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OPTIMAL SIZING OF STANDALONE HYBRID WIND/PV POWER SYSTEMS
USING GENETIC ALGORITHMS
Daming Xu
Xian Jiaotong Uni.
[email protected]
Longyun Kang
Xian Jiaotong Univ.
[email protected]
Liuchen Chang
Uni. of New Brunswick
email: [email protected]
Binggang Cao
Xian Jiaotong University
[email protected]
Abstract
Proper design of standalone renewable energy powersystems is a
challenging task, as the coordination amongrenewable energy
resources, generators, energy storages andloads is very
complicated. The types and sizes of wind turbinegenerators (WTGs),
the tilt angles and sizes of photovoltaic(PV) panels and the
capacity of batteries must be optimizedwhen sizing a standalone
hybrid wind/PV power system, whichmay be defined as a mixed
multiple-criteria integerprogramming problem. In our research, we
investigated thegenetic algorithm (GA) with elitist strategy for
optimally sizing
a standalone hybrid wind/PV power system. Our objective
isselected as minimizing the total capital cost, subject to
theconstraint of the Loss of Power Supply Probability (LPSP).The
LPSP of every individual of the GAs population iscalculated by
simulation of 8760 hours in a year. Studies haveproved that the
genetic algorithm converges very well and themethodology proposed
is feasible for optimally sizingstandalone hybrid wind/PV power
systems.
Keywords: Wind/PV; standalone power systems;
optimalconfiguration; genetic algorithms; mixed multiple
criteriainteger programming.
1. Introduction
Global environmental concerns and the ever-increasing need
for energy, coupled with a steady progress in renewable
energy
technologies are opening up new opportunities for
utilization
of renewable energy resources. Hybrid wind/ photovoltaic
(PV)
power systems are one important type of standalone renewable
energy power systems. The hybrid combination of PV panels
and wind turbine generators (WTGs) improves overall energy
output and reduces energy storage requirements [1].
Proper design of standalone renewable energy power
systems is a challenging task, as the coordination among
renewable energy resources, generators, energy storages and
loads is very complicated. Generally the main objectives of
the
optimization design are power reliability and cost.In this paper
an optimal sizing method using the genetic
algorithm (GA) is proposed. The types and sizes of wind
turbine generators, the tilt angles and sizes of
photovoltaic
panels and the capacity of batteries can be optimized when
sizing a standalone hybrid wind/PV power system, which may
be defined as a mixed multiple-criteria integer programming
problem.
2. Loss of Power Supply Probability
2.1. System Configuration
The configuration of standalone hybrid wind/PV power
systems is shown in Fig. 1. In this paper, we investigated
the
case that a system has only one type of WTGs.
.
.
WTG
1
WTG
N
.
.
.
.
. .
. .
Charge/Discharge
Controller
Battery
1,1
Battery
M,1
Battery
1,N
Battery
M,N
DC Bus
InverterAC
Load
DC
Load
Dump
Load
Control
System
MPPT
. .
. .
.
.
.
.
PV
1,1
PV
M,1
PV
1,N
PV
M,N
Figure 1. Schematic of standalone hybrid wind/PV power
systems.
2.2. Calculation of Wind and Solar Energy
The wind speed to a particular hub height is given [2] as:
( )2 2 1 1V H H V
= (1)
where:
iV wind speed at height i ( iH ),
surface roughness factor (1/7 for open land).It is necessary to
estimate the solar radiation incident on a
tilted solar panel surface when only the total radiation on
ahorizontal surface is known. The total radiation on the tilted
surface is the sum of a set of radiation streams including
beam
radiation, diffuse radiation from the sky and
ground-reflected
radiation, where the diffuse radiation is composed of three
parts as isotropic, circumsolar diffuse and horizon
brightening.
The Hay-Davies-Klucher-Reindl (HDKR) anisotropic model
described by Duffie and Beckman [3] is employed to calculate
the incident radiation on the tilted PV panel surface.
0-7803-8886-0/05/$20.00 2005 IEEE
CCECE/CCGEI, Saskatoon, May 2005
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2.3. Models of System Components
A power curve can be used to represent the relationship
between the average power from a wind turbine and average
hub-height wind speed over an average time interval. This
curve is a function of the turbine design and normally
obtained
from the wind turbine manufacturer. Power curves are
represented by a piecewise cubic spline interpolation in the
calculation.The output power from a PV panel can be calculated
by an
analytical model given by France Lasnier and Tony Gan Ang
[4], which defines the current-voltage relationships based
on
the electrical characteristics of the PV panel. This model
includes the effects of radiation level and panel temperature
on
the output power. With a maximum power point tracker
(MPPT), the output power from a PV panel is given as:
( )
( )
mp mp mp
mp mp,ref V,oc c c,ref
Tmp mp,ref sc,ref I,sc c c,ref
ref
P V I
V V T T
GI I I T TG
=
= +
= + +
(2)
where:
refG irradiance of 1000 W/m2 at reference operating
conditions,
TG average irradiance on a tilted surface (W/m2),
mpI PV panel current at the maximum power point (A),
mp,refI mpI at reference operating conditions (A),
sc,refI short circuit current at reference operating
conditions
(A),
mpP PV panel power at the maximum power point (W),
cT PV panel operating temperature (),
c,refT PV panel temperature of 25 at reference operating
conditions,
mpV PV panel voltage at the maximum power point (V),
mp,refV mpV at reference operating conditions (V),
I,sc temperature coefficient for short circuit current (A/),
V,oc temperature coefficient for open circuit voltage (V/).
Lead acid batteries are main energy storage devices in
standalone power systems. The battery charge efficiency is
set
equal to the round-trip efficiency, and the discharge
efficiency
is set equal to 1. The maximum battery life can be obtained
if
the depth of discharge (DOD) is set equal to 30%50%, for
example DOD=50%. The batteries are normally installed
inside a building where the temperature is not expected to
change drastically, so the temperature effects are not
considered in this paper. The energy stored in batteries at
any
hour tB,tE is subjected to the following constraint:
Bmin B, BmaxtE E E (3)
where:
BmaxE battery maximum allowable energy level,
BminE battery minimum allowable energy level.
LetBmaxE as batterys nominal capacity with the value of the
battery state of charge (SOC) as 1, then
Bmin Bmax(1 DOD)E E= (4)
The MPPT, the battery controller, the inverter and
distribution lines are assumed to have constant
efficiencies.
Assume the efficiencies of the MPPT, the battery controller
and distribution lines as 1 and that of the inverter as 0.9.
2.4. Loss of Power Supply Probability
The Loss of Power Supply Probability (LPSP) [2], which is
defined in terms of the SOC, is the power reliability index of
a
system. LPSP can be defined as the long-term average
fraction
of the load that is not supplied by the standalone power
system.
The SOC of the batteries at any time t1depends on the SOCin the
previous moment t0and the sequence of generated power
and load demand levels in the time interval t1-t0. The SOC
is
used as a decision variable for the control of over charge
and
over discharge. This is important to prevent batteries from
shortening their life or even their destruction.
In terms of the SOC, the LPSP can be defined [2] as:
{ }B, BminLPSP Pr ; fortE E t T= (5)
2.5. Operation Simulation
The logistic model and time series method [5] are employed
for simulation studies. Logistical models are used primarily
for
long-term performance predictions, for component sizing, andfor
providing input to economic analyses. An essential feature
of the time series method is that it employs an energy
balance
approach within each time step. This assures that energy is
conserved throughout the entire simulation, and that the
model
is internally consistent. In particular the sum of all
energy
sources must equal the sum of all sinks.
The simulation period is one year and the time step is one
hour. The load, wind energy and solar energy are assumed to
be constant during a time step. The energy generated by the
WTGs and PV array for hour t,G,tE , can be expressed as:
G, WTG WTG, PV PV,t t tE N E N E= + (6)
where:
PVE energy generated by the PV array,
WTGE energy generated by the WTGs,
PV number of PV panels in the PV array,
WTGN number of WTGs.
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If the generated energy from the WTGs and the PV array
exceeds that of the load demand, the batteries will be
charged
with the round-trip efficiency:
( )B, B, 1 G, L, inv bat1t t t t E E E E = + (7)
where:
B,tE energy stored in the batteries in hour t,
B, 1tE energy stored in the batteries in previous hour,
L,tE load demand in hour t,
at round-trip efficiency of the batteries,
inv inverter efficiency,
self-discharge rate per hour of the batteries.When the load
demand is greater than the available energy
generated, the batteries will be discharged by the amount
that
is needed to cover the deficit. This can be expressed as:
( )B, B,t-1 L, inv G,1t t tE E E E = (8)
When the available energy generated and stored in batteries
is
insufficient to satisfy the load demand for hour t, that
deficitcalled Loss of Power Supply (LPS) for hour tcan be
expressed
as:
L, G, B, 1 Bmin invLPSt t t t E E E E = + (9)
The LPSP for a considered period T is the ratio of all LPS
tvalues for that period to the sum of the load demand, as
defined by [2]:
L,
1 1
LPSP LPST T
t t
t t
E= =
= (10)
3. Optimal Sizing Using the Genetic Algorithm
3.1. Problem Description and Sizing Procedures
The reliability and cost are two objectives of sizing
standalone hybrid wind/PV power systems. The cost index is
the capital cost [4] in this paper. The types and sizes of
WTGs,
the tilt angles and sizes of PV panels and the capacity of
batteries have a considerable influence upon the power
reliability and capital cost and can be optimized. Except the
tilt
angle, which is a real variable, others are integer variables.
So
optimization of standalone hybrid wind/PV power systems is a
mixed multiple criteria integer programming problem [6].
For multiple criteria programming, one method is to retain
only one main objective and to converter other objectives to
constraints. The power reliability is in conflict with the
capital
cost. The requirements of power reliability are different in
systems that have different load characteristics. Usually
the
LPSP is not required equal to 1. Let the total capital cost
of
WTGs, PV panels and batteries,WPBC , as the objective, the
power reliability as the constraint, then the problem of
sizing
standalone hybrid wind/PV power systems is changed to single
criteria programming as follows:
TypeWPB WTG WTG PV PV bat bat
set
WTG
PV
bat
min
. .
LPSP LPSP
Type
0,1,2,
0,1,2,
0,1,2,
C C N C N C N
s t
N
N
N
= + +
=
=
=
=
(11)
where:
atC cost of the batteries,
PVC cost of the PV panel,
TypeWTGC cost of a certain type of WTG,
LPSP set according to the load characteristics,
at number of the batteries,
Type code of a certain type of WTG.
The total capital cost is given as follows [2]:
total WPB 0C C C= + (12)
where 0C is the total constant costs including the cost of
power conditioning equipment, design and installation etc.
In the optimization model, the tilt angle is a variable of
the
HDKR model that is used in computing LPSP. The amount of
radiation received using the optimum fixed tilt angle is
only
slightly less than that using a monthly adjustable tilt angle.
The
fixed tilt angle method may be preferred because it would
involve cheaper equipment and less work [7]. The optimum
fixed tilt angle rests on geographical and meteorological
conditions of the location and the load characteristics as well
as
the system configuration. In this paper the fixed tilt angle is
setas an integer in degrees. The range of optimization of the
tilt
angle is obtained by rounding off the latitude value then
plus-
minus 0for south-facing panels with a limiting range of
[090]For a chosen configuration, tilt angles adjacent to
the optimal tilt angle can make the system fulfill .
So the optimal tilt angle of the system must be recalculated
according to the optimized configuration.
The optimization procedure is to determine the sizes of PV
panels and capacity of batteries in series, then to use the GA
to
compute the type and sizes of WTGs, the tilt angle and sizes
of
PV panels and the capacity of batteries, and then to
recalculate
the optimal fixed tilt angle of the PV panels.
3.2. The Genetic Algorithm
The GA is a stochastic global search method that mimics the
metaphor of natural biological evolution and does not
require
derivative information or other auxiliary knowledge. It is
important to note that GA provides a number of potential
solutions to a given problem and the choice of final solution
is
left to the user [8].
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In this paper, integer encoding and the elitist strategy are
employed. The form of the individual of the GAs population
is [ ]WTG PV batType N N N , where is thefixed tilt angle. The
LPSP of every individual is calculated by
simulations for 8760 hours.
4. Application Example
The typical meteorological year data sets (TMY2s) contain
hourly values of solar radiation and meteorological elements
for a one-year period [9]. The location of Daggett,
California
of Latitude 34 is chosen. So the range of optimization
of the fixed tilt angle is [5 5 ]. The data of
extraterrestrial horizontal radiation, global horizontal
radiation,
diffuse horizontal radiation, temperature and wind speed in
the
TMY2s are utilized. Generally, the ground reflectance is
0.2.
The FD series WTGs made by Tianfeng Green Energy
Company of China were considered. The turbines with rated
power of 1KW, 3KW, 5KW, 7.5KW and 10KW were coded as
I, II, III, IV, and VThe power curves of the WTGs are shown
in Fig. 2. A 50Wpeak
PV panel made by Yunnan Semiconductor
Device Factory in China was used for this simulation study.
The capacity of a single battery used was 200Ah. That
battery
has a round-trip efficiency of 0.7 and DOD=50%.
Figure 2. Power curves of the WTGs (The symbols represent data
sampled
from the power curve graphs given by the manufacturer).
The load was assumed constant year round [4]. Let the load
as 2000W, LPSP=0.01. The numbers of PV panels and
batteries in series are determined as 3 and 24 previously.
The
GAs results are [ 10 523 1524] with the totalcapital cost of
WTGs, PV panels and batteries, WPBC , as
593400 Chinese Yuan. The type WTG, FD1KW, yields thelowest cost
for the system, and thus Type=. is in therange of [5862]
he optimal configuration is [ 10 59 523 1524]
with LPSP=0.0099565. The Loss of Power Supply in the one-
year simulation is shown in Fig. 3 and this is in accordance
with the situation that both the solar energy and wind
energy
are abundant in summer at this location.
Figure 3. The Loss of Power Supply of configuration
[ 10 59 523 1524].
5. Conclusions
A methodology of sizing standalone hybrid wind/PV power
systems using the genetic algorithm is proposed in this
paper.
Studies have proved that the genetic algorithm converges
verywell and the methodology proposed is feasible for sizing
standalone hybrid wind/PV power systems.
Acknowledgements
This research was supported by the Research Project (No.
2004EA105003) of P. R. China.
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