Low-Voltage Ride-Through Strategy to Doubly-Fed Induction Generator with Passive Sliding Mode Control to the Rotor-Side Converter

Abstract

The doubly-fed induction generator (DFIG) is vulnerable to overcurrent at the stator winding and overvoltage at the DC link due to voltage drop after the grid fault. The large wind farm may have a capacity of several million MWs, whose tripping yields a notable power imbalance and frequency drop in the power systems, which may be avoided by the low-voltage ride-through (LVRT) strategies implemented with the hardware or software. The latter has the merits of low cost and easy to realize, thus studied in this paper. Considering the grid fault uncertainty and DFIG parameters’ correlation, this paper newly introduces the sliding mode structure into the passive control to improve the performance of the inner current control loop of the rotor-side converter (RSC), thus proposing a passive sliding mode control (P-SMC) based RSC control strategy to improve the LVRT capability of the DFIG. The time domain analysis with different fault severities, i.e., voltage drops, at the point of public coupling (PCC) is performed. The simulation results with the P-SMC control or not are obtained and compared to verify the control effect and the robustness of the proposed LVRT strategy. This study is beneficial for maintaining power system security against fast-increasing wind power.

1. Introduction

1.1. Background of This Paper

With the overuse of fossil fuels, wind and solar energies are now paying more attention [1,2,3]. At present, the popular type of wind turbine generator (WTG) is the double-fed induction generator (DFIG) and the permanent magnet synchronous generator. The DFIG has the merits of variable speed, flexible control and low cost for the converters [4,5].

The low-voltage ride-through (LVRT) code requires the WTGs to maintain grid integration against voltage drop at the point of common coupling (PCC) [6,7,8]. Unlike thermal synchronous generators with strong excitation capacity, conventional wind turbines cannot provide reactive power support for the grid when the voltage drops at the integrated point, so they may be taken off the grid under the action of low-voltage protection or overcurrent protection. Due to the increasing penetration rate of wind power, the off-grid state of the WT will aggravate the fault degree of the power system. Therefore, the wind farm grid-connected specification puts forward the requirements of low-voltage crossing for wind turbines [9,10,11,12]. At present, there are also many studies aimed at improving the LVRT characteristics of DFIG.

At present, the research on the implementation of low-voltage ride-through in DFIG mainly focuses on four aspects: (1) Improving the hardware structure of DFIG and improving its ability to cope with electromagnetic shock and electromechanical disturbance when the grid voltage drops. For example, adding crowbar resistance, using series rotor brake resistance, etc.; (2) Improving the traditional control strategy of the DFIG converter, improving the dynamic characteristics and response-ability of the control system, and suppressing the rotor overcurrent when the grid voltage drops; (3) Adding shunt capacitor banks, SVC, STATCOM and other reactive power compensation devices to improve the low-voltage ride-through capability of DFIG; (4) Study the interaction between power grid and DFIG that realizes LVRT, and determine the best ride-through scheme.

1.2. Literature Review and Comparison

In terms of hardware, the most commonly used method is to attach a crowbar to the rotor side of DFIG [13,14]. Based on research into the protection switching scheme for pry rods [15] indicated that the impact of pry rod input on the system includes maintaining a connection between the wind farm and the grid, which facilitates system recovery. However, once the pry bar is engaged, the turbine operates asynchronously and absorbs reactive power, hindering system recovery. The authors of [16] analyzed the operational mechanism of DFIG in case of power grid failure. By incorporating the threshold value of rotor side current for DFIG, a two-stage division is established for DFIG wind farm operation with and without engaged pry bars, along with an equivalent model to accurately represent parameter changes such as voltage during power grid failure. In [17], focusing on the accurate calculation of short circuit current resulting from delayed engagement of pry bar protection when voltage drops during asymmetric faults, mathematical analysis was conducted before and after activation of pry bar protection to derive expressions for short circuit current throughout the fault process. The influence of timing for pry bar protection activation on DFIG short-circuit current characteristics is examined to provide guidance for setting speed parameters for pry bar protection activation.

Crowbar protection is low-cost and easy to implement. However, the DFIG cannot provide reactive power and needs to absorb a large amount of reactive power to supplement AC excitation when the protection is used [8]. Aiming at the deficiencies of crowbar protection, reference [18] proposed a rotor series damping resistance control strategy to rationally distribute active and reactive power of DFIG during LVRT and improve the recovery speed of voltage drop. Considering that it is difficult for a single fixed resistor to satisfy the LVRT effect of DFIG when all voltage drop depths are met, a fuzzy switching control strategy for rotor tandem dual dynamic resistor is proposed in the literature [19]. To improve the LVRT performance of DFIG, a more comprehensive and accurate dual resistor input rule is formulated by comprehensively weighing the voltage drop depth and rotor current threshold.

One study [20] simulated and analyzed the transient output characteristics of double-fed wind turbines with SVC under different fault types of the power grid and found that SVC increased the output voltage of DFIG while increasing the short-circuit current provided to the system. Another study [4,21] proposed a strategy for low-voltage ride-through using DFIG assisted by the dynamic voltage regulator. The authors of [22] proposed a DFIG low-voltage ride-through scheme for supercapacitor energy storage. The authors of [23,24] found that series brake resistances or STATCOM can increase the terminal voltage of a DFIG machine, thereby improving its LVRT capability.

In terms of software, the control strategy of the grid-side converter (GSC) is improved to suppress direction current (DC) overvoltage caused by rotor current fluctuation. In literature [25], a compensation item that can reflect the instantaneous power change on the rotor side is added to the reference value of the GSC current inner loop to suppress DC voltage fluctuations. Aiming at the three-phase voltage symmetric low-drop fault at the junction point [26] improved the control of wind turbines and proposed an independent pitch control strategy, which enhanced the flexibility of pitch angle adjustment and reduced the capture of wind energy during LVRT. The authors of [27] propose a new grid-connection strategy based on the active disturbance rejection controller, which enhances the LVRT capability of the unit and reduces the influence of grid faults on the unit. Other studies [28,29] put forward a new control strategy that changed the control mode of the systems’ grid-side converter to give full play to the role of the full-power converter and adjust the generator stator voltage, stator voltage and DC capacitor voltage to be controlled by the machine-side converter, while the grid-side converter tracks the change of wind energy. The authors of [30] adjusted the control method of the side-converter and adopted type-2 fuzzy control during LVRT to convert the unbalanced power into the mechanical energy of the motor rotor and stabilize the DC voltage. The authors of [31] proposed a power balance joint control strategy to coordinate the control of the rotor-side converter (RSC) and GSC to improve the transient DC voltage control characteristics.

However, the above literature adopts the traditional dual-loop PI control literature, which has slow dynamic response characteristics and shows difficulty in meeting the requirements of DC voltage adjustment. Therefore, it is necessary to improve the original dual-loop control structure of GSC. One study [32] improved the GSC current inner loop control structure based on the passive theory. From the perspective of the energy forming of the system, an energy storage function related to the controlled physical quantity was established, and energy distribution was designed to achieve global stability of the system, thus improving the LVRT capability of the unit. However, passive control needs the mathematical model and parameters of the system, which are easily disturbed in practical engineering, resulting in uncertainty of the balance point of the system operation. The classification of the existing literature is shown in

Table 1. Literature Comparison.

LVRT Measure		Literature	Comments
Hardware	Crowbar	[15,16,17]	Merit: Reliable, suitable for different scenarios. Drawback: High cost and cannot provide reactive power.
	Resistance or SVC	[4,8,18,19,20,21,22,23,24]	Merit: Var support during LVRT. Drawback: High cost.
Software	Improved GSC control	[25]	Merit: Little cost. Drawback: Control complexity. Limited capacity compared with hardware. Strong parameter dependence and weak anti-interference ability
	Independent pitch control	[26]
	Grid-connection strategy based on active disturbance rejection controller	[27]
	Control mode of GSC	[28,29,30]
	Joint control of the power balance	[31]
	GSC inner current loop control based on passive theory	[32]
	P-SMC	This paper	Compared with hardware measures, the cost is lower. Compared with other software measures, P-SMC has the advantages of both passive control and sliding mode variable structure, with stronger robustness and faster convergence speed.

.

1.3. Key Problems, Contribution, and Layout of This Paper

This paper focuses on several key issues:

(1)

How to analyze sliding mode variable structure control from the perspective of energy is the key to combining passive control with sliding mode variable structure control;

(2)

How to design a P-SMC model based on the current inner loop structure of the original RSC.

Considering the problems of PI control, such as strong system parameter dependence and weak anti-interference ability, this paper introduces the sliding mode variable structure with fast response and strong robustness into passive control, establishes a P-SMC model and improves the RSC current inner loop structure based on this model. While improving the LVRT capability of DFIG, the sensitivity of the control structure to system parameters and external changes is reduced.

P-SMC combines the advantages of passive control and sliding mode control, has good robustness and dynamic performance, and can overcome the jitter problem of sliding mode control so that the system performance is significantly improved. The application of this control strategy in power electronic circuits, such as DC/DC converters and current-type AC power amplifiers, has achieved a good control effect, which proves its effectiveness and superiority in practical application. In addition, P-SMC is insensitive to model errors, parameter changes and external disturbances, which allows it to maintain stable control performance in the face of complex and uncertain systems. With the development of technology and application, P-SMC will play an important role in more fields, especially in systems requiring high precision and high reliability. For example, in intelligent manufacturing, aerospace, new energy, and other fields, P-SMC is expected to become one of the key technologies that will improve system performance. In addition, with the development of artificial intelligence and big data technology, P-SMC is expected to be combined with these technologies to further improve the intelligence level of the system and achieve more accurate and efficient control.

In Section 2, a transient model of a wind power system with DFIG is presented as the basis for subsequent control design. In Section 3, a P-SMC control model is established, and the current RSC inner loop structure is improved based on the model. In Section 4, simulation results are presented to verify the effectiveness of the proposed P-SMC model. In Section 5, some brief conclusions and outlooks are given.

2. Modeling to the DFIG

As shown in Figure 1, a DFIG includes the WT with the pitch angle control (PAC), the transfer shaft between the WT and the induction generator (IG), the RSC and the GSC connected by the DC capacitor, and the transformer or filter between the GSC and the stator. Where U_s, I_s, U_g, I_g, U_r, and I_r are stator, GSC and rotor voltage and current, respectively, U_DC is DC voltage, U_pcc is DFIG’s integrated voltage, and v_w is DFIG’s capture wind speed.

2.1. Wind Turbine

The captured power of the wind turbine is given by (1), where ρ is the air density, r_t is the radius of the wind turbine and P_N is the rated power. The wind power utilization coefficient C_p is decided by the tip speed ratio λ and the pitch angle β, as shown in (2).

$$P_{\mathrm{wt}}={\displaystyle \frac{1}{2P_{\mathrm{N}}}}\rho \pi {r_{\mathrm{t}}}^2{v_{\mathrm{w}}}^3{C}_{\mathrm{p}}$$

(1)

$$\left\{\begin{array}{l}{C}_{\mathrm{p}}(\lambda ,\beta )=c_1\left({\displaystyle \frac{c_2}{{\lambda }_{\mathrm{i}}}}-c_3\beta -c_4{\beta }^{c_5}-c_6\right)e^{{\displaystyle \frac{-c_7}{{\lambda }_{\mathrm{i}}}}}\\ {\displaystyle \frac{1}{{\lambda }_{\mathrm{i}}}}={\displaystyle \frac{1}{\lambda +c_8\beta }}-{\displaystyle \frac{c_9}{{\beta }^3+1}}\\ \lambda ={\displaystyle \frac{{\omega }_{\mathrm{t}}{r}_{\mathrm{t}}}{p\eta v_{\mathrm{w}}}}{\omega }^{*}\end{array}\right.$$

(2)

where λ_i is the intermediate variable, c₁~c₉ are fitting coefficients, ω_t denotes turbine speed and p and η denote the number of induction motor poles and gearbox growth ratio, respectively.

The wind turbine adopts pitch angle control, and the governing equation is shown in Equation (3):

$$\left\{\begin{array}{l}{\beta }^{*}=\left(k_{\mathrm{p}0}+{\displaystyle \frac{k_{\mathrm{i}0}}{s}}\right)\left({\omega }_{\mathrm{t}}-{\omega }_{\mathrm{t}}^{*}\right)=\left(k_{\mathrm{p}0}+{\displaystyle \frac{k_{\mathrm{i}0}}{s}}\right)(S_{\mathrm{t}}^{*}-S_{\mathrm{t}})\\ \beta ={\displaystyle \frac{1}{s{T}_s}}\left({\beta }^{*}-\beta \right)\end{array}\right.$$

(3)

where T_s is the pitch angle time constant, k_p0 and k_i0 are the PI control parameters, respectively, S_t is the fan slip rate and the superscript * indicates the reference value.

2.2. Induction Motor and Drive Train

The induction motor and drive shaft are described by the 4th-order electromagnetic transient equation and the 3rd-order mechanical transient equation.

The wind turbine captures the wind energy to drive the induction motor through the transmission shaft, and the transmission system is composed of a high-speed shaft, a gearbox and a low-speed shaft. In this paper, the wind turbine and low-speed shaft are taken as one mass block, and the gearbox and high-speed shaft are taken as one mass block:

$$\left\{\begin{array}{l}{\displaystyle \frac{\mathrm{d}{\omega }_{\mathrm{t}}}{\mathrm{d}t}}={\displaystyle \frac{T_{\mathrm{m}}}{2H_{\mathrm{t}}}}-{\displaystyle \frac{K\gamma }{2H_{\mathrm{t}}}}-{\displaystyle \frac{D({\omega }_{\mathrm{t}}-{\omega }_{\mathrm{r}})}{2H_{\mathrm{t}}}}\\ {\displaystyle \frac{\mathrm{d}{\omega }_{\mathrm{r}}}{\mathrm{d}t}}={\displaystyle \frac{T_{\mathrm{e}}}{2H_{\mathrm{r}}}}+{\displaystyle \frac{K\gamma }{2H_{\mathrm{r}}}}+{\displaystyle \frac{D({\omega }_{\mathrm{t}}-{\omega }_{\mathrm{r}})}{2H_{\mathrm{r}}}}\\ {\displaystyle \frac{\mathrm{d}\gamma }{\mathrm{d}t}}={\omega }_{\mathrm{r}}^{*}({\omega }_{\mathrm{t}}-{\omega }_{\mathrm{r}})\end{array}\right.$$

(4)

where ϒ is the relative torsion angle between the two masses, and ω_r denotes the rotor speeds of DFIG. H_t and H_r are the inertia time constants of the wind turbine and DFIG, respectively. K and D are the stiffness and damping coefficients, respectively. T_m and T_e are mechanical and electromagnetic torque, respectively, as shown in Equation (5):

$$\left\{\begin{array}{l}{T}_{\mathrm{e}}=-L_{\mathrm{m}}\left(I_{\mathrm{rq}}{I}_{\mathrm{sd}}-I_{\mathrm{rd}}{I}_{\mathrm{sq}}\right)\\ T_{\mathrm{m}}={\displaystyle \frac{P_{\mathrm{wt}}}{{\omega }_{\mathrm{t}}}}\end{array}\right.$$

(5)

where L_m is the excitation inductance; I_sd and I_sq are the stator current dq axis components, respectively; I_rd and I_rq are the rotor current dq axis components, respectively.

With the stator current flowing into the induction motor in a positive direction, the fixed, rotor flux and voltage equations are shown as follows in the dq two-phase rotating coordinate system:

$$\left\{\begin{array}{l}{\psi }_{\mathrm{sd}}=L_{\mathrm{s}}{I}_{\mathrm{sd}}+L_{\mathrm{m}}{I}_{\mathrm{rd}}\\ {\psi }_{\mathrm{sq}}=L_{\mathrm{s}}{I}_{\mathrm{sq}}+L_{\mathrm{m}}{I}_{\mathrm{rq}}\\ {\psi }_{\mathrm{rd}}=L_{\mathrm{r}}{I}_{\mathrm{rd}}+L_{\mathrm{m}}{I}_{\mathrm{sd}}\\ {\psi }_{\mathrm{rq}}=L_{\mathrm{r}}{I}_{\mathrm{rq}}+L_{\mathrm{m}}{I}_{\mathrm{sq}}\end{array}\right.$$

(6)

$$\left\{\begin{array}{l}{U}_{\mathrm{sd}}=R_{\mathrm{s}}{I}_{\mathrm{sd}}+{\displaystyle \frac{\mathrm{d}{\psi }_{\mathrm{sd}}}{\mathrm{d}t}}-{\omega }_{\mathrm{s}}{\psi }_{\mathrm{sq}}\\ U_{\mathrm{sq}}=R_{\mathrm{s}}{I}_{\mathrm{sq}}+{\displaystyle \frac{\mathrm{d}{\psi }_{\mathrm{sq}}}{\mathrm{d}t}}+{\omega }_{\mathrm{s}}{\psi }_{\mathrm{sd}}\\ U_{\mathrm{rd}}=R_{\mathrm{r}}{I}_{\mathrm{rd}}+{\displaystyle \frac{\mathrm{d}{\psi }_{\mathrm{rd}}}{\mathrm{d}t}}-s_{\mathrm{r}}{\psi }_{\mathrm{rq}}\\ U_{\mathrm{rq}}=R_{\mathrm{r}}{I}_{\mathrm{rq}}+{\displaystyle \frac{\mathrm{d}{\psi }_{\mathrm{rq}}}{\mathrm{d}t}}+s_{\mathrm{r}}{\psi }_{\mathrm{rd}}\end{array}\right.$$

(7)

where ψ is the flux link, S_r is induction motor rotor slip, L_s and L_r are fixed, rotor side self-induction, respectively, R_s and R_r are fixed, and rotor resistance, respectively; U_sd and U_sq are the stator voltage dq axis components, respectively; U_rd and U_rq are the rotor voltage dq axis components, respectively.

2.3. Control to Back-to-Back Converters

The back-to-back converter is composed of RSC, GSC and intermediate DC capacitance and is connected to the power grid through the GSC transformer. Among them, RSC controls the active and reactive power of DFIG stators. GSC maintains DC capacitance-voltage stability and controls the DFIG power factor. The DC capacitance is responsible for the RSC and GSC active power balance.

The voltage converter GSC, by adding PI control and feedforward compensation, realizes the decoupling control of the voltage on the network side and the current of the dq axis on the network side. The current reference value is obtained by the power outer loop PI control, which realizes the decoupling control of DC voltage and reactive power at the network side. The governing equations of GSC’s power outer loop and current inner loop are as follows:

$$\left\{\begin{array}{l}{U}_{\mathrm{gd}}=(k_{\mathrm{pr}3}+{\displaystyle \frac{k_{\mathrm{ir}3}}{s}})(I_{\mathrm{gd}}^{*}-I_{\mathrm{gd}})-X_{\mathrm{T}}{I}_{\mathrm{gq}}+U_{\mathrm{sd}}\\ U_{\mathrm{gq}}=(k_{\mathrm{pr}4}+{\displaystyle \frac{k_{\mathrm{ir}4}}{s}})(I_{\mathrm{gq}}^{*}-I_{\mathrm{gq}})+X_{\mathrm{T}}{I}_{\mathrm{gd}}\\ I_{\mathrm{gd}}^{*}=-(k_{\mathrm{pr}1}+{\displaystyle \frac{k_{\mathrm{ir}1}}{s}})(U_{\mathrm{dc}}^{*}-U_{\mathrm{dc}})\\ I_{\mathrm{gq}}^{*}=-(k_{\mathrm{pr}2}+{\displaystyle \frac{k_{\mathrm{ir}2}}{s}})(Q_{\mathrm{g}}^{*}+Q_{\mathrm{g}})\end{array}\right.$$

(8)

where k_pr1, k_pr2, k_pr3, k_pr4, k_ir1, k_ir2, k_ir3, k_ir4 are PI control parameters of GSC power outer loop and current inner loop, respectively; U_gd and U_gq are the dq axis components of the voltage at the grid side, respectively; I_gd and I_gq are the dq axis components of the current at the grid side, respectively; X_T denotes transformer equivalent reactance; Q_g is reactive power output on the network side; U_dc denotes DC capacitance voltage.

In voltage converter RSC, the rotor voltage is controlled by pulse width modulation (PWM) pulse signal, and then the rotor current is controlled. Therefore, by adding PI control and feedforward compensation, the decoupling control of rotor voltage to rotor dq axis current is realized; that is, I_rd and I_rq are separately controlled by U_rd and U_rq. I_rd, I_rq Reference values $I_{\mathrm{rd}}^{*}$, $I_{\mathrm{rq}}^{*}$ can be controlled by the power outer loop PI to achieve active power and reactive power decoupling control. The governing equations of RSC’s power outer loop and current inner loop are as follows:

$$\left\{\begin{array}{l}{U}_{\mathrm{rd}}=\left(k_{\mathrm{p}3}+{\displaystyle \frac{k_{\mathrm{i}3}}{s}}\right)\left(I_{\mathrm{rd}}^{*}-I_{\mathrm{rd}}\right)-S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rq}}-S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sq}}\\ U_{\mathrm{rq}}=\left(k_{\mathrm{p}4}+{\displaystyle \frac{k_{\mathrm{i}4}}{s}}\right)\left(I_{\mathrm{rq}}^{*}-I_{\mathrm{rq}}\right)+S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rd}}+S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sd}}\\ I_{\mathrm{rd}}^{*}=-\left(k_{\mathrm{p}1}+{\displaystyle \frac{k_{\mathrm{i}1}}{s}}\right)\left(P_{\mathrm{s}}^{*}-P_{\mathrm{s}}\right)\\ I_{\mathrm{rq}}^{*}=\left(k_{\mathrm{p}2}+{\displaystyle \frac{k_{\mathrm{i}2}}{s}}\right)\left(Q_{\mathrm{s}}^{*}-Q_{\mathrm{s}}\right)\end{array}\right.$$

(9)

where k_p1 and k_p2 are the outer loop proportional coefficients; k_p3 and k_p4 are the inner loop proportional coefficients, and k_i1–k_i4 are the corresponding integral coefficients; P_s and Q_s denote output active and reactive power for the stator side, respectively.

In this paper, the RSC double loop control structure is improved: the voltage outer loop is retained, the P-SMC is used to replace the current inner loop, and the voltage outer loop output, RSC current feedback and stator current are taken as the input of P-SMC, and the RSC voltage is taken as the output. It overcomes the disadvantages of strong dependence on PI control parameters and weak anti-interference ability. The derivation of the P-SMC model and the improvement of the current inner loop structure are presented in Section 3 of this paper.

3. P-SMC Design to RSC

The original control of RSC adopts the conventional PI structure, which has problems such as strong parameter dependence and many tuning parameters. These series of deficiencies make the low-voltage traverse characteristics of DFIG poor, and it is urgent to improve the original control structure. In this paper, P-SMC is applied to the RSC control structure of DFIG for the first time, overcoming the problems of weak anti-interference ability and strong parameter dependence of the original RSC control structure and improving the LVRT characteristics of DFIG. As a nonlinear control, passive control solves the problems of the original PI linear control, and sliding mode variable structure control can further overcome the disadvantages of passive control in uncertain scenarios. Therefore, the passive sliding mode RSC control model is established by improving the RSC current inner loop structure by combining passive control with sliding mode variable structure control. The design of RSC’s current inner loop control structure based on P-SMC needs to solve the following two difficulties: there are systematic error terms in the passive control structure and error terms in the sliding mode variable structure. Coordinating and unifying the two control error terms is also the key to combining the two kinds of control; improving the P-SMC structure according to the input and output characteristics of RSC’s original PI control is the current inner loop.

3.1. Sliding Mode Control

Considering the nonlinear characteristics of the system, the traditional linear sliding mode is abandoned, and the integral sliding mode with good tracking characteristics is selected:

$$\left\{\begin{array}{c}{s}_1=k_{\mathrm{ps}1}{e}_1+k_{\mathrm{is}1}{\displaystyle \int e_2}\\ s_2=k_{\mathrm{ps}2}{e}_1+k_{\mathrm{is}2}{\displaystyle \int e_2}\end{array}\right.$$

(10)

where k_ps1, k_is1, k_ps2, and k_is2 are the sliding mode surface control coefficient and e₁ and e₂ are the control system error as given by Equation (11):

$$\left\{\begin{array}{c}{e}_1=I_{\mathrm{rd}}-I_{\mathrm{rd}}^{*}\\ e_2=I_{\mathrm{rq}}-I_{\mathrm{rq}}^{*}\end{array}\right.$$

(11)

In order to improve the chattering problem of sliding mode control, the sat(·) function is selected to replace the sgn(·) function. The saturation function expression is as follows:

$$\mathrm{sat}(x)=\left\{\begin{array}{c}1, x>\Delta \\ kx,\left|x\right|\le \Delta ,k={\displaystyle \frac{1}{\Delta }}\\ -1, x<-\Delta \end{array}\right.$$

(12)

where Δ is the boundary layer thickness of the sliding mode surface, and Δ = 1 is selected in this paper.

Choose the exponential reaching law:

$$\left\{\begin{array}{l}{\dot{s}}_1=-{\epsilon }_1\mathrm{sat}(s_1)-k_1{s}_1\\ {\dot{s}}_2=-{\epsilon }_2\mathrm{sat}(s_2)-k_2{s}_2\end{array}\right.$$

(13)

where: ε₁, ε₂, k₁ and k₂ are the reaching law coefficients, and aimed at ensuring $s\cdot \dot{s}$ < 0, the reaching law coefficients are all positive.

The derivative of the control system error with respect to time is derived by derivation of Equation (17) and the combining of Equations (11) and (13):

$$\left\{\begin{array}{l}{\dot{e}}_1={\dot{I}}_{\mathrm{rd}}={\displaystyle \frac{-[k_{i\mathrm{s}1}{e}_1+k_1{s}_1+{\epsilon }_1\mathrm{sat}(s_1)]}{k_{p\mathrm{s}1}}}\\ {\dot{e}}_2={\dot{I}}_{\mathrm{rq}}={\displaystyle \frac{-[k_{i\mathrm{s}2}{e}_2+k_2{s}_2+{\epsilon }_2\mathrm{sat}(s_2)]}{k_{p\mathrm{s}2}}}\end{array}\right.$$

(14)

Based on the original current inner loop control characteristics of GSC (Equation (15)), an improved current inner loop control model (Equation (16)) is established:

$$\left\{\begin{array}{c}{U}_{\mathrm{rd}}+S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sq}}=L_{\mathrm{r}}{\dot{I}}_{\mathrm{rd}}-S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rq}}+R_{\mathrm{r}}{I}_{\mathrm{rd}}\\ U_{\mathrm{rq}}-S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sd}}=L_{\mathrm{r}}{\dot{I}}_{\mathrm{rq}}+S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rd}}+R_{\mathrm{r}}{I}_{\mathrm{rq}}\end{array}\right.$$

(15)

$$\left\{\begin{array}{c}{U}_{\mathrm{rd}}+S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sq}}={\displaystyle \frac{-L_{\mathrm{r}}[k_{i\mathrm{s}1}{e}_1+k_1{s}_1+{\epsilon }_1\mathrm{sat}(s_1)]}{k_{p\mathrm{s}1}}}+R_{\mathrm{r}}{I}_{\mathrm{rd}}-S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rq}}\\ U_{\mathrm{rq}}-S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sd}}={\displaystyle \frac{-L_{\mathrm{r}}[k_{i\mathrm{s}2}{e}_2+k_2{s}_2+{\epsilon }_2\mathrm{sat}(s_2)]}{k_{p\mathrm{s}2}}}+R_{\mathrm{r}}{I}_{\mathrm{rq}}+S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rd}}\end{array}\right.$$

(16)

3.2. Design to Passive Sliding Mode Controller

Aimed at obtaining a passive sliding mode controller by combining passive control theory with sliding mode control, the input of the current inner loop control model improved by sliding mode control is taken as the expected stable equilibrium point of the passive control system:

$${\mathit{E}}^{*}=\left[\begin{array}{c}{I}_{\mathrm{rd}}^{*}\\ I_{\mathrm{rq}}^{*}\end{array}\right]$$

(17)

The system error is ${\mathit{E}}_e=\mathit{E}-{\mathit{E}}^{*}$, where $\mathit{E}=$$\left[\begin{array}{c}{I}_{\mathrm{rd}}\\ I_{\mathrm{rq}}\end{array}\right]$. The current inner loop control improved by sliding mode control is rewritten into Euler-Lagrange form:

$$\mathit{M}\dot{\mathit{E}}+\mathit{J}\mathit{E}+\mathit{R}\mathit{E}=\mathit{u}$$

(18)

where $\mathit{M}=\left[\begin{array}{cc}{L}_{\mathrm{r}}& 0\\ 0& L_{\mathrm{r}}\end{array}\right]$; $\mathit{R}=\left[\begin{array}{cc}{R}_{\mathrm{r}}& 0\\ 0& R_{\mathrm{r}}\end{array}\right]$; $\mathit{J}=\left[\begin{array}{cc}0& -S_{\mathrm{r}}{L}_{\mathrm{r}}\\ S_{\mathrm{r}}{L}_{\mathrm{r}}& 0\end{array}\right]$; $\mathit{u}=\left[\begin{array}{c}{U}_{\mathrm{rd}}+S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sq}}\\ U_{\mathrm{rq}}-S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sd}}\end{array}\right]$.

The EL form of system error under passive control can be derived according to Equation (18):

$$\mathit{M}{\dot{\mathit{E}}}_{\mathrm{e}}+\mathit{J}{\mathit{E}}_{\mathrm{e}}+\mathit{R}{\mathit{E}}_{\mathrm{e}}=\mathit{u}-\mathit{M}{\dot{\mathit{E}}}^{*}-\mathit{J}{\mathit{E}}^{*}-\mathit{R}{\mathit{E}}^{*}$$

(19)

Increasing the system damping R_a to improve the rate of convergence to the desired equilibrium point, where the system damping is R_d:

$${\mathit{R}}_d=\mathit{R}+{\mathit{R}}_a$$

(20)

where ${\mathit{R}}_{\mathrm{a}}=\left[\begin{array}{cc}{R}_{\mathrm{a}1}& 0\\ 0& R_{\mathrm{a}2}\end{array}\right]$.

The EL form of the system error with increased damping is derived. Add R_aE_e to both sides of Equation (19) on the left side RE_e + R_aE_e = (R + R_a)E_e = R_dE_e. Move the JE_e on the left side of the equation to the right side: −JE* − JE_e = −J(E* + E_e) = −JE. Based on the above derivation, Equation (21) can be obtained:

$$\mathit{M}{\dot{\mathit{E}}}_{\mathrm{e}}+{\mathit{R}}_{\mathrm{d}}{\mathit{E}}_{\mathrm{e}}=\mathit{u}-\mathit{M}{\dot{\mathit{E}}}^{*}-\mathit{J}\dot{\mathit{E}}-\mathit{R}{\mathit{E}}^{*}+{\mathit{R}}_{\mathrm{a}}{\mathit{E}}_{\mathrm{e}}$$

(21)

Aimed at realizing control decoupling, the passive control law of the current inner loop model improved by sliding mode control is selected based on Equation (21):

$$\mathit{u}=\mathit{M}{\dot{\mathit{E}}}^{*}+\mathit{J}\dot{\mathit{E}}+\mathit{R}{\mathit{E}}^{*}-{\mathit{R}}_{\mathrm{a}}{\mathit{E}}_{\mathrm{e}}$$

(22)

According to Equation (22), the passive control law of the dq axis of the current inner loop model improved by sliding mode control can be derived:

$$\left\{\begin{array}{c}{U}_{\mathrm{rd}}+S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sq}}=R_{\mathrm{r}}{I}_{\mathrm{rd}}^{*}-S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rq}}-R_{\mathrm{a}1}(I_{\mathrm{rd}}-I_{\mathrm{rd}}^{*})\\ U_{\mathrm{rq}}-S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sd}}=R_{\mathrm{r}}{I}_{\mathrm{rq}}^{*}+S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rd}}-R_{\mathrm{a}2}(I_{\mathrm{rq}}-I_{\mathrm{rq}}^{*})\end{array}\right.$$

(23)

The analytical formula of the system error is derived by combining Equations (16) and (23):

$$\left\{\begin{array}{c}{I}_{\mathrm{rd}}-I_{\mathrm{rd}}^{*}={\displaystyle \frac{L_{\mathrm{r}}[k_1{s}_1+{\epsilon }_1\mathrm{sat}(s_1)]}{k_{\mathrm{ps}1}(R_{\mathrm{a}1}+R_{\mathrm{r}})-k_{\mathrm{is}1}{L}_{\mathrm{r}}}}\\ I_{\mathrm{rq}}-I_{\mathrm{rq}}^{*}={\displaystyle \frac{L_{\mathrm{r}}[k_2{s}_2+{\epsilon }_2\mathrm{sat}(s_2)]}{k_{\mathrm{ps}2}(R_{\mathrm{a}2}+R_{\mathrm{r}})-k_{\mathrm{is}2}{L}_{\mathrm{r}}}}\end{array}\right.$$

(24)

The RSC current inner loop control model improved by the passive sliding mode controller is derived by substituting Equation (24) into Equation (23):

$$\left\{\begin{array}{c}{U}_{\mathrm{rd}}=R_{\mathrm{r}}{I}_{\mathrm{rd}}^{*}-S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sq}}-S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rq}}-{\displaystyle \frac{R_{a1}{L}_{\mathrm{r}}[k_1{s}_1+{\epsilon }_1\mathrm{sat}(s_1)]}{k_{\mathrm{ps}1}(R_{\mathrm{a}1}+R_{\mathrm{r}})-k_{\mathrm{is}1}{L}_{\mathrm{r}}}}\\ U_{\mathrm{rq}}=R_{\mathrm{r}}{I}_{\mathrm{rq}}^{*}+S_{\mathrm{r}}{L}_{\mathrm{m}}{I}_{\mathrm{sd}}+S_{\mathrm{r}}{L}_{\mathrm{r}}{I}_{\mathrm{rd}}-{\displaystyle \frac{R_{a2}{L}_{\mathrm{r}}[k_2{s}_2+{\epsilon }_2\mathrm{sat}(s_2)]}{k_{\mathrm{ps}2}(R_{\mathrm{a}2}+R_{\mathrm{r}})-k_{\mathrm{is}2}{L}_{\mathrm{r}}}}\end{array}\right.$$

(25)

If the coupling quantity between dq is ignored, the control block diagram of the d and q axis of the inner loop of the P-SMC current is shown in Figure 2, where the green area represents the control block diagram of the RSC P-SMC structure. Compared with the GSC control block diagram, the improvement idea of the RSC current inner loop can be clearly seen: the original voltage outer ring is retained, the output of the voltage outer ring is taken as the integral sliding mode, and the exponential reaching law is selected according to the integral sliding mode, and then the dq axis component of the rotor side voltage is output through passive control.

3.3. Discussions

The passive control is a nonlinear control strategy. It changes the control manner from traditional signal processing to energy processing, which is intuitive and easy for power system engineers to accept. The SMC can treat the uncertainty of the system and has the advantage of fast response, strong robustness, and simple control law. Therefore, in this paper, they are combined to propose the P-SMC model for the LVRT of the DFIG. One drawback of the SMC is that the system size is limited in determining the energy function.

The thermal stress of the DFIG during grid fault is critical to the fault ride-through [33]. Since the temperature rise of the DFIG is related to spatial and ventilation conditions, the thermal stress is often quantified by the thermal effect, which is defined as the integral of the square of the current within the fault duration. Whatever, the LVRT measures help to reduce the stator current and the thermal stress after the fault.

4. Case Studies

To verify the effectiveness of the passive sliding mode improved RSC current inner loop control strategy proposed in this paper, the time domain simulation analysis is carried out. The single-DFIG infinite system model was built in MATLAB(2021b)/Simulink. The parameters of DFIG are shown in the following

Table 2. Parameters of DFIG.

Wind Turbine	Blade Radius	34 m	Inertial Time Constant	3.5 s
Driving shaft	Stiffness coefficient	0.8 p.u./rad	Mutual damping coefficient	3.4 p.u.
Pitch angle	kp1 = 6                        ki1 = 2.5 × 10−4
Induction machine	Rated power	2 MW	Rated voltage	690 V
	Stator resistance	0.03 p.u.	Stator reactance	0.44 p.u.
	Rotor resistance	0.045 p.u.	Rotor reactance	0.45 p.u.
	Excitation reactance	6.55 p.u.	Inertial time constant	3 s
Direct current capacitance	Capacitance voltage	1200 V	Capacitance value	0.5 F
RSC	Control inner loop	kp2 = 0.57, ki2 = 0.042, kp3 = kp2, ki3 = ki2
	Control outer loop	kp4 = 0.048, ki4 = 2.1 × 10−4, kp5 = kp4, ki5 = ki4
GSC	Control inner loop	kp6 = 0.57, ki6 = 0.042, kp7 = kp6, ki7 = ki6
	Control outer loop	kp8 = 0.048, ki8 = 2.1 × 10−4, kp9 = kp8, ki9 = ki8
	Transformer reactance	0.08 p.u.

.

Assume that the three-phase short-circuit fault occurs in the system at 1 s, and the voltage drop depth of the node is 20%, 40%, and 80%, respectively. The fault lasts for 0.5 s and is removed at 1.5 s.

To verify the superiority and robustness of P-SMC, the traditional PI control strategy before P-SMC and the additional P-SMC strategy are used to simulate the transient processes of DFIG DC voltage and rotor current when the voltage drop depth is 20%, 40% and 80%, respectively.

4.1. Control Effect with Voltage Drop of 20% at PCC

4.1.1. Transient Change of DC Voltage

Figure 3 shows the DFIG DC voltage transient process results obtained when the voltage drop depth is 20%, where P-SMC denotes the passive SMC, k_ps1 and k_ps2 have the same value, so the abbreviation is k_ps and k_is are also the same). When DFIG integrated voltage drops, DFIG DC voltage overshoots, which is consistent with the theoretical derivation above. By comparing the voltage overshoot amplitude, voltage oscillation frequency, oscillation time and oscillation amplitude before and after the additional P-SMC, it can be seen that P-SMC significantly improves the transient characteristics of DFIG DC voltage during LVRT. By comparing the transient characteristics of U_dc with different values of k_ps and k_is, it can be found that the selection of control parameters has little influence on the effect of P-SMC, indicating that P-SMC has strong robustness.

Table 3. Dynamic Evaluation Index of U_dc When Voltage Drops by 20%.

	Oscillation Peak (V)	Oscillation Time (s)
Without P-SMC	1301.1	0.12
P-SMC kps = 20, kis = 200	1269.3	0.07
P-SMC kps = 5, kis = 25	1269.5	0.07
P-SMC kps = 100, kis = 1200	1269.5	0.07

shows the specific values of DFIG to measure the transient characteristics of DC capacitance-voltage in the process of the voltage drop of node connection by 20% when P-SMC is not attached, and P-SMC with different PI parameters is attached.

With the P-SMC, the oscillation peak value of DFIG DC capacitance voltage is lower than that of traditional PI control, and the oscillation convergence time is also shortened. At the same time, setting different parameters for P-SMC has little effect on oscillation peak and convergence time, which indicates that the control parameter is adaptable.

4.1.2. Transient Change of dq Components of Rotor Current

Figure 4 and Figure 5 show the transient process results of DFIG rotor current d and q axis components when the voltage drop depth is 20%, respectively. When DFIG is in the LVRT process, its rotor current will increase sharply, which is consistent with theoretical derivation. The DFIG with P-SMC has smaller current overshooting and oscillation amplitude and shorter oscillation convergence time. In the process of rotor current oscillation, after the power grid fault is removed, the rotor current overshooting of DFIG with additional P-SMC is also significantly smaller than that of the unit without additional P-SMC, and the overall oscillation amplitude is significantly smaller, and the convergence time is shorter, and the selection of parameters has little influence on the control effect. Therefore, additional P-SMC can suppress the rotor current fluctuation and improve the rotor current transient characteristics during LVRT in DFIG.

Table 4. Dynamic Evaluation Index of I_rd When Voltage Drops by 20%.

	Oscillation Peak (p.u.)	Oscillation Time (s)
Without P-SMC	0.93	0.38
P-SMC kps = 20, kis = 200	0.61	0.11
P-SMC kps = 5, kis = 25	0.61	0.11
P-SMC kps = 100, kis = 1200	0.61	0.11

and

Table 5. Dynamic Evaluation Index of I_rq when Voltage Drops by 20%.

	Oscillation Peak (p.u.)	Oscillation Time (s)
Without P-SMC	−0.06	0.43
P-SMC kps = 20, kis = 200	−0.18	0.16
P-SMC kps = 5, kis = 25	−0.19	0.16
P-SMC kps = 100, kis = 1200	−0.18	0.16

show the specific value of the rotor current transient characteristic index of DFIG in the process of the voltage drop of node connection by 20% when P-SMC is not attached and P-SMC with different PI parameters is attached.

As seen from Table 4 and Table 5, the current transient characteristics of the DFIG rotor with P-SMC are obviously better than those of traditional PI control, and the peak value of oscillation and convergence time are obviously improved. Compared with Table 3, the introduction of P-SMC has a better effect on the rotor current transient characteristics than on the DC capacitance voltage.

4.1.3. Transient Change of Rotor Voltage

In this paper, the rotor voltage transient characteristics of DFIG under traditional PI control and P-SMC are compared. Since the measurement is a three-phase component, it is difficult to make a direct comparison. Therefore, the three-phase component is analyzed by a fast Fourier transform to compare the total harmonic distortion of rotor voltage under different controls.

Figure 6 and Figure 7 show the FFT analysis of DFIG rotor voltage under traditional PI control and P-SMC, respectively. The fundamental wave content of rotor voltage in DFIG under P-SMC is significantly higher than that under traditional PI control during low-voltage crossing, while the harmonic content is significantly lower than that under traditional PI control. This shows that the rotor voltage quality of DFIG with P-SMC is significantly higher than that of traditional PI control during low-voltage crossing.

4.2. Control Effect with Voltage Drop of 40% at PCC

4.2.1. Transient Change of DC Voltage

The power grid fault degree is aggravated, the voltage drop depth of DFIG nodes is increased to 40%, and the DFIG DC voltage transient process shown in Figure 8 is derived:

Comparison between Figure 3 and Figure 8 shows that DFIG DC voltage overshoot amplitude increases when the voltage drop degree deepens. The voltage drop depth of the DFIG unit DC voltage after overshooting without attached P-SMC is obviously greater than that of the DFIG unit DC voltage drop depth when the voltage drop depth is 20%. The U_dc drop depth of the unit with P-SMC is almost not affected by the drop depth of U_pcc, and the drop depth is small.

Table 6. Dynamic Evaluation Index of U_dc When Voltage Sag of 40%.

	Oscillation Peak (V)	Oscillation Time (s)
Without P-SMC	1347.5	0.21
P-SMC kps = 20 kis = 200	1283.7	0.07
P-SMC kps = 5 kis = 25	1284.1	0.07
P-SMC kps = 100 kis = 1200	1283.4	0.07

shows the specific values of DFIG to measure the transient characteristics of DC capacitance-voltage in the process of 40% voltage drop in node connection when P-SMC is not attached, and P-SMC with different PI parameters is attached:

As seen from Table 6, when the voltage drop depth is increased, the DFIG DC capacitance-voltage transient characteristics with P-SMC are still better than those of traditional PI control. Compared with Table 3, when the voltage drop depth is low, the deepening of the voltage drop degree has little influence on the transient characteristics of DC capacitance-voltage under P-SMC.

4.2.2. Transient Change of dq Components of Rotor Current

Figure 9 and Figure 10, respectively, show the transient process results of DFIG rotor current d and q axis components when the voltage drop depth is 40%. According to Figure 4, Figure 5, Figure 9 and Figure 10, when the U_pcc drops more deeply, the rotor current oscillation is intensified, and the current overshoot and oscillation amplitude increase more significantly. At this time, the overrush value of the rotor current oscillation in the power grid with P-SMC attached after fault removal is also significantly smaller than that in the unit without additional control, that is, the transient characteristics of the rotor current in DFIG after additional control is completely better than that before additional control.

4.3. Control Effect with Voltage Drop of 80% at PCC

Aiming to study the control characteristics of P-SMC under extreme power grid fault scenarios, the U_pcc drop depth was increased to 80%.

4.3.1. Transient Change of DC Voltage

The U_dc transient process, as shown in Figure 11, is derived. When the power grid failure is relatively serious, and the U_pcc drops too deeply, the U_dc without the attached P-SMC has sustained oscillation of up to 0.3 s within 0.5 s of LVRT, and the amplitude of oscillation is very large. In this case, DFIG is in danger of becoming off-grid. The unit with additional P-SMC is not affected by the drop depth of U_pcc, and still maintains relatively good transient characteristics. However, it is worth noting that when the 1.5 s voltage is restored, the DFIG DC capacitance voltage with P-SMC has a higher oscillation amplitude and convergence time during the recovery process, which is worthy of further study.

Table 7. Dynamic Evaluation Index of U_dc with Voltage of 80%.

	Oscillation Peak (V)	Oscillation Time (s)
Without P-SMC	1605.3	0.27
P-SMC kps = 20, kis = 200	1362.5	0.08
P-SMC kps = 5, kis = 25	1361.8	0.08
P-SMC kps = 100, kis = 1200	1362.2	0.08

shows the specific values of DFIG to measure the transient characteristics of DC capacitance-voltage in the process of 80% voltage drop in node connection when P-SMC is not attached and P-SMC with different PI parameters is attached:

As seen from Table 7, when the voltage drop depth is very high, DFIG DC capacitance-voltage under traditional PI control shows poor transient characteristics, i.e., higher oscillation amplitude and longer convergence time, while DFIG under P-SMC still shows good transient characteristics.

4.3.2. Transient Change of dq Components of Rotor Current

Figure 12 and Figure 13, respectively, show the transient processes of the d- and q-axes components of the rotor current in DFIG when the U_pcc drops 80%. By combining Figure 9, Figure 10, Figure 12 and Figure 13, it is found that when extreme faults occur in the power grid, current oscillation is further intensified. The P-SMC still plays a role in suppressing the current fluctuation of the DFIG rotor under severe fault conditions.

Table 8. Dynamic Evaluation Index of I_rd with a Voltage Sag of 80%.

	Oscillation Peak (p.u.)	Oscillation Time (s)
Without P-SMC	2.23	0.38
P-SMC kps = 20, kis = 200	1.84	0.12
P-SMC kps = 5, kis = 25	1.84	0.12
P-SMC kps = 100, kis = 1200	1.84	0.12

and

Table 9. Dynamic Evaluation Index of I_rq with a Voltage Sag of 80%.

	Oscillation Peak (p.u.)	Oscillation Time (s)
Without P-SMC	1.42 p.u.	0.36
P-SMC kps = 20, kis = 200	1.89 p.u.	0.13
P-SMC kps = 5, kis = 25	1.89 p.u.	0.13
P-SMC kps = 100, kis = 1200	1.89 p.u.	0.13

show the specific value of the rotor current transient characteristic index of DFIG in the process of 80% voltage drop of node connection when P-SMC is not attached, and the P-SMC with different PI parameters is attached:

As seen from Table 8 and Table 9, when the voltage drop depth is deep, the current transient characteristics of the DFIG rotor under PI control are obviously worse than those of the DFIG rotor with P-SMC. The depth of voltage drop influences the transient characteristics of rotor current, but the effect is less than that of DC capacitance voltage.

4.3.3. Validation of the RSC’s Constraints

To verify whether the rotor voltage and the apparent power of the RSC with the additional P-SMC exceed the limit during the LVRT, the three-phase component of the rotor voltage and the apparent power of the rotor side are measured when the voltage drop depth is 80%. If the constraints are not violated, the results with a smaller average are acceptable to the DFIG, otherwise the control parameters of the P_SMC will change, or the capacity of the RASC will be extended.

The rotor voltage is shown in Figure 14 Its steady-state and peak values are shown in

Table 10. Steady-state value of Vrabc and oscillation peak of Vrabc with a voltage sag of 80%.

	Steady State Value (V)	Oscillation Peak (V)
Vrabc	1197	1659

. As can be seen from Table 10, the peak value of the rotor voltage is only 1.39 times the steady-state value, and the duration time is quite short. According to the requirements for low-voltage crossing in China’s power grid guidelines, the rotor voltage of DFIG does not exceed the limit during the low-voltage ride-through.

According to the low-voltage ride-through standard of the power grid code. At a steady state, the apparent power of the rotor is 50% of the rated capacity. As can be seen from Figure 15, the peak oscillation value of the apparent power does not exceed the rated capacity of the rotor-side converter during the low-voltage crossing of DFIG.

Combined with the rotor voltage and apparent power transient process diagram, no rotor voltage and apparent power overruns occur in DFIG under P-SMC during low-voltage ride-through.

4.4. Reactive Power Injected into the Grid during LVRT

Because grid codes demand reactive power infeed during the LVRT, scenarios of voltage drop depth at different nodes are set, and the changes of reactive power injected into the system by DFIG under different scenarios were compared and analyzed. (The voltage drop depth is 5%, 10% and 15%, respectively). The result is shown in Figure 16, the reactive power injected by DFIG into the system will increase when the voltage of the node is dropped, and the deeper the drop is, the more reactive power will increase.

4.5. Robustness of P-SMC

To verify the robustness of P-SMC, the transient change of the DC voltage under P-SMC, passive control and traditional PI control are compared in the time domain under different voltage drop depths (10%, 40%, 60%).

Comparison to Figure 17, Figure 18 and Figure 19 shows that under different voltage drop depth scenarios, the control effect of P-SMC is always better than the other two kinds of control, and it has good robustness.

5. Conclusions and Outlook

5.1. Conclusions

In this paper, P-SMC is considered to improve the LVRT characteristics of DFIG units, but there are problems, such as strong system parameter dependence and weak anti-interference ability. Therefore, the robust sliding mode control is introduced into passive control, and the RSC current inner loop control structure is improved based on P-SMC. By comparing the DC voltage and rotor current transient characteristics of DFIG units with no P-SMC and additional P-SMC during LVRT when the voltage drop depth of DFIG nodes is 20%, 40% and 80%, respectively, the following conclusions can be drawn:

(1)

P-SMC can effectively improve the transient process of internal parameters in the LVRT process of DFIG units; that is, oscillation amplitude, oscillation frequency and convergence time are reduced, and the value of control parameters has little influence on the control effect, and the control robustness is strong.

(2)

When the voltage drop-depth of the integrated point increases, the internal parameter transient characteristics of DFIG units without additional P-SMC deteriorate faster, and when the drop depth is too large, the internal parameter transient instability is more likely. When P-SMC is added, the transient characteristics of the internal parameters of DFIG will still deteriorate, but the deterioration rate is slower, and the transient characteristics remain relatively good.

The simulation results show that the proposed control strategy can effectively suppress the DC voltage and rotor current fluctuations of DFIG during LVRT, improve the LVRT characteristics of DFIG units, and the control has good robustness.

5.2. Outlook for Future Study

P-SMC belongs to offline control. The disadvantages of offline control mainly include data synchronization that is not timely and data loss. Because the data is not synchronized in real-time, the control instructions may not be updated in time, which affects the real-time and accuracy of the control. In addition, offline control may also face the risk of data loss, especially in the process of feedback signal transmission or processing problems, which may lead to the loss of important control information and then affect the normal operation of the system.

The authors considered adding an online control part to P-SMC. Online control can improve the observability and tracking support ability of the system, and has the advantages of good real-time performance, high reliability and strong adaptability.