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A least squares induction motor
parameters identification based on three
level system
Bianchunyuan1,a,Liuhaijing1,b, Caoruixia1,c, Songchonghui1,d
1,2,3,4
School of Information Science & EngineeringˈNortheastern University
Shenyang ,China
a
[email protected], b [email protected],[email protected]
d
[email protected] ise.neu.edu.cn
method, model reference adaptive method, Kalman filter,
genetic algorithm and neural networks [ 3] . In recent years,
wavelet theory applied in the motor parameter identification
has been applied [ 2 ] .
Abstract—In recent years, with parameter self-tuning of the
drive is concerned by national experts and scholars, which has
become the focus of research. Because the induction motor has a
strong coupling, nonlinear, operating parameters and other
II.
significant characteristics change, many scholars do a lot of
PARAMETERS
research on the induction motor parameters identification, the
parameters identification theory, many of the results of modern
A.
Three-level system architecture
In Figure 1, A, B, C three terminals are connected with
induction motor. U-phase bridge inverter is a wall with
anti-parallel diode ( D1 ~ D4 ) of the four source switch
( S1 ~ S4 ) component. In a real system, switching devices are
IGBT. The midpoint of the two DC capacitor is given in
inverter DC side. DZ 1 and DZ 2 are the clamping diodes.
Common three-phase bridge arm 12 and the continued flow of
power electronic switching diodes
control theory are applied directly to vector control systems to
develop into a high-precision vector converter. This article
describes an experiment based on single-phase improved
methods, the least square off-line identification, only one
experiment can measure the motor parameters. According to the
simulation results , we obtain a satisfactory result.
Keywords-least square; induction motor;
identification
I.
LEAST SQUARE IDENTIFICATION OF MOTOR
parameter
INTRODUCTION
At present, the inverter plays a more and more important
role in energy saving and speed control so that it has been
experienced rapid development and wide application. The
application of higher voltage and better performance inverter
gets more and more attention. Therefore, three-level inverter
based on space vector control is a hot topic in the future
development.
This study is based on the three-level system to research
the motor parameter identification. Accuracy of motor
parameters is an important factor in determining the inverter
performance.
The inverter with parameter identification technology
research can be divided into offline and online identification[1
2 ] two research directions. Offline parameter identification is
mainly used to complete the self-setting, identification of the
parameters of which is higher initial value of precision, or the
direct use value under not very high work environment.
Online identification key is used to track changes in the motor
parameters, calibration of electrical parameters to meet the
operating environment of relatively high precision. The main
methods used in domestic vector inverter are the least squares
978-1-4577-0321-8/11/$26.00 ©2011 IEEE
Fig. 1 T Diagram of three-level NPC inverter
and six clamping diodes, all the same as the pressure tubes.
The two capacitors of the DC parameters are the same, the
voltage is half of the DC voltage[6]. Capacitance for two
capacitors is limited, the midpoint of the capacitor charge and
discharge current will produce the mid-point voltage drift[4 5
7].
29
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ls Rr + lr Rs
RR
R
1
, n0 = r s , m1 =
, m0 = r , we can
σ ls lr
σ ls lr
σ ls
σ ls lr
see n1 , n0 , m1 , m0 the four parameters are closely related to
the motor parameters ,so we must first identify the four
parameters. In order for this least squares transfer function
model parameters identification, which must be turned into a
linear form of variables, we should get their differential from
the stator voltage and current signals, here we use
second-order filter to replace differential. We can select the
filter in the form:
B. Linear model of induction motor parameters
n1 =
The core of this method is to detect the rotor stationary
motor parameters, here we use two-phase stationary reference
frame of the motor mathematical model, expressing as
formula (1) - (2).
Voltage equation:
Lm p
0
0
ªusα º ª Rs + Ls p
º ªisα º
«u » «
» «i »
R
L
p
L
p
0
+
0
s
s
m
« sβ » = «
» « sβ » (1)
«uγα » « Lm p
Rr + Lr p
ω Lm
ω Lr » «iγα »
« » «
»« »
Lm p
Rr + Lr p ¼ «¬ iγβ »¼
−ω Lr
«¬ uγβ »¼ ¬ −ω Lm
s 2 iα s
1
1
=
, making z =
,
H ( s ) ( s + ω0 )( s + ω1 )
( s + ω0 )( s + ω1 )
According to the definition of z , we can get
Flux equation:
ªψ sα º ª Ls
«ψ » «
« sβ » = « 0
«ψ γα » « Lm
«
» «
¬«ψ γβ ¼» ¬ 0
0
Ls
0
Lm
Lm
0
Lr
0
0 º ªisα º
« »
Lm »» «isβ »
0 » «iγα »
»« »
Lm ¼ ¬« iγβ ¼»
(10)
(2)
Here
is a integral part, commonly used in practice to
s2
be replaced by low-pass filter, to avoid saturation points, so
1
we
used
instead.
We
can
get
H (s)
For the squirrel cage induction motor with rotor measured
voltage is 0. From the mathematical model of induction motor
voltage and flux equations, derived a linear induction motor
model in (2) into (1), we can obtain state equation of the stator
currents is and rotor flux ψ r :
<
ψ γα =
<
ψ γβ =
lm
τr
lm
τr
isα −
isβ −
<
i sα = −γ isα +
1
τr
K
τr
<
i sβ = −γ isβ +
1
τr
ψ γα − ωψ γβ
(3)
ψ γβ + ωψ γα
(4)
(5)
ψ γβ − K ωψ γα + α s usβ
(6)
K
(ω1 + ω0 ) s + ω1ω0
z
H ( s)
(ω + ω0 − n1 ) s + (ω1ω0 − n0 )
m s + m0
iα s + 1
uα s
= 1
H (s)
H (s)
iα s = z +
iα s = θ T X
l
Rs lm2 Rr
1
+
, K = m , αs =
. If only the
σ ls
σ ls lr
σ ls σ ls lr2
α -axis exciting, this time the motor does not turn, in this case
uβ = 0, iβ =ψ β =0, we get formula (7) and formulas (8)
<
<
lm
τr
isα −
i sα = −γ isα +
1
ψ γα
(7)
ψ γα + α s usα
(8)
τr
K
τr
We can get the domain transfer function S, such as formula
(9)
isα
m s + m0
= 2 1
isβ s + n1s + n0
(12)
ª m0 − m1ω1 º
ª 1
º
«
»
« s + ω usα »
− ω1
ω
0
1
«
»
«
»
»
ª x1 º « 1
ª a1 º « m1ω1 − m0 »
usα »
»
«
«
»
«a » «
−
ω
ω
0
1
«
»
»
« x2 » = « s + ω0
θ = « 2» = «
2»ˈX =
»
« x3 » « 1
« a3 »
−n0 + n1ω1 − ω1
»
usα »
« » «
« » «
ω0 − ω1
»
¬ a4 ¼ «
¬ x4 ¼ « s + ω1
»
«
»
«
»
2
1
« n0 − n1ω1 + ω1 »
usα »
«
«
»
¬« s + ω0
¼»
ω0 − ω1
¬
¼
Where θ is the parameter vector which can be identified,
X is measurable signal, these signals can all be measured
through the first order filter, the model has been simplified. In
the calculation , We assumed the stator and rotor leakage
inductance are equal. These parameters and the actual
relationship of the motor parameters:
Where γ =
ψ γα =
(11)
Using some fractions, we obtained following the linear model:
ψ γα + K ωψ γβ + α s usα
τr
1
(9)
Where
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n1 = ω1 + ω0 − a3 − a4
n0 = ω1ω0 − ω0 a3 − ω1a4
m1 = a1 + a2
2) The determination of filter parameters: We
transformed the form above to avoid the differential, but the
introduction of the integrator, which uses second-order
low-pass filter to replace the second integral, in the
transformation of the various models, we get the first-order
low-pass filter with model the equivalent of first-order points.
a)
First-order low-pass filter equivalent to the
(13)
m0 = ω0 a1 + ω1a2
The relationship between the above we can get:
n
Rs = 0
m0
n
Rr = 1 − Rs
m1
lr = ls =
(14)
We can draw the low-pass filter cutoff frequency of the
input signal frequency is not the same time, low-pass filter of
the following approximate relationship:
(15)
Rr m1
m0
(16)
ls
m1
(17)
lm = ls2 −
principle of the integrator
When ωe ωc , G ( s ) ≈
b)
First-order low-pass filter parameter selection
Obtained by the above analysis, the larger of ωc , the
smaller of τ =
1
ωc
ωe
= 5 or 6 to meet
ωc
. We choose
requirement.
3) Sampling time selection: In order to make
algorithm on the actual realization of digital controller,
system must be discretized. We often select under
experience formula of the sampling frequency; as follows
the empirical formula of sampling frequency:
a)
Selected in accordance with transition time T p
The following we analysis the role of the state vector
SVPWM switching time. We conducted the analysis from the
above, Vβ = 0. Vα > 0, the interaction vector for the OOO,
POO, PON, PNN, NNN; Vα <0, the interaction vector for the
NNN, NNO, NNP, NOP, OOP, OOO.
D. The resolution of the key technology in linear induction
Ts = (1/15 ~ 1/ 5)T p
motor model
the
the
the
are
(21)
b)
Selected in accordance with main time constant of
the system Tls
In the concrete realization of the process, many specific
needs of key technologies need to solve, as following we will
introduce.
Ts = (0.05 ~ 0.1)Tls
1) Stimulus selection: In the parameter identification
process, the selection of stimulus parameters play a decisive
role in whether the convergence.
The continuous transfer function of Identification of the
object is:
1 + a1 s + ! an s n
1
;
s
to a pure integrator.
Three level work vector analysis
In this paper, an improved on the basis of a single-phase
experiments were carried out off-line least squares
identification. Three-level inverter switching state the main
use of PNN and NNN, as in the P-type in the SVPWM vector
and N-type vector can not be switched directly to the
transition through the zero vector.
G (s) =
, when, ωe ωc , G ( s ) ≈
ωc
ωe
we can get, when
1 , Low-pass filter can be equivalent
ωc
C.
b0 + b1s + ! + bm s m
1
(22)
c)
Selected in accordance with minimum time
constant of the system Tmin
Ts = (1 ~ 2)Tmin
(23)
Combination of the above calculation, and considering the
actual situation, the final choice of the sampling time is
0.0005s.
(18)
III.
PARAMETERS IDENTIFICATION OF
INDUCTION MOTOR SIMULATION BASED ON LEAST
SQUARES ALGORITHM
We can see transfer function contain (m + n + 1)
parameters, Therefore, in order to identification
(m + n + 1) parameters, the persistent excitation signal shall
include
different
frequency
components
at
least: j ≥ (m + n + 1) / 2 . By simplifying the transfer function,
we can get the requirement of different frequency number
j ≥ (2 + 1 + 1) / 2 = 2 . Therefore, the selected excitation signal
is a linear combination of three different frequency signals.
Discussed above analysis, under the Matlab / Smiulink
environment build a simulation model of least squares.
We used in the experiment AC motor nameplate:
YB2-100L1-4, Pe =2.2KW,
U 1e =380V/660V( Δ / Y )
31
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I1e =5.05/2.92A( Δ / Y ), ne =1410rpm, cos ϕ =0.82, Continuous
duty GB series of parameters required λm =2.1.
Calculated by the motor electrical parameters calculation
module, we get the simulation. Here we can see a1, a2, a3, a4
has a good convergence in Figure 3.
Fig.3 Waveform for the parameters of the induction machine
with system
From the figure, we can conclude the effect of
convergence is satisfactory. This result was confirmed by
using the proposed method in practice for the feasibility of
induction motor parameter identification.
ACKNOWLEDGEMENT
The auther would like to thank the reviewers constructive
comment. Thank the National Science Foundation(60974141)
and the Natural Science Foundation of Liaoning Province
(20092007) to support this project.
REFERENCES
[1]
[2]
Fig.2 Waveform for the intermediate variables
The following simulation experiment we added a
three-level inverter and svpwm module. We conducted
simulation results shown in Figure 3.
[3]
[4]
[5]
[6]
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32
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