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Solar Energy 84 (2010) 691–702
Reliability analysis of solar photovoltaic system using hourlymean solar radiation data
Ravindra M. Moharil a,*, Prakash S. Kulkarni b
a Department of Electrical Engineering, Yeshwantrao Chavan College of Engineering, Nagpur, Maharashtra, Indiab Department of Electrical Engineering, Visvesvaraya National Institute of Technology, South Ambazari Road, Nagpur 440011, Maharashtra, India
Received 18 April 2008; received in revised form 14 August 2009; accepted 27 January 2010Available online 25 February 2010
Communicated by: Associate Editor Elias Stefanakos
Abstract
This paper presents the hourly mean solar radiation and standard deviation as inputs to simulate the solar radiation over a year.Monte Carlo simulation (MCS) technique is applied and MATLAB program is developed for reliability analysis of small isolated powersystem using solar photovoltaic (SPV). This paper is distributed in two parts. Firstly various solar radiation prediction methods alongwith hourly mean solar radiation (HMSR) method are compared. The comparison is carried on the basis of predicted electrical powergeneration with actual power generated by SPV system. Estimation of solar photovoltaic power using HMSR method is close to theactual power generated by SPV system. The deviation in monsoon months is due to the cloud cover. In later part of the paper variousreliability indices are obtained by HMSR method using MCS technique. Load model used is IEEE-RTS. Reliability indices, additionalload hours (ALH ) and additional power (AP ) reduces exponentially with increase in load indicates that a SPV source will offset maximumfuel when all of its generated energy is utilized. Fuel saving calculation is also investigated. Case studies are presented for SagardeepIsland in West Bengal state of India.� 2010 Elsevier Ltd. All rights reserved.
Keywords: Hourly mean solar radiation (HMSR); Loss of health expectation (LOHE); Monte Carlo simulation (MCS); Small isolated power system(SIPS); Solar photovoltaic (SPV); Reliability indices
1. Introduction
Solar photovoltaic (SPV) produces electrical power fromclean, quiet, pollution free sustainable renewable energysource that is accessible whenever there is regular sunshine.SPV arrays are recognized as feasible alternatives to energysources for meeting electric energy demands in remote, iso-lated un-electrified locations (Billinton and Karki, 2003).
SPV systems are subject to failure modes. Loose or cor-roded connections, battery failure, controller failure and
0038-092X/$ - see front matter � 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.solener.2010.01.022
* Corresponding author. Address: 37, L.I.C. Colony, Ajni Chowk,Khamla Road, Nagpur 440015, Maharashtra, India. Tel.: +91 7122233128; fax: +91 7104 232372.
E-mail addresses: [email protected] (R.M. Moharil),[email protected] (P.S. Kulkarni).
module failure represent a few of the things that mightgo wrong in a SPV system. SPV systems do have a factorthat affects system performance to which conventionalsystems are not subjected – unpredictable cloud cover(Messenger and Ventre, 2000).
Inclusion of wind turbine generator (WTG) and SPV inconventional small isolated power system (SIPS) signifi-cantly reduce operating cost by offsetting costly fuel con-sumed by diesel generators. Limitations in the energyavailable from SPV system and their intermittent behav-iour degrade the system reliability. Therefore cost benefitanalysis associated with application of SPV is incompletewithout corresponding reliability assessment (Billintonand Karki, 2001).
Many authors have contributed papers on reliabilityanalysis of system including renewable energy sources. Jain
Nomenclature
A;B;C ASHRAE model constantsAP additional power (kW)ALH additional load hours (h)a, b constants for a sitea1, b1 constants based on sunrise hour angle (xs)CA cell area (m2)Ci capacity outage of state i for the unit being
added (kW)Cia available capacity at hour i (kW)ECj energy not able to supply (kWh)FS fuel saving (liters)Gh hourly solar radiation (W=m2)ðGhÞmean hourly mean solar radiation (W=m2)ðGhÞrnd random hourly solar radiation (W=m2)�Hg monthly average of the daily global radiation on
a horizontal surface at a location (kJ=m2 � day)�Ho monthly average of the daily extra-terrestrial
radiation which would fall on a horizontal sur-face at the location under consideration(kJ=m2 � day)
HR heat-rate (kWh=liter)ISF incident solar flux (W=m2)Ibhc, Idhc, I corrected values of monthly-mean-hourly
beam, diffused and global radiation on horizon-tal surface (kJ=m2 � h)
Ibn beam radiation in the direction of rays(kJ=m2 � h)
�Ig monthly average of the hourly global radiationon a horizontal surface (kJ=m2 � h)
Ig, Ib, Id hourly global, beam and diffuse radiation(kJ=m2 � h)
�Io monthly average of the hourly extra-terrestrialradiation on a horizontal surface (kJ=m2 � h)
IT solar radiation falling on a tilted surface(kJ=m2 � h)
LOLE loss of load expectation, days=yearLOEE loss of expected energy (kWh=year)LOHE loss of health expectation (h/year)LOLH loss of load hours (h)Lia forecast peak load at hour i (kW)LAT local area time (hh:mm:ss)MTTF mean time to failure (h)
MTTR mean time to repair (h)m month parameterN number of sample yearsn number of unit statesnðHÞ number of healthy statends number of days under studyP power output of SPV array (kW)P Gd power generated in a day (kW)P Dd power demand in a day (kW)P Dmh maximum hourly load demand of the day (kW)P j individual probability of jth capacity statePðHÞ healthy state probabilityP d electric power available for distribution (kW)P iðCiahLiaÞ probability of loss of load for an hour iPðX Þ cumulative probability of capacity X kW outP 0ðX � CiÞ cumulative probability of capacity (X � Ci)
kW out before adding the new generatorPCi SPV array capacity available at instant ip modified month parameterpi probability of existence of the unit in state iq time correction factorrb, rd , rr tilt factor of beam, diffuse and reflecting radia-
tion�S monthly average of the sunshine hours per day
at location (h)�Smax monthly average of the maximum possible sun-
shine hours per day at the location (h)std standard deviationtðHÞ duration of healthy state (h)u number of generating unitsx hour angle (�)xs sunrise hour angle (�)gc conversion efficiencygi inverter efficiencygb battery efficiencyhz angle of incidence on a horizontal surface (�)kb, kd rainfall correction factor for beam and diffused
radiationlb, ld time correction factor for beam and diffused
radiation
692 R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702
et al. (1995) presented an economic analysis of the systemin terms of conventional fuel savings due to use of the pho-tovoltaic system. The fluctuating nature of the energy pro-duced by the photovoltaic generation system had adifferent effect on the overall system reliability than theenergy produced by conventional units. Shrestha and Goel(1998) discussed the issues in optimizing the use of isolatedsmall SPV power generation in SIPS. Loss of load hour(LOLH ), energy loss and total cost were the parameters
used for evaluation of different schemes. Nehrir et al.(2000) reported development of computer approach forevaluating general performance of stand-alone wind/SPVsystem and used to predict the behaviour based on avail-able wind, solar and load data. Billinton and Karki (Karkiand Billinton, 2001; Billinton and Karki, 2001, 2003) intheir work evaluated generation capacity requirements forSIPS using deterministic methods such as percent reservemargin, the loss of the largest unit (LLU ), etc. The number
R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702 693
of random variables and system complexities increasedwhen renewable energy sources were added to the systemdue to the fluctuating capacity levels of these sources. Theyalso utilized the well-being approach for SIPS containingrenewable energy such as SPV and wind. They had furtherconducted relevant cost and reliability studies and assessedthe actual benefits of SPV energy in power generating sys-tems. Bagen and Billinton (Bagen and Billinton, 2005a,b;Billinton and Bagen, 2006) presented sequential simulationtechnique to evaluate different operating strategies forSIPS. They extended conventional well-being approach torenewable generating system using energy storage andapplied the technique to several SIPS and carried out thegenerating capacity adequacy evaluation.
India is a tropical country with latitude lying between 7�and 37� N. It receives an annual average intensity of solarradiation between 16,700 and 29,260 kJ/m2/day. Thereforesolar energy utilization technology can be profitablyapplied to this region (Mani, 1980). Several authors hadcarried out work on estimation of solar radiation in India.
Empirical equations are given in the ASHRAE Hand-book (ASHRAE, 1972, 1985). Parishwad et al. (1997,1998) developed new sets of values of the constants (A; Band C), which were used in the ASHRAE equations, suit-able for Indian locations. It was observed that the esti-mated solar radiation data closely matched in the drymonths, but differed with corresponding measured valuesdue to cloudiness, which was related to rainfall. The proce-dure was developed for calculating the rainfall correctionfactor and estimating hourly global (Ig) and diffuse (Id)radiation on a horizontal surface at any location in India,during both dry and wet months, with reasonable accuracy.
Systematic data collection was started in India fromyear 1957 to 1958. Indian Meteorological Department(IMD) created the national radiation network with 25 sta-tions. IMD published mean hourly global solar radiation,mean hourly diffuse solar radiation, mean hourly directsolar radiation, mean solar elevation, solar azimuth andrelative air mass for each hour of every month. The meanbright sunshine hours were given for the twelve monthsof the year. The measured data for 21 years was compiledand is available in the form of tables (Mani, 1980).
Moharil and Kulkarni (2006) investigated the effect ofazimuth angle on solar radiation received by photovoltaicpanel connected to a water pump and stated that changein azimuth angle thrice a day increases the water dischargerate.
In this paper HMSR method is proposed for solar radi-ation simulation over a year. This method is useful for anysite in the world where HMSR and standard deviation areknown. Various solar radiation estimation methods men-tioned in the literature along with HMSR method are com-pared on the basis of actual power generated by SPVsystem. Effects of penetration of SPV energy in the conven-tional system are studied. Investigations regarding reliabil-ity analysis of Sagardeep Island SPV system are carriedout.
1.1. Site details
The Sagardeep Island is located in Sunderban area ofWest Bengal. Sunderban is a part of the vast delta of theriver Ganga. It is an abode of famous Royal Bengal Tiger.Sagardeep Island is a part of 24 Pargana district of WestBengal in India. There are 46 villages in Sagardeep Island,where river Hoogly falls onto the sea at Bay of Bengal.Fig. 1 shows the map locating Gangasagar (SagardeepIsland) in 24 Pargana district of West Bengal. SagardeepIsland is the place of pilgrimage for devotees with a popu-lation of 150 thousand people (www.censusindia.net;www.mapsofindia.com; Chaurey, 2000).
Sagardeep Island is 96 km. away from Kolkata by roadand further at 6 km-ferry distance by river route. Area ofSagardeep Island is 300 Sq. km. out of which 50% of theland is under agriculture, 40% is non-cultivable andremaining 10% comprises of waterways, embankments,etc. Economy is developing through hard working people,who are engaged in agriculture, fishing, deep-freeze stor-age, betel vine and chilli cultivation, tourism, etc. Theremote villages and hamlets of the southern part of theSunderban suffer from chronic shortage of energy due tonon-availability of grid power. It is extremely difficult toextend high-tension transmission line network to theseareas as most of the places are separated from the main-land and from each other by wide rivers and creeks. Sinceit is highly cost prohibitive to draw transmission linesacross very wide rivers and creeks SPV system was consid-ered to be the right choice by West Bengal RenewableEnergy Development Agency (WBREDA) for providingclean energy to these remote settlements. The average solarinsolation at site is 15,622.83 kJ/m2/day. For lighting pur-pose the people used kerosene as a main energy source.Firewood was used as a fuel for cooking. There were num-ber of battery operated radio and musical systems prior tothe extension of electric connection through SPV (Bhatta-charjee, 2002, 2004, 2006a,b; Chaurey, 2000; Moharil andKulkarni, 2009).
2. Evaluation model
The power output of a SPV array depends on the ran-dom variability of the available solar intensity, incidenceangle, ambient temperature, reflectance, tracking abilityof the SPV array and its design parameters. The reliabilityevaluation of SPV system involves three consecutive steps;atmospheric data modeling, SPV energy conversion and sys-
tem adequacy assessment (Billinton and Karki, 2003).
2.1. Solar radiation data modeling
The quantity of solar radiation reaching earth’s surfaceduring a day is governed by (a) the solar elevation at noon;(b) the duration of the day as determined by astronomicaland geographical factors; (c) the turbidity of the air; (d)total amount of water vapour in the air; and (e) the type
Fig. 1. Map of South 24 Pargana district of West Bengal state of India.
694 R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702
and amount of clouds. Solar flux striking a collector is acombination of direct beam radiation, scattered or diffusedradiation and reflected radiation. First attempt of estimat-ing solar radiation was done by Angstrom who suggestedrelationship between solar radiation and sunshine. Ang-strom’s regression equation relates monthly average dailyradiation to clear day radiation at a particular locationand average fraction of possible sunshine hours. This rela-tionship was then further modified by J.K. Page and givenby Eq. (1). The solar radiation at a site can be estimated ifthe latitude of location, longitude of location and altitudeof location is known. The relevant equations are given byEqs. (1)–(4). (Page, 1961; Sukhatme, 2004) are
Hg
H o¼ aþ b
�S�Smax
� �ð1Þ
a; b constant depends on site
�Ig
�Io¼
�Hg
�Hoða1 þ b1 cos xÞ ð2Þ
where a1 ¼ 0:409þ 0:5016 � sinðxs � 60�Þ andb1 ¼ 0:6609� 0:4767 � sinðxs � 60�Þ
Ig ¼ Ibn � cos hz þ Id ð3Þ
The flux falling on the tilted surface at any instant is givenby
IT ¼ Ib � rb þ Id � rd þ ðIb þ IdÞ � rr ð4Þ
In the ASHRAE model, it is postulated that
Ibn ¼ A exp½�B= cos hz� ð5Þ
and
Id ¼ C � Ibn ð6Þ
where A is apparent solar irradiation in (W/m2), B is atmo-spheric extinction coefficient (dimensionless) and C is diffu-sion radiation factor (dimensionless) are constants whichwere determined on a month-wise basis. These values ini-tially were given in ASHRAE handbook. These values ofA, B and C were then revised for Indian cities and are givenin Table 1 (ASHRAE, 1972, 1985; Parishwad et al., 1997,1998; Sukhatme, 2004).
Based on climatologically available data on rainfall,India is broadly divided into four regions (1) region ofheavy rainfall (HR) with total annual average rainfall(TAAR) > 1800 mm), (2) region of medium rainfall (MR)(1100 mm < TAAR < 1800 mm), (3) region of low rainfall(LR) (500 mm < TAAR < 1100 mm), and (4) region ofvery low rainfall (VLR) (TAAR < 500 mm). These limits
Fig. 2. Basic steps involved in WATGEN.
Table 1Values of constants A, B and C obtained for predicting hourly solarradiation in India (Parishwad et al., 1998).
S. No. Day A (W/m3) B C
1 21-January 708 0 0.1922 21-February 732.2 0.01 0.2093 21-March 767.86 0.046 0.2294 21-April 713.35 0.131 0.3855 21-May 798.39 0.15 0.256 21-June 440.71 0.398 1.1087 21-July 222.87 0.171 1.7218 21-August 240.8 0.148 1.6249 21-September 396.21 0.074 0.748
10 21-October 644.73 0.02 0.25611 21-November 666.6 0.008 0.21312 21-December 692.52 0 0.193
Fig. 3. Basic steps involved in HMSR method.
R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702 695
are not very strict. A polynomial of third order was foundsuitable as a correction factor for rainfall (Parishwad et al.,1998).
Separate empirical constants in these equations areobtained for monthly-mean-hourly beam and diffused radi-ation on horizontal surfaces. In order to make the curve fit-ting easier the year is divided into two halves, and origin onthe month-axis is taken at the middle of the half-year inwhich the month under consideration lies. The relevantequations are given by (Eqs. (7)–(13)) (Parishwad et al.,1998).
p ¼ m� 3:5 for m 6 6
p ¼ m� 9:5 for m > 6ð7Þ
For Medium RainðMRÞkb ¼ 0:8884� 0:0544p þ 0:0034p2 þ 0:0073p3 m 6 6
kd ¼ 1:0459� 0:0628p þ 0:0077p2 þ 0:0044p3 m 6 6 ð8Þ
kb ¼ 0:9319� 0:2926p þ 0:0296p2 � 0:0319p3 m > 6
kd ¼ 1:0663þ 0:0948p þ 0:0179p2 � 0:0039p3 m > 6
Due to time correction factor, beam and diffused radia-tion are obtained by the following equations
q ¼ LAT � 12:0 ð9Þlb ¼ 1:0042þ 0:0693q� 0:0090q2 � 0:0009q3
ld ¼ 1:2330þ 0:0242q� 0:0289q2 � 0:0002q3ð10Þ
Ibhc ¼ Ib � kb � lb ð11ÞIdhc ¼ Id � kd � ld ð12ÞI ¼ Ibhc þ Idhc ð13ÞThe monthly-mean of the hourly values of each of thebeam- and diffused radiation are calculated for Januaryto December, separately by using
(i) Eqs. (1)–(4) with specified a; b parameters of thelocation.
(ii) Eqs. (5) and (6) for ASHRAE model using A, B and Cparameters.
(iii) Eqs. (7)–(13) with the effect of rainfall consideredusing A, B and C parameters of the ASHRAE model.
A computer program known as WATGEN has beendeveloped at the University of Waterloo based on themathematical models. This program is widely used to con-duct performance and design assessments on solar energyconversion systems. Many researchers have used this pro-gram in their research to generate hourly solar radiationdata for the sequential Monte Carlo simulation studies.The overall procedure for generating synthetic hourly solarradiation data in the program is a two-step process, asshown in Fig. 2. The first step involves generating dailyradiation data from the monthly mean values at the partic-ular site location. The second step is the generation ofhourly solar radiation for a calendar year from the dailyvalues generated in the first step. WATGEN requiresmonthly average meteorological data, monthly averagevalues of solar radiation on the horizontal surface, thewind speed and the ambient temperature at a specific sitelocation as its input for the simulation of the solar radia-tion process at that site (Bagen, 2005; Billinton and Bagen,2006).
But the difficulty with the WATGEN software is that itis not easily available to all researchers across the worldeasily, hence an attempt is made to develop a program(HMSR method) in MATLAB software, which is easilyavailable across the world. For HMSR method, MonteCarlo simulation technique is used to develop a programin MATLAB for reliability analysis of small isolated powersystem using solar photovoltaic. The input data matrixconsists of hourly mean solar radiation (HMSR), standarddeviation, maximum and minimum value for every hour ofa day of the month (24 � 12 matrix each), the mean brightsunshine hours in month (1 � 12 matrix). MATLAB func-tion normrnd available in MATLAB Statistical toolbox(http://www.mathworks.com/) is used which requires argu-ments as hourly mean solar radiation and standard devia-tion to predict the solar radiation at a site. The commandline is as given in Eq. (14). Output solar radiation isobtained for 365 days i.e. (1 � 8760 matrix). Fig. 3 showsthe basic steps involved in HMSR method.
ðGhÞrnd ¼ normrndððGhÞmean; stdÞ ð14Þ
696 R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702
If the ðGhÞrnd obtained is less than the minimum value orgreater than the maximum value it is set to minimum andmaximum value, respectively. Another random variable isgenerated and compared with the sunshine data matrix todeclare whether the hour is with a cloud cover or not. Ifthe hour is with a cloud cover then the radiation at thathour is assumed minimum.
2.2. Solar photovoltaic energy conversion
Fig. 4a shows the I–V characteristic of SPV panel of75 Wp installed at Sagardeep Island site. The power outputfrom the SPV array is given by
P ¼ ISF � CA� gc ð15Þ
The main factors that determine the output power ofSPV are: (i) SPV system conversion efficiency, (ii) radiationintensity, and (iii) temperature of solar cell. The SPV sys-tem efficiency means the output power of SPV per unit
Fig. 4. (a) I–V characteristics of SPV system installed at Sagardeep Island.(b) Actual and predicted power of SPV system located at SagardeepIsland.
radiation of solar cell. The SPV system efficiency is depen-dent on two factor namely solar radiation and temperature.Every degree centigrade rise in temperature above the ref-erence temperature the silicon cell power output decreasesby about 0.5% approximately. This is because increase incurrent is much less than the decrease in voltage, the neteffect is a decrease in power at higher operating tempera-ture. The efficiency of SPV system increases with increasein solar radiation intensity. The typical power curve ofSPV system for different radiation intensities is shown inFig. 4b. At first, a small increase in the radiation producesa significant increase in the SPV’s efficiency, solely the effectof increase in solar radiation since the ambient temperatureis well below the reference temperature. After a certainradiation point, known as knee point, further increases inradiation produce relatively smaller increase in the powerbecause rise in temperature effect is more predominant thanrise in solar radiation (Cha et al., 2004; Patel, 2006).
P ¼ �0:0622 � ðGhÞ2 þ 36:5073 � ðGhÞ þ 351:2967 0 < Gh < 220
¼ ð0:002 � ðGhÞ þ 4:8821Þ � 103 221 < Gh < 1000
ð16Þ
The power from SPV panel can be predicted using Eq. (16).The actual and predicted graph was plotted for 25 kWpSPV array located at Sagardeep Island is shown inFig. 4b. The graph is obtained by assuming solar radiationof 220 W/m2 as a knee point. This value of knee point isobtained by using a trial and error method (Moharil andKulkarni, 2009).
The electric power available for distribution by the SPVarray is given by
P d ¼ P � gi � gb ð17Þ
2.3. Reliability modeling
The conventional and SPV generator (SPV system) aretreated as two different sub-systems and the probabilitymodel is developed for each subsystem. Fig. 5 shows thereliability model of conventional and SPV generator. Theconventional generator three-state model includes a singlederated state in addition to the rated capacity and zerocapacity states. The HMSR method is capable to considerany number of derated states. The power from SPV gener-ator is possible only when solar radiation is available andpower conditioning unit, battery, and SPV unit are work-ing satisfactorily. Derating of SPV generator is due to fail-ures of cells connected in series or/and parallel, shadow onparts of SPV array etc. Solar radiation is categorised intono radiation, less than knee point radiation and radiationgreater than knee point radiation. A combined generationmodel for cumulative probability is obtained.
PðX Þ ¼Xn
i¼1
piP0ðX � CiÞ ð18Þ
LOLEi ¼ P iðCiahLiaÞ ð19Þ
Fig. 5. Reliability models of conventional and SPV generator.
R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702 697
The index LOLE for the entire period is given as
LOLE ¼Xnds
i¼1
LOLEi ð20Þ
The capacity outage probability table and LOLE index canbe obtained using Eqs. (18)–(20). The loss of load hours(LOLH ) is the summation of loss of load expectation(LOLE) events. These events are expressed in hours overa specified time (usually one year) that the photovoltaicpower system is unable to meet the load requirementsdue to lack of power at that hour. LOEE is obtained usingload duration curve and the generating unit capacity data(Billinton and Allan, 1996).
LOEE ¼Xu
j¼1
ECj � P j ð21Þ
P ðHÞ ¼PnðHÞ
i¼1 tðHÞiN �Year in hours
ð22Þ
The value of health state probability can be obtained usingEq. (22). An index designated as the loss of health expecta-tion (LOHE) is defined, as the expected number of hours ina year the power system does not meet the capacity reserverequirement specified by the deterministic criterion. LOHEis calculated using Eq. (23) (Billinton and Karki, 2003).
LOHE ¼ ð1� P ðHÞÞ ð23Þ
The additional power (AP ) and additional load hours(ALH ) available can be obtained when the commitmentof power supply is for fixed number of hours and powergeneration is more than power requirement for that dayusing the following formulae.
AP ¼ P Gd � P Dd ð24ÞALH ¼ AP=P Dmh ð25Þ
The customer will get power for additional hours. The sav-ing in fuel energy is expected in a SPV-Diesel System due toALH .
If PCi is the total additional power available in i th yeardue to increase in SPV capacity for year i, and if the simu-lation is run for N sample years and heat-rate is knownthen fuel saving per year is given by Eq. (26) (Billintonand Karki, 2003).
FS ¼PN
i¼1PCi
N � HRð26Þ
The methodology for composite power system reliabilityevaluation using MCS is briefly summed up in the follow-ing steps (Billinton and Li, 1994):
(i) Specify the initial state of each component (all dieseland SPV generator). Normally it is assumed that allcomponents are initially in the up state.
(ii) Simulate the duration of each component residing inits present state using the inverse transform methodf ðtÞ ¼ ke�kt and the distribution functions of thecomponent failure and repair rates. The sample valueof the state duration (T ) is T i ¼ � lnðUiÞ=ki, where Ui
is the uniformly distributed random number [0 1] cor-responding to the ith component; ki is a failure rate orrepair rate depending on the current state of the ithcomponent.
(iii) Repeat step (ii) in a given time span. A chronological‘up’ and ‘down’ state for each component is thenconstructed in a given time span. The simulated
698 R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702
operation is assessed for each hour during a giventime span. At the end of each simulated year the reli-ability indices are calculated and updated.
Fig. 6 shows the flow chart for simulation process usingHMSR method. Fig. 7 shows the reliability evaluation ofLOLH with HMSR method described in flow chart of Fig. 6.
3. Simulation results
At the Sagardeep Island, (22.66� N, 88.45� E), an aver-age rainfall per year is 1800 mm. It is placed in the medium
Fig. 6. Flow chart of MCS simulatio
rainfall category for calculation of rainfall correction fac-tor. The constants a and b considered for Sagardeep Islandare 0.28 and 0.42, respectively, for a–b method. Values ofconstants A, B and C obtained for predicting hourly solarradiation in India is shown in Table 1 is used for A–B–C
no rain method. Eqs. (7)–(13) were used to plot ABC rainfallcorrection. Fig. 8 shows the predicted power output fromSPV system by different solar radiation methods (a–b,
ABC no rainfall correction, ABC rainfall correction and
HMSR) and actual power generation.When these different method are compared with actual
It is observed that the three methods namely a–b constant,
n technique for HMSR method.
Fig. 7. MCS characteristic for LOLH using HMSR method at SagardeepIsland.
R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702 699
A–B–C no rain and A–B–C rainfall have higher estimationof power generation with respect to actual values. ABCwithout rain consideration (ABC no rain) has the highestestimated output power ranging from 141% to 272% withactual power. ABC with rainfall correction (ABC rainfall)has higher estimated values for non-monsoon months (Jan-uary to May and October to December) over a–b constantmethod. During monsoon months ABC rainfall has lowerpower estimation than a–b constant and ABC no rain inthe range of 203–236% of actual power. For the proposedHMSR method the estimated SPV power output of singleiteration of MCS is represented in Fig. 8. The power esti-mations by HMSR method deviates ±10% from actualpower generation for non-monsoon months (January toMay and October to December). The prediction deviates15–20% during monsoon months (June to September)due to a cloud cover effect.
3.1. Case I
The developed HMSR method is applied to a base sys-tem with three diesel generating units, two 40 kW each and
Fig. 8. Comparison of power generation pr
one 80 kW (with 4% Forced Outage Rate {FOR}, MTTF1920 h, MTTR 80 h). In this study the LOHE is obtainedby considering loss of largest unit LLU in the system. Thehourly chronological load shape of the RBTS and IEEE-RTS (Billinton et al., 1989; IEEE Committee Report,1979) is used with a peak load of 60 kW. The system isassumed to be located at Sagardeep Island with monthlysolar radiation data given by Mani (1980). Four differentcases are considered as follows (i) base case; (ii) base casewith addition of 40.5 kWp SPV arrays (built by assembling540 panels of 75 Wp modules with 4% FOR); (iii) base casewith addition of one diesel unit of 40 kW with FOR ¼ 0:04;and (iv) base case with addition of 40.5 kWp SPV arraysand removal of one diesel unit of 40 kW.
Fig. 9 compares the system degree of comfort in meetingthe LLU criterion for the four cases using HMSR method.It is observed that the system health increases for eachcapacity addition case but not to the same degree. Fig. 9shows that health state probability of additional conven-tional diesel generator (case 3) is better than the additionof SPV system (case 2) in terms of system reliability forhigher load. Replacement of diesel unit by same capacityof SPV (case 4) reduces health state probability. This isbecause during evening hours no power is available fromSPV system.
3.2. Case II
West Bengal Renewable Energy Development Agency(WBREDA) is the state level organization planning andpromoting the use of renewable energy technologies(RET) in West Bengal. In order to satisfy the growing aspi-rations of the remote rural customers, and to serve the pop-ulation with AC electricity such that they can use easily forend use appliances. WBREDA and Ministry of New andRenewable Energy (MNRE) has been promoting theinstallation of centralized SPV power plants, which supplyAC electricity to the village for fixed duration (Moharil andKulkarni, 2009). The load model in per unit form is given
ediction with actual power generation.
Fig. 9. Variation in health state probability for Case-I.
700 R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702
in Table 2 for the Sagardeep Island. The peak load on dis-tribution system is considered as 10 kW.
The load model is based on the load survey of theregion. The region already has eleven such power plantsand some more have been planned in future. These powerplants are used for rural village electrification. The SPVpanel will charge the battery during the daytime. At pres-ent, there is no daytime supply as there is not sufficient day-time load. The battery of (2 � 800 Ah) capacity is used tostore the total energy received from the sun during theday. The plant through a battery bank and inverter sup-plies AC electricity for a fixed duration from 5:00 pm to11:00 pm throughout the year. During rainy season inabsence of solar energy people use the kerosene lamps.No diesel generators are provided at the site (Mohariland Kulkarni, 2009).
Table 3 shows the various reliability indices obtained byHMSR method using MCS technique for Sagardeep
Table 2Load model on per unit basis for Sagardeep Island.
Time Load on per unit basis
Season
Rainy Winter Summer
5:00 pm to 6:00 pm 0.66 0.615 0.6866:00 pm to 7:00 pm 0.856 0.732 0.7817:00 pm to 8:00 pm 0.766 0.815 0.7968:00 pm to 9:00 pm 0.792 0.773 19:00 pm to 10:00 pm 0.732 0.736 0.93210:00 pm to 11:00 pm 0.634 0.6113 0.687
Island. The variation in the system load in the above studyhas been modeled by increasing the peak load while main-taining the same load shape given in Table 2. Table 3 indi-cates that reliability indices LOLE, LOLH and LOEEincrease with increase in load. LOLE increases linearly forlower load and saturates at higher loads. LOLH increaseslinearly for increase in load. LOEE increases exponentiallyinitially for lower load and linearly for higher load. ALHand AP reduce exponentially with increase in load andbecomes zero for load more than 13 kW. Reduction inALH with increase in load indicates that a SPV source willoffset maximum fuel when all of its generated energy is uti-lized. The energy available from SPV source may notalways be consumed due to a lower power demand. Table 4shows the effect of increase in SPV system capacity on var-ious reliability indices for 10 kW peak load on the system.
Table 3Reliability indices using MCS technique on 25 kWp SPV system forvarying peak load.
Peak load(kW)
LOLE
(days/year)LOLH
(h)LOEE
(kWh/year)ALH (h) AP (kW)
08 141.25 336 1536 323.1 258509 176.37 436 2256 184.1 165710 222.4 550 3161 91.4 91411 276.9 68I 4298 36.6 40212 324.6 813 5670 10.5 12613 353.2 936 7215 1.79 2314 362.6 1040 8841 0.124 1.7415 363.98 1122 10,488 0.0010 0.0150
R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702 701
It is observed from Table 4 that with the rise in genera-tion capacity by 60% (i.e. from 25 to 40 kWp) the reliabilityindices LOLE, LOLH and LOEE reduce to 1/3 of their basevalue and ALH and AP increase seven times to their basevalues.
Fig. 10a and b show the LOLH during different monthsof the year for 25 and 40 kWp SPV system, respectively,with a peak load of 10 kW. It is observed that increase incapacity has reduced LOLH by one hour during the rainyseason (line A and line C i.e. from 4 to 3 h) and by twohours during rest of the year (line B and line D i.e. from2 to 0 h). It indicates that just the increase in the capacityof SPV system is not the solution to improve the reliabilityduring the rainy season but the use of some other sourceeither renewable or conventional is the solution.
Table 4Reliability indices using MCS technique with increase in capacity of SPVsystem on 10 kW peak load.
PV systemrating (kWp)
LOLE
(days/year)LOLH
(h)LOEE
(kWh/year)ALH
(h)AP
(kW)
25 222.4 550 3161 91.4 91427.5 180 445.7 2563 173.9 173930 152.3 369 2111 271 270932.5 131.7 308.2 1749 377 377235 115.86 262 1451 489 489737.5 100.50 220.7 1203 607.2 607240 88.4 184.8 998 729 7290
Fig. 10. Loss of load hours during different months of the year for (a)25 kWp and (b) 40 kWp SPV system.
Fig. 11. Effect of SPV capacity addition on fuel saving in base case.
Fig. 11 shows the fuel saving with increasing SPV pene-tration, assuming a heat-rate of 2.85 kWh/liter (Chakrabartiand Chakrabarti, 2002) at Sagardeep Island. The rate ofrise of fuel saving reduces with increase in installedcapacity.
4. Conclusions
In this paper HMSR method is proposed for predictionof solar radiation. The results predicted by HMSR methoddeviates ±10% from actual values for non-monsoonmonths. The deviation in monsoon months is more dueto cloud cover. Another advantage of HMSR method isthat it can be used as a probabilistic method for MCS tech-nique. From the reliability analysis using HMSR method itis concluded that increase in installed capacity will reducethe LOLH during rainy seasons (June to September) andadditional hours will be available during the summer per-iod (February to May). ALH and AP reduce exponentiallywith increase in load and becomes zero at higher load.Increased installed capacity of SPV also ensures the reduc-tion in the consumption of petroleum product (e.g. Dieselor kerosene). The HMSR method with MCS techniquepresented in this paper, together with related cost analysis,should prove useful as valuable inputs for system planning.
Websites
http://www.mapsofindia.com/maps/westbengal/dis-tricts/south24-parganas.htm.
http://www.censusindia.net.http://www.mathworks.com.
Acknowledgements
Authors are grateful to MHRD New Delhi for sanction-ing the R&D scheme with title; “Operation control & sta-bility of an integrated power system” vide their letter No.
702 R.M. Moharil, P.S. Kulkarni / Solar Energy 84 (2010) 691–702
F.26-14/2003 dated 14/01/2004. They are also thankful tothe authorities of Y.C.C.E. & V.N.I.T. for granting permis-sion to carry out the above research work.
Annexure A
The details of 75 Wp SPV panel are as given below:
Peak power =75 Wp
Voc = 21.0 V
Vmp = 17.0 VIsc = 4.8 A
Imp = 4.4 A NOCT = 42 �C O.C. voltagetemperaturecoefficient= �0.08 V/�C
Fill factor = 74%
Dimensions =1210 � 526 � 35 mmReferences
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