In the context of increasingly scarce energy resources and rising prices, the global energy utilization pattern is shifting toward high quality, low cost, clean, and low-carbon solutions. With the continuous advancement of power electronics technology, photovoltaic (PV) power generation has developed rapidly and has become one of the primary directions of new energy development. The quasi-Z-source cascaded multilevel photovoltaic grid-connected inverter (QZS-CMI) can simultaneously accomplish DC-DC conversion and DC-AC inversion through single-stage power conversion, and it enables independent maximum power point tracking (MPPT) control for each module. When applied in PV systems, this topology can enhance system reliability and grid-connected current quality while reducing the cost of PV power generation. This paper focuses on the quasi-Z-source cascaded multilevel photovoltaic grid-connected inverter and investigates its modulation and grid-connected control strategies in depth.
1. Introduction and Background
The global energy landscape has undergone profound changes in recent years. According to the BP World Energy Outlook released in 2023, despite efforts since the Paris Climate Conference in 2015, global carbon emissions have continued to rise year by year except for 2020. The share of new energy in the energy mix is increasing, and wind and solar PV installations are growing rapidly. In China, the National Energy Administration reported that by the end of 2022, the total installed power generation capacity reached approximately 2.56 billion kW, with PV installed capacity reaching about 390 million kW, representing a year-on-year growth of 28.1%. The newly added PV installed capacity in 2022 was 86.4 GW, an increase of about 57% compared with the previous year. These statistics underscore the critical role of PV systems in the transition toward a carbon-neutral society.
PV grid-connected inverters are the key equipment for energy conversion and control in PV systems. They must achieve three main tasks: (1) adjusting the output voltage of PV arrays so that they operate near the maximum power point voltage, (2) ensuring high-quality grid-connected current and avoiding islanding effects, and (3) satisfying user load demands. Among various inverter topologies, multilevel inverters have attracted significant attention because they can output near-sinusoidal voltage waveforms with low total harmonic distortion (THD), use lower voltage rating devices, and reduce the size of output filters. The cascaded H-bridge multilevel inverter is particularly attractive for PV applications due to its modular structure, independent MPPT capability, and low electromagnetic interference.
A major problem of the traditional cascaded H-bridge PV inverter is the need for a separate DC-DC converter to boost the PV voltage, which increases system cost and complexity. The quasi-Z-source inverter (QZS-I), introduced by Peng Fangzheng and his team, overcomes this limitation by using a unique impedance network that allows shoot-through states. The QZS-I can boost voltage in a single stage, eliminating the dead-time issue, improving reliability, and reducing system volume. Combining the quasi-Z-source network with the cascaded H-bridge structure yields the quasi-Z-source cascaded multilevel inverter (QZS-CMI), which inherits the advantages of both topologies. Each H-bridge unit is fed by an independent PV panel through a quasi-Z-source impedance network, enabling independent MPPT and DC-link voltage control.
However, in practical applications, partial shading, aging, and manufacturing tolerances cause power mismatch among PV modules. Since the same grid current flows through all cascaded units, power imbalance leads to over-modulation of units with higher power output. This over-modulation distorts the grid-connected current and threatens system stability. Therefore, this paper proposes an optimal third-harmonic compensation strategy to expand the operating range and suppress over-modulation under severe power imbalance. The key contributions are summarized as follows:
- Detailed modeling and analysis of the QZS-CMI PV grid-connected system, including the derivation of small-signal transfer functions.
- An improved carrier phase-shifted SPWM strategy that fuses the shoot-through duty cycle with the single-arm chopper modulation scheme.
- A comprehensive control strategy comprising independent MPPT, DC-DC dual-loop control, independent DC-link voltage balance control, grid-connected current control, and an optimal third-harmonic compensation control for power imbalance.
- Real-time simulation and experimental validation on a prototype.
2. Modeling and Analysis of the QZS-CMI PV System
2.1 Operating Principle of the Quasi-Z-Source Inverter
The topology of a single-phase quasi-Z-source inverter is illustrated in the system diagram. It consists of a quasi-Z-source impedance network (inductors \(L_1\), \(L_2\), capacitors \(C_1\), \(C_2\), and a diode) and a standard H-bridge inverter. The impedance network permits the H-bridge to operate in a shoot-through state, during which both switches in the same leg are turned on. This state is forbidden in a conventional voltage-source inverter, but in the QZS-I it is exploited to boost the DC-link voltage.
Assuming ideal components and continuous conduction mode, the inverter operates in two states: shoot-through state (duration \(T_0\)) and non-shoot-through state (duration \(T_1\)). The switching period is \(T = T_0 + T_1\), and the shoot-through duty ratio is defined as \(D = T_0/T\).
During the shoot-through state, the equivalent circuit yields:
$$
\begin{aligned}
L_1 \frac{di_{L1}}{dt} &= v_{PV} + v_{C2} \\
L_2 \frac{di_{L2}}{dt} &= v_{C1} \\
C_1 \frac{dv_{C1}}{dt} &= -i_{L2} \\
C_2 \frac{dv_{C2}}{dt} &= -i_{L1}
\end{aligned}
\tag{2.1}
$$
During the non-shoot-through state:
$$
\begin{aligned}
L_1 \frac{di_{L1}}{dt} &= v_{PV} – v_{C1} \\
L_2 \frac{di_{L2}}{dt} &= -v_{C2} \\
C_1 \frac{dv_{C1}}{dt} &= i_{L1} – i_{PN} \\
C_2 \frac{dv_{C2}}{dt} &= i_{L2} – i_{PN}
\end{aligned}
\tag{2.2}
$$
Applying the volt-second balance principle to the inductors and ampere-second balance to the capacitors, the steady-state capacitor voltages are obtained as:
$$
v_{C1} = \frac{1-D}{1-2D} v_{PV}, \quad v_{C2} = \frac{D}{1-2D} v_{PV}
\tag{2.3}
$$
The peak DC-link voltage across the H-bridge is:
$$
v_{PN} = v_{C1} + v_{C2} = \frac{1}{1-2D} v_{PV} = B \cdot v_{PV}
\tag{2.4}
$$
where \(B = 1/(1-2D)\) is the boost factor. The peak AC output voltage of the H-bridge is then:
$$
\hat{v}_{out} = M \cdot v_{PN} = M \cdot B \cdot v_{PV}
\tag{2.5}
$$
where \(M\) is the modulation ratio.
2.2 Design of the Quasi-Z-Source Impedance Network
The impedance network parameters directly determine the performance of the QZS inverter. The design must ensure acceptable voltage and current ripples while maintaining fast dynamic response. The maximum voltage gain is determined by the grid voltage and the minimum PV voltage:
$$
G_{max} = \frac{2V_g}{V_{PV\_min}}
\tag{2.6}
$$
The minimum modulation ratio is:
$$
M_{min} = \frac{G_{max}}{2G_{max}-1}
\tag{2.7}
$$
Using the small-ripple approximation, the capacitance is chosen based on the allowed capacitor voltage ripple \(\alpha\):
$$
C_1 \ge \frac{D \cdot \bar{i}_{L2}}{f_s \cdot \alpha \cdot v_{C1}}
\tag{2.8}
$$
With a 20 mV voltage ripple specification, 5 mF capacitors were selected. Similarly, the inductance is chosen based on the current ripple \(\beta\):
$$
L_2 \ge \frac{D \cdot v_{C1}}{f_s \cdot \beta \cdot \bar{i}_{L2}}
\tag{2.9}
$$
With a 1 A current ripple specification, 1 mH inductors were selected. The diode must withstand the peak DC-link voltage during the shoot-through state and conduct the sum of the two inductor currents during the non-shoot-through state. The design parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Inductors \(L_1\), \(L_2\) | 1 mH |
| Capacitors \(C_1\), \(C_2\) | 5 mF |
| Switching frequency \(f_s\) | 20 kHz |
| Maximum shoot-through duty \(D_0\) | 0.316 |
2.3 State-Space Model of a Single QZS-HBI Unit
Since the QZS-CMI system is highly modular, the dynamic model of a single quasi-Z-source H-bridge inverter (QZS-HBI) unit can represent the whole system. The state variables are chosen as the two inductor currents, the two capacitor voltages, and the PV voltage:
$$
\mathbf{x} = [i_{L1}, i_{L2}, v_{C1}, v_{C2}, v_{PV}]^T
\tag{2.10}
$$
During the shoot-through state, the state equation is:
$$
\mathbf{F} \frac{d\mathbf{x}}{dt} = \mathbf{A}_1 \mathbf{x} + \mathbf{B}_1 \mathbf{u}
\tag{2.11}
$$
where \(\mathbf{u} = [i_{PV}, i_{PN}]^T\), \(\mathbf{F} = \operatorname{diag}(L_1,L_2,C_1,C_2,C_{PV})\). The matrices are:
$$
\mathbf{A}_1 = \begin{bmatrix}
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 0
\end{bmatrix}, \quad
\mathbf{B}_1 = \begin{bmatrix}
0 & 0 \\
0 & 0 \\
0 & 0 \\
0 & 0 \\
0 & 1
\end{bmatrix}
\tag{2.12}
$$
During the non-shoot-through state:
$$
\mathbf{F} \frac{d\mathbf{x}}{dt} = \mathbf{A}_2 \mathbf{x} + \mathbf{B}_2 \mathbf{u}
\tag{2.13}
$$
with
$$
\mathbf{A}_2 = \begin{bmatrix}
0 & 0 & -1 & 0 & 1 \\
0 & 0 & 0 & -1 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 0
\end{bmatrix}, \quad
\mathbf{B}_2 = \begin{bmatrix}
0 & 0 \\
0 & 0 \\
0 & -1 \\
0 & -1 \\
1 & 0
\end{bmatrix}
\tag{2.14}
$$
Using the state-space averaging method:
$$
\mathbf{A} = D \mathbf{A}_1 + (1-D) \mathbf{A}_2, \quad \mathbf{B} = D \mathbf{B}_1 + (1-D) \mathbf{B}_2
\tag{2.15}
$$
Introducing small-signal perturbations \(\hat{x}\), \(\hat{u}\), and \(\hat{d}\), and linearizing, the resulting transfer function from the shoot-through duty cycle to the inductor current \(i_{L2}\) is:
$$
G_1(s) = \frac{\hat{i}_{L2}(s)}{\hat{d}(s)} = \frac{(v_{C1}+v_{C2}) + (I_{L1}-I_{L2}-I_{PN})}{LCs^2 + (1-2D)^2}
\tag{2.16}
$$
The transfer function from the inductor current to the PV voltage is:
$$
G_2(s) = \frac{\hat{v}_{PV}(s)}{\hat{i}_{L2}(s)} = \frac{LCs^2 + (1-2D)^2}{LCs^2(2LCs^2+1) + (2D^2-2D+1)Cs}
\tag{2.17}
$$
These transfer functions form the basis for designing the DC-DC dual-loop controller.
2.4 Equivalent Model of the QZS-CMI Grid-Connected System
The overall system consists of \(N\) QZS-HBI units connected in series on the AC side. The total output voltage is the sum of each unit’s output:
$$
v_o = \sum_{n=1}^{N} v_{on} = \sum_{n=1}^{N} S_n \cdot v_{PNn}
\tag{2.18}
$$
where \(S_n \in \{-1,0,1\}\) is the switching function of the \(n\)-th H-bridge. The grid-side voltage equation is:
$$
v_o = v_g + L_g \frac{di_g}{dt}
\tag{2.19}
$$
The equivalent circuit model is shown in the conceptual diagram. Under steady state, the output power of the \(n\)-th unit is:
$$
P_n = v_{PVn} i_{PVn} = \frac{v_{PNn} M_n I_g}{2}
\tag{2.20}
$$
The total power is \(P_T = \sum_{n=1}^{N} P_n = V_g I_g\). Thus the power ratio is:
$$
\frac{P_n}{P_T} = \frac{v_{PNn} M_n}{2 V_g}
\tag{2.21}
$$
This equation reveals that when the total power \(P_T\) decreases (e.g., due to shading of some units), the grid current \(I_g\) decreases, causing the modulation ratio \(M_n\) of the healthy units to increase. If \(M_n\) exceeds the maximum allowable value \(1-D_0\), the unit enters over-modulation, which distorts the grid current and destabilizes the system.
3. Modulation Strategy for the QZS-CMI System
3.1 Switching States of a Single QZS-HBI Unit
The H-bridge of a QZS-HBI unit has four switches. Besides the two active states (the output voltage is \(+v_{PN}\) or \(-v_{PN}\)) and two traditional zero states (output voltage is 0), the QZS-CMI adds shoot-through zero states where both switches in the same leg are simultaneously on. Since the shoot-through zero state also produces zero voltage across the AC side, it can be inserted into the traditional zero-state interval without affecting the active state duration. This is the fundamental principle of the QZS-CMI modulation.
| State | S1 | S2 | S3 | S4 | Output voltage |
|---|---|---|---|---|---|
| Active 1 | 1 | 0 | 1 | 0 | +\(v_{PN}\) |
| Active 2 | 0 | 1 | 0 | 1 | \(-\)\(v_{PN}\) |
| Traditional zero | 1 | 1 | 0 | 0 | 0 |
| Traditional zero | 0 | 0 | 1 | 1 | 0 |
| Shoot-through | 1 | 1 | 1 | 0 | 0 |
| Shoot-through | 1 | 0 | 1 | 1 | 0 |
| Shoot-through | 1 | 1 | 1 | 1 | 0 |
3.2 Comparison of Multilevel Carrier-Based SPWM Strategies
Two main categories of carrier-based SPWM strategies are used for cascaded multilevel inverters: phase-vertical-shift SPWM and phase-horizontal-shift (phase-shifted carrier) SPWM. In the vertical-shift strategy, \(N-1\) triangular carriers are stacked vertically with the same phase. In the horizontal-shift strategy, \(N\) carriers with equal amplitude and a phase shift of \(2\pi/N\) are used. The phase-shifted carrier SPWM has the advantage of equal power distribution among modules and a high equivalent switching frequency. Therefore, it is the preferred method for QZS-CMI systems.
3.3 Improved Carrier Phase-Shifted SPWM with Shoot-Through Fusion
The traditional fused shoot-through carrier-based SPWM generates a shoot-through signal by comparing the constant level \(1-D\) with the triangular carrier. This method is simple but suffers from high switching losses and unbalanced device stress. To improve the performance, this paper adopts a single-arm chopper modulation with complementary same-arm driving. In this scheme, the high-frequency bridge arm switches \(S_2\) and \(S_3\) operate complementarily, while the low-frequency arm switches \(S_1\) and \(S_4\) are combined with the shoot-through signals. The shoot-through signals are generated by comparing the carrier with \(1-D\) during the positive half-cycle of the modulation wave and with \(-(1-D)\) during the negative half-cycle.
The improved strategy can be expressed as follows. For unit \(n\), the modulation signal is \(m_n = M_n \sin(\omega t + \theta_n)\). The shoot-through signals are:
$$
\begin{cases}
S_{ST1} = 1, & \text{if } c_{n} > 1-D_n \text{ and } \sin(\omega t) \ge 0 \\
S_{ST2} = 1, & \text{if } c_{n} < -(1-D_n) \text{ and } \sin(\omega t) < 0
\end{cases}
\tag{3.1}
$$
The final driving signals for \(S_1\) and \(S_4\) are obtained by adding the shoot-through signals to the conventional low-frequency arm signals. This method ensures that only one arm switches at high frequency, reducing switching losses and improving efficiency. The carrier phase shift between adjacent units is \(\pi/N\) for the single-polarity mode, resulting in an equivalent switching frequency of \(2Nf_s\).
4. Grid-Connected Control Strategy
4.1 Front-Stage Control
4.1.1 Independent MPPT Control
Each QZS-HBI unit is connected to an independent PV panel, so the maximum power point of each panel must be tracked separately. This paper uses the perturbation and observation (P&O) method due to its simplicity and effectiveness. The algorithm compares the current power \(P_{PV}(n)\) with the previous value \(P_{PV}(n-1)\) and adjusts the reference voltage \(v^*_{PV}\) by a fixed step \(\Delta v = 0.1\) V. The control frequency is 20 Hz. The P&O algorithm ensures that each PV panel operates at its own maximum power point even under non-uniform irradiance.
4.1.2 DC-DC Dual-Loop Control
The DC-DC conversion from the PV voltage to the required DC-link voltage is achieved by controlling the shoot-through duty ratio \(D_n\). The control structure consists of an inner inductor current loop and an outer PV voltage loop, as shown in the control block diagram. The inner current loop uses a PI controller \(G_{PI2}(s) = 0.15 + 500/s\). The open-loop transfer function of the current loop is:
$$
T_{i\_ol}(s) = G_{PI2}(s) \cdot G_1(s) \cdot M(s) \cdot H_{n1}(s)
\tag{4.1}
$$
The open-loop Bode plot after compensation exhibits a crossover frequency of 2.4 kHz and a phase margin of about 78°, ensuring stable current control.
The closed-loop current transfer function is:
$$
T_{i\_cl}(s) = \frac{G_{PI2}(s) M(s) G_1(s) H_{n1}(s)}{1 + G_{PI2}(s) M(s) G_1(s) H_{n1}(s)}
\tag{4.2}
$$
The outer voltage loop uses the PI controller \(G_{PI1}(s) = 0.045 + 0.1/s\). The open-loop transfer function is:
$$
T_{v\_ol}(s) = G_{PI1}(s) \cdot T_{i\_cl}(s) \cdot G_2(s) \cdot H_{n2}(s)
\tag{4.3}
$$
After compensation, the crossover frequency is 0.4 Hz with a phase margin of 45°, achieving good voltage regulation without interaction with the 100 Hz ripple.
4.2 Back-Stage Control
4.2.1 Independent DC-Link Voltage Control
The DC-link voltage of each QZS-HBI unit is given by:
$$
v_{PNn} = v_{C1n} + v_{C2n}
\tag{4.4}
$$
Instead of directly measuring the pulsed DC-link voltage, the sum of the two capacitor voltages is used. The power outer-loop control compares the filtered sum \(v_{C1n} + v_{C2n}\) with the reference \(v^*_{PN}\), and the error is processed by a PI controller with \(K_p = 0.1\), \(K_i = 0.001\). The output of this controller is multiplied by \(v_{PN}\) to obtain the power reference \(P_n\). This mechanism maintains the DC-link voltage of each unit constant and ensures voltage balance among all units.
4.2.2 Grid-Connected Current Control
The total power \(P_T = \sum_{n=1}^{N} P_n\) is used to generate the amplitude of the grid current reference. The reference current is:
$$
i_g^* = \frac{P_T}{V_M} \cdot 2\sin\theta
\tag{4.5}
$$
where \(V_M\) and \(\theta\) are obtained from the phase-locked loop (PLL). The current error is processed by a PI controller with \(K_p = 40\), \(K_i = 400\). The output is added to the grid voltage \(v_g\) to form the total inverter voltage reference \(v_H^*\). The open-loop transfer function of the current inner loop is:
$$
G_{gc\_ol}(s) = \frac{K_p s + K_i}{L_g s^2}
\tag{4.6}
$$
After compensation, the crossover frequency is about 1 kHz with a phase margin above 60°. The closed-loop transfer function exhibits nearly zero steady-state error and zero phase shift at 50 Hz.
4.2.3 Power Imbalance Control: Optimal Third-Harmonic Compensation
When severe power imbalance occurs, units with higher power output may enter over-modulation. To extend the linear modulation range, an optimal third-harmonic voltage is injected into the over-modulated units. The modulated wave with third-harmonic injection can be expressed as:
$$
m(t) = M \sin(\omega t) + k M \sin(3\omega t)
\tag{4.7}
$$
Let \(\varphi = \omega t\). Then the modulation wave becomes:
$$
m(\varphi) = M \left[ \sin\varphi + k \sin(3\varphi) \right]
\tag{4.8}
$$
By analyzing the maximum value of the term \(\sin\varphi + k \sin(3\varphi)\), it is found that the minimum possible maximum value occurs at \(k = 1/6\), where:
$$
\max_{\varphi} \left[ \sin\varphi + \frac{1}{6} \sin(3\varphi) \right] = \frac{\sqrt{3}}{2} \approx 0.866
\tag{4.9}
$$
Consequently, the modulation ratio can be increased from \(1-D_0\) to \(0.790\) without entering over-modulation, expanding the operating range by about 15.5%.
For a given over-modulated unit with modulation ratio \(M_n\), the optimal third-harmonic compensation coefficient \(k_n\) is calculated using the polynomial fitting curve:
$$
k_n = A_0 + A_1 M_n + A_2 M_n^2 + A_3 M_n^3 + A_4 M_n^4 + A_5 M_n^5
\tag{4.10}
$$
The fitting coefficients are given in Table 3.
| Coefficient | Value |
|---|---|
| \(A_0\) | -5686.1898 |
| \(A_1\) | 40173.8322 |
| \(A_2\) | -113456.7850 |
| \(A_3\) | 160087.3579 |
| \(A_4\) | -112849.4621 |
| \(A_5\) | 31793.5754 |
After injecting the optimal third harmonic into the over-modulated units, the total third-harmonic voltage injected into the system is:
$$
V_3^{T} = \sum_{n=1}^{x} k_n M_n v_{PNn}
\tag{4.11}
$$
To prevent the third harmonic from appearing in the grid current, an equal amount of reverse third-harmonic voltage must be injected into the non-over-modulated units. The allowable maximum third-harmonic voltage in the \(n\)-th non-over-modulated unit is:
$$
V_{n}^{(max)} = (1-D_0 – M_n) v_{PNn}
\tag{4.12}
$$
The third-harmonic voltage assigned to each non-over-modulated unit is proportional to its available margin:
$$
V_{3}^{NTHn} = \frac{V_{n}^{(max)}}{\sum_{j=x+1}^{N} V_{j}^{(max)}} \cdot V_3^{T}
\tag{4.13}
$$
Thus the final modulation signal for the \(n\)-th non-over-modulated unit is:
$$
m_n(t) = M_n \sin(\omega t) – \frac{V_{3}^{NTHn}}{v_{PNn}} \sin(3\omega t)
\tag{4.14}
$$
This strategy ensures that all units operate within the linear modulation range while the injected positive and negative third harmonics cancel each other in the total output voltage, leaving the grid-connected current free of third-harmonic distortion.
5. Real-Time Simulation and Experimental Verification
5.1 Real-Time Simulation Setup
The real-time simulations were carried out using the RT-LAB platform. The system model was built in Matlab/Simulink and then compiled and downloaded to the RT-LAB simulator. A three-unit QZS-CMI system was modeled with the parameters listed in Table 4.
| Parameter | Value |
|---|---|
| Quasi-Z-source inductance \(L_1\), \(L_2\) | 1 mH |
| Quasi-Z-source capacitance \(C_1\), \(C_2\) | 5 mF |
| Filter inductance \(L_g\) | 2 mH |
| Grid voltage peak \(V_M\) | 120 V |
| Grid frequency \(f\) | 50 Hz |
| Switching frequency \(f_s\) | 20 kHz |
| PV module maximum power | 300 W |
| PV module MPP voltage | 36.8 V |
| PV module MPP current | 8.27 A |
5.2 MPPT and DC-DC Control Results
Initially, all three PV modules were exposed to an irradiance of 1000 W/m² and a temperature of 25°C. At \(t=2\) s, the irradiance of unit 2 was changed to 700 W/m² and that of unit 3 to 500 W/m², while unit 1 remained at 1000 W/m². The MPPT control successfully tracked the new maximum power point within 0.14 s after the disturbance. The PV voltages returned to the MPP voltage (36.8 V), confirming that each unit independently achieves MPPT.
The capacitor voltages \(v_{C1n}\) and \(v_{C2n}\) of the three units are shown in the simulation results. At steady state, \(v_{C1n} \approx 62\) V and \(v_{C2n} \approx 38\) V, summing to the DC-link peak voltage of approximately 100 V. The ripple magnitude is within 5%, satisfying the design specification. The inductor current \(i_{L1n}\) contains no significant double-frequency ripple, indicating effective decoupling.
5.3 Grid-Connected Operation under Power Imbalance
To test the system under severe power imbalance, at \(t=2\) s the irradiance of unit 2 was changed to 500 W/m² and unit 3 to 300 W/m², while unit 1 remained at 1000 W/m². Without third-harmonic compensation, the modulation ratio of unit 1 exceeded the limit \(1-D_0 = 0.684\), causing over-modulation. The grid-connected current waveform became distorted, with THD rising to 10.98%. This confirms the theoretical analysis of over-modulation.
With the proposed optimal third-harmonic compensation, the same power imbalance was applied. The modulation wave of unit 1 was no longer clipped, and all units remained within the linear modulation range. The grid-connected current THD was only 2.39%, which meets the IEEE 519 standard. The grid voltage and current remained in phase, confirming unity power factor operation.
The simulation results are summarized in Table 5.
| Condition | THD before disturbance | THD after disturbance |
|---|---|---|
| Without compensation | 1.87% | 10.98% |
| With optimal third-harmonic compensation | 1.87% | 2.39% |
5.4 Experimental Results
A two-unit QZS-CMI experimental platform was constructed. Each QZS-HBI unit was built on a separate PCB with the designed impedance network and H-bridge. The control was implemented using a YXSPACE-SP2000 controller based on DSP-F28377. The DC input was set to 35 V to emulate the PV module voltage, and the shoot-through duty ratio was 0.318. The measured DC-link voltages of the two units were both approximately 90 V, showing good voltage balance. The output voltage waveform of the two-unit cascaded system confirmed the operation of the improved modulation strategy. Although only open-loop results were obtained due to laboratory limitations, the experimental results validate the boost capability and the feasibility of the proposed modulation approach.
6. Conclusion
This paper has presented a comprehensive study on the grid-connected control strategy of the quasi-Z-source cascaded multilevel photovoltaic inverter. The main contributions and conclusions are as follows:
- The operating principle and boost mechanism of the quasi-Z-source inverter were analyzed in detail. The impedance network parameters were designed based on ripple specifications, and a state-space model of a single QZS-HBI unit was derived. The small-signal transfer functions provide a solid foundation for controller design.
- An improved carrier phase-shifted SPWM strategy that fuses the shoot-through duty cycle with single-arm chopper modulation was proposed. This strategy reduces switching losses while maintaining the boost capability of the QZS-CMI system.
- A complete two-stage control strategy was designed. The front stage achieves independent MPPT and DC-DC dual-loop control for each unit. The back stage implements independent DC-link voltage balance control, grid-connected current control, and power imbalance control. Controller parameters were designed using Bode analysis to ensure adequate stability margins.
- An optimal third-harmonic compensation strategy was proposed to address severe power imbalance. The polynomial fitting method was used to determine the optimal compensation coefficient. By injecting the optimal third harmonic into over-modulated units and an equal reverse third harmonic into non-over-modulated units, the operating range is expanded without introducing third-harmonic distortion into the grid current.
- Real-time simulations on the RT-LAB platform verified the effectiveness of the proposed control strategies. Under severe power imbalance, the grid current THD was reduced from 10.98% to 2.39%, meeting grid standards. Experimental results on a two-unit prototype further validated the theoretical analysis and the feasibility of the design.
Future work will focus on closed-loop experimental verification of the complete system, extension to more than three units, and the application of advanced model predictive control methods to improve the dynamic response of the quasi-Z-source cascaded multilevel photovoltaic inverter.