Sliding Mode Controller-Based BFCL for Fault Ride-Through Performance Enhancement of DFIG-Based Wind Turbines

Department of Electrical Engineering, Faculty of Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran Department of Electrical Engineering, University of Zanjan, Zanjan, Iran Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran


Introduction
Due to the increment of energy demand and depletion of fossil fuels, the demand for electric power generations from renewable energy resources (RESs) is gradually growing [1,2]. e electric power generation from wind energy is growing so quickly, which can be mostly credited to DFIG-based wind turbines (WTs) due to some advantages such as using partial converter ratings (25-30%) of the nominal-rated wind generator, decoupled active and reactive power control, variable speed operation, low cost, and weight [3]. However, under grid fault conditions, the stator current increases due to the direct connection of the DFIG stator windings to the grid. It results in the transient rotor overcurrent and DC-link overvoltage due to magnetically coupling of the stator and rotor circuit.
is may lead to damage in the rotor-side converter (RSC) of the DFIG and disconnecting from the grid [4,5]. is contrasts with the fault ride-through (FRT) requirement.
is requirement states that the WTs must stay connected when the connecting point voltage remains above limit line 1, as shown Figure 1. Also, in the above limit line 2, all WTs should be able to experience a fault without disconnection [6].
e research results confirm that SFCLs offer a promising solution to meet the FRT requirements of the DFIGs. However, they require high construction cost.
In [28], the BFCL with a discharging resistor in the DC side is used to enhance the FRT performance for the first time. In [29,30], scholars have changed the BFCL configuration by inserting the discharging resistor in the AC side of the BFCL as the limiting impedance to enhance the FRT performance of the DFIG. From this view, BFCLs with different limiting impedances from the ones used in [28] have been proposed. In [31], a parallel resonance circuit is used as the limiting impedance instead of the discharging resistor to enhance the FRT performance of the DFIG. Kartijkolaie et al. and Firouzi and Gharehpetian [32,33] proposed a capacitor as the limiting impedance to provide the reactive power for supporting the DFIG terminal voltage under fault condition.
In all of them, the BFCL inserts the limiting impedance in the fault path to reduce the voltage sag at the coupling point voltage for FRT enhancement under fault conditions. However, the power system has dynamic nonlinear characteristics, especially under fault conditions. Furthermore, the connection of DFIG-based WTs by the nonlinear power electronic converters makes it more nonlinear [17]. erefore, the integration of a nonlinear controller to the BFCL instead of the conventional linear controllers can enhance the FRT performance of the DFIG under fault conditions. Considering this matter, this paper presents a sliding mode controller-(SMC-) based BFCL to enhance the FRT performance of the DFIG. To achieve this, a nonlinear SMC is designed and implemented to the BFCL to enhance the FRT response of the DFIG under grid fault condition. e efficiency of the SMCbased BFCL is verified by time-domain simulations in the PSCAD/EMTDC software environment. Also, the FRT performance of the SMC-based BFCL is compared with the conventional and PI controller-based BFCL under both symmetrical and asymmetrical short-circuit faults. e wind turbine, drive train, generator model, and its controller are the main parts of the DFIGbased WT and are modelled as follows.

Aerodynamic Modeling of the Wind Turbine.
ere are two wind turbine models in the master library of PSCAD/ EMTDC software. In this study, the mode 2 wind turbine model is used. In this model, the captured mechanical power (P m ) from the conversed wind power is expressed by the following equation [34]: where ρ, R, and V w represent the air density, radius of blades, and wind speed, respectively. C p is the power coefficient and is expressed by where λ and β are the tip speed ratio and pitch angle, respectively. Also, the drive train model used in this study is based on the commonly two-mass model [35] as demonstrated in Figure 2(b), which is described by the following:  where T t and T g are the mechanical turbine and electromagnetic generator torque, respectively, H t and H g are the equivalent turbine-blade and the generator inertia, respectively, ω t and ω g are the turbine and the generator angular speed, respectively, and K tg , D tg , and δ tg are the shaft stiffness, the damping constant, and the angular displacement between two ends of the shaft, respectively [34,35]. Figure 2(a), the DFIG consists of the wounded rotor induction generator (WRIG), the rotor-side converter (RSC), DC link, and grid-side converter (GSC). Considering the equivalent circuit of the DFIG as depicted in Figure 2(c) and using the dq synchronous reference frame, the d-q components of the voltage and flux equations of the DFIG are expressed as follows [7]: Complexity 3

DFIG Model and Control System. As demonstrated in
where L s � L s L m /(L s + L m ) and L r � L r L m /(L r + L m ). i dqs and i dqr are the d-q components of the stator and rotor currents. ω s and ω r are the supply and rotor angular frequencies, respectively. Also, the GSC and DC link dynamic equations are expressed as follows: In this case, P g and Q g are In addition, the active and reactive output power of the DFIG is defined as follows: Figure 2(c) demonstrates the control system of the DFIG under steady-state condition. e main objective of the RSC is controlling the output active power (P s ) and reactive power (Q s ) by regulating q-and d-axis components of the rotor currents (i.e., i qr and i dr ), respectively. To achieve this capability, the GSC regulates the DC link and coupling point voltage in the reference values by controlling the q-and daxis components of the stator currents (i.e., i qs and i ds ), respectively.

SMC-Based BFCL
In [28], the application of the BFCL is proposed to enhance the FRT performance of the wind turbine for the first time. In this structure, the limiting resistor is configured in the DC side of the BFCL. It can control the DC reactor current to regulate the PCC voltage. In this paper, a SMC is implemented to the BFCL to regulate the terminal voltage at the determined value for different voltage sag levels by controlling the DC reactor current. e power circuit, principle operation, and designing of SMC for the BFCL are described as follows.

BFCL Power Circuit.
e power circuit of the BFCL is illustrated in Figure 3. It includes the following elements: (1) A three-phase bridge rectifier including diodes D 1 -D 6 (2) An IGBT switch, which is represented by T to switch the limiting resistor (3) A DC reactor L D to limit the rate of increasing of fault current and di/dt (4) A limiting resistor (R) (5) ree single-phase series coupling transformers (T a , T b , and T c )

Principle Operation of the BFCL.
Based on the situation of the IGBT switch, two paths, low impedance path (LIP) and high impedance path (HIP), are provided to carry the normal and fault operation mode currents. Figure 3 Figure 3(c) demonstrates the DC reactor current path in this mode. In this condition, the BFCL generates some power losses and voltage drop due to the BFCL switches and DC reactor resistance, which are negligible. When a fault occurs, the line current and subsequently the DC reactor current start to increase. Figure 3(c) demonstrates the DC reactor current path in this mode (t 0 < t < t 1 ).
When the DC reactor current reaches to i 1 , the control system of the BFCL opens T to insert the limiting resistor in the fault path. In this condition (t > t 1 ), i d flows through the HIP. erefore, i d and subsequently i L are limited under fault condition [36][37][38][39].

PI and Conventional Controller-Based BFCL.
In the conventional control approach of the BFCL, the PCC voltage is used as a control signal. Figure 4(a) demonstrates the conventional control system of the BFCL. Under the steadystate operation of the system V PCC > V TH , T is turned on, and the LIP carries the line current. When V PCC < V TH , T is turned off to force the fault current towards the HIP and limits the fault current. Figure 4(b) demonstrates the PI control system of the BFCL. In this approach, the PI controller is used to regulate the terminal voltage at the reference value.

Design and Implementation of the SMC to the BFCL.
In recent years, nonlinear controllers due to their good performances in parametric uncertainties and unmodeled dynamics are extended. One of the main powerful controllers is SMC which has a robust performance for unmodeled and noisy systems [40][41][42][43]. Consider the single input-single output system by the following state equation: 4 Complexity Complexity where x and u are the state variable and system input, respectively. f(x) and b(x) are bounded nonlinear functions of state variables. Let x � x − x d be the trajectory error in state x. e time-varying sliding surface for the system is chosen as where Λ is a strictly positive constant and n is the order of the system. By satisfying the following term, the trajectories of the system are remained in the sliding surface: where µ is strictly positive. e above equation can be rewritten as follows: According to (17), the reaching time will be as follows: where t reach is the reaching time. To satisfying (17), generally, _ s is considered as follows: where K is the positive constant. In [42], to decrease the reaching time and the chattering phenomenon in the input controller, the variable gain was used which was known as the exponential reaching law (ERL). Hence, according to Firouzi et al. [43], (16) can be rewritten as where where 0 < α < 1, 0 < β. Hence, the reaching time will reduce to the following term: In order to design the BFCL controller, the average model of the system is used. By using Kirchhoff's voltage law (KVL) in the DC side of the BFCL circuit, it can be written for each phase the following equation: where i d is the reactor DC current, V d is the DC side voltage. It should be note that the value of R D can be varied by the value of the modulation index (M i ). Hence, M i can be defined as follows: By inserting (25) in (24), (24) can be rewritten as follows: e sliding surface of the DC-link current of the BFCL is defined as By taking the time derivative of (27), it becomes To eliminate the tracking error, the sliding surface and time derivative of it must be zero. Hence, it can be written as Stability proof: to prove the stability of the controller, (14) should be satisfied. Hence, by using (27)-(29), (14) will be satisfied as follows: It shows that the designed controller is stable. To provide the T gate signal, the modulation index (M i ) obtained from (29) is compared with the triangular signal. e triangular frequency is set to be 1 kHz as shown in Figure 4(c).

DC Reactor Design.
e main purpose of using the DC reactor in the BFCL circuit is limiting the rate of increase of fault current before fault detection time. e cost and inductance of the DC reactor are decisive factors. High value of the DC reactor inductance results in high power losses and cost, which are not acceptable. However, the inductance value of the DC reactor should be sufficient to achieve this purpose. Considering Figure 3(c), which presents the equivalent circuit during t 0 < t < t 1 time, the DC reactor current is approximately given by the following equation: where r � r D and L � L D . Considering (t 1 -t 0 ) as the necessary time for increasing fault current from i 0 to i 1 and solving (31), the inductance value of the DC reactor is obtained by the following equation: V D is the mean value of the source voltage on the DC side of the bridge circuit and is approximately as follows: where V m is the magnitude of the source voltage. Furthermore, by determining t 1 and i 1 , the DC reactor inductance is designed.

Complexity
3.6. Limiting Resistance Design. When a fault occurs, the BFCL inserts the limiting resistor (R D ) in the fault path to dissipate the excess output active power of the DFIG (P G ) during the fault. To make sure the least disturbance reaches to the DFIG during the fault, R D should be sufficient to dissipate the active power transferred by the faulted line. erefore, the active power dissipated by the BFCL (P D ) should be equal with P G during the fault. P D is determined as follows: Using (34), the minimum value of R D can be derived as follows:

Simulation and Discussion
To verify the proposed SMC-based BFCL performance, the system shown in Figure 5 is used. It includes a 2 MW DFIGbased wind turbine, which is connected to the main grid through a step-up 0.7 kV/13.8 kV transformer. Both symmetrical three-line-to-ground (3LG) and asymmetrical single-line-to-ground (SLG) short-circuit faults were applied at the PCC bus to evaluate the capability of the proposed SMC-based BFCL. e simulated system and DFIG parameters are illustrated in Table 1. Both short-circuit faults occur at t � 10s and continue for 150 ms. V T represents the terminal voltage in Figure 5. Simulations were performed for the following cases: Case A: using the conventional-controller BFCL Case B: using the PI-controller BFCL Case C: using the sliding mode controller BFCL Figure 6 demonstrates the performance of the BFCL for three cases under 3LG fault condition. In this condition, the PCC voltage drops to zero, approximately. As demonstrated in Figure 6(a), the BFCL performances in three cases have the same trend in response to severe voltage sag. However, the SMC-controlled BFCL has the lowest voltage sag and oscillation in the fault period. Figure 6(b) demonstrates the DFIG active power for three cases. In cases A and B, the active power drops to 0.8 pu in the fault period, approximately. Also, it is increased to 1.5 pu after fault clearance in case A. However, it has the lowest fluctuation in case C by using the SMC-controlled BFCL. Figure 6(c) demonstrates the DFIG speed under this condition. It demonstrates the least rotor speed deviation for case C. Figure 6(d) demonstrates the DC link voltage of the DFIG under this condition. It can be seen from this figure that the DC link voltage remains constant during and after fault by using the SMCcontrolled BFCL. Figure 7 demonstrates the DFIG stator current under this condition. It can be seen from this figure that the fault current is limited in 0.4 pu. In cases B and C, the fault current is 0.5 pu, and they have the same trend. However, the SMCcontrolled BFCL has superior performance in both ends of the fault period.     using the SMC-based BFCL, the terminal voltage is controlled at the reference level by controlling the DC reactor current. Figure 8 Figure 9 demonstrates the DFIG stator current for three cases under this condition. In case A, the fault current is lower than the per-fault current due to full insertion of the limiting impedance in the fault path. In cases B and C, the fault current is limited in 0.5 pu; however, the SMC-based BFCL has superior performance under fault condition.

Conclusions
In this paper, a sliding mode controller has been designed to control the BFCL for enhancing the FRT capability of the DFIG-based wind turbine under severe and low voltage sag levels. e DC reactor current of the BFCL has been considered as a state variable in the SMC to control the DFIG terminal voltage. Also, to show the efficiency of the proposed SMC-based BFCL, its performance has been compared with the PI-and conventional controller-based BFCL. Based on the PSCAD/EMTDC simulation results, the following points are obtained: Data Availability e PSCAD file data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.