In recent years, the escalating climate crisis, rising global oil prices, and the rapid depletion of non-renewable energy resources have compelled nations worldwide to enact new regulations promoting the adoption of renewable energy sources. Solar energy, as a clean and abundant resource, has garnered significant attention due to its vast reserves, ubiquitous availability, and economic viability. Projections indicate that by 2030, the total installed capacity of photovoltaic (PV) systems in China is expected to reach 1.2 terawatts, and globally, renewable energy is anticipated to supply up to 41% of total energy demand by 2040. Photovoltaic power generation, characterized by its cleanliness and wide applicability, has emerged as a crucial measure to alleviate the shortage of conventional fossil fuels and mitigate environmental pollution. The on-grid inverter serves as the core power conversion equipment in PV systems. However, PV panels exhibit a soft load characteristic, necessitating that the subsequent inverter stage can operate over a wide input voltage range and track the system’s maximum power point under varying conditions such as irradiance and temperature. This capability is essential to reduce energy curtailment, lower the cost of grid-connected PV power, and enhance overall system efficiency. Inverter topologies are primarily categorized into two types: single-stage (direct DC/AC conversion) and multi-stage (typically DC/DC followed by DC/AC). Single-stage inverters draw power directly from the PV array, offering relative simplicity but suffering from significant DC-side voltage fluctuations and lower efficiency. Multi-stage inverters, on the other hand, regulate the DC voltage from the PV array to a stable level before conversion to AC, achieving higher conversion efficiency, precise control over the DC/AC conversion process, improved output voltage quality, and enhanced safety by preventing potential short circuits between power sources. To meet the functional requirements of a single-phase PV grid-connected system and implement maximum power point tracking (MPPT) control, this design adopts a two-stage non-isolated topology. The first stage is a DC/DC Boost converter responsible for MPPT, and the second stage is a DC/AC H-bridge inverter. This structure allows independent control of each stage, simplifying the control strategy and offering flexibility in application. The on-grid inverter must ensure high-quality power injection into the grid, making the analysis and design of its main circuit and control system paramount.
The overall system block diagram is conceptualized as follows. The system comprises two main parts: the front-end DC/DC stage and the rear-end DC/AC stage. The first stage is a Boost converter. The MPPT controller samples the PV panel output voltage $U_{pv}$ and current $I_{pv}$, calculates the voltage $U_{pvc}$ corresponding to the maximum power point at that instant, compares it with $U_{pv}$, and generates a modulation signal $U_{conp}$ to control the duty cycle of the Boost converter’s power switch. This enables the PV system to dynamically adjust its operating point to follow the maximum power point. The second stage is an H-bridge DC/AC inverter. The DSP control board samples the Boost output DC voltage $U_d$ via isolation, performs analog-to-digital conversion, and compares it with a reference DC bus voltage $U_{dref}$. The error is processed by a PI controller, the output of which serves as the amplitude reference for the grid-connected current. After filtering high-frequency components, a phase-locked loop extracts the grid phase angle to generate a sinusoidal current reference $i_{ref}$ that is synchronous with the grid voltage. This dual-loop control strategy not only facilitates grid connection but also maintains stable voltage on the inter-stage capacitor with minimal ripple, meeting the requirements for inverter grid integration. The performance of this on-grid inverter hinges on precise modeling and parameter design.
To analyze the PV source, we begin with the mathematical model of a solar cell. A PV panel is composed of numerous interconnected cell units. Based on the physics of photovoltaic conversion, the equivalent circuit model of a solar cell is presented. The key parameters are: $I_{ph}$ (photo-generated current), $I_{d}$ (dark saturation current), $C_j$ (junction capacitance), $R_{sh}$ (shunt resistance), $I_L$ (load current), $R_s$ (series resistance), and $V_{pv}$ (output voltage). Deriving from the equivalent circuit, the I-V characteristic for a combination of series and parallel cells is given by:
$$ I = I_{ph} – I_{0} \left[ \exp\left( \frac{q(V_{pv} + R_s I)}{n k T} \right) – 1 \right] – \frac{V_{pv} + R_s I}{R_{sh}} $$
where $I_0$ is the reverse saturation current, $q$ is the electron charge ($1.6 \times 10^{-19}$ C), $n$ is the diode ideality factor, $k$ is Boltzmann’s constant ($1.38 \times 10^{-23}$ J/K or $8.617 \times 10^{-5}$ eV/K), and $T$ is the absolute temperature. The output power $P$ is:
$$ P = V_{pv} I = V_{pv} I_{ph} – V_{pv} I_{0} \left[ \exp\left( \frac{q(V_{pv} + R_s I)}{n k T} \right) – 1 \right] – \frac{V_{pv}(V_{pv} + R_s I)}{R_{sh}} $$
Typically, $R_{sh}$ is very large and $R_s$ is very small, allowing simplification 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 practicality, to avoid complex computations and expedite response, the model is often linearized using key parameters: short-circuit current $I_{sc}$, open-circuit voltage $V_{oc}$, voltage at maximum power point $V_m$, and current at maximum power point $I_m$. Introducing variables for irradiance $S$ and temperature $T$, the empirical characteristics are:
$$
\begin{aligned}
I_{sc} &= I_{scref} \frac{S}{S_{ref}} (1 + a \cdot \Delta T) \\
V_{oc} &= V_{ocref} (1 – c \cdot \Delta T) \ln(1 + b \cdot \Delta S) \\
I_m &= I_{mref} \frac{S}{S_{ref}} (1 + a \cdot \Delta T) \\
V_m &= V_{mref} (1 – c \cdot \Delta T) \ln(1 + b \cdot \Delta S) \\
\Delta T &= T – T_{ref} \\
\Delta S &= S – S_{ref}
\end{aligned}
$$
Here, $S_{ref}$ is the reference irradiance (1000 W/m²), $T_{ref}$ is the reference temperature (25°C), and $a$, $b$, $c$ are compensation coefficients. For simulation and experimental purposes, a PV panel model is defined with parameters as summarized in Table 1.
| Parameter | Value |
|---|---|
| Open-circuit voltage, $V_{oc}$ (V) | 65.0 |
| Short-circuit current, $I_{sc}$ (A) | 2.7 |
| Voltage at MPP, $V_m$ (V) | 50.0 |
| Current at MPP, $I_m$ (A) | 2.4 |
| Maximum power, $P_{max}$ (W) | 120 |
The efficiency of PV panels is generally low, often below 25%, and their cost remains significant. Therefore, to improve the economic viability of PV systems, it is crucial to maximize the power extracted from the panels under varying environmental conditions. Maximum Power Point Tracking (MPPT) algorithms are employed for this purpose. In this design, an improved variable-step-size Perturb and Observe (P&O) method is utilized. The algorithm operates by adjusting the operating point based on the observed changes in power and voltage. The core principle is to introduce a perturbation in the PV voltage, measure the resulting change in power $\Delta P$ and voltage $\Delta V_{pv}$, and use the signs of these changes to determine the direction and magnitude of the next perturbation, steering the operating point toward the maximum power point. The MPPT principle is illustrated conceptually: the power-voltage curve exhibits a single peak, and the algorithm seeks that peak. The variable-step-size MPPT control flow is as follows: the reference current $I_{ref}$ for the inverter, the perturbation step size $step$, and a constant $cn$ are defined. After acquiring the DC/DC output signals, the changes in PV output power $\Delta P$ and voltage $\Delta V_{pv}$ are computed. Based on $\Delta P$, the step size is adjusted: if $\Delta P \geq 0$, the step size remains unchanged from the previous cycle; otherwise, $step(k)$ is set to $step(k-1) – cn$. The product $\Delta P \cdot \Delta V_{pv}$ determines the perturbation direction: if $\Delta P \cdot \Delta V_{pv} > 0$, the direction is maintained; if < 0, the direction is reversed; if = 0, no perturbation is applied. This cycle repeats until the step size reduces to zero, indicating convergence to the MPP. When a change in environmental conditions is detected (i.e., a significant $\Delta V_{pv}$), the step size is reinitialized, and the process restarts. This method reduces power oscillations around the MPP compared to fixed-step P&O, enhancing the efficiency of the on-grid inverter.
The control system for the DC/AC inverter stage employs a dual-loop strategy comprising an outer voltage loop and an inner current loop. The output of the voltage loop serves as the amplitude reference for the current loop, which in turn generates the PWM signals to drive the H-bridge. The current loop must have fast dynamic response to ensure accurate tracking of the current reference. Assuming the feedback and reference processing delays are equal, the current loop control block diagram is constructed. The PWM stage is modeled as $\frac{K_{PWM}}{T_s s + 1}$, where $K_{PWM}$ is the gain and $T_s$ is the sampling period. $K_{if}$ is the current feedback gain, $T_{if}$ is the current sampling delay, $i^*_L$ is the current reference, $i_L$ is the actual current, and $u_s$ represents grid voltage disturbance. The PI controller for the current loop is:
$$ G_c(s) = K_{iP} + \frac{K_{iI}}{s} = \frac{K_{iP} (\tau_i s + 1)}{\tau_i s} $$
where $K_{iP}$ is the proportional gain, $K_{iI}$ is the integral gain, and $\tau_i = K_{iP}/K_{iI}$. Using grid voltage feedforward to cancel disturbance, the open-loop transfer function of the current loop is:
$$ G_{io}(s) = \frac{K_{if} K_{iI} K_{PWM} (\tau_i s + 1) / R}{s (T_{if} s + 1)(T_s s + 1)(L s / R + 1)} $$
where $L$ is the filter inductance and $R$ represents parasitic resistances. Setting $\tau_i = L/R$ and applying the second-order optimum design method, 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 derived:
$$
\begin{aligned}
K_{iI} &= \frac{R}{3 T_s K_{PWM}} \\
K_{iP} &= \frac{L}{3 T_s K_{PWM}}
\end{aligned}
$$
The voltage outer loop control block diagram includes the current closed-loop transfer function $G_{ic}(s)$, a delay $T_{vf}$ in the voltage feedback path, and a gain $K_{vf}$ (set to 1). The plant includes the DC-bus capacitor $C$. Defining $T_h = 3T_s + T_{vf}$, the voltage open-loop transfer function is:
$$ G_{vo}(s) = \frac{K_{vI} (\tau_v s + 1) / C}{s^2 (T_h s + 1)} $$
where $K_{vP}$ and $K_{vI}$ are the voltage PI controller parameters, and $\tau_v = K_{vP}/K_{vI}$. Designing the voltage loop as a type II system, the symmetric optimum method yields the relations:
$$ \frac{K_{vP}}{C \tau_v} = \frac{h_v + 1}{2 h_v^2 T_h^2} $$
Choosing $h_v = 5$, the voltage PI parameters are:
$$
\begin{aligned}
K_{vI} &= \frac{3C}{25 T_h^2} \\
K_{vP} &= \frac{3C}{5 T_h}
\end{aligned}
$$
This control design ensures stable DC bus voltage and high-quality grid current for the on-grid inverter.
The hardware parameters of the system are designed based on operational specifications. The system is intended for a low-power single-phase on-grid inverter application. The design specifications are: PV input voltage range $U_{PVmin} = 30$ V to $U_{PVmax} = 80$ V; DC bus voltage setpoint $U_d = 80$ V; Boost converter switching frequency $f_{Boost} = 40$ kHz; system efficiency $\eta = 96\%$; output power $P_o = 120$ W; maximum inductor current $I_L = 2.5$ A; inverter switching frequency $f_{inv} = 20$ kHz; maximum MOSFET current $I_{mos} < 3$ A. The calculations for key components are detailed below.
A. Boost Inductor $L_1$ Design
The maximum duty cycle $D_{max}$ occurs at the minimum input voltage:
$$ D_{max} = \frac{U_d – U_{PVmin}}{U_d} $$
In continuous conduction mode, the average inductor current $I_{L1o}$ at full load is:
$$ I_{L1o} = \frac{P_o}{\eta U_{PV}} $$
where $U_{PV}$ is the nominal PV voltage. The inductor current ripple $\Delta I_{Lo}$ is typically chosen as 30% of the average current. The inductance is calculated using:
$$ L_1 = \frac{D U_{PV}}{2 I_{Lo} f_{Boost}} $$
where $I_{Lo}$ is related to the average current. Substituting values ($D_{max} \approx 0.625$ for $U_{PV}=30$ V, $I_{L1o} \approx 4.17$ A for $P_o=120$ W at $U_{PV}=30$ V, $\Delta I_{Lo}=1.25$ A, $I_{Lo}=2.085$ A), we obtain $L_1 \approx 0.55$ mH.
B. DC-Link Capacitor $C_{Bus}$ Design
The DC-link capacitor smoothens the voltage and supplies energy to the inverter. The allowable DC voltage ripple $\Delta U_d$ is usually within 5% of $U_d$. For a single-phase system, the capacitor is sized based on the power balance at double the grid frequency (100 Hz):
$$ C_{Bus} = \frac{P_o}{4 \pi f_{grid} \Delta U_d U_d} $$
With $f_{grid}=50$ Hz, $\Delta U_d = 0.05 \times 80 = 4$ V, calculation gives $C_{Bus} \approx 298$ µF. Considering a safety margin of 1.5-2 times, a standard value of 450 µF/300 V is selected.
C. Inverter Output Filter Inductor $L_2$ Design
The inverter output is a PWM waveform requiring filtering to produce a sinusoidal grid current. The filter inductor $L_2$ limits the current ripple. The voltage across the inductor is $U_{L2} = L_2 di/dt$. Over a switching period $T_{inv} = 1/f_{inv}$, the peak-to-peak current ripple $\Delta i$ is maximum when the output voltage is at its peak $U_{L2max}$. From the inductor equation:
$$ \Delta i = \frac{U_{L2max}}{L_2} D T_{inv} $$
Using the volt-second balance, the duty cycle at the peak is $D = (U_d – U_{L2max})/U_d$. Substituting:
$$ L_2 = \frac{U_{L2max} (U_d – U_{L2max}) T_{inv}}{\Delta i U_d} $$
For a grid voltage peak of $40\sqrt{2} \approx 56.57$ V (assuming 40 Vrms grid), $U_d=80$ V, $\Delta i$ chosen as 20% of peak grid current (peak current for 120 W at 40 Vrms is about 4.24 A, so $\Delta i \approx 0.85$ A), and $T_{inv}=50$ µs, we compute $L_2 \approx 1.3$ mH. For a symmetric L filter, this can be split into two inductors of 0.65 mH each.
D. Output Filter Capacitor $C_o$ Design
An LC filter is used to attenuate switching harmonics. The resonant frequency $f_s$ should be much lower than the switching frequency and well above the grid frequency to avoid resonance issues. Typically:
$$ 10 f_{grid} \leq f_s = \frac{1}{2\pi \sqrt{L_2 C_o}} \leq \frac{1}{5} f_{inv} $$
With $f_{grid}=50$ Hz and $f_{inv}=20$ kHz, the bounds are 500 Hz $\leq f_s \leq$ 4 kHz. Solving for $C_o$:
$$ C_o \geq \frac{1}{L_2 (2\pi f_{inv}/5)^2} $$
Using $L_2=1.3$ mH, the lower bound from the upper frequency limit is very small. To provide sufficient attenuation and considering practical aspects, a value of $C_o = 10$ µF is selected, which yields $f_s \approx 1.4$ kHz, within the desired range. Table 2 summarizes the key hardware parameters.
| Component | Symbol | Designed Value |
|---|---|---|
| Boost inductor | $L_1$ | 0.55 mH |
| DC-link capacitor | $C_{Bus}$ | 450 µF / 300 V |
| Output filter inductor (total) | $L_2$ | 1.3 mH (0.65 mH each for symmetric design) |
| Output filter capacitor | $C_o$ | 10 µF |
| Boost switching frequency | $f_{Boost}$ | 40 kHz |
| Inverter switching frequency | $f_{inv}$ | 20 kHz |
To validate the proposed design, a simulation model was built using PSIM software. The model includes the PV array emulator, Boost converter with MPPT, H-bridge inverter, dual-loop controllers, and grid connection. The PV emulator parameters are as per Table 1. The simulation results demonstrate the system performance. Upon startup, the PV voltage tracks the MPPT reference, and the grid current increases gradually. The DC bus voltage stabilizes at the setpoint of 80 V after reaching the maximum power point. The PV output power rises and settles at the maximum of 120 W. The grid current is sinusoidal and in phase with the grid voltage, with low total harmonic distortion (THD), confirming the effectiveness of the control strategy for the on-grid inverter.
An experimental prototype was constructed to further verify the design. The test platform consists of a programmable DC power supply (GW Instek PSW 160-7.2) to emulate the PV array, a single-phase AC source (APS-300) representing the grid, the power circuits, and a DSP (TMS320F28335) based control board. The DC power supply is programmed to output the I-V characteristics of the PV model. The MOSFETs are Infineon IPP075N15N3G, chosen for their low on-resistance (7.5 mΩ max) and high current capability (100 A), suitable for high-frequency switching. The Boost diode is an MBR1660 fast recovery diode for low forward drop and high efficiency. The passive components are selected as per the design calculations. The experimental procedure involves enabling the auxiliary power, then the DC source, AC source, and finally the gate drive signals. The waveforms are monitored using an oscilloscope.
Under steady-state conditions with the PV emulator set to curve 1 (120 W maximum power), the system successfully tracks the MPP. The input power from the DC supply is measured as 120.2 W, and the output power to the grid is 117.3 W, yielding an efficiency of 97.58%. The grid voltage and current waveforms show clean sinusoids in phase. To test dynamic response, the PV emulator is switched to curve 2 with parameters: $V_{oc2}=58.5$ V, $I_{sc2}=2.43$ A, $V_{m2}=45$ V, $I_{m2}=2.16$ A, and $P_{max2}=97.2$ W. This simulates a sudden change in irradiance. The system rapidly re-tracks the new MPP, with the power, voltage, and current settling to the new values within a few hundred milliseconds. The input power is 97.48 W, output power is 94.75 W, and efficiency is 97.2%. The grid current remains sinusoidal during the transition. These results validate the robustness and efficiency of the two-stage non-isolated single-phase on-grid inverter design.
In conclusion, this work presents a comprehensive analysis and design of a two-stage non-isolated single-phase photovoltaic on-grid inverter. The topology, comprising a front-end Boost converter and a rear-end H-bridge inverter, is well-suited for low-voltage renewable energy systems requiring wide input voltage range operation. The mathematical modeling of the PV source provides a foundation for simulation and control. The improved variable-step-size perturb and observe MPPT algorithm effectively minimizes power oscillations and ensures rapid tracking under changing environmental conditions. The dual-loop control strategy, with an inner current loop and outer voltage loop, guarantees stable DC bus voltage and high-quality grid current injection. Detailed hardware parameter design based on instantaneous power balance ensures optimal performance of passive components. Simulation and experimental results corroborate the design, showing high steady-state accuracy, good dynamic response, and overall efficiency above 97%. The proposed on-grid inverter design offers a practical and efficient solution for small-scale grid-connected PV systems, with potential for further optimization and scaling. The integration of advanced control techniques and robust hardware design makes this on-grid inverter a reliable component in the renewable energy infrastructure, contributing to the broader adoption of solar power generation.