RU2293422C2 - ASYMMETRIC THREE-PHASE FRACTIONAL-SLOT WINDING WITH 2p = 6c POLES PLACED IN z = 39c SLOTS - Google Patents

Abstract

FIELD: electrical and electromechanical engineering; three-phase induction and synchronous machines including slip-ring induction motors.

SUBSTANCE: proposed double-layer fractional-slot winding with m = 3 phases, m' = m = 3 bands, 2p = 6c poles in z = 39c slots, and slot number per pole per phase q = z/3p = 13/3 has 3pc coil groups with coil grouping 5 4 4 4 4 5 4 5 4 repeated c times. Novelty is that slot pitches of concentric coils y_si = 10 - 2(i - 1) and turn numbers (1 - x)w_c for coils with i' = 1, 5 and turn number (1 + x)w_c for coil with i' = 3 in five-coil groups 1G, 6G, 9G; slot pitches y'_si = 9 - 2(i' - 1) and turn number (1 + x)w_c for coil with i' = 2 in all four-coil groups; turn number equals (1 - x)w_c for coil with i = 4 in coil groups 3G, 4G, 7G, 9G, and for coil groups 2G, 5 G at slot pitch y_si = 6 turn number equals (1 - x)w_c for coil with i = 4 in coil group 2G and for coil with i = 1 in coil group 5G; turn number in remaining coils of coil groups equals w_c, where c = 1, 2, 3 ...; i = 1 - 5 and i' = 1 -4 are coil numbers in coil groups starting from external one; w_c is turn number in slots completely filled with winding.

EFFECT: reduced asymmetry and differential scatter ratios.

1 cl

Description

The invention relates to three-phase windings of electrical AC machines - asynchronous motors (HELL) and synchronous generators (SG).

Known two-layer loop m = 3-phase fractional windings are known, performed at 2p poles in z grooves from m′p coil groups with equal-step or concentric coils with an average pitch of grooves y _to ≈z / 2p, the number of grooves per pole and phase q = z / m′p = b + c / d, where m ′ = 2m = 6 or m ′ = m = 3 is the number of phase zones per pair of poles, c / d <1; according to symmetry conditions, the 2p / d ratios are integer, d / m are non-integer [Voldek A.I. Electric cars. L .: Energy, 1978, S. 392-394].

Grouping coils in groups of fractional asymmetric (d / m - integer) windings are given in rows and depend on c / d [Livshits-Garik M. Windings of AC machines. / Per. from English L .: SEI, 1959, p. 254], for example 5 4 4 4 4 5 4 5 4 for q = 13/3; Due to phase asymmetry, differential scattering increases.

The invention aims to reduce the asymmetry coefficients, differential scattering of an asymmetric m ′ = 3-zone winding at q = 13/3.

The solution of this problem is achieved by the fact that for m = 3-phase asymmetric test winding with 2p = 6s poles in z = 39s grooves, a two-layer m ′ = 3-zone with the number of grooves per pole and phase q = z / 3p = 13 / 3 of 3pc coil groups 1G ... 9G with a group of 5 4 4 4 4 5 4 5 4, repeated with time:

concentric coils have _groove steps y _pi = 10-2 (i-1) with numbers of turns (1-x) w _to coils with i = 1, 5 and (1 + x) w _to coils with i = 3 for five-coil groups 1Г, 6Г, 8Г, у _pi = 9-2 (i'-1) with the number of turns (1 + x) w _{to the} coil with i ′ = 2 for all four-coil groups with (1) w _{to the} turns of the coil with i ′ = 4 groups in 3G, 4G, 7G, 9G, and for groups 2G, 5G with y _n = 6- (1-x) w _{to the} coil turns with i '= 4 in 2G and with i' = 1 in 5G when w _to in the other coils of the groups, where c = 1, 2, 3, ..., i = 1 ... 5 and i '= 1 ... 4 are the numbers of coils in the groups, starting from the outer, x = 0 , 5, and 2w _to - the number of turns of grooves, completely filled with a winding.

Figure 1 shows a scan of the groove layers of the proposed winding with c = 1, 2p = 6, z = 39 with numbers 1 ... 39 from the bottom, 3p = 9 groups with numbers 1G ... 9G from above, alternating phase zones A-B - From the upper, XYZ lower layers and the blackened grooves contain (2) w _to turns at 2w _to turns in the remaining grooves, and the shifts of the axes of the groups are marked from below; figure 2 is a diagram of the shifts of groups, their EMF phases E _A , E _B, E _With respect to the axis of symmetry 8G; figure 3, 4 on a triangular grid constructed polygons of the MDS winding for coils equal- (figure 3) and unequal (figure 4). The winding (Fig. 1) is connected in series-consonant inclusion of groups: 1G, 4G, 7G in phase I, 2G, 5G, 8G in phase II, 3G, 6G, 9G in phase III with beginnings of 1G, 2G, 3G; phases can mate in Y and Δ. With c = 2, 3, ... the winding has 2p = 6s = 12, 18, ... poles, z = 39s = 78, 117, ... grooves and 3pc = 18, 27, ... groups.

K_нес%=(F/D) [Петров Г.Н. Электрические машины, ч.2. Асинхронные и синхронные машины. М.-Л.: ГЭИ, 1963, с.162] вычисляется коэффициент несимметрии К_нес%=0,79% при К_об=(Е_АС+2Е_ВА)/

·39=0,8148.For winding (1) groups EMF determined by the coefficients of shortening concentric coils K _yi = sin (90y _pi / τ _n) = sin _(pi at 180 ° / 13) with the pole pitch τ _p = z / 2p = 6.5; By _yi = (1-x) 0.663123 (y _pi = 10), (1 + x) 0.992709 (y _pi = 6), (1-x) 0.464723 (y _pi = 2) at E _{r .b} = 3.878555-x0.135137 for groups of five-coil (large), (1 + x) 0.992709 (y ′ _pi = 7) (1-x) 0.663123 (y ′ _pi = 3) with E _{g .m} = 3.413832 + h0,329586 groups 3G, 4G, 7G, 9G chetyrehkatushechnyh (small). The diagram of Fig. 2 is constructed for 2p = 6, z = 39. α _p = 360 ° / z = 120 ° / 13 and the shift angles of the axes of the groups of FIG. 1: 8G → 9G = 4.5α _p p = 120 ° + 0.5α _p and 8G → 7G = 240 ° -0.5α _n ; 8G-1G = 9α _p p = 240 ° + α _p and 8G → 6G = 120 ° -α _p ; 8G → 2G = 13.5α _p p = 360 ° + 1.5α _p and 8G → 5G = 360 ° -1.5α _p ; 8G → 3G = 17.5α _p p = 120 ° + 0.5α _p and 8G → 4G = 240 ° -0.5α _p , according to which: E _B = E _{8G (b)} + 2E _{2G (m)} cos1.5α _n = 10,50782 + x0,6647423 is the vertical vector, where for non-concentric groups 2G, 5G - 2x [cos1,5α _n -cos (1,5-1,5 · 3) α _n ] = + x0,79988; E ² _A = (2E _{4G (m)} ) ² + E ² _{1G (b)} -4E _{4G (m)} E _{1G (b)} cos (180 ° -1.5α _n ) - by the cosine theorem and for x = 0 - E _A = E _c = 10.6341, the angle γ (2) is defined by the sine theorem E _4G / sinγ = E _A / sin (180 ° -1,5α _n) where γ = 8,8387 ° angles and then the phase EMF shifts are φ _BA = φ _BC = 120 ° -α _p + γ = 119.6079 and φ _AC = 120.7841 °. From the phase EMF and shear angles, the linear EMF a = E _BA = b = E _BC = 18.2733, c = E _AC = 18.4911 are determined and then by the expressions: S = a + b + c, A = (a ² + b ² + c ² ) / 6,

K _carried% = (F / D) [Petrov G.N. Electric cars, part 2. Asynchronous and synchronous machines. M.-L.: SEI, 1963, p.162] the asymmetry coefficient is calculated K _carried% = 0.79% at K _about = (E _AC + 2E _VA ) /

39 = 0.8148.

(z-3x)=0,8702 и z'=39-3x=37,5 - эквивалентное число полностью заполненных обмоткой пазов, т.е. она имеет больший К_об и меньший К_нес% (в 0,79/0,35=2,26 раза).Similarly, for the non-uniform winding of FIG. 1 at x = 0.5: E _B = 10.8402, E _A = E _C = 10.8957, γ = 9.0446 °, φ _VA = φ _BC = 119.8138 ° , φ _AC = 120.3724 °, a = E _BA = b = E _BC = 18.8062, c = E _AC = 18.9073, K _carried% = 0.35, K _rev = (E _AC + 2E _VA )

(z-3x) = 0.8702 and z '= 39-3x = 37.5 is the equivalent number of grooves completely filled by the winding, i.e. it has a larger K _about and a smaller K _carried% (0.79 / 0.35 = 2.26 times).

From the MDS polygons of Figs. 3, 4 (with unit current vectors of phase zones A-Z-B-X-C-Y in the center) according to a triangular grid and the relations

the differential scattering coefficient σ _D% is determined, which characterizes the quality of the winding by the harmonic composition of the MDS with the square of the average radius j = 1 ... z of the groove points R ² _d , the radius R _{o of the} circle for the main harmonic [Popov V. Determination and optimization of the parameters of three-phase windings along the MDS polygons // Electricity, 1997, No. 9, p. 53-55]:

According to (1) - (2): at x = 0, K _rev = 0.8148 - R ² _d = 477/39, R _o = 39 · 0.8184 / 3π and σ _D% = 7.60; at x = 0.5 and K _rev = 0.8702 - R ² _d = 486.75 / 39, R _o = 37.5 · 0.8702 / 3π, σ _D% = 4.11%, i.e. σ _D% decreases by 7.60 / 4.11 = 1.85 times. Given the changes in K _about , K _carried% , σ _{d%, the} winding of Fig. 1 with x = 0.5 has a high efficiency K _eff = (0.8708 / 0.8148) (0.79 / 0.35) (7 60 / 4.11) (37.5 / 39) = 4.3; at optimal x = x _opt , K _nes = 0 is achieved.

The proposed m ′ = 3-zone winding, in comparison with m ′ = 6-zone at z = 39, 2p = 6, q = z / 6p = 13/6, for _n = 5, grouping 322222232222223222, К _ob = 0, 8912, K _carried% = 0.43 and σ _D% = 4.27, has reduced K _carried and σ _D with half as many groups.

Its application allows to reduce additional losses in the rotor and magnetic noise in the blood pressure with short-circuit rotor, improve the shape of the voltage curve in the SG.

Claims (1)

Three-phase asymmetric fractional winding at 2p = 6s poles in z = 39s grooves, performed by a two-layer m ′ = 3-zone with the number of grooves per pole and phase q = z / 3p = 13/3 of 3pc coil groups with a group of 5 4 4 4 4 5 4 5 4, repeated with times, characterized in that the concentric coils have _groove steps y _pi = 10-2 (i-1) and the number of turns (1-x) w _k for coils with i ′ = 1.5 and the number of turns (1 + x) w _k for a coil with i = 3 for five-coil groups 1Г, 6Г, 8Г, groove steps y ′ _пi = 9-2 (i′-1) and the number of turns (1 + х) w _к for a coil with i ′ = 2 for all four-coil groups, with the number of turns equal to (1) w _k for a coil with i = 4 dl I of coil groups 3G, 4G, 7G, 9G, and for coil groups 2G, 5G with a pitch in the grooves of _n = 6, the number of turns is (1) w _k for the coil with i = 4 in the coil group 2G and for the coil with i = 1 in the 5G coil group, while the number of turns in the remaining coils of the coil groups is w _k , where c = 1, 2, 3, ...; i = 1 ... 5 and i ′ = 1 ... 4 are the numbers of coils in the coil groups, starting from the outside; 2w _to - the number of turns in the grooves, completely filled with a winding; x = 0.5.

Images