Resonance and Multilevel converters
Industrial Electrical Engineering and Automation Lund University, Sweden
Conventional 2-level Inverter • Topology reference • Two level output: ±Vdc/2 • High dv/dt (=
𝑉𝑑𝑐 ) 𝑡𝑠𝑤
• Few components • Easy to control • EMC reducing implementation required
One phase leg of a 2-level inverter
Multilevel Inverters Introduction: • Inverters with 3+ voltage levels are called multilevel inverters • m-1 capacitors split the DC voltage into m levels (m-1 levels in the line voltage) • The switches select the correct level • The output only changes 1 level 𝑑𝑣 𝑉 /(𝑚−1) up/down at a time ( 𝑑𝑡 = 𝑑𝑐 𝑡 ) 𝑠𝑤
Example in figure: Assume m = 5 which means 4 capacitors are used to split up the DC voltage. Then the output shown in the figure is: 𝑉𝑑𝑐 𝑉𝑑𝑐 𝑉𝑑𝑐 𝑉𝑜𝑢𝑡 = − = 2 4 4
Simplified m-level
Multilevel Inverters pros/cons
Benefits: • Less total harmonic distortion • Can run on lower switching frequency • Less component stress • Lower component voltage rating
Drawbacks: • Higher complexity • Higher amount of components
Neutral Point Clamped Multilevel Inverter (NPCMLI ) Principle: • The DC voltage is split into smaller levels by the capacitors. • Diodes are used to clamp each switch to one capacitor voltage level. • Switch state determines output voltage Components: • Number of capacitors: m-1 • Number of clamping diodes: (m1)(m-2) per phase • Number of switches: 2(m-1) per phase • All components must have voltage rating higher than Vdc/(m-1)
5-level Natural Point Clamped Inverter
NPCMLI pros/cons Benefits: • Easy to control.
Drawbacks: • High amount of clamping diodes when number of voltage levels is high. • Capacitor unbalance occurs when transferring real power. 3-level Natural Point Clamped Converter
Capacitor Clamped Multilevel Inverter (CCMLI ) Principle: • Same basic principle as the NPCMLI • Capacitors are used to clamp the device voltage to one voltage level • Has redundant switching states, which makes capacitor balancing possible. Components: • Number of DC-bus capacitors: m-1 • Number of clamping capacitors: (m1)(m-2)/2 per phase • Number of switches: 2(m-1) per phase • All components must have voltage rating higher than Vdc/(m-1)
CCMLI pros/cons
Benefits: • Redundant switch combinations makes voltage balancing possible Drawbacks: • High amount of clamping capacitors when number of voltage levels is high • Capacitors are more expensive and bulky than diodes • Balancing modulation is very complicated and requires high switching frequency resulting in high switching losses
Modular Multilevel Inverter (MMI) Principle: • Modularized setup with submodules. • Each submodule have a capacitor charged to Vdc/(m-1). • The submodules can be inserted to make their capacitor contribute to the output. • Has redundant switching states, which makes capacitor balancing possible. Components: • Number of capacitors: 2(m-1) per phase +2 • Number of switches: 4(m-1) per phase • 2 inductors per phase (to take up voltage difference when switching occurs)
MMI pros/cons Benefits: • Modularized setup • Redundant switch combinations makes voltage balancing possible • The number of required components dose not grow quadratic with number of levels. Drawbacks: • Complicated balancing modulation
Matrix Converter • Three VARYING levels IN • Modulation to any number of potentials OUT • No intermediate Energy Storage • Simple modulation • Sort the three input levels in [min med max] and ”think 3level” • Difiicult Switching © Mats Alaküla
L5 – 3-phase modulation
Star C Principle: • The switches generate block-shaped voltage pulse • The pulse is shaped to a semi-sinusoidal pulse • This pulse is fed to the output capacitor for one of the phases
The Star C topology got two different approaches: a) The series resonant (soft switched) and b) the inductive (hard switched).
Star C pros/cons •
Benefits: Low number of semiconductor switches (compared to MLI:s) • Very low output voltage derivatives
Drawbacks of series resonant Star C: • May run in to problems if the load is unsymmetrical
Drawbacks of inductive Star C: • Higher switching losses as a result of hard switching
2- and 3-level inverter simulations
One phase leg of the 2-lvl inverter
One phase leg of the 3-lvl inverter
Modulation - Control of voltage time area va +
uk 0
va s 1 v c
vb
Electric Drives
R, L
s 0
u
vb +
i
e
va when s 1 vc vb when s 0 uk when s 1 u s va vb s uk 0 when s 0
15
Output voltage vc
va
t vb
0 u
uk
y1
y2
T
Electric Drives
y3
2T
16
3T t
Control with both flanks u
y ym
uk y+
* y3
+
T/2
T /2
Y0
uk dt
-
T y+
0
y( + , ) y+ + y Electric Drives
y
* y3
ym *
y3
y 0
0
y
* y3
y
T /2
+
+
0
uk dt Y0 uk dt
T / 2 +
uk dt
T /2
17
+
T 2
-
T
Industrial Electrical Engineering and Automation Lund University, Sweden
To Simulink !
© Mats Alaküla
L5 – 3-phase modulation
Balancing the capacitor clamped inverter
Available switch states and corresponding voltage evolution (from “Flying Capacitor Multilevel Inverters and DTC Motor Drive Applications” by M. Escalante, J. Vannier, A. Arzandé)
One phase leg of a 5-lvl capacitor clamped inverter
Simulation work to do • Add the motor model • Balancing modulation for the Modular Multilevel Inverter • Balancing circuit for the Diode Clamped Multilevel Inverter • Adjust all simulations to specifications
One phase leg of the 5-lvl diode clamped inverter
One phase leg of the 5-lvl modular inverter
Capacitor Clamped MLI
- Kapacitanser i serie - Mäta alla kapacitans värden - Look-up Table i Spice
CCMLI - Balansering
Modular MLI
- Balansera en fas som i CCMLI - Balansera tre faser – Se modular.pdf
Natural Point Clamped MLI - 3-level version (simulering) - Fler nivåer => Balanserings problem - Balansera med extra krets
NPCMLI - Balansering
Two quadrant DC converters : II u U dc,max Udc
um u*
0
T
2T
3T
t
u U dc,max
+ Udc
-
U dc y
+ i u 0
y
1
T
y 3
2
2T
27
3T
t
The generic 3-phase load ia
R
+ ib
R
+ ic
+
R
L
+ ea
ua
L
+ eb
ub L
+ ec
di 2 u a R i a + L a + ea 3 dt
uc
2 di 2 e 3 ub R ib + L a + eb j
3 +
dt
4 di 2 e 3 u c R i c + L a + ec j
3
dt
di u Ri + L + e dt © Mats Alaküla
L5 – 3-phase modulation
Vectors in 3-phase systems b ib
di 2 u a R i a + L a + ea 3 dt
2 j e 3
4 j e 3
ic
1
2 di 2 e 3 ub R ib + L a + eb j
ia
3
a +
dt
4 di 2 e 3 u c R i c + L a + ec j
3
dt
di u Ri + L + e dt
Effekt-invarians
p(t ) ua i a + ub ib + uc ic ua ia + u b i b © Mats Alaküla
L5 – 3-phase modulation
Symmetric emf ia
R
+ ib
R
+ ic
R
+
L
+ ea
ua
L
+ eb
ub L
+ ec
uc
e eˆ cos t a 2 ˆ e e cos t b 3 4 ˆ e e cos t c 3 © Mats Alaküla
L5 – 3-phase modulation
Example, grid voltage vector 2 4 j j 2 e ea + eb e 3 + ec e 3 3
2 2 eˆ cos t + cos t 3 3
3 4 1 + j + cos t 2 3 2
3 1 j 2 2
cos t + cos t cos 2 + sin t sin 2 1 + j 3 2 3 3 2 2 eˆ 3 3 4 4 1 + cos t cos + sin t sin j 3 3 2 2
2 1 1 3 3 eˆ cos t 1 + + + j sin(t t ) + 3 4 4 4 4
3 eˆ cos t + j sin(t t ) E e jt 2
© Mats Alaküla
L5 – 3-phase modulation
Rotating reference frame
Use the integral of The grid back emf vector:
b q e
e e dt E e j t dt j
t
d
t
0
0
© Mats Alaküla
i
t t
2
a
j t E 2 e
L5 – 3-phase modulation
Voltage equation in the (d,q)-frame
di u R i + L + j L i + e dt
© Mats Alaküla
L5 – 3-phase modulation
Active power ... di u R i + L + j L i + e dt * * di * * * p(t ) Re u i ReR i i + L i + j L i i + e i dt diq did 2 2 Rid + Riq + L id + L iq + eq iq dt dt
1
Resistive losses
3
2
Energizing inductances
Power absorbed by the grid back emf
Stationarity: 3 ˆ p( t ) E i cos( ) E i phase cos( ) 3 E I rms, phase cos( ) 2 © Mats Alaküla
L5 – 3-phase modulation
3-phase converters – 8 switch states ( 0 ,0 ,0 )
(1,0,0 )
(1,1,0 )
( 0,1,0 )
(1,1,1)
( 0 ,1,1)
( 0 ,0,1)
(1,0,1)
u ( 0 ,1,0 )
u (1,1,0 )
2 u (1,0 ,0 ) U dc u ( 0 ,1,1) 3 2
u (1,0 ,0 )
u (1,1,1)
u ( 0 ,1,1)
u ( 0 ,0 ,0 )
j 2 u ( 0 ,1,0 ) U dc e 3 u (1,0 ,1) 3 4
j 2 u ( 0 ,0 ,1) U dc e 3 u (1,1,0 ) 3 u ( 0 ,0 ,0 ) 0 u (1,1,1)
u ( 0 ,0 ,1) © Mats Alaküla
u (1,0 ,1) L5 – 3-phase modulation
3-phase converters - sinusoidal references * u u * e jt u * cos(t ) + j sin(t ) ua* + j u b*
2 * ua 3 1 * 1 * * ub ub ua 2 6 1 * 1 * * uc ub ua 2 6 ua*
© Mats Alaküla
ua* ub* uc*
L5 – 3-phase modulation
2 * u cos(t ) 3
2 * 2 u cos(t ) 3 3
2 * 4 u cos(t ) 3 3
3-phase converters modulation Simplest with sinusoidal references... 400 200
0 -200
-400 0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
... but the DC link voltage is badly utilized.
© Mats Alaküla
L5 – 3-phase modulation
0.018
0.02
3-phase converters – symmetrization 3 phase potentials, only 2 vector components. One degree of freedom to be used for other purposes.
* v az u a* v *z * vbz ub* v *z * vcz u c* v *z
© Mats Alaküla
L5 – 3-phase modulation
3-phase symmetrized modulation * * * * * * max( u , u , u ) + min( u * a b c a , ub , u c ) vz 2 400 200
0 -200
-400 0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Maximum phase voltage with sinusoidal modulation : Udc/2 Maximum phase-to phase voltage with symmetrized modulation : Udc -> Phase voltage Udc/sqrt(3), i.e. 2/sqrt(3)=1.15 times larger than with sinusoidal modulation. © Mats Alaküla
L5 – 3-phase modulation
3-phase minimum switching modulation
U dc * * * U dc * * * v z * min max u a , ub , uc , min u a , ub , uc 2 2 400
200
0
-200
-400
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
One phase is not switching for 2 60 degree intervals ...
© Mats Alaküla
L5 – 3-phase modulation
Modulation sequence vs. ripple b
um
u b*
u (1,1,0 ) va
1
u* 0
u (1,1,1) u ( 0 ,0 ,0 )
u (1,0 ,0 )
vb
1 0 vc
1 0
© Mats Alaküla
u a*
L5 – 3-phase modulation
u c*
Modulation sequence vs. ripple
b q
e
i
d L
e dt
u dc
i
u
e
0
a
di u e dt L
Current ripple in the (d,q)-frame 1
1
1
0
0
0
-1
-1
-1
-1
© Mats Alaküla
0
1
-1
L5 – 3-phase modulation
0
1
-1
0
1
