1

A New Wind Turbine Generation System Based on Matrix Converter S. M. Barakati, M. Kazerani, Senior Member, IEEE, and X. Chen

Abstract-- At a given wind velocity, the mechanical power available from a wind turbine is a function of its shaft speed. To maximize the power captured from the wind, the shaft speed has to be controlled. In low-cost wind energy conversion systems, the turbine shaft speed is not regulated and a squirrel-cage induction generator is used to convert the turbine mechanical power to electric power. Power electronic converters are used to interface the induction generator with the grid and maximize the power captured from the wind. In this paper, a wind energy conversion scheme based on the matrix converter topology is proposed. As the commutation problems in the conventional nine-bidirectional switch matrix converter topology impairs its performance in industrial applications, an improved topology which does not have any commutation problems, has been adopted for the system presented in this paper. Through matrix converter, the terminal voltage and frequency of the induction generator can be controlled in such a way that the wind turbine is operating at its maximum power point for all wind velocities. The power factor at the interface with the grid is also controlled by the matrix converter to ensure purely active power injection into the grid for optimal utilization of the installed wind turbine capacity. Furthermore, the reactive power requirements of the induction generator are satisfied by the matrix converter to avoid selfexcitation capacitors. Theoretical analysis and simulation results are used to support the claims made on the advantages of the proposed scheme. Index Terms-- Wind energy, squirrel cage Induction generator, matrix converter, maximum power point tracking.

I. INTRODUCTION

D

UE to the increasing demand on electrical energy and environmental concerns, a considerable amount of effort is being made to generate electricity from renewable sources of energy. The major advantages of using renewable sources are abundance and lack of harmful emissions. Wind is one of the most abundant renewable sources of energy in nature. The wind energy can be harnessed by a wind energy conversion system (WECS), composed of a wind turbine, an electric

S. M. Barakati is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (email: [email protected]). M. Kazerani is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (e-mail: [email protected]). X. Chen is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, as a visiting scholar from Harbin Institute of Technology, China (e-mail: [email protected]).

generator, a power electronic converter and the corresponding control system. Based on the types of components used, different WECS structures can be realized. However, the objective in all structures is the same, i.e., the wind energy at varying wind velocities has to be converted to electric power at the grid frequency [1]. Wind turbine configurations for extracting energy from the wind are categorized based on horizontal or vertical axis, number of blades and power rating. Modern wind turbines are of horizontal-axis type, normally have three blades, and their output power can be as high as 2MW per machine [2]. To choose other components of WECS, the strategy of speed control should be known. It has been shown that, for grid connected wind turbine systems, the efficiency of constant-speed systems is lower than that of variable-speed systems. Therefore, despite the extra cost of power electronics, the life-cycle cost is lower. Many different configurations of variable-speed wind turbines have been introduced in the literature [3],[4],[5]. Reference [3] introduces a high-performance configuration, commonly known as Scherbius drive, composed of a doubly-fed induction generator (DFIG) and a PWM AC/DC/AC converter connected between the stator and rotor terminals to implement variable speed operation. Another configuration for variable-speed wind turbines has been introduced in [4]. This system is composed of a DFIG with a matrix converter connected between the stator control winding and the main stator terminals. Variable speed is implemented through control of the matrix converter. The main advantage of the configurations reported in [3] and [4] is in employing a pilot converter to perform shaft speed control. The main disadvantage of these schemes is the high cost of the doublyfed induction generator. Recently, the use of squirrel-cage induction generator (SCIG) for direct grid-connection of WECS has been well established, due to the low cost in comparison with other types of electric machines [6],[7],[8]. The most common configuration of power converters for WECS based on variable-speed wind turbine and SCIG is that composed of two back-to-back voltage source converters with a large capacitor on the dc-link. The power flow of the grid side converter is controlled in order to keep the dc-link voltage constant, while the control of the generator side is set to satisfy the SCIG magnetization demand and control the speed or torque. A technical advantage of this topology is the capacitor decoupling between the grid converter and the

2

generator converter. Besides providing some protection, this decoupling facilitates independent control of the two converters, allowing compensation of asymmetries on both the generator and the grid sides. However, the dc-link capacitor is bulky and exhibits relatively reduced lifetime [7]. The matrix converter (MC) provides direct AC-AC conversion and is considered an emerging alternative to the conventional two-stage AC-DC-AC converter topology [9],[10]. A matrix converter provides a large number of control levers that allows for independent control on the output voltage magnitude, frequency and phase angle, as well as the input power factor. When compared with the AC-DCAC converter system, the bold feature of MC is elimination of the DC-link reactive elements, e.g., bulky capacitors and/or inductors. However, this topology has not yet found its appropriate place in industrial applications. The main reasons behind this are the potential commutation problems, requiring complex control and snubber circuits, unavailability of monolithic bi-directional switches, lack of decoupling between the two ac sides of the converter, and low voltage gain. A novel MC topology with advantages over the conventional nine-bidirectional-switch topology has been developed by Wei and Lipo [11]. The improved topology has the same performance as the conventional MC, but does not have any commutation problems. In addition, voltage gain is improved and control is simplified. This paper proposes a new wind energy conversion system in which the AC-DC-AC converter has been replaced by an improved MC topology and the doubly-fed induction machine has been replaced by a less costly SCIG machine. In this paper, first, a brief description of WECS is provided. Then, it is demonstrated how the wind energy can be optimally captured and converted to electric energy using a wind turbine, a SCIG and a matrix converter. Finally, some simulation results based on the proposed WECS are presented to support the theoretical expectations. II. THE PROPOSED SCHEME Fig. 1 shows a block diagram of the proposed wind energy conversion scheme. As the entire power generated by the wind turbine is transferred through the matrix converter, this work targets low-to-medium-power wind turbines. For medium-to-high-power wind turbines, doubly-fed induction generator with a pilot converter connected to the auxiliary winding will be more appropriate. The wind turbine is followed by a gear box which steps up the shaft speed. Note that working at a low shaft speed translates into a low induction generator terminal frequency which can result in core saturation unless a low terminal voltage is imposed. At low terminal voltages, the operating current will be high, making the scheme impractical. The matrix converter interfaces the SCIG with the grid and implements shaft speed control to achieve maximum power point tracking at varying wind velocities. It also performs power factor control at the grid interface and satisfies the Var demand at the induction generator terminals. The proposed scheme allows for

connecting individual wind turbines to the grid. It also permits paralleling the outputs of several wind turbine generation units at the grid interface. The power handling capability of the system can be enhanced by adopting a multi-converter approach. In the following sections, different elements of the system will be described.

Gear Box

SCIG

Matrix Converter

Grid

Fig. 1 Schematic diagram of proposed wind energy conversion scheme.

III. WIND TURBINE The mechanical power generated by a wind turbine is given by Equation (1) [12]. 1 P = ρ C p Ar Vw3 (1) 2 where P is the power in W, ρ the air density in g/m3, Cp a dimensionless factor called power coefficient, Ar the turbine rotor area in m2 ( Ar = π Rr2 , where Rr is the rotor blade radius) and Vw the wind speed in m/s. The power coefficient is related to the tip speed ratio λ and rotor blade pitch angle θ according to Equation (2) [12]. ⎛ 151 ⎞ − 0.58θ − 0.002θ 2.14 − 13.2 ⎟ e−18.4 / λi (2) C p (λ ,θ ) = 0.73 ⎜ ⎝ λi ⎠ where 1 λi = (3) 1 0.003 − 3 λ − 0.02θ θ + 1 and

λ=

ωr Rr

(4)

Vw

In (4), ωr is the angular speed of the turbine shaft. The theoretical limit for Cp is 0.59 according to Betz’s Law [13], but its practical range of variation is 0.2-0.4. In this paper, the rotor pitch angle is assumed to be fixed. Fig. 2 shows a typical Cp versus λ curve [6]. 0.4

l ) λ( p C T N E I C I F F E O C R E W O P

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0

1

2

3

4 5 6 Tip Speed Ratio (λ )

7

8

9

10

Fig. 2 A typical Cp versus λ curve

As Equations (1)-(4) suggest, the mechanical power generated by the wind turbine at a given wind velocity is a function of the shaft speed. In this paper, a wind turbine

3

model has been created in PSIM simulation package based on the equations (1)-(4) [6]. The block diagram of the model is shown in Fig. 3 and a typical P versus ωr curve produced by the model is shown in Fig. 4.

ωr V

corresponding to the pushover torque. ωs is related to the induction generator terminal frequency fe dictated by the matrix converter through Equation (5). 300

λ

Nm

C( λ )

200

R

ρ

100

Pw

0

Tw

e u q r o T

Operating Region

-100 -200

Fig. 3 Block diagram of the wind turbine model in PSIM: ω r: shaft speed, V: wind velocity, R: radius of the shaft, ρ :Air Density.

-300 -400

140

*

Vw3>Vw2>Vw1

120

Vw 3

-500 0

50

100

150

200

250

300

350

400

wm

Fig. 5 A Typical Te versus ωr curve for SCIG. )t a W K ( R E W O P E N I B R U T

100

*

Vw 2

60

40

*

Vw 1

20

0

0

1

2

3 4 5 SPEED(rad/Sec.)

4π fe (5) p where p is the number of poles of the induction generator. Fig. 6 shows the Pw - ωr and Tw - ωr curves of the wind turbine, as well as a family of Tc - ωr curves for the induction generator for different ωs values. As shown in Fig. 6, by varying fe and thus ωs, the Tc - ωr curve can be shifted to the right or left with respect to the torque-speed curve of the wind turbine to assume a wide range of possible steady-state operating points defined by the intersections of the two curves. Obviously, one of the operating points corresponds to maximum power. To move from one operating point to another, fe is changed in steps (small enough to maintain generating mode) and the difference between the wind turbine torque Tw and the new counter torque of the induction generator Tc at the operating speed will accelerate or decelerate the shaft according to Equation (6) until the new steady-state operating point is reached. d ωr Tw − Tc = J (6) dt

ωs =

80

6

7

8

Fig. 4 Typical P versus ωr curves for different wind velocities (* = PMax).

As seen from Fig. 4, at any given wind velocity, maximum power can be captured from the wind if the shaft speed is adjusted at the value corresponding to the peak power. The idea in this paper is to change the terminal frequency of the induction generator through matrix converter frequency control to track the shaft speed corresponding to the maximum turbine power at all times. The maximum power tracking can be achieved through perturbing the shaft speed in small increments or decrements and observe the direction of changes in the power till the maximum power, at which dP/dωr=0, is reached. The method suggested in this paper for maximum power tracking is perturbation and Observation which is commonly used in photovoltaic energy conversion systems for capturing the maximum power from the solar array under different insolation levels.

T

T

w

P

c

w

2.5 Wind Velocity V*

w

2 1.5

OP1 Tw

IV. SQUIRREL-CAGE INDUCTION GENERATOR Fig. 5 shows a typical torque-speed curve for a SCIG. In Fig. 5, Te is the induced torque in the induction machine. The sign of the torque in the motoring and generating regions has been specified based on the convention that: Tmotor > 0 and Tgenerator < 0. The magnitude of the counter torque that is developed in the induction generator as a result of the load connected at the machine’s stator terminals is then Tc = - Te. The theoretical range of operation in the generator mode is limited between the synchronous angular speed ωs and the ωr

) u p( e u q r o T

1

OPm OP2

1 )

u p( r e w o P

Pw

.5

ws1 w w sm s2 0 -.5 -1 -1.5 0

.33

.66

1

wr (PU)

1.33

Fig. 6 Maximizing captured wind power by shifting Te - ωr curve.

1.66

wr /wrm

4

A. Accelerating Shaft Towards Maximum Power Point In Fig. 6, OPm is the operating point corresponding to maximum power captured from wind at the wind velocity of Vw*. At this point, Pw =1 pu, Tw =1 pu, and ωr = ωrm =1 pu, where ωrm is the angular shaft speed corresponding to maximum power point. Assuming the present operating point to be OP1, corresponding to ωs1, the shaft should speed up so that the operating point OPm can be assumed by the system. This can be achieved by increasing ωs from ωs1 to ωsm through an increase in the SCIG terminal frequency. The SCIG terminal voltage is also adjusted by the matrix converter according to the constant V/f strategy. The frequency adjustment is performed in steps small enough for the induction machine to keep operating as a generator throughout the transition period. This action makes Tw-Tc>0 and accelerates the shaft according to Equation (6) towards maximum power point. B. Decelerating Shaft Towards Maximum Power Point Assuming the present operating point to be OP2, corresponding to ωs2, the shaft should slow down so that the system assumes the operating point OPm. This can be accomplished by decreasing ωs from ωs2 to ωsm through a decrease in the SCIG terminal frequency and voltage according to constant V/f strategy, in steps small enough to restrict operation within the stable generating region. This action makes Tw-Tc

A New Wind Turbine Generation System Based on Matrix Converter S. M. Barakati, M. Kazerani, Senior Member, IEEE, and X. Chen

Abstract-- At a given wind velocity, the mechanical power available from a wind turbine is a function of its shaft speed. To maximize the power captured from the wind, the shaft speed has to be controlled. In low-cost wind energy conversion systems, the turbine shaft speed is not regulated and a squirrel-cage induction generator is used to convert the turbine mechanical power to electric power. Power electronic converters are used to interface the induction generator with the grid and maximize the power captured from the wind. In this paper, a wind energy conversion scheme based on the matrix converter topology is proposed. As the commutation problems in the conventional nine-bidirectional switch matrix converter topology impairs its performance in industrial applications, an improved topology which does not have any commutation problems, has been adopted for the system presented in this paper. Through matrix converter, the terminal voltage and frequency of the induction generator can be controlled in such a way that the wind turbine is operating at its maximum power point for all wind velocities. The power factor at the interface with the grid is also controlled by the matrix converter to ensure purely active power injection into the grid for optimal utilization of the installed wind turbine capacity. Furthermore, the reactive power requirements of the induction generator are satisfied by the matrix converter to avoid selfexcitation capacitors. Theoretical analysis and simulation results are used to support the claims made on the advantages of the proposed scheme. Index Terms-- Wind energy, squirrel cage Induction generator, matrix converter, maximum power point tracking.

I. INTRODUCTION

D

UE to the increasing demand on electrical energy and environmental concerns, a considerable amount of effort is being made to generate electricity from renewable sources of energy. The major advantages of using renewable sources are abundance and lack of harmful emissions. Wind is one of the most abundant renewable sources of energy in nature. The wind energy can be harnessed by a wind energy conversion system (WECS), composed of a wind turbine, an electric

S. M. Barakati is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (email: [email protected]). M. Kazerani is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (e-mail: [email protected]). X. Chen is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, as a visiting scholar from Harbin Institute of Technology, China (e-mail: [email protected]).

generator, a power electronic converter and the corresponding control system. Based on the types of components used, different WECS structures can be realized. However, the objective in all structures is the same, i.e., the wind energy at varying wind velocities has to be converted to electric power at the grid frequency [1]. Wind turbine configurations for extracting energy from the wind are categorized based on horizontal or vertical axis, number of blades and power rating. Modern wind turbines are of horizontal-axis type, normally have three blades, and their output power can be as high as 2MW per machine [2]. To choose other components of WECS, the strategy of speed control should be known. It has been shown that, for grid connected wind turbine systems, the efficiency of constant-speed systems is lower than that of variable-speed systems. Therefore, despite the extra cost of power electronics, the life-cycle cost is lower. Many different configurations of variable-speed wind turbines have been introduced in the literature [3],[4],[5]. Reference [3] introduces a high-performance configuration, commonly known as Scherbius drive, composed of a doubly-fed induction generator (DFIG) and a PWM AC/DC/AC converter connected between the stator and rotor terminals to implement variable speed operation. Another configuration for variable-speed wind turbines has been introduced in [4]. This system is composed of a DFIG with a matrix converter connected between the stator control winding and the main stator terminals. Variable speed is implemented through control of the matrix converter. The main advantage of the configurations reported in [3] and [4] is in employing a pilot converter to perform shaft speed control. The main disadvantage of these schemes is the high cost of the doublyfed induction generator. Recently, the use of squirrel-cage induction generator (SCIG) for direct grid-connection of WECS has been well established, due to the low cost in comparison with other types of electric machines [6],[7],[8]. The most common configuration of power converters for WECS based on variable-speed wind turbine and SCIG is that composed of two back-to-back voltage source converters with a large capacitor on the dc-link. The power flow of the grid side converter is controlled in order to keep the dc-link voltage constant, while the control of the generator side is set to satisfy the SCIG magnetization demand and control the speed or torque. A technical advantage of this topology is the capacitor decoupling between the grid converter and the

2

generator converter. Besides providing some protection, this decoupling facilitates independent control of the two converters, allowing compensation of asymmetries on both the generator and the grid sides. However, the dc-link capacitor is bulky and exhibits relatively reduced lifetime [7]. The matrix converter (MC) provides direct AC-AC conversion and is considered an emerging alternative to the conventional two-stage AC-DC-AC converter topology [9],[10]. A matrix converter provides a large number of control levers that allows for independent control on the output voltage magnitude, frequency and phase angle, as well as the input power factor. When compared with the AC-DCAC converter system, the bold feature of MC is elimination of the DC-link reactive elements, e.g., bulky capacitors and/or inductors. However, this topology has not yet found its appropriate place in industrial applications. The main reasons behind this are the potential commutation problems, requiring complex control and snubber circuits, unavailability of monolithic bi-directional switches, lack of decoupling between the two ac sides of the converter, and low voltage gain. A novel MC topology with advantages over the conventional nine-bidirectional-switch topology has been developed by Wei and Lipo [11]. The improved topology has the same performance as the conventional MC, but does not have any commutation problems. In addition, voltage gain is improved and control is simplified. This paper proposes a new wind energy conversion system in which the AC-DC-AC converter has been replaced by an improved MC topology and the doubly-fed induction machine has been replaced by a less costly SCIG machine. In this paper, first, a brief description of WECS is provided. Then, it is demonstrated how the wind energy can be optimally captured and converted to electric energy using a wind turbine, a SCIG and a matrix converter. Finally, some simulation results based on the proposed WECS are presented to support the theoretical expectations. II. THE PROPOSED SCHEME Fig. 1 shows a block diagram of the proposed wind energy conversion scheme. As the entire power generated by the wind turbine is transferred through the matrix converter, this work targets low-to-medium-power wind turbines. For medium-to-high-power wind turbines, doubly-fed induction generator with a pilot converter connected to the auxiliary winding will be more appropriate. The wind turbine is followed by a gear box which steps up the shaft speed. Note that working at a low shaft speed translates into a low induction generator terminal frequency which can result in core saturation unless a low terminal voltage is imposed. At low terminal voltages, the operating current will be high, making the scheme impractical. The matrix converter interfaces the SCIG with the grid and implements shaft speed control to achieve maximum power point tracking at varying wind velocities. It also performs power factor control at the grid interface and satisfies the Var demand at the induction generator terminals. The proposed scheme allows for

connecting individual wind turbines to the grid. It also permits paralleling the outputs of several wind turbine generation units at the grid interface. The power handling capability of the system can be enhanced by adopting a multi-converter approach. In the following sections, different elements of the system will be described.

Gear Box

SCIG

Matrix Converter

Grid

Fig. 1 Schematic diagram of proposed wind energy conversion scheme.

III. WIND TURBINE The mechanical power generated by a wind turbine is given by Equation (1) [12]. 1 P = ρ C p Ar Vw3 (1) 2 where P is the power in W, ρ the air density in g/m3, Cp a dimensionless factor called power coefficient, Ar the turbine rotor area in m2 ( Ar = π Rr2 , where Rr is the rotor blade radius) and Vw the wind speed in m/s. The power coefficient is related to the tip speed ratio λ and rotor blade pitch angle θ according to Equation (2) [12]. ⎛ 151 ⎞ − 0.58θ − 0.002θ 2.14 − 13.2 ⎟ e−18.4 / λi (2) C p (λ ,θ ) = 0.73 ⎜ ⎝ λi ⎠ where 1 λi = (3) 1 0.003 − 3 λ − 0.02θ θ + 1 and

λ=

ωr Rr

(4)

Vw

In (4), ωr is the angular speed of the turbine shaft. The theoretical limit for Cp is 0.59 according to Betz’s Law [13], but its practical range of variation is 0.2-0.4. In this paper, the rotor pitch angle is assumed to be fixed. Fig. 2 shows a typical Cp versus λ curve [6]. 0.4

l ) λ( p C T N E I C I F F E O C R E W O P

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0

1

2

3

4 5 6 Tip Speed Ratio (λ )

7

8

9

10

Fig. 2 A typical Cp versus λ curve

As Equations (1)-(4) suggest, the mechanical power generated by the wind turbine at a given wind velocity is a function of the shaft speed. In this paper, a wind turbine

3

model has been created in PSIM simulation package based on the equations (1)-(4) [6]. The block diagram of the model is shown in Fig. 3 and a typical P versus ωr curve produced by the model is shown in Fig. 4.

ωr V

corresponding to the pushover torque. ωs is related to the induction generator terminal frequency fe dictated by the matrix converter through Equation (5). 300

λ

Nm

C( λ )

200

R

ρ

100

Pw

0

Tw

e u q r o T

Operating Region

-100 -200

Fig. 3 Block diagram of the wind turbine model in PSIM: ω r: shaft speed, V: wind velocity, R: radius of the shaft, ρ :Air Density.

-300 -400

140

*

Vw3>Vw2>Vw1

120

Vw 3

-500 0

50

100

150

200

250

300

350

400

wm

Fig. 5 A Typical Te versus ωr curve for SCIG. )t a W K ( R E W O P E N I B R U T

100

*

Vw 2

60

40

*

Vw 1

20

0

0

1

2

3 4 5 SPEED(rad/Sec.)

4π fe (5) p where p is the number of poles of the induction generator. Fig. 6 shows the Pw - ωr and Tw - ωr curves of the wind turbine, as well as a family of Tc - ωr curves for the induction generator for different ωs values. As shown in Fig. 6, by varying fe and thus ωs, the Tc - ωr curve can be shifted to the right or left with respect to the torque-speed curve of the wind turbine to assume a wide range of possible steady-state operating points defined by the intersections of the two curves. Obviously, one of the operating points corresponds to maximum power. To move from one operating point to another, fe is changed in steps (small enough to maintain generating mode) and the difference between the wind turbine torque Tw and the new counter torque of the induction generator Tc at the operating speed will accelerate or decelerate the shaft according to Equation (6) until the new steady-state operating point is reached. d ωr Tw − Tc = J (6) dt

ωs =

80

6

7

8

Fig. 4 Typical P versus ωr curves for different wind velocities (* = PMax).

As seen from Fig. 4, at any given wind velocity, maximum power can be captured from the wind if the shaft speed is adjusted at the value corresponding to the peak power. The idea in this paper is to change the terminal frequency of the induction generator through matrix converter frequency control to track the shaft speed corresponding to the maximum turbine power at all times. The maximum power tracking can be achieved through perturbing the shaft speed in small increments or decrements and observe the direction of changes in the power till the maximum power, at which dP/dωr=0, is reached. The method suggested in this paper for maximum power tracking is perturbation and Observation which is commonly used in photovoltaic energy conversion systems for capturing the maximum power from the solar array under different insolation levels.

T

T

w

P

c

w

2.5 Wind Velocity V*

w

2 1.5

OP1 Tw

IV. SQUIRREL-CAGE INDUCTION GENERATOR Fig. 5 shows a typical torque-speed curve for a SCIG. In Fig. 5, Te is the induced torque in the induction machine. The sign of the torque in the motoring and generating regions has been specified based on the convention that: Tmotor > 0 and Tgenerator < 0. The magnitude of the counter torque that is developed in the induction generator as a result of the load connected at the machine’s stator terminals is then Tc = - Te. The theoretical range of operation in the generator mode is limited between the synchronous angular speed ωs and the ωr

) u p( e u q r o T

1

OPm OP2

1 )

u p( r e w o P

Pw

.5

ws1 w w sm s2 0 -.5 -1 -1.5 0

.33

.66

1

wr (PU)

1.33

Fig. 6 Maximizing captured wind power by shifting Te - ωr curve.

1.66

wr /wrm

4

A. Accelerating Shaft Towards Maximum Power Point In Fig. 6, OPm is the operating point corresponding to maximum power captured from wind at the wind velocity of Vw*. At this point, Pw =1 pu, Tw =1 pu, and ωr = ωrm =1 pu, where ωrm is the angular shaft speed corresponding to maximum power point. Assuming the present operating point to be OP1, corresponding to ωs1, the shaft should speed up so that the operating point OPm can be assumed by the system. This can be achieved by increasing ωs from ωs1 to ωsm through an increase in the SCIG terminal frequency. The SCIG terminal voltage is also adjusted by the matrix converter according to the constant V/f strategy. The frequency adjustment is performed in steps small enough for the induction machine to keep operating as a generator throughout the transition period. This action makes Tw-Tc>0 and accelerates the shaft according to Equation (6) towards maximum power point. B. Decelerating Shaft Towards Maximum Power Point Assuming the present operating point to be OP2, corresponding to ωs2, the shaft should slow down so that the system assumes the operating point OPm. This can be accomplished by decreasing ωs from ωs2 to ωsm through a decrease in the SCIG terminal frequency and voltage according to constant V/f strategy, in steps small enough to restrict operation within the stable generating region. This action makes Tw-Tc