CN107273647A - Low-speed gear case Double-feed wind power set optimization design method based on direct current transportation - Google Patents

Abstract

The invention relates to an optimal design method of a low-speed gearbox doubly-fed wind turbine based on direct current transmission, which belongs to the field of wind power. This method uses a doubly-fed wind power generation system topology to optimize the design and control of doubly-fed wind turbines including gearboxes, doubly-fed generators (DFIG) and DC converters; firstly, the stator flux vector oriented control is used Strategy, find the ratio of the stator-rotor current, total current and DC converter total current of the DFIG before and after optimization; secondly find the total cost C _s2 of the doubly-fed wind turbine after optimization; finally find the optimal design parameters of the wind turbine: according to C _s2 Formula, draw the C _s2 ‑λ curve, λ is the ratio of the gear box speed-up ratio before and after optimization, and obtain the minimum value of C _s2 and the optimal value of λ, so as to obtain the optimized gear box speed-up ratio and the stator-rotor of DFIG Current, synchronous speed, stator rated frequency. The invention reduces the speed-up ratio of the gear box, reduces the failure rate and cost, and improves the operating reliability of the system.

Description

Optimal design method of low-speed gearbox doubly-fed wind turbine based on DC transmission

technical field

The invention relates to an optimal design method, in particular to an optimal design method for a low-speed gearbox doubly-fed wind turbine based on DC transmission, and belongs to the technical field of wind power generation.

Background technique

The doubly-fed wind power generation system is mainly composed of a wind turbine, a gearbox, a doubly-fed wind generator (DFIG), and a converter. DFIG is a high-speed, small-sized generator. Since the wind turbine operates at low speed, a speed-up gearbox with a high speed-up ratio is usually used to increase the low speed of the wind turbine to a high-speed rotor speed. The higher the speed-up ratio of the gearbox, the smaller the volume and cost of DFIG; but the larger the speed-up ratio of the gearbox, the higher the volume and cost of the gearbox, the greater the energy loss and failure rate, and the reliability of the whole system worse. The main loss of the doubly-fed wind power generation system comes from the gearbox and converter system, and about 65% of the annual system loss comes from the gearbox. Therefore, it is necessary to study the gearbox with a low speed-up ratio in order to reduce the cost and loss of the system and improve the reliability of the system operation. However, the traditional DFIG stator is usually directly connected to the AC grid. DFIG must adopt a constant voltage and constant frequency operation mechanism to ensure that the frequency of the stator is consistent with the frequency of the grid, so a gearbox with a low speed-up ratio cannot be used.

At present, DC transmission technology has attracted much attention due to its many advantages such as reliable operation, long distance, low cost, and low loss. It has become an ideal technology for connecting long-distance large-scale wind farms and power grids, and is widely used in wind power transmission systems. Utility model patent ZL201420171452.1 discloses a doubly-fed wind turbine converter topology for flexible direct current transmission systems. The converter includes a stator-side converter, a machine-side converter, and a grid-side DC-DC The converter can directly connect the output power of the doubly-fed wind turbine to the DC grid, and the stator-side converter is connected to the stator of the DFIG to realize rectification, that is to say, the stator of the DFIG is not connected to the AC grid, so the output of the stator The voltage and frequency do not require constant voltage and constant frequency. The converter can flexibly adjust the stator frequency and stator voltage, which makes the frequency of the stator lower than the grid frequency (such as 50Hz), so the synchronous speed of the generator can be reduced, so that low-increase Gearbox with speed ratio. However, the reduction of the gearbox speed ratio and the reduction of the synchronous speed will lead to the increase of the DFIG stator and rotor current, and the increase of the gearbox volume and cost. For this reason, the optimization design and control problems of the whole system must be solved.

Contents of the invention

The main purpose of the present invention is to: aim at the deficiencies and gaps in the prior art, and according to the characteristics of the flexible direct current transmission system, propose a method for optimizing the design of double-fed wind turbines by selecting the best gear ratio Increase the speed ratio, reduce the cost of doubly-fed wind turbines, and improve system reliability.

In order to achieve the above purpose, the present invention provides an optimal design method for low-speed gearbox doubly-fed wind turbines based on direct current transmission, using a DC transmission-based doubly-fed wind power generation system topology to optimize the design of doubly-fed wind turbines and control, the doubly-fed wind power generation system includes a wind turbine, a gearbox, a doubly-fed wind generator, a DC converter, and a DC bus, and the DC converter includes a stator-side converter and a rotor-side converter , the doubly-fed wind turbine includes the gearbox, the doubly-fed wind generator and the DC converter, characterized in that it includes the following steps:

Step 1, assuming that the power of the wind turbine before and after optimization remains unchanged, the number of pole pairs of the double-fed wind turbine and the inductance of the stator, the inductance of the rotor and the mutual inductance between the stator and rotor remain unchanged, and the stator Keeping the magnetic flux constant, let:

λ=M/N (1)

In the formula, N and M are the speed-up ratio of the gearbox before optimization and the speed-up ratio of the gearbox after optimization, respectively, and M<N, λ is the speed-up ratio of the gearbox after optimization and before optimization The ratio of the speed-up ratio of the gear box;

Using the stator flux vector oriented control strategy, the ratio of the stator current, rotor current, total current and the total current of the DC converter before and after optimization of the doubly-fed wind turbine is calculated, and the calculation formulas are respectively:

In the formula, I _s1 , I _sd1 , I _sq1 , I _r1 , and I _t1 are the stator current, stator current d-axis component, stator current q-axis component, rotor current, total current , I _c1 is the total current of the DC converter before optimization; I _s2 , I _sd2 , I _sq2 , I _r2 , I _t2 are the stator current and stator current d-axis of the doubly-fed wind turbine after optimization respectively component, stator current q-axis component, rotor current, total current, I _c2 is the total current of the DC converter after optimization; β is the stator self-inductance L _s and stator-rotor mutual inductance L of the double-fed wind turbine The ratio of _m , namely β=L _s /L _m ; α=I _rd1 /I _sq1 .

Step 2, establishing a calculation model of the total cost of the doubly-fed wind turbine after optimization; the calculation model is:

In the formula, C _s2 is the total cost of the DFIG after optimization, C _t1 , C _g1 , and C _c1 are the cost of the DFIG before optimization, the cost of the gearbox, and the cost of the DFIG respectively. The cost of the DC converter, k ₀ , k ₁ , k ₂ , and k ₃ are the fitting coefficients of the cost curve of the gearbox respectively.

Step 3, seeking the optimal design parameters of the doubly-fed wind turbine according to the calculation model described in step 2, specifically comprising the following steps:

1) With λ as the abscissa and cost as the ordinate, draw a curve according to formula (6) to obtain the minimum value C _s2min of the total cost C _s2 of the DFIG, that is, the DFIG after optimization The optimal cost of the unit, and the corresponding λ is the ratio λ _opt of the optimal gearbox speed-up ratio;

2) Substituting λ=λ _opt into formula (1), obtain the speed-up ratio M=λ _opt N of the gear box after optimization;

3) Substituting λ= _λopt into formulas (2) and (3) respectively, the stator current I _s2 and rotor current I _r2 of the double-fed wind turbine after optimization are obtained as follows:

4) According to the ratio of the synchronous speed of the doubly-fed wind turbine after optimization and before optimization:

In the formula, n _1N and n _1M are the synchronous speeds of the DFIG before and after optimization, respectively, and ω _m1 and ω _m2 are the DFIGs before and after optimization, respectively. Rotor speed, n _w is the speed of the wind turbine;

Substituting λ=λ _opt into formula (9) to obtain the optimized synchronous speed n _1M =λ _opt n _1N of the doubly-fed wind power generator;

5) According to

In the formula, n1 is the synchronous rotational speed _of the doubly _- fed wind power generator, f1 is the rated frequency of the stator of the doubly-fed wind power generator, and _np is the number of pole pairs of the doubly-fed wind power generator ;

Substitute n ₁ =n _1M =λ _opt n _1N into formula (10) to obtain the optimized stator rated frequency f _1N =n _p λ _opt n _1N /60 of the doubly-fed wind turbine.

The beneficial effect of the present invention is that: with the reduction of the speed-up ratio of the gearbox, the volume of the gearbox is reduced, the cost is reduced, and the failure rate is reduced, thereby reducing the cost of the whole machine system and improving the reliability of system operation.

Description of drawings

FIG. 1 is a schematic diagram of the topological structure of a doubly-fed wind power generation system adopted in the present invention.

Figure 2 is a curve diagram of the optimized cost-gearbox speed ratio ratio λ.

Among them, 1-wind turbine; 2-gearbox; 3-double-fed wind generator; 31-stator of double-fed wind generator; 32-rotor of double-fed wind generator; 4-DC converter; 41-stator side converter; 42-rotor side converter; 5-DC bus

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

As shown in Figure 1, the doubly-fed wind power generation system adopted in the present invention includes a wind turbine 1, a gear box 2, a doubly-fed wind generator 3, a DC converter 4, and a DC bus 5; the DC converter 4 includes a stator The side converter 41 and the rotor side converter 42 ; the gear box 2 , the doubly-fed wind power generator 3 and the DC converter 4 are collectively referred to as a doubly-fed wind turbine. One end of the gearbox 2 is connected to the wind turbine 1, and the other end is connected to the rotor 32 of the doubly-fed wind power generator; one end of the stator-side converter 41 is connected to the stator 31 of the doubly-fed wind power generator, and the other end is respectively connected to the rotor-side converter 42. The DC bus 5 is connected; the other end of the rotor-side converter 42 is connected to the rotor 32 of the doubly-fed wind power generator.

The present invention is based on the low speed-up ratio double-fed wind turbine optimization design method of DC transmission, adopts a double-fed wind power generation system topology to optimize the design and control of the double-fed wind turbine, and specifically includes the following steps:

Step 1, assuming that the power of the wind turbine 1 remains unchanged before and after optimization, the number of pole pairs n _p of the doubly-fed wind turbine (DFIG) 3 and the inductance L _s of the stator 31, the inductance L _r of the rotor 32 and the stator-rotor The mutual inductance L _m between remains unchanged, and the magnetic flux ψ _s of the stator 31 remains unchanged, so that:

λ=M/N (1)

In the formula, N and M are the speed ratios of the gearbox 2 before and after optimization, respectively, and M<N, λ is the ratio of the speed ratio of the gearbox 2 after optimization to the speed ratio of the gearbox 2 before optimization.

Using the stator flux vector oriented control strategy, the ratios of the stator current, rotor current, total current and the total current of the DC converter 4 before and after optimization are calculated. The specific process is as follows:

According to the stator flux vector orientation control strategy, in the stator flux vector orientation coordinate system, if the stator flux vector direction is consistent with the d-axis of the coordinate system, then:

In the formula, ψ _s is the stator flux, ψ _sd , ψ _sq are the d-axis and q-axis components of ψ _s respectively; I _sd , I _rd are the d-axis components of the stator current and rotor current respectively; I _sq , I _rq are respectively is the q-axis component of stator current and rotor current; β is the ratio of stator self-inductance L _s to stator-rotor mutual inductance L _m , namely: β=L _s /L _m ;

From the second equation of formula (11), it can be obtained: I _sq =-I _rq /β, then the output power P of the doubly-fed wind turbine 3, the stator flux ψ _s and the current have the following relationship:

In the formula, _ωm is the rotor speed.

In the case that the power and stator flux remain unchanged before and after optimization, formula (12) has:

In the formula, ω _m1 and ω _m2 are the rotor speeds before and after optimization, respectively, I _sq1 and I _rq1 are the q-axis components of the stator current and rotor current before optimization, respectively, and I _sq2 and I _rq2 are the stator current and The q-axis component of the rotor current.

According to Equation (13), Equation (9), and Equation (11), the ratios of the q-axis current of the stator 31 and the q-axis current of the rotor 32 before and after optimization can be obtained as follows:

The stator side of the double-fed wind turbine 3 usually operates in the unit power factor mode, that is, the reactive current of the stator 31 is 0, and the rotor 32 provides the excitation current for the system. Combined with formula (11), there is:

In the formula, I _sd1 , I _rd1 are the d-axis components of the stator current and rotor current before optimization, respectively, and I _sd2 , I _rd2 are the d-axis components of the stator current and rotor current after optimization, respectively.

According to formula (14) and formula (15), the ratio of stator current before and after optimization can be obtained as:

In the formula, I _s1 and I _s2 are the DFIG stator currents before and after optimization, respectively.

According to formula (13) and formula (14), the ratio of rotor current before and after optimization can be obtained as:

which is:

In the formula, I _r1 and I _r2 are the rotor currents of the doubly-fed wind turbine 3 before and after optimization respectively, and α is the ratio of the rated rotor d-axis excitation current I _rd1 before optimization to the stator q-axis active current I _sq1 , namely: α =I _rd1 /I _sq1 , once the doubly-fed wind power generator 3 is determined, the value of α remains constant.

According to formula (14) and formula (15), the ratio of the total current of the doubly-fed wind turbine 3 before and after optimization can be obtained as:

which is:

In the formula, I _t1 and I _t2 are the total current of the doubly-fed wind turbine 3 before and after optimization, respectively.

According to formula (14) and formula (15), the ratio of the total current of the DC converter 4 before and after optimization can be obtained as:

which is:

In the formula, I _c1 and I _c2 are the total current of the DC converter 4 before and after optimization respectively.

Step 2, establishing the calculation model of the total cost C _s2 of the optimized DFIG, the specific process is as follows:

Assuming that before the optimization design, the cost of the doubly-fed wind turbine 3 is C _t1 , the cost of the gearbox 2 is C _g1 , the cost of the DC converter 4 is C _c1 , and the total cost of the doubly-fed wind turbine is C _s1 , Then there are:

C _s1 ＝C _t1 +C _g1 +C _c1 (16)

After the optimized design, the cost of DFIG 3 is C _t2 , the cost of gearbox 2 is C _g2 , the cost of DC converter 4 is C _c2 , and the total cost of DFIG is C _s2 , then there is

C _s2 ＝C _t2 +C _g2 +C _c2 (17)

In the case of constant power P, the cost C _g2 of the gearbox 4 is mainly determined by its gear ratio and torque. With the decrease of λ, it can be estimated as

C _g2 ＝C _g1 (k ₀ +k ₁ λ+k ₂ λ ² +k ₃ λ ³ ) (18)

In the formula, k ₀ , k ₁ , k ₂ , and k ₃ are the fitting coefficients of the cost curve of the gearbox 4, which are used to fit the cost curve of the gearbox that varies with λ, so that it coincides with the actual cost curve of the gearbox.

In the case of the same voltage level, the cost of DFIG 3 and DC converter 4 is related to its current level, so the optimized cost C _t2 of DFIG 3 can be estimated as:

Substituting formula (4) into formula (19), then:

The cost C _c2 of the optimized DC converter 4 can be estimated as:

Substituting formula (5) into formula (21), then:

Substituting Equation (18), Equation (20), and Equation (22) into Equation (17), the total cost C _s2 of the doubly-fed wind turbine after the gear ratio is reduced is:

Step 3, according to the calculation model formula (6) of the total cost C of the _doubly -fed wind turbine after optimization, the optimal design parameters of the doubly-fed wind turbine are obtained, specifically including the following steps:

1) As shown in Figure 2, with λ as the abscissa and the cost as the ordinate, the cost C _g2 -λ of the gearbox 2 is plotted according to Equation (18), Equation (20), Equation (22) and Equation (6) curve, cost C _t2 -λ curve of double-fed wind turbine 3, cost C _c2 -λ curve of DC converter 4, total cost C _s2 -λ curve of double-fed wind turbine, and find the minimum value of C _s2 C _s2min is the optimal cost of the optimized doubly-fed wind turbine, and the corresponding λ is the ratio λ _opt of the optimal gearbox speed-up ratio;

2) According to formula (1), obtain the speed-up ratio M=λ _opt N of the gearbox 2 after optimization;

3) Substituting λ= _λopt into formula (2) and formula (3) respectively, the stator current I _s2 and rotor current I _r2 of the optimized doubly-fed wind turbine 3 are obtained as follows:

4) According to the ratio of synchronous speed after optimization and before optimization:

In the formula, n _1N and n _1M are the synchronous speeds of DFIG 3 before and after optimization respectively, ω _m1 and ω _m2 are the rotor speeds before and after optimization respectively, and n _w is the speed of wind turbine 1 ;

Substituting λ=λ _opt into formula (9) to obtain the synchronous rotational speed n _1M =λ _opt n _1N of the optimized doubly-fed wind turbine 3;

5) According to

In the formula, n ₁ is the synchronous speed of DFIG, f ₁ is the rated frequency of the stator, and n _p is the number of pole pairs of DFIG;

Substituting n ₁ =n _1M =λ _opt n _1N into formula (10), the optimized stator rated frequency f _1N =n _p λ _opt n _1N /60 of DFIG is obtained.

The present invention will be further described below with an example.

Example:

Taking the double-fed wind turbine produced by a certain company as an example, its main parameters are: P=3MW, V _s ＝1650V (stator voltage), I _s ＝600A, I _r ＝608A, n _1N ＝1000rpm, n _p ＝3 , gearbox speed ratio N=80, L _m ＝99mH, L _s ＝99.99mH; gearbox cost C _g1 ＝220,000 Euro (Euro), DFIG cost C _t1 ＝60,000 Euro, converter cost C _c1 = 86,700 euros, the total cost of the three C _s1 =366,700 euros; k ₀ =0, k ₁ =0.2, k ₂ =0.35, k ₃ =0.45, β=1.01, α=0.0884.

First, draw the optimized gearbox cost C _g2 -λ curve, DFIG cost C _t2 -λ curve, DC converter cost C The _c2 -λ curve and the total cost C _s2 -λ curve of the above three in the doubly-fed wind turbine are shown in Figure 2. It can be seen from Fig. 2 that the cost C _g2 of the gearbox gradually decreases with the decrease of λ; the cost of the converter and DFIG (C _c2 , C _t2 ) increases gradually with the decrease of λ; the total cost C _s2 First, it gradually decreases with the decrease of λ, and then gradually increases with the decrease of λ, and there is a minimum value. Find the minimum point A in the figure, this point is the optimal point, its corresponding abscissa value λ is the ratio of the optimal gearbox speed-up ratio λ _opt = 0.7, and its corresponding ordinate C _s2 value is the optimized The optimal cost C _s2min = 311kEuro = 311,000 Euros for the rear doubly-fed wind turbine, which saves 55,700 Euros and reduces the cost by 15.2%.

Secondly, by substituting λ _opt =0.7 into formula (1), the transmission ratio M=56 of the optimized gearbox can be obtained, and the gearbox can be selected according to the power level.

Thirdly, substituting λ _opt =0.7 into Equation (7) and Equation (8) respectively, the optimized stator current I _s2 and rotor current I _r2 are respectively obtained: I _s2 =857A, I _r2 =867A.

Fourth, substituting λ _opt =0.7 into formula (9) to obtain the optimized synchronous speed n _1M of DFIG =700rpm;

Finally, substituting n ₁ =n _1M =700rpm into formula (10), the optimized stator rated frequency f _1N =35Hz of DFIG is obtained.

Claims (4)

1. Optimal design method of low-speed gearbox doubly-fed wind turbine based on direct current transmission, adopting a doubly-fed wind power generation system topology based on direct current transmission to optimize design and control of doubly-fed wind turbine, said doubly-fed The wind power generation system includes a wind turbine, a gearbox, a double-fed wind generator, a DC converter, and a DC bus. The DC converter includes a stator-side converter and a rotor-side converter. The double-fed wind power The unit includes the gearbox, the doubly-fed wind generator and the DC converter, and is characterized in that it includes the following steps: Step 1, assuming that the power of the wind turbine before and after optimization remains unchanged, the number of pole pairs of the double-fed wind turbine and the inductance of the stator, the inductance of the rotor and the mutual inductance between the stator and rotor remain unchanged, and the stator The magnetic flux remains unchanged; the stator flux vector oriented control strategy is adopted to obtain the ratio of the stator current, rotor current, total current and the total current of the DC converter before and after optimization; Step 2, establishing a calculation model of the total cost of the doubly-fed wind turbine after optimization; Step 3, calculating the optimal design parameters of the doubly-fed wind turbine according to the calculation model described in step 2. 2. according to claim 1, based on the low-speed gearbox doubly-fed wind turbine optimization design method for DC transmission, it is characterized in that, in the step 1, order: λ=M/N (1) In the formula, N and M are the speed-up ratios of the gearbox before and after optimization, respectively, and M<N, λ is the speed-up ratio of the gearbox after optimization and the speed-up ratio of the gearbox before optimization The ratio of the stator current, the rotor current, the total current and the total current of the DC converter before and after the optimization are calculated respectively according to the following formula: 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<mrow><mfrac><msub><mi>I</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msub><mi>I</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>I</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>I</mi><mrow><mi>r</mi><mn>2</mn></mrow></msub></mrow><mrow><msub><mi>I</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>I</mi><mrow><mi>r</mi><mn>1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mrow><msup><msub><mi>I</mi><mrow><mi>s</mi><mi>d</mi><mn>2</mn></mrow></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>I</mi><mrow><mi>s</mi><mi>q</mi><mn>2</mn></mrow></msub><mn>2</mn></msup></mrow></msqrt><mo>+</mo><msqrt><mrow><msup><msub><mi>I</mi><mrow><mi>r</mi><mi>d</mi><mn>2</mn></mrow></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>I</mi><mrow><mi>r</mi><mi>q</mi><mn>2</mn></mrow></msub><mn>2</mn></msup></mrow></msqrt></mrow><mrow><msqrt><mrow><msup><msub><mi>I</mi><mrow><mi>s</mi><mi>d</mi><mn>1</mn></mrow></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>I</mi><mrow><mi>s</mi><mi>q</mi><mn>1</mn></mrow></msub><mn>2</mn></msup></mrow></msqrt><mo>+</mo><msqrt><mrow><msup><msub><mi>I</mi><mrow><mi>r</mi><mi>d</mi><mn>1</mn></mrow></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>I</mi><mrow><mi>r</mi><mi>q</mi><mn>1</mn></mrow></msub><mn>2</mn></msup></mrow></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mrow><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;lambda;</mi><mn>2</mn></msup><msup><mi>&amp;alpha;</mi><mn>2</mn></msup></mrow></msqrt></mrow><mrow><mi>&amp;lambda;</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mrow><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;alpha;</mi><mn>2</mn></msup></mrow></msqrt><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mrow> In the formula, I _s1 , I _sd1 , I _sq1 , I _r1 , and I _t1 are the stator current, stator current d-axis component, stator current q-axis component, rotor current, total current , I _c1 is the total current of the DC converter before optimization; I _s2 , I _sd2 , I _sq2 , I _r2 , I _t2 are the stator current and stator current d-axis of the doubly-fed wind turbine after optimization respectively component, stator current q-axis component, rotor current, total current, I _c2 is the total current of the DC converter after optimization; β is the stator self-inductance L _s and stator-rotor mutual inductance L of the double-fed wind turbine The ratio of _m , namely β=L _s /L _m ; α=I _rd1 /I _sq1 . 3. according to claim 1, based on the low-speed gearbox doubly-fed wind turbine optimization design method of DC transmission, it is characterized in that, in the step 2, the calculation model of the total cost of the doubly-fed wind turbine after optimization is: : <mrow><msub><mi>C</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>C</mi><mrow><mi>t</mi><mn>1</mn></mrow></msub><msqrt><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>)</mo><mo>+</mo><msup><mi>&amp;lambda;</mi><mn>2</mn></msup><msup><mi>&amp;alpha;</mi>mi><mn>2</mn></msup></mrow><mrow><msup><mi>&amp;lambda;</mi><mn>2</mn></msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;alpha;</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></mfrac></msqrt><mo>+</mo><msub><mi>C</mi><mrow><mi>g</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mi>k</mi><mn>0</mn></msub><mo>+</mo><msub><mi>k</mi><mn>1</mn></msub><mi>&amp;lambda;</mi><mo>+</mo><msub><mi>k</mi><mn>2</mn></msub><msup><mi>&amp;lambda;</mi><mn>2</mn></msup><mo>+</mo><msub><mi>k</mi><mn>3</mn></msub><msup><mi>&amp;lambda;</mi><mn>3</mn></msup><mo>)</mo></mrow><mo>+</mo><msub><mi>C</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mrow><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;lambda;</mi><mn>2</mn></msup><msup><mi>&amp;alpha;</mi><mn>2</mn></msup></mrow></msqrt></mrow><mrow><mi>&amp;lambda;</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mrow><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;alpha;</mi><mn>2</mn></msup></mrow></msqrt><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow> 1 In the formula, C _s2 is the total cost of the DFIG after optimization, C _t1 , C _g1 , and C _c1 are the cost of the DFIG before optimization, the cost of the gearbox, and the cost of the DFIG respectively. The cost of the DC converter, k ₀ , k ₁ , k ₂ , and k ₃ are the fitting coefficients of the cost curve of the gearbox respectively. 4. The low-speed gearbox doubly-fed wind turbine optimization design method based on direct current transmission according to claim 1, wherein the step 3 specifically comprises the following steps: 1) With λ as the abscissa and cost as the ordinate, draw a curve according to formula (6) to obtain the minimum value C _s2min of the total cost C _s2 of the DFIG, that is, the DFIG after optimization The optimal cost of the unit, and the corresponding λ is the ratio λ _opt of the optimal gearbox speed-up ratio; 2) Substituting λ=λ _opt into formula (1), obtain the speed-up ratio M=λ _opt N of the gear box after optimization; 3) Substituting λ= _λopt into formulas (2) and (3) respectively, the stator current I _s2 and rotor current I _r2 of the double-fed wind turbine after optimization are obtained as follows: <mrow><msub><mi>I</mi><mrow><mi>s</mi><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mn>1</mn><msub><mi>&amp;lambda;</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msub></mfrac><msub><mi>I</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo>mo></mrow></mrow> <mrow><msub><mi>I</mi><mrow><mi>r</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>I</mi><mrow><mi>r</mi><mn>1</mn></mrow></msub><msqrt><mfrac><mrow><msup><msub><mi>&amp;lambda;</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msub><mn>2</mn></msup><msup><mi>&amp;alpha;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;beta;</mi><mn>2</mn></msup></mrow><mrow><msup><msub><mi>&amp;lambda;</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msub><mn>2</mn></msup><mrow><mo>(</mo><msup><mi>&amp;alpha;</mi><mn>2</mn></msup><mo>+</mo><msup><mi>&amp;beta;</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></mfrac></msqrt><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mrow> 4) According to the ratio of the synchronous speed of the doubly-fed wind turbine after optimization and before optimization: <mrow><mfrac><msub><mi>n</mi><mrow><mn>1</mn><mi>M</mi></mrow></msub><msub><mi>n</mi><mrow><mn>1</mn><mi>N</mi></mrow></msub></mfrac><mo>=</mo><mfrac><msub><mi>&amp;omega;</mi><mrow><mi>m</mi><mn>2</mn></mrow></msub><msub><mi>&amp;omega;</mi>mi><mrow><mi>m</mi><mn>1</mn></mrow></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>n</mi><mi>w</mi></msub><mi>M</mi></mrow><mrow><msub><mi>n</mi><mi>w</mi></msub><mi>N</mi></mrow></mfrac><mo>=</mo><mfrac><mi>M</mi><mi>N</mi></mfrac><mo>=</mo><mi>&amp;lambda;</mi><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow> In the formula, n _1N and n _1M are the synchronous speeds of the DFIG before and after optimization, respectively, and ω _m1 and ω _m2 are the DFIGs before and after optimization, respectively. Rotor speed, n _w is the speed of the wind turbine; Substituting λ=λ _opt into formula (9) to obtain the optimized synchronous speed n _1M =λ _opt n _1N of the doubly-fed wind power generator; 5) According to <mrow><msub><mi>n</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mn>60</mn><msub><mi>f</mi><mn>1</mn></msub></mrow><msub><mi>n</mi><mi>p</mi></msub></mrow>mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow> In the formula, n1 is the synchronous rotational speed _of the double _- fed wind generator, f1 is the rated frequency of the stator of the double-fed wind generator, and _np is the number of pole pairs of the double-fed wind generator ; Substituting n ₁ =n _1M =λ _opt n _1N into formula (10), the optimized stator rated frequency f _1N =n _p λ _opt n _1N /60 of the doubly-fed wind turbine is obtained.