永磁直驱风力发电系统的MATLAB建模

Abstract —The paper presents the dynamic model and control schemes of a variable speed pitch wind turbine with permanent magnet synchronous generator (PMSG). The model incl udes a PMSG model, a pitch-angled controlled wind turbine model and a drive train model. The drive train model uses one-mass model

to represent the mechanical characteristics of the generator set.

The generator mode l is estab l ished in the dq –synchronous rotating reference frame. The wind turbine model detail s the mechanism of variable speed operation of the turbine by a pitch control. The control schemes in the paper incl ude a pitch angle

contro l for the wind turbine and a speed contro l for the generator. The pitch angle control uses wind speeds and electric power output as the input signals to ensure normal operation in high wind speed. The speed contro is rea ized through fie d orientation where the d -axis current is set to zero and the q -axis current is used to control the rotational speed of the generator

according to the variation of wind speed. In order to verify the presented mode l and the contro

l strategy, simu l

ations with MATLAB/Simul ink software have been conducted. Simul ation results prove the validity of the model and the control schemes.

Index Terms —Permanent magnet synchronous generator, Wind turbine, Vo l tage source converter, Speed contro l

, Integration I. I NTRODUCTION IT H its abundant, inexhaustible potential, its increasingly competitive cost, and environmental advantage, wind energy is one of the best technologies available today to provide a sustainable supply to the world development. By the end of 2003, the total installed capacity of the wind turbines has reached as much as 39.234GW and will exceed 110GW by the year of 2012 [1]. In depth understanding and investigation of wind energy related technologies, such as wind power generators, wind farm integration, grid code and etc., is very meaningful. In terms of the generators for wind-power application, there are different concepts in use today. The major distinction among them is made between fixed speed and variable speed wind turbine generator concepts. In the early stage of wind power development, fixed-speed wind turbines and induction generators were often used in wind farms. But the limitations of such generators, e.g. low efficiency and poor power quality, This work was supported in part by National Natural Science Foundation

of China under grant 50577018.

The authors are with the Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education, North China Electric Power University, Changping 102206, Beijing, P.R.China

(e-mail: routouter@https://www.360docs.net/doc/6c12650910.html,, ligy@https://www.360docs.net/doc/6c12650910.html,, zhouming@https://www.360docs.net/doc/6c12650910.html,,

chengyongzhao@https://www.360docs.net/doc/6c12650910.html,).

adversely influence their further application. With large-scale

exploration and integration of wind sources, variable speed wind turbine generators, such as doubly fed induction generators (DFIGs) and permanent magnetic synchronous generators (PMSGs) are emerging as the preferred technology [2]. In contrast to their fixed-speed counterparts, the variable

speed generators allow operating wind turbines at the optimum tip-speed ratio and hence at the optimum power efficient for a wide wind speed range.

As the penetration of wind power increases, integrating large wind farms to power grids and the relevant influences on the host grids needs to be carefully investigated. So, accurate and reliable model of variable speed wind turbine generators are urgently needed for power system simulation analysis. The paper is dedicated to analyzing the complete model of a variable speed wind turbine with permanent magnet

synchronous generator and developing control schemes for the wind turbine generator. The modeled system consists of a

PMSG model, a pitch-angled controlled wind turbine model and a drive train model. The control schemes include a pitch angle control and a speed control of the generator. The pitch angle control uses wind speed signals and power output of the generator as the inputs. The speed control the concept of

vector control is implemented for the speed control of the

generator in the dq -synchronous rotating reference frame. The

field orientation is realized by setting i dref =0. The q -axis component of the current i q controls the rotational speed. Simulations have been conducted with the software MATLAB/Simulink to validate the model and the control schemes. II. M ODEL OF W IND T URBINE WITH PMSG Traditionally, a wind turbine with PMSG is connected to the AC grid through back-to-back full converters. Nowadays, with the evolution of power electronics, voltage source converter based HVDC (VSC-HVDC) [3] has been considered as a feasible solution to integrating wind farms to grids due to its favorable features [4]. The analysis in the paper is under the background of VSC-HVDC. The topology of this method is depicted in Fig.1 where VSC 1

is the machine side power

converter; T 1 is the interface transformer and L 1

is the

inductance of the transformer (the resistance of the transformer is omitted). u g is the output voltage of the power

converter that should be referred to the machine side and f e is the electric frequency that should vary with the variation of wind speed. When VSC-H VDC is implemented for wind power transmission, the machine side power converter (VSC 1) Modeling of the Wind Turbine with a Permanent Magnet Synchronous Generator for Integration

Ming Yin, Student Member , IEEE , Gengyin Li, Member , IEEE , Ming Zhou, Member , IEEE ,

Chengyong Zhao, Member , IEEE

W

1-4244-1298-6/07/$25.00 ?2007 IEEE.

to VSC2

Fig. 1. Block diagram of PMSG with VSC-HVDC

operates to adjust the speed of the generator according to the variation of wind speed. The power converter (VSC 2) on the other end of the DC Link connects AC grids and takes the onus of controlling the DC voltage and the output AC voltage

or the reactive power [5]. The paper will address the control strategy for the machine-side power converter. A. Aerodynamic Model

The wind turbine extracts power from wind and then

converters it into mechanical power. The amount of aerodynamic torque is related to the wind speed as follows λγθρπ/),(5.023P

w

w

C V R T = (1)

where ρ is the air density, R is the turbine radius, V w is the

wind speed and C P is the power coefficient, θ is the pitch angle of rotor, γ=ωw R/V w is the tip speed ratio and ωw is the turbine rotor speed.

C P can be determined by [6]

βθβ5

.12exp )54.0116(22.0???=p C (2)

where β is calculated by

1035.008.0113

+?+=

θθλβ (3) The relationship between C P and γ for the given values of

pitch angle is visually displayed in Fig. 2.

γ

C p

Fig. 2. Power coefficient C P (θ, γ) curves.

The extracted aerodynamic power is given by

w w w T P ω= (4)

The drive train of PMSG consists of five parts, namely, rotor, low speed shaft, gearbox, high-speed shaft and generator. In the analysis, other parts of wind turbines, e.g.

tower and flap bending modes can be reasonably neglected.

When the interest of study varies the complexity of the drive train differs. For example, when the problems such as torsional fatigue are studied, dynamics from both sides of gearbox have to be considered. So, two-lumped mass or more sophisticated models are required. But when the study focuses on the interaction between wind farms and AC grids the drive train can be treated as one-lumped mass model for the sake of time efficiency and acceptable precision. So, the drive train takes the form of the latter one in the paper and is displayed in Fig.2 in which the parameters have been referred to the generator side. ???????=??=g g eq g m g w e g

dt

d J B T T dt d ωα

ωω/)(_ (5) where ‘g ’ represent the parameters of the generator side, J eq is the rotational inertia of generator which is derived from J eq =

J g +J w /2

g

n , n g is the gear ratio, B m is the rotating damping, T e is the electromagnetic torque, αg is the mechanical angle of the generator, T w_g is the aerodynamic torque that has been transferred to the generator side by T w_g =T w /n g , and ωg is the mechanical angular speed.

B. Generator Model

The dynamic model of PMSG is derived from the two-phase synchronous reference frame in which the q -axis is 90° ahead of the d -axis with respect to the direction of

rotation. The synchronization between the dq -rotating reference frame and the abc -three phase frame is maintained

by a phase locked loop (PLL) [7]. The electrical model of PMSG in the synchronous reference frame is given in (6). ???????++??=++?=q q q d q d e q q a q d d q d q e d d a d u L L i L L i L R dt

di

u L i L L i L R dt di 1)1(10λωω (6)

where subscripts ‘d ’ and ‘q ’ refer to the physical quantities that have been transformed into the dq -synchronous rotating reference frame; R a is the armature resistance; ωe is the electrical rotating speed which is related to the mechanical rotating speed of the generator as ωe =n p ωg where n p is the number of pole pairs; λ0 is the permanent magnetic flux. The electric frequency is determined by f e =ωe /2π. The frequency is obtained by PLL. The inductances, L d and L q are the summation of the inductances of the generator on the d - and

q -axis and the inductance of the transformer L 1, respectively. u d and u q are, respectively, the d - and q -axis components of u g in Fig.1.

The q -axis counter electric potential e q =ωe λ0 and the d -axis counter electric potential e d =0. In the paper, we assume L d =L q =L and (6) can be rewritten as

???????++??=++?=q d e q a q d q e d a d u L L i i L R dt

di

u L i i L R dt di 1)1(10λωω

Fig.3 shows the equivalent circuit of the PMSG on the

dq -rotating reference frame.

(a) q -axis equivalent circuit

(b) d -axis equivalent circuit

Fig. 3. Equivalent circuit of PMSG in the synchronous frame

The electromagnetic torque can be derived from

))((5.

10λq q d q d p e i i i L L n T +?=As the inductances on the d - and q -axis are equal, the electromagnetic torque can be regulated by i q as

05.1λq p e i n T =Equations (7) can be supplemented by the mechanical

equations for the drive train given in (5) to form the model of PMSG used in this paper.

So, the Simulink based models of the drive train and the generator are given in Fig.4 and Fig.5, respectively.

Fig. 4. Model of the drive train

Fig. 5. Model of the generator

III. C ONTROL S CHEMES

As a type of variable speed wind turbines, PMSGs have two control goals in accordance with variations of wind speeds. In details, in light wind, the maximum power coefficient is maintained by keeping a constant maximum tip speed ratio (power optimization section). In strong wind, the control goal is to keep the machine at the rated output power [8] (power limitation section). In this case, the pitch angle will increase, and the rotor speed will go up and so will the tip speed ratio. According to Fig.3, the power coefficient will drop to maintain the rated output power. The relationships between the generator speed and the electric power and the torque are illustrated in Fig.6.

Speed (pu)

T o r q u e , P o w e r (p u )

Fig. 6. Torque and electric power for different wind speeds.

Meanwhile, the relationship between the power coefficient C P and wind speeds is visualized in Fig.7. There are two control schemes for PMSG to realize the two control goals: pitch control and speed control. The pitch control is implemented to regulate the aerodynamic power extracted from the wind. The pitch angle controller plays the role of a governor in conventional generator, which aims to prevent the generator from exceeding its rated power. This goal is achieved by applying either speed or power feedback. The speed control is utilized to guarantee the machine to follow the predefine speed curve. This goal is achieved by controlling the full power converter on the machine side.

Wind speed (m/s)

P o w e r c o e f f i c i e n t

Fig. 7. Power coefficient C p for different wind speeds.

A. Pitch Angle Control

The pitch angle has significant influence on the power coefficient C P . It plays the role of a governor in conventional generators [9]. In low and medium wind speeds, the pitch control is rarely actuated and only set to the optimum value, e.g. 2°. In high wind speeds, the pitch angle control effects to regulate the extracted wind power so that the design limits of the turbine will not be breached. In the paper, the pitch angle controller is shown in Fig. 8.

Fig. 8. Pitch angle controller

In the pitch angle controller, V wrated is the rated wind speed, e.g. 12m/s. V w is the actual wind speed. P eref is the power

reference value. When power losses are neglected P eref is determined by (1) and (4), i.e. P eref =P w . P e is the actual power which is determined by P e =T e * ωe . The philosophy behind the controller is that wind speed signals are used for feed forward compensation and the power signals for feedback control through a proportional-integral control (PI1 in the figure). In

the controller, “max” is used for selecting the maximum of the

input to ensure that the pitch angle controller actuates only

when the actual wind speed is greater than its rated value.

Therefore, the complete model of wind turbine is obtained, as shown in Fig.9. In the figure, “P_angle control” is the proposed pitch angle controller as in Fig.9; “C P cal” functions to calculate power coefficient according to (2) and (3); “f 1()” aims to calculate ωeref , the reference values of electric angular speed according to (10) [9]. The reference is used to control the speed of PMSG. R n n V p g w eref /γω= (10)

“f 2()” represents the calculation of T w in accordance with (1). In Fig.9, “SW” means a switch that is controlled by wind speed V w . In more detail, when V w is below the rated wind speed, the switch connects to the position “0”; otherwise, to the position “1”.

P V

Fig. 9. Model of the wind turbine

B. Speed Control

As in Fig.1, the full-load frequency converter VSC 1 takes the duty to adjust the rotational speed of the generator that corresponds to the variation of wind speed. The converter generates the voltage phasor u g and the electric frequency f e . So, the machine side converter operates as a voltage source converter.

As the generator is excited by permanent magnets, there is no exchange of reactive power between the generator and the machine side power converter. Therefore, the concept of vector control is implemented for the speed control of the generator in the dq -synchronous rotating reference frame. In

order to obtain field orientation, i dref is set to zero. The torque

command current i qref is derived from the q -axis speed controller. It is known from (6) that there are cross-coupling terms

between the d - and q -axis, namely, ωe i d and ωe i q . Feed forward technique is recommended to compensate the cross-coupling terms. Here, two new inputs and are defined d q e d u Li v +=ω (11)

q q d e q u e Li v +??=ω (12) Therefore, two independent first-order models in the d - and q -axis directions are obtained [10] d a d i R sL v )(+= (13) q a q i R sL v )(+= (14) where s is the Laplace operator. Based on the models, two separate current loops are resulted which have two similar PI controllers designated PI2 and PI3 in Fig. 10. Two control loops are used: the inner loop regulates the currents and the outer loop controls the speed. In the proposed speed controller, i dref =0 and ?ω is the deviation of the electric angular speed from its reference,

namely, ?ω=ωeref ?ωe where ωeref is obtained from the wind turbine model in Fig.9. After the process of the speed

controller, the two generated voltage signals u d and u q are input into the PMSG model as given in (7) to generate the two-axis current components i d and i q , T e , and e q .

d i u d

e q q ?u q

q

q

Fig. 10. Speed controller

So, the model of variable speed wind turbine with PMSG and the proposed control strategy are obtained, which is illustrated in Fig.11. In the figure, “Speed Ctrl” represents the proposed speed controller as shown in Fig.10; “PMSG” is the permanent magnet synchronous generator model; “Drive_T” is the drive train model expressed in (5); “Wind_T” represents the wind turbine model depicted in Fig.9.

Fig. 11. Overall control scheme of wind turbine with PMSG

C. Phase Locked Loop (PLL)

The phase locked loop, in dependence on the sensed value of the angular frequency ω of the AC source and of the phase position of the AC system voltage, generates a synchronizing signal ξ

. The synchronizing signal has the importance in synchronizing the dq -reference plane with the AC source voltage abc -system. Thus, when ξ is in synchronism with the phase of the source voltage, the rotating dq -reference plane is locked and maintained in synchronism with the three-phase abc -system.

IV. S IMULATION S TUDIES

The proposed model of the variable speed wind turbine with PMSG is constructed with MATLAB/Simulink. This

paragraph presents the simulated responses of the system under variable wind speeds. In order to test the proposed model in the paper, a simulation case has been performed with MATLAB/Simulink. In the case, natural wind speed suddenly steps up from 8m/s to

14m/s at t =1s and the reference value of the d -axis current component i dref is set to zero. Simulation results are given in Fig. 12 to Fig. 20.

V w (m /s )

Time (s)

Fig. 12. Wind speed model

P e (M W )

Time (s)

e

Time (s)

Fig. 13. PMSG output power Fig. 14. Electrical rotational speed

P i t c h (o)

Time (s)

T

i p s p e e d r a t i o λ

Time (s)

Fig. 15. Pitch angle Fig. 16. Tip speed ratio

C p

Time (s)

e q (k V )

Time (s)

Fig. 17. Power coefficient Fig. 18. q -axis counter electric potential

i d , i q (A )

Time (s)

Time (s) d q

Fig. 19. dq -axis current components Fig. 20. dq -axis voltage components

It is shown from the simulation results when the wind speed is 8m/s, the initial pitch angle θ keeps the value of 2o, the tip speed ratio γ maintains the optimal value 7, and the

power coefficient C P is the maximum around 0.4.

Just after the wind speed steps from 8m/s to 14m/s, due to the inertia of the wind turbine, the rotational speed can’t keep up with the change of wind speed. Therefore, the tip speed ratio has a drop. Meanwhile, because the wind speed is up the rated wind speed the operation of the pitch angle control is actuated and the pitch angle rises to lower the extracted wind power. At the same time, the rotational speed of the wind turbine goes up, which helps transfer the surplus wind power to mechanical energy. As the rotational speed increases, the q-axis counter electric potential e q increases proportionally, too. As is clearly shown in the equivalent circuit of PMSG (Fig.3), the d- and q-axis components of VSC1’s output voltage u d and u q increases accordingly. So, the performance of the variable speed wind turbine with PMSG can be reasonably explained.

V. C ONCLUSIONS

The paper presents the complete model of the variable speed wind turbine with PMSG that is scheduled to connect an AC grid through VSC-HVDC. The complete model consists of a PMSG model, a pitch-angled controlled wind turbine model and a drive train model. At the same time, the paper addresses control schemes of the wind turbine in terms of pitch angle and generator rotational speed. The pitch angle control is actuated in high wind speeds and uses wind speed signals and electric power as the inputs. The generator rotational speed control scheme features the concept of vector control in the dq-synchronous rotating reference frame. MATLAB/Simulink is implemented to build the dynamic model of the wind turbine with PMSG and simulations have been conducted to validate the model and the proposed control schemes.

From the point of view of integration, comprehensive impact studies should be performed carefully before the wind turbines are added to grids. Under this background, the work in this paper is meaningful.

VI. A PPENDIX

The parameters of the PMSG used in the paper are listed below

Rated power: 2MW;

Rated wind speed: 12m/s;

Resistance: R a=0.1Ohm;

Inductance: L=0.005H;

Gear ratio: n g=77;

Number of pole pairs: n p=2;

Radius of wind turbine rotor: R=41m;

Equivalent inertia: J=8000kg.m2;

Rotational damping: B=0.

VII. A CKNOWLEDGEMENTS

The authors are especially grateful to J. Charles Smith, executive director of UWIG, for his help.

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IX. B IOGRAPHIES

Ming Yin (S’06)was born in Hebei Province, China, on April 22, 1974. He received the B.S. degree in power system and its automation from North China Electric Power University (NCEPU) in 1996. Now he is pursuing Ph. D. degree at NCEPU. H is fields of interest include H VDC, wind power technology and flexible AC transmission system (FACTS).

Gengyin Li (M’03)was born in Hebei Province, China. He received the B.S., M.S. and Ph.D. degrees, all in Electrical Engineering, from North China Electric Power University (NCEPU) in 1984, 1987 and 1996, respectively. Since 1987, Dr. Li has been with the School of Electrical Engineering at NCEPU, where he is currently a professor and vice director of the Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education. His research interests include power quality, electricity markets, analysis and control of power systems, and new transmission and distribution technologies.

Ming Zhou (S’03, M’06) was born in Hubei Province, China. She received the B.S., M.S. and Ph.D. degrees, all in Electrical Engineering, from North China Electric Power University (NCEPU) in 1989, 1992 and 2006, respectively. Since 1992, Ms. Zhou has been with the School of Electrical Engineering at NCEPU, where she is currently an associate professor. H er areas of interest include electricity markets, power quality, AI applications to power systems, and power system operation and management.

Chengyong Zhao (M’05) was born in Zhejiang Province, China. He received the B.S., M.S. and Ph.D. degrees in power system and its automation from North China Electric Power University (NCEPU) in 1988, 1993 and 2001 respectively. H is fields of interest include power system harmonics, power quality, power electronics and flexible AC transmission system (FACTS).