In searching for methods to increase the power capacity of wind power generation system, superconducting synchronous generator (SCSG) has appeared to be an attractive candidate to develop largescale wind turbine due to its high energy density and unprecedented advantages in weight and size. In this paper, a hightemperature superconducting technology based largescale wind turbine is considered and its physical structure and characteristics are analyzed. A simple yet effective single neuronadaptive PID control scheme with Delta learning mechanism is proposed for the speed control of SCSG based wind power system, in which the RBF neural network (NN) is employed to estimate the uncertain but continuous functions. Compared with the conventional PID control method, the simulation results of the proposed approach show a better performance in tracking the wind speed and maintaining a stable tipspeed ratio, therefore, achieving the maximum wind energy utilization.
With the fast development of wind power generation systems, the generating capacity of wind turbines is expected to reach up to 10 MW [
Comparison of nacelle sizes for technology options for large systems (image from American Superconductor).
Among various issues related to SCSG wind power generation systems, speed control represents one of the most crucial ones. Because of the inherent nonlinear and uncertain characteristics of the system, traditional PID control, although simple in structure and used widely in industry, is difficult to achieve reliable variable speed control performance in the blowrated speed region.
To address this issue, several advanced control approaches have been studied, such as single neuronadaptive PID control approach, BP neural network PID control approach, fuzzy RBF neural network PID control approach, genetic algorithm PID control approach, and adaptive fuzzy PID control approach. However, previous studies show that the response time of single neuronadaptive PID is comparatively long, and most of the existing algorithms are computationally expensive, and some of them even lead to larger overshoot than traditional PID. The neural network control approach with selflearning and strong selfadaptive characteristics can effectively reduce the negative impact arising from the system parametric uncertainties and stochastic disturbances. Motivated by this fact, in this paper, a single neuronadaptive PID controller based on Delta learning regulation is introduced, in which the RBF neural network is employed to estimate the uncertain but continuous function. Analysis and simulation results show that the proposed control approach has better performance in terms of robustness, stability, and computational cost as compared with other modified PID methods, thus being mode suitable for the speed control of SCSG wind turbine systems.
The SCSG for wind turbine system has a multiple synchronous hightemperature superconducting (HTS) field winding for direct drive train and has been widely studied worldwide. Figure
Physical properties of the designed SCSG.
Items  Value  Items  Value 

Rated power  10 MW  Number of poles  24 
Rated line to line voltage  13.8 kV  Rated frequency  2 Hz 
Rated armature current  418 A  Number of phases  3 
Rated field current  100 A  Length of HTS wire  919 km 
Rated rotating speed  10 RPM  Operating temperature  20 K 
Electrical properties of the designed SCSG.
Items  Value 

Turns of stator coil  28 
Number of slots  144 
Number of slots per pole per phase  2 
Current density of stator wire  5 A/mm^{2} 
Space factor of stator wire  0.4 
Turns of field coil  1500 
Configuration of the 10 MW SCSG system.
It is well known that the expression for power produced by a wind turbine is simply given by
Note that the tipspeed ratio is defined by
In the lowerrated wind speed region, the maximum power point tracking (MPPT) control approach is adopted. The maximum power of the wind turbine is expressed as [
Table
Model parameters of the designed SCSG.
Items  Symbol  Value 

Rated power 

10 MW 
Rated rotor speed 

10 RPM 
Rotor radius 

85 m 
Maximum power coefficient 

0.48 
Optimum tipspeed ratio 

7 
Air density 

1.225 kg/m^{3} 
For the purpose of the studies presented in this paper, a standard (
In the rotor
Assume
According to formula (
The voltage balance equations of stator and rotor windings are shown in (
The electromagnetic torque expression is shown in formula
Figure
Equivalent circuits of the modeled SCSG for
In order to allow operation at different speeds, the designed SCSG model is linked to the power grid via a fullscale frequency inverter. The frequency converter consists of a generator side converter, a grid side rectifier, and a DClink. The generator side converter executes the MPPT control through the control of the
Structure of the fullscale frequency inverter.
Controller implementation of the fullscale frequency inverter.
The simulation model of the generator drive used in this paper utilizes ideal voltage sources representing the fundamental frequency component of a PWMtype variable speed drive. It includes a current control and a speed control. The control target of the speed control is to keep the expected steady state and dynamic characteristic of the rotor speed
Structure diagram of overall wind turbine generation system.
Equations of the incremental PID control approach are defined as follows:
Combining single neuron to the incremental PID can address the challenge of realtime adjustment of control parameters. The single neuronadaptive PID control structure is illustrated in Figure
The block diagram of the single neuronadaptive PID controller.
Improved single neuronadaptive PID control algorithm based on Delta learning rule implements the adjustment of the three weights in incremental PID controller, therefore, achieving adaptive control.
Delta learning rule based on the steepest descent method completes the aim to adjust the three weights by minimizing the introduced performance indicator.
Assume the weight value at time
Each time the amendments are to meet
Firstorder Taylor expansion of
In the above formula,
The value of
Introducing a gain factor
Neural network (NN) is a powerful approach to linearize and approximate any continuous nonlinear control system, in which radial basis function (RBF) network is a threelayer forward network. RBF network is composed of an input layer, a single hidden layer with nonlinear nodes, and an output layer with a linear node. The topological structure of a typical RBF network is depicted in Figure
Topological graph of RBF neural network.
The control block diagram of a typical RBF neural network is illustrated in Figure
Control block diagram of RBF neural network.
In RBF network,
The output of the
The performance of network can be evaluated by
Using the gradient descent method, we can get the iterative algorithm of output weight, central vector of mode, and base width constant expressed as follows:
At time
According to the universal approximation ability of the RBF neural network [
The proposed neuronadaptive PID speed control system of SCSG based on RBF neural network identification is depicted in Figure
Simulation module of the SCSG wind generation system.
Simulation module of SCSG.
To verify the dynamic and static performances of the neuronadaptive PID controller based on RBF NN proposed in this paper, simulation tests are designed in two cases: (1) noload operation with a given speed of 10 r/min;
SCSG speed response curve to noload operation with traditional PID controller.
Figures
SCSG speed response curve to noload operation with neuronadaptive PID controller with RBF NN.
Figures
SCSG speed response curve to a sudden load with traditional PID controller.
SCSG speed response curve to a sudden load with neuronadaptive PID controller with RBF NN.
PID parameters adaptive tuning curve.
Figure
Figures
Simulation results of the speed control for SCSG wind turbine with conventional PID controller.
Simulation results of the speed control for SCSG wind turbine with neuronadaptive PID controller with RBF NN.
In this paper, the 10 MW class superconducting wind turbine generator has been studied, and a single neuronadaptive PID controller based on Delta learning regulation is proposed, using the RBF neural network to estimate the uncertain continuous function. Analysis and simulation results show that the proposed control approach in SCSG system has a strong robustness and good dynamic performance by keeping a stable output in the presence of disturbances. Furthermore, comparative study between the proposed controller and the conventional PID controller in the speed control of SCSG wind turbine system has also been conducted. Overall, the proposed control approach is able to achieve smooth and satisfactory rotor speed tracking, achieving the maximum wind energy utilization, in the belowrated wind speed region, and outperforms the traditional PID.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the Major State Basic Research Development Program 973 (no. 2012CB215202) and the National Natural Science Foundation of China (no. 51205046).