Mutual inductance calculation method of arbitrary space positioned coils

Transcript

1 Eectri c Machines and Contro Vo. 0 No. 6 Jun DOI /j. emc TM 153 TM 551 A X Mutua inductance cacuation method of arbitrary space positioned cois XIE YuePAN Wei-ing Department of Eectrica and Mechanica Engineering China Jiiang University Hangzhou China Abstract The magnetic couping resonant wireess power transfer technoogy reaizes the power transfer wireessy by means of eectromagnetic couping between space-separated cois. The different sizes and reative position change of couping cois may cause the mutua inductance magnitude variation which can thereby infuence the performance of wireess power transfer system. Taking the common rectanguar cross section air-core cois as the anaysis object the cacuation method of mutua inductance between arbitrary space positioned cois was researched and the reevant theoretica formua was derived based on Neumann equation and method of subdivision and superposition. The cacuation formua can give the support to the design of both static and dynamic wireess power transfer systems. The correctness of the proposed cacuation method was proved by the consistency of the experimenta resuts and the formua programming cacuation resuts under the condition of different space positions such as different axia distances radia distances and rotation anges between the couping cois. Keywords wireess power transfer mutua inductance of cois arbitrary reative space position rectanguar cross section method of subdivision and superposition cacuation method

2 Oxyz O z O'x'y'z' O'z' O'x'y'z' O'z' Oxyz X s Y s Z s z' = ax +by + cz r xo - r xi h x 8 h x r xo - r xi Fig. 1 Spatia mutua inductance mode of rectanguar cross section air - core circuar cois 14 ARM Cortex - M3 STM3F T p + 1 Q p + 1 T s + 1 Q s xoy 1 P mn m = - T p 0 T p n = - Q p 0 Q p P mn 0 h p n N x r xo r xi h x x = p x = s Q p + 1 P mn

3 6 65 n' = r pmn = r po + r pi + r po - r pi T p + 1 m 1 P mn N pmn = N p T p + 1 Q p + 1 S m'n' m' = - T s 0 T s - Q s 0 Q s Oxyz O' X s Y s Z s z' = ax + by + cz S m'n' X sm'n' Y sm'n' Z sm'n' X s + ch s n' Q s + 1 S m'n' X - s r sm'n' = r so + r si ah s n' Q s + 1 Y s + bh s n' Q s + 1 Z s + + r so - r si m' 3 T s + 1 S m'n' N sm'n' = N s T s + 1 Q s = X sm'n' /r pmn Y - s = Y sm'n' /r pmn Z - s = Z sm'n' - Z pmn /r pmn r - s = r sm'n' /r pmn C 1 C IR110 C R 0 M mnm'n' = N pmn N sm'n' μ 0 r sm'n' π π A[ ( 1 - ) k K k - E k dφ 0 ] IR110 5 L + Y - sab sinφ + r - sc A = Y- sccosφ - X - s V = 3 k 槡 V r - s 1 - b c { [ ( ) cos φ + c sin φ + abc sin φ ] + k = Y - s + Z - s - r- s ( ) } 1 槡 4V / B + V B = 1 + r - s + X - s + X - sab - Y - s + Z - sbc cosφ + X - sc - M mnm'n' = - N pmnn sm'n' μ 0 r sm'n' π π Y - sbsinφ 0 3 k 槡 V [ ( 1 - ) k K k - E k dφ ] Z - sa sinφ 06 μh R 0 = 0. 5 ± 0. 0% Ω = 0 z'y 50kHz Z s Z s X s Z s 6 V = X - s + Y - s + r - s cos φ - r - sx - sbcosφ 1 B = 1 + r - s + X - s + Y - s + Z - s - r - s X - sbcosφ - Z - ssinφ M ps N p r po r pi h p N s r so r si h s T p X s Y s Z s a b c = Q p T s Q s m = -T p n = -Q p m'= T s n'= -Q s M mnm'n' 7 M ps N p r po r pi h p N s r so r si h s 6 X s Y s Z s a b c 3 14 P mn S m'n' N P mn z = 槡 1 - b p N s ARM Cortex - M3 STM3F103 MOSFET IRF840 VT 1 VT i p t u s X - s + Y - s - r - X - sab - Y - s s cosφ + X- sc sinφ 3 K k E k k N p = 5 r po = 178 mm r pi = 159 mm h p = 10 mm N s = 5 r so = 141 mm r si = 160 mm h s = 10mm L =

4 66 0 X s X s θ a b c 5% 4 c X s 0 Matab θ X s 10 cm0 cm θ 5 5% Fig. Schematic diagram of cois' mutua inductance measurement experiment system 3 Fig. 3 Measurement experiment patform of mutua inductance between arbitrariy positioned cois 4 4 a Z s 4 b Z s 10 cm 0 cm 30 cm X s 4 c Z s 0 cm X s 0 10 cm 0 cm y' 4 a Z s 5% 4 b Z s X s X s > 15 cm 0 μh Z s

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