Y -Source Inverter Yam P. Siwakoti, Graham E. Town
Poh Chiang Loh, Frede Blaabjerg
Department of Engineering Macquarie University NSW-2109, Australia
[email protected],
[email protected]
Department of Energy Technology Aalborg University Pontoppidanstnede 101, 9220 Aalborg, Denmark
[email protected],
[email protected]
Abstract-This paper introduces a new 3-phase Y-source inverter
whose
gain
is
presently
not
matched
by
classical
impedance-network-based inverters operating at the same duty ratio. The proposed network uses a tightly coupled transformer with three windings. By squeezing the shoot-through range while keeping higher boost, the inverter can operate at a higher modulation index, thereby minimizing switching device stress and providing better output power quality. In addition, the inverter has more degrees of freedom for setting the voltage gain and modulation index than other classical impedance-source networks. This design flexibility was proven mathematically, and
impedance network is proposed in [20] to realize a very-high gain DC/DC converter. The same Y-so�rce imped�nce network is implemented in this paper to realize a very-hlgh gain 3-phase inverter as shown in Fig. 1, whose versatility is demonstrated by implementing different winding factors, turns ratios and ranges of shoot-through duty cycle to achieve a higher modulation index. A mathematical derivation is documented in Section II, which is validated by simulation results in Section III and finally concluded with all anticipated results.
is supported by simulations carried out to prove the concept and
D1
validate the analysis.
N1:N2:N3
51
Index Terms-Y-source network, DC/AC power conversion, impedance network, distributed generation.
I.
Ym
978-1-4799-5115-4/14/$31.00 ©2014 IEEE
5
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+
C1
INTRODUCTION
An impedance network provides an efficient means of power conversion between source and load in a wide ran�e of electric-power conversion applications. The most promment among them is probably the Z-source impedance network introduced in [1]. Although the Z-source impedance network was first tested with a dc-ac inverter, its usage is not limited, and has in fact been tried with many types of energy converters as demonstrated in [2], [3] and [4] for DC/DC converters, [7], [8] for DC/AC converters, [5] for AC/AC converters, and [6] for AC/DC converters. This flexibility has also been shown with other impedance networks proposed subsequently, including the quasi-Z [7], [8], embedded-Z [9], [10], series-Z [11], switched-inductor [12], [13], tapped inductor [14], cascaded [15], T-source [16], [17], trans-Z source [18] and r-source [19] networks. Among them, the latter three networks, with magnetic coupling, are slightly more unique in the sense that they use a coupled inductor or transformer with two windings to achieve higher voltage gain, while keeping a minimum component count. They differ only in their winding placements which, although simple rearrangements, can lead to different winding requirements, as explained in [19]. Each of these networks has its own characteristic features, which might at times be helpful depending on the application under consideration [23]. It is thus not fair to favor any particular networks, but more appropriate to look for an alternative that can merge all the preferred characteristics. To achieve that, a unique Y-source
53
52
54
56
'---�""'....+.....-� ...
Fig. I. Proposed Y-source three-phase inverter
II.
MATHEMATICAL DERryATION
The proposed inverter consists of a Y-source network on the input side, a 3-ph bridge inverter and a filter at the output stage. The Y-source impedance network in its elementary form consists of a passive diode D" a capacitor C, and, most importantly, a three-winding transformer (N" N2, N3) for introducing a high boost at a small duty ratio. As the transformer is connected directly to the inverter bridge and D" its coupling must be tight to minimize leakage inductances seen at its windings. This can be done by following the winding style associated with a bifilar coil [21]. Like a traditional impedance-source inverter, the Y-source inverter has an extra shoot-through zero state and non-shoot through state that consist of six active states and two zero states. The shoot-through state can be achieved by short circuiting both the upper and lower switching devices of any/all phase leges) of the inverter. By ensuring that, the equivalent circuit during the shoot-through across the inverter bridge, i.e. dSTT, is shown in Fig. 2(a) and can be written as (1), where n12 NdNz and n13 NdN3 are the turns ratios of the transformer. The diode DI is open circuit in this interval. =
VCl
+
vd nl Z -Vdn13
=
=
0
(1) On the other hand, during any non-shoot-through state interval (1-dST )T, diode DJ is conducting and the inverter bridge is modeled as an equivalent current source, as shown in Fig. 2(b); the circuit expressions change to (2). VIn
=
VL + VCl + vL/n1Z
(2)
vac -
MBVln Z
_
-
M(1-KdST)Vln
The gain derived from (5), together with those of the related impedance networks [16]-[19], is summarized in Table II. They are all ideal expressions derived by ignoring the parasitic elements. Now comparing the first and fourth expressions from Table I, it can be seen that the gain of the Y source inverter can be set higher than that of the traditional Zsource inverter if the inequalities of
Performing the state-space averaging, the voltage across the capacitor C I can be deduced to be
=>
VC1
=
VIn (1-dST) /
(1
_
n12(n13+1)dST n12-n'3
)
(5)
Z
K
=
N3+N, > N3-Nz
2 and
N3 - Nz > 0 are satisfied. These inequalities translate to the winding design requirements spelled out in (6) and (7) for the Y-source inverter when compared with the traditional Z source inverter. N1
(3)
+
2Nz
>
N3
(6)
Nz < N3 and N3
>
1
(7)
Moreover, by setting the denominator of (4) to be greater than zero, the range of variation for dST of the Y-source inverter can be determined as in (8). The range in (8) can certainly be made narrower than the 0�dST < 0.5 of the traditional Z-source inverter if the conditions in (6) and (7) are satisfied. The Y-source inverter is therefore capable of producing a high gain at a small duty ratio.
o " � =
J
O
a)
0�dST < dsT,max
=
I/K
(8)
and the corresponding modulation index is M Vdc-link
b) Fig. 2. Equivalent circuit of the V-source inverter during (a) shoot through and (b) non-shoot-through state.
Referring now to the dc-link voltage across the inverter bridge (Vdc-link), its peak value Vdc-link during the non shoot-through states can be written as (4), from which the network voltage boost B Vdc-link/Vln can be determined in terms of the transformer winding factor K defined as K =
=
N3+N, N3-Nz
Vdc-link
- (1 +.2...) . - V /[1
=
V1n
=> Vdc-lmk �
n13 VL
In
-
=
V1n
-
]
(1+ n13)dsT I-nZ3
where the boost factor B
=
c l nk fj d - i Vln
(
n13+1 n13
VIn =
/[1
)(
) (V1n - VCl) ] - BV
� n
-
12 +1
(N3+N1)dsT N3-Nz
[1-KdST ] -1
In
(4)
The peak value of the ac voltage per phase from the inverter output can be derived as
=
1.15(1-dST) '
(9)
So by squeezing the range of shoot-through range, the range of modulation index can be extended to achieve lower device stress and better spectral performance. This means that higher voltage boost can be achieved at a smaller shoot through duty cycle and high modulation index simultaneously according to (9). To further illustrate how the Y-source inverter voltage gain varies with different winding factors K and shoot-through duty cycles dST, Fig. 3 can be plotted using (5), where the curve corresponding to K 2 also represents the voltage gain of the traditional Z-source inverter. The curves plotted clearly show that the Y-source inverter can produce the desired gain with many different combinations of K and dST' Besides K and dST' the winding turns of the transformer can also be flexibly chosen so long as they give the specified K, while yet meeting design constraints faced by individual users. To illustrate this by Table I it can be seen that, for each K value chosen for a certain gain Gv and range for dST, there are more than one combination of winding turns (N1: N z: N 3) to select from. The flexibility of the Y-source network in providing the desired gain is thus demonstrated, which presently, is not =
10
8 ;;;
7
;3
6
� E g
,
' --
\ \ \ \ "-
4 3 2
K L =
K=3 K=4
TABLE IT
K=5
SUMMARY OF VOLTAGE GAINS FROM DIFFERENT IMPEDANCE-NETWORK
--
K=6
--
1M)
0.9
0.7 Modulation Index
1.1
TABLE T
Y-SOURCE INVERTER WHEN REALIZED WITH DIFFERENT WINDING FACTORS K AND TURNS RATIOS (N ,'N2 'N3)
VOLTAGE GAIN OF
=
o < dST < dST.max
Voltage Gain
2
0< dST < 1/2
O.5M(1- 2dsT)-1
3
0< dST < 1/3
0.5M(1- 3dsT)-1
4
0< dST < 1/4
0.5M(1- 4dST)-1
5
0< dST < 1/5
0.5M(1- 5dsT)-1
6
0< dST < 1/6
0.5M(1- 6dsT)-1
N,+N3 N,-Nz
VaclVln
Nt:Nz:N3
I: I :3, 2: I :4, 1:2:5,
3:1:5, 4:1:6, 1:3:7 1:1:2, 3:1:3, 2:2:4, 1:3:5, 4:2:5 2:1:2, 1:2:3, 5:1:3, 4:2:4, 8:1:4 3:1:2, 2:2:3, 1:3:4, 7:1:3, 6:2:4 4:1:2, 3:2:3, 2:3:4, 1:4:5, 9:1:3
VaclVln
Voltage Gain
Z-, Quasi-Z- and Embedded-Z-Source [ I ], [7], [23] T- and Trans-Z-Source [16]-[18]
Fig. 3. Theoretical voltage gain (Gv = M B) of the Y-source inverter obtained with different duty cycle dST and winding factor K.
K
BASED INVERTERS
Impedance Network
o 0.5
will lead to a higher switching voltage in addition to a reduction in gain.
--
\ \ \ \ \ \ \\ '\. \. \\ -..... ....... " " -
5
