Wind turbine employs pitch angle control to maintain captured power at its rated value when the wind speed is higher than rated value. This work adopts a perturbation observer based sliding-mode control (POSMC) strategy to realize robust variable-pitch control of permanent magnet synchronous generator (PMSG). POSMC combines system nonlinearities, parametric uncertainties, unmodelled dynamics, and time-varying external disturbances into a perturbation, which aims to estimate the perturbation via a perturbation observer without an accurate system model. Subsequently, sliding mode control (SMC) is designed to completely compensate perturbation estimation in real-time for the sake of achieving a global consistent control performance and improving system robustness under complicated environments. Simulation results indicate that, compared with vector control (VC), feedback linearization control (FLC), and nonlinear adaptive control (NAC), POSMC has the best control performance in ramp wind and random wind and the highest robustness in terms of parameter uncertainty. Specially, the integral absolute error index of

Energy is an essential material basis and support for human survival and social-economic development [

Currently, permanent magnet synchronous generator (PMSG) is an attractive choice of wind turbine (WT) due to its large thrust, low loss, high-efficiency density, and high energy conversion efficiency [

Various variable pitch control techniques have been reported in publications during the past decades so far. Conventional vector control (VC) using proportional-integral (PI) and proportional-integral-derivative (PID) control are widely adopted in industrial processes owing to its strengths of simple configuration and convenient implementation [

In this work, a perturbation observer based sliding-mode control (POSMC) is adopted for PMSG to limit the turbine output power and generator speed in Region 3. Firstly, the perturbation observer generates the new perturbation via combining the system nonlinearities, parametric uncertainties, unmodelled dynamics, and time-varying external disturbances. Then sliding mode control is utilized to completely compensate the perturbation estimation in real-time. The proposed POSMC retains the strong robustness of sliding-mode control (SMC), and only require the measurements of d-q axis current and mechanical rotation speed. Three case studies are studied by Matlab/Simulink, e.g., ramp wind speed, random wind speed, and parameter uncertainty. Simulation results validate that, compared with VC control, feedback linearization control (FLC) and nonlinear adaptive control (NAC), POSMC can achieve satisfactory robust control performance under various operating conditions.

The rest of this article is organized as follows: Section 2 gives the model of PMSG system; Section 3 introduces the theory of POSMC; Section 4 develops the detailed design of POSMC for variable-pitch PMSG. In Section 5, case studies results are discussed and analyzed. And the last Section summarizes this work and draws conclusions.

A representative topology of PMSG system is described in

The tip speed ratio

where

According to aerodynamic theory, the electrical power extracted by the WT can be described as

where

The voltage and torque equations of PMSG can be denoted as

where _{d} and _{q} represent d-q axis stator voltages, _{d} and _{q} are d-q axis stator currents, _{d} and _{q} are d-q axis inductances, _{e} is the electromagnetic torque, _{e} is the permanent magnetic flux.

The dynamics model of mechanical shaft system can be represented by

where _{m} is the mechanical torque, _{e} has a much faster response than _{m}, thus let

Pitch angel control actuator could regulate the blade pitch based on the required value. And the first-order linear model of pitch angel control actuator without considering the delay characteristics can be given as [

where

An uncertain nonlinear system is denoted as

where

The perturbation of system

where _{0} is constant control gain.

Based on _{n} of system

Define a fictitious state _{n+1} to denote perturbation

Define the extended state vector

_{0} is selected to meet

Suppose _{1} is the sole measurable state, a (

where

An estimated sliding surface is defined as

where the estimated sliding surface gains

Finally, POSMC of system is given as

where

The state-space equation of PMSG is represented by

where

where _{s} is the stator resistance, _{d} and _{q} are d-q axis stator voltages, and

Differentiate control output

where

where

Note that

Define perturbation

where

Define tracking error

Then, a third order sliding-mode state and perturbation observer (SMSPO) is adopted to estimate

where positive constants

The estimated sliding surface of system

Finally, the POSMC of system

where

Differentiate control output

where

Note that

Define perturbation

where

Define tracking error

Then, two second order sliding-mode perturbation observers (SMPOs) are adopted to estimate

where positive constants

The estimated sliding surface of system

Finally, the POSMC of system

where

At this end, the overall block diagram of POSMC is shown in

As described in Assumption 2, the perturbation and its derivative are locally bounded. And the deduction of these bounds is given as

Hence, the validity of the developed perturbation observer is demonstrated.

Three cases, e.g., ramp wind speed, random wind speed, and parameter uncertainty, are undertaken to assess the performance of POSMC compared with that of VC [

Parameters | Values | Units | Parameters | Values | Units |
---|---|---|---|---|---|

Actuator time constant _{β} |
1 | s | Air density |
1.205 | kg/m^{3} |

Blade radius |
39 | m | d-axis inductance _{d} |
5.5 | mH |

d-axis stator current reference _{mdr} |
0 | A | Field flux _{e} |
136.25 | V∙s/rad |

Mechanical rotation speed reference | 2.2489 | rad/s | Number of pole pairs |
11 | |

Pitch angle rate _{rate} |
±10 | degree/s | q-axis inductance _{q} |
3.75 | mH |

q-axis stator current reference _{mqr} |
593.3789 | A | Rated electromagnetic torque reference | 889326.7 | Nm |

Rated output power _{r} |
2 | MW | Rated wind speed _{r} |
12 | m/s |

Stator resistance _{s} |
50 | Total inertia _{tot} |
10000 | kg∙m^{2} |

Pitch angle control | ||||
---|---|---|---|---|

Generator control | ||||

A ramp wind signal changing from 18 m/s to 14 m/s is exerted to WECS, as shown in _{m}, and _{m} during running period which needs full state measurements. Meanwhile, NAC has the highest overshoot of _{md} and _{mq} compared with other three methods. And POSMC can obtain the satisfactory control performance with the fast convergence speed and the small tracking error. Specially, the convergence time of VC, FLC, NAC, and POSMC in terms of _{m} of VC, FLC, NAC and POSMC is 8.70% and 3.55%, 1.25% and 0.15%, respectively. Meanwhile, the errors between the estimations and actual values of the designed observers are shown in

The random wind curve is denoted in _{m} and _{m} around their rated value during all the simulation time with the smallest overshoot and consistent control performance. Meanwhile, VC, FLC, and POSMC have the nearly similar control performace of _{md} and _{mq}. And

In this case, the variation of field flux _{e} from 1 (p.u.) at _{md} because of the simple mechanism, they have the worst control performance in other seven output variables. And the maximum overshoot of

Integral absolute error index

Scenario | IAE index | Controller | |||
---|---|---|---|---|---|

VC | FLC | NAC | POSMC | ||

Ramp wind | IAE |
0.4137 | 0.1555 | 4.312E-2 | 6.237E-4 |

IAE |
9.727E-15 | 1.025E-13 | 1.506E-2 | 2.84E-4 | |

IAE |
8.554E-13 | 6.97E-12 | 3.196E-2 | 2.753E-2 | |

Random wind | IAE |
1.317 | 1.273 | 1.017 | 0.154 |

IAE |
1.003E-14 | 1.075E-13 | 7.848E-2 | 7.295E-2 | |

IAE |
9.604E-13 | 7.155E-12 | 7.655E-2 | 2.436E-2 | |

Parameter uncertainty | IAE |
5.284E-2 | 0.207 | 2.742E-3 | 4.919E-5 |

IAE |
9.469E-15 | 1.24E-13 | 1.32E-3 | 7.168E-4 | |

IAE |
67.7 | 1957 | 0.2213 | 0.1841 |

In this paper, POSMC is applied in variable-pitch control of PMSG to limit generator’s output power at its rated value when the wind speed is higher than rated value. The main novelties/contributions can be concluded as follows:

POSMC combines nonlinearities, parametric uncertainties, unmodelled dynamics, and time-varying external disturbances into a new perturbation estimating via the perturbation observer. Subsequently, sliding mode control is designed to completely make up for the perturbation estimation in real-time for the sake of realizing a global consistent control performance and improving the robustness of the system under various operation conditions.

Compared with VC, POSMC is designed based on nonlinear architecture which is not affected by the changed system operating points.

Compared with FLC, POSMC only requires the measurements of d-q axis current and mechanical rotation speed

Compared with NAC, POSMC has the better control performance in ramp wind and random wind, the higher robustness in terms of parameter uncertainty, the smaller IAE indexes and overall control costs. Specially, the IAE

Future studies will be focused on carrying out the HIL experiment of variable-pitch PMSG to further prove the implementation feasibility of POSMC.