With the increasing severity of climate change, rising global oil prices, and the depletion of non-renewable resources, countries worldwide are enacting new regulations to promote the development of renewable energy. Solar energy, as a clean and sustainable source, offers numerous advantages such as vast reserves, widespread availability, and economic benefits, attracting significant attention from governments and researchers. By 2030, the total installed capacity of new energy photovoltaic systems in China is projected to reach 1.2 terawatts, and globally, renewable energy is expected to account for 41% of total energy demand by 2040. Solar power, due to its cleanliness and versatility, has become a key solution to alleviate the shortage of conventional fossil fuels and mitigate environmental pollution.
The solar inverter is a core component in the energy conversion process of photovoltaic systems. However, the soft load characteristics of battery arrays require the inverter to operate over a wide input voltage range, track the maximum power point under varying conditions like irradiance, and reduce energy waste, thereby lowering the cost of grid-connected solar power and improving efficiency. Inverters are primarily categorized into single-stage (DC/AC) and multi-stage (e.g., DC/DC followed by DC/AC) topologies. Single-stage inverters directly draw power from the solar panels, offering simplicity but suffering from significant DC-side voltage fluctuations and lower efficiency. Multi-stage inverters, on the other hand, regulate the DC voltage before inversion, enabling higher conversion efficiency, precise control, and enhanced safety by preventing short circuits between power sources. For single-phase grid-connected systems, a two-stage non-isolated topology is often preferred to achieve maximum power point tracking (MPPT) and stable grid integration. The first stage typically employs a Boost converter for MPPT, while the second stage uses an H-bridge inverter for DC/AC conversion. This structure allows independent control of each stage, simplifying implementation and improving flexibility.
The system design, as illustrated in the block diagram, consists of two main parts: a front-end DC/DC Boost converter and a rear-end DC/AC H-bridge inverter. The Boost converter samples the photovoltaic (PV) panel’s output voltage \(U_{pv}\) and current \(I_{pv}\), computes the reference voltage \(U_{pvc}\) for maximum power, and generates a modulation signal \(U_{conp}\) to control the switch duty cycle, enabling dynamic MPPT. The inverter stage isolates and samples the DC bus voltage \(U_d\), compares it with a set value \(U_{dref}\), and processes the error through a PI controller to determine the grid current amplitude. After filtering high-frequency components, a phase-locked loop (PLL) extracts the grid phase angle to generate the reference current \(i_{ref}\), ensuring synchronization with the grid. This dual-loop control strategy not only facilitates grid connection but also maintains stable voltage across the inter-stage capacitor, minimizing fluctuations.
Mathematical Modeling of Photovoltaic Cells
Solar panels are composed of multiple photovoltaic cells connected in series and parallel to meet power requirements. Based on the working principle of PV cells, the equivalent circuit model includes a photocurrent source \(I_{ph}\), a diode representing the PN junction, a shunt resistance \(R_{sh}\), a series resistance \(R_s\), and a junction capacitance \(C_j\). The output current \(I\) and voltage \(V_{pv}\) of the PV array can be derived as:
$$I = I_{ph} – I_0 \left[ \exp\left(\frac{q(V_{pv} + R_s I)}{n k T}\right) – 1 \right] – \frac{V_{pv} + R_s I}{R_{sh}}$$
where \(I_0\) is the reverse saturation current, \(q\) is the electron charge (1.6 × 10^{-19} C), \(n\) is the ideality factor, \(k\) is Boltzmann’s constant (0.86 × 10^{-4} eV/K), and \(T\) is the absolute temperature. The output power \(P\) is given by:
$$P = V_{pv} I = V_{pv} I_{ph} – V_{pv} I_0 \left[ \exp\left(\frac{q(V_{pv} + R_s I)}{n k T}\right) – 1 \right] – \frac{V_{pv}(V_{pv} + R_s I)}{R_{sh}}$$
In practice, \(R_{sh}\) is very large, and \(R_s\) is small, so the equations simplify to:
$$I = I_{ph} – I_0 \left[ \exp\left(\frac{q V_{pv}}{n k T}\right) – 1 \right]$$
$$P = V_{pv} I_{ph} – V_{pv} I_0 \left[ \exp\left(\frac{q V_{pv}}{n k T}\right) – 1 \right]$$
For engineering applications, simplified models use key parameters like short-circuit current \(I_{sc}\), open-circuit voltage \(V_{oc}\), maximum power point voltage \(V_m\), and current \(I_m\). Incorporating irradiance \(S\) and temperature \(T\) variations, the PV characteristics are modeled as:
$$
\begin{aligned}
I_{sc} &= I_{scref} \frac{S}{S_{ref}} (1 + a \cdot \Delta T) \\
V_{oc} &= V_{ocref} (1 – c \cdot \Delta T) \ln(1 + b \cdot \Delta S) \\
I_m &= I_{mref} \frac{S}{S_{ref}} (1 + a \cdot \Delta T) \\
V_m &= V_{mref} (1 – c \cdot \Delta T) \ln(1 + b \cdot \Delta S) \\
\Delta T &= T – T_{ref} \\
\Delta S &= S – S_{ref}
\end{aligned}
$$
where \(S_{ref} = 1000 \, \text{W/m}^2\), \(T_{ref} = 25^\circ \text{C}\), and \(a\), \(b\), \(c\) are compensation coefficients. For simulation and experimentation, a PV module with a power rating of 0–360 W is used, with parameters summarized in Table 1.
| Parameter | Value |
|---|---|
| Open-circuit voltage (V) | 65.0 |
| Short-circuit current (A) | 2.7 |
| Voltage at maximum power point (V) | 50.0 |
| Current at maximum power point (A) | 2.4 |
Variable-Step Perturb and Observe MPPT Control
Photovoltaic cells have low conversion efficiency, typically below 25%, and high costs, making it essential to maximize power output under varying conditions. An improved variable-step perturb and observe (P&O) method is employed for MPPT, adjusting the step size dynamically within each control cycle. The algorithm works by introducing a perturbation in the PV voltage, observing changes in power (\(\Delta P\)) and voltage (\(\Delta V_{pv}\)), and determining the direction and magnitude of the next perturbation to converge toward the maximum power point. The control logic is as follows: if \(\Delta P \geq 0\), the step size remains unchanged; otherwise, it is reduced by a constant \(c_n\). The product \(\Delta P \cdot \Delta V_{pv}\) dictates the perturbation direction: if positive, the direction is maintained; if negative, it is reversed; if zero, no perturbation is applied. This process repeats until the step size approaches zero, ensuring precise tracking. If environmental changes cause significant voltage fluctuations, the step size is reinitialized to restart the tracking process.
The MPPT control enhances the efficiency of solar inverters by minimizing power loss and oscillations. The reference current for the grid-connected inverter \(I_{ref}\) is derived from the MPPT output, and the perturbation step size \(step\) is updated cyclically. This approach allows the solar inverter to adapt quickly to irradiance and temperature variations, maintaining optimal performance.
Voltage and Current Dual-Loop Control Design
The control system for the solar inverter employs a voltage outer loop and a current inner loop to regulate the DC bus voltage and grid current. The current inner loop ensures fast tracking of the reference current, while the voltage outer loop maintains stable DC-link voltage. The current control loop, as shown in the block diagram, includes a PWM block with gain \(K_{PWM}\) and time constant \(T_s\), a current sampling gain \(K_{if}\), and a time delay \(T_{if}\). The PI controller for the current loop is represented as:
$$G(s) = K_{iP} + \frac{K_{iI}}{s} = \frac{K_{iP} (\tau_i s + 1)}{\tau_i s}$$
where \(K_{iP}\) is the proportional gain, \(K_{iI}\) is the integral gain, and \(\tau_i = K_{iP} / K_{iI}\). With grid voltage feedforward to cancel disturbances, the open-loop transfer function of the current loop is:
$$G_{io}(s) = \frac{K_{if} K_{iI} K_{PWM} (\tau_i s + 1) / R}{s (T_{if} s + 1)(T_s s + 1)(L s / R + 1)}$$
Setting \(\tau_i = L / R\) and applying second-order optimum design, the closed-loop transfer function simplifies to:
$$G_{ic}(s) = \frac{K_{iI} K_{PWM} / (1.5 T_s R)}{s^2 + s / (1.5 T_s) + K_{iI} K_{PWM} / (1.5 T_s R)}$$
With a damping ratio \(\xi = 0.707\), the PI parameters are:
$$
\begin{aligned}
K_{iI} &= \frac{R}{3 T_s K_{PWM}} \\
K_{iP} &= \frac{L}{3 T_s K_{PWM}}
\end{aligned}
$$
The voltage outer loop control, as depicted in its block diagram, includes the current loop transfer function \(G_{ic}(s)\), a time delay \(T_{vf}\), and a feedback gain \(K_{vf} = 1\). The DC-link capacitor \(C\) is considered, and the total delay \(T_h = 3T_s + T_{vf}\) is defined. The open-loop transfer function for the voltage loop is:
$$G_{vo}(s) = \frac{K_{vI} (\tau_v s + 1) / C}{s^2 (T_h s + 1)}$$
Designing the voltage controller as a type II system with \(h_v = 5\), the PI parameters are:
$$
\begin{aligned}
K_{vI} &= \frac{3C}{25 T_h^2} \\
K_{vP} &= \frac{3C}{5 T_h}
\end{aligned}
$$
This dual-loop strategy ensures robust performance of the solar inverter, with low steady-state error and high dynamic response.
Hardware Parameter Design and Selection
The system operates under the following conditions: front-end DC/DC input voltage range of 20–80 V, DC bus voltage \(U_d = 80\) V, Boost switching frequency \(f_{Boost} = 40\) kHz, efficiency \(\eta = 96\%\), and output power \(P = 120\) W. The maximum current through the inductor \(I_L\) is 2.5 A, and the inverter switching frequency is 20 kHz, with MOSFET current rating below 3 A.
A. Boost Inductor \(L_1\) Design
The maximum duty cycle \(D_{max}\) is calculated as:
$$D_{max} = \frac{U_{PVmax} – U_{PVmin}}{U_{PVmax}}$$
The average inductor current \(I_{L1o}\) at full load is:
$$I_{L1o} = \frac{P_0}{\eta U_{PV}}$$
Assuming a ripple current \(\Delta I_{Lo} = 30\%\) of the average current, the inductor value is:
$$L_1 = \frac{D U_{PV}}{2 I_{Lo} f_{Boost}}$$
Substituting parameters yields \(L_1 \approx 0.55\) mH.
B. DC-Link Capacitor \(C_{Bus}\) Design
The DC-link capacitor filters the output and supplies energy to the inverter. With a ripple voltage \(\Delta U_d = 5\%\) of \(U_d\), the capacitance is:
$$C_{Bus} = \frac{P_o}{4 \omega \Delta U_d U_d}$$
Calculated as 298 μF, and with a safety margin of 1.5–2 times, \(C_{Bus} = 450\) μF is selected.
C. Filter Inductor \(L_2\) Design
The output filter inductor limits current ripple. The voltage across the inductor \(U_{L2}\) relates to current by:
$$U_{L2} = L_2 \frac{di}{dt}$$
The peak ripple current \(\Delta i\) occurs at maximum output voltage \(U_{L2max}\):
$$\Delta i = \frac{U_{L2max}}{L_2} D T$$
Using the duty cycle \(D = (U_d – U_{L2max}) / U_d\) and setting \(\Delta i = 20\%\) of maximum current, the inductance is:
$$L_2 = \frac{U_{L2max} (U_d – U_{L2max}) T}{\Delta i U_d}$$
This gives \(L_2 = 1.3\) mH, split symmetrically into two 0.65 mH inductors.
D. Filter Capacitor \(C_o\) Design
An LC filter is used, with the corner frequency \(f_s\) satisfying:
$$10 f_g \leq f_s = \frac{1}{2\pi \sqrt{L_2 C_o}} \leq \frac{1}{5} f_H$$
where \(f_g = 50\) Hz is the grid frequency, and \(f_H = 20\) kHz is the inverter switching frequency. Thus,
$$C_o \geq \frac{100}{L_2 (2\pi f_H)^2}$$
With design margins, \(C_o = 10\) μF is chosen.
Table 2 summarizes the key hardware parameters for the solar inverter system.
| Component | Parameter | Value |
|---|---|---|
| Boost Inductor | \(L_1\) | 0.55 mH |
| DC-Link Capacitor | \(C_{Bus}\) | 450 μF |
| Filter Inductor | \(L_2\) | 0.65 mH (each) |
| Filter Capacitor | \(C_o\) | 10 μF |
| Switching Frequency (Boost) | \(f_{Boost}\) | 40 kHz |
| Switching Frequency (Inverter) | \(f_H\) | 20 kHz |
Simulation and Experimental Validation
Based on the above analysis, a simulation model of the two-stage non-isolated single-phase solar inverter was developed in PSIM, incorporating modules for PLL, variable-step MPPT, and dual-loop control. The PV module was simulated with parameters: \(V_{oc} = 65\) V, \(I_{sc} = 2.7\) A, \(V_m = 50\) V, \(I_m = 2.4\) A, and maximum power 120 W. The Boost converter operated at 40 kHz, and the inverter at 20 kHz. Simulation results demonstrate that the PV output voltage tracks the reference, the grid current increases smoothly, and the DC bus voltage stabilizes at the maximum power point, confirming effective MPPT.
An experimental prototype was built to validate the design. The PV array was emulated using a programmable DC source (GW Instek PSW160-72) with a maximum output of 360 W, 160 V, and 7.2 A. A single-phase AC source (APS-300) provided grid emulation at 40 V RMS and 50 Hz. The MOSFETs used were Infineon IPP075N15N3G with low on-resistance (7.5 mΩ) and high current capacity (100 A), suitable for high-frequency switching. The Boost inductor was 0.55 mH, DC-link capacitor 450 μF, and filter inductors 0.65 mH each. A TI TMS320F28335 DSP served as the controller, ensuring real-time processing.
Tests with two PV curves (Curve 1: \(P_{max} = 120\) W; Curve 2: \(P_{max} = 97.2\) W) showed that the system rapidly tracks the maximum power point. For Curve 1, the input power was 120.2 W, output power 117.3 W, and efficiency 97.58%. When switching to Curve 2, the system adjusted quickly, with input power 97.48 W, output power 94.75 W, and efficiency 97.2%. The grid current and voltage were synchronized, with low harmonic distortion, meeting grid standards.
These results verify that the solar inverter design achieves high steady-state accuracy, fast dynamic response, and excellent efficiency, making it suitable for practical applications.
Conclusion
This work presents the analysis and design of a two-stage non-isolated single-phase solar inverter for low-voltage renewable energy systems. The variable-step P&O MPPT method minimizes power oscillations and losses, while the voltage-current dual-loop PI control ensures stable DC bus voltage and precise grid current tracking. Mathematical modeling of PV cells, combined with hardware parameter design based on instantaneous power balance, results in an optimized system. The LC filter effectively attenuates high-frequency harmonics, improving power quality. Simulations and experiments confirm that the solar inverter efficiently tracks the maximum power point under varying conditions, with efficiency exceeding 97%. The design offers high performance, reliability, and practical value for grid-connected solar applications.