European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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European Journal of Control
journal homepage: www.elsevier.com/locate/ejcon
AC Ward Leonard drive systems: Revisiting the four-quadrant operation
of AC machines$
Qing-Chang Zhong n
Dept. of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, UK
art ic l e i nf o
a b s t r a c t
Article history:
Received 13 May 2013
Accepted 13 May 2013
Recommended by Alessandro Astolfi
In this paper, the problem of controlling the speed of AC machines in four quadrants is revisited from a
completely new viewpoint, based on the idea of powering an AC machine with a synchronous generator
that generates a variable-voltage–variable-frequency supply. This is a natural, mathematical, but not
physical, extension of the conventional Ward Leonard drive systems for DC machines to AC machines.
As a result, AC drives can be regarded as generator-motor systems, which facilitate the analysis of AC
drives and the introduction of other special functions because a system consisting of a generator and a
motor is easier to be handled than the conventional AC drive that consists of an inverter and a motor.
Control strategies, with and without a speed sensor, are proposed to implement this idea and the
experimental results are presented to demonstrate the feasibility.
& 2013 European Control Association. Published by Elsevier Ltd. All rights reserved.
Keywords:
Variable speed drives
Ward Leonard drive systems
AC machines
Synchronverters
Inverters that mimic synchronous
generators
Speed-sensorless
1. Introduction
Motors consume the majority of electricity, of which 50–70% is
consumed by asynchronous electric motors and 3–10% by synchronous electric motors.1 Variable speed drives (VSD), often equipped
with inverters, are hence widely used nowadays to save energy,
increase productivity and improve quality in many applications, such
as home appliances, robots, pumps, fans, automotive, railway,
industrial processes and, recently, renewable energy. AC motors are
the main driving force in industry because of their small size,
reliability, low cost and low maintenance [4,5,12,18]. Due to the
advancement of power electronics, digital signal processing (DSP),
etc., the technology of VSD for AC motors is matured and AC drives
have replaced DC drives in many application areas. There are mainly
three approaches developed for AC drives [4,6,12]:
(1) V/f control: The idea is to generate a variable-voltage–variablefrequency sinusoidal power supply from a constant DC power
source. The control variables are voltage and frequency while
maintaining their ratio constant to provide (almost) constant
☆
Some preliminary results of this work were presented at the 5th IET International Conference on Power Electronics, Machines and Drives (PEMD) held in April
2010 in Brighton, UK and at the 20th International Symposium on Power
Electronics, Electrical Drives, Automation and Motion (SPEEDAM) held in June
2010 in Pisa, Italy.
n
Tel.: +44 114 22 25630; fax: +44 114 22 25683.
E-mail addresses: Q.Zhong@Sheffield.ac.uk, zhongqc@ieee.org
1
http://encyclopedia2.thefreedictionary.com/Power+System+Load.
flux. It is widely used in open-loop drives, where the requirement of performance, e.g. speed accuracy and response, is not
high and/or the controller needs to be simple [25]. This is also
called scalar control because only the amplitude of the voltage
is controlled. It is possible to add feedback, e.g. speed, torque
and/or flux, to improve the performance [2,24].
(2) Vector control: The idea is to control AC motors in a way similar
to controlling separately excited DC motors, after introducing
some transformations. The three phase currents are converted
into d, q current components id and iq, which correspond to the
field and armature currents of DC motors, respectively. If id is
oriented (aligned) in the direction of the rotor flux and iq is
perpendicular to it, then the control of id and iq is decoupled, as
in the case of DC motors. The frequency is not directly controlled
as in the scalar control but indirectly controlled; the torque is
controlled indirectly via controlling the current. The advantage of
vector control is that it provides good performance that is similar
to DC drives. The drawbacks of vector control are: (i) the flux
estimation and field orientation are dependent on motor parameters, which change in reality (e.g. with temperature); (ii) the
controller is very complicated and (iii) the inverter is often
current controlled via hysteresis-band PWM, which makes the
system analysis difficult [3,9,11,16,22]. A lot of patches have been
developed for vector control to improve the performance
[1,7,10,14,15,17,19,20,27].
(3) Direct torque (and flux) control: The torque (and stator flux) are
directly controlled via selecting appropriate inverter voltage
space vectors through a look-up table but the frequency is
indirectly controlled [8,26,30,28]. It uses hysteresis-based control,
0947-3580/$ - see front matter & 2013 European Control Association. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ejcon.2013.05.013
Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines,
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which generates flux and torque ripples, and the switching
frequency is not constant. It also needs motor parameters to
estimate the torque (and stator flux) [13,23,29]. Again, the
hysteresis-based control makes system analysis very difficult.
These three schemes have been further advanced for a long period
with the development of related technologies in e.g. control theory
and microelectronics. They are suitable for different applications
because of their different characteristics [4,12,21]. The vector
control and direct torque (and flux) control provide very good
performance but the control algorithms involve several transformations and are very complicated. What is worse is that look-up
tables are used in the direct torque (and flux) control, which
makes the analytical analysis of the system very difficult. The high
order of the resulting complete system from these approaches also
means that the system stability is difficult to guarantee. V/f control
is simple but the performance needs to be improved. Hence, a
simple high-performance AC drive that facilitates the analytical
analysis of the system is desirable.
From the viewpoint of control system design, the AC motor is
simply the load to an inverter. The main control objective of a
drive is to regulate the speed and the torque to obtain fast and
good response and the change of the motor parameters (including
the load) should not impose a major problem to the system. Such
an attempt is made in this paper, following the concept of
operating inverters to mimic synchronous generators [33–35]
and motivated by the conventional Ward Leonard drive systems
(WLDS). The physical interpretation of this is that the AC motor is
powered by a synchronous generator (SG) driven by a variablespeed prime mover. The synchronous generator and the prime
mover are then replaced by an inverter that behaves as a
synchronous generator. The torque and speed of the AC motor
are then controlled via controlling the torque and frequency of the
synchronous generator. The resulting control scheme is very
simple as it does not involve vector transformations nor the
estimation of flux. No complicated concepts, e.g. vector control
and field orientation, are needed and the scheme is very easy to
understand. This also unifies the drive for synchronous motors
(SM) and induction motors (IM). In the proposed scheme, the
attention of how to design AC drives has shifted from motororiented to inverter-oriented. This has led to an extremely simple
controller. It can also be treated as the proposed AC drive is
powered by a synchronous generator while the vector-controlled
AC drives are powered by a DC generator with some transformations. Another important advantage is that the complete system
can be described by the analytic mathematical models of the
generator and the motor, which facilitate the analytical analysis of
the system. The comparison of the different types of VSDs is given
in Table 1.
The rest of the paper is organised as follows. The concept of the
DC Ward Leonard drive systems is reviewed and then extended to AC
machines in Section 2. The mathematical model of synchronous
generators is described in Section 3 and a control scheme is proposed
in Section 4 to implement the concept. Experimental results are
shown in Section 6 and conclusions are made in Section 7.
Table 1
Comparison of control types for AC VSDs.
Load
Prime
mover
Variable
speed
Constant
speed
Controllable field
Fixed field
Fig. 1. Conventional (DC) Ward Leonard drive systems.
2. Ward Leonard drive systems
Induction motors, particularly those of the squirrel-cage type,
have been the principal workhorse for long time. However, until the
beginning of 1970s, they had been operated in the constant-voltage–
constant-frequency (CVCF) uncontrolled mode, which is still very
common nowadays. VSDs were dominated by DC motors in the
Ward Leonard arrangement. Ward Leonard drive systems, also
known as Ward Leonard Control, were widely used DC motor speed
control systems introduced by Harry Ward Leonard in 1891. A Ward
Leonard drive system, as shown in Fig. 1, consists of a motor (prime
mover) and a generator with shafts coupled together. The motor,
which turns at a constant speed, may be AC or DC powered. The
generator is a DC generator, with field windings and armature
windings. The field windings are supplied with a variable DC source
to produce a variable output voltage in the armature windings, which
is usually used to power a second DC motor that drives the load.
A natural analogy is to replace the DC generator with a synchronous generator and the DC motor with an AC machine (an induction
motor or a synchronous motor); see Fig. 2(a). This configuration is
called AC Ward Leonard drive systems [31,32]. It is worth noting that
the physical implementation of an AC Ward Leonard drive system is
of limited use, as described below. The prime mover in a DC WLDS
maintains a constant speed and the flux of the generator is variable;
the prime mover in an AC WLDS needs to have a variable speed (so
that the frequency of the output can be varied) and the flux of the
generator is constant. The output of the generator (voltage) in a DC
WLDS is varied via controlling the field voltage and the output of the
generator (voltage and frequency) in an AC WLDS is varied via
controlling the speed of the prime mover. If the speed of the prime
mover could be varied, it could have been used to drive the load
straight-away and hence there is no need to have a physical AC
WLDS. Instead of having a physical synchronous generator that is
driven by a variable-speed prime mover, an inverter that captures the
main dynamics of the physical system (the synchronous generator,
the variable-speed prime-mover and its controller), as shown in
Fig. 2(b), can be used to power the motor, following the synchronverter concept of operating inverters to mimic synchronous
generators [33–35]. Ideally, if the motor has the same pole number
as the generator and there was no loss, the torque of the generator
would be the same as the torque of the motor. Hence, the torque of
the motor could be controlled via controlling the torque entering the
synchronous generator.
3. Model of a synchronous generator
Control type
Frequency control
Torque control
Flux control
V/f control
Vector control
Direct torque control
AC WLDS
Direct
Indirect
Indirect
Direct
None
Indirect
Direct
Direct
None
Direct
Direct
Open-loop
The model of synchronous generators is very well documented
in many textbooks and other literature. Here, some changes are
made to the model developed in [34], assuming that the flux
established in the stator by the field windings is sinusoidal
and that the stator winding resistance and inductance are zero.
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The saturation effect of the machine is introduced by limiting the
voltage to the rated value, as shown in Fig. 3. When the field
current If is constant, the generated voltage e ¼ ½ea eb ec T is
The mechanical dynamics of the machine is governed by
~ θ
e ¼ λθ_ sin
where J is the moment of inertia of all parts rotating with the rotor,
Dp is the damping factor, Tm is the mechanical torque applied to
the synchronous generator by the prime mover and Te is the
electromagnetic torque given by
ð1Þ
where θ is the electrical rotor position (hence θ_ is the electrical
angular speed), λ is the amplitude of the mutual flux linkage
~ θ is
between the stator winding and the rotor winding, and sin
the vector ½ sin θ sin ðθ−ð2π=3ÞÞ sin ðθ−ð4π=3ÞÞT : In fact, λ is also
the ratio of the generated voltage (amplitude) to the speed
(angular) and λ ¼ M f I f , where Mf is the maximum mutual
inductance between the stator winding and the rotor winding.
~ θ⟩:
T e ¼ pλ⟨i; sin
ð2Þ
Here, p is the number of pole pairs per phase, i ¼ ½ia ib ic T is the
state current vector and ⟨; ⟩ denotes the conventional inner
~ φ then
product. It is worth noting that if i ¼ I sin
0
~ φ; sin
~ θ⟩ ¼ 3 pλI cos ðθ−φÞ;
T e ¼ pλI 0 ⟨ sin
0
2
Variable
speed
Prime
mover
_
J θ€ ¼ T m −T e −Dp θ;
SG
Load
SM/IM
which is a constant DC value. This is a very important property,
from which a simple control strategy can be designed to regulate
the speed of the AC machine.
Variable
speed
Fixed field
4. Control scheme with a speed sensor
Inverter
4.1. Control structure
Variable
speed
VDC
Prime
mover
SG
SM/IM
Load
Variable
speed
Fixed field
Fig. 2. AC Ward Leonard drive systems. (a) Natural implementation. (b) Proposed
implementation.
Fig. 3. Mathematical model of a synchronous generator.
As explained before, the idea of the AC Ward Leonard drive system
is to power the AC motor with a synchronous generator, driven by a
variable-speed prime mover that is implemented via an inverter.
Hence, the focus of the control system is to control the generator
instead of the motor. The mechanical torque Tm applied to the
generator can be easily generated by a speed controller (governor),
e.g. a PI controller, that compares the actual speed θ_ f with the
reference speed θ_ r . If the motor is synchronous, then the actual speed
can be directly taken from the generator without a speed sensor as the
_ If the motor is inductive, then
motor runs at the synchronous speed θ.
the actual speed (mechanical) can be measured from the motor and it
should be converted to the electrical speed via multiplying it with the
number of pole pairs p. Usually this involves a low-pass filter to reduce
the measurement noise. Another aspect could be easily taken into
account is the voltage drop on the stator winding of the motor,
particularly, when the speed is low. It can be compensated via a feedforward path containing the stator winding resistance Rs from current
i to the generated voltage e. Thus, the resulting complete controller
consists of a synchronous generator model, a speed measurement
unit, a speed controller and a current feed-forward controller, as
shown in Fig. 4. In order to speed up the system response and to
minimise the number of tuning parameters, it is advantageous
to choose the inertia of the generator to be J¼0 (i.e., zero inertia).
Fig. 4. Control structure for AC WLDS with a speed sensor. θ_ r , θ_ f and θ_ are all electrical speed.
Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines,
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Fig. 5. Control structure for AC WLDS without a speed sensor.
This also reduces the system order by one, which helps improve
system stability.
It is worth noting that the λ of the generator is always kept
constant. When the speed of the generator exceeds the rated speed,
the generated voltage is bounded by the rated voltage so that the
insulation of the motor is not damaged (the voltage boost due to the
current feed-forward path should not exceed the margin allowed,
which is normally the case). It should be pointed out that p, λ and Rs
should be chosen the same as those of the motor.
The output u of the controller, which is the sum of the generated
voltage and the compensated voltage drop on the motor stator
winding, can be passed though a three-phase inverter, after appropriate scaling according to the DC-link voltage, to power the AC motor.
The switches in the inverter are operated so that the average values of
the inverter output over a switching period should be equal to u,
which can be achieved by many known pulse-width-modulation
(PWM) techniques. Because of the inherent low-pass filtering effect
of the motor, it may not necessary to connect LC filters to improve the
total harmonic distortion.
4.2. System analysis and selection of parameters
In order to simplify the analysis, assume that the speed feedback
_ i.e., θ_ f ¼ ð1=ðτs þ 1ÞÞθ.
_ The torque Te can be regarded
is taken from θ,
as a disturbance to simplify the analysis. The transfer function from
_ assuming zero load, is then
the speed reference θ_ r to the speed θ,
ðK P s þ K I Þðτs þ 1Þ
:
H θ_ ðsÞ ¼
Dp τs2 þ ðDp þ K P Þs þ K I
For a step change of θ_ r , the speed θ_ jumps by ðK P =Dp Þθ_ r , which is
normally regarded as aggressive, and then settles down. In order to
avoid this, take KP ¼ 0. Hence
H θ_ ðsÞ ¼
K I ðτs þ 1Þ
:
Dp τs2 þ Dp s þ K I
This is a second order system and the poles are
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
−1 7 1−4τK I =Dp
:
s1;2 ¼
2τ
If KI is chosen as
KI ¼
Dp
;
4τ
then the two poles are s1;2 ¼ −1=2τ and
H θ_ ðsÞ ¼
τs þ 1
ð2τs þ 1Þ2
:
This would leave enough margin for the controller to cope with
uncertainties and parameter variations. The transfer function from
Fig. 6. An experimental AC drive.
Table 2
Parameters of the motor.
Parameters
Values
Parameters
Values
Rs
p
Rated voltage (line-to-line)
0:17 Ω
2
30 VRMS
Rated frequency
Rated speed
Rated torque
128 Hz
3621 rpm
0.528 Nm
torque −T e (regarded as a disturbance) to the speed θ_ is
H T ðsÞ ¼
4τsðτs þ 1Þ
Dp ð2τs þ 1Þ2
;
which means that any step change in the (load) torque does not cause
_ If there is a step change Te in the torque,
a static error in the speed θ.
the speed jumps by ð1=Dp ÞT e and then recovers. Hence, in order to
reduce the impact of the load on the speed, Dp should not be too small.
The speed response is directly related to the time constant of
the low-pass filter used in the speed measurement unit. The
smaller the time constant, the faster the system response.
The above analysis is approximate because the loop involving
the motor that affects Te is not fully considered and the speed
feedback is not exactly taken from the motor. However, it does
offer some insightful understanding to the system and, in principle, reflects the system dynamics as can be seen from the
experimental results to be shown in the next section. It is worth
noting that, although the above design leads to a non-oscillatory
response, the closed-loop system in real implementation could be
oscillatory because of the reasons mentioned above.
The four-quadrant operation of AC machines comes automatically with the proposed AC WLDS. There is no need to add any
extra effort or device; the change of the sign of the speed reference
changes the direction of the motor rotation. A positive frequency
Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines,
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Fig. 7. Reversal at high-speed without a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
Fig. 8. Reversal at high-speed with a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
5
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Fig. 9. Reversal at low-speed without a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
(speed) reference leads to a positive speed and a negative
frequency (speed) reference leads to a negative speed. A change
of the frequency from negative to positive, or from positive to
negative, leads to the reversal of the motor rotation.
In summary, the speed response is determined by the time
constant τ of the speed measurement unit and the torque response
is determined by Dp. The parameters of the controller can be
chosen as follows:
(1) Choose p, λ and Rs the same as, or close to, those of the motor
and choose J ¼0.
(2) Determine the time constant τ to meet the requirement of the
speed response (also the requirement of the measurement
noise) and Dp to meet the requirement of the torque response.
(3) Choose KP ¼0 and K I ¼ Dp =4τ.
5. Control scheme without a speed sensor
5.1. Control structure
If the motor is synchronous, then there is no need to have a
speed sensor because the speed of synchronous motor converges
to the speed θ_ of the generator, which is internally available in the
controller for feedback. Even for induction motors, θ_ is the
synchronous speed and can be used to reflect the actual motor
speed (the difference is the slip). In this case, Dp can be chosen as 0.
The slip of an induction motor can be compensated to some extent as
well. It is well known that the speed drop θ_ s is in proportion to the
torque over a wide speed range, i.e.
θ_ s ¼ K T T e :
This can be obtained from the torque–speed characteristics of the
motor. For synchronous motors, KT ¼ 0. This load (torque) effect can be
compensated via adding KTTe to the speed reference θ_ r . The resulting
speed-sensorless control scheme for AC machines is shown in Fig. 5. It
consists of the model of a synchronous generator, a speed controller, a
load-effect compensator and a current feed-forward controller, which
is a feed-forward path containing the stator winding resistance Rs
from current i to the generated voltage e. This scheme is applicable for
both synchronous (with KT ¼ 0) and induction motors. For synchronous motors, it provides zero-static-error speed control; for induction
motors, there is normally a small static error depending on the
compensation accuracy of the load (torque) effect. The accuracy can
be improved via using a two-dimensional table to determine KT
according to the torque–speed characteristics of the motor, taking into
account both the synchronous speed and the torque.
5.2. System analysis and selection of parameters
In order to simplify the exposition below, consider the case
when the motor is synchronous, i.e., KT ¼0. The transfer function
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Fig. 10. Reversal at low-speed with a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
_ assuming zero load, is
from the speed reference θ_ r to the speed θ,
H θ_ ðsÞ ¼
KPs þ KI
Js2 þ K P s þ K I
and the transfer function from torque −T e (regarded as a disturbance) to the speed θ_ is
H T ðsÞ ¼
s
Js2 þ K P s þ K I
:
The system is of second order and the poles are
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
−1 7 1−4K I J=K 2P
s1;2 ¼
:
2J=K P
Increasing KI tends to make the system response oscillatory. Define
τ ¼ J=K P , i.e., K P ¼ J=τ. If KI is chosen as
KI ¼
KP
J
¼ 2;
4τ
4τ
then the two poles are s1;2 ¼ −1=2τ. Under this set of parameters
H θ_ ðsÞ ¼
H T ðsÞ ¼
4τs þ 1
ð2τs þ 1Þ2
;
4τ2 s
Jð2τs þ 1Þ2
:
The speed response can be tuned by changing τ and the torque
response can be tuned by changing J.
In summary, the control parameters can be chosen as follows:
(1) Choose p, λ and Rs the same as, or close to, those of the motor
and choose Dp ¼0.
(2) Determine the time constant τ to meet the requirement of the
speed response and J to meet the requirement of the torque
response.
(3) Choose K P ¼ J=τ and K I ¼ K P =4τ.
(4) Choose KT according to the torque–speed characteristics of the
motor (KT ¼0 for synchronous motors).
6. Experimental results
The proposed AC WLDS was verified on an experimental
system, as shown in Fig. 6. The system consists of an inverter, a
board consisting of current sensors, a dSPACE DS1104 R&D controller board equipped with ControlDesk software, and an induction motor. The motor parameters are given in Table 2. According
to the parameters, it can be found that λ ¼ 0:0305 and KT ¼86.82.
The inverter has the capability to generate PWM voltages from a
constant 42 V DC voltage source and the motor is equipped with a
bi-directional encoder with 1000 lines for speed measurement.
6.1. Case 1: with a speed sensor for feedback
The control parameters were chosen as τ ¼ 0:1 s and Dp ¼0.08,
which results in KI ¼0.2. Many experiments were carried out to
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Fig. 11. Reversal at an extremely low speed without a load. (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
Fig. 12. Reversal at high-speed without a load (without a speed sensor). (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
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test the performance of the system and some of the results are
shown here.
that the sequence of the three phase currents/voltages changed at
around t¼0.8 s.
6.1.1. Reversal at high-speed without a load
The reference speed was changed from −3600 rpm to 3600 rpm
at around t¼0.6 s. The responses (speed, torque, current and
voltage) are shown in Fig. 7. The motor quickly reversed from
−3600 rpm to 3600 rpm and settled down in about 1.2 s. There
was a very short period of over-current around 70%; the voltage
dropped when the reversal was started and then gradually built up
after the reversal. The phase sequence of the currents was changed
at around 0.85 s, which corresponds to the change of the rotating
direction of the magnetic field, to enable the reversal.
6.1.4. Reversal at low-speed with a load
The reference speed was changed from −300 rpm to 300 rpm at
around t ¼2.2 s. The responses are shown in Fig. 10. The motor
quickly reversed from −300 rpm to 300 rpm in about 2 s. There
was a noticeable stop in the middle of the reversal process. The
over current was about 50%.
6.1.2. Reversal at high-speed with a load
The reference speed was changed from −1800 rpm to 1800 rpm
at around t ¼1 s. The responses are shown in Fig. 8. The motor
quickly reversed from −1800 rpm to 1800 rpm in about 1.5 s,
which is slightly longer than the case without a load. There was
about 11% overshoot in the speed and the over current increased
to about 150%.
6.1.3. Reversal at low-speed without a load
The reference speed was changed from −150 rpm to 150 rpm at
around t ¼0.6 s. The responses are shown in Fig. 9. It took about
1.5 s to complete the reversal and settle down. The over-current
was only about 15% and the speed overshoot was about 6%. Note
6.1.5. Reversal at an extremely low speed without a load
The reference speed was changed from −4.5 rpm to 4.5 rpm at
around t¼ 5 s. The responses are shown in Fig. 11. It took about 15 s
to complete the reversal and settle down due to the extremely low
speed. There were some ripples in the measured speed, which was
owing to the error in the measurement unit (the motor actually
rotated smoothly). The motor speed dropped to 0 quickly but
remained standstill for about 12 s, during which the torque increased
almost linearly, before the torque was accumulated high enough to
start the motor. Once the current gradually increased to a level that is
enough to generate the required torque, the motor started rotating.
6.2. Case 2: without a speed sensor for feedback
The control parameters were chosen as τ ¼ 0:1 s and J¼ 0.08,
which results in KP ¼ 0.8 and KI ¼2. Many experiments were
carried out and some of the results are shown here.
Fig. 13. Reversal at high-speed with a load (without a speed sensor). (a) Speed. (b) Torque of the generator. (c) Current. (d) Voltage.
Please cite this article as: Q.-C. Zhong, , AC Ward Leonard drive systems: Revisiting the four-quadrant operation of AC machines,
European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i
10
Q.-C. Zhong / European Journal of Control ∎ (∎∎∎∎) ∎∎∎–∎∎∎
6.2.1. Reversal at high-speed without a load
The reference speed was changed from −3600 rpm to 3600 rpm
at around 0.7 s. The responses are shown in Fig. 12. The motor
quickly reversed from −3600 rpm to 3600 rpm in about 1.3 s.
There was a very short period of over 100% over-current and the
speed overshoot was about 14%. The static error was almost zero.
6.2.2. Reversal at high-speed with a load
The reference speed was changed from −1800 rpm to 1800 rpm
at around t ¼0.4 s. The responses are shown in Fig. 13. It took
about 1.6 s to complete the reversal and there was about 200%
over-current.
7. Conclusions and discussions
The concept of the conventional DC Ward Leonard drive
systems is extended to AC machines. Instead of implementing it
physically, it is implemented mathematically and an inverter is
controlled to replicate the dynamics of the physical set of a
variable-speed prime mover and a synchronous generator. This
leads to the smooth operation of AC machines in four quadrants.
The change of the sign of the frequency set-point leads to the
change of the phase sequence of the current and, furthermore, the
change of the rotational direction. Two control schemes, one with
a speed sensor and the other without a speed sensor, are proposed
for the system, which is then validated with the experimental
results. The main purpose of this paper is to propose and validate
the concept. Some further studies, e.g. the comparison with other
approaches, detailed analysis of the complete system and the
application of the strategy, are left for future research.
While it is vital for some applications to achieve the fastest
possible torque response, this may have been aggressively pushed
for some applications where the response speed is not critical. For
the formal case, it is often achieved via controlling the current
provided by the inverter, but for the latter case, the speed
regulation can be achieved by controlling the voltage provided
by the inverter. In other words, AC drives can be classified as
current-controlled AC drives and voltage-controlled AC drives.
Vector control and direct torque control belong to the currentcontrolled AC drives while V/f control and the proposed AC WLDS
belong to the voltage-controlled AC drives. Similarly to AC dives,
the inverters in smart grid integration can be current-controlled or
voltage-controlled; see [33] for detailed and systematic treatment
of controlling inverters for renewable energy and smart grid
integration.
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European Journal of Control (2013), http://dx.doi.org/10.1016/j.ejcon.2013.05.013i