The 14th International Conference on Intelligent System Applications to Power Systems, ISAP 2007
November 4 - 8, 2007, Kaohsiung, Taiwan
Stability and Performance of an Autonomous
Hybrid Wind-PV-Battery System
Li Wang, Senior Member, IEEE, and Tsung-Jen Lin
delivered and supplied by the proposed hybrid power
generation and energy storage system with appropriate control
and effective coordination among various subsystems. Due to
the international technological progress and promoted
experience on wind power generation system, the cost of
generating of the wind power has already been reduced and
the cost of electricity-generating of wind power generation
systems may close to the one of traditional fossil-fuel energies
[1-3].
On the other hand, with the improvement of
semiconductor manufacture technology, photovoltaic (PV)
cells have enhanced efficiency, the cost of PV becomes much
lower and the installed capacity becomes much higher in
recent years. However, PV systems have lower energy
conversion efficiency, lower power density, and higher cost
compared with wind turbine generators. Large PV may
generate enough electricity for supplying isolated loads or
delivering energy to a utility grid through DC-to-DC boost
converters and DC-to-AC converters [4-6].
The energy storage systems play an important role in a
hybrid system to perform both functions of storing and
Index
Terms--small-signal
stability,
steady-state releasing energy at an adequate time. The battery stores the
characteristics, dynamic performance, synchronous generator electric energy in DC form and it requires rectifier circuits
(SG), PV module, battery system, AC-to-DC converter, DC-to- (AC-to-DC converters), charging circuits, and DC-to-AC
inverters to exchange energy with the AC system. There are
DC boost converter, DC-to-AC inverter, eigenvalue.
dozens of utility-scaled battery plants built for load-leveling
and dynamic applications. During the past decades, progress
I. INTRODUCTION
NERGY shortage problems jointed with high petroleum with sealed, recombinant lead-acid battery technology and
price has led to severe impacts to several important advanced compounds has extended the scope and future of
technical aspects recently. Efficiency enhancement of high- potentially economic utility applications of battery [7].
Since both wind energy and PV energy are random in
power equipment, development of alternative energy resources,
nature,
they can be combined together to compensate the
exploration of integrated various renewable energy resources,
etc., have also been eagerly progressing. During the past shortage of each other and supply the required energy to loads
decades, huge amount of natural resources has been in remote autonomous areas. When battery is added to the
unlimitedly dissipated and our living environment has been combined wind and PV system, the energy can be effectively
severely polluted. Global environmental protection concerns controlled to delivery to the connected loads or the utility grid
have been widely developed and several new forms of through the employed AC-to-DC converters, DC-to-DC
renewable resources such as photovoltaic systems (PV) and converters, and DC-to-AC inverters. Combining the abovewind power generation systems (WPGS) to supplement fossil mentioned various renewable energy resources with different
fuels have been extensively examined, integrated, and energy storage systems, converters, and inverters in a hybrid
developed in the whole world today.
system, the generated electric energy can be effective
Hybrid power generation and energy storage system distributed and controlled to meet the energy requirement of
may combine all different kinds of available renewable energy the connected loads. The above hybrid power generation and
associated with available energy storage apparatuses. The energy storage system has exhibited several advantages to
required power for the connected loads can be effectively control electrical energy absorbed by the connected loads [811]. This paper is organized as follows. Section II introduces
the d-q axis models for the subsystems of the studied windLi Wang and Tsung-Jen Lin are with the Department of Electrical
Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R. O.
PV-battery system. Steady-state and dynamic simulated and
Abstract--This paper presents small-signal stability, steadystate characteristics, and dynamic performance of an
autonomous hybrid wind-PV-battery system feeding an isolated
single-phase load. To improve the inherent variable frequency,
variable voltage, and loading effects of the studied wind
synchronous generator (SG) under random wind speeds, an ACto-DC converter and a battery system are employed to combine
distinct generated energies from the wind SG and a PV module.
The stored energy in the battery is converted into a single-phase
source with constant voltage and constant frequency to supply
isolated single-phase loads by means of a DC-to-DC boost
converter and a DC-to-AC inverter. The d-q axis equivalentcircuit models for the SG, AC-to-DC converter, DC-to-AC
inverter, DC-to-DC boost converter, PV module, and battery
system are respectively derived to establish the complete dynamic
system equations of the studied hybrid system. Experimental
results obtained from a laboratory 300 W SG, a 24 V, 1.5 kW PV
module, and a 24 V, 250 Ah battery system are compared with
the simulated results to validate the proposed system model.
Small-signal stability of the studied system under various
operating points and different disturbance conditions is also
carried out by using eigenvalue analysis and dynamic simulations,
respectively.
E
C. (e-mail: liwang@mail.ncku.edu.tw).
221
The 14th International Conference on Intelligent System Applications to Power Systems, ISAP 2007
SG
AC-to-DC
Converter
XCR
SW
iqds
iqd1
vqds
LR
RR
LE
IR
C1
rS
VR
PV Module
iSC
RE
Rsh
XCI
RI
II
iqd2
vqd2
VI
C2
Load
C
DC-to-DC Boost
Converter
battery
Battery
System
vo
LI
RC
vC
io
DC-to-AC
Inverter
D1
iE
VDC
November 4 - 8, 2007, Kaohsiung, Taiwan
Fig. 1 Equivalent-circuit model of the studied wind SG fed to a single-phase load through an AC-to-DC converter (Rectifier), a DC-to-AC inverter, a PV
module, a battery system, and a DC-to-DC boost converter.
measured results as well as system eigenvalue analysis are
presented in Section III. Specific conclusions are drawn in
Section IV.
2Hp(ωr ) = Tm − Te
p(θ r ) = ωr
(2)
(3)
where H is the inertia of SG, ωr is rotor speed of SG, θr is
angle of SG, Tm is input mechanical torque of SG, and Te is the
per-unit electromagnetic torque of SG which can be expressed
by
II. SYSTEM MODEL
The equivalent-circuit model of a variable-speed wind
synchronous generator (SG) combined with a photovoltaic
module (PV) and a battery system fed to a single-phase load
through an AC-to-DC converter, a DC-to-DC boost converter,
and a DC-to-AC inverter is shown in Fig. 1. The stator
terminals of SG are directly connected to the AC-to-DC
converter to transfer randomly time-varying AC energy
generated by SG to a DC voltage. Since the battery system is
connected in parallel to the output terminals of the PV module,
the energy from SG and the energy from PV are combined
together to store in the battery system whose stored energy is
sent to a single-phase AC load through a DC-to-DC boost
converter, a single-phase DC-to-AC inverter, and a harmonic
L-C filter. A step-up transformer, which is employed to step
up the low output-voltage level of the DC-to-AC inverter to
match the required voltage level of the connected load, located
between the DC-to-AC inverter and the connected load is not
shown in Fig. 1.
The employed mathematical models for each subsystem
of the studied system are respectively described as below.
Te = −(3/ 2)  Lmd ( −ids + iF )iqs − Lmq ( −iqs )ids 
(4)
The voltage-current equations of the capacitor C1 connected to
the terminals of the stator windings of SG are given by
iqs   pC1 ωC1  vqs  iq1 
 =
⋅ +  
ids  −ωC1 pC1  vds  id1 
(5)
The employed SG has the following specifications: rated
power of 300 W, rated line voltage of 400 V, rated frequency
of 60 Hz, three-phase Y-connected windings, 4 poles, and
rated rotational speed of 1800 rpm.
B. AC-to-DC converter model
The per-unit output voltage of the AC-to-DC converter
shown in Fig. 1 can be expressed by [13-16]
VR = VqRcosαR – (π/6)XCRIR
(6)
A. SG model
The d-q axis voltage-current equations of the studied SG where VR and IR are respectively the output voltage and current
shown in Fig. 1 can be expressed in matrix form as below [12]. of the converter at DC side, αR is the firing angle of the
converter, XCR is the commutation-choke reactance of the
− ωr Ld
0
ωr Lmd  iqs
vqs − Rs − pLq
converter, and VqR is the AC-side per-unit voltage to which

v   ω L
− Rs − pLd
0
pLmd  ids (1) converter is connected and it can be expressed by
r q
 ds = 
⋅
v0s  
  
vF  
0
0
− Rs − pLls
0
− pLmd
0


RF + pLF 
0
 i0 
 
iF 
VqR =
where p is the differential operator with respect to time t while
subscripts 0, d, q, and F are respectively referred to the
quantities of zero-axis, d-axis, q-axis, and field windings of
the SG. The per-unit torque equations of the studied SG can be
written as
2
2
vds
+ vqs
2
(7)
The practical AC-to-DC converter in the studied system can
accept both DC and AC input variable voltages to convert into
the required DC voltage level for the next stage.
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The 14th International Conference on Intelligent System Applications to Power Systems, ISAP 2007
C. PV model
Each practical PV panel of the studied system has the
following specifications: BP275UU, rated power of 75 W,
rated voltage of 17 V, rated current of 4.45 A, open-circuit
voltage of 21.4 V, and short-circuit current of 4.5 A. Two PV
panels are connected in series to form a 24 V branch and total
10 branches are connected in parallel to form a PV module of
rated 1.5 kW. The equivalent-circuit model of a PV module
shown in Fig. 1 includes an equivalent short-circuit current
source iSC in parallel with a diode and a shunt resistor Rsh. The
output of the PV shown in Fig. 1 is connected in parallel with
the output terminals of the battery system via a wire with
series resistance of Rs and inductance of Ls. The equivalentcircuit model of the PV module shown in Fig. 1 can be
expressed by the following equations [7]
vo = vPV – Rsio
is the AC-side per-unit voltage to which the inverter is
connected.
G. Formulation of system equations and linearized equations
When proper and common voltage and capacity bases for
all the subsystems of the studied hybrid system are selected,
the above equations can be expressed in terms of per-unit
quantities to constitute a set of nonlinear system equations.
The system equations of the studied hybrid wind-PV-battery
system with the AC-to-DC converter, DC-to-DC boost
converter, DC-to-AC inverter, filter, and load shown in Fig. 1
can be properly written in terms of matrix form as below [20].
p[X] = f([X], [U], t)
(13)
where [X] is the state vector, [U] is the control input vector,
and f is the nonlinear function of the studied system. Equation
(13) can be further linearized around a selected nominal
operating condition to obtain a set of linear system equations
of the form
(8)
io = isc(PI/1000) – ID[exp(qvPV/AkT) – 1] – vPV/Rsh
November 4 - 8, 2007, Kaohsiung, Taiwan
(9)
where vPV is the output voltage of the PV module, q is the
charge of an electron (q = -1.602×10-19 C), k is Boltzmann
constant (k = 1.38×10-23 J/°K), T is temperature in °K, A is the
quality factor which is a constant, ID is the reverse saturation
current of the diode, PI is the insolation level in W/m2, and isc
is the short-circuit current at 1000 W/m2 solar radiation.
p[∆X] = [A][∆X] + [B][∆U]
(14)
where [A] is the system matrix and [B] is the control matrix.
The characteristic equation of [A] is defined as
det ( [A] − λ[I] ) = 0
(15)
D. Battery model
In the studied system, four 6 V, 250 Ah batteries are
connected in series to form a 24 V branch and two 24 V
branches are connected in parallel to constitute a 24 V, 250 Ah
battery system. The equivalent circuit of the battery system is
simulated by a resistor of rs in series with a DC voltage of VDC.
where [I] is an identity matrix of appropriate dimensions and
λ is one of the system eigenvalues of [A]. If one of the
eigenvalues of [A] has positive real part or is located on the
right half of the complex plane, the system subject to a small
disturbance may become unstable.
E. DC-to-DC boost converter model
The equations of the employed DC-to-DC boost
converter can be expressed by [17-18]
To validate the proposed SG model under various
loading conditions, the measured and simulated line voltages
of the no-load SG suddenly connected to a resistive load of
0.407 pu under 1800 rpm are shown in Figs. 2(a) and 2(b),
respectively. It can be found from Fig. 2 that the peak line
voltages of the SG are suddenly dropped from about 480 V to
about 200 V at t = 7.0 s. The amplitude and frequency of the
measured voltage response are very close to the ones of the
simulated voltage.
Fig. 3 also shows the measured voltage-load steadystate characteristic curve of the studied SG under the rotor
speed of 1800 rpm. It is found from Fig. 3 that the no-load line
voltage Vab is dropped from about 340 Vrms (Y = 0 S) to as
low as 40 Vrms (Y = 10 S). Hence, large voltage variations on
the output voltage of the studied SG can be clearly observed
from Fig. 3 while proper energy storage unit such as a battery
unit should be employed to store the generated energy from
SG for voltage transformation.
Table 1 lists the simulated and measured voltages and
frequencies as well as the measured output powers of the
studied SG under four different resistive loads when the rotor
speed is kept at 1800 rpm. The errors between the simulated
and measured voltages and frequencies are also listed in Table
1. It can be clearly found from Table 1 that the maximum error
of both voltage and frequency is less than 1.2% and the
validation of the proposed SG model is obtained.
 RE + (1 − D)( RC // R )
−
LE
 piE  
=


(1 − D ) R
 pvC  

( R + RC )C

(1 − D ) R 
 1
LE ( R + RC )   i E  
 ⋅   + LE
  vC  
1
−
 0

( R + RC )C 
−

v E =  (1 − D )( RC // R )

R   iE 
 ⋅ 
R + RC   vC 

v
 g

(10)
(11)
where (10) and (11) are respectively the state equation and
output equation of the converter, iE is the current flowing
through inductance LE, vC is the voltage across capacitor C, vE
is the output voltage of the converter, D is the duty cycle of
the transistor which acts as a switch to transform input 24 V
voltage to a higher level for the next stage, i.e., the DC-to-AC
inverter..
F. DC-to-AC inverter model
The per-unit output voltage of the DC-to-AC inverter
shown in Fig. 1 can be expressed by [19]
VI = VqIcosγI – (π/6)XCIII
(12)
where VI and II are respectively the voltage and current at DC
side of the inverter, γI is the extinction angle of the inverter,
XCI is the commutation-choke reactance of the inverter, and VqI
223
III. CHARACTERISTIC ANALYSIS OF THE STUDIED SYSTEM
The 14th International Conference on Intelligent System Applications to Power Systems, ISAP 2007
G of the previous Section. To ensure system stability under the
selected operating conditions, it is necessary to check that all
system eigenvalues are completely located on the left half of
the complex plane. The variations of system eigenvalues are
also very important to determine the sensitivity of system
eigenvalues subject to the variation of one of the system
parameters or operating conditions. It can be clearly found
from Table 2(a) that all system eigenvalues may be affected
by the changes of loading resistance RL but only eigenvalues
λ6,7 are closest to the imaginary axis and they have the trend to
move toward the right half of the complex plane by the
changes of the loading resistance and rotor speed. When the
loading resistance decreases or the rotor speed increases, the
damping of λ6,7 decreases accordingly and it will make the
system become less stable.
Since the output voltage, frequency, and system
eigenvalues of the studied wind SG are severely affected by
the rotor speed and loading conditions of the SG as listed in
Tables 1-2, the generated energy from the SG can be
combined with the generated energy from the PV module and
then send to a battery system for energy storage. The stored
energy in the battery system can also transfer to a single-phase
load through a DC-to-DC boost converter, a DC-to-AC
inverter, and an L-C harmonic filter as shown in Fig. 1.
(a) Measured voltage (Y-axis: 200 V/div, X-axis: 1 s/div)
Vab (V)
800.00
400.00
0.00
-400.00
-800.00
2.00
4.00
6.00
8.00
10.00
12.00
t (sec)
Table 2 System eigenvalues (rad/s) under various loading conditions.
(a)Various loading resistance RL with fixed rotor speed ωr of 1800 rpm.
RL (pu)
λ1,2
λ3,4
λ5
λ6,7
-1.119
0.407
-218±j374.7
-3.25±j13.48
-92437±j315.5
0.201 -187464±j372.7
-1.244
-122.1±j373.09
-3.19±j13.48
-1.274
0.138 -273118±j369.2
-92.97±j369.76
-3.16±j13.49
0.098 -384639±j365.6
-1.289
-74.45±j366.22
-3.12±j13.50
(b)Various SG rotor speed ωr with fixed loading resistance RL of 0.407 pu
λ1,2
λ3,4
λ5
λ6,7
ωr (RPM)
1046
-92437±j215.5 -217.8±j214.89 -0.91137 -3.52±j13.40
1247
-92437±j258.3 -217.9±j257.85 -0.98558 -3.42±j13.42
1674
-92437±j348.4 -218.0±j384.12 -1.09595 -3.28±j13.47
1800
-92437±j374.9 -218.0±j374.69 -1.11933 -3.25±j13.48
(b) Simulated voltage
Fig. 2 Dynamic responses of the studied SG fed to a resistive load.
Vab (V)
400.00
300.00
200.00
The following analyzed results assume that the
irradiation of sunlight is maintained at 38000 lux and the
output power of PV is kept at 200 W. Table 3(a) lists the
measured electrical quantities of the SG under various rotor
speeds. Table 3(b) lists the active powers of load, SG, and
battery under various values of loading resistance. It is found
Table 3(a) that when the SG’s rotor speed gets higher, the
output voltage, frequency, and output power of the SG become
higher accordingly. As listed in Table 3(b), when the loading
resistance becomes lower, the load absorbs higher power from
battery since the battery with a fixed DC voltage decouples the
wind SG and the inverter while the SG’s output power is kept
at a constant value under the fixed rotor speed. Because the
studied system is an autonomous hybrid system with wind, PV,
and battery, the measured results listed in Tables 3(a) and 3(b)
should be carefully determined to meet power balance
conditions. Especially, the voltages, frequencies, and powers
of the studied system under various operating conditions can
not be easily obtained by conventional three-phase power flow
method since converters and inverters are included in the
hybrid system.
100.00
0.00
0.00
4.00
8.00
12.00
Y=1/Z
Fig. 3 Measured voltage-load characteristic curve of the studied SG.
Table 1 Simulated and measured results and associated errors of the studied
SG under 1800 rpm.
Loading
Resistance
RL (pu)
Measured
Voltage
VM (V)
No Load 336
0.407
126.7
0.201
66.9
46.9
0.138
0.098
33.6
Simulated
Voltage
VS (V)
Voltage
Error
VE (%)
334.6
127.3
66.5
46.5
33.2
0.42
-0.47
0.60
-0.86
1.19
Measured Simulated Frequency
Error
Frequency Frequency
FE (%)
FM (Hz)
FS (Hz)
60
59.9
59.8
59.7
59.6
60
59.9
59.9
59.8
59.7
0
0
-0.17
-0.17
-0.17
November 4 - 8, 2007, Kaohsiung, Taiwan
Output
Power
PSG (W)
0
76.81
43.33
30.94
22.29
To examine small-signal stability of the studied system
subject to small perturbed conditions, Tables 2(a) and (b)
respectively list all system eigenvalues of the studied SG
feeding a resistive load under different values of loading
resistance RL and rotor speed ωr using the linearized smallperturbed d-q axis system model described in the Subsection
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The 14th International Conference on Intelligent System Applications to Power Systems, ISAP 2007
IV. CONCLUSIONS
Table 3 Steady-state measured electrical quantities of the studied system
(a) Various SG rotor speeds
No-load
Loaded
No-load
Loaded
Output
Rotor
Voltage
Voltage Frequency
Frequency
Power
Speed
VNL(V)
VL(V)
FNL(Hz)
FL(Hz)
PSG(W)
ωr(RPM)
1046
192
153
34.9
33.7
67.8
220
157
41.6
40.5
78.3
1247
300
163
55.8
54.8
92.6
1674
1800
336
165
60
59
102.8
(b) Different values of loading resistance
Loading
Output
Supplied Power
Absorbed
Resistance
Power of Load
Power of SG
of Battery
PL (W)
PSG (W)
PBatt (W)
RL (Ω)
418.2
115.73
102.8
12.93
206.6
234.27
102.8
131.47
340.85
102.8
238.05
142.0
100.6
481.11
102.8
378.31
Tables 4(a) and (b) respectively list system eigenvalues
of the studied system under various values of rotor speed ωr
and loading resistance RL. It is obviously found from Table 4
that most of the system eigenvalues can be maintained as
stable modes regardless of the changes of various values of ωr
and RL. Only eigenvalues λ9,10 and λ11 have obvious
variations due to the changes of RL but all system eigenvalues
are located on the left half of the complex plane. Again, to
ensure system stability under the selected operating conditions,
it is necessary to check that all system eigenvalues are
completely located on the left half of the complex plane under
different operating conditions. Hence, the AC-to-DC converter,
DC-to-AC inverter, and battery system can render better
small-signal damping effect to the hybrid wind-PV-battery
system under drastically changed operating conditions.
Figs. 4(a)-(c) respectively show the simulated results
of the output voltage of the SG, the inverter output voltage,
and the load voltage when the SG is suddenly connected to the
AC-to-DC converter when ωr = 1800 rpm and RL= 0.407 pu. It
is found from Fig. 4(a) that the AC-to-DC converter and the
battery system constitute an equivalent load of the SG whose
peak terminal voltage suddenly drops from no-load voltage of
420 V to about 200 V. It is seen from Fig. 4(b) that the output
voltage of the DC-to-AC inverter is a PWM voltage waveform
with peak value of 23 V. This nonsinusoidal voltage can be
effectively filtered out to be a nearly sinusoidal voltage
waveform using the L-C filter and then step up to a new
voltage with peak value of 300 V using the step-up
transformer as shown in Fig. 4(c).
ωr (RPM)
1046
1247
1674
1800
λ1,2
-37229±j195
-37229±j242
-37229±j336
-37229±j364
RL (pu)
10
5
3
1
λ1,2
-37229±j364
-37229±j364
-37229±j364
-37229±j364
November 4 - 8, 2007, Kaohsiung, Taiwan
This paper has presented small-signal stability with
eigenvalue analysis, steady-state performance, and dynamic
responses of a practical autonomous hybrid wind-PV-battery
system using experimental and simulated results to validate
the proposed model. The employed wind synchronous
generator (SG) has combined with a PV module to supply
energy to an isolated single-phase load through the
employment of an AC-to-DC converter, a battery system, a
DC-to-DC boost converter, a single-phase DC-to-AC inverter,
an L-C harmonic filter, and a step-up transformer. The
connected load can obtain good voltage and frequency profiles
from the output of the DC-to-AC inverter regardless the
inherent random characteristics of wind speed and irradiation
of sunlight. From small-signal stability analysis using
eigenvalue analysis, it is clearly found that the AC-to-DC
converter, DC-to-DC boost converter, DC-to-AC inverter, and
battery system can render better damping effect and enhance
dynamic stability of the hybrid wind-PV-battery system under
drastically changes operating conditions.
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[11] A. Emadi, S.S. Williamson, and A. Khaligh, “Power electronics
Table 4 System eigenvalues (rad/s) of the studied system.
(a) Various SG rotor speeds with fixed loading resistance of 1.0 pu
λ3,4
λ5
λ6,7
λ8
λ9,10
-0.62155
-26.53730
-499±j192.69
-3.18 ±j13.53
-215 ±j1307
-0.66882
-25.52713
-499±j239.58
-3.17 ±j13.54
-215 ±j1307
-0.76979
-24.51413
-499±j334.73
-3.14 ±j13.54
-215±j1307
-0.79835
-23.27105
-499±j362.27
-3.13 ±j13.54
-215±j1307
(b) Different values of loading resistance with fixed SG rotor speed of 1800 RPM
λ3,4
λ5
λ6,7
λ8
λ9,10
-0.79835
-23.27105
-499±j362.27
-3.13 ±j13.54
-50 ±j1003.79
-0.79835
-23.27105
-499±j362.27
-3.13 ±j13.54
-100 ±j1015.7
-0.79835
-23.27105
-499±j362.27
-3.13 ±j13.54
-164±j1046
-0.79835
-23.27105
-499±j362.27
-3.13 ±j13.54
-215±j1307
225
λ11
-569.84026
-569.84026
-569.84026
-569.84026
λ12,13
-71.6±j70.18
-71.6 ±j70.19
-71.6±j70.19
-71.6 ±j70.19
λ11
-9900
-4800.34
-2671.7
-569.84026
λ12,13
-71.6 ±j70.19
-71.6 ±j70.19
-71.6±j70.19
-71.6 ±j70.19
The 14th International Conference on Intelligent System Applications to Power Systems, ISAP 2007
[14]
[15]
[16]
[17]
[18]
[19]
[20]
400.00
Vab(V)
[13]
800.00
0.00
-400.00
-800.00
3.00
2.00
4.00
5.00
t (s)
(a) SG’s terminal voltage
25.00
20.00
15.00
10.00
5.00
PW
M(V)
[12]
intensive solutions for advanced electric, hybrid electric, and fuel cell
vehicular power systems,” IEEE Transactions on Power Electronics,
vol. 21, pp. 567-577, May 2006.
P.C. Krause, Analysis of Electric Machinery, New York: Mc-Graw Hill
Inc., 1987.
L. Wang, “A comparative study of damping schemes on damping
generator oscillations,” IEEE Transactions on Power Systems, Vol. 8,
No. 2, 1993, pp. 613-619.
Y.-Y. Hsu and L. Wang, "Damping of a parallel ac-dc power system
using PID power system stabilizers and rectifier current regulators,"
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1988.
Y.-Y. Hsu and L. Wang, "Modal control design of an HV DC system for
the damping of subsynchronous oscillations," IEE Proceedings, Part C,
Vol. 136, No. 2, 1989, pp. 76-86.
S.-C. Kuo and L. Wang, “Analyses of an isolated self-excited induction
generator feeding a rectifier load,” IEE Proceedings-Generation,
Transmission, and Distribution, vol. 149, no. 1, pp. 90-97, January 2002.
L. Wang and Y.-H. Lin, “Dynamic stability of a photovoltaic array
connected to a large utility grid,” Paper 2000WM-173, IEEE/PES 2000
Winter Meeting, Singapore, January 2000.
L. Wang and Y.-H. Lin, “Random fluctuations on dynamic stability of a
grid-connected photovoltaic array,” Paper 2001WM-104, IEEE/PES
2001 Winter Meeting, Columbus, Ohio, USA, January 2001.
S.-C. Kuo and L. Wang, “Analysis of voltage control for a self-excited
induction generator using a current-controlled voltage source inverter
(CC-VSI),” IEE Proceedings, Generation, Transmission, and
Distribution, vol. 148, no. 3, pp. 1-8, September 2001.
D.-J. Lee and L. Wang, “Small-signal stability analysis of an
autonomous hybrid renewable energy power generation/energy storage
system, Part I: Time-domain simulations,” accepted for future
publication on IEEE Transactions on Energy Conversion, July 2007.
November 4 - 8, 2007, Kaohsiung, Taiwan
0.00
-5.00
-10.00
-15.00
-20.00
-25.00
3.00
3.02
3.04
3.06
3.08
3.10
(b) Inverter’s output voltage
400.00
VI. NOMENCLATURE
200.00
Vload(V)
General and Abbreviation
synchronous generator
SG
PV
photovoltaic module
ωr , θr
rotor speed and rotor angle of SG
electromagnetic torque of SG
Te
Tm
mechanical input torque of SG
H
inertia of SG
V, I, F voltage, current, and frequency
R, L, C resistance, inductance, and capacitance
D
duty cycle of DC-to-DC boost converter
λ
system eigenvalue
α, γ
firing angle and extinction angle
XC
commutation chock reactance
p
differential operator with respect to time t
loading resistance
RL
Z, Y
loading impedance and admittance
0.00
-200.00
-400.00
0.00
2.00
t (s)
4.00
6.00
(c) Load voltage
Fig. 4 Dynamic simulated results of the studied hybrid system.
VII. BIOGRAPHIES
Li Wang (S87-M88-SM05) was born in Changhua, Taiwan, on December 20,
1963. He received a Ph. D. degree from Department of Electrical Engineering,
National Taiwan University, Taipei, Taiwan, in June 1988. Since August
1988, he has joined the faculty of the Department of Electrical Engineering,
National Cheng Kung University, Tainan, Taiwan where he was an associated
professor. Since August 1995, he has been a professor at the Department of
Electrical Engineering, National Cheng Kung University, Tainan, Taiwan. He
was a visiting scholar of School of Electrical and Computer Engineering,
Purdue University, West Lafayette, IN, USA from February 1 to July 31,
2000. He was a visiting scholar of School of Electrical and Computer
Engineering, Washington State University, Pullman, WA, USA from August
1, 2003 to January 31, 2004. At present, his interests include power system
(control, stability, dynamics, controllers design), electric machinery (induction
machine, reluctance machine, synchronous machine, permanent machine,
power transformer, motorcycle’s AC generator and starting DC motor),
industrial electronics (battery chargers and voltage regulator), and power
electronics (inverters, electronic ballasts, motor-speed control). He is an IEEE
Senior Member.
Subscripts
quantities of AC-to-DC converter (rectifier)
R
I
quantities of DC-to-AC inverter
PV
quantities of PV module
d, q
quantities of d- and q-axis of SG
F
quantities of field winding of SG
m
quantities of mutual inductance
NL
quantities of no-load conditions
L
quantities of loaded conditions
M
quantities of measured results
SG
quantities of synchronous generator (SG)
S
quantities of simulated results
Batt
quantities of battery system
E
quantities of error between measured and simulated
results
Tsung-Jen Lin was born in Taipei County, Taiwan, on September 20, 1976.
He obtained his B.Sc. degree from National Kaohsiung Institute of
Technology and Commerce, Kaohsiung City, Taiwan in 1996 and entered FuWei University of Technology, Yunlin, Taiwan, in 1999. He received his
M.Sc. degree from Department of Electrical Engineering, National Cheng
Kung University, Tainan, Taiwan in 2002. His interests are hybrid power
generation and energy storage systems.
226