Download Hexagon Voltage Manipulating Control (HVMC) for AC Motor Drives

Hexagon Voltage Manipulating Control (HVMC) for
AC Motor Drives Operating at Voltage Limits
JUL-KI SEOK
Senior Member, IEEE
SEHWAN KIM
Student Member, IEEE
Power Conversion Lab.
Yeungnam University, KOREA
[email protected],
http://yupcl.yu.ac.kr
Abstract – This paper proposes a hexagon voltage
manipulating control (HVMC) method for ac motor drives
operating at voltage limits. The command output voltage can be
simply determined by the torque command and the hexagon
voltage boundary in the absence of PI control gains, additional
MTPV tracking controllers, and observers for closed-loop
control. These attributes reduce the time and effort required for
the calibration of the controller in the nonlinear voltage-limited
region. The proposed hexagon voltage manipulating controller
(HVMC) accomplishes the “true” maximum available voltage
utilization, allowing a higher efficiency than that of the current
vector controller (CVC) alone in the MTPV domain. Modelbased voltage control (MVC) or CVC can be performed under
the MTPA region and control authority is handed automatically
over to the proposed HVMC in the voltage shortage region.
Successful application of the control approach has been
corroborated by a graphical and analytical analysis. The
proposed control approach is potentially applicable to a broad
family of control designs for ac drives.
Index Terms-- Ac motor drives operating at voltage limits,
hexagon voltage manipulating control (HVMC), maximum
available voltage utilization, model-based voltage control (MVC).
I.
INTRODUCTION
The growing penetration of ac motor drives into
commercial, industrial, and transportation applications has
made current technology continue to move toward the voltage
constrained regions. The good examples that are experiencing
this trend are ultra-high-speed (>120,000 r/min), high
efficiency, and high-power-density drives, such as
electrically-assisted turbo chargers [1-2], turbo compressors
[3-4], white goods applications [5-6] and reduced dc-link
capacitor technology for heating-ventilating-air-conditioning
(HVAC) systems [7-9].
The PI-type current vector control (CVC) is the most
widely used approach for achieving decupling control of an
air-gap torque and flux linkage of ac motors [10]. It has a
well-developed reach in technology and has been a market
success because of its robustness and simplicity. While it has
been found to be excellent in the maximum-torque-perampere (MTPA) operation, the performance requirements are
satisfied with the help of multiple-objective sub-control
978-1-4799-5776-7/14/$31.00 ©2014 IEEE
actions at voltage limits, such as maximum-torque-pervoltage (MTPV) or flux weakening control, anti-windup
control, and over-modulation scheme. As a result, one major
difficulty under the MTPV or voltage-limited region arises
from the fact that sub-control actions conflict in subtle ways
[11]. In addition, there are certain current limitations or load
angle constraints which must be considered when designing
the MTPV tracking controller. Therefore, the CVC strategy
becomes more complicated under voltage-limited conditions
because it requires extra control function and tuning gains,
which should be selected carefully based on the complex
trade-off between drive system stability and control dynamics.
Furthermore, realization of the maximum voltage utilization
fails, because it needs to consider the voltage limit as a circle
instead of a hexagon. Consequently, this control methodology
increases the copper loss and requires multiple control laws
for the transition between flux weakening and maximum
voltage utilization.
As alternatives, some modified direct torque and flux
control (DTFC) schemes have been exploited for high
performance ac motor drives [12-13]. Despite their improved
control performance over classical direct torque control
algorithms, the same limitations associated with their voltage
constraints as those in the CVC are still remained. These
adverse consequences arise from the adherence to the control
structure using the PI-type torque and flux regulator at the
hexagonal voltage limit. One of the main reasons for using
the PI regulator is the nonlinear cross-coupling of the voltage
manipulated input, yielding both an air-gap torque and stator
flux linkage, which is not solvable directly and cannot be
decoupled in continuous time.These have a closed-loop
feedback structure to regulate the motor air-gap torque and
stator flux linkage. Therefore, the control performance is
directly influenced by a stator flux linkage and torque
observer design based on the motor model.
Recently, a finite-settling-step DTFC (FSS-DTFC) method
associated with the inverter voltage and current constraints
for interior permanent-magnet synchronous motors
1707
(IPMSMs) was proposed [11]. The FSS -DTFC suggests that
the intersection of the current limited ellipse and the rotating
hexagon becomes a feasible voltage vector at the next
sampling instant. A closed-loop Volt-sec solution can
correctly decouple the nonlinear cross-coupling of the applied
voltage in the discrete time without adopting a PI-type
regulator. Here, the control law dynamically scales voltage
vectors on the hexagonal voltage boundary to ensure
maximum torque capabilities at a given operating condition,
while simultaneously regulating the stator flux linkage
magnitude to meet flux-weakening requirements. The
automatic transition to the MTPV mode is achieved with a
single voltage selection rule. Besides the stator flux linkage
and torque observer, a closed-loop stator current observer is
mandatory to accurately track and estimate the change in
current in each switching period. The complicated design of
multiple observers and the need to solve the complex
equation between exact motor model and rotating hexagon
may prohibit its implementation on a low-cost processor.
This paper focuses on developing a hexagon voltage
manipulating control (HVMC) method for ac motor drives
operating at voltage limits. The command voltage vector at
each discrete time step can be simply determined by the
torque command and the hexagon voltage boundary without
requiring PI control gains, additional MTPV tracking
controllers, and observers for closed-loop torque and flux
control. These attributes reduce the time and effort required
for the calibration of the controller in the nonlinear voltagelimited region. The proposed HVMC accomplishes the “true”
maximum available voltage utilization, allowing a higher
efficiency than that of CVC alone in the MTPV domain.
Model-based voltage control (MVC) or CVC is performed
under the MTPA region and motor control is handed
automatically over to the proposed HVMC in the voltage
shortage region. The automatic transition from MTPA to
MTPV mode provides new opportunities in a small dc-link
capacitor inverter fed by diode-bridge rectifiers, which
experiences frequent dc-bus voltage shortages. Successful
application of the control approach has been corroborated by
a graphical and analytical analysis. The proposed structure
can offer further flexibilities in motor design and ac drive
control operating at voltage limits.
II.
HVMC DESIGN FOR AC MOTORS UNDER MTPV REGION
In this paper, an ac motor is referred to salient when the daxis inductance is not equal to the q-axis inductance while
non-salient if the d-axis inductance is identical to the q-axis
inductance.
A.
permanent magnet (PM) motors can be expressed as
v ds = R s i ds − ω r L s i qs
(1a)
v qs = R s i qs + ω r L s i ds + ω r λ pm
(1b)
where v dqs and i dqs are the stator voltage and current
vector in the synchronous coordinate, respectively. R s is
the stator resistance, ω r is the rotor angular velocity, λ pm
is the flux linkage of the PM, and L s denotes the stator
inductance. Then, the q-axis stator current can be obtained as
⎛ ωr Ls
i qs = −⎜
⎜ R 2 + ω 2 L2
r s
⎝ s
ω r R s λ pm
−
R s2 + ω 2r L2s
⎞
⎛
Rs
⎟v + ⎜
ds
⎟
⎜ R 2 + ω 2 L2
r s
⎠
⎝ s
⎞
⎟v
⎟ qs
⎠
.
(2)
The motor torque command can be described as a function
of the rotor speed and the d-q axis voltage as follow:
3P
Te* =
λ pm i qs
22
⎤
⎡ ⎛ ω L
⎞
r s
⎟v
⎥
⎢− ⎜
ds
⎥ , (3)
⎢ ⎜⎝ R s2 + ω 2r L2s ⎟⎠
3P
⎥
=
λ pm ⎢
22
⎞
⎢ ⎛
ω r R s λ pm ⎥
R
s
⎟v −
⎥
⎢+ ⎜ 2
qs
R s2 + ω 2r L2s ⎥⎦
⎢⎣ ⎜⎝ R s + ω 2r L2s ⎟⎠
where P denotes the number of poles.
Fig. 1 shows a graphical representation of the stator
voltage solutions between torque command lines and rotating
hexagon in the synchronously rotating d-q volt plane. The
boundary of each rotating hexagon sector can be modeled as
a straight line in the d-q volt plane [11]
v qs (k ) = M n v ds (k ) + B n
(4)
where M n and B n are constant values given by the
boundary of each hexagon sector.
The corresponding hexagon boundary and the torque
command of (3) can provide two possible stator voltage
solutions that produce the desired output torque, as shown in
Fig. 1. Here, the command voltage vector v *dqs is chosen as
a feasible solution because it is the only voltage to satisfy the
desired stator flux magnitude. A selected voltage vector at
every sampling time can be uniquely expressed as
v *ds
Non-salient PM Motors
At steady-state, the stator voltage equation of non-salient
1708
ω r R s λ pm
Te*
Rs
+
− Bn
2
2
2
2
3P
R s + ω 2r L2s
λ pm R s + ω r L s
.
=− 2 2
ωr Ls
Rs
− Mn
R s2 + ω 2r L2s
R s2 + ω 2r L2s
(5a)
v *qs
⎛
ω r R s λ pm
Te*
Rs
⎜
+
− Bn
2
2 2
2
⎜ 3P
R s + ω 2r L2s
λ pm R s + ω r L s
⎜
= −M n ⎜ 2 2
ωr L s
Rs
⎜
− Mn
⎜
2
2 2
2
R s + ωr L s
R s + ω 2r L2s
⎜⎜
⎝
⎞
⎟
⎟
⎟
⎟ + Bn .
⎟
⎟
⎟⎟
⎠
k d3 = −
k q2 =
(5b)
In the proposed HVMC method, the intersection of the
torque line and the rotating hexagon becomes the command
voltage vector at the next sampling instant.
Salient PM Motors
The stator voltage equation of salient ac motors can be
expressed as
v ds = R s i ds − ω r L q i qs
(6a)
v qs = R s i qs + ω r L d i ds + ω r λ pm
(6b)
, and k q 3 = −
+ ω 2r L d L q
,
ω r R s λ pm
R s2 + ω 2r L d L q
.
0
-100
⎞
⎛
Rs
⎟v + ⎜
⎟ ds ⎜ R 2 + ω 2 L L
r d q
⎠
⎝ s
Te* [p.u.]
-150
-200
-150
-100
-50
0
50
d − axis [V]
100
150
200
Fig. 1. Voltage selection principle for HVMC operation of non-salient PM
motors.
(7a)
150
100
q − axis [V]
⎤
⎞
⎟v ⎥
⎟ ds ⎥
⎠
⎥
⎞ ⎥
⎟v ⎥ .
⎟ qs ⎥
⎠ ⎥
⎥
⎥
⎥
⎥⎦
⎞
⎟v
⎟ qs
⎠
. (7b)
50
0
-50
-100
Then, the motor torque command can be described as a
function of the rotor speed and the d-q axis voltage as follow:
(
Te* [p.u.]
)
Te*
= λ pm k q1 v ds + k q 2 v qs + k q 3 +
3P
22
)(
(L d − L q ) k d1 v ds + k d 2 v qs + k d 3 k q1v ds + k q 2 v qs + k q3
k d1 =
R s2 + ω 2r L d L q
ωr L d
R s2
-50
⎡ ⎛
ωr L d
⎢− ⎜
⎢ ⎜ R 2 + ω2 L L
r d q
⎢ ⎝ s
⎢ ⎛
ωr L q ⎢ ⎜
Rs
1
i ds =
v ds +
+
Rs
R s ⎢ ⎜ R s2 + ω2r L d L q
⎢ ⎝
⎢
ω r R s λ pm
⎢−
⎢ R 2 + ω2 L L
s
r d q
⎢⎣
(
Rs
, k q1 = −
50
(6), the d-q axis stator current can be obtained as
(8)
where
+ ω 2r L d L q
100
where L dq indicates the d-q axis stator inductance. From
⎛
ωr L d
i qs = −⎜
⎜ R 2 + ω2 L L
r d q
⎝ s
ω r R s λ pm
−
2
R s + ω 2r L d L q
R s2
150
q − axis [V]
B.
ω 2r L q λ pm
ω 2r L d L q
ωr L q
1
, k d2 =
,
−
R s R s (R s2 + ω 2r L d L q )
R s2 + ω 2r L d L q
-150
-200
-150
-100
-50
0
50
d − axis [V]
100
150
200
Fig. 2. Voltage selection principle for HVMC operation of salient PM
motors.
)
Fig. 2 shows the stator voltage solutions in the d-q volt
plane, where a torque command trajectory forms a hyperbolic
curve. A feasible voltage vector at the intersection between
(4) and (8) can be obtained as
1709
v *ds =
− β − β 2 − 4αγ
⎛ 1
⎞
ω e2 L s L σ
⎟v
−
λ *dr = L m ⎜
2
2
⎜ R s R (R + ω L L ) ⎟ ds
s
s
e s σ ⎠
⎝
.
ωe Lσ
+ Lm
v qs
R s2 + ω e2 L s L σ
(9)
2α
v *qs = M n v *ds + B n
where
{
}
α = (L d − L q ) k d1k q1 + k d 2 k q 2 M 2n + (k d1k q 2 + k d 2 k q1 )M n ,
The motor torque command can be obtained as follow:
3 P Lm
Te* =
k d1_IM v ds + k d2_IM v qs ⋅
2 2 Lr
(14)
(
(k
⎧⎪2k d 2 k q 2 M n B n + (k d1k q 2 + k d 2 k q1 )B n
⎫⎪
β = (L d − L q )⎨
⎬
⎪⎩+ k d1 k q3 + k d3 k q1 + k d 2 k q3 + k d3 k q 2 M n ⎪⎭ ,
+ λ pm k q1 + λ pm k q 2 M n
(
)
(
)
+ k q2_IM v ds
.
C.
Induction Motors
At the steady-state, the motor air-gap torque command and
the rotor flux linkage of the rotor-flux oriented-controlled
(RFO) IM can be expressed as
3 P Lm
(10a)
Te =
λ i qs
2 2 L r dr
λ dr ≅ L m i ds
(10b)
where λ dr represents the d-axis rotor flux linkage vector.
Lr
represent
the
ωe Lσ
k d2_IM = L m
In (9), a single voltage solution, which falls on the
hexagonal voltage boundary, can be chosen as a feasible
solution because only one solution is achievable at the next
sampling time.
and
⎞
⎛ 1
ωe2 Ls L σ
⎟,
k d1_IM = L m ⎜
−
⎜ R s R (R 2 + ω2 L L ) ⎟
s s
e s σ ⎠
⎝
+ k d 2 k q3 + k d3 k q 2 B n + k d 3 k q3 )
magnetizing
and
R s2
and k q2_IM = −
+ ω e2 L s L σ
, k q1_IM =
ωe Ls
R s2
Rs
R s2
v ds = R s i ds − ω e σL s i qs
(11a)
v qs = R s i qs + ω e L s i ds
(11b)
150
100
1
Te* [p.u.]
50
0.5
0
-1
0
-0.5
Rotating
hexagonal
voltage limit
-50
-100
-150
-200
-100
0
d − axis [V]
100
200
Fig. 3. Voltage selection principle for HVMC operation of induction motors.
A feasible voltage vector can be obtained as
where σL s is the stator transient leakage inductance.
By combining (10) and (11), the torque and rotor flux
linkage command can be obtained as a function of the
synchronous speed:
ωeLs
⎛
⎞
v ds ⎟
⎜−
2
2
⎟
3 P L m * ⎜ R s + ωe Ls L σ
Te* =
λ dr ⎜
(12)
⎟.
Rs
2 2 Lr
⎜+
v qs ⎟
⎜ R 2 + ω2L L
⎟
s
e s σ
⎝
⎠
,
.
+ ω e2 L s L σ
rotor
inductance, respectively.
By combining (10) and (11), the torque and rotor flux
linkage command can be obtained as a function of the
synchronous speed
The stator voltage equation can be also simplified as
+ ω e2 L s L σ
Fig. 3 shows the stator voltage solutions in the d-q volt
plane.
q − axis [V]
= ( L d − L q )(k d 2 k q 2 B 2n
T*
+ λ pm k q 2 B n + λ pm k q 3 − e
3P
22
Lm
q1_IM v qs
)
)
where
and
γ
(13)
v*ds =
v*qs
=
− β + β 2 − 4αγ
(15)
2α
M n v*ds
+ Bn
where
1710
α = k d1_IM k q2_IM + k d2_IM k q1_IM M 2n
+ (k d1_IM k q1_IM + k d2_IM k q2_IM )M n
β = 2k d2_IM k q1_IM M n B n
+ (k d1_IM k q1_IM + k d2_IM k q2_IM )B n
,
, and
γ = k d2_IM k q1_IM B 2n −
2
⎧⎪k
⎫⎪
d1_RM k q1_RM + k d2_RM k q2_RM M n
α = (L d − L q ) ⎨
⎬,
⎪⎩+ k d1_RM k q2_RM + k d2_RM k q1_RM M n ⎪⎭
Te*
.
3 P Lm
2 2 Lr
(
D.
Synchronous Reluctance Motors
The torque command of synchronous reluctance motors
can be expressed as
)
(
Te*
= (L d − L q ) k d1_RM v ds + k d2_RM v qs ⋅
3P
22
(k
q1_RM v ds
+ k q2_RM v qs
(16)
)
ωr Lq
Although the HVMC can achieve the minimum stator
current or maximum voltage utilization operation in the
MTPV region, this is not the best strategy under the
unconstrained region, compared to an MTPA method. Fig. 5
shows the stator current vector of a salient ac motors in the dq current plane for a given torque requirement when the
motor is operated below a base speed ( ω base ).
k q1_RM = −
k q2_RM =
,
+ ω 2r L d L q
ωr Ld
R s2
+ ω 2r L d L q
Rs
R s2
+ ω 2r L d L q
Te*
.
3 P
2 2
III. CONTROLLER DESIGN FOR AC MOTORS UNDER MTPA
REGION
ω 2r L d L q
1
k d1_RM =
−
,
R s R s (R s2 + ω 2r L d L q )
R s2
⎧⎪2k d2_RM k q2_RM M n B n
⎫⎪
β = (L d − L q ) ⎨
⎬,
⎪⎩+ (k d1_RM k q2_RM + k d2_RM k q1_RM )B n ⎪⎭
and
γ = (L d − L q )(k d2_PM k q2_PM B 2n ) −
where
k d2_RM =
)
, and
ω < ω base
i qs [A]
.
Fig. 4 shows the stator voltage solutions of synchronous
reluctance motors in the d-q volt plane.
150
i ds [A]
q − axis [V]
100
50
1
0
Te* [p.u.]
-1
-0.5
0.5
Fig. 5. Stator current vector of MTPA and HVMC in the non-limited region.
0
In this regard, this paper suggests a hybrid structure for
minimum copper loss control over the entire operating range.
This paper introduces an MVC for the non-limited voltage
operation [9]. When the stator voltage remains within
-50
Rotating
hexagonal
voltage limit
-100
-150
-200
-100
0
d − axis [V]
100
Vdc / 3 (circular voltage boundary), which is called the
200
Fig. 4. Voltage selection principle for HVMC operation of synchronous
reluctance motors.
v *dqs _ MVC nears the circular voltage boundary, the control
A feasible voltage vector can be calculated as
v*ds =
v*qs
where
=
− β − β 2 − 4αγ
2α
M n v*ds
+ Bn
MVC operation, the intersection between the constant flux
linkage and desired torque command in the d-q Volt plane
becomes the feasible voltage command at the next sampling
time. Fig. 6 presents MVC solution trajectories of the
induction motor with the rotor speed elevation. Once
(17)
switches to the proposed HVMC that generates the desired
air-gap torque as closely as possible, while simultaneously
regulating the flux linkage magnitude under a fieldweakening operation.
One caveat of the MVC mode is that the flux level is not
1711
100
v*dqs_MVC
λ*s
or v*dqs_CVC
Te*
ωe ↑
60
v *dqs
40
20
i dqs
v dqs
θr
v*dqs_HVMC
v*dqs_MVC
0
-100
θr
-50
0
100
50
d - axis[V]
Fig. 6. Voltage trajectories of MVC mode
Fig. 7. Proposed hybrid control configuration for copper loss minimization control.
maintained properly when the machine-parameters drift due
to magnetic saturation and initial errors. On the other hand,
the automatic transition to the HVMC mode can be achieved
with a single voltage selection rule. Thus, the transparent and
streamlined controller can be designed under a single control
law, and reduces the time and effort required for the
calibration of the controller in the entire operating region.
The CVC operation is rather robust against the parameter
errors, but it requires an additional effort for the control mode
transition. A smooth transition between CVC and HVMC
could be achieved by resetting the CVC integrator whenever
the mode switching occurs [14]. Using the proposed hybrid
voltage control, the minimum copper loss operation is
achieved over the entire operating space. Fig. 7 shows an
example of the hybrid control configuration, where the MVC
or CVC is responsible for the MTPA operation.
Note that the precise torque regulation in the MVC and
HVMC mode can be achieved provided there is no drift of
the motor parameter. In practice, however, this is not always
the case, and the motor parameters should be estimated and
updated in real situations [9, 14-15].
IV. SIMULATION AND EXPERIMENTAL RESULTS
The basic feasibility of the proposed controller was
verified on a 900 W salient PM motor, a 600W non-salient
PM motor which is coupled to a 1.0 kW servo motor, and a
1.5kW induction motor with a small dc-link capacitor
inverter fed by three-phase diode front-end rectifiers, as
described in Table I, II, and III.
The simulated test result for the salient PM motor is
depicted in Fig. 8(a) when the rotor speed travels to 200% of
the base speed and the 35% of the rated torque is regulated in
the tested motor. The rotor speed, command/controlled airgap torque, d-q axis stator current, and stator flux linkage are
200
100
q - axis [V]
2
ω rpm [p.u.] 1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.45
Te*
0.5
0
-100
Te
Te [p.u.] 0.35
-200
-200
-100
0
100
d - axis [V]
0.25
200
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
150
2
i ds
1
i qs
100
i *dqs [p.u.] 0
-1
-2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1.57
*
v sdqs
[V]
q - axis[V]
80
50
0
-50
-100
λ̂ s [p.u.] 0.9
-150
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
-200
Time [5ms/div]
Time[s]
(a)
(b)
Fig. 8. Simulated result of the proposed HVMC for salient PM motor (CVC+HVMC operation).
1712
200
illustrated from the top to bottom. Precise air-gap torque
control is performed in the flux weakening domain while an
automatic transition occurs between the MTPA (CVC) and
MTPV (HVMC) mode. Torque distortions were rarely found
during the transition between CVC and HVMC mode. The xy locus [Fig. 8(b)] shows that the proposed HVMC scheme
achieves the maximum voltage utilization under voltagelimited conditions.
TABLE I
Ratings and Known Parameters of 900W IPMSM
Ratings and Parameters
Value
maximum speed. No additional distortion was found in the
output phase voltage waveform. It can be confirmed from the
x-y locus [Fig. 9(b)] that the resulting HVMC achieves the
maximum voltage utilization under the voltage limited
condition.
2
ω̂ rpm [p.u.]
0
Unit
Rated torque
2.9
Number of poles
Ld
8
8.5
mH
Lq
20.2
mH
λ pm
0.115
Wb
1
Te[ p.u.]
Nm
0.35 0
2
i dqs [p.u.]
0
−2
1.55 λ̂ s [p.u.]
0
TABLE II
Ratings and Known Parameters of 600W SPMSM
Value
Unit
Rated torque
1.9
Nm
Number of poles
Ls
8
4.6
mH
0.065
Wb
λ pm
(a)
v*qs [50V/div]
Ratings and Parameters
Time [1s/div]
v*ds [50V/div]
TABLE III
Ratings and Known Parameters of 1.5kW IM
Ratings and Parameters
Rated voltage
Rated speed
R s / R r @ 25D C
L m / σL s
200 Unit
*
vsdqs
220
1500
V
r/min
[50V/div]
2.47/0.7
Ω
134/12.6
mH
Value
0
− 200 Time [5ms/div]
(b)
Fig. 9. Test result of the proposed HVMC for non- salient PM motor
(CVC+HVMC operation).
A motoring test result for the 600 W non-salient PM motor
is depicted in Fig. 9(a), where the rotor speed, the measured
torque, the measured d-q stator current, and the estimated
stator flux linkage are illustrated from the top to bottom. In
this test, the dc-link voltage was set to 150 V and the motor
drive was operated from 0 to 200% of the base speed. The
coupled servo drive was operated in the speed-control mode
while 35% of the rated torque was regulated in the tested
motor. Fig. 9(b) shows the selected d-q command voltage
waveforms of (5) in the stationary reference frame at the
Validation of the theoretical developments presented
above was performed on a 1.5 kW IM drive with a 20μF film
capacitor fed by a three-phase diode rectifier through a real
test. The nominal input line-to-line voltage was set to 210 V.
Fig. 10(a) presents a test result in the motoring operation,
where the measured dc-link voltage, flag signal, estimated
air-gap torque, and estimated rotor flux linkage are illustrated
from top to bottom. The “mode_HVMC” is 1 if the HVMC
mode activates and 0 otherwise (MVC mode). In this test, the
1713
IM drive was operated with 90% of the base speed while the
rated load torque was applied. The dc-link voltage fluctuates
with six times the input grid voltage frequency. The
waveform of the flag signal and air-gap torque show a
smooth and rapid transition occurs between the MVC and
HVMC operation. The x-y locus [Fig. 10(b)] shows that the
resulting controller can achieve the maximum voltage
utilization at the periodic voltage dropping region.
in applications experiencing frequent dc-bus voltage
shortages. The performance of the proposed HVMC was
illustrated both in simulations and on a real ac drive, showing
the combination of a graphical and analytical analysis. The
proposed control approach is potentially applicable to a broad
family of control designs for ac drives.
REFERENCES
[1]
[2]
Vdc_measure 300
[12V/div]
[3]
1
mode_HVMC
0
T̂e
[0.5p.u./div]
[4]
1
[5]
[6]
λ̂ edr
[0.2Wb/div]
0.5
[7]
Time [5ms/div]
(a)
vsqs* [50V/div]
[8]
[9]
[10]
vsds* [50V/div]
[11]
*
v sdqs
[12]
[50V/div]
[13]
Time [10ms/div]
(b)
Fig. 10. Test result of the proposed HVMC for induction motor.
(MVC+HVMC operation).
V.
[14]
CONCLUSIONS
[15]
This paper proposes a hexagon voltage manipulating
control (HVMC) method for ac motor drives operating at
voltage limits. The command output voltage can be simply
determined by the torque command and the hexagon voltage
boundary in the absence of PI control gains, additional
MTPV tracking controllers, and observers for closed-loop
control. This performance criterion is particularly important
1714
C. Bell, Maximum boost: Designing, Testing and Installing
Turbocharger Systems. Bentley Publishers, 1997.
S. H. Kim and J. K. Seok, “Comprehensive PM motor controller
design for electrically assisted turbo-charger systems,” Proc. of
IEEE ECCE Conf., 2013, pp. 860-866.
B. H. Bae, S. K. Sul, J. H. Kwon, and J. S. Byeon,
“Implementation of sensorless vector control for super high speed
PMSM of turbo-compressor,” IEEE Trans. Ind. Appl., vol. 39, no.
3, pp. 811–818, May/Jun. 2003.
S. Chi and L. Xu, “Development of sensorless vector control for a
PMSM running up to 60,000 rpm,” in IEEE-IEMDC Conf, 2005,
pp. 834–839.
I. Boldea, “Control issues in adjustable speed,” IEEE Ind. Electron.
Mag., vol. 2, no. 3, pp. 32–50, Sep. 2008.
A. Tenconi, S. Vaschetto, and A. Vigliani, “Electrical machines for
high-speed applications: design considerations and tradeoffs,”
IEEE Trans. Trans. Ind. Electron., vol. 61, no. 6, pp. 3022-3029,
June 2014.
Altivar 21 User’s Manual. Schneider Electric Industries S.A.S.,
2006.
A. Yoo, S. K. Sul, H. Kim, and K. S. Kim, “Flux-weakening
strategy of an induction machine driven by an electrolyticcapacitor-less inverter,” IEEE Trans. Ind. Appl., vol. 47, no. 3, pp.
1328–1336, May/June 2011.
S. H. Kim, G. R. Kim, A. Yoo, and J. K. Seok, “Induction motor
control with small DC-link capacitor inverter fed by threephase diode front-end rectifiers,” to be presented in Proc. IEEE
ECCE 2014.
H. Kim, M. W. Degner, J. M. Guerrero, F. Briz, and R. D. Lorenz,
“Discrete-time current regulator design for AC machine drives,”
IEEE Trans. Ind. Appl., vol. 46, no. 4, pp. 1425-1435, July/Aug.
2010.
C. H. Choi, J. K. Seok, and R. D. Lorenz, “Wide-speed direct
torque and flux control for interior PM synchronous motors
operating at voltage and current limits,” IEEE Trans. Ind. Appl.,
vol. 49, no. 1, pp. 109-117, Jan./Feb. 2012.
I. Boldea, M. C. Paicu, G. D. Andreescu, and F. Blaabjerg, “Active
flux DTFC-SVM sensorless control of IPMSM,” IEEE Trans.
Energy Convers., vol. 24, no. 2, pp. 314-322, June. 2009.
G. Foo and M. F. Rahman, “Sensorless direct torque and fluxcontrolled IPM synchronous motor drive at very low speed without
signal injection,” IEEE Trans. Ind. Appl., vol. 57, no. 1, pp. 395403, Jan. 2010.
S. H. Kim, C. H. Choi, and J. K. Seok, “Voltage disturbance statefilter design for precise torque-controlled interior permanent
magnet synchronous motors,” in Proc. IEEE ECCE 2011, pp.
2445-2451.
S. H. Kim and J. K. Seok, “Maximum voltage utilization of
IPMSMs using modulating voltage scalability for automotive
applications,” IEEE Trans. Power Electron, vol. 28, no.124, pp.
5639–5646, Dec. 2013.