In recent years, the global energy landscape has shifted toward renewable sources due to the depletion of fossil fuels and environmental concerns. Solar energy, in particular, offers a clean and abundant alternative, making solar inverters critical components in photovoltaic (PV) systems. These solar inverters convert DC power generated by PV panels into AC power for consumer use. However, when solar inverters operate independently in islanded mode to supply nonlinear loads, challenges such as output voltage distortion and high harmonic content arise. Nonlinear loads introduce harmonic currents that cause voltage drops across the inverter’s internal impedance, leading to significant waveform distortion. Traditional control strategies, like proportional-integral (PI) controllers, often fall short in mitigating these issues, necessitating advanced approaches. This paper proposes a novel control strategy based on an improved neural network algorithm, optimized using genetic algorithms (GAs), to enhance the performance of solar inverters under nonlinear load conditions. The strategy focuses on improving convergence speed and reducing harmonic distortion, validated through experimental results from a 10 kW prototype.
The topology of a single-phase full-bridge solar inverter is commonly used in distributed PV systems. It employs unipolar pulse width modulation (PWM) for efficient operation. The structure includes power switches (V1 to V4), filter inductors (L1 and L2) with equivalent series resistances, a filter capacitor (C), and the load. The DC input voltage (U_dc) is derived from the PV array after boost conversion, and the output PWM voltage (u_i) is controlled via the duty cycle (d). Key variables include the filter capacitor voltage (u_c), output voltage (u_o), output current (i_1), capacitor current (i_c), and load current (i_2). The relationship between these parameters can be expressed using differential equations that model the inverter’s dynamics. For instance, the output voltage is influenced by the duty cycle and load conditions, as described by:
$$ u_o = d \cdot U_{dc} – L_1 \frac{di_1}{dt} – R_1 i_1 $$
This equation highlights the impact of nonlinear loads, which introduce harmonics that distort u_o. The control objective is to regulate d to maintain a sinusoidal output voltage despite load variations.
Neural networks, particularly backpropagation (BP) networks, have gained traction in power electronics for their ability to model complex nonlinear systems. A standard three-layer BP neural network consists of an input layer, a hidden layer, and an output layer. The input-output relationship for such a network is given by:
$$ s_j = f\left( \sum_{i=1}^{n} w_{ji} x_i + b_j \right) $$
$$ y_k = g\left( \sum_{j=1}^{h} w_{kj} s_j + b_k \right) $$
where x_i represents the input neurons, s_j the hidden layer outputs, y_k the output neurons, w_{ji} and w_{kj} are weights, b_j and b_k are biases, and f and g are activation functions (e.g., tan-sigmoid and purelin). In the context of solar inverters, the BP network can be trained to predict the duty cycle based on inputs such as DC voltage, filter capacitor voltage, load current, and output voltage. However, traditional BP networks suffer from slow convergence and susceptibility to local minima. To address this, genetic algorithms (GAs) are employed to optimize the initial weights and thresholds of the BP network. GAs use principles of natural selection, including encoding, fitness evaluation, crossover, and mutation, to find global optima. The fitness function for the GA is defined as the mean squared error between the predicted and actual duty cycles. The optimization process involves encoding the BP parameters into a population, iterating through generations, and selecting the best individuals. The GA-BP hybrid approach ensures faster convergence and higher accuracy, as demonstrated by a reduction in training iterations from 19,682 to 3,112 for the same error target.
The proposed control strategy for solar inverters utilizes the GA-BP neural network to generate the PWM duty cycle. The neural network model has five inputs: the current DC voltage U_dc(k), filter capacitor voltage u_c(k), load current i_2(k), duty cycle d(k), and output voltage u_o(k). The output is the next duty cycle d(k+1). The hidden layer contains seven neurons with tan-sigmoid activation, while the output layer uses a linear function. The GA optimizes the initial weights and biases, enhancing the network’s ability to handle nonlinearities. The training process involves 60,000 samples, with 2,000 used for testing, and a target error of 10^{-6}. The improved convergence is evident from the faster training cycles and reduced prediction errors compared to standard BP. The control law for the solar inverter can be summarized as:
$$ d(k+1) = NN \left( U_{dc}(k), u_c(k), i_2(k), d(k), u_o(k) \right) $$
where NN denotes the GA-BP neural network function. This approach allows the solar inverter to adapt dynamically to load changes, minimizing harmonic distortion.
Experimental validation was conducted on a 10 kW solar inverter prototype with parameters including L1 = 5.2 mH, switching frequency f_s = 20 kHz, filter capacitor C = 7.3 μF, output voltage u_o = 220 V, L2 = 1.4 mH, and U_dc = 500 V. The performance of the GA-BP control was compared to traditional PI control under various load conditions. For purely resistive loads, both strategies maintained low voltage total harmonic distortion (THD), with PI control achieving 1.37% and GA-BP achieving 1.09%. However, under nonlinear loads, such as rectifier-based loads, the GA-BP strategy significantly outperformed PI control. The voltage THD was reduced from 4.26% with PI to 2.38% with GA-BP, demonstrating superior harmonic suppression. Additionally, the GA-BP controller showed faster response to load transients, such as sudden connection or disconnection of nonlinear loads, ensuring stable output voltage. The following table summarizes the key performance metrics:
| Control Strategy | Load Type | Voltage THD (%) | Convergence Time (iterations) |
|---|---|---|---|
| PI Control | Resistive | 1.37 | N/A |
| GA-BP Control | Resistive | 1.09 | 3,112 |
| PI Control | Nonlinear | 4.26 | N/A |
| GA-BP Control | Nonlinear | 2.38 | 3,112 |
The enhanced performance of solar inverters with GA-BP control is attributed to the neural network’s ability to learn and compensate for nonlinearities in real-time. The mathematical formulation of the harmonic reduction can be expressed using Fourier analysis, where the output voltage u_o(t) is decomposed into harmonic components:
$$ u_o(t) = \sum_{n=1}^{\infty} \left[ a_n \cos(n\omega t) + b_n \sin(n\omega t) \right] $$
The GA-BP controller minimizes the higher-order harmonics (n > 1), resulting in lower THD. Furthermore, the robustness of solar inverters under varying operating conditions is improved, as the neural network adapts to changes in solar irradiance and load dynamics. For instance, the duty cycle prediction error over samples is significantly lower with GA-BP, as shown in the following equation representing the error reduction:
$$ \text{Error} = \frac{1}{N} \sum_{k=1}^{N} \left( d_{\text{pred}}(k) – d_{\text{actual}}(k) \right)^2 $$
where N is the number of samples, and the error is reduced by up to 50% compared to standard BP.
In conclusion, the integration of GA-optimized neural networks into solar inverter control systems offers a promising solution for islanded operation with nonlinear loads. The proposed strategy enhances the convergence speed and accuracy of duty cycle prediction, leading to significant reductions in voltage harmonic distortion. Experimental results from a 10 kW prototype confirm the effectiveness of the GA-BP approach, with THD values below 2.5% under nonlinear loads, compared to over 4% with PI control. This advancement contributes to improved power quality and reliability in distributed PV systems, enabling wider adoption of solar energy. Future work could explore the application of this control strategy to three-phase solar inverters and integration with grid-support functions.