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285 | Abdulabbas & Salih
the technique employed to regulate the inverter. Typically, the C2
control process consists of two main objectives: producing ac-
tive states and generating shoot-through states. While the first L1 -+ L2
task is accomplished by typical control methods, the latter can iL1 vC2
be readily achieved using the simple boost control technique vin
outlined in [9]. D iL2 + S1 S3 S5 ioa Loa
The qZSI investigations focus on single-phase grid-linked Lia iia vga
systems [10–12], uninterruptible power supply systems [13–
15], three-phase grid-tied systems [16], [17], and three-phase C1 + a Lib iib iob Lob vgb
four-leg uninterruptible power supply systems [18]. A control b ioc Loc vgc
approach is proposed in [10] for effectively managing a grid- vC1 Vdc
tied cascaded multilevel qZSI solar power plant. The proposed - S2 c Lic iic
control method, as described in [11], effectively reduces the S4 S6
necessary capacitance value in the impedance network by im-
plementing improved modulation and double-frequency ripple - + C+ b +
suppression techniques. In [12], a hybrid pulsewidth modula- vb-c
tion (HPWM) technique is suggested, which mixes the pulse- vac Ca vcc Cc
width modulation and pulse-amplitude modulation schemes.
The current ripple damping control is introduced in [13]. The - -
control methods described in references [12]and [13] result in
a decrease in the required inductance and capacitance values Fig. 1. The overall configuration of a three-phase
in the impedance network. However, in all of the aforemen- quasi-Z-source inverter (qZSI) connected to a grid with an
tioned approaches suggested for single- and three-phase grid-
tied systems, the Voltage Source Inverter (VSI) is connected LCL filter.
to the grid using an L filter instead of an LCL filter.
This work investigates the suitability of using a Lyapunov- II. MATHEMATICAL DEPICTION OF THE
function-based control technique to regulate a three-phase SYSTEM
grid-tied qZSI with an LCL filter. The LCL filter is widely
recognized for introducing two extra poles into the system, Fig. 1 depicts a three-phase grid-tied LCL-filtered quasi-Z-
which poses challenges in designing the control technique source inverter (qZSI). The mathematical representations of
due to the potential for instability and the need for resonant the quasi-source network and voltage source inverter are pro-
damping. Ensuring global stability for such a system is crucial vided in the subsequent sections.
because of the inherent stability difficulty with the LCL filter.
A recent study [19] has demonstrated that the control approach 1) Quasi-Z-Source Inverter Circuit modeling
based on Lyapunov functions ensures global stability of the
three-phase grid-tied LCL-filtered VSI, even when subjected Similar to the conventional ZSI, the qZSI also has two op-
to significant perturbations deviating from the operational erational states on the DC side: the active state (which in-
point. The inverter current and capacitor voltage reference cludes the six active states and two conventional zero states of
are determined by a proportional-resonant (PR) control mech- the traditional VSI) and the shoot-through state (where both
anism. In contrast to the work described in reference [19], switches in at least one phase conduct simultaneously). When
this study proposes a method to establish inverter current and observed from the DC side, the inverter bridge behaves like a
capacitor voltage references of three-phase inverter by employ- current source in cases of the active state. Two states can be
ing basic equations derived from synchronous reference frame. represented by their respective equivalent circuits, which are
The capacitor voltage and inductor current reference of qZSI illustrated in Fig. 2. The shoot-through state is not allowed
are produced by a two proportional-resonant (PR) controller in the conventional Voltage Source Inverter (VSI) due to the
that is linked to the output of the primary controller manip- risk of short-circuiting the voltage source, which might result
ulating the inductor current error, with the inverter current in device damage. The qZSI and ZSI, when combined with
reference being generated by the initial proportional-resonant the LC and diode network, alter the functioning of the circuit,
(PR) controller. Theoretical considerations are validated using enabling the shoot-through state.
computer simulations. For general analysis, the input voltage, vin, is selected as the
system input, which is related to the input current, iL1. The
reason for this is that RES does not possess the same rigid
output characteristics as an ideal voltage source or current
source. In DC-side modeling, the three-phase inverter bridge
and external AC load are simplified as a single switch and
current source connected in parallel [20]. The asymmetric
quasi-Z-source network has four state variables: The currents
flowing through the inductors are denoted as iL1 and iL2, The
voltage over the capacitors vC1 and vC2. The independent load
current, iload, operates as an additional input or disturbance
to the quasi-Z-source network. Select vC1 and i (also known
