A fuzzy logic CC PWM three phase AC DC converter

The proposed control system satisfies sinusoidal input currents, unity power factor and constant output voltage by means of an optimised management of the energy exchanged between the

A Fuzzy Logic CC-PWM Three-phase A C D C Converter

A Dell'Aquila, M Liserre

Dipartimento di Elettrotecnica ed Elettronica

Politecnico di Bari Bari, Italy

Abstract - The paper deals with a PWM A O C converter based

on the fuzzy control of the output capacitor chargeldischarge

process The proposed control system satisfies sinusoidal input

currents, unity power factor and constant output voltage by

means of an optimised management of the energy exchanged

between the AC supply and the output capacitor The

simulations show a very good dynamic behaviour of the system

at both start-up and load current step variations

I INTRODUCTION Three-phase, PWM controlled rectifiers are gaining more

and more attention in those applications where performance,

energy consumption and components optimisation are

important issues [ 11

components size reductions (mainly capacitor and

reactors) ;

constant voltage operations at variable load current;

sinusoidal currents and unity power factor on the AC side

Standard ACDC converter controllers cannot usually

achieve the simultaneous optimisation of both line currents

and capacitor charge-discharge process

Recent works focus their analysis to some aspects such as

capacitor size reduction [ 11, stability analysis [2], energy con-

sumption reduction and so forth Many approaches including

Lyapunov-based [2], sliding-mode [3] and others including an

interesting feed forward current control [4], have been

proposed in literature but fuzzy logic control has not yet been

fully investigated In fact, it has been used only for PID

regulator fuzzyfication and/or for the reduction of the

computational complexity [ 5 ] without degrading system

performance

This paper proposes a "true" fuzzy logic controller that

allows simultaneous control of the voltage and of the power

factor during load current variations

The simulation results show that the capacitor

charge/discharge processes are well managed even at start-up

which is one of the worst operating conditions for such a

system

A good design should allow:

11 SYSTEM ANALYSIS The mathematical model of the system shown in Fig.1 is

based on the following assumptions:

the converter switches are considered ideal;

C Cecati, A Ometto

Dipartimento di Ingegneria Elettrica Universid degli Studi di LAquila LOC Monteluco di Roio, LAquila, Italy

the load is modeled as an ideal current source;

the supply voltages are sinusoidal:

2K

3

eb ( t ) = E COS(W~ - -)

4K

e , ( ? ) = Ecos(ot )

Assuming ideal switches, the converter can be modelled by

three switching functions p, each one associated with the

switch S, (j = a, b, c) The switching functions are defined as:

p,=+l when the switch SI imposes v,'l=vh;

p,=-l when the switch S, imposes vI=vI

Then the input phase voltages v,, V b n , v , and the output

current i, can be written as function of S, and of v, and input currents i,, ib, i, (irr+ib+ic=O)

n

Fig 1 Three-phase PWM AClDC rectifier

By introducing:

L

%

L

_

L

-

L

-

111 VOLTAGE AND POWER FACTOR CONTROL The PWM technique has been introduced in rectifiers control in order to obtain almost sinusoidal input currents and unity power factor in each physically possible working condition i.e for each value of the chosen output voltage that

is compatible with the value of the supply voltage

If these requirements are actually fulfilled the PWM

rectifier can be modelled as a black box with imposed

sinusoidal input currents and constant output voltage

Let's consider the AC side inductive elements (i.e the transformer inductance or other inductance included to make the system working properly) and the DC side capacitive element With these conservative elements connected to the ideal PWM rectifier, the system can be studied as a parallel between a current and a voltage source connected by means

of the black box that controls the energy flow (Fig 2)

In effect, the voltage control loop will be designed under

energy considerations [ 6 ] but a fuzzy controller will be used

to take into account the actual evolution of the electric quantities

Neglecting the converter losses, the rms value of the input cuprent can be computed by means of the power balance:

ideal

== v o

rectifier

are the vectors of the rectifier input voltages and currents, and

P(t) = [Pa 0) P b W P c cor

is the vector of the switching functions

following relation is obtained for the AC side:

On the other hand, from the Kirchooff voltage law, the

di ( t )

dt

vs(t) = e ( t ) - L i - R i , ( t )

where R and L are the values of the phase resistance and

inductance and e(t) = [ e , ( t ) e b ( t ) e c ( t ) r is the supply

voltages vector

Then, from the Kirchooff current law, the following

relation is obtained for the DC side:

By substituting ( 6 ) in (4) and (7) in (5) leads to:

(7)

(8)

- = is( t )+-e( t )- k , p( t ) v,,( t )

1

d v ( t ) 0 - 1 - - l o ( f ) - - l L ( f )

Obviously the quantities that have to be controlled: i,(f) and

v,(t) are not independent and that makes their control a hard

task In fact, the same control variable p(t) is responsible of

two regulation actions: the first one on the input currents and

the other one on the load voltage

That can be seen if equations (8) and (9) are written as:

where the control variable p(t) is pointed out as system input

where P, is the converter output power:

From equation (1 1) the input current is:

if the following relation is satisfied:

3E2

Po 5-

4R

At steady state operating conditions the capacitor current is zero thus the converter output power is:

988

and the maximum load current that can be delivered is

obtained [2]:

c

Va

P W M ACDC CAPACITOR

_c c LOAD

3 E 2

IL" = -

4RVo

mathematical

reference CONTROL +

Unfortunately, the three-phase converter must be able to

impose the energy exchange and to fulfil the constraints on

the input currents and output voltage even in transient

conditions

In such a system both load current and output voltage

reference changes cause transient-operating conditions More

in detail, positive or negative variations of the voltage

reference result in charge or discharge processes of the output

capacitor Increases of the load current result in voltage

undershoot while its decreases result in voltage overshoot So,

from the point of view of the output voltage control, load

current changes result in voltage variations that must be

compensated by charge or discharge processes

During these operations the main goal is to obtain a fast

dynamic response without involving high current overshoot

In fact, the current and voltage ratings of power devices for

PWM converter are mainly chosen considering efficiency and

safety operations So, it is important to fully utilise the device

capability to avoid under utilisation that results in a non cost-

effective converter On the other hand, the switch current

cannot exceed the maximum current rating of the device

because it can result in severe faults

If the output voltage is different from its reference value

Vorer, the amount of energy that the capacitor must receive to

come back at the set point is:

The power corresponding to this energy is:

where kT, , expressed as function of the supply period T O , is

the time in which the voltage has to reach the reference value

Therefore the converter output power must be:

and the rms value of the current is:

2 R

So, the current reference depends on both load power and

output voltage error as shown in Fig 3

This current value is used as reference for a current

controller such as a hysteresis controller that offers good

dynamic performance suitable for the high dynamic control of

the DC voltage [7] The scheme of the control and of the

system under investigation is reported in Fig 4

The charge/discharge process can be chosen either quick or slow depending on the power term A& that is affected by the factor k Actually, such a factor allows the

charge/discharge speed to be controlled

A fast dynamic can be generally obtained choosing kS1 in order to deliver the energy needed to the capacitor charge/discharge process as quick as possible

This control technique works quite well if the input currents are actually sinusoidal and the power factor is close

to unity, i.e the input current tracks the reference one In effect, the controller can loose the control of the input currents during transient-operating conditions It happens when the needed voltage across the inductance (di/dt )

cannot be imposed due to the finite gain of the physical system or to the too small value of the output voltage

In such a case there is a current overshoot that can be caused by integrator wind up phenomenon if a standard PI regulator is used as controller The overshoot can last for quite a long time because the delivered power depends on the

steady state energy

balance

Rg 3 Current reference calculation (rms value)

I feedback currents

generation

output voltage and load current

Fig 4 Schematic diagram of proposed CC-PWM

AC/DC

actual power factor PF and can be much smaller than the

theoretical one, computed for P F = 1 This behaviour can be

recognised in Fig 5 that shows the system evolution at start-

up, with such a controller

A conditional integrator, a limited integrator and a tracking

anti wind up controller, are commonly used among other

solutions However none has faced this problem investigating

the actual cause of the overshoot: the design of the control

loop that imposes the required output voltage is carried out

assuming ideal AC side operating conditions, i.e sinusoidal

currents and unity power factor On the other hand the design

of the control loop that imposes the required input currents is

carried out assuming constant load voltage

Iv THE PROPOSED FUZZY LOGIC CONTROLLER

In order to overcome the previous drawbacks, a control

technique based on the fuzzy logic is proposed Such a

controller is able to manage the energy exchange by taking

into account the actual evolution of the electric quantities and

to impose sinusoidal input currents, unity power factor and

constant output voltage

The voltage control is based on the analysis of the previous

section In particular, the current reference is computed by

considering both load and chargeldischarge processes power

Then the equations (15), (17), (18) and (20) are used in the

control scheme (Fig 6)

It has been recognised that the main problem of the system

occurs when the actual currents cannot track the reference

values Most of the times this situation can be avoided by

slowing down the chargeldischarge process of the output

capacitor when the current error is large Increasing the factor

k in order to impose a long time to recovery the energy AWc

can do it In other words, it is useless to impose current

references that cannot be tracked since the chargeldischarge

process would be slow anyway due to the small power factor

A faster chargeldischarge process can be achieved with lower

currents and unity power factor

Unfortunately, a large value of k affects the system

dynamic even when the currents track the reference values

and the current error is very small In this case, it is possible

to speed up the charge process as the power factor is close to

unity and the computed current reference is correct Therefore

the factor k can be small in order to achieve a fast dynamic

behaviour

A good control of the system can be only obtained by

adapting the factor k on line A fuzzy logic controller has

been used for the regulation of the chargeldischarge speed by

taking into account both input current and output voltage

errors (Fig 6)

The fuzzy controller consists of a first section that

generates the inputs and a fuzzy core that performs

fuzzyfication, inference and defuzzyfication More in detail,

the fuzzy output represents the time assigned to the

chargeldischarge process normalised to the supply voltage

period

time (s)

0

time (s)

1

I

8 0.5

E

g o

EL

-0.5

time (s)

0

fig 5 Voltage, currents and power factor at start up

CONTROL

I

-)

I

E q S W

Fig 6 The control block diagram of the voltage loop

The fuzzy labels chosen to define the current and the

voltage errors are zero (Z), small (S), medium (M), large (L) and extra large (EL) The output variable expresses how quick the capacitor energy control must be so it is appropriate to choose fuzzy labels as quick (Q), medium (M) and slow (S) with intermediate value as (QM) between quick and medium

and (MS) between medium and slow

990

The membership functions for input and output variables are reported in Fig 7, Fig 8 and Fig 9 The amplitude of the current space vector error normalised to a value depending on the rectifier rated power is considered as current error The voltage error is normalised to the reference voltage

The output is given by an inferential process in which fuzzy conditional statements relate the input variables in the antecedents and output process control variables in the consequent So the fuzzy rules that realise the explained control are schematically reported in Table I

0 l

Fig 7 dc voltage error membership functions [0 11

The control factor k is updated every quarter of the line voltage period Fig 10 shows the output voltage error, the absorbed ac currents and the power factor during the start-up with fuzzy compensation In contrast with Fig 5, obtained without fuzzy logic control, here the reference currents are

well smoothed and both current tracking and P F z I are

satisfied around the end of the second period

Fig 11 shows the system behaviour for a stepwise variation

of the load current (0 up to 2.5 A): these curves highlight that

the output voltage variation is very limited (5 2%) and both a

fast recovery of the rated DC voltage and the accurate input currents tracking are obtained

Finally the control has been tested for a reference voltage

step change with 2 A load current as reported in Fig 12: Fig

13 shows both input currents and voltages, while Fig 14

shows the power factor These results confirm the satisfactory behaviour of the proposed PWM rectifier, too

0 '

; 0 0.2 0.4 0.6 1

Fig 8 Current error membership functions [0 11

Fig 9 Quickness of the chargeldischarge process membership functions [l 121

TABLE I

FUZZY RULES FOR THE CHARGUDISCHARGE PROCESS CONTROL

U

Voltage error

The proposed PWM fuzzy controlled rectifier has been verified by means of simulations All presented results have been obtained using the following values: J! = 3 0 V , U = 100 rads, L = 15.5 mH, R = O S R, C=3000 pF The reference DC

voltage is 100 V and the fuzzy logic controller samples the

time (s)

eference current

s

B

2

- -10

c)

E o ."

time (s)

Fig 10 Voltage, currents and power factor at start up

obtained with the fuzzy control of the charge process

(C=3000uF R=0.5R Ir15.15mH)

-capacitor charge with frequencyf,= 1 kHz

- 100’

L

~

i

time (s)

time (s)

Fig I 1 Voltage and line currents for a step change of the current

drained by the load, obtained with the fuzzy control

of the charge process (C=3000pF R=0.5R d-15.15mH)

0

U

60

0 0.1 0.2 0.3 0.4 0.5

time (s) Fig 12 dc voltage for a step change in the

reference voltage(C=3000pF R d S R k15.15mH)

40

I

-40 I

time(s)

Fig 13 Line voltage and line current for 2 A load current and

80 V reference voltage (C=3000pF R=0.5R k15.15mH)

’

time (s) Fig 14 Power factor for 2 A load current and

80 V reference voltage (C=3000pF R=OSR d-15 15mH)

This paper addresses the problem of the optimization of the capacitor charge/discharge process in a PWM AC/DC converter, aiming to obtain the simultaneous control of the output voltage and of the power factor, even during various kind of perturbations For such a goal, a fuzzy logic controller has been designed The proposed system changes the capacitor charge/discharge speed on the basis of the voltage and current errors

The controller is very simple and its practical implementation is inexpensive since it does not require additional hardware with respect to a common PWM rectifier

The reported simulation results highlight satisfactory behaviour of the system in all tested operating conditions

Work is in progress in order to experimentally verify the

obtained results on an actual system

VII REFERENCES

L Malesani, L Rossetto, P Tenti and P Tomasin: “ACIDCIAC PWM Converter with Reduced Energy Storage in the DC Link”, IEEE Trans

on Ind Applications, vol 31, NO 2, MarcWApril 1995 pp 287-292

H Komurcugil, 0 Kukrer: “Lyapunov-based control for Three-phase

PWM ACDC Voltage-Source Converters”, IEEE Trans on Power

Electronics, vol 13 No 5 , September 1998 pp 801-813

J F Silva: “Sliding-Mode control of Boost-Type Unity-Power-Factor PWM Rectifiers”, IEEE Trans on Ind Electronics, vol 46, No 3, June

H Komurcugil, 0 Kukrer: “A Novel Current-Control Method for Three-phase PWM ACDC Voltage-Source Converters”, IEEE Trans

on Ind Electronics, vol 46, No 3, June 1999 pp 544-553

S Saetieo, D A Torrey, “Fuzzy Logic Control of a Space-Vector PWM Current Regulator for Three-phase Power Converters”, IEEE Trans on Power Electronics, vol 13, NO 3, May 1998 pp419-426

M.-T Tsai, W I Tsai: “Analysis and design of Three-phase AC-to-DC Converters With High Power Factor and Near-Optimum Feedforward”, IEEE Trans on Ind Electronics, vol 46, No 3, June 1999, pp, 535-543

A Dell’Aquila, M Liserre, P Zanchetta, C Cecati, N Rotondale “An Overview on Nonoptimal, Optimal, Preoptimized and Fuzzy Current Controlled PWM techniques”, in Proc ISIE’99, Bled

1999, pp 594-603 ,

992