Solar energy, as a green and renewable source, has gained significant attention due to its pollution-free and inexhaustible nature. Among its applications, photovoltaic (PV) systems are widely studied, with micro PV systems representing a distinct category compared to traditional large-scale integrated systems. Micro PV systems feature individual solar panels connected to low-power inverter modules, and they can be classified into various types of solar inverter configurations, such as micro off-grid and micro grid-tied systems. This article focuses on micro off-grid PV systems, which operate independently and consist of PV panels, batteries, and micro-inverters. These systems are crucial for powering remote areas, mobile base stations, and street lighting. The core component, the micro-inverter, converts DC power from panels or batteries to AC, and its control strategy is vital for system stability and efficiency. In this work, we explore advanced control methods for micro off-grid inverters, specifically integrating feed-forward compensation with proportional-integral (PI) control to address issues like measurement interference and enhance output quality. We begin by modeling an ideal flyback converter, derive its small-signal transfer functions, and then detail the software and experimental implementation. Our results demonstrate that this approach yields stable sinusoidal outputs with low total harmonic distortion (THD), validating its effectiveness for various types of solar inverter applications.
Micro off-grid PV systems are designed to operate autonomously, providing power to local loads without grid connection. During the day, PV panels convert solar energy to DC electricity, which the micro-inverter uses to supply loads and charge batteries; at night, batteries discharge through the inverter to maintain power. This setup contrasts with micro grid-tied systems, which can feed excess power into the grid, requiring synchronization with grid voltage and frequency. The key difference lies in the control strategies, where off-grid inverters prioritize voltage and frequency stability under varying loads. Among the different types of solar inverter topologies, the flyback converter is popular in micro-inverters due to its isolation and step-up capabilities. However, its nonlinear nature demands precise control. Common challenges include output distortion under load changes, which we address by combining feed-forward and PI control. This combination compensates for disturbances and improves dynamic response, making it suitable for the diverse types of solar inverter systems used in off-grid scenarios.
To understand the control design, we first model an ideal flyback converter. The circuit includes a transformer with turns ratio N, an input inductor Lm, an output capacitor Co, a filter inductor Lf, and a load resistance Rload. The state variables are the magnetizing inductor current Im, the output capacitor voltage Vac, and the output current Iac. Using state-space averaging, we derive the average equations over a switching period, where d is the duty cycle and d’ = 1 – d. The Kirchhoff’s voltage and current laws yield:
$$ V_{LM} = L_m \frac{d(i_m)}{dt} = d \cdot v_{pv} – d’ \cdot \frac{v_{ac}}{N} $$
$$ V_{Lf} = v_{ac} – i_{ac} R_f – v_{load} $$
$$ i_c = C_o \frac{d(v_{ac})}{dt} = d \cdot \left( -\frac{v_{load}}{R_{load}} \right) – d’ \cdot \left( \frac{i_m}{N} – \frac{v_{load}}{R_{load}} \right) $$
$$ i_{pv} = d \cdot i_m $$
$$ v_{load} = R_{load} \cdot i_{ac} $$
Linearizing around a steady-state operating point, we define the state vector x = [i_m, i_ac, v_ac]^T, input vector u = [d, v_load, v_pv]^T, and output y = i_ac. Perturbing these variables (e.g., x = X + x̃) and ignoring higher-order terms, we obtain the small-signal model:
$$ \tilde{v}_{LM} = L_m \frac{d(\tilde{i}_m)}{dt} = D \cdot \tilde{v}_{pv} – D’ \cdot \frac{\tilde{v}_{ac}}{N} + \tilde{d} \left( v_{pv} + \frac{v_{ac}}{N} \right) $$
$$ \tilde{i}_c = C_o \frac{d(\tilde{v}_{ac})}{dt} = \frac{D’ \cdot \tilde{i}_m}{N} – \frac{\tilde{v}_{load}}{R_{load}} – \frac{I_m \cdot \tilde{d}}{N} $$
$$ \tilde{v}_{Lf} = L_f \frac{d(\tilde{i}_{ac})}{dt} = \tilde{v}_{ac} – \tilde{i}_{ac} R_f – \tilde{v}_{load} $$
This leads to the AC small-signal equivalent circuit, and from the state-space representation, we derive the transfer function from control input to output current. The state matrix A and input matrices B1, B2, B3 are:
$$ A = \begin{bmatrix} 0 & 0 & -\frac{D’}{L_m N} \\ 0 & -\frac{R_f}{L_f} & \frac{1}{L_f} \\ \frac{D’}{N C_o} & -\frac{1}{C_o} & 0 \end{bmatrix}, \quad B_1 = \begin{bmatrix} 0 \\ 0 \\ -\frac{I_m}{N C_o} \end{bmatrix}, \quad B_2 = \begin{bmatrix} \frac{D}{L_m} \\ 0 \\ 0 \end{bmatrix}, \quad B_3 = \begin{bmatrix} 0 \\ -\frac{1}{L_f} \\ 0 \end{bmatrix} $$
The output equation is Y = C X with C = [0, 1, 0]. The transfer function G_id(s) = i_ac(s) / d(s) is:
$$ G_{id}(s) = \frac{I_m}{C_o L_f} \frac{s}{s^3 + \frac{R_f}{L_f} s^2 – \frac{L_m + L_f}{C_o L_m L_f} s – \frac{D^2 R_f}{C_o L_m L_f N^2}} $$
This transfer function exhibits a right-half-plane zero, characteristic of buck-boost topologies, complicating control design. To achieve stable operation in micro off-grid inverters, we propose a control strategy combining feed-forward and PI compensation. The feed-forward part provides the steady-state duty cycle D(t) based on the voltage conversion ratio of the flyback converter:
$$ D = \frac{V_o}{V_o + V_i N} $$
where V_i is the input voltage and V_o is the output voltage. This compensates for input variations, while the feedback PI controller handles dynamic tracking. The overall duty cycle d(t) is:
$$ d(t) = D(t) + D_d(t) $$
where D_d(t) is the output of the PI controller, which processes the error between the reference current i_ac_ref and the measured output current i_ac. The PI controller transfer function is:
$$ G_c(s) = K_p + \frac{K_i}{s} $$
This dual approach ensures robustness against load disturbances and measurement noise, common in various types of solar inverter systems. The control structure is implemented in software using a digital signal controller, as described next.
For software implementation, we selected the dsPIC33FJ16GS504 digital signal controller due to its high-speed PWM modules and ADC capabilities. The main program initializes system clocks, I/O ports, ADC, comparators, PWM, and timers. After enabling interrupts, it enters a loop waiting for ADC interrupts, which occur every 17.5 μs. The interrupt service routine samples PV panel voltage, inverter output current, and output voltage, computes the next PWM duty cycle, and updates the SPWM waveform. Key algorithms include the PI control and feed-forward compensation. The PI control flowchart involves sampling i_ac, calculating error e(t) = i_ac(t) – i_ac_ref(t), and computing the control output u(t) using:
$$ u(k) = K_i \cdot e(k) + K_p \cdot (e(k) – e(k-1)) $$
with anti-windup measures for saturation. The feed-forward compensation uses sampled V_pv and V_ac to compute D(t) as per the voltage ratio formula. This combination allows real-time adjustment of the duty cycle for the flyback MOSFETs, ensuring a stable 50 Hz sinusoidal output. The software also includes a phase-locked loop for frequency synchronization and protection mechanisms for over-current and over-voltage.
To validate the control strategy, we built an experimental setup with a programmable DC source (Chroma 62006P-300-8) simulating PV panels, a resistive load of 300 Ω, and a Tektronix TPS2024B oscilloscope for waveform analysis. The micro-inverter prototype uses an active-clamp flyback converter for DC-DC step-up and a full-bridge unfolder for DC-AC conversion. With the DC source set to 36 V and 1.5 A, the output waveforms were captured. The flyback output shows a high-frequency switched waveform, while the full-bridge output produces a clean sinusoidal voltage at 50 Hz.
For quantitative analysis, we exported output waveform data to MATLAB and performed FFT analysis. The THD was calculated to be 3.29%, well below the 5% limit set by standards. The output frequency remained stable at 50 Hz with minimal distortion, demonstrating the effectiveness of the feed-forward and PI control. This performance is crucial for reliable operation in various types of solar inverter applications, especially off-grid systems where load variations are common.
In summary, we have developed a control strategy for micro off-grid PV inverters that integrates feed-forward compensation with PI current feedback. The small-signal model of the flyback converter provided insights into system dynamics, enabling precise controller design. Software implementation on a dsPIC controller facilitated real-time control, and experimental results confirmed stable sinusoidal outputs with low THD. This approach enhances the performance of micro off-grid inverters, a key category among the types of solar inverter systems, and can be extended to other topologies. Future work could explore adaptive control for varying environmental conditions and integration with battery management systems.
| Inverter Type | Control Method | Typical THD (%) | Applications |
|---|---|---|---|
| Micro Off-Grid | Feed-Forward + PI | 3.29 | Remote areas, street lighting |
| Grid-Tied | MPPT + Synchronization | <5 | Residential, commercial |
| Central Inverter | Vector Control | <3 | Large-scale PV farms |
The table above highlights how different types of solar inverter systems employ distinct control strategies to meet specific requirements. Our focus on micro off-grid inverters with feed-forward and PI control underscores the importance of tailored solutions for enhanced power quality. As solar technology evolves, further innovations in control algorithms will continue to improve the efficiency and reliability of all types of solar inverter configurations.