# Intelligent Design of ZVS Single-Ended DC/AC Converter Based on Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Principle of Operation of the Single-Ended Resonant DC/AC Converter

_{D}, as shown in Figure 2). After the change in the direction of the current, the transistor T begins to conduct (for the interval from t

_{D}to t

_{i}). A characteristic of this stage is that for the entire interval, an increasing current with a shape close to linear flows through the LR load, and the capacitor C has a voltage close to 0 (the voltage drop of the unblocked reverse diode D and transistor T).

_{i}to t

_{2}): it begins at the moment when the transistor T turns off. If resonance conditions are met in the series RLC circuit (and this is necessary for the normal operation of the power circuit), a sinusoidal current with a non-zero initial value I

_{0}begins to flow through the load (according to Figure 2). This initial value of current through the load is the value reached when the first stage of operation of the circuit has ended. Due to the presence of resonant processes, resonant capacitor C is charged according to an oscillatory law to a voltage higher than the voltage of the DC power source. After that, a discharge process begins in the circuit, and when the voltage on the capacitor C reaches the value of the input voltage U

_{d}, the current through the inductance has a value close to the maximum, although with the opposite sign. Thus, the energy stored in inductance L causes the further discharge of resonant capacitor C. When the capacitor voltage becomes equal to zero and tends to go negative, the reverse diode is turned on, which ends this interval of circuit operation, and the next period begins.

_{0}is turned off.

#### 2.2. Modeling of Operation of the Single-Ended Resonant DC/AC Converter

_{0}.

_{d}= 25 V, active resistance R = 1 Ω, capacitance C = 10 μF, and inductance L = 1 μH. The value of the current I

_{0}was chosen to be 15A. Figure 3 shows the obtained time diagrams of the current through the inductance and of the voltage on the capacitor. These circuit parameter values were obtained using the design methodology presented in [28].

## 3. Results

#### 3.1. Formulation of the Task

_{aver}, Δi, u

_{aver}and Δu as the input for the network allowed us to change some of the values of the circuit elements R, L, and C, as well as the values of i

_{aver}, Δi, u

_{aver}and Δu. Thus, the considered design task was reduced to a static one. This is what allowed the use of the forward NN for the automated design of the DC/AC converter. To visualize the design process, we called this network the inverse neural network model of the converter. If the design task had not been reduced to a static one, it would have required the use of recurrent neural networks in the role of an inverse neural network model. This would have significantly complicated the task, as it is not known whether it is possible to realize the modeling of the desired process with a recurrent neural network. On the other hand, the static task risked that the neural model would turn out to be inadequate for our applications (too simplistic). The results presented below show that, fortunately, this was not the case.

#### 3.2. Preparing the Data for Training the Neural Network

_{aver}, Δi, u

_{aver}and Δu, as shown in Figure 4.

- -
- First, the condition for the resonance of the series circuit is satisfied: $R<2\sqrt{\frac{L}{C}}$;
- -
- Secondly, within a pseudo-period, the voltage on the capacitor u becomes negative and as a result, current flows through the reverse diode for some time.

_{aver}, Δi, u

_{aver}and Δu) were calculated. The result of this calculation with the model is shown in Figure 6.

_{aver}, Δi, u

_{aver}and Δu have averaged values, and at the output, the values of the circuit elements R, L and C are determined. Schematically, this model is shown in Figure 7. To train this network (the inverse network), we needed a large amount of diverse input and output data. With the data generated by the previous step of the automated design, the NN—inverse model was trained (shown in Figure 7).

^{6}, 1 × 10

^{5}, and 1, respectively. The values for C, L and R are plotted precisely at this normalized scale in Figure 5.

_{aver}, Δi, u

_{aver}, and Δu from the mathematical model. Then, i

_{aver}, Δi, u

_{aver}and Δu were fed as input to the neural network. In general, if the network is well-selected and well-trained, a good match between the C, L and R values given as input to the mathematical model and obtained as output of the neural network should be expected. The results given in Figure 10 show that such a match was achieved.

#### 3.3. Single-Ended DC/AC Converter Design Example

_{aver}= 15 V and i

_{aver}= 2 A.

_{aver}, Δi, u

_{aver}and Δu were calculated. The calculation was performed with formulas (3) and (4). Of course, only the values of the state variables i and u in the established mode were used, as shown in Figure 11. The results were as follows:

_{aver}= 13.5835, and i

_{aver}= 1.8292 A.

_{aver}, Δi, u

_{aver}and Δu with the values that were chosen for the input of the neural network at the beginning of this section. We found that they were extremely close (the difference was less than 5%). A certain (not large) deviation was observed only for the value of u

_{aver}. However, this was most likely due to the fact that the values of i

_{aver}, Δi, u

_{aver}and Δu are mutually dependent and cannot be set arbitrarily (at the beginning, this was not taken into account when setting the values of the design parameters). These values were chosen according to the subjective desire of the designer. However, as a result of the analysis of the obtained results, it should be noted that an arbitrary combination between them cannot be achieved. Based on this, it should be concluded that the design of the DC/AC converter was successful and the set goal of applying neural networks for the automated design of power electronic devices was fully achieved.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- (a)
- minmax(z) is a standard command that finds the minimum and maximum values of each of the inputs, and this data is then used to initialize the weights of the two layers $W,\hspace{0.33em}B,\hspace{0.33em}V,\hspace{0.33em}D$;
- (b)
- [60,3] shows that the network has two layers. The first (input) consists of 60 neurons (the number of neurons in this layer is not fixed in advance; this number determines the power of the network, and in the process of experimentation, a value of 60 neurons was selected) and the second (output) consists of 3 neurons (the number of neurons in the last layer is equal to the number of outputs, so there can only be 3 neurons here);
- (c)
- {‘logsig’,‘purelin’}… show that the activation functions of the first and second layers are, respectively, logsig and purelin (subpoint “b” and “c” also determine the structure of the network shown in Figure 8).

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**Figure 2.**Timing diagrams describing the operation of a series resonant inverter. From top to bottom: control pulses, load current, and voltage on the capacitor and the transistor (on the reverse diode).

**Figure 3.**Timing diagrams of the DC/AC converter state variables: (

**a**) current through the inductance; (

**b**) voltage across the capacitor.

**Figure 6.**Output data for state variables: (

**a**) current through the inductance L- i

_{aver}and Δi; (

**b**) voltage across the capacitor C- u

_{aver}and Δu.

**Figure 11.**State variable results of the neural network-designed DC/AC converter: (

**a**) current form through the inductance with parameters i

_{aver}and Δi; (

**b**) voltage across the capacitor with parameters u

_{aver}and Δu.

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**MDPI and ACS Style**

Hinov, N.; Gilev, B.
Intelligent Design of ZVS Single-Ended DC/AC Converter Based on Neural Network. *Inventions* **2023**, *8*, 41.
https://doi.org/10.3390/inventions8010041

**AMA Style**

Hinov N, Gilev B.
Intelligent Design of ZVS Single-Ended DC/AC Converter Based on Neural Network. *Inventions*. 2023; 8(1):41.
https://doi.org/10.3390/inventions8010041

**Chicago/Turabian Style**

Hinov, Nikolay, and Bogdan Gilev.
2023. "Intelligent Design of ZVS Single-Ended DC/AC Converter Based on Neural Network" *Inventions* 8, no. 1: 41.
https://doi.org/10.3390/inventions8010041