A novel-strategy controller design for maximum power extraction in stand-alone windmill systems

Energy xxx (2014) 1e10

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

A novel-strategy controller design for maximum power extraction in stand-alone windmill systems Soheil Ganjefar*, Ali Akbar Ghasemi Department of Electrical Engineering, Bu Ali Sina University, Hamedan, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 January 2014 Received in revised form 28 July 2014 Accepted 6 August 2014 Available online xxx

This paper proposes a new control strategy for an optimal extraction of output power from stand-alone windmill systems. The system consists of a variable-speed wind turbine directly coupled to a PMSG (permanent magnet synchronous generator), a diode bridge rectifier, a DC-to-DC boost converter, and a battery bank. This control method, with its higher speed, directly creates a control signal for handling DC-to-DC converters. Adding an ESN (echo state network) to this method can result in extracting maximum power from the wind turbine without measuring the wind speed. This system is then simulated using MATLAB-SIMULINK software. The obtained simulation results show that the objective of extracting maximum power from the wind is reached. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Intelligent control Stand-alone windmill Calculus of variations Echo state networks Optimization

1. Introduction Although most previous studies in this field have focused on the development of utility-scale wind powers, small-sized wind turbines (1e100 kW) have recently received more attention due to the variety of their usage. The most important application of these small wind-turbines lies in their capability in providing electricity in remote places with no access to a power grid or with impractical lost-cost access to the power grid [1,2]. The amount of energy capture from a WECS (wind energy conversion system) depends not only on the wind at the site, but on the control strategy used for the WECS as well as on the conversion efficiency. Thus, the question “how to offer more power to electrical utilities through promoting the efficiency of the wind power” is still a major concern for all researchers of this field. Due to the characteristics of the wind turbine, the power captured from a turbine for a certain wind-speed is maximum at a certain value of the rotor speed. On the other hand, the wind speed is instantaneously varying; therefore the optimum wind-energy extraction is achieved by running the WTG (wind-turbine generator) in a variable-speed mode [2]. There are several possible configurations of power electronic converters and electrical generators for variable-speed wind turbine systems. Among the

* Corresponding author. E-mail addresses: [email protected], [email protected] (S. Ganjefar).

electric generators, PMSG (permanent magnet synchronous generator) is preferred due to its efficiency, reliability, power density; gearless construction, light weight, and self-excitation features [1,3]. Controlling the PMSG to achieve the MPP (maximum power point) can be performed by varying its output voltage. In this regard, a boost converter is one of the possible solutions in which, by controlling the duty cycle of the converter, the output voltage of the generator (and consequently the shaft speed) will be adjusted [1,4]. It is commonly desirable to operate this kind of systems at the point of maximum power extraction; the wind-power, however, mainly depends on geographic and weather conditions, thus varying from time-to-time; on the other hand, the behavior of the overall system is described by a highly coupled set of nonlinear differential equations [5] and, as a result, the maximum power output cannot be easily obtained. Moreover, to achieve such a goal, it is necessary to know the wind speed, which is usually not easily measurable. Therefore, it is desirable to present a control method which is fast enough and does not require an anemometer for a physical measurement of the wind speed. The structure of the previous researches consists of two main sections. In the first section, a MPPT (maximum power point tracking) algorithm is used with an aim to find the set point which has obtained the maximum power. In the second section, the control signal for handling the power electronic converter is created through different control methods such as PI control [2,6], vector control [7], passivity-based and sliding mode control [8], high order sliding mode control [9], radial basis function network

http://dx.doi.org/10.1016/j.energy.2014.08.024 0360-5442/© 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

2

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

control [10], fuzzy neural network control [11], adaptive fuzzy neural network control [12], adaptive passivity-based control [5], fuzzy-PI control [13], Elman neural network control [12] and quantum neural network control [14] to force the system to track the set point obtained in the first section. Therefore, we are confronted with two problems if one of which is not designed properly, the purpose cannot be obtained. The first problem is the design of MPPT algorithm. MPPT algorithms researched so far can be classified into three types, namely, TSR (tip speed ratio), PSF (power signal feedback), and HCS (hill-climb searching). Among these MPPT algorithms, MPPTTSR and MPPT-PSF algorithms are more efficient than MPPT-HCS algorithm, but they are limited by difficulty in wind speed measurements and knowledge of the turbine's characteristics. Also, these algorithms are competed with one another from other viewpoints as efficiency, speed, simplicity, accuracy that increases the difficulty in selection. The references [15,16] present the details of these methods as well as their comparisons. Second problem is the design of the controller. The wind turbine system is a complex dynamic system with a highly nonlinear behavior, and a nonlinear control strategy is required. Moreover, efficiency of the controller is influenced by MPPT algorithm type designed in the first section. Therefore, if a control method is employed that directly creates a control signal for handling DC-to-DC converters, the aforementioned problems can be solved. In Ref. [17] a method based on Perturbation and Observation of the duty cycle of the boost converter has been proposed. But this method is less efficient compared to other methods and has difficulty determining the optimum step-size [16]. The purpose of the present paper is to propose a new control strategy for achieving maximum electrical power from small-scale wind energy systems so as to directly create a control signal for handling power electronic converters. This method is based on a calculus of variations and allows the generator to track the optimal operation points of the wind-turbine system under fluctuating the wind conditions and speeding up the tracking process over time. As the unknown wind-speed enters into the controller dynamics in a nonlinear way, we decided to use the neural network with the aim to remove this drawback. The ESN (echo state network) is preferred for this purpose since it doesn't have the limitations of feed forward neural network as in MLP (Multi-Layer Perceptron) Network or RBF (Radius Basis Function) Network , and its training process is easier and requires less computational effort compared to the regular RNN (Recurrent Neural Network) which has the same size [18]. ESN has been successfully applied for simple-function approximations, system identifications, and direct adaptive controls [19]. This paper is organized as follows. Section 2 presents the windturbine aerodynamics and its overall dynamic model. Section 3 presents a brief introduction to the calculation of variations, and then the controller is designed considering the known wind-speed. In Section 4, designed controller is meliorated using the echo state neural network and wind speed estimator. Section 5 provides the simulation results with an aim to assess the performance of the proposed control method. Finally, Section 6 will conclude the paper.

Fig. 1. Schematic of a battery charging windmill system.

2.1. Aerodynamic model of wind turbine The aerodynamic model of turbine can be characterized by the cp(l,b) curves. Cp is the power coefficient, which is a function of the tip speed ratio l and the pitch angle b. The tip speed ratio l is given by.

l¼

um r v

(1)

where um is the rotational speed of the turbine (rad=s), v is the wind speed (m=s), r is the radius of the swept area (m). The relationship between CP and “l and b” can be described as:

  c5
 c Cp l; b ¼ c1 2  c3 b  c4 e li þ c6 l li

(2)

1 1 0:035  ¼ li l þ 0:08b b3 þ 1 where the coefficients c1 to c6 are: c1 ¼ 0.5176, c2 ¼ 116, c3 ¼ 0.4, c4 ¼ 5, c5 ¼ 21, c6 ¼ 0.0068 . When the wind speed is below the rated wind speed, the pitch angle is fixed to zero. Hence, the characteristics of the Cp mainly depends on only the l and thus can be rewritten as:

 cp1
 cp2  cp3 e l þ cp4 l Cp l ¼ l

(3)

The coefficients cp1 to cp4 are defined in Table 1. Fig. 2 shows the power coefficient of the turbine as a function of the mechanical speed at various wind speeds. The power coefficient for a certain wind speed is maximum at a certain value of the rotor speed. Therefore, to achieve the maximum power, it is necessary that the system be operating at this optimum point. The maximum value of Cp(Cpmax ¼ 0.4801) is achieved for lopt ¼ 8.1. Moreover, if v is known, the optimum mechanical speed can be calculated using Eq. (4). This work has been made for different wind speeds in Fig. 2.

um;opt ¼

lopt v r

(4)

2. Analysis of wind generation system The configuration of the overall system is presented in the schematic diagram of Fig. 1. The fixed-pitch wind turbine was directly coupled to a multi pole PMSG which, from the electric point of view, was connected through a rectifier and a DC/DC converter to a DC (Direct Current) bus. This configuration contributes to control the turbine operation point and consequently to handle the duty cycle of the DC/DC converter in its power generation.

Table 1 Windmill/battery system parameters. Pole pairs

P ¼ 28

Blades radius

r ¼ 1.84 m

Synchronous resistance Synchronous reactance Flux

Rs ¼ 0.3676 U

Inertia

J ¼ 7.856 kg/m2

Ls ¼ 3.55 mH

Turbine parameters Battery voltage

cp1 ¼ 21, cp2 ¼ 125.22 cp3 ¼ 9.7792, cp4 ¼ 0.0068 vdc ¼ 48 V

f ¼ 0.2867 Wb

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

3

Fig. 2. Power coefficient curves as a function of rotor speed.

According to the aerodynamic characteristics of the turbine, the amount of power captured by the wind turbine delivered by the rotor is given by Refs. [5,9]:

pw ¼

1 rACp ðlÞv3 2

(5)

where r is the air density (kg=m3 ), A is the blades swept area (m2). From Eq. (1), the expression of the driving torque can be obtained as:

Tw ¼

pw 1 ¼ rArCt ðlÞv2 um 2

(6)

where Ct ðlÞ ¼ Cp ðlÞ=l is the torque coefficient of the turbine. 2.2. Overall dynamic model The PMSG is linked to a battery bank through a passive rectifier and a DC/DC converter, as shown Fig. 1. It is noteworthy that in modeling the small-scale windmill systems, the generator dynamics cannot be neglected, as usually done for large wind turbines [5]. Moreover, this configuration presents a pure active power load to the generator terminals (cos(f) ¼ 1). In this paper, we used the proper model presented in Refs. [5] and [9]. The modeling considered the following assumptions:  the friction terms in the mechanical equation is neglect;  in actual radial flux PMSGs with a smooth air gap, it holds Ld y Lq y Ls  DC to DC converter and battery are ideal.

where Rs and Ls are the synchronous resistance and inductance, respectively, f is the flux linked by the stator windings, id and iq are the direct and quadrature stator currents, P is the number of poles, and J is the inertia of the rotating parts; ue is the electrical angular speed related to the mechanical angular speed via

ue ¼

P um 2

The voltage at the generator's terminals is determined by the battery voltage (vdc) and the duty ratio of the DC/DC converter, denoted D, as:

   ! pvdc D  Vs  ¼ pffiffiffi   3 3 By decomposing the terminal voltage Vs in the rotor dq frame, incorporating the electric torque expression (7)e(10), and considering the unity power factor, the dynamics of the overall system can be rewritten as:

Rs iq pv iq D ue f qffiffiffiffiffiffiffiffiffiffiffiffiffiffi i_q ¼  ue i d þ  pffiffiffi dc Ls Ls 3 3L i2 þ i2 s

q

d

Rs id pv id D qffiffiffiffiffiffiffiffiffiffiffiffiffiffi i_d ¼ þ ue iq  pffiffiffi dc Ls 3 3L i2 þ i2 s

P

3P Tt  fiq u_ e ¼ 2J 22

q

d



Also, by considering the third assumption, the current injected by the PMSG on the DC bus can be expressed as:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi i2q þ i2d D

The dynamic model of PMSG can be expressed in a dq rotor reference frame by Ref. [20]:

p idc ¼ pffiffiffi 2 3

 1
i_q ¼  RS iq  ue Ls id þ ue f  vq Ls

In order to write these dynamics in a compact form, the following notations can be defined:

 1
 RS id þ ue Ls iq  vd i_d ¼ Ls u_ e ¼

P ðTt  Te Þ 2J

Te ¼

3P fiq 22

(7)

x1 ≡ id

x2 ≡ iq

x3 ≡ rum

(8)

(9)

(10)

D p rA PLs L1 ≡ R ≡ Rs L ≡ Ls u ≡ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M ≡ pffiffiffi C1 ≡ Mvb C2 ≡ 3 2r 2 2 3 3 x1 þ x2
 pf 2J 3v M v3 x  J1 ≡ 2 K ≡ dc F x3 ; v ≡ C 2 C P 3 f1 ≡ 2r 2 x3 v 3r Therefore, the system state equations can be written as [5]:

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

4

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

x_1 ðtÞ ¼

1 ð  Rx1 ðtÞ þ Lx2 ðtÞx3 ðtÞ  C1 x1 ðtÞuðtÞÞ L

x_2 ðtÞ ¼

1 ð  Rx2 ðtÞ  L1 x1 ðtÞx3 ðtÞ þ f1 x3 ðtÞ  C1 x2 ðtÞuðtÞÞ L

(11)

(12) x_3 ðtÞ ¼

1 ð  f1 x2 ðtÞ þ Fðx3 ðtÞ; vÞÞ J1

(13)

Also in this form, the current injected on DC bus can be rewritten as:


 3



 idc t ¼ M x21 t þ x22 t u t 2




 3



 Pe t ¼ vdc t idc t ¼ Mvdc x21 t þ x22 t u t 2

Ztf JðuÞ ¼

Calculus of variations is a branch of mathematics considered as a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc. for which a given function has a stationary value. A functional is a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving the unknown functions and their derivatives. The interest is in extremal functions that make the functional attain a maximum or minimum value, in which the rate of change of the functional is precisely zero. The problem is to find an admissible control U* resulting in the system described by the state equation.

Z gðXðtÞ; UðtÞ; tÞdt ¼

(20)

Ztf (15)

t0

where X(t) and U(t) represent the n  1 state vector and m  1 control vector, respectively. The functions of f and g are differentiable with respect to both X(t) and U(t). The aim is to find U(t) as a function of X(t), so that the control can be implemented as a feedback. Now Hamiltonian function H defined as:





 


 


  H X t ; u t ; P t ; t ¼ g X t ; u t ; t þ PT f X t ; u t ; t (16) Using this notation, the necessary conditions can be written as [21],

vHðXðtÞ; UðtÞ; PðtÞ; tÞ ¼0 vU

(17)

vHðXðtÞ; UðtÞ; PðtÞ; tÞ _ ¼ PðtÞ vX

(18)

vHðXðtÞ; UðtÞ; PðtÞ; tÞ _ ¼ XðtÞ vP

(19)

(21)

  K x21 ðtÞ þ x22 ðtÞ uðtÞdt

t0

As for Eq. (16) and to convert the maximization problem to a minimization problem, Hamiltonian function can be written as:

  p ðtÞ HðXðtÞ;uðtÞ;PðtÞ;tÞ ¼  K x21 ðtÞ þ x22 ðtÞ uðtÞ  1 ð  Rx1 ðtÞ L p ðtÞ þ Lx2 ðtÞx3 ðtÞ  C1 x1 ðtÞuðtÞÞ  2 ð  Rx2 ðtÞ L  L1 x1 ðtÞx3 ðtÞ þ f1 x3 ðtÞ  C1 x2 ðtÞuðtÞÞ 

p3 ðtÞ ð  f1 x2 ðtÞ þ fðx3 ðtÞ;vÞÞ J1 (22)

(14)

To follow an admissible trajectory X*, from an initial point X(t0) to a desired final point X(tf), while minimizing a desired cost, function J is given by:

gðXðtÞ; UðtÞ; tÞdt

In this study, the purpose of control is to extract the maximum power from small wind-turbine systems. The amount of the electrical power delivered to DC bus is given by:

  gðXðtÞ; uðtÞ; tÞ ¼ K x21 ðtÞ þ x22 ðtÞ uðtÞ

3.1. Calculus of variations

JðuÞ ¼

3.2. Designing the control method based on calculus of variations

Therefore, the desired cost function is defined as:

3. The proposed control method based on calculus of variations





  X_ t ¼ f X t ; U t ; t

synthesis of optimal control. Some of the broad classes of the problems include fixed initial and final states, fixed initial and free final state, etc. Further details can be found in Ref. [21].

Co-state equations can be obtained from Eq. (22) and Eq. (18) as follows:

vHðXðtÞ; uðtÞ; PðtÞ; tÞ ¼ p_ 1 ðtÞ vx1 ðtÞ vHðXðtÞ; uðtÞ; PðtÞ; tÞ ¼ p_ 2 ðtÞ vx2 ðtÞ vHðXðtÞ; uðtÞ; PðtÞ; tÞ ¼ p_ 3 ðtÞ vx3 ðtÞ p_ 1 ðtÞ ¼ 

R þ C1 uðtÞ L x ðtÞ p1 ðtÞ  1 3 p2 ðtÞ þ 2Kx1 ðtÞuðtÞ L L

(23)

R þ C1 uðtÞ L x ðtÞ f p2 ðtÞ  1 3 p1 ðtÞ  1 p3 ðtÞ þ 2Kx2 ðtÞuðtÞ p_ 2 ðtÞ ¼  L L J1 (24) p_ 3 ðtÞ ¼ 

L1 x2 ðtÞ L x ðtÞ f vfðx3 ðtÞ; vÞ p1 ðtÞ  1 1 p2 ðtÞ þ 1 p3 ðtÞ þ L L vx3 ðtÞ L (25)

These equations are called optimal control equations, co-state equations, and state equations, respectively and have to be solved simultaneously along with appropriate boundary conditions for the

where final term of Eq. (25) is given by:

  vfðx3 ðtÞ;vÞ C v3 C v2 CP1 C ¼  22 Cp ðlÞ þ 2 e l  P2 vx3 ðtÞ x ðtÞ x3 ðtÞ l2 3    C CP2  CP3 þ CP4 þ P1 l l2

(26)

For optimal control equation, Eq. (17), the necessary condition for optimality is given by:

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

vHðXðtÞ; uðtÞ; PðtÞ; tÞ ¼0 vuðtÞ


 p ðtÞ
 p ðtÞ
 K x21 t þ x22 t þ 1 C1 x1 t þ 2 C1 x2 t ¼ 0 L L

(27)

Neglecting the converter loss, the generator power (i.e. the power delivered to DC bus) can be written as:

Pe ¼ Pem  Pgloss

(28)

where Pem and Pgloss are the input powers to generator and generator loss, respectively, being given by:

Pem ¼

3 Te um 2

Pgloss ¼

 3 2 R iq þ i2d 2

Combining Eq. (28) and Eq. (20) and the defined notations obtained as:




 3

 3 

 K x21 t þ x22 t u t ¼ f1 x2 t x3 t  R x21 t þ x22 t 2 2 (29) Thus, the control signal is derived from Eq. (29) and Eq. (27) as follows:



 3  2

 3 2
 2 f 1 x2 t x3 t  2 R x1 t þ x2 t u t ¼
 p2 ðtÞ
 p1 ðtÞ L C 1 x1 t þ L C 1 x2 t *

¼

Vx2 ðtÞx3 ðtÞ 3R  p1 ðtÞx1 ðtÞ þ p2 ðtÞx2 ðtÞ 2K

(30)

where V is defined as V≡3Lf1 =2C1 . Therefore, the desired control signal u* is a function of the state variables X(t) and the co-state variables P(t); on the other hand, from the Eqs. 23e25, the co-state variables are dependent on X(t) so that the control can be implemented as a feedback of the state variables.

4. Improving the designed control method As it can be observed in Eq. (26) and Eq. (25), the wind speed enters into the controller equations in a highly nonlinear way, causing the controller to be dependent on measuring the windspeed. In order to remove such a deficiency and improve designed control method, two methods are used in this section: (1) Improving the proposed control method using echo state network (method 2), (2) Improving the proposed control method using online wind speed estimator (method 3).

5

4.1.1. Echo state networks ESN (echo state network) is a special type of recurrent neural networks. In order to maintain the high modeling capability of the ordinary recurrent neural networks, a large (e.g. 100 hidden neurons) RNN is used as a “DR (Dynamic Reservoir)” in the hidden layer of the ESN, which can be excited by suitably presented input and/or feedback of the output. The typical structure of ESN consists of three layers: input, internal (or hidden), and output layers as shown in Fig. 3. The internal layer as the dynamical reservoir often contains sigmoid neurons (e.g. with tan h functions) while the other two layers have linear neurons. At the time step(n þ 1), the reservoir state vector X, i.e. the vector of the outputs of all neurons across the reservoir and ESN outputs Y, are given as:





 X n þ 1 ¼ F Win U n þ 1 þ WX n þ Wofb Y n

(31)

 h

 
iT  Y n þ 1 ¼ G Wout U T n þ 1 ; X T n þ 1

(32)

where Win(of size Nx  Nu), W (of size Nx  Nx), Wofb (of size Nx  Ny) and Wout (of size Ny  (Nu þ Nx)) are respectively the input-internal, internaleinternal, output-internal, and output weight matrices. U and Y are input and output vectors, respectively. F ¼ [f1,f2,...,fNx]T and G ¼ [g1,g2,...,gNy]T are the vector of activation functions of output neurons (often linear functions) and the vector of activation functions of internal neurons, respectively. When the network is updated according to Eq. (31), under certain conditions, the network state becomes asymptotically independent of the initial conditions. If this condition holds, the reservoir network state will asymptotically depend only on the input history and the network is said to have the echo state property. A sufficient condition for the echo state property is contractively of W. In practice it was found following steps [18]: Step 1: Generate an initial internal weight matrix W0 randomly; Step 2: Normalize W0 to obtain W1 with unity spectral radius, that is, W1 ¼ W0/lmax where lmax is the spectral radius of W0; Step 3: Scale W1 as W ¼ aW1 and a < 1, so the spectral radius of W will be a. Being randomly generated from a uniform distribution, Win and Wofb are mostly dense are remain unchanged during the training process. The general procedure to train the ESN is to minimize the MSE (mean square error) between the desired outputs and the real outputs of ESN for the applied time series of inputs in order to obtain the optimal Wout. Initially, the training data is fed to the ESN and the

4.1. Improving the proposed control method using echo state network Since the artificial neural networks (ANNs) are renowned as effective universal function approximators in this section, instead of Eq. (26), we apply a neural network (NN). Thus, the wind-speed is extracted from the dynamic of the system, causing the controller not to require an anemometer. Finally, due to the ESN's high modeling capability of complex dynamic systems, it was selected to be used in this paper.

Fig. 3. The structure of ESN.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

6

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

internal dynamic reservoir states are computed according to Eq. (31) at each sampling step. Then the data from initial transient, for each time shorter than an initial washout time T0, is dismissed and the remaining input plus network states (Uteach(n),Xteach(n)) rowwise are collected into a matrix S. In the end, one has obtained a state collecting matrix of size (TT0 þ 1)  (Nx þ Nu). Simultaneously, the remaining training teacher output Yteach(n) row-wise is collected into a teacher collection matrix D to end up with a teacher collecting matrix D of size (TT0 þ 1)  Ny. Then the output weight (Wout) is calculated using Eq. (33).

Wout ¼ ðpseudoinverseðSÞ  DÞT

(33)

4.1.2. Designing the ESN One of the significant aspects of applying a NN to any particular problem is to formulate the inputs and outputs of the NN structure under study. According to Eq. (5), wind velocity can be estimated from turbine power (Pm) and generator speed (um). On the other hand, the derivative of the mechanical power into the generator speed (vf(x3(t),v)/vx3(t)) is a complexity function of the wind speed and the generator speed. Therefore, Eq. (26) can be estimated from the turbine power and the generator speed, as shown in Fig. 4. The turbine power Pm can be generated from the generator power Pe and the generator speed um as follows:

Pm ¼ Jum

dum þ Pe dt

(34)

assumption. In this section, we use it to remove wind speed measurement in the designed control method. For the sake of completeness, a slight variation of main result of [22] e suitable for our objective e is given below. The interested reader is referred to this reference for the proof of the proposition. Proposition: consider the windmill system with equations (11)e(13). The I&I estimator.

g b v ðtÞ þ gx3 ðtÞÞÞ v_ ðtÞ ¼ ðf1 x2 ðtÞ  Fðx3 ðtÞ; ðb J1 where g > 0 is an adaptation gain, asymptotically consistent, so that




 v t þ gx3 t ¼ v t lim b

t/∞

If the condition below holds:

3
 vCP ðlÞ C l > l P vl

(35)

The estimator is globally convergent if the power coefficient verifies (35). In the normal operating region of wind turbine, it is desirable to keep the torque coefficient with a negative slope [23]. It is easy to show that:

vCT ðlÞ vCP ðlÞ 1 vC ðlÞ 1 ¼  CP ðlÞ  00 P  CP ðlÞ vl vl l vl l Then, the condition (33) does hold. This condition will be checked numerically in Section 5.3.

where the derivative operation is approximated as: 5. Simulation results

dum ðtÞ um ðtÞ  um ðt0 Þ z dt t  t0 For the present paper, the data was obtained by simulating the small-scale windmill system. The simulation was carried out at random wind-speeds and sample dates Pm, um, and vf(x3(t),v)/ vx3(t) were collected as the training data for the ESN. 4.2. Improving the proposed control method using on-line wind speed estimator Currently, for the disadvantages of wind speed sensor, many wind speed estimators have been proposed. In Ref. [22], an estimator based on I&I (immersion and invariance) technique has been applied to solve the wind estimation problem. It has shown that I&I estimator can be globally consistent under a monotonicity

Computer simulations were conducted with the aim to evaluate the performance of the proposed controller. The plant was modeled with a comprehensive full order model detailed in Eqs. 11e13. The simulation condition is shown in Table 1. This simulation data for the battery-charging windmill system was taken from Ref. [5]. All simulations were executed using the Matlab Simulinks mathematical analysis software. The simulation model of the entire system is shown in Fig. 5. The proposed methods are separated with a switch in it. 5.1. Validation of the proposed controller based on method 1 In this section, having assumed that the wind speed was known and vf(x3(t),v)/vx3(t) was calculated according to Eq. (26) before

Fig. 4. Proposed training scheme for ESN based vfðx3 ðtÞ; vÞ=vx3 ðtÞ estimation.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

Fig. 5. Simulation model of the entire system.

being applied to the controller, the validity of the proposed controller was evaluated. To achieve this goal, a random windspeed profile with a maximum of 12 m/s and a minimum of 7 m/ s, as shown in Fig. 6, was applied to the battery-charging windmill system. The mechanical speed, the power coefficient, the duty ratio of the boost converter, and the active power output are shown in Fig. 6. It is delineated that the mechanical speed well-tracked the optimal speeds specified in Fig. 2. Further details on the system's responses are provided in Fig. 7, where the evolution of the all states of the system is presented. It should be considered that the state variablex3 is a coefficient of the mechanical speed. As it can be observed, the overall system's behavior was as desired: (1) the converter's duty ratio stayed within 0e100%, and (2) the power coefficient was very close to its optimal value, and hence the maximum power was extracted for all varying wind-speeds. 5.2. Validation of the proposed controller based on method 2 To evaluate the performance of the proposed controller when it is independent of the measuring wind speed, the trained echo state network was then replaced with the Eq. (26). A wind profile without taking into account the tower shadow effect defined as Eq. (36) was selected for this purpose [24].

vðtÞ ¼ 0:9ð10 þ 2 sinðuw tÞ þ 2 sinð3:5uw tÞ þ sinð12:5uw tÞ þ 0:2 sinð35uw tÞÞ þ whitenoise (36) The frequency uw depending on the desired test time was given as:

uw ¼

2p ttest

In this case, the test time was chosen as ttest ¼ 600 s. This wind profile is shown in Fig. 9(a). In Fig. 8, the performance of the considered system with methods 2 is presented. To verify the validity of the ESN, its actual output is compared with its desired output in Fig. 8(a) and (b). It can be seen that a value close to vf(x3(t),v)/vx3(t) is output in ESN at all wind speeds. The difference between the actual mechanical speed and the optimum mechanical speed is depicted in Fig. 8(c) for method 2. The

Fig. 6. Responses of the proposed control in wind-speed variations.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

7

8

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

Fig. 7. Evolution of all states of the system.

optimum speed was obtained from Eq. (4) and Eq. (36) regardless of the noise term of Eq. (36). This figure shows that, if ESN is employed, the mechanical speed can well track the optimal speeds. The value of power coefficient is depicted in Fig. 8(d). It is concluded that the proposed controller based on method 2 works well where the value of power coefficient keeps its optimum value equal to 0.48 with changes of the wind speed to obtain MPPT. 5.3. Validation of the proposed controller based on method 3 In this method, wind speed is estimated using the online windspeed estimator presented in Section 4.2 before being applied to the controller. After many trails, the value of g was selected as 0.15 to give enough speed to the estimator to track time-varying average value of the wind speed. The performance of the proposed controller based on method 3 is evaluated at the same wind speed represented in Fig. 9(a). To investigate condition (35), the derivative of the mechanical power into the generator speed is rewritten as follow:

  vfðx3 ðtÞ; vÞ C2 v2 vCP ðlÞ 1  CP ðlÞ ¼ vx3 ðtÞ vl l l As shown in Fig. 8(a) the value of vf(x3(t),v)/vx3(t) for a wide range of wind speed is negative. It is easy to show that:

vfðx3 ðt Þ; vÞ <0 vx3 ðt Þ

/

vCP ðlÞ 3
 < CP l vl l

Therefore, this key condition is satisfied. Fig. 9(a) shows the actual and estimated wind-speed. The error between the actual and estimated wind-speed is found less than 0.45 as shown in Fig. 9(b). Fig. 9(c) indicates the difference between the actual mechanical speed and the optimum mechanical speed for method 3. It is clear that the actual mechanical speed tracking error is low due to use of proposed controller based on method 3. Fig. 9(d) shows, if estimator is employed, the power coefficient is close to its maximum value during the whole wind speed profile. 5.4. Comparison of performance The simulation results show that by using the new proposed MPPT control system, the actual wind turbine power can track its desired value closely, and the maximal wind energy can be

Fig. 8. Performance of the considered system using method 2.

captured. The performance comparison between proposed methods and other methods is presented in this subsection. In beginning, the performance of the proposed controller based on method 2 and method 3 is compared and then proposed controller performance is compared with PID (Proportional Integral Derivative) and APBC (adaptive passivity-based control) methods which used MPPT-TSR algorithm.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

9

Fig. 10. Comparison of the performances of the three methods.

method 2 in comparison with method 3 is variable (i.e. sometimes more and sometimes less) as shown in Fig. 11. Therefore, to numerically compare these methods, the average value of the generated power using both methods was calculated through Eq. (37):

Fig. 9. Performance of the considered system using method 3.

In Fig. 10, the generated power, the rotor speed, and the duty ratio are compared with their attributed values when the wind speed was known (method 1) and when the wind speed measurement was removed by using an ESN (method 2) and when the wind speed was estimated with an estimator (method 3). The details of Fig. 10(a), for the generated electrical power are shown in Fig. 11. It can be seen that the generated electrical power with

Fig. 11. Details of the generated electrical power with the three methods.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024

10

S. Ganjefar, A.A. Ghasemi / Energy xxx (2014) 1e10

Table 2 Performance for various control methods. Controller type

Average Minimum Mean squared errors Decreasing error ¼ um,optum mean squared power (W) power coefficient errors (%)

Proposed method 3.5463 APBC method 4.9720 with MPPT-TSR algorithm 7.8285 PID method with MPPT-TSR algorithm

54.7 36.49

1587.3 1578.6

0.3662 0.3576

e

1575

0.3358

system which converter loss is not negligible; (3) The combination of the proposed control method with an ESN to remove measuring the wind-speed was more efficient compared to the time the control method is equipped with wind-speed estimator due to the ESN's high modeling capability of complex dynamic systems. For a better appreciation about the proposed controller assets, its performance was compared with that of PID and APBC methods. Performance comparison showed that by using proposed control method the windmill system is more efficient than the time it is equipped with PID and APBC methods. References

Zttest   1 Pout average ¼ Pout ðtÞdt ttest

(37)

0

Pout ðaverageÞcmthod2 $100% ¼ 99:9986 Pout ðaverageÞcmthod1 Pout ðaverageÞcmthod3 $100% ¼ 99:8843 Pout ðaverageÞcmthod1 It is concluded that method 2 is more efficient in comparison to method 3. It is so because the obtained mechanical speed of method 2 is closer to the optimum speed compared to that of method 3 as shown in Figs. 8(c) and 9(c). Now, the proposed controller is replaced with the PID controller and APB (Adaptive Passivity Based) controller. In order to challenge methods, a rapid wind speed profile with test time 200 s in Eq. (36) is applied to the stand-alone windmill system. Average power, mean squared error between actual mechanical speed and the optimum mechanical and minimum power coefficient from each control method are summarized in Table 2. It is concluded that the proposed method has better performance compared to other methods. 6. Conclusion In this paper, a new MPPT control method was proposed for a stand-alone windmill system, directly driven by a permanent magnet synchronous generator system. The MPPT control method was employed with the aim to harvest the maximum power from the available wind power. The control method was presented based on the calculus of variations, directly creating the control signal for handling the power electronic converter. In beginning, the controller was designed considering the known wind-speed and then the dependence of the controller on the anemometer was removed using a combination of the proposed control method with an echo state neural network as well as with the wind-speed estimator. Finally, the proposed control schemes were simulated in MATLAB/Simulink environment. Simulation results confirmed the validity and performance of the suggested MPPT control method, showing that our proposed method had the capability to reach the objective of extracting maximum power from the air stream at any wind-speed without needing to know the speed itself. advantages of the new proposed control method are addressed as following; (1) This method was designed based on nonlinear calculus of variation to cope with the intrinsic nonlinear behavior of wind turbines/generators; (2) This method was considered output electrical power of the generator as a cost function to decrease generator and converter losses as well as increase wind turbine power. This advantage is cleared in high power wind turbine

[1] Mittal R, Sandu KS, Jain DK. Isolated operation of variable speed driven PMSG for wind Energy conversion system. Int J Eng Technol (IACSIT) 2009;1:3. [2] Li H, Shi KL, McLaren P. Neural network based sensorless maximum wind energy capture with compensated power coefficient. IEEE Trans Ind Appl 2005;41:6. [3] Li S, Haskew TA, Xu L. Conventional and novel control designs for direct driven PMSG wind turbines. Electr Power Syst Res 2010;80:328e38. [4] Amei K, Takayasu Y, Ohji T, Sakui M. A maximum power control of wind generator system using a permanent magnet synchronous generator and a boost chopper circuit. Proc Power Convers Conf 2002;3:1447e52. [5] Mancilla F, Ortega R. Adaptive passivity-based control for maximum power extraction of stand-alone windmill systems. Elsevier Control Eng Pract 2012;20:173e81. [6] Kesraoui M, Korichi N, Belkadi A. Maximum power point tracker of wind energy conversion system. Elsevier Renew Energy 2011;36:2655e62. [7] Thongam JS, Bouchard P, Beguenane R, Fofana I, Ouhrouche M. Sensorless control of PMSG in variable speed wind energy conversion systems. In: International Power Electronics Conference (IPEC); 2010. p. 2254e9. [8] Valenciaga F, Puleston PF, Battaiotto PE, Mantz RJ. Passivity/sliding mode control of a stand-alone hybrid generation system. IEEE Proc Control Theory Appl 2000;147:680e6. [9] Valenciaga F, Puleston PF. High-order sliding control for a wind energy conversion system based on a permanent magnet synchronous generator. IEEE Trans Energy Convers 2008;23:3. [10] Lin WM, Hong CM. Intelligent approach to maximum power point tracking control strategy for variable-speed wind turbine generation system. Energy 2010;35:592e601. [11] Lin WM, Hong CM, Cheng FS. Fuzzy neural network output maximization control for sensorless wind energy conversion system. Energy 2010;35: 592e601. [12] Hong CM, Ou TC, Lu KC. Development of intelligent MPPT (maximum power point tracking) control for a grid-connected hybrid power generation system. Energy 2013;50:270e9. [13] Aissaoui AG, Tahour A, Essounbouli N, Nollet F, Abid M, Chergui MI. A fuzzy-PI control to extract an optimal power from wind turbine. Energy Convers Manag 2013;65:688e96. [14] Ganjefar S, Ghasemi AA, Ahmadi MM. Improving efficiency of two type maximum power Point tracking methods of tip-speed ratio and optimum torque in wind turbine system using a quantum neural networks. Energy 2014;67:444e53. [15] Kot R, Rolak M. Comparison of maximum peak power tracking algorithms for a small wind turbine Malinowski. Math Comput Simul 2013;91:29e40. [16] Abdullah MA, Yatim AHM, Tan CW, Saidur R. A review of maximum power point tracking algorithms for wind energy systems. Renew Sustain Energy Rev 2012;16:3220e7. [17] Koutroulis E, Kalaitzakis K. Design of a maximum power tracking system for wind-energy-conversion applications. IEEE Trans Ind Electron 2006;53: 486e94. [18] Jaeger H. Tutorial on training recurrent neural networks, covering BPTT, RTRL, EKF and the ‘Echo State Network’ approach. GMD Report 159. Sankt Augustin: German National Research Center for Information Technology; 2002. [19] Dai J, Venayagamoorthy GK, Harley RG. An introduction to the Echo state network and its applications in power system. In: IEEE international Conference on Intelligent System Applications to Power Systems; 2009. p. 1e7. [20] Krause P, Wasynczuk O, Sudhoff S. Analysis of electric machinery. Piscataway, NJ: IEEE Press; 1995. [21] Kirk DE. Optimal control theory an introduction. Dover Publications; 2004. [22] Ortega R, Mancilla-David F, Jaramillo F. A wind speed estimator for windmill systems. In: International conference on renewable energy and power quality (ICREPQ'11); 2011. Las Palmas, Canary Islands, Spain. [23] Cigre. Technical brochure, modeling and dynamic behavior of wind generation as it relates to power system control and dynamic performance. Working Group 601 of Study Committee C4, Final Report; 2007. [24] Gonzalez LG, Figueres E, Garcera G, Carranza O. Maximum-power-point tracking with reduced mechanical stress applied to wind-energy-conversionsystems. Elsevier Appl Energy 2010;87:2304e12.

Please cite this article in press as: Ganjefar S, Ghasemi AA, A novel-strategy controller design for maximum power extraction in stand-alone windmill systems, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.08.024