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This paper investigates the application of the axial flux machine (AFM) to the wind energy conversion systems (WECS) to obtain high power and torque at reduced cost. By developing mathematical equations using the phase and active transformations, the three-phase model is transformed to two-phase equations by making both the stator and rotor as reference frames, finally converting to arbitrary reference frame, which is useful for the modelling of the axial flux machine. The torque, current, and voltage equations are expressed to improve the simulation reliability. Based on the developed equations, the mathematical model for the axial flux machine is developed using the MATLAB/Simulink. Starting with the axial flux motor model, when the load on the motor increases, how the parameters like torque, current, and speed of the motor vary are explored in this paper. Then for the axial flux generator model, when the wind speed exceeds the rated speed how the torque, line voltages, currents, power and speed of the generator behave are investigated and presented in this paper. The developed model in this paper could be extended to a twin-rotor axial flux synchronous machine, which will lead to the development of more efficient WECS.

Renewable Energy Resources are the future scope for the generation of the power due to the decrease in availability of the conventional energy sources and the environmental problems that are associated while the generation of power is from them. Many trends are developed in the past two decades for the generation of power using the renewable energy resources of which the Wind Energy Conversion System (WECS) plays a prominent role. WECS is the only renewable energy resource which can be placed and developed around the globe due to its main advantage of using the wind energy for the generation of power [

・ Efficient in terms of cooling is considered for the machine.

・ For the torque production large axial length is not at all required.

・ Constant tooth flux-density.

・ Rotor core is utilized efficiently.

・ The different speed operation can be achieved at a time by using the multi air-gap technology.

Different type of topologies is considered for the axial flux machines, namely, the single sided machine, double sided machine, and the motor with multi air-gaps. Various types of elements are used for the motor manufacture. The core magnets of the AFM’s are made from the Magneto dielectrics, Iron or Amorphous. Very rarely superconductors are used in the building of motor. These topologies are only made possible by varying the direction of the main air-gap flux.

Section 2 of this paper describes the components, technology and overview of the WECS. WECS’s design characteristics and the aerodynamic design followed by their power characteristics are presented. The different types of converters were used in the WECS and their control strategies are also presented in this section. Section 3 presents the necessary equations that are used to develop the axial flux machines model and the phase transformations that are made to facilitate the system modelling in MATLAB/Simulink. Section 4 presents the testing results for the developed model under different conditions. Finally, a conclusion is presented in section 5.

Wind Energy Conversion Systems (WECS) takes the prior position among the other renewable energy technologies and becoming popular and important day-by-day. The power production from the wind energy has become success and is showing rapid growth from last ten years when mainly compared to solar energy. The technology which is used in the early stages to produce power in wind turbines was Squirrel-cage induction generators (SCIG) and is connected directly to the grid. As the usage time of the SCIG increasing the consistent production of power is decreasing due to disadvantages it is showcasing in the wind turbine. To get more power from the wind energy, the Doubly fed induction generators (DFIG) are used as a replacement for the SCIG and the DFIG is consisting of the gear box. In the starting stages the usage of gear box has shown some advantages but as the time proceeds, the mechanical losses are increasing and make the system durability low. To get rid of all these disadvantages, after carrying many researches on the synchronous machines, the axial flux machines are chosen as the best generator for the power production in the wind turbine. The installation of the axial flux machines to wind turbines is done only when the proper care is taken for the components of the wind turbine and the technology of the power electronic components that are used.

When the wind turbine conversion process is considered, the available kinetic energy from the wind is converted to the mechanical energy and this conversion process plays a prominent role in the wind energy conversion system. The captured kinetic energy is converted into electrical energy by the help of an electro mechanical subsystems, which is a generator. Finally, the electrical subsystems adapt the energy and pushes into the grid [

Wind turbine has several components involved in the conversion of kinetic energy available from wind to the electrical energy. The installed rotor hub on the main shaft is responsible for the conversion of kinetic energy of wind to mechanical energy with the help of mounted blades the mechanical energy is transferred to the generator through the drive chain. The drive chain consists of low speed shaft, gear box and high-speed shaft. This mechanical energy is converted to the electrical energy in the generator. If required, the power converters are used to decouple the supplied power generator from the grid. In addition to these parts, there are some other parts like mechanical brake, pitch system, wind speed sensor, wind direction sensor, yaw system, power distribution cables, tower, nacelle and foundation which are not involved directly but are important for proper, efficient and reliable operation.

The aerodynamic operation of the turbine blades is explained by the Bernoulli’s principle, which states that as the speed of the moving fluid increases, the pressure within the fluid decreases. The curve shape of the blade creates the pressure difference between the air flowing above and below the blade i.e., the air flow above the blade is faster than the air flow below the blade which creates the inverse effect of the pressure [

The wind power P W is moving at a speed of V W through an area A can be calculated as

P W = 1 2 ρ A V W 3 (1)

where ρ is the density of air which is approximately 1.2 Kg/m^{3}, A is the swept area in square meters, V W is the speed of wind in m/s.

The mechanical power Pm converted by the turbine from the captured wind power Pw can be calculates as

P M = P W × C P = 1 2 ρ A V w 3 C P (2)

where C_{p} is the coefficient of power, which is obtained from the blade has a maximum of 0.59 theoretical value. For modern wind turbine, the C_{p} value is in between 0.2 to 0.5 which is function of blade number and rotational speed of the turbine. From the above equation we can observe that the mechanical power can be supervised by varying any of these three parameters: Swept are of turbine A, Wind velocity and power co-efficient. Wind velocity V W is uncontrollable but or better and steadier wind conditions the regions like offshores can be selected. Area swept by the wind turbine A is given by π l 2 , where l is the length of the blade from pivot. With the increase in l there is a quadratic increase in the area A and thus increase the mechanical power output P_{M}. The third possible parameter C_{p} is the function of TSR and angle of attack.

In the generator control mode, the MPPT control has the vital role and is the reason where the axial flux generators have the more torque control, power density and optimum tip speed ratio. The control over MPPT can be done by three types:

MPPT with power profile of turbine: In this control the turbine power profile is given by the user. With the help of the power profile at various speeds of the wind, the reference mechanical power of the generator is generated and is compared with the measured power Pm from the generator to generate the signals that can be controlled by the power converters [

MPPT with optimal TSR: In this control, the MPPT operation is achieved by keeping the tip speed ratio to its optimal value λ T o p t . The reference generator (AFG) speed is obtained by measuring the speed of wind and setting the TSR at its optimal value. By controlling the generator speed to its reference vale using power converters [

MPPT with optimal torque control: From the relation between the speed and torque, the maximum power point is obtained by calculating the reference torque. The reference turbine speed is generated by measuring the speed of wind and by setting the optimal tip speed ratio to its optimal value. When a gear ratio is considered, neglecting the mechanical losses of the gear box, the turbine speed ω M is converted to the generated speed ω m . The reference torque is obtained by calculating optimum torque co-efficient and reference generator (AFG) speed. By comparing the reference torque and torque of the generator, the control signals are generated to the power converters [

Since 1980’s the usage of the power electronics in the wind turbine systems are increased rapidly and the main operation of the power electronic device in Wind turbine system is for the soft starting of the system by using the thyristor which is by-passed and by that soft start, the direct operation of the generator to the grid made easy. From the middle of 1990’s, a diode bridge is used as a switching device for the control of rotor resistance and later it was replaced by the power converter which is connected in back-to-back mode and firstly used in DFIG’s. The better solution for the system of wind turbine when the power converters are considered is the usage of double 2-level voltage source converters with the configuration of back-to-back mode and this mode of configuration is started using the axial flux machines and is showing the better output power compared to that of the DFIG. For the alliance between the power grid and the generator (AFG) of the wind turbine, the manufacturer requirements must be satisfied by the wind power converter to both the sides. When the generator side is considered, the adjustment of the torque and rotational speed can be controlled by the stator generator when there is enough current flow in it and improves the balance of the active power when the generator is operating normally and extracting the wind turbine’s maximum power. To vary the voltage amplitude and fundamental frequency of the generator, the converter must be properly installed in the turbine. When we consider the grid side accordance with the generator link, the converter should act in accordance with the codes of the grid no matter what the speed of the wind is available to the turbine and should possess the special feature to control the capacitive and inductive power Q and the response of the active power P should be very fast. At a low level, the maintenance of the rotor currents total harmonic distortion should be done. So, the converter must be operated to meet the requirement of satisfying the grid side and generator side cost and maintenance problems and for satisfying these requirements, the converter must have high power-density, modularity and reliability. The active power storing and boosting the voltage from the side of the generator to the grid is also done by the wind power converter.

AC machines must be modelled to get the perfect output before implementing the prototype model so that what are the possible errors which may be included in the machine can be detected and can be removed by the help of the modelling. Linear transformation plays a vital role in the modelling of AC machines. All the rotating electrical machines are made equivalent to a primitive machine model in the process of obtaining the mathematical model. In primitive machine models, the magnetic field is invariant with respect to time. Many polyphase AC machines are constructed in different manner than a primitive machine. These polyphase AC machines have distinct phase windings on stator and rotor which produce the rotating magnetic field when they are excited by the polyphase supply. Hence the machine inductances change especially in non-uniform air-gap machines with respect to the rotor position which is a function of time. The Linear Transformation is the process of representing poly phase windings on stator and rotor by d, q axes coils of primitive machine. The term Linear Transformation means the transformation from old to new set of variables or vice versa governed by Linear equations. The general form of transformation is

[ New variables ] = [ Transformation matrix ] × [ old variables ] (3)

Phase transformation is also known as transformation from a, b, c to α, β, 0 transformation. Using Phase Transformation, a 3φ machine is transformed into an equivalent 2φ model with additional zero sequence system [

F_{a}, F_{b}, F_{c} are maximum values of mmf’s shown along their respective phase axis. These 3φ’s is excited by 3φ currents.

When the equations for the current and voltage are considered for the axial flux machines with the help of the phase transformations, they are as follows:

I a = I m cos ω t (4)

I b = I m cos ( ω t − 120 ∘ ) (5)

I c = I m cos ( ω t − 240 ∘ ) (6)

When the equations for the current fed by the 3-phase supply in the active transformations, they are as follows:

I α = I m cos ω t (7)

I β = I m cos ( ω t − 90 ∘ ) = I m sin ω t (8)

When the phase transformation from 3-phase to 2-phase is considered by the method of changing both the current magnitudes and the turns ratio, the necessary equations that are obtained are

After the transformation of the matrix and the simplified form of the main torque equation is given by

T e = 3 2 p 2 L m [ i d r i q s − i q r i d s ] (9)

where the factor 3/2 is introduced to obtain power invariance between 3φ machine and d-q model and the parameters are as follows:

P = Number of poles.

L m = Mutual Inductance

i d r = Rotor current at d-axis

i q s = Stator current at q-axis

i q r = Rotor current at q-axis

i d s = Stator current at d-axis

In this section the simulation of the axial flux machine is presented.

・ At rated wind speed i.e., at a wind speed of 12 m/s, how the voltage, current, torques, rotor speed and output power of Axial flux generator possess the characteristics is presented here. These are shown in

・ At above rated wind speed i.e., at a wind speed of 20 m/s, how the voltage, current, torques, rotor speed and output power of Axial flux generator possess the characteristics is presented here. These are shown in

・ At no load condition, that is when there is no load applied on motor, how the currents, speed and torque possess the characteristics are presented here. These are shown in

・ At loaded condition, that is when there is load applied on motor, how the currents, speed and torque possess the characteristics are presented here. These are shown in

It can be concluded from the testing results of the simulated model for the axial flux machine that the developed model has behaved as expected under different conditions for both generation and motoring modes.

The simulation and analysis for complete axial flux synchronous machines using the mathematical modelling from the MATLAB environment were presented in this paper. Axial flux synchronous machines in WECS could avoid the use of gear box. This reduces the weight and cost of the wind turbine. Therefore, it leads to the elimination of the complicated foundation and tower design of the turbine.

A background research for the axial flux machines has been carried out. By exhibiting the features of having more pole pairs, the AFMs are perfectly opted for the direct-drive and low-speed applications. A single air-gap axial flux synchronous machine is modelled in MATLAB/Simulink environment and its torque, speed and respective current curves are plotted for both the generator and motor. For motor, the speed, torque, and current are presented for no load condition. Then, when the load was applied, how the speed, torque and current changes are also analysed and presented in this work. For generator, the line voltages and current, power, torque and speed are presented for the rated wind speeds. Then, how these parameters changed when the wind speed changes abruptly; the results are analysed and presented in this work.

The developed system of equations in this paper for the modelling of AFM’s model can be extended to twin-rotor axial flux synchronous machine. Where, in variable speed WECS applications, controllers and power converters can be designed for twin rotor axial flux generators to maximise output power.

The authors declare no conflicts of interest regarding the publication of this paper.

Al-Bahadly, I. and Neppalli, S.C. (2019) Enhancement of Wind Energy Conversion Using Axial Flux Generator. Journal of Power and Energy Engineering, 7, 43-58. https://doi.org/10.4236/jpee.2019.72004