Research on Neural Network Global Optimization of Hybrid Full-Bridge Push-Pull Topology Based on Genetic Algorithm

Abstract

The traditional control strategies for bidirectional power supply full-bridge push-pull DC-DC topologies still face limitations in efficiency, dynamic response, and output stability. To address this, this paper proposes an integrated modulation strategy combining neural network optimization and closed-loop control, which adjusts the phase-shift angle and switching timing through online learning to significantly improve dynamic and steady-state performance. Simulations show that the current peak value was reduced from 16A to 15.2A, the output voltage ripple was significantly suppressed from 90% to 30%, and the system efficiency, calculated through multiple iterations, gradually increased. This paper first analyzes the problems of traditional control strategies, then presents a new control framework, modeling, and simulation. Finally, simulation verification was performed under typical operating conditions. The results show that this strategy is suitable for high-efficiency energy storage systems.

1. Introduction

The international community is accelerating the transformation of the energy structure, driven by the global strategic goals of ‘carbon peak’ and ‘carbon neutrality’. Conferences such as the United Nations Climate Change Conference (COP28), the World Sustainable Energy Summit, and the International Power Electronics and Drives Conference (EPE) have identified efficient electric power conversion and intelligent control technologies as key to achieving green energy goals. As a major consumer of fossil fuels, China’s energy-related carbon dioxide emissions account for one-third of global annual emissions, reaching 10 billion tons [1]. Furthermore, during the 2020 United Nations General Debate, the General Secretary announced that China would implement more robust policies and measures to strive for carbon neutrality by 2060 [2]. Power electronics technology plays a critical role, especially in renewable energy systems. For example, in wind and solar energy systems and energy storage integration, power electronics technology enables these renewable energies to be effectively integrated into the grid while ensuring high efficiency and stability in power transmission. Reference [3] describes the design of a 350 kW DC charger that optimizes the relationship between efficiency and cost, enabling the platform to achieve sustainable energy management. Furthermore, reference [4] focuses on the application of smart grid technologies for integrating sustainable energy into the grid, including the intelligent control of power electronics systems and voltage regulation. Meanwhile, the rapid development of electric vehicles, energy storage systems and renewable energy in recent years has also led to broader prospects for DC-DC converters in these areas [5].

The Phase-Shifted Full Bridge (PSFB) converter has been widely applied in renewable energy fields, hybrid vehicles, and bidirectional power supplies due to its advantages, such as zero voltage switching (ZVS) to reduce switching losses, high power density to enhance efficiency, and the high power handling capacity and support for high switching frequencies of MOSFETs [6,7]. However, optimizing the dynamic performance and minimizing the losses of PSFB converters under complex operating conditions remains a key challenge in international research [8].

In recent years, the rapid development of artificial intelligence, particularly in the area of neural network technology for nonlinear system modeling and intelligent control, has provided new approaches to solving this issue. Intelligent controllers (such as fuzzy neural control) can process uncertain information using fuzzy logic and leverage the learning capabilities of artificial neural networks for online optimization [9]. Therefore, applying neural networks to power converters can overcome the linear assumptions of traditional PI/PID control, enabling the system’s dynamic characteristics to be adapted and optimized online, thereby maintaining high efficiency under complex load and disturbance conditions.

International research has shown that Lin et al. proposed a digital signal processor (DSP)-based probabilistic fuzzy neural network (PFNN) control strategy for a two-stage AC-DC lithium battery charger. This significantly improved voltage and current discontinuities, as well as transient response performance during the constant current-constant voltage (CC-CV) mode switching process [10]. Nirmahas proposed a method that effectively addresses the issue of fault detection and classification in hybrid microgrids by employing a neural network training model [11]. From a topological perspective, Coelho explored how to achieve high efficiency in isolated DC-DC converters within renewable energy systems. He noted that using wide-bandgap devices (SiC/GaN) and intelligent control algorithms is a key trend for future high-power-density systems [12]. Furthermore, in their study of neural network uncertainties, Gawlikowski pointed out the insufficient confidence of traditional deterministic neural networks under parameter drift and external disturbances, emphasizing the importance of optimizing model robustness and generalization capabilities [13]. These studies have laid the theoretical and experimental foundation for intelligent control in the field of efficient energy conversion.

In China, Xiaobing Zhang optimized PID parameters using BP neural networks to achieve adaptive regulation of DC-DC converters, significantly improving steady-state accuracy [14]. Wang Lei introduced a PSO-BP hybrid algorithm in a bidirectional DC conversion system to effectively reduce output voltage ripple and overshoot [15]. Chinese researchers have also employed neural networks for vector control of grid-connected inverters and for current and voltage optimization control [16].

Most studies optimize PSFB under a fixed load or operating point, failing to capture its nonlinear behavior under dynamic conditions. Some neural network control methods do not address issues like sample distribution bias and uncertainty propagation. Traditional control algorithms combined with neural networks have limitations in real-time performance and interpretability. These methods often confuse system nonlinearity with parameter uncertainty, limiting control accuracy and hindering broader application. Therefore, an efficient neural network optimization strategy is needed. This paper proposes a strategy combining neural network optimization with closed-loop control, enabling real-time adjustment of key parameters like phase shift angle and duty cycle, improving the efficiency and stability of the PSFB system. The innovations in this paper are only at the simulation stage. This research offers an effective solution for future power management and energy storage development.

2. Working Principle

The Phase-Shifted Full-Bridge (PSFB) converter is a voltage-mode topology that is commonly found in medium- to high-power isolated DC conversion systems. The circuit consists of four power switches (Q1, Q2, Q3 and Q4) that form the main power bridge arms. Diodes (D1, D2, D3 and D4) and parasitic capacitors (C1, C2, C3 and C4) are inherent components of these switches. L_r is the primary-side resonant inductor, while L_c and C are the secondary-side filtering inductance and capacitance, respectively. Diodes D5 and D6 form the secondary-side rectifier bridge and are responsible for rectifying the AC voltage from the secondary-side transformer. N represents the transformer turns ratio. This topology achieves electrical isolation between the input and output via a high-frequency transformer and uses the secondary-side rectifier circuit and output filter to complete the energy conversion. The input is connected to a DC source (U_in) and the output provides a smooth DC voltage (U_o). The input DC voltage (U_in) enters the converter and is modulated through phase-shifted switching. The switches Q1–Q4 operate according to a control sequence. The phase difference between the switches (e.g., Q1 and Q4, or Q2 and Q3) determines the effective duty cycle and thus controls the energy transferred to the transformer. This phase shift controls the output power and voltage. The transformer controls the flow of energy by switching the primary side switches (Q1 and Q4).

The AC voltage induced in the primary windings is transferred to the secondary windings of the transformer, where it is rectified and filtered to produce a stable DC output voltage. On the secondary side, energy is rectified through diodes (D1–D4). This energy is then stored in capacitors and output inductors, which smooth out any fluctuations and provide a stable DC output voltage. The PSFB converter effectively adjusts power by controlling the phase shift of the primary side switches, thus regulating the energy transferred through the transformer. The efficient transfer of energy, precise duty cycle control, and electrical isolation provided by the transformer work together to deliver high efficiency. This is particularly effective when combined with Zero Voltage Switching (ZVS) as it minimizes switching losses. The transformer, rectifiers, and phase-shift modulation are key components that work together to ensure the converter operates efficiently and reliably under various operating conditions.

3. Control Strategy Optimization Scheme

3.1. Traditional Control Strategies

In traditional PI control strategies, a common approach is to introduce a PI (Proportional-Integral Control) controller to construct a “outer voltage loop + inner current loop” double closed-loop structure, as shown in Figure 1. The outer loop PI controller compares the output voltage U_o with the reference value U_ref to generate the reference value for inductor current or power, I_ref. The inner loop PI controller ensures that the actual current (or equivalent control variable, such as the current corresponding to the phase-shift duty cycle) quickly tracks I_ref. Ultimately, phase-shift control is employed to drive the switching devices, thereby suppressing load disturbances and bus voltage fluctuations.

Traditional PI control exposes deficiencies in terms of efficiency, dynamic performance, and control accuracy in topologies such as the hybrid full-bridge push-pull. First, in terms of efficiency, as wide bandgap devices (e.g., SiC and GaN) increase the switching frequency, the “optimal operating point” for timing and modulation becomes more sensitive. Traditional PI control is unable to precisely align the gate drive timing with the soft-switching window, resulting in increased switching losses. Second, traditional PI control presents a trade-off between speed and accuracy in dynamic response, particularly during load transients, where the recovery speed is slow and prone to overshooting. Under high-frequency or wide bandwidth conditions, PI control may also become unstable due to sensor interference or measurement errors [17,18]. Finally, PI control exhibits poor robustness to parameter uncertainties and operating point drift, making it difficult to improve steady-state accuracy and voltage/current ripple, which must be addressed through a variable gain mechanism that adjusts automatically with load changes [19,20].

3.2. Introduction of Intelligent Control Algorithms

To further improve the performance of the control system, intelligent control algorithms such as fuzzy control and neural network control are introduced, building upon traditional dual-loop control. Fuzzy control uses fuzzy reasoning and decision-making based on the system’s real-time state and experiential knowledge without requiring an exact mathematical model. It is highly adaptable to nonlinearity and uncertainty in the system. Neural network control, on the other hand, can learn the system’s dynamic characteristics through large amounts of training data, enabling more precise control. Combining intelligent control algorithms with traditional control methods effectively enhances the system’s dynamic performance and steady-state accuracy.

The paper develops a feedforward neural network model, beginning with the definition of the core parameters of the system. The network consists of two hidden layers. The first hidden layer contains 8 neurons, while the second layer contains 4 neurons. The structure is illustrated in Figure 2. This network architecture is relatively simple, making it suitable for control optimization tasks. During training, the maximum number of training epochs is set to 150, with a learning rate of 0.02 for updating the network weights at each iteration. The phase shift angle ranges from 0.1 to 0.6, and the target error is set to 1 × 10⁻⁶, indicating that the training process will terminate early when the network error reaches this value. Subsequently, the train function in MATLABR2024a is used to train the neural network with input and target data in order to minimize the difference between the output and the target.

The key difference from traditional PI closed-loop control is that the data are not directly fed back to the input layer, rather they are propagated through the backpropagation process, where they are fed back into the weight functions of the neural network to optimize the weights within the network. Specifically, the feedback of data mainly occurs during the backpropagation phase, where the error gradients are computed, and the weight functions adjust the weights of each layer in the neural network based on the error. The following section provides a detailed explanation of how the data are fed back within the neural network.

During the forward propagation phase of training, data start from the input layer and undergo computations through each layer until the output layer generates the predicted value (i.e., the output of the neural network). In this phase, the input data (load resistance R) are passed through the neurons of each layer, where they are weighted, summed, and processed by activation functions, ultimately resulting in the network’s output. After obtaining the network output through forward propagation, the error between the output and the target value is calculated. The error is represented using a loss function (MSE).

$$MSE={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{(y_{pred}(i)-y_{true}(i))}^2}$$

(1)

Here, y_pred(i) is the predicted output value of the i-th sample in the network, and y_true(i) is the actual output corresponding to the i-th sample in the target function. N represents the number of samples, which was 50 in this study.

The output of the neural network in this study is defined by the following equation:

$$eff={\displaystyle \frac{P_{out}(i)}{P_{in}(i)}}$$

(2)

$$targets(i)=D(i)\cdot {\displaystyle \frac{eff(i)}{best\_eff}}$$

(3)

Here, targets(i) is the y_true(i) mentioned earlier, P_out(i) is the output power at the ith phase shift angle, P_in(i) is the corresponding input power, D(i) is the value of the ith phase shift angle, eff(i) is the efficiency at the ith phase shift angle, and best_eff is the maximum efficiency value across all phase shift angles.

The goal of backpropagation is to update the weights in the network based on the errors calculated during forward propagation, so that the network output becomes increasingly closer to the target value. The backpropagation process is carried out through gradient descent. After each backpropagation step, the gradients are calculated and the weights are updated. The network adjusts the weights iteratively to reduce the error until the predefined stopping conditions are met, such as the maximum training epochs of 150 or a target error of 1 × 10⁻⁶. In summary, the training process of the neural network in this study can be described as a sequence of repeated forward propagation, error calculation, backpropagation, and weight updates. Through this process, the neural network ultimately learns the optimal relationship between load resistance and phase shift angle, enabling it to output the optimal phase shift angle to improve the efficiency of the DAB converter. The flowchart of the entire process is shown in Figure 3.

Compared to traditional voltage-current dual-loop control, the neural network optimization algorithm enhances the system’s performance in several key areas. Firstly, traditional voltage-current dual-loop control typically relies on fixed parameters and preset control strategies, making it incapable of dynamically and precisely adjusting in response to load variations or system disturbances. While dual-loop control can maintain voltage and current stability to some extent, its strong dependency on parameters often prevents it from achieving optimal energy transfer efficiency. Current and voltage waveforms may exhibit significant ripple under traditional control strategies, and efficiency tends to be lower, as reflected in the simulation results. The peak-to-peak value of the current is high and the output voltage ripple rate is also high, meaning that the system’s stability requirements are not met.

In contrast, the neural network optimization algorithm continuously learns and adaptively adjusts the phase shift angle, thereby minimizing current and voltage fluctuations as much as possible. Through multiple iterations, the neural network automatically adjusts the phase shift angle during load variations and optimizes the system’s energy transfer efficiency in real-time. This results in more symmetrical current waveforms and a significant reduction in the voltage ripple rate. For instance, in the optimized simulation, the peak-to-peak value of the inductive current decreases, the voltage fluctuation range narrows, and the ripple rate drops considerably. These results demonstrate that neural network optimization can substantially improve a system’s dynamic characteristics, enabling it to maintain high stability and low power loss under varying load conditions.

Furthermore, neural network optimization not only optimizes the phase shift angle, but also adjusts it based on the system’s actual operating conditions. This is in contrast to traditional dual-loop control, which relies solely on preset control rules and proportional constants. The parameter adjustments in traditional dual-loop control are often inflexible and unable to address nonlinear relationships or dynamic operating environments in complex systems. Neural networks, in contrast, can adapt to different loads, switching frequencies and external disturbances through learning and adjustment. This allows the system to maintain optimal operating conditions and thus outperforms traditional control methods in terms of overall efficiency, stability and waveform symmetry.

Furthermore, the neural network optimization algorithm can more accurately identify the optimal operating point through rapid optimization and fine-tuning during the iterative process. This adaptive adjustment approach enables the system to adjust its parameters in real-time in response to dynamic load variations, thereby maintaining efficient operation. Traditional control methods, in contrast, may fail to make timely adjustments under significant load changes, resulting in a decline in system efficiency and stability. Therefore, the neural network optimization algorithm enables the system to operate in a wider range of application scenarios through automated intelligent learning and control, exhibiting better adaptability and higher overall performance.

4. Simulation and Experimental Results Analysis

4.1. Simulation Model Setup

A bidirectional power supply simulation model consisting of a left-side full-bridge circuit and a right-side push-pull circuit was constructed using MATLABR2024a/Simulink software, as shown in Figure 4. The specific parameter settings of the simulation model are shown in

Table 1. Simulation Parameters of the Hybrid Full-Bridge Push-Pull Circuit.

Parameter	Value
Uin/V	200
R/Ω	5, 10, 15, 20
Uo/V	50
Resonant Inductance Lr/μH	500
Filter Capacitor Value C/μF	100
Filter Inductor Lc/μH	150
Switching Frequency fs/kHz	100
Turns Ratio N	2

. Based on this model, a control program was developed according to the optimized control strategy to simulate and analyze the system’s performance under different operating modes. The simulation parameters were set according to the actual design requirements, including input and output voltages, load resistance, and switching frequency, among others.

To validate the effectiveness of the proposed neural network-optimized control strategy for the hybrid full-bridge push-pull topology, we used MATLABR2024a/Simulink software to create a simulation model of a bidirectional power supply comprising a full-bridge on the left and a push-pull on the right.

This model accurately simulates the actual working conditions of the bidirectional DC-DC converter, including driving power switches, electromagnetic conversion in the high-frequency transformer and output filtering. The model components and parameter settings are as follows:

The main circuit model consists of a full-bridge section comprising four power switches (Q1, Q2, Q3 and Q4), taking into account the parasitic capacitance and body diode effects of each switch. The push-pull section generates a DC output through diode rectification and capacitor filtering to simulate the rectification and filtering processes of the actual circuit. The high-frequency transformer is configured with an appropriate turns ratio (N), as well as primary and secondary resonant inductances (L_r), filtering inductance (L_c) and capacitors (C), to simulate the electromagnetic conversion and filtering effects within the actual transformer.

The corresponding control program was developed based on the optimized neural network control strategy. This program ensures precise control of the phase shift angle, duty cycle, and timing, optimizing the system’s dynamic performance and steady-state accuracy. The neural network module was trained offline to obtain optimized weights and biases, which were then adjusted during the simulation to accommodate the system’s requirements under different operating modes.

The simulation parameters were set according to the actual design requirements, using the input DC voltage Vin and the desired output DC voltage Vo. Various load resistance values (5 Ω, 10 Ω, 15 Ω and 20 Ω) were selected to simulate the system’s performance under different load conditions. The switching frequency was chosen to optimize the balance between system efficiency, dynamic response and switching losses. During the initialization phase of the simulation process, the parameters were configured and the weights and biases of the neural network module were initialized. During the operational phase, the simulation was launched and the model generated driving signals based on the control program to manage the switching actions of the full-bridge and push-pull sections while monitoring key system parameters, such as current and voltage.

Key data such as inductive current, output voltage and phase shift angle were recorded during the simulation process, followed by subsequent analysis and processing. By constructing the above simulation model and setting the parameters, we were able to simulate the performance of the bidirectional DC-DC converter comprehensively under different operating modes.

4.2. Results Analysis

Based on observations of the neural network MSE curve, the Mean Squared Error (MSE) exhibited a significant exponential decline during the initial phase of training (iterations 1 to 2). This reflects the neural network’s ability to optimize rapidly within the parameter space. The sharp variation in this phase is due to the large deviations caused by the randomization of the initial weights. These initial weights are usually generated using a particular distribution, such as He or Xavier initialization, and often differ significantly from the actual data distribution. This results in a larger adjustment space for the gradient direction. The network uses the backpropagation algorithm to calculate the error gradient layer by layer via the chain rule, updating the weights along the negative gradient direction using gradient descent. This accumulation of parameter corrections results in a sharp decrease in error during the initial phase.

Firstly, in terms of neural network MSE (see Figure 5), it is clear that the system exhibits significant advantages after neural network optimization. As the number of iterations increases, the mean squared error (MSE) value decreases rapidly and then stabilizes, indicating that the neural network effectively reduces prediction errors during training and quickly converges to the optimal solution. This suggests that the neural network is highly efficient at optimizing and has strong fitting capabilities when adjusting circuit parameters. During the initial training stage (iterations 1 to 2), the MSE value dropped rapidly from approximately 0.02, demonstrating that the neural network efficiently optimizes the model parameters and enhances its ability to fit during this phase. The neural network quickly learns the effective parameters, leading to a substantial improvement in system performance over a short period. As training progresses (iterations 2 to 4), the rate of error reduction gradually decreases, but the MSE remains low, confirming that the neural network does not overfit with continued training and that the optimization process remains stable.

In conclusion, the low MSE value indicates that the circuit can effectively reduce errors during optimization and highlights the rapid convergence of the neural network, enabling the system to achieve optimal performance with fewer iterations. This demonstrates the powerful advantages of neural networks in circuit optimization. Throughout the neural network training process, we closely monitored the variation in MSE. Initially, due to the random initialization of network weights and biases, the MSE was relatively high. However, as the number of iterations increased, the MSE decreased rapidly and stabilized. Specifically, in the first 100 iterations, the MSE fell from an initial value of around 0.02 to below 0.0005 and remained at this extremely low level in subsequent iterations. This indicates that the neural network has strong learning capabilities and optimization potential, enabling it to converge quickly to the global optimal solution. The low MSE value means that the neural network can accurately predict the system’s dynamic characteristics, providing a solid basis for precisely implementing the control strategy.

Figure 6 compares the dynamic response characteristics of the inductive current and the output voltage in a power electronics system, showing the difference between the initial and optimized states. This clearly illustrates the significant improvement in system performance that is achieved through parameter optimization or control strategy enhancement. A comparison of the inductive current shows that in the initial state, it exhibited intense high-frequency oscillations with peak values close to ±10 A. The waveform also showed significant phase lag and distortion. After optimization, however, the current waveform’s amplitude was reduced to approximately ±8 A, representing a 20% reduction in fluctuation amplitude. The waveform was also significantly smoother, indicating enhanced stability and disturbance rejection capability in the system’s dynamic response. This improvement may be due to the fine-tuning of control parameters (e.g., PID parameters) or the use of new control algorithms (e.g., model predictive control or sliding mode control), enabling the system to adjust the duty cycle more quickly in response to load transients and suppress overshoot and oscillations in the inductive current. Additionally, optimizing circuit parameters (such as inductance and switching frequency) may have reduced the system’s equivalent impedance, thereby decreasing current ripple.

In terms of the output voltage response, the initial voltage waveform exhibited significant overshoot and steady-state error, with peak fluctuations approaching 8 V and a longer settling time. Following optimization, however, the overshoot was significantly reduced, the steady-state fluctuations were controlled to within 2 V and the waveform was much closer to an ideal sine or DC reference signal. These improvements demonstrate breakthroughs in the system’s voltage regulation accuracy and dynamic tracking performance. The optimization strategy may have increased the system’s resilience to input disturbances and load transients by introducing feedforward compensation, load current observers or enhanced modulation techniques, such as space vector modulation. For example, increasing the bandwidth of the voltage and current loops in the dual-loop control enables the system to respond more quickly to changes in output voltage, reducing the time required to return to steady state. Furthermore, the optimized system is likely to exhibit lower total harmonic distortion (THD) in the output voltage, which is essential for the stable operation of sensitive loads, such as communication equipment and precision instruments.

In terms of energy conversion efficiency, reducing inductive current fluctuations lowers conduction losses in switching devices and copper losses in magnetic components. Meanwhile, improved output voltage stability reduces energy fluctuation losses at the load end. These effects combined significantly enhance the system’s overall efficiency, particularly in high-frequency switching scenarios. The optimization also has engineering value in terms of controlling temperature rise and extending the lifespan of the devices. Furthermore, the optimized system performed better in terms of electromagnetic compatibility (EMC), as the reduced rate of change of current and voltage (di/dt and dv/dt) helps to decrease the intensity of electromagnetic interference (EMI), thus simplifying the design of filtering circuits.

However, it is worth noting that slight oscillations remain in the optimized response curve, potentially due to hardware parameters (e.g., sensor accuracy, switching device response speed) or unmodeled dynamics (e.g., the nonlinear characteristics of parasitic resistances and capacitances). Future research could integrate hardware-in-the-loop (HIL) simulations and adaptive control algorithms to further explore the system’s performance potential. In summary, the optimization strategy demonstrates substantial enhancements in dynamic response, steady-state accuracy, and energy efficiency, offering a valuable reference for the high-performance design of power electronics systems.

Figure 7 shows the relationship between the optimal phase shift angle and efficiency when load resistance varies under different load conditions. This analysis provides valuable insights into the dynamic performance of power electronics converters and similar energy conversion systems. Two key characteristics can be observed from the figure: first, within the load resistance range of 5 Ω to 20 Ω, the system’s optimal phase shift angle remained relatively stable, with the phase shift angle at all four test points consistently around 0.1, with minimal fluctuation. Second, system efficiency showed a negative correlation with load resistance. As load resistance increased from 5 Ω to 20 Ω, efficiency decreased from approximately 0.025 to 0.012, representing a reduction of over 50%.

From a control strategy perspective, the stability of the phase shift angle can be attributed to the system’s closed-loop control algorithm. As the load resistance changes, the controller maintains stability by adjusting the switching timing in real-time. This is a characteristic commonly observed in resonant topologies, such as LLC converters, during parameter design. A stable phase shift angle helps to maintain soft-switching conditions and reduce switching losses. However, the chart shows that this control strategy does not stop the efficiency from decreasing. This suggests that as the load resistance increases, the system may be experiencing an issue with an increasing proportion of conduction losses. As the load resistance increases, the output current decreases accordingly; however, losses related to current, such as copper losses in magnetic components (e.g., transformers) and wiring, may not decrease proportionally. This leads to an increased proportion of losses under light-load conditions. Furthermore, if the system has fixed standby power losses, their impact becomes more pronounced under light-load conditions.

The pattern of the efficiency curve revealed the performance characteristics of the system across a wide load range. Under heavy load conditions (5 Ω), the system is likely operating at full capacity, where conduction losses dominate; however, the relatively high output power results in a higher efficiency value. As the load resistance increases to 20 Ω, the system enters a light-load state. While switching losses may decrease due to frequency or phase adjustments, fixed losses (e.g., control circuit power consumption and core losses) become more significant, causing a continuous decline in efficiency. This phenomenon is particularly important in the design of practical power supplies, where engineers must often strike a balance between heavy-load efficiency and light-load standby power losses.

From a perspective of optimizing system design, these data suggest that dynamically adjusting the operating parameters could improve efficiency across the full load range.

Through multiple iterations of neural network optimization under varying load conditions (Figure 8), the system achieved more precise adaptive control of the output voltage. During the training process, the neural network gradually learned the mapping relationship between ‘load–optimal phase shift angle–output voltage’, such that under different loads ranging from 5 Ω to 20 Ω, the output voltage increased with load but maintained good periodicity and phase consistency overall, thus avoiding distortion and instability caused by load variations. Secondly, as the iterations progressed, the output voltage waveform, which was initially characterized by significant fluctuations, gradually converged to a smoother, more ideal sine wave-like periodic waveform. The voltage ripple rate decreased significantly, and the optimal voltage curve that emerged in later iterations exhibited higher peak values and the best stability. This demonstrates the neural network’s ability to effectively suppress voltage ripple, improve voltage utilization and enhance output quality under varying load conditions after several iterations, thus significantly improving the converter’s voltage output performance in dynamic load scenarios.

Following multiple iterations of neural network optimization, both the inductive current and the output voltage exhibited significant stabilization and regularity. Following 17 iterations (see Figure 9), the inductive current exhibited a characteristic periodic ‘square-wave’ pattern. It rapidly rose to a peak value of approximately 8 A within each cycle then maintained a stable interval before decreasing symmetrically to a trough value of approximately −8 A, repeating this process. Throughout the entire time range of 0–500 μs, the peak and trough values and cycle durations remained highly consistent, indicating that the inductive current had converged to a regular, stable operating state. After 18 iterations (Figure 10), the output voltage exhibited near-sinusoidal periodic fluctuations, slowly rising from 0 V to a peak of approximately 3.8 V, then dropping to a trough of about 0.8 V before rising again. The peak-to-trough values and cycle durations across multiple cycles were also highly consistent, demonstrating that the output voltage waveform was smooth with controllable fluctuations and good periodicity.

In summary, the advantages of the neural network iterations are primarily reflected in the transformation of the inductive current and output voltage waveforms from ‘potentially large fluctuations’ to ‘stable amplitude and consistent rhythm’ periodic waveforms. This significantly improves the stability of both the current and the voltage. Second, the system quickly converged to an ideal operating point under the given conditions, ensuring smooth, controllable energy transfer and enhancing the converter’s overall output quality and operational reliability.

Through neural network optimization, the convergence trend of the phase shift angle (Figure 11) and the efficiency improvement curve (Figure 12) demonstrate the significant impact of this optimization on the two parameters. In Figure 11, the circles indicate the step-by-step reduction of the phase-shift angle after each iteration; the more circles, the greater the reduction. As the number of iterations increased, the phase shift angle gradually converged from an initial range of 0.26 to 0.3 to a range of 0.1 to 0.12. This indicates that the neural network optimized and adjusted the phase shift angle, thereby reducing the system’s energy loss and improving energy transfer efficiency. Regarding efficiency improvement, there was initially little change; however, from the third iteration onwards, efficiency increased rapidly from 0.1% to 1.9%, showing that neural network optimization significantly enhanced the system’s overall performance in the later stages. Convergence of the phase shift angle led to more precise energy transfer, reducing power losses and unnecessary current fluctuations within the system and directly contributing to efficiency improvement. As the phase shift angle was continuously optimized, current fluctuations and peak values gradually diminished, stabilizing energy transfer and effectively improving system efficiency. During the iterative optimization process, the convergence of the phase shift angle enhanced the circuit’s stability and directly facilitated efficiency improvements. Therefore, neural network optimization can be seen to achieve higher conversion efficiency by precisely controlling the phase shift angle, with the two factors forming a mutually reinforcing optimization relationship.

Next, a detailed analysis of the current optimization process was conducted. This focused on changes in peak current values and compared current at different stages of iteration. This revealed the profound impact of neural network optimization on current control. An in-depth examination of these data provided a more comprehensive understanding of the neural network’s role in optimizing current, especially with regard to reducing fluctuations, lowering peak values and improving stability. Figure 13 shows the gradual decrease in the current peak, which was a direct result of the neural network optimization. Initially, the current peak stabilized at around 16 A. As the iterations progressed, the current peak began to decrease gradually after the third iteration, ultimately dropping to 15.2 A after the fourth iteration. This change indicates not only a reduction in the amplitude of current fluctuations, but also demonstrates the neural network’s fine control over the current during the optimization process. By adjusting the control parameters, the neural network effectively reduces excessive current fluctuations, thereby preventing high peak currents from imposing an excessive load on the system or causing energy wastage. This trend indicates an improvement in the system’s ability to control current fluctuations, stabilizing its response to load changes while reducing thermal management pressure and extending the system’s lifespan.

Figure 14 provides a more detailed analysis of current changes, illustrating how the current waveform and peak values evolve at different stages of iteration. In the early stages (iterations 2–10), the current waveform remained stable and consistent, peaking at around 8 A. This indicates that the current output characteristics are good and that the system is operating stably. During this phase, the periodicity and symmetry of the current waveform remain unaffected, indicating that the system’s current control is stable. However, as the number of iterations increased, particularly in the mid-stage (iterations 12–20), variations in the current waveform began to emerge, with the current peak tending towards 8A. Meanwhile, the waveform’s smoothness and symmetry improved. This suggests that the neural network optimization is beginning to exhibit more refined adjustment capabilities during this phase, enabling the system to control the current output more precisely and avoid excessive fluctuations and unnecessary load responses. In the later stages (iterations 22–30), the stability of the current waveform improved further, with reduced differences between peak and trough values. The current waveform also became smoother and more consistent. This is a particularly crucial change, as it indicates that the neural network effectively optimized the current regulation algorithm. The result is a more stable and symmetrical current output with smaller fluctuations. It also suggests that after multiple rounds of optimization, the system can precisely control the current waveform, reducing unnecessary energy losses and improving the stability of the current output. The enhanced smoothness and consistency of the current output make the system more stable under dynamic load conditions, enabling more efficient energy transmission and avoiding thermal losses and efficiency degradation caused by current fluctuations.

Combining the data from Figure 13 and Figure 14 for analysis reveals that neural network optimization reduces current peak value fluctuation and, more importantly, enhances current stability and controllability through precise adjustments. The connection between the two sets of data is particularly significant. The downward trend in current peak values reflects improved current regulation precision due to neural network optimization. The progression of the current waveform—from stable in the early stages to gradual changes in the mid-stage and finally a smoother waveform in the later stages—further demonstrates that the neural network gradually achieved more efficient and precise current control during optimization. Specifically, as the neural network optimization deepened, the system was able to reduce current peak values and avoid overloading or excessively high currents, thereby optimizing energy transmission efficiency.

Next, a detailed analysis of the voltage aspect was conducted, focusing on changes in the voltage ripple rate and the evolution of the voltage waveform. These demonstrate the significant impact of neural network optimization on voltage control. Analyzing these two datasets provides a deeper understanding of the advantages of neural networks in optimizing voltage output, and of how these changes enhance the system’s overall performance. Figure 15 shows that the voltage ripple rate improved significantly after multiple iterations. During the initial stage (iterations 1–2), the voltage ripple rate remained stable at around 90%, indicating substantial voltage fluctuations and poor stability. However, between iterations 2 and 3, the voltage ripple rate decreased rapidly, eventually stabilizing at 30%, which showed a significant improvement in voltage stability. This suggests that as neural network optimization progresses, the system can control voltage fluctuations more precisely, reducing voltage ripple and improving the smoothness and quality of the voltage output. The sharp drop in ripple rate during the transition from iterations 2 to 3 reflects the neural network’s successful optimization of the voltage regulation algorithm, resulting in more uniform voltage fluctuations and further enhancing voltage stability.

Figure 15 illustrates the evolution of the voltage waveform at different stages of the iteration process. During the initial iterations (2–10), the waveform remained consistent, with peak and trough values of approximately 3.8 V and 0.8 V, respectively. Both the cycle duration and waveform shape were also consistent during this phase. This indicates that during this phase, the voltage output characteristics are stable and the circuit is operating smoothly, with no significant changes to the waveform and relatively uniform voltage fluctuations. However, as the iterations progressed into the mid-stage (iterations 12–20), the voltage waveform began to change. The peak gradually approached 3.8 V and the waveform became smoother and more symmetrical, leading to better voltage output stability. In the later stages (iterations 22–30), the voltage waveform showed significant optimization, with the peak reaching 7.5 V. Compared to earlier stages, the amplitude and stability of the waveform were significantly improved, indicating that following optimization, the stability and amplitude of the voltage output were greatly increased and the system’s voltage control capability had been significantly enhanced.

Combining the information from Figure 15 and Figure 16 shows that neural network optimization plays a key role in reducing voltage ripple and improving stability. Figure 13 shows that the reduction in voltage ripple rate reflects a decrease in voltage fluctuations, while Figure 14 shows that the improvement in waveform smoothness and stability significantly enhances the quality of the voltage output. This demonstrates that reducing voltage ripple directly contributes to smoothing the voltage waveform and enhancing stability, thereby improving the system’s power conversion efficiency and reliability.

In the previous analysis, we examined the optimization processes for current and voltage. We focused particularly on the impact of neural network iterations on current fluctuations, peak reduction, and the reduction in the voltage ripple rate. These optimizations enhanced the stability of the current and voltage, and laid the foundation for improving the system’s overall efficiency. Stable current and smooth voltage output ensure efficient energy conversion during the transfer process, minimizing unnecessary energy losses. This provides a robust basis for the subsequent analysis of power characteristics and system efficiency.

Figure 17 present the changes in power characteristics, normalized errors and efficiency during the iteration process, detailing the key role of neural network optimization in power conversion and enhancing system performance. Analyzing these data provides a clearer understanding of how neural networks optimize power characteristics through continuous iterations, reduce errors and significantly improve system efficiency.

Figure 17 first illustrates the power characteristics during the iteration process, particularly the changes in input and output power. According to the data, the input power remained at around 400 W during iterations 1 to 2, then dropped to approximately 350 W during iterations 2 to 3, and finally decreased further to 250 W after iterations 3 to 4.

This indicates that as the neural network iterates, the system’s input power requirement gradually decreases. The system continually optimizes the energy conversion efficiency in each iteration, reducing unnecessary energy consumption and achieving more efficient energy transfer and processing.

In terms of output power, it stabilized at around 0.5W in the early iterations (1–2). However, after the third iteration, the output power began to increase substantially, reaching approximately 2.5 W by the fourth iteration. This demonstrates that as the neural network optimizes, the system’s energy conversion capability is significantly enhanced and the output power increases substantially. This indicates that following optimization, the system can utilize input power more effectively, thereby improving the circuit’s power transmission capacity. From this perspective, the contrast between the decrease in input power and the increase in output power highlights the significant improvement in energy conversion efficiency brought about by neural network optimization. While input power is gradually reduced, the system is able to effectively increase the output power. This demonstrates that the neural network has successfully improved the power conversion efficiency through optimized control strategies, reducing energy losses and achieving more efficient power conversion.

Next, the code stores the mean squared error (MSE) at each iteration of the neural network training process. By dividing the training error at each node by the maximum value of the MSE, a normalized error value is obtained, which scales the error to a range from 0 to 1, facilitating comparison with other performance metrics. The normalized efficiency is calculated by dividing the efficiency value at each iteration by the initial efficiency, providing a relative efficiency value that reflects the improvement in performance during the optimization process.

Figure 18 illustrates the changes in normalized error and efficiency throughout the neural network optimization process. According to the data, the normalized error remains at an extremely low level, close to zero, throughout the entire iteration process. This indicates that the error in the system remains consistently stable and low throughout the iterations, demonstrating the neural network’s precise adjustment capability during the optimization process. The system is able to maintain an error close to zero through continuous optimization, reflecting the neural network’s exceptional data-fitting and model-optimization capabilities.

Meanwhile, changes in the normalized efficiency also demonstrate significant improvement during the optimization process. Normalized efficiency remained stable during iterations 1 to 3 and then began to increase gradually after the third iteration. Notably, there was a substantial improvement in efficiency in the fourth iteration. According to the data, the system’s normalized efficiency increases as the number of iterations rises. This indicates that during the optimization process, the neural network reduces errors and effectively enhances the system’s energy utilization efficiency. This increase in efficiency is consistent with the gradual decrease in input power and significant increase in output power, which further validates the critical role of neural network optimization in enhancing energy conversion efficiency.

Combining the content of Figure 17 and Figure 18 shows that neural network optimization achieved significant progress in power conversion efficiency and reduced system errors, improving overall performance. Specifically, the decrease in input power and the increase in output power complement each other, demonstrating that the system achieved more efficient energy conversion through optimized control strategies. Concurrently, the dual enhancement of low error and high efficiency further proves the neural network’s ability to refine adjustments during the optimization process, enabling the system to reach an optimal state in terms of energy conversion and efficiency improvement.

5. Conclusions

This paper proposes an integrated control strategy that combines neural network optimization algorithms with closed-loop control. By introducing a neural network-based optimization method, the strategy enables precise control over the phase shift angle, duty cycle, and switching timing through intelligent learning and online adjustment. This approach significantly enhances both the dynamic performance and steady-state control accuracy of the system.

Experimental results demonstrate that the implementation of neural network-based online optimization leads to substantial improvements in key control variables and performance metrics. As the optimization process progressed, the optimal phase shift angle rapidly converged to a range of 0.10 to 0.12. Additionally, the quality of both current and voltage was notably enhanced: the current peak decreased from 16 A to 15.2 A, while the voltage ripple rate dropped from approximately 90% to around 30%, indicating effective suppression of output fluctuations and a marked increase in stability.

Regarding power characteristics, the input power demand decreased with iterations: from 400 W in the first iteration to 350 W, reflecting improved energy utilization and power conversion efficiency. In terms of error and overall efficiency indicators, the normalized error approached zero and remained stable throughout iterations 1 to 4. The normalized efficiency remained stable from iterations 1 to 3, began to rise after the third iteration, and significantly improved to 13 in the fourth iteration.

In conclusion, neural network optimization enables effective convergence of the phase shift angle within fewer iterations, simultaneously reducing the current peak and voltage ripple, lowering input power demand, increasing output power and efficiency while maintaining a low and stable error level, thereby significantly enhancing the system’s stability and energy conversion performance.