Page 297 - 2024-Vol20-Issue2

293 | Abdulabbas & Salih

S1 TABLE I.
S2 SYSTEM PARAMETERS
S3
Control of Lyapunov Symbol Value
function S4 800 V
S5 DC link voltage, Vdc 1.4 mH
??????* ??????* GPR2(s) DST - S6 Inductance on the side of
?????? GPR1(s) 0.5 mH
comparator the inverter, Li
?????? + Inductance on the grid 50µ F

- side, Lo 0.1?
Capacitance of the filter, 0.05?
comparator 12.5 kHz
-1 + C
v
Carrier Inverter inductor 230 * 2
wave resistors, ri
500µ H
Fig. 9. Control using a Lyapunov function that incorporates Grid inductor resistors, ro
shoot through states. Switching frequency 400µ F

sen as ?, then the PR controller, as specified in equation (44), Amplitude of the grid
provides an infinite gain at the resonant frequency ?. This voltage, Vg
ensures that the grid current precisely follows its reference
without any inaccuracy in the steady-state [19]. Nevertheless, Inductances of the gZS
it is impractical to implement a PR controller with unrestricted network, Ll, L2
gain. Hence, the subsequent imperfect transfer function is
employed in practical applications. Capacitances of the gZZ
network, C1, C2

GPR(s) = Kp + s2 2 Kr?cs ?2 (45) of the suggested control technique. The simulations were
+ 2?cs + done using Matlab/Simulink. A phase locked loop (PLL) is
utilized to produce the current reference that is synchronized
The system utilizes two proportional-resonant (PR) controllers with the grid voltage and frequency. The switching function
that function based on errors in capacitor voltage and inductor of the proposed control method is computed after produc-
current as described below. ing the requisite reference signals iid*, iiq*, vcd* and vcq*
and used Lyapunov function based control. Next, the PWM
GPR1( s) = IL1 * = Kp1 + s2 2 Kr1?cs (46) signals are generated by comparing the calculated switching
vC1 * - VC1 + 2?cs + ?2 function with a carrier wave that has a frequency of 12.5
kHz . The controller gains were assigned the following val-
and ues: Kd = Kq = -0.004, Kcd = Kcq = 4, Kp1 = 1.5, Kp2 =
3, Kr1 = 80, Kr2 = 500, and ?c = 1rad/s. The system param-
GPR2( s) = DST = Kp2 + s2 2 Kr2?cs 2 (47) eters are shown in Table. I.
IL1 * - IL1 + 2?cs + ? Figures (10)-(12) illustrate the dynamic behaviour of the
grid voltages and currents when the grid current reference
The cut-off frequency is represented by ?c, the resonant fre- amplitude ( I*o ) is increased from 15 A to 30 A at 0.3 sec .
quency is represented by ?, and Kp1, Kp2, Kr1 and Kr2 are pro- Fig. 10 displays the simulated steady-state responses of the
portional and resonant gains, respectively. The shoot-through grid voltage and current produced using the Lyapunov-based
control method with proportional-resonant (PR) control of
states may be produced by comparing the complement of the qZSI (without capacitor voltage loop). It is assumed that the
duty cycle ( 1 - DST ) with the triangular carrier waveform estimated lower control limit (LCL) parameters are in agree-
used for generating PWM signals for the inverter switches as ment with the actual parameters. The relationship between
the injected grid current and the grid voltage is evident as they
shown in Fig. (9). are in phase. The oscillations observed in the grid current
indicate that the Lyapunov-based control technique, using PR
III. RESULTS OF THE SIMULATION control of qZSI, fails to effectively mitigate the resonance.
Fig. 11 displays the simulated steady-state responses of the
The simulations of qZSI with LCL-filter-based three-phase grid voltage and current achieved by the suggested control
grid-connected VSI demonstrate the effectiveness and utility approach with the capacitor voltage loop, assuming that the