Fractional-order Sliding Mode Control of Hybrid Drive Wind Turbine for Improving Low-voltage Ride-through Capacity

Ziwei Wang; Wenliang Yin; Lin Liu; Yue Wang; Cunshan Zhang; Xiaoming Rui

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Fractional-order Sliding Mode Control of Hybrid Drive Wind Turbine for Improving Low-voltage Ride-through Capacity PDF

- ORCID：
Ziwei Wang
✉
- ORCID：
Wenliang Yin
✉
- ORCID：
Lin Liu
✉
- ORCID：
Yue Wang
✉
- ORCID：
Cunshan Zhang
✉
- ORCID：
Xiaoming Rui
✉

School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo 255000, China； School of Electrical and Data Engineering, University of Technology Sydney, NSW 2007, Australia； School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China

Updated：2023-09-20

DOI：10.35833/MPCE.2022.000701

OUTLINE

Abstract

A hybrid drive wind turbine equipped with a speed regulating differential mechanism can generate electricity at the grid frequency by an electrically excited synchronous generator without requiring fully or partially rated converters. This mechanism has extensively been studied in recent years. To enhance the transient operation performance and low-voltage ride-through capacity of the proposed hybrid drive wind turbine, we aim to synthesize an advanced control scheme for the flexible regulation of synchronous generator excitation based on fractional-order sliding mode theory. Moreover, an extended state observer is constructed to cooperate with the designed controller and jointly compensate for parametric uncertainties and external disturbances. A dedicated simulation model of a 1.5 MW hybrid drive wind turbine is established and verified through an experimental platform. The results show satisfactory model performance with the maximum and average speed errors of 1.67% and 1.05%, respectively. Moreover, comparative case studies are carried out considering parametric uncertainties and different wind conditions and grid faults, by which the superiority of the proposed controller for improving system on-grid operation performance is verified.

Keywords

Sliding mode controller (SMC); extended state observer (ESO); low-voltage ride through (LVRT); synchronous generator (SG); speed regulation; wind power; wind turbine

I. Introduction

PURSUING carbon neutrality and peak emissions has contributed to the continuous investment in and development of a low-carbon, safe, and efficient energy market [

1]. Meanwhile, grid-connected wind power generation systems have relatively good technical foundations and prospects for large-scale utilization, thereby providing a feasible solution to the global energy transition [2], [3]. However, owing to the intermittency and volatility of wind, new challenges to power grids in terms of operating safety and stability inevitably arise if large-scale and high-proportion wind power is integrated [2]-[4]. Therefore, strict technical requirements for grid connection of wind farms, especially regarding output electricity frequency and low-voltage ride-through (LVRT) capacity, are being adopted by power grid companies worldwide [5], [6].

To maximize the energy capture capacity and reduce the impact of wind power fluctuations on the grid, most wind farms produce electricity using the variable-speed constant-frequency strategy through doubly-fed induction generators (DFIGs) or direct drive synchronous generators (DDSGs) [

7], [8]. In addition, efficient equipment including static synchronous compensators [9], dynamic voltage restorers [10], and energy storage systems [11], [12] endowed with advanced control schemes is used to enhance the dynamic performance and LVRT capacity. However, wind turbines (WTs) based on the DFIG or DDSG require partially or fully rated converters to ensure that the output current frequency is consistent with the power grid frequency [7], [8]. Coupled with auxiliary devices, the energy dissipation, investment and maintenance costs, and control complexity of existing WTs increase, especially during LVRT operation [13]. Furthermore, harmonic pollutants can also be excited by the rectifier-inverter links of WT converters, possibly reducing the power quality in the power grid [14], [15].

Hybrid drive WTs provide an alternative solution to generating grid-frequency electricity without power-consuming converters. These WTs often use a dedicated speed regulating differential mechanism (SRDM) consisting of differential gear sets and hydraulic/electrical actuators to continuously adjust the output speed of the transmission chain. Thus, these WTs can be directly connected to the power grid with an electrically excited synchronous generator (SG). Considering hybrid drive WTs, [

16] proposed an electrical continuously variable transmission composed of multiple planetary gear trains (PGTs) and speed regulating motors. Reference [17] combined a single-stage gear transmission with a hydraulic pump to retain the output torque stability when wind speed changes. Reference [18] calculated the energy efficiency of a novel wind power generation system that integrates a three-axis planetary gear set and servomotor. Reference [19] established a detailed dynamic model of the hybrid drive transmission and described its power flow characteristics. Reference [20] designed an adaptive neuro-fuzzy controller to achieve the maximum power tracking. Reference [21]-[23] designed a hybrid drive scheme based on the SRDM and then investigated control strategies for accurate SRDM speed control considering the uncertainties of various parameters and external disturbances. Reference [24] analyzed the compatibility and reliability of a 50 MW on-grid wind farm composed of hybrid drive WTs [24].

The aforementioned developments greatly promote the advancement and application of the hybrid drive WT with continuously variable transmission. However, regarding operational control schemes, researchers have paid more attention to guaranteeing the maximum energy capture efficiency and desired speed adjusting accuracy of SRDMs, often neglecting excitation control to maintain stable SG operation under wind changes and LVRT operation. Moreover, although hybrid drive WTs have unique advantages for grid-friendly connection with wind farms, the inherent volatility of wind power remains a serious challenge for developing modern power systems with large-scale and high-proportion renewable power integration. Thus, theoretical and experimental studies are still needed to improve the operation safety, stability, and economy of both hybrid drive WTs and the connected power systems.

SG excitation control allows to flexibly adjust the output voltage and power, thus improving the transient and steady-state grid-connected operation performance of SRDM-based hybrid drive WTs. Recently, [

25] and [26] synthesized an adaptive robust excitation controller for ensuring the voltage stability and reactive power carrying capacity of hybrid drive WTs. The nonlinear effects caused by the strong coupling in the transmission system were reduced by including additional error compensators, but the required accurate system parameters are difficult to obtain. To deal with model uncertainties, [27] performed compensation and feedback linearization of SG disturbances by designing an extended state observer (ESO). However, as all the system nonlinear factors are regarded as a single disturbance signal, the information of state variables is neglected.

An ESO can perform state estimation in a nonlinear system under parameter uncertainty and external disturbances [

28]. Reference [29] and [30] designed a nonlinear robust controller based on an ESO, thereby improving the drivetrain torsional oscillation of a WT, and demonstrated that the ESO can handle disturbances under extreme operation environments of a wind power generation system. By combining various advanced algorithms such as the adaptive fuzzy algorithm [31], additional observer [32], and high-order theory [33], sliding mode controllers (SMCs) [34] provide unique advantages including simple derivation, fast response, and strong robustness, ideally meeting technical requirements for adequate WT excitation control. Meanwhile, targeting drawbacks in convergence properties and undesirable chattering effects, fractional calculus theory can be applied to SMC to avoid improper power dispersion and mechanical vibrations in a control system [35], [36].

In our previous work [

21]-[23], a novel SRDM-based hybrid drive WT was developed to obtain constant-frequency electric power without requiring converters. Speed regulation control and parameter optimization were investigated. Moreover, the feasibility and superiority of the proposed WT were confirmed through numerical simulations and experimental platforms. The main contributions of this paper can be summarized as follows.

1) Considering unique transmission features such as dual-power inputs, continuously variable speed ratio, and time-varying steering of SRDM-based hybrid drive WTs, this paper proposes an improved fractional-order SMC (FOSMC) for SG excitation to improve the grid-connected operation performance of SRDM-based hybrid drive WTs, especially under LVRT operation.

2) An ESO with the proposed controller is designed to suitably estimate the system parametric uncertainties and internal/external disturbances in real time. By using the ESO, the proposed excitation controller could better adapt to the complex and varying operation of WTs.

3) A dedicated simulation model of a 1.5 MW SRDM-based hybrid drive WT is established and validated using an experimental platform. In addition, comparative case studies of the control functions among FOSMC with ESO (FOSMC-ESO), SMC with ESO (SMC-ESO), and proportional-integral-derivative (PID) control with power system stabilizer (PSS) (PID-PSS) are evaluated. The results confirm the effectiveness and superiority of the designed controller in improving continuous on-grid operation performance of an SRDM-based hybrid drive WT under changing wind speeds, parameter uncertainties, and grid faults.

The remainder of this paper is organized as follows. Section II describes the transmission principles and the modeling of the SRDM-based hybrid drive WT. In Section III, the design procedure and theory of the proposed controller are detailed. The dedicated simulation model is established and then verified using the experimental platform in Section IV. In addition, case studies are evaluated to validate the satisfactory performance of the synthesized SG excitation control. Finally, conclusions are drawn in Section V.

II. Transmission Principles and Modeling of SRDM-based Hybrid Drive WT

A. Transmission Principles of SRDM-based Hybrid Drive WT

Figure 1 shows a diagram of the proposed SRDM-based hybrid drive WT consisting of wind wheel, differential gearbox, SRDM system, SG, transformer, and power grid. The wind wheel captures random wind energy and generates initial time-varying speed and torque, which are the dominating inputs to the generation unit. Meanwhile, a permanent magnet synchronous motor (PMSM), working as the power source of the SRDM, provides speed regulating inputs. Based on a precise control algorithm and compound function of the PGT, the SG can receive a relatively stable input speed to produce electricity at a constant frequency to the power grid.

Fig. 1 Diagram of proposed SRDM-based hybrid drive WT.

Figure 2 shows the speed relations between components in the PGT.

Fig. 2 Speed relations between components in PGT.

By using the reverse rotation method [

37], the transmission ratio between the sun and ring gears can be calculated as:

i_{S R}^{C} = \frac{n_{S}^{C}}{n_{R}^{C}} = \frac{n_{S} - n_{C}}{n_{R} - n_{C}} = - k

(1)

where $n_{C}$ , $n_{S}$ , and $n_{R}$ are the rotation speeds of the planet carrier, sun gear, and ring gear, respectively; $n_{S}^{C}$ ( $n_{S}^{C} = n_{S} - n_{C}$ ) and $n_{R}^{C}$ ( $n_{R}^{C} = n_{R} - n_{C}$ ) are the rotation speeds of the sun and ring gears with respect to the planet carrier, respectively; and k is the structural parameter of the PGT.

Hence, we can obtain:

n_{S} = (1 + k) n_{C} - k n_{R}

(2)

According to the parameter optimization results in [

22], the transmission ratio between the sun gear and SG should be set to be 1. Then, (2) can be rewritten as:

n_{g} = (1 + k) n_{C} - k n_{R} = (1 + k) n_{w} i_{C r} - k n_{m} i_{R m}

(3)

where n_w, n_m, and n_g are the rotation speeds of the wind wheel, PMSM, and SG, respectively; i_Cr is the speed increasing ratio between the wind wheel and planet carrier; and i_Rm is the transmission ratio between the PMSM and ring gear. For an actual SRDM-based hybrid drive WT, k, i_Cr, and i_Rm are inherent properties of the transmission system with constant values.

According to (3), if the speed of the wind wheel is acquired and transmitted to the control system in real time, the SG can receive a constant input speed by adjusting the speed of the PMSM.

B. Mathematical Model of SG

To investigate control strategies, various studies have shown that a third-order mathematical model of SG is sufficient to satisfy engineering demands considering the complexity of control law modeling. In this case, the model of an electrically excited SG is given by [

26], [27]:

\{\begin{array}{l} {\dot{δ}}_{g} = ω_{g} - ω_{g 0} \\ {\dot{ω}}_{g} = \frac{ω_{g 0}}{H_{g}} (P_{g i} - P_{g e}) - \frac{D_{g}}{H_{g}} (ω_{g} - ω_{g 0}) \\ {\dot{E}}_{g q}^{'} = - \frac{1}{T_{g d 0}} E_{g q} + \frac{1}{T_{g d 0}} E_{g f} \end{array}

(4)

P_{g e} = \frac{E_{g q}^{'} U_{g s}}{X_{g d Σ}^{'}} s i n δ_{g}

(5)

where $δ_{g}$ is the SG power angle; $ω_{g}$ is the rotor speed; $ω_{g 0}$ is the steady-state rotor speed; H_g is the inertia time moment; P_gi is the compound input mechanical power; P_ge is the electromagnetic power; D_g is the damping coefficient; $E_{g f}$ is the excitation voltage; U_gs is the bus voltage; E_gq and $E_{g q}^{'}$ are the steady- and transient-state electric potential of the SG in the q axis, respectively; $T_{g d 0}$ is the steady-state open-circuit time constant of excitation winding in the d axis; and $X_{g d Σ}^{'}$ is the total equivalent reactance values in the d axis.

Given that $E_{g q}^{'}$ is always difficult to measure and P_ge describes most of the nonlinearity in the SG, in combination with (4) and (5), the time derivative of P_ge is given by:

{\dot{P}}_{g e} = \frac{U_{g s} E_{g q}^{'} (ω_{g} - ω_{g 0}) c o s δ_{g}}{X_{g d Σ}^{'}} - \frac{U_{g s} E_{g q} s i n δ_{g}}{X_{g d Σ}^{'} T_{g d 0}} + \frac{U_{g s} E_{g f} s i n δ_{g}}{X_{g d Σ}^{'} T_{g d 0}}

(6)

Let

\{\begin{array}{l} x_{1} = Δ δ_{g} = δ_{g} - δ_{g 0} \\ x_{2} = Δ ω_{g} = ω_{g} - ω_{g 0} \\ x_{3} = Δ P_{g e} = P_{g i} - P_{g e} \end{array}

(7)

where $δ_{g 0}$ is the steady-state power angle of the SG. Then, (4) can be rewritten in the state-space form as:

\{\begin{array}{l} {\dot{x}}_{1} = x_{2} \\ {\dot{x}}_{2} = \frac{ω_{g 0}}{H_{g}} x_{3} - \frac{D_{g}}{H_{g}} x_{2} \\ {\dot{x}}_{3} = f (x, d) + b_{0} u \end{array}

(8)

where $f (x, d)$ is the lumped disturbance; b₀ is a constant related to $δ_{g 0}$ ; and u is the control input for $E_{g f}$ .

\{\begin{array}{l} \begin{array}{l} f (x, d) = {\dot{x}}_{3} - b_{0} u = {\dot{P}}_{g i} - \frac{U_{g s} E_{g q}^{'} (ω_{g} - ω_{g 0}) c o s δ_{g}}{X_{g d Σ}^{'}} + \\ \frac{U_{g s} E_{g q} s i n δ_{g}}{T_{g d 0} X_{g d Σ}^{'}} - \frac{U_{g s} (s i n δ_{g} + s i n δ_{g 0})}{X_{g d Σ}^{'} T_{g d 0}} u \end{array} \\ b_{0} = \frac{U_{g s} s i n δ_{g 0}}{X_{g d Σ}^{'} T_{g d 0}} \end{array}

(9)

III. Design Procedure and Theory of FOSMC-ESO

A. Feedback Linearization Based on ESO

As observed from (8) and (9), the nonlinear factors in the SG model are described by ${\dot{x}}_{3}$ . Thus, it is complicated to design an SG excitation controller using direct feedback linearization. To address this problem, a two-order ESO is designed to estimate the lumped disturbances and nonlinear dynamics in the SG model [

28], [29]:

\{\begin{array}{l} σ = z_{1} - P_{g e} \\ {\dot{z}}_{1} = z_{2} - β_{1} \cdot f a l (σ, γ_{1}, ξ) + b_{0} u \\ {\dot{z}}_{2} = - β_{2} \cdot f a l (σ, γ_{2}, ξ) \end{array}

(10)

where z₁ and z₂ are the estimates of P_ge and $f (x, d)$ , respectively; $β_{1}$ , $β_{2}$ , $γ_{1}$ , $γ_{2}$ , and $ξ$ are the ESO parameters; and function $f a l (σ, γ_{x}, ξ)$ ( $x = 1,2$ ) is defined as [

28], [29]:

f a l (σ, γ_{x}, ξ) = \{\begin{array}{l} \frac{σ}{ξ^{γ_{x} - 1}} | σ | \leq ξ \\ | σ |^{γ_{x}} s i g n (σ) | σ | > ξ \end{array}

(11)

s i g n (σ) = \{\begin{array}{l} 1 σ > 0 \\ 0 σ = 0 \\ - 1 σ < 0 \end{array}

(12)

Thus, in combination with (8) and (10), linearization for SG excitation unit can be achieved for the following control input:

u = \frac{{\dot{x}}_{3} - z_{2}}{b_{0}}

(13)

B. Design of FOSMC-ESO

Define a fractional calculus operator ${}_{a} D_{t}^{α}$ as [

38]:

{}_{a} D_{t}^{α} f (t) = \{\begin{array}{l} \frac{d^{α} f (t)}{d t^{α}} R e (α) > 0 \\ f (t) R e (α) = 0 \\ \int_{a}^{t} {}_{a} D_{t}^{α + 1} f (t) d t R e (α) < 0 \end{array}

(14)

where a and t are the lower and upper limits of the fractional calculus operator, respectively; and $α$ is the operator order.

By using the Caputo fractional calculus approach, the $α^{t h}$ -order fractional derivative of a continuous function can be calculated with (15) if $m - 1 < α < m$ holds [

38].

{}_{a} D_{t}^{α} f (t) = \frac{1}{Γ (m - α)} \int_{a}^{t} \frac{f^{(m)} (τ)}{{(t - τ)}^{α - m + 1}} d τ

(15)

where m is an integer; and $Γ$ is the Gamma function given by:

Γ (z) = \int_{0}^{\infty} e^{- t} t^{z - 1} d t

(16)

For simplicity, we denote ${}_{a} D_{t}^{α}$ compactly as $D_{t}^{α}$ when the lower and upper limits of the fractional calculus operator are not involved. The design of the FOSMC comprises the design of the sliding surface and switching control law. According to (7), (8), and (10), the tracking error vector $e (t)$ can be set as:

e (t) = [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} Δ δ_{g} \\ Δ ω_{g} \\ Δ P_{g e} \end{matrix}]

(17)

Then, the sliding surface function $s (t)$ can be expressed as [

34]-[36]:

s (t) = C e (t) + K D_{t}^{- α} e (t)

(18)

where $C = [c_{1}, c_{2}, c_{3}]$ and $K = [k_{1}, k_{2}, k_{3}]$ are the constant vectors. The derivative of (18) is then given by:

\dot{s} (t) = \frac{d}{d t} (C e (t) + K D_{t}^{- α} e (t)) = C \dot{e} (t) + K D_{t}^{- α} \dot{e} (t)

(19)

D_{t}^{α} \dot{s} (t) = D_{t}^{α} (C \dot{e} (t) + K D_{t}^{- α} \dot{e} (t)) = C D_{t}^{α + 1} \dot{e} (t) + K \dot{e} (t)

(20)

To ensure that the system can quickly approach the sliding mode, the exponential approach law is selected for FOSMC:

\dot{s} (t) = - ε_{1} s i g n (s (t)) - ε_{2} s (t)

(21)

where $ε_{1}$ and $ε_{2}$ are the positive constants. According to (20) and (21), we can obtain:

\dot{s} (t) = D_{t}^{α} (- ε_{1} s i g n (s (t)) - ε_{2} s (t)) = C D_{t}^{α + 1} e (t) + K \dot{e} (t)

(22)

Combining (8), (16), and (22), we can obtain:

\begin{array}{l} K \dot{e} (t) = k_{1} {\dot{x}}_{1} + k_{2} {\dot{x}}_{2} + k_{3} {\dot{x}}_{3} = k_{1} x_{2} + k_{2} (\frac{ω_{g 0}}{H_{g}} x_{3} - \frac{D_{g}}{H_{g}} x_{2}) + \\ k_{3} (z_{2} + b_{0} u) = D_{t}^{α} (- ε_{1} s i g n (s (t)) - ε_{2} s (t)) - C D_{t}^{α + 1} e (t) \end{array}

(23)

Therefore, the system control law can be expressed as:

\begin{array}{l} u = - \frac{z_{2}}{b_{0}} + \frac{1}{b_{0} k_{3}} [\overset{}{D_{t}^{α} (- ε_{1} s i g n (s (t)) - ε_{2} s (t)) -} \\ C D_{t}^{α + 1} e (t) - (k_{1} - \frac{k_{2} D_{g}}{H_{g}}) x_{2} - \frac{k_{2} ω_{g 0}}{H_{g}} x_{3}] \end{array}

(24)

The reaching condition and convergence of the proposed controller must be satisfied to guarantee the final tracking performance. In this case, we select the following Lyapunov function:

V = \frac{1}{2} s^{2} (t)

(25)

Prerequisite $\dot{V} < 0$ is required to ensure that the designed FOSMC-ESO is stable and can reach the switching surface in finite time.

Owing to the complex operation scenarios of WTs, we define a time-varying parameter $Δ z$ , which represents the error between the actual and observed values of P_ge, to express the amount of lumped disturbance. Hence, according to (12), (18), (21), and (25), $\dot{V}$ can be obtained as:

\begin{array}{l} \dot{V} = s (t) \dot{s} (t) = s (t) (C \dot{e} (t) + K D_{t}^{- α} \dot{e} (t) + c_{3} Δ z + k_{3} D_{t}^{- α} Δ z) = \\ s (t) (- ε_{1} s i g n (s (t)) - ε_{2} s (t) + c_{3} Δ z + k_{3} D_{t}^{- α} Δ z) = \\ - ε_{1} | s (t) | - ε_{2} s^{2} (t) + s (t) (c_{3} Δ z + k_{3} D_{t}^{- α} Δ z) \leq \\ - ε_{1} | s (t) | + s (t) (c_{3} Δ z + k_{3} D_{t}^{- α} Δ z) \end{array}

(26)

To make sure that $\dot{V} < 0$ always holds, the following condition should be satisfied:

- ε_{1} | s (t) | + s (t) (c_{3} Δ z + k_{3} D_{t}^{- α} Δ z) < 0

(27)

In this case, if the values of c₃, k₃, and $ε_{1}$ are selected according to (28), the proposed controller is asymptotically stable.

| c_{3} Δ z + k_{3} D_{t}^{- α} Δ z | \leq c_{3} | Δ z | + k_{3} | D_{t}^{- α} Δ z | < ε_{1}

(28)

A linear proportional link u_add is also supplemented into the control law to eliminate the impacts of terminal voltage changes and achieve voltage regulation:

u_{a d d} = c_{4} (U_{g t} - U_{g t 0})

(29)

where U_gt and U_gt₀ are the output and steady-state terminal voltages of the SG, respectively; and c₄ is a positive constant.

The control block diagram of the improved FOSMC-ESO is shown in Fig. 3.

Fig. 3 Block diagram of improved FOSMC-ESO.

IV. Experimental and Simulation Evaluations

A. Experimental Validation of Simulation Platform

In [

22], we established a detailed simulation model of an SRDM-based hybrid drive WT based on derived triaxial dynamic equations. However, the analysis concerning the structural characteristics and transmission principles of the SRDM was implemented considering the ideal condition without mechanical transmission losses.

To ensure high simulation accuracy, we evaluated case studies in a dedicated experimental platform described in the Appendix A to verify the correctness of the simulation models. In this subsection, specific parameters of the testbed are used to build the simulation model. Four normal turbulent models with mean wind speeds of 5 m/s, 10 m/s, 13 m/s, and 21 m/s shown in Fig. 4(a) are simulated as experimental and simulation inputs by using the FAST software. The wind wheel speed profiles are shown in Fig. 4(b).

Fig. 4 Profiles of different wind speeds and wind wheel speeds. (a) Wind speeds. (b) Wind wheel speeds.

The desired rated speed of the SG is set to be 300 r/min, and the experiments last for 100 s. The results of the SG input speeds for the four normal turbulent models are shown in Fig. 5.

Fig. 5 Results of SG input speeds for four normal turbulent models. (a) Results at wind speed of 5 m/s. (b) Results at wind speed of 11 m/s. (c) Results at wind speed of 13 m/s. (d) Results at wind speed of 21 m/s.

After reaching the steady-state operation, the SG driving speeds obtained from the experiments and simulations are distributed in the range of [295, 305]r/min. The maximum and average steady-state errors in the experiments are less than 2.40% and 1.66%, respectively, while those in the simulations are within 1.34% and 1.02%, respectively, at different wind speed inputs. These results demonstrate the desired behavior and accuracy of the simulation approach, which could be used for subsequent performance evaluations of controllers.

B. Performance Evaluation of FOSMC-ESO

To verify the effectiveness of the proposed FOSMC-ESO, a simulation model with a 1.5 MW SRDM-based hybrid drive WT is built considering the experimental validation of the simulation platform. Comparisons are conducted to verify the on-grid performance of the SRDM-based hybrid drive WT using the proposed FOSMC-ESO, PID-PSS, and SMC-ESO under random wind speeds and various grid voltage drop faults.

The key parameters of SG are listed in Table I, and the control parameters are provided below.

TABLE I Key Parameters of SG

Symbol	Quantity	Value
P_grate	Rated power	1.5 MW
f_gr	Frequency	50 Hz
X_gd	d-axis steady reactance	1.81 p.u.
$X_{g d}^{'}$	d-axis transient reactance	0.3 p.u.
T_gd₀	Open-circuit time constant	4.5 s
H_g	Inertia time constant	3.2 s
D_g	Damping coefficient	0
X_TR	Transformer reactance	0.16 p.u.
X_TL	Transmission line reactance	0.263 p.u.

1) FOSMC: $c_{1} = 0.1$ , $c_{2} = 20$ , $c_{3} = 0.2$ , $c_{4} = 10$ , $k_{1} = k_{2} = k_{3} = 1$ , $α = 0.05$ .

2) SMC: $c_{1} = - 1$ , $c_{2} = - 6$ , $c_{3} = 1$ .

3) PID: $k_{p} = 0.2$ , $k_{i} = 2$ , $k_{d} = 0.01$ .

4) ESO: $γ_{1} = 0.5$ , $γ_{2} = 0.25$ , $β_{1} = 2000$ , $β_{2} = 300$ , $ξ = 0.1$ .

The steady-state operation point parameters of the SG are set as follows: $P_{g e 0} = 0.75$ p.u., $δ_{g 0} = 25.2 °$ , $ω_{g 0} = 314$ rad/s, and $U_{g t 0} = 1.01$ p.u..

1)　Evaluation Under Mechanical Power Fluctuations

Because the input mechanical power fluctuations of an SRDM-based hybrid drive WT can be induced by changes of wind speed, an energy backlog occurs on the generator shaft under power imbalance, seriously affecting the WT operation safety. Therefore, case studies with different types of changing wind speeds are evaluated to determine the performance of the proposed FOSMC-ESO to compensate for deviations between input mechanical power and output electromagnetic power.

Three typical wind models are generated and used for evaluation, and their main characteristics are summarized as follows.

1) Case 1: a normal turbulent model with 10 m/s basic wind speed and 20% turbulence density.

2) Case 2: an extreme turbulent model with 13 m/s basic wind speed and 40% turbulence density.

3) Case 3: a coherent gust model with 10 m/s initial wind speed, 14.88 m/s gust amplitude, and -72° change in direction.

Figures 6-8 show the power deviations using different controllers during a 15 s simulation in cases 1-3, respectively.

Fig. 6 Wind wheel input of case 1 and power deviations using different controllers in case 1. (a) Wind wheel input. (b) Power deviation.

As observed from Fig. 6, the power imbalance peak of SG obtained by using the proposed FOSMC-ESO is only 0.08 p.u., while the peaks obtained by SMC-ESO and PID-PSS are 0.2 p.u. and 0.26 p.u., respectively. Meanwhile, as shown in Fig. 7, the power imbalances of SG substantially increase and reach around 0.3 p.u. for SMC-ESO, 0.5 p.u. for PID-PSS, and 0.2 p.u. for the proposed FOSMC-ESO. Nevertheless, the average power gap for FOSMC-ESO is small (less than 0.07 p.u.), being only 35% and 25% of the gaps for SMC-ESO and PID-PSS, respectively. As shown in Fig. 8(b), under coherent gust, although the SRDM-based hybrid drive WT suffers a power shock of about 0.4 p.u., the SG equipped with the proposed FOSMC-ESO could release the excess power quickly (less than 1 s), helping to protect the equipment and handle the resulting power imbalance effects. These results demonstrate the effectiveness and advancement of the proposed FOSMC-ESO in relieving energy backlog.

Fig. 7 Power deviations using different controllers in case 2. (a) Wind wheel input of case 2. (b) Power deviation.

Fig. 8 Power deviations using different controllers in case 3. (a) Wind wheel input of case 3. (b) Power deviation.

2)　Evaluation Under Different Grid Faults

Most grid codes for monitoring the behaviors of wind farms require reliable LVRT capability. Hence, the on-grid performance of the SRDM-based hybrid drive WT by adopting the three evaluated controllers are compared and analyzed under symmetrical and asymmetrical grid faults. The wind wheel input in case 1 shown in Fig. 6(a) is used as the system input.

At $t = 0.375$ s, a three-phase short-circuit symmetrical fault is simulated on the high-voltage side of the transformer, causing the on-grid point voltage to drop by 80% of the rated value for 0.625 s. The corresponding SG indicators of terminal voltage, rotor speed, and output active and reactive power values for the three controllers are recorded, as shown in Fig. 9(a). For generality, the same indicators under three-phase short-circuit symmetrical faults with a 50% voltage drop for 0.625 s and an 80% voltage drop for 0.2 s are shown in Fig. 9(b) and (c), respectively.

Fig. 9 Results under three-phase short-circuit symmetrical faults. (a) 80% voltage drop for 0.625 s. (b) 50% voltage drop for 0.625 s. (c) 80% voltage drop for 0.2 s.

The comparative analysis of the excitation control performance is also studied under critical single-phase-to-ground short-circuit asymmetrical faults. The corresponding results of the above-mentioned indicators are shown in Fig. 10. For clarity, the data analysis of Figs. 9 and 10 containing all the oscillation amplitudes and the time for indicator recovery are listed in Table II, where E_STA represents the standard deviation of the state variables after fault removal, t_r is the time required for recovery, and six cases are considered.

Fig. 10 Results under single-phase-to-ground short-circuit asymmetrical faults. (a) 80% voltage drop for 0.625 s. (b) 50% voltage drop for 0.625 s. (c) 80% voltage drop for 0.2 s.

As shown in Fig. 9, during three-phase short-circuit symmetrical faults, the indicators obtained by the proposed FOSMC-ESO return faster to their steady states with the smallest oscillation peaks than those obtained by SMC-ESO and PID-PSS. As listed in Table II, the four indicators take around 1.25 s, 1.07 s, 0.59 s, and 1.08 s for recovery obtained by FOSMC-ESO, being approximately 70%-80% and 30%-40% of the recovery time obtained by SMC-ESO and PID-PSS, respectively. The recovery responses are also smoother and directly reach steady states obtained by the proposed FOSMC-ESO.

After the fault is removed, the SG rotor speed obtained by FOSMC-ESO has only 0.992 p.u. of shock bottom, while the speeds endure derivations of 0.013 p.u. and 0.026 p.u. obtained by SMC-ESO and PID-PSS, respectively. Moreover, as shown in Fig. 9(a) and Table II, around 0.4 p.u. of additional reactive power could be provided by using SMC-ESO or FOSMC-ESO, possibly contributing to restoring the grid-connected point voltage during LVRT operation. The analysis of Fig. 9(b) and (c) leads to similar findings.

TABLE Ⅱ Data Analysis of Results for Different Grid Faults Shown in Figs. 9 and 10

Variable	Controller	Case 1		Case 2		Case 3		Case 4		Case 5		Case 6
Variable	Controller	E_STA (p.u.)	t_r (s)	E_STA (p.u.)	t_r (s)	E_STA (p.u.)	t_r (s)	E_STA (p.u.)	t_r (s)	E_STA (p.u.)	t_r (s)	E_STA (p.u.)	t_r (s)
Voltage	PID-PSS	0.048400	2.70	0.023900	2.51	0.038600	2.84	0.028800	3.76	0.027000	3.63	0.017800	3.05
	SMC-ESO	0.037800	1.53	0.023200	1.52	0.030600	1.59	0.014500	1.20	0.010600	1.18	0.007800	1.25
	FOSMC-ESO	0.037300	1.25	0.022600	1.17	0.030400	1.21	0.016800	1.01	0.012200	0.97	0.008300	1.07
Speed	PID-PSS	0.007528	3.47	0.000862	2.88	0.001671	3.36	0.000963	3.96	0.000840	3.89	0.001374	3.22
	SMC-ESO	0.002751	1.43	0.000486	1.25	0.000736	1.37	0.000952	1.43	0.000703	1.54	0.000622	1.38
	FOSMC-ESO	0.001836	1.07	0.000196	0.98	0.000512	1.15	0.000456	1.18	0.000339	1.18	0.000451	1.17
Active power	PID-PSS	0.497100	3.13	0.088400	2.64	0.129500	2.83	0.084700	2.75	0.055000	2.83	0.098800	2.85
	SMC-ESO	0.224600	1.17	0.070000	1.03	0.124900	1.29	0.083100	1.19	0.056400	1.21	0.081800	1.17
	FOSMC-ESO	0.188200	0.59	0.069300	0.65	0.124300	0.65	0.073900	0.59	0.049200	0.75	0.079400	0.87
Reactive power	PID-PSS	0.327300	2.96	0.148900	2.73	0.278300	3.47	0.320100	3.61	0.301400	3.77	0.215600	3.13
	SMC-ESO	0.235000	1.45	0.132400	1.37	0.156100	1.51	0.182100	1.37	0.132100	1.27	0.119800	1.44
	FOSMC-ESO	0.256400	1.08	0.135500	1.01	0.164400	1.18	0.205500	1.03	0.149100	0.95	0.124700	1.09

As shown in Fig. 10, when asymmetrical faults occur, the terminal voltage and active and reactive power values experience serious oscillations under single-phase-to-ground short-circuit faults owing to the harmonic pollutants in the SG stator and rotor currents. As shown in Fig. 10(a) and Table II, the indicators obtained by using FOSMC-ESO require the shortest time for recovery with small shock peaks compared with the other controllers. The maximum fluctuation of the rotor speed is less than 0.003 p.u., while that of active power remains within 1.03 p.u., and that of reactive power remains within $- 1.92$ p.u.. The recovery time for the SG parameters using FOSMC-ESO is much shorter than that of the other controllers and could be reduced to approximately 1.01 s for the terminal voltage, 1.18 s for the rotor speed, 0.59 s for the active power, and 1.03 s for the reactive power. The average deviations of the four SG indicators can be reduced by approximately 20%-40% compared with those obtained by PID-PSS. As shown in Fig. 10(b) and (c), the control performance of the proposed FOSMC-ESO is also much better than that of PID-PSS.

It should be mentioned that the SMC-ESO is suitable for SG excitation control. However, chattering could not be eliminated. Furthermore, FOSMC-ESO achieves superior performance for suppressing the oscillation regions and accelerating the recovery time of the indicators. As listed in Table II, the recovery time and shock peaks obtained obtained by SMC-ESO are approximately one-quarter and one-third larger than those obtained by the proposed FOSMC-ESO, respectively. Enough reactive power can also be provided by the proposed FOSMC-ESO.

V. Conclusion

Considering SRDM-based hybrid drive WTs, this paper proposes an improved FOSMC-ESO for accurate control of SG excitation, thus enhancing the on-grid operation performance of WT under changing wind speeds, parameter uncertainties, and various grid voltage drop faults. The satisfactory functions of the SRDM in SG speed regulation and superiority of the proposed controller in excitation adjustment are verified by comparative experimental and simulation case studies.

We can draw the following conclusions from this study.

1) The simulation platform is applicable and accurate. The maximum and average steady-state errors of SG input wind speed in the simulation are less than 1.34% and 1.02%, respectively.

2) The proposed controller can considerably alleviate the power imbalance between the SG input and output. Under different wind speeds, the average power gap is only 0.07 p.u., being much smaller than the gaps obtained by SMC-ESO and PID-PSS.

3) An SRDM-based hybrid drive WT equipped with the proposed FOSMC-ESO has an outstanding LVRT capability under symmetrical and asymmetrical grid faults. Compared with conventional controllers, the SG indicators of terminal voltage, rotor speed, and output active/reactive power can quickly recover their steady states with the smallest oscillation amplitudes by using the proposed controller. Moreover, enough reactive power can be generated for grid-voltage restoration during fault periods.

This study provides a convincing theoretical basis for the practical application of hybrid drive WTs. Future works concerning experimental validations in high-power testbeds should be considered to further improve the operation of SRDM-based hybrid drive WTs and proposed FOSMC-ESO.

Appendix

Appendix A

Figure A1 shows the experimental platform of the SRDM-based hybrid drive WT.

Fig. A1 Experimental platform of SRDM-based hybrid drive WT.

The differential gear box, treated as a core equipment of the testbed, consists of a single-stage planetary gear and a pair of synchronous belt wheels. Servo motors A and B are connected to the planet carrier and ring gear of the differential gear box to provide the dominating input and speed regulation power source, respectively. Sensors A and B acquire torque and speed signals in real time for transmission to an industrial personal computer (IPC) to complete speed control. The DAQNavi, MATLAB, and LabVIEW software packages connect the software and hardware components.

References

K. Hu, C. Raghutla, K. R. Chittedi et al., “The effect of energy resources on economic growth and carbon emissions: a way forward to carbon neutrality in an emerging economy,” Journal of Environmental Management, vol. 298, no. 3, p. 113448, Nov. 2021. [Baidu Scholar]

A. Attya, J. L. Dominguez-Garcia, and O. Anaya-Lara, “A review on frequency support provision by wind power plants: current and future challenges,” Renewable & Sustainable Energy Reviews, vol. 81, pp. 2071-2087, Jan. 2018. [Baidu Scholar]

B. K. Sahu, “Wind energy developments and policies in China: a short review,” Renewable & Sustainable Energy Reviews, vol. 81, pp. 1393-1405, Jan. 2018. [Baidu Scholar]

X. Liang, “Emerging power quality challenges due to integration of renewable energy sources,” IEEE Transactions on Industry Applications, vol. 53, no. 2, pp. 855-866, Mar.-Apr. 2017. [Baidu Scholar]

R. A. Oliveira and M. Bollen, “Susceptibility of large wind power plants to voltage disturbances-recommendations to stakeholders,” Journal of Modern Power Systems and Clean Energy, vol. 10, no. 2, pp. 416-429, Mar. 2022. [Baidu Scholar]

F. Wang, J. Chen, B. Xu et al., “Improving the reliability and energy production of large wind turbine with a digital hydrostatic drivetrain,” Applied Energy, vol. 251, p. 113309, Oct. 2019. [Baidu Scholar]

Y. Chang, I. Kocar, J. Hu et al., “Coordinated control of DFIG converters to comply with reactive current requirements in emerging grid codes,” Journal of Modern Power Systems and Clean Energy, vol. 10, no. 2, pp. 502-514, Mar. 2022. [Baidu Scholar]

M. K. K. Prince, M. T. Arif, A. Gargoom et al., “Modeling, parameter measurement, and control of PMSG-based grid-connected wind energy conversion system,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 5, pp. 1054-1065, Sept. 2021. [Baidu Scholar]

M. Saqib and A. Saleem, “Power-quality issues and the need for reactive-power compensation in the grid integration of wind power,” Renewable & Sustainable Energy Reviews, vol. 43, pp. 51-64, Mar. 2015. [Baidu Scholar]

C. Wessels, F. Gebhardt, and F. Fuchs, “Fault ride-through of a DFIG wind turbine using a dynamic voltage restorer during symmetrical and asymmetrical grid faults,” IEEE Transactions on Power Electronics, vol. 26, no. 3, pp. 807-815, Mar. 2011. [Baidu Scholar]

T. P. Teixeira and C. L. T. Borges, “Operation strategies for coordinating battery energy storage with wind power generation and their effects on system reliability,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 1, pp. 190-198, Jan. 2021. [Baidu Scholar]

S. Ghosh and S. Kamalasadan, “An integrated dynamic modeling and adaptive controller approach for flywheel augmented DFIG based wind system,” IEEE Transactions on Power Systems, vol. 32, no. 3, pp. 2161-2171, May. 2017. [Baidu Scholar]

R. Hiremath and T. Moger, “Comprehensive review on low voltage ride through capability of wind turbine generators,” International Transactions on Electrical Energy Systems, vol. 30, no. 10, p. e12524, Jul. 2020. [Baidu Scholar]

M. A. Hannan, H. M. S. Lipu, P. J. Ker et al., “Power electronics contribution to renewable energy conversion addressing emission reduction: applications, issues, and recommendations,” Applied Energy, vol. 251, p. 113404, Oct. 2019. [Baidu Scholar]

L. Sainz, L. Monjo, J. Pedra et al., “Effect of wind turbine converter control on wind power plant harmonic response and resonances,” IET Electric Power Applications, vol. 11, no. 2, pp. 157-168, Feb. 2017. [Baidu Scholar]

M. Idan and D. Lior, “Continuous variable speed wind turbine: transmission concept and robust control,” Wind Engineering, vol. 24, no. 3, pp. 151-167, May 2000. [Baidu Scholar]

Y. Lin, L. Tu, H. Liu et al., “Hybrid power transmission technology in a wind turbine generation system,” IEEE-ASME Transaction on Mechatronics, vol. 20, no. 3, pp. 1218-1225, Jun. 2015. [Baidu Scholar]

X. Zhao and P. Maißer, “A novel power splitting drive train for variable speed wind power generators,” Renewable Energy, vol. 28, no. 13, pp. 2001-2011, Oct. 2003. [Baidu Scholar]

D. Li, W. Cai, P. Li et al., “Dynamic modeling and controller design for a novel front-end speed regulation (FESR) wind turbine,” IEEE Transactions on Power Electronics, vol. 33, no. 5, pp. 4073-4087, May 2018. [Baidu Scholar]

D. Petković, Ž. Ćojbašić, and V. Nikolić, “Adaptive neuro-fuzzy maximal power extraction of wind turbine with continuously variable transmission,” Energy, vol. 64, pp. 868-874, Jan. 2014. [Baidu Scholar]

X. Rui, W. Yin, Y. Dong et al., “Fractional‐order sliding mode control for hybrid drive wind power generation system with disturbances in the grid,” Wind Energy, vol. 22, no. 1, pp. 49-64, Jan. 2019. [Baidu Scholar]

W. Yin, Z. Dong, L. Liu et al., “Self-stabilising speed regulating differential mechanism for continuously variable speed wind power generation system,” IET Renewable Power Generation, vol. 14, no. 15, pp. 3002-3009, Oct. 2020. [Baidu Scholar]

W. Yin, X. Wu, and X. Rui, “Adaptive robust backstepping control of the speed regulating differential mechanism for wind turbines,” IEEE Transactions on Sustainable Energy, vol. 10, no. 3, pp. 1311-1318, Jul. 2019. [Baidu Scholar]

H. Müller, M. Pöller, A. Basteck et al., “Grid compatibility of variable speed wind turbines with directly coupled synchronous generator and hydro-dynamically controlled gearbox,” in Proceeding of the 6th International Workshop on Large-scale Integration of Wind Power and Transmission Networks for Offshore Wind Farms, Delft, Netherlands, Oct. 2006, pp. 307-315. [Baidu Scholar]

X. Li, H. Dong, H. Li et al., “Optimization control of front-end speed regulation (FESR) wind turbine based on improved NSGA-II,” IEEE Access, vol. 7, pp. 45583-45593, Apr. 2019. [Baidu Scholar]

H. Dong, N. Chen, X. Li et al., “Improved adaptive robust control for low voltage ride-through of front-end speed regulation wind turbine,” IEEE Access, vol. 8, pp. 55438-55446, Mar. 2020. [Baidu Scholar]

T. Li, J. Zhu, M. Yuan et al., “Design of a robust excitation controller based on differential homeo-morphic mapping and extended state observer,” Power System Technology, vol. 36, no. 2, pp. 131-135, Feb. 2012. [Baidu Scholar]

J. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900-906, Mar. 2009. [Baidu Scholar]

B. Liu, J. Zhao, Q. Huang et al., “Robust nonlinear controller to damp drivetrain torsional oscillation of wind turbine generators,” IEEE Transactions on Sustainable Energy, vol. 12, no. 2, pp. 1336-1346, Apr. 2021. [Baidu Scholar]

B. Liu, J. Zhao, Q. Huang et al., “Robust nonlinear controller for wind turbine generator drivetrain torsional oscillation under large disturbances,” in Proceeding of 2021 IEEE PES General Meeting (PESGM), Washington DC, USA, Jul. 2021, pp. 1-5. [Baidu Scholar]

E. Nechadi, M. N. Harmas, A. Hamzaoui et al., “A new robust adaptive fuzzy sliding mode power system stabilizer,” International Journal of Electrical Power & Energy Systems, vol. 42, no. 1, pp. 1-7, Nov. 2012. [Baidu Scholar]

M. Ouassaid, M. Maaroufi, and M. Cherkaoui, “Observer-based nonlinear control of power system using sliding mode control strategy,” Electric Power Systems Research, vol. 84, no. 1, pp. 135-143, Mar. 2012. [Baidu Scholar]

X. Liu and Y. Han, “Decentralized multi-machine power system excitation control using continuous higher-order sliding mode technique,” International Journal of Electrical Power & Energy Systems, vol. 82, pp. 76-86, Nov. 2016. [Baidu Scholar]

V. Utkin, “Sliding mode control design principles and applications to electric drives,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 23-36, Feb. 1993. [Baidu Scholar]

S. Huang, L. Xiong, J. Wang et al., “Fixed-time fractional-order sliding mode controller for multimachine power systems,” IEEE Transactions on Power Systems, vol. 36, no. 4, pp. 2866-2876, Dec. 2020. [Baidu Scholar]

V. Patel, D. Guha, and S. Purwar, “Neural network aided fractional-order sliding mode controller for frequency regulation of nonlinear power systems,” Computers & Electrical Engineering, vol. 96, p. 107534, Dec. 2021. [Baidu Scholar]

M. Luo, Planetary Gear Mechanism. Nanjing: Southeast University Press, 2019, pp. 23-41. [Baidu Scholar]

D. Valério and J. Costa, “Introduction to single-input single-output fractional control,” IET Control Theory and Applications, vol. 5, no. 8, pp. 1033-1057, May 2011. [Baidu Scholar]

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