Download Open-Loop Torque Boost and Simple Slip Frequency Compensation

Open-Loop Torque Boost and Simple Slip Frequency
Compensation for General Propose V/f Inverters
Jutarat Pongpant
E-mail:[email protected]
Sakorn Po-ngam
E-mail:[email protected]
Power Electronics & Motor Drives Laboratory (PEMD)
Department of Electrical Engineering, Faculty of Engineering
King Mongkut's University of Technology Thonburi
91 Prachauthit Road, Bangmod, Thungkhru District, Bangkok 10140 Thailand.
ABSTRACT
In this paper, the performance improvement of the
constant V/f control induction motor drive is proposed.
This proposed scheme fully compensates for the stator
resistance voltage drop by vectorially modifying the stator
voltage and keeping the magnitude of the stator flux
constant. The simple slip frequency compensation, based
on an estimation of the air-gap power and a linear torquespeed approximation, is also introduced. This method
reduces the steady-state speed error to almost zero. The
nameplate data and only the stator resistance are required
in this control scheme. The validity of this control scheme
is verified by simulation results.
Keywords: Torque boost, V/f control, Induction motor
1. INTRODUCTION
The speed controls of induction motor with V/f
inverters have been widely known. However, it is torquespeed characteristic at low speeds does not function well
enough because maximum-torque will be decreased. Due
to stator resistance voltage drop affecting the low speed
range, the stator resistance voltage drop compensation
that is called “Torque boost” is used. The weak point of
torque boost by manual magnitude of voltage
modification is that it is done on a trial-and-error basis. If
over voltage is adding, the magnetic flux will cause
saturation to occur, which resulting in the increase power
loss in the motors. Therefore, the popular methods of an
automatic torque boost for V/f inverters are introduced,
that is the close-loop magnitude flux control. Such as the
magnitude air-gap flux control method [1]; the induced
voltage control from stator flux, air-gap flux, and rotor
flux respectively [2], [3], [4]. Although, these close-loop
control methods can improve the performance of V/f
inverters, they require the accuracy parameters of motor
[3-4]. In addition, the without pattern for gain of
controller (PI) design is a drawback when using it in the
implementation. The research in [5] introduced an
automatic torque boost method based on close-loop
control of magnitude stator flux that required only the
parameter of motor which is the stator resistance and also
introduced the pattern for gain design of PI controller.
However, PI controller in order to design, we should have
adequate knowledge of motor model. The research in [5]
presented the use of reducing order model (based on full
order model estimation) as well as reducing the linear
order model estimation.
Therefore, this paper presents the open-loop torque boost
method that use the steady-state model of induction motor
to supply voltage to motor (based on vector method).
Only the stator resistance which is a parameter of motor
and nameplate data are used in this study. In addition, the
simple slip frequency compensation is presented; it
provides the actual speed value to close the command
speed value in steady state that is the high-performance
modification of V/f inverters. The simulation results show
performance of induction motor drive V/f control system
is improved even if it is in low speed range.
2. THEORY AND PRINCIPLE
2.1 Open-loop torque boost
The main reason for proposing the use of torque
boost in induction motor V/f control is the stator
resistance voltage drop compensation because it keeps the
Em/f magnitude constant. If this method can control the
stator magnitude constant, the torque-speed characteristic
of motor will depend only on slip frequency. The
induction motor steady-state equivalent circuit and phasor
diagram are shown in Fig.1 and Fig.2, respectively.
LR
IR
M
σ LS
RS
IS
I mR
US
Em
2
⎛ M ⎞ RR
⎜ ⎟
⎝ LR ⎠ s
M2
LR
Fig.1: Induction Motor Steady-State Equivalent Circuit
Em
I S .RS
φ
φ
E − ( I S .RS .sin φ )
2
m
2
US
I S .RS .cos φ
IS
Fig.2: Phasor Diagram of Current and Voltage
Fig.1 can be used to find the relationship between torque
and slip frequency as seen in equation (1) [4].
⎛E ⎞
A
i m⎟
Tm = 2
2 ⎜
A + B ⎝ ω1 ⎠
The 3-phase quantities are transformed to space vector
quantities by using relative transform matrix as shown in
equation (3), where γ = 2π / 3[ rad ] .
2
(1)
iS = isu + isv e jγ + iswe j 2γ
1
⎡
1 −
⎢
⎡isα ⎤
2
⎢i ⎥ = ⎢
3
⎣ sβ ⎦ ⎢ 0
⎢⎣
2
where
(ωS M ) , B = σ L + R M / LR
RR
i
S
2
ωS RR2 + (ωS LR )2
RR2 + (ωS LR )
2
A=
2
R
2
According to equation (1), if we keep proportion of
magnitude Em/f constant, the motor torque varies directly
proportional to the slip frequency and torque-speed
characteristic of motor is the same as at all speed range.
2
⎛ E × ωe∗ ⎞
2
= I S .RS .cos φ + ⎜ mR
⎟ − ( I S .RS .sin φ )
⎝ ωeR ⎠
iS = is2α + is2β
I S = isu ( RMS ) =
2
⎛ E × ωe∗ ⎞ ⎡
2
2
= I S .RS .cos φ + ⎜ mR
⎟ − ⎣( I S .RS ) − ( I S .RS .cos φ ) ⎤⎦
ω
eR
⎝
⎠
Where “*” is a command value, ø is a load angle, and the
subscript R is indicated the rated value.
From equation (2), the RMS value of the stator
current Is, stator resistance Rs, cosø, sinø are necessary.
By using the zero crossing method to calculate the power
factor, we will have problems with high-frequency noise
from an inverter so the solution to the problem is
transforming current on stationary reference frame into
synchronous rotating reference frame. The RMS value of
the stator current (Is) is calculated by using space vector
quantities of current, which is expressed as:
uS
isd
isq
φ
ρ
d : Synchronous rotating ref
ω frame
e
dρ
= ωe
dt
α : Stationary ref frame
Fig.3: Voltage and Current Component on the
Synchronous Rotating Reference Frame
(4)
isu ( peak )
⎡isd ⎤ ⎡ cos ωet
⎢i ⎥ = ⎢
⎣ sq ⎦ ⎣ − sin ωet
(2)
iS
(3)
2
=
2
iS
3
(5)
Then, we will show how to calculate Is·cosø as in
equation (6) after transforming the stator current on
synchronous rotating reference frame. Fig.1 can be used
to calculate Is·cosø (Real part of Is) as shown in equation
(7). Fig.4 shows the block diagram of the voltage
calculation that is supplied to the motor.
U S = I S .RS .cos φ + Em2 − ( I S .RS .sin φ )2
β
⎤ ⎡i ⎤
⎥ ⎢ su ⎥
⎥ ⎢isv ⎥
⎥⎢ ⎥
⎥⎦ ⎣isw ⎦
Consequently,
With reference to the phasor diagram in Fig.2,
voltage supplies to motor can be found from equation (2)
[6].
q
1
2
3
−
2
−
I S .cos φ =
isu
isv
sin ωet ⎤ ⎡isα ⎤
⎢ ⎥
cos ωet ⎥⎦ ⎣isβ ⎦
2
isq
3
(7)
IS
Eq (3) − (5)
ωe∗
iS
Eq (2)
Eq (6) − (7)
(6)
I S cos φ
Fig.4: Block Diagram of the Voltage Calculation
Supplied to the Motor
US
ωm∗
ωe∗
ωe∗
+
+
PWM
U
Eq (2)
1
τ s +1
ωS
PAirgap 3φ
Eq (10 )
Tm
Eq (9)
Eq (8)
∗
S
IM
VSI
isu
IS
I S cos φ
Eq (6)
iS Eq (3) − (5) isv
& (7)
Fig.5: Block Diagram of the Control System as is Presented
2.2 Slip frequency compensation
For convenience, we will estimate the slip frequency
which varies directly proportional to the motor torque
after controlling the stator flux magnitude to constant.
The power across airgap, motor torque, and slip
frequency value can be calculated as in equation (8)-(10),
respectively. However, the result of positive feedback is
the cause of instability in the system. So we must contain
a first order lag in the slip frequency compensation loop
to reduce the result of positive feedback. The block
diagram of all control system is shown in Fig.5.
PAir − gap 3φ = 3 ⎡⎣U S .I S .cos φ − I S2 .RS ⎤⎦ − Core loss
of the convergent speed is around 200 ms. The RMS
voltage supplies to motor is increased after taking load to
compensate the stator resistance voltage drop. Fig.8 is
shown the simulation by using the decoupling control
method at commanded speed 300 rpm which have the
torque, current, and speed response values as close as
those shown in Fig.7.
Tm ( actual )
0
Tm ( cal )
5 Nm
0
ωm
5 Nm
(8) 100
100 rpm
isu
0
p
Tm = ×
2
PAir − gap 3φ
ωe
(9)
5A
US
10
⎛ ωSR ⎞
⎟iTm
⎝ TmR ⎠
ωS = ⎜
10 V
(10)
The 2-phase current sensors, the nameplate data of
motor, the stator resistance, and core loss of motor are
also used, as shown in the block diagram in Fig.5. The
stator resistance and core loss coefficients of motor
(varies as f & f2) were available at an initial program in
the implementation.
3. SIMULATION RESULTS
This topic confirms that this presented method is
possible to be implemented. The simulations were carried
out using Matlab/Simulink as shown in Fig.(6)-(8).
Fig.(6)-(7) are the simulation results while the step
load change at rated torque 10 Nm., commanded speed
100 rpm and 300 rpm, respectively, which show the
motor is an excellent to drive loads. The torque
calculation from equation (9) equals to the actual torque
of motor in steady state. The speed error is nearly zero
even if at low speed range and rated load torque. The time
1 sec
Fig.6: Simulated the Step Load Change at Rated Torque
10 Nm., Commanded Speed 100 rpm.
Tm ( actual )
0
5 Nm
Tm ( cal )
5 Nm
0
300
ωm
100 rpm
isu
5A
0
0
US
20 V
1 sec
Fig.7: Simulated the Step Load Change at Rated Torque
10 Nm., Commanded Speed 300 rpm.
6. APPENDIX
The motor’s parameters and rating shown as follow:
Tm ( actual )
0
5 Nm
isq
0
ωm
300
RR = 0.963 Ω , RS = 2.15 Ω.
100 rpm
7. REFERENCES
5A
1 sec
Fig.8: Simulated the Step Load Change at Rated Torque
10 Nm., Commanded Speed 300 rpm., Including
Decoupling Control
4. CONCLUSION
The performance improvement of the induction
motor drive with V/f inverters is presented in this paper
based on open-loop torque boost and simple slip
frequency. This method requires the only parameter
which is the stator resistance and the nameplate data of
motor. This proposed method has the nearly response to
the vector control and use to implement in the high
performance applications. Simulation results are given to
verify the validity of the proposed method.
5. LIST OF SYMBOL
uS : stator voltage space vector
iS : stator current space vector
RS : stator resistance
RR : rotor resistance
LS : stator –self inductance
LR : rotor –self inductance
ω m : mechanical rotor speed
M : mutual inductance
p : numbers of pole
s : slip
ωS : slip frequency
Tm : motor torque
ωe : synchronous speed
σ = 1−
M2
LS .LR
[ ]d , [ ]q
: total leakage
: denote the d and q components on the
synchronous rotating reference frame
[ ]α , [ ]β : denote the α and β components on the
synchronous rotating reference frame
J = 0.021 kg im 2 , M = LR = 93.4 mH
5A
isu
0
2HP , 220 / 380 V , 50 Hz , 6.3 / 3.7 A , 1430 rpm , 4 poles ,
,
LS = 104.9 mH
,
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