The evolution of distributed generation, particularly photovoltaic (PV) systems, has placed stringent demands on the power electronic interfaces that connect them to the grid or local loads. A primary challenge stems from the inherent variability of the PV panel’s output voltage, which fluctuates significantly with irradiance and temperature. Conventional voltage-source inverters (VSIs), while prevalent, are fundamentally limited to a buck (step-down) operation. This necessitates a relatively stable and high DC input voltage, often achieved through a preceding DC-DC boost stage or the use of bulky electrolytic capacitors for filtering. This multi-stage approach or reliance on short-lived electrolytic components compromises system efficiency, power density, reliability, and cost-effectiveness. Therefore, the development of efficient, compact, and reliable single-stage solar inverters with inherent buck-boost capability is of paramount importance for modern renewable energy systems.
This article presents a detailed examination of a novel single-stage, non-isolated inverter topology derived from the classic Buck-Boost DC-DC converter principle. The proposed architecture is specifically designed to address the wide input voltage range characteristic of solar applications. The core advantage lies in its ability to provide a balanced and linearized buck-boost inversion in a single power conversion stage, eliminating the need for heavy line-frequency transformers or cascaded converter stages. The topology employs a minimal number of active and passive components. Notably, it does not require large electrolytic capacitors for DC-link stabilization, instead utilizing a small inductor for energy storage and a film capacitor for AC output filtering. This contributes directly to enhanced longevity, reduced volume, and lower cost. A key innovation discussed herein is the implementation of a specialized nonlinear Pulse Width Modulation (PWM) strategy. This strategy effectively linearizes the inherently nonlinear input-to-output voltage gain relationship of the basic Buck-Boost cell, simplifying control system design and enabling pure sinusoidal output waveforms. We will systematically explore the operational principles, modulation technique, dynamic modeling, control design, and validation through simulation and experimental results of this promising solar inverter topology.
Topology and Operational Principles
The proposed single-stage non-isolated Buck-Boost inverter topology is illustrated in the conceptual diagram below. It can be conceptually deconstructed into two functional sections: a DC transformation section and a polarity reversal section. The DC transformation section is responsible for processing the input PV voltage ($U_{dc}$) and comprises the switches $S_4$, $S_5$, and the storage inductor $L_{dc}$. The polarity reversal section, which operates at the output line frequency, directs the processed energy to the load with the correct AC polarity. This section ingeniously reuses switch $S_4$ and employs switches $S_1$, $S_2$, and $S_3$ along with diodes $VD_1$, $VD_2$, and $VD_3$ to form the AC output bridge. The output $LC$ filter ($L_1$, $C_1$) smoothens the switched voltage to produce a sinusoidal voltage $u_o$ across the load $Z$.
The operation of this solar inverter alternates between two primary modes within each half-cycle of the output AC waveform. The four distinct switching states are summarized in Table 1 and described thereafter.
| State | Active Switches | Inductor $L_{dc}$ | Energy Flow | Output Half-Cycle |
|---|---|---|---|---|
| 1 | $S_4$, $S_5$ | Charging from $U_{dc}$ | Input to Inductor | Positive |
| 2 | $S_2$, $S_3$ | Discharging | Inductor to Load | Positive |
| 3 | $S_4$, $S_5$ | Charging from $U_{dc}$ | Input to Inductor | Negative |
| 4 | $S_1$, $S_4$ | Discharging | Inductor to Load | Negative |
State 1 (Positive Half-Cycle, Inductor Charging): During the positive output half-cycle, when switches $S_4$ and $S_5$ are turned on simultaneously, a charging loop is established: $U_{dc}^+ \rightarrow S_5 \rightarrow L_{dc} \rightarrow S_4 \rightarrow U_{dc}^-$. The input source $U_{dc}$ directly charges the inductor $L_{dc}$, causing its current $i_L$ to increase linearly. Meanwhile, the output filter capacitor $C_1$ supplies energy to the load, maintaining the output voltage.
State 2 (Positive Half-Cycle, Inductor Discharging): When switches $S_2$ and $S_3$ are turned on, the energy stored in $L_{dc}$ is transferred to the load and the output capacitor. The current path is: $L_{dc} (n) \rightarrow VD_2 \rightarrow S_2 \rightarrow L_1 \rightarrow Load \rightarrow VD_3 \rightarrow S_3 \rightarrow L_{dc} (m)$. This delivers a positive voltage to the load.
State 3 (Negative Half-Cycle, Inductor Charging): Similar to State 1, $S_4$ and $S_5$ are turned on to charge the inductor $L_{dc}$ from the input source. During this period, the output voltage is negative, and the filter capacitor $C_1$ discharges through the load, sustaining the output waveform.
State 4 (Negative Half-Cycle, Inductor Discharging): To generate the negative output voltage, switches $S_1$ and $S_4$ are turned on. The inductor discharge path is: $L_{dc} (n) \rightarrow S_4 \rightarrow Load \rightarrow L_1 \rightarrow S_1 \rightarrow VD_1 \rightarrow L_{dc} (m)$. This effectively applies a negative voltage across the load terminals.
This operational sequence reveals that the inductor current $i_L$ is a rectified sinusoidal waveform at twice the output frequency, superimposed on a high-frequency switching ripple. This characteristic differentiates it from traditional current-source inverters which require a constant DC current, allowing for a significantly smaller and lower-loss inductor $L_{dc}$ in this topology.
Modulation Strategy for Linearized Gain
A fundamental challenge in applying Buck-Boost derived topologies as solar inverters is their intrinsic nonlinear voltage gain. The classical steady-state relationship for a DC-DC Buck-Boost converter is $V_o = \frac{D}{1-D} V_{in}$, where $D$ is the duty cycle. Direct application of sinusoidal PWM (SPWM) to the proposed inverter, using $d(t) = m_1 |\sin(\omega t)|$ where $m_1$ is the modulation index, results in an output voltage given by:
$$ u_o(t) = \begin{cases}
+\frac{m_1 |\sin(\omega t)|}{1 – m_1 |\sin(\omega t)|} U_{dc}, & 0 < \omega t < \pi \\
-\frac{m_1 |\sin(\omega t)|}{1 – m_1 |\sin(\omega t)|} U_{dc}, & \pi < \omega t < 2\pi
\end{cases} $$
The peak voltage gain $M_{SPWM}$ becomes:
$$ M_{SPWM} = \frac{U_{o,peak}}{U_{dc}} = \frac{m_1}{1-m_1} $$
While this confirms buck-boost capability ($M<1$ for $m_1<0.5$, $M>1$ for $m_1>0.5$), the output waveform $u_o(t)$ is not a pure sinusoid due to the nonlinear distortion introduced by the $\frac{m_1 |\sin(\omega t)|}{1 – m_1 |\sin(\omega t)|}$ term. This complicates control and filter design.
To achieve a linear and controllable input-output relationship essential for high-performance solar inverters, a nonlinear PWM (NPWM) strategy is adopted. The desired relationship is a pure sinusoidal modulation: $u_o(t) / U_{dc} = m_1 \sin(\omega t)$. By equating this with the Buck-Boost gain formula $u_o(t) / U_{dc} = \frac{d(t)}{1-d(t)} \cdot \text{sgn}(\sin(\omega t))$, we can solve for the required duty cycle function $d(t)$:
$$ d(t) = \frac{m_1 |\sin(\omega t)|}{1 + m_1 |\sin(\omega t)|} $$
This $d(t)$ becomes the modified modulation wave. The peak gain with NPWM is simply:
$$ M_{NPWM} = m_1 $$
This is a crucial result. It demonstrates that with the proposed NPWM, the inverter’s gain is linear and directly equal to the modulation index $m_1$. The solar inverter operates in buck mode when $m_1 < 1$, boost mode when $m_1 > 1$, and unity gain when $m_1 = 1$. The control system can now linearly command the output voltage amplitude by adjusting $m_1$, greatly simplifying the controller design for applications with widely varying PV voltage. The switching logic derived from this modulation scheme ensures that only one switch ($S_5$) operates at high frequency continuously, while others operate at either high frequency during one half-cycle or at line frequency, leading to reduced switching losses compared to full-bridge VSIs where all switches operate at high frequency.
Dynamic Modeling and Controller Design
To ensure stable operation and high-quality output from the solar inverter under varying load and input conditions, a closed-loop control system is essential. Designing an effective controller requires a dynamic model of the system. The model is derived considering the output $LC$ filter and the averaging effect of the PWM modulator. The control-to-output transfer function $G_o(s)$, which relates the modulating signal $V_m(s)$ to the output voltage $U_o(s)$, can be expressed as the product of the modulator gain and the filter transfer function:
$$ G_o(s) = \frac{U_o(s)}{V_m(s)} = \frac{U_o(s)}{I_h(s)} \cdot \frac{I_h(s)}{V_m(s)} = \frac{1}{L_1 C_1 s^2 + R C_1 s + 1} \cdot \frac{U_{dc}}{V_{tri}} $$
where $I_h(s)$ is the current injected into the filter, $V_{tri}$ is the peak amplitude of the triangular carrier wave, $L_1$ and $C_1$ are the filter inductance and capacitance, and $R$ is the load resistance. For a designed filter with $L_1 = 3 \text{ mH}$, $C_1 = 2.2 \mu\text{F}$, $R = 50 \Omega$, $U_{dc} = 100 \text{ V}$, and $V_{tri} = 1 \text{ V}$, the transfer function becomes:
$$ G_o(s) = \frac{100}{6.6 \times 10^{-9} s^2 + 1.1 \times 10^{-4} s + 1} $$
Analysis of the open-loop Bode plot of $G_o(s)$ reveals a phase margin of only about 7.78°, indicating poor stability and a sluggish transient response. This necessitates compensation.
For single-phase solar inverters, a Proportional-Resonant (PR) controller is highly effective because it provides near-infinite gain at the fundamental AC frequency (e.g., 50/60 Hz), ensuring zero steady-state error in tracking the sinusoidal reference. The ideal PR controller transfer function is:
$$ G_c(s) = K_P + \frac{2K_R \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
where $K_P$ is the proportional gain, $K_R$ is the resonant gain, $\omega_0$ is the resonant frequency (fundamental angular frequency), and $\omega_c$ is a small cutoff frequency to improve robustness. After tuning for stability and performance, the compensated open-loop transfer function $G_c(s)G_o(s)$ shows significantly improved characteristics: a phase margin over 75° and a gain margin over 25 dB. The high gain at $\omega_0$ ensures accurate reference tracking, while the sufficient phase and gain margins guarantee stability under parameter variations and disturbances common in PV systems, such as sudden changes in irradiance (input voltage $U_{dc}$) or load connection/disconnection.
For grid-connected operation of the solar inverter, the control structure shifts from voltage control to grid-current control. The PR controller is similarly employed but its reference is the desired sinusoidal grid current, often derived from a Maximum Power Point Tracking (MPPT) algorithm. The output of the current controller generates the modulation signal for the NPWM block, forcing the inverter to inject a high-quality, in-phase current into the utility grid.
Simulation and Experimental Verification
The theoretical analysis, modulation strategy, and controller design for the proposed Buck-Boost solar inverter were validated through detailed simulation and a scaled-down experimental prototype. The key system parameters are summarized in Table 2.
| Parameter | Symbol | Value |
|---|---|---|
| Input DC Voltage Range | $U_{dc}$ | 80 – 120 V |
| Rated Output AC Voltage | $u_o$ | 100 Vrms / 141 Vpeak |
| Output Frequency | $f$ | 50 Hz |
| Switching Frequency | $f_{sw}$ | 20 kHz |
| DC Inductor | $L_{dc}$ | 1.5 mH |
| Filter Inductor | $L_1$ | 3 mH |
| Filter Capacitor | $C_1$ | 2.2 µF |
| Rated Power | $P_{rated}$ | 200 W |
Simulation Results: Initial simulations compared SPWM and NPWM. With $U_{dc}=60V$ and SPWM ($m_1=0.5$), the output was a distorted sinewave with a 60V peak, confirming the nonlinear gain. With NPWM, setting $m_1=1$ yielded a perfect 60V peak sinewave, $m_1=0.5$ yielded a 30V peak (buck operation), and $m_1=1.5$ yielded a 90V peak (boost operation), validating the linear $M=m_1$ relationship. Closed-loop simulations demonstrated robust performance. With a 100V peak voltage reference, a step in input voltage from 80V to 120V and back was rejected within a few cycles with minimal overshoot. Similarly, step changes in load from 100% to 50% and back were handled effectively, with the output voltage quickly recovering to its reference. Grid-connected simulations showed the inverter successfully injecting a sinusoidal current with low total harmonic distortion (THD) into the grid, even during input voltage transients.
Experimental Results: A 200W laboratory prototype was built. Open-loop tests clearly demonstrated the buck-boost functionality. With $U_{dc}=60V$ and appropriate modulation, output peaks of 80V (boost) and 25V (buck) were achieved, with the inductor current $i_L$ visibly pulsating at 100 Hz as predicted. Closed-loop experimental waveforms confirmed the dynamic performance. For a 100V peak reference, a sudden input voltage step from 80V to 120V caused a minor, fast-recovering disturbance in the output. Load step changes also resulted in stable, well-damped transients. The inverter consistently produced a high-quality sinusoidal output voltage. The measured efficiency curve of the prototype, under hard-switching conditions, is shown in Table 3. The peak efficiency exceeds 94%, which is notable for a single-stage converter. This high efficiency is attributed to the low component count, the use of only one continuously high-frequency switch, and the absence of lossy electrolytic capacitors. Efficiency could be further improved with optimized magnetic components and the use of modern wide-bandgap semiconductor devices.
| Output Power (W) | Efficiency (%) |
|---|---|
| 200 | 94.2 |
| 180 | 94.5 |
| 160 | 94.7 |
| 140 | 94.8 |
| 120 | 94.6 |
| 100 | 94.1 |
Conclusion
This article has presented a comprehensive study of a novel single-stage non-isolated Buck-Boost inverter topology, highlighting its particular suitability for solar energy applications characterized by a wide input voltage range. The topology achieves a balanced buck-boost capability within a single power conversion stage, leading to a system with high component count efficiency, reduced volume, and potentially lower cost due to the elimination of a front-end DC-DC stage and large electrolytic capacitors. The introduction of a specific nonlinear PWM strategy was crucial, as it successfully linearized the control characteristic, allowing the output voltage amplitude to be directly and linearly controlled via the modulation index. This greatly simplifies the design of the control system for these solar inverters. Detailed dynamic modeling and PR controller design ensured system stability and excellent reference tracking under disturbances. Both simulation and experimental results on a 200W prototype validated all theoretical claims, demonstrating satisfactory steady-state and dynamic performance for both standalone and grid-connected operations. The topology exhibits clear advantages in efficiency and simplicity, making it a compelling candidate for small to medium-power photovoltaic systems, micro-inverters, and other renewable energy interfaces where input voltage variation is a primary concern. Future work may focus on optimizing the magnetic design, implementing soft-switching techniques to push efficiency even higher, and developing advanced MPPT algorithms integrated seamlessly with the proposed NPWM control for these innovative solar inverters.