Page 293 - 2024-Vol20-Issue2

289 | Abdulabbas & Salih

Vcarrie vb* vc*
Vp
t
r

va*
-Vn

Fig. 6. Changing of duty cycle with constant outer S1
parameters in qZSI. t

this approach, the duration of shoot-through time remains con- S2
sistent for each switching cycle, ensuring a steady boost factor. t
The shoot-through duty ratio drops as the modulation index
M increases in this manner. Therefore, the highest possible S3
shoot-through duty ratio is restricted to (1 - M). When the t
value of M grows to its maximum, the shoot-through duty
ratio reaches zero, causing the inverter to operate in the same S4
way as the typical VSI. The direct current (DC) inductor cur- t
rent and capacitor voltage do not exhibit any fluctuations that
are linked to the output frequency. S5
t

S6
t

Shoot
through
region

Fig. 7. Simple boost modulation of qZSI circuit.

Vg = vga vgb vgc T, Li = Lia Lib Lic ,
Lo = Loa Lob Loc , and C = Ca Cb Cc respectively.

The three-phase grid voltage are given by vga = Vg cos(?t) ,
2p 2p
vgb = Vg cos ?t - 3 , andvgc = Vg cos ? t + 3 since the

current injected into the grid is required to be sinusoidal

and in phase with the grid voltage so the reference grid

current should be selected as following ioa* = I*o cos(?t) ,
iob* = I*o cos 2p , and ioc* = I*o cos 2p
4) Three-phase grid-tied VSI ? t - 3 ?t + 3 .
Fig. 1 clearly shows that the dc-link voltage of the VSI corre-
sponds to the output voltage of the qZS network. The Voltage The pole voltages can be obtained as VIN = 1 (1 + sk)Vdc as
Source Inverter (VSI) is linked to the electrical grid through a 2
Low Pass Filter (LCL). By utilising Kirchhoff’s voltage and
current rules to analyse the circuit depicted on the right of the k=a,b,c and sk is switching function given by the following
qZS network, one can derive the subsequent set of differential
equations. equation

sk = +1 if si is closed
-1 if si is closed

L1 di1 + r1i1 = Vinv - VC (8) Since Vinv = ViN - VnN
dt So, The phase to neutral voltage expressions in terms of input

voltage and switching function

Lo dio + roio = VC - Vg (9) Vinv = ? 2 -1 -1 ? ? sa ? (11)
dt 1 -1 2 -1 ? ? sb ?
6 Vdc ? -1 -1 2 sc

C dVC = ii - io (10) It can be transformed the three-phase quantity to the syn-
dt chronous reference dq frame oriented by d-axis and neglected

Where the matrices are given by ii = iia iib iic T ,Vinv = zero sequence component so the all AC quantities become DC
hence this purpose using Park transformation to obtain differ-
van vbn vcn T , VC = vca vcb vcc T, io = ioa iob ioc Te, nt variables of this circuit. Applying this transformation can