高周波電圧信号重畳による誘導機ドライプシステムで利用する信号分離用フィルタの設計

高周波電圧信号重畳による誘導機ドライプシステム

で利用する信号分離用フィルタの設計

著者

窪田 涼介

雑誌名

福岡工業大学総合研究機構研究所所報

巻

3

ページ

11-15

発行年

2020-12-25

URL

http://hdl.handle.net/11478/00001582

㧗࿘Ἴ㟁ᅽಙྕ㔜␚࡟ࡼࡿㄏᑟᶵࢻࣛ࢖ࣈࢩࢫࢸ࣒࡛฼⏝ࡍࡿ

ಙྕศ㞳⏝ࣇ࢕ࣝࢱࡢタィ

❑⏣ ᾴ௓㸦⚟ᒸᕤᴗ኱Ꮫ▷ᮇ኱Ꮫ㒊᝟ሗ࣓ࢹ࢕࢔Ꮫ⛉㸧

Design of Filter utilizing IM Drive System with High Frequency Voltage Signal Injection

KUBOTA Ryosuke㸦Department of Information and Multimedia Technology, FIT Junior College㸧

Abstract

This paper reports the design and its analysis of various filters used for signal separation for the induction machine drive system with high frequency voltage signal injection. The designed filters are notch filter in addition to 1st_{, 2}nd_{, and 4}th _{order low-pass filters.}

For the analysis method, the simulation is carried out by constructing an indirect type vector control system. Also, the stability analysis is carried out for the current controller with the filter. As the results, it is clarified that the fundamental component and the high frequency amplitude can be accurately extracted by using notch filter as compared with other low-pass filters.

Keywords㸸Filter Design, High Frequency Signal Injection, Induction Machine, Stability Analysis,

 ࡲ࠼ࡀࡁ ㄏᑟᶵ㸦IM㸧ࡣ㸪ࡑࡢᵓ㐀ୖ㸪Ᏻ౯࠿ࡘሀ∼࡜࠸࠺≉㛗ࢆ ᭷ࡋ㸪⌧ᅾ㸪⏘ᴗ⏺࡛᭱ࡶ฼⏝ࡉࢀ࡚࠸ࡿ஺ὶ㟁ືᶵ࡛࠶ ࡿࠋࡲࡓ㸪㧗⢭ᗘ࡞ࢺࣝࢡ࣭㏿ᗘไᚚࢆᚲせ࡜ࡍࡿ⏝㏵࡟࠾ ࠸࡚ࡣ㸪ᅇ㌿Ꮚ㸦஧ḟ㸧☢᮰࡟ྠᮇࡋࡓdq ྠᮇᗙᶆୖ࡛ไ ᚚࢆ⾜࠺࣋ࢡࢺࣝไᚚࡀᐇ⏝ࡉࢀ࡚࠸ࡿ(1)_{ࠋ࣋ࢡࢺࣝไᚚ࡛} ࡣ㸪ࡑࡢไᚚཎ⌮ୖ㸪ᅇ㌿㏿ᗘࢆไᚚ⣔࡬ࣇ࢕࣮ࢻࣂࢵࢡࡋ ࡞ࡅࢀࡤ࡞ࡽࡎ㸪ࡑࢀᨾ㸪㍈➃࡟㏿ᗘࢭࣥࢧࢆྲྀࡾ௜ࡅࡿᚲ せࡀ࠶ࡿࠋࡑࡢࡓࡵ㸪ࢥࢫࢺࡢቑຍࡸᨾ㞀➼࡟ࡼࡿಙ㢗ᛶࡢ పୗࢆᣍࡁ㸪IM ᮏ᮶ࡢ≉㛗ࢆᦆ࡞࠺ࡇ࡜࡟࡞ࡿࠋࡲࡓ㸪⏝ ㏵࡟ࡼࡗ࡚ࡣ୧㍈ࢆ౑⏝ࡍࡿࡇ࡜ࡶ࠶ࡾ㸪㏿ᗘࢭࣥࢧ⮬య ࢆྲྀࡾ௜ࡅࡽࢀ࡞࠸ሙྜࡀ࠶ࡿࠋࡑࡇ࡛㸪ࡇࢀࡽࡢㄢ㢟࡟ᑐ ࡍࡿゎỴ⟇࡜ࡋ࡚㸪㏿ᗘࢭࣥࢧࢆせࡋ࡞࠸㸪࠸ࢃࡺࡿ㏿ᗘࢭ ࣥࢧࣞࢫ࣋ࢡࢺࣝไᚚ㸦ࢭࣥࢧࣞࢫไᚚ㸧ࡀ⪃᱌ࡉࢀ㸪ᐇ⏝ ࡟౪ࡉࢀ࡚࠸ࡿ(2)_{ࠋIM ࡢࢭࣥࢧࣞࢫไᚚ࡛ࡣ㸪஧ḟ☢᮰఩} ⨨࡜ᅇ㌿㏿ᗘࢆ᥎ᐃࡍࡿᚲせࡀ࠶ࡾ㸪࣋ࢡࢺࣝไᚚ㥑ື࡟ ࠾ࡅࡿ㧗⢭ᗘ࡞ࢺࣝࢡ࣭㏿ᗘ≉ᛶࢆᐇ⌧ࡍࡿࡓࡵ࡟㸪ከࡃࡢ ᥎ᐃ᪉ᘧࡀሗ࿌ࡉࢀ࡚࠸ࡿ(3)~(9)_ࠋ ࡇࢀࡲ࡛࡟ሗ࿌ࡉࢀ࡚࠸ࡿࢭࣥࢧࣞࢫไᚚἲࡣ㸪኱ูࡍ ࡿ࡜ IM ࡢᇶᮏἼࣔࢹࣝ࡟❧⬮ࡋࡓࢭࣥࢧࣞࢫ᪉ᘧ࡜࣮ࣔ ࢱࣔࢹࣜࣥࢢ࡟࠾࠸࡚⪃៖ࡉࢀ࡚࠸࡞࠸≀⌮⌧㇟ࢆ฼⏝ࡋ ࡓࢭࣥࢧࣞࢫ᪉ᘧࡀ࠶ࡿࠋ๓⪅ࡢ᪉ᘧࡣ㸪୍⯡࡟⏝࠸ࡽࢀࡿ ᪉ᘧ࡛࠶ࡾ㸪᥎ᐃ⢭ᗘࡢ㧗⢭ᗘ໬ࢆᅗࡿほⅬ࠿ࡽ✀ࠎࡢ᥎ ᐃ࢔ࣝࢦࣜࢬ࣒ࡀᥦ᱌ࡉࢀ࡚࠸ࡿ(3)~(5)_{ࠋࡋ࠿ࡋ࡞ࡀࡽ㸪ᇶᮏ} Ἴࣔࢹࣝ࡟ᇶ࡙࠸࡚ᵓ⠏ࡉࢀ࡚࠸ࡿࡓࡵ㸪≉࡟ప㏿࣭ᅇ⏕㡿 ᇦࡢ㞽࿘Ἴᩘ࡜࡞ࡿ㐠㌿≧ែ࡟࠾࠸࡚஧ḟഃࡢㄏ㉳㟁ᅽࢆ ⾲ࡍ㡯ࡀࢮࣟ࡜࡞ࡾ㸪஧ḟഃࡢ≧ែࢆ᥎ᐃࡍࡿࡇ࡜ࡀᅔ㞴 ࡟࡞ࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿࠋ୍᪉㸪ᚋ⪅ࡢ᪉ᘧࡣ㸪IM ᶵෆ ࡢ☢Ẽ㣬࿴ࡸᅇ㌿Ꮚࢫࣟࢵࢺ㧗ㄪἼࢆ฼⏝ࡍࡿ᪉ᘧ࡛࠶ ࡾ㸪ᇶᮏἼࣔࢹࣝࢆ⏝࠸࡞࠸ࡓࡵ㸪㞽࿘Ἴᩘ㐠㌿࡟࠾࠸࡚ ࡶ㸪᥎ᐃཎ⌮ୖ㸪Ᏻᐃࡋࡓືసࡀྍ⬟࡜ࡉࢀ࡚࠸ࡿࠋ☢Ẽ㣬 ࿴ࢆ฼⏝ࡍࡿ᪉ἲࡣ㸪஧ḟ☢᮰఩⨨ࡢ᥎ᐃ࡟฼⏝ࡉࢀ㸪୺☢ ᮰ࡢ㣬࿴࡟㉳ᅉࡋ࡚⏕ࡌࡿ✺ᴟᛶࢆ᳨ฟࡍࡿࡇ࡜࡛᥎ᐃࢆ ⾜࠺(6)(7)_{ࠋࡲࡓ㸪ᅇ㌿Ꮚࢫࣟࢵࢺ㧗ㄪἼࢆ฼⏝ࡍࡿ᪉ἲࡣ㸪} ᅇ㌿㏿ᗘࡢ᥎ᐃ࡟฼⏝ࡉࢀ㸪IM ࡢᅇ㌿Ꮚᵓ㐀࡟㉳ᅉࡋ࡚⏕ ࡌࡿࢫࣟࢵࢺࣜࣉࣝࢆ᳨ฟࡍࡿࡇ࡜࡛᥎ᐃࡀ⾜ࢃࢀࡿ(8)(9)_ࠋ 㣬࿴✺ᴟᛶࡸ㧗⢭ᗘ࡞ᅇ㌿Ꮚࢫࣟࢵࢺ㧗ㄪἼࡢ᳨ฟ࡟㛵ࡋ ࡚ࡣ㸪㧗࿘Ἴಙྕࢆ㔜␚ࡍࡿࡇ࡜࡟ࡼࡗ᳨࡚ฟྍ⬟࡜࡞ࡿࠋ IM ࡢ㧗࿘Ἴಙྕ㔜␚࡟ࡼࡿࢭࣥࢧࣞࢫไᚚ࡛ࡣ㸪㧗࿘Ἴ ಙྕࢆᇶᮏἼ࡟㔜␚ࡋ㸪ࡑࡢሙྜ࡟ ᐃࡉࢀࡿಙྕ࠿ࡽ㧗 ࿘Ἴᡂศࢆᢳฟࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪஧ḟ☢᮰఩⨨࠾ࡼࡧᅇ ㌿㏿ᗘࢆ᥎ᐃࡍࡿࠋࡑࡢ㝿㸪㧗࿘Ἴᡂศࢆᢳฟࡍࡿࡓࡵ࡟ ࣇ࢕ࣝࢱࡀ⏝࠸ࡽࢀࡿࠋ୍᪉㸪㧗࿘ἼಙྕࡣᇶᮏἼࡢไᚚಙ ྕ࡟࡜ࡗ࡚ࡣእ஘࡛࠶ࡾ㸪ࡲࡓ㸪ᗈᖏᇦࡢ㟁ὶไᚚჾࢆタィ ࡋ࡚࠸ࡿሙྜ࡟ࡣ㧗࿘Ἴᡂศࡲ࡛⿵ൾࡉࢀࡿࡓࡵ㸪ࡑࢀࡽ ࡢᙳ㡪ࢆ㜵ࡄࡓࡵ࡟ᇶᮏἼᡂศࡢࡳࢆᢳฟࡍࡿࣇ࢕ࣝࢱࡀ ᚲせ࡜࡞ࡿࠋ㧗࿘Ἴᡂศࡢᢳฟ࡟⏝࠸ࡽࢀࡿࣇ࢕ࣝࢱࡢᵓ ᡂ࡜ࡋ࡚ࡣ㸪BPF㸦Band Pass Filter㸧ࢆ⏝࠸࡚㧗࿘Ἴಙྕࢆ

ᢳฟࡋ㸪ࡇࢀ࡟ྠ୍ࡢ࿘Ἴᩘᡂศࢆ᥃ࡅྜࢃࡏࡓᚋ㸪LPF

㸦Low Pass Filter㸧ࢆ⏝࠸࡚㧗࿘Ἴಙྕࡢ᣺ᖜࡢࡳࢆᢳฟࡍ

ࡿ᪉ἲࡀ࠶ࡿ(6)_{ࠋ୍᪉㸪ᇶᮏἼᡂศࡢᢳฟ࡟⏝࠸ࡽࢀࡿࣇ࢕}

ࣝࢱ࡟㛵ࡋ࡚ࡣLPF ࡀከ⏝ࡉࢀ࡚࠸ࡿࠋࡋ࠿ࡋ࡞ࡀࡽ㸪ୖ

グࡢ㧗࿘ἼࡸᇶᮏἼࡢᢳฟ㐣⛬࡛⏝࠸ࡽࢀࡿLPF ࡣ㸪ไᚚ

ᛂ⟅㏿ᗘࡢほⅬ࠿ࡽᖏᇦࢆୗࡆࡿࡇ࡜ࡀ࡛ࡁࡎ㸪ࡲࡓ㸪₇⟬ ࿘ᮇࡢほⅬ࠿ࡽඛ㗦ᗘࢆ㧗ࡃ࡛ࡁ࡞࠸➼ࡢၥ㢟ࡀ࠶ࡿࠋ

❑⏣ ᾴ௓ ࡑࡇ࡛㸪ᮏ✏࡛ࡣ㧗࿘Ἴ㟁ᅽಙྕ㔜␚࡟࠾ࡅࡿಙྕศ㞳

࡟฼⏝ࡍࡿࣇ࢕ࣝࢱࡢタィ࡜ࡑࡢゎᯒ࡟ࡘ࠸࡚ሗ࿌ࡍࡿࠋ タィࢆ⾜࠺ࣇ࢕ࣝࢱ࡟㛵ࡋ࡚ࡣ㸪୍⯡࡟⏝࠸ࡽࢀࡿ୍ḟࡢ LPF ࡟ຍ࠼࡚㸪஧ḟཬࡧᅄḟࡢ LPF㸪ࡲࡓ㸪BSF㸦Band Stop Filter㸧ࡢ୍✀࡛࠶ࡿ NF㸦Notch Filter㸧ࢆᑐ㇟࡜ࡋ࡚タィࢆ ⾜࠺ࠋタィࡉࢀࡓࣇ࢕ࣝࢱࡢゎᯒ࡟㛵ࡋ࡚ࡣ㸪㛫᥋ᙧ࣋ࢡࢺ ࣝไᚚ⣔࡟⤌ࡳ㎸ࢇࡔሙྜࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ຍ࠼㸪タ ィࡋࡓࣇ࢕ࣝࢱ࡜㟁ὶไᚚჾ࡟㛵ࡍࡿఏ㐩㛵ᩘ࠿ࡽᴟ㞽Ⅼ ࢆồࡵࡿࡇ࡜࡟ࡼࡗ࡚Ᏻᐃᛶゎᯒࢆᐇ᪋ࡍࡿࠋࡑࡢ⤖ᯝ㸪ᮏ ࢩࢫࢸ࣒࡛ࡣᇶᮏἼᡂศࢆᢳฟࡍࡿࡓࡵ࡟⏝࠸ࡿࣇ࢕ࣝࢱ ࡜ࡋ࡚㸪NF ࢆ⏝࠸ࡓሙྜ࡟௚ࡢ LPF ࡜ẚ㍑ࡋ࡚㧗࿘Ἴࡢᙳ 㡪ࢆ᭱ࡶపῶࡋ࡚ᇶᮏἼᡂศࢆᢳฟ࡛ࡁࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ ࡋࡓࠋࡲࡓ㸪㧗࿘Ἴᡂศࡢ᣺ᖜࢆᢳฟࡍࡿࡓࡵ࡟⏝࠸ࡿࣇ࢕ ࣝࢱ࡟㛵ࡋ࡚ࡶ㸪NF ࢆ⏝࠸ࡓሙྜ࡟㧗࿘Ἴ᣺ᖜࢆ⢭ᗘⰋࡃ ᢳฟྍ⬟࡛࠶ࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓࡢ࡛ሗ࿌ࡍࡿࠋ  ࣇ࢕ࣝࢱタィ  ྛ✀ࣇ࢕ࣝࢱࡢᵓᡂ ᮏ᳨ウ࡟࠾ࡅࡿᇶᮏἼᡂศ࡜㧗 ࿘Ἴᡂศࡢಙྕศ㞳࡟⏝࠸ࡿࣇ࢕ࣝࢱࡣ㸪୍ḟ㸪஧ḟཬࡧ ᅄḟࡢLPF ࡟ຍ࠼࡚㸪NF ࢆᑐ㇟࡟タィࢆ⾜࠺ࠋྛ✀ࣇ࢕ࣝ ࢱࡢఏ㐩㛵ᩘࡣ㸪ୗᘧ࡛⾲ࡉࢀࡿࠋ ܩଵೞ೟௅௉ிൌ ௄ఠ ௦ାఠ ... (1) ܩଶ೙೏௅௉ிൌ ௄ఠమ ௦మ_ାഘ ೂభ௦ାఠమ ... (2) ܩସ೟೓௅௉ிൌ ௄భఠమ ௦మ_ାഘ ೂమ௦ାఠమ ή ௄మఠమ ௦మ_ାഘ ೂయ௦ାఠమ ... (3) ܩேிൌ ௄൫௦మ_ାఠ ಿಷ మ _൯ ௦మ_ାഘಿಷ ೂభ௦ାఠಿಷమ ... (4)  ࡇࡇ࡛㸪㸦1㸧ᘧࡣ୍ḟ LPF㸪㸦2㸧ᘧࡣ஧ḟ LPF㸪㸦3㸧ᘧࡣ ᅄḟLPF ཬࡧ㸦4㸧ᘧࡣ NF ࡢఏ㐩㛵ᩘ࡛࠶ࡿࠋ 㸦1㸧ᘧ㹼㸦4㸧ᘧ࡛⾲ࡉࢀࡿྛࣇ࢕ࣝࢱࡢఏ㐩㛵ᩘࢆᇶ࡟㸪 ᇶᮏἼᡂศཬࡧ㧗࿘Ἴᡂศࢆᢳฟྍ⬟࡜ࡍࡿࣃ࣓࣮ࣛࢱࡢ タィࢆ⾜࠺ࠋ  タィ௙ᵝ ⾲ 1 ࡟ᇶᮏἼᡂศᢳฟ⏝࡟タィࡋࡓྛࣇ࢕ ࣝࢱࡢࣃ࣓࣮ࣛࢱࢆ♧ࡍࠋ⾲1 ࡼࡾ㸪ྛ LPF ࡢ࢝ࢵࢺ࢜ࣇ ࿘Ἴᩘࡣ㟁ὶไᚚჾࡢタィ್࡟౫Ꮡࡋ㸪ᮏ᳨ウ࡟࠾࠸࡚⏝ ࠸ࡿ㟁ὶไᚚჾࡢᖏᇦ࿘Ἴᩘࡀ⣙159 Hz ࡛࠶ࡿࡇ࡜ࢆ⪃៖ ࡋ࡚ỴᐃࡋࡓࠋNF ࡢ࢝ࢵࢺ࢜ࣇ࿘Ἴᩘ࡟㛵ࡋ࡚ࡣ㸪ࡑࡢື స≉ᛶୖ㸪㔜␚࿘Ἴᩘ࡟ᑐᛂࡋࡓ್࡜ࡍࢀࡤⰋࡃ㸪500 Hz ࡜ ࡋ࡚タィࡋࡓࠋࡲࡓ㸪ᅄḟLPF ࡟㛵ࡋ࡚ࡣ㸪ࣂࢱ࣮࣡ࢫ≉ ᛶ࡜࡞ࡿࡼ࠺࡟タィࢆ⾜ࡗࡓࠋᅗ1 ࡟ྛ LPF ࡢ࣮࣎ࢻ⥺ᅗ ࢆ♧ࡋ㸪ᅗ2 ࡟ NF ࡢ࣮࣎ࢻ⥺ᅗࢆ♧ࡍࠋᅗ 1 ཬࡧᅗ 2 ࡼ ࡾ㸪タィ㏻ࡾࡢ≉ᛶࡀᚓࡽࢀ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ㧗࿘Ἴᡂ ศᢳฟ࡟࠾ࡅࡿࣃ࣓࣮ࣛࢱ࡟㛵ࡋ࡚ࡣ㸪⾲ 1 ࡟♧ࡉࢀࡓ ࢝ࢵࢺ࢜ࣇ࿘Ἴᩘ࡟ᑐࡋ࡚㔜␚࿘Ἴᩘࢆ⪃៖ࡋ࡚タィࡍࡿ ࡇ࡜࡛Ỵᐃࡉࢀࡿࠋ ⾲1 タィࣃ࣓࣮ࣛࢱ

Table 1. Design parameters.

Parameters Gain Cut-off frequency

[rad/s] Quality factor 1st _{Order LPF ܭ ൌ ͳ ߱ ൌ ʹɎ ή ʹͷͲ} 2nd _{Order LPF ܭ ൌ ͳ ߱ ൌ ʹɎ ή ʹͷͲ} ܳଵൌ ͳ ξʹ 4th _{Order LPF} ܭ_ଵൌ ͵ െͳ ܳ_ଶ ܭ_ଶൌ ͵ െͳ ܳ_ଷ ߱ ൌ ʹɎ ή ʹͷͲ ܳ_ଶൌ ͳ ʹ …‘•ߨ_ͺ ܳ_ଷൌ ͳ ʹ …‘•͵ߨ ͺ NF ܭ ൌ ͳ ߱ேிൌ ʹɎ ή ͷͲͲ ܳଵൌ ͳ ξʹ



Fig. 1. Bode diagram for each LPF. Frequency [Hz]

ᅗ2 NF ࡟㛵ࡍࡿ࣮࣎ࢻ⥺ᅗ

Fig. 2. Bode diagram for NF. Frequency [Hz]

 ゎᯒ᪉ἲ  ࢩ࣑࣮ࣗࣞࢩࣙࣥࣔࢹࣝࡢᵓᡂ ᅗ 3 ࡟ᇶᮏἼᡂศᢳ ฟࣇ࢕ࣝࢱࢆ௜ຍࡋࡓࢩ࣑࣮ࣗࣞࢩࣙࣥࣔࢹࣝࢆ♧ࡍࠋᅗ3 ࡼࡾ㸪ᮏ᳨ウ࡛ࡣ㛫᥋ᙧ࣋ࢡࢺࣝไᚚ⣔࡟ࡼࡾㄏᑟᶵࢆື సࡉࡏ㸪㧗࿘Ἴ㟁ᅽಙྕࢆ d ㍈୍ḟ㟁ᅽᣦ௧್࡟㔜␚ࡍࡿ ᵓᡂ࡜ࡋࡓࠋ㔜␚ࡍࡿ㧗࿘Ἴ㟁ᅽಙྕࡣୗᘧ࡛⾲ࡉࢀࡿࠋ ݒ_ଵௗ௛௙ൌ ܸ_ଵ௛௙•‹൫߱௛௙ݐ൯ ... (5)  ࡇࡇ࡛㸪ܸ_ଵ௛௙ࡣ㔜␚ಙྕࡢ᣺ᖜ㸪߱௛௙ࡣ㔜␚࿘Ἴᩘ࡛࠶ࡿࠋ ㄏᑟᶵࡢไᚚ࡟࠾࠸࡚ࡣ㸪㧗࿘Ἴᡂศࡣእ஘࡛࠶ࡿࡓࡵ㸪 ᇶᮏἼᡂศᢳฟࣇ࢕ࣝࢱࢆ⏝࠸࡚㧗࿘Ἴᡂศࢆ㝖ཤࡍࡿᚲ せࡀ࠶ࡿࠋලయⓗ࡟ࡣ㸪ㄏᑟᶵࣔࢹࣝࡼࡾᚓࡽࢀࡿ㧗࿘Ἴᡂ ศࢆྵࡴ dq ㍈୍ḟ㟁ὶ್࡟ᑐࡋ࡚ᇶᮏἼ㟁ὶࡢࡳࢆᢳฟ ࡋ㸪㟁ὶไᚚჾ࡬ࣇ࢕࣮ࢻࣂࢵࢡࡍࡿᵓᡂ࡛࠶ࡿࠋᮏ᳨ウ࡛ ࡣ㸪ᅗ3 ࡟♧ࡉࢀࡓࢩ࣑࣮ࣗࣞࢩࣙࣥࣔࢹࣝࢆ⏝࠸࡚㸪๓❶ ࡛タィࡋࡓྛࣇ࢕ࣝࢱࡢᣲືࢆゎᯒࡍࡿࠋ㧗࿘Ἴᡂศࡢ᣺ ᖜᢳฟࣇ࢕ࣝࢱࡢᵓᡂ࡟ࡘ࠸࡚ࡣḟ❶࡛㏙࡭ࡿࠋ  Ᏻᐃᛶゎᯒ ᅗ 4 ࡟ᇶᮏἼᡂศᢳฟࣇ࢕ࣝࢱࢆ௜ຍࡋ ࡓd ㍈㟁ὶไᚚჾࡢᵓᡂࢆ♧ࡍࠋᅗ 4 ࡼࡾ㸪㟁ὶไᚚჾࡣ PI㸦ẚ౛✚ศ㸧ไᚚ࡛ᵓᡂࡉࢀ㸪ࡑࡢฟຊࢆ㟁ᅽᣦ௧್࡜ࡋ ࡚ࣉࣛࣥࢺ࡛࠶ࡿㄏᑟᶵࣔࢹࣝ࡟ධຊࡍࡿࠋࡑࡢᚋ㸪ࣉࣛࣥ ࢺࡢฟຊ࡛࠶ࡿ㟁ὶ್࡟ᑐࡋ࡚ࣇ࢕ࣝࢱࢆ௓ࡋ࡚ࣇ࢕࣮ࢻ ࣂࢵࢡࡍࡿࠋྛࣇ࢕ࣝࢱ࡟ᑐࡍࡿᏳᐃᛶࡢ᳨ウࡣ㸪ᅗ4 ࡟♧ ࡉࢀࡓ⣔࡟╔┠ࡋ࡚⾜࠺ࠋලయⓗ࡟ࡣ㸪㛢࣮ࣝࣉఏ㐩㛵ᩘࢆ ồࡵ㸪ᴟ㞽Ⅼࢆィ⟬ࡍࡿࡇ࡜࡛Ᏻᐃᛶࡢ᳨ウࢆ⾜࠺ࠋ  ゎᯒ⤖ᯝ  ᇶᮏἼᡂศࡢᢳฟ ᅗ5 ࡟ྛ LPF ࡟࠾ࡅࡿᇶᮏἼᡂศ ࡢᢳฟ࡟㛵ࡍࡿ d ㍈୍ḟ㟁ὶࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࢆ♧ Current PI Control with Decoupling Control 1 ref d

v

v

Z

i

i

i

I

i

Z

y

Z

d-axis high frequency

voltage injection dq IM model including mechanical system Filter for fundamental component extraction TL ᅗ3 ࢩ࣑࣮ࣗࣞࢩࣙࣥࣔࢹࣝ

Fig. 3. Simulation model.

ᅗ4 ᇶᮏἼᡂศᢳฟࣇ࢕ࣝࢱ௜ࡁd㍈㟁ὶไᚚჾ

Fig. 4. d-axis current controller with fundamental extraction filter.

PI regulator Plant Each Filter (a) ࣇ࢕ࣝࢱ࡞ࡋ㸪୍ḟ LPF ฟຊ (b) ஧ḟ LPF ฟຊ㸪ᅄḟ LPF ฟຊ ᅗ5 d㍈୍ḟ㟁ὶ

Fig. 5. d-axis stator current.

(a) ࣇ࢕ࣝࢱ࡞ࡋ㸪୍ḟ LPF ㏻㐣㟁ὶධຊ

(b) ஧ḟ LPF ㏻㐣㟁ὶධຊ㸪ᅄḟ LPF ㏻㐣㟁ὶධຊ

ᅗ6 d㍈୍ḟ㟁ᅽ

❑⏣ ᾴ௓ ࡋ㸪ᅗ6 ࡟ྛ LPF ࠿ࡽࡢฟຊࢆ㟁ὶไᚚჾ࡬ࣇ࢕࣮ࢻࣂࢵ ࢡࡋࡓሙྜࡢd ㍈୍ḟ㟁ᅽࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࢆ♧ࡍࠋ ᅗ5㸦a㸧ཬࡧᅗ 6㸦a㸧ࡣ㸪ࣇ࢕ࣝࢱࢆ⏝࠸࡞࠸ሙྜ࡜୍ḟ LPF ࢆ⏝࠸ࡓሙྜࡢ⤖ᯝࢆ♧ࡋ࡚࠾ࡾ㸪ᅗ 5㸦b㸧ཬࡧᅗ 6 㸦b㸧ࡣ㸪஧ḟ LPF ࢆ⏝࠸ࡓሙྜ࡜ᅄḟ LPF ࢆ⏝࠸ࡓሙྜࡢ ⤖ᯝࢆ♧ࡋ࡚࠸ࡿࠋᅗ5㸦a㸧ࡼࡾ㸪୍ḟ LPF ࢆ⏝࠸ࡓሙྜ㸪 ࣇ࢕ࣝࢱ࡞ࡋࡢ⤖ᯝ࡜ẚ㍑ࡋ࡚㧗࿘Ἴᡂศࡀ㝖ཤࡉࢀ㸪ᇶ ᮏἼᡂศࢆᢳฟࡋ࡚࠸ࡿࡀᢳฟ⢭ᗘࡀప࠸ࡇ࡜ࡀศ࠿ࡿࠋ ࡑࡢࡓࡵ㸪ᅗ6㸦a㸧ࡼࡾ㸪㟁ὶไᚚჾࡢฟຊ࡛࠶ࡿ୍ḟ㟁ᅽ ࡣ㧗࿘Ἴᡂศࡲ࡛⿵ൾࡉࢀ㸪㧗࿘Ἴ㟁ᅽᣦ௧್௨ୖࡢ㟁ᅽ ࡜࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ୍᪉㸪ᅗ5㸦b㸧ࡼࡾ㸪 ஧ḟ LPF ࡜ᅄḟLPF ࢆ⏝࠸ࡓሙྜ㸪ᮏ᮶࡞ࡽࡤࣇ࢕ࣝࢱḟᩘࢆ㧗ࡃ ࡍࡿ࡜ᢳฟ⢭ᗘࡀ㧗ࡃ࡞ࡿࡣࡎ࡛࠶ࡿࡀ㸪୙Ᏻᐃ࡞ᣲື࡟ ࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋࡑࡢࡓࡵ㸪ᅗ 6㸦b㸧࡟࠾࠸࡚ࡶ 㟁ὶไᚚჾࡢୖ㝈ࡲ࡛㐩ࡋ㸪୙Ᏻᐃ࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ ࠿ࡿࠋࡇࡢཎᅉࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵ㸪ᅗ4 ࡟♧ࡉࢀࡓ⣔࡟ᑐ ࡍࡿᏳᐃᛶゎᯒࢆ⾜ࡗࡓࠋᅗ 7 ࡟ᴟ㞽Ⅼ࡟ࡼࡿゎᯒ⤖ᯝࢆ ♧ࡍࠋࡇࡇ࡛㸪͆™͇ࡣᴟ࡛࠶ࡾ㸪͆ࠐ͇ࡣ㞽Ⅼ࡛࠶ࡿࠋᅗ7 㸦a㸧ࡣ㸪୍ḟ LPF ࢆ⏝࠸ࡓሙྜࡢ⤖ᯝࢆ♧ࡋ࡚࠾ࡾ㸪ྠᅗ 㸦b㸧ࡣ㸪஧ḟ LPF ࢆ⏝࠸ࡓሙྜࡢ⤖ᯝࢆ♧ࡋ࡚࠸ࡿࠋࡲࡓ㸪 ྠᅗ㸦c㸧ࡣ㸪ᅄḟ LPF ࢆ⏝࠸ࡓሙྜࡢ⤖ᯝࢆ♧ࡋ࡚࠸ࡿࠋ ᅗ7㸦a㸧ࡼࡾ㸪୍ḟ LPF ࢆ⏝࠸ࡓሙྜ࡟ࡣᏳᐃ࡛࠶ࡿ࡜ุ ู࡛ࡁ㸪ᅗ5㸦a㸧࡟ᑐᛂࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋᅗ 7㸦b㸧 ཬࡧ㸦c㸧ࡼࡾ㸪஧ḟཬࡧᅄḟ LPF ࢆ⏝࠸ࡓሙྜ࡟ࡣ୙Ᏻᐃ 㡿ᇦ࡟ᴟࡀ఩⨨ࡋ࡚࠾ࡾ㸪ᅗ5㸦b㸧࡟ᑐᛂࡋ࡚࠸ࡿࡇ࡜ࡀ ศ࠿ࡿࠋࡇࡢ௦⾲᰿ࡣ㸪タィࣃ࣓࣮ࣛࢱࡢ࢝ࢵࢺ࢜ࣇ࿘Ἴᩘ ࢆ኱ࡁࡃࡍࡿ࡜Ᏻᐃ㡿ᇦ࡟⛣ືࡋ㸪ᑠࡉࡃࡍࡿ࡜୙Ᏻᐃ㡿 ᇦ࡬⛣ືࡍࡿࠋࡇࢀࡼࡾ㸪஧ḟཬࡧᅄḟLPF ࢆ⏝࠸ࡓሙྜ ࡟୙Ᏻᐃ࡞ᣲື࡟࡞ࡿཎᅉࡣ㸪㟁ὶไᚚჾࡢᖏᇦ࡟ᑐࡋ࡚ 㐺ษ࡞࢝ࢵࢺ࢜ࣇ࿘Ἴᩘ࡜࡞ࡗ࡚࠸࡞࠸ࡇ࡜ࡀཎᅉ࡛࠶ࡿ ࡜ゝ࠼ࡿࠋ஧ḟཬࡧᅄḟLPF ࢆ⏝࠸࡚Ᏻᐃ࡟ືసࡉࡏࡓ࠸ ሙྜ࡟ࡣ㸪࢝ࢵࢺ࢜ࣇ࿘Ἴᩘࢆ኱ࡁࡃࡍࢀࡤⰋ࠸ࡀᢳฟ⢭ ᗘࡀపࡃ࡞ࡿࡓࡵ㸪ᮏ᮶ࡢព࿡ࢆ࡞ࡉ࡞࠸ࡇ࡜࡜࡞ࡿࠋ୍ ᪉㸪ᅗ8 ཬࡧᅗ 9 ࡟ NF ࢆ⏝࠸ࡓሙྜࡢ⤖ᯝࢆ♧ࡍࠋᅗ 8 ࡣ㸪ࣇ࢕ࣝࢱࢆ⏝࠸࡞࠸ሙྜ࡜NF ࢆ⏝࠸ࡓሙྜࡢ d ㍈୍ḟ 㟁ὶࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࢆ♧ࡋ࡚࠾ࡾ㸪ᅗ9 ࡣ NF ࠿ࡽ (a) ୍ḟ LPF ࢆ⏝࠸ࡓሙྜ (b) ஧ḟ LPF ࢆ⏝࠸ࡓሙྜ (c) ᅄḟ LPF ࢆ⏝࠸ࡓሙྜ ᅗ7 LPF ࡜㟁ὶไᚚჾ࡟㛵ࡍࡿᴟ㞽Ⅼ

Fig. 7. Pole-Zero for LPF and current controller.

ᅗ8 d㍈୍ḟ㟁ὶ㸦NF ฟຊ㸧

Fig. 8. d-axis stator current (output of NF).

ᅗ9 d㍈୍ḟ㟁ᅽ㸦NF ㏻㐣㟁ὶධຊ㸧

Fig. 9. d-axis stator voltage (input of current passed through NF).

ࡢฟຊࢆ㟁ὶไᚚჾ࡬ࣇ࢕࣮ࢻࣂࢵࢡࡋࡓሙྜࡢ d ㍈୍ḟ 㟁ᅽࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࢆ♧ࡋ࡚࠸ࡿࠋᅗ8 ࡼࡾ㸪NF ࢆ⏝࠸ࡓሙྜ㸪ᇶᮏἼᡂศࢆ⢭ᗘⰋࡃᢳฟ࡛ࡁ࡚࠸ࡿࡇ࡜ ࡀศ࠿ࡿࠋࡲࡓ㸪ᅗ9 ࡼࡾ㸪NF ࡢฟຊࢆ㟁ὶไᚚჾ࡬ࣇ࢕ ࣮ࢻࣂࢵࢡࡋࡓሙྜ࡟࠾࠸࡚ࡶ㧗࿘Ἴ㟁ᅽᣦ௧್࡜୍⮴ࡋ ࡓ㟁ᅽ࡜࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ ௨ୖࡢ⤖ᯝࡼࡾ㸪NF ࢆ⏝࠸ࡓሙྜ࡟௚ࡢ LPF ࡜ẚ㍑ࡋ࡚ ⢭ᗘⰋࡃᇶᮏἼᡂศࢆᢳฟ࡛ࡁࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ  㧗࿘Ἴ᣺ᖜࡢᢳฟ ᅗ10 ࡟㧗࿘Ἴᡂศࡢ᣺ᖜࢆᢳฟࡍ ࡿࣇ࢕ࣝࢱࡢᵓᡂࢆ♧ࡍࠋ㧗࿘Ἴ᣺ᖜࡣ㸪㧗࿘Ἴಙྕ㔜␚࡟ ࡼࡿࢭࣥࢧࣞࢫไᚚ࡟࠾࠸࡚㸪஧ḟ☢᮰఩⨨ཬࡧ㏿ᗘࡢ᥎ ᐃ࡟ᚲせ࡜࡞ࡿࡓࡵ㸪㧗⢭ᗘ࡟ᢳฟࡍࡿࡇ࡜ࡀ㔜せ࡜࡞ࡿࠋ ᅗ10 ࡼࡾ㸪㧗࿘Ἴᡂศࢆ㔜␚ࡋࡓ㟁ᅽࢆㄏᑟᶵ࡟༳ຍࡋࡓ ሙྜ㸪ࡑࡢฟຊ࡛࠶ࡿ㟁ὶࡣ㧗࿘Ἴᡂศࢆྵࡴࡇ࡜࡜࡞ࡿࠋ ࡑࡇ࡛㸪BPF ࢆ⏝࠸࡚㧗࿘Ἴᡂศࡢࡳࢆᢳฟࡋ࡚ྠ୍ࡢ࿘ Ἴᩘᡂศࢆ᥃ࡅྜࢃࡏ㸪ࡑࡢᚋ㸪㧗࿘Ἴ᣺ᖜᢳฟ⏝࡟タィࡉ ࢀࡓNF ࡟㏻ࡍࡇ࡜࡛᣺ᖜࡢᢳฟࢆ⾜࠺ࠋᅗ 11 ࡟㧗࿘Ἴᡂ ศ࡟㛵ࡍࡿ d ㍈୍ḟ㟁ὶࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࢆ♧ࡍࠋ ࡇࡇ࡛㸪ᅗ11 ࡣ BPF ࡢฟຊ࡜ NF ࡢฟຊࢆ♧ࡋ࡚࠸ࡿࠋᅗ 11 ࡼࡾ㸪NF ࢆ⏝࠸ࡓሙྜ㸪BPF ࡢฟຊ࡛࠶ࡿ㧗࿘Ἴ㟁ὶ࠿ ࡽࡑࡢ᣺ᖜࢆ⢭ᗘⰋࡃᢳฟ࡛ࡁ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ  ࡲ࡜ࡵ ᮏ✏࡛ࡣ㸪㧗࿘Ἴ㟁ᅽಙྕ㔜␚࡟ࡼࡿㄏᑟᶵ㥑ືࢩࢫࢸ ࣒࡛฼⏝ࡍࡿಙྕศ㞳⏝ࣇ࢕ࣝࢱࡢタィ࡜ࡑࡢゎᯒ࡟ࡘ࠸ ࡚ሗ࿌ࡋࡓࠋ⤖ᯝ࡜ࡋ࡚㸪୍ḟ㸪஧ḟཬࡧᅄḟࡢLPF ࡜ẚ ㍑ࡋ࡚ NF ࢆ⏝࠸ࡓሙྜ࡟ᇶᮏἼᡂศཬࡧ㧗࿘Ἴ᣺ᖜࢆ⢭ ᗘⰋࡃᢳฟྍ⬟࡛࠶ࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓࠋ ௒ᚋ㸪ᮏ᳨ウ࡟࠾࠸࡚タィࡋࡓNF ࢆ FPGA ࢆ⏝࠸ࡓࢹ ࢕ࢪࢱࣝࣇ࢕ࣝࢱ࡜ࡋ࡚ᐇ⿦ࡋ㸪㧗࿘Ἴ㟁ᅽಙྕ㔜␚࡟ࡼ ࡿ☢Ẽ㣬࿴✺ᴟᛶ࡜ࢫࣟࢵࢺ㧗ㄪἼࢆ฼⏝ࡍࡿࢭࣥࢧࣞࢫ ࣋ࢡࢺࣝไᚚ⣔ࡢᵓ⠏ࢆ┠ᣦࡍࠋ ᮏ◊✲ࡣᮏᏛ࢚ࣞࢡࢺࣟࢽࢡࢫ◊✲ᡤࡢ2019 ᖺᗘ᪂௵ࢫ ࢱ࣮ࢺ࢔ࢵࣉᨭ᥼ไᗘ࡟ࡼࡾᐇ᪋ࡋࡓࡶࡢ࡛࠶ࡿࠋ  ᩥ   ⊩

㸯R. Kurosawa : “The Basic Theory and the System Configration of Vector Control for Induction Machine. II. The System Configuration of High Performance Vector Control.”, IEEJ Trans. IA, Vol.117, No.5, pp.538-540 (1997-5) (in Japanese)

㯮⃝Ⰻ୍㸸ࠕㄏᑟᶵࡢ࣋ࢡࢺࣝไᚚࡢᇶ♏࡜ไᚚࢩࢫࢸ࣒ࡢᐇ㝿ᵓ

ᡂ II㸬㧗ᛶ⬟࣋ࢡࢺࣝไᚚࢩࢫࢸ࣒ࡢᐇ㝿ᵓᡂࠖ㸪㟁Ꮫㄽ D㸪

Vol.117㸪No.5, pp.538-540 (1997-5)

㸰 H. Umida : “The Basic Theory and the System Configration of Vector Control for Induction Machine. III. The System Configuration of Speed Sensorless Vector Control.”, IEEJ Trans. IA, Vol.117, No.5, pp.541-543 (1997-5) (in Japanese)

ᾏ⏣ⱥಇ㸸ࠕㄏᑟᶵࡢ࣋ࢡࢺࣝไᚚࡢᇶ♏࡜ไᚚࢩࢫࢸ࣒ࡢᐇ㝿ᵓ ᡂIII㸬㏿ᗘࢭࣥࢧࣞࢫ࣋ࢡࢺࣝไᚚࢩࢫࢸ࣒ࡢᐇ㝿ᵓᡂࠖ㸪㟁Ꮫㄽ D㸪Vol.117㸪No.5, pp.541-543 (1997-5)

㸱 T. Ohtani, E. Watanabe, H. Takasaki, and N. Takada : “Approach of Vector-Controlled Induction Motor Drives without Speed Sensor”, IEEJ Trans.IA, Vol.107, No.2, pp.199-206 (1987-2) (in Japanese)

኱㇂⥅฼࣭Ώ㎶ⱥྖ࣭㧗ᓮ⚽⣖࣭㧗⏣ᚨᖾ㸸ࠕ࣋ࢡࢺࣝไᚚ࡟ࡼࡿㄏ

ᑟ㟁ືᶵࡢ㏿ᗘࢭࣥࢧࣞࢫࢻࣛ࢖ࣈࠖ㸪㟁ᏛㄽD㸪Vol.107㸪No.2, pp.199-206 (1987-2)

㸲H. Sugimoto, S. Tamai, and M. Yano : “Speed Sensor-Less Vector Control of Induction Motor Using Model Reference Adaptive System”, IEEJ

Trans.IA, Vol.108, No.3, pp.306-313 (1988-3) (in Japanese)

ᮡᮏⱥᙪ࣭⋢஭ఙ୕࣭▮㔝ᫀ㞝㸸ࠕࣔࢹࣝつ⠊㐺ᛂࢩࢫࢸ࣒ࢆ㐺⏝ࡋ

ࡓㄏᑟ㟁ືᶵࡢ㏿ᗘࢭࣥࢧࣞࢫ࣋ࢡࢺࣝไᚚࠖ㸪㟁ᏛㄽD㸪Vol.108㸪 No.3, pp.306-313 (1988-3)

㸳H. Kubota, M. Ozaki, K. Matsuse, and T. Nakano : “Direct Field Oriented Control of Induction Motor without Speed Sensors using Adaptive Flux Observer”, IEEJ Trans.IA, Vol.111, No.11, pp.954-960 (1991-11) (in Japanese)

ஂಖ⏣ᑑኵ࣭ᑿᓮṇ๎࣭ᯇ℩㈉つ࣭୰㔝ᏕⰋ㸸ࠕ㐺ᛂ஧ḟ☢᮰࢜ࣈࢨ

࣮ࣂࢆ⏝࠸ࡓㄏᑟ㟁ືᶵࡢ㏿ᗘࢭࣥࢧࣞࢫ┤᥋ᙧ࣋ࢡࢺࣝไᚚࠖ㸪㟁 ᏛㄽD㸪Vol.111㸪No.11, pp.954-960 (1991-11)

㸴D.W. Chung, J.I. Ha, S.K. Sul, K. Ide, I. Murokita, and T. Sawa : “Controller Design of Sensorless Induction Machine by High Frequency Voltage Injection”, IEEJ Trans.IA, Vol.120, No.11, pp.1257-1264 (2000-11) (in Japanese)

D.W. Chung࣭J.I. Ha࣭S.K. Sul࣭஭ᡭ⪔୕࣭ᐊ໭ᗄ☻࣭ἑಇ⿱㸸ࠕㄏᑟ

㟁ືᶵࡢ㧗࿘Ἴ㟁ᅽ㔜␚࡟ࡼࡿ㏿ᗘࢭࣥࢧࣞࢫ࣋ࢡࢺࣝไᚚࠖ㸪㟁Ꮫ

ㄽD㸪Vol.120㸪No.11, pp.1257-1264 (2000-11)

㸵C. Caruana, G.M. Asher, and M. Sumner : “Performance of HF Signal Injection Techniques for Zero-Low-Frequency Vector Control of Induction Machines Under Sensorless Conditions”, IEEE Trans.IE, Vol.53, No.1, pp.225-238 (2006-2)

㸶H. Kiyotake, K Shinohara, and K. Yamamoto : “Rotor Speed Detection Method for Vector Control of Induction Motor without Speed Sensor Utilizing Slot Harmonics”, IEEJ Trans.IA, Vol.127, No.7, pp.739-746 (2007-7) (in Japanese)

ΎṊ༤ᩥ࣭⠛ཎ຾ḟ࣭ᒣᮏྜྷ㑻㸸ࠕㄏᑟ㟁ືᶵ㏿ᗘࢭࣥࢧࣞࢫ࣋ࢡࢺ

ࣝไᚚ࡟࠾ࡅࡿࢫࣟࢵࢺ㧗ㄪἼࢆ฼⏝ࡋࡓ㏿ᗘ᳨ฟἲࠖ㸪㟁ᏛㄽD㸪

Vol.127㸪No.7, pp.739-746 (2007-7)

㸷R. Raute, C. Caruana, C.P. Staines, J. Cilia, M. Sumner, and G.M. Asher : “Sensorless Control of Induction Machines at Low and Zero Speed by Using PWM Harmonics for Rotor-Bar Slotting Detection”, IEEE Trans.IA, Vol.46, No.5, pp.1989-1998 (2010-9/10)

ᅗ10 㧗࿘Ἴ᣺ᖜᢳฟࣇ࢕ࣝࢱࡢᵓᡂ

Fig. 10. Constitution of high frequency amplitude extraction filter.

dq IM

model BPF NF

ᅗ11 㧗࿘Ἴᡂศ࡟㛵ࡍࡿd㍈୍ḟ㟁ὶ

Fig. 11. d-axis stator current for high frequency component.