LOSS MINIMIZATION OF INDUCTION GENERATORS WITH

ADAPTIVE FUZZY CONTROLLER

Durval de Almeida Souza*, José Antonio Dominguez Navarro**

* Federal Center for Technology Education of Bahia – CEFET-BA/ UE de Vitória da Conquista

3150 Zabelê, 45030-220, Vitória da Conquista, Bahia, Brazil

Jesús Sallán Arasanz

** University of Zaragoza, Department of Electrical Engineering, Calle Maria de Luna s/n

50018 Campus del Actur, Zaragoza, Spain

Keywords: Inverter-fed induction generator, loss minimization, vector control, fuzzy controller, adaptive control.

Abstract: In this paper a new technique for efficiency optimization of induction generator working at variable speed

and load is introduced. The technique combines two distinct control methods, namely, on-line search of the

optimal operating point, with a model based efficiency control. For a given operating condition,

characterized by a given turbine speed (ω

) and electric torque (T

), the search control is implemented via

the “Rosenbrock” method, which determines the flux level that results in the maximum output power. Once

the optimal flux level has been found, this information is used to update the rule base of a fuzzy controller,

which plays the role of an implicit mathematical model of the system. Initially, for any load condition the

rule base yields the rated flux value. As the optimum points associated with the different operating

conditions are identified, the rule base is progressively updated, so that the fuzzy controller learns to model

the optimal operating conditions for the entire torque-speed plane. After every rule base update, the

Rosenbrock controller output is reset, but it is kept active to track possible minor deviations of the optimum

point.

1 INTRODUCTION

In the last decade, wind power is integrated into the

electrical grid and accounts for a noticeable share of

the total power generation (

Kumar, 2007). In this

context the inverter-fed induction generator has been

identified as a possible source of energy to be used

in modern micro and high power applications

(

Leidhold, 2002). The presence of a converter in a

drive system enables an extra degree of freedom,

namely, flux adjustment. In fact, efficiency

optimization in adjustable speed drives is usually

obtained by machine flux control. This is due to the

fact that in electric machines, maximum efficiency is

achieved when the copper losses become equal to

the core losses. Typically, under partial load

operation, rated flux condition results in relatively

large core losses, small copper losses, and poor

efficiency. By decreasing the flux, core losses are

reduced, whereas an increase in copper losses takes

place. The total losses, however, are reduced, and

the efficiency is improved (

Sousa, 1995). In this

work, a new efficiency optimization technique is

introduced. It is applicable to any adjustable speed

drive, but it is illustrated here for an induction

generator under field-oriented control. The

technique combines two distinct control strategies,

namely, on-line search and model base control. For a

given operating condition, characterized by a given

turbine speed (ω

) and electric torque (T

), the

search control is implemented via the Rosenbrock

method, which determines the flux level that results

in maximum output power. Once the optimal flux

level has been found, this information is used to

update the rule base of a fuzzy controller, which

plays the role of an implicit mathematical model of

the system. Figure 1 shows the scheme of the

Inverter-Fed Induction Generator used in this

research.

de Almeida Souza D., Antonio Dominguez Navarro J. and Sallán Arasanz J. (2008).

LOSS MINIMIZATION OF INDUCTION GENERATORS WITH ADAPTIVE FUZZY CONTROLLER.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - ICSO, pages 13-19

DOI: 10.5220/0001482500130019

 SciTePress

Figure 1: Inverter-fed induction generator connected to

grid. Figure adapted by (Rüncos).

2 EFFICIENCY OPTIMIZATION

2.1 Search Control

In steady state with constant torque and speed, the

flux component of the chain is decreased whereas

the torque component is increased. Initially a

reduction in total stator current occurs (I

= i

- j i

and consequently a reduction in stator copper losses,

but rotor copper losses are increased. As the

reduction in both stator and iron losses are higher

than the increase in rotor losses, the total losses are

reduced. If i

is continuously reduced, a reduction in

the total losses will occur until the moment when the

increase in copper losses becomes higher that the

reduction in core losses, that is, the point minimum

losses will be exceeded. The determination of this

point, of minimum losses, that corresponds to

optimum efficiency, can be performed using

different procedures. This philosophy is illustrated in

figure 2.

A turbine is submitted to a load proportional to the

square of the angular speed of the wind. Thus, in

weak wind conditions, below 7 m/s, the generator

works typically with light rotor load. In such

conditions the intensity of the rotor flux of the

induction generator (IG), commanded in vector

control for i

, can be reduced to values below

nominal flux, reducing reactive circulation,

diminishing iron losses and consequently increasing

global efficiency of both inverter and machine

(Sousa,1995), something essential at low wind speed

to improve power extraction capacity, (Simões,

1999).

Figure 2: Philosophy for search method of efficiency

optimization.

As mentioned before, rated flux results in excessive

core losses and poor efficiency under light load

conditions. Another aspect worth mentioning is the

need to prevent machine torque disturbances during

the efficiency optimization control. Under vector

control, the developed torque can be expressed as:

qsrte

ikT

(1)

where: λ

is the rotor flux and i

is the torque

component of the stator current, and k

is a constant.

If the flux is reduced to improve efficiency, i

must

be increased accordingly, such that their product

remains constant at any given time.

2.1.1 The Rosenbrock Method

This is a very simple method, and guaranteed to

converge. The reference for the flux component of

the stator current (i

) is modified in small steps in a

given direction, while the system approaches the

optimum efficiency point, i.e., the measured change

in output power in the n-th step is positive (ΔP(n) >

0). When the method recognizes that an “overshoot”

has occurred (ΔP(n) < 0), it reverses the search

direction, with a reduced step size, (J. Moreno-

Eguilaz, 1997,). The search process can be

mathematically expressed as in (2):

0P(n) if ;

0P(n) if ;1

);()()1(

***

⎪

⎩

⎪

⎨

⎧

<Δ−=

>Δ=

Δ+=+

niknini

dsdsds

(2)

where:

P(n) = P(n) – P(n-1)

and

(n) =

*(n) – i

*(n-1) .

Gear

box

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3 THE PROPOSED SYSTEM

The indirect method of vector control is applied to

the IG. It derives the reference for the torque

component of the stator current (i

) from the speed

error, utilizing a conventional proportional-Integral

(PI) controller. As the system operates with variable

flux, a compensation block is introduced at the

output of the speed PI controller. Essentially, this

block multiplies the original PI controller output by

the ratio rated flux / actual flux (estimate).

The reference for the flux component of stator

flux (i

) is not kept constant here, as in the majority

of high performance IM drive systems. It is defined

as the sum of two block outputs: i

(k) = i

’*

(k) +

ΣΔi

*’

. The first term (i

’

) is obtained from a fuzzy

controller, that from two inputs (speed (ω

) and

estimate load torque(T

), derives a preliminary

reference (i

’*

) through fuzzy inference. The second

one (ΣΔi

’

) is the actual output of a search

controller, based on the Rosenbrock method. Its

value represents the accumulated control actions

taken by the controller during the search process up

to the current iteration (n), as can be seen in Fig. 3.

When the system is turned on for the first time,

the rule base of the fuzzy controller contains rated d-

axis current reference (i

’

) for all rules, i.e. for any

speed and load torque point. When a steady state

condition is detected, the search controller becomes

active. After a few steps, it reaches the optimum

efficiency point by imposing the ΣΔi

’

change to

the original reference (i

’

) from the fuzzy

controller. Once the controller recognizes this

optimum condition, the rule base can be updated to

reflect the knowledge of the optimum flux level for

this particular operating point (load torque and

speed). At the same time, the search controller

output must be reset, to prevent erroneous operation.

When the optimum point is found, the rule base is

updated, and the output of the search controller

reset, such that, effectively, i

opt

= i

’*

Figure 3: Hybrid efficiency controller.

As the optimum efficiency points related to the

several operating conditions are identified, the rule

base is progressively updated, such that the fuzzy

controller “learns” the optimum flux level for the

entire torque-speed plane. Once completed the

learning process, the output of the fuzzy controller

already reflects the optimum flux level, and the

fuzzy controller is capable of driving the system at

optimum efficiency without delays. To prevent sub-

optimal operation, the search controller remains

active to track possible deviations of the optimum

point. Under transient conditions, the search process

is cancelled, and the flux reference is solely derived

from the fuzzy controller. It is worth noticing that no

switching of strategies is required, since higher

torques demands are normally met by imposing

higher flux levels, i.e., the optimum level of flux for

higher torques is close to the rated flux value. This

methodology is summarized in Figure 4.

Figure 4: State diagram for efficiency controller.

3.1 The Fuzzy Efficiency Controller

The fuzzy sets for the input variables are shown in

Figure 5. Both utilize normalized universes of

discourses, to make the controller easier to port for

different machine ratings. The output variable (i

’*

)

is represented by singletons, and is not shown here.

The rule base for the fuzzy controller is illustrated in

LOSS MINIMIZATION OF INDUCTION GENERATORS WITH ADAPTIVE FUZZY CONTROLLER

Table 1. It is typically initialized with rated

’

(1 p.u.), and it is progressively updated to

incorporate the knowledge of the maximum

efficiency points as they are found by the search

controller, as previously described.

Table 1: Rule base for the fuzzy controller.

The primary flux reference current i

’*

is obtained

by fuzzy sup-min inference, and the height method

of defuzzification:

(1)

in Ri

∗

∑

(3)

At steady state condition, whenever the search

controller identifies an optimum flux level, the rule

base must be updated. This process can be

summarized as follows:

1) Identify the fired rules in the Rule Base (e.g.,

rules A,B,C,D in Table 1);

2) Compute the degree of truth for each rule, by

applying the minimum (min) operator over the

degree of membership for the input variables T

and

: μ

= min(μ

, μ

ωr

);

3) Evaluate the proportionality factor K, given

by (4);

()

Ri ds

ipu

×Δ

∑∑

∑

(4)

4) Compute the correction term ΔI

(n)=Kxμ

for

each fired rule as the product of its degree of truth

and factor K;

5) Get the new value for each fired rule i

(i=A,B,C,D) by (5).

(1) () ()

iii

In In In

=+Δ

(5)

3 SIMULATION RESULTS

In this simulation a 4 kW squirrel-cage induction

machine was used (220/380V, p=2). A reference

speed step of 0.88 p.u, 0.40 p.u, 0.88 p.u and 0.40

p.u is applied at t=1s, t=30s, t=45s and t=55s,

respectively, as shown in Figure 6 (A). After the

initial transient, at t=6s, the search begins. At t = 15s

the controller identifies that an optimum point has

been found, and proceeds to update the rule base. Up

to this point, the output of the fuzzy controller (i

’*)

was the rated value for magnetizing current, but

from this time on, its output is made equal to the

optimum value. Simultaneously, the output of the

search controller is reset (∑Δi

= 0), as can be seen

in Figure 6 (B). The rotor flux response follows a

first order filter profile of the reference current (i

as expected, and is shown here multiplied by a factor

of 10, Figure 6 (C). The changes in flux level have a

direct impact on the output power, Figure 6 (E), as

well as in the torque component of stator current

reference (i

), as expected, but the electromagnetic

torque is unaffected, due to proper feed-forward

compensation in i

, as shown in Figure 6 (D). At

t=45s and t=55s when a previous reference speed

step is applied, the rule base recognize and the

system operate directly with optimum efficiency.

Figures 6 (F) and (G) shown the voltages and

currents on the phases A, B and C, respectively.

(p.u.)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5

(a)

(b)

(p.u.)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5

Figure 5: Fuzzy sets for the input variables: (a) load

torque and (b) speed.

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0 10 20 30 40 50 60

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60

200

400

600

800

1000

1200

1400

Turbine Speed (r.p.m.)

t (s)

(r.p.m.)

0 10 20 30 40 50 60

-4

-2

t (s)

Current (A)

ΣΔ

0 10 20 30 40 50 60

200

400

600

800

1000

1200

Out P ower (W )

t (s)

(W)

0 10 20 30 40 50 60

-150

-100

-50

100

150

t (s)

Voltage (V)

Va, Vb and Vc (Volts)

0 10 20 30 40 50 60

Flux (Wb) and Flux Component (A)

(A)

(Weber)

t (s)

0 10 20 30 40 50 60

-20

-15

-10

-5

Torque (N.m) and Torque Component (A)

(Nm)

(A)

t (s)

LOSS MINIMIZATION OF INDUCTION GENERATORS WITH ADAPTIVE FUZZY CONTROLLER

Figure 6: Results of simulation for operation of the fuzzy

controller: A) Reference and actual speed on the axis of

turbine in r.p.m.; B) Components of d-axis current; C)

Components of d-axis current and rotor flux; D)

Components of q-axis current and torque estimate; E) Out

power; F) Voltage in the phases A, B and C; F) Current in

the phases A, B and C.

4 CONCLUSIONS

The proposed control strategy consists of a more

effective way to implement the efficiency

optimization via flux control in an induction

machine. From the analysis of literature can be

observed that in the comparative study of the diverse

known search techniques, none of them results on a

process as fast as the one achieved with the present

method. This implies a great energy save, because

the system can be tuned all the time and operate at

maximum efficiency. Another noteworthy point is

that the transition from steady to transitory state

occurs without abrupt changes in the system, or

without any topological control change, since the

displacement from a low torque point to one of

higher torque or vice-versa is already programmed

in the base of rules. The salient features of this

technique are summarized next: i) It is applicable to

any machine size, and does not require knowledge of

machine parameters; ii) The rule base self tuning is

progressive, and does not need any intervention

from the operator; iii) Once tuned, the system is

capable of operating all the time at optimum

efficiency, without delay from one steady state

condition to another, with significant energy saving;

iv) During transients the rule base is kept active and,

as a consequence there is no switching from one

control strategy (for steady state) to another (during

transients), provided that the tuning has been

completed; v) Proper disturbance compensation is

included, such that no correction is needed to keep

torque and speed constant during the optimization

process; and vi) The system is capable of tracking

slow parameter deviations, guaranteeing true

optimum efficiency.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the support of Fha

– Foundation for the Development of New

Technologies of Hydrogen in Aragón; CIRCE –

Centre of Research for Energy Resources and

Consumption; as well as CEFET-BA and University

of Zaragoza.

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t (s)

Current (A)

Ia,Ib and Ic (A)

G )

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LOSS MINIMIZATION OF INDUCTION GENERATORS WITH ADAPTIVE FUZZY CONTROLLER