Fractional Integral Terminal Sliding Mode MPPT Control Technique for Permanent Magnet Synchronous Ge

8

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https://doi.org/10.22214/ijraset.2020.32473

December 2020

International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com

Fractional Integral Terminal Sliding Mode MPPT Control Technique for Permanent Magnet Synchronous Generator Wind Energy Conversion System Zahid Ullah1, Umar Habib Khan2, Khalid Mahmood3, Hamid Maqsood4 1, 3

Department of Electrical Engineering, Abasyn University Peshawar, Pakistan.

Department of Electrical Engineering, Comsats University Abbottabad, Pakistan.

4 Department of Electrical Technology, Govt. Polytechnic Institute, Karak, Pakistan.

2

Abstract: The stochastic and random wind nature makes the entire wind energy conversion system (WECS) highly intermittent.

To achieve the maximum amount of wind energy, an advanced control technique is required. In such a scenario, the controller aims to maximize power extraction. The aim of this research is to extract the maximum amount of energy from the generator by tracking the generator reference speed. This paper presents a nonlinear fractional integral terminal sliding mode control technique for the extraction of maximum power. The simulation results show the method is simple and has high precision of control, and the system has good characteristics in steady state and during transients with permanent magnet synchronous generator. The MATLAB / Simulink tool has been used to test the suggested controller under various wind curves. The simulation result validates the robustness of the control scheme and also it shows better results than the feedback linearization (FBLC) control technique.

Keywords: FITSMC, MPPT, PMSG, WECS, FBLC. I. INTRODUCTION Over the past few decades, renewable energy is the fastest growing technology due to environmental effect and decrease in natural resources like fuel, coal and gases etc. [1]. Due to intense development in the economy of world, there is rapid increase in Electrical Energy demand. On the top of list in Power generation, now a days renewable Energy has become a priority for all countries to solve the problems relate with energy crisis as well as environmental pollutions [2]. The need for generation of electrical energy is increasing day by day but this is insufficient to meet the requirement so the increase in energy is always a demanding factor[3].

The renewable energy for example wind energy has gained advancement in technology. According to the report of Global Wind Energy Council (GWEC), in 2017 more than 54 GW of aerodynamic energy have been installed across the 90 countries. This increase is 12.6% higher than the previous year [4]. By the end of 2020, aerodynamic energy across the globe is estimated to be 850 GW. It has been predicted that by the end of 2025, up to 12% of the world’s electricity will rely on wind power. Developed countries established Wind turbines (WT) that ranges from 20 kW to MWs [5]. The fast growing energy resource in today’s world is the wind energy. The use of wind energy in grid system has decrease the toxic emission of gases..

Though the installation cost for wind energy system is high but it is environment friendly. One of the main problem that exhibit in it include varying wind speed which result low efficiency. For the system to be an efficient, it must run at the maximum power point (MPP). Chasing the (MPP) is the main task of a WECS, a lot of research work has been done in this area to design efficient and reliable MPPT controllers [6, 7]. There are many control methods that has been used to achieve MPP [8]. To achieve this goal, tracking and extraction of MPP at variable wind speed is the most challenging task due to stochastic nature of wind [9]. Conventional methods and intelligent methods are two main MPPT techniques. Among all the methods, Hill climbing search (HCS) is the easiest one in conventional methods [10]. Conventional PI controller is not reliable control method and is sensitive to changes [11]. The speed of wind in uncontrollable due to its stochastic nature. Therefore, the use of variable speed wind turbine is necessary which can change its rotation speed according to wind speed and is called the optimal speed ratio (TSR) [12]. Feedback linearization control based particle swarm optimization method is suitable for WECS but the main drawback is that it is very delicate to change in system parameters that occurs and requires system specific modelling [13]. Sliding mode control technique has been proposed. It has proven a good technique which has advantages over conventional PI controller.

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com It has the feature which include order reduction, simple design and resilient to disturbance but it has chattering issue [14, 15].

Research into back stepping non-linear control illustrates the potential of simple structure, fast and accurate tracking but this method is less robust to any change in parametric uncertainties in real time [16]. One of the proposed control technique that shows advantage in achieving robustness, stability and high efficiency is the second order sliding mode [17]. The usefulness of this technique is applicable to synchronous machine as well. The limitation of this method is that it need extra information about higher derivatives of Sliding and because of high gain the actuator may damage. In [18] research into the use of robust sliding mode control of PMSGWECS eectively exhibits the potential intensity of this control strategy. The quality of hearty sliding mode control originates from the capacity to control high-arrange frameworks, while displaying strength against unsettling influences and varieties in model parameters. Result shows that this control technique suffers from chattering issues that causes high mechanical wear and low accuracy. Studies on Integral Sliding Mode Control (ISMC) show that this method eliminates the arrival phase of the system [19].

The order of a system is equal to the order of ISMC, which causes the system to run in full state in ISMC [20]. In modern era, most of the researchers are attracted towards soft computing methods that includes the artificial intelligence methods. Compared to conventional methods, these proposed controllers show rapid convergence at different wind speeds. Other methods can include feedback control (PSF) [22], power signal optimal torque (OPC) [23], perturbation and observation method (P&O) [24], incremental conductance and optimal base relation (ORB) [25], Indirect Power Controllers (IPC) and Direct Power Controllers (DPC) [26, 27].

The intelligent control methods like RBF Neural-Network-Control and artificial neural network control [28] used to make an effective controller but these control methods require time-consuming calculations.

In this research, a novel non-linear fractional integral MPPT controller for PMSG-WECS has been proposed. The proposed technique not only reduce the oscillation with fast convergence but also ensures MPPT. The rest of the work is structured as: Section II provides PMSG-WECS and turbine modelling. Section III gives the input output conversion of the system. Stability analysis is given in section IV. FITSMC control MPPT algorithm is analyzed in section V. Section VI discussed simulation results. Final conclusion is given in Section VII. II. PMSG-WECS MODELLING PMSG-WECS can be divided into two parts, first is the wind turbine (WT) modelling and second is the PMSG modelling.

A. Wind Turbine Modelling The wind turbine is the most import part in wind energy transformation system, other system includes the generator, gearbox, low speed and high speed shaft and the control mechanism. The generators that includes in WECS are the synchronous generator, permanent magnet synchronous generator (PMSG), squirrel cage generator, wound rotor type generator and doubly fed induction generator (DFIG). In low and medium power turbines permanent magnet, squirrel cage type generator are used due to low cost and reliability. In high power requirements PMSG, wound field synchronous and induction generators are used [21]. Figure 1 shows a typical model for wind power plant.

Figure 1: Schematic diagram for PMSG based WECS

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com The mechanical formula extracted from the wind turbine depends upon the available wind speed and the power curve of the system provided by the manufacturer is given by the following formula: ( , )

= 0.5

(1)

Where is the mechanical power extracted from the wind turbine, ρ is the density of air, A is area of wind turbine blades, is the wind speed and is the wind turbine power coefficient as a function of tip speed ratio and the pitch angle of the blade . The tip speed ratio is given by: (2)

= Where

is the speed of the turbine rotor.

From (2), while keeping the rotor speed constant ( ), any variation in wind speed ( ) will change the tip speed ratio ( ) due to which the power extracted from the WT changes. To obtain the MPP from the wind turbine, the rotor speed ( ) is made relative to the wind speed variation. As a result the tip speed ratio is preserved at optimum point . The reference of the turbine rotor can be presented by the .

(3)

= Several numerical approximation exist for

( , )

. This relation is given by [6]. =

(4) − 9.7477 10 − 6.541 10 − +1.3032 10 6 − 4.54 10 is a function of λ and β. has some optimal point called at optimal tip speed ratio . For simulation purpose, the wind turbine has = 7 and value of = 0.476. Assuming that both and are known, the optimum power is given as: 0.0061 − 0.0013

+ 0.0081

(5) 2 Therefore, the speed of the rotor should be kept at optimal value of TSR ( = 7). If the wind speed changes, the rotor speed should be adjusted accordingly. The mechanical torque generated by the turbine rotor is given by the below relation: =

(6)

= =

(7)

2

B. PMSG Modelling By understanding and studying how PMSG behaves and works, PMSG is expressed in a mathematical form. The PMSG stator consists of three windings with equal number of turns , therefore they have the same resistance . These windings are distributed in the stator in such a way that the induced magnetic flux is sinusoidal and the displacements of the three windings is 120 electrical degrees. In this way, three phases are formed, and the voltage equation can be expressed as: =

+

(8)

Where ,

are the voltages of the three-phase winding

,

are the currents of the three-phase winding ,

are the flux linkages of the three-phase winding

These flux linkages are the sum of the self-inductance and mutual-inductance and can be represented as follows:

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com ( +

=

)

(

−

)

(

+

)

(9)

Where is the permanent magnet rotor flux are the electrical displacement angle and ,

represent the self-inductances of phases ,

The mutual inductances of phase a are represented as PMSG can be represented in the space vector as follows:

respectively. ,

and same to mutual inductances of the other two phases. The

2 (10) ( + ) + 3 2 (11) = ( + + ) 3 2 (12) = ( + + ) 3 Where represents the phase shift of 120 electrical degrees between the windings. The dynamic model of PMSG was developed in the synchronous reference frame, in which the − is aligned with the magnet axis and the − orthogonal to the daxis with respect to the direction of rotation. Figure 2 shows the transformation stages and axis. These transformation has been done in two stages. The first stage is the Clarke transformation, in which the three-phase fixed coordinates are transformed into twoaxis fixed coordinate (α−β). =

Figure 2. Transformation from abc axis to dq axis (13)

i =i =

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2 √3

+

2

(14)

√3

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com The second stage is the Park transformation in which the two-axis fixed coordinates ( − ) are transformed to a synchronous rotating coordinate ( ), which rotates at the synchronous speed, by introducing the mechanical rotor displacement angle at = . cos( ) +

=

sin( )

(15)

cos( )

(16)

= − sin( ) +

The PMSG can be represented in d-q axis synchronous reference frame as follows:

=

(17)

+

Where (18)

=

(19)

= cos( ) + sin( ) =ω

(20)

+

(21)

Therefore, = =

+

+

(22)

ψ

Rearranging the equation by representing the inductance, we get = = where

are the self-inductance and

(

+ +

and

)

+

−ω

+ω (

+

(23)

+ )

+

+ω ψ

(24)

are the mutual inductances between the d and q-axis. By introducing = =

+

(25)

+

(26)

We got, = =

+

(27)

−ω

+

+ω (

+ψ

(28)

)

The mechanical Torque of the generator is as follows: =

+

ω

(29)

+ ω

(30)

= = 1.5 (

+ (

where and are the electrical and mechanical torques respectively. number of pole pair is .

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−

)

)

(31)

and are the fractional and the inertia of PMSG and the

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com III. INPUT OUTPUT CONVERSION The input out form of PMSG based WECS as given as: (32)

̇ = ( )+ ( )

(33)

= ℎ( ) Where ε

represent the state vector.

ε

the output and ℎ is the scalar smooth feld on

is the control input and

(34)

= +

⎡ ( ) = ⎢1 ⎢ ( ⎣

+

+

+

+

1 ⎡− ⎢ ( )=⎢ 1 − ⎢ ⎣ 0 ℎ( ) = =

+

⎤ ⎥ )⎥ ⎦

⎤ ⎥ ⎥ ⎥ ⎦

(37) (38) (39)

= ℎ( ) = ℎ( ) =

(35)

(36)

=

=

.

+

+

−

(40) (41)

= Where, ,

,

are the coordinates transform form.

IV. MPPT CONTROL LAW DESIGN In this section, fractional integral terminal sliding mode control law is designed to get the maximum power from the wind energy conversion system WECS. For designing the controller, stabilize it (42)

̇ ̇= ̇ =

ℎ( ) +

=

+ ̇+

ℎ( ).

(43)

/

(44)

Where u is the control input.

Assuming sliding surface as below:

Where =

−

̇= ̇ − ̇

(45) (46)

Put Error! Reference source not found.) in Error! Reference source not found., we get

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com − ̇

(47)

̈= ̇ − ̈

(48)

̇=

As =

+ ̇+

/

(49)

/

(50)

/

(51)

Taking derivative of Error! Reference source not found.), we have ̇=

̇+ ̈+

Rearranging, ̇= ̈+

̇+

̇= ̇ − ̈ + ̇= By putting ̇ = 0 and calculating

(52)

/

̇+

ℎ( ). − ̈ +

̇+

/

−1 ( ℎ( ) − ̈ + ℎ( )

̇+

/

ℎ( ) +

(53)

, we have =

=

−1 ℎ( )

= −

−

=

+

)

(54)

(55)

( )

ℎ( ) − ̈ +

(56) /

̇+

−

−

( )

(57)

V. STABILITY ANALYSIS The stability of the proposed system be proved by the Lyapunov equation.

Lyapunov stability is given by: =

1 2

(58)

Taking derivative, we have ̇ = S= ̇= ̇ =

ℎ( ) + ℎ( ) +

(59) ̇

(60)

/

+ ̇+

ℎ( ) − ̈ +

̇+

ℎ( ) − ̈ +

̇+

(61)

/ /

(62)

Selecting u such that, 1 / ℎ( ) − ̈ + ̇ + − − ( ) ℎ( ) Putting the value of u in Error! Reference source not found. and after simplification, we’ll get =−

(63)

After simplification we have ̇ =−

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−

∗

( )

(64)

̇ =− | |

(65)

̇ <0

(66)

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com VI. SIMULATON AND RESULTS This section briefly describes the results of the proposed model FITSMC, the effectiveness of the FITSMC has been shown over the feedback linearization control (FBLC) technique. Simulation results has been carried out (over a period of 100 s) in Matlab/Simulink environment.

Different parameters of the proposed controller have been shown below from Table 1 to Table 3.

Table 1. Wind Turbine Parameters Parameters Values Density of the air 1.25 / Blade radius 0.25 Power coefficient 0.47 Tip Speed Ratio (Optimal) 7 Table 2. PMSG Parameters Parameters Values Resistance of stator 3.3 inductance of â&#x2C6;&#x2019; 0.04156 q-axis inductance 0.04156 Load inductance 0.08 Magnetic Flux 0.43 Speed of High Shaft Inertia 0.0552 / Table 3. FITSMC Parameters Parameters Values 11 28 650 0.08 70 10 The effectiveness of the proposed controller has been checked under stochastic nature of wind speed Figure 3. The wind speed varies stochastically and average wind speed has been taken as 7 sec. The stochastic wind speed demonstrates various characteristics, such as characteristics of ramp, gust and noise simultaneously. Furthermore, developed control scheme fractional integral terminal sliding mode (FITSMC) has been compared with the Feedback Linearization (FBLC) MPPT controller.

Figure 3. Wind Speed Profile

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com Figure 4 shows tracking of the high speed shaft rotational speed the for proposed controller scheme and it has been shown that the FITSMC converges at 0 while FBLC exhibit a steady error of 0.6 and FITSMC tracks every optimal point for each wind speed. Ratio of tip speed has its optimum value of = 7 which is successfully tracked by the FITSMC and is shown in Figure 5 while FBLC oscillates from the optimum value and its value is 8 approximately. Hence FITSMC guarantees MPP. The power coefficient has its optimum value near to 0.47 which is ensured by our propose model in the simulation and is given below in Figure 6. Figure 7 shows the low speed shaft WT mechanical power , the figure clearly shows that the optimal regime characteristics (ORC) and the operating points for FITSMC is very closed as compared to the FBLC. Figure 8 shows mechanical power of the wind turbine vs ratio of tip speed, it can be clearly seen that the low speed shaft power lies at optimum value 7 while in case of FBLC, deviation occurs.

Mechanical power on generator side, has been shown in Figure 9. The electromagnetic torque, of the generator is depicted in Figure 10 and it can be clearly seen that it tracks the optimum speed ratio.

Figure 4. High speed shaft rotational speed

Figure 5. Tip speed ratio

Figure 6. Power coefficient

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com

Figure 7. Speed of low shaft rotational speed vs speed of shaft WT mechanical power

Figure 8. Low speed shaft power

Figure 9. High speed shaft power

Figure 10. Mechanical torque

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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 8 Issue XII Dec 2020- Available at www.ijraset.com VII. CONCLUSION FITSMC has been successfully developed for PMSG-based WECS non-linear systems. Through the above design and analysis, we have proven that FITSMC can reduce the chattering caused by the FBLC. The proposed controller can ensure that the system state always reaches to optimum operating point and FITSMC can also reduce the tracking error to zero in a limited time. From the results, it can be clearly seen that the performance of FITSMC is far better than FBLC. In addition, the simulation results of the standalone PMSG-based WECS system show that the proposed FITSMC technique achieves excellent tracking performance.

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