CC BY
41Electronic Journal «Technical Acoustics» http://webcenter.ru/~eeaa/ejta/
2004, 8 H. Bounoua, A. Bounoua
School of electrical engineering, University of Sidi Bel Abbes,
22000, Sidi Bel Abbes, Algeria, e-mail: [email protected]
The utilization of the PWM inverter feeding in the asynchronous motor command
Received26.01.2004, published 04.07.2004
In this paper, the acquisition of new control tools and the improvement of the PWM inverter feeding in the asynchronous motor command are considered. In the asynchronous machine, the directions flow and the electromagnetic torque are closely tied. The scalar command law allows to maintaining the flow and consequently the electromagnetic torque constant for high frequencies. However, this law is very insufficient at low frequencies, what leads us to proceed with the field-oriented asynchronous pulse-width modulation, for high-performance asynchronous machine drives operating at low frequency. The performances of this command are evaluated by using results of simulation realized by the MATLAB software under the SIMULINK environment. The obtained simulation results prove the efficiency of the PWM signal in the command and give excellent electrical magnitude performances of the system. With this easy model, the simulated system, constituted by the asynchronous machine and the two levels voltage inverter, is achieved in a very short time interval and the obtained results are interesting.
INTRODUCTION
Up to date, the numerical command of asynchronous machines remains of interest as shown in the most recent research works [1, 2]. In our paper, the acquisition of new control tools and the improvement of command are considered. During a varying speed drive (asynchronous machine - voltage inverter), the ideal command is to be able to find an adjustment characteristic of the electromagnetic torque identical to that the continuous current machine.
In this paper, we study the control of the electromagnetic torque while maintaining a constant flow [3]. Before any synthesis of numerical command laws, it is necessary to analyze the process to control, to establish an adapted modeling and to interpret its dynamics. The choice of the simulation program and the equations simplifications lead us to establish an information graph for the command. It indicates clearly the blocks articulation and the command meaning [4].
In an asynchronous machine, the directions flow and the electromagnetic torque are closely tied. It is necessary to be able to untie them in order to suitable choose the regulators parameters. On the other hand, the scalar command law V /F = constant only allows to maintain the flow constant and consequently the electromagnetic torque constant for high frequencies. However, this law is very insufficient at low frequencies, what leads us to
proceed with the vector command with the orientation of the flow. This allows to improve the performances of the system asynchronous machine-voltage inverter, either in the course the transient regime or in the course of the permanent regime despite the disturbances that are able to intervene while the system operates. As area of applications of the association "asynchronous machine-inverter" and for small powers less then 10 kW, one uses them in the electro-spits, centrifuge. As for average and high powers greater than 1 MW, they are used in pumps, ventilators, compressors, mixers, machines-tools [5].
1. PRINCIPLE
Electrical machines feed by static converters are used as rotary actuators in a many industrial equipments of varying speed. The actuator characteristics depend at the same time on the machine, its feeding and the command of the whole system [6]. These characteristics are:
• A torque with the minimum possible undulation;
• Controlled by the smallest variables number;
• A large range of varying speed;
• Small electrical and mechanical time constants.
The dynamic control of the asynchronous motor is a more delicate but recent works [2, 3] on the vector control have already shown its feasibility. Beside the used technology, one is always interested in the ratio quality/price, thus one tries realize the high performances of the most economical product. Because of the PWM structure of the variator, it presents a major disadvantage in the noise level that is very high. As its structure of command is entirely numerical, the PWM modulator of the variator is directly linked to the variator. The success of the variator speed has a good optimization of the PWM system. For that, it is necessary [2, 7, 8]:
• To make the good choice of the commutation elements;
• To have a good numerical structuring of its command allowing an adaptability of the MATLAB software under the SIMULINK environment.
2. BLOCK DECOMPOSITION OF THE SYSTEM
The principle is based on the decomposition of the system to study in blocks and in under blocks and to establish relationships between them [1, 3]. Then, the following formulae have been established, describing the operation of the system under study (see Fig. 1).
2.1. Asynchronous machine subsystem
The system to study is a not linear system [8]. Our objective is to render it a linear model for the purpose of facilitating the command techniques utilization. Because of the complexity of the asynchronous machine model, it is desirable to apply the PARK transformation so as to undertake a change of three phased axis (a, b, c) in a two phased referential (d, q) (see Fig. 2).
Figure 1. Command of the associated PWM inverter-asynchronous machine
system voltage feed
&-
Clock
To Workspaces
Figure 2. Asynchronous machine subsystem
The state vector is:
[lsd; Isq; O rd; O rq; ®m] T.
We write Ird, I , Osd, Osq with the state variables chosen. Settlement form of the
machine state equations:
r rd M
Ird = X ~ T!
O
Iq = rq
rq
L,,
MI
L sq
(1)
(2)
O d = IsdLsa +
O
rd 5
O = I L a +------------O ,
sq sq s l rq?
(3)
(4)
where Ord, Orq are the components torque of the rotor respectively to axis d and q; Isd, Isq,
Ird, Ird are the components current of the stator and the rotor respectively of axis (d, q); a is the dispersion coefficient:
a = 1 - M V L,Lr.
The mathematical model is:
dIsd _ 1
f f
dt aL„
dIsq _ 1
M
A
V V
LrTr j
MM
Isd +a(0sLsLsq + O rd + L am O rd + Vsd
LrTr Lr j
f
dt aL„
V v
dO rd MId O r
M2 ^
LrTr j
T T T M , M , T- ^
Isq ~a(°SLsLsd + LT O rq-------------L~&m O rd + Vsq
LrTr Lr j
sd rd
dt Tr Tr
dO q MIq O „
sq rq
dt T T
+ (,-®m )O
rd
(5)
(6)
(7)
(8) (9)
where Vrd , Vrq are the components voltage of the rotor of axis d and q respectively and
Vsd , Vsq are the components voltage of the stator of axis d and q respectively; Rs , Rr are the stator and the rotor resistance and Ls, Lr are the stator and the rotor self-induction; as is the pulsating of the stator field; M is the mutual of the self-induction; Ts , Tr are the time
constant to stator and rotor respectively.
The mechanical equation of the induction machine is:
= PML( I -O Id)-) -K^
dt JLr rd sq rq sd ’ J J
(10)
where o>m is the pulsating of the rotor field.
The equation of electromagnetic torque is:
C. = PM (O -O qId ),
Lr
where Ce is the electromagnetic torque and p is the number of pair pole.
This modeling has shown a strong coupling between the flow and the electromagnetic torque. It is therefore interesting to use the indirect vector command of rotor flow orientation so as to improve their performances in dynamic regime [5, 10].
2.2. Inverter Sub-System
It is composed a three phased bridge of six power switches, essentially thyristors (see Fig. 4). Its main role is to deliver a power signal as close as possible to the command signal coming from the regulation and command sub-block. [9]. Before any synthesis of command laws, it is necessary to analyze the process to control, to establish a adequate modeling and to interpret its proper dynamics. The digital algorithmic command envisaged to operate the converter, necessitates the sampling and the quantification of magnitudes [3, 5, 9]. Others constraints are present as for example, the imperfection of the source, the sampling of the converter, the delay due to the opening time and closing time of the thyristors. To each switch Kci corresponds a connection function fd [3, 4] with:
fa = 0 ^ Kci°Pen , (11)
fci = 1 ^ Kci cloSed . (12)
One defines the connection function as follows:
fd + fc 2 = 1. (13)
Each inverter arm is formed of two complementary switches in such away that that it realizes the connection function [4] (see Fig. 3). The following equations for PWM inverter feeding: (phased-neuter voltage/axis (a, b, c)) [5, 9]:
; (14)
2 ----------3-------- > (15)
(16)
and following the referential (a, ft):
Vsa = Van ; (17)
v - vb
vft=-S^3bL, (18)
where vsa, vsft are the components voltage of the stator to follow the axis (a, ft).
Following the referential ( d, q ):
vsq = van ; (19)
vsd =}jj(vcn - vbn ^ (20)
where vsq ; vsd are the components voltage respectively of the stator to follow to axis (d, q).
u f 2va 1 v - vc
2 V 3
u f-v a + 2vb +1
= 2 V 3
=u f-v a - vb + 2v
=2 V 3
d>
S1
©■
S2
©■
S3
O—
Vs1
Switch
Switchl
Swi tch2
Mux K Demux
Matrix
Gainl
♦o
Va
-KD
Vb
-*©
Mux7
Demux
Vc
Figure 3. PWM inverter feeding
2.3. Rectifier sub-block
The rectifier sub-block is a three phased bridge formed of six diodes placed at the output of the alternative three phased network, its role is to deliver a waved rectified continuous voltage that will be (L, C) filtered.
2.4. Input filter and output filter sub-block
The input filter plays an essential role in the power under block of the inverter. Its role is to filter the waved continuous voltage to the rectifier output.
2.5. Auxiliary power feeding sub-block
The sub-block of the auxiliary power feeding is under the form of a transformer to multiple secondary.
2.6. Regulation and command sub-block
The regulation and command sub-block is formed by (see Fig. 4):
• Measures and collector system;
• Modulation systems;
• Algorithmic command;
• User interface.
The PWM command block is composed at: [3, 5, 9]:
• Carrier block;
• Reference block;
• Compared digital block;
• Digital command block.
m
Repeating
Sequence
N
□
-*o
■*0
Figure 4. PMW command
The signal of carrier wave has amplitude u and frequency f , so the equations system
are:
u
X = -3u + 4—-t;
1 Pji
X2 = + Up — 4 — t;
2 pT
The reference signal has amplitude um and frequency fm
Uml = Um sin®t ;
Um2 = Um sin(t — 2n/3);
Um3 = Um sin(®t — 4nl3);
(21)
(22)
(23)
(24)
(25)
(26)
a = 2nfm is the pulsating of the reference signal.
(27)
Constant14
out 2
Constantl 3
3. SIMULATION RESULTS
The performances of this command are evaluated by using results of simulation realized by the MATLAB software. The figures below evaluate the obtained results quality in either open loop or closed loop. In the indirect vector command of the inverter-asynchronous motor system voltage feed, the obtained results quality shows the decoupling efficiency between the flow and the torque:
• In the open loop, the control between the flow and the electromagnetic torque is perfectly realized. Curves show that the decoupling affects weakly the flow where controlled magnitudes are isd and isq (see Fig. 6);
• In the closed loop, the speed response time is really reduced comparing with the preceding case. Despite the abrupt variations of the torque, the flow components O rd and O rq remain constant which shows the perfect decoupling between the flow and the torque (see Fig. 7).
By following the comparative test of the main control laws, one observes that the speed evolution is better which is to the benefit of the indirect command law in low and averages speed.
CONCLUSIONS
The simplicity of the used model in the simulation of the system constituted of the asynchronous machine and the two levels voltage inverter to PWM has allowed us to realize simulations in a very short time interval. The obtained simulation results prove the efficiency of PWM signal in the command and give excellent electrical magnitude performances of the system. In the open loop, the simulations results show that the torque responses are highly corrupted with noise and are weak of amplitude namely at low speeds. In closed loop the simulation shows high performances. Our current results concern the improvement of results obtained during the simulation in order to make the control of the speed and of the position more reliable at very low frequencies.
REFERENCES
1. Haddad S. Contribution au developpement d’un generateur automatique de programme de simulation de procedes electromecaniques. Thesis, INPL, Loraine, France, 1990.
2. Bodson M., Chiassn J. N., Novotnak R. T. A systematic approach to selecting flux references for torque maximization in induction motors. IEEE Trans. On control system tech., 1995, Vol. 3, N°4, pp. 388-397.
3. Abid M. Modelisation et simulation de l’association onduleur de tension a MLI-machine asynchrone. Master, University of Sidi Bel Abbes, Algeria, 1997.
4. Hautier J. P. Modelisation et commande de la machine asynchrone. Collection Sciences et Technique, 1993.
5. Benbakhti K. Controle vectoriel par orientation du flux rotorique d'une machine asynchrone pilotee par un onduleur de tension MLI. PFE, Electrical Engineering Department, University of Sidi Bel Abbes, Algeria, 1999.
6. Leonhard W. Control of electrical drive. Springer-Verlag, 1985.
7. Bowes S. R. Harmonic minimization in microprocessor controlled current-fed PWM inverter drives. IEEE, 1987.
8. Subrahmanyam V., Surendran K. Performance characterization of a new discrete pulse-modulated current regulator. IEEE, 1984, Vol. 25, N°6, pp. 1139-1148.
9. Belhadef H. Etude et controle de tension de sortie d'un onduleur a PMW. PFE, Electrical Engineering Department, University of Sidi Bel Abbes, Algeria, 1998.
1G. Habbadi A. Commande numёrique d’une machine asynchrone alimentёe par un onduleur de tension. Thesis, INP, Toulouse, France, 1988.
(a)
Figure 6. Electrical and mechanical values of the system (open loop): speed (a); electromagnetic torque (b); component of the flow to axis q (c); component of the flow to axis d (d)
(a)
(b)
Time (s)
Time (s)
(c)
(d)
Time (s)
Time (s)
Figure 7. Electrics and mechanics values of system (in closed loop): plot of components current to axes d and q (a); plot of the flow (b); plot of the torque (c); plot of speed (d)
APPENDIX
SYMBOLS AND NOTATIONS
o , o s’ r Flow respectively to stator and rotor
o d, o sd ^ sq Components flow of the stator respectively to axis d and q
o d, o ra i rq Components flow of the rotor respectively to axis d and q
V, V sr Voltage respectively of the Stator and the rotor
Vrd , Vrq Components voltage of the rotor respectively of axis d and q
Vsa, Vsq: Components voltage of the stator respectively of axis d and q
r Current respectively of the Stator and the rotor
sq sa Components current of the stator respectively of axis d and q
q r Components current of the rotor respectively of axis d and q
r Resistance of the stator and the rotor
Ls, 4 Self-induction respectively of the stator and the rotor
T, Tr Time constant respectively to stator and rotor
C Electromagnetic torque
