Research ArticleOptimized Sizing, Selection, and Economic Analysis of BatteryEnergy Storage for Grid-Connected Wind-PV Hybrid System
Hina Fathima and K. Palanisamy
School of Electrical Engineering, VIT University, Vellore Campus, Vellore District, Tamil Nadu 632 014, India
Correspondence should be addressed to Hina Fathima; [email protected]
Received 21 September 2015; Revised 13 November 2015; Accepted 22 November 2015
Academic Editor: Elio Chiodo
Copyright ยฉ 2015 H. Fathima and K. Palanisamy. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.
Energy storages are emerging as a predominant sector for renewable energy applications. This paper focuses on a feasibility studyto integrate battery energy storage with a hybrid wind-solar grid-connected power system to effectively dispatch wind power byincorporating peak shaving and ramp rate limiting. The sizing methodology is optimized using bat optimization algorithm tominimize the cost of investment and losses incurred by the system in form of load shedding and wind curtailment. The integratedsystem is then tested with an efficient battery management strategy which prevents overcharging/discharging of the battery. In thestudy, five major types of battery systems are considered and analyzed.They are evaluated and compared based on technoeconomicand environmentalmetrics as per Indian powermarket scenario. Technoeconomic analysis of the battery is validated by simulations,on a proposed wind-photovoltaic system in a wind site in Southern India. Environmental analysis is performed by evaluating theavoided cost of emissions.
1. Introduction
India has been suffering from power shortages for threedecades. Government organizations all over the world arevowing for a cleaner energy policy and promoting renewablepower to combat growing power demands. According tothe Renewables Global Status Report (2015) [1] 19.1% ofworld energy consumption in 2013 was met by renewableenergy alone. Hybrid Renewable Energy Systems (HRES)are emerging as the key solutions to overcome the unpre-dictability and variability in renewables by combining twoor more power sources, enabling the system to be reliableand cost-effective. Butmany problems arise in their planning,operation, and scheduling. Energy storages are needed tobalance load, bridge power gap, and improve power quality.Initiation of energy storage demonstration projects by theMNRE, Government of India in August, 2015 [2], has raisedhopes to revolutionize the Indian energy storagemarket. Gridlevel storages for implementing renewable energy integra-tion, experimenting with energy arbitrage, and supportingancillary services need to be explored under Indian powermarkets.
Battery Energy Storage Systems (BESS) are the mostmature storage technology and they offer a wide rangeof characteristics for varied applications. BESS comprisemultiple electrochemical cells connected in arrays to deliverelectricity at desired capacity and potential. As the energyis stored in form of electrochemical energy, the entire bulkof the battery is prone to chemical reactions. Hence, theyrequire high maintenance which presented a major setback.Developing technology and material science enabled designofmaterials which allow this ingress of reactions up to severalthousand times, thus evolving rechargeable batteries withreduced maintenance. Recent times have seen tremendousadvancements in BESS with the emergence of advancedrechargeable valve-regulated lead-acid batteries, sodium bat-teries, lithium batteries, and flow batteries. Governmentsand research agencies are making large scale investmentsimplementing batteries for both grid and transport applica-tions. There are yet many challenges to be addressed for safeintegration, operation, and disposal of batteries.
Many studies could be found in the literature on inclusionof energy storages with HRES. Zhao et al. [3] presenteda review of planning, operating, and controlling studies in
Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2015, Article ID 713530, 16 pageshttp://dx.doi.org/10.1155/2015/713530
2 Modelling and Simulation in Engineering
wind and energy storage integrated systems. Poullikkas [4]gave a detailed economic overview of battery storage systemsfor large-scale electricity storage. Maleki and Askarzadeh[5] optimally sized a PV-Wind-Diesel-Battery hybrid systemwith discrete harmony search algorithm. Further expansionof the HRES with a fuel cell hydrogen storage system [6]was attempted and the results proved the batteries to be abetter investment option. Prodromidis and Coutelieris [7]simulated and analyzed nine types of HRES with storageslike batteries and flywheels based on the net present costsof systems. These results also proved the batteries to be astandard choice for HRES integration. These studies wereconducted on standalone systems and the authors evaluatedthe economic costs of BESS. However, the current studydeals with grid-connected systems and is scheduled to matcha predetermined power dispatch, failing of which leads toload shedding and losses. Integrating BESS with renewablesnecessitates optimizing battery capacity so as to minimizeinvestment and operation costs and increase battery lifetime.A deep analysis and understanding of the characteristicsof the different batteries available is important to justifyselection of a battery for a particular application. Varioustypes of BESS and their applications in wind systems wereexplored prior to this study and a detailed overview of it canbe seen in [8]. Inverters of flooded lead-acid batteries haveseen widespread domestic installations in India. Keeping inview Indiaโs geographical, economic, and energy scenarios,five batteries have been identified for analysis in this paperand will be explained in the next sections.
Gitizadeh and Fakharzadegan [9] proposed sizing ofBESS for a grid-connected PV system using the GeneralAlgebraic Modeling System (GAMS) to minimize the costof the battery. Bahmani-Firouzi and Azizipanah-Abarghooee[10] implemented an improved bat algorithm to evaluate thesize of a BESS with theminimum operation andmaintenancecosts. Li et al. [11] developed a dispatch strategy to maximizethe lifetime of the battery by ensuring maximum charge-discharge in each cycle. However, scheduling dispatch basedon State of Charge (SOC) of storages may not be appropriatewhile dispatching wind power with the grid. Johnson et al.[12] explored an online scheduling problem using batteriesto harvest peak shaving with optimization algorithms. Abovestudies aim at only optimizing the battery costs but do notconsider the expense of losses, which may increase if thebattery size selected is too small. In an effort to balancethe investment cost of battery and losses, a multiobjectiveoptimization function to reduce investment costs and lossesis presented here.
Dicorato et al. [13] discussed the effect of battery storagesizing on the planning and operation of the hybrid system.The results proved that a higher rating of BESS can aidin higher renewable penetration and gain more advantagesby controlling power bids. But, if the nominal size of theBESS exceeds that of the system it may cause more expensesand design issues. Brekken et al. [14] explored the effectof power flow control strategy on sizing of energy storageby imposing fuzzy and artificial neural network controlstrategies. Ma et al. [15] published a feasibility study for wind-PV-battery HRES using HOMER and portrayed the effects of
individual system configurations on the HRES performance.These studies provide a benchmark for the current studyin terms of sizing results for the battery system. Economicanalysis and feasibility studies have been attempted in manyapplications for power systems from a long time [16]. In [17],the authors exhibited an excellent cost analysis for solar PVsystems based on payback periods. A study by Kaabecheand Ibtiouen [18] proposed an optimal configuration of awind-PV HRES considering economic metrics including netpresent costs, cost of energy, and energy deficits. Dufo-Lopez [19] concluded that, for introducing storage to ACgrids, an adequate TOU tariff and drop in battery costsare crucial to ensure profitability. The presented case studyexplores the economic aspects of investing in energy storagesunder Indian markets which are governed by fixed tariffrates. Also, many system metrics including payback periodsand net present costs are explored for battery storages toinvestigate the investment feasibility. Additionally, this paperalso evaluates an avoided cost of emissions to point out thesignificance of investing in emission free storage technology.
This paper presents a feasibility study of integratingbattery storage to a Wind-PV HRES. The HRES is scheduledto meet a power dispatch curve which implements peakshaving and ramp rate limiting to avoid power surges inthe grid. An optimized sizing methodology for evaluatingthe battery capacity and cost which successfully satisfiesall power constraints is proposed. The sizing methodologyis then validated with a 275 kW grid-connected wind-PVhybrid renewable system and tested with five different typesof batteries.The performance of each battery is simulated andcomparisons are made based on technoeconomic metrics.Simulations are carried out in MATLAB and all evaluationsare done based on Indian power market scenario. Hence,the aim of peak shaving is to improve power delivery andnot energy arbitrage. A further exploration of profits gainedby avoiding emissions is also included to emphasize theenvironmental benefits of adopting battery storage in theHRES. The paper is structured as follows. Section 2 entailsmodeling of system components and scheduling of powerdispatch. A brief summary of types of battery systems andthe sizing methodology are explained in detail in Section 3.The performance and economic analysis of different batteriesare entailed in Section 4. The last section summarizes thesimulation results and comparative analyses of the batterysystems.
2. Modeling of System Components
The Hybrid Renewable Energy System shown in Figure 1consists of a 200 kW wind turbine MICONM450-200 whichhas an asynchronous machine operating at 400V whosespecifications can be seen at [20]. A 75 kW PV panel isconnected to the HRES through a rectifier to producealternating current. It is assumed that the proposed wind-PV system acts as a power injection system to the powergrid and lacks the features to exert any kind of power qualitycontrol on the power generated. The power generated bythe wind turbine is directly pumped via AC grid to thedistribution station.The power from the solar panels is fed to
Modelling and Simulation in Engineering 3
Wind turbine
DC-ACconverter
AC grid to distribution
station
Bidirectionalcharge controller
Battery storage
M450-200400V
75kW PV panel600V DC 120V DC
200 kW MICON
Figure 1: Schematic diagram of Hybrid Renewable Energy System.
the grid via DC-AC converter. A bidirectional charge con-troller charges/discharges the battery and takes care of theAC-DC conversion and voltage boosting. The unpredictablenature of renewable sources makes the system incapable ofmeeting the power dispatch standards of the load dispatchcentres. Also, at times of high wind availability the turbinesare forced to shut down due to lack of power evacuation facil-ities. Integrating battery with the HRES will help to store thespilled energy and deliver it at times of peak power demandsthus improving the system reliability. The methodology usedfor sizing and analysis is shown in Figure 2.
Initially, power generated by the HRES is calculated bymodeling the system components. A simple power dispatchstrategy is evaluated to remove all intermittences in thegenerated power. It also enables storage of energy at lowdemand periods and delivering it at times of peak load, thatis, peak shaving and ramp rate limiting to avoid suddensurges entering the grid.The battery capacity needed to meetthis power dispatch is estimated and optimized using batalgorithm. The optimized results are tested by operating fivedifferent types of batteries with the HRES. A simple energymanagement strategy is also included to avoid over charg-ing/discharging of the battery. From the results obtained,analysis and comparisons are made to identify the mostsuitable battery for the HRES.
2.1. Wind Turbine Modeling. The power generated in awind turbine is evaluated using (1) [21]. The turbine startsgenerating power at wind speeds greater than cut-in speed Vci.๐ถ๐(๐, ๐ฝ) is the power coefficient of the wind turbine which isa function of pitch angle ๐ฝ and tip-speed ratio ๐ and is plottedin Figure 3. The turbine continues to produce rated powerafter attaining rated speed and at reaching cut-out speeeds theturbine is stalled. The power curve thus obtained is shown inFigure 4. Consider
๐๐ค (V) ={{{
{{{
{
0, V โค Vci or V โฅ Vco0.5๐๐ด๐ถ๐ (๐, ๐ฝ) V
3, Vci โค V โค V๐
๐rated-wt, V๐ โค V โค Vco.(1)
2.2. PV System. A silicon PV module output depends onmany variables including the type of material, temperature,and solar radiance incident on the surface of the module. Itsoutput can be expressed as [22]
๐pv = ๐pv๐pv๐บ๐
๐บSTC[1 + ๐ผ (๐๐ โ ๐STC)] . (2)
๐บSTC and ๐STC are taken to be 1000W/m2 and 25โC,respectively. ๐ผ and ๐pv are considered as 0.4% and 97%,respectively.
2.3. Power Dispatch Curve. Renewable power systems cannotbe considered as a dispatchable generation due to theiruncontrolled and intermittent nature. On the contrary, loaddispatch centers demand a 15-minute time block at theleast for scheduling and dispatch of power to the grid [23].However, energy storages can be employed in making thisintermittent power dispatchable. In this study, power dispatchis scheduled for every 30 minutes (computation for two timeblocks) and any mismatch of generated power in this timeinterval is nullified by the battery storage. Thus, the poweroutput from the hybrid system will be constant for 30min.Let ๐gen be the total power generated by the hybrid systemgiven as below. Here the efficiencies take into account theefficiency of the power generating system and its connectedpower converters. One has
๐gen (๐ก) = (๐๐ค (๐ก) ร ๐wt) + (๐pv (๐ก) ร ๐pv) . (3)
The power dispatch curve ๐dem(๐ก) includes peak shavingand ramp rate limiting. The dispatch curve is obtained byfollowing an average of ๐gen(๐ก) generated per day, denotedby ๐๐บav(๐), where โ๐โ is the day of month. At times of off-peak demand, some of the energy generated is stored inbatteries and the rest is delivered. And during peak load,this saved energy is dispatched as shown in Table 1. This isto ensure optimum usage of the energy storage device whileimplementing peak shaving. Whenever ๐gen(๐ก) experiencessurges due to wind gusts, it may affect the grid stability,
4 Modelling and Simulation in Engineering
Start
Evaluate deficit/surplus power
Evaluate battery capacity using bat optimization algorithm
Stop
Implement proposed energy management strategy and evaluate system performance
Conduct economic analysis for the hybrid system and evaluate battery system payback
From the results obtained compare the battery systems considered
Evaluate Pw , Ppv, and Pgen
Evaluate dem based on Pgen
Figure 2: Energy storage sizing methodology.
0 2 4 6 8 10 120
0.050.1
0.150.2
0.250.3
0.35
Tip-speed ratio
Pow
er co
effici
entC
p
Figure 3: ๐ถ๐ curve.
2 4 6 8 10 12 14 16 18 200
40
80
120
160
200
Wind speeds (m/s)
Pow
er (k
W)
Figure 4: Wind turbine power curve.
Table 1: Dispatch curve evaluation.
Hour of day Demand period Dispatch (๐dem(๐ก))00.00 to 07.00 Morning off-peak ๐gen(๐ก)/207.00 to 11.00 Morning peak ๐๐บav(๐) + (๐gen(๐ก)/2)11.00 to 19.00 Midday off-peak (๐gen(๐ก) + ๐๐บav(๐))/219.00 to 23.00 Evening peak ๐๐บav(๐) + (๐gen(๐ก)/2)23.00 to 0.00 Evening off-peak ๐gen(๐ก)/2
thereby necessitating ramp rate control. In case of anyunscheduled power surge/fall (occurring at times other thanscheduled ramp changes of load shifting from off-peak topeak and vice versa) of more than ยฑ5% of rated power, theexcess/deficit power is directed to the battery. Figure 5 showsthe power dispatch curve ๐dem(๐ก) plotted against the ๐gen(๐ก)curve.
3. Optimal Sizing of Energy Storage
3.1. Selection of Battery Energy Storage Systems (BESS). BESSare made of multiple electrochemical cells connected inseries or stacks to get the desired voltage and capacity,
Modelling and Simulation in Engineering 5
Table 2: Properties of batteries [8, 24, 25].
Technology Capital costin $/kWh
Dischargetime
Energyrating(MWh)
Specificenergy(Wh/kg)
Cyclingcapability, @
% DoDLife (yrs) Energy ๐
(%)
Self-discharge
(%)
Operatingtemperature
in โC
Pb-acid 50โ150 Sec.-hrs 0.001โ40 35โ50 500โ2000@ 70 5โ15 70โ80 <0.2 โ5 to 40
Na-S 200โ600 Sec.-hrs 0.4โ244.8 100โ175 2500 @ 100 10โ20 75โ89 No 325Ni-Cd 400โ2400 Sec.-hrs 6.75 30โ80 3500 @ 100 10โ20 70 0.2โ0.3 โ40 to 50
Li-ion 900โ1300 Sec.-hrs 0.001โ50 100โ200 1500โ3500 @80 14โ16 75โ95 1โ5 โ30 to 60
VRB 600 Sec.-10 hrs 2โ120 30โ50 100โ13000 @75 10โ20 65โ85 Very low 0 to 40
ZBB 500 Sec.-10 hrs 0.1โ4 60โ85 2000โ2500 8โ10 65โ85 No 0 to 40
PSB 300โ1000 Sec.-10 hrs 0.005โ120 >400 100โ13000@ 75 15 60โ75 No 0 to 40
Table 3: Battery energy storage system ratings (per module).
S.number Type Commercial
product Rating Voltage Life time inyrs
Chargingefficiency in
%
Dischargingefficiency in
%
Depth ofdischarge % Cost
Energycost
coeff. inRs/kWh
1 Lead-acid
TrojanT105-RE 225Ah 6 10 95 80 70 160 $/module 6,222
2 PSB 50 kW 48 15 90 75 75 500 $/kWh 36,0003 VRB 50 kW 48 18 98 85 75 600 $/kWh 36,0004 NaS 50 kW 48 20 99 88 100 400 $/kWh 9,000
5 LiPeO4Smart battery
SB300 300Ah 12 14 99 95 80 3500 $/module 30,000
0
50
100
150
200
250
Hour of day
Pow
er (k
W)
DemPgen
Morningpeak Evening peak
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Figure 5: Dispatch curve.
respectively. Each cell is composed of an electrolyte withpositive and negative electrodes. Electrochemical reactionsoccur at the electrodes to generate free electrons, whichmove around generating electrical energy. The amount ofenergy that can be stored depends upon the mass/volumeof electrodes while the power capacity is determined by thecontact area of electrodes with the electrolyte. Many batterytypes are available for integrating renewable systems andtheir characteristics are tabulated after extensive study in
Table 2. A deeper knowledge on the types of BESS and theircharacteristics could be gained from [8]. Nickel-cadmiumbatteries suffer from โmemory effectโ [26] and are verycostly and cause health risks. They are also banned in somecountries and are now replaced with other batteries [27].This study compares five types of batteries which include theconventional (lead acid), Lithium-ion, and fast developingbattery systems like sodium and flow batteries. Rechargeablelead-acid batteries have been in the market for more thana decade now. Low self-discharge, easy availability, and lowcost make them highly suitable for renewable integrationapplications. Flow batteries find improved applications inrenewable systems for long term storage of energy.This is dueto improved scalability, reliability, and recycling capability[28]. Sodium sulphide (NaS) batteries have high energydensity and excellent energy efficiency. Lithium-ion batterieshave the highest energy density and their portable featuresand light weight enhance their flexibility and modularity. Ofthe five batteries, only lead-acid and lithium-ion batteriesare available commercially. The characteristics of these areobtained from their data sheets [29] and [30], respectively.The flow batteries and the NaS batteries are assumed to beimplemented in 50 kWmodules [31].The data in Table 3 havebeen obtained using the data sheets of commercial batteriesand other assumptions are taken according to data fromTable 2.
6 Modelling and Simulation in Engineering
3.2. Sizing of BESS. Let ๐ธbatt be the average energy require-ment for the battery per day in kWh per day. It is evaluatedfrom the maximum power surplus/deficit (๐diff (๐ก)) calculatedas below where ๐dem(๐ก) is the power that is to be dispatchedover a time period ฮ๐ก. Let๐ depict the number of days in thesimulation period. Consider
๐diff (๐ก) = ๐gen (๐ก) โ ๐dem (๐ก)
๐ธbatt (kWh) = max{๐
โ
๐=1
๐diff ร ฮ๐ก} .(4)
A simple model of battery is implemented to evaluate thenominal size of the battery system [32]. The model needs totake into account the depth of discharge (DoD%), days ofautonomy (๐ท), and battery aging. DoD is optimally selectedfor each battery to ensure its longevity and efficiency. It can beseen from Table 3 that NaS batteries have 100% DoD as theycan be completely drained to 0% SOC, but lead-acid batteriesshow degraded performance with such a high DoD. โDaysof autonomyโ indicate the duration for which the batteryis capable of meeting the dispatch as a back-up withoutcharging that is assumed to be 2 days in this study. Theoperating temperatures and aging also affect the operationof the BESS. Hence, from [33] the temperature correctionfactor for an average operating temperature of 28โC (fromFigure 7) is found to be 0.964.The aging characteristics of thebattery are considered by assuming an aging factor of 15%. Acommon correction factor is evaluated in (5) and included in(6) for battery sizing as follows:
Correction factor for effect of temperature & aging
= (0.964 โ 1.15) = 1.108 โ 110%(5)
Required Battery capacity in kWh: ๐ธbatt(max) (kWh)
=110๐ธbatt (kWh/day)๐ท
DoD%
(6)
Required Battery capacity in Ah: ๐ธcap (Ah)
=๐ธbatt(max) (kWh)๐ ร 1000
.
(7)
๐ธcap is the required capacity of battery in Ah. The ratioof ๐ธcap to the Ah rating of the individual battery module/cellyields the number of batteries to be connected in parallel(๐๐). The ratio of system voltage to the voltage rating of theindividual battery module/cell gives the number of batteriesto be connected in series (๐๐ ), to form the battery bank.Battery size obtained is minimized further by implementingan optimization algorithmby considering๐ธcap as amaximumboundary limit for the population selection.
3.3. Bat Optimization Algorithm. The underlying idea inmost of the optimization algorithms is to emulate a naturalprocess to evaluate the optimum result. Some of the examplesof these are genetic algorithm, particle swarm, and simulatedannealing algorithms. Bat algorithm is new metaheuristic
optimization technique formulated by Yang in 2010 [34] andits literature review and applications are listed in [35]. It isinspired from the prey locating technique called echolocationin flying bats used extensively by microbats.They emit soundpulses and listen for their reflected echo, to infer theirsurroundings and prey. In bat algorithm, a population ofbats is initiated with a fixed pulse emitting frequency, rate,and loudness. Velocities and position of the bats are updatedsimilar to particle swarm optimization. Loudness and rate ofpulse emission are updated based on distance from the prey.The pseudocode of the algorithm is shown in Pseudocode 1:
Minimize Annualized Cost = Battery Cost + Losses
Battery Cost = (๐ธbess ร ๐) ร (1 + ๐พ) ร CRF(8)
(see [36]), where Capital Recovery Factor is
CRF = idr (1 + idr)๐
(1 + idr)๐ โ 1.
idr = 1 + ir1 + if r
โ 1.
(9)
Here ir denotes interest rate, if r is the inflation rate, idris the discount rate, and ๐ denotes the lifetime of battery.The objective function is to minimize investment costs andlosses and is formulated as summation of two terms. First isbattery cost which is a function of battery size ๐ธbess in kWh,which is the optimization variable in the equation. Secondterm โLossesโ include losses incurred due to wind powerspilling and load shedding caused by inadequate storage. Asthe losses have an inversely proportionate relationship withthe battery size (a larger battery ensures greater reliabilityand lesser losses and vice versa), they are included in thecost minimization function. The constraints bounding theoptimization problem are as follows:
(1) Power balance constraints is ๐gen(๐ก) = ๐dem(๐ก) + ๐๐(๐ก).(2) Battery power limit constraints is ๐๐,min โค ๐๐(๐ก) โค๐๐,max.
(3) Battery SOC constraints is SOCmin โค SOC(๐ก) โคSOCmax, where SOC(๐ก) = SOC(๐ก โ 1) + ๐๐(๐ก) ร(ฮ๐ก/๐ธbess).
(4) Battery energy limit constraints is ๐ธ๐,min โค ๐ธ๐(๐ก) โค๐ธ๐,max.For discharging, ๐ธ๐(๐ก) = max{(๐ธ๐(๐ก โ 1) + (ฮ๐ก ร๐๐(๐ก))/๐dis), ๐ธ๐,min}.For charging, ๐ธ๐(๐ก) = min{(๐ธ๐(๐ก โ 1) + (ฮ๐ก ร ๐๐(๐ก)) ร๐chg), ๐ธ๐,max}.
4. Performance and Economic/EnvironmentalAnalysis of Battery Storage
The battery operates in charge/discharge mode based onthe power surplus/deficit occurring in the HRES. Let ๐๐(๐ก)be the power exchange to and from the battery duringcharge/discharge, respectively (positive for charging andnegative for discharging). The energy management strategyof the HRES system is depicted in the flow chart of Figure 6.
Modelling and Simulation in Engineering 7
Initialize bat population.Evaluate the objective function for each bat individual.Specify loudness ๐ด ๐, rate of emission ๐๐ and frequency limits (๐min and ๐max) for emitting pulses.Generate bat population for battery size using ๐ธbatt(max) as the maximum boundary limit and evaluate theobjective function for each individual.Identify the best solution ๐ฅโ.while (iteration count <max. iterations)Vary frequency (๐๐) and update velocity (V๐) and location (๐ฅ๐) using the below equations๐๐ = ๐min + (๐max โ ๐min) ๐ฝ
V๐ก๐= V๐กโ1๐+ (๐ฅ๐ก
๐โ ๐ฅโ) โ ๐๐
๐ฅ๐ก
๐= ๐ฅ๐กโ1
๐+ V๐ก๐
if (rand > ๐๐)Generate local solutions around the best solution.
end ifif (rand < ๐ด ๐ & ๐๐ < ๐min)
Include newly generated individuals and increase ๐๐ and reduce ๐ด ๐.end if
Prioritize bat individuals based on their loudness (proximity to solution).end while
Pseudocode 1
4.1. SystemMetrics. A feasibility study of the HRES project isdetermined by evaluating its economic system metrics. Thetariff fixed for wind power by the Tamil Nadu ElectricityRegulatory Commission [37] is Rs. 2.75 per kWh. Assumingthe same to be the price of the HRES power output, thefollowing system metrics are evaluated.
4.1.1. Revenue Losses (RL). Thewind-PV system incurs lossesunder three conditions.
(i) Wind Power Curtailment. Tamil Nadu faces instances ofwind power curtailment due to creaky T&D infrastructure.This condition occurs when there is sufficient wind, yet thewind turbines are either stalled or generating below ratedpower due to lack of power evacuation or load-demandmismatch [38].The actual wind power generated by the windturbine per day for themonth of June 2013 is denoted by๐๐คavg.The curtailed wind power ๐๐คcurt and the resulting revenueloss are evaluated as below where โ๐โ denotes the day of themonth:
๐๐คcurt (๐) = ๐๐คavg (๐) โ ๐๐คact (๐)
RL๐คcurt =30
โ
๐=1
๐๐คcurt ร ๐๐ ws ร ๐ก.(10)
(ii) Power Spilled. This condition occurs when ๐gen > ๐demand the excess power generated is spilled. Revenue lost dueto spilling is calculated for the entire simulation period ๐ asfollows:
๐spil (๐ก) = ๐gen (๐ก) โ ๐dem (๐ก)
RLspil =๐
โ
๐ก=1
๐spil ร ๐๐ ws ร ๐ก.(11)
In this case, the power spilled is assumed as the powerwhich is generated but not dispatched due to lack of demand.It differs fromcurtailedwindpower in the fact that the latter ispower in the wind which was not harvested at all as explainedabove.
(iii) Power Shed. This condition occurs when ๐gen < ๐dem.Without storage, the HRES fails to meet the dispatch curve,hence leading to load shedding.The deficit power is assumedto be met by an alternative energy source like diesel power.A diesel generator meets the excess load at a cost of ๐๐ ๐assumed to be Rs. 22 per kWh. Then the revenue loss to becalculated is
๐shed (๐ก) = ๐dem (๐ก) โ ๐gen (๐ก)
RLshed =๐
โ
๐ก=1
๐shed ร ๐๐ ๐ ร ๐ก.(12)
Thus, the total revenue loss is obtained by summing upindividual losses:
RL = RL๐คcurt + RLspil + RLshed. (13)
4.1.2. Payback Period. From the revenue earnings and lossesevaluated, the profit gained by adding the battery storage canbe calculated. Benefits gained here are limited to increase inearnings and reduction in losses due to inclusion of battery.Consider
BGA = [(RE๐ค๐ โ RE๐ค๐๐) + (RL๐ค๐๐ โ RL๐ค๐)] . (14)
Simple Payback Period (SPBP) is the ratio of investmentof battery cost (Inv) to the annual benefits gained from itsusage. As this does not include any interest rates, a discountedpayback period is also evaluated as in (15). It considers rate of
8 Modelling and Simulation in Engineering
Start
Evaluate battery capacity required to improve system using bat optimization algorithm
Evaluate battery SOC(t)
Battery is fully charged so excess power is spilled Battery is charged with excess
powerBattery is discharged to meet
deficit power
Battery is fully drained so unmet demand is shed
End of simulation
time
Stop
Next iteration
Yes No
Yes No
YesNo
No
Yes
Evaluate Pw , Ppv, and Pgen
Evaluate dispatch Pdem
t = 1
Pgen(t) > Pdem(t)
t = t + 1
SOC(t) > SOCmax SOC(t) < SOCmin
Pb(t) = 0,Pspil(t) = Pgen(t) โ Pdem(t)
Pdel(t) = Pdem(t)
SOC(t) = SOCmaxEb(t) = Ebmax
Pb(t) = Pgen(t) โ Pdem(t)
Pdel(t) = Pgen(t) โ Pb(t)
Eb(t) = Eb(t โ 1) + (๐ch โ Pb(t))
Pb(t) = Pgen(t) โ Pdem(t)
Pdel(t) = Pgen(t) โ Pb(t)
Eb(t) = Eb(t โ 1) + (Pb(t)/๐dis)
Pb(t) = 0,Pshed(t) = Pdem(t) โ Pgen(t)
Pdel(t) = Pgen(t)
SOC(t) = SOCminEb(t) = Ebmin
Figure 6: Energy management flowchart.
interest, rate of inflation [39], andmaintenance and operationcharges for the battery as shown in Table 4. One has
๐ = โln (1 โ (idr ร Inv) / (BGA โ (๐พ ร Inv)))
ln (1 + idr). (15)
4.1.3. Net Present Value (NPV). The difference betweenpresent value of the benefits gained and costs incurred in aninvestment is termed as the net present value of the system.This is an important economicmeasure as it includes the timefactor with the interest rate. It is always unique irrespectiveof the cash flow patterns. The formula to calculate NPV is asbelow.The investment is deemed to be profitable for a positive
NPV and conversion; a negative NPV indicates a financialloss [40]. Consider
NPV = (BGA) [ (1 + ๐)๐โ 1
๐ (1 + ๐)๐ ] โ Inv. (16)
4.1.4. Loss of Power Supply Probability (LPSP). It is a reliabilityindex which indicates the measure of energy deficit (DE) in apower system. It is a ratio of the energy deficit in the systemto the total energy delivered:
LPSP =โ๐
๐ก=1DE (๐ก)
โ๐
๐ก=1๐del (๐ก) โ ฮ๐ก
. (17)
Modelling and Simulation in Engineering 9
Table 4: Economic analysis parameters.
Symbol Parameter Value๐๐ ws Wind energy selling price Rs. 2.75 per kWh
๐๐ ๐Diesel energy generation
price Rs. 22 per kWh
ir Rate of interest 12%ifr Inflation rate 7%
idr Discounted rate of interest (1 + ir1 + ifr
) โ 1
omr O&M charges of battery as% of investment cost 3%
4.1.5. Benefit-Cost Ratio (BCR). The ratio of the benefits tothe costs associated with a project investment is its BCR. Fora project to be viable, it must yield a BCR ratio greater thanunity. It is a profitability indexwhich ismost easily interpretedby investors:
BCR = ( BGA ร CRFInv ร (1 + ๐พ ร CRF)
) . (18)
4.1.6. AvoidedCost of Emission (ACE). An analysis on the costof emission of carbon dioxide is included here. The cost ofcapture is defined as the incremental levelized capture costsin a given year divided by the volume of CO2 captured for agiven year. It is generally expressed as the change in levelizedcost of power for a year, between the capture case and thereference case, divided by the volume of CO2 captured in ayear. The standard formula is
ACECO2
=COEhigh โ COElow
CO2cap, (19)
where COE is the Levelized Cost of Energy from the genera-tion plant. Consider the wind-PV system to be the referencehigh emission system and the wind-PV-battery system as thelow emission system [41]. COE gives the price per unit ofenergy and is calculated as the sum of the total investmentcost of the system and the annual fuel cost of the system[42]. When the load is high the excess load is to be metwith a diesel generator, whose rating matches the maximumdeficit power. From๐diff evaluated, themaximumpower shedcan be calculated, that is, for cases ๐diff < 0. This will givethe required rating for the diesel generator. In this case, itis 121 kW. The investment cost (DGinv) for a 100 kW dieselgenerator is taken to be 6000$ [43] with an average life of 5years and interest rate of 10% [41]. Consider
COEhigh = (CRFhigh ร DGinv) + FCann, (20)
where FCann is the annual fuel cost for meeting the loadand ๐ธdel is the energy delivered by the diesel generator at acost of ๐๐ ๐ Rs/kWh. Similarly, CRFlow and COElow are alsoevaluated.
CO2cap is evaluated as the difference between the amountsof CO2 emitted by the reference high emission system and thelow emission battery system. Fuel consumption is assumed
3 6 9 12 15 18 21 24 250100200300400500600700800900
Hour of the day0
253035
Tem
pera
ture
(โC)
Temperature (โC)Solar irradiance (W/m2)
Sola
r irr
adia
nce (
W/m
2)
Figure 7: Solar irradiance and temperature in 24 hrs.
to be 0.33 litres of fuel per kWh energy delivered [44] and9.63๐ โ 3 tons of CO2 emitted per gallon of fuel. Thus (0.33 ร0.264172 ร 9.63๐ โ 3) 0.8395๐ โ 3 tons of CO2 is emitted perkWh energy delivered. Then annual emissions will be
CO2cap = CO2high โ CO2low. (21)
5. Results and Discussions
5.1. System Description. The specifications of the MICON450-200 wind turbine are listed in Table 5 [20]. Solar andwind data are recorded over a period of one year at a windsite in Southern India. The solar irradiation data for 24 hrsis shown in Figure 7. The wind data measured (at 30mheight) for every 10min is shown in Figure 8. In India, windgeneration is possible only in the windy seasons, that is,May to September. During other months, the generation istoo low for consideration. It was observed from site datathat the power generated by the wind-PV HRES in oneyear (inclusive of wind power for 5 months and PV for12 months) is approximately equal to 5 times the powergenerated by the system in June alone. Hence, to reducecomputational complexity, June is considered as the modelmonth for running the simulation.
5.2. Simulation Results and Discussion. The wind-PV systemgenerated 145.77MW power in June 2013; of this 90% wasfrom the wind turbine. The power graph of the wind-PVsystem without BESS (Figure 9(a)) shows that the deliveredpower is unable to meet the scheduled dispatch curve.Revenue losses occurring in the system include losses due towind power curtailment, load spilling, and shedding. Theselosses add up to a sum of Rs. 450,531.64 annually with a LPSPratio of 19.72%.
For selection of battery storage systems, five types of bat-teries, namely lead-acid, sodium sulphide, vanadium redox,polysulphide bromide, and lithium-ion batteries, are consid-ered. Using (6)-(7), the size and investment costs requiredfor each battery are evaluated and the results are tabulated inTable 6. Results illustrate that NaS batteries required the leastcapacity as compared to others. VRB batteries are found tobe the costliest of all other considered options. The batterysize is further optimized using bat optimization algorithmto minimize the investment costs and losses incurred. The
10 Modelling and Simulation in Engineering
Table 5: Specification of MICONM450-200 wind turbine.
S. number Specification Value S. number Specification Value1 Rated power 200 kW 8 Cut-off speed 25m/s2 Rotor diameter 24m 9 Voltage 400V3 Swept area 452m2 10 Freq. 50 hz4 Blade length 12m 11 Air density 1.2258 kg/m3
5 Tip-speed ratio 52.2m/s 12 Pitch angle 10 deg.6 Cut-in speed 5m/s 13 Efficiency 95%7 Rated speed 13m/s
Table 6: Sizing of batteries without optimization.
Type Rating inAh/module Capacity in Ah Number of
modules Inv. in $ Inv. in INR
Pb-acid 225 2700 240 $35,520 2,131,200PSB 1042 3126 9 $225,000 13,500,000VRB 1042 3126 9 $270,000 16,200,000NaS 1042 2084 6 $120,000 7,200,000Li-ion 300 2400 80 $280,000 16,800,000
2468
101214161820
Time (hours)
Win
d sp
eed
(m/s
)
Wind speed
0 24 48 72 96 120
144
168
192
216
240
264
288
312
336
360
Figure 8: Wind speed at 30m height.
loudness and the pulse rate of the bat algorithm are setas 0.5. Results obtained after optimizing are as in Table 7.Optimization of battery size resulted in significant changesin investment costs (Figure 10), payback periods, and BCRvalues of the system. In case of NaS batteries, the size isreduced to 50% as opposed to the battery size evaluatedusing (7). In other batteries the size is reduced to 30โ40%.The battery sizes thus evaluated are about 4โ7.5% (4% forNaS being the smallest and 7.5% for flow batteries being thelargest) of the rating of the wind-PV HRES. These results areconsistent and, in some cases, better than the results obtainedin previous literatures. In [45], the battery size evaluatedusing optimization was 6โ10% and in [14], fuzzy and neuralcontrollers were used to size the energy storage to be 30โ34%. A feasibility study by Ma et al. in [15] proposed abattery size about 24% of size of the wind-PV isolated system.Another study by Teleke et al. [46] suggests that a battery ofsize 15โ25% ofHRES capacity would be sufficient for effectivepower dispatch. Thus in the current study, a battery of muchsmaller size about 4โ7.5% is proved to be sufficient.
Energy delivered and profits gained before and afterintegration of BESS with the HRES are compared. Energy
storage helped to increase the power delivered by 24.56%and enabled the HRES to meet the scheduled dispatch curveat all times thus reducing the LPSP to zero as illustratedin Figure 9(b). It can be seen that after inclusion of batterystorage the power delivered curve follows the dispatch curvescheduled earlier. Losses due to spilling andwind curtailmentare reduced to zero and the energy thus saved is utilized tomeet peak demand. Tamil Nadu has a fixed wind power tariffrate [37]; hence the profits earned are based on reductionof power losses alone and no additional incentives for timeshifting have been considered. Thus, a future introductionof TOU tariffs or incentives may increase the profitability ofstorages implementing peak shaving.
The total power discharged from the battery to the gridfor the duration of the simulation is 28MW that contributedto 19.72% of the total power delivered by the wind-PV-battery HRES. Graphs plotted in Figures 11(a) and 11(b)show the power charged and discharged from the battery.The SOCs of the batteries, plotted in Figure 12(a), give anindication on the performance of the battery storages. TheSOC values vary within 90โ30% depending on the DoDof each battery indicating effective utilization of the batterysize over the period of simulation. Observing the changein SOC for over 48 hrs as shown in Figure 12(b) showsthe deeper charges/discharges occurring in a NaS batterydue to its maximum DoD. Flow batteries show identicalperformance but lag behind other batteries due to lowerDoD and efficiencies. The life of battery storage systemsdepends greatly on the cycles of operation preformed. FromFigure 12(a), the number of charge/discharge cycles per yearin the current study can be evaluated to be about 300โ350.Assuming the lifecycle limits of batteries to be 10,000 cyclesfor flow batteries and 2,000โ3,000 cycles for other batteries(as all batteries considered are deep-cycle batteries), lifetimeof batteries in years is evaluated to be 6 for Pb-acid, 8.33 forNaS, 10 for Li-ion, and >20 for flow batteries. Li et al. [11]
Modelling and Simulation in Engineering 11
Table 7: Sizing of batteries with optimization.
Type Rating in Ah Capacity in Ah Number of modules Inv. in $ Inv. in INRPb-acid 225 1800 160 $23,680 1,420,800PSB 1042 2084 6 $150,000 9,000,000VRB 1042 2084 6 $180,000 10,800,000NaS 1042 1042 3 $60,000 3,600,000Li-ion 300 1500 50 $175,000 10,500,000
0 3 6 9 12 15 18 21 240
50
100
150
200
250
Hour of day
Pow
er (k
W)
Wind powerSolar power
Load powerDelivered power
(a)
0 3 6 9 12 15 18 21 24โ100
โ500
50100150200250
Hour of day
Pow
er (k
W)
Wind powerLoad powerDelivered power
Battery powerSolar power
Battery charging Battery discharging
(b)
Figure 9: (a) Hybrid system output without battery storage. (b) Hybrid system output with battery storage.
3552
0
2250
00 2700
00
1200
00
2800
00
2368
0
1500
00
1800
00
6000
0 1750
00
050000
100000150000200000250000300000
Pb-acid PSB VRB NaS Li-ion
Inve
stmen
t ($)
Types of batteries
Investment for BESS
Before optimizationOptimized
Figure 10: Investment for BESS.
developed a dispatch strategy to maximize the lifetime of thebattery and simulation results showed an estimated batterylife of 2.10 years. Thus, current study results indicate a betterlifetime operation of batteries than those shown in earlierliterature. It is also to be noted that though the VRB batterywas the most expensive it also has highest number of cycles.
The performance of battery system is then evaluatedbased on operating conditions discussed in [47]. Ah through-put of a battery is the cumulative Ah discharged from batteryafter normalization with battery capacity. In the currentstudy, the partial cycling index for all the batteries lies inthe range of 58โ60% and Ah throughput index was foundto be 67%. โTime at low SOCโ value is the percentageoperating time for which the battery SOC is below 30%and is found to be 1.3%. These findings indicate an optimalbattery operation (category 5) with lowmedium risk of aging.
Thus, the sizing strategy with the energymanagement systemresults in optimal and intelligent use of battery storage.
System metrics evaluated based on simulation resultswere tabulated in Tables 8 and 9. Investment costs are shownin rupees with exchange rate assumed to be Rs.60/- perdollar. As the delivered power is the same for all batterycases, the monetary benefits gained remain equal. As BCRratios for all batteries are positive it can be assured that allbattery systems operate profitably. NaS batteries have thelowest capacity requirements with high efficiency. Pb-acidbatteries are the cheapest needing investment of only 59% ofthe cost of NaS batteries. Hence, they have the lowest paybackperiod (see Figure 13) of less than a year and highest BCR (seeFigure 14) of 10.95. However, NaS batteries have maximumNPV (see Figure 15), thus indicating that they can be aneconomically sound choice with zero maintenance. This isfurther supported by the fact thatNaS battery has nearly twicethe lifetime of lead-acid battery. The drawback of the NaSbattery is that it can be operated only at high temperaturesand require adequate thermal management.
Flow batteries and Li-ion battery have longer paybackperiods and higher investment costs. This makes them theleast favorable compared to lead-acid and NaS batteries.However, the payback periods are only a quarter of theirlifetimes, beyond which all benefits earned will be consideredas profits. Any reduction in prices of these batteries in thenear future may attract investments. Also, VRB and PSBshowed the longest cycle life based on operating cycles.Recently, VRB batteries are being installed commercially andare attracting investors due to the recyclability of electrolyteand low maintenance issues (maintenance required only for
12 Modelling and Simulation in Engineering
020406080
100120
Time (hours)
Pow
er (k
W)
Power charged to the battery3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96
(a)
Pow
er (k
W)
โ100โ90โ80โ70โ60โ50โ40โ30โ20โ10
0
Time (hours)
Power discharged from the battery
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96
(b)
Figure 11: (a) Power charged to the battery. (b) Power discharged from the battery.
0 100 200 300 400 500 600 7002030405060708090
100
Time (hours)
SOC
(%)
Battery SOC
N(1, 1) ยท PSOC = lead acidN(1, 2) ยท PSOC = PSBN(1, 3) ยท PSOC = VRB
N(1, 4) ยท PSOC = NaSN(1, 5) ยท PSOC = LiFePO4
(a)
0 5 10 15 20 25 30 35 40 45505560657075808590
Time of day
SOC
(%)
Battery SOC
N(1, 1) ยท PSOC = lead acidN(1, 2) ยท PSOC = PSBN(1, 3) ยท PSOC = VRB
N(1, 4) ยท PSOC = NaSN(1, 5) ยท PSOC = LiFePO4
(b)
Figure 12: (a) SOC of batteries. (b) SOC of batteries for 48 hrs.
Table 8: Economic analysis without optimization.
TypeEnergy
delivered inkWh
Revenueearned (INR)
Benefits inINR for June
Annualbenefits in
INRNPV SPBP in yrs DPBP in yrs BCR ACE in INR
Pb-acid 73,049 200,884 490,146 2,450,730 16,595,301 0.87 0.93 7.30 21,539.00PSB 73,049 200,884 490,146 2,450,730 8,211,364 5.51 8.07 1.46 โ5,005.00VRB 73,049 200,884 490,146 2,450,730 7,365,298 6.61 10.66 1.33 โ9,180.00NaS 73,049 200,884 490,146 2,450,730 21,438,573 2.94 3.57 3.15 11,836.00Li-ion 73,049 200,884 490,146 2,450,730 2,879,398 6.86 11.30 1.13 โ14,142.00
Table 9: Economic analysis after optimization.
TypeEnergydeliveredin kWh
Revenueearned(INR)
Benefits inINR for June
Annualbenefits in
INRNPV SPBP in yrs DPBP in yrs BCR ACE in INR
Pb-acid 73,049 200,883.85 490,146.05 2,450,730.23 17,472,912.71 0.58 0.61 10.95 2,3618.00PSB 73,049 200,883.85 490,146.05 2,450,730.23 14,144,121.35 3.67 4.69 2.19 5,923.00VRB 73,049 200,883.85 490,146.05 2,450,730.23 14,708,352.93 4.41 5.93 2.00 3,140.00NaS 73,049 200,883.85 490,146.05 2,450,730.23 26,422,617.02 1.47 1.63 6.30 19,806.00Li-ion 73,049 200,883.85 490,146.05 2,450,730.23 11,089,989.38 4.28 5.72 1.81 15,78.00
Modelling and Simulation in Engineering 13
0
5
10
15
20
Pb-acid PSB VRB NaS Li-ion
0.87 5.
51 6.61
2.94
6.86
0.58 3.67 4.41
1.47 4.
28
12 15
18
20
14
Payb
ack
and
life (
year
s)
Types of batteries
Payback period and lifetime of batteries
Before optimizationOptimizedLife
Figure 13: Payback period and lifetime of batteries.
7.30
1.46 1.33
3.15
1.13
10.9
5
2.19 2.00
6.30
1.81
0123456789
101112
Pb-acid PSB VRB NaS Li-ion
Bene
fit-c
ost r
atio
Types of batteries
Benefit-cost ratio
Before optimizationOptimized
Figure 14: Benefit-cost ratios.
165.95
82.11
73.65
214.39
28.79
174.73
141.44
147.08
264.23
110.90
0 50 100 150 200 250 300
Pb-acid
PSB
VRB
NaS
Li-ion
Net present value (Rs. in lakhs)
Type
of b
atte
ries
Net present value
OptimizedBefore optimization
Figure 15: Net present value.
21.54
(โ5.01)(โ9.18)
11.84
(โ14.14)
23.62
5.92 3.14
19.81
1.58
โ20โ15โ10โ50
51015202530
Pb-acid PSB VRB NaS Li-ion
Type of batteries
Avoided cost of emission
Before optimizationOptimized
Avoi
ded
costs
(Rs./
ton
CO2)
ร103
Figure 16: Avoided cost of emission.
the pump systems of the battery). Flow batteries thus are avery promising solution for grid-integrated systems.
It is difficult to justify the investments in green energyor any other sustainable energy which usually requires highinvestments. It is difficult to set a price for a pollution-freeenvironment. However, introduction of terms like avoidedcost of emissions and avoided costs of energy have made itpossible to show the profits gained by adopting green power.Hence, to further the idea of integrating energy storages,an environmental analysis is done based on ACE. A dieselgenerator to meet deficit power in the absence of storage isassumed to be the reference higher emission system.The totalannual CO2 emissions from a diesel generator are assumed tobe 60.466 tons for calculating the ACE.The chart in Figure 16shows the avoided cost of emissions obtained by adoptingbattery systems in the HRES before and after optimization.Prior to optimization, only Pb-Acid and NaS batteries exhibitsavings. However, on optimizing the size of the batteries,the cost of energy for the battery reduces below that of thediesel generator system, thus giving a positive ACE. Theavoided costs can also be looked up as savings as they are thedifference in cost of energy values of the two systems.
6. Conclusion
India is poised for a significant transformation in therenewable power sector. This further emphasizes the neces-sity of energy storages tomake renewable power dispatchable.This study outlines an optimized sizing methodology forbattery storage to implement peak shaving and ramp rate lim-iting features in the power dispatch.Theoptimization uses batalgorithm to effectivelyminimize the cost of the battery underfixed tariff. It is then validated in a Wind-PV grid-connectedhybrid system to eliminate power curtailment losses andimprove power evacuation.Themethodology is tested on fivetypes of battery systems from conventional lead-acid and Li-ion to upcoming flow batteries and NaS battery. Economicand environmental parameters are evaluated to analyze the
14 Modelling and Simulation in Engineering
feasibility of the HRES. The following conclusions could bedrawn:
(1) The dispatch strategy and the sizing methodologyincorporated peak shaving and ramp rate limiting toeffectively optimize the battery size. Consistent andcompetitive results were obtained, as compared toother referred literature studies.
(2) Though battery storage systems require high initialinvestments, this study proves that the benefits gainedin form of increased reliability and reduced lossesjustify investments. Profits gained by cutting downon spilling and shedding losses (with 0% LPSP) wereused as payback for recovering the investments.
(3) The lead-acid battery is found to have the least invest-ment costs and shortest payback periods. However,NaS battery outperformed the lead-acid battery inSOC characteristics with highest NPV. Hence, theyprovide a better solution with reduced maintenanceproblems and longer life.
(4) Though Li-ion batteries are highly efficient, the highcapital investment costs make them least favorable.Flow batteries proved to be less beneficial with highinitial costs but are still an intelligent choice withhighest cycle life.
Thus, battery storages are a viable and profitable optionfor aiding Indian renewable power projects. Future deregula-tion of power markets and introduction of time based profitswill prove beneficiary to systems integrating energy storages.Future workmay focus on integration, operation, and controlof the battery system with the grid-connected HRES.
Nomenclature
๐ผ: Temperature coefficient of PV panel๐ฝ: Pitch angles in degrees๐พ: Ratio of maintenance cost to the fixed cost
of the battery๐: Rotor speed in rad/s๐: Air density in kg/m3๐: Tip-speed ratio of the wind turbine๐: Energy cost coefficient of the battery in
Rs/kWh๐wt: Efficiency of the wind turbine๐pv: Efficiency of solar inverter๐ch and ๐dis: Charging/discharging efficiency of the
battery๐ด: Swept area in m2๐ถ๐(๐, ๐ฝ): Power coefficient of the wind turbine๐ธ๐(๐ก): Energy stored in the battery at time ๐ก in
kWh๐ธbess: Capacity of battery energy storage system
in kWh๐pv: Derating factor for solar panel๐บ๐: Solar irradiance incident on the panel in
W/m2
๐บSTC: Solar irradiance incident on the panelunder standard test conditions in W/m2
๐: Discounted payback period in years๐๐(๐ก): Power charged/discharged to/from the
battery at time ๐ก๐del: Power delivered at time ๐ก๐dem: Power to be dispatched to the load center
in kW๐gen: Power generated by the wind-PV
generation system in kW๐pv: Power generated by the solar panel in kW๐rated-wt: Rated power of the wind turbine in kW๐shed: Load shed due to unavailability of power
in kW๐spil: Wind power lost due to spilling in kW๐๐ค: Power generated by wind turbine in kW๐๐คact: Actual wind power extracted from turbine
in kW๐๐คavg: Average wind power generated as per
power curve equation in kW๐๐ ๐: Diesel power cost in Rs/kWh๐๐ ws: Selling price of wind power in Rs/kWh๐ : Length of blade in mSOC(๐ก): State Of Charge of the battery at time ๐ก๐๐: PV panel temperature in โC๐STC: PV panel temperature under standard test
conditions in โCV: Wind speed in m/sVci: Cut-in speed in m/sVco: Cut-off speed in m/sV๐: Rated wind speed of turbine in m/s๐pv: Rating of solar panel in kW.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
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