Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.

Wind power generation has widely grown during the last decades and nowadays is the most competitive form of renewable energy [

Wind turbines (WTs) are usually designed to withstand extreme winds statically so that they can survive a storm. However, such property keeps true only when the turbine is not spinning. At very large rotational speeds, the forces on the blades and other parts of the turbine are enormous and they will literally tear the turbine apart. In order to deal with the mechanical stress posed to the turbines during high wind speed, pitch-regulated and stall-regulated strategies are proposed and have been employed in the commercial WTs [

Configuration of pitch regulation subsystem in the WT.

The typical power curves of the pitch and the stall-regulated WECS are shown in Figure

Power curves of fixed pitch and variable pitch wind turbines.

As analyzed in [

This paper analyzed the nonlinear property of the real WT and compared the typical linear and nonlinear strategies employed in the WT pitch control from the engineering point of view. The procedure of parameter design for each strategy is introduced and the final controller is applied in the digital simulations. The performance and engineering practice of different strategies are then compared with the simulation results.

The configuration of a typical WECS is shown in Figure

Configuration of a typical WECS (with full-capacity power converters).

Usually, pitch system can be hydraulic or electrical. The electrical pitch system uses the converter driven servomotor to regulate the pitch angle, which provides simpler structure, smaller size, and more convenient maintenance compared with the hydraulic one. The typical configuration of the electrical pitch system is illustrated in Figure

Configuration of pitch regulation control system in the WECS.

Compared with the pitch system, other subsystems have different response time scales. For example, the electrical system of the power generation responds quickly (in milliseconds) due to the small time constant determined by the stator and rotor impedance. In contrast, the turbine speed varies slowly (in multiminutes) because of the large inertia. Therefore, the pitch regulator is slower than the electrical response but much rapider than the mechanical response.

Considering the time-scale difference between different subsystems, the system modeling can be simplified. Specifically, the electrical dynamic can be ignored in the evaluation of pitch and mechanical dynamics. And the pitch actuator dynamic can be simply represented by a first-order model [

Based on the above assumption, the mathematical model of the pitch-regulated WECS can be expressed as

In (

The torque coefficient

Typical torque coefficient curve.

The WT characteristic shown in Figure

Equation (

The alternative choice to obtain the WT characteristics is to fit Figure

As indicated by the above analysis from the engineering point of view, it is concluded that the nonlinear property, the parameter uncertainty, and the implementation cost are the main difficulties of the pitch control.

Generally, the control scheme can be designed based on a linear or nonlinear system model. Taking account of the controller property, there are four controller design principles, linear controller based on linear system model (LCLM), nonlinear controller based on linear system model (NCLM), linear controller based on nonlinear system model (LCNM), and nonlinear controller based on nonlinear system model (NCNM). Since the real property of the WT aerodynamic characteristics is highly nonlinear, NCLM is not an efficient way to solve the pitch control problem. In the left three principles, LCLM is employed in early WECSs and the proportional-integral (PI) controller is normally used. The PI parameters are designed based on the linearized system model and try and error methods are necessary to obtain the satisfactory performance in the real pitch system. However, such strategy is proven to be noneffective when the operation point of the WECS deviates from the linearized working point [

LCNM is studied to avoid the performance deterioration of LCLM at different operation points [

In this method, several operation points at different wind speed are firstly selected, for example, 12 m/s, 15 m/s, 18 m/s, 21 m/s, and 25 m/s. It is noted that selection of the operating point is critical to ensure the aerodynamic stability and pitch regulation performance in the system. Principles in details can be found in [

Based on the linear model described by (

The frame of the gain scheduled LCNM is illustrated in Figure

System frame of LCNM based scheme.

With gain scheduling, the controller can provide satisfactory performance. However, the implementation cost of the scheme is great. Plenty of simulations or even experiment tests should be executed to get the PI parameters at different working points [

In contrast to LCNM, NCNM based scheme seems more effective in the inherent nonlinear WECS. Generally, NCNM can be classified into two categories. One is the scheme depending on the system model and the other is the one independent of the nonlinear model.

In [

Reference [

System frame of model dependent NCNM scheme.

In Figure

In contrast to model dependent NCNM scheme, model independent NCNM strategy employs adaptive nonlinear controller to fit the system nonlinear feature especially when the operation point drifts. Artificial neural network (ANN) is a good choice to achieve the control objective. In [

Topology of the 3-level BP neural network.

The discrete aerodynamic experimental data from the turbine manufactory is used as the training data for the neural network. As shown in Figure

Basically, the ANN controller utilizes the neuron to identify the nonlinear system model or inverse model and applies the identification results into the control. Figure

System frame of model independent NCNM scheme.

As the nonlinear feature is identified in the controller, it can show a convincing performance as shown in [

Simulations are carried out using MATLAB/SIMULINK to compare the performance of three above different pitch controllers (with frame shown in Figures

The steady-state operation points are varied with the change of wind speed. In the simulation, the wind speed (above the rated value) is step changing with the profile in Figure

Input wind speed.

System responses with different pitch controllers in the step wind situation.

As indicated by Figure

Parameter uncertainties are very common in the WECS which should be evaluated in the controller design. Uncertainties can come from the measurement and control errors or parameter deviations. In this section, simulation with measurement error of the wind speed is implemented. On the one hand, such error is inevitable in the real applications. On the other hand, control errors because of other parameter uncertainties can always be considered as the equivalent deviation on the wind speed. Moreover, from the simulation point of view, such scenario is easier to implement.

In the simulation, it is assumed that the real wind speed

Real and measured wind speed.

System responses with different pitch controllers considering parameter uncertainties.

Figure

As compared by the above analysis and simulation results, different control structure for system with nonlinear dynamics, such as the WECS, has its advantages and disadvantages. The comparisons are indicated in Table

Comparisons of different control schemes.

Schemes | Comparison | |||
---|---|---|---|---|

Control performance | Practical application | |||

Steady-state error | Robustness | Complexity | Industrial acceptance | |

LCNM | Large | Good | Low | Good |

NCNM1 | Small | Better (with robust compensation) |
High | Bad |

NCNM2 | Smallest | Best | Highest | Worst |

Nominal Parameters of the WECS.

Parameters | Value |
---|---|

Blade radius [m] | 40 |

Air density [kg·m^{3}] |
1.25 |

Cut in wind speed [m/s] | 3 |

Cut out wind speed [m/s] | 25 |

Rated wind speed [m/s] | 12.6 |

Turbine Inertia [kg·m^{2}] |
90 × 10^{6} |

Rated Turbine Speed [rad/s] | 1.5 |

Generator Inertia [kg·m^{2}] |
90 |

Gearbox Ratio | 100 |

Generator Rated Torque [N·m] | 1 × 10^{6} |

Generator Rated Power [MW] | 1.5 |

Response time of the pitch actuator [s] | 0.5 |

Considering the control performance, nonlinear scheme taking account of the system nonlinear feature provides smaller control errors compared with linear schemes. In all the nonlinear schemes, the one independent of system models has better performance because it can adaptively vary the control parameters on the basis of the system response. In contrast, nonlinear schemes based on system models cannot work well if the model parameters drift. The robust compensations, such as in Figure

From the engineering point of view, linear scheme with gain scheduling is attractive to the commercial products. Most of the time, the control performance is acceptable. More importantly, for the field engineers, it is easy to understand the principle of the scheme; therefore, the cost of field service and technique training is saved. Also, such scheme has already been applied in the products for many years and the reliability is widely accepted by the industry and consumers, which is a benefit to the business marketing. As for the cost, such scheme requires more efforts on the design of control parameters. Usually, try and error methods are used and plenty of simulations or experiments are necessary. If the consistency of the product parameters can be guaranteed, such scheme is a good choice. In contrast to linear scheme, the NCNM schemes increase the controller complexity. Although powerful digital processor can easily execute the nonlinear scheme nowadays, the reliability of such scheme needs time to be accepted by the industry.

This paper discusses the controller design of the pitch control for WTs from both the theoretical and the engineering point of view. Because of the highly nonlinear WT aerodynamics, linear controller with unique parameters cannot provide satisfactory performance. Sometimes, it results even in instability. Linear controller with gain scheduled parameter is a good choice from both implementation cost and industrial acceptance perspectives. If the better performance is required, nonlinear schemes are necessary. Essentially, the nonlinear strategies improve the control performance by employing the system nonlinear features. Strategies adaptive to the variation of system parameters or structures are deserved to get better results while the ones depending on the system models result in control errors when the model deviates. Selection of the control scheme is a comprehensive job affected by the ongoing techniques, performance, costs in terms of implementation, training, maintenance, and so forth.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the National Natural Science Foundation of China (NSFC) under Grants 61104046, 61273045, and 51361135705, Tsinghua University Initiative Scientific Research Program, grants from Beijing Higher Education Young Elite Teacher Project, Delta Scholar Program in Power Electronics, Delta Environmental, and Educational Foundation.

_{∞}control for wind energy conversion system