シャドーイング練習: 26 - How does harmonic phase shifting work including a detailed mathematical explanation to reduce s - 動画で英語スピーキングを学ぶ

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In this video we're going to talk about a subject that a lot of people ask questions about, harmonic cancellation with phase shifting transformers.

So with two variable frequency drives connected to a common bus and motors connected to those drives,

the harmonics that come out of those typical six pulse drives will have a current waveform that look like this.

So the drives will look like this and what happens is the total current is basically just two times that.

So it's one plus one equals two.

Before we put isolation transformers and phase shifting transformers in here to get cancellation, we're going to demonstrate how harmonics add up on power systems.

So we're going to go to a part of the system

over here where we're actually going to show you how that works.

And we're going to actually combine these harmonics from drives.

We're going to put two different drives on and show how those harmonics add up together.

So we'll turn one on.

We'll take a look at the waveform and you see the harmonics coming out of one of the drives.

And now if we take a look at the harmonic spectrum,

the harmonic spectrum from that has your typical fifth and seventh harmonics, what you'd expect.

And so the fifth harmonic right now is about 10 .9 amps.

Now if I turn on the second drive what we end up with is about twice that amount of harmonic current.

So as expected one plus one equals two and that's the harmonics that come out of both drives.

Now, what we're going to do is we're going to turn those drives off.

And we're going to go back to the paper

and we're going to describe what happens when we put two drives on but with phase shifting transformers.

OK.

So now with phase shifting transformers, we would put in this situation where we have,

for example, a delta y on one side, delta y on one side.

And this could be a delta delta, or in fact, it could be a delta zigzag, which effectively gives you a zero degree phase shift.

So you get zero degrees here, and you get 30 degrees here.

So the same harmonics come out of these drives that we saw in the other picture.

OK?

But what happens up here is this transformer has zero degree phase shift.

The harmonics come out the same.

This transformer, the harmonics kind of look like this, or the waveform kind of looks like this.

And so when you add these two together, we get what's not now a six -pulse system,

but rather a 12 -pulse system and we end up with a current that looks fairly linear.

So let me show you that in the actual waveforms that we can see from the two drives coming on.

So I'm going to turn this over to a combination where we put one drive on

and if we look at that situation, we have the isolation transformer where we're going around.

It's a delta -delta transformer.

Now if we look at the actual waveforms from that, the harmonics look very similar.

But if we look at the actual waveforms, the harmonics look the same.

But then when we put on the fourth drive, or the other drive, where we have the phase shifting, or the 30 degree phase shift,

you can see that now we have what's similar to a 12 pulse situation.

So now if I go to my harmonic spectrum, we actually have the fifth and seventh go away.

Now if we turn drive number one off,

what we're going to see is the harmonic currents come back from that drive that's now on,

the one that went through the delta Y transformer, and we can now see that the wave shape is,

as I showed you, a little bit different.

Now what's interesting about this is let's just look at one of the harmonics, the fifth harmonic.

Okay, and what we're going to do is we're going to look at the fifth harmonic here on phase A.

And the fifth harmonic is 9 amps at minus 62 degrees.

Now what we're going to do is we're going to turn that drive off, and we're going to turn drive number one back on.

and we'll see that the harmonic currents from that drive come in at about the same amount or magnitude,

about almost 9 amps again, but the phase angle is about 114 degrees.

So now if we put both of them on together, we put the other drive on with it,

now we get that fifth and seventh to cancel out, but your eleventh and thirteenth basically adds up together.

So going back to the paper now, let's talk about how that worked.

Again, we had no phase shift here, so we expect the wave shape to add up to be similar,

or to go through the transformer and look very similar.

This one here, the wave shape changed.

And this is a 30 degree phase shift.

So we're saying the 5th and 7th from here cancel with the 5th and 7th from here.

And what happens is we don't end up with 5th and 7th flowing this way.

So no 5th and 7th going this way, but we do end up with 11th and 13th, which ends up being this 12 -pulse system.

How does that work?

Well, if you take each harmonic order, the positive, negative, and zero sequence harmonics for each, we say plus, minus, zero,

plus, minus, zero, and that pattern continues.

Plus, minus, zero, plus, minus.

So if we look at just the fundamental, the fundamental we say is a vector,

a phasor, that rotates in this direction.

So phase A is at zero, rotates this direction, phase B follows, and phase C follows that.

So a negative sequence harmonic would actually rotate the opposite direction.

So how do we get the fifth and seventh to cancel from one side to the other?

First of all, all of these harmonics on the left side stay exactly the same.

The fifth harmonic on the right side is five times as fast as the 60 hertz, so the phase shift is 5 times 30 degrees,

but it's actually in the opposite direction.

It's a negative sequence harmonic.

It's in the opposite direction of the 60 Hertz.

So if the 60 Hertz is going ahead 30 degrees, and this one goes the other direction 30 degrees,

but times 5, we end up with 150 degrees this way and 30 degrees this way the net effect is 180 degrees.

It's like we always talk about two vehicles leaving at the same time, going opposite directions.

One goes 30 this way, 30 miles this way or whatever, and we say the other one goes 150 miles this way.

The difference in that is 180 miles.

In this case, we're 180 degrees out of phase.

And so what that actually means is when the fifth harmonic comes up from the bottom on this side, the fifth harmonic looks like this.

And when the fifth harmonic comes up from this side, it looks like exactly the opposite.

So those two added together in this path up here go away because they add up to zero.

And the seventh harmonic, because the seventh harmonic is a positive sequence harmonic,

it actually rotates the same direction as the 60 hertz.

So imagine 210 degrees or 7 times 30 going this way, 210 degrees.

And we're going the same direction or 30 degrees with the fundamentals.

So the net difference again is 180 degrees.

So as we look at the 5th and 7th coming up through power system, we're actually canceling out the 5th and 7th from both sides.

So as we wrap up, the key point here is we take two six -pulse drives, we put them through phase -shifting transformers,

and we create a 12 -pulse system.

Seems complicated, but at the end of the day, as we saw with the minus 61 or so degrees and 114,

115 degrees positive, you saw the fifth harmonic was exactly almost equal and opposite or 180 degrees apart, and that's how it works.

Thank you.

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このレッスンの語彙とスピーキングのポイント

このスピーキングレッスンは、動画「26 - How does harmonic phase shifting work including a detailed mathematical explanation to reduce s」を教材にしています。繰り返し出てくる語は次のとおりです：harmonic, drive, degree, phase, fifth。この動画には、シャドーイング用の文が95文、単語が1342語あります。音声の長さは9:00です。話す速さは1分あたり約149語で安定しており、シャドーイングしやすいペースです。単語の85%は英語の頻出3,000語に含まれます。残りは練習の前に確認しておきましょう。

この動画の重要語彙

動画に出てくる覚えておきたい単語15語を、発音と意味つきで紹介します。

単語	発音	意味
delta 名詞	/ˈdɛltə/	デルタ
pulse 名詞	/pʌls/	脈, 脈搏
seventh 形容詞	/ˈsɛvənθ/	七番目
minus	/ˈmaɪ.nəs/	引く
sequence 名詞	/ˈsiː.kwəns/	順序
cancel 動詞	/ˈkæn.sl̩/	取り消す, 取り止める
rotate 動詞	/ˈɹoʊ.teɪt/	回る
fundamental 形容詞	/ˌfʌn.dəˈmɛn.təl/	基本的な
spectrum 名詞	/ˈspɛktɹəm/	スペクトル, 分光
connect 動詞	/kəˈnɛkt/	繋げる
isolation 名詞	/ˌaɪsəˈleɪʃən/	隔離, 孤立
cancellation 名詞	/kænsəˈleɪʃən/	取り消し, 削除
complicated 形容詞	/ˈkɑm.plɪˌkeɪ.tɪd/	複雑な
angle 名詞	/ˈæŋ.ɡəl/	角度
frequency 名詞	/ˈfɹiːkwənsi/	頻度

動画に出てくる句動詞

単語	発音	意味
go away 動詞		去る, 出る
come out 動詞	/ˌkʌm ˈaʊt/	出る
come up 動詞		上がる, 登る
go ahead 動詞	/ˌɡoʊ əˈhɛd/	どうぞお先に

注意したい発音

話し手はwe're, we'll, don'tなど、短縮形や弱形を27回使っています。聞こえたとおりの短い形で発音しましょう。

「th」の音: seventh /ˈsɛvənθ/, eleventh /ɪˈlɛv.ənθ/, thirteenth /ˌθɝˈtiːnθ/
「sh」と「zh」の音: isolation /ˌaɪsəˈleɪʃən/, cancellation /kænsəˈleɪʃən/
長い単語（アクセントの位置に注意）: fundamental /ˌfʌn.dəˈmɛn.təl/, isolation /ˌaɪsəˈleɪʃən/, cancellation /kænsəˈleɪʃən/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/

日本語話者が苦手な音：

/r/ と /l/ の区別 — /l/ は舌先を歯茎につけ、/r/ はどこにもつけない: linear /ˈlɪn.i.əɹ/, variable [ˈvæɹ.i.ə.bl̩]
/v/ — /b/ にならないように、上の歯を下唇に当てる: seventh /ˈsɛvənθ/, variable [ˈvæɹ.i.ə.bl̩], vector /ˈvɛktɚ/, eleventh /ɪˈlɛv.ənθ/
/f/ — 「フ」ではなく、上の歯と下唇で出す: fundamental /ˌfʌn.dəˈmɛn.təl/, frequency /ˈfɹiːkwənsi/, transformer /tɹænsˈfoɹməɹ/

この動画での練習方法

まず声を出さずに動画を最後まで聞き、知らない単語をメモします。
通常の速度で一文ずつシャドーイングし、話し手のリズムに合うまで繰り返します。
自分の声を録音して元の音声と比べます。delta, pulse, seventhなどの単語に特に注意しましょう。

シャドーイングとは？英語上達に効果的な理由

シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。

シャドーイングのやり方: ステップ別の完全ガイドを読む →

シャドーイング練習: 26 - How does harmonic phase shifting work including a detailed mathematical explanation to reduce s - 動画で英語スピーキングを学ぶ

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