energies
Article
A Proportional Resonant Control Strategy for
Efficiency Improvement in Extended Range
Electric Vehicles
Xiaoyuan Wang 1 , Haiying Lv 1 , Qiang Sun 2, *, Yanqing Mi 1 and Peng Gao 1, *
1
2
*
Institute of Electrical Engineering & Automation, Tianjin University, No. 92 Weijin Road, Tianjin 300072,
China; [email protected] (X.W.); [email protected] (H.L.); [email protected] (Y.M.)
College of Engineering and Technology, Tianjin Agricultural University, Tianjin 300384, China
Correspondence: [email protected] (Q.S.); [email protected] (P.G.); Tel.: +86-22-27406705 (P.G.)
Academic Editor: K.T. Chau
Received: 14 November 2016; Accepted: 22 January 2017; Published: 10 February 2017
Abstract: The key to control the range extender generation system is to improve the efficiency
and reduce the emissions of the electric vehicle (EV). In this paper, based on the purpose of
efficiency optimization, both engine and generator are matched to get a public high efficiency
region, and a partial power following control strategy was presented. The engine speed is constant in
the defined power range, so the output power regulation of the range extender is only realized by
the adjustment of the torque of the generator. Engine speed and generator torque were decoupled.
An improved proportional resonant (PR) controller is adopted to achieve fast output power regulation.
In order to ensure the response characteristics of the control system and to improve the robustness,
the impacts on system’s characteristics and stability caused by PR controller and parameters in the
inner-current loop were analyzed via frequency response characteristics. A pre-Tustin with deviation
compensation is proposed for PR controller’s discretization. A stable and robust power following
control method is obtained for the range extender control system. Finally, simulation and experiment
of the proposed control strategy illustrated its feasibility and correctness.
Keywords: electric vehicle; range extender; efficiency improvement; pulse width modulation (PWM)
voltage source converter; proportional resonant controller; stability
1. Introduction
Due to the lower combustion efficiency of fuel and stricter regulations on the emissions of
traditional vehicles, the automotive industry is actively developing environmentally friendly and
green energy vehicles. Electric vehicles (EVs) are considered to be a green solution, due to their zero
emissions advantages. Due to the restrictions of the current battery technology, the driving range
is limited by their one-time charge cycle. In order to overcome the disadvantages of the pure EV,
Extended Range Electric Vehicles (EREVs) were developed as a feasible and low cost solution [1].
The block diagram for the architecture of the widely used EREV is shown in Figure 1.
The range extender (RE) is composed of an internal combustion engine, a permanent magnet
synchronous generator (PMSG) and a pulse width modulation (PWM) voltage source converter
(VSC). The propulsion of the EREV is provided only by the electric motor, so the RE is decoupled from
the wheels of the EV, one benefit of this series parallel electric vehicle architecture is lower driving
noise, and another is the higher efficiency due to the fact the RE is operating continuously in its
high efficiency region. Compared with conventional hybrid electric vehicles (HEVs), EREVs have
advantages in fuel economy, engine efficiency and emissions [2].
Energies 2017, 10, 204; doi:10.3390/en10020204
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Battery
Battery
batbat11
e  gen
eng,,
PPeng
gen
e
ICE
ICE
eng
eng
G
G
batbat22
con
con
invinv
PWM
PWM
Converter
Converter
Inverter
Inverter
Electrical connection
Electrical connection
Mechanical connection
Mechanical connection
mot
mot
M
M
Range Extender(RE)
Range Extender(RE)
Figure 1. Block diagram for the architecture of an EREV.
Figure
Figure 1.
1. Block
Block diagram
diagram for
for the
the architecture
architecture of
of an
an EREV.
EREV.
The key to control the RE generation system is to improve its efficiency and to reduce the
The key to control the RE generation system is to improve its efficiency and to reduce the
The key
control
thepresent,
RE generation
system
is to improve
efficiency
to reduce(CS)
the emissions
emissions
oftothe
EV. At
the Charge
Depleting
(CD)itsand
Chargeand
Sustaining
mode are
emissions of the EV. At present, the Charge Depleting (CD) and Charge Sustaining (CS) mode are
of
the
EV.
At
present,
the
Charge
Depleting
(CD)
and
Charge
Sustaining
(CS)
mode
are
mainly
in
mainly used in EREV applications [2]. The vehicle operates in CD mode while the state ofused
charge
mainly used in EREV applications [2]. The vehicle operates in CD mode while the state of charge
EREV
[2]. The
vehiclethan
operates
in CD mode
while the
statethe
of charge
of thetobattery
(SoC) applications
of the battery
is greater
a designed
threshold.
Once
battery(SoC)
depletes
some
(SoC) of the battery is greater than a designed threshold. Once the battery depletes to some
ispredefined
greater than
a designed
the battery
depletes
to operates
some predefined
threshold,
the two
RE
threshold,
the threshold.
RE will be Once
switched
on and the
vehicle
in CS mode.
There are
predefined threshold, the RE will be switched on and the vehicle operates in CS mode. There are two
will
be
switched
on
and
the
vehicle
operates
in
CS
mode.
There
are
two
operating
strategies
in
CS
operating strategies in CS mode: one is the constant power control, which means that RE generates
operating strategies in CS mode: one is the constant power control, which means that RE generates
mode:
one is therated
constant
power
control,
which can
means
RE generates
the efficient
maximum
ratedhowever
power,
the maximum
power,
so that
the system
be that
operated
at the most
point,
the maximum rated power, so that the system can be operated at the most efficient point, however
so
that
the
system
can
be
operated
at
the
most
efficient
point,
however
the
battery
will
be
charged
and
the battery will be charged and discharged frequently, which reduces the service life of the battery
as
the battery will be charged and discharged frequently, which reduces the service life of the battery as
discharged
frequently,
which
reduces
the
service
life
of
the
battery
as
a
drawback.
The
other
strategy
a drawback. The other strategy is the power following control, under which the output power of the
a drawback. The other strategy is the power following control, under which the output power of the
isRE
theispower
following
control,
which
the demands.
output power
the RE is of
changed
according
the
changed
according
to theunder
driving
power
The of
advantage
this mode
is the to
minor
RE is changed according to the driving power demands. The advantage of this mode is the minor
driving
power
demands.
The
advantage
of
this
mode
is
the
minor
fluctuation
of
the
battery
SoC,
fluctuation of the battery SoC, so the battery lifetime will be extended. Its disadvantage is that the
fluctuation of the battery SoC, so the battery lifetime will be extended. Its disadvantage is that the
so
the battery
lifetime
will be extended.
disadvantage
is that the
efficiency
of the RE
generation
efficiency
of the
RE generation
system isItslow
when the demand
power
is relatively
small,
because
efficiency of the RE generation system is low when the demand power is relatively small, because
system
low when
the demand
power
relativelyregion.
small, In
because
thecompare
RE cannot
maintained in
the RE is
cannot
be maintained
in the
highisefficiency
order to
thebe
characteristics
of
the RE cannot be maintained in the high efficiency region. In order to compare the characteristics of
the
high
efficiency
region.
In
order
to
compare
the
characteristics
of
the
two
operating
strategies,
the two operating strategies, the performance of
EREV is analyzed over repeated new European
the two operating strategies, the performance of the EREV is analyzed over repeated new European
the
performance
of the EREV
is analyzed
repeatedSoC
newvariation
Europeanfor
driving
cycle (NEDC).
Figure
2
driving
cycle (NEDC).
Figure
2 shows over
the battery
the different
strategies.
The
driving cycle (NEDC). Figure 2 shows the battery SoC variation for the different strategies. The
shows
the
battery
SoC
variation
for
the
different
strategies.
The
range
RE
is
switched
on
when
the
SoC
range RE is switched on when the SoC depletes to 22%. In Figure 2a, the blue line shows the SoC
range RE is switched on when the SoC depletes to 22%. In Figure 2a, the blue line shows the SoC
depletes
22%.
Figure power
2a, the control
blue line
shows and
the SoC
variation
for the
powersignal
control
variationtofor
the In
constant
strategy
the red
line shows
theconstant
switch on/off
of
variation for the constant power control strategy and the red line shows the switch on/off signal of
strategy
and
line
shows
thewas
switch
on/off
signaland
of the
can befluctuated
seen that cyclically.
the RE was
the RE. It
canthe
bered
seen
that
the RE
started
six times
theRE.
SoCItcurve
In
the RE. It can be seen that the RE was started six times and the SoC curve fluctuated cyclically. In
started
andline
the shows
SoC curve
fluctuated
cyclically.
Figure
2b, the blue
linestrategy
shows the
Figure six
2b, times
the blue
the SoC
variation
for the In
power
following
control
andSoC
the
Figure 2b, the blue line shows the SoC variation for the power following control strategy and the
variation
for thethe
power
following
controlItstrategy
and
thethe
redRE
line
shows the switch
on/off
red line shows
switch
on/off signal.
illustrates
that
continuously
operates
in CSsignal.
mode
red line shows the switch on/off signal. It illustrates that the RE continuously operates in CS mode
Itand
illustrates
the RE continuously
operates
the SoCthat
fluctuates
within a small
range. in CS mode and the SoC fluctuates within a small range.
and the SoC fluctuates within a small range.
Threshold
Threshold
switch on/off
switch on/off
Range extender
Range extender
on/off signal
on/off signal
SOC%
SOC%
80
80
60
60
40
40
Threshold
Threshold
switch on/off
switch on/off
Range extender
Range extender
on/off signal
on/off signal
80
80
60
60
40
40
20
20
0
0
100
100
SOC%
SOC%
100
100
20
20
50
50
100
t/min 100
t/min
(a)
(a)
150
150
0
0
50
50
100
t/min 100
t/min
150
150
(b)
(b)
Figure 2. EREV control methods in CD-CS operation mode (a) Constant power control strategy; (b)
EREVcontrol
controlmethods
methodsininCD-CS
CD-CS
operation
mode
Constant
power
control
strategy;
Figure 2. EREV
operation
mode
(a) (a)
Constant
power
control
strategy;
(b)
Power following control strategy.
(b)
Power
following
control
strategy.
Power following control strategy.
In this paper, the high efficiency operating region is determined by the engine fuel consumption
In this paper, the high efficiency operating region is determined by the engine fuel consumption
curves and the generator efficiency map. A power following control strategy is adopted in the high
curves and the generator efficiency map. A power following control strategy is adopted in the high
efficiency region; constant power control is adopted in the external efficiency region. This strategy
efficiency region; constant power control is adopted in the external efficiency region. This strategy
Energies 2017, 10, 204
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In this paper, the high efficiency operating region is determined by the engine fuel consumption
curves and the generator efficiency map. A power following control strategy is adopted in the high
efficiency region; constant power control is adopted in the external efficiency region. This strategy
ensures that the engine and the generator operate in the high efficiency region together; at the same
time it can also reduce the SoC fluctuations, preventing the battery from charging and discharging
frequently and thus prolonging the battery lifetime.
There are two main structures in RE generation systems: one consists of the electrical excitation
synchronous motor and uncontrolled rectifier, whose output power can be regulated by adjusting the
excitation current of generator. Although this structure is a low cost solution, the electrical excitation
machine does not meet the requirements of high power density in EV applications [3–6]. The other
form is composed of a PMSG and PWM rectifier, which can control both the generator operating in
motor state and the generator state [7–9]. This form features a simple structure, high power density
and synchronous control of engine speed and motor torque, so it’s an ideal solution. At present,
because of simple control and good stability of PI controllers, they is widely used in engine and
synchronous motor control. In [10,11], a PI predictive control method was adopted to achieve the
output voltage and power adjustment. As the current loop of PMSG control with coupled dq current,
it had to add a compensation to improve the dynamic performance, which leads control structure
complexity and a lack of robustness. Some references also designed robust, for instance, in [8], a global
efficiency optimization of sliding mode control is proposed, in which two chattering-free sliding mode
controllers are utilized to control engine speed and PMSG torque; in [12,13], adopts a fuzzy logic
control; in [14–16] a Dynamic Programming (DP) technology is used to obtain an optimal solution.
However, these control strategies such as DP algorithm are not suitable for EREV real-time control;
because they are based on masses of driving cycle and a lot of data processing.
Mechanically coupled connection between engine and generator determines that the output
power is related to engine speed and generator torque. Therefore, to design a control strategy which
can decouple the engine and generator control and optimize power generation efficiency is the key
to get an efficient RE generation system. In this paper, a fast response and high robustness control
method is presented based on decoupling, simplifying algorithm and improving RE efficiency. The PR
controller is introduced into RE power generation control. PR could simplify coordinate transformation
and replace feed-forward compensation. The impacts on system characteristics and stability caused by
PR controller and parameters in generator control were analyzed via frequency response characteristics,
and the PR controller is discretized by pre-Tustin transform to obtain a stable and high robustness
power following control strategy. Finally, simulation and experiment of the proposed control strategy
illustrated its well dynamic response and steady state performance.
2. EREV Efficiency Improvement Design
The proposed RE generation system is design to satisfy with the requirement of the city’s compact
EV, the requirement and performance of the EREV is shown in Table 1. A 17 kW engine model and a
13 kW PMSG are selected [17].
Table 1. Required EREV performance characteristics.
Symbol
Description
Values
Reference
MV
V1
t
V2
V3
α
fr
CD
Af
Total mass
Maximum velocity at ER switch on
Acceleration time (0–50 km/h)
Maximum velocity at 4% slope
Maximum velocity at 12% slope
Gradeability
Rolling resistance coefficient
Aerodynamic drag coefficient
Front area of the vehicle
≤1400 kg
≥80 km/h
≤7 s
≥70 km/h
≥40 km/h
≥20%
0.013
0.4
1.96 m2
GB/T 19596
GB/T28382 4.5.1
GB/T 28382 4.5.2
GB/T28382 4.5.3
GB/T28382 4.5.3
GB/T 28382 4.5.3
Asphalt pavement
Energies 2017, 10, 204
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The mechanically decoupled structure between RE and the wheel of EV leads to a strong point
Energies
10, 204 characteristics of the RE are not related to vehicle traction performance,
4 ofand
16 the
whereby
the2017,
output
Energies 2017, 10, 204
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output power is only needed to meet the driving requirements. Therefore, one of the main objectives
is to keep the RE operating in the high efficiency region. Firstly, both the engine and the generator
is to keep
the RE
operating
in the
high efficiency
region.
Firstly,both
boththe
the
engine
the
generator
is to keep
RE operating
in the
efficiency
region. region.
Firstly,
engine
andand
the
generator
should
be the
matched
to achieve
thishigh
common
operating
The PMSG
efficiency
map
of the
should
be
matched
to
achieve
this
common
operating
region.
The
PMSG
efficiency
map
of
the
should be
matched
to achieve
this common
region.
PMSG efficiency
map85%
of selected
the
selected
generator
is shown
in Figure
3, where operating
it can be seen
that The
the efficiency
is more than
in
generator
is
shown
in
Figure
3,
where
it
can
be
seen
that
the
efficiency
is
more
than
85%
in
almost
selected
generator
is
shown
in
Figure
3,
where
it
can
be
seen
that
the
efficiency
is
more
than
85%
in 70%
almost 70% of the operating region. In the designed RE system, this region is defined as a high
almost
70%
of
the
operating
region.
In
the
designed
RE
system,
this
region
is
defined
as
a
high
of theefficiency
operating
region.
In
the
designed
RE
system,
this
region
is
defined
as
a
high
efficiency
region
region where the speed is limited to 2000–4000 rpm, and the torque is limited to
efficiency
where
speed isrpm,
limited
rpm, and
torque
where15–40
the speed
is limited
to the
2000–4000
and to
the2000–4000
torque is limited
to the
15–40
N·m.is limited to
N·m.region
15–40 N·m.
95
90
95
85
90
80
85
79
80
78
79
77
78
76
77
75
76
74
75
73
74
72
73
71
72
70
71
60
70
0
6000 60
6000 0
Torque/N.m
Torque/N.m
40
40
30
30
20
20
10
10
0
0
3000
4500
Speed/rpm
3000
4500
Speed/rpm
Figure 3. Permanent magnet synchronous generator efficiency map.
Figure
3. Permanent
magnet
generatorefficiency
efficiency
map.
Figure
3. Permanent
magnetsynchronous
synchronous generator
map.
1500
1500
Both the efficiency and emissions of the engine are nonlinear, so online efficiency optimization
Torque/N.m
Torque/N.m
Both thewould
efficiency
emissions
the engine
areimportant
nonlinear,tosodefine
efficiency
optimization
calculations
take
aemissions
lot
of time.
Therefore
it are
is
an
optimum
operating
Both
the efficiency
andand
ofof
the
engine
nonlinear, soonline
online
efficiency
optimization
calculations
would
take
a
lot
of
time.
Therefore
it
is
important
to
define
an
optimum
operating
region.
The
efficiency
map
of
the
selected
engine
is
shown
in
Figure
4.
The
engine
speed
is
between
calculations would take a lot of time. Therefore it is important to define an optimum operating
region.
region.
The
efficiency
map
of the
selected
engine
is
shown
in 25
Figure
4.
The45engine
speed
is between
2500
rpm
and
4000
rpm,
while
the
engine
torque
is
between
Nm
and
Nm,
the
region
that
is rpm
The efficiency
map
of
the
selected
engine
is
shown
in
Figure
4.
The
engine
speed
is
between
2500
2500 rpm
rpm, while
the engine
torque operating
is betweenarea
25 Nm
and 45narrow
Nm, the
region that
is
defined
asand
the 4000
fuel economy
region.
The engine
is relative
compared
with
and 4000
rpm,
while
theeconomy
engine torque
isThe
between
25
N℘m and
45is N
℘m, the
regioncompared
that is defined
as
defined
as
the
fuel
region.
engine
operating
area
relative
narrow
with
PMSG [18].
the fuel
economy
PMSG
[18]. region. The engine operating area is relative narrow compared with PMSG [18].
50
50
45
45
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
51492
1492
300
300
290
290
300
300 280
280
310
310
340
340
490
490
12
10 12
8 10
380 8
380
590
590
18
16
14 16 18
14
380
380
420
420
Power/ kW
Fuel
consumption
g/ kWh
Power/
kW
Fuel consumption g/ kWh
2042 2592
2042 2592
3142 3692 4242 4792 5303
3142
3692 4242 4792 5303
Speed/rpm
Speed/rpm
Figure 4. Engine efficiency map.
Figure 4. Engine efficiency map.
Figure 4. Engine efficiency map.
Considering the advantages and disadvantages of constant power control and power following
Considering
the advantages
disadvantages
of constant
power
control
and powerWhen
following
control,
a partial power
followingand
control
strategy within
efficiency
region
is proposed.
the
control,
a
partial
power
following
control
strategy
within
efficiency
region
is
proposed.
When
the
Considering
the
advantages
and
disadvantages
of
constant
power
control
and
power
following
demanded power is lower than Pthreshold, a constant power control strategy is adopted. The strategy
demanded
power
is
lower
than
P
threshold, a constant power control strategy is adopted. The strategy
control,
a partial
following
control
within
efficiency
regionthe
is demanded
proposed. power
When the
splits
the RE power
power output
between
the strategy
driving motor
and
battery. When
splits is
the
RE power
output
the
driving
motor
and
When
demanded
power
value
between
Pthreshold
and Pbetween
max
, a power
following
control
is battery.
adopted.
Pthresholdthe
is the threshold
demanded
power
is lower
than
P
, a constant
power
control
strategy
ishere
adopted.
The
strategy
threshold
value that
is between
Pthreshold
and
, a powerinfollowing
control ismode.
adopted.
here
is the threshold
determines
the
RE Pismax
operating
power
following
The PPthreshold
threshold
is determined
usingvalue
splitsvalue
the RE power
output
between
the driving
motor
and battery. When
the demanded
power
value
that determines
the RE is operating
in power
following mode. The Pthreshold is determined using
the
optimization
method
the fuel
consumption.
is between
Pthreshold and
Pmax ,toa minimize
power following
control is adopted. Pthreshold here is the threshold value
the optimization
method
to
minimize
the
fuel
consumption.
The fuel consumption rate can be described as the function of the engine power and engine
that determines
RE is operating
in power
following
The
is determined
using the
threshold
The fuelthe
consumption
rate can
be described
as themode.
function
of Pthe
engine
power and engine
speed:
optimization
method
to
minimize
the
fuel
consumption.
speed:
Energies 2017, 10, 204
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Energies
2017,
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204
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The
fuel
rate can be described as the function of the engine power and engine speed:
= ff PPeng (tt), ,ωe (t)t  
mme e(tt) 
e
 eng

(1)
(1)
where m
consumption, P
(t) is
is the
the engine
engine power, ωee(t)
(t) is
is the
the engine
engine speed.
speed. The
The relation
mee(t) is the fuel consumption,
Peng
eng(t)
(t) and
and P
Peng
(t)atat defined
defined ωωe eisisshown
shown in
in Figure
Figure 5.
5. Although
Although the
the engine
engine has
has better fuel
eng(t)
between m
mee(t)
economy at a speed of 2000
rpm,
the
maximum
output
power
is
limited.
Considering
the engine
2000 rpm, the maximum output power is limited.
output power range and economic fuel consumption, a speed of 3000 rpm is defined as the constant
speed for the power following control.
Fuel consumption rate/g/kwh
700
600
2000 rpm
3000 rpm
2500 rpm
3500 rpm
500
4000 rpm
400
300
15
200
4
6
8
10
Power/kW
12
14
16
Figure
Figure 5.
5. Fuel
Fuel consumption
consumption rate
rate of
of the
the engine
engine at
at defined
defined engine
engine speeds.
speeds.
The vehicle demand power can be expressed as following Equation (2):
The vehicle demand power can be expressed as following Equation (2):
Preq (t )   (t ) Fd (t )
Preq (t) = υ(t) Fd (t)
The driving force Fd(t) can be expressed as Equation (3):
The driving force Fd (t) can be
F expressed
(t )  F (t )as Equation
F (t )  F(3):
(t )  F (t )
d
f
w
i
j
(2)
(2)
(3)
Fd (rolling
t) = Ffresistance;
(t) + Fw (t)F+
Fi (ist)air
+ resistance;
Fj (t)
(3)
where υ(t) is vehicle speed; Ff(t) is
w(t)
Fi(t) is climbing resistance
and Fj(t) is accelerating resistance. The total driving force can be calculated as follows:
where υ(t) is vehicle speed; Ff (t) is rolling resistance; Fw (t) is air resistance; Fi (t) is climbing resistance
1
d (t )
2
and Fj (t) is accelerating
calculated
Fd (t ) resistance.
MV gf r cosThe
 total adriving
CD Af force
(t ) can
MVbe
g sin
  MVas
 follows:
(4)
2
dt
1
dυ(t)
2
where g is gravity F
acceleration,
is air
density
isVthe
rotational
f racos
α +mass
ρa C
t) +δM
g sin
α + MV δinertia factor. According
(4)
D A f υ (and
d ( t ) = MV g ρ
2
dt
to the path of power flow, the demand power Preq at the t moment can be expressed as follows:
where g is gravity acceleration, ρa is air mass density and δ is the rotational inertia factor. According to
Peng (t ),
Preq  Pthreshold

a0a2power
the path of power flow,
Preq at the t moment can
be expressed as follows:
P the
(t )demand

(5)

(
a0a2 Peng (t )  a0a1a2 Peng (t ), Preq  Pthreshold
a a2 Peng (t),
Preq > Pthreshold
Preqpower
(t) = ratio0 of
where  is the driving
RE
output
power,

is
charging
power
ratio, and there is  + (5)
=
a0 a2 λPeng (t) + a0 a1 a2 ξPeng (t), Preq ≤
Pthreshold
1. The equivalent efficiency factor can be defined as follows:
where λ is the driving power ratio of RE output power, ξ is charging power ratio, and there is λ + ξ = 1.
a0  eng gen con
The equivalent efficiency factor can be defined
as follows:

a


(6)
bat1  bat 2
  1


ηeng × ηgen × ηcon
 a0a=
 2  inv mot , Pthreshold
(6)
a1 = ηbat1 × ηbat2

the
a2 engine;
= ηinv ×ηηgenmot
, Pthreshold efficiency; ηcon, PWM VSC efficiency;
where ηeng, transmission efficiency of
, generator
ηbat1, charge efficiency of the battery; ηbat2, discharge efficiency of the battery; ηinv, efficiency of the
motor controller; ηmot, drive motor efficiency.
The instantaneous fuel consumption rate me(t) is not suitable for representing how economically
the engine fuel is utilized. When the Preq is lower than Pthreshold, part of the engine power is transmitted
req
Energies 2017, 10, 204
6 of 16
where η eng , transmission efficiency of the engine; η gen , generator efficiency; η con , PWM VSC efficiency;
η bat1 , charge efficiency of the battery; η bat2 , discharge efficiency of the battery; η inv , efficiency of the
motor controller; η mot , drive motor efficiency.
Energies 2017, 10, 204
6 of 16
The instantaneous fuel consumption rate me (t) is not suitable for representing how economically
the engine fuel is utilized. When the Preq is lower than Pthreshold , part of the engine power is transmitted
to charge the battery and will be used by the driving motor in the future. Considering the charge and
to charge the battery and will be used by the driving motor in the future. Considering the charge and
discharge consumption of the battery, the equivalent fuel consumption can be expressed as follows:
discharge consumption of the battery, the equivalent fuel consumption can be expressed as follows:
R0t me  t  dt
FC 
0 me (t)dt
   bat1bat 2invmot   
FC = enggencon invmot
ηeng ηgen ηcon ηinv ηmot · λ + ηbat1 ηbat2 ηinv ηmot · ξ 
(7)
(7)
 R tt f Peng  t  , e dt  !
 min  00 f  Peng (t), ω e dt  FCminFC=minmin
a0aa0a2 (2 (1
 a )  a a a  
  1 − a1 1 )λ +0 a10 a2 1 a2
(8)
(8)
t


where
which can
can be
be calculated
calculated on
on aa given
given driving
driving cycle.
cycle.
where λ𝜆̅ is
is an
an equivalent
equivalent driving
driving power
power ratio
ratio which
When
the
range
[4,13],
then
corresponding
parameter
λ can
be calculated
in
When P
Pthreshold
threshold isis
setsetinin
the
range
[4,13],
then
thethe
corresponding
parameter
𝜆̅ can
be calculated
in the
the
range
under
a given
driving
The value
ofobtained
λ is obtained
through
data lookup
range
(0.9,(0.9,
0.6) 0.6)
under
a given
driving
cycle.cycle.
The value
of 𝜆̅ is
through
a dataalookup
table.
table.
The corresponding
fuel consumption
can
be obtained
a different
value
Pthreshold
set.
The corresponding
fuel consumption
can be
obtained
whenwhen
a different
value
of Pof
threshold
is set.isThe
The
minimum
consumption
is achieved
when
Pthreshold
is closed
to 8 kW.
minimum
fuel fuel
consumption
is achieved
when
Pthreshold
is closed
to 8 kW.
The flow chart of the control is shown in Figure 6.
The
RE
is
switched
on when the battery SoC
6.
falls to
22%.
The
controller
determines
whether
to
carry
out
power
following
control
according
to the
to 22%. The controller determines whether to carry out power following
control
according
to
power
demand
of theofEV.
generation
systemsystem
constantly
outputsoutputs
8 kW when
thewhen
power
the power
demand
theThe
EV.RE
The
RE generation
constantly
8 kW
thedemand
power
is
lower than
8 kW;than
when
is greater
than
kW, thethan
power
following
control
strategy
demand
is lower
8 the
kW;power
whendemand
the power
demand
is 8greater
8 kW,
the power
following
is
adopted
to ensure
minimum
fuel consumption.
control
strategy
is adopted
to ensure
minimum fuel consumption.
Start
CS operating mode
ER switch on
SOC < 22%?
YES
NO
CD operating
mode
Preq > Pthreshold ?
NO
YES
Power following
Pthreshold < Preq ≤ 13kW
n=3000 rpm
25Nm < T ≤ 42Nm
NO
Constant
power output
Pout = Pthreshold
SOC > 30%?
YES
switch off
Figure
Figure 6.
6. State
State chart
chart of
of the
the partial
partial power
power following
following strategy.
strategy.
3. Development
of the
the Control
Control Strategy
Strategy
3.
Development of
3.1. Modeling
of the
the Generator
Generator Control
Control
3.1.
Modeling of
The optimal
optimal operating
operating region
region is
is defined
defined in
in the
the last
last section.
section. The
engine speed
speed receives
receives aa fixed
fixed
The
The engine
speed
reference
and
the
generator
torque
is
regulated
with
the
power
demand.
The
output
power
speed reference and the generator torque is regulated with the power demand. The output power
regulation of
ofthe
theRE
RE
realized
by engine
speed
and generator
control.
The engine
speed
regulation
is is
realized
by engine
speed
and generator
torquetorque
control.
The engine
speed control
control
is realized
by adjusting
the electronic
throttle,
using anPR
improved
PRtocontroller
to
is
realized
by adjusting
the electronic
throttle, and
using and
an improved
controller
achieve fast
achieve
fast
regulation
of
generator
torque.
The
engine
speed
is
constant
in
the
defined
power
range,
regulation of generator torque. The engine speed is constant in the defined power range, so the output
so the regulation
output power
the REbyisthe
only
realized of
bythe
thetorque
adjustment
of the torque
power
of theregulation
RE is only of
realized
adjustment
of the generator.
Thereofisthe
no
generator.between
There is
no coupling
between
speed
control
andTo
generator
torque
control.
To
coupling
engine
speed control
andengine
generator
torque
control.
design the
generator
torque
design the generator torque control algorithms for RE generation system, the mathematical model of
generator will be introduced. The PMSG can be described as Equation (9) in a rotating dq coordinate
linked with a rotor:
Energies 2017, 10, 204
7 of 16
Energies 2017, 10, 204
7 of 16
control algorithms for RE generation system, the mathematical model of generator will be introduced.
diq

The PMSG can be described as Equation
linked with a rotor:
uq  (9)
 Rsin
iq aLrotating
 edq
Ld icoordinate
q
d  e f


d
t
( 
(9)
di
d ωe L d i d + ωe ψ f
uq =
iq i−LLq dtdq i−
ud−RsR
 e Lqiq
s d
d
(9)
= −Rs i − L did
dt
+ ωe L q i q
u 
d
d
d dt
where ud, uq, id, iq are the stator voltage and current in d-axis and q-axis coordinates respectively; Ld,
where ud , uq , id , iq are the stator voltage and current in d-axis and q-axis coordinates respectively; Ld ,
Lq are the d-axis and q-axis inductance; Rs is the stator resistance, ωe = pn·ωr is the angular frequency
Lq are the d-axis and q-axis inductance; Rs is the stator resistance, ωe = pn ·ωr is the angular frequency
of the rotating field, ωr is the rotor speed; pn is the number of pole pairs.
of the rotating field, ωr is the rotor speed; pn is the number of pole pairs.
The electromechanical torque:
The electromechanical torque:
Tem  0.75 phn  f iq  ( Ld  Lq )id iqi
(10)
Tem = 0.75pn ψ f iq + ( Ld − Lq )id iq
(10)
By controlling the d-axis current to be zero id = 0, then the electromechanical torque could be
written
as:
By controlling
the d-axis current to be zero id = 0, then the electromechanical torque could be
written as:
Tem 1.5 pn f iq
(11)
Tem = 1.5pn ψ f iq
(11)
According to the above Equation (11) and mechanical characteristics, the output power control
According to the above Equation (11) and mechanical characteristics, the output power control
can be realized via adjusting the q-axis current:
can be realized via adjusting the q-axis current:
2k1Pe
iq  2k1 P
e
iq = 3 pn f e
(12)
(12)
3pn ψ f ωe
The next section will discuss how to realize RE output power/current control to diminish static
The next section will discuss how to realize RE output power/current control to diminish static
errors and obtain a stable and high robustness control system.
errors and obtain a stable and high robustness control system.
3.2. Design of PR Controller
3.2. Design of PR Controller
The PR controller with power regulation is employed for the EREV, as shown in Figure 7. The
The PR controller with power regulation is employed for the EREV, as shown in Figure 7.
reference Preq* in the outer loop is the required power, thus good dynamic and steady state
The reference Preq * in the outer loop is the required power, thus good dynamic and steady state
characteristics can be obtained through real-time adjustment of the instantaneous power [19–21].
characteristics can be obtained through real-time adjustment of the instantaneous power [19–21].
The controlled object in the inner loop is alternating current, and a PR regulator is introduced to
The controlled object in the inner loop is alternating current, and a PR regulator is introduced to
eliminate the steady state errors of the control system, where iα* and iβ* are the given input current
eliminate the steady state errors of the control system, where iα * and iβ * are the given input current
under the stationary αβ frame for the PWM converter.
under the stationary αβ frame for the PWM converter.
Rload
+
IC
Engine
Cdc
PMSG
-
ωe
Vdc
Idc
Ua
Uc
ia ib ic
SPLL
abc/αβ
Ub
PI
θ
ωe*
Define ωe
according to
efficiency map
iα
SVM
iβ
-
iq*
Preq*
+
Preq
PI
id *
uα*
iα* +
dq
αβ
PR
-
iβ* +
PR
αβ
u
β*
P
abc
Figure7.7.Power
Powerfollowing
followingvector
vectorcontrol
controlstrategy
strategywith
withPR
PRcontroller.
controller.
Figure
The transfer function of an ideal PR controller is shown in the following Equation [22]:
Energies 2017, 10, 204
8 of 16
Energies 2017, 10, 204
8 of 16
The transfer function of an ideal PR controller is shown in the following Equation [22]:
2K s
GPR ( s )  K p  2 R 2
(13)
2K s
s
GPR (s) = K p + 2 R02
(13)
s + ω0
where KP and KR are the proportional and resonant coefficients, and ω0 is the resonant frequency.
where
KP and
are the proportional
andthe
resonant
coefficients,
ω 0 is
theand
resonant
frequency.
Compared
withKaR traditional
PI controller,
PR regulator
has an and
infinite
gain
a 90° phase
shift
Compared
with a traditional
PIωcontroller,
the PR
has an infinite
gainfrequencies.
and a 90◦ phase
at the fundamental
frequency
0, and it has
littleregulator
gain magnitude
at other
As toshift
the
at
the fundamental
frequency
ω 0 , achieve
and it has
gain
magnitude
other
to the
closed-loop
control system,
it can
zerolittle
static
error
in phase at
and
gainfrequencies.
for tracking As
given
an
closed-loop
control
system,
it canfrequency.
achieve zero
static error
phasefluctuation
and gain for
tracking
given
an
alternating signal
with
a specific
However,
wheninspeed
of the
engine
occurs,
alternating
signal with
a specific
frequency.
However,
speed
of theofengine
occurs,
the output current
frequency
of the
generator
will be when
variable
andfluctuation
the bandwidth
the ideal
PR
the
outputisn’t
current
frequency
of the gain
generator
will be
bandwidth
the ideal PR
controller
sufficient,
so that
magnitude
ofvariable
the openand
loopthe
is reduced,
andofaccordingly
a
controller
sufficient,
so that
the gain magnitude
the stability.
open loopInis order
reduced,
and accordingly
a
non-error isn’t
steady
state can’t
be achieved
due to theofbad
to solve
the stability
non-error
achieved
duean
to the
bad stability.
In order to can
solvebe
theused
stability
problems steady
causedstate
bycan’t
an be
infinite
gain,
optimized
PR regulator
in problems
practical
caused
by an infinite
gain,
an optimized
PR regulator
canensure
be used
in practical
implementations
with
implementations
with
a finite
gain, but high
enough to
a small
static error.
The improved
PRa
finite
gain,isbut
highinenough
to ensure
a small
controller
given
the following
form
[23]: static error. The improved PR controller is given in the
following form [23]:
2K  s
G
(ss)) =
K
 2 2KRRωccs 2
(14)
PR (
GPR
K pp +
(14)
 2ω
2ccss+ ω
20
ss2 +
0
Based on the control principle of the PMSG, the current loop of generator control is shown in
Figure 8, iαα* and iαα are
are the generator
generator current
current reference
reference value and actual value, respectively, in α-β
α-β
coordinates;
stator
voltage
of the
GPR (s)GisPRthe
functionfunction
of the PRof
controller;
coordinates; eαeαisisthe
the
stator
voltage
of generator;
the generator;
(s) transfer
is the transfer
the PR
G
function
signal sampling
and PWM
switch
controller;
P(s) is the
transfer considering
function considering
signal sampling
and
PWMdelay;
switchGdelay;
GDbe
(s)
P (s) is theGtransfer
D (s) can
expressed
as a timeas
delay
considering
A/D sampling
transmission;
GVSC (s) can be
expressed
as
can be expressed
a time
delay considering
A/Dand
sampling
and transmission;
GVSC
(s) can be
-ωT
/2
delay
considering
duty
cycle
updating
of
PWM
waveform;
G
(s)
is
the
transfer
function
of
the
expressed
as
-ωT
s
/2
delay
considering
duty
cycle
updating
of
PWM
waveform;
G
L
(s)
is
the
transfer
s
L
control
functionobjective.
of the control objective.
i 
+-
GD (s)
G PR ( s )
*
2K Rc s U
Kp  2
e  sTd
s  2c s  02
GVSC ( s )
U +
K PWM
TPWM s  1
-
GP ( s )
e
GL ( s )
1 i
LsR
Figure 8. Control block diagram of the inner current loop.
Figure 8. Control block diagram of the inner current loop.
Considering
and
disturbance
input
simultaneously,
the transfer
function
of current
Considering reference
referenceinput
input
and
disturbance
input
simultaneously,
the transfer
function
of
control
loop
can
be
written
as
follows:
current control loop can be written as follows:
 GP P(s()s)· GGLL((ss)) ∗*
GG
G G (s()s·) G
L (Ls()s )
i  PRPR

e eα
iα =
iiα −
1+
(s()s)· GGPP((ss))·G
) ·L G
1 GG
GLL(ss))
11+GG
( s()s)G·PG( sP)(sG
( sL)(s)
PRPR
PRPR
(15)
(15)
As the gain of the control system is much greater than 1 at the resonant frequency point
PR(s)·
(GPR
(s)·GGPP(s)·
(s)G
·GL(s)
>>1),1),the
thecoefficient
coefficientofofthe
thefirst
firstterm
termon
onthe
theright
rightisisapproaching
approaching 11 and
and the other is
L (s)>>
can be
be seen
seen from
fromEquation
Equation(15)
(15)that
thatiαiα≈
≈ iαα*.
approximately zero. Therefore, it can
*. It
It can
can be deduced that
error.
the PR controller can eliminate the static error.
controleffect
effect
is mainly
determined
byparameters
the parameters
of the controller.
Therefore,
the
The control
is mainly
determined
by the
of the controller.
Therefore,
the influence
influence
of each on
parameter
on effect
the control
effect was
analyzed
detail. K
The
variables
K
P
and
KR
of
each parameter
the control
was analyzed
in detail.
The in
variables
and
K
were
adjusted
P
R
were adjusted
to observeby
the
influence
by Bode diagram.
respectively
to respectively
observe the influence
Bode
diagram.
From Figure 9a, the amplitude margin at the resonant frequency does not change significantly
with the increase of the KPP, while the amplitude margin increases at other frequencies. This indicates
of of
thethe
PRPR
control
at resonant
frequency
andand
affect
the
that the
the excess
excess KKPPwill
willweaken
weakenthe
theadvantage
advantage
control
at resonant
frequency
affect
bandwidth
andand
stability
of the
controller.
It can
be seen
from
Figure
9b 9b
that
thethe
amplitude
gain
at
the
bandwidth
stability
of the
controller.
It can
be seen
from
Figure
that
amplitude
gain
resonant
frequency
increases
with
at
resonant
frequency
increases
withincreasing
increasingKRKRwhich
whichserves
servestotoeliminate
eliminatethe
thesteady-state
steady-state error.
error.
Therefore, the PR controller parameter design needs to take into account the various parameters on
the influence of the dynamic and static performance. The rule of parameter design is that KP and KR
Energies 2017, 10, 204
9 of 16
KP =2
KP =1.5
KP =1
KP =0.5
KP =0.2
20
-30
-80
100
40
30
20
10
0
100
50
0
-50
-100
100
Gain/dB
40
30
20
10
0
70
KR =140
KR =110
KR =80
KR =50
KR =20
Phase/deg
Phase/deg
Gain/dB
Energiesthe
2017,PR
10, controller
204
9 of 16 on
Therefore,
parameter design needs to take into account the various parameters
the influence of the dynamic and static performance. The rule of parameter design is that KP and KR
are adjusted to meet the dynamic, static performance and stability demands; the cut-off frequency ωc
are adjusted
to meet the dynamic, static performance and stability demands; the cut-off frequency ω c
is adjusted to suppress the disturbances caused by the signal fluctuation. ωc reflects the ability of the
is adjusted to suppress the disturbances caused by the signal fluctuation. ω c reflects the ability of the
controller to track signals in real time, the bandwidth should be wide enough to achieve fast
controller
to track signals in real time, the bandwidth should be wide enough to achieve fast dynamic
dynamic response. However, the excessive bandwidth will introduce high-frequency noise such as
response.
the excessive
bandwidth
will need
introduce
high-frequency
suchonasthe
PWM
PWM However,
switching frequency,
so parameter
design
to consider
the mutual noise
influence
switching
frequency,
so
parameter
design
need
to
consider
the
mutual
influence
on
the
control
effect.
control effect.
102
101
Frequency/Hz
103
(a)
102
101
Frequency/Hz
103
(b)
Figure 9. Frequency response considering parameter variation of PR controller. (a) Bode diagram at
Figure 9. Frequency response considering parameter variation of PR controller. (a) Bode diagram at KP
KP variation; (b) Bode diagram at KR variation.
variation; (b) Bode diagram at KR variation.
3.3. Design of Control Stability
3.3. Design of Control Stability
To improve the dynamic and static behavior of the converter, it is important to analyze the
stability
of thethe
presented
control
According
to the current
model in Figure
8 and the
To
improve
dynamic
andsystem
static [24,25].
behavior
of the converter,
it loop
is important
to analyze
Equation
the transfer
function
of current
loop can
be written
follows:
stability
of the(15),
presented
control
system
[24,25].control
According
to the
currentasloop
model in Figure 8 and
Equation (15), the transfer function of current
control loop can be written as follows:
i
G( s)  * a  GPR ( s)  GD ( s )  GVSC ( s )  GL ( s )
(16)
i i
ia a a
= GPR (s) · GD (s) · GVSC (s) · GL (s)
(16)
G (s) = ∗
i a −ofi asignal sampling and hold.
GD(s) is the transfer function
As A/D sampling and transmission
will lead to a time delay of calculation, GD(s) can be expressed as follows:
GD (s) is the transfer function of signal sampling and
hold. As A/D sampling and transmission
Td s
GDcan
( s)be
K
(17)
de
will lead to a time delay of calculation, GD (s)
expressed
as follows:
It can be expressed by Taylor expansions:
GD (s) = Kd e−Td s
(17)
Kd
Kd
GD  s   K d e
 Td s 
1
1
2
3
(18)
e
It can be expressed by Taylor expansions:
1  Td s  Td s   Td s   
2!
3!
Kexpressed
d and then GD(jω) can be
d
− Td s by K
In Equation
as:
GD(18),
= jω,
=
(18)
(s) s=isKreplaced
de
T
s
1
d
e
1 + Td s + 2! ( Td s)2 + 3!1 ( Td s)3 + · · ·
Kd
GD ( j ) 
1
1
1
2
4
5 as: 
(19)
In Equation (18),
s is replaced by jω, andthen GD (jω)1 can be3 expressed
1  2! Td    4! Td      j Td   3! Td    5! Td    
Kd
h frequency of sampling signal isi much
h higher than the frequency of controlled
i
GBecause
(19)
D ( jω ) =the
2
4
3
5
1
1
1
1
1
−
T
ω
+
T
ω
−
·
·
·
+
j
T
ω
−
T
ω
+
T
ω
−
·
·
·
(
)
(
)
(
)
(
)
d
d
d
d
d
3!
5!
current, the following2!relationship 4!can be derived:
 Td s
1 signal
1 higher
2
3
Because the frequency of sampling
is 1,
much
current,
Td the frequency of controlled(20)
Td  
Td  than
2!
3!
the following relationship can be derived:
Based on the above analysis, the GD(s) can be written as a first-order delay function:
1
1
( T ω )2 << 1,
( T ω )3 << Td ω
2! d
3! Kdd
GD ( s) 
Based on the above analysis, the GD (s) can be written
Td s  1 as a first-order delay function:
GD ( s ) ≈
Kd
Td s + 1
(20)
(21)
(21)
Energies
Energies2017,
2017,10,
10,204
204
Energies
2017,
10,
204
10
10of
of16
16
10
of
16
At the
the same
same time,
time, duty
duty cycle
cycle updating
updating of
of the
the PWM
PWM waveform
waveform also
also brought
brought aa ωT
ωTss/2
/2 delay,
delay, so
so the
the
At
At series
the same
time, duty
cyclefor
updating
of the
PWM waveform
also
brought a ωTs /2 delay, so the
Taylor
expansion
is
used
modeling
approximations
of
the
G
p(s) as follows:
Taylor series expansion is used for modeling approximations of the Gp(s) as follows:
Taylor series expansion is used for modeling approximations of the Gp (s) as follows:
K PWM
Kd
K PWM
K
K
d
GP((ss))  eeTTddss  K K PWM
 K
 KKPWM
 K DDK
G



P
PW
M
PW
M
TPWMss 11≈ TTdssd11 · TTPWMss 11 ≈
TTiiss D11
GP (s) = e−Td s · T

d
PWM
TPWPWM
s
+
1
T
s
+
1
T
s
+
1
∑ Ti s + 1
M
PW M
d
(22)
(22)
(22)
where is
is the
the ∑T
∑Tii is
is the
the equivalent
equivalent delay
delay factor;
factor; K
KDD is
is the
the equivalent
equivalent gain
gain coefficient;
coefficient; TTdd is
is time
time delay
delay of
of
where
where
is
the
T
is
the
equivalent
delay
factor;
K
is
the
equivalent
gain
coefficient;
T
is
time
delay
∑
D
i
d
sample and
and hold;
hold; K
Kdd is
is time
time delay
delay coefficient
coefficient of
of sample
sample and
and hold;
hold; TTPWM
PWM is the delay time of the pulse
sample
is the delay time of the pulse
of
sample
and hold; KKPWM
time
delay
coefficient
ofof
sample
and hold;
Tmodulation.
the
PWM is the delay
d is is
width
modulation;
the
delay
coefficient
the
pulse
width
The time
time of
delay
width modulation; KPWM is the delay coefficient of the pulse width modulation.
The
time
delay
pulse
widththe
modulation;
is the delay
coefficient
of the pulse
modulation.
The time delay
PWM transport
including
sampling Kand
and
delay
is generally
generally
givenwidth
by ∑T
∑T
i = 1.5 Ts, it will have a
including
the sampling
transport delay
is
given
by
i = 1.5 Ts, it will have a
including
the
sampling
and
transport
delay
is
generally
given
by
T
=
1.5
T
,
it
will
have
a significant
∑
s
i
significant impact
impact on
on the
the control
control stability.
stability. The
The influence
influence of
of the
the delay
delay factor
factor on
on the
the current
current
control is
is
significant
control
impact
on
the
control
stability.
The
influence
of
the
delay
factor
on
the
current
control
is
depicted
in
depicted
in
Figure
10.
It’s
shown
that
the
design
needs
to
consider
a
sufficient
stability
margin
to
depicted in Figure 10. It’s shown that the design needs to consider a sufficient stability margin to
Figure
10.the
It’s
shown that
the
design
to consider a sufficient stability margin to enhance the
enhance
robustness
and
avoid
sideneeds
effects.
enhance
the robustness
and
avoid
side
effects.
robustness and avoid side effects.
50
50
00
-50
-50
-100
-100
-150
-150
00
00
-90
-90
-180
-180
Gain/dB
Gain/dB
without delay
delay
without
Phase/deg
Phase/deg
with delay
delay
with
-270
-270
-360
-360
10-3-3
10
without delay
delay
without
with delay
delay
with
10-2-2
10
10-1-1
1000
10
10
Frequency/kHz
Frequency/kHz
1022
10
1011
10
Figure 10.
10. Frequency
Frequency response
response influence
influence on
on current
current control
control performance
performance for
for variation
variation of
of time
time delay.
delay.
Figure
Figure 10. Frequency response influence on current control performance for variation of time delay.
Imaginary
Imaginary
Imaginary
Imaginary
Figure 11
11 shows
shows the
the frequency
frequency response
response characteristic
characteristic curve
curve of
of closed-loop
closed-loop control.
control. It
It can
can be
be
Figure
Figure
11
shows
the
frequency
response
characteristic
curve
of
closed-loop
control.
can
be
used
used
to
discuss
the
stability
margin
of
the
control
system.
Angular
frequency
ω
s is It
the
crossover
used to discuss the stability margin of the control system. Angular frequency ωs is the crossover
to
discuss the
stability
margin
of the
control
Angular
frequency
ω scrossover
is the crossover
frequency
frequency
of the
the
amplitude
gain
at point
point
M11system.
angular
frequency
ωcscs is
is the
the
crossover
frequency
of the
the
frequency
of
amplitude
gain
at
M
;; angular
frequency
ω
frequency
of
of
the
amplitude
gain
at
M
;
angular
frequency
ω
is
the
crossover
frequency
of
the
phase
gain
phase
gain
at
point
M
2. point
It
can
be
seen
from
Figure
11a,b
that
the
point
(−1,
j0)
isn’t
encircled
in
the
cs
1
phase gain at point M2. It can be seen from Figure 11a,b that the point (−1, j0) isn’t encircled in the
at
point M
canω
seen from
Figure
11a,b
that the
point
(−coordinate
1,
j0) isn’t encircled
the Nyquist
Nyquist
curve
as
ωbe
increases,
and
no poles
poles
appear
in the
the
right
coordinate
plane. In
In in
Figure
11c, the
the
2 . It as
Nyquist
curve
increases,
and
no
appear
in
right
plane.
Figure
11c,
curve
as ω increases,
poles appear
in the
the amplitude
amplitude
margin is
isand
20lg|𝐺𝑗𝜔
dBright
andcoordinate
the phase plane.
marginInisFigure
𝛾 = 𝜋11c,
+ ∠𝐺(𝑗𝜔
𝑐𝑠 | = 14.5
𝑐𝑠 ) = 48.
amplitude
margin
hh == no
20lg|𝐺𝑗𝜔
𝑐𝑠 | = 14.5 dB and the phase margin is 𝛾 = 𝜋 + ∠𝐺(𝑗𝜔𝑐𝑠 ) = 48.
◦ . Considering
margin
is
h
=
−
20lg
Gjω
=
14.5
dB
and
the
phase
margin
is
γ
=
π
+
∠
G
jω
=
48
(
)
|
|
Considering
the
parameter
deviation
between
the
real
system
and
the
physical
model,
the
cs
cs
Considering the parameter deviation between the real system and the physical model, the
the
parameter
deviation
between
the
real
system
and
the
physical
model,
the
requirements
of
the
requirements
of
the
stability
margin
are
30°
≤
PM
≤
60°
and
GM
>
6
dB.
As
shown
in
the
Bode
requirements of the stability margin are 30° ≤ PM ≤ 60° and GM > 6 dB. As shown in the Bode
◦ ≤ PM ≤ 60◦ and GM > 6 dB. As shown in the Bode diagram, it is found that
stability
are 30
diagram,margin
is found
found
that
the bandwidth
bandwidth is
is wide
wide enough
enough to
to meet
meet the stability
stability margin
margin requirements
requirements
diagram,
itit is
that
the
the
bandwidth
is
wide
enough
to
meet
the
stability
margin
requirements
for
the
generator
output
for
the
generator
output
current
control,
even
if
the
generator
output
current
frequency
is between
between
for the generator output current control, even if the generator output current frequency is
current
control,
even
if
the
generator
output
current
frequency
is
between
100
Hz
and
200
Hz.
100 Hz
Hz and
and 200
200 Hz.
Hz.
100
hh
ωcscs
ω
(-1, j0)
j0)
(-1,
γγ
ωss
ω
Real
Real
Real
Real
(a)
(a)
(b)
(b)
Figure 11. Cont.
Energies 2017, 10, 204
Energies 2017, 10, 204
Phase/deg
Gain/dB
11 of 16
11 of 16
50
0
-50
-100
-150
-200
00
0
-90
-180
-270
-360
10-3
M1
GM=0dB
PM=48°
GM=14.5dB
PM=-180°
M2
10-2
10-1
100
Frequency/kHz
101
102
(c)
Figure 11. Frequency response. (a) Nyquist curves; (b) Enlarged drawing of the Nyquist curves; (c)
Figure 11. Frequency response. (a) Nyquist curves; (b) Enlarged drawing of the Nyquist curves;
Bode diagram.
(c) Bode diagram.
3.4. Implementation of PR Controller
3.4. Implementation of PR Controller
In order to realize digital control, the proposed PR controller is discretized using the
In order to realize digital control, the proposed PR controller is discretized using the pre-Tustin
pre-Tustin transformation method which can realize the mapping between s-domain and the
transformation method which can realize the mapping between s-domain and the z-domain [26,27]:
z-domain [26,27]:
ss=
ω
11−zz−11
tan(ωTs /2) 1 + z−11
tan Ts / 2  1  z
(23)
(23)
Ts and ω are sampling time and resonant frequency, respectively. Compared with the traditional
Ts and ω are sampling time and resonant frequency, respectively. Compared with the
Tustin discretization, the correction factor ω/tan(ωTs ) is used to replace 2/Ts to avoid frequency
traditional Tustin discretization, the correction factor ω/tan(ωTs) is used to replace 2/Ts to avoid
aliasing distortion and phase shift. Substituting Equation (23) into GPR (s), the transfer function of PR
frequency aliasing distortion and phase shift. Substituting Equation (23) into GPR(s), the transfer
regulator in z-domain can be deduced as follows:
function of PR regulator in z-domain can be deduced as follows:
b2 z−2 2 + b1z1−1 + b0
GPR (z) = b2 z −
bz b
GPR ( z )  a2 z 2 +1a1 z−1 +0 1
where
where
a2 z
2
1
 a1 z  1
(24)
(24)
2ω02 − 2γ2
a1 = 22
2
2𝜔γ0 −
+ 2γ
2ωc γ + ω02
𝑎1 = 2
2
γ + 2𝜔
𝑐 γ + 𝜔0
2−
2
γ
2ω
γ
c
2+ ω0
a2γ2=− 2𝜔
𝑐 γ + 𝜔0
𝑎2 = 2 γ2 + 2ωc γ2+ ω02
γ + 2𝜔𝑐 γ + 𝜔0
2𝐾𝑅 𝜔2K
𝑐 γR ωc γ
𝑏0 =b0𝐾𝑃=+K P2+
2
2
2
γ + γ2𝜔+
+𝜔
𝑐 γ2ω
c γ0 + ω0
2
2
(2𝜔0 − 2γ
)𝐾𝑃 𝑏1 = 2
2ω02 − 2γ22 K P
bγ1 =+ 2𝜔
𝑐 γ + 𝜔0
2
γ2𝜔+
2 2ωc γ + ω0
(γ2 − 2𝜔𝑐 γ +
𝑅
0 )𝐾𝑃 − 2𝜔𝑐 γ𝐾
𝑏2 =
2 + 2𝜔 γ + 2𝜔 2
2
γ
γ − 2ωc γ𝑐+ ω0 0K P − 2ωc γK R
b2 =
𝜔0
γ = γ2 + 2ωc γ + ω02
𝜔 𝑇
tan⁡( 0 𝑠ω
)
2 0 γ=
ω0 Ts
Above Equation (24) can be transformed into
analytic function as follow:
tan differential
2
y (n)  a1  y (n  1)  a2  y (n  2)  b0  u(n)  b1  u(n  1)  b2  u(n  2)
(25)
Above Equation (24) can be transformed into differential analytic function as follow:
Equation (25) is implemented by using digitization. It is shown in Figure 12 where u(n) and
y(nand
) = output
− a1 · y(ofn the
− 1)PR
− regular
a2 · y ( n −
) +nth
b0 ·sampling
u(n) + b1 time.
· u(n − 1) + b2 · u(n − 2)
(25)
y(n) are input
at 2the
Energies 2017, 10, 204
12 of 16
Equation (25) is implemented by using digitization. It is shown in Figure 12 where u(n) and y(n)
12 of 16
of the PR regular at the nth sampling time.
12 of 16
Energies 2017, 10, 204
are input
and
output
Energies
2017,
10, 204
u(n) bb0
u(n)
0 

b1
b1 
Z
1
1
Z
Z 11
Z

b2
b2 

y(n)
y(n)
-a1
-a1
Z 11
Z
-a
2
 -a2

Z 11
Z
Figure
Figure12.
12.Digital
Digitalimplementation
implementationdiagram
diagramofof
ofcontroller.
controller.
Figure
12.
Digital
implementation
diagram
controller.
It’s important to select the optimum sampling frequency during discretization. The
select
the optimum
sampling
frequencyfrequency
during discretization.
The performance
It’s important
importantto to
select
the optimum
sampling
during discretization.
The
performance of the controller is poor when the selected sampling frequency is low. It’s better to set
of
the
controller
is
poor
when
the
selected
sampling
frequency
is
low.
It’s
better
to
set
the
frequency
performance of the controller is poor when the selected sampling frequency is low. It’s better to set
the frequency as large as possible. However higher sampling rates imply a higher data rate. In
as large
as possible.
However
higherHowever
samplinghigher
rates imply
a higher
rate.
In orderdata
to select
the
frequency
as large
as possible.
sampling
ratesdata
imply
a higher
rate. an
In
order to select an optimum sampling frequency, an oversampling method whose sampling
optimum
oversampling
method
samplingmethod
frequency
is greater
than
order
to sampling
select an frequency,
optimum an
sampling
frequency,
an whose
oversampling
whose
sampling
frequency is greater than the Nyquist frequency is adopted to keep the sampling frequency away
the Nyquist
is adopted
to keep
the sampling
frequency
away
the resonant
frequency.
frequency
is frequency
greater than
the Nyquist
frequency
is adopted
to keep
thefrom
sampling
frequency
away
from the resonant frequency. As shown in Figure 13, the influence of the sampling frequency on the
As shown
in Figurefrequency.
13, the influence
of the
on the
the designed
PR
from
the resonant
As shown
insampling
Figure 13,frequency
the influence
ofperformance
the samplingoffrequency
on the
performance of the designed PR controller is discussed by root locus plots.
controller is discussed
by rootPR
locus
plots. is discussed by root locus plots.
performance
of the designed
controller
(a)
(a)
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1.0
-1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0
0 0.2 0.4 0.6 0.8 1.0
-1.0 -0.8 -0.6 -0.4 -0.2
Real axis
Real axis
Imaginaryaxis
axis
Imaginary
Imaginaryaxis
axis
Imaginary
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1.0
-1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0
0 0.2 0.4 0.6 0.8 1.0
-1.0 -0.8 -0.6 -0.4 -0.2
Real axis
Real axis
(b)
(b)
Figure 13. Root locus plot of control system at different sampling frequency. (a) Sampling frequency
Figure 13. Root locus plot of control system at different sampling frequency. (a) Sampling frequency
13.(b)
Root
locus plot
of control
isFigure
2.0 kHz;
Sampling
frequency
is system
4.0 kHz.at different sampling frequency. (a) Sampling frequency is
is 2.0 kHz; (b) Sampling frequency is 4.0 kHz.
2.0 kHz; (b) Sampling frequency is 4.0 kHz.
From the root plot we can see that the high or low sampling frequency will lead to poor
From the root plot we can see that the high or low sampling frequency will lead to poor
stability
of the
control
thethe
sampling
frequency
is selected
in the range
2 kHz
to 3
From
plotsystem.
we canWhen
see
that
high or low
sampling
toofof
poor
stability
stability
of the
theroot
control
system.
When
the sampling
frequency
is frequency
selected inwill
the lead
range
2 kHz
to 3
kHz,
even
if the
gain coefficient
over a wideisrange,
it canthe
meet
theofrequirement
of system
of the
control
system.
the changes
sampling
range
2 kHz to 3 kHz,
even if
kHz,
even
if the
gain When
coefficient
changes frequency
over a wide selected
range, itincan
meet
the requirement
of system
stability
andchanges
reduce aliasing
distortion.
the gainmargin,
coefficient
a wide
range, it can meet the requirement of system stability margin,
stability
margin,
and reduceover
aliasing
distortion.
and reduce aliasing distortion.
4. Simulation and Experimental Results
4. Simulation and Experimental Results
4. Simulation and Experimental Results
4.1. Simulation Results
4.1.
4.1. Simulation
Simulation Results
Results
According to the control strategy of Figure 7, a simulation system is built to verify the
According
to the
control
strategyFigure
of Figure
7, a simulation
built
to verify the
According
control
strategy
7,The
a simulation
issystem
built to is
verify
the
effectiveness
of to
thethedesigned
controlofmethod.
speed ofsystem
the engine-generator
set effectiveness
is defined
effectiveness
of control
the designed
control
method.
The speed of the set
engine-generator
set isgenerator
defined
of theon
designed
method.
Thethe
speed
defined
based
generator
torque
to realize
RE of
in the
theengine-generator
most efficient regioniswhen
thebased
RE ison
running in
based
on
generator
torque
to
realize
the
RE
in
the
most
efficient
region
when
the
RE
is
running
in
torquefollowing
to realize the
RE in
the control
most efficient
regionpower
when the
RE is running
in power
power
mode,
then
the output
regulation.
The outer
loopfollowing
obtainedmode,
the
power
following
mode,
then
control
the
output
power
regulation.
The
outer
loop
obtained
the
then control
output
power regulation.
Thevoltage
outer loop
power
value by detecting
actual
power the
value
by detecting
the DC bus
andobtained
current; the
the actual
inner loop
introduced
the PR
actual
power
value
by
detecting
the
DC
bus
voltage
and
current;
the
inner
loop
introduced
the the
PR
the DC bus
voltage
anddepict
current;
inner loop
introduced
the PR with
controller.
Figure 14a,b
depict
controller.
Figure
14a,b
the the
proposed
PR strategy
compared
the traditional
Space
Vector
controller. Figure 14a,b depict the proposed PR strategy compared with the traditional Space Vector
Modulation (SVM) of the generator output current tracking reference value, respectively. The
Modulation (SVM) of the generator output current tracking reference value, respectively. The
reference current is almost exactly the same as the actual output current using the PR strategy.
reference current is almost exactly the same as the actual output current using the PR strategy.
Energies 2017, 10, 204
13 of 16
proposed PR strategy compared with the traditional Space Vector Modulation (SVM) of the generator
output current tracking reference value, respectively. The reference current is almost exactly the same
2017, 10,
204 current using the PR strategy.
13 of 16
asEnergies
the actual
output
Energies 2017, 10, 204
Reference i
*
Reference
Actual i i
Actual i
1
1
2
2
60
60
40
40
20
20
0
0
-20
-20
-40
-40
-60
-60 0
0
*
Current/A
Current/A
Current/A
Current/A
60
60
40
40
20
20
0
0
-20
-20
-40
-40
-60
-60 0
0
13 of 16
4
3
4
3
Time/ms
Time/ms
5
5
6
6
Reference i*
*
Reference
Actual i i
Actual i
1
1
2
2
(a)
(a)
4
3
4
3Time/ms
Time/ms
5
5
6
6
(b)
(b)
Figure 14. Vector
Vector waveformofofgenerator’s
generator’s outputcurrent.
current. (a)
(a)Proposed
Proposedstrategy;
strategy;(b)
(b) Traditional
Figure
Figure 14.
14. Vector waveform
waveform of generator’s output
output current. (a)
Proposed strategy;
(b) Traditional
Traditional
SVM
strategy.
SVM
SVM strategy.
strategy.
The simulation system tests the dynamic performance when the power demand changes to
The simulation
thethe
dynamic
performance
when
the power
demand
changes
to ensure
simulationsystem
systemtests
tests
dynamic
performance
when
the power
demand
changes
to
ensure the dynamic response performance. According to the control state chart of Figure 6, RE
the
dynamic
responseresponse
performance.
According
to the control
state
chart state
of Figure
REFigure
maintains
a
ensure
the dynamic
performance.
According
to the
control
chart6,of
6, RE
maintains a constant 8 kW when the vehicle power demand value is lower than 8 kW. When the
constant
when the
vehicle
demand
valuedemand
is lowervalue
than 8iskW.
When
vehicle
power
maintains8 akW
constant
8 kW
whenpower
the vehicle
power
lower
thanthe
8 kW.
When
the
vehicle power demand is more than 8 kW, the current reference is obtained via the power demand.
demand
is more
than 8 is
kW,
thethan
current
reference
is obtained
viaisthe
power via
demand.
As shown
in
vehicle power
demand
more
8 kW,
the current
reference
obtained
the power
demand.
As shown in Figure 15, the current varies fast when the power demand changes, and the system
Figure
15, the
current15,
varies
when
the power
demand
changes,
and thechanges,
system reaches
steady
As shown
in Figure
the fast
current
varies
fast when
the power
demand
and thea system
reaches a steady state in a short time without overshoot appearing.
state
in aa short
time
without
overshoot
appearing.
reaches
steady
state
in a short
time without
overshoot appearing.
80
80
12
12
9
9
6
6
3
3
0
0 0
0
Power/kVA
Power/kVA
15
15
Current/A
Current/A
160
160
0
0
-80
-80
-160
-160 0
0
36
18
18 Time/ms 36
Time/ms
(a)
(a)
54
54
Reference Preq*
Reference
Actual PreqPreq*
Actual Preq
10
10
20
20
30
40
30Time/s
40
Time/s
(b)
50
50
60
60
70
70
(b)
Figure 15. Simulation waveforms of transient response at Preq* change. (a) Generator output current;
Figure 15.
15. Simulation
Simulation waveforms
waveforms of
of transient
transient response
response at
at PPreq** change.
(a) Generator output current;
Figure
(b) Output
power.
req change. (a) Generator output current;
(b)
Output
power.
(b) Output power.
4.2. Experimental Results
4.2. Experimental
Results
4.2.
Experimental Results
Experiments with the designed PR controller were conducted on a lab sample. The test bench is
Experiments with
with the designed
designed PR
PR controller
controller were
were conducted on
on a lab
lab sample.
sample. The
The test bench
bench is
is
Experiments
shown
in Figure 16. Asthe
shown in Figure
17, a dynamic conducted
response of thea generator
controltest
is observed.
shown in
in Figure
Figure 16.
16. As
in Figure
aa dynamic
response
of
control is
observed.
shown
As shown
shown
Figure 17,
17,
dynamic
response
of the
the generator
generator
The proposed
method
realizesingenerator
current
control
with fast
response.
Thiscontrol
is due is
toobserved.
the direct
The
proposed
method
realizes
generator
current
control
with
fast
response.
This
is
due
to
the direct
direct
The
proposed
method
realizes
generator
current
control
with
fast
response.
This
is
due
to
the
current control by the current loop of Figure 8 and the high gain of the PR controller at the resonant
current control
control by
by the
the current
current loop
loop of
of Figure
Figure 88 and
and the high
high gain of
of the
the PR
PR controller
controller at
at the
the resonant
resonant
current
frequency. Figure
17b depicts
the actual
power the
tracking gain
reference,
where
there is no
significant
frequency.
Figure
17b
depicts
the
actual
power
tracking
reference,
where
there
is
no
significant
frequency.
17b depicts
the power
actual following
power tracking
where
thereloop
is no
significant
fluctuation.Figure
It is shown
that the
controlreference,
by the fast
current
improves
the
fluctuation. ItItisisshown
shownthat
that
the
power
following
control
byfast
thecurrent
fast current
loop improves
the
fluctuation.
the
power
following
control
by
the
loop
improves
the
system
system response. Figure 18 shows the generator efficiency at different speed settings with the
system response.
18
the efficiency
generator at
efficiency
at
different speed
settings
with the
response.
18Figure
showsWhen
theshows
generator
different
speed
with
the proposed
proposedFigure
PR controller.
the output
power value
is lower
thansettings
8 kW, the
operating
pointsPR
are
proposed
PR
controller.
When
the
output
power
value
is
lower
than
8
kW,
the
operating
points
are
controller.
the output
power
valuebut
is lower
8 kW, the
operating
arethan
outside
of the
outside ofWhen
the high
efficiency
region;
when than
the output
power
valuepoints
is more
8 kW,
the
outside
of the region;
high efficiency
region;
but power
when value
the output
power
is more
thanefficiency
8 kW, the
high
efficiency
when
the90%.
output
is more
than
8value
kW,
the
generator
is
generator
efficiency isbut
more
than
The generator
efficiency
trend
under
different
speed settings
generator
efficiency
is
more
than
90%.
The
generator
efficiency
trend
under
different
speed
settings
more
than 90%.
The generator efficiency trend under different speed settings is basically the same.
is basically
the same.
is basically the same.
Energies 2017, 10, 204
Energies2017,
2017,10,
10,204
204
Energies
Energies 2017, 10, 204
14 of 16
1414ofof1616
14 of 16
torquemeter
meter
torque
torque meter
powermeter
meter
power
power meter
load
load
load
converter
converter
converter
drive
drive
motor
drive
motor
motor
PMSG
PMSG
PMSG
Figure16.
16.The
Thetest
testbench
benchfor
forRE
REpower
powergeneration
generationsystem.
system.
Figure
Figure
Figure16.
16.The
Thetest
testbench
benchfor
forRE
REpower
powergeneration
generationsystem.
system.
13.0
13.0
13.0
Power/kVA
Power/kVA
Power/kVA
11.0
11.0
11.0
Current/A
Current/A
Current/A
9090
90
6060
60
3030
30
00
0
-30
-30
-30
-60
-60
-60
-90
-90
-9000
0
Referencepp* *
Reference
Reference p* Measurement
Measurementpp
Measurement p
9.0
9.0
9.0
7.0
7.0
7.0
3030
30
120
6060
9090 120
60 Time/ms
90
120
Time/ms
Time/ms
150 180
180
150
150 180
00
0
22
2
(a)
(a)
(a)
44
4
Time/s
Time/s
Time/s
66
6
88
8
(b)
(b)
(b)
Figure 17.
17. Dynamic
Dynamic response
response atat load
load change.
change. (a)
(a) generator
generator output
output current;
current; (b)
(b) reference
reference and
and
Figure
Figure
17. Dynamic
response
at load(a)change.
(a)output
generator
output
current;
(b)
reference and
Figure
17.
Dynamic
response
at
load
change.
generator
current;
(b)
reference
and
measurement
power.
measurementpower.
power.
measurement
measurement power.
Efficiency/%
Efficiency/%
Efficiency/%
98%
98%
98%
94%
94%
94%
90%
90%
90%
86%
86%
86%
82%
82%
82%
78%
78%
78%
74%
74%
74%
70%
70%
70%00
0
η%@2500rpm
η%@2500rpm
η%@2500rpm
η%@3000rpm
η%@3000rpm
η%@3000rpm
η%@3500rpm
η%@3500rpm
η%@3500rpm
10
15
55
10
15
5Power/kW
15
Power/kW 10
Power/kW
Figure
18.
Generator
efficiency
curves
at
different
rotatingspeed
speedwith
withdesigned
designedcontrol
controlstretagy.
stretagy.
Figure
18.
Generator
efficiency
curves
at
different
Figure 18.
18. Generator
Generator efficiency
efficiency curves
curves at
at different
differentrotating
rotating
speed
Figure
rotating
speed with
with designed
designed control
controlstretagy.
stretagy.
Conclusions
5.5.Conclusions
5.
5.Conclusions
Conclusions
In this
this study,
study, toto optimize
optimize the
the overall
overall efficiency
efficiency ofof RE,
RE, the
the efficient
efficient operating
operating region
region isis
1.1. In
1.
to optimize
the overall
efficiency
of RE, the
is determined,
1. In
In this
thisstudy,
study,
to optimize
the overall
efficiency
of efficient
RE, theoperating
efficient region
operating
region is
determined,
and
a
partial
power
following
control
strategy
is
designed
for
an
urban
EREV
determined,
a partial
powercontrol
following
control
strategy is
designed
an urban
EREV
and
a partialand
power
following
strategy
is designed
an urbanfor
EREV
application.
determined,
and
a partial
power following
control
strategy for
is designed
for
an urban
EREV
application.The
Thethreshold
thresholdpower
powerthat
thatdetermines
determinesthe
theRE
REoperation
operationininpower
powerfollowing
followingmode
modeisis
application.
The
threshold
power
that determines
the RE operation
power following
is obtained
application.
The
threshold
power that determines
the REinoperation
in power mode
following
mode is
obtainedusing
usingthe
theevaluation
evaluationofofminimum
minimumfuel
fuelconsumption.
consumption.The
Thecontrol
controlstrategy
strategyachieved
achieved
obtained
using
the using
evaluation
of minimum
fuel consumption.
The control
strategy
obtained
the evaluation
of minimum
fuel consumption.
The
controlachieved
strategyelectrical
achieved
electrical decoupling
decoupling between
between the
the engine
engine speed
speed control
control and
and generator
generator torque
torque control.
control. The
The
electrical
decoupling
between the
engine the
speed
control
and control
generator
control.
The control.
engine was
electrical decoupling
between
engine
speed
andtorque
generator
torque
The
enginewas
wascontrolled
controlledtotooperate
operateatatconstant
constantspeed
speedwithin
withinthe
thehigh
highefficiency
efficiencyregion,
region,and
andthe
the
engine
controlled
operate attoconstant
within
the high
efficiency
andregion,
the generator
engine wastocontrolled
operate speed
at constant
speed
within
the highregion,
efficiency
and the
generatorcurrent
currentwas
wasregulated
regulatedtotoachieve
achievepower
powerfollowing
followingcontrol.
control.
generator
current
was
regulated
achieve power
following
generator
current
wasto
regulated
to achieve
powercontrol.
following control.
proportionalresonance
resonancecontroller
controllerbased
basedon
onα-β
α-βcoordinates
coordinatesisisintroduced
introducedinto
intothe
thecurrent
current
2.2. AAproportional
2. A proportional resonance controller based on α-β coordinates is introduced into the current
controlloop
looptotorealize
realizeRE
REpower
powerfollowing
followingcontrol.
control.ItIthas
hasfast
fastresponse
responseand
andstrong
strongrobustness
robustness
control
control loop to realize RE power following control. It has fast response and strong robustness
characteristics.
characteristics.
characteristics.
Energies 2017, 10, 204
2.
3.
4.
15 of 16
A proportional resonance controller based on α-β coordinates is introduced into the
current control loop to realize RE power following control. It has fast response and strong
robustness characteristics.
Using frequency response analysis, the relationship between the main parameters of the proposed
control strategy and the stability margin were discussed and summarized. A general method
for control system parameter design and stability design is proposed by using the control theory
criterion, and the pre-Tustin is used for discretization of the PR controller.
Simulation and experimental results show that the proposed control strategy has excellent
stability and robustness. It can effectively balance the stability margin and transient performance
to achieve better real-time tracking effects.
Acknowledgments: The research work described in this paper is supported by the National High Technology
Research and Development Program of China (2011aa11a239).
Author Contributions: Xiaoyuan Wang and Haiying Lv proposed the concrete idea of the described strategy,
Haiying Lv conducted the main work of the systematic process of design and simulation and also drafted the
paper. Qiang Sun and Peng Gao provided insightful suggestions on the research and simulation results analysis.
Yanqing Mi designed the experiments.
Conflicts of Interest: The authors declare no conflict of interest.
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