A New Low Cost Cc-Pwm Inverter Based On Fuzzy Logic.pdf

A NEW LOW COST CC-PWM INVERTER BASED ON FUZZY LOGIC

A. Dell'Aquila, M. Liserre, P Zanchetta,

Politecnico di Bari, Italy

ABSTRACT

Nevertheless if few fuzzy rules and simple non-fuzzy

calculations are used, it is possible to realise a high

dynamic current control of a three-phase converter.

In the paper the authors develop a new current control

strategy in order to better exploit the low cost fuzzy

microcontroller resources. The control have been tested

on a CC-PWM inverter feeding a three-phase load:

simulation and experimental results have been reported.

The paper presents a space-vector current control of a

PWM inverter based on a fuzzy logic estimation of the

power devices duty cycles, implemented on a low cost

fuzzy logic dedicated microcontroller. The simulation

analysis carried out in Simulink environment and the

experimental results show the good performances of the

proposed fuzzy logic current control.

SYSTEM ANALYSIS AND CURRENT CONTROL

INTRODUCTION

The voltage equation of a three phase load such as an

induction motor is :

v = Ri + Lpi + eo (1)

Substituting the current deviation vector Ai = i* - i in

eq.(l), neglecting Ri and considering a three phase

voltage source inverter feeding the load we obtain:

In the last twenty years power electronics equipment

had a very wide diffusion in several applications.

Among them current controlled pulse width modulation

(CC-PWM) schemes for d.c.1a.c. power conversion

received much attention and they have been the subject

of many researches above all in the field of variable

speed induction motor drives (see Fig. 1).

The development of relatively low cost CC-PWM

inverters has been possible thanks to the great diffusion

of the new high performances power devices able to

work at very high switching frequency and to the quick

evolution of microcontrollers of the new generation. In

recent years fuzzy dedicated microprocessor have been

proposed too and generally they offer a good solution

for process control. The use of these fuzzy pP in high

dynamic converter control is limited by the too long

computing time, due to the on-line evaluation of fuzzy

rules and to the non-fuzzy mathematical operations.

LpAi = e - v

(2)

where:

e = Lpi* + eo

(3)

and v is the voltage supplied by the VSI to the stator

windings.

The most important term in eq.(2) for the current control

is LpAi, determined by the choice of v = v(k), that

represents one of the possible inverter output voltages.

In order to make Ai smaller, it is necessary to choose

v(k) so that the corresponding @Ai)k has an opposite

component on the Ai direction.

An optimum current control can be realised by means of

an on-line or off-line implementation of the eq.(2) in

each working condition as shown by Kazmierkowski

and Malesani (1). So for each of the possible inverter

output voltages, the corresponding control action can be

evaluated, but it is necessary to estimate eo or at least its

phase, eventually with an iterative process. However the

value of eo could depend on the load parameters. Many

of the current control techniques use this approach for a

correct estimation of the voltage that drives the current

towards its reference. Then a classical space-vector

PWM inverter supplies the desired voltage to the load.

The main drawback of this approach lies in the use of

the current control eq.(2) (with the estimation of eo) that

is computing hard and in the use of the space-vector

PWM that approximates well the voltage only at high

sampling frequencies.

INVERTER

AAA

DRIVING SIGNAL

Figure 1 : Schematic diagram of the current controlled

PWM inverter

Power Electronics and Variable Speed Drives, 18-19 September 2000, Corlference Publication No. 475 0 1EE 2000

466

However high sampling frequencies are often

incompatible with the use of eq.(2) that needs too long

computing time especially in low cost applications, thus

with reduced hardware resources.

The use of a fuzzy approach can solve many of the

problems previously listed, using:

0 a direct choice of the inverter voltage vectors, on the

base only of the phase error sign knowledge;

a fuzzy regulation of the voltages duty cycle.

In the following a simple analysis to obtain an optimum

pattern and the principle of the duty cycle fuzzy

regulation will be shown.

Among the three voltage vectors of each sector one

reduces the error with a high dynamic and the other with

a slow one. In fact L@Ai)klAl grows as Ai approaches to

v(k), hence the vector to which Ai is nearer produces a

higher dynamic because it acts strongly on the error (i.e.

with the major derivative on it).

Let's consider the example in Fig. 3: the current error

vector Ai belongs to ranges A, B and C, hence the three

vectors will be v(2), v(1) and v(6). In the sector

obtained by A, B and C overlapping v(1) reduces the

error quickly.

The previous analysis leads to the optimum pattern

choice shown in Fig. 4.

THE OPTIMUM PATTERN

Big current derivative

Let's consider the eq.(2) neglecting the emf e influence:

LpAi '5 - vQ

(4)

With eq.(4) it is possible to choose an optimum pattern

for the current control. Let's consider for each voltage

vector v(k) a range of 180" centred on it. If the current

error Ai is detected in this range, the corresponding

voltage will reduce the error because LpAi component

on it (L@Ai)llAJ has an opposite versus, as shown in

Fig. 2.

3- I

,6;4.

....................................

p------.

.....................

I ........

Figure 4 : Three switching patterns for each phase

angle sector and their effects

The emf e neglected in eq.(4) produces a change in

LpAi magnitude and phase. This results in a sectors

modification that can produce some troubles in the

control only if the error is in the transition area between

two of the six sectors. However two neighbouring

sectors have two of the three reducing error vectors in

common. So only one vector can produce a light

increase of the error. On the contrary when the error is

detected far from the sector boundary the emf e can only

change how (strongly or lightly) each of the three

voltage vectors acts on the error.

Figure 2 : 180' range around the voltage vector v(1) and

its influence on the current error in the range

For each of the six non-zero voltage vectors, a 180'

range can be considered. Then six sectors come out,

each of them from three 180" ranges overlapping as can

be seen in Fig. 3.

____-------_____

_---

,,--

THE OPTIMUM PATTERN CHOICE

On the basis of the previous analysis it is possible to

choose the optimum pattern for each position of the

current error vector using only the phase current error

sign knowledge.

Let's consider the current space-vectors:

i* = - (i; + ai; + a2il)

i=-(i,

+ai, +a2i,)

-._

---________----

(6)

Figure 3 : Current error sectors and the

corresponding voltage vectors

i, + aAi, + a2Ai,)

Ai=-(A

(7)

461

In the following we use a for Aia,b for Aib and c for Ai,.

Considering a = - 1/2 + j&/2 , a' = - 1/2 - j&/2

and

a+b+c=O:

Ai=a+j-(2b+a)

(8)

So Ai is in the sector of v(1) or v(4) if a is positive or

respectively negative (Fig. 5):

--.

f----

Figure 6 : Optimum pattern choice algorithm

THE PATTERN ARRANGEMENT

The choice of the switching sequence comes from the

results of the analysis developed in the previous

sections. We can summarise:

Figure 5 : Current error on phase a positive implies that

Ai is in the v(1) sector

for each current error phase sector three non-zero

patterns reduce differently the error (one quickly

and two slowly);

the zero voltage vectors play an intermediate role.

In fact the v(1) sector is between -90" and 90"and the

v(4) sector is supplementary . For the couple v(5) v(2)

the analysis is a bit more complex, because the sector is

between -30" and 150" but we can shift the current error

vector with a 60" delay and consider the sector between

-90" and 90" as for v(1). The eq.(8) becomes:

Then all the three non-zero pattems for each sampling

period are applied:

0 to have two types of reduction action for each

sampling period;

0 to be sure of a good current reduction even when

the emf e influence changes the error reduction

action produced by each vector.

The sampling period is divided in five parts: three for

the non-zero voltage vectors (one will produce a quick

reduction of the error and the other two a slow one) and

two for the zero voltage vectors as shown in Fig. 7. The

two zero-vectors are applied at the beginning and at the

end of the sampling period as for the traditional space-

vector technique. In fact Holtz (2) has noted that the

vector trajectory of the harmonic current content passes

through zero while the zero vector is on.

The time of application of the three non-zero vectors

may be decided with fuzzy logic.

- 1

-e-J6''=(a+b)+j-(b-a)

(9)

So Ai is in the sector of v(5) or v(2) if a+b is positive or

respectively negative. Also for the couple v(3) v(6) we

can consider a phase shift of 120° and obtain:

= (- b)+ jz(b + 2a)

(10)

So Ai is in the sector of v(3) or v(6) if b is negative or

respectively positive.

These results can be obtained also considering Ai on

L@Ai)k direction (equal to v(k) direction, see eq.(4))

and not the vector L@Ai)k on the Ai direction. Hence the

current error sign on phase a will decide between v(1)

and v(4), the current error sign on phase b will decide

between v(3) and v(6) and the current error sign on

phase c will decide between v(5) and v(2).

The result of this analysis in the pattern choice can be

summarised in Table 1 and the consequent algorithm in

Fig. 6 with each pattern arranged to minimise the

commutations.

zero

quick

slow

zero

voltage

voltage voltage

voltage

vector

Figure 7 : The switching sequence

TABLE 1 - Pattern choice based

on current error sign

THE FUZZY LOGIC CONTROL

The fuzzy control chooses each state weight in the

sampling period division. It carries out two strategies

(high dynamic action or slow one) for each sampling

b 2 (<) 0

a+b 1 (<) 0

v(3) (~(6))

v(2) (~(5))

468

’

how long each of them will be applied.

ontrol action is based on the evaluation

of the current error, i.e. on these two control regulation

principles:

if the magnitude of the error is big, the high

dynamic action sampling period portion will be big

and the slow dynamic action one will be little;

if the magnitude of the error is little, the high

dynamic action sample period portion will be little

and the slow dynamic action current action one will

be’big.

In fact if the error is too big, it is necessary a strong

action to reduce it quickly; on the contrary if it is little, a

short application time of the strong action is sufficient,

as shown by Dell’Aquila et a1 (3). Vice versa it is

possible to apply the slow action for a long time only if

the error is not big. In fact a too long application of a

slow action, can cause loss of control.

The control chooses at first the switching sequence, then

optimises the state arrangement in the sampling period

to minimise the commutation number.

Each phase current error is normalised to the range [-1

11 then it’s enough to define one triangular membership

function ZE as shown in Fig. 8. For the output duty

cycle [0 11 two singletons have been defined: one S

(chosen if the current error is zero) corresponds to the

5% of the sampling time (15% of one third of the

sampling time) and the other one L (chosen if the

current error is not zero) to the 29% (87% of one third

of the sampling time) as shown in Fig. 9.

TEST SETUP

As a demonstration of the effectiveness of the proposed

fuzzy control, we have tested it on an inverter feeding a

three phase load.

A hardware circuit for the voltage-source PWM

converter has been constructed and tested in our

laboratory using the ST52x301 microcontroller. A

suitable mother board for the microcontroller has been

built (Fig. 10) together with different acquisition and

conditioning modules for all the signals. The software

has been developed with FUZZYSTUDIO@as shown in

Fig. 11. We have used only 6 rules and few simple

mathematical functions to optimise the microcontroller

time of calculation.

For the sake of a coherent comparison with the

experimental results, all the simulations (Matlab-

Simulink-Fuzzy environment) reported in this paper are

carried out considering the delay produced by the AID

converter of the ST52x301 microcontroller and its

calculation times (Fig. 12).

:,.

Figure 8 : Current error (normalised) membership

functions [-1 13

Figure 10 : ST52x301 mother board

1j3

Figure 9 : Output duty cycle singletons [0 11

Once decided the optimum pattern (see the algorithm in

Fig. 6) the choice of each state duty cycle is based on

the following fuzzy rules for the phase a current error:

1. if (a is ZE) then (1 -4 duty cycle is S)

2. if (a is not ZE) then (1-4 duty cycle is L)

Similar rules can be written for the other phases.

So the inferential process decides which voltage vector

is the quick one and how long it must be applied. In fact

the bigger is the error Aia (a) the nearer is the vector Ai

to the vector v(1) and so this vector produces the quick

action and it will be applied for the longer time that can

be maximum the 87% of one third of the sampling time.

Figure 11 : FUZZYSTUDIO@main program

469

I-

range [OV 2.W]

8 bit

+-q&@+u

input

conversion

coneFion

output

delay

gain

.............. ”

: ......................................................................................................... - I

~~52w301

.........................................

....................................

” ........

.....................

i’v

FUZZY INPUTS

R*U)AD

&CONmTER+

DETERMINATION

S+GATEPmE

-i-*

STATE

GENERATION?

............................................................................................................

b SEQUENCE

;

FEEDBACK

CURRENTS

+b+

..............................................................................................................................................................

REFERENCES

RESULTS

Kazmierkowski M. P., Malesani L., 1998, IEEE

In Fig. 13 the 25 Hz experimental reference and

feedback currents (obtained at 5 kHz sampling

frequency with a 40 V d.c. voltage) are reported.

Simulation results have been obtained with a 40 V

feeding voltage and reference currents in the range [0.1

13 A and with a 5 kHz sampling frequency. A good

current control has been obtained even in the worst case

(reference current 0.1 A) as Figs. 14, 15 and 16 show.

Then the fuzzy control has been compared with two

traditional ones (all simulated considering a digital

implementation on ST52x301 and with 1 A reference

current) and the results are always the better in terms of

current THD (Fig. 17) while the switching frequency

has a medium value (Fig. 18).

Vol. 45,691-703.

J. Holtz, “Pulsewidth Modulation for Electronic

Power Conversion”,

1994, Proceews of the

m,w.

Dell’Aquila A., Liserre M., Zanchetta P., “A Fuzzy

Logic Calculation of the Duty Cycle for the Space-

Vector Current Controlled PWM” 1999, =.

Cecati C., Corradi S., Rotondale N., “A Fuzzy

Logic-based Adaptative PWM Technique”, 1997

ECON, 1142-1147.

Dell’Aquila A., Liserre M., Zanchetta P., Cecati C.,

Rotondale N., “An Overview on Nonoptimal,

Optimal,

CONCLUSIONS

Preoptimized

and

Fuzzy

Current

Controlled PWM techniques”, 1999, m, 1322-

1327.

A novel fuzzy logic space-vector current control has

been developed to regulate a voltage source inverter.

This new strategy allows us to obtain an appropriate

current control action.

The proposed fuzzy control results very flexible because

it can be easily adapted to the requirements of the

different applications simply changing via software the

fuzzy rules.

Finally it is important to note that this new control is

completely independent on the load parameters: it needs

only the knowledge of the values of current error

magnitude and phase. Moreover the control is very

simple so it needs reduced hardware and software

resources; in fact it has been implemented on a low cost

fuzzy dedicated microcontroller. Nevertheless its

simplicity the control gives good performances on the

tested system.

Figure 13 : Experimental currents (reference and

feedback) at 5 kHz sampling frequency with 40 V d.c.

voltage

470

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: