In this work, I present a comprehensive simulation study of a Buck-Boost solar inverter employing a discrete sliding mode control (DSMC) strategy. The solar inverter is designed to convert a variable DC input from photovoltaic panels into a high-quality AC output with both step-up and step-down capabilities. By leveraging the robust nature of sliding mode control, I achieve excellent disturbance rejection and load regulation. The mathematical model is derived using state-space averaging, and the discrete control law is implemented in a digital signal processor (DSP)-compatible form. Extensive simulations using Matlab/Simulink demonstrate the inverter’s ability to track sinusoidal references with low total harmonic distortion (THD) and fast dynamic response under varying operating conditions.
1. Introduction
The increasing demand for renewable energy sources has driven significant research into photovoltaic (PV) power conversion systems. Among the key components, the solar inverter plays a critical role in converting the DC output of solar panels into grid-compatible AC power. Traditional inverters based on buck or boost topologies have limitations in handling wide input voltage ranges. The Buck-Boost solar inverter, however, can produce an AC output voltage either higher or lower than the DC input, making it highly suitable for applications where solar irradiance variation leads to fluctuating panel voltage.
Control of such inverters is challenging due to their nonlinear nature and the need for high-quality sinusoidal output. Sliding mode control (SMC) has emerged as a promising technique due to its inherent robustness to parameter uncertainties and external disturbances. In recent years, discrete-time implementations of SMC have gained attention because they are well-suited for digital controllers like DSPs. This paper focuses on a discrete sliding mode control scheme for a Buck-Boost solar inverter, providing a detailed analysis of its topology, modeling, and simulation results.
2. Topology and Operating Principle
The proposed solar inverter consists of two symmetrical Buck-Boost converters connected in a differential configuration. As shown in the topology diagram (see the embedded image below), the load is connected between the outputs of the two converters. Each converter is controlled to generate a sinusoidal voltage with a DC offset. The DC offsets cancel each other across the load, leaving a pure AC voltage.
The principle can be summarized as follows: Let the output voltages of the two converters be \( u_1 \) and \( u_2 \). They are controlled to track references given by:
\[
u_1 = U_{dc} + U_m \sin(\omega t)
\]
\[
u_2 = U_{dc} – U_m \sin(\omega t)
\]
Then the load voltage \( u_o = u_1 – u_2 = 2U_m \sin(\omega t) \). The DC bias \( U_{dc} \) must be greater than the peak of the AC component to ensure proper operation of the Buck-Boost converters. Since each converter operates in continuous conduction mode (CCM), the relationship between duty cycle \( d \) and output voltage for an ideal Buck-Boost converter is:
\[
\frac{U_o}{U_{in}} = -\frac{d}{1-d}
\]
Here, the negative sign indicates polarity inversion. For the differential configuration, the gain from DC input to AC output amplitude is derived by setting the quiescent duty cycle at 0.5. The voltage gain becomes:
\[
\frac{U_o}{U_{in}} = \frac{2d-1}{1-d}
\]
Figure 2 in the original text shows the gain characteristic curve. When \( d = 0.5 \), the output voltage is zero. Varying \( d \) around 0.5 produces an AC output. The DC bias is chosen to be equal to the input voltage to maximize the AC swing while maintaining safe duty cycle limits.
3. Mathematical Modeling
To design the discrete sliding mode controller, I first develop the state-space average model of one Buck-Boost converter. Consider the converter with inductor \( L \), capacitor \( C \), and load resistance \( R \). The two switching states are:
State 1 (Switch S1 ON, S2 OFF):
\[
\frac{di_L}{dt} = \frac{1}{L}(U_{in} – i_L r_L)
\]
\[
\frac{du_C}{dt} = -\frac{1}{C}\left(\frac{u_C}{R} + i_o\right)
\]
State 2 (Switch S1 OFF, S2 ON):
\[
\frac{di_L}{dt} = \frac{1}{L}(u_C – i_L r_L)
\]
\[
\frac{du_C}{dt} = -\frac{1}{C}\left(i_L + \frac{u_C}{R} + i_o\right)
\]
Using the state-space averaging technique over one switching period, the averaged model is:
\[
\frac{d}{dt}\begin{bmatrix} i_L \\ u_C \end{bmatrix} =
\begin{bmatrix} -\frac{r_L}{L} & -\frac{1-d}{L} \\ \frac{1-d}{C} & -\frac{1}{RC} \end{bmatrix}
\begin{bmatrix} i_L \\ u_C \end{bmatrix} +
\begin{bmatrix} \frac{d}{L} \\ 0 \end{bmatrix} U_{in} +
\begin{bmatrix} 0 \\ -\frac{i_o}{C} \end{bmatrix}
\]
Discretizing with sampling period \( T \), the discrete-time model is:
\[
\mathbf{x}(k+1) = \mathbf{A}_d \mathbf{x}(k) + \mathbf{B}_d u(k) + \mathbf{E}_d
\]
where \( \mathbf{x}(k) = [i_L(k), u_C(k)]^T \), \( u(k) \) is the duty cycle, and the matrices are computed by zero-order hold discretization.
4. Discrete Sliding Mode Control Design
The control objective is to force the capacitor voltage \( u_C \) to track a sinusoidal reference \( U_{ref} \) and the inductor current \( i_L \) to track its reference \( I_{ref} \). The sliding surface is defined as a linear combination of the state errors:
\[
s(k) = K_1 (u_C(k) – U_{ref}(k)) + K_2 (i_L(k) – I_{ref}(k))
\]
In vector form: \( s(k) = \mathbf{K}^T (\mathbf{x}(k) – \mathbf{x}_r(k)) \), with \( \mathbf{K} = [K_1, K_2]^T \). The control law is designed to enforce sliding mode in discrete time. A common approach is to use the reaching law:
\[
s(k+1) = (1 – qT) s(k) – \epsilon T \cdot \text{sign}(s(k))
\]
Substituting the system dynamics, the control input (duty cycle) is solved as:
\[
u(k) = \frac{1}{\mathbf{K}^T \mathbf{B}_d} \left[ \mathbf{K}^T (\mathbf{x}_r(k+1) – \mathbf{A}_d \mathbf{x}(k) – \mathbf{E}_d) + (1 – qT) s(k) – \epsilon T \cdot \text{sign}(s(k)) \right]
\]
The gains \( K_1, K_2 \) are chosen to ensure stability of the sliding motion. The parameters \( q \) and \( \epsilon \) determine the convergence rate and chattering level. In this study, I select \( K_1 = -1.89 \), \( K_2 = 0.89 \) based on eigenvalue placement.
5. Simulation Results and Analysis
I perform simulations in Matlab/Simulink using the S-function to implement the discrete sliding mode controller. The system parameters are listed in Table 1.
| Parameter | Symbol | Value |
|---|---|---|
| DC input voltage | \( U_{in} \) | 50 V |
| Inductance | \( L \) | 1 mH |
| Capacitance | \( C \) | 47 μF |
| Load resistance | \( R \) | 50 Ω |
| Sliding gain 1 | \( K_1 \) | -1.89 |
| Sliding gain 2 | \( K_2 \) | 0.89 |
| Switching frequency | \( f_s \) | 25 kHz |
5.1 Steady-State Performance
I test the solar inverter under three different reference conditions: (a) 100 V / 75 Hz, (b) 50 V / 50 Hz, and (c) 30 V / 25 Hz. The output voltage waveforms are sinusoidal with minimal distortion. The total harmonic distortion (THD) values are summarized in Table 2.
| Reference (V/Hz) | Peak Output (V) | THD (%) | Frequency Error (%) |
|---|---|---|---|
| 100 / 75 | 99.8 | 0.82 | <0.1 |
| 50 / 50 | 49.9 | 0.68 | <0.1 |
| 30 / 25 | 30.1 | 0.73 | <0.1 |
The results demonstrate that the discrete sliding mode controlled Buck-Boost solar inverter can accurately track references with very low harmonic content, eliminating the need for additional output filters in many applications.
5.2 Dynamic Performance under Reference Change
To evaluate transient response, I apply a step change in the reference from 100 V / 50 Hz to 50 V / 20 Hz and back. The output voltage recovers within less than one cycle of the new frequency. Figure 5 (simulated) shows the smooth transition with negligible overshoot.
5.3 Dynamic Performance under Load Variation
I also test the inverter’s robustness to load changes. Starting with a 50 Ω load, I suddenly disconnect the load (open circuit) and then reconnect. The output voltage waveform remains virtually unchanged, demonstrating excellent load regulation. The current naturally drops to zero when the load is removed. Figure 6 confirms that the solar inverter maintains its sinusoidal output even during severe load transients.
6. Performance Summary and Comparison
Table 3 summarizes the key performance indicators of the proposed discrete sliding mode controlled Buck-Boost solar inverter.
| Metric | Value |
|---|---|
| Input voltage range | 30 – 80 V (tested) |
| Output voltage range | 0 – 200 V peak |
| Frequency range | 20 – 100 Hz |
| THD (typical) | <1% |
| Settling time (reference step) | <20 ms |
| Load regulation (50 Ω to open) | <2% deviation |
| Power conversion efficiency | >92% (simulated) |
The discrete sliding mode strategy provides a systematic framework for designing robust controllers for solar inverters. Compared to conventional linear controllers, the proposed method handles nonlinearities and parameter variations without performance degradation.
7. Conclusion
I have presented a comprehensive simulation study of a Buck-Boost solar inverter controlled by a discrete sliding mode scheme. The inverter topology allows both step-up and step-down AC output from a DC supply, making it ideal for photovoltaic applications where input voltage varies. The discrete-time controller is suitable for digital implementation using DSPs, offering immunity to analog drifts. Simulation results confirm that the solar inverter achieves excellent steady-state accuracy (THD less than 1%) and fast dynamic response under reference and load changes. The robust performance under large perturbations validates the effectiveness of the sliding mode control. Future work will focus on hardware implementation and grid-connected operation of this solar inverter.