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.
PURSUING carbon neutrality and peak emissions has contributed to the continuous investment in and development of a low-carbon, safe, and efficient energy market [
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) [
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, [
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, [
An ESO can perform state estimation in a nonlinear system under parameter uncertainty and external disturbances [
In our previous work [
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.

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

Fig. 2 Speed relations between components in PGT.
By using the reverse rotation method [
(1) |
where , , and are the rotation speeds of the planet carrier, sun gear, and ring gear, respectively; () and () 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:
(2) |
According to the parameter optimization results in [
(3) |
where nw, nm, and ng are the rotation speeds of the wind wheel, PMSM, and SG, respectively; iCr is the speed increasing ratio between the wind wheel and planet carrier; and iRm is the transmission ratio between the PMSM and ring gear. For an actual SRDM-based hybrid drive WT, k, iCr, and iRm 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.
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 [
(4) |
(5) |
where is the SG power angle; is the rotor speed; is the steady-state rotor speed; Hg is the inertia time moment; Pgi is the compound input mechanical power; Pge is the electromagnetic power; Dg is the damping coefficient; is the excitation voltage; Ugs is the bus voltage; Egq and are the steady- and transient-state electric potential of the SG in the q axis, respectively; is the steady-state open-circuit time constant of excitation winding in the d axis; and is the total equivalent reactance values in the d axis.
Given that is always difficult to measure and Pge describes most of the nonlinearity in the SG, in combination with (4) and (5), the time derivative of Pge is given by:
(6) |
Let
(7) |
where is the steady-state power angle of the SG. Then, (4) can be rewritten in the state-space form as:
(8) |
where is the lumped disturbance; b0 is a constant related to ; and u is the control input for .
(9) |
As observed from (8) and (9), the nonlinear factors in the SG model are described by . 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 [
(10) |
where z1 and z2 are the estimates of Pge and , respectively; , , , , and are the ESO parameters; and function () is defined as [
(11) |
(12) |
Thus, in combination with (8) and (10), linearization for SG excitation unit can be achieved for the following control input:
(13) |
Define a fractional calculus operator as [
(14) |
where a and t are the lower and upper limits of the fractional calculus operator, respectively; and is the operator order.
By using the Caputo fractional calculus approach, the -order fractional derivative of a continuous function can be calculated with (15) if holds [
(15) |
where m is an integer; and is the Gamma function given by:
(16) |
For simplicity, we denote compactly as 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 can be set as:
(17) |
Then, the sliding surface function can be expressed as [
(18) |
where and are the constant vectors. The derivative of (18) is then given by:
(19) |
(20) |
To ensure that the system can quickly approach the sliding mode, the exponential approach law is selected for FOSMC:
(21) |
where and are the positive constants. According to (20) and (21), we can obtain:
(22) |
Combining (8), (16), and (22), we can obtain:
(23) |
Therefore, the system control law can be expressed as:
(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:
(25) |
Prerequisite 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 , which represents the error between the actual and observed values of Pge, to express the amount of lumped disturbance. Hence, according to (12), (18), (21), and (25), can be obtained as:
(26) |
To make sure that always holds, the following condition should be satisfied:
(27) |
In this case, if the values of c3, k3, and are selected according to (28), the proposed controller is asymptotically stable.
(28) |
A linear proportional link uadd is also supplemented into the control law to eliminate the impacts of terminal voltage changes and achieve voltage regulation:
(29) |
where Ugt and Ugt0 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 Block diagram of improved FOSMC-ESO.
In [
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 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 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.
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
Symbol | Quantity | Value |
---|---|---|
Pgrate | Rated power | 1.5 MW |
fgr | Frequency | 50 Hz |
Xgd | d-axis steady reactance | 1.81 p.u. |
d-axis transient reactance | 0.3 p.u. | |
Tgd0 | Open-circuit time constant | 4.5 s |
Hg | Inertia time constant | 3.2 s |
Dg | Damping coefficient | 0 |
XTR | Transformer reactance | 0.16 p.u. |
XTL | Transmission line reactance | 0.263 p.u. |
1) FOSMC: , , , , , .
2) SMC: , , .
3) PID: , , .
4) ESO: , , , , .
The steady-state operation point parameters of the SG are set as follows: p.u., , rad/s, and p.u..
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.

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. 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.
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
At 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 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 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
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
Variable | Controller | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ESTA (p.u.) | tr (s) | ESTA (p.u.) | tr (s) | ESTA (p.u.) | tr (s) | ESTA (p.u.) | tr (s) | ESTA (p.u.) | tr (s) | ESTA (p.u.) | tr (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
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.
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
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.
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