﻿ 六相双Y30°绕组感应电机建模与控制技术研究
 舰船科学技术  2020, Vol. 42 Issue (8): 140-144    DOI: 10.3404/j.issn.1672-7649.2020.08.026 PDF

Research on modeling and control technology of six-phase induction motor with double Y-connected 3-phase symmetrical windings displaced in turn by 30°
WANG Xian-ming, CHENG Han, HE Lu, WU Jian-feng
The 722 Research Institute of CSSC, Wuhan 430205, China
Abstract: The six-phase induction motor has a series of advantages such as low torque ripple, low motor loss, large motor limit capacity, and high energy density. Based on the mathematical model expression of αβ two-phase stationary coordinate system of three-phase induction motor, the spatial magnetic field distribution of six-phase double Y30° winding induction motor is equivalent to the spatial synthesis of two sets of three-phase motor windings. Coordinates 6/2 vector transformation expression, and designed a six-phase double Y30° winding induction motor vector control system are given. The double loop control system of speed outer loop and current inner loop is adopted. Through theoretical analysis and simulation, the effectiveness of the mathematical model, coordinate transformation and control strategy of the motor is verified.
Key words: induction motor     six-phase     rotor flux-oriented     vector control
0 引　言

1 六相双Y30°绕组感应电机模型

1.1 物理结构模型

 图 1 六相双Y30°绕组感应电机绕组物理结构 Fig. 1 Winding physical structure of six-phase winding induction motor with double Y30°
1.2 三相感应电机数学模型

 \left\{ \begin{aligned} & {\psi _{s\alpha }} = {L_s}{i_{s\alpha }} + {L_m}{i_{r\alpha }}\text{，} \\ & {\psi _{s\beta }} = {L_s}{i_{s\beta }} + {L_m}{i_{r\beta }}\text{，} \\ & {\psi _{r\alpha }} = {L_r}{i_{r\alpha }} + {L_m}{i_{s\alpha }}\text{，} \\ & {\psi _{r\beta }} = {L_r}{i_{r\beta }} + {L_m}{i_{s\beta }}\text{；} \\ \end{aligned} \right. (1)

 \left\{ \begin{aligned} & {u_{s\alpha }} = {R_s}{i_{s\alpha }} + p{\psi _{s\alpha }} = {R_s}{i_{s\alpha }} + {L_s}p{i_{s\alpha }} + {L_m}p{i_{r\alpha }} \text{，} \\ & {u_{s\beta }} = {R_s}{i_{s\beta }} + p{\psi _{s\beta }} = {R_s}{i_{s\beta }} + {L_s}p{i_{s\beta }} + {L_m}p{i_{r\beta }} \text{，}\\ & 0 = {R_r}{i_{r\alpha }} + {\omega _r}{\psi _{r\beta }} + p{\psi _{r\alpha }} \text{，} \\ & 0 = {R_r}{i_{r\beta }} - {\omega _r}{\psi _{r\alpha }} + p{\psi _{r\beta }}{\rm{ }} \text{。} \\ \end{aligned} \right. (2)

 $\small \begin{array}{*{20}{l}} \begin{gathered} \left[ {\begin{array}{*{20}{l}} {p{i_{s\alpha }}} \\ {p{i_{s\beta }}} \\ {p{\psi _{r\alpha }}} \\ {p{\psi _{r\beta }}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - \displaystyle\frac{a}{b}}&{{\text{0}}}&{\displaystyle\frac{{{R_r}{L_m}}}{{{L_r}b}}}&{\displaystyle\frac{{{\omega _r}{L_m}}}{b}} \\ 0& {- \displaystyle\frac{a}{b}}&{ - \displaystyle\frac{{{\omega _r}{L_m}}}{b}}&{\displaystyle\frac{{{R_r}{L_m}}}{b}} \\ {\displaystyle\frac{{{R_r}{L_m}}}{{{L_r}}}}&{{\text{0}}}&{ - \displaystyle\frac{{{R_r}}}{{{L_r}}}}&{ - {\omega _r}} \\ 0&{\displaystyle\frac{{{R_r}{L_m}}}{{{L_r}}}}&{{\omega _r}}&{ - \displaystyle\frac{{{R_r}}}{{{L_r}}}} \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{i_{s\alpha }}} \\ {{i_{s\beta }}} \\ {{\psi _{r\alpha }}} \\ {{\psi _{r\beta }}} \end{array}} \right] + \hfill \\ \quad \quad \quad \quad \quad \left[ {\begin{array}{*{20}{l}} {\displaystyle\frac{{{L_r}}}{b}}&{{\text{0}}} \\ 0&{\displaystyle\frac{{{L_r}}}{b}} \\ 0&{{\text{0}}} \\ 0&{0} \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{u_{s\alpha }}} \\ {{u_{s\beta }}} \end{array}} \right]\text{。} \hfill \\[-10pt] \end{gathered} \end{array}$ (3)

1.3 六相双Y30°绕组感应电机数学模型

 ${u_{6s}} = {R_{6s}}{i_{6s}} + p{\psi _{6s}}\text{，}$ (4)

 $\small\left[ \begin{array}{l} {u_A} \\ {u_B} \\ {u_C} \\ {u_D} \\ {u_E} \\ {u_F} \\ \end{array} \right] = R\left[ \begin{array}{l} 1\;\;\;0\;\;\;0\;\;\;0\;\;\;0\;\;\;0 \\ 0\;\;\;1\;\;\;0\;\;\;0\;\;\;0\;\;\;0 \\ 0\;\;\;0\;\;\;1\;\;\;0\;\;\;0\;\;\;0 \\ 0\;\;\;0\;\;\;0\;\;\;1\;\;\;0\;\;\;0 \\ 0\;\;\;0\;\;\;0\;\;\;0\;\;\;1\;\;\;0 \\ 0\;\;\;0\;\;\;0\;\;\;0\;\;\;0\;\;\;1 \\ \end{array} \right]\left[ \begin{array}{l} {i_A} \\ {i_B} \\ {i_C} \\ {i_D} \\ {i_E} \\ {i_F} \\ \end{array} \right] + p\left[ \begin{array}{l} {\psi _A} \\ {\psi _B} \\ {\psi _C} \\ {\psi _D} \\ {\psi _E} \\ {\psi _F} \\ \end{array} \right]\text{。}$ (5)

 图 2 六相静止与两相静止坐标系示意图 Fig. 2 Schematic diagram of six-phase stationary and two-phase stationary coordinate system
 \small\left\{ \begin{aligned} & {F_\alpha } = {F_A} + {F_B}\cos ({\text π} /6) + {F_C}\cos (2{\text π} /3) +\\ & \quad \quad\; {F_D}\cos (5{\text π}/6) + {F_E}\cos (4{\text π} /3) \text{，} \\ & {F_\beta } = {F_B}\sin ({\text π} /6) + {F_C}\sin (2{\text π} /3) + \\ & {\rm{ }}{F_D}\sin (5{\text π} /6) + {F_E}\sin (4{\text π} /3) - {F_F} \text{。} \\ \end{aligned} \right. (6)

 $\left[\!\! \begin{array}{l} {F_\alpha }\\ {F_\beta } \end{array} \!\! \right] = \left[ \!\!{\begin{array}{*{20}{l}} 1&{\sqrt 3 /2}&{ - {\rm{1/2}}}&{ - \sqrt 3 /2}&{ - {\rm{1/2}}}&{\rm{0}}\\ 0&{1/2}&{\sqrt 3 /2}&{{\rm{1/2}}}&{ - \sqrt 3 /2}&{ - {\rm{1}}} \end{array}} \!\!\right]{F_{6s}} \text{。}$ (7)

 \begin{aligned} & {C_{6s/2s}} = \frac{1}{{\sqrt 3 }} \times \\ & \left[ {\begin{array}{*{20}{l}} 1&{\sqrt 3 /2}&{ - {\text{1/2}}}&{ - \sqrt 3 /2}&{ - {\text{1/2}}}&{{\text{0}}} \\ 0&{1/2}&{\sqrt 3 /2}&{{\text{1/2}}}&{ - \sqrt 3 /2}&{ - {\text{1}}} \\ 1&{ - \sqrt 3 /2}&{ - {\text{1/2}}}&{\sqrt 3 /2}&{ - {\text{1/2}}}&{{\text{0}}} \\ 0&{1/2}&{ - \sqrt 3 /2}&{{\text{1/2}}}&{\sqrt 3 /2}&{ - {\text{1}}} \\ 1&{0}&{1}&{0}&{1}&{0} \\ 0&{1}&{0}&{1}&{0}&{1} \end{array}} \right] \text{，} \end{aligned} (8)

 \begin{aligned} & {C_{2s/6s}} = C_{6s/2s}^T = \frac{1}{{\sqrt 3 }} \times \\ & \left[ {\begin{array}{*{20}{l}} 1&{0}&{1}&{0}&{1}&{0} \\ {\sqrt 3 /2}&{1/2}&{ - \sqrt 3 /2}&{{\text{1/2}}}&{0}&{1} \\ { - {\text{1/2}}}&{\sqrt 3 /2}&{ - {\text{1/2}}}&{ - \sqrt 3 /2}&{1}&{0} \\ { - \sqrt 3 /2}&{1/2}&{\sqrt 3 /2}&{{\text{1/2}}}&{0}&{1} \\ { - {\text{1/2}}}&{ - \sqrt 3 /2}&{ - {\text{1/2}}}&{\sqrt 3 /2}&{1}&{0} \\ 0&{ - 1}&{0}&{ - 1}&{0}&{1} \end{array}} \right] \text{，} \end{aligned} (9)

 ${C_{6s/2s}} \times {C_{2s/6s}} = \left[ \begin{array}{l} 1\;\;\;0\;\;\;0\;\;\;0\;\;\;0\;\;\;0 \\ 0\;\;\;1\;\;\;0\;\;\;0\;\;\;0\;\;\;0 \\ 0\;\;\;0\;\;\;1\;\;\;0\;\;\;0\;\;\;0 \\ 0\;\;\;0\;\;\;0\;\;\;1\;\;\;0\;\;\;0 \\ 0\;\;\;0\;\;\;0\;\;\;0\;\;\;1\;\;\;0 \\ 0\;\;\;0\;\;\;0\;\;\;0\;\;\;0\;\;\;1 \\ \end{array} \right] \text{。}$ (10)

 图 3 两相静止坐标系与两相旋转坐标系示意图 Fig. 3 Schematic diagram of two-phase stationary and two-phase rotating coordinate system
 $\left[ \begin{array}{l} {i_d}\\ {i_q} \end{array} \right] = \left[ {\begin{array}{*{20}{c}} {\cos (\theta )}&{{\rm{sin(}}\theta {\rm{)}}}\\ { - \sin (\theta )}&{{\rm{cos(}}\theta {\rm{)}}} \end{array}} \right]\left[ \begin{array}{l} {i_\alpha }\\ {i_\beta } \end{array} \right] \text{，}$ (11)

 ${C_{2s/2r}} = \left[ {\begin{array}{*{20}{l}} {{\rm{cos(}}\theta {\rm{)}}}&{{\rm{sin(}}\theta {\rm{)}}}&0&0&0&0\\ { - {\rm{sin(}}\theta {\rm{)}}}&{\cos (\theta )}&0&0&0&0\\ 0&0&1&0&0&0\\ 0&0&0&1&0&0\\ 0&0&0&0&1&0\\ 0&0&0&0&0&1 \end{array}} \right] \text{。}$ (12)

 $\small\begin{split} &{C_{6s/2r}} = {C_{2s/2r}} \times {C_{6s/2s}} = \displaystyle\frac{1}{{\sqrt 3 }}\times \\ & \left[{\begin{array}{*{20}{l}} {{\rm{cos(}}\theta {\rm{)}}}&{\cos (\theta - \displaystyle\frac{\text π }{6})}&{{\rm{cos(}}\theta - \displaystyle\frac{{2{\text π}}}{3}{\rm{)}}}\\ {{\rm{ - sin(}}\theta {\rm{)}}}&{{\rm{ - sin}}(\theta - \displaystyle\frac{\text π}{6})}&{{\rm{ - sin(}}\theta {\rm{ - }}\displaystyle\frac{{2{\text π}}}{3}{\rm{)}}}\\ 1&{{\rm{ - }}\sqrt 3 /2}&{ - {\rm{1/2}}}\\ 0&{1/2}&{ - \sqrt 3 /2}\\ 1&0&1\\ 0&1&0 \end{array}}\right.\\ &\left. {\begin{array}{*{20}{l}} {{\rm{cos(}}\theta - \displaystyle\frac{{5{\text π}}}{6}{\rm{)}}}&{{\rm{cos(}}\theta - \displaystyle\frac{{4{\text π}}}{3}{\rm{)}}}&{{\rm{cos(}}\theta - \displaystyle\frac{{3 {\text π}}}{2}{\rm{)}}}\\ {{\rm{ - sin(}}\theta {\rm{ - }}\displaystyle\frac{{5{\text π}}}{6}{\rm{)}}}&{{\rm{ - sin(}}\theta {\rm{ - }}\displaystyle\frac{{4{\text π}}}{3}{\rm{)}}}&{{\rm{ - sin(}}\theta {\rm{ - }}\displaystyle\frac{{3{\text π}}}{2}{\rm{)}}}\\ {\sqrt 3 /2}&{ - {\rm{1/2}}}&{\rm{0}}\\ {{\rm{1/2}}}&{\sqrt 3 /2}&{ - {\rm{1}}}\\ 0&1&0\\ 1&0&1 \end{array}}\right]\text{。} \end{split}$ (13)

2 六相双Y30°绕组感应电机仿真 2.1 仿真模型构建

 图 4 六相感应电机控制系统主电路 Fig. 4 Control system main circuit of six-phase induction motor

 图 5 六相双Y30°绕组感应电机仿真模型 Fig. 5 Simulation model of six-phase winding induction motor with double Y30°
 $\small \begin{gathered} \left[ {\begin{array}{*{20}{l}} {{u_{s\alpha }}} \\ {{u_{s\beta }}} \end{array}} \right] = \frac{1}{{\sqrt 3 }}\times \hfill \\ \left[ {\begin{array}{*{20}{l}} 1&{\sqrt 3 /2}&{ - {\text{1/2}}}&{ - \sqrt 3 /2}&{ - {\text{1/2}}}&{{\text{0}}} \\ 0&{1/2}&{\sqrt 3 /2}&{{\text{1/2}}}&{ - \sqrt 3 /2}&{ - {\text{1}}} \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{u_A}} \\ {{u_B}} \\ {{u_C}} \\ {{u_D}} \\ {{u_E}} \\ {{u_F}} \end{array}} \right] \text{，} \end{gathered}$ (14)
 $\small \left[ \begin{array}{l} {i_{sa}}\\ {i_{ib}}\\ {i_{sc}}\\ {i_{sd}}\\ {i_{se}}\\ {i_{sf}} \end{array} \right] = \frac{1}{{\sqrt 3 }}\left[ {\begin{array}{*{20}{l}} 1&0\\ {\sqrt 3 /2}&{1/2}\\ { - {\rm{1/2}}}&{\sqrt 3 /2}\\ { - \sqrt 3 /2}&{1/2}\\ { - {\rm{1/2}}}&{ - \sqrt 3 /2}\\ 0&{ - 1} \end{array}} \right]\left[ \begin{array}{l} {i_{s\alpha }}\\ {i_{s\beta }} \end{array} \right] \text{。}$ (15)

 图 6 六相双Y30°绕组感应电机矢量控制原理框图 Fig. 6 Vector control block diagram of six-phase winding induction motor with double Y30°
2.2 系统仿真结果

 图 7 六相双Y30°绕组感应电机矢量控制仿真波形 Fig. 7 Vector control simulation waveforms of six-phase winding induction motor with double Y30°
3 结　语

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