adaptive control pmsg

1446 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 3, MAY 2014

An Adaptive Control Strategy for a Wind Energy

Conversion System Based on PWM-CSC and PMSGEduardo Giraldo, Member, IEEE, and Alejandro Garces, Member, IEEE

AbstractThis paper proposes a new adaptive control strategy

for a wind energy conversion system based on a permanent

magnet synchronous generator and a pulse-width modulated cur-

rent source converter. Most of the studies on wind farms are based

on double fed induction technology. Nevertheless, the proposed

conversion system is a good alternative due to its high efciency

and reliability. Electrolytic capacitors are not required in this

type of converter and the voltage in the DC-link as well as the

generated reactive power can be dynamically modied according

to the wind velocity, being even negative if required. However, it is

challenging from the control and stability standpoint. Capacitive

lters placed on the AC side, which are required for safe commu-

tation, can create resonances with the power grid. Reactive power

is generated according to the capacity of the converter, the wind

velocity and the load prole. The adaptive control strategy uses an

adaptive PI which is self-tuned based on a linear approximation

of the power system calculated at each sample time. A model ref-

erence is also proposed in order to reduce the post-fault voltages.

Simulation results demonstrate the advantages of the proposed

control.

Index TermsAdaptive control, permanent magnet generators,

pulse-width modulated current source converter, reference model,

wind energy.

NOMENCLATURE

Mechanical power.

Wind velocity.

Area swept by the blades.

Air density.

Tip ratio.

Pitch angle.

Coefcient of power.

Rotational speed.

Stator phase resistance of the machine.

Armature inductance.

Inductance in the PWM-CSC.

Voltage in the output of the diode rectier.

Manuscript received May 03, 2013; revised August 15, 2013; accepted

September 25, 2013. Date of publication October 08, 2013; date of current

version April 16, 2014. Paper no. TPWRS-00521-2013.

The authors are with the Department of Electrical Engineering, Universidad

Tecnolgica de Pereira, Pereira, Colombia (e-mail: [email protected]; ale-

[email protected]).

Color versions of one or more of the gures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identier 10.1109/TPWRS.2013.2283804

Current in the DC link.

Voltage in the input of the PWM-CSC (DC side).

Voltage in the output of the PWM-CSC (AC side).

Modulation index.

Angle of the modulated current.

I. INTRODUCTION

M ODERN wind power applications require efcient andexible technologies that adapt to changes in load andgeneration. These challenges can be met by a combination of

non-conventional energy conversion systems and improved

adaptive control strategies.

In terms of the energy conversion system, most of the wind

turbines for on-land emplacements use double fed induction

generators due to their economic advantages (i.e., high ef-

ciency, improved controllability and reduced rating of the

converter [1]). Nevertheless, other energy conversion sys-

tems and generator technologies have been proposed recently

[2][4]. One of the most promising of them is the permanent

magnet synchronous generator (PMSG) which has clear ad-

vantages in terms of efciency and power density. Integration

into the grid of this type of generators requires a full rated

AC/AC converter which, in most cases, is based on the voltage

source converter technology (VSC). Another possible type of

converter is the pulse-width modulated current source con-

verter (PWM-CSC) which has potentially more advantages for

medium size wind turbines [5]. It is capable of controlling the

DC current according to the wind velocity independently of

the DC voltage. This characteristic is exploited in this paper

to create an adaptive control which does not require measure

of the rotational speed. In addition, it permits the use of a full

bridge diode rectier in the side of the machine and hence,

efciency and reliability are improved.

Adaptive control allows the integration of wind resources as

plug-and-play devices in electric power systems. As a result,

this type of control is a key technology in smart-grids and elec-

tric energy systems with non-dispatchable generating sources

[6].

Several design procedures for control of power systems are

well known for cases in which the resulting control system is

time invariant. However, these procedures require a detailed

knowledge of the process dynamics and must be redesigned

if the process is time varying [7]. On the other hand, adaptive

0885-8950 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

GIRALDO AND GARCES: ADAPTIVE CONTROL STRATEGY FOR A WIND ENERGY CONVERSION SYSTEM 1447

control techniques that perform identication and control of dy-

namic systems can be adapted to highly-complex dynamic sys-

tems in order to auto-adjust the controller parameters. However,

thesemethods require an adequate initialization of the controller

parameters and detailed system data [8].

Specically, PI controls has been widely used for control of

power systems, but the tuning of these controllers is a highly

demanding task when the parameters of the controlled process

either are poorly known or vary during normal operation [9].

An adaptive PI control can be designed in order to achieve

high-performance control systems [10]. However, during

normal operation where the controlled process are almost time

invariant, a xed PI control may have similar performance in

terms of reference tracking. Additionally, since the process is

nonlinear, by using linear estimators it is possible to obtain

a time varying linear approximation which can be used to

self-tune the controller.

This paper proposes a new adaptive control strategy for a

wind energy conversion system based on a permanent magnet

synchronous generator and a pulse-width modulated current

source converter. The proposed conversion system is a good

alternative due to its high efciency and reliability. The control

strategy uses an adaptive PI which is self-tuned based on a

linear approximation of the power system and a desired closed

loop response.

The paper is organized as follows: In Section II the energy

conversion system is presented. Advantages of each component

are also described. Next, in Section III the proposed adaptive

control is deduced. After that, simulation results are presented.

Finally, conclusions are presented in Section V.

II. ENERGY CONVERSION SYSTEM

The proposed energy conversion system is based on PMSG.

This type of machine has three main features which are rele-

vant for wind power applications: there are no signicant losses

generated in the rotor; magnetization provided by the perma-

nent magnets allows soft start; and there is no consumption of

reactive power. The rst characteristic implies an improvement

in efciency while the second and third effect the power elec-

tronic converter which does not require bidirectional power ca-

pability. Hence, a full bridge diode rectier is enough for the

AC/DC conversion. In addition, PMSGs allow smaller, exible

and lighter designs as well as lower maintenance and operating

costs. A gear box is not required if it is designed appropriately

with a high number of poles.

A PMSG requires a full rated converter which is usually a

back-to-back conguration with voltage source converters as

shown in Fig. 1(a). This type of converter is efcient for in-

tegrating induction generators since it controls reactive power

in the rectier as well as in the inverter. However, a PMSG

does not require reactive power and hence the rectier can be

replaced by a diode rectier [11]. Nevertheless, the DC voltage

in a VSC must remain within certain limits in order to maintain

stability. As a consequence of this, a DC/DC boost converter

is required for controlling the power in the electric machine as

depicted in Fig. 1(b). The use of a three-phase diode rectier

improves the efciency and reliability of the energy conversion

system but the boost converter could have an opposite effect.

Fig. 1. Three possible congurations for PMSG integration: (a) back to

back converter with VSCs, (b) diode-bridge rectier and boost converter, and

(c) proposed energy conversion system with PWM-CSC.

Any power electronic converter based on forced commutations

has two types of losses: conduction losses and switching losses.

Conduction losses depend mainly on the collector current while

switching losses are mainly related to the switching frequency.

Usually converters are designed in such a way that conduction

and switching losses are equal. A full-bridge can be considered

as a device with only conduction losses since switching occurs

only once during each cycle.

A third option is to integrate the PMSG to the main grid

through a diode rectier and a PWM-CSC as given in Fig. 1(c).

Variation on the DC voltage is not a limitation on the PWM-

CSC; hence the power can be controlled directly by the inverter.

In addition, a PWM-CSC does not require an electrolytic capac-

itor as the VSC. This impacts the reliability of the systems since

30% of failures on AC converters are related to the electrolytic

capacitor [12].

PWM-CSC technology has been applied successfully in a

wide range of applications such as motor drives [13], power

quality conditioners [14] and HVDC transmission for offshore

wind generation [15][17]. Unlike the line commutated con-

verter a PWM-CSC is based on forced commutation and con-

sequently it is able to control active and reactive power. In ad-

dition, it has an inherent short-circuit protection capability [18].

A PWM-CSC requires semiconductor devices with reverse

voltage blocking capability. This can be added to a standard in-

sulated-gate bipolar transistor (IGBT) using a diode connected

in series as shown in Fig. 2. Another alternative is the new

type of semiconductor devices such as reverse blocking IGBTs

(RB-IGBT) or integrated gate commutated thyristors (IGCTs).

The latter alternative is promising for PWM-CSCs [19].

The DC current is directly controlled by the converter. This

feature is specially important for low wind velocities when

voltage in the machine is greatly reduced. While a voltage

source converter requires a constant voltage on the DC side, a

PWM-CSC is able to adapt its voltage according to the wind

velocity. Efciency is improved due to this capability.

The unity power factor is achieved by the modulation itself.

This is done by using space vector modulation [5]. In addition,


Fig. 2. Pulse-width modulated current source converter.

output voltage presents low harmonic distortion and the perfor-

mance for weak grids is guaranteed.

Nevertheless, PWM-CSC has some challenges related to the

control of the converter [20]. The lter placed in the AC side

can create resonances with the grid so that active damping tech-

niques are required. However, these techniques reduce the band

width of the control [21]. In addition, the voltage on the DC

side must be controlled according to the wind velocity in order

to improve efciency and guarantee stability.

III. PROPOSED ADAPTIVE CONTROL FOR PWM-CSC

A hierarchical control is proposed for integration of the wind

turbine into the grid as depicted in Fig. 4. First, the maximum

tracking point algorithm is modied in terms of the DC cur-

rent in the PWM-CSC. Therefore, the reference for this current

is modied dynamically according to the wind velocity. Next,

an adaptive PI control is designed in order to track this refer-

ence. Finally, a model reference control is included in order to

reduce the over-voltages resulting from a fault in the grid. Space

vector modulation (SVM) is used to modulate the current of the

converter.

A. Maximum Tracking Point

The power generated by a wind turbine is proportional to the

cube of the wind velocity as given in (1):

(1)

Maximum power transference is achieved by an optimal

value of . Consequently the rotational speed must be

proportional to the wind velocity and hence, power must be

proportional to the cube of the rotational speed as given in (2):

(2)

On the other hand, the PMSG is modeled on the rotor refer-

ence frame as follows:

(3)

(4)

Fig. 3. Reference for using a maximum tracking point algorithm.

The voltage on the diode rectier (see Fig. 2) is propor-

tional to the voltage in the terminals of the machine which in

turn is given by (5) where is a proportional constant:

(5)

This expression was obtained by replacing (2) in the model

of the PMSG in stationary state and ignoring the voltage drop

in the inductance. This approximation will be demonstrated nu-

merically on Section IV. A speed sensor is not required when

using this expression since the voltage is measured.

The generated power is given by (PMSG losses

are ignored). As a result, the optimal to achieve maximum

tracking is given by (6):

(6)

where is a proportional value which can be approximated as

follows:

(7)

This equation establishes a set point for current as given

in Fig. 3. A low pass digital lter (LPF) is required to smooth

voltage . The cut-off frequency is set below commutation

frequency.

On the other hand, the dynamics of depends on the in-

ductance as follows:

(8)

Each element in this equation is given in Fig. 2. The modula-

tion of the converter depends on the current which varies

according to the wind velocity but cannot be zero. Therefore,

(8) can be written in terms of power as given in (9):

(9)

where is the power delivered by the converter which in turn

depends on the modulation index as follows:

(10)

where is the angle of the output current. This angle must be

equal to the angle of the grid voltage in order to achieve a unity

power factor. A phase locked loop is required as illustrated in

Fig. 4. Therefore, the only control variable is as given in (11):

(11)


Fig. 4. Proposed hierarchical strategy for adaptive control of the energy conversion system based on a pulse-width modulated current source converter.

Fig. 5. Adaptive control and identier.

The output power beyond the capacitive lter is approxi-

mately equal to . Usually, the control in current source con-

verters is made in two stages, one controlling the active power

and the other controlling the voltage in the AC side. This ap-

proach directly controls the active power and the reactive power

is maintained by the modulation itself. Therefore, the possible

resonances on the controls are reduced. The resulting nonlinear

system requires an adaptive control as will be demonstrated in

the next subsection.

B. Adaptive Control

This paper means by adaptive control any control strategy

which uses parameter estimation of the plant in real time by

using recursive identication. The adaptive controller to be de-

signed is based on the certainty equivalence principle: design

the controller as long as the plant parameters are known. How-

ever, since these are unknown at time , they are replaced by

an estimate given by an online identier [22].

This adaptive controller is easy to implement, since for the

controlled plant, only the output signal is needed for feedback.

An adaptive PI control is designed where the plant parameters

are estimated by an online identier, as shown in Fig. 5.

In continuous time, a PI controller can be dened as

(12)

being the control signal, and the error signal (repre-

sented by the difference between the reference and the output

signals). In this case, these variables are given as follows:

(13)

(14)

In discrete time, the PI controller can be dened as

(15)

(16)

being the sample time , and the error

and the integral error at time respectively, and the

integral error at time . By dening a delay operator

such as . Equation (15) can be rewritten as

follows:

(17)

(18)

(19)

Therefore, the control signal at time can be expressed as

(20)

(21)

(22)

(23)

Obtaining the following expression for the PI controller in dis-

crete time

(24)

where the parameters and of the PI controller in con-

tinuous time can be related to the controller in discrete time, as

follows:

(25)

(26)

Since the process to be identied is nonlinear, the identied

model is a linear approximation of the nonlinear model at time

instant . A simplied rst order model is selected, described

by a discrete transfer function, as

(27)

where the unknown parameters to be estimated are and .


Fig. 6. Diagram block using transformation.

Equations (24) and (27) can be rewritten by using the trans-

formation as follows:

(28)

and

(29)

By using (28) and (29) it is possible to formulate the block

diagram of Fig. 6. From this gure it is possible to obtain the

closed loop transfer function, as follows:

(30)

(31)

(32)

(33)

If dening desired closed loop poles, given by

(34)

where and are the discrete time roots of (34), which can

be related to the continuous time roots and by using

(35)

(36)

It is possible to obtain the controller parameters by comparing

the closed loop poles with the desired closed loop poles of (34)

as follows:

(37)

(38)

(39)

(40)

Therefore, the controller parameters can be obtained from

(34) as

(41)

(42)

where it is evident that and are related to the linear ap-

proximation model of the nonlinear process, represented by the

discrete transfer function (29).

In order to estimate the plant parameters (29), a simplied

identication algorithm, known as projection algorithm, de-

scribed in [22] is proposed. When the projection algorithm is

applied in (29) for the estimation of and , the following

actualization rule is obtained:

(43)

(44)

(45)

where and are the estimated parameters at time

, and and are the estimated parameters at

time .

Since the controller parameters are dependent on and

according to (41), a time varying parameters for each can be

obtained as follows:

(46)

(47)

where and are automatically tuned according to

the desired closed loop poles.

Finally, the controller parameters and can be calcu-

lated from (25) by

(48)

(49)

Therefore, the resultant controller is an adaptive PI controller

calculated for each . The behavior of the controller can be

determined by the selection of the desired closed loop poles of

(34) and the sample time , according to (35).

C. Model Reference Adaptive Control

Reference current is modied during a short circuit in

order to improve the short circuit behavior of the converter. A

slightly different current in which the desired output is gen-

erated by a linear reference model is proposed. The reference

model can be selected with an order less than or equal to the

order of the process. In this work, a zero order model is used in

pre-fault , no control during the fault

and a rst order model after the fault as follows:

(50)

(51)

where must be selected as a stable root , where

it is clear that the reference model must be selected as a stable

model with unitary gain. However, the selection of the reference

model and the pole placement technique are separate problems,


Fig. 7. Simulated primary feeder with the proposed energy conversion system.

TABLE I

PARAMETERS OF THE SYSTEM

so it is evident that by using a reference model the exibility of

the control system in the assignment of the closed loop poles is

increased. The fault condition is detected using the voltage .

IV. RESULTS

A detailed switching model of the proposed energy conver-

sion system was simulated using Matlab-Simulink. The system

consists of a 13.2-kV distribution feeder with a 2-MWwind tur-

bine as shown in Fig. 7. Parameters of this system are shown in

Table I.

The discrete time roots were selected in order to

achieve steady state in 20 ms. On the other hand, the reference

model for short circuit condition was calculated for 400 ms.

Wind velocity for 15-s simulation is depicted in Fig. 8. Base

wind velocity is 12 m/s. A gust is simulated in order to demon-

strate the maximum tracking point capability of the proposed

control. Wind velocity prole was created using a detailed

model which considers stochastic behavior [23]. Rotational

speed and voltage are plotted in Fig. 8. These two vari-

ables are proportional as expected. Fig. 9 shows voltage

with respect to rotational speed for the aforementioned simu-

lation. The linear approximation given in (5) is more accurate

for low wind velocities. At high wind velocities, the generated

power increases the current and hence, the voltage drop on the

inductance inuences the generated voltage. Nevertheless, the

linear approximation is accurate enough from a practical point

Fig. 8. Wind velocity, rotational speed and DC voltage.

Fig. 9. Voltage versus rotational speed.

Fig. 10. Generated power in the point of common coupling.

of view and maximum tracking is achieved as shown in Fig. 10.

High inertia of the set turbine-generator produces a delay in

the rotational-speed tracking capability but also a smoothing

effect. This is expected in almost all type of controls for wind

energy.

Generated power is shown in Fig. 10. Wind velocity is again

shown in this gure. An almost perfect tracking characteristic

is achieved in as illustrated in Fig. 11.

The control strategy changes dynamically according to the

wind conditions as shown in Fig. 12. If a time invariant PI con-

trol is used the performance could be similar at least at nominal

wind velocity. In that case, the proposed algorithm can be used

as a tuning technique.

Three-phase voltages and currents in the PWM-CSC are

shown in Fig. 13. Small harmonic distortions are present in


Fig. 11. DC current and reference .

Fig. 12. Values of the adaptive controls and .

Fig. 13. Three-phase voltages and currents on the PWM-CSC.

three-phase voltages due to the commutation process. They

are attenuated by the transformer and hence, the voltage

in the point of common coupling is completely sinusoidal.

A smoother waveform can be achieved by increasing the

switching frequency at the expense of higher switching losses.

Transient behavior of the proposed control was also tested

in the same distribution feeder. Wind velocity was maintained

constant in 12 m/s. A three-phase short circuit at Node 3 was

simulated in (see Fig. 7). Results are shown in Fig. 14.

The voltage on the grid dropped to almost zero [Fig. 14(a)]. Cur-

rent increased due to the drop on the grid voltage in Node

3. The converter still worked in this condition maintaining the

unity power factor. The reference model enter into operation

by maintaining . This allows for energy storage in

Fig. 14. Response for a three-phase fault in the grid. (a) Grid voltages. (b)Mod-

ulation index and DC current. (c) Control variables. (d) Voltages at the primary

of the transformer. (e) Output currents.

the inductance during a fault. The reference for changes

smoothly since it depends on the wind velocity. The modula-

tion index increases up to the point of over-modulation. Conse-

quently, the parameters of the control decreases. These parame-

ters return to their normal values after the fault is cleared. Notice

that the voltages and currents after the fault are within the max-

imum limits due to the introduction of the reference model.

V. CONCLUSIONS

An adaptive control for a PWM-CSC-based energy conver-

sion system particularly designed for wind power applications

adaptive control pmsg

Documents