In recent years, the rapid depletion of conventional energy resources and escalating environmental concerns have significantly hindered global development. Photovoltaic (PV) power generation has emerged as a pivotal solution due to its inherent safety, low operational and maintenance costs, and widespread applicability. The performance of renewable energy generation systems is critically influenced by the efficacy of their control strategies. Among various configurations, two-stage single-phase grid-connected solar inverter systems are prevalently adopted. The front-end typically comprises a Boost converter for maximum power point tracking (MPPT) and voltage elevation, while the rear-end involves a DC/AC inverter for grid integration. However, grid-connected current distortion caused by factors such as dead-time effects, DC-side voltage fluctuations, and grid voltage harmonics poses a significant challenge, deteriorating power quality and complicating controller design. To address this, we propose an adaptive harmonic elimination current control strategy, leveraging selective characteristic harmonic compensation and an enhanced neural network for dynamic gain adjustment. This approach aims to optimize current waveforms, enhance tracking performance, and ensure compliance with grid standards.
The two-stage single-phase solar inverter system, as illustrated, consists of a Boost DC/DC converter and a full-bridge DC/AC inverter. The Boost stage elevates the PV array voltage and implements MPPT using perturbation and observation methods, providing a stable DC-link voltage. The inverter stage converts DC to AC, synchronized with the grid. Key parameters include grid voltage (220 V), frequency (50 Hz), filter inductance (800 μH), filter capacitance (50 μF), DC-link capacitance (1000 μF), and reference DC voltage (400 V). The control system employs a dual-loop proportional-integral (PI) structure in the synchronous reference frame (d-q coordinates) to regulate voltage and current. However, traditional PI controllers struggle to mitigate low-order harmonics, necessitating advanced compensation techniques.
To model the inverter in d-q coordinates, we first construct a virtual orthogonal variable for the single-phase system. Let the actual physical quantity be \(X_{\alpha}\) and its virtual counterpart be \(X_{\beta}\), delayed by a quarter period. The transformation from stationary to rotating coordinates is given by:
$$ \begin{bmatrix} X_d \\ X_q \end{bmatrix} = \begin{bmatrix} \cos(\omega t) & \sin(\omega t) \\ -\sin(\omega t) & \cos(\omega t) \end{bmatrix} \begin{bmatrix} X_{\alpha} \\ X_{\beta} \end{bmatrix} $$
where \(X_d\) and \(X_q\) are the d-axis and q-axis components, respectively, and \(\omega\) is the grid angular frequency. This transformation enables the representation of AC quantities as DC values, facilitating PI control. The state-space model of the inverter in d-q coordinates is derived as:
$$ \frac{d}{dt} \begin{bmatrix} U_d \\ U_q \end{bmatrix} = \begin{bmatrix} 0 & \omega \\ -\omega & 0 \end{bmatrix} \begin{bmatrix} U_d \\ U_q \end{bmatrix} – \frac{1}{C} \begin{bmatrix} I_d \\ I_q \end{bmatrix} + \frac{1}{C} \begin{bmatrix} I_{0d} \\ I_{0q} \end{bmatrix} $$
$$ \frac{d}{dt} \begin{bmatrix} I_d \\ I_q \end{bmatrix} = \begin{bmatrix} 0 & \omega \\ -\omega & 0 \end{bmatrix} \begin{bmatrix} I_d \\ I_q \end{bmatrix} – \frac{1}{L} \begin{bmatrix} U_d \\ U_q \end{bmatrix} + \frac{1}{L} \begin{bmatrix} D_d U_{dc} \\ D_q U_{dc} \end{bmatrix} $$
Here, \(U_d\), \(U_q\) and \(I_d\), \(I_q\) are the voltage and current components; \(I_{0d}\), \(I_{0q}\) are load currents; \(D_d\), \(D_q\) are duty cycles; \(L\) and \(C\) are filter inductance and capacitance; and \(U_{dc}\) is the DC-link voltage. The model reveals cross-coupling terms (\(\omega L I_q\) and \(\omega L I_d\)) and disturbances from grid voltage, which degrade performance. To address this, we implement decoupling feedforward and dual-loop PI control. The current inner loop equations are:
$$ U_{df} = \left( K_{ip} + \frac{K_{iv}}{s} \right) (I_d^* – I_d) – \omega L I_q + U_d $$
$$ U_{qf} = \left( K_{ip} + \frac{K_{iv}}{s} \right) (I_q^* – I_q) + \omega L I_d + U_q $$
where \(K_{ip}\) and \(K_{iv}\) are PI gains, and \(I_d^*\), \(I_q^*\) are reference currents from the voltage outer loop:
$$ I_d^* = \left( K_{op} + \frac{K_{oi}}{s} \right) (U_d^* – U_d) $$
$$ I_q^* = \left( K_{op} + \frac{K_{oi}}{s} \right) (U_q^* – U_q) $$
with \(K_{op}\) and \(K_{oi}\) as voltage loop PI gains. The reference voltages are \(U_d^* = U_{dc}^*\) and \(U_q^* = 0\) for unity power factor. This control structure, while effective for fundamental tracking, fails to suppress harmonics, leading to distorted grid currents. Therefore, we integrate a selective harmonic compensation scheme.
Harmonic detection is crucial for compensation. The grid current \(i_{\alpha}\) is decomposed into Fourier series to identify characteristic harmonics (e.g., 3rd, 5th, 7th, 9th), which dominate distortion due to nonlinearities in solar inverters. The current is expressed as:
$$ i_{\alpha}(t) = \sum_{l=1,3,5,\ldots}^{N} [A_l \sin(l\omega t) + B_l \cos(l\omega t)] $$
where \(A_l = X_l \cos \phi_l\), \(B_l = X_l \sin \phi_l\), with \(X_l\) and \(\phi_l\) being the amplitude and phase of the \(l\)-th harmonic. Using FFT and a phase-locked loop (PLL), we extract \(X_l\) and \(\phi_l\), then reconstruct each harmonic component \(i_{l\alpha}\) for compensation. Instead of compensating all harmonics, which may amplify high-frequency noise, we selectively target low-order harmonics to improve efficiency.
The adaptive compensation mechanism employs a Levenberg-Marquardt backpropagation (LM-BP) neural network to dynamically adjust compensation gains. The detected harmonic currents \(i_{l\alpha}\) (for \(l = 3,5,7,9\)) form an input vector \(\mathbf{X}_{\alpha} = [i_{3\alpha}, i_{5\alpha}, i_{7\alpha}, i_{9\alpha}]^T\). A weight vector \(\mathbf{W}_{\alpha} = [a_3, a_5, a_7, a_9]^T\), initialized to ones, scales these inputs to generate a compensation signal \(y_{\alpha} = \mathbf{W}_{\alpha}^T \mathbf{X}_{\alpha}\). The error between the desired current (from full harmonic detection) and \(y_{\alpha}\) is minimized using the LM algorithm, which enhances convergence and avoids local minima. The error function for the \(n\)-th sample is:
$$ \varepsilon(n) = \frac{1}{2} e_{\alpha}^2(n) = \frac{1}{2} (i_{h\alpha}(n) – y_{\alpha}(n))^2 $$
The weight update rule combines gradient descent and Newton’s method:
$$ \Delta \mathbf{W}_{\alpha} = -[\mathbf{H}(e_{\alpha}) + \mu \mathbf{I}]^{-1} \nabla e_{\alpha} $$
where \(\mathbf{H}(e_{\alpha})\) is the Hessian matrix, \(\nabla e_{\alpha}\) is the gradient, \(\mu\) is a damping factor, and \(\mathbf{I}\) is the identity matrix. This ensures robust adaptation to grid variations. The compensated voltage signal \(\Delta U_{\alpha}\) is derived via harmonic impedance \(\omega L\) and added to the PWM modulator, reconstructing the waveform to cancel harmonics.
To validate our strategy, we conducted simulations in MATLAB/Simulink and experimental tests on a 2 kW solar inverter platform. The system parameters are summarized in Table 1.
| Component | Parameter |
|---|---|
| Grid Voltage | 220 V |
| Grid Frequency | 50 Hz |
| Filter Inductance | 800 μH |
| Filter Capacitance | 50 μF |
| DC-link Capacitance | 1000 μF |
| Reference DC Voltage | 400 V |
| Switching Frequency | 10 kHz |
| MPPT Method | Perturb and Observe |
Under conditions of dead-time (2 μs) and DC voltage fluctuations (±6 V), we compared traditional PI control, Newton-based harmonic compensation, and our LM-BP adaptive method. The grid current total harmonic distortion (THD) served as the key metric. Simulation results are summarized in Table 2.
| Control Method | THD (%) | 3rd Harmonic (%) | 5th Harmonic (%) | 7th Harmonic (%) | 9th Harmonic (%) |
|---|---|---|---|---|---|
| Traditional PI | 3.52 | 1.8 | 1.2 | 0.7 | 0.5 |
| Newton-Based Compensation | 2.10 | 0.9 | 0.6 | 0.4 | 0.3 |
| LM-BP Adaptive Compensation | 1.32 | 0.4 | 0.3 | 0.2 | 0.1 |
The LM-BP method reduced THD by over 60% compared to traditional PI, demonstrating superior harmonic suppression. Current waveforms showed significant smoothing, with minimal distortion at peaks and troughs. Experimental results on a lab-scale solar inverter, using a DSP-based controller, corroborated the simulations, yielding a THD of 1.35% under similar conditions. The adaptive gains converged within 0.5 seconds, ensuring real-time efficacy.
Further analysis involves the impact of varying solar irradiance and grid impedance on compensation performance. We derived a transfer function for the compensated system to assess stability margins. The open-loop transfer function \(G(s)\) of the current loop with compensation is approximated as:
$$ G(s) = \frac{K_{ip} K_{pwm}}{L s + R} \cdot \frac{1 + \frac{s}{\omega_z}}{1 + \frac{s}{\omega_p}} $$
where \(K_{pwm}\) is the PWM gain, \(R\) is parasitic resistance, and \(\omega_z\), \(\omega_p\) are zeros and poles introduced by the harmonic compensator. Bode plots confirmed a phase margin above 45°, ensuring robustness. Additionally, we formulated the harmonic rejection ratio \(H_{rr}\) for the \(l\)-th harmonic:
$$ H_{rr}(l) = 20 \log_{10} \left( \frac{|I_l|}{|I_{l0}|} \right) $$
where \(|I_l|\) and \(|I_{l0}|\) are harmonic amplitudes with and without compensation. Our method achieved \(H_{rr}\) values below -20 dB for targeted harmonics, indicating effective attenuation.
The adaptive nature of our solar inverter control strategy allows it to handle non-ideal grid conditions, such as voltage sags or frequency deviations. The neural network continuously updates weights based on real-time current error, minimizing the need for manual tuning. This is particularly beneficial for solar inverters deployed in diverse environments, where grid parameters may fluctuate. Moreover, the selective compensation reduces computational load on the DSP, making it feasible for cost-effective implementations.
In conclusion, we have developed an adaptive current control strategy for single-phase solar inverters that integrates selective harmonic elimination with LM-BP neural network-based gain adjustment. This approach effectively mitigates low-order harmonics caused by dead-time, DC fluctuations, and grid distortions, enhancing current tracking and power quality. Simulations and experiments validate the method, showing THD reductions to below 1.5%. Future work will extend this to three-phase solar inverter systems and explore integration with advanced MPPT algorithms for holistic optimization. The proposed strategy underscores the potential of adaptive control in renewable energy systems, paving the way for smarter and more efficient solar inverter technologies.
Throughout this discussion, the term “solar inverter” has been emphasized to highlight its centrality in photovoltaic systems. The solar inverter serves as the critical interface between PV panels and the grid, and its performance directly impacts overall system efficiency. By refining control strategies like adaptive harmonic compensation, we can unlock greater potential from solar energy, contributing to a sustainable energy future. The continuous evolution of solar inverter designs, incorporating real-time adaptation and intelligent algorithms, will be key to meeting the growing demands of modern power networks.