# Neuron-Adaptive PID Based Speed Control of SCSG Wind Turbine System

Authors: Shan Zuo; Yongduan Song; Lei Wang; Zheng Zhou
Journal: Abstract and Applied Analysis
 (2014)

---

## Abstract

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 large-scale wind turbine due to its high energy density and unprecedented advantages in weight and size. In this paper, a high-temperature superconducting technology based large-scale wind turbine is considered and its physical structure and characteristics are analyzed. A simple yet effective single neuron-adaptive 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 tip-speed ratio, therefore, achieving the maximum wind energy utilization.


---

## Body

## 1. Introduction

With the fast development of wind power generation systems, the generating capacity of wind turbines is expected to reach up to 10 MW [1]. Consequently, the wind turbine weight and size have to be increased simultaneously, with the bald diameter reaching up to 10 meters [2], as shown in Figure 1, which imposes technical difficulty in designing, transporting, and installing such large turbine blades. To address this challenge, novel concept of wind turbine generators with high energy density is urgently needed. High-temperature superconducting (HTS) technology is an expected solution. The research of wind turbines with SCSG has gained worldwide attention during the past decade [3–11].Figure 1
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 blow-rated speed region.To address this issue, several advanced control approaches have been studied, such as single neuron-adaptive 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 neuron-adaptive 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 self-learning and strong self-adaptive 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 neuron-adaptive 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.


## 2. Dynamic System Modeling

### 2.1. Configuration of the Superconducting Generator

The SCSG for wind turbine system has a multiple synchronous high-temperature superconducting (HTS) field winding for direct drive train and has been widely studied worldwide. Figure2 shows the configuration of the 10 MW SCSG wind power generation system, including the wind turbine, the generator, and the convertor [12]. Physical properties and electrical properties of the designed SCSG are given in Tables 1 and 2, respectively [1].Table 1
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 KTable 2
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/mm2
Space factor of stator wire
0.4
Turns of field coil
1500Figure 2
Configuration of the 10 MW SCSG system.


### 2.2. Modeling of the Superconducting Synchronous Generation System

It is well known that the expression for power produced by a wind turbine is simply given by(1)PS=12Cp(λ,β)ρπR2v3,
where ρ is air density, R is the radius of rotor, and v is wind speed passing the rotor. Cp denotes power coefficient of wind turbine, which is a function of the tip-speed ratio λ and the pitch angle β [13].Note that the tip-speed ratio is defined by(2)λ=vTipv=Rωv,
where vTip is the tip-speed and ω is the rotor speed.In the lower-rated wind speed region, the maximum power point tracking (MPPT) control approach is adopted. The maximum power of the wind turbine is expressed as [14]
(3)Pmax⁡=12ρπR5Cp_max⁡λopt3ω3.Table3 shows the specifications of the modeled 10 MW SCSG wind turbine [2].Table 3
Model parameters of the designed SCSG.
Items
Symbol
Value
Rated power
P
N
10 MW
Rated rotor speed
n
r
10 RPM
Rotor radius
R
85 m
Maximum power coefficient
C
p
_
max
⁡
0.48
Optimum tip-speed ratio
λ
opt
7
Air density
ρ
1.225 kg/m3For the purpose of the studies presented in this paper, a standard (dq-frame) synchronous machine simulation model has been used with parameters resembling the main characteristics of a notional 10 MW HTS generator along with the associated controls. This notional simulation model of the HTS generator is loosely based on the parameters of an actual prototype in order to safeguard the proprietary information of the manufacturer. The mechanical input for the notional HTS generator originates from the wind turbine model.In the rotordq-rotating coordinate system, the generator flux model is shown in (4)
(4)Ψsd=Lsσid+(Lmdid+Msfif+MsDiD),Ψsq=Lsσiq+(Lmqiq+MsQiQ),Ψf=Lfσif+(32Msfid+Lmfif+MfDiD),ΨD=LDσiD+(32MsDid+LmDiD+MfDif),ΨQ=LQσiQ+(32MsQiq+LmQiQ).Ψ
s
d, Ψsq are the orthogonal axes flux of the stator; Ψf is rotor excitation flux; ΨD, ΨQ are orthogonal axes flux of the damping winding; id, iq are the orthogonal axes currents of the stator; if is rotor excitation current; iD, iQ are orthogonal axes currents of damper winding. Lsσ, Lfσ, LDσ, and LQσ are leakage inductances, respectively, for stator winding, field winding, and orthogonal axis damper winding. Lmd, Lmq are armature reaction inductances for orthogonal axis. Msf, MsD, and MsQ are mutual inductances between the stator winding, rotor field winding, and the orthogonal axis damper winding. Lmf, LmD, and LmQ are inductances corresponding to the main magnetic circuit in the self-inductance of the field winding and the orthogonal axis damper winding.Assume(5)Ld=Lsσ+Lmd,Lq=Lsσ+Lmq,Lf=Lfσ+Lmf,LD=LDσ+LmD,LQ=LQσ+LmQ,
where Ld, Lq are the orthogonal axis inductances of the motor; Lf is the self-inductance of the rotor field winding; LD, LQ are the self-inductances of orthogonal axis damper winding.According to formula (5), the flux mathematical model in formula (4) could be further simplified.The voltage balance equations of stator and rotor windings are shown in (6)
(6)ud=rsid+dΨsddt-Ψsqdθrdt,uq=rsiq+dΨsqdt+Ψsddθrdt,uf=rfif+dΨfdt,rDiD+dΨDdt=0,rQiQ+dΨQdt=0,
where rs, rf, rD, and rQ are the resistances of the stator winding, rotor field winding, and orthogonal axis damping winding, respectively.The electromagnetic torque expression is shown in formula(7)Te=32p(Ψsdiq-Ψsqid),
where p is the number of pole pairs of the generator.Figure3 shows the d-q equivalent circuit model of the designed SCSG based on Park’s transformations.Figure 3
Equivalent circuits of the modeled SCSG fordq-axes.In order to allow operation at different speeds, the designed SCSG model is linked to the power grid via a full-scale frequency inverter. The frequency converter consists of a generator side converter, a grid side rectifier, and a DC-link. The generator side converter executes the MPPT control through the control of theq-axis current. The grid side rectifier performs reactive power control and constant DC voltage control through control of the d-axis and q-axis currents. Figure 4 depicts the structure of the full-scale frequency inverter. Figure 5 shows controller implementation of the generator side converter and the grid side rectifier.Figure 4
Structure of the full-scale frequency inverter.Figure 5
Controller implementation of the full-scale frequency inverter.The simulation model of the generator drive used in this paper utilizes ideal voltage sources representing the fundamental frequency component of a PWM-type 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 speedω. The paper utilizes a single neuron-adaptive PID control approach based on RBF to achieve this control goal [15]. Figure 6 represents the overall structure diagram of the SCSG wind turbine generation system mounted with associated controllers.Figure 6
Structure diagram of overall wind turbine generation system.


## 2.1. Configuration of the Superconducting Generator

The SCSG for wind turbine system has a multiple synchronous high-temperature superconducting (HTS) field winding for direct drive train and has been widely studied worldwide. Figure2 shows the configuration of the 10 MW SCSG wind power generation system, including the wind turbine, the generator, and the convertor [12]. Physical properties and electrical properties of the designed SCSG are given in Tables 1 and 2, respectively [1].Table 1
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 KTable 2
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/mm2
Space factor of stator wire
0.4
Turns of field coil
1500Figure 2
Configuration of the 10 MW SCSG system.


## 2.2. Modeling of the Superconducting Synchronous Generation System

It is well known that the expression for power produced by a wind turbine is simply given by(1)PS=12Cp(λ,β)ρπR2v3,
where ρ is air density, R is the radius of rotor, and v is wind speed passing the rotor. Cp denotes power coefficient of wind turbine, which is a function of the tip-speed ratio λ and the pitch angle β [13].Note that the tip-speed ratio is defined by(2)λ=vTipv=Rωv,
where vTip is the tip-speed and ω is the rotor speed.In the lower-rated wind speed region, the maximum power point tracking (MPPT) control approach is adopted. The maximum power of the wind turbine is expressed as [14]
(3)Pmax⁡=12ρπR5Cp_max⁡λopt3ω3.Table3 shows the specifications of the modeled 10 MW SCSG wind turbine [2].Table 3
Model parameters of the designed SCSG.
Items
Symbol
Value
Rated power
P
N
10 MW
Rated rotor speed
n
r
10 RPM
Rotor radius
R
85 m
Maximum power coefficient
C
p
_
max
⁡
0.48
Optimum tip-speed ratio
λ
opt
7
Air density
ρ
1.225 kg/m3For the purpose of the studies presented in this paper, a standard (dq-frame) synchronous machine simulation model has been used with parameters resembling the main characteristics of a notional 10 MW HTS generator along with the associated controls. This notional simulation model of the HTS generator is loosely based on the parameters of an actual prototype in order to safeguard the proprietary information of the manufacturer. The mechanical input for the notional HTS generator originates from the wind turbine model.In the rotordq-rotating coordinate system, the generator flux model is shown in (4)
(4)Ψsd=Lsσid+(Lmdid+Msfif+MsDiD),Ψsq=Lsσiq+(Lmqiq+MsQiQ),Ψf=Lfσif+(32Msfid+Lmfif+MfDiD),ΨD=LDσiD+(32MsDid+LmDiD+MfDif),ΨQ=LQσiQ+(32MsQiq+LmQiQ).Ψ
s
d, Ψsq are the orthogonal axes flux of the stator; Ψf is rotor excitation flux; ΨD, ΨQ are orthogonal axes flux of the damping winding; id, iq are the orthogonal axes currents of the stator; if is rotor excitation current; iD, iQ are orthogonal axes currents of damper winding. Lsσ, Lfσ, LDσ, and LQσ are leakage inductances, respectively, for stator winding, field winding, and orthogonal axis damper winding. Lmd, Lmq are armature reaction inductances for orthogonal axis. Msf, MsD, and MsQ are mutual inductances between the stator winding, rotor field winding, and the orthogonal axis damper winding. Lmf, LmD, and LmQ are inductances corresponding to the main magnetic circuit in the self-inductance of the field winding and the orthogonal axis damper winding.Assume(5)Ld=Lsσ+Lmd,Lq=Lsσ+Lmq,Lf=Lfσ+Lmf,LD=LDσ+LmD,LQ=LQσ+LmQ,
where Ld, Lq are the orthogonal axis inductances of the motor; Lf is the self-inductance of the rotor field winding; LD, LQ are the self-inductances of orthogonal axis damper winding.According to formula (5), the flux mathematical model in formula (4) could be further simplified.The voltage balance equations of stator and rotor windings are shown in (6)
(6)ud=rsid+dΨsddt-Ψsqdθrdt,uq=rsiq+dΨsqdt+Ψsddθrdt,uf=rfif+dΨfdt,rDiD+dΨDdt=0,rQiQ+dΨQdt=0,
where rs, rf, rD, and rQ are the resistances of the stator winding, rotor field winding, and orthogonal axis damping winding, respectively.The electromagnetic torque expression is shown in formula(7)Te=32p(Ψsdiq-Ψsqid),
where p is the number of pole pairs of the generator.Figure3 shows the d-q equivalent circuit model of the designed SCSG based on Park’s transformations.Figure 3
Equivalent circuits of the modeled SCSG fordq-axes.In order to allow operation at different speeds, the designed SCSG model is linked to the power grid via a full-scale frequency inverter. The frequency converter consists of a generator side converter, a grid side rectifier, and a DC-link. The generator side converter executes the MPPT control through the control of theq-axis current. The grid side rectifier performs reactive power control and constant DC voltage control through control of the d-axis and q-axis currents. Figure 4 depicts the structure of the full-scale frequency inverter. Figure 5 shows controller implementation of the generator side converter and the grid side rectifier.Figure 4
Structure of the full-scale frequency inverter.Figure 5
Controller implementation of the full-scale frequency inverter.The simulation model of the generator drive used in this paper utilizes ideal voltage sources representing the fundamental frequency component of a PWM-type 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 speedω. The paper utilizes a single neuron-adaptive PID control approach based on RBF to achieve this control goal [15]. Figure 6 represents the overall structure diagram of the SCSG wind turbine generation system mounted with associated controllers.Figure 6
Structure diagram of overall wind turbine generation system.


## 3. Design of Controller

### 3.1. Incremental PID Control Approach

Equations of the incremental PID control approach are defined as follows:(8)u(k)=u(k-1)+Δu(k),Δu(k)=kp[e(k)-e(k-1)]+kie(k)+kd[e(k)-2e(k-1)+e(k-2)].
Equation (8) shows that the three control parameters (kp, ki, and kd) cannot be real-time adjusted, which result in a decrease in the response speed of system.


### 3.2. Single Neuron-Adaptive PID Controller Algorithm

Combining single neuron to the incremental PID can address the challenge of real-time adjustment of control parameters. The single neuron-adaptive PID control structure is illustrated in Figure7.Figure 7
The block diagram of the single neuron-adaptive PID controller.Improved single neuron-adaptive 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 timek in the incremental PID controller is to be expressed as wj(k), j=p,i,d, and the weight value adjusting formula of next moment is expressed as
(9)wj(k)=wj(k-1)+Δwj(k),
where Δwj(k) is the weight increment. Introduce the output error square function as the performance indicator, namely,
(10)F[wj(k)]=12[r(k)-y(k)]2=12[z(k)]2,
where r(k) and y(k) are input and output of the reference.Each time the amendments are to meet(11)F[wj(k)]<F[wj(k-1)].First-order Taylor expansion ofF[wj(k)] is expressed as
(12)F[wj(k)]=F[wj(k-1)+Δwj(k)]≈F[wj(k-1)]+gT(k)Δwj(k),
where g(k)=∇F[wj(k)].In the above formula,g(k) is the gradient vector of F[w] when w=wj(k). Assume Δwj(k)=-ηjg(k), where ηj is the learning rate, which is a small positive value. Formula (11) is bound to meet.The value ofΔwj(k) is expressed as
(13)Δwj(k)=wj(k)-wj(k-1)=-ηj∂F(w)∂wj(k)=ηjz(k)∂y(k)∂Δu(k)∂Δu(k)∂wj(k),
where (∂y(k))/(∂Δu(k)) is unknown and in the case when calculation accuracy is not strictly required, replace it with the sign function sgn⁡((∂y(k))/(∂Δu(k))). Standardizing the above algorithm, we can get
(14)wp(k)=wp(k-1)+ηpz(k)sgn⁡(∂y(k)∂Δu(k))x1(k),wi(k)=wi(k-1)+ηiz(k)sgn⁡(∂y(k)∂Δu(k))x2(k),wd(k)=wd(k-1)+ηdz(k)sgn⁡(∂y(k)∂Δu(k))x3(k),
where
(15)sgn⁡(x)={+1,x≫0-1,x<0.Introducing a gain factorK, we can get
(16)u(k)=u(k-1)+K[wp(k)x1(k)+wi(k)x2(k)+wd(k)x3(k)].


### 3.3. Improved Single Neuron PID Using RBF Neural Network

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 three-layer 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 Figure8.Figure 8
Topological graph of RBF neural network.The control block diagram of a typical RBF neural network is illustrated in Figure9.Figure 9
Control block diagram of RBF neural network.In RBF network,X=[x1,x2,…,xn]T is the input vector and hg is activation function, which is given by
(17)hg=exp⁡(-∥X-Cg∥22bg2),g=1,2,…,m,
where Cg=[C1g,C2g,…,Cig,…,Cng]T is the central vector of gth hidden neuron. B=[b1,b2,…,bg,…,bm]T is the basis-width vector, bg>0 is the base width constant of gth mode, and the weight vector of the network is w=[w1,w2,…,wg,…,wm]T.The output of themth neuron in the output layer at time k is defined as
(18)ym(k)=wH=w1h1+w2h2+⋯+wmhm.The performance of network can be evaluated by(19)E=12[y(k)-ym(k)]2.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:(20)wg(k)=wg(k-1)+β(y(k)-ym(k))hg+α[wg(k-1)-wg(k-2)],Δbg=[y(k)-ym(k)]wghg∥X-Cg∥2bg3,bg(k)=bg(k-1)+βΔbg+α[bg(k-1)-bg(k-2)],Δcig=[y(k)-ym(k)]wgxg-cigbg2,cig(k)=cig(k-1)+βΔcig+α[cig(k-1)-cig(k-2)],
where α is the momentum factor and β is the learning rate.At timek, (∂y(k))/(∂Δu(k))≈(∂ym(k))/(∂Δu(k)), since X is a one-dimensional vector, containing Δu; therefore ∂X/∂Δu=1; then, we can write the Jacobian matrix of the control system as follows:
(21)∂ym(k)∂Δu(k)=∂∑g=1mwghg∂Δu(k)=∑g=1mwg∂exp⁡(-∥X-Cg∥2/2bg2)∂Δu(k)=∑g=1mwghg((Cg-X)/bg2)∂X∂Δu(k)=∑g=1mwghgCg-Xbg2.According to the universal approximation ability of the RBF neural network [16–28], we can conclude that
(22)∥ym(k)-y(k)∥<ε,
where ε is a bounded positive constant.


## 3.1. Incremental PID Control Approach

Equations of the incremental PID control approach are defined as follows:(8)u(k)=u(k-1)+Δu(k),Δu(k)=kp[e(k)-e(k-1)]+kie(k)+kd[e(k)-2e(k-1)+e(k-2)].
Equation (8) shows that the three control parameters (kp, ki, and kd) cannot be real-time adjusted, which result in a decrease in the response speed of system.


## 3.2. Single Neuron-Adaptive PID Controller Algorithm

Combining single neuron to the incremental PID can address the challenge of real-time adjustment of control parameters. The single neuron-adaptive PID control structure is illustrated in Figure7.Figure 7
The block diagram of the single neuron-adaptive PID controller.Improved single neuron-adaptive 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 timek in the incremental PID controller is to be expressed as wj(k), j=p,i,d, and the weight value adjusting formula of next moment is expressed as
(9)wj(k)=wj(k-1)+Δwj(k),
where Δwj(k) is the weight increment. Introduce the output error square function as the performance indicator, namely,
(10)F[wj(k)]=12[r(k)-y(k)]2=12[z(k)]2,
where r(k) and y(k) are input and output of the reference.Each time the amendments are to meet(11)F[wj(k)]<F[wj(k-1)].First-order Taylor expansion ofF[wj(k)] is expressed as
(12)F[wj(k)]=F[wj(k-1)+Δwj(k)]≈F[wj(k-1)]+gT(k)Δwj(k),
where g(k)=∇F[wj(k)].In the above formula,g(k) is the gradient vector of F[w] when w=wj(k). Assume Δwj(k)=-ηjg(k), where ηj is the learning rate, which is a small positive value. Formula (11) is bound to meet.The value ofΔwj(k) is expressed as
(13)Δwj(k)=wj(k)-wj(k-1)=-ηj∂F(w)∂wj(k)=ηjz(k)∂y(k)∂Δu(k)∂Δu(k)∂wj(k),
where (∂y(k))/(∂Δu(k)) is unknown and in the case when calculation accuracy is not strictly required, replace it with the sign function sgn⁡((∂y(k))/(∂Δu(k))). Standardizing the above algorithm, we can get
(14)wp(k)=wp(k-1)+ηpz(k)sgn⁡(∂y(k)∂Δu(k))x1(k),wi(k)=wi(k-1)+ηiz(k)sgn⁡(∂y(k)∂Δu(k))x2(k),wd(k)=wd(k-1)+ηdz(k)sgn⁡(∂y(k)∂Δu(k))x3(k),
where
(15)sgn⁡(x)={+1,x≫0-1,x<0.Introducing a gain factorK, we can get
(16)u(k)=u(k-1)+K[wp(k)x1(k)+wi(k)x2(k)+wd(k)x3(k)].


## 3.3. Improved Single Neuron PID Using RBF Neural Network

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 three-layer 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 Figure8.Figure 8
Topological graph of RBF neural network.The control block diagram of a typical RBF neural network is illustrated in Figure9.Figure 9
Control block diagram of RBF neural network.In RBF network,X=[x1,x2,…,xn]T is the input vector and hg is activation function, which is given by
(17)hg=exp⁡(-∥X-Cg∥22bg2),g=1,2,…,m,
where Cg=[C1g,C2g,…,Cig,…,Cng]T is the central vector of gth hidden neuron. B=[b1,b2,…,bg,…,bm]T is the basis-width vector, bg>0 is the base width constant of gth mode, and the weight vector of the network is w=[w1,w2,…,wg,…,wm]T.The output of themth neuron in the output layer at time k is defined as
(18)ym(k)=wH=w1h1+w2h2+⋯+wmhm.The performance of network can be evaluated by(19)E=12[y(k)-ym(k)]2.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:(20)wg(k)=wg(k-1)+β(y(k)-ym(k))hg+α[wg(k-1)-wg(k-2)],Δbg=[y(k)-ym(k)]wghg∥X-Cg∥2bg3,bg(k)=bg(k-1)+βΔbg+α[bg(k-1)-bg(k-2)],Δcig=[y(k)-ym(k)]wgxg-cigbg2,cig(k)=cig(k-1)+βΔcig+α[cig(k-1)-cig(k-2)],
where α is the momentum factor and β is the learning rate.At timek, (∂y(k))/(∂Δu(k))≈(∂ym(k))/(∂Δu(k)), since X is a one-dimensional vector, containing Δu; therefore ∂X/∂Δu=1; then, we can write the Jacobian matrix of the control system as follows:
(21)∂ym(k)∂Δu(k)=∂∑g=1mwghg∂Δu(k)=∑g=1mwg∂exp⁡(-∥X-Cg∥2/2bg2)∂Δu(k)=∑g=1mwghg((Cg-X)/bg2)∂X∂Δu(k)=∑g=1mwghgCg-Xbg2.According to the universal approximation ability of the RBF neural network [16–28], we can conclude that
(22)∥ym(k)-y(k)∥<ε,
where ε is a bounded positive constant.


## 4. Simulations and Analysis

The proposed neuron-adaptive PID speed control system of SCSG based on RBF neural network identification is depicted in Figure6. The entire control module of the SCSG wind generation system is presented in Figure 10 and the simulation module of SCSG is depicted in Figure 11. Parameters of SCSG used in the simulation are listed in Tables 1, 2, and 3. The reference model used in the simulation is taken as a constant speed. The simulation is tested with the MATLAB/Simulink and FAST (FAST is a fully coupled aero-hydro-servo-elastic code, freely available and developed at the National Renewable Energy Laboratory and used to simulate the loads and performance of modern wind turbines).Figure 10
Simulation module of the SCSG wind generation system.Figure 11
Simulation module of SCSG.To verify the dynamic and static performances of the neuron-adaptive PID controller based on RBF NN proposed in this paper, simulation tests are designed in two cases: (1) no-load operation with a given speed of 10 r/min;(2) system starts with no-load, after being in a steady state, given a sudden load Tl=10MN·m at t=2s. Simultaneously compared with the conventional PID controller, available system speed control response curves are demonstrated from Figure 12 to Figure 16. Furthermore, after verifying the validity of the proposed control approach, the paper applies the proposed controller in the speed control of SCSG wind generation system in the below-rated wind speed region to better track wind speed and maintain a stable tip-speed ratio, therefore, achieving the maximum utilization of wind energy.Figure 12
SCSG speed response curve to no-load operation with traditional PID controller.Figures12 and 13 show that compared with the conventional PID controller, the speed response with the proposed controller is more rapid and smooth, with a smaller overshoot and no static error, solving the contradiction between response time and overshoot of the conventional PID control.Figure 13
SCSG speed response curve to no-load operation with neuron-adaptive PID controller with RBF NN.Figures14 and 15 depict that compared with the conventional PID controller, system with the proposed controller is more robust. When the parameter perturbation occurs, the entire system is stable, with better transient characteristics and nonsteady state static error, and has a strong ability to inhibit the impact of load disturbance to generator speed.Figure 14
SCSG speed response curve to a sudden load with traditional PID controller.Figure 15
SCSG speed response curve to a sudden load with neuron-adaptive PID controller with RBF NN.Figure 16
PID parameters adaptive tuning curve.Figure16 shows the adaptive tuning curve of PID parameters (kp,ki,kd).Figures17 and 18 show the compared simulating results of two algorithms in speed control of SCSG tracking wind speed in wind power generation system. Obviously, the proposed control approach makes the SCSG speed better track the wind speed and achieve a more stable tip-speed ratio when the wind speed is below the rated wind speed 12 m/s, such that the SCSG wind power generation system makes better use of wind energy.Figure 17
Simulation results of the speed control for SCSG wind turbine with conventional PID controller.Figure 18
Simulation results of the speed control for SCSG wind turbine with neuron-adaptive PID controller with RBF NN.


## 5. Conclusion

In this paper, the 10 MW class superconducting wind turbine generator has been studied, and a single neuron-adaptive 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 below-rated wind speed region, and outperforms the traditional PID.



---

*Source: 376259-2014-05-19.xml*