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損失電流による水トリー検出のシミュレーション

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(1)

៊ᄬ㔚ᵹߦࠃࠆ᳓࠻࡝࡯ᬌ಴ߩࠪࡒࡘ࡟࡯࡚ࠪࡦ

દ⮮ ᷕ

㧖,1

㧘㋈ᧁ 㓷ผ

**

㧘㋈ᧁ ᥍ᒾ

㧘ศ᧛ ᣹

**

㧔2006 ᐕ 4 ᦬ 11 ᣣฃઃ㧘2006 ᐕ 11 ᦬ 22 ᣣฃℂ㧕

Simulation of Water Tree Detection by Loss Current

Atsushi ITO*

,1

, Masafumi SUZUKI**, Haruhiko SUZUKI* and Noboru YOSHIMURA**

(Received April 11, 2006 ; Accepted November 22, 2006)

Degradation of XLPE cable by water trees is still one of the serious factors of the cable accident.

Therefore, not only the prevention of water tree but also the detection of water tree at early stage is very

important. Until now, a lot of methods which can detect water trees have been studied. In these

techniques, the loss current measurement is paid to attention as a method that can detect water trees by

nondestructive. Many studies have been carried out including numerical simulations, in order to understand

the mechanisms of loss current generation and the relationship between the progress of water tree and the

loss current. In the previous studies, the shape of water tree was not considered though the length of water

tree had been considered in the simulation of loss current measurements. However, water tree changes it’s

shape by the situation, therefore, in water tree’s simulation, it is necessary to consider not only the length of

water tree but also it’s shape.

In the present paper, we examined the possibility of the detection of water

tree by the loss current measurement while changing the shape and the length of water tree.

䋱㪅 䈲䈛䉄䈮 ᨞ᯅࡐ࡝ࠛ࠴࡟ࡦ㧔XLPE㧕ࠤ࡯ࡉ࡞ߦ߅ߌࠆ᳓࠻࡝࡯ ഠൻߪ㧘੹ߥ߅ࠤ࡯ࡉ࡞੐᡿ߩਥⷐߥේ࿃ߩ৻ߟߣߥߞߡ ޿ࠆ㧚ࠤ࡯ࡉ࡞ߩ⛘✼⎕უߦ઻߁஗㔚੐᡿ߪ␠ળ⊛ߦ߽ᄢ ߈ߥ໧㗴ߣߥࠆߎߣ߆ࠄ㧘᳓࠻࡝࡯ߩ⊒↢ᛥ೙ߪ൩⺰ߩߎ ߣ㧘ᣢ⸳ߩࠤ࡯ࡉ࡞ߦ߅޿ߡᣧᦼߦ᳓࠻࡝࡯ߩ⊒↢ࠍ⍮ࠆ ߎߣߪᭂ߼ߡ㊀ⷐߢ޽ࠆ㧚ߎߩߚ߼㧘⋥ᵹṳࠇ㔚ᵹ㧘⺃㔚 ․ᕈ㧘ᱷ⇐㔚⩄ߥߤߦᵈ⋡ߒߚ㕖ᵴ✢ߢߩഠൻ⸻ᢿᴺ߿⋥ ᵹ㊀⇥㧘ᵴ✢tanǬ㧘៊ᄬ㔚ᵹߥߤߦ⌕⋡ߒߚᵴ✢ߢߩഠൻ ⸻ᢿᴺ߇⎇ⓥߐࠇߡ޿ࠆ㧚ߎࠇࠄߩഠൻ⸻ᢿᴺߩਛߢ,៊ᄬ 㔚ᵹ᷹ቯᴺߪᵴ✢⁁ᘒߢ㕖⎕უߦࠃࠅ᳓࠻࡝࡯ᬌ಴ߩน⢻ ᕈ߇޽ࠆᚻᴺߣߒߡᵈ⋡ߐࠇߡ޿ࠆ㧚 ᳓࠻࡝࡯⊒↢⹜ᢱߩ៊ᄬ㔚ᵹࠍ᷹ቯߒߚ႐ว㧘៊ᄬ㔚ᵹ ᵄᒻߦᱡ߇⷗ࠄࠇ㧘ߎߩࠃ߁ߥᵄᒻߩᱡߺߦࠃࠆ㜞⺞ᵄ߇ ⊒↢ߔࠆ㧚․ߦ㜞⺞ᵄߩ߁ߜᦨᄢߢ޽ࠆ╙㧟㜞⺞ᵄ㔚ᵹߣ ᳓࠻࡝࡯ኸᴺ㧘੤ᵹ⎕უ㔚࿶╬ߣߩ㑆ߦߪ⋧㑐㑐ଥ߇޽ࠆ ߣ⸒ࠊࠇߡ޿ࠆ㧚៊ᄬ㔚ᵹߩᱡߺߪ᳓࠻࡝࡯ߩ㕖✢ᒻߥ㔚 ᳇વዉ․ᕈߦ⿠࿃ߔࠆߣ⠨߃ࠄࠇ㧘ߎߩࠃ߁ߥ⃻⽎ࠍ⺑᣿ ߔࠆߚ߼ࠪࡒࡘ࡟࡯࡚ࠪࡦᚻᴺࠍ฽߻ᄙߊߩ⎇ⓥ߇ߥߐࠇ ߡ޿ࠆ㧚଀߃߫㧘Ꮉ੗ࠄߪ᳓࠻࡝࡯ߩ㕖✢ᒻߥ㔚࿶㧙㔚ᵹ ․ᕈࠍ෺ᦛ✢㑐ᢙ߿ᄙ㗄ᑼߦࠃࠅࡕ࠺࡞ൻߒ㧘᳓࠻࡝࡯⊒ ↢⹜ᢱࠍᧂഠൻㇱߣഠൻㇱߩ㧞ጀ߆ࠄߥࠆࡑࠢࠬ࠙ࠚ࡞㧙 ࡢࠣ࠽࡯ဳߩ⺃㔚૕ߣߺߥߒߡ៊ᄬ㔚ᵹߩ⸃ᨆࠍ⹜ߺߡ߅ ࠅ㧘ࡕ࠺࡞ߩࡄ࡜ࡔ࡯࠲ࠍㆡಾߦ⸳ቯߔࠆߣㆊ෰ߦႎ๔ߐ ࠇߡ޿ࠆ៊ᄬ㔚ᵹߩ․ᓽ߇ౣ⃻ߢ߈ࠆߎߣࠍ᣿ࠄ߆ߦߒߡ ޿ࠆ1)㨪4) ߒ߆ߒߥ߇ࠄ㧘᳓࠻࡝࡯ߪߘߩ⊒↢▎ᚲ߿⊒↢᧦ઙߦࠃ ࠅߘߩᒻ⁁ࠍ᭽ޘߦᄌ߃ࠆ㧚ᓥߞߡ㧘╩⠪ࠄߪ᳓࠻࡝࡯ߩ િ߮ߣ៊ᄬ㔚ᵹߩ㑐ଥߩߺࠍ⼏⺰ߔࠆߩߢߪߥߊ㧘ߘߩᒻ ⁁ߩ㆑޿߹ߢ߽⠨ᘦߒߚࠪࡒࡘ࡟࡯࡚ࠪࡦ߇ᔅⷐߢ޽ࠆߣ ⠨߃╬ଔ࿁〝ࡕ࠺࡞ࠍ↪޿ߚ⎇ⓥࠍⴕ޿㧘᳓࠻࡝࡯ߩિ߮ ߇หߓߢ޽ߞߡ߽ߘߩᒻ⁁߇⇣ߥࠆߣⷰኤߐࠇࠆ៊ᄬ㔚ᵹ ᵄᒻߦ㆑޿߇޽ࠆน⢻ᕈࠍ⷗಴ߒߚ5)㧚 ࠠ࡯ࡢ࡯࠼㧦᳓࠻࡝࡯㧘╬ଔ࿁〝㧘ࠪࡒࡘ࡟࡯࡚ࠪࡦ㧘៊ ᄬ㔚ᵹ * ⑔ፉᎿᬺ㜞╬ኾ㐷ቇᩞ㔚᳇Ꮏቇ⑼㧔970-8034 ޿ࠊ߈Ꮢ ᐔ਄⨹Ꮉሼ㐳የ30㧕

Fukushima National College of Technology, 30 Nagao Kamiarakawa Taira, Iwaki, 970-8034, Japan

** ⑺↰ᄢቇᎿቇ⾗Ḯቇㇱ㔚᳇㔚ሶᎿቇ⑼㧔010-8502 ⑺↰

Ꮢᚻᒻቇ࿦↸1-1㧕

Engineering and Resource Science, Akita University 1-1 Tegata Gakuenmachi, Akita 010-8502, Japan

(2)

ᵄᢙߩ⇣ߥࠆᱜᒏᵄ੤ᵹ㔚࿶ࠍශടߒߚ႐วߤߩࠃ߁ߥ៊ ᄬ㔚ᵹ߇ᓧࠄࠇࠆ߆ࠍࠪࡒࡘ࡟࡯࡚ࠪࡦߒ㧘ߎߩ⚿ᨐ߆ࠄ ࠃࠅᣧߊ᳓࠻࡝࡯ࠍᬌ⍮ߢ߈ࠆ᧦ઙࠍ᣿ࠄ߆ߦߔࠆߎߣࠍ ⋡⊛ߣߒߚ㧚 䋲㪅 ╬ଔ࿁〝䊝䊂䊦 ᧄ⎇ⓥߦ߅޿ߡ߽㧘వߩ⺰ᢥ5)ߣห᭽ߦ࿑㧝ߦ␜ߔࠃ߁ ߥෘߐ1mm ߩ XLPE ⹜ᢱߦ᳓࠻࡝࡯߇⊒↢ߒߚ⁁ᘒࠍᮨ ᡆߔࠆ㧚⹦⚦ߪవߩ⺰ᢥߦ⹦ߒߊㅀߴࠄࠇߡ޿ࠆߩߢߎߎ ߢߪഀᗲߔࠆ߇㧘⹜ᢱߩෘߐߪ᏷ߦᲧߴߡ⭯ߊ㧘㔚⇇ߪ❑ ᣇะߢ޽ࠆߚ߼㧘᳓࠻࡝࡯ࠍ࿑㧝ߩࠃ߁ߦ਄ㇱ᳓㔚ᭂࠍ฽ ߻㔚⇇ߦᐔⴕߥᢿ㕙ߦᛩᓇߒߚ2 ᰴరࡕ࠺࡞ߢ⠨߃ࠆߎߣ ߦߔࠆ㧚߹ߚ㧘XLPE ⹜ᢱߪᮮᣇะߦ 60 ಽഀ㧘❑ᣇะߦ 30ಽഀߐࠇߡ߅ࠅߘࠇߙࠇߩႺ⇇ㇱಽߦᛶ᛫R෸߮ࠦࡦ࠺ ࡦࠨC ߩਗ೉࿁〝߆ࠄߥࠆࠗࡦࡇ࡯࠳ࡦࠬ Z ࠍ㈩⟎ߔࠆ㧚 ᛶ᛫R ෸߮ࠦࡦ࠺ࡦࠨ C ߩ୯ߪ XLPE ⹜ᢱߩታ᷹࠺࡯࠲ࠍ ၮߦ㧘R=1.0Tǡ㧘C=0.012pF ߣ᳿ቯߐࠇߚ㧚 ታ㓙ߩCV ࠤ࡯ࡉ࡞ߢߪ㧘ౝ↰ࠄ6)㧘ᾢỈࠄ7)ߩႎ๔ߦ߽ ޽ࠆࠃ߁ߦ㧘ᒻ⁁߇౞ᒻߦㄭ޿᳓࠻࡝࡯߿㔚⇇ᣇะߦ⚦㐳 ߊિ߮ߚ᳓࠻࡝࡯ߥߤ߇ⷰኤߐࠇߡ޿ࠆ㧚᳓࠻࡝࡯ᒻ⁁ߪ㧘 ߘߩ⊒↢⿠ὐ߿㔚࿶ශട᧦ઙߥߤߦࠃࠅ᭽ޘߦᄌൻߔࠆߣ ᕁࠊࠇࠆ߇㧘ᧄ⎇ⓥߢߪ਄⸥ߩႎ๔ߦ޽ࠆᒻ⁁ࠍෳ⠨ߦ㧘 ◲නൻߩߚ߼XLPE ⹜ᢱߦ࿑㧞(a)ߩࠃ߁ߦ౞ᒻߦ᳓࠻࡝࡯ ߇ ⊒ ↢ 㧘 િ ዷ ߒ ߚ ࡕ ࠺ ࡞ 㧘(b)ߩࠃ߁ߦᮮ㐳ߩᬦ౞ᒻ 㧔L1:L2=1:1.5㧕ߦ᳓࠻࡝࡯߇⊒↢ߒߚࡕ࠺࡞㧘(c)ߩࠃ߁ߦ

OO



O

O

XLPE



O

O

࿑㧝 ᳓࠻࡝࡯ߩ᭎⇛࿑ Fig.1 Schematics of water tree.

ᵹߩ㑐ଥࠍᲧセߔࠆߚ߼ߦ઒ቯߐࠇߚ㧚߹ߚ㧘઒ቯߒߚࡕ ࠺࡞(b)ߣ(c)ߦ߅޿ߡᬦ౞ߩ⍴ゲߣ㐳ゲߩᲧ߇⇣ߥࠆ߇㧘ߎ ߎߢߪ⍴ゲߣ㐳ゲߩᲧ₸ߦࠃࠆ៊ᄬ㔚ᵹߩ㆑޿ࠍᬌ⸛ߔࠆ ߩߢߪߥߊ㧘ᒻ⁁ߩ㆑޿ߦࠃࠆ៊ᄬ㔚ᵹߩ㆑޿ߦ⌕⋡ߒߚ ߚ߼㧘ࡕ࠺࡞૞ᚑߩኈᤃߥᲧ₸ࠍណ↪ߒߚ㧚ߥ߅㧘᳓࠻࡝ ࡯ߩ㐳ߐߪߘࠇߙࠇߩࡕ࠺࡞ߦ߅޿ߡ㔚ᭂ㑆㐳ߦኻߒߡ 20㧑㧘40㧑㧘60㧑㧘80㧑߹ߢિዷߒߚࡕ࠺࡞ࠍ⠨߃ߚ㧚ߎ ߎߢ㧘᳓࠻࡝࡯ౝߦ฽߹ࠇࠆࠗࡦࡇ࡯࠳ࡦࠬZ ࠍᣂߚߦ㔚 ࿶ଐሽဳᛶ᛫ߦ឵߃㧘࿁〝ࠪࡒࡘ࡟࡯࠲(PSpice)ࠍ↪޿ߡ⸃ ᨆࠍⴕߞߚ㧚ߥ߅㧘㔚࿶ଐሽဳᛶ᛫ߩ㔚࿶㧙㔚ᵹ․ᕈߪᧄ ੗ࠄߩ⽾ㅢ᳓࠻࡝࡯ߩ㔚࿶㧙㔚ᵹ․ᕈߩታ᷹୯ 8)ࠃࠅ᳿ቯ ߒߚ5)㧚 䋳㪅 ⸘▚⚿ᨐ䈫ᬌ⸛ ೨ㅀߩࠃ߁ߦ᳿ቯߐࠇߚ3 ⒳㘃ߩᒻ⁁㧘4 ⒳㘃ߩિ߮㧔⸘ 12 ⒳㘃㧕ߩ᳓࠻࡝࡯ࡕ࠺࡞ߘࠇߙࠇߦኻߒߡ㧘ᱜᒏᵄ੤ᵹ 㔚࿶ߩ๟ᵄᢙࠍ50Hz㧘100Hz㧘200Hz㧘400Hz㧘600Hz㧘800Hz㧘 1kHz㧔7 ㅢࠅ㧕㧘ታല୯ࠍ 1kV㧘2kV㧘4kV㧘6kV㧘8kV㧘10kV 㧔6 ㅢࠅ㧕ߣᄌ߃ߚ㧘ว⸘ 42 ⒳㘃ߩ㔚࿶ශട᧦ઙߢ៊ᄬ㔚 ᵹࠍ᳞߼ߚ㧚એਅߦ㧘᳓࠻࡝࡯ߩᒻ⁁ߏߣߦ߹ߣ߼ߡ⚿ᨐ ࠍᢛℂߔࠆ㧚 䋳㪅䋱 ౞ᒻ䊝䊂䊦 ࿑㧟ߦ▚಴ߐࠇߚ៊ᄬ㔚ᵹߩ৻଀ߣߒߡ㧘᳓࠻࡝࡯߇㔚ᭂ 㑆ߩ20㧑߹ߢિዷߒߚ႐วߦ๟ᵄᢙ 200Hz㧘ታല୯ 1kV㧘2kV㧘 4kV㧘6kV㧘8kV㧘10kV ߩ㔚࿶ࠍශടߒߚ႐วࠍ␜ߔ㧚࿑ࠃࠅ㧘 ߎߩ๟ᵄᢙ㧔200Hz㧕ߦ߅޿ߡߪ㧘៊ᄬ㔚ᵹߩ୯ߪ߶߷ශട㔚 ࿶ߦᲧ଀ߒߡჇടߒߡ޿ࠆ੐߇ಽ߆ࠆ㧚߹ߚ㧘ߎߩ࿑߆ࠄߪ ៊ᄬ㔚ᵹᵄᒻߩᄢ߈ߥᱡߺߪ⹺߼ࠄࠇߥ޿㧚៊ᄬ㔚ᵹ߇ᱡ߻ ᄢ߈ߥේ࿃ߣߒߡ㧘╙3 㜞⺞ᵄߩሽ࿷߇ᜰ៰ߐࠇߡ߅ࠅ㧘ߎ ߩ╙3 㜞⺞ᵄߩሽ࿷ࠍᬌ⍮ߔࠆߎߣߢ㧘᳓࠻࡝࡯ߩሽ࿷ࠍᬌ ⍮ߢ߈ࠆน⢻ᕈ߇޽ࠆ㧚 ߘߎߢ㧘ᧄ⎇ⓥߢߪᓧࠄࠇߚ៊ᄬ㔚ᵹᵄᒻࠍࡈ࡯࡝ࠛᄌ឵ߒ㧘 ╙3 㜞⺞ᵄߩ୯ࠍၮᧄᵄߢഀࠆߎߣߢ╙ 3 㜞⺞ᵄߩᲧ₸ࠍ᳞ 㪉 㪇䋦 㪋 㪇䋦 㪍 㪇䋦 㪏 㪇䋦 㪣 㪈 㪣 㪉 㪉 㪇䋦 㪋 㪇䋦 㪍 㪇䋦 㪏 㪇䋦 㪣 㪈 㪣 㪉 㪉 㪇䋦 㪋 㪇䋦 㪍 㪇䋦 㪏 㪇䋦 㪣 㪈 㪣 㪉 (a)౞ᒻࡕ࠺࡞ (b)ᮮ㐳ᬦ౞ᒻࡕ࠺࡞ (c)❑㐳ᬦ౞ᒻࡕ࠺࡞ ࿑㧞 ᳓࠻࡝࡯ࡕ࠺࡞ Fig.2 Water tree model.

(3)

࿑㧟 ៊ᄬ㔚ᵹᵄᒻާ200Hz㧘20㧑િዷި Fig.3 Loss current waveform.

߼ߚ㧚࿑㧠(a)㨪(d)ߦ᳓࠻࡝࡯߇ 20%㨪80㧑߹ߢિዷߒߚ㓙ߩ ╙3 㜞⺞ᵄߩᲧ₸ࠍශട㔚࿶ߩ๟ᵄᢙ㧘ታല୯ࠍࡄ࡜ࡔ࡯࠲ ߣߒߡ␜ߔ㧚ߎࠇࠄߩ࿑ࠃࠅ㧘޿ߕࠇߩ᳓࠻࡝࡯િዷഀวߢ ߽ශട㔚࿶߇㜞޿߶ߤ㧘߹ߚ๟ᵄᢙ߇㜞޿߶ߤ╙3 㜞⺞ᵄߩ ഀวߪᄢ߈ߊߥߞߡ߅ࠅ㧘៊ᄬ㔚ᵹᵄᒻߩᱡ߇ᄢ߈ߊߥߞߡ ޿ࠆ੐߇ಽ߆ࠆ㧚ߎࠇߪ᳓࠻࡝࡯߇㕖✢ᒻߥ㔚᳇વዉ․ᕈࠍ ᜬߞߡ޿ࠆߚ߼ߢ㧘ශട㔚࿶ࠍ਄ߍࠆߎߣߦࠃࠅ㔚ᵹ߇㕖✢ ᒻߦჇടߒߚߚ߼ߢ޽ࠆ㧚ห᭽ߦ๟ᵄᢙࠍ਄ߍࠆߎߣߦࠃࠅ ᧂഠൻߩXLPE ㇱಽߩ㔚࿶ಽᜂ߇ᷫࠅ㧘᳓࠻࡝࡯ഠൻㇱߩ㔚 ࿶ಽᜂ߇਄᣹ߒ㧘㔚ᵹ߇㕖✢ᒻߦჇടߔࠆߎߣߦࠃࠅᱡߺ߽ ᄢ߈ߊߥࠆ㧚ߒ߆ߒ㧘หߓિዷഀวߢᲧセߔࠆߣ㧘ශട㔚࿶ ߹ߚߪ๟ᵄᢙߩჇടߦኻߔࠆ╙3 㜞⺞ᵄߩഀวߩჇടߪ㘻๺ ௑ะ߇⷗ࠄࠇࠆ㧚଀߃߫િዷഀว߇20㧑ߩ႐วߦ߅޿ߡශട 㔚࿶ࠍ10kV ߣߒߚ႐ว㧘๟ᵄᢙ߇ 100Hz ߆ࠄ 600Hz ߹ߢߪ ╙3 㜞⺞ᵄߩᲧ₸߇ᄢ߈ߊჇടߒߡ޿ࠆߩߦ㧘600Hz એ਄ߢ ߪჇട௑ะ߇㊰ൻߒߡ޿ࠆ㧚ห᭽ߦශട㔚࿶ߩ๟ᵄᢙࠍ1kHz ߦ࿕ቯߔࠆߣ㧘ශട㔚࿶߇1kV ߆ࠄ 6kV ߹ߢߪ╙ 3 㜞⺞ᵄߩ Ყ₸߇ᕆჇߒߡ޿ࠆ߇㧘ߘࠇએ਄ߢߪ߿߿㊰ൻߩ௑ะ߇⷗ࠄ ࠇࠆ㧚 ᳓࠻࡝࡯િዷߦኻߔࠆ╙3 㜞⺞ᵄߩᲧ₸ߩᄌൻࠍ⷗ࠆߣ㧘 ޿ߕࠇߩශട㔚࿶᧦ઙߦ߅޿ߡ߽᳓࠻࡝࡯િዷߦ઻޿Ყ₸ߪ Ⴧടߒߡ޿ࠆ㧚ߎࠇ߆ࠄ᳓࠻࡝࡯ߩિዷߣ╙3 㜞⺞ᵄߩᲧ₸ ߦߪ㑐ㅪ߇޽ࠆ੐߇⏕⹺ߐࠇࠆ㧚಴᧪ࠆߛߌ᳓࠻࡝࡯⊒↢ߩ ೋᦼᲑ㓏ߢߎࠇࠍ៊ᄬ㔚ᵹߩᱡ߆ࠄᬌ಴ߔࠆߎߣࠍ⋡⊛ߣߔ ࠆߣ㧘៊ᄬ㔚ᵹߩ᷹ቯߪ಴᧪ࠆߛߌ㜞޿㔚࿶㧘๟ᵄᢙߢⴕ߁ ੐߇ᦸ߹ߒ޿㧚ߒ߆ߒ㧘ታ↪ᕈࠍ⠨߃ࠆߣ಴᧪ࠆߛߌශട㔚 ࿶෸߮๟ᵄᢙߪᛥ߃ߚ޿㧚᳓࠻࡝࡯ߩ㔚᳇․ᕈߪ᭽ޘߢ޽ࠆ ߇㧘੹࿁઒ቯߒߚ᳓࠻࡝࡯ߢߪ200Hz㧘6kV ޽ࠆ޿ߪ 100Hz㧘 8kV⒟ᐲߩශട㔚࿶ߢၮᧄᵄߦኻߔࠆ╙3㜞⺞ᵄߩᲧ₸߇1% ࠍ⿥߃㧘៊ᄬ㔚ᵹߩᱡ߆ࠄ᳓࠻࡝࡯ሽ࿷ߩᬌ⍮ߩน⢻ᕈ߇޽ ࠆߣ⠨߃ࠄࠇࠆ㧚 㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(a) Water tree expanded to 20%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(b) Water tree expanded to 40%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(c) Water tree expanded to 60%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪩 㪸㫋 㫀㫆 䋨䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(d) Water tree expanded to 80%

࿑㧠 ╙3 㜞⺞ᵄߩᲧ₸

Fig.4 Ratio of third harmonics. 㪄㪊㪅㪇㪜㪄㪇㪏 㪄㪉㪅㪇㪜㪄㪇㪏 㪄㪈㪅㪇㪜㪄㪇㪏 㪇㪅㪇㪜㪂㪇㪇 㪈㪅㪇㪜㪄㪇㪏 㪉㪅㪇㪜㪄㪇㪏 㪊㪅㪇㪜㪄㪇㪏 㪇㪅㪇㪇㪌 㪇㪅㪇㪇㪍 㪇㪅㪇㪇㪎 㪇㪅㪇㪇㪏 㪇㪅㪇㪇㪐 㪇㪅㪇㪈 㪫㫀㫄㪼䋨䌳䋩 㪣 㫆 㫊㫊 㪺 㫌 㫉㫉 㪼 㫅 㫋䋨 㪘 䋩 㪈㫂㪭 㪉㫂㪭 㪋㫂㪭 㪍㫂㪭 㪏㫂㪭 㪈㪇㫂㪭

(4)

ᭂ㑆ߩ20㧑߹ߢિዷߒߚ႐วߦ๟ᵄᢙ 200Hz ߩ㔚࿶ࠍශ ടߒߚ႐วࠍ␜ߔ㧚ߎߩ᧦ઙߪ࿑㧟ߦ␜ߒߚ౞ᒻߩ᳓࠻࡝ ࡯ࡕ࠺࡞ߦട߃ߚ㔚࿶ߣหߓߢ޽ࠆ㧚࿑㧡ࠃࠅ㧘ᮮ㐳ߩᬦ ౞ᒻ᳓࠻࡝࡯ࡕ࠺࡞ߢ߽િዷഀว߇20㧑ߩ႐วߪ㧘៊ᄬ㔚 ᵹߪ߶߷ශട㔚࿶ߦᲧ଀ߒߡჇടߒߡ޿ࠆ੐߇ಽ߆ࠆ㧚߹ ߚ㧘⋡ⷞ߆ࠄߪᄢ߈ߥᵄᒻߩᱡߺߪ⹺߼ࠄࠇߥ޿㧚 㪄㪊㪅㪇㪜㪄㪇㪏 㪄㪉㪅㪇㪜㪄㪇㪏 㪄㪈㪅㪇㪜㪄㪇㪏 㪇㪅㪇㪜㪂㪇㪇 㪈㪅㪇㪜㪄㪇㪏 㪉㪅㪇㪜㪄㪇㪏 㪊㪅㪇㪜㪄㪇㪏 㪇㪅㪇㪇㪌 㪇㪅㪇㪇㪍 㪇㪅㪇㪇㪎 㪇㪅㪇㪇㪏 㪇㪅㪇㪇㪐 㪇㪅㪇㪈 㪫㫀㫄㪼䋨䌳䋩 㪣 㫆 㫊㫊 㪺 㫌 㫉㫉 㪼 㫅 㫋䋨 㪘 䋩 㪈㫂㪭 㪉㫂㪭 㪋㫂㪭 㪍㫂㪭 㪏㫂㪭 㪈㪇㫂㪭 ࿑5 ៊ᄬ㔚ᵹᵄᒻާ200Hz㧘20㧑િዷި

Fig.5 Loss current waveform.

ߎߎߢ߽㧘౞ᒻߩ᳓࠻࡝࡯ࡕ࠺࡞ߩ⸃ᨆߣห᭽ߦ㧘៊ᄬ 㔚ᵹᵄᒻࠍࡈ࡯࡝ࠛᄌ឵ߒ㧘╙3 㜞⺞ᵄߩၮᧄᵄߦኻߔࠆ Ყ₸ࠍ᳞߼ߚ㧚⚿ᨐࠍ࿑㧢(a)㨪(d)ߦ␜ߔ㧚᳓࠻࡝࡯ߩિዷ ߦኻߔࠆ╙3 㜞⺞ᵄߩഀวߩᄌൻ㧘㔚࿶ශട᧦ઙߩ㆑޿ߦ ࠃࠆ╙3 㜞⺞ᵄߩഀวߩᄌൻߪ᭎ߨ౞ᒻߩ᳓࠻࡝࡯ࡕ࠺࡞ ߩ႐วߣห᭽ߢ㧘᳓࠻࡝࡯߇િ߮ࠆ߶ߤ╙3 㜞⺞ᵄߩഀว ߪჇടߒ㧘ශട㔚࿶୯߿๟ᵄᢙ߇Ⴧടߔࠆ߶ߤ╙3 㜞⺞ᵄ ߩഀวߪჇടߔࠆ㧚߹ߚ㧘࿑㧠ߦ␜ߒߚ౞ᒻߩ᳓࠻࡝࡯ࡕ ࠺࡞ߩ╙3 㜞⺞ᵄߩᲧ₸ߣᲧセߔࠆߣ㧘଀߃߫ 200Hz㧘6kV ߩ᧦ઙߦ߅޿ߡ㧘᳓࠻࡝࡯߇20%િዷߒߚ႐วߪ౞ᒻࡕ࠺ ࡞ߢ╙3 㜞⺞ᵄߩᲧ₸߇ 1.40 ߢ޽ߞߚ߽ߩ߇ᮮ㐳ᬦ౞ࡕ࠺ ࡞ߢߪ 0.92㧘80%િዷߒߚࡕ࠺࡞ߢߪ౞ᒻࡕ࠺࡞ߩ႐วߩ 9.78%߇ᮮ㐳ᬦ౞ࡕ࠺࡞ߢߪ 7.95%ߣ㧘หߓ᳓࠻࡝࡯િዷഀ วߦ߅޿ߡ㧘ᮮ㐳ᬦ౞ᒻ᳓࠻࡝࡯ࡕ࠺࡞ߩ╙3 㜞⺞ᵄߩᲧ ₸ߪ߿߿ᷫዋߒߡ޿ࠆ㧚ߎࠇߪ㧘᳓࠻࡝࡯߇ᐢ߇ߞߚߎߣ ߢ᳓࠻࡝࡯ㇱಽߩ㔚࿶ಽᜂ߇ᷫዋߒߚߚ߼㧘㔚࿶㧙㔚ᵹ․ ᕈߩ㕖✢ᒻᕈ߇ᷫዋߒߚߚ߼ߢ޽ࠆ㧚ߎࠇࠃࠅ㧘หߓ᳓࠻ ࡝࡯ߩિዷഀวߢ޽ߞߡ߽㧘᳓࠻࡝࡯߇㔚⇇ߦု⋥ߥᣇะ ߦᐢ߇ࠅߥ߇ࠄિዷߒߚ႐วߦߪ៊ᄬ㔚ᵹᵄᒻߩᱡ߇ዋߥ ߊߥࠆ੐߇ಽ߆ࠆ㧚៊ᄬ㔚ᵹߩᱡ߆ࠄ᳓࠻࡝࡯ሽ࿷ߩ᦭ή ࠍᬌ⍮ߒࠃ߁ߣߔࠆ㓙ߦߪߎߩ㆑޿ߪ㊀ⷐߢ޽ࠅ㧘㔚⇇ߦ ኻߒߡု⋥ᣇะߦᐢ߇ߞߚ᳓࠻࡝࡯ߪᬌ಴߇ᄙዋ㔍ߒߊߥ ࠆน⢻ᕈ߇޽ࠆ㧚 ౞ᒻࡕ࠺࡞ߩ႐วߣห᭽ߦ㧘᳓࠻࡝࡯ߩೋᦼᲑ㓏ߢߩᬌ 㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(a) Water tree expanded to 20%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪩 㪸㫋 㫀㫆 䋨䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐㩿㪟㫑㪀 㪭㫆㫃㫋㪸㪾㪼㩿㪭㪀

(b) Water tree expanded to 40%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪩 㪸㫋 㫀㫆 䋨䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐㩿㪟㫑㪀 㪭㫆㫃㫋㪸㪾㪼㩿㪭㪀

(c) Water tree expanded to 60%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐㩿㪟㫑㪀 㪭㫆㫃㫋㪸㪾㪼㩿㪭㪀

(d) Water tree expanded to 80%

࿑㧢 ╙3 㜞⺞ᵄߩᲧ₸

(5)

಴ߩน⢻ᕈࠍᬌ⸛ߔࠆߚ߼㧘િዷഀว20㧑ߩ႐วߦᵈ⋡ߔ ࠆߣ㧘200Hz㧘6kV ߩ㔚࿶ࠍශടߒߡ៊ᄬ㔚ᵹࠍ᷹ቯߒߚ ႐ว㧘╙3 㜞⺞ᵄߩᲧ₸ߪ౞ᒻࡕ࠺࡞ߩ႐วࠃࠅ 10%߶ߤ ૐਅߔࠆ߇㧘ၮᧄᵄߦኻߒߡ0.9%⒟ᐲߪ޽ࠅ㧘߹ߛᬌ಴ߩ น⢻ᕈߪ޽ࠆߣ⠨߃ࠄࠇࠆ㧚 䋳㪅䋳 ❑㐳ᬦ౞ᒻ䊝䊂䊦 ᰴߦ㧘࿑㧞(c)ߦ␜ߒߚ❑㐳ߦિዷߒߚ᳓࠻࡝࡯ࡕ࠺࡞ߦ ߟ޿ߡห᭽ߦ៊ᄬ㔚ᵹᵄᒻߩ⸃ᨆࠍⴕߞߚ㧚ߎߩࡕ࠺࡞ߢ ߪ㐳ㄝ㧔L1㧕ߣ⍴ㄝ㧔L2㧕ߩᲧ߇ 1:0.5 ߢ޽ࠅ㧘᳓࠻࡝࡯ ߩ㕙Ⓧߪ౞ᒻࡕ࠺࡞ߩ1/2㧘ᮮ㐳ᬦ౞ᒻࡕ࠺࡞ߩ 1/3 ߣߥࠆ㧚 ▚಴ߐࠇߚ៊ᄬ㔚ᵹߩ৻଀ߣߒߡ㧘ߎࠇ߹ߢߣห᭽ߦ㧘 ᳓࠻࡝࡯߇20%િዷߒߚ႐วߦ㧘200Hz㧘1kV ߆ࠄ 10kV ߩ 㔚࿶ࠍශടߒߡ▚಴ߒߚ៊ᄬ㔚ᵹᵄᒻࠍ࿑㧣ߦ␜ߔ㧚࿑ࠃ ࠅ៊ᄬ㔚ᵹߩ୯ߪශട㔚࿶ߦ߶߷Ყ଀ߒߡჇടߒߡ޿ࠆ㧚 ߹ߚ㧘࿑㧟ߩ౞ᒻ᳓࠻࡝࡯ࡕ࠺࡞㧘࿑㧡ߩᮮ㐳ᬦ౞ᒻࡕ࠺ ࡞ߣᲧセߒߡ㧘៊ᄬ㔚ᵹߩᄢ߈ߐߦߪ߶ߣࠎߤᄌൻ߇ߥ޿㧚 ߎࠇ߆ࠄ㧘៊ᄬ㔚ᵹߩᄢ߈ߐߪߘߩ⊒↢ೋᦼᲑ㓏ߢߪ㧘᳓ ࠻࡝࡯ߩ㕙Ⓧߩᓇ㗀ߪ߶ߣࠎߤฃߌߕ㧘િዷഀวߦࠃߞߡ ߩߺ᳿ቯߐࠇࠆߣ⠨߃ࠄࠇࠆ㧚 ᰴߦ౞ᒻ߅ࠃ߮ᮮ㐳ᬦ౞ᒻ᳓࠻࡝࡯ࡕ࠺࡞ߣห᭽ߦ៊ᄬ 㔚ᵹᵄᒻߦ߅ߌࠆ╙3 㜞⺞ᵄߩၮᧄᵄߦኻߔࠆᲧ₸ࠍ㧘᳓ ࠻࡝࡯િዷഀวߏߣߦ࿑㧤ߦ␜ߔ㧚❑㐳ߩᬦ౞ᒻ᳓࠻࡝࡯ ࡕ࠺࡞ߦ߅ߌࠆ╙3 㜞⺞ᵄߩഀวߪ㧘వ⒟ߣห᭽ߦ 200Hz㧘 6kV ߩ᧦ઙࠍ଀ߦขࠆߣ㧘᳓࠻࡝࡯߇ 20%િዷߒߚ႐ว 1.99㧘80%િዷߒߚ႐ว 13.17 ߣઁߩ౞ᒻ߿ᮮ㐳ᬦ౞ᒻ᳓࠻ ࡝࡯ࡕ࠺࡞ߩߘࠇࠃࠅᄢ߈ߊ㧘 40%㨪100㧑⒟ᐲᄢ߈ߥ୯ ߣߥߞߡ޿ࠆ㧚❑㐳ᬦ౞ᒻࡕ࠺࡞ߢߪ㧘᳓࠻࡝࡯ㇱߩ㕙Ⓧ ߪઁߩࡕ࠺࡞ߦᲧߴߡዊߐ޿߇㧘᳓࠻࡝࡯ㇱߩ㔚࿶ಽᜂ߇ 㜞޿㧔㔚⇇߇㓸ਛߔࠆ㧕ߚ߼ߦ㧘㔚࿶㧙㔚ᵹ․ᕈߩ㕖✢ᒻ ᕈ߇ᒝߊ⴫ࠇߚ⚿ᨐߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚 ߎߩ⚿ᨐ߆ࠄ㧘㔚⇇ᣇะߦ㍈ߊિዷߒߚ᳓࠻࡝࡯ߢߪ៊ ᄬ㔚ᵹߩᱡ߇ᄢ߈ߊ㧘៊ᄬ㔚ᵹᵄᒻߩᱡ߆ࠄ᳓࠻࡝࡯ߩᬌ 㪄㪊㪅㪇㪜㪄㪇㪏 㪄㪉㪅㪇㪜㪄㪇㪏 㪄㪈㪅㪇㪜㪄㪇㪏 㪇㪅㪇㪜㪂㪇㪇 㪈㪅㪇㪜㪄㪇㪏 㪉㪅㪇㪜㪄㪇㪏 㪊㪅㪇㪜㪄㪇㪏 㪇㪅㪇㪇㪌 㪇㪅㪇㪇㪍 㪇㪅㪇㪇㪎 㪇㪅㪇㪇㪏 㪇㪅㪇㪇㪐 㪇㪅㪇㪈 㪫㫀㫄㪼䋨䌳䋩 㪣 㫆 㫊㫊 㪺㫌 㫉㫉 㪼㫅 㫋䋨 㪘 䋩 㪈㫂㪭 㪉㫂㪭 㪋㫂㪭 㪍㫂㪭 㪏㫂㪭 㪈㪇㫂㪭 ࿑7 ៊ᄬ㔚ᵹᵄᒻާ200Hz㧘20㧑િዷި

Fig.7 Loss current waveform.

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪊㪌 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(a) Water tree expanded to 20%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪊㪌 㪩 㪸㫋 㫀㫆 䋨䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐䋨㪟㫑䋩 㪭㫆㫃㫋㪸㪾㪼䋨㪭䋩

(b) Water tree expanded to 40%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪊㪌 㪩 㪸㫋 㫀㫆 䋨䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐㩿㪟㫑㪀 㪭㫆㫃㫋㪸㪾㪼㩿㪭㪀

(c) Water tree expanded to 60%

㪌㪇 㪈㪇㪇 㪉㪇㪇 㪋㪇㪇 㪍㪇㪇 㪏㪇㪇 㪈㫂 㪈㫂 㪋㫂 㪏㫂 㪇 㪌 㪈㪇 㪈㪌 㪉㪇 㪉㪌 㪊㪇 㪊㪌 㪩 㪸㫋 㫀㫆 䋨 䋦 䋩 㪝㫉㪼㫈㫌㪼㫅㪺㫐㩿㪟㫑㪀 㪭㫆㫃㫋㪸㪾㪼㩿㪭㪀

(d) Water tree expanded to 80%

࿑8 ╙ 3 㜞⺞ᵄߩᲧ₸

(6)

㜞⺞ᵄߩഀวߣ᳓࠻࡝࡯ߩિ߮ߦߪ৻ቯߩ㑐ଥ߇޽ࠅ㧘᳓ ࠻࡝࡯߇ㅴዷߔࠆߦߟࠇߡ╙3 㜞⺞ᵄߩഀว߇Ⴧടߔࠆ੐ ߇ಽ߆ࠆ㧚ߒ߆ߒ㧘ߘߩᄌൻߪ᳓࠻࡝࡯ߩᒻ⁁ߦࠃࠅ⇣ߥ ࠅ㧘㔚⇇ߦု⋥ߥᣇะߦᐢ߇ߞߚ᳓࠻࡝࡯ߪ㔚⇇ᣇะߦ㍈ ߊિዷߒߚ᳓࠻࡝࡯ࠃࠅ៊ᄬ㔚ᵹߩᱡ߇ዊߐߊ㧘᳓࠻࡝࡯ ߩᬌ಴߇㔍ߒ޿੐߇ಽ߆ࠆ㧚 ߹ߚ㧘੹࿁઒ቯߒߚ᳓࠻࡝࡯ࡕ࠺࡞ߢߪ㧘޿ߕࠇ߽200Hz㧘 6kV ⒟ᐲߩ㔚࿶ࠍශടߒߡ៊ᄬ㔚ᵹࠍ᷹ቯߔࠆߎߣߢ㧘╙ 3 㜞⺞ᵄߩᲧ₸߇ 1%ࠍ⿥߃㧘᳓࠻࡝࡯⊒↢ߩᲧセ⊛ೋᦼᲑ 㓏ߦ߅޿ߡ㧘᳓࠻࡝࡯ሽ࿷ߩ᦭ή߇ᬌ⍮ߢ߈ࠆߩߢߪߥ޿ ߆ߣ⠨߃ࠄࠇࠆ㧚 䋳㪅䋴 ᳓䊃䊥䊷ᒻ⁁䈫៊ᄬ㔚ᵹᵄᒻ ߎࠇ߹ߢߪ᳓࠻࡝࡯ᬌ಴ߩน⢻ᕈࠍតࠆߚ߼㧘᳓࠻࡝࡯ િዷഀว20㧑ߩೋᦼᲑ㓏ߦߟ޿ߡਥߦ⼏⺰ߒߡ߈ߚ㧚ߎߩ ߚ߼࿑㧟㧘࿑ 5㧘࿑㧣ߩ៊ᄬ㔚ᵹᵄᒻߦߪ⋡ⷞߢߩᄢ߈ߥ ᱡߪ⏕⹺ߢ߈ߥ޿㧚৻ᣇߢ╩⠪ࠄߪ᳓࠻࡝࡯ߩિዷഀว߇ หߓߢ߽㧘ᒻ⁁ߦࠃࠅ៊ᄬ㔚ᵹߩᱡߺ߇⇣ߥࠆߎߣࠍႎ๔ ߒߚ 5)㧚ߎߩߚ߼㧘੹࿁઒ቯߒߚࡕ࠺࡞ߢ߽ߎߩ⃻⽎߇⃻ ࠇࠆ߆⏕⹺ߒߚ㧚ߎߎߢߪᲧセ⊛ᱡߩᄢ߈ߥ㧘᳓࠻࡝࡯િ ዷഀว߇80㧑㧘ශട㔚࿶ߩ 10kV㧘๟ᵄᢙ 1kHz ߩ႐วߦߟ ޿ߡ㧘౞ᒻ㧘ᮮ㐳࡮❑㐳ᬦ౞ᒻߩ᳓࠻࡝࡯ࡕ࠺࡞ߩ៊ᄬ㔚 ᵹࠍ࿑㧥ߦ␜ߔ㧚࿑ࠃࠅ㧘޿ߕࠇߩࡕ࠺࡞ߦ߅޿ߡ߽៊ᄬ 㔚ᵹᵄᒻߪᱜᒏᵄߩࡇ࡯ࠢ߇ߟ߱ࠇ㧘ੑߟߩࡇ࡯ࠢ߇⷗ࠄ ࠇࠆࠃ߁ߦߥߞߡ޿ࠆ㧚ߒ߆ߒ㧘౞ᒻߩ᳓࠻࡝࡯ࡕ࠺࡞ߣ ᮮ㐳ᬦ౞ᒻࡕ࠺࡞ࠍᲧセߔࠆߣ㧘ᮮ㐳ᬦ౞ᒻࡕ࠺࡞ߩᣇ߇ ᓟࠈߩࡇ࡯ࠢ߇⓭಴ߒߡ޿ࠆ㧚৻ᣇ㧘౞ᒻࡕ࠺࡞ߣ❑㐳ᬦ ౞ᒻࡕ࠺࡞ߩᲧセߢߪ㧘❑㐳ᬦ౞ᒻࡕ࠺࡞ߩ៊ᄬ㔚ᵹߪ೨ ߩࡇ࡯ࠢ߇ࠃࠅ⓭಴ߒߡ޿ࠆ੐߇ಽ߆ࠆ㧚ߎߩࠃ߁ߦ㧘੹ ࿁ߩࠪࡒࡘ࡟࡯࡚ࠪࡦ߆ࠄ߽᳓࠻࡝࡯ߩિዷഀว߇หߓߢ ߽㧘ߘߩᒻ⁁߇⇣ߥࠆߣ៊ᄬ㔚ᵹᵄᒻߪ⇣ߥࠆ੐߇⏕⹺ߐ ࠇߚ㧚߹ߚ㧘㔚ᵹ୯ߪ㧘ᮮ㐳ᬦ౞ᒻࡕ࠺࡞㧪౞ᒻࡕ࠺࡞㧪 㪄㪉㪅㪇㪜㪂㪇㪇 㪄㪈㪅㪌㪜㪂㪇㪇 㪄㪈㪅㪇㪜㪂㪇㪇 㪄㪌㪅㪇㪜㪄㪇㪈 㪇㪅㪇㪜㪂㪇㪇 㪌㪅㪇㪜㪄㪇㪈 㪈㪅㪇㪜㪂㪇㪇 㪈㪅㪌㪜㪂㪇㪇 㪉㪅㪇㪜㪂㪇㪇 㪈㪅㪇 㪈㪅㪉 㪈㪅㪋 㪈㪅㪍 㪈㪅㪏 㪉㪅㪇 Time(ms) Lo ss cu rr en t(µ A ) 㪺㫀㫉㪺㫃㪼 㪼㫃㫃㫀㫇㫊㪼㩿㫎㫀㪻㪼㪀 㪼㫃㫃㫀㫇㫊㪼㩿㫅㪸㫉㫉㫆㫎㪀 ࿑㧥 ฦࡕ࠺࡞ߩ៊ᄬ㔚ᵹᵄᒻ

Fig.9 Loss current waveform of each model.

䋴㪅 䉁䈫䉄 ᧄ⎇ⓥߢߪ㧘᳓࠻࡝࡯ߩሽ࿷ࠍߘߩ⊒↢ೋᦼߦ៊ᄬ㔚ᵹ ߩᱡ߆ࠄᬌ಴ߔࠆน⢻ᕈߦߟ޿ߡᬌ⸛ߔࠆߚ߼㧘ᒻ⁁ߩ⇣ ߥࠆ3 ⒳㘃ߩ᳓࠻࡝࡯ࡕ࠺࡞ߦ߅޿ߡ╬ଔ࿁〝ࡕ࠺࡞ࠍ↪ ޿ߚࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕߞߚ㧚߹ߚ㧘᳓࠻࡝࡯ߩિ߮ߩ ߺߥࠄߕ㧘ߘߩᒻ⁁ߦࠃࠅ៊ᄬ㔚ᵹᵄᒻߦ㆑޿߇⷗ࠄࠇࠆ ߆ࠍ⏕⹺ߒߚ㧚᳓࠻࡝࡯ߩિ߮߿ᒻ⁁ߪ⊒↢⿠ὐ߿㔚࿶ශ ട᧦ઙߢ᭽ޘߦᄌൻߔࠆߚ߼㧘ᧄ⎇ⓥߢᓧࠄࠇߚ⚿ᨐߪో ߡߩ᳓࠻࡝࡯ᒻ⁁ߦኻߒߡㆡ↪ߢ߈ࠆࠊߌߢߪߥߊ㧘ᒻ⁁ ࠍᮨᡆߒߚ৻ㇱߩ᳓࠻࡝࡯ᒻ⁁ߦኻߒߡ␜ߐࠇߚߎߣߢ޽ ࠆ㧚એਅߦᧄ⎇ⓥߢᓧࠄࠇߚᚑᨐࠍ߹ߣ߼ࠆ㧚 (1)᳓࠻࡝࡯⊒↢ߩೋᦼᲑ㓏㧔િዷഀว 20㧑㧕ߢߪ㧘៊ᄬ㔚 ᵹᵄᒻࠍࡈ࡯࡝ࠛᄌ឵ߒߚ⚿ᨐ㧘㔚⇇ᣇะߦ⚦ߊિዷߒ ߚ᳓࠻࡝࡯ߪᐢߊિዷߒߚ᳓࠻࡝࡯ߦᲧߴ╙3 㜞⺞ᵄߩ ഀว߇ᄢ߈޿੐߇ಽ߆ߞߚ㧚 (2)઒ߦ╙ 3 㜞⺞ᵄߩၮᧄᵄߦኻߔࠆഀว߇ 1%⒟ᐲߣߥࠆ ᧦ઙࠍ᳞߼ࠆߣ㧘ᧄ⎇ⓥߢ↪޿ߚࡕ࠺࡞ߢߪ200Hz㧘6kV ⒟ᐲߩශട㔚࿶߇ᔅⷐߣᕁࠊࠇࠆ㧚ߒ߆ߒ㧘೨ㅀߩࠃ߁ ߦ᳓࠻࡝࡯ߩᒻ⁁ߦࠃࠅ╙3 㜞⺞ᵄߩഀวߪ⇣ߥࠅ㧘㔚 ⇇ᣇะߦ⚦ߊિዷߒߚ᳓࠻࡝࡯ߢߪ㧘ᄙዋૐ޿㔚࿶ߢ߽ ╙3 㜞⺞ᵄߩഀวߪ 1%ߦߥࠆ㧚ታ㓙ߩࠤ࡯ࡉ࡞ߦ߅޿ ߡߤߩࠃ߁ߥ᧦ઙ߇ᦨㆡ߆ߪᦝߦᬌ⸛ߔࠆᔅⷐ߇޽ࠆ㧚 (3)᳓࠻࡝࡯߇ 80%⒟ᐲㅴዷߔࠆߣ㧘៊ᄬ㔚ᵹᵄᒻߪ㧘િዷ ഀว߇หߓߢ߽᳓࠻࡝࡯߇⊒↢ߒߡ޿ࠆ㕙Ⓧ㧔૕Ⓧ㧕߇ Ⴧടߔࠆ߶ߤჇ߃ࠆ㧚߹ߚ㧘᳓࠻࡝࡯ߩᒻ⁁߇⇣ߥࠆߣ ᵄᒻߩᒻ⁁ߪᄢ߈ߊ⇣ߥࠆ㧚 ෳ⠨ᢥ₂ 1)Ꮉ੗ੑ㇢㧘ຠᎹẢ৻㧘ਛ᧛ୃᐔ㧘Ỉ੖㇢㧦㔚ቇ⺰ A,119 (1999),92 2)Ꮉ੗ੑ㇢㧘⩆ፉߺࠁ߈㧘᧘ ⧷㧘ຠᎹẢ৻㧘ᶏ⠧ᴧᐽశ㧘 ਛ᧛ୃᐔ㧘Ỉ੖㇢㧦㔚ቇ⺰A,120 (2000),92 3)Ꮉ੗ੑ㇢㧦㕒㔚᳇ቇળ⹹,24(2000)245 4)ਛ᧛ୃᐔ㧘દ᧲ೣᐘ㧘Ꮉ੗ੑ㇢㧘ຠᎹẢ৻㧘ᶏ⠧ᴧᐽశ㧦 㔚ቇ⺰A,120 (2000),1114 5)㋈ᧁ㓷ผ㧘દ⮮ᷕ㧘ศ᧛᣹㧦㔚ቇ⺰ A,125(2005)367 6)ౝ↰సᏆ㧘ጟᧄ㆐Ꮧ㧦㔚ቇ⺰ A,124(2004)935 7)ᾢỈቁᄦ, ၳ↰᣽ᒄ㧘᧖ጊ⌀৻㧘ᯅ⹣ବᚑ㧘⼱ᕡᄦ㧦 㔚ቇ⺰B,117(1997)1538 8)ᧄ੗⷗ੑ㧘ᒄᵤ⎇৻㧘⚦ᳯൎᐢ㧘ᓼਣ੉㢬㧘᧻↢ືᴦ㧦 㔚᳇ቇળ⺃㔚࡮⛘✼᧚ᢱ⎇ⓥળ⾗ᢱ㧘DEI-95-37(1995)

参照

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A wave bifurcation is a supercritical Hopf bifurcation from a stable steady constant solution to a stable periodic and nonconstant solution.. The bifurcating solution in the case

Related to this, we examine the modular theory for positive projections from a von Neumann algebra onto a Jordan image of another von Neumann alge- bra, and use such projections

[25] Nahas, J.; Ponce, G.; On the persistence properties of solutions of nonlinear dispersive equa- tions in weighted Sobolev spaces, Harmonic analysis and nonlinear

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

Abstract The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S 3 − K ,