Tuning PI Controller Based on Multiobjective Optimization Approaches for Speed Control of PMSG Wind Turbine.

(1)

Tuning PI Controller Based on Multiobjective Optimization Approaches

for Speed Control of PMSG Wind Turbine

Ratna Ika Putri

1, 2

, Lie Jasa

, Margo Pujiantara

, Ardyono Priyadi

, Mauridhi Hery P.

Abstract

–

This paper presents a particle swarm optimization (PSO) method for determining

proportional integral (PI) controller parameters for a variable speed wind turbine driven by a

permanent magnet synchronous generator. Generator speed is controlled to obtain optimal power.

The performance of the PSO-PI controller is compared to that of a PI controller based on pole

assignment and simulation results show that the PSO method can successfully tune the PI

controller to achieve better performance than the PI controller.

Copyright © 2015 Praise Worthy

Prize S.r.l. - All rights reserved.

Keywords

:

Permanent Magnet Synchronous Generator, Particle Swarm Optimization, PI

Controller, Wind Turbine

Nomenclature

P

Wind Turbine Power (watt)

Cp

The Coefficient of turbine power conversion

ρ

The Air density (kg/m

)

λ

The tip speed ratio

R

The blade radius (m)

V

The wind speed (m/s)

β

The pitch angle

ω

The turbine angular speed (rad/s)

J

The inertia moment (kg m

)

F

The friction coefficient (N)

T

The mechanical torque (Nm)

T

The wind turbine torque (Nm)

i

,i

d and q axis current (A)

u

,u

d and q axis stator voltage (V)

Rs

The winding resistance (Ω)

L

, L

q and d-axis inductance (H)

ψr

Permanent magnetic flux (Wb)

P

Pole pairs

ω

The angular velocity of the generator (rad/s)

Te

Electromagnetic torque (Nm)

X

(

t

)

Position of ith particle

P

best

The best position of each particle

G

best

The best position of the whole swarm

v

(

t

)

velocity of ith particle

w

The constriction factor

C

, C

learning factors

r

, r

random numbers generated uniformly

Mp

Maximum overshoot

Ess

Steady state error

t

Rise time

t

Settling time

α

The weight value

Kp

d,q

Proportional constant for the d and q-axis

current controller

t

id,q

the constant of integration time for the d-axis

current controller

ζ

The damping coefficient

Wn

The natural frequency

I. Introduction

In Indonesia, the use of electrical energy has been

increasing every year by 6.2% [1]. The use of fossil fuels

in national power plants causes environmental damage

due to CO2 gas emissions.

In an effort to diversify the energy supply away from

dwindling fossil fuels and to reduce the environment

impact of the fossil energy, the use of renewable energy

is increasing. Wind energy has great potential in

Indonesia and has been developed quickly [2]. Based on

the wind speed data from various regions, wind energy

resources in Indonesia range from 2.5 to 5.5 m/s at a

height of 24 m above ground level.

This classifies wind speed in Indonesia in the

low-to-medium grade [3]. Although wind energy is clean,

pollution free, and inexhaustible, the amount of energy

generation fluctuates and the supply is intermittent.

The conversion of wind energy into electrical energy

requires an electric generator. Some electrical generators

that can be used in the wind energy conversion system

are permanent magnet synchronous generators (PMSG),

doubly fed induction generators (DFIG), and induction

generators. Currently, PMSG is used widely in wind

energy conversion systems because it has several

advantages: high reliability, lightweight components, low

volume, high performance, and high efficiency.

PMSG are cost effective and suitable for small-scale

applications. The use of PMSG for variable-speed wind

turbines is being investigated, particularly with respect to

optimizing the efficiency of the system [4]-[11].

(2)

Changes in wind speed affect the PMSG output power

and system performance. A control system is required to

improve the efficiency and performance by ensuring that

the generator operates at the maximum power point.

By controlling the PMSG rotor speed, this maximum

power point can be achieved. Several speed control

strategies have been developed. Proportional integral (PI)

controller has been widely used in industrial processes,

because it is simple and easy to implement. PI controllers

have shown good performance for PMSG speed control

[12]. However, the determination of the PI control

parameter is very difficult, so the necessary tuning

parameters PI. This can be done by several methods,

including neural networks, fuzzy logic, B-spline

networks, genetic algorithms, heuristic optimization

methods, and particle swarm optimization (PSO)

[13]-[20], [28]-[30]. Aissaoui et al [13] tuned PI controllers

using a fuzzy logic method to control the speed of a

PMSG. Based on simulation results, a PI controller tuned

by fuzzy logic can determine the maximum power with

better performance than the PI controller alone. However,

the success of the fuzzy logic method is highly dependent

on the determination rule and membership function used.

Tuning PI controller parameters with a heuristic

method for PMSG speed control has shown to have

better performance with fewer errors [17]. However, the

use of a heuristic method is a long process and is difficult

to implement in practice. To improve performance PI

controller , in this paper, the parameters of PI controller

tuned by using PSO. PSO is a multiobjective

optimization that can tune the parameters PI for the

PMSG speed control based on error steady state,

maximum overshoot, rise time and settling time.

Compared with genetic algorithms and the linear

quadratic regulator (LQR) method, PSO produces better

dynamic performance for linear brushless DC motors

[21]. PSO is also a very simple method that is easy to

implement and code using a computer, and for these

reasons has been widely studied [14]-[20]. This paper

presents the use of PSO for tuning a PI controller for the

speed control of a PMSG-driven wind turbine.

Speed control using the PSO-PI system is compared to

using the PI controller with pole assignment. This paper

is organized as follows: in Section 2 the variable speed

wind turbine and the PMSG models are described.

In Section 3, an overview of particle swarm

optimization is presented. In Section 4, the control

strategy is described (how PSO is used to optimally tune

the PI controller for speed control of the PMSG). In

Section 5, we compare the performance of the PSO-PI

controller and PI controller via simulation results. In

Section 6 we show our final conclusions of the paper.

II. Modeling of a Variable Speed

Wind Turbine

The wind energy conversion system of interest here

consists of a wind turbine, permanent magnet

synchronous generator (PMSG), control rectifiers, a

pulse width modulation (PWM) system and electronic

filters. Kinetic energy from the wind is converted into

rotational energy using the turbine, which is then

converted into electrical energy by the attached

three-phase generator. Three-three-phase electric energy is rectified

by a circuit controlled by PWM. Here, modeling of the

wind conversion systems will be undertaken using dq

models and description of the control systems to obtain

optimum power.

II.1.

Wind Turbine Model

The power and torque produced by a wind turbine are

dependent on the wind speed. Wind power (

P

) and

torque (

T

) are expressed as follows [13], [22], [23]:

P

= 0.5

πρCp

(

λ,β

)

R

v

(1)

=

0,5

( , )

(2)

where

ρ

is air density,

Cp

is the coefficient of turbine

power conversion,

λ

is the tip speed ratio, R is the blade

radius, and

v

is the wind speed.

Cp

can be expressed as

follows where

β

is the pitch angle:

= 0.5176

116 −

0.4 −

5 + 0.0068

(3)

1 =

1 + 0.08

−

0.035 + 1

(4)

The tip speed ratio compares the turbine angular speed

(

ω

) and the wind speed, expressed as follows:

=

(5)

The dynamic equation of the wind turbine can be

expressed by:

= (1/ )[

−

]

(6)

where

J

is the inertia moment,

F

is the friction

coefficient,

T

is the torque that is produced by the

turbine, and

T

is generator torque. Fig. 1 shows the

characteristics of turbine output power as a function of

turbine speed for different wind speeds with a pitch angle

of 0

. It is clear that different wind speeds produce very

different maximum output power values.

II.2.

Permanent Magnet Synchronous

Generator Model

PMSG can be modeled using a dq equivalent circuit as

shown in Figs. 2 [9], [22]-[24]. Based on this equivalent

circuit a mathematical model in a synchronous reference

frame can be expressed as follows:

(3)

=

−

+

1 (7)

=

−

1 +

1 (8)

where

i

is the d-axis stator currents,

i

is the q-axis stator

current,

v

is d -axis stator voltage,

v

is the q-axis stator

voltage,

Rs

is the winding resistance (Ω),

L

is winding

inductance on the d-axis (H),

L

is the winding

inductance on the axis

q

(H),

ψr

is permanent magnetic

flux (Wb), and

ω

is the electrical rotating speed of the

PMSG (rad/s).

The angular speed of the electric generator is

dependent on the number of pole pairs (P) and the

angular velocity of the generator (

ω

) which can be

expressed by Eq. (9):

ω

= P

∙ ω

(9)

Electromagnetic torque produced by the PMSG in

terms of the dq model can be expressed as follows:

T

= 1.5

P

((

L

-

L

) ∙

i

(

t

) ∙

i

(

t

) +

i

(

t

)

ψ

)

(10)

III. Overview of Particle Swarm

Optimization (PSO)

PSO is an evolutionary computing technique for

optimization [21], [28]-[30]. PSO was developed by Dr.

Kennedy and Dr. Eberhart based on a social-psychology

theory of the behavior of flocking animals such as ants,

termites, bees and birds. Social behavior consists of

individual actions influenced by others in the group.

Fig. 1. Turbine Power Characteristics

(a) q- axis equivalent circuit (b) q- axis equivalent circuit Figs. 2. Equivalent circuit of a PMSG

Every individual, for example a bird, is expressed as a

particle that has two characteristics, namely position and

velocity. The iterations of the model proceed as each

particle is randomly moved through the search space,

where the movement of a particle depends on its local

best-known location as well as that of the swarm.

Based on the optimum position of one particle, other

particles in the group will adjust their position and

velocity [14], [15], [18]-[20].

PSO is initialized to a random solution, an iterative

search for the optimal value based on an objective

function. If a particle in d- dimensional space is

expressed by

X

= {

X

,

X

,…,

X

} and the best position

of each particle is Pbest. The best position of the whole

swarm is called Gbest. The velocity and position of the

ith particle can be defined according to the following

equations:

v

(

t

)

= w v

(

t-

1)

+ C

r

(

Pid – X

(

t-

1)) +

+ C

r

(

Pid – X

(

t-

1))

(11)

X

(

t

)

= X

(

t-

1)

+ v

(

t

)

(12)

where

v

(

t

) is velocity of ith particle,

X

(

t

) is position of

ith particle,

w

is the constriction factor,

C

and

C

are

learning factors,

r

and

r

are random numbers generated

uniformly in the range [0 1] [21].

IV. Control Strategy

A block diagram of the wind energy conversion

system is shown in Fig. 3 which consists of the PMSG,

wind turbines, control rectifiers, PWM module, current

controller, and a speed controller. As each wind speed

produces a different power curve, a control system is

required in order to modify the generator speed to

achieve optimum power with fluctuating wind speeds.

The PMSG speed controller consists of two stages; a

current controller (inner loop) and a speed controller

(outer loop).

In this paper, the speed controller was a PSO - PI

controller while the current controller for the d-axis and

q-axis was a PI controller based on pole assignment.

Fig. 3. Schematic of speed and current controller components

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

1 pu Max. power at base wind speed (12 m/s) and beta = 0 deg

6 m/s 7.2 m/s

8.4 m/s 9.6 m/s

10.8 m/s 12 m/s

13.2 m/s 14.4 m/s

Turbine speed (pu of nominal generator speed)

(4)

IV.1. Speed Control Using a PSO-PI Controller

The speed controller regulates the PMSG speed based

on a reference value obtained through maximum power

point tracking calculations. Based on the characteristics

of the WECS, the generator must rotate at an optimum

speed to achieve maximum power. Based on the method

of tip speed ratio (TSR), the optimum speed can be

determined by the wind speed, the length of the blade (R)

and the optimum tip speed ratio (

λ

opt

) as described by Eq.

(13):

=

· (13)

Here we assumed an optimum tip speed ratio of 8.1. A

block diagram of the speed controller components is

shown in Fig. 4. The speed controller input is the

difference between the reference speed and generator

speed while the controller output is the q-axis current that

will be referenced in the q-axis current controller.

Fig. 4. Speed control using the PSO-PI controller

The PI controller used a PSO algorithm to tune the

parameters Kp and Ki to get a suitable output transient

response. Every particle in PSO method has two

dimensions consisting of Kp and Ki. The initial value for

each particle is determined randomly and the speed and

position are updated based on equations (11) and (12).

The objective function at PSO is based on criteria

performance of controller.

The most common performance criteria are the

integrated absolute error (IAE), the integrated square

error of time (ITSE) and the integrated square error

(ISE), which were evaluated in the frequency domain.

These performance criteria have some disadvantages

where minimization can result in a response with a small

overshoot. Settling time becomes greater because the ISE

performance criterion weighs all errors equally

independent of time. The ITSE performance criteria can

overcome these shortcomings but the derivative

processing of the ITSE formula becomes more complex

and time-consuming [21].

Therefore the performance criteria used in this paper

to evaluate the PI controller are based on the time

domain. Performance criteria in the time domain include

maximum overshoot (

M

), steady state error (

E

), rise

time (

t

) and settling time (

t

). These can be used in the

PSO algorithm as follows [21]:

W

(

K

)

=

(1

– e

(-α)

)

· (

M

+E

)

+ e

(-α)

· (

t

-t

)

(14)

Fig 5. Flowchart of the PSO-PI controller method

In this study, to reduce overshoot and steady state

error, the weight value

α can be set to a value greater

than 3. For reducing the rise time and settling time, the

α

value can be set to less than 3.

The value of the fitness function using the PSO

method is determined based on the minimum value

achieved from performance criteria.

A flowchart of the PSO-PI control used in this study is

shown in Fig. 5. The PI controller tuned by PSO had the

following parameters; number of iterations = 20, size of

the swarm = 20,

C

=

C

= 1.2, and a constriction factor

(

w

) = 0.45.

IV.2. Current Controller

Current controller functions to regulate the d-axis (

I

)

and q-axis (

I

) current and to generate a controller output

in the form of a d-axis (

V

) and q-axis (

V

) voltage. In

this study,

I

dref

is zero and

I

qref

is the speed controller

output. The current controller used a proportional

integrator (PI) based on pole assignment.

A block diagram of the PI control for the d-axis and q-

axis is shown in Figs. 6. Based on the dynamic model

generator and PI controller outputs,

V

to control the

d-axis current can be expressed by Eq. (15):

( ) =

( )

−

( ) +

(1)

Changes in wind speed affect the PMSG output power

and system performance. A control system is required to

improve the efficiency and performance by ensuring that

the generator operates at the maximum power point.

By controlling the PMSG rotor speed, this maximum

power point can be achieved. Several speed control

strategies have been developed. Proportional integral (PI)

controller has been widely used in industrial processes,

because it is simple and easy to implement. PI controllers

have shown good performance for PMSG speed control

[12]. However, the determination of the PI control

parameter is very difficult, so the necessary tuning

parameters PI. This can be done by several methods,

including neural networks, fuzzy logic, B-spline

networks, genetic algorithms, heuristic optimization

methods, and particle swarm optimization (PSO)

[13]-[20], [28]-[30]. Aissaoui et al [13] tuned PI controllers

using a fuzzy logic method to control the speed of a

PMSG. Based on simulation results, a PI controller tuned

by fuzzy logic can determine the maximum power with

better performance than the PI controller alone. However,

the success of the fuzzy logic method is highly dependent

on the determination rule and membership function used.

Tuning PI controller parameters with a heuristic

method for PMSG speed control has shown to have

better performance with fewer errors [17]. However, the

use of a heuristic method is a long process and is difficult

to implement in practice. To improve performance PI

controller , in this paper, the parameters of PI controller

tuned by using PSO. PSO is a multiobjective

optimization that can tune the parameters PI for the

PMSG speed control based on error steady state,

maximum overshoot, rise time and settling time.

Compared with genetic algorithms and the linear

quadratic regulator (LQR) method, PSO produces better

dynamic performance for linear brushless DC motors

[21]. PSO is also a very simple method that is easy to

implement and code using a computer, and for these

reasons has been widely studied [14]-[20]. This paper

presents the use of PSO for tuning a PI controller for the

speed control of a PMSG-driven wind turbine.

Speed control using the PSO-PI system is compared to

using the PI controller with pole assignment. This paper

is organized as follows: in Section 2 the variable speed

wind turbine and the PMSG models are described.

In Section 3, an overview of particle swarm

optimization is presented. In Section 4, the control

strategy is described (how PSO is used to optimally tune

the PI controller for speed control of the PMSG). In

Section 5, we compare the performance of the PSO-PI

controller and PI controller via simulation results. In

Section 6 we show our final conclusions of the paper.

II. Modeling of a Variable Speed

Wind Turbine

The wind energy conversion system of interest here

consists of a wind turbine, permanent magnet

synchronous generator (PMSG), control rectifiers, a

pulse width modulation (PWM) system and electronic

filters. Kinetic energy from the wind is converted into

rotational energy using the turbine, which is then

converted into electrical energy by the attached

three-phase generator. Three-three-phase electric energy is rectified

by a circuit controlled by PWM. Here, modeling of the

wind conversion systems will be undertaken using dq

models and description of the control systems to obtain

optimum power.

II.1.

Wind Turbine Model

The power and torque produced by a wind turbine are

dependent on the wind speed. Wind power (

Pw

) and

torque (

Tw

) are expressed as follows [13], [22], [23]:

Pw

= 0.5

πρCp

(

λ,β

)

R

vw

(1)

=

0,5

( , )

(2)

where

ρ

is air density,

Cp

is the coefficient of turbine

power conversion,

λ

is the tip speed ratio, R is the blade

radius, and

vw

is the wind speed.

Cp

can be expressed as

follows where

β

is the pitch angle:

= 0.5176

116 −

0.4 −

5 + 0.0068

(3)

1 =

1 + 0.08

−

0.035 + 1

(4)

The tip speed ratio compares the turbine angular speed

(

ω

) and the wind speed, expressed as follows:

=

(5)

The dynamic equation of the wind turbine can be

expressed by:

= (1/ )[

−

]

(6)

where

J

is the inertia moment,

F

is the friction

coefficient,

Tm

is the torque that is produced by the

turbine, and

TL

is generator torque. Fig. 1 shows the

characteristics of turbine output power as a function of

turbine speed for different wind speeds with a pitch angle

of 0

. It is clear that different wind speeds produce very

different maximum output power values.

II.2.

Permanent Magnet Synchronous

Generator Model

PMSG can be modeled using a dq equivalent circuit as

shown in Figs. 2 [9], [22]-[24]. Based on this equivalent

circuit a mathematical model in a synchronous reference

frame can be expressed as follows:

(2)

=

−

+

1 (7)

=

−

1 +

1 (8)

where

id

is the d-axis stator currents,

iq

is the q-axis stator

current,

vd

is d -axis stator voltage,

vq

is the q-axis stator

voltage,

Rs

is the winding resistance (Ω),

Ld

is winding

inductance on the d-axis (H),

Lq

is the winding

inductance on the axis

q

(H),

ψr

is permanent magnetic

flux (Wb), and

ω

is the electrical rotating speed of the

PMSG (rad/s).

The angular speed of the electric generator is

dependent on the number of pole pairs (P) and the

angular velocity of the generator (

ω

) which can be

expressed by Eq. (9):

ω

r = P

∙ ω

(9)

Electromagnetic torque produced by the PMSG in

terms of the dq model can be expressed as follows:

Te

= 1.5

P

((

Ld

-

Lq

)

∙

id

(

t

)

∙

iq

(

t

) +

iq

(

t

)

ψ

)

(10)

III. Overview of Particle Swarm

Optimization (PSO)

PSO is an evolutionary computing technique for

optimization [21], [28]-[30]. PSO was developed by Dr.

Kennedy and Dr. Eberhart based on a social-psychology

theory of the behavior of flocking animals such as ants,

termites, bees and birds. Social behavior consists of

individual actions influenced by others in the group.

Fig. 1. Turbine Power Characteristics

(a) q- axis equivalent circuit (b) q- axis equivalent circuit

Figs. 2. Equivalent circuit of a PMSG

Every individual, for example a bird, is expressed as a

particle that has two characteristics, namely position and

velocity. The iterations of the model proceed as each

particle is randomly moved through the search space,

where the movement of a particle depends on its local

best-known location as well as that of the swarm.

Based on the optimum position of one particle, other

particles in the group will adjust their position and

velocity [14], [15], [18]-[20].

PSO is initialized to a random solution, an iterative

search for the optimal value based on an objective

function. If a particle in d- dimensional space is

expressed by

Xi

= {

Xi

,

Xi

,…,

XiD

} and the best position

of each particle is Pbest. The best position of the whole

swarm is called Gbest. The velocity and position of the

ith particle can be defined according to the following

equations:

vid

(

t

)

= w vid

(

t-

1)

+ C

r

(

Pid – Xid

(

t-

1)) +

+ C

r

(

Pid – Xid

(

t-

1))

(11)

Xid

(

t

)

= Xid

(

t-

1)

+ vid

(

t

)

(12)

where

vid

(

t

) is velocity of ith particle,

Xid

(

t

) is position of

ith particle,

w

is the constriction factor,

C

and

C

are

learning factors,

r

and

r

are random numbers generated

uniformly in the range [0 1] [21].

IV. Control Strategy

A block diagram of the wind energy conversion

system is shown in Fig. 3 which consists of the PMSG,

wind turbines, control rectifiers, PWM module, current

controller, and a speed controller. As each wind speed

produces a different power curve, a control system is

required in order to modify the generator speed to

achieve optimum power with fluctuating wind speeds.

The PMSG speed controller consists of two stages; a

current controller (inner loop) and a speed controller

(outer loop).

In this paper, the speed controller was a PSO - PI

controller while the current controller for the d-axis and

q-axis was a PI controller based on pole assignment.

Fig. 3. Schematic of speed and current controller components

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

1 pu Max. power at base wind speed (12 m/s) and beta = 0 deg

6 m/s 7.2 m/s

8.4 m/s 9.6 m/s

10.8 m/s 12 m/s

13.2 m/s 14.4 m/s

Turbine speed (pu of nominal generator speed)

(3)

IV.1. Speed Control Using a PSO-PI Controller

The speed controller regulates the PMSG speed based

on a reference value obtained through maximum power

point tracking calculations. Based on the characteristics

of the WECS, the generator must rotate at an optimum

speed to achieve maximum power. Based on the method

of tip speed ratio (TSR), the optimum speed can be

determined by the wind speed, the length of the blade (R)

and the optimum tip speed ratio (

λ

opt

) as described by Eq.

(13):

=

· (13)

Here we assumed an optimum tip speed ratio of 8.1. A

block diagram of the speed controller components is

shown in Fig. 4. The speed controller input is the

difference between the reference speed and generator

speed while the controller output is the q-axis current that

will be referenced in the q-axis current controller.

Fig. 4. Speed control using the PSO-PI controller

The PI controller used a PSO algorithm to tune the

parameters Kp and Ki to get a suitable output transient

response. Every particle in PSO method has two

dimensions consisting of Kp and Ki. The initial value for

each particle is determined randomly and the speed and

position are updated based on equations (11) and (12).

The objective function at PSO is based on criteria

performance of controller.

The most common performance criteria are the

integrated absolute error (IAE), the integrated square

error of time (ITSE) and the integrated square error

(ISE), which were evaluated in the frequency domain.

These performance criteria have some disadvantages

where minimization can result in a response with a small

overshoot. Settling time becomes greater because the ISE

performance criterion weighs all errors equally

independent of time. The ITSE performance criteria can

overcome these shortcomings but the derivative

processing of the ITSE formula becomes more complex

and time-consuming [21].

Therefore the performance criteria used in this paper

to evaluate the PI controller are based on the time

domain. Performance criteria in the time domain include

maximum overshoot (

Mp

), steady state error (

Ess

), rise

time (

tr

) and settling time (

ts

). These can be used in the

PSO algorithm as follows [21]:

W

(

K

)

=

(1

– e

(-α)

)

· (

Mp+Ess

)

+ e

(-α)

· (

ts-tr

)

(14)

Fig 5. Flowchart of the PSO-PI controller method

In this study, to reduce overshoot and steady state

error, the weight value

α

can be set to a value greater

than 3. For reducing the rise time and settling time, the

α

value can be set to less than 3.

The value of the fitness function using the PSO

method is determined based on the minimum value

achieved from performance criteria.

A flowchart of the PSO-PI control used in this study is

shown in Fig. 5. The PI controller tuned by PSO had the

following parameters; number of iterations = 20, size of

the swarm = 20,

C

=

C

= 1.2, and a constriction factor

(

w

) = 0.45.

IV.2. Current Controller

Current controller functions to regulate the d-axis (

Id

)

and q-axis (

Iq

) current and to generate a controller output

in the form of a d-axis (

Vd

) and q-axis (

Vq

) voltage. In

this study,

Idref

is zero and

Iqref

is the speed controller

output. The current controller used a proportional

integrator (PI) based on pole assignment.

A block diagram of the PI control for the d-axis and q-

axis is shown in Figs. 6. Based on the dynamic model

generator and PI controller outputs,

Vd

to control the

d-axis current can be expressed by Eq. (15):

( ) =

( )

−

( ) +

(4)

where

Kp

is a proportional constant for the d-axis

current controller and

ti

is the constant of integration

time for the d-axis current controller.

The output of the q-axis current controller (

Vq

) can be

expressed by:

( ) =

( )

−

( ) +

+

( )

−

( )

+

( )

( ) +

( )

(16)

where

Kp

is the proportional constant for the q-axis

current controller and

ti

is the constant of integration

timefor the q-axis current controller.

(a) d-axis current controller

Iq +

-PI Controller

+ Iqref

r d d

r r

Vq(t)

(b) q-axis current controller

Figs. 6. PI control of (a) d-axis and (b) q-axis currents

The PI controller design is determined by pole

assignment then the proportional gain and the integration

time constant for d-axis and q-axis current are calculated

as follows:

Kp

=

2 ζL

–

Rs

(17)

=

2 −

(18)

Kp

=

2 ζWnL

q – Rs

(19)

=

2 −

(20)

where ζ is the damping coefficient selected to be 0.707

and

Wn

is the natural frequency which was selected

based on the desired closed loop settling time. The larger

the value of

Wn

, the shorter the closed loop settling time.

V. Results and Discussion

For the developed model based on a variable-speed

wind turbine system we assumed an 8.5kW PMSG

system.

To test the performance of the PSO-PI controller

method, we used a Simulink simulation in MATLAB

with sampling time is 20 μs, where simulations were

performed with both constant and variable wind speeds.

Fig. 7 shows the generator speed response at constant

wind conditions of 10 m/s, where the PSO-PI and PI

controllers are compared. Both controllers are able to

follow the set-point but the PSO-PI controller produced

no overshoot and had a lower settling time.

Figs. 8 show the d-axis and q-axis current controller

responses for the PI and PSO-PI controllers. Both

controllers were able to follow the d-axis current

reference at zero. However the PSO-PI controller

generated a closer response. Fig. 9 shows the error rate in

the speed control. The PSO-PI controller showed a lower

error compared to the PI controller based on pole

assignment.

Fig. 7. Generator speed response

(a) PI controller

(b) PSO-PI controller

Figs. 8. q-axis and d-axis current responses

Fig. 9. Error rate of the speed controllers over time

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

5 10 15 20 25 30

X: 0.0959 Y: 26.72

Time(s)

(

)

PID Reference Optimized PSO

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -1

0 1x 10

-15

(

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

100 200 300

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

100 200 300

Time(s)

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -5

0 5 10x 10

-16

(

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

100 200 300

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

100 200 300

Time(s)

(

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -5

0 5 10 15 20 25 30

Time (s)

)

PSO-PI PI

(5)

Fig. 10 shows the response speed with a change in

wind speed and Figures 11 show the response current.

The PSO-PI controller followed changes in wind

speed. Table I compares the performance of the PSO-PI

and PI controllers.

TABLE I

PERFORMANCE OF PSO-PIAND PICONTROLLER

PSO-PI PI

P 8.4969 7.1 I 324.3317 460 Mp(%) 0 3.5 Ess 0.1 0.18 Tr (ms) 0.018 0.018 Ts(ms) 0.048 0.0719

Fig. 10. Generator speed response with changes in wind speed

(a) PI controller

(b) PSO-PI controller

Figs. 11. q-axis and d-axis current response with changes in wind speed

VI. Conclusion

A control strategy for a variable-speed wind turbine

driven by a PMSG was presented, including a speed

controller as the outer loop and a current controller as the

inner loop. The speed controller used PSO-PI while the

current controller used PI based on pole assignment.

The overall system was simulated for two different

wind speeds and it was shown that the PSO algorithm

succeeded in tuning the PI controller parameter. The use

of the PSO-PI controller showed better performance than

the PI controller.

Future work will include further development of the

control technique and validation by an experimental

study.

Appendix

Density of Air: 1.225 kg/m

, Area swept by blades:

3m

, stator resistance (Rs): 0.08Ω, Inductance (L

d, Lq):

0.0066H, number of pole: 5.

Acknowledgements

The authors gratefully acknowledge the contributions

of the Directorate General of Higher Education in

Indonesia (DIKTI) for the support of this work.

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Time (s)

(

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PI Reference Optimized by PSO

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100 200 300

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

100 200 300

Time(s)

(

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -1

0 1 2x 10

-15

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

100 200 300

)

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100 200 300

Time(s)

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eering 1 Sura 2 3 c Tec in c Ph.D. Nov hyd netwo Nov Ele rene curre rese iden Osa Lab Iden Tec Artific ene 1_Electric Surabay 2_Electric 3_Electric currently Technol in contr

Ph.D. d Novemb hydro p network Novemb Electric renewab currently research identific

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Ph.D. degre November, hydro powe network

November Electrical En renewable e

currently a research inte identificatio

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Electrical Dep Surabaya.

Electrical Depa

Electrical Engin

urrently pursui Technology S in control, powe

Ph.D. degree in November, Sur hydro power g

November (ITS Electrical Engin renewable energ

currently a lect research interest identification of

Osaka city Univ Laboratory of Identification a Technology Sep Artificial Intelli energy, conditio

Electrical Departm

Electrical Departme

Electrical Engineerin

pursuing th hnology Sepuluh ontrol, power ele

D. degree in Ele vember, Surabay ro power gener

vember (ITS), In ctrical Engineerin ewable energy,

lecturer earch interest is ntification of pow

ka city University oratory of Instr ntification and

hnology Sepulu rtificial Intelligent rgy, condition an

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cal Department

cal Department, P

cal Engineering De

pursuing the P epuluh No ol, power electro

egree in Electric ber, Surabaya. Hi power generatio

ber (ITS), Indon al Engineering ble energy, protec

lecturer at h interest is powe cation of power s

city University, Ja tory of Instrum

cation and a p logy Sepuluh N al Intelligent, N , condition and mo

Authors

Department, In

epartment, Polit ngineering Depa Ratn borne receiv degre Brawi 1994 lectur Nege rsuing the Ph.D.

epuluh Novemb ower electronics Lie Indon his Engin Nove degre Techn 1996 ree in Electrical E

Surabaya. His er generation sy

Marg java receiv Syste Sepu maste Band degre (ITS), Indonesia Engineering Dep

protection Ardy java receiv Syste Sepu maste Syste Univ lecturer at Elec terest is power

n of power systems

Mau

Bang 16, 1 from Techn 1984 Engin 1989 University, Japa of Instrumenta n and a profe Sepuluh Novem Intelligent, Neura

dition and monito

thors’

partment, Instit

rtment, Politekni

neering Departme

Ratna Ik

borneo of received degree Brawijaya 1994 and lecturer o Negeri ing the Ph.D. deg

uluh November, r electronics and

Lie Jasa

Indonesia his bac Engineeri Novembe degree f Technolo 1996, wh Electrical Engi abaya. His curre

eneration system,

Margo P

java of received h System E Sepuluh master’s Bandung degree ), Indonesia in ineering Departme

protection and

Ardyono

java of I received h System E Sepuluh master an System Universit turer at Electrica st is power transi power systems

Mauridh

Bangkala 16, 1958 from Technolo 1984 an Engineeri 1989, and versity, Japan in

Instrumentation nd a professor puluh November, igent, Neural Ne

n and monitoring

thors’

ment, Institut

ment, Politeknik Ne

ring Department, U

Ratna Ika P

borneo of Ind received her degree in Brawijaya 1994 and 20 lecturer of ele Negeri Malan he Ph.D. degree

November, Sura ctronics and rene

Lie Jasa

Indonesia on his bachelo Engineering November, S degree from Technology 1996, where h ectrical Engineeri a. His current ration system, re

Margo Pujia

java of Ind received his b System Engi Sepuluh Nov master’s de Bandung (IT degree from Indonesia in 20

ring Department and iden

Ardyono Pr

java of Indon received his b System Engi Sepuluh Nov master and P System E University, J r at Electrical E s power transient

er systems.

Mauridhi H

Bangkalan 16, 1958. He from Elec Technology 1984 and m Engineering 1989, and P rsity, Japan in 199

strumentation, M a professor of h November, t, Neural Netwo

d monitoring syst

thors’ inform

t, Institut Tek

Politeknik Negeri

Department, Uday

atna Ika Putri

orneo of Indone received her bac egree in Ele

Unive 994 and 2006. lecturer of electro

Malang, h.D. degree in Ele vember, Surabay

renewab

was Indonesia on Dec

is bachelor's Engineering Ins

ovember, Sura egree from Ele Technology Sepu 996, where he is cal Engineering His current rese n system, renew

Margo Pujiantar

java of Indonesia received his bache

ystem Engineer epuluh Novemb aster’s degree Bandung (ITB),

egree from I esia in 2011.

Department, ITS and identific

rdyono Priyad

java of Indonesia is bache ystem Engineer epuluh Novemb aster and Ph.D ystem Engin niversity, Japan Electrical Engin er transient sta

Mauridhi Hery

Bangkalan east ja 6, 1958. He re from Electrica Technology Sepu 984 and mast Engineering Osa 989, and Ph.D. Japan in 1995. w

entation, Measu rofessor of Ele ovember, Surab eural Network, onitoring system

informati

Institut Teknolo

iteknik Negeri Ma

artment, Udayana

a Ika Putri was eo of Indonesia o ved her bachelo ee in Electri University and 2006. rer of electronics

Malang, East . degree in Electric ber, Surabaya

renewable e

was born nesia on Decemb bachelor's de neering Institute mber, Surabaya ee from Electric nology Sepuluh , where he is cur Engineering Insti current research system, renewable

go Pujiantara

of Indonesia ved his bachelor

m Engineering luh November (ITS er’s degree fro

ung (ITB), Indo ee from Institu

in 2011. H partment, ITS.

and identificatio

ono Priyadi

of Indonesia on is bachelor m Engineering luh November (ITS er and Ph.D. de

m Engineerin ersity, Japan in ctrical Engineerin

transient stability

ridhi Hery Pu

east java o 1958. He receiv

Electrical nology Sepuluh and master's neering Osaka c

h.D. degr n in 1995. wher tion, Measurem ssor of Electric Surabaya. l Network, Ima toring system.

informatio

stitut Teknologi

ik Negeri Malang

ent, Udayana Uni

was bo f Indonesia on O her bachelor’s d in Electrical

University, Ea 2006. Since 2 f electronics Dep Malang, East Jav gree in Electrical Surabaya. Her cu renewable energ

was born in on December, chelor's degree ing Institute T r, Surabaya in rom Electrical gy Sepuluh No ere he is currently ineering Institute rent research inte

m, renewable e

Pujiantara was b Indonesia on his bachelor degr Engineering from

November (ITS), degree from (ITB), Indonesia

from Institut 2011. He is c ment, ITS. His identification of

was b ndonesia on Sep is bachelor degr Engineering from

November (ITS), nd Ph.D. degree

Engineering y, Japan in 20 al Engineering D sient stability, re

i Hery Purn

east java of In . He received Electrical En gy Sepuluh No d master's deg ing Osaka city

h.D. degree in 1995. where he , Measurement r of Electrical

Surabaya. His etwork, Image P

information

Teknologi Sep

egeri Malang, Ind

Universi

was born donesia on Octob r bachelor’s degr Electrical En niversity, East Ja

Since 2000 ectronics Departm ng, East Java, I in Electrical Eng . Her curren ewable energy.

as born in Ta December, 18 1 or's degree

Institute Tech Surabaya in 19 Electrical Eng Sepuluh Novem he is currently w ring Institute Tec research interests renewable energ

was born onesia on Marc

achelor degree in ineering from I

ember (ITS), In gree from In (ITB), Indonesia in Institut Tek e is curre t, ITS. His rese

ntification of pow

was born nesia on Septem achelor degree in ineering from I

ember (ITS), In Ph.D. degree in Engineering fro

apan in 2008 a Engineering Depa t stability, renew

ery Purnomo

st java of Indone e received his trical Engine Sepuluh Novem master's degree Osaka city Uni .D. degree in Po 95. where he is Measurement and

Electrical Eng urabaya. His re rk, Image Proce

formation

nologi Sepuluh

ri Malang, Indone

University, I

was born in Ba sia on October, 2 helor’s degree ectrical Engine rsity, East Java Since 2000, sh nics Department East Java, Indo lectrical Enginee

. Her current rese ble energy.

born in Tabana cember, 18 1966

degree from titute Technolo baya in 1990 ectrical Enginee uluh November, s currently worki Institute Techno arch interests in wable energy, a

was born in sia on March18 elor degree in Ele ring from Instit

er (ITS), Indon from Institu Indonesia in 199 Institut Teknolo e is currently S. His researc cation of power s

was born in a on September elor degree in Ele ring from Instit

er (ITS), Indon .D. degree in Ele eering from n in 2008 and eering Departm bility, renewable

Purnomo

va of Indonesia ceived his bach al Engineerin uluh November, er's degree fro ka city Universi degree in Power where he is curr urement and Po ectrical Enginee

aya. His researc Image Processin

gi Sepuluh No

lang, Indonesia

University, Indo

in Balikp on October, 22 1 r’s degree and rical Engineerin , East Java Ind ce 2000, she ha s Department at P st Java, Indonesi

trical Engineering . Her current researc

in Tabanan ber, 18 1966. He egree from

nology a in 1990 and cal Engineering November, Sura rrently working to

itute Technology interests includ le energy, and

as born in Pasu on March18, 1 r degree in Electr

from Institut T (ITS), Indonesia from Institut T

nesia in 1995 a tut Teknologi

is currently a le His research in n of power syste

was born in Nga September 27, r degree in Electri from Institut T (ITS), Indonesia egree in Electric ng from Hi

2008 and 201 ng Department, y, renewable en

was f Indonesia on S ed his bachelor'

Engineering November, Sura

degree from city University, ree in Power syst re he is currently ment and Power cal Engineering . His research i ge Processing, r

Sepuluh Nope

, Indonesia.

iversity, Indonesi

in Balikpapan ctober, 22 1977. degree and ma

Engineering ast Java Indonesi 2000, she has b partment at Polit va, Indonesia. l Engineering Inst urrent research in

Tabanan Ba 18 1966. He rec e from Elec nology Se 1990 and ma Engineering Inst vember, Surabay ly working towar

Technology Se erests include mi nergy, and com

born in Pasuruan March18, 1966 ree in Electrical P m Institut Tekn ), Indonesia in Institut Tekn sia in 1995 and

Teknologi Se urrently a lectur s research intere f power systems

born in Nganjuk ptember 27, 1973 ree in Electrical P m Institut Tekn ), Indonesia in e in Electrical P

from Hirosh 08 and 2011. H Department, ITS renewable energy

was bor donesia on Septe his bachelor's d gineering Inst vember, Surabay gree from Elec

University, Japa in Power system e is currently an and Power Sy

Engineering Inst s research intere Processing, renewa

uluh Nopembe

rsity, Indonesia

n Balikpapan east er, 22 1977. ee and master’ ngineering from Java Indonesia i

, she has been ment at Politekni Indonesia. She i gineering Institut nt research interest

banan Bali o 966. He receive from Electrica nology Sepulu 90 and master's ineering Institut ber, Surabaya i working toward th chnology Sepulu ts include micro y, and compute

in Pasuruan eas rch18, 1966. H ical Powe nstitut Teknolog donesia in 1985 stitut Teknolog 1995 and Ph.D. knologi Sepulu

ntly a lecturer a search interest i

er systems

in Nganjuk eas ber 27, 1973. He n Electrical Powe nstitut Teknolog donesia in 1997 Electrical Powe from Hiroshim and 2011. He i artment, ITS. Hi able energy, an

was born i esia on Septembe bachelor's degre ering Institut ber, Surabaya i from Electrica iversity, Japan i ower system from

currently an hea d Power System

ineering Institut search interest i essing, renewabl Nopember,

Indonesia.

alikpapan east 22 1977. She and master’s eering from Indonesia in e has been a t at Politeknik She is ering Institute search interest

an Bali of . He received Electrical ogy Sepuluh and master's ring Institute Surabaya in ing toward the logy Sepuluh include

micro-and computer

Pasuruan east 8, 1966. He ical Power stitut Teknologi esia in 1985, t Teknologi 95 and Ph.D. logi Sepuluh a lecturer at h interest is

Nganjuk east 27, 1973. He ectrical Power stitut Teknologi esia in 1997, ctrical Power Hiroshima 2011. He is ent, ITS. His e energy, and

as born in on September helor's degree g Institute Surabaya in m Electrical sity, Japan in r system from ently an head ower System ring Institute rch interest is ssing, renewable opember,

apan east She master’s g from onesia in as been a Politeknik She is g Institute ch interest

Bali of e received Electrical Sepuluh master's Institute rabaya in toward the y Sepuluh -computer

ruan east 1966. He ical Power Teknologi in 1985, Teknologi and Ph.D. Sepuluh ecturer at nterest is

njuk east 1973. He trical Power Teknologi in 1997, al Power Hiroshima 1. He is ITS. His ergy, and

born in eptember r's degree Institute rabaya in Electrical Japan in stem from y an head r System Institute interest is renewable