Direct Fractional-Order Adaptive Control Design for Cascaded Doubly-

Fed Induction Generator (CDFIG) in a Wind Energy System

SIHEM DJEBBRI1, SAMIR LADACI2,*

20 August 1955 University,

Elhadaiek, Skikda 21000,

ALGERIA

Abstract: - This paper is devoted to a fractional-order model reference adaptive control (FO-MRAC) synthesis

for the independent control of the active and reactive power flows in the cascaded doubly fed induction

generator (CDFIG) in wind energy systems. The proposed adaptive control law combines a second-order-like

fractional reference model and a direct MIT adaptation law using a fractional order integrator. This generator

configuration can be an interesting alternative to standard double-output wound rotor induction generators. It is

made up of two identical wound rotor induction motors such that their rotors are mechanically and electrically

coupled. Using two cascaded induction machines permits the elimination of the brushes and copper rings in the

traditional doubly-fed induction generator DFIG, which makes the system more resistant and reduces

maintenance costs. In the first step, we propose a classical PI controller synthesis to regulate the active and

Key-Words: - MRAC, FOMRAC, Direct fractional adaptive control, Cascaded Doubly Fed Induction

For more than three centuries, a great number of

researchers have concentrated on fractional calculus,

[1]. Since its beginning in 1695, fractional calculus

fractional order control and its application in

renewable energy systems and electrical machines

have been the subjects of a sustained research effort

bringing several innovations to increase efficiency

and the effectiveness of these systems, [3], [4], [5],

[6], [7].

Induction Generators using a fractional-order PIλ

controller, [17]. Recently, fractional adaptive

control schemes based on fractional order identified

models have been developed with interesting

results, [18], [19], [20], [21], [22]. Today wind

parks occupy a very considerable place in the field

of the production of electrical energy, [23]. Indeed,

thanks on the one hand to the sensitivity and the

importance of the sector of energy production and

on the other hand to the development and

economic requirements.

with asynchronous machines with double-fed

induction generators (DFIG) functioning at variable

speeds, [27], [28], [29]. Unfortunately, in this

structure of conversion, the presence of the system

ring brushes reduces the reliability of the machine,

[30]. However, with regard to this work, we propose

to study the performance of windmill chains where

parameters is not a simple task and usually needs a

continuous correction. Besides, the parameters

obtained analytically or by simulation usually fail in

disturbances mainly because the stator flux is not

constant [17].

Fig. 1: CDFIG configuration for wind power

generation

and implementation of a FOMRAC controller for

2.1 Electric Equations

First machine:

(7)

(9)

(10)

(11)

(12)

(13)

(15)

The CDFIG is connected to the network via its first

stator while controlling the sizes of the second

stator. We control the active and reactive power

which transit by stator 1, not to overload stator 1 in

the case where the aerodynamic power is higher

Where,

(22)

an efficient approach for automatic controller

adjustment in real-time, aiming to achieve or to

maintain a specified level of performance in

the presence of unknown or slowly varying

parameters.

objective function of the system behavior using the

input, the states, the outputs, and the known

disturbances. The main concept in Model Reference

Adaptive control is to make the closed-loop control

converge to ideal values and thus, the plant output

tracks the desired response.

updating law is based on a fractional order integral

and aims to improve the plant behavior, [39].

The description equation of a fractional order

process may be given in the frequency domain as:

where,

α: fractional exponent.

p: fractional pole which is the cut frequency,

s: Laplace operator.

The literature presents a number of works that

demonstrate the advantage of using fractional-order

systems with their inherent good properties in

dynamics performance and robustness, [40].

real number such that 0<α<1,

which leads to the following blocs scheme of Figure

6.

There are several mathematical definitions for the

integration and the fractional order derivation.

These definitions always do not lead to identical

for the realization of a discrete algorithm, [44].

Let

integral of f, of lower bound c is defined as:

(32)

With

, and

With,

: Sampling Period.

4.1 PI Controllers

The simulation results using the classical PI

controller are given in Figure 8, Figure 9, Figure 10,

Figure 11, Figure 12 and Figure 13.

with PI regulator

Fig. 10: CDFIG active power Ps1, Ps2 for direct

control with PI regulator

Fig. 11: Zoom of CDFIG active power Ps1, Ps2 for

direct control with PI regulator

of the cascaded doubly fed generator whereas

Figure 15 represents its Bode diagram.

Fig. 14: Step response of the open-loop of cascaded

doubly fed induction Generator power system

the integer order MRAC control.

Fig. 16: Active power output control of Power

machine Ps1 with integer order reference model

MRAC

Power Machine Ps1 and Control Machine Ps2 with

integer order reference model MRAC.

Fig. 22: Active power output of Power Machine Ps1

and Control Machine Ps2 with integer order

reference model MRAC

Fig. 23: Reactive power output control of Power