An Aggregate Model of PMSG-based, Grid Connected ...

An Aggregate Model of PMSG-based, Grid Connected Wind Farm Investigation of LVRT capabilities Mohamed ABBES (1,2) (1)

Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR11ES15 Laboratoire de Systèmes Electriques, 1002, Tunis,Tunisie (2) Ecole Nationale Supérieure d’Ingénieurs de Tunis, 1008, Tunis. [email protected]

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Keywords — Wind Farm; PMSG; Aggregate Model; LVRT; Ancillary Services.

INTRODUCTION

As a result of economic and environmental concerns, Transmission System Operators (TSOs) are relying more and more on wind power. Consequently, for many countries, wind energy penetration in power systems has undergone a significant increase over the past few years. In terms of annual electricity production, Denmark remains the country with the highest penetration level which reaches 27.1%, followed by Portugal (16.8%) and Spain (16.3%) [1]. The high share of wind power in the electricity systems requires that modern wind plants participate effectively to Grid Support Services (GSS). As defined by most grid codes, the required GSS include voltage and frequency control, and certain function for system restoration during grid disturbances. To deliver such services, fundamental changes might be needed in the way that wind farms are operated and controlled. For example, recent studies show that a power reserve capacity of 1-15% is required to achieve a penetration level of 10%, and 4-18% at a penetration level of 20% [2]. Nonetheless, the most current This work was supported by the Tunisian Ministry of High Education, Research and Technology.

978-1-4799-7947-9/15/$31.00 ©2015 IEEE

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Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR11ES15 Laboratoire de Systèmes Electriques, 1002, Tunis,Tunisie (2) Ecole Nationale Supérieure d’Ingénieurs de Tunis, 1008, Tunis. [email protected]

Abstract —Large scale integration of wind power has become one of the most important challenges of wind industry. To increase wind power penetration on power systems, modern wind farms are required to operate like conventional generating unit. They should participate to frequency and voltage control and stay connected to the grid during severe disturbances. In this context, an aggregate model of a grid connected wind farm is developed in this paper. The wind farm includes 25 direct drive wind turbines of 2 MW rating each. The cluster or multi-machine equivalent representation was used to achieve the necessary accuracy under different incoming winds. This model will be used to investigate the behavior of power systems including wind farms and to improve the planning and the exploitation of electricity systems. A hierarchical control approach is developed to manage wind farm active and reactive generation during voltage dips and to investigate its Low Voltage Ride-Through (LVRT) capacity.

I.

OthmanB.k HASNAOUI (1,2)

Mehdi ALLAGUI (1,2)

Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR11ES15 Laboratoire de Systèmes Electriques, 1002, Tunis,Tunisie (2) Ecole Nationale Supérieure d’Ingénieurs de Tunis, 1008, Tunis. [email protected]

operating wind farms are controlled to achieve maximum power production regardless of the power system state. This fact highlights the need to develop enhanced control strategies for wind farms to achieve better integration into the electrical grid. In this context, this paper proposes an aggregated model of grid connected wind farm, which uses the direct drive technology. Up to now, most of investigations on wind farm models have focused on the fixed speed configuration and the doubly fed induction generators configuration. However, due to the intriguing performances of the direct drive technology, the need to develop aggregated models for PMSG based wind farms has arisen. Commonly, wind farms with large number of wind turbines have been aggregated in a single equivalent wind generator. Rated apparent power of this equivalent generator is rescaled to reach the total power capacity of individual turbines. However, this method ignores that, in real conditions, wind turbines are exposed to different wind speeds as consequence of wake effect, turbulence and terrain orography. Such simplification does not reflect effectively the difficulty to manage the production of multiple wind turbines with different operating points. Therefore, in this work, the cluster representation is used to achieve the necessary accuracy. The model is intended to develop an innovative supervision scheme for PMSG-based wind farms to accommodate more wind energy in the electrical grid. It also can be used for power stability investigations. The next section of this paper presents the equivalent model of a single wind turbine. The third section introduces the control scheme for the PMSG wind turbine including grid side converter (GSC) control and the generator side converter control. Section four gives the detailed model of the wind farm achieved using the cluster approach. Finally, the fifth section presents the supervision strategy of the wind farm. It aims to manage wind farm production during faults. The performances are evaluated by simulation and the results are compared to the GCR defined by the German Transmission System Operators (TSO), E. ON Netz. II.

WIND TURBINE MODEL

The structure of the 2 MW, pitch-regulated, wind turbine is shown in Fig. 1. This generating system is divided into a

number of subsystems where each subsystem represents a physical phenomenon. Dynamics of each component are described by differential equations and the detailing degree of the model is adapted according to the investigation objectives.

u Drive Train

Power Electronic Interface

PMSG

β

Ω

MPPT Algorithm & Pitch Mechanism

u

LCL filter & Grid

J tot

torque produced by the generator.

A. Aerodynamic Subsystem According to the actuator disk theory, the mechanical torque extracted from the wind is expressed by [3]: 1 3 2 C p (λ ,β ) ρΠR U λ 2

(1)

In (1), U is the wind speed, R is the rotor radius and ρ is the air density. C p expresses the power coefficient which is a function of the tip speed ratio λ and the blade pitch angle β : ΩR λ= U

(2)

Ω is the blade angular speed. Power coefficient C p is approximated by the analytical equation (3). Model parameters ci are detailed in [4]. ⎛c ⎞ C p ( λ , β ) = c1 ⎜ 2 − c3 β − c4 β c5 − c6 ⎟ e ⎝ λi ⎠ c 1 1 With : = + 9 . λi λ + c8 β β 3 + 1

c7

λi

(3)

Power coefficient curves C p ( λ , β ) of the considered model

are depicted in Fig. 2: 0.5

0 deg Power coefficient Cp

0.4

0.3

10 deg 15 deg

0.2

C. Permanent magnets synchronous generator The PMSG is represented by means of the well-known third order model written in the dq reference frame. The d axis is aligned with the rotor flux ψˆ v a. In the generator convention, voltage equations are expressed as [4]: i

vgd = − Rg igd +ψ gd −ψ gq pΩ

(5)

i

vgq = − Rg igq +ψ gq +ψ gd pΩ

(6)

The stator flux components are given by: ψ gd = − Ld igd +ψˆ v

(7)

ψ gq = −Lq igq

(8)

In (5) and (6), Rg is the resistance of stator windings and p is the number of pole pairs. The generator electromagnetic torque is calculated as: Tem = p (ψˆ v igq + ( Lq − Ld )igq igd )

(9)

D. Power converters In the direct drive topology, the generator is decoupled from the grid through tow fully rated, back-to-back converters. Switched models which give instantaneous output voltages in function of the switching signals are usually used to describe accurately the operation of power converters. These models are well suited to analyze control algorithms and power quality of grid connected renewable energy sources [6]. However, to investigate the dynamic behavior of wind farms on power systems, simplified models are required to reduce the computation time. In this work, the two-level converters are represented by averaged equivalent circuits as illustrated in Fig. 3.

2 deg 20 deg

0

2

4

mid ( t )

5 deg

0.1

0

(4)

Dmp is the damping coefficient and Tem is the electromagnetic

Controller of Power Converters

−

dΩ + Dmp Ω = Tmec − Tem dt

In (4), J tot is the total inertia of the rotor and the generator,

Pulses

Fig. 1. Structure of the pitch regulated, PMSG wind turbine.

Tmec =

the generator. A two mass model is then used to represent the drive train [5]. However, in this work, a one-mass model is used to represent the drive train system in order to simplify the wind turbine modeling. Shaft dynamic is described by the following equation:

6

8 lambda

10

12

14

16

Fig. 2. Power coefficient curves of pitch regulated wind turbines.

B. Drive train For high power wind turbines, flexible shaft couplings are usually used to achieve the connection between the rotor and

vid

udc (t ) mPWM miq ( t ) Fig. 3. Averaged model of power converters.

viq

According to this representation, mid and miq are the modulation functions which vary between ⎡⎣ − 3 2, 3 2 ⎤⎦ . mPWM is the modulation coefficient which depend on the used modulation technique. It takes the value 3 for the space vector modulation. Consequently, the voltage ripple in the DC link is given by: du 1 ⋅ ( Prec − Pinv ) (10) Cdc ⋅ dc = dt udc In relation (10), Prec is the active power delivered by the rectifier and Pinv is the active power at the inverter output. By neglecting converter losses, their expressions are given by:

Prec = ( udc mPWM ) ⋅ ( mrd ⋅ igd + mrq ⋅ igq ) Pinv = ( udc mPWM ) ⋅ ( mid ⋅ i fd + miq ⋅ i fq )

(11) (12)

In the above expressions, v fd and v fq are the capacitor voltages. igrd and igrq are the grid currents components. III.

This section presents the control scheme of a single PMSG wind turbine. In the conventional control strategy, the main objectives are to maximize the energy capture and to control reactive and active powers delivered to the grid. Therefore, two independent control blocks are generally used: The generator side converter control and the grid side converter control. A brief description of these controllers is given in this section.

A. Control of the generator side converter As above mentioned, generator rotational speed should be controlled in order to maximize power extraction. This objective is achieved by a nested speed-torque algorithm as shown in Fig. 5.

In the above expression, i fd and i fq are the current component

Current control

at the grid side converter output.

vi

R1 , L1

PMSG Model

ωgψ gq

igr R2 , L2

Cf

+ * igd =0

* igq

+

-

PI

PI

-

+

−ωgψ gq

v*gd

v*gq

-

Rectifier & SVM

E. Grid connection model In this work, the wind generating system is connected to the grid through an LCL filter since it offers a butter harmonic rejection compared to a simple L filter [7]. Fig. 4 shows the topology of the used filter. Herein, the grid is assumed to have an infinite short circuit capacity since our objective is to develop an enhanced control strategy for wind farms which allows a better wind energy integration. Therefore the grid is represented by a simple e.m.f denoted egr .

if

CONTROL SCHEME OF THE PMSG WIND TURBINE

vgd -

+

1 + (Ld / Rg )s igd

vgq

1/ Rg

+

+

−ωgψ gd

1/ Rg

igq

1+ (Lq / Rg )s

ωgψ gd

Fig. 5. Conventional decoupled vector current control of PMSG [7].

This algorithm is developed based on PMSG model present in section 2. The torque is regulated through a decoupled control of stator currents igd and igq using PI-regulation.

egr

* According to (9), torque reference Tem* is related to i g q

Fig. 4. Single phase representation of the LCL filter connected to the grid.

through:

According to this model, transient state equations describing the LCL filter dynamics are given by:

1 * (19) Tem pψˆ v The torque reference is generated by the MPPT algorithm.

i

L1 ⋅ i fd = mid ⋅ ( udc mPWM ) − R1 ⋅ i fd + L1ω gr i fq − v fd i

L1 ⋅ i fq = miq ⋅ ( udc mPWM ) − R1 ⋅ i fq − L1ω gr i fd − v fq i

C f ⋅ v fd = C f ω gr v fq + i fd − igrd i

C f ⋅ v fq = −C f ω gr v fd + i fq − igrq i

L2 ⋅ igrd = − R2 ⋅ igrd + L2ω gr igrq + v fd − egrd i

L2 ⋅ igrq = − R2 ⋅ igrq − L2ω gr igrd + v fq − egrq

(13) (14) (15) (16) (17) (18)

* igq =

B. Control of the grid side converter This controller is synchronized with the grid through a Phase Loocked Loop. A vector current control is then used to control grid currents at the connexion point of each turbine. * * and igrq , are generated through the grid Reference currents igrd voltages and active and reactive power references according to the following expressions: Pgr* ⋅ vgrd + Qgr* ⋅ vgrq * (20) igrd = 2 2 vgrd + vgrq

* igrq =

Pgr* ⋅ vgrq − Qgr* ⋅ vgrd

(21)

2 2 vgrd + vgrq

Grid currents are controlled using PI-regulation [8]. According to the LCL filter differential equations, there is a cross coupling between d and q components. Therefore, axes decoupling is performed by subtracting compensation expressions ecomp _ d and ecomp _ q from regulator outputs as depicted in Fig. 6.

ecomp _ d * igrd

+-

PI

vid*

- vid

+

ecomp _ d + +

K2 1+τ 2s

igrd

power coefficient C p . Assuming that all aggregated turbines receive practically the same wind speed, the mechanical torque e of the equivalent wind turbine Tmec can be approximated by [10]: e Tmec

With : K 2 = 1 R2 and τ 2 = L2 R2 . Likewise, DC bus is controlled through a PI regulator which forms an external control loop. Details of controller design are presented in [8].

IV. WIND FARM EQUIVALENT MODEL Many aggregation methodologies for wind farms have been presented in literature [9]. The main requirement for an aggregate model of a wind farm is that apparent power produced at the main connection point should be the same as that produced by individual wind turbines. In addition, the aggregate model should accurately simulate the dynamic behavior of the wind farm during grid disturbances. The single unit representation presents an aggregation technique which can satisfy the above requirements if all the wind turbines are exposed to the same operating conditions such wind speed, direction and rotor rotational speed. Thus, the wind farm is represented by a single equivalent generator which is rescaled to reach the total power production of single turbines. This method is well suited for power system investigation since it can significantly reduce the computation time. However, when it comes to investigate and develop a supervision strategy for wind farms, this method is no more suited since it does not reflect the difficulty to control many wind turbines with different incoming winds. The cluster representation is another aggregation technique which was developed to overcome this difficulty. According to this method wind turbines with similar winds are modeled with a simplified wind turbine model. This solution is acceptable since wind farms are generally organized in rows perpendicular to the prevailing wind direction. Thus, wind turbines belongings to the same row usually undergo the same wake effect and consequently, the same incoming wind. Therefore, in this paper, the study case wind farm was represented with five equivalent clusters, as shown in Fig.7. Each cluster presents an equivalent wind turbine with a rated power equal to n-times the rated power of individual turbines. n is the number of aggregated turbines which equals to 5 in this case. The equivalent wind turbine shares the same rotor model as single turbines, with identical rotor radius R and

(22)

i Tmec

corresponds to the torque of individual PMSG wind With turbine calculated according to relation (1). The equivalent mechanical torque is applied to an equivalent wind turbine that present the same generator and power converters models as those presented in section 2. The same electrical and mechanical data are retained for the generator. However, the total inertia of the rotating system is replaced by an equivalent value n-time bigger than that of single turbines. Thus, the drive train equation is given by: n ⋅ J tot

Fig. 6. Grid current control by PI regulator according to the d axis [8].

i = n ⋅T mec

dΩ e + n ⋅ Dmp Ω = Tmec − Tem dt

(22)

Finally, capacitance Cdc of the equivalent model is multiplied by n since the transmitted powers through the DC link are ntime bigger than those of individual wind turbines. Consequently, voltage ripple in the DC link is given by: n ⋅ Cdc ⋅

5

dudc 1 = ⋅ ( Prec − Pinv ) dt udc

3

4

2

(23)

1 Bus Bar

Group 1 Group 3

Group 4

Group 2 2

2

Group 5 25

24

23

22

21

Fig. 7. The PMSG, 50 MW wind farm modeled by the cluster representation.

The 50 MW wind farm presented in Fig. 7 was modeled using the cluster representation as explained above. Fig. 8 presents the operation of the five clusters which receive different incoming winds. The first cluster represents the upwind row of the wind farm and receive a wind speed equals to the rated value. The other clusters present the downstream turbines.

Consequently, they experience the wake effect of upwind turbines. Therefore, incoming winds for downstream clusters are calculated according to the classical wake model developed by Jensen [10]. Fig. 8.a and Fig. 8.b show the produced active and reactive powers during normal operating conditions. Fig. 8.c shows that the five clusters operate at different rotational speeds in order to maximize power extraction. Reference rotational speeds are generated by MPPT algorithms of each cluster.

Cluster 1

u Drive Train

u Ω

MPPT Algorithm

TemMPPT

Active Power [W]

10 Cluster 1

6

Cluster 2

4

Cluster 3 Cluster 4

2 0

Cluster 5

0

0.5

1

1.5

2

2.5

3

3.5

4

6

Reactive Power [VAr]

2

x 10

Drive Train

Cluster 2

1.5

Cluster 3 Cluster 5

u

0.5 0

Ω 0

0.5

1

1.5

2

2.5

3

3.5

MPPT Algorithm

TemMPPT

Dc-Link Voltage [V]

Cluster 1

2

Qgrs 5

Qgr*

Cluster 4 Cluster 5

0

1

2

3

Control Law 1

4

Fig. 8. The PMSG-based, 50 MW wind farm operation during normal operating conditions.

SUPERVISION STRATEGY AND LVRT PERFORMANCES

This section presents the supervision strategy for the whole wind farm. According to the GCR of the German operator E. ON Netz, wind farms should stay connected during voltage dips with time duration of 3s [11]. In addition, a reactive current equal to 2% I n per 1% U n voltage dip is required. To satisfy these grid codes, the supervision strategy of Fig. 9 is proposed. It includes two control modes, switched according to the dip magnitude: ⇒ L1: vgr ≥ 0.9VN : This mode is activated in absence of voltage faults. The torque reference Tem* is generated by the MPPT algorithm. Reactive power reference is fixed by the TSO and it is subdivided equally on the five clusters: ⎧⎪Tem* = TemMPPT ⎨ s TSO ⎪⎩Qgr ,i = Qgr n

Qgrs ,i

Tems ,i

Cluster 2 Cluster 3

V.

Controller of Power Converters

Tems 5

3000

2500

Pulses

Tem*

1

4

3500

LCL filter/ Grid

Power Electronic Interface

PMSG

Cluster 4

1

Qgrs 1

Cluster 5

u

Cluster 1

Controller of Power Converters

…...............................

Tems 1

x 10

8

Pulses

Tem*

1 2

6

12

LCL filter/ Grid

Power Electronic Interface

PMSG

(24)

n is the number of clusters or, generally, the number of wind turbines.

1

Qgrs

2

5

Control Law 2

Qgrs ,i 1

2

Vgr Grid voltage

egr

2

0%

1

90%

egr

Supervisory control block

Ω

Egr

QgrTSO

Fig. 9. Supervision algorithm for the whole wind farm.

⇒ L2 : 0.0VN ≤ vgr < 0.9VN : The fault mode is activated

when the grid voltage falls under 90% of the nominal value. In this case, the wind turbine should support the grid voltage by delivering reactive current. However, current at the converter output should not exceed nominal ratings of power semiconductors. Therefore, reactive power reference is calculated by: ⎛ egr ⎞ ⎟ (25) Qgrs = 6 egr I N ⎜1 − ⎜ EN ⎟ ⎝ ⎠ Qgrs is used to calculate the maximum active power that the wind farm can produce:

Pgrs =

(3 e

gr

IN

) − (Q ) 2

s 2 gr

(38)

To simplify the supervision strategy, the calculated power is fairly distributed over the wind turbines. Therefore, when a voltage dip is detected, torque reference switches to another value given by: Tems ,i =

Pgrs / n

(39)

Ωi

Grid Voltage RMS[V]

500 400 300 200

VI.

100 0

0

1

2

3

4

5

6

7

8

9

10

6

Active power [W]

x 10 10

Clust1 Clust2

5

Clust3 Clust4

0

1

2

3

4

5

6

7

8

9

In this work, a supervision control strategy for PMSG-based wind farms was proposed. Simulation results show that the wind farm can deliver GSS during voltage dips. LVRT capacity of the wind farm complies with GCR. The supervisory control algorithm can be optimized to deliver more active power during voltage drops. In addition, new units can be included to achieve voltage and frequency primary control. REFERENCES

10

6

[1]

x 10 10

Clust1

5

Clust2

[2]

Clust3 Clust4

[3]

Clust5

[4]

0 0

1

2

3

4

5

6

7

8

9

10

[5]

DC bus voltage [kV]

3.2 3.1 3

[6]

2.9

[7]

2.8

Grid current RMS [kA]

0

rotational speed [rd/s]

CONCLUSION

Clust5

0

[Var]

Fig. 10 shows the response of the wind farm during a 50% symmetrical voltage dip. Wind speeds are considered constant since the fault time duration is significantly lower than wind dynamics. Simulation results show that the over-voltage on the DC links for the five clusters do not exceed 5% of the rated value. In addition, the wind farm stay connected and supports the grid voltage by delivering reactive current. Grid currents are limited to the nominal values as shown by Fig10.e. The maximum active power that the wind farm can export is reduced in proportion to the grid voltage reduction. Finally, it is noted that rotor rotational speeds increase during the fault since they are no longer controlled by the MPPT algorithms. However, Fig.10.f shows that they do not deviate considerably and return gradually to their initial values.

1

2

3

4

5

6

7

8

9

10

10

[8]

5

[9]

0

0

1

2

3

4

5

6

7

8

9

10

[10]

3

[11] 2.5

[12]

2

[13] 1.5

0

1

2

3

4

5

6

7

8

9

10

Time [s]

Fig. 10. Wind farm operation during a symmetrical fault of 50% magnitude.

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