IEEE Transactions on Energy Conversion, Vol. 12, No. 1, March 1997
79
UNIT SIZING AND CONTROL OF HYBRID
WIND-SOLAR POWER SYSTEMS
Riad Chedid, Member IEEE
Department of Electrical & Computer Engineering
American University of Beirut,
850 Third Avenue, New York N.Y. 10022, IJSA
Abshxct- The aim ofthis paper is to provide the core of a CAn/CAA tool
that can help designers detennine the optimal design of a hybrid wind-solar
power system for either autonomous or grid-linked applications. The
proposed analysis einploys linear programming techniques to minimize the
average production cost of electricity while meeting the load requircinents
in a reliable manner, and takes environmental factors into consideration
both in the design and operation phases. While in autoiionious systems, the
environmental credit gained as compared to diesel alternatives can be
obtained through direct optimization, in grid-linked systems eiiiission is
another variable to be minimized such that the use of renewable energy
can be justified. A controller that monitors the operation of the
autonornoudgrid-linkedsystem is designed. Such a colitloller dctei miles
the energy available from each of the system components atid the
environmental credit of the system. It then gives details relatcd to cost,
uninet arid spilled energies, and battery charge and discharge losses.
I. Introduction
The increased interest in environmental issues has led recently to
extensive research for ha~uessingrenewable energy resc)urces. In
[I] a linear programming (LP) model for the design of integrated
renewable energy systems has been developed, and in [2] a similar
LP model was used to arrive at an optimal mix of wind and
photovoltaics for system design. In [3] a computer model
RAPSODY that facilitates the design, sizing and operation of a
remote area power supply is described. This software is capable of
simulating the operation of systems that use various combinations
of renewable energy sources taking into account the variability of
the energy source, the capital cost, and the operating and
maintenance costs of system components. In [4], a trade-off
approach is used to design a stand alone power system under
uncertain conditions. The authors d e h e several scenarios to
account for variation in load growth, renewable resources and
hardware availability; and use decision set analysis to an-ive at the
optimal plan. A knowledge-based approach to design integrated
renewable energy systems is presented in [5]; the authors use a
databm and a search algorithm to find the combination of P V and
wind energy conversion system ratings and the size of energy
Saifur Rahman, Senior Member IEEE
Center for Energy and the Global Environment
Virginia Polytechnic Institute and State University
Blacksburg, VA 2406 1-011 I , USA
storage that minimizes the capital cost while maintaining the
required loss of power supply probability. Finally, a computer
package that assists planners to determine the optimal expansion
plan of an autonomous generation system, is presented in [6]. This
package takes into account the stochastic nature of meteorological
conditiolis and load.
In all of the above studies, either probabilistic techniques have
been implemented, or optimal designs have been arrived at without
taking into Consideration the operational characteristics of the
proposed systems. The aim of this paper is to provide a
deterministic analysis to produce the optimal design of a hybrid
wind-solar power system for either autonomous or grid-linked
applications. Such a power systetn is mainly composed of solar,
wind and battery sets; and depending on the application, either
diesel engines or a jqid option are considered for back-up
purposes. The part related to autonomous applications has been
reported U1 [7], and will be briefly introduced here for comparison
purposes.
11. Problem Definition
The major concern in the design of an electric power system that
utilizes renewable energy sources is the accurate selection of
system components that can economically satisf) the load
demand. While in autonomous systems, the environmental credit
gained as compared to diesel alternatives can be obtained
through direct optimization; in grid-linked systems, emission is
another variable to be minimized for the use of renewable energy
be justified. Hence, system's components are found subject to:
I.
2.
3.
minimizing the electricity production cost ($/KWh),
ensuring that the load is served according to a certain
reliability criteria, and
minimizing the power purchased from the grid.
The cost fiinction is defined as [8]:
4
A paper recommended and approved by the IEEE
Energy Development and Power Generation Committee of the IEEE
Power Engineering Society for presentation at the 1996 IEEUPES
Summer Meeting, July 28 - August 1, 1996, Denver, Colorado.
Manuscript submitted August 28, 1995;made available for printing June
25, 1996.
96 S M 572-8 EC
f=(c
k= I
1
Ik-SPk+OA4 )Pk E,.N
where the index k is made to account for wind, solar, diesel
generators or grid connection, and batteries.
0885-8969/97/$10.00 0 1996 IEEE
80
The proposed analysis is composed of three modules, iiaiiiely, the
preprocessor, the optimization tool and the control module. To
meet the above objectives, the user should have data on load
demand, solar and wind resources averaged over several years as
well as economic and technical data. Such irlformatioil is analyzed
and brought to the required format through the preprocessor. The
selection of system components will be achieved via the
optimization module and then the whole design will be tested in the
control module through which tlie size of the storage will be
determined as well as the environmental credit of the system Foithis a chronological set of hourly load and resource data is assumed
to be available. Detailed analysis and a case study will be presented
in the following sections.
111. Optimization Coeficients
A. Wind Turbine
or a solar panel; hence, it might be necessary to purchase additional
diesel generators before the life span of the project comes to an
end. If adis the initial cost in $KW, the present worth of all the
initial investments is:
(7)
where L, is the life-time of diesel generators and x, is the number
of times where diesel generators are purchased.
Tlie salvage value of the diesel generator is assumed to decrease
linearly fi-oin a,($KW) if the generator operates for zero years, to
S, ($/KW) if the generator operates along its life-time Ld. If the
project life comes to an end before the diesel generators have
reached the end of their life span, then the diesel sets could be sold
at SI,, ($/KW),
which is a value greater than S,:
S
pd
The design vmable of the wind tm bine is the total I otoi ai ea, Aw,
m m2.Given a, the mtial cost ($/in2) of tlie wind tuibine, the first
term of equation (1) becomes a , 4 , With a salvage value of
Sw($/in2), tlie total salvage value would be Sw Aw and the present
worth 1s
SI,
=
Sw Aw facl
(2)
'd-'d
= (-).yenrs+ad
where 'years' indicates tlie number of years of operation between
the installation of the last diesel set and the end of the project life
span. The present worth of all the salvage values is found by:
Xd-l
Finally, with a yearly operation and i~iaiiiteiiancecost (( )M)of
aoMw($/m2/year),the total yearly operation and maintenance cost
would be a,,,.Aw,
and the present woitli of all tlie yearly costs
would be.
(
)MI,,=CI omAw.fac2
(3)
where,
N
(1 + e # - (1 +es)
f a e 2 = ~ --.(1-(-)
y = l (1 +.y
(r-4
1 +es
I +r
) for
r=es
(4)
and fac2=N if i-=es. Here 'es' is the escalation rate.
B. Solar Puriels
The design variable here is the total solar panels' area, As, in i d .
With an initial cost of a,($/111*), the total initial investment would
be a&. The salvage value would be %.As, where Ss is the selling
price per m2, and the present worth of the selling price would be:
S,,,=Ss.As.fac1
(5)
With a yearly OM cost of aoMs($/ni'/yeai-), the total yearly OM
cost would be a,,,As with a global present worth of
OM,,= CI ,,.As.fac:!
C. Diesel Gerrerutors
The design variable here is the capacity R, in KW. The life- time
of a diesel engine L, is usually shoi-ter than that of a wind turbine
1i j %.L
lij N
(-)
d + S .Rd.(-)
'
Sp3=Sd.Rd.
x-1
where f a c l = ( l + ~ ) ~ / ( l + r )and
~ , 'J' and 'r' aie the iilfjatioii and
interest rate respctively
(8)
Ld
l+r
pd
(9)
l+r
Tlie yearly OM cost can be divided into two parts. Labor and parts
cost (a .,,),$/KWh),
and fuel cost (a,,,,$/KWh). The present
woitli of tlie total yearly OM cost is:
CL Mcn+aoc,).R,.total number
of hours.fac2
(1 0 )
D.Grid Connection
If gi id is available, then utilizing renewable energy sources can
only be justified on the basis that reduction in utility emissions is
dew able This awai eness takes the form of a utility management
program for promoting for environmentally friendly
technologies On the customer side, the use of renewable energy
niay become attiactive if in the future, customers would have to
pay not only for the cost of generating the power they use, but
a l w for it5 transniission, distIibution and the indirect cost of
envii onniental cleanup and health effects[9] The design variable
in this case is the rating of the substation R, (KW), which makes
tlie connection with the hybrid power system Given ag,the
initial cost ($/KW), tlie total capital cost becomes a&
With
ablly
defining the cost of pui chased electricity ($/kWh), the yearly
costs would be.
O M , = ~ ~ ~ , ~ ~ , . R number
~ . ( t o t aof
l hours) + 12aDc.Rg
If regulations allow a utility to buy power from private
suppliers, tlien equation (1 1) should modified as follows:
C)M~=(CIb,,y.I~~-arell.Rercerr).(total
number of hours) + 12aDc.R,
81
of the whole system at that point (see section VI).
The above equation has a present worth of
OM,,,=( )Ms.fac2
V. Controller Design
E. Storage Batteries
The design variable in the case of storage batteries is their size
R, in KWh. As in the case of diesel generators, the life-time of a
battery (Lb) is expected to be less than that of the wholc project.
Hence batteries of sizes R, are to be purchased at regular
intervals of L,. The total present worth of the capital investments
on batteries (with k=4 in (I)) is given by:
While average load demand and supply patterns are used at the
design stage, the system is subject to fluctuating wind speeds and
solar insolation as well as to varying load demand during
operation. Hence, a controller is essential to determine how
inuch energy is available from each component and how much to
use of each. At the end of the operation period, the controller
gives full information regarding the status of the system such as
cost, energy available from each unit, environmental credit,
uninet and spilled energies, and battery charge and discharge
losses.
where xb is the number of times battei ies should be purchased
during the project life-time and a bIS the capital cost ($/KWi)
A . Operntironpolicies.
Case I Autonoinom System
The salvage value of the batteries is assumed negligible. With an
operation and maintenance cost of aoMB
($/KWldyear), the present
worth of the total yearly cost would be:
The operation policy of the proposed system implies that the
available energy from the wind turbines and solar panels in each
subperiod be used first, and excess energy to be stored in
batteries. If the renewable energy is not sufficient to supply the
load in a given subperiod, two control policies are implemented
to iill the void. In control policy I (CPI), energy is first drawn
from the storage system. If this is not enough, the diesel
generators should provide the remaining portion of the load. In
control policy 2 (CP2), if the load cannot be met by the
renewable supply, energy is drawn first from the diesel engines
and, if possible, the batteries supply the remaining part of the
demand. The main difference between the two approaches is that
in C1' I , the storage system acts as a fuel saver since batteries are
used before the diesel engines. This is done at the expense of
having batteries that are already discharged in periods where
diesel engines are not sufficient to supply the load. Hence the
unniet load is expected to be smaller in CP2 but fuel costs are
higher. In sorne subperiods, all of the available supply is not
sufficient to serve the load; in such a case, the difference
between the deiiiand and tlie available energy is shed and an
underflow cost is incuned.
IV.Load Constraints
The load must be satisfied according to a certain rcliability
criteria. Hence, for an autonomous system,
ew(i).Aw+es(i).As+duration.R,+ x.RI>-(I -EENS) Load(i) (1 6 )
ew(i).Aw+es(i).As-tduration.R,+x.Ri,
ILoad(i)
( I 7)
where, EENS is the expected energy not served, i is the period, x
is the fraction of the battery capacity expected to discharge in
each period, and ew and es are the wind and solar energy
produced per m2 respectively. ew and es are calculated based on
the monthly averaged wind speed and solar iiradiance input data
[7]. For a grid-linked system, the teiiii R, shuuld be replaced by
R,. Additional constraints to be imposed are:
Case 2 . Grid-Liiked Systetn
0 < Aw <&,ax
0 i As c A,,,,
01 R b
01 R d &,
(18)
(for autonomous systems)
Or Rg CR,,,~
(for grid linked-systems)
It is to be noted that although the I ) r o b h formulation for both
autonomous and grid-liilked systems is identical, the procedure of
obtaining tlie optimal design differs substantially in the case of a
grid-lmked system, because it is the minimization of both cost and
grid energy demand which is of conceiii here. However, these two
objectives cannot be achieved simultaneously because t h y conflict
with each other. Therefore a trade-off curve of cost versus energy
demanded from grid is required for unit sizing. The choice of :in
operating point on the trade-off curve depends on the
environmental credit it oEers and on the operational characteristics
The control strategy for grid-linked systems is similar to the one
discussed in case I above in the sense that renewable energy
must he exploited first and excess energy should be stored in
b:ltteries, However, if there is still excess energy
_.then, the latter
should be sold to the grid. Real spilled energy is the energy that
cannot go to the grid because of the rating limit of the electric
substation. If the renewable energy is not sufficient to supply the
load in a given subperiod, then the two control policies
discussed in case 1 are applied but with the grid now replacing
tlie diesel engines. It is to be mentioned that the concept of fuel
saving in CP 1 as discussed in case I , leads to the concept of grid
energy deniand saving in case 2. Hence better conditions for the
environment are guaranteed.
82
B. Diesel Generator Control
VI. Results and Discussion
Each generator has in addition to the rating Pg,,,,,, a minilnuin
allowable loading Pglllinto ensm'e the coi+ect engine operating
temperature. On the other hand, tlie efficiency of diesel engines
varies with the fraction of the rating at which they are operating.
This dependence is taken into consideration by calculating the cost
rate for each engine 'i' as [ 1 11:
A. IJnit Sizing.The proposed techniques are applied to a location
in Lebanon where the load is defined as 800KW from the 5-th to
the 9-th months, and 550KW for the rest of the year. The hourly
wind speeds vary between 2.96 and 5.63 d s and the hourly solar
irradiance vary between 0 and 0.7 KW/m2. The values of the
parameters involved in this case study are given in Appendix I.
Riming the optimization routine gives well defined results for the
autonomous system. However, for the grid-linked system, it is the
task ofthe designer to choose an option near the knee of the tradeoff curve sliown in Fig. 1 such that the EENS is not exceeded. This
c i n e was geiierated under restrictions on space available for solar
and wind units, and limited storage (4000m' for wind units,
1 OOO0iii2for solar units and 1OOOKWh for storage). Under such
restrictions, the options located in the upper part of the knee of the
curve are not appropriate because they do not satisfy the
requirement in EENS which is set at 5%.
Cr(i>=a(i)+b(i).Pg(i)+c(i).Pg'(i)
(19)
where a(;), b(i), c(i) are coeficients that should be available
from the engine's specifications, and Pg(i) is tlie power output
level of the generator.
A variable called average production cost (apc) is defined for
each generator 'i' as follows.
Results of optunization for both systems are shown in Table 1. Had
tlie load been satisfied only by diesel engines or through a grid
connection, tlie required capacity would have been 760 KW.
Therefore, the use of renewable energy has resulted in 50.26%
savings in diesel capacity and 44.7% savings in grid capacity. The
emission savings are calculated based on the emission rates given
Mode 0: the generators are never allowed to be shut-down; if not in [ 131 for oil type utilities, mid in [ 141 for diesel fuel. Although the
needed, they should be kept on hot reserve. This mode is costs sliown in tllis table do not iiiclude the emission cost, as is the
applicable when the generators have high starting costs rendering ciment pi-actice in many countries, we anticipate that the real cost
uneconoinical the slid down process, or when their minimum of electricity should be calculated according to the following
down and start-up times are relatively large (umeliable operation). procedure. Calculate through a chronological analysis the
In this case, even if no power is taken from the generators, a hot consumption of electric energy associated with the grid (or diesel
reserve cost will be incurred equals to a(;) ($Amur) for each generators) and find the cost due to CO,, NO, and SO, emissions.
generator 5'.
The cost ofthe latter vary from country to country. For example in
tlie TJSA some estimates show these to be 1.78 centsKWh for
Mode 1 : the generators are allowed to be shut down when no CO2,0.80 centsKWh for SO,, and 1.66 centsKWh for NO, [ 1.51.
power is needed from them. This is peimissible only when the By adding the emission cost to tlie operation cost of the system
mininiuni down and up tinies are negligible with respect to the concerned, the actual cost of producing lKWh can then be
length of the considered subpeiiod. C)peratioii under mode 1 causes obtained by running the optimization routine as described'in this
additional start-up costs accounting for extra fuel.
paper. Finally, it can be seen from Table 1 that optimization
suggests that no storage is necessary in the design phase for both
systems. However to cater for the fluctuations in both the input
energy and the load, storage is introduced by running the controller
Ena gy fi-om battenes is needed whenevei the I enewable energy is with batteries of different capacities for a day having maximum
~m.fEclentto supply the load (CP I), oi when both the ienewable possible load under worst possible weather conditions. The battery
system and diesel generaturs (or gild i n tlie case of g~~d-lii&cd size which is consistent with constraints (1 7- 18) is selected.
systems) fail to meet the total demand (CP2) On the other hand,
energy is stored whenever tlie supply from the I enewable <y\teiii H. Controller rmnning. 111 this section we show the hourly
exceeds the load demand (CPI and CP2), and when the diesel operation ofthe controller over a sununer day (see Appendix I for
engines are capable of chai ging the batteries (c'P2) (No battery a listing of the necessary inputs)
charging will be done from the grid i n eithei CP I or CP2) The
maximum allowable enei gy taken or added to the battei le\ is How by Hour Er1ei-pResults.for the Grid-Linked System. Figs 2usually 10% of RI,per hour [ 3 ] The conti oller specifies tlie amount the energy demand under both control policies The unmet load
ofenagy stored or dischmged by the battcries and the storage level eneigy iuider both policies is shown in Fig 4 From Figs 2-4, it can
at each subpei iod It also identifies the charging and discharging he noticed that the system performance IS highly affected by the
losses of the batteries
The above equation is used to identify which generator has a
cheaper operation so that diesel engines are committed starting
with those having smallest apc. Diesel engines are allowed to
operate in one of two possible modes
83
Table 1
Optimization Results
Wind, mz
Solm,mz
Battery,KWh
Diesel, KW
Grid, KW
CO,, Kg/yew
NO, Kg/yew
SO,, Kg/year
Cost, $/KWh
Autonomous system
Grid-linkedsystem
4000
10000
0
378
1846
10000
0
i 400
300
w
100
420
2.29~10~
5.8~10'
14.92~10'
0.1016
0.244~10~
0.297~10'
3.36~10'
0.1574
200
0
-1 00
8
4
state of the solar insolation. In fact, the energy drawn from the wind
turbine is almost constant throughout the day; however, the energy
from the solar PV system reaches zero at nights and peaks at noon.
Hence, some unniet energy is encountered during nights while
some energy is being spilled and therefore sold back to utility
during mid-days (see Fig.5). The uuunet energy encountered in CP I
(Fig.4) is reduced in CP2 because, in the latter case, the grid would
meet the load before the storage batteries, and when a shortage is
encountered, batteries will be able to supply more energy (The
m e t energy is 162.5KWh in CPI and 128.26 KWh in 0 2 ) . As
a result, the grid energy in CP I, shown in Fig.6, is lower and hence
less pollution is envisaged (For the day under consideration, the
extra savings in emissions due to CPI are 26.7Kg in CO,,
0.0684Kg in NO, and 0.174Kg in SC)J.
+Load
+
4Solar
--)c
Grid
20
16
24
Battery
-€I-
Wind
Fig.:! Hourly Operation Under CP1
12
6
4
H o w By Hour Diesel Cost.for the Ai~tononious,(;ysteirr. Fig.7
illustrates the diesel operational costs incutred during the day in the
two control policies CP 1 aid CP2. It is noticed that less energy is
being drawn from the diesel engines while operating wider CP 1
and hence less hiel price is being paid, and less enviroiiniental
daniage is encountered (For the day under consideration, the extra
savings in emissions due to CP 1 are 32.07Kg in Cbz, 0.44Kg in
SO2 and 0.039Kg in NOX).This is because batteries back-up the
renewable system before the diesel engines. The daily fie1 costs
sum up to $544.26 under CP 1 and $556. I under CP2. The start-up
costs, shown in Fig.8, sun up to $5 16 for both CP I and (21'2.
12
lime, t!i
16
24
20
Time, Hr
--t
Load
-t
Grid
-e- Battery
--r Wind
--t Solor
Fig.3 Hourly Operation LJnder CP2
60
50
c
40
x
9 30
wC
20
10
0
0.55-
6
12
16
20
24
I
IEZICP~
RCP~
$ 0.25-
>
5
4
Time, Hr
0.3 -
Fig.4 Llnniet Energy [Jnder CP1 and CP2
02-
0
0.150.1
VII. Conclusions
-
o'os'O
' 100 ' 200 ' 300 ' 400 ' 500 ' 600
Grid Power. KW
'
700
'
'
Fig 1 . Trade-off Curve of Cost Versus Grid Power
This paper has presented a technique to design and analyze a
hybrid wind-solar power system for either autonomous or p d linked applications This technique uses linear programming
principles to reduce the cost of electricity while meeting the load
84
’““IT
1
140
120-
3
y
100-
>-
;80C
60-
‘Oi
20
I
0
24
1
4
8
Time,
Hr
(mcPImcP2
I
Fig 5 Spilled Energy LJiider CPl and CP2
450
Time, Hr
j m C P 1 a c P 2
1
Fig.8 Stat-up Diesel Cost under CP1 and CP2
I
- The use of renewable energy offers substantial environmental
credit when compared to diesel or grid altematives. The level of
penetration of renewables in grid-linked systems depends on
system’s reliability which should be strictly satisfied,
- The envirc~ilmentalcredit of both systems can be improved in the
operation phase tl~roughappropriate control policies. In this study,
CP 1 was found to be suitable for both systems.
- The proposed analysis allows the user to study the interaction
ainong eeononuc, operational and environmental factors and hence
it offers a useful tool for the design and analysis of hybrid solarwind power systems.
Time, Hr
1Fig.6 Grid Power Under CPl nnd CP2
45
VIII. Aclcnowledgment
-1
:L
\I
351
I/
IO
5
4
I
1
24
8
12
- Time,
CP1
16
Hr
CP2
20
Fig 7 Diesel Operating Cost Under CPI and CP2
requirements in a reliable manner. A controller that monitors the
operation ofthe autonoInaus/grid-liIlked systeiiis is designed Such
a controller determines the energy available fiom each of the
system components and the environrnental credit of the system. It
then gives details related to cost, uimet and spilled energies, and
battery losses. From the results obtained above, the following
conclusions can be made.
Tlus research was partly done during tbe summer visit made by the
first author to Virginia Tech The financial support of the URB at
the American ‘IJniversity of Beirut is gratefully acknowledged.
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NOMENCLATURE
initial investment
present worth of the salvage value of each component
present worth of the operation and maintenance costs
yearly energy demand
life-time of the project.
interest and inflation rates respectively
solar panels' and wind rotor areas respectively
diesel rating and battery capacity respectively
cost rate for generator (i)
average production cost for generator (i)
CP 1,CP2 control policies 1 and 2 respectively
ew, es wind and solar energy respectively
aoc
demand charge in $/(KW.niontli)
asell
electricity sold ($/kWh)
Rexosss excess energy that cannot be stored in batteries
a,, a, wind and solar initial costs respectively
ad,a, diesel and grid initial costs respectively
Saifur Rahman (IEEE S-7.5, M-78, SM-83) graduated from the
Bangladesh IJniversity of Engineering and Technology in I973
with a B.Sc degree in Electrical Engineering. He obtained his M.S
degree in Electrical Sciences from the State University of New
York at Stony Brook in 1975. His Ph.D degree (1978) is in
Electrical Engineering from the Virginia Polytechnic Institute and
State University.
Saifur Rahman has taught in the Department of Electrical
Engineering, the Bangladesh University of Engineering and
Technology, the Texas A&M University and the Virginia
Polytechnic Institute and State University where he is a Full
Professor. He also directs the Center for Energy and the Global
Environment at VPI. His industrial experience includes work at the
Brookhaven National Laboratory, New York, the Carolina Power
and Light Company, and the Tokyo Electric Power Company,
Japan. He is a member of the IEEE Power Engineering and
Computer Societies. He serves on the System Planning and
Deinand Side Management subcommittees, and the Load
Forecasting and the Photovoltaics working groups of the IEEE
Power Engineering Society. His areas of interest are demand side
management, power system planning, alternative energy systems
and environmental systems. He has authored more than 180
technical papers and reports in these areas.
Appendix I
Input Data for the Optimization and Control Routines
Efficiency of solar system
Inflation or escalation rate
Interest rate
Project life span
Battery life span
Diesel life span
Solar panel price
Wind turbine price
Battery price
Diesel engine price
Grid connection
Solar panel salvage value
Wind turbine salvage value
Diesel engine salvage value
Solar panels' OM costs
Wind tu1bine' OM costs
Batteries' OM costs
Riitd Chedid was born in Lebanon in 1960. He received his M.S
Grid energy charge
degree (with distinction) in Electrical Engineering from Moscow Demand charge (grid)
Power Engineering Institute in 1986. In 1992 he obtained his 11'1 D Diesel engines Maintenance
in Electrical Engineering from the University of London, and the Fuel cost
DIC from Imperial College of Science Tecluiology and Medicine, Batteiy eftkiency
1J.K. At present, Dr. Chedid is an Assistant Prof. at the Dcpart~nent Loss of load cost
of Electrical and Computer Engineering, Arnerican IJniversity of Pgmax for diesel engines
Beirut. His research interests include alternative energy systems, Pgmm for diesel engines
Cost late constants for
low qxed drives, finite element analysis of electric machinery and each generator
neural networks applications in electrical engineering.
Startup costs of diesels
0.12
0 09
0.12
20 years
5 years [ 101
8 years [3]
450$/m2 [ 12 (12$/Wp for 20 MJ/mZ/day
100$/m2 [ 121 (1$/Wp for 5 5 m/s speed)
1OO$/KWh I IO]
SOO$/KWh [ 101
SOO$/KW
45$/ni2
10$/m2
80$/KW
4.3$/m2/year[ 161
2.5$/m2/year[ 3 ]
IO$/KWh [3]
0.08$/KWh
lS%/KW.month
0.023%/KWh
0.196 $KWh
0 78
0.8$/KWh[3]
[200 100 100 100 3001
[40 20 20 20 751
a=[l.l 1.0 1.0 1.0 1.21
b=[0.125 0.122 0.122 0.122 0.131
c=[0.14 0.13 0.13 0.13 0.16]x103
[62 5 5 55 55 661