A Comparison of the Response and Voltage Regulation Performance of the Single-Channel DC/DC Boost Converter Circuit with Artificial Neural Networks, Fuzzy Logic and PID Controllers

In this section, we describe the details and relevant principles of the research presented. Considering Figure 1, in the first section on the left, it is found that it is the part of the initial set of powers that comprises wind turbines, gear blocks (GB) and generators (SCIG) with rotors are squirrel cage type. When the generator produces AC voltage, it passes through the mechanism of the full wave rectifier (REC) that filters the ripples to achieve a DC voltage with minimal ripples. However, for the second part, there will be an important component of the research article topic: single-channel DC/DC boost converter with switch device control (MOSFET) with three forms of control algorithms consisting of: artificial neural networks controller (ANNC), fuzzy logic controller (FLC), and PID controller (PIDC). This DC/DC boost converter controls the DC voltage and undergoes ripple filtration again. For constant voltage control, the principle of output voltage detection at the link point (DC-Bus) is used before entering the three-phase inverter. For inverters, it is the third segment that uses the principle of switching device operation control (IGBT) with the principle of SVPWM closed loop speed control and contains algorithmic ANNC, FLC, and PID controller. Consequently, the Induction motor (SCIM) is therefore loaded to test the response and voltage control performance of the single-channel DC/DC boost converter. There are three forms of controlled algorithms based on the proposed objectives of this research paper.

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Figure 1. Proposed mechanism of the single-channel converter DC/DC boost

The next section discusses the mathematical principles involved in the research, including the single-channel DC/DC boost converter and the principle of the algorithmic ANNC, FLC, and PID controller. Notwithstanding, the simulation results are compared with the prototype mechanism produced, in order to verify the results and verify their validity for conclusions.

2.1 Wind turbine blades

Wind turbine blades are the dominant and important components of wind turbines. It is also the main mechanism for the most important operation of energy conversion with the process of converting wind kinetic energy into rotary mechanical energy. Wind turbine blades have evolved in aerodynamic design and materials from very early wind turbines. Modern wind turbine blades are usually made of aluminum, fiberglass or carbon fiber composites that provide a high ratio of strength to weight required. Generally, for a given wind turbine blade, the lifting force (F_w) can be adjusted to the degree of angle. When this angle is equal to zero, that is, the absence of lifting force or torque that causes the turbine blades to rotate. Thus, the power of air masses flowing at speed (v_w) through cross-sectional space (A) can be calculated by

$P_w=\frac{1}{2} \rho A v_w^3$     (1)

Eq. (1), which ρ is the density of air in kg/m³, A is the sweeping area in m² and v_w is the wind speed in m/s. The density of air ρ is an element of air pressure and air temperature. Wind energy captured by wind turbine blades and converted into mechanical energy can be calculated by

$P_M=\frac{1}{2} \rho A v_w^3 C_p$     (2)

where, C_p is the power coefficient of the wind turbine blades. According to the Betz limit, with today's technology, the energy coefficient of modern turbines usually ranges from 0.2 to 0.5, which performs the function of rotation, speed and number of wind turbine blades. The energy produced is 2 MW at a wind speed of 12 m/s, and the air density ρ = 1.225 kg/m³. However, from Eq. (2) in the increase in energy captured by wind turbines, there are three possibilities: wind speed v_w, C_p energy coefficient and sweep area A. Based on the Eqns. (1)-(2), wind turbines can be designed with a larger sweeping area to capture more energy. Depending on the area A=πl², where l is the length of the wind turbine blades designed by the manufacturer in each model. Increasing the length of the wind turbine blades has the effect of squaring in the sweeping area and capturing energy. However, for this research, the wind turbines used were designed by manufacturers that improved the energy coefficients of turbine blades according to aerodynamics in accordance with international standards.

2.2 Induction generator models

The classification of inductions applied to generators in wind turbine systems is divided into two types: double-fed induction generators. (DFIGs) and squirrel cage induction generators (SCIGs) both generators have the same stators but only different rotor structures. However, for this research paper, SCIG type rotors are used, with structures consisting of laminated cores and rotor bars. The rotor bar is embedded inside the rotor. When the stator coil is connected to a three-phase power supply, it creates a rotating magnetic field in the air gap. Because the rotor band shorts circuits, the voltage of the induction rotor produces a rotor current, which reacts with the rotating field to produce an electromagnetic field.

Nevertheless, for writing dynamic models commonly used for induction generators, they are divided into two. Based on space vector theory, it is a dq-axis model derived from vector model space. This space vector model has a compact mathematical expression and a single equivalent circuit. Instead, it uses variables that are both real and imaginary. Whereas the dq-frame model consists of two equivalent circuits for each axis. These models have a convenient relationship for analyzing the temporal performance and static state of the induction generator.

2.3 Space-vector model

The development of the induction generator space vector model is based on two hypothetical points: the induction generator is symmetrical in structure and three-phase equilibrium. The second point is that the magnetic core of the stator and rotor will be linear with a slight loss in the core. This induction generator space vector model generally consists of three sets of equations: the voltage equation, the flux link equation, and the motion equation [4, 5]. The voltage equations for the stator and rotor of the generator in the frame of reference are written as equations to be obtained.

$\vec{v}_s=R_s \vec{i}_s+p \vec{\lambda}_s+j \omega \vec{\lambda}_s$     (3)

$\vec{v}_r=R_r \vec{i}_r+p \vec{\lambda}_r+j\left(\omega-\omega_r\right) \vec{\lambda}_r$     (4)

where, $\vec{v}_s, \vec{v}_r$ are stator and rotor voltage vectors $(\mathrm{V}), \vec{\imath}_s, \vec{\imath}_r$ are stator and rotor current vectors (A), $\vec{\lambda}_s, \vec{\lambda}_r$ are stator and rotor flux-linkage vectors $(\mathrm{wb}), R_s, R_r$ are stator and rotor winding resistances $(\Omega), \omega$ is the rotating speed of the arbitrary reference frame $(\mathrm{rad} / \mathrm{s}), \omega_r$ is rotor electrical angular speed $(\mathrm{rad} / \mathrm{s}), p$ is derivative operator $(p=d / d t)$. The terms $j \omega \vec{\lambda}_s$ and $j\left(\omega-\omega_r\right) \vec{\lambda}_r$ on the right-hand side of Eqns. (3) and (4) are referred to as speed voltages, which are induced by the rotation of the reference frame at the arbitrary speed of a $\omega$. Similarly, an equation for the stator and rotor flux linkages can be written a

$\vec{\lambda}_s=\left(L_{l s}+L_m\right) \vec{i}_s+L_m \vec{i}_r=L_s \vec{i}_s+L_m \vec{i}_r$     (5)

$\vec{\lambda}_r=\left(L_{l r}+L_m\right) \vec{i}_r+L_m \vec{i}_s=L_r \vec{i}_r+L_m \vec{i}_s$     (6)

where, L_s= L_ls + L_m is stator self-inductance (H), L_r= L_lr + L_m is rotor self-inductance (H), L_ls + L_lr is stator and rotor leakage inductance (H), L_m is magnetizing inductance (H). All the rotor-side parameters and variables, such as R_r, L_lr, $\vec{l}_r$ and $\vec{\lambda}_r$, in the above equations are referred to the stator side. The third set of equations is the equation of motion, which describes the dynamics and behavior of the mechanical velocity of the rotor in terms of mechanics and electromagnetism torque as

$\vec{v}_s=v_{d s}+j v_{q s} ;\quad \vec{i}_s=i_{d s}+j i_{q s} ; \quad \vec{\lambda}_s=\lambda_{d s}+j \lambda_{q s}$     (7)

$J \frac{d \omega_m}{d t}=T_e-T_m$     (8)

$T_e=\frac{3 P}{2} \operatorname{Re}\left(j \vec{\lambda}_s \vec{i}_s^*\right)=-\frac{3 P}{2} \operatorname{Re}\left(j \vec{\lambda}_r \vec{i}_r^*\right)$     (9)

where, J is the moment of inertia of the rotor (kgm²), P is the number of pole pairs, T_m is the mechanical torque from the generator shaft (N•m), T_e electromagnetic torque (N•m), ω_m is the rotor mechanical speed, ω_m=ω_r/P (rad/sec). The above equation is a space vector model of an induction generator, which shows an equivalent circuit, as in Figure 2, the generator model is in an arbitrary frame of reference, rotating in space at an arbitrary speed ω.

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Figure 2. Space-vector equivalent circuit of an induction generator

From the space vector model of the induction generator, as shown in Figure 2, the principle of motor operation is applied by considering the direction of the stator current flowing into the stator. This convention is widely accepted since inductors are mainly used as motors. However, if there is no loss of space vector models, these equations can be used to model inductors, whether motors or generators.

2.4 Dq reference frame model

This topic describes the dq-axis model of an induction generator by decomposing space vectors in the components of the d-axes and q-axes, as shown in Figure 3.

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(a) d-axis circuit

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(b) q-axis circuit

Figure 3. Induction generator dq-axis model in the reference frame.

Figure 3 writes the voltage equations of the stator and rotor as equations as

$\vec{v}_s=v_{d s}+j v_{q s} ;\quad \vec{i}_s=i_{d s}+j i_{q s} ; \quad \vec{\lambda}_s=\lambda_{d s}+j \lambda_{q s}$     (10)

$\vec{v}_r=v_{d r}+j v_{q r} ; \quad\vec{i}_r=i_{d r}+j i_{q r} ; \quad\vec{\lambda}_r=\lambda_{d r}+j \lambda_{q r}$     (11)

Moreover, the groups the real and imaginary components as

$v_{d s}=R_s i_{d s}+p \lambda_{d s}-\omega \lambda_{q s}$     (12)

$v_{q s}=R_s i_{q s}+p \lambda_{q s}+\omega \lambda_{d s}$     (13)

$v_{d r}=R_r i_{d r}+p \lambda_{d r}-\left(\omega-\omega_r\right) \lambda_{q r}$     (14)

$v_{q r}=R_r i_{q r}+p \lambda_{q r}+\left(\omega-\omega_r\right) \lambda_{d r}$     (15)

Similarly, substituting Eqns. (10) and (11) into Eqns. (3) and (4), the dq-axis flux linkages are obtained:

$\lambda_{d s}=\left(L_{l s}+L_m\right) i_{d s}+L_m i_{d r}=L_s i_{d s}+L_m i_{d r}$     (16)

$\lambda_{q s}=\left(L_{l s}+L_m\right) i_{q s}+L_m i_{q r}=L_s i_{q s}+L_m i_{q r}$     (17)

$\lambda_{d r}=\left(L_{l r}+L_m\right) i_{d r}+L_m i_{d s}=L_r i_{d r}+L_m i_{d s}$     (18)

$\lambda_{q r}=\left(L_{l r}+L_m\right) i_{q r}+L_m i_{q s}=L_r i_{q r}+L_m i_{q s}$     (19)

The electromagnetic torque T_e in Eq. (9) can be represented by dq-axis flux, linkage and current are the same. However, mathematical manipulation of several expressions for torque can be obtained. The most commonly used expressions are as follows:

$T_e=\left\{\begin{array}{l}\frac{3 P}{2}\left(i_{q s} \lambda_{d s}-i_{d s} \lambda_{q s}\right) \quad (a)\\ \frac{3 P L_m}{2}\left(i_{q s} i_{d r}-i_{d s} i_{q r}\right) \quad (b)\\ \frac{3 P L_m}{2 L_r}\left(i_{q s} \lambda_{d r}-i_{d s} \lambda_{q r}\right)\quad (c)\end{array}\right.$     (20)

However, from Eqns. (10) to (20) together with equations of motion (8)-(9) instead of axes. dq. The form of the induction generator in the frame of reference and related. The dq-axis equivalent circuit is shown in Figure 3. To obtain a dq-axis model in synchronous and stationary reference frames, the speed of the W reference frame can be set to the synchronous frequency (stator) WS of the generator and zero, respectively.

2.5 Single-channel boost converter

A typical circuit diagram for a single-channel boost converter, as shown in Figure 4, would show that a boost converter is a power converter with a DC voltage output rather than an input. This single-channel boost converter circuit consists of switches, diodes, inductors, and filters, namely capacitors. For capacitors, the output filter must be sufficiently large, and the output voltage of the converter must be free of ripples.

Figure 4 briefly describes the principle of operation, namely when the switch is on. The diode has a reverse bias, and the output is equal to the input, since the circuit is turned on. When the switch is turned off the diode is forward biased, and the energy stored in the inductor is released by flowing through the diode. In this case, the output voltage is the sum of the input voltage and the inductor voltage [6-9], resulting in the output voltage of the converter being higher than the input voltage.

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Figure 4. The single-channel boost converter

However, the operation of this converter will depend on the continuation of the induction current. As for the operation of the converter, it can be divided into two modes of operation, consisting of continuous-current mode (CCM) and discontinuous-current mode (DCM), and it is found that when the boost converter is operates in CCM, the inductive current does not fall to zero.

In steady-state operation of the converter, the integral of the induction voltage. Over time period (t_s) it must be zero, meaning that the average voltage across the inductor must be greater than the interval to zero and write the basic equations of the converter as

$V_i t_{\text {on }}=\left(V_o-V_i\right) t_{\text {off }}$     (21)

from which

$\frac{V_o}{V_i}=\frac{1}{1-D} \quad$ for $0 \leq D<0$     (22)

where, D is the duty cycle converter defined by D=t_on/t_s,  t_s is the switching period, and the ton and toff are the switch turn-on (t_on) and turn-off (t_off) respectively. The above expression indicates that the output voltage of the converter is always higher than the input voltage.

The relationship between the converter input current and output current can be derived from V_iI_i=V_oI_o from which

$\frac{I_o}{I_i}=1-D  \quad for \quad 0 \leq D< 1$     (23)

However, for calculating ripple currents in inductors and designing inductors and capacitors is not explained at this research article.

2.6 The control algorithm of the single-channel boost converter

2.6.1 Artificial neural networks controller

The relationship between machine learning and neural networks replaces the model with explanatory learning rules, the learning rules for neural networks can be found in Figure 5.

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Figure 5. The relationship between machine learning and the neural network

However, learning something about the human brain will be a way of retaining knowledge. Although they both store their data with different mechanisms, the computer stores the data according to the location of the memory. While the human brain uses a method of altering neuronal relationships, in which the neurons themselves do not have the ability to store them, they use the method of transmitting signals from one place of the neuron to the other. The human brain is therefore a gigantic network of these neurons, and the relationships of neurons are therefore applied in a specific information model called the neural network [10-13]. Similarly, it can be further explained using the mechanisms of neural networks for better understanding by considering them as nodes of conditions obtained as three inputs, as shown in Figure 6.

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Figure 6. A node that receives three inputs

Figure 6 shows that the circle and arrows of the figure show the nodes and flows of x₁, x₂, and x₃ signals, respectively, which are input signals. Likewise, w₁, w₂ and w₃ are the weight of the corresponding signals, and finally, b is the bias, which is another relevant factor of data storage, which is the information of the neural net that is stored in the form of weights and bias. However, the input signal from the outside is multiplied by the weight before that to the node. When a weighted signal is collected at the node [14-17]. These values are added as weighted sums. This weighted sum is written as

$v=\left(w_1 \times x_1\right)+\left(w_2 \times x_2\right)+\left(w_3 \times x_3\right)+b$     (24)

The equation of the weighted sum can be written with matrices as

$v=w x+b$     (25)

where, w and x are defined as

$w=\left[\begin{array}{lll}w_1 & w_2 & w_3\end{array}\right] \quad x=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$     (26)

Finally, the node enters the weighted sum into its activation and output function [18]. The activation function determines the behavior of the node.

As part of the neural network design of the single-channel boost converter, for this research, a mathematical model by the MATLAB/Simulink program was used to create a feed forward neural network control block. This control block uses coaching by entering the input conditions of dc voltage, DC voltage output and output current, defined as duty cycle value [19-21]. However, for better understanding, it is shown as a model used in the coaching of neural networks as shown in Figure 7.

In Figure 7, this neural network model defines the input as a three-parameter value consisting of voltage, current, and power. The second part, the Hidden SCBC section, this procedure contains 15 sets, which is a machine learning process, and the tangent sigmoid transfer function, which is a function that accepts both positive and negative input parameters. The third part is a linear output transfer function with 1 machine learning process used for linear estimation. However, when modeling neural networks neatly. The next step will be the process of bringing input data sets and target datasets to be coached to the neural network. This network coaching network is divided into 3 components with a 70% coaching section, 15% monitoring part, 15% test part. Nevertheless, weights and bias are adjusted during coaching to reduce neural network errors.

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Figure 7. Neural network models used in single-channel boost converter coaching

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Figure 8. Neural network models used in space vector pulse width modulation coaching

Similarly, for a three-phase inverter. Determination of the input voltage of the load to control the operation of the speed of the three-phase induction motor, which is the output voltage of the three-phase inverter. Determining the output of a neural network is the modulation index value and frequency of the model in coaching, as shown in Figure 8.

Consequently, from both models of neural networks, there are multiple layers of conditions. The first layer is the part of the input, which receives the parameter values, variables and conditions. The second layer is the hidden section. This layer contains 15 sets and has a tangent sigmoid transfer function, in which this function receives positive and negative input signals. The third layer is the output part, there is a certain amount, the neural has a linear transfer function. However, once the neural network model is defined, the input dataset and target dataset will be used to further coach the neural network.

2.6.2 Fuzzy logic controller

In engineering, vague fuzzy logic and reasoning algorithms are used to control systems. Using the fuzzy logic algorithm to control the output voltage of the single-channel boost converter, there is a basis for the processing of the fuzzy logic algorithm as shown in Figure 9. For this research, fuzzy logic algorithms were used to detect changes in output voltage and current and process them to generate a single-channel boost converter control duty signal [22-24]. However, for the fuzzifier part, it defines variables and imports voltage and output current change data and duty cycle values.

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Figure 9. Fuzzy logic algorithm diagram

However, for fuzzy conditions, the logic algorithm to control the duty cycle can be divided into five variables comprising NB (Negative Big), NS (Negative Small), ZE (Zero), PS (Positive Small) and PB (Positive Big) [25-28]. The single-channel boost converter control uses the basic conditions voltage variable, current variable input and duty cycle output as shown in Figure 10.

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Figure 10. Control of the basic conditions of fuzzy logic

2.6.3 PID controller

This topic explains the basic application of PID control algorithms for Single-Channel Boost Converter and controls the angular position of three-phase induction motor drive [29-31]. However, this research uses the following two basic command transfer functions as

$\frac{Y(s)}{U(s)}=\frac{b}{s(s+a)}$     (27)

An ideal PID controller has the transfer function.

$C(s)=K_c\left(1+\frac{1}{\tau_1 s}+\tau_D s\right)$     (28)

where, K_c is the proportional gain, τ₁ is the integral time constant and τ_D is the derivative gain. We rewrite the PID controller given in (30) into the transfer function form.

$C(s)=\frac{c_2 s^2+c_1 s+c_0}{s}$     (29)

By comparing (30) with (31), we have the relationships,

$K_c=c_1 ; \quad \tau_1=\frac{c_1}{c_0} ; \quad \tau_D=\frac{c_2}{c_1}$     (30)

Consequently, in the design of the single-channel boost converter and controls the angular position of the three-phase induction motor. The first step is to find the parameters in (31), and then convert them to the PID controller using the necessary parameters in the next execution step [32]. However, this research paper summarizes the application of PID algorithms as Flowchart diagrams as shown in Figure 11 and Figure 12 respectively.

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Figure 11. Diagram of single-channel boost converter with PID controlling

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Figure 12. Diagram of SVPWM with PID controlling

Present the above research, literature, and principles. This research has produced prototypes starting from the design of the voltage regulator circuit of wind turbines, single-channel boost converter circuits, three-phase inverters connecting induction motor. This prototype consists of DC voltage capacitors, current filter inductors, MOSFET circuits, gate drive circuits, delay circuits, current detection circuits, voltage detection circuits, and three-phase inverter designs. Consequently, write commands for processing with mathematical model functions of the MATLAB/Simulink program into the microcontroller. The following sections will present the results of the prototype compared to the MATLAB/ Simulink program. It also analyzes the results for further development and application.

Prototyping mechanisms and experiments compare the response and voltage control performance of single-channel DC/DC Boost Converter circuits with ANNC, FLC and PID algorithms. After proving the theoretical principle with mathematical simulation of the MATLAB/Simulink program with the prototype, the mechanism can be summarized as follows:

Part 1: Single-channel DC/DC boost converter designed and prototyped mechanisms for voltage control with ANNC, FLC and PID algorithms were found to be capable of satisfying voltage control according to the intended purpose and hypothesis. Responding to voltage changes from generators to wind turbines, it was found that the control of switching of basic power electronics produced a ripple condition of high output voltage of more than 5%. Similarly, responses to voltage changes controlled using the ANNC, FLC and PID algorithms showed ripples of output voltage less than 5%. However, for the ANNC and PIDC algorithms, voltage and speed control performance is very good, even if it is not equal to FLC. Moreover, if one considers the input current of the three-phase induction motor, it is found that during increased load modifications, the FCL algorithm generates more surge current than the ANNC and PIDC algorithms.

Part 2: The three-phase inverter designed and prototyped mechanism for the drive of the three-phase induction motor found that PWM control with the ANNC, FLC and PID algorithms can control the speed of the three-phase induction motor according to the specified conditions. Similarly, the ANNC, FLC and PID algorithms with the initial state response experiments of motor start showed that ANNC and PIDC algorithms can control overshoot better than FCL algorithms.

However, for the input voltage obtained from the generator (SCIG) of a constant speed wind turbine with a function controller topology, it allows the wind turbine to start smoothly by reducing the current flow, thus reducing the occurrence of alternating voltage surges before entering the single-channel DC/DC boost converter mechanism well. Although this research article does not go into detail on the part of the generator (SCIG) of a fixed-speed wind turbine. Consequently, the research team will continue to study and analyze it in the future and will present it on the next occasion. However, by comparing the performance and performance of the algorithms described above, it can be further developed by defining additional conditions and accompanying variables to make the algorithm more accurately responsive.