COMPARATIVE STUDY OF TWO ROBUST CONTROL STRATEGIES APPLIED ON A WIND CONVERSION SYSTEM BASED ON A HYBRID EXCITATION SYNCHRONOUS GENERATOR

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CONVERSION SYSTEM BASED ON A HYBRID EXCITATION SYNCHRONOUS GENERATOR

Amina Mseddi, Sandrine Le Ballois, Helmi Aloui, Lionel Vido

To cite this version:

Amina Mseddi, Sandrine Le Ballois, Helmi Aloui, Lionel Vido. COMPARATIVE STUDY OF TWO

ROBUST CONTROL STRATEGIES APPLIED ON A WIND CONVERSION SYSTEM BASED

ON A HYBRID EXCITATION SYNCHRONOUS GENERATOR. ELECTRIMACS 2017, Jul 2017,

Toulouse, France. �hal-01687797�

C OMPARATIVE STUDY OF TWO ROBUST CONTROL STRATEGIES APPLIED ON A

W ^IND C ^ONVERSION S YSTEM BASED ON A H ^YBRID E ^XCITATION S YNCHRONOUS

G ^ENERATOR

Amina Mseddi ^1,2 , Sandrine Le Ballois ¹ , Helmi Aloui ² , Lionel Vido ¹

1. SATIE Laboratory, University of Cergy Pontoise, 5 Mail Gay Lussac, 95031 Cergy Pontoise, France 2. Laboratory of advanced Electronic Systems & Sustainable Energy, ISEM team, ENET’COM, Sfax, Tunisia

Tel : +33/644072717

E-mail : [email protected]

Abstract - This paper deals with a Wind Conversion System (WCS) based on a Hybrid Excitation Synchronous Generator (HESG) connected to an isolated load.

The set is modeled under Matlab-Simulink. To ensure an efficient and reliable use of the system, a tight control remains vital. In fact, the dynamic equations of a turbine are strongly nonlinear as are the ones of a HESG; most of the system parameters are highly uncertain, and, at last, a WCS is always affected by unknown disturbance sources. To address these problems, robust control methods must be adopted. In this paper, two control strategies for the maximization of the wind turbine extracted power are investigated. First, a H

∞

controller is implemented. Then, a second- generation CRONE controller is designed. The performance of the two regulators is compared in relation to the tracking of the optimal power outputs and their robustness to the uncertainty of the parameters.

Keywords – WCS, HESG, H

∞

controller, 2

^nd

generation CRONE controller 1. I NTRODUCTİON

Faced with the limitations, high cost and pollution concerns of fossil fuels on the one hand, and with the worldwide demand for the reduction of carbon dioxide emissions and for the nature conservation on the other, the use of renewable energies such as solar, geothermal and wind power is now absolutely necessary. Among these alternatives, wind power is one of the most cost effective. It is also one of the cleanest: while producing energy, wind turbines pollute neither the waters, nor the soils, and they don’t propagate any greenhouse gas effects [1].

However, because of the stochastic nature of the wind and the inevitable uncertainties of a WCS, wind turbines have operated with a low efficiency for many years. Previously, classical controllers such as P, PI and PID based on linearized models were used [2] [3]. Nowadays, the design of robust controllers with a capability of tracking smoothly and more efficiently the optimal energy extracted is of great interest for the wind power industry.

In this work, the focus is on the second operating region [4], i.e. the area with a wind speed below the rated speed, where the turbine must operate with an optimal efficiency to extract the maximum power.

The present work considers a HESG. In this type of generators, the excitation flux is created by permanent magnets and DC coils. The optimal rotation speed tracking is achieved by adjusting the excitation winding current, which adds a degree of freedom to the WCS architecture. The control of the considered structure is ensured by an internal current loop and an external speed loop. A PI controller was designed in [5] for the current loop. Its effectiveness and robustness to the uncertainties of the parameters were proven in the same work. In this paper, linear robust control techniques are applied for the regulation of the generator velocity loop. Among the robust techniques that could be used for the speed control, a H

∞

controller based on the Normalized Coprime Factors robust stabilization problem and a 2

^nd

generation CRONE controller are investigated and tested in presence of parameters’ uncertainties and nonlinearities of the WCS model.

For various wind profiles (including step ones and stochastic ones), the two controllers are compared considering their ability to track the desired set-point.

2. D YNAMİC MODEL OF THE WCS

A WCS converts wind energy into electrical one. Its

main parts are the turbine, the gearbox and the

generator. The choice of the latter and its control remain a crucial factor. Before dealing with the control concepts, we shall describe below the dynamic models and the nonlinear equations governing the studied system (Fig 1). Fig 8 shows a complete Matlab/Simulink model of this architecture.

Fig 1 : Architecture of the wind generator [4]

2.1. W İND T URBİNE DYNAMİCAL MODEL As in Fig 1, in the presence of an aerodynamic torque C

t

(1), the gearbox, connected between the turbine and the generator, adapts the turbine rotation speed Ω

t

to the one of the generator Ω

g

[2],[4].

3 3

0.5 ( , )

t p w t

C   C       S V   ⁽¹⁾ V

w

is the wind velocity, ρ is the air density and S is the surface swept by the turbine blades radius R

p

. C

p

is the turbine performance coefficient. It’s a function of the pitch angle β and the tip speed ratio λ (2):

t

R V

p w

     ⁽²⁾

In order to take into account a possible mechanical torsion between the slow shaft and the fast one, a two masses mechanical model of the wind turbine is considered. The mechanical behavior is described in the reference of the slow shaft and given by (3) and (4) [2].

(

^g

) (

^g

)

t

t t ls t ls t t t

p p

J d C D K K

dt m m

 

 

        (3)

( ) ( )

g ls g ls g

g em t t g g

p p p p

d D K

J C K

dt m m m m

 

 

        (4)

θ

g

and θ

t

are the angular positions of the generator and of the turbine, J

g

and J

t

are the inertias of the generator and of the turbine, K

g

, K

t

and K

ls

are respectively the generator, the turbine and the slow shaft viscous friction coefficients and D

ls

is the torsion coefficient of the slow shaft. Finally, m

p

is the coefficient of the multiplier.

2.2. WCS ELECRİCAL PARTS ’ ^MODELS The described parts include the HESG, the rectifier, the resistive load and the DC/DC converter.

2.2.1. HESG Model

Among the inevitable uncertainties affecting in a

significant way the power quality extracted from the wind, one can mention the generator’s current harmonics [7]. It’s a common practice to neglect this phenomenon. For instance, in [2] [5], the generators are modeled in a d-q reference frame and a first harmonic model is considered. However, the distortion in the currents and armature voltages wave forms are due mainly to the harmonics. These harmonics also cause torque rippling [5] and can lead to a bad reference tracking. Therefore, their impact on the wind extracted power needs further consideration.

To take into account harmonics effects, the HESG is modeled drawing on the results presented and proved in [8]. For example, for the a phase, the stator inductance is expressed as in (5), the flux as in (6) and the mutual inductance as in (7). Then, the generator is modeled in Concordia reference frame.

0 2

cos(2 )

4

cos(4 )

6

cos(6 )

aa s s s s

L  L  L p   L p   L p  (5)

1

2 cos( )

3

cos(3 )

ea a

p

a

p

       (6)

0 2 4

2 4

cos(2 ) cos(2 )

3 3

ab s s s

M  M  L p     M p    (7)

With L

_s0

 ( L

_d

 L

_q

) 3 , L

_s2

 ( L

_d

 L

_q

) 3 ,

4 2

s s

L  L ,

6

0.7

2

s s

L  L , M

_s0

  L

_s0

3 , M

_s4

 0.3 L

_s2

, 

_a3

 0.15 

_a1

. L

d

and L

q

are the d and q-axis inductances. 

_a1

is the effective value of the flux created by the magnets in the armature coils and 

_ea

is the flux created by the magnets in the DC field excitation coils. p is the number of pole pairs.

2.2.2. Converters and load models The excitation coils of the HESG are controlled by a DC/DC converter and the resistive load is connected to the WCS through a full bridge rectifier.

SimPowerSystem tools are used for the modeling of the converters. They allow to take into account the commutations effects and test the controllers in a realistic environment [5].

The resistive load R

c

is also implemented using

SimPowerSystem blocks. A value of 15Ω is selected

because it matches both the maximum power and the

current limitations of the HESG. Indeed, the

maximum value of the stator currents is 10A and the

nominal power of the generator is 3kW, the resistive

load should thus not surpass a value 30Ω. Moreover,

the maximum value of the excitation current that can

be supported is 6A. For security reasons and in order

to avoid a possible overheating of the excitation

coils, this value is limited to 5A. At last, for the

rated rotation speed, Fig 2 shows that the resistive

load should be limited to 18Ω to avoid possible

damage for the excitation coils.

Fig 2 : Excitation current for different R

c

3. C ONTROL OF THE WCS

The control system of a wind turbine should secure appropriate reference tracking, while minimizing its dynamic error. For a maximum power extraction using a HESG, the optimal turbine rotation speed may be tracked by controlling the excitation current of the generator [5]. However, control design for a non-linear system such as a WCS is a hard task. This can be overcome by adopting sophisticated control methods. Robust controllers such as H

∞

and CRONE regulators can be a good choice. In this section, both controllers are developed.

3.1. WCS LİNEARİSATİON

As said before, the present study is performed in zone 2 (from 4 to 11.5m/s). In this area, the blades pitch angle  is constant and equal to 0°. The performance coefficient C

p

is also constant and is set at its optimal value [5]. For the synthesis of both the CRONE and the H

∞

velocity controllers, the non- linear model described in Fig 8 must be linearized.

Some assumptions should then be made to get a linear model. The non-linear model will be used for the validation of the controllers while the linearized model is used only for the controllers design.

An identification process is conducted on a simplified model for four operating points in zone 2.

The wind speed is set to 4, 6.5, 8.5 and 11 m/s respectively. A set of linear transfer functions from the input i

eref

to the output 

g

is then derived and an average model is selected.

First, to simplify the non-linear model of Fig 8, the following assumptions are made:

 The converters are modeled as pure gains:

the commutations are not taken into account,

 The HESG is modeled in the d-q reference frame, a first harmonic model is considered,

 The turbine torque C

t

is constant and it is set to its operating point value.

To get the model of Fig 4, the electromagnetic torque is expressed in the d-q frame as in (8) [5] then equations (3) and (4) are combined to obtain (9).

   

em q

3

a e d q d

C    p i      Mi  L  L i    ⁽⁸⁾

3

3 2 1 0 1 0

2 2

2 1 0 2 1 0

² ( )

_t

g em

e s e s e s e a s a C f s f s f b s b s b C

   

  

   

(9)

2 2 2

3 2

2 2 2

1

2 0

2 2 2

2 1 0 1

0 2 1 0

, ( ) ( )

( )( )

( ) 2 ( )

, ( ) , ,

, , ,

g t p g ls t p t ls g p

ls t g ls p ls ls g p ls t

ls t ls ls ls ls g p ls

t p ls t p ls p ls p

ls p t ls t ls

e J J m e J D K m J D K m

e K J J K m D D K m D K

e D K K K D D K m K

f J m f D K m f K m a D m a K m b J b D K b K

    

     

     

    

    

The angular velocity’s open loop model is then derived from (8) and (9). The closed loop is given in Fig 4 where K



(s) is the velocity controller to synthesize. The identification simulations are performed for different values of the excitation current i

eref

corresponding to the four operating points defined previously.

Fig 3 : Identified Bode diagrams

The average model transfer function is for 6.5 m/s (see Fig 3) and is given in (10).

( ) 33.66

( ) ( ) 1 1 6.73 s

g n

eref n

s G

G s i s T s

 

  

    ⁽¹⁰⁾

Fig 4 : Angular velocity closed-loop

In the present work, the settling time of the angular

velocity’s closed loop is set to 4s which is

mechanically coherent for a WCS [9]. The inner

current loop needs to be at least 10 times faster than

the outer velocity loop. This is verified in the present

case where the current settling time is about 25ms [5]. Making the assumption that the velocity closed loop is tuned as a second order system, the desired settling time gives the closed loop bandwidth



0

to achieve. A sufficiently damped closed loop response is obtained with a damping factor of  =0.6.

Using the relation 

0

t

r

=f(), mixing the damping ratio, the bandwidth frequency and the settling time of a second order system, one can deduce that 

0

is around 0.75rd/s.

3.2. H

∞

CONTROL STRATEGY

The H

∞

control theory includes two main approaches.

The first one is based on closed loop specifications and it is known as the standard H

∞

problem. The second one, known as the Normalized Coprime Factors (NCF) robust stabilization problem [10] [11], is based on open loop specifications and it is considered in the present work.

As the H

∞

method based on the NCF robust stabilization problem does not address performance directly, pre and post compensators W

1

(s), W

2

(s) must be added to the nominal model to give the wanted open-loop shape. The augmented model is defined by G

a

(s)=W

2

(s)G(s)W

1

(s). In the studied case, the model to control is a SISO one, so only a pre- compensator W

1

(s) is necessary. The latter has to ensure that the open loop has a high gain in low frequencies and a low gain in high frequencies to secure a good reference tracking and a good disturbance rejection. To do so, a PI compensator W

PI

(s) is selected (11). The integral action of W

PI

(s) stops around the cut-off frequency of (10) so T

1

=T

n

.

1 1

1

( ) 1

PI

W s K T s T s

   (11)

In addition, the natural slope of (10) is -20dB/decade (Fig 3) which is not enough to have a satisfying roll- off. Thus, a low-pass filter is added. The time constant of the filter must be much smaller than T

n

(a ratio of 10 is usual) to not modify the natural phase margin of (10) around 

0

so, T

f

=0.025T

n

. Finally, W

1

(s) is given as:

1

1 1

1

1 1

( ) 1

_f

W s K T s

T s T s

   

 (12)

The H

∞

controller is computed for G

a

(s)=G(s)W

1

(s) with the Matlab ncfsyn function. It is given by (13).

A very good phase margin of 89° is achieved.

3 2

4 3 2

6.225s 250.91 74.138 5.496

( ) s 81.7 1672 246.6

s s

K s

^

s s s

   

   

(13)

3.3. C RONE CONTROL STRATEGY

CRONE control (French abbreviation of non-integer order robust control) is a frequency approach for a robust control methodology. In such an approach,

the corrected open loop transfer function has a non- integer (fractional) order, real or complex, that allows to define the optimal open-loop transfer function in terms of overshoot, rapidity and precision with few high-level parameters. The CRONE control includes three generations [12]. The first generation is based on a constant phase of the controller around the desired open loop cross-over frequency w

0

. The second one is used when there are variations of gain of the nominal model to control, as well as transitional frequencies variations. The third generation should be used when the frequency response of the model to control has uncertainties of various kinds (other than gain and phase types) [12].

Considering the Bode shapes of Fig 3, the second generation seems to be a good choice. It consists in determining, for the nominal state of the plant, the open-loop’s transfer function  ( ) s , defined by (14), which ensures the required specifications [12]:

( ) s K

_CRONE

( ) s G s ( )

   ⁽¹⁴⁾

1

1 1

( ) 1

1

h

n n

l h

u n

l l

h

s s

w w

s K

s s s

w w w



     

   

   

      

      

     

(15)

Where G(s) is the uncertain plan model (10), K

CRONE

(s) is the controller, K

u

is a constant ensuring unity gain at the desired frequency 

0

. w

h

and w

l

are the transitional high and low frequencies. w

l

and w

h

are geometrically distributed around 

0

. n

h

, n

l

and n are respectively the order at high frequencies, low frequencies and around the crossover frequency.

The constraints defined in the 3.1 section are used in the CRONE toolbox [13] to synthetize the desired controller given by (16). A good phase margin of 86.4° is achieved around the crossover frequency.

2

3 2

3.583s 0.6178 0.0127

( ) s 23.88

CRONE

K s s

s

  

   ⁽¹⁶⁾

4. C OMPARAİSON OF THE TWO CONTROLLERS

The performance and robustness of the two regulators are now compared, based on simulations conducted using the complete WCS model of Fig 8.

In a first test, an artificial wind made of 5 levels is injected to the nonlinear model. Fig 5 shows the obtained rotation speeds and Table I summarizes the overshoots and settling times for each level.

It turns out that, with the H

∞

controller, the static

error tends to 0 and the oscillations in the transient

state are damped for all operating points with a

maximum overshoot of 27%. A similar behavior is observed with the CRONE controller, yet with more overshoot which can reach 33% in the worst case, showing lesser stability than the H

∞

controller. This is due to the fact that the CRONE controller phase margin is smaller than the one of the H

∞

controller.

Regarding the settling time, the same performance is registered for all considered speed levels. In the worst case, it is 19s for the two controllers. While higher than expected, this value remains acceptable.

Fig 5 : Rotation speed versus time Table I Comparison with a step wind profile

H

∞

CRONE

V

w

(m/s) Over-

shoot Settling time (s) Over-

shoot Settling time (s) 1 5.9 25.08% 19 33.02% 19 2 5.25 20.95% 17 27.45% 17 3 8.5 26.68 % 17 31.54% 14

4 6 21.6% 16 27.5% 16

5 7.2 24.31% 15 29.64% 15 The second test focuses on the robustness of the controllers to the generator parameters’ uncertainty.

The harmonics effects are neglected and the electric parameters vary as follows:

 Case 1: nominal values

 Case 2: M=0.9M

e

, L

d

=0.9L

dnom

, L

q

=0.9L

qnom

, R

s

=1.2R

snom

, R

e

=1.2 R

enom

, ɸ

a

=ɸ

anom

 Case 3: M=0.8M

e

, L

d

=0.7L

dnom

, L

q

=0.7L

qnom

, R

s

=1.5R

snom

, R

e

=1.5R

enom

, ɸ

a

=0.8ɸ

anom

R

s

, R

e

are respectively the stator and the excitation resistances. M is the mutual inductance. In the considered cases, M

e,

L

dnom

, L

qnom

, R

snom

, R

enom

and ɸ

anom

are the nominal parameters and M, L

d

, L

q

, R

s

, R

e

and ɸ

a

are the ones used for the simulations.

Table II Comparison for the robustness tests

H

∞

CRONE

Overshoot

(%) Settling

time (s) Overshoot

(%) Settling time (s)

1 31.16 18.2 37.72 18.8

2 30.82 18.18 37.59 18.9

3 30.45 18.15 37.62 19

During the previous tests, stepped wind profiles

were considered. Such tests are not sufficient to validate the controllers. They do not represent a real wind in a meteorological context. Therefore, the studied architecture is now tested on the advanced model of Fig 8 with a stochastic wind profile (Fig 7).

One can remark that both controllers provide a good reference tracking. In fact, they handle correctly the commutations of the full bridge rectifier and DC/DC converter and are also robust to the generator’s current harmonic perturbations.

Fig 6 : Robustness analysis for a wind varying from 4.5m/s to 8.5m/s (velocity reference : black – case 1:

red – case 2: blue – case 3: green)

Fig 7 : Rotation speed under a realistic wind profile

5. C ONCLUSİON AND P ERSPECTİVES

The present paper presents two robust control

strategies for a HESG in a wind conversion system

connected to an isolated load. The two approaches

are introduced and a comparison between a CRONE

controller and a H

∞

controller is presented. The

comparison examines both performance and

robustness to the inevitable uncertainties of the parameters of the generator as well as to the space harmonics, the electronic commutations and the wind brutal variations. The simulation results show that the H

∞

regulator has better performance regarding the parametric variations which testify its robustness. Regarding the optimal rotation speed tracking, similar performances are obtained.

As the purpose of the present research is to evaluate the contribution of a HESG in wind applications, a WCS emulator with a 3kW HESG generator is under construction. The wind, gearbox and turbine rotor are replaced with a 7kW asynchronous motor connected to the HESG through a torque-meter. For the control and measurements, a Humusoft real-time interface and Matlab-Simulink real-time control software are used. The hybrid generator is connected to a resistive load through a full bridge rectifier and its excitation coils are controlled by a full bridge DC/DC converter. Implementation is ongoing to prove the efficiency of the control strategy.

6. R EFERENCES

[1] Moradi H, Vossoughi G: Robust control of the variable speed wind turbines in the presence of uncertainties: A comparison between H

∞

and PID controllers, Oct 2015, pp 1508-1521.

[2] Boukhezzar B, Lupu L, Siguerdidjane H, Hand M: Multivariable control strategy for variable speed, variable pitch wind turbines.

Renew Energy. July 2007, pp 1273-1287.

[3] Hand M: Variable-speed wind turbine controller systematic designs methodology: a comparison of nonlinear and linear model- based designs. NREL report. USA; July 1999.

[4] Berkoune K, Ben Sedrine E, Vido L, Le Ballois S: Control and operating point optimization of hybrid excitation synchronous generator applied for wind application Electrimacs, Valence, 2014.

[5] Berkoune K, Ben Sedrine E, Vido L, Le Ballois S: Robust Control of Hybrid Excitation Synchronous Generator for Wind Applications, Mathematics and Computers in Simulation Journal, Jan 2017, pp 55-75.

[6] Mseddi A, Le Ballois S, Vido L, Aloui H:

An integrated Matlab-Simulink platform for a wind energy conversion system based on a hybrid excitation synchronous generator, 11

^th

International Conference on Ecological Vehicles and Renewable Energies, Monaco, 2016.

[7] Abdul Jabbar Khan R, Akmal M:

Mathematical Modeling of Current Harmonics Caused by Personal Computers. International Journal of Electrical and Computer Engineering 2008, pp 3-14.

[8] Vido L: Etude d'actionneurs électriques à double excitation destinés au transport : dimensionnement de structures synchrones.

PHD Thesis, ENS Cachan, 2004. France.

[9] Khezami N : Commande multimodèle optimale des éoliennes : application à la participation des éoliennes au réglage de la fréquence. PHD Thesis, Lille, France, Tunis, Tunisia, Oct. 2011.

[10] McFarlane D, Glover K: Robust controller design using normalized coprime factor plant descriptions, lecture notes in control and information sciences. Springer Verlag (1990).

[11] McFarlane D, Glover K: A loop shaping design procedure using H



synthesis. IEEE Transactions on Automatic Control, Jun 1992 pp 759-769.

[12] Sabatier J, Lanusse P, Feytout B, Gracia S:

“CRONE control based anti-icing/deicing system for wind turbine blades”. Control Engineering Practice, Nov 2016, pp 200-209.

[13] Web-site:http://cronetoolbox.ims- bordeaux.fr, Dec 2017.

Fig 8 : WCS under Matlab/Simulink [5]