Artificial neural network analysis on an axial flux permanent magnetgenerator having variable air gap and power regime

ADEM TEKEREK1,* and EROL KURT2

1Computer Engineering Department, Technology Faculty, Gazi University, Ankara, Turkey2Electrical and Electronics Engineering Department, Technology Faculty, Gazi University, Ankara, Turkey

e-mail: atekerek@gazi.edu.tr; ekurt@gazi.edu.tr

MS received 27 August 2021; revised 8 October 2021; accepted 8 October 2021

Abstract. In the present study, an artificial neural network (ANN) design has been proposed to analyze and

estimate the output quantities of a newly manufactured generator, namely axial flux permanent magnet generator

(AFPMG). The machine has been designed with a maximum power of 3 kW for the household electric power

generation. As one of the innovative points, this machine has a variable air gap between the stator and the rotors,

thereby the maximal power scale can be determined easily by adjusting the air gap between 2 mm and 7 mm. It

means that the maximal power has values between 3 kW and 1.5 kW. ANN approach for such a machine is

important in the sense that the estimation of output power, voltage and current values under various speeds and

electrical loads are vital for the optimum operation of the machine. The designed ANN algorithm has been

successful to estimate the output power and voltage of the newly produced generator for different air gap and

speed and electrical load parameters.

Keywords. Artificial neural network; generator; axial flux; air gap; power.

1. Introduction

Permanent magnet generators (PMGs) are easy to construct

and reliable with a sinusoidal output waveform if an opti-

mized magnetic flux path is designed and implemented [1].

According to the previous works, there exist mainly two

types of permanent magnet generators, namely radial flux

(RF) and axial flux (AF) [2–4]. AF machines have certain

superiorities over the RF ones [5]. RF machines have hard

design and construction processes, in addition, they have

worse ratio of power-to-weight compared to the AF

machines. Thereby, especially for vertical-operating wind

turbine systems, AF devices have more preferable solu-

tions. There exist various types of AF machines in the lit-

erature: They can be both core-free and cored structure

[6, 7]. While the cored machines have high flux densities,

core-free ones have lower cogging torque values [8, 9]. The

coreless AF devices frequently operate in low scale energy

solutions [10]. But it is a reality that they suffer from low

power outputs if they are compared to the cored machines.

By looking at the earlier works, AF generators were

designed and practiced in different AF topologies: Tor-

oidal, single side, funnel, multi-side, double side

[6, 7, 11–13].

The generated power of AF devices strictly depends on

windings mass, air gap, and volume of the machine

[14, 15], indeed the volume (or outer diameter of the

device) cannot be increased more because of the envi-

ronmental restrictions inside a usage area. In the litera-

ture, Ishikawa et al [11] designed a machine with axial

and radial flux morphology and performed some analyses

on flux and reluctance structures. The engineers do not

deal with only the flux or reluctance; in addition, opti-

mization of machine at high speeds which is also vital. It

has been known that high speed operation causes

warming in the windings, back-irons and cores. In such

scenario, Li et al [16, 17] studied the temperature

dependence of the machine components. They have

proven that the temperature of the machine has an

increasing trend from 50 �C to 150 �C at high speeds.

Thus, such a temperature increase results certain prob-

lems in magnetic components due to the decreasing

magnetization. Beside the efficient cooling procedure,

various mechanical issues (i.e. acoustic noises and

vibrations, mechanical frictions) are other vital points in

order to decrease the artifacts of a machine and have a

more efficient device [2]. In that point, to obtain maxi-

mum efficiency, the minimization of loses in electro-

magnetic and mechanical manner is also important. In

this manner, Vansompel et al [18] studied the core

geometry, mass, and lamination type and recorded their

effects to machine efficiency. According to their work,

the variation in air gap decreased the loses stem from the

machine core with a rate 8%. [19].*For correspondence

Sådhanå (2021) 46:240 � Indian Academy of Sciences

https://doi.org/10.1007/s12046-021-01768-0Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

A quick look to the literature proves that AF devices

have different power densities over the volume. The power

densities vary from 10 to 100 kW/m3 [20–22]. One of our

different designs, a single phase 12 poles AF permanent

magnet generator had a value of 28.5 kW/m3 [2]. Wind

turbine blades usually rotates at low speeds (i.e. about

400 rpm or less). Therefore, high number of pole pairs are

generally used in the market in order to get 50 Hz fre-

quency from the output [23]. Especially, in the cases of

developing countries, the rural populations require small

and cheap electrical power solutions. They can be either

off-grid solutions, or on-grid applications for wind energy

promoting regions.

The present AF device has different power densities

because of its adjustable air gap. The maximum power

density has been examined as 111.7 kW/m3 for the air gap

value 2 mm [24]. This result is a promising value, when

one compare it with the RF machines in the literature. The

RF devices have high total harmonic distortion, but our

design and prototype generate outputs within 4% maximum

total harmonic distortion. Apart from our earlier laboratory

works, the volume of the new device is larger and it gen-

erates more energy. The characteristic features are to use

thinner air gap (i.e. 2 mm) with new magnet positioning

strategy and to have higher active electromagnetic volume

for windings and cores. When the above-mentioned points

are combined together, the device reaches to a higher power

value (i.e. P = 3 kW). The current device also operates

well under various load conditions, electrically. To sum up,

by following the present strategy (with high power density,

having easy-maintenance, stability, low cogging torque and

self-cooling units), a good machine has been constructed,

however, exploration of all those parameters in laboratory

condition is hard job, and it can be simplified by ANN

analyses for many system parameters mentioned above.

One of the aims of the present study is to prove this idea.

This paper is organized as follows: In section 2, a liter-

ature review on the ANN applications of electric machines

is presented. In section 3, the methodology is described.

Next section gives the main design issues of the innovative

machine together with the algebraic modeling. Section 4

gives the results of the electromagnetic design of the

machine. Section 5 reports the results of experimental

works. The general background of ANN modeling is dis-

cussed in section 6. Section 7 gives the ANN analysis

results and discusses the findings for various air gap and

power stages of the generator. Finally, the concluding

remarks are given in section 8.

2. ANN applications in electrical machines

There exist many studies on the applications of ANN to the

electric machines. For instance, Ding et al, developed an

expert system for traditional time-frequency analysis

diagnostic methods [25]. In their work, authors have pro-

posed an intelligent diagnostic method for a rotating elec-

trical machine based on Generative Adversarial Network

using small samples. According to their findings, their

approach has achieved higher accuracy and low volatility

diagnosis results over other diagnosis methods. In the

proposed method, even if a small number of training data is

used, it can stably differentiate fault determinations under

different operating conditions [26]. Ref. [27], the authors

proposed an ANN-based method for the detection of dis-

tributed synchronous generators. In the proposed method,

ANN was used as pattern classifiers. Islanding is deter-

mined on the basis of the voltage samples measured in the

distributed generator, which is more advantageous than

ANN-based ant dedication methods [26]. Bouzid and G.

Champenois proposed a study an automatic and intelligent

stator diagnostic model for magnet generators. In proposed

system a multi-layer ANN with feed-backward feed for-

ward is used. The obtained results with ANN have diag-

nosed different stator errors under variable load conditions

for variable speed, variable fault current and noisy signals

and harmonics in the machine to eliminate errors [27].

In Ref. [28], the authors have proposed a method to

prevent ANN constraints for monitoring distributed sys-

tems. With ANN-based model, it can be done with fewer

measurements than traditionally required. The contribution

of their study consists of a scenario maker and a method to

generate useful educational data using a series of hyper

parameters that define the ANN architecture [28].

In another study [29], a method has been proposed to

determine the real-time stability status and identification of

compatible generator groups by estimating the rotor angle

after a major distortion through the radial function neural

network. Within the framework of the studies, the first six

cycles of post-failure data measurements synchronized

from the Phasor Measurement Units (PMU), consisting of

rotor angles and voltages of generators, input data to the

ANN were determined to predict the state of the signal.

Baptista et al proposed an Automated General Purpose

Neural Hardware Generator to assist with ANN hardware

implementation. ANN trained solar radiation provides a

good solution to estimate the generated power values of a

photovoltaic system in real time. Although ANN can run on

a computer, it is expensive to have a computerized control

room for small photovoltaic installations. The proposed

tool allows an automated configuration system that allows

the user to configure the ANN and release the user from the

details of the physical application [30].

In another study, authors proposed intelligent control as

the maximum power monitoring system for the switched

generator driven by the variable speed wind turbine to

select maximum power. The ANN controller and fuzzy

logic (FL) used together to developed a hybrid controller

[31].

In a different study, the authors proposed flow phenom-

ena through rotor dynamic performance analysis of an axial

240 Page 2 of 16 Sådhanå (2021) 46:240

fan and permanent magnet generator. As a result of their

simulation, the optimum straight angle of the blade is

determined since it has the highest speed value from the

output of the simulation. According to the results, the

highest velocity is calculated as 1.86 m / s and power 0.46

Wat 65-degree blade [32].

Ref. [33] proposed an ANN based system to control the

voltage and frequency of a self-excited induction generator.

An external excitation circuit containing a power-switched

inductance or capacitor is used to compensate for the pro-

posed system reagent demand. The proposed ANN model is

used to obtain the inverse model of the self-excited

induction generator and is trained using output voltage,

load and wind turbine speed as an input vector, and the

required capacitor value as the target output.

In-service inspection of complex systems such as nuclear

steam generator tubes and surrounding support structures,

and overlapping decay modes are taken into account.

Tension data is processed with a modified master compo-

nent analysis to reduce data size, and modified master

component analysis points are taken as input to an ANN

that simultaneously targets the support structure bore size,

tube dimensions in two dimensions, and four parameters

associated with the pitch. When using curtain depth as an

input, hole ID and tube position estimates are improved

[34].

The authors have proposed a new model to predict sit-

uations and load torque to implement a multivariable con-

troller for the sensorless three-phase squirrel cage induction

machine [35]. In their work, state prediction significantly

improves the performance of the model reference adapta-

tion system based on rotor flux in the variable speed

working region. The proposed model uses the Kalman filter

as a rotor flux observer and an ANN adaptation mechanism

to estimate the rotor speed. State estimation requires only

measurement of stator voltages and currents.

In another study, the authors propose an ANN algorithm

for a magnet synchronous generator (PMSG) connected to a

wind turbine to generate maximum power using ANN. The

actual power generated by the generator has been found to

depend on the internal characteristics of the wind turbine,

such as speed and power factor [34].

In some other more works, type-2 fuzzy [36, 37], swarm

optimization [38] and bee colony algorithms [39] for a

Figure 1. (a) The design of the machine in axial direction, (b) photos of Rotor-1 and (c) Rotor-2. The screw attached at the rotors

enable one to adjust the air gaps.

Sådhanå (2021) 46:240 Page 3 of 16 240

power electronic converter systems, respectively. They

have found that both algorithms have been successful for

the optimization of the above-mentioned systems.

3. Electromagnetic design of the generator

The generator is presented in figures 1(a)-(c). The AF

device has one double-sided stator and two rotors at each

side. The design has an easy construction unit for two back

irons on two lateral regions of rotors. There exist 12 cores

wand 24 coils in total. Two sides of the stator are actively

used in order to get an efficient power generation. Two

rotors having different active diameters are used, because

the permanent magnets are located different radial positions

of rotors. Frankly speaking, Rotor 1 and Rotor 2 has higher

and lower active diameters as seen in figures 1(b) and (c),

respectively. Rotors have 16 magnets shaped as disk type

and made by rare-earth Ne magnets in order to achieve high

flux densities. The back iron units located on the outer sides

of rotors and the cores are made by M19 material. In the

construction phase, M19 materials are axially laminated.

Therefore, they have low eddy current effects as also

known from literature.

All materials and dimensions are given in table 1,

explicitly. Two rotors have back irons located nearby the

PMs as shown in figures 1(b and c). Since the magnetic flux

loops inside the back iron components, it is obvious that the

reluctance is expected to be low. However, in the coreless

device, the reluctance becomes higher compared to the first

case. In addition, the back iron enables to form a natural

housing for the PMs and this produces a stable rotor

structure. Therefore, the voltage waveform quality becomes

better for high wind speeds such as 1000 rpm. The overall

characteristics of the machine is given in table 1. The

output characteristics of the machine can change substan-

tially when one adjusts different air gap values.

By considering the algebraic explanation of the structure,

we refer to Ref. [25], which mentions about the low pow-

ered machine. The total reluctance of machine has been

calculated as R = 3.99 9 105 A/Wb from that algebraic

modeling and a value of 42.0 mWb has been found from

the theoretical model for looping magnetic flux. Note that

the core magnetic permeability is 2800 and the PMs create

a magnetic field strength of H = 10.53 kOe in this respect.

4. Electromagnetic simulations

The finite element analysis has been applied to the designed

generator. The simulations have been performed in 2D and

3D environment of Ansys Maxwell. In this frame, the

magnetostatic and magnetodynamic simulations have been

completed. Note that this package is capable of finding out

output waveforms, magnetic fluxes, power, iron losses and

copper losses with good accuracy, if the mesh structure of

the designed volumes are produced perfectly. In this sec-

tion, we only report the values with 4 mm airgap.

Figure 2 shows the magnetostatic results from the

designed machine. It is clear that the flux density reaches to

the maximum value B = 0.65 T. The high flux values

increase the voltage amplitude positively, therefore the

back irons at the top and the bottom play important roles.

The flux density reaches to B = 0.8 T inside the back iron

unit.

Figure 3 shows the magnetic flux over a single winding.

Here, the fluxes exhibit two sinusoidal waveforms for dif-

ferent rotor structures (with or without back iron). The rotor

structure having back iron has high flux (i.e. 40 mWb).

Whereas, the rotors without back iron gives less flux values

(i.e. 16 mWb). This proves that we use back iron compo-

nent in our innovative design to maximize the flux. The

simulated flux values are nearly same with the analytical

findings discussed in the previous section. It is clear that the

Table 1. Characteristic parameters of the designed and con-

structed generator.

Components Features

Outer radius of rotor R2 (mm) 105

Outer radius of rotor R1(mm) 150

Inner radius of rotor R2 (mm) 75

Inner radius of rotor R1 (mm) 120

Inner radius of stator disc (mm) 70

Thickness of back iron (mm) 10

Outer radius of stator disc (mm) 155

Inner radius of stator disc (mm) 70

Rotor filling material Aluminum

Stator filling material Aluminum

Outer radius of back iron 1 (mm) 150

Outer radius of back iron 2 (mm) 105

Inner radius of back iron 1 (mm) 120

Inner radius of back iron 2 (mm) 75

Coil outer diameter (mm) 40

Coil inner diameter (mm) 30

Winding turns 200

Wire diameter (mm) 0.75

Coil number 24

Electrical phase 3

Magnet type NdFeB

Magnet diameter (mm) 30

Magnet thickness (mm) 5

Magnet shape Circular

Magnet number 32

Core/back iron material M19

Core type Axially/ radially laminated

Core number 12

Air gap (mm) 2–7

Core coefficients (W/m3)

Kh/Kc/Ke/Kdc 164.2/1.3/1.72/0

240 Page 4 of 16 Sådhanå (2021) 46:240

reluctance value decreases because of back irons and that

causes a substantial enhancement in flux. In fact, the flux

enhances three times. This situation increases the amplitude

of the voltage waveform and currents flowing the coils.

From the terminals, finally higher power values can be

obtained.

In figure 4, the maximum phase voltages are shown at the

operation with 1000 rpm rotor speed. Note that various

ohmic electric loads are used. While the phase voltage

increases from 40 V to 88 V at the back ironless device, the

voltage increases from 57 V to 139 V for the device with

back - iron. Low reluctance essentially causes an increase

in flux and the variation in flux is enhanced by the rotor

speed. This result gives an advantage in the voltage output

from each phase. The voltage increases till the optimum

Figure 2. Flux paths from the designed generator.

Figure 3. The magnetic flux of a winding for rotor speed 1000

rpm from the design with back irons and without back-irons.

Figure 4. The maximum phase voltage at 1000 rpm from the

generator with back-iron and without back iron.

Figure 5. Phase voltage output versus time. The rotor speed and

electrical load are 1000 rpm and 40 ohm, respectively.

Sådhanå (2021) 46:240 Page 5 of 16 240

electrical load (i.e. 40 ohms) is satisfied. This value,

indeed, is close to the impedance of the machine.

Two sample waveforms are shown in figure 5. The plots

are formed at the rotor speed 1000 rpm, when an electrical

load 40 ohm is attached at the terminals. In the terminal,

the voltage waveform shape is sinusoidal without any dis-

tortion. That gives a superiority to the device for having no

total harmonic distortion.

Figure 6(a) shows the results core- loss analyses. For this

analysis, the results at various rotor speeds are considered.

The core- losses have an increasing trend till the impedance

load 40 Ohm. Obviously the losses go from 0.85 W to

1.18 W. However, since the output power increases at 40

ohms, the loss of 1.18 W is not considered a high loss, as

will be discussed later in the power and efficiency graphs.

The increase in core loss in the machine due to the increase

in core material is reasonable. Copper loss is shown in

figure 6(b) for various rotor speeds. Copper loss drops from

20 W to 5 W less for optimized load.

In figure 7, the output power of the designed machine is

plotted various speeds. In 300 rpm working condition, the

generated power is about 145 W. In the case of 500 rpm,

optimal power is found as 302 W. When the rotation speed

reaches to 1000 rpm, 728 W is obtained.

5. Experimental study

The experimental setup is founded as in figure 8. Indeed,

there are two basic aims to perform the experimental work.

Initially, testing the design parameters found in the theory,

second, making a feed-back to tune the parameters for the

use in real world. As seen in figure 1, the device situates at

the front and right hand-side on a specific table. During the

experiments, an induction motor having a controller is

Figure 6. (a) Core and (b) copper losses, respectively. The rotorspeeds are 300 rpm, 500 rpm and 1000 rpm.

Figure 7. Power versus ohmic load for the designed machine.

Figure 8. The experimental setup with the AFPMG.

240 Page 6 of 16 Sådhanå (2021) 46:240

coupled to the axis of the generator as shown in figure 1.

The coupling apparatus is designed to be light enough to

convey the mechanical rotation to the generator. The aim is

to operate the induction motor under different rotor speeds

by using the controller. Thereby, one can have the char-

acteristic outputs. The main devices sit on the measurement

table for the experiments. Beside the controller, there are

Yokogawa DLM4038 oscilloscope, a Fluke 434 Series II

power analyzer and Delorenzo DL1017R, DL1017L,

DL1017C electrical loads with resistive, inductive and

capacitive type, respectively. Power analyzer measures and

records the phase voltage, current and power,

synchronizingly. At the same time, the oscilloscope mea-

sures and records the waveforms.

Table 1 gives the machine characteristics. The most

attractive point is that one can obtain the characteristics of

the machine under various air gaps. This is a superiority for

our design in the sense that one can easily change the air

gap via a basic screw system. In this case, one can prefer a

low, moderate or high power regime depending on the

usage purpose.

We have constructed a machine with 1.3 mm air gap, but

it has produced high cogging torque values. Especially for

low wind speeds, high cogging torque is not preferable in

Figure 9. The oscilloscope patterns of voltage waveforms with no-load condition at 1400 rpm under the air gap configurations in the

cases of (a) 3 mm and (b) 7 mm.

Sådhanå (2021) 46:240 Page 7 of 16 240

the field. Therefore, air gaps 2 mm and 3 mm have been

tested to have a chance to use in low speeds such as 30 rpm.

According to table 1, the machine has characteristic

geometric features and parameters such as core structure,

back iron structure, rotor and stator geometry. Therefore, an

ANN model can be a good tool to identify the relation

among all these parameters as found in some earlier works

(i.e. Refs. [26, 28, 32, 35, 36]).

Two representative oscilloscope images are shown in

figures 9(a) and (b). These are the generated voltage

waveforms and received at no-load case. Note that it fits to

the theoretical expectations in terms of waveform, which is

ideal sinusoidal. Note that while figure 9(a) was measured

from the machine configuration having 3 mm air gap, fig-

ure 9(b) was taken under the condition of 7 mm air gap. It

is obvious that there is 120-degree phase difference among

the phases.

Figure 10 shows the measurements of the rms values of

output voltage per phase for different speed scenarios from

100 rpm to 1300 rpm under no-load conditions. The gen-

erator generates more voltage as parallel to the theory when

the air gap decreases. Strictly speaking, the rms phase

voltage is measured as 355.2 V at 1400 rpm under 7 mm

and 437.6 V under 3 rpm and 517.3 rpm under 2 mm air

gap conditions. That gives us a structural factor that a factor

of 0.42 decrease in air gap results 1.23 increase in voltage.

Figure 10 shows a net linear increase at the same rate as the

theoretical explanation of Faraday’s Law. As a structural

feature of the proposed machine, the slopes of the stress

curves decrease significantly with increasing air gap.

6. Method

In this section, ANN method study is briefly explained, and

steps of obtaining data, cleaning the unnecessary and noise

data and normalizing the data process are described. Then,

the data is divided as training and test data, and the creation

of the ANN model is explained.

6.1 Artificial neural networks and data

The problem encountered here is highly nonlinear since

magnetic hysteresis effect yields to different results in the

experiments and that causes distortions in waveforms. In

addition, the electromotive force strictly depends on the air

gap. Because the reluctance stem from the airgap mostly.

All those factors make the present problem difficult in

terms of nonlinearity. It should be also mentioned that the

variables of the system depend on each other nonlinearly.

As a solution methodology, such problems with determin-

istic methods cannot be fully used. Indeed, the problems

mentioned here require many configurations of parameter

0

100

200

300

400

500

600

100 300 500 700 900 1100 1300

PH

AS

E V

OL

TA

GE

(V

)

SPEED (RPM)

Air Gap=2 mm

Air Gap=3 mm

Air Gap=7 mm

Figure 10. The experimental voltage plots depending on the

rotor speed for the no-load condition of the generator for 2 mm, 3

mm and 7 mm air gap.

Figure 11. A simple ANN network.

Figure 12. Feed forward Artificial Neural Network.

240 Page 8 of 16 Sådhanå (2021) 46:240

sets. This reality also affects the solution time. The ANN

analyses make the optimum solutions clear in a short time

duration. This shows that the heuristic methods are more

preferable for nonlinear problems. Here, ANN as one of the

heuristic methods, is a machine learning method with basic

intelligence qualities obtained as a result of modeling the

nervous system structure in living things. ANN has the

ability to make decisions under similar conditions by

learning how to react under certain conditions as in living

things. By training through ANN datasets; ability to asso-

ciate, predict, classify, generalize, improve and character-

ize. ANN’s fast working, adaptable, trainable and easy to

design make it a highly preferred algorithm. One of the

most important features of ANN is that it is successful in

solving nonlinear problems. Since the neuron structure,

which is the basic business process element of ANN, is not

linear, the ANN formed by the combination of neurons is

also nonlinear. With this feature, it has become the most

important machine learning algorithm in solving complex

and nonlinear problems. ANN is a machine learning algo-

rithm that is modeled according to the biological neuron

cell structure and has a self-learning feature. ANN can be

used in many different applications such as pattern recog-

nition, medicine, signal processing, prediction and espe-

cially system modeling. ANN is formed by connecting

neurons to each other. ANN learns by making inferences

from the data and thus new information is predictable and

used in the solution of nonlinear problems. The data have

divided into two groups as training and test sets. The pur-

pose of the training is to minimize the error level by

adjusting the weights in the neural network. The training

process continues until the intended output is achieved. The

performance of the training process is obtained by testing

the data not used in training in the neural network. In fig-

ure 11, a simple ANN network scheme presented.

The ANN network given in figure 11 can be defined

mathematically in Eq. (1) and follows:

uk ¼Xn

j¼1

wkjxj

vk ¼ uk þ bk

yk ¼ u uk þ bkð Þyk ¼ u vkð Þ

ð1Þ

ANN is a combination of neurons with connections. It is

trained using the training data and can therefore make new

inferences and predictions. ANN is used to solve non-linear

problems. To train the ANN network, the data is divided

into training and test datasets. The aim of the training

process is to reduce or minimize the error level by adjusting

the weights in the neural network. This process continues

until the intended output is obtained. The performance level

of the training process is obtained by testing the data not

used during training in the neural network. In train of the

neural network, the feed forward back propagation archi-

tecture is effective. The feed forward neural network moves

in one direction from the input layer of the model to the

output layer. The feed forward ANN model consists of

primarily input layer, one or two hidden layers, and output

layer (figure 12).

The training of the neural network is done by randomly

assigning weights between neurons and optimizing the

weight values. This process is calculated with the error

function presented in equation (2). (dj: intended result, oj:

actual result).

Ep ¼ 1

2

X

j

dpj � opj

� �2

ð2Þ

In Eq. (2), the error function is given. This equation is

used to rearrange the weights,

Dpwji ¼ �goEp

owji

� �ð3Þ

Table 2. Sampling of data structure obtained from the electric generator.

Air Gap

(mm)

Ohmic Load

(ohm)

Generator Speed

(rpm)

RMS Phase Voltage

(V)

RMS Phase Current

(A)

Total Output Power

(W)

2 1055 100 66.40 0.060 11.95

2 775 100 67.10 0.085 17.11

2 445 600 217.00 0.482 313.78

2 305 500 185.00 0.609 338.00

3 127 600 151.00 1.19 538.606

3 152 800 191.00 1.26 720.020

3 218 400 132.00 0.61 239.780

3 305 1300 328.00 1.08 1058.203

3 445 1000 289.00 0.65 563.063

3 775 800 259.00 0.33 259.668

3 1055 1000 313.00 0.30 278.585

Sådhanå (2021) 46:240 Page 9 of 16 240

In Eq. (3), for the g constant (learning rate) any value

can be assigned. Eq. (4) is used to rearrange the weights:

wij t þ 1ð Þ ffi wij tð Þ þ g dj ii ð4Þ

In Eq. (4) wij(t) is weight, i result value of node or error

term of dj with j node. Output layer node error is dj iscalculated by,

dj ffi oj 1� oj� �

dj � oj� �

ð5Þ

Here, j is a hidden node and the error term is calculated

by,

dj ffi oj 1� oj� �X

k

dkwjk ð6Þ

The weight changes can be revised by adding any amoment term,

wij t þ 1ð Þ ffi wij tð Þ þ g dj � oj� �

ii þ a wij tð Þ þ wij t � 1ð Þ� �

ð7Þ

Feedforward backpropagation neural network structure is

one of the most effective methods used in the training of

artificial neural networks. The feed forward neural network

moves from the input layer of the model to the output layer

in one direction. The feedforward ANN model consists of

the input layer first, then one or two hidden layers and

finally the output layer.

The data used in the study were collected using an

electric generator. The dataset consists of a total of 392

lines data. Dataset consist of five feature, such as air gap (in

mm), ohmic load (in Ohm), generator speed (in rpm), rms

phase voltage (in Volt), rms phase current (in Amper) and

total output power (in Watt). In table 2, a sampling of data

structure is presented for the clarity.

Table 3. The results of different ANN Model Experiments.

No. Model

Training

Function

Activation

Function

Hidden

Layer

Hidden Layer

Neuron

Performance Criteria

Train R

Rate

Test R

Rate

Mean Squared

Error

1 3-5-2 Trainlm Tansig 1 5 0.9788 0.9582 0.04

2 3-10-2 Trainlm Tansig 1 10 0.9999 0.9998 0.00011

3 3-20-2 Trainlm Tansig 1 20 0.9846 0.9687 0.02

4 3-5-5-2 Trainlm Tansig 2 5-5 0.9892 0.9857 0.004

5 3-10-10-2 Trainlm Tansig 2 10-10 0.9746 0.9602 0.04

6 3-20-20-2 Trainlm Tansig 2 20-20 0.9609 0.9658 0.04

Figure 13. Suggested ANN structure.

240 Page 10 of 16 Sådhanå (2021) 46:240

6.2 ANN model

Before ANN model was created, the features which are

selected as ANN model inputs were determined. Ohmic

load, generator speed (RMS), and air gap, phase current

(A), which are the experimental results of the electric

generator, are considered for prediction of phase voltage

and output power.

(a) Normalizing of data: The data are normalized in

order to prevent unnecessary repetition. The data is rear-

ranged to the 0-1 range and increase the performance of the

ANN model. In the normalization process, the min-max

method was used. In Eq. (8), Xr represents the actual value

of the input, Xmin represents the minimum input value and

Xmax represents the maximum input value.

Xn ¼Xr � Xmin

Xmax � Xminð8Þ

(b) The training and testing process: After the normal-

ization process, train and test operations are carried out

using the MATLAB program. Dataset is divided in two

group, 70% of data is selected for training and 30% of is

selected for testing randomly. Many attempts have been

made in different ways to create the proposed model.

According to the test result, the best model (high R and low

error rate) is selected. In the training process, different

ANN models are developed and experiments are conducted

for the best training result. The ANN model developed in

table 3 gives training function, activation function, hidden

layer count, hidden layer neuron count and performance

criteria. According to the performance criteria, it is obvious

that the best results are obtained from the 3-10-2 ANN

model.

Figure 14. (a) Training, (b) validation, (c) test and

(d) regression.

Figure 15. Performance error rate graph of the model.

Sådhanå (2021) 46:240 Page 11 of 16 240

The ANN model structure is given in Figure 13.

According to the test results, the model has high per-

formance and low error rate. In this ANN model, Speed

(RMS), Current (A) and air gap are the input variables of

the network, and Voltage (V) and Power (W) are the output

variables. There are 10 neurons in the hidden layer with the

hyperbolic tangent activation function, which is also used

for the output neuron. In this model, biased nodes with

3-10-2 plus relative activation functions are used.

7. ANN results and discussion

The optimum model was created as a result of the experi-

ments performed after the training regression rate: 0.9999,

test regression ratio: 0.99988, validation regression ratio:

0.99989 and mean square error rate is 1.1711 9 10-5, and

a multi-layered structure regression and low error rate.

According to the experimental results, the ANN model

structure (3-10-2) has a very low performance while it is a

one hidden layer with 10 neurons.

Figure 16. Comparison of laboratory experimental and predicted values of (a) output power and (b) output voltages in the case of 2 mm

air gap.

240 Page 12 of 16 Sådhanå (2021) 46:240

The obtained values were tested with test data to measure

the memorization status and performance level of the

model. Train-test regression values and error graph of the

determined model are given in figures 14(a-d).

According to the test results, the lowest error rate and

best validation performance were determined in 228 itera-

tions. In figure 15, training, validation and test performance

error rate graph is presented. The error results are very well

diverging by epochs.

A comparative representation of some of the real and

predictive values obtained from the model is given in

figures 16(a) and (b) and figures 17(a), (b). It has been

determined that the estimation results with the ANN

experiments largely overlap with the actual results and the

error rates are very low (close to zero).

In figures 16(a) and (b), the power and voltage outputs

have been predicted for 2 mm air gap. While the power

plots increase parabolic as in the experimental findings with

respect to rotor speed, voltage results are linear with the

speed, reasonably. Indeed, those trends fulfill well-known

Faraday’s Equation, where the speed causes the output

voltage linearly as shown in figure 16(b). Since power

Figure 17. Comparison of laboratory experimental and predicted values of (a) output power and (b) output voltages in the case of 3 mm

air gap.

Sådhanå (2021) 46:240 Page 13 of 16 240

mainly changes with the square of voltage, figure 16(a) also

fulfils the analytical electric machine features.

In the case of 3 mm air gap, the plots have slightly lower

values for the same rotor speed compared to fig-

ures 16(a) and (b). Because in electric machines, the

increase in air gap causes an increase on the reluctance,

which is indeed a resistance towards the magnetic flux,

thereby this effect decreases the flux and that is reflected to

the values of voltage directly. Since voltage decreases,

power also decreases at the same time as in Fig-

ures 17(a) and(b). Note that the trends of the plots resemble

to the ones in figures 16(a) and (b), respectively. Since the

ANN gives an overall solution on the problem, the design

can give us output results for the unmeasured values for

different speeds, too. Besides, one can also predicts the

power and phase voltage values for different resistances.

Since in figures 16(a) and (b) and figures 17(a) and (b), we

aimed to compare the real values with the ANN findings,

we have only focused on the defined resistances.

In order to show you the reliability of the model, we have

also run the code for the air gap value of 2.5 mm. Since the

data for this value were not given at the training phase, we

Figure 18. Predicted values of (a) output power and (b) output voltage in the case of 2.5 mm air gap.

240 Page 14 of 16 Sådhanå (2021) 46:240

should clearly understand whether the model gives accurate

results. Strictly speaking, for the same output resistances,

the results for a = 2.5 mm should be between a = 2 mm

and a = 3 mm are reasonable. Thus, that would be good a

test for us to evaluate the accuracy of the model. The results

of that numerical measurement are depicted in fig-

ures 18(a) and (b).

It is obvious from the plots that the ANN analysis gives

reasonable values for a = 2.5 mm, although the experi-

mental data were not given into the input of the model for

this air gap value. Indeed, the aim of this study has been

fulfilled by these data, because one can easily predict the

output of various air gaps of this new generator. Thus, one

does not need to make long experimental procedure, one

can use that model to have the values of voltage and power

for different values of electrical loads, i.e. resistances.

8. Conclusions

In the present study, we have implemented a new neural

network model in order to predict the voltage and power

outputs of a newly-implemented 3 kW maximum powered

axial flux permanent magnet generator, having variable air

gaps. With this model, we implemented a feed forward

network solution with an input layer, a hidden layer, and an

output layer. Since the generator has a variable air gap, we

have performed a detailed study on the prediction of power

and voltages under various air gaps. For the training data

set, experimental air gap values a = 2 mm and 3 mm have

been considered for the training purposes. Then the con-

structed model has been validated for many different

resistances. The proposed ANN model works well for the

newly implemented maximum 3 kW generator for different

output electrical loads, speeds and air gap. This is the

unique and comprehensive study for such an axial flux

permanent magnet machine providing the most accurate

results for many system parameters, namely air gap, resis-

tance and speed. It has been already known that those 3

parameters are very important to characterize the output

phase voltage and power of the generator. Therefore, by

using the proposed ANN method, one can predict accu-

rately the output power and output phase voltage without

any time consuming experiments. For this, especially we

have studied the air gap a = 2.5 mm, which was not

experimented at all for the didactic point of view. After

looking at the results of ANN model, one can understand

that our ANN model is suitable for the prediction of output

values, even for the characterization of the generator pre-

experimental laboratory works. To conclude, according to

the ANN findings, the error becomes too low within the

value of 0.1 % for many cases.

Acknowledgement

The Scientific and Technological Research Council of

Turkey (TUBITAK) has supported this work with grant No.

MAG-315M483. Two patents with Nos. TR 2015 04164 B

and TR 2013 13062 B exist in Turkish Patent Institute

(TPE).

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