Page 292 - 2024-Vol20-Issue2

288 | Abdulabbas & Salih

they are discarded. By the small-signal model, the transfer

functions from d0 to the voltage across capacitors vC1 and vC2
are the same and expressed as vC, indicated as Eq. (7).

G1 = vC(s) =
d0(s) ˜iload =0

vin =0

(VC1 + VC2 - RIload ) (1 - 2D0) + (Iload - 2IL) (Ls + r + R)
LCs2 + C(r + R)s + (1 - 2D0)2

(7)

To accurately depict the changing properties of the quasi-Z- Fig. 4. Changing of inductance with constant outer
source network, we analyse several root loci of the transfer parameters in qZSI (a) pole-zero mapping ,(b) step response.
function G(s) by systematically varying the parameters L, C,
and D0. The system parameters are listed as follows: L = 500
µH, C = 400 µF, R = 0.03 ?, r= 0.47 ?, D0= 0.25, Iload =
9.9 A, and Vin= 130 V. Fig. 2 demonstrates the movement of
poles and zeros towards the imaginary axis as the inductance
L is changed from 200 µH to 500 µH.
At an inductance value of 100 µH, the poles become equal,
resulting in the system being in critical damping, and increas-
ing the inductance to 100 µH results in the emergence of
imaginary component the poles, leading to under-damping.
Thus, when examining the step response of the function see in
Fig. 4, the output waveform exhibits inconsistent overshoot at
100 µH. As the inductance increases, both the overshoot and
settling time also increase. The moving of zeros increases the
non-minimum-phase undershoots, while the shifting of poles
enhances the system settling time and response.

By increasing the capacitance C from 100 µF to 500 µF,
Fig.5 demonstrates the vertical movement of the poles towards
real axis while the zeros remain unchanged. Increasing system
damping has been seen to decrease the amplitude of overshoot
and undershoot, but it will also increase the rising time. To
ensure appropriate performance and stability, it is crucial to
analyze the movements of zero and pole for sources with more
comprehensive operating ranges. The same conclusion can be
obtained when changing the value of cycle period shown in
Fig. 6.
The selection of L and C values in a quasi-Z-source network
can be based on a compromise between the damping response
and settling time of the transfer function G(s), as determined
from the pole-zero maps and step signal test of the derived
transfer function.

3) Simple Boost Modulation Fig. 5. Changing of capacitance with constant outer
The simple boost approach [20] utilises two straight lines that parameters in qZSI(a) pole-zero mapping ,(b) step response.
have a value equal to or greater than the peak value of the
three phase references as shown in Fig. 7. These lines are
utilised to insert the shoot-through duty ratio. By following