In this work, we address the challenges of unstable zero dynamics and nonlinear characteristics in quasi-Z-source inverters (qZSI) used for grid-connected photovoltaic systems under DC-side voltage fluctuations. These issues lead to system oscillations, slow dynamic response, and complex control design. We propose an integral compensation fixed-frequency current integral sliding mode (ISM) control strategy enhanced by a radial basis function (RBF) neural network. The RBF network adaptively tunes controller parameters and approximates the nonlinear model, effectively reducing chattering and improving robustness. Simulation results in MATLAB/Simulink demonstrate that our RBF-ISM method achieves faster dynamic response and superior disturbance rejection compared to conventional sliding mode control (SMC). This study contributes to the advancement of high-performance types of solar inverter technologies, particularly for renewable energy integration.
1. Introduction
With the global push toward carbon neutrality and the expansion of distributed generation, grid-connected inverters play a pivotal role in photovoltaic (PV) systems. Among various types of solar inverter, the quasi-Z-source inverter (qZSI) has gained attention due to its single-stage buck-boost capability, low harmonic distortion, shoot-through immunity, and high reliability. However, qZSI systems exhibit nonlinear dynamics and right-half-plane zeros in the transfer function under continuous conduction mode (CCM), which degrade transient performance and limit control bandwidth. Conventional linear controllers like PI or PR often fail to maintain stability under wide input voltage variations.
Sliding mode control (SMC) is a robust nonlinear method well-suited for power converters due to its inherent switching nature. Nevertheless, standard SMC suffers from chattering and sensitivity to parameter uncertainties. To overcome these limitations, we integrate an integral sliding surface with RBF neural network adaptation. The RBF network dynamically adjusts the switching gain, providing smooth control action while preserving robustness. Our approach is specifically designed for types of solar inverter operating in grid-connected mode, ensuring fast dynamic response and excellent steady-state performance.
2. Quasi-Z-Source Inverter Modeling
2.1 System Configuration
The three-phase qZSI system consists of a PV module, a quasi-Z-source network (inductors L1, L2; capacitors C1, C2; diode D), an inverter bridge, and an LCL filter. The network operates in two states: shoot-through (ST) and non-shoot-through (NST), enabling voltage boost.
2.2 Large-Signal Model
Assuming symmetrical components \( L_1 = L_2 = L \), \( C_1 = C_2 = C \), the state-space equations for ST and NST states are:
Shoot-through state:
$$
\frac{di_{L1}}{dt} = \frac{u_{C2} + V_{in}}{L}, \quad \frac{di_{L2}}{dt} = \frac{u_{C1}}{L}, \quad \frac{du_{C1}}{dt} = \frac{i_{L2}}{C}, \quad \frac{du_{C2}}{dt} = \frac{i_{L1}}{C}
$$
Non-shoot-through state:
$$
\frac{di_{L1}}{dt} = \frac{V_{in} – u_{C1}}{L}, \quad \frac{di_{L2}}{dt} = \frac{-u_{C2}}{L}, \quad \frac{du_{C1}}{dt} = \frac{i_{L1} – i_{dc}}{C}, \quad \frac{du_{C2}}{dt} = \frac{i_{L2} – i_{dc}}{C}
$$
By introducing a switching function \( u \) (1 for ST, 0 for NST), the unified model is:
$$
\dot{X} = A + B u
$$
where \( X = [i_{L1}, i_{L2}, u_{C1}, u_{C2}]^T \), and matrices A, B are derived from the above equations. This model forms the basis for our control design, which is applicable to all types of solar inverter utilizing qZSI topology.
3. RBF Neural Network Integral Sliding Mode Controller
3.1 Sliding Surface Design
We select the following state variables for the sliding surface:
$$
x_1 = i_{L1} – i_{L1}^*, \quad x_2 = u_{C1} – u_{C1}^*, \quad x_3 = \int [(i_{L1} – i_{L1}^*) + (u_{C1} – u_{C1}^*)] dt
$$
The sliding surface is defined as:
$$
S = \alpha_1 x_1 + \alpha_2 x_2 + \alpha_3 x_3
$$
where \( \alpha_1, \alpha_2, \alpha_3 \) are sliding coefficients. The reference current \( i_{L1}^* \) is generated by a PI-type compensator to eliminate steady-state error:
$$
i_{L1}^* = K_i \int (u_{C1} – u_{C1}^*) dt + K_p (u_{C1} – u_{C1}^*)
$$
3.2 Equivalent Control Law
Taking the derivative of S and substituting the system dynamics yields the equivalent control \( u_{eq} \):
$$
u_{eq} = \frac{(u_{C1} – V_{in}) + k_1(u_{C1} – u_{C1}^*) – k_2(i_{L1} – i_{dc}) – k_3[i_{L1} – K_i\int(u_{C1} – u_{C1}^*) dt]}{(u_{C1} + u_{C2}) + k_2(i_{dc} – i_{L1} – i_{L2})}
$$
with parameters \( k_1, k_2, k_3 \) chosen to ensure reachability and stability. The equivalent control is directly used as the shoot-through duty ratio \( D \) (0 < D < 0.5). This control law is independent of specific types of solar inverter and can be generalized to similar topologies.
3.3 Existence Condition
To guarantee the sliding mode exists, we require:
$$
\lim_{S \to 0^+} \dot{S} < 0, \quad \lim_{S \to 0^-} \dot{S} > 0
$$
Using steady-state approximations, the existence condition simplifies to:
$$
\begin{cases}
V_{in,max} – k_1(u_{C1,ss} – u_{C1}^*) + k_2(i_{L1,min} – i_{dc,ss}) + k_3[i_{L1,min} – K_i\int(u_{C1,ss} – u_{C1}^*) dt] < u_{C1,ss} \\
V_{in,min} – k_1(u_{C1,ss} – u_{C1}^*) – k_2 i_{L2,max} + k_3[i_{L1,max} – K_i\int(u_{C1,ss} – u_{C1}^*) dt] < -u_{C2,ss}
\end{cases}
$$
These conditions are verified over the expected operating range of the types of solar inverter we consider.
3.4 Stability Analysis
The ideal sliding dynamics are obtained by substituting \( u_{eq} \) into the system model. Linearizing around the equilibrium point yields the characteristic equation:
$$
\det(A_s – \lambda I) = 0
$$
Proper selection of \( \alpha_1, \alpha_2, \alpha_3 \) ensures all eigenvalues lie in the left half-plane, guaranteeing asymptotic stability. Our design methodology applies to various types of solar inverter with different ratings.
3.5 RBF Neural Network for Gain Adaptation
To mitigate chattering, we employ an RBF neural network that adaptively adjusts the switching gain \( \varepsilon \). The network has a 2-3-1 structure: inputs \( [S, \dot{S}]^T \), hidden layer with Gaussian activation functions, and output \( \varepsilon \). The output is:
$$
y_m = \varepsilon = \mathbf{w}^T \mathbf{h}(x)
$$
where \( \mathbf{w} = [w_1, w_2, w_3]^T \) are weights, and \( h_i(x) = \exp\left(-\frac{\|x – c_i\|^2}{2b_i^2}\right) \) are Gaussian functions. The weights, centers, and widths are updated via gradient descent to minimize \( E = \frac{1}{2} e^2 \) where \( e = S \). The update laws are:
Weight update:
$$
\Delta w_i = \eta \, e \, \text{sgn}(S) \, h_i(x) \, \text{sgn}(w_i h_i(x))
$$
$$
w_i(t) = w_i(t-1) + \Delta w_i(t) + \alpha (w_i(t) – w_i(t-1))
$$
Center update:
$$
\Delta c_{ij} = \eta \, e \, \text{sgn}(S) \, w_i \, \frac{\partial h_i}{\partial c_{ij}}, \quad c_{ij}(t) = c_{ij}(t-1) + \Delta c_{ij}(t) + \alpha (c_{ij}(t) – c_{ij}(t-1))
$$
Width update:
$$
\Delta b_i = \eta \, e \, \text{sgn}(S) \, w_i \, \frac{\partial h_i}{\partial b_i}, \quad b_i(t) = b_i(t-1) + \Delta b_i(t) + \alpha (b_i(t) – b_i(t-1))
$$
This adaptive mechanism ensures robust performance across different operating conditions for all types of solar inverter.
4. Simulation Results
We implement our RBF-ISM controller in MATLAB/Simulink and compare it with conventional SMC. System parameters are given in Table 1.
| Parameter | Value |
|---|---|
| qZSI inductance \( L \) | 3 mH |
| qZSI capacitance \( C \) | 500 μF |
| Filter inductance | 3 mH |
| Filter capacitance | 2 μF |
| Switching frequency | 10 kHz |
| DC input voltage (\( V_{in} \)) | 500 V → 600 V (step at 1 s), back to 500 V (1.5 s) |
The test scenario involves a sudden change in DC input voltage to emulate real-world PV fluctuations. Figure 1 shows the grid-connected current waveforms under both controllers.
Performance Comparison: Table 2 summarizes key performance metrics during the voltage step change at 1 s.
| Metric | SMC | RBF-ISM |
|---|---|---|
| Settling time (ms) | 15 | 8 |
| Overshoot in DC-link voltage (%) | 12 | 3 |
| Current THD (%) | 4.5 | 2.8 |
| Chattering amplitude (A) | 0.8 | 0.2 |
As observed, our RBF-ISM controller achieves faster transient recovery with significantly reduced overshoot and chattering. The active and reactive power tracking is also smoother, as shown in the simulation data. These results validate the effectiveness of the proposed method for various types of solar inverter in grid-connected applications.
5. Conclusion
We have developed a novel RBF-ISM control strategy for quasi-Z-source inverters in photovoltaic systems. By combining integral sliding mode with RBF neural network adaptation, the controller effectively mitigates chattering while preserving robustness against DC-side voltage fluctuations. The theoretical analysis covers sliding surface design, existence conditions, and stability proof. Simulation comparisons demonstrate superior dynamic response, lower THD, and improved disturbance rejection over conventional SMC. This work provides a practical solution for enhancing the performance of types of solar inverter, particularly in grid-connected renewable energy systems where reliability and fast response are critical.
Future work will extend the approach to multi-inverter parallel operation and consider grid fault conditions. The adaptive nature of RBF-ISM makes it a promising candidate for next-generation types of solar inverter in smart grids.