A Low Voltage Ride Through Strategy of DFIG based on Explicit Model Predictive Control

Electrical Power and Energy Systems 119 (2020) 105783

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A Low Voltage Ride Through Strategy of DFIG based on Explicit Model Predictive Control ⁎

T

⁎

Jia Luo , Haoran Zhao , Shuning Gao, Mingzhe Han School of Electrical Engineering, Shandong University, Jinan 250061, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Doubly Fed Induction Generators (DFIG) Demagnetization control Explicit Model Predictive Control (E-MPC) Low Voltage Ride Through (LVRT)

In this paper, an improved demagnetization control, based on Explicit Model Predictive Control (E-MPC) is proposed to improve Low Voltage Ride Through (LVRT) capability of Doubly Fed Induction Generators (DFIGs). By injecting an additional rotor current component, the demagnetization control can efficiently eliminate the free and negative flux to avoid saturation of the rotor converter. The conventional demagnetization control is based on fixed scaling factors, whose control performance can’t be guaranteed for different fault conditions. The proposed E-MPC approach can fully explore the potential of rotor side converter. Besides, the control parameters of E-MPC are derived offline and very efficient for online control. In addition, the proposed E-MPC structure is simple and easy to be implemented. The mechanism of proposed E-MPC is presented in detail and verified in Matlab/Simulink. The results show that the proposed control scheme has a good performance and can improve the LVRT capability of DFIGs under various fault conditions, especially unbalanced faults.

1. Introduction WITH the increasing penetration of wind power, the integration of wind farms to the grid and their dynamic behavior under grid faults have become an important issue in recent years [1,2]. According to the grid codes, to keep the system stability, the wind turbine should always be connected to the grid during and after faults, especially Low Voltage Ride Through (LVRT). The Doubly Fed Induction Generator (DFIG) is widely used in wind power generation systems due to its high reliability and low cost [3,4]. However, it is excessive sensitivity to grid disturbances since the stator is directly connected to the grid. The sudden voltage fault may cause problems of DFIG such as rotor side over-current and over-voltage at DC bus [5]. The situation gets even worse for the unbalanced cases, due to the rotor voltage induced by free and negative sequence flux, which will cause activation of protection devices and even disconnection of DFIG from the grid [6]. It is of highly importance to study the improvement of LVRT capability of DFIG [7]. To protect the DFIG against voltage dips, the primary solution is using hardware protection devices, such as crowbar and chopper [8]. However, during the activation of crowbar, the DFIG absorbs a large amount of reactive power from the power grid, which can’t help and even deteriorate the voltage recovery [9]. Crowbar should be timely

removed to support reactive power to the grid [10]. Dynamic voltage restorer is installed between the stator and the grid to compensate the drop in the grid voltage by providing reactive power during the fault [11,12]. However, the application of hardware in these methods increases the system cost and control complexity [13]. Many studies have focused on the improvement of converter control methods to reduce the usage or shorten the activation time of hardware protection devices. Part of the methods improve the dynamic performance of DFIG by changing the control parameters. Obviously, the rational design of the control parameters is crucial for the control of the DFIG [14]. Appropriate tuning the proportional integral (PI) controllers is also shown to affect the DFIG LVRT [15]. In addition, it is also a mainstream LVRT solution to change the control structure of the rotor side controller. Ref. [16] proposed the demagnetization control to eliminate the induced voltage by injecting a rotor current opposite to the free and negative flux. In [17], the measurement of negative sequence and free component flux was improved to avoid the delay caused by low pass filter. Ref. [18] proposed a scaled current tracking control for rotor-side converter to enhance its LVRT capacity without flux observation. In [19], virtual resistance is introduced to enlarge the control range, but still can’t adjust the demagnetizing current flexibly. An improved demagnetization control, immune to system parameter variation, is proposed to shorten the

This work was supported by the National Key Research and Development Program of China (2018YFB0904004). ⁎ Corresponding author. E-mail addresses: [email protected] (J. Luo), [email protected] (H. Zhao), [email protected] (S. Gao), [email protected] (M. Han). https://doi.org/10.1016/j.ijepes.2019.105783 Received 16 September 2019; Received in revised form 10 December 2019; Accepted 12 December 2019 0142-0615/ © 2020 Elsevier Ltd. All rights reserved.

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dynamic process [20], but only applied to balanced faults. In [21], the rotor flux linkage is controlled to track a reduced fraction of the changing stator flux linkage. However, the reactive power required by grid code is not involved. The cooperation of the crowbar and the demagnetization are studied in the article [22]. However, the control parameters of the aforementioned control strategies are fixed, which can’t be adjusted flexibly for different grid conditions. Thus, their control performance can’t be guaranteed. To overcome this problem, a demagnetization control based on Explicit Model Predictive Control (E-MPC) is proposed. Model Predictive Control (MPC) can predict future output over a specific prediction horizon based on the system model [23,24]. The main advantage of using MPC is computing the optimal control action while considering system constraints [25]. However, during LVRT, the fault time is very short and MPC is difficult to handle the fast online calculation [26]. In this study, E-MPC is applied to calculate the optimization problem offline and suitable for online calculation [27]. The main contributions of this paper are twofold. Firstly, the demagnetizing current can be optimally derived for various fault conditions to fully explore the capacity of the rotor side converter. Secondly, a simple E-MPC control structure without additional measurement requirements is designed and described in detail. This paper is organized as follows. Section 2 describes the dynamic model of DFIG. Section 3 analyzes the dynamical performance of DFIG under unbalanced conditions. In Section 4, the working principle of conventional demagnetization control is elaborated. The proposed demagnetization control based on E-MPC is designed and presented in detail in Section 5. To verify the proposed strategy, the simulation are carried out in Section 6. The conclusion is drawn in Section 7.

−

isd Rs

ωs ψsq

+

+ Lls +

usd −

+

ωs ψsd

+ usq

− Lls

usq = Rs i sq + urd = Rr i rd + urq = Rr i rq +

dt dψrd dt dψrq dt

ψrd = L m i sd + Lr i rd ψrq = L m i sq + Lr i rq

+ urq

dψrq dt

−

Rr irq

−

−

dψ

dird dt

+

dirq

+ ωr Lm ψsd + Lm dt s  s   erq

dt

L

L

m sd − ωr Lm ψsq Ls dt s   erd

L

L

dψsq

, (3)

L2 Lr − m Ls

is the leakage inductance coefficient. The induced where σ ≜ Lr rotor voltage caused by the stator flux linkage in dq reference frame are denoted by erd and erq , respectively. 3. Dynamical performance of DFIG under unbalanced conditions Due to the direct connection to the grid, it can be considered that →s the stator voltage V s is determined by the grid [28]. By ignoring the →s stator resistance Rs , V s can be written as the sum of the positive sequence and the negative sequence in stator reference frame without considering the zero sequence component,

,

(1)

→s V s = V1 e jωs t + V2 e−jωs t ,

where the flux linkages for stator and rotor are derived by,

ψsd = Ls i sd + L m i rd ψsq = Ls i sq + L m i rq

+

+ Lm

urd = Rr i rd − ωr σLr i rq + σLr

− ωr ψrq + ωr ψrd

ωr ψrd

where usd , usq , i sd , i sq , ψsd , ψsq are stator voltage, current and flux linkage vector in dq reference frame, respectively. urd , urq , i rd , i rq , ψrd , ψrq represent rotor voltage, current and flux linkage vector in dq reference frame, respectively. Rs and Ls are stator resistance and self inductance. Rr and Lr are rotor resistance and self inductance, respectively. L m indicates the mutual inductance, ωs and ωr are grid synchronous angular frequency and the electrical angular frequency of rotor respectively. By substituting (2) into (1), the rotor voltages urd and urq can be calculated by,

− ωs ψsq + ωs ψsd

urd −

Fig. 2. Model of DFIG in dq frame.

The basic structure of DFIG with crowbar and chopper is shown in Fig. 1. The mathematical modelling of DFIG under synchronous rotating reference frame (dq) can be expressed as follows. The equivalent circuits are shown in Fig. 2. dt dψsq

Llr −

+

2. Dynamical model of DFIG

dψsd

Rr ird +

−

dψsq dt

−

−

dψrd dt

−

isq Rs

ωr ψrq

+ Lm

dψsd dt

urq = Rr i rq + ωr σLr i rd + σLr

usd = Rs i sd +

Llr +

(4)

where V1 and V2 denote the amplitudes of the positive and negative sequence of the stator voltage. To be noticed, the superscript “s” in variables represents the stator reference frame. ⎯→ ⎯ s ⎯→ ⎯ s The corresponding generated flux linkages ψ s1 and ψ s2 can be written as,

, (2)

⎯→ ⎯ s ⎯→ ⎯ s V V2 −jωs t ψ s1 = 1 e jωs t , ψ s2 = e . jωs −jωs

(5)

Since the flux linkage should be continuous, the induced free ⎯→ ⎯ component of stator flux linkage after fault ψsf t = 0+ can be derived by,

⎯→ ⎯ s ψf

+

t=0

⎯→ ⎯ s = ψ s1

−

t=0

⎯→ ⎯ s − ψ s1

+

⎯→ ⎯ s − ψ s2

t=0

. t = 0+

(6)

⎯→ ⎯ s ⎯→ ⎯ s ⎯→ ⎯ s Fig. 3 illustrates the relation between ψ s1, ψ s2 , ψ sf under unbalanced fault condition (single phase voltage drop). ⎯→ ⎯ s According to (5) and (6), ψ s during the fault can be expressed by, ⎯→ ⎯ s ⎯→ ⎯ s V e jωs t V e−jωs t + 2 + ψf ψs = 1 −jωs jωs

Fig. 1. The structure of DFIG. 2

t = 0+ e

−t / τ ,

(7)

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R s + Rr

σLr

irrf +

s1

|

s1

| |

s2

+ −

|

s

errf

r vrf

−

s2

s

axis

sf

|

s1

| |

s2

Fig. 5. Rotor equivalent circuit of free component.

|

very large, which result in the over-current on the rotor side and overvoltage on the DC bus. 4. Conventional demagnetization control r r v r2 and → v rf , the demagnetization To counteract the induced voltage → control which injecting a rotor current opposite to the free and negative flux is employed. This method avoids rotor converter saturation and reduces DC bus over-voltage and rotor over-current. ⎯→ ⎯ s ⎯→ ⎯ s → r r v r2 and → v rf are caused by ψ s2 and ψ sf , the current i rde opSince → ⎯→ ⎯ s ⎯→ ⎯ s posite to ψ s2 and ψ sf can be used as the injected demagnetizing current,

axis Fig. 3. The flux linkage when the single phase voltage drops to 0.2 p.u.

where τ =

Ls Rs

is time constant. ⎯→ ⎯ s ⎯→ ⎯ s To study the effect on the rotor side, ψ s2 and ψ sf are transformed to r r ⎯→ ⎯ ⎯→ ⎯ ψ s2 and ψ sf in the rotor reference frame,

e−j (ωs + ωr ) t

e−jωs t

⎯→ ⎯ r V V ψ s2 = 2 e−jωr t = 2 −jωs −jωs

,

⎯→ ⎯ r ⎯→ ⎯ r →r i rde = −k ψ sf − k ψ s2.

(8)

⎯→ ⎯ r ⎯→ ⎯ s ψ sf = ψ sf e−jωr t ,

(9)

where the superscript “r” in variables represents the rotor reference ⎯→ ⎯ r ⎯→ ⎯ r frame. According to the superposition principle, ψ s2 and ψ sf are analyzed separately. ⎯→ ⎯ r r v r2 induced by ψ s2 is According to (3), the rotor voltage → r → v r2 =

+ ⎡Rr + ⎢ ⎣

⎯→ ⎯ r ⎯ r ⎯→ ⎯ r ⎯→ ⎯ r →r L ⎯→ ψ r = m ⎜⎛ ψ s − kσLr ψ sf − kσLr ψ s2⎟⎞ + σLr i r . Ls ⎝ ⎠

Lm 2 Rs ⎛⎜ωr Ls

( )

⎝

5. Demagnetization control based on E-MPC

. →r

→r di + ωs⎞⎟ ⎤ i r2 + σLr dtr2 ⎥ ⎠⎦

The control structure of proposed E-MPC based demagnetization control is shown in the Fig. 8. To be noticed, the following variables are all in the rotor reference frame. Therefore the superscript “r” is ignored

(10)

Considering that (ωr + ωs) is approximately equal to 2, the equivalent circuit of negative sequence can be obtained and shown in Fig. 4. ⎯→ ⎯ r r v induced by ψ is According to (3), the rotor voltage → rf

sf

→r 2 ⎤ →r ⎡ ⎯→ ⎯ s d i rf r L L → v rf = − m jωr ψ f e−jωr t + ⎢Rr + ⎛ m ⎞ Rs ωr ⎥ i rf + σLr dt Ls → ⎥ ⎢ ⎝ Ls ⎠  erf ⎦ ⎣ ⎜

s1

⎟

(11)

s s

σLr

axis

Considering that ωr is approximately equal to 1, the equivalent circuit of free component can be obtained and shown in Fig. 5. →r →r According to (10) and (11), the induced voltage v r2 and v rf can be

Rr + 2Rs

(13)

The control diagram of conventional demagnetization control is shown in Fig. 7.

Lm ⎡ ⎛ ⎜ωr Ls ⎢

+ ωs⎟⎞ V2 e−j (ωr + ωs) t ⎤ ⎥ ⎣⎝ ⎠  ⎦→   er2

(12)

⎯→ ⎯ → The demagnetizing current i rde produces a magnetic flux ψdef to ⎯→ ⎯ opposite the free flux linkage and a magnetic flux ψde2 to opposite the ⎯→ ⎯ negative flux linkage. These effects on ψs are shown in Fig. 6. ⎯→ ⎯ →r The rotor flux ψr with i rde can be derived by,

irr2

s2

sf def

de2

+ + −

err2

r vr2

− axis Fig. 4. Rotor equivalent circuit of negative sequence.

Fig. 6. Flux linkage with demagnetizing current. 3

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filter. Since ψsf is DC amount, there is no error in the phase. Accordingly, ψs2 can be obtained by subtracting ψsf which has no error in the phase. In such way, the effect of demagnetization control can be improved. 5.2. Predictive model By substituting (2) into (1), the state space model can be derived as,

⎧

dψsd dt

⎨ dψsq ⎩

dt

= usd −

Rs ψ Ls sd

+

Lm Rs i Ls rd

+ ωs ψsq

= usq −

Rs ψ Ls sq

+

Lm Rs i Ls rq

− ωs ψsd ∗ i rd

The control input references

Fig. 7. Control diagram of conventional demagnetization control. ∗ ⎧i rd i∗ ⎨ ⎩ rq

∗ i r1d ∗ i r1q

= =

+ +

∗ i r2d ∗ i r2q

+ +

.

and

(16) ∗ i rq

∗ i rfd ∗ . i rfq

are composed by,

(17)

are used to suppress free flux component and are where used to suppress negative flux component. According to the symmetrical component method, the negative and free components of (16) can be expressed separately, ∗ ∗ i r2d , i r2q

∗ ∗ i rfd , i rfq

⎧

dψs2d dt

⎨ dψs2q ⎩

dt

dψsfd

= us2d−

Rs ψ Ls s2d

+

Lm Rs i Ls r2d

+ ωs ψs2q

= us2q−

Rs ψ Ls s2q

+

Lm Rs i Ls r2q

− ωs ψs2d

=−

Rs ψ Ls sfd

+

Lm Rs i Ls rfd

+ ωs ψsfq

⎨ dψsfq = − ⎩ dt

Rs ψ Ls sfq

+

Lm Rs i Ls rfq

− ωs ψsfd

⎧

dt

, (18)

. (19)

It should be noted that the stator voltage usd , usq does not contain a free component. By introducing incremental variables (labelled by Δ ), (18) and (19) can be transformed into,

Fig. 8. Control diagram of E-MPC based demagnetization control.

for simplicity.

⎧ 5.1. Free and negative flux measurement

⎩

∫ ⎛vs − Rs is⎞ dt. ⎜

⎟

⎝

⎠

⎧ ⎨ ⎩

ψs −

= ψs1 + ψs2 + ψsf −

= ψs1 + ψs2 + ψsf −

⎝ = 2ψs2 + ψsf

− jψs2⎞⎟ ⎠

Lm Rs Δi r2d Ls

+ ωs Δψs2q

R − L s Δψs2q s

Lm Rs Δi r2q Ls

− ωs Δψs2d

s

dt

=

dΔψsfd dt dΔψsfq dt

+

R

= − L s Δψsfd + s

R

= − L s Δψsfq + s

,

Lm Rs Δi rfd Ls

+ ωs Δψsfq

Lm Rs Δi rfq Ls

− ωs Δψsfd

(20)

. (21)

x ≜ [Δψs2d , Δψs2q , Δψsfd , Δψsfq]T u ≜ [Δi r2d , Δi r2q , Δi rfd , Δi rfq]T .

(22)

By applying the sampling time Ts , according to the discretization method described in [29]. The LTI system (22) can be transformed into a discrete-time form,

⎛ ⎞ ⎜ψs1 + ψs2 + ψsf ⎟ ⎝ ⎠

1 ⎛ ⎜jψs1 jωs

R

x ̇ = Ax + Bu y = I4 × 4 x

(14)

1 d jωs dt

= − L s Δψs2d +

The state space form of the Linear Time-Invariant (LTI) system can be finally written as,

The ψsf can be extracted through the low-pass filter. A linear combination of these two quantities ψsf + 2ψs2 can be directly estimated by stator current i s and stator voltage vs . 1 dψs jωs dt

dt

⎨ dΔψs2q

It is key to accurately measure free flux (ψsfd , ψsfq ) and negative flux (ψs2d , ψs2q ) in proposed method. The low pass filter can cause amplitude and phase errors during LVRT. In this study, the low pass filter is only used for ψsf . The measurement method adopted in this paper is shown in Fig. 9. The total stator flux is obtained by

ψs =

dΔψs2d

.

⎧ x (k + 1) = Ad x (k ) + Bd u (k ) , ⎨ y (k ) = Cd x (k ) ⎩ (15)

(23)

where Ad , Bd , Cd are the discrete forms of A, B, I4 × 4 in (22), respectively.

In order to get their respective values, ψsf is measured by a low pass

5.3. Constraints of E-MPC ∗ ∗ The rotor current references i rd and i rq are limited by the capacity of the rotor side converter, ∗2 ∗2 i rd + i rq ⩽ ilim ,

Fig. 9. Measurement structure of flux. 4

(24)

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Δψs2d (k ) = S1 y (k ), S1 = [1, 0, 0, 0] Δψs2q (k ) = S2 y (k ), S2 = [0, 1, 0, 0] Δψsfd (k ) = S3 y (k ), S3 = [0, 0, 1, 0] Δψsfq (k ) = S4 y (k ), S4 = [0, 0, 0, 1]

, (30)

the MPC problem at time t can be formulated as follows, np

min u

⎛ 2 2 ⎜ ‖ψs2d (k ) + S1 y (k )‖Q T + ‖ψs2q (k ) + S2 y (k )‖Q T , ⎝ + ‖ψsfd (k ) + S3 y (k )‖Q2 F + ‖ψsfq (k ) + S4 y (k )‖Q2 F )

∑

k=0

(31)

subject to (23) and (26), k ∈ [0, …, n p]. 5.5. Implementation of E-MPC In this part, the control rule of E-MPC is derived. The partitions that are calculated offline are highly correlated with the prediction horizon n p and sampling time Ts . Too many partitions will increase the time for online search and slow down the calculation. Under the premise of guaranteeing the effect, n p is chosen as 3 and Ts is set to 0.0005 s. The state partition map and the corresponding optimal control algorithm are obtained by offline calculation. In this paper, 29 regions are divided. The partition map of E-MPC is shown in Fig. 11. Each different color region represents an optimized control algorithm. In online calculation, the corresponding optimal control algorithm can be found by finding the partition in which the current state variable of the system is located. Thereby E-MPC greatly reduce the solution time and meet the calculation requirements of the transient period.

Fig. 10. Constraints of rotor current references. ∗ ∗ ⎧i rd = i r1d + i r2d + i rfd + Δi r2d + Δi rfd . ∗ ∗ i = i r1q + i r2q + i rfq + Δi r2q + Δi rfq ⎨ ⎩ rq

(25)

The nonlinear constraint (24) can be considered as a circle with i rd and i rq as the horizontal and vertical axis. The radius of the circle is ilim . In order to be implemented in E-MPC, Eq. (24) can be approximately represented by a series of linear constraints. In this study, 8 linear constraints surrounding the circle is used, as shown in Fig. 10.

⎧ − ⎪ ⎪ − ⎨ ⎪ ⎪ ⎩

∗ ∗ 2 ilim ⩽ i rd + i rq ⩽

2 ilim

∗ i rd

2 ilim

2 ilim ⩽

−

∗ i rq

⩽

∗ − ilim ⩽ i rd ⩽ ilim ∗ − ilim ⩽ i rq ⩽ ilim

.

6. Cases study (26)

A 1.5-MW DFIG-based system is built in MATLAB/ Simulink to verify the proposed control strategy. The DFIG parameters are shown in Table 1. To show the control performance, simulation is carried out under both balanced and unbalanced faults with three controllers: without demagnetization (labelled by “Control 1”), conventional demagnetization control (labelled by “Control 2”) and E-MPC.

5.4. Design of cost function The goal of E-MPC is to minimize ψs2d , ψs2q , ψsfd and ψsfq . The objective function can be written as follows,

‖ψs2d + Δψs2d ‖Q2 T + ‖ψs2q + Δψs2q ‖Q2 T + ‖ψsfd + Δψsfd ‖Q2 F + ‖ψsfq + Δψsfq ‖Q2 F

6.1. Balanced faults

, (27)

In this part, a balanced voltage drop at the grid side is set to 0.5 p.u. at t = 1 s , and the simulation results are shown in Fig. 12. From the results, it can be seen that the proposed control method reduces the

where Q T and QF are the weighting factors. Ideally, the free flux component (ψsfd , ψsfq ) and negative flux component (ψs2d , ψs2q ) are expected to be all minimized. However, there → → exist control input constraints (26). The induced voltages er2 and erf by negative and free flux components are different. According to (10), (11) → → the ratio of er2 and erf is,

→ er2 = → e rf

Lm ⎡ ⎛ ⎜ωr Ls ⎢

+ ωs⎟⎞ V2 e−j (ωr + ωs) t ⎤ ⎥ ⎠ ⎦, ⎯→ ⎯ s −jωr t ⎞ Lm ⎛ ⎜ − jωr ψ f e ⎟ Ls ⎝ ⎠

⎣⎝

(28)

where ωr = 1 − s, ωs = 1, and s ∈ [−0.3, 0.3]. Accordingly, Eq. (28) can be approximated as,

⎯→ ⎯ ⎯→ ⎯ → (ωr + ωs) ψs2 2 ψs2 er2 ≈ ≈ ⎯→ ⎯ . ⎯→ ⎯ → esr ωr ψsf ψsf

(29)

According to (29), it is obvious that the induced voltage caused by ⎯→ ⎯ ⎯→ ⎯ ψs2 is twice than that caused by ψsf . For the perspective of the induced voltage minimization, the optimal weighting factor ratio of Q T and QF can be set as 4:1. The prediction horizon is n p and k indicates the prediction index. By defining,

Fig. 11. Reduced partition for E-MPC for ψs2d and ψs2q (other variables are set to 0). 5

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Table 1 Parameters of 1.5-MW DFIG. Rated power Stator voltage Mutual inductance Stator leakage inductance Rotor leakage inductance Stator resistance Rotor resistance

1.5 MW 575 V 2.9 p.u. 0.18 p.u. 0.16 p.u. 0.023 p.u. 0.016 p.u.

Fig. 13. Single phase fault to 0.8 p.u. (a) Stator active power. (b) Stator reactive power. (c) Electromagnetic torque. (d) Amplitude of rotor current. (e) DC bus voltage.

the conventional vector control, the ripple of electromagnetic torque exceeds 1 p.u. during the entire failure. When a balanced fault occurs, only the free component flux is induced. Among these controllers, since there is no demagnetization control in Controller 1, the damping speed of the free component ψsf is quite slow. Comparably, the damping speed of ψsf based on E-MPC is the fastest, as shown in Fig. 12(d). The similar phenomenon can also be observed in Fig. 12(e) and (f). E-MPC shows the best performance. The oscillations of rotor current Ir and DC bus voltage VDC are damped rapidly and significantly. The range of VDC can be limited within 1130 V to 1160 V after t = 1.1 s . During the faults, the energy flowing into the DC link can be reduced effectively with EMPC, and the DC chopper and crowbar has to be activated for only a short period. 6.2. Single phase faults Fig. 12. Balanced fault to 0.5 p.u. (a) Stator active power. (b) Stator reactive power. (c) Electromagnetic torque. (d) Amplitude of ψsf . (e) Amplitude of rotor currnet. (f) DC bus voltage.

The most common fault in the power grid is single phase fault. Negative sequence components and free components will generate simultaneously in the stator flux linkage. A single phase voltage drop at the grid side is set to 0.8 p.u. at t = 1 s , and the simulation results are shown in Fig. 13. It can also be seen that the stator active and reactive power output will oscillate smaller during the fault with the E-MPC. Different from the symmetric fault, because the negative sequence component always exists, it must

output of stator active power and increases the output of stator reactive power. Therefore, it can support the recovery of the terminal voltage after the fault occurs 0.05s. The electromagnetic torque is smooth under the proposed control strategy as shown in Fig. 12(c). In contrast, with 6

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Fig. 15. Single phase fault to 0.4 p.u. (a) Amplitude of rotor current. (b) DC bus voltage.

Fig. 14. Single phase fault to 0.6 p.u.. (a) Amplitude of rotor current. (b) DC bus voltage.

always be offset by the demagnetizing current, and it can not send more reactive power during the fault. The oscillation of the electromagnetic torque under the proposed control method is much smaller as shown in Fig. 13(c). The magnitude of the oscillation is reduced by about 40 percent. Among all these controllers, the damping speed of the rotor current Ir is the fastest as shown in Fig. 13(d). In comparison, it has better demagnetization effect than Control 2. Similarly, E-MPC can best suppress the oscillation of DC bus voltage compared with Control 1 and Control 2 in Fig. 13(e). The Ir can always be limited within 1 p.u. while VDC does not exceed 1170 V. In the following, due to space limitations, only the rotor current and DC bus voltage values will be displayed under different fault levels. A single phase voltage drop at the grid side is set to 0.6 p.u. at t = 1 s , and the simulation results are shown in Fig. 14. The Ir of Control 1 oscillates at 1.5 p.u.. Control 2 has a little demagnetization effect, but still can not meet the current value requirements. Compared with the other two controls, the oscillations of rotor current Ir based on E-MPC is damped rapidly and significantly. After t = 1.1 s, Ir can be limited within 1 p.u.. The proposed control can reduce the time of activation of the crowbar, thereby providing reactive power and supporting grid voltage recovery. As shown in Fig. 14(b), the same phenomenon which E-MPC has the best control effect can also be observed. Among three controllers, the oscillation amplitude of VDC using E-MPC is the minimum. A single phase voltage drop at the grid side is set to 0.4 p.u. at t = 1 s , and the simulation results are shown in Fig. 15. Ir of Control 1 is the largest, and Ir of E-MPC is slightly lower than Control 2 as shown in Fig. 15(a). Compared with other controllers, E-MPC can better suppress VDC oscillation as shown in Fig. 15(b). In addition to the moment the fault begins, VDC can be limited within 1200 V. However, the magnitude of the current of all controllers have exceeded the limit of the rotor side converter. It is indicated that the limit of the capacity of the rotor side converter has been reached at this time, and crowbar need be put into use to achieve LVRT.

Fig. 16. Phase to phase fault to 0.8 p.u.. (a) Amplitude of rotor current. (b) DC bus voltage.

shown in Fig. 16(b). E-MPC enables the DFIG to have better dynamics behaviours during unbalanced faults. A phase to phase voltage drop at the grid side is set to 0.6 p.u. at t = 1 s , and the simulation results are shown in Fig. 17. Compared with Control 1 and Control 2, E-MPC has the best effect which can limit Ir to less than 1 p.u. after t = 1.1 s as shown in Fig. 17(a). Capability of the rotor-side converter can be fully explored to achieve LVRT. And the oscillation of VDC can be significantly suppressed as shown in Fig. 17(b). Under this circumstance, crowbar will not be activated so that the rotor side converter will not lose control and the DFIG is able to provide reactive power during the fault. A phase to phase voltage drop at the grid side is set to 0.4 p.u. at t = 1 s , and the simulation results are shown in Fig. 18. E-MPC can better suppress Ir compared to Control 1 and Control 2 as shown in Fig.18(a). However, Ir of the three controllers all exceed the limit value, which means that at such a fault depth, it is not possible to rely solely on the rotor converter to complete the LVRT. Hardware

6.3. Phase to phase faults A phase to phase voltage drop at the grid side is set to 0.8 p.u. at t = 1 s , and the simulation results are shown in Fig. 16. Comparably, the damping speed of Ir based on E-MPC is the fastest, as shown in Fig. 16(a). The oscillation of VDC can be significantly suppressed as 7

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and reduce the activation time of the crowbar and the chopper. 7. Conclusion In this paper, the demagnetization control based on E-MPC is proposed to enhance the LVRT capability of DFIGs. The proposed E-MPC can flexibly adjust the demagnetizing current under different fault conditions and fully explore the capability of rotor side converter. Based on the offline derived calculation parameters, the designed EMPC can speed up solving the optimization problem significantly, which is very suitable for online control application. The control structure of proposed E-MPC is simple and easy to be implemented. The simulation results show that the proposed E-MPC can significantly reduce the free and negative sequence flux. Accordingly, rotor over-current and DC bus over-voltage can be effectively suppressed. With the proposed E-MPC, the usage of the hardware protection such as crowbar can be largely reduced. So that the rotor converter will not lose control during the fault period, and the DFIG will output reactive power to support grid voltage recovery. Declaration of Competing Interest Fig. 17. Phase to phase fault to 0.6 p.u.. (a) Amplitude of rotor current. (b) DC bus voltage.

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Fig. 18. Phase to phase fault to 0.4 p.u.. (a) Amplitude of rotor current. (b) DC bus voltage.

protection such as crowbar must be activated. The similar phenomenon can also be observed in Fig. 18(b). E-MPC shows the best performance. The oscillation of VDC is damped rapidly. 6.4. Discussion As shown above, under symmetrical faults, the proposed control scheme can significantly suppress the oscillation of the electromagnetic torque DC bus voltage and suppress the amplitude of the rotor current. Under asymmetrical faults, simulation experiments were performed to verify the reliability of E-MPC at different depths. Obviously, under the three fault depths, the E-MPC can effectively reduce the amplitude of the rotor current and suppress the oscillation of the DC bus voltage. However, when the fault level reaches 0.4, although the E-MPC can play a demagnetizing effect, the rotor current and DC bus voltage still exceed 1p.u. and 1200 V. Therefore, the proposed E-MPC can improve the demagnetization effect within the limit of the converter capacity 8

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