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Modeling and control design of a stand alone wind energy conversion system based on functional model predictive control

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Abstract

This paper investigates the application of the model predictive control (MPC) approach to control the voltage and frequency of a stand alone wind generation system. This scheme consists of a wind turbine which drives an induction generator feeding an isolated load. A static VAR compensator is connected at the induction generator terminals to regulate the load voltage. The rotor speed, and thereby the load frequency are controlled via adjusting the mechanical power input using the blade pitch-angle. The MPC is used to calculate the optimal control actions including system constraints. To alleviate computational effort and to reduce numerical problems, particularly in large prediction horizon, an exponentially weighted functional model predictive control (FMPC) is employed.

Digital simulations have been carried out in order to validate the effectiveness of the proposed scheme. The proposed controller has been tested through step changes in the wind speed and the load impedance. Simulation results show that adequate performance of the proposed wind energy scheme has been achieved. Moreover, this scheme is robust against the parameters variation and eliminates the influence of modeling and measurement errors.

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Abbreviations

v ds ,v qs :

d-q stator voltages

i ds ,i qs :

d-q stator currents

i dr ,i qr :

d-q rotor currents

R s ,R r :

stator and rotor resistances per phase

L s ,L r ,L m :

stator, rotor and magnetizing inductances

C o :

self excitation capacitance per phase

ω s :

angular stator frequency of the induction generator

ω m :

angular rotor speed (electrical rads/s) of the induction generator

ω t :

angular rotor speed of the turbine

J :

moment of inertia

f :

friction coefficient

p :

differential operator d/dt

L o :

physical inductance of the reactor in the SVAR

α tcr :

firing angle of the SVAR

β :

turbine blade pitch angle

i dL ,i qL :

d-q load current

\(i_{dL_{o}},i_{qL_{o}}\) :

d-q reactor current in the SVAR

λ :

turbine tip speed ratio

P :

number of pole pairs

C p :

turbine power coefficient

L eq :

equivalent inductance of the reactor of the FCTCR

v ref :

reference voltage

P ref :

reference power

v t :

generator’s terminal voltage

R L :

load resistance

L L :

load inductance

N p :

prediction horizon

N c :

control horizon

VAR:

voltage automatic regulator

MPC:

model predictive control

SEIG:

self excited induction generator

GPC:

generalized predictive control

RHC:

receding horizon control

WT:

wind turbine

IG:

induction generator

GB:

gear box

FMPC:

functional model predictive control

FCTCR:

fixed-capacitor thyristor-controlled reactor

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Authors and Affiliations

  1. Electrical. Dep., Beni-Suef University, Beni Suef, Egypt

    Ahmed M. Kassem

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  1. Ahmed M. Kassem
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Correspondence to Ahmed M. Kassem.

Appendices

Appendix A: System parameters

Wind turbine:

Rating::

1 kw, 450 rpm (low speed side) at V w =12 m/s.

Size::

height = 4 m, equator radius = 1 m, swept area = 4 m2, ρ=1.25 kg/m2.

Induction machine:

Rating::

3-phase, 2 kw, 120 V, 10 A, 4-pole, 1740 rpm.

Parameters::

R s =0.62 Ω, R r =0.566 Ω, L s =L r =0.058174 H, L m =0.054 H, J=0.0622 kg m2, f=0.00366 Nm/rad/s.

FC-TCR::

C o =176 μF, L o =0.127 H.

Appendix B: Operating point values [29]

I qs :

7.35 A

I ds :

0.81 A

I qr :

−0.06 A

I dr :

−1.12 A

ω mo :

291 rad/sec

V ds :

118 V

I qL :

1.106 A

I dL :

0.41 A

\(I_{qL_{o}}\) :

0.57 A

\(I_{dL_{o}}\) :

0.23 A

α tcro :

146 deg

β o :

10.6 deg

Appendix C: Linearization matrix parameters

The elements a ij of the 12×12 matrix A are:

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Kassem, A.M. Modeling and control design of a stand alone wind energy conversion system based on functional model predictive control. Energy Syst 3, 303–323 (2012). https://doi.org/10.1007/s12667-012-0051-3

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  • DOI: https://doi.org/10.1007/s12667-012-0051-3

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