as a doubly-fed wind turbine. One end of the gear box 2 is connected with the wind turbine 1, and the other end of the gear box is connected with the rotor 32 of the doubly-fed wind generator; one end of the stator-side converter 41 is connected with the stator 31 of the doubly-fed wind generator, and the other end of the stator-side converter is respectively connected with the rotor-side converter 42 and the direct-current bus 5; the other end of the rotor-side converter 42 is connected to the doubly-fed wind generator rotor 32.
The invention relates to a low-speed-ratio double-fed wind turbine generator optimal design method based on direct-current transmission, which adopts a topological structure of a double-fed wind turbine generator system to optimally design and control a double-fed wind turbine generator, and specifically comprises the following steps:
step 1, assuming that the power of the wind turbine 1 is unchanged before and after optimization, the number n of pole pairs of a doubly-fed wind generator (DFIG)3pAnd inductance L of stator 31 thereofsThe inductance L of the rotor 32rAnd mutual inductance L between stator and rotormThe magnetic flux psi of the stator 31 remains unchangedsKeeping unchanged, and making:
in the formula of λ ═ M/N (1), N, M indicates the gear ratios of the pre-optimization gearbox 2 and the post-optimization gearbox 2, respectively, and M < N, λ is the ratio of the speed-increasing ratio of the post-optimization gearbox 2 to the speed-increasing ratio of the pre-optimization gearbox 2.
And (3) optimizing the ratio of the stator current, the rotor current and the total current of the front and rear double-fed wind driven generators 3 to the total current of the direct current converter 4 by adopting a stator flux vector directional control strategy. The specific process is as follows:
according to the stator flux vector directional control strategy, in a stator flux vector directional coordinate system, the direction of a stator flux vector is consistent with the d axis of the coordinate system, and the method comprises the following steps:
Figure BDA0001371766770000041
in the formula, #sFor stator flux,. psisd、ψsqAre respectively psisD-axis and q-axis components of (1); i issd、IrdD-axis components of the stator current and rotor current, respectively; i issq、IrqQ-axis components of stator and rotor currents, respectively, β being stator self-inductance LsMutual inductance L with stator and rotormI.e. β -Ls/Lm；
From the second equation of equation (11): i issq＝-Irq/β, output power P and stator flux psi of the doubly-fed wind generator 3sAnd current have the following relationships:
Figure BDA0001371766770000042
in the formula, ωmIs the rotor speed.
Under the condition that the power and the stator magnetic flux remain unchanged before and after optimization, the method has the following formula (12):
Figure BDA0001371766770000043
in the formula, ωm1、ωm2Before and after optimization, respectivelysq1、Irq1For optimising the q-component, I, of the stator and rotor currents respectivelysq2、Irq2The q-axis components of the optimized stator and rotor currents, respectively.
From equations (13), (9) and (11), the ratio of the q-axis current of the front and rear stators 31 to the q-axis current of the rotor 32 can be optimized as follows:
Figure BDA0001371766770000051
the doubly-fed wind generator 3 normally operates in unity power factor mode on the stator side, i.e. the reactive current of the stator 31 is 0 and the rotor 32 supplies the excitation current to the system, in combination (11), with:
Figure BDA0001371766770000052
in the formula Isd1、Ird1D-axis components, I, of optimized front stator and rotor currents, respectivelysd2、Ird2The d-axis components of the optimized stator and rotor currents, respectively.
Then, according to equations (14) and (15), the ratio of the stator currents before and after optimization can be obtained as:
Figure BDA0001371766770000053
in the formula Is1、Is2Respectively, the DFIG stator current before and after optimization.
According to the equations (13) and (14), the ratio of the rotor currents before and after optimization can be:
Figure BDA0001371766770000054
namely:
Figure BDA0001371766770000055
in the formula Ir1、Ir2The rotor currents of the double-fed wind driven generator 3 before and after optimization are respectively α is the rated rotor d-axis exciting current I before optimizationrd1Active current I with stator q axissq1I.e. α ═ Ird1/Isq1Once the doubly fed wind generator 3 is determined, the α value remains constant.
According to the formulas (14) and (15), the ratio of the total current of the front and rear double-fed wind driven generators 3 can be optimized as follows:
Figure BDA0001371766770000056
Figure BDA0001371766770000061
namely:
Figure BDA0001371766770000062
in the formula It1、It2The total current of the double-fed wind driven generator 3 before and after optimization is respectively.
According to the equations (14) and (15), the ratio of the total current of the dc converters 4 before and after optimization can be:
Figure BDA0001371766770000063
namely:
Figure BDA0001371766770000064
in the formula Ic1、Ic2The optimized total current of the front and rear direct current converters 4 is respectively.
Step 2, establishing the total cost C of the optimized double-fed wind turbine generators2The specific process of the calculation model is as follows:
before the optimization design is set, the cost of the double-fed wind driven generator 3 is Ct1The cost of the gear case 2 is Cg1The cost of the DC converter 4 is Cc1And the total cost of the double-fed wind turbine generator is Cs1Then, there are:
Cs1＝Ct1+Cg1+Cc1(16)
after the optimization design is designed, the cost of the double-fed wind driven generator 3 is Ct2The cost of the gear case 2 is Cg2The cost of the DC converter 4 is Cc2And the total cost of the double-fed wind turbine generator is Cs2Then there is
Cs2＝Ct2+Cg2+Cc2(17)
Cost C of the gearbox 4 with constant power Pg2Mainly determined by the gear ratio and the torque, and can be estimated as the reduction of lambda
Cg2＝Cg1(k0+k1λ+k2λ2+k3λ3) (18)
In the formula, k0、k1、k2、k3Fitting coefficients, respectively, of the cost curve of the gearbox 4 are used to fit a gearbox cost curve that varies with lambda to coincide with the actual gearbox cost curve.
Under the condition of the same voltage class, the cost of the doubly-fed wind generator 3 and the cost of the DC converter 4 are related to the current class, so the cost C of the optimized doubly-fed wind generator 3t2It can be estimated that:
Figure BDA0001371766770000071
when formula (4) is substituted for formula (19), there are:
Figure BDA0001371766770000072
cost C of the optimized dc converter 4c2It can be estimated that:
Figure BDA0001371766770000073
when formula (5) is substituted for formula (21), there are:
Figure BDA0001371766770000074
by substituting formula (18), formula (20) and formula (22) into formula (17), the total cost C of the doubly-fed wind turbine can be obtained after the gear ratio is reduceds2Comprises the following steps:
Figure BDA0001371766770000075
step 3, according to the total cost C of the double-fed wind turbine generator set after optimizations2The calculation model formula (6) is used for solving the optimal design parameters of the doubly-fed wind turbine generator, and the method specifically comprises the following steps:
1) as shown in fig. 2, the cost C of the gear case 2 is plotted according to equations (18), (20), (22) and (6) with λ as the abscissa and the cost as the ordinateg2-cost C of lambda curve, doubly-fed wind generator 3t2Lambda curve, cost C of the DC converter 4c2-lambda curve, total cost of doubly-fed wind turbine Cs2Lambda curve, find Cs2Minimum value of (C)s2minI.e. the optimal cost of the optimized double-fed wind turbine generator, and the corresponding lambda is the ratio lambda of the speed increasing ratio of the optimal gearboxopt；
2) The optimized step-up ratio M ═ λ of the gear case 2 is obtained from the equation (1)optN；
3) Changing λ to λoptRespectively substituting the formula (2) and the formula (3) to obtain the optimized stator current I of the doubly-fed wind generator 3s2And rotor current Ir2Respectively as follows:
Figure BDA0001371766770000076
Figure BDA0001371766770000077
4) according to the ratio of the synchronous rotating speed after optimization to the synchronous rotating speed before optimization:
Figure BDA0001371766770000078
in the formula, n1N、n1MBefore and after optimization, respectively, the synchronous speed omega of the double-fed wind driven generator 3m1、ωm2Before and after optimization, respectivelywThe rotation speed of the wind turbine 1;
changing λ to λoptSubstituting into formula (9), and obtaining the optimized synchronous rotating speed n of the doubly-fed wind generator 31M＝λoptn1N；
5) According to
Figure BDA0001371766770000081
In the formula, n1For DFIG synchronous speed, f1For stator rated frequency, npIs the polar pair number of DFIG;
n is to be1＝n1M＝λoptn1NSubstituting the formula (10) to obtain the stator rated frequency f of the DFIG after optimization1N＝npλoptn1N/60。
The invention is further illustrated below by means of an example.
Example (b):
taking a doubly-fed wind turbine generator produced by a certain company as an example, the main parameters are as follows: p is 3MW, Vs1650V (stator voltage), Is＝600A，Ir＝608A，n1N＝1000rpm，npThe step-up ratio N of the gearbox is 80 and L is 3m＝99mH，Ls99.99 mH; cost of gearbox Cg122 ten thousand Euro (Euro), DFIG cost Ct16 ten thousand euros, converter cost Cc1Total cost of 8.67 ten thousand euros, Cs136.67 ten thousand euros; k is a radical of0＝0，k1＝0.2，k2＝0.35，k3＝0.45，β＝1.01，α＝0.0884。
First, the optimized gear box cost C is plotted according to the expressions (18), (20), (22), and (6)g2-lambda curve, DFIG cost Ct2-lambda curve, DC converter cost Cc2-lambda curve, double-fed wind turbine set as described aboveTotal cost of three components Cs2Lambda curve, as shown in figure 2. As can be seen in FIG. 2, the cost C of the gearboxg2Gradually decreases as λ decreases; cost (C) of converter and DFIGc2、Ct2) Gradually increasing as λ decreases; total cost Cs2There is a minimum value that first gradually decreases with decreasing λ and then gradually increases with decreasing λ. Finding out the minimum A point as the optimal point, and the corresponding x value as the ratio of the speed increasing ratio of the optimal gear boxopt0.7, its corresponding ordinate Cs2The value is the optimal cost C of the optimized double-fed wind turbine generators2min311kEuro is 31.1 ten thousand Euros, 5.57 ten thousand Euros are saved, and the cost is reduced by 15.2%.
Secondly, let λ beoptThe formula (1) is substituted by 0.7, and the gear ratio M of the optimized gearbox is determined to be 56, and the gearbox is selected according to the power class.
Thirdly, will lambdaoptFormula (7) and formula (8) were substituted with 0.7, respectively, and optimized stator current I was obtaineds2And rotor current Ir2Respectively as follows: i iss2＝857A，Ir2＝867A。
Fourthly, aoptCalculating the synchronous rotating speed n of the optimized DFIG (DFIG) (0.7 substituted formula (9))1M＝700rpm；
Finally, n is added1＝n1MThe stator rated frequency f of the DFIG after optimization is obtained after 700rpm is substituted into the formula (10)1N＝35Hz。

Claims (3)

1. The low-speed gear box double-fed wind turbine generator optimal design method based on direct-current transmission adopts a double-fed wind turbine generator system topological structure based on direct-current transmission to optimally design and control the double-fed wind turbine generator system, the double-fed wind turbine generator system comprises a wind turbine, a gear box, a double-fed wind turbine generator, a direct-current converter and a direct-current bus, the direct-current converter comprises a stator side converter and a rotor side converter, the double-fed wind turbine generator system comprises the gear box, the double-fed wind turbine generator and the direct-current converter, and the method is characterized by comprising the following steps:
step 1, assuming that the power of the wind turbine is unchanged before and after optimization, the pole pair number of the doubly-fed wind generator, the inductive reactance of a stator of the doubly-fed wind generator, the inductive reactance of a rotor of the doubly-fed wind generator and the mutual inductance between the stator and the rotor of the doubly-fed wind generator are kept unchanged, and the magnetic flux of the stator is kept unchanged; a stator magnetic flux vector directional control strategy is adopted to obtain the ratio of stator currents of the doubly-fed wind driven generator before and after optimization, the ratio of rotor currents of the doubly-fed wind driven generator before and after optimization, the ratio of total currents of the doubly-fed wind driven generator before and after optimization and the ratio of total currents of the direct current converter before and after optimization;
step 2, establishing an optimized calculation model of the total cost of the doubly-fed wind turbine generator:
Figure FDA0002548815380000011
in the formula, Cs2To optimize the total cost of the doubly-fed wind turbine, Ct1、Cg1、Cc1Before optimization, the cost of the doubly-fed wind generator, the cost of the gearbox, the cost of the DC converter, k0、k1、k2、k3Lambda is the ratio of the speed increasing ratio of the gearbox after optimization to the speed increasing ratio of the gearbox before optimization, α is the ratio of the rotor current d-axis component and the stator current q-axis component of the doubly-fed wind generator before optimization, and β is the ratio of the stator self-inductance of the doubly-fed wind generator to the mutual inductance between the stator and the rotor;
and 3, solving the optimized design parameters of the doubly-fed wind turbine generator according to the calculation model in the step 2.
2. The direct-current transmission based low-speed gearbox doubly-fed wind turbine generator optimization design method according to claim 1, wherein in the step 1, the steps of:
λ＝M/N (1)
wherein N, M is the speed increasing ratio of the gearbox before and after optimization, respectively, and M < N, λ is the ratio of the speed increasing ratio of the gearbox after and before optimization; respectively calculating the ratio of the stator currents of the doubly-fed wind generator before and after optimization, the ratio of the rotor currents of the doubly-fed wind generator before and after optimization, the ratio of the total currents of the doubly-fed wind generator before and after optimization and the ratio of the total currents of the direct current converter before and after optimization according to the following formulas:
Figure FDA0002548815380000012
Figure FDA0002548815380000013
Figure FDA0002548815380000014
Figure FDA0002548815380000021
in the formula Is1、Isd1、Isq1、Ir1、Ird1、Irq1、It1Before optimization, the stator current d-axis component, the stator current q-axis component, the rotor current d-axis component, the rotor current q-axis component and the total current I of the doubly-fed wind generator are respectivelyc1The total current of the direct current converter before optimization; i iss2、Isd2、Isq2、Ir2、Ird2、Irq2、It2The optimized stator current, the optimized d-axis component of the stator current, the optimized q-axis component of the stator current, the optimized rotor current, the optimized d-axis component of the rotor current, the optimized q-axis component of the rotor current, the optimized total current Ic2β is the stator self-inductance L of the doubly-fed wind generatorsMutual inductance L between stator and rotormThe ratio of (β) to (L)s/Lmα is optimized by the ratio of the d-axis component of the rotor current to the q-axis component of the stator current of the double-fed wind generator, i.e. α ═ Ird1/Isq1。
3. The direct-current transmission based low-speed gearbox doubly-fed wind turbine generator optimization design method according to claim 2, wherein the step 3 specifically comprises the following steps:
1) taking lambda as abscissa and optimizing total cost C of the doubly-fed wind turbine generators2Drawing a curve according to the formula (6) for the ordinate, and solving the total cost C of the optimized doubly-fed wind turbine generators2Minimum value of (C)s2minI.e. the optimized optimal cost of the double-fed wind turbine generator, and the corresponding lambda is the ratio lambda of the speed increasing ratio of the optimal gearboxopt；
2) Changing λ to λoptSubstituting the formula (1), and obtaining the speed increasing ratio M ═ lambda of the gearbox after optimizationoptN；
3) Changing λ to λoptRespectively substituting the formula (2) and the formula (3), and obtaining the optimized stator current I of the doubly-fed wind generators2And rotor current Ir2Respectively as follows:
Figure FDA0002548815380000022
Figure FDA0002548815380000023
4) according to the ratio of the synchronous rotating speeds of the double-fed wind driven generator after optimization to the synchronous rotating speeds of the double-fed wind driven generator before optimization:
Figure FDA0002548815380000024
in the formula, n1N、n1MBefore and after optimization respectively, the synchronous rotating speed omega of the doubly-fed wind generatorm1、ωm2Are respectively optimizedRotor speed n of the double-fed wind driven generator before and after optimizationwThe rotating speed of the wind turbine;
changing λ to λoptSubstituting into formula (9), and obtaining the optimized synchronous rotating speed n of the doubly-fed wind generator1M＝λoptn1N；
5) According to
Figure FDA0002548815380000025
In the formula, n1Synchronous speed, f, obtained for said doubly-fed wind generator1For the stator nominal frequency, n, of said doubly-fed wind generatorpThe number of pole pairs of the doubly-fed wind generator is;
n is to be1＝n1M＝λoptn1NSubstituting into formula (10), and obtaining the stator rated frequency f of the doubly-fed wind generator after optimization1N＝npλoptn1N/60。
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