i. voltage source inverter (vsi) ii. metode...
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I. Voltage Source Inverter (VSI)A. Six-Step VSI
B. Pulse-Width Modulated VSI
II. Metode PWM
A. Sinusoidal PWM
B. Hysteresis (Bang-bang)
C. Space Vector PWM
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Voltage Source Inverter Tiga Fasa Six Step
Gambar 1 Three phase voltage source inverter
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Gambar 1 Three-phase voltage source inverter.
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Sinyal gate, urutan switching dan tegangan line ke negatif.y g , g g g g
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Voltage Source Inverter (VSI)Six-Step VSISix-Step VSI
Urutan Switching: 561 (V ) → 612 (V ) → 123 (V ) → 234 (V ) → 345 (V ) → 456 (V ) → 561 (V )dimana, 561 berarti S5, S6 and S1 di-ON-kan sedangkan switch lainnya OFF
561 (V1) → 612 (V2) → 123 (V3) → 234 (V4) → 345 (V5) → 456 (V6) → 561 (V1)
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Voltage Source Inverter (VSI)Six-Step VSISix-Step VSI
Tegangan line-to-line (Vab, Vbc, Vca) dan tegangan line-to-neutral (Van, Vbn, Vcn)g g ( ab bc ca) g g ( an bn cn)
V b = V N - VbN
Tegangan line-to-line
Vab VaN VbN
Vbc = VbN - VcN
V = V VVca = VcN - VaN
Tegangan fasa
Van = 2/3VaN - 1/3VbN - 1/3VcN
Vbn = -1/3VaN + 2/3VbN - 1/3VcNbn aN bN cN
Vcn = -1/3VaN - 1/3VbN + 2/3VcN
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Voltage Source Inverter (VSI)Six-Step VSISix-Step VSI
Amplitud tegangan line to line (Vab, Vbc, Vca)p g g ( ab, bc, ca)
Komponen frekuensi fundamental (Vab)1
dcdcdc V78.0V62
V423
≈==ππ
(rms))(V 1ab
Komponen frekuensi harmonik (Vab)h
: amplitud harmonik menurun dengan naiknya orde harmoniknya: amplitud harmonik menurun dengan naiknya orde harmoniknya
V78.0dcab =
h(rms))(V h
3 )21(16hdi ±
h
3,.....)2,1,(n16nhdimana, =±=
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Voltage Source Inverter (VSI)Six-Step VSISix-Step VSI
Karakteristik VSI Six Stepp
Disebut “inverter six-step” karena adanya enam step pada bentuk
gelombang tegangan line-to-netral (fasa) nya.
H ik d 3 d k li t 3 tid k l d t li tHarmonik orde 3 dan kelipatan 3 tidak muncul pada tegangan line-to-
line dan line-to-neutral. Konsekuensinya juga tidak muncul pada
arusnya.
Amplitud output inverter tiga fasa dapat dikontrol hanya denganAmplitud output inverter tiga fasa dapat dikontrol hanya dengan
mengubah tegangan DC-link nya (Vdc).
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Sasaran PWM
Mengontrol tegangan output inverter
Mengurangi harmonik
Kekurangan dari PWM
R i i it hi ik k f k i PWM ti iRugi-rugi switching naik karena frekuensi PWM yang tinggi
Tegangan output menjadi berkurang
Problem interferensi elektromagnetik (EMI) disebabkan harmonik ordetinggi
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Pulse Width Modulation (PWM)Pulse-Width Modulation (PWM)
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Tegangan output inverterTegangan output inverter
Jika vcontrol > vtri, VA0 = Vdc/2
Jika vcontrol < vtri, VA0 = -Vdc/2
Kontrol tegangan output inverter
Amplitud dikontrol oleh harga puncak vcontrol
Frekuensi PWM sama dengan frekuensi vtri
p g p control
Frekuensi fundamental dikontrol oleh frekuensi vcontrol
10 ,2/
)(puncak AcontrolV
Vvm ==∴
Indeks modulasi (m)
/35 A01A0 V dari lfundamenta frekuensikomponen :)(Vdimana,2/dctri Vv
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Sinusoidal PWMSinusoidal PWM
Hysteresis Band PWMyste es s a d
Space Vector PWMp
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Three phase inverterThree-phase inverter
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Bentuk Gelombang v v v vg
frekuensi vtri = fs
Frekuensi vtri dan vcontrol
vtri vcontrol_A vcontrol_B vcontrol_C
frekuensi vcontrol = f1
dimana, fs = frekuensi PWM
f1 = frekuensi fundamental
Tegangan output inverter
jika vcontrol > vtri, VA0 = Vdc/2
Tegangan output inverter
dimana, VAB = VA0 – VB0
V = V – V
jika vcontrol < vtri, VA0 = -Vdc/2
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VBC = VB0 – VC0
VCA = VC0 – VA0
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Rasio Modulasi Amplitud (ma)Rasio Modulasi Amplitud (ma)
10 ,2/
)(
dc
A
tri
controla V
Vpuncaknilaivamplitudvpuncakamplitudm ==∴
A01A0 V lfundamenta frekuensikomponen :)(Vdimana,
Rasio modulasi frekuensi (mf)
lfundamentafrekuensifdanPWMfrekuensifdimana,, 1s ===ffm s
f ,, 1s1f
f
mf seharusnya bilangan bulat ganjilJika mf bukan bilangan bulat mungkin ada subharmonik pada output teganganJika mf bukan bilangan bulat, mungkin ada subharmonik pada output teganganJika mf bukan ganjil, komponen DC masih ada dan harmonik pada tegangan output
m seharusnya adalah kelipatan 3 untuk inverter PWM 3 fasa
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mf seharusnya adalah kelipatan 3 untuk inverter PWM 3 fasaHarmonik kelipatan 3 ganjil dan harmonik genap dihilangkan
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Inverter Tiga fasa untuk Kontrol Arus HysteresisInverter Tiga fasa untuk Kontrol Arus Hysteresis
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Kontroler arus HysteresisKontroler arus Hysteresis
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Karakteristik Kontrol Arus HysteresisKarakteristik Kontrol Arus Hysteresis
Keunggulan
R di ik t b ikRespon dinamik yang sangat baik
Biaya rendah dan mudah diterapkan
Kelemahan
Riak arus yang besar pada steady-state
Variasi pada frekuensi switching
Tidak ada inter-komunikasi antara masing-masing kontroler histerisis dariketiga fasa, dan akibatnya tidak ada cara untuk membangkitkan vektortegangan nol. Hasilnya, frekuensi switching bertambah pada indeksmodulasi yang lebih rendah dan sinyal akan melewati pita histeresis setiap
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kali vektor nol ON.Proses modulasi membangkitkan komponen sub-harmonik.
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Tegangan outpur inverter tiga fasa (1)Tegangan outpur inverter tiga fasa (1)
dimana, transistor atas: S1, S3, S5transistors bawah: S4, S6, S2
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4 6 2vektor variabel switching: a, b, c
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Tegangan outputTegangan output
S1 sampai S6 adalah 6 transistor yang membentuk tegangan output
P d t k l t ON k l b h d k ki h OFFPada saat sakelar atas ON, sakelar bawah pada kaki yang harus sama OFF
Menghasilkan 8 kombinasi pola ON-OFF bagi transistor-transistor atas (S1, S3, S5)
ab a011V⎥⎤
⎢⎡⎥⎤
⎢⎡ −
⎥⎤
⎢⎡
Vektor tegangan line-to-line [Vab Vbc Vca]t
tdc
ca
bc c]b[aswitchingvariabelvektordimana,cb
101110V
VV
⎥⎥⎥
⎦⎢⎢⎢
⎣⎥⎥⎥
⎦⎢⎢⎢
⎣−−=
⎥⎥⎥
⎦⎢⎢⎢
⎣V t t li t t l (t f ) [V V V ]t
⎥⎤
⎢⎡⎥⎤
⎢⎡ −−
⎥⎤
⎢⎡ a112
1Van
Vetor tegangan line-to-netral (tegangan fasa) [Van Vbn Vcn]t
/35⎥⎥⎥
⎦⎢⎢⎢
⎣⎥⎥⎥
⎦⎢⎢⎢
⎣ −−−−=
⎥⎥⎥
⎦⎢⎢⎢
⎣ cb
211121V
31
VV dc
cn
bn
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Tegangan outputTegangan output8 vektor teganganganinverter (V0 to V7)
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8 kombinasi, tegangan fasa dan tegangan line output
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Prinsip Space Vector PWMPrinsip Space Vector PWM
Memperlakukan tegangan sinusoidal sebagai sebuah vektor amplitud konstanyang berputar pada frekuensi konstan
Teknik PWM ini memperkirakan tegangan referensi Vref lewat kombinasi
yang berputar pada frekuensi konstan
kedelapan pola switching (V0 - V7)
Perubahan Koordinat (kerangka referensi abc menjadi kerangka d-q stasioner)Perubahan Koordinat (kerangka referensi abc menjadi kerangka d q stasioner) : Vektor tegangan tiga fasa ditransformasikan menjadi vektor pada kerangka koordinat d-q
stasioner yang mewakili penjumlahan vektor ruang dari ketiga tegangan fasa
Vektor-vektor (V1 - V6) membagi bidang menjadi 6 sektor (masing-masing 60 derajat)
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Vref dibangkitkan oleh dua vektor bukan nol yang berdekatan dan dua vektor nol
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D kt d kt it hiDasar vektor dan sektor switching
6 vektor aktif (V1,V2, V3, V4, V5, V6)
Sumbu heksagonal
Tegangan DC link disuplay ke beban
Masing-masing sektor (1 - 6): 60
derajat
2 vektor nol (V0, V7)Pada titik asal
Tidak ada tegangan yang disuplay ke beban
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Perbandingan Sinusoidal PWM dan Space Vector PWMPerbandingan Sinusoidal PWM dan Space Vector PWM
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Gambar. Perbandingan lokus tegangan kontrol linier maksimum pada SPWM dan SVPWM
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Perbandingan Sinusoidal PWM dan Space Vector PWM
Space Vector PWM membangkitkan distorsi harmonik lebih sedikit padaoutput tegangan atau arus dibanding sinusoidal PWM
Perbandingan Sinusoidal PWM dan Space Vector PWM
output tegangan atau arus dibanding sinusoidal PWM
Space Vector PWM menghasilkan penggunaan tegangan suplay yang lebihefisien dibanding sinuosoidal PWMefisien dibanding sinuosoidal PWM
Sinusoidal PWM: Lokus vektor referensi berada di dalam lingkaran dengan radius 1/2 Vdc
Space Vector PWM: Lokus vektor referensi berada di dalam lingkaran dengan radius 1/√3 Vdc
∴ Utilisasi tegangan: Space Vector PWM = 2/√3 kali Sinusoidal PWM
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P S V t PWMPenerapan Space Vector PWM
Langkah 1 Tentukan V V V dan sudut (α)Langkah 1. Tentukan Vd, Vq, Vref, dan sudut (α)
Langkah 2. Tentukan durasi waktu T1, T2, T0
Langkah 3. Tentukan waktu switching masing-masing transistor (S1 to S6)
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Langkah 1. Menentukan Vd, Vq, Vref, dan sudut (α)
cnbnan
cnbnand
V21V
21V
cos60Vcos60VVV
−−=
⋅−⋅−=
Langkah 1. Menentukan Vd, Vq, Vref, dan sudut (α)
Transformasi koordinat: abc dq
cnbnq
cnbnan
cos30Vcos30V0V
22
⋅−⋅+=
⎤⎡⎤⎡ V111
cnbnan V23V
23V −+=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−−=⎥
⎦
⎤⎢⎣
⎡∴
cn
bn
an
q
d
VVV
23
230
21
211
32
VV
⎦⎣ 22
V
VVV
q1
2q
2dref +=
/35 l)fundamentafrekuensif(dimana,
t2ππtω)VV
(tanα
s
ssd
q1
=
=== −Gambar: Vektor ruang tegangan dan komponennyadalam (d, q).
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Step 2 Menentukan durasi waktu T T T (1)Step 2. Menentukan durasi waktu T1, T2, T0 (1)
Gambar. Vektor referensi sebagai kombinasi vektor-vektor berdekatan padasektor 1.
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Step 2. Menentukan durasi waktu T1, T2, T0
durasi waktu switching pada sektor 1TTTT T z21z 1
∫∫∫ ∫+
p 1, 2, 0
)VTV(TVT
VdtVdtVV
2211refz
TT0
T12
0 01ref
21
⋅+⋅=⋅∴
++= ∫∫∫ ∫+
)60α0(dimana)3/(sin)3/(cos
V32T
01
V32T
)(sin)(cos
VT dc2dc1refz
°≤≤
⎥⎦
⎤⎢⎣
⎡⋅⋅⋅+⎥
⎦
⎤⎢⎣
⎡⋅⋅⋅=⎥
⎦
⎤⎢⎣
⎡⋅⋅⇒
ππ
αα
)60α0(dimana, ≤≤
⋅⋅=∴−
⋅⋅=∴ 21 )3/(sin)(sin
)3/(sin)3/(sin aTTaTT zz π
απ
απ
⎟⎟⎟⎞
⎜⎜⎜⎛
==+−=∴ref
z210 2V
aandf1Twhere,),(
)3/(sin)3/(sin
TTTT z
ππ
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⎟⎟⎠
⎜⎜⎝ dcs V
32f
29
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Langkah 2. Menentukan durasi waktu T1, T2, T0
Durasi waktu switching pada setiap sektor
Langkah 2. Menentukan durasi waktu T1, T2, T0
⎞⎛⎞⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −
+−⋅⋅
=∴
33
31
3sin
31
fVTfVT
nV
refVTT
dc
zπαπ
⎟⎠⎞
⎜⎝⎛ −
⋅⋅=⎟
⎠⎞
⎜⎝⎛ −
⋅⋅= sin
3coscos
3sin
3
3sin
3 nnV
refVTnV
refVT
dc
z
dc
zαπαπαπ
⎟⎠⎞
⎜⎝⎛ −
⋅+−
⋅−⋅
=⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −
−⋅⋅
=∴3
1cossin3
1sincos3
31sin
32
nnV
refVTnV
refVTT
dc
z
dc
zπαπαπα
⎟⎟⎠
⎞⎜⎜⎝
⎛°≤≤
=−−=∴
60α06)sampai(sektor16sampai1ndimana,
,210 TTTT z
/35
⎠⎝ ≤≤ 60α0
30
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Langkah 3. Menentukan waktu switching masing-masing transistor (S1 - S6)Langkah 3. Menentukan waktu switching masing masing transistor (S1 S6)
(a) Sektor 1. (b) Sektor 2.
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Gambar. Pola switching space Vector PWM pada tiap sektor
31
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L k h 3 M t k kt it hi i i t i t (S S )Langkah 3. Menentukan waktu switching masing-masing transistor (S1 - S6)
(c) Sektor 3. (d) Sektor 4.
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Gambar. Pola switching space Vector PWM pada tiap sektor
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L k h 3 M t k kt it hi i i t i t (S S )Langkah 3. Menentukan waktu switching masing-masing transistor (S1 - S6)
(e) Sektor 5. (f) Sektor 6.
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Gambar. Pola switching space Vector PWM pada tiap sektor
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Langkah 3 Menentukan waktu switching masing-masing transistor (S1 - S6)Langkah 3. Menentukan waktu switching masing-masing transistor (S1 - S6)
/35 Tabel waktu switching pada tiap sektor34
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[1] N Mohan W P Robbin and T Undeland Power Electronics: Converters[1] N. Mohan, W. P. Robbin, and T. Undeland, Power Electronics: Converters,Applications, and Design, 2nd ed. New York: Wiley, 1995.
[2] B K Bose Power Electronics and Variable Frequency Drives:Technology[2] B. K. Bose, Power Electronics and Variable Frequency Drives:Technology and Applications. IEEE Press, 1997.
[3] H W d B k H C Sk d l d G V St k “A l i d[3] H.W. van der Broeck, H.-C. Skudelny, and G.V. Stanke, “Analysis and realization of a pulsewidth modulator based on voltage space vectors,” IEEE Transactions on Industry Applications, vol.24, pp. 142-150, 1988.
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