Electrical Power and Energy Systems 64 (2015) 1017–1024

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Energy storage model with gridable vehicles for economic load dispatchin the smart grid

http://dx.doi.org/10.1016/j.ijepes.2014.09.0040142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +61 431530999, +61 863045318; fax: +61863045811.

E-mail addresses: u.debnath@ecu.edu.au (U.K. Debnath), i.ahmad@ecu.edu.au(I. Ahmad), d.habibi@ecu.edu.au (D. Habibi), aysaber@ieee.org (A.Y. Saber).

Uttam Kumar Debnath a,⇑, Iftekhar Ahmad a, Daryoush Habibi a, Ahmed Yousuf Saber b

a Smart Energy Research Group, School of Engineering, Edith Cowan University, Joondalup, WA 6030, Australiab R&D Department, Operation Technology, Inc., ETAP, Lake Forest, CA 92630, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 June 2014Received in revised form 24 August 2014Accepted 4 September 2014Available online 20 September 2014

Keywords:Battery lifetimeEnergy storageGridable vehiclesParticipation rateRenewable energySmart grid

The intermittent nature of renewable energy sources (RESs) and unpredictable variable load demandshave necessitated the inclusion of energy storage devices in the smart grid environment. Electric vehicles(EVs) and plug-in hybrid electric vehicles (PHEVs), with vehicle-to-grid capability, referred to as ‘‘gridablevehicles’’ (GVs), have become an option as storage devices. However, unsupervised use of GVs as storagedevices presents new challenges due to concerns over battery lifetime and cost effectiveness of this two-way power transfer. These issues reduce the participation rate of GVs in the vehicle-to-grid dischargeprogram. In this study, we present a system model, for GVs to act as distributed storage devices, whichmitigates concerns over battery lifetime, and provides GV owners with a transparent cost-benefit analysisof their participation in the vehicle-to-grid discharge program. With this model in place, fuel and emis-sions cost has been reduced, as shown using particle swarm optimization. Simulation results show thatup to 52% of GVs might be discharging at a net loss. In contrast, our proposed system ensures that no GVsare at loss when discharging to the grid. This factor alone is expected to increase the participation rate ofGVs by a significant margin, and ensure economic load dispatch.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Sustainable energy systems have become a priority for almostall countries in the world. A smart grid is meant to provide suchan energy system by integrating extra operational capabilitiesand renewable energy sources (RESs) into the power system. RESssuch as wind and solar power are well accepted sustainable energysources. However, unreliability in continuous energy productionfrom RESs has been a major problem. A straightforward solutionto this problem is to use conventional energy storage systems, suchas electrochemical accumulators, which tend to be very costly. Avariety of energy storage provisions have been proposed to flattenthe cost [1], although achieving an acceptable cost of storage is stilla very active area of research. In recent times, gridable vehicles(GVs) have emerged as a significant contender, for dealing withthe uncertainty of RESs, in order to keep the utility grid unaffected.Research trends indicate that the use of GVs as energy storagedevices will bring about a breakthrough in the way that RESs aremanaged.

Recently, researchers [2] have been working on modeling thebenefits of using vehicle energy. Others are working on the charg-ing and discharging algorithms for GVs [3]. Modeling of chargingdemand from GVs and the impact of charging load have beenaddressed in some recent research [4,5]. Some other researchers[6] have addressed the economic load dispatch (ELD) problem withGVs as storage devices. Two major limitations of these works arethe implied assumptions that: (i) there exists a linear relationshipbetween a charging/discharging cycle and the lifetime of a GV bat-tery; and (ii) GVs will discharge at any time required by the grid.While such assumptions may be valid in an ideal situation, in prac-tice, they do not accurately reflect real-world conditions. The rea-sons include: (i) GVs are dependent on the performance of theirbatteries, and battery lifetime depends on its remaining capacityafter frequent use as a source and load; (ii) the cost of owningand maintaining a GV is still high; and (iii) the cost of a singlecharging/discharging cycle for each GV is dependent on the rateof capacity degradation. None of the research thus far has consid-ered battery capacity degradation in the cost model, or in theobjective function of the economic load dispatch model.

While GVs solve a major problem regarding storing and deliver-ing energy, battery capacity degradation and the actual cost ofenergy from GVs in the real-time, put a limit on how often a GVcan be used as a storage device. Participation rate of GVs in the grid

Nomenclature

Wdep/Wpre departure/present state of chargeWmin/Wmax min./max. state of chargef system efficiency (battery)FCi()/ECi() fuel/emission cost function of unit iwi emission penalty factor of unit iwc/we weight factors for fuel/emission costD(t) load demand at time tH scheduling hoursN number of thermal generating unitsNGV(t) no. of vehicles connected to the grid at hour tNGV-Dsch(t) no. of vehicles discharging to the grid at hour tNGV

max total vehicles in the systemPi(t) power of unit i at time tPwind(t) power from wind farm at time tPpv(t) power from solar photovoltaic panels at time tPi

max/Pimin max./min. output limit of unit i

Pvj capacity (power) of vehicle jR(t) system reserve requirement at hour tNcycle cycle number of a batteryCDremaining capacity degradation as a percentage of the initial

capacityCDstorage capacity degradation due to storage fadeCDcycling capacity degradation due to cycling fadeCcycle cost per charging/discharging cycleCopp/Cdgdn opportunity/capacity degradation cost per cyclewopp/wdgdn weight factors for Copp/Cdgdn

Vc(t) total cost of energy from vehiclesEs(t) energy supplied from s-th vehicle at time tps(t) price of energy of s-th vehicle at time tpbest/gbest particle’s best position/global best positionIte/MaxIte current iteration/maximum No. of iterations

1018 U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024

discharge program is still low due to this limitation, which hindersthe realization of a sustainable energy system. An intelligent sys-tem is thus required to relate battery capacity with the charging/discharging cycle in order to use GVs as a viable storage option;which provides the motivation for this research.

Problem description

In the smart grid, along with conventional thermal generators,the system consists of RESs, mainly wind and solar power sources,and GVs such as plug-in hybrid electric vehicles (PHEVs) and elec-tric vehicles (EVs). RESs are considered to be the compulsorysources of generation to reduce emissions and running costs alongwith the thermal generators, and GVs are considered to be distrib-uted storage devices to help balance loads. After considering all thesources including GVs, an optimization method is used to generatean intelligent schedule for cost and emissions reduction.

One of the representative objective functions for cost-emissionoptimization is [6], subject to some constraints:

minXN

i¼1

XH

t¼1

½wcðFCiðPiðtÞÞÞ þweðwiECiðPiðtÞÞÞ� !

ð1Þ

Two essential constraints of this optimization model, givingconsideration to load balancing and providing adequate spinningreserves, are given below in (2) and (3).

With GVs as sources of energy the load balance equation withreserve capacity is given as [6]:

XN

i¼1

Pmaxi ðtÞ þ PpvðtÞ þ

XNGV ðtÞ

j¼1

fPvjðWpre �WdepÞ

þ PwindðtÞP DðtÞ þ Lossesþ RðtÞ ð2Þ

And with GVs as loads or storages the load balance equationwith reserve capacity is given as [6]:

XN

i¼1

Pmaxi ðtÞ þ PpvðtÞ þ PwindðtÞP DðtÞ þ Lossesþ RðtÞ

þXNGV ðtÞ

j¼1

fPv jðWdep �WpreÞ ð3Þ

From (2) and (3), it is evident that power transfer to/from the GVs isthe only determining factor for ensuring maximum utilization of

RESs, and achieving a load balance condition. A high participationrate of GVs is thus necessary for the successful implementation ofa smart grid with RESs. However this cannot be achieved unless amodel is developed which provides transparent information, andinstills enough confidence in the owners that they will not end uplosing out if they participate in the grid-discharge program.

The aim of this work is to design an intelligent system model,taking both the battery condition and capacity degradation issuesinto consideration, and making the actual cost of GV energy trans-parent to the owners; assisting them to make a decision on dis-charging. Such a model is expected to significantly increase theparticipation rate, and to create a valuable contribution towardsthe realization of a sustainable smart grid system.

Proposed system model for efficient and economic use of GVs

The main contributions of this paper are two-fold. First, wemodel the capacity degradation cost of a battery, based on its num-bers of cycles that have already been spent, and include this in thecost of a single charging/discharging cycle of the GV, at variousstages of its lifetime. This model is then used to make a trade-offbetween the cost involved in a charging/discharging cycle, andthe real-time power available from a GV; in order to decidewhether it should discharge or not, and in what amount. Second,we develop an economic load dispatch model, where the objectivefunction takes the cost of using the GVs’ energy into account, inconjunction with the cost of fuel and emissions for thermal gener-ators. By using these two models, we ensure a cost-effective use ofthe battery energy, which is expected to enhance the participationrate of the GVs.

A. Modeling capacity degradation and actual cost of using GVs asstorages

Battery capacity degradation depends on a number of factors,such as spent depletion cycles, age, temperature at which it hasbeen used, size and type, and battery chemistry. As the vehiclescontinue using the batteries, capacity degradation is believed tofall in two categories; namely cycling degradation and storage deg-radation. Research shows that these two broad categories of losscover most of the factors concerning capacity degradation, andcan be represented as a function of the number of spent cycles[7]. If the current cycle number of a battery is Ncycle, the capacity

0 500 1000 1500 2000 2500 3000 3500 400088

90

92

94

96

98

100

Cycle Number

Rem

aini

ng C

apac

ity (

%)

Curve for Source Data

Curve for Fitted Equation

Fig. 1. A plot of the total capacity fading of a battery against the number of cyclesboth from [7] and the fitted Eq. (7). The quality of the fit is given by R2 = 0.9985.

U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024 1019

degradation as a percentage of the initial capacity, CDremaining, canbe given as in (4), further details being described in the followingsections.

CDremaining ¼ f ðNcycleÞ ð4Þ

The real-time energy available from a GV is justified against thecurrent cycle number, to make a trade-off, so that a GV does notpay more in terms of its capacity degradation.

The actual cost of GV energy consists of the capacity degrada-tion cost, and the opportunity cost, both of which are describedbelow. Opportunity cost is the initial cost of purchasing the bat-tery. Capacity degradation cost is the cost incurred for the actualdegradation of the battery capacity due to energy discharging frombattery to the grid. A combination of both these costs has beenused in this study to account for the initial capital cost as well asthe capacity degradation cost that is variable to individual energytransfer scenarios. With both these cost items included in the bat-tery energy cost calculation, vehicle owners are given more free-dom to set their own battery energy price that would ultimatelyencourage them to accept this business model towards adoptingthe grid discharge program.

If this actual cost is beneficial with respect to the current energypricing, a GV will discharge; otherwise the GV can denydischarging.

Capacity degradation costThe capacity loss of batteries has been observed by many

researchers and been stated that the fraction of capacity loss canbe measured per cycle of charging and discharging [8]. Degradationin current cycle number has thus been used in this study as one ofthe representative measure of the capacity losses during continu-ous cycling of batteries, as it has been shown on various experi-mental results [7]. To make a closer approximation of theconventional Li-ion battery capacity degradation trajectory, repre-sentative experimental results have been taken [7] to demonstratehow to determine the capacity degradation from the current cyclenumber. Each vehicle is expected to charge and discharge onlyonce a day, after giving consideration to both the battery lifetimeissues and the charging–discharging time. Urban driving profilehas been considered to reflect the driving profile of a usual vehicleowner.

In order to relate capacity degradation to cycle number, we usethe experimental results graphs [7] showing capacity degradationduring storage, and cycling against time and cycle numbers. Ulti-mate capacity fade is determined from the minimum of thesetwo capacity fading effects [7]. Reformulating the graphs (cyclenumbers in the X-axis) and assuming each battery will dischargeat most once a day, we get (5) and (6).

For storage, the capacity fade equation becomes

CDstorage ¼ 2� 10�6N2cycle � 0:008Ncycle þ 100:8 ð5Þ

For cycling, the capacity fade equation becomes

CDcycling ¼ 4� 10�8N2cycle � 0:003Ncycle þ 99:82 ð6Þ

Using 4000 cycles as a benchmark, and taking the minimum valueof capacity from (5) and (6), we find (7) and the corresponding fit-ted graph in Fig. 1 (R2 = 0.9985). We have used R2, which is the‘‘Coefficient of Determination’’ to quantify the ‘‘goodness of fit’’ ofa nonlinear model with an experimental result. R2 is computed fromthe sum of the squares of the distances of the points from the best-fit curve determined by nonlinear regression.

CDremaining ¼ 2� 10�16N5cycle � 2� 10�12N4

cycle þ 5� 10�9N3cycle

� 5� 10�6N2cycle � 0:0038Ncycle þ 99:961 ð7Þ

To find out the number of cycles already spent by the battery, weuse the battery internal management system records. We use thecapacity degradation versus cycle number graph in Fig. 1 to findthe capacity degradation at that particular cycle number. This infor-mation can now be used to calculate the real-time degradation as apercentage of the original capacity.

Costing for the degradation caused by the current charging-dis-charging cycle can be calculated using established battery perfor-mance data. As a battery cannot be used for vehicle-to-gridpower transfer once the remaining capacity drops below 80% ofthe initial capacity [9,10], cost of the battery should be distributedto the range between 80% and 100% of the original capacity.

When using the GV batteries, the end-of-life (EOL) require-ments of the batteries must also be addressed. When dischargingthe batteries, the state-of-charge (SOC) window should not crossa certain limit [11] to ensure the expected longevity and safetyof the battery. Because of the EOL requirements of the battery,owners are always concerned about the depth-of-discharge(DOD) while discharging. The owners also look at the DOD rangewhen selecting their weight factors for different cost items; asdescribed in the following sections.

Battery opportunity costThe cost to manufacture lithium-ion batteries depends on the

time, size, and volume of the production run. Currently the oppor-tunity cost is approximately $1000/kW h [12,13].

Both the opportunity cost and the degradation cost are con-verted into a cost per cycle, and are then added together to findthe per cycle charging-discharging cost. The cost per charging/dis-charging cycle, Ccycle, can thus be modeled as:

Ccycle ¼ woppCopp þwdgdnCdgdn ð8Þ

Weighting factors (ranging from 0 to 1) are selected by the owner,depending on the current cycle number and the DOD the batteriesare required to operate up to. Before discharging a vehicle, anowner/owner’s agent can look at this costing per cycle and corre-sponding battery capacity to analyze the revenue and battery life-time. If the current price of selling energy to the grid exceedsCcycle, the GV may decide to discharge; otherwise it should declinedischarging. The flowchart for the decision making process is givenin Fig. 2.

Selecting the weight factors is the owners’ choice as to whichcost concerns them the most, and they should be given the free-dom of choosing the weight factors that may help reduce their rev-enue concerns.

Fig. 2. Flowchart for discharging decision by the owner of GVs in the smart gridusing proposed model.

1020 U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024

It is possible to find an objective choice for these parameters,but that might push the vehicle owners towards a confusion asto who decides on the use of their own assets. A range of valuesfor each of these parameters have been proposed in this study.

Copp and Cdgdn in Eq. (8) are computed in three steps: first, totalopportunity cost and total capacity degradation cost are deter-mined for the whole automotive lifetime of a vehicle battery. Thenuseful life of the battery is determined on the basis that the batterywill cease to be suitable for automotive purpose once the capacitydegrades below 80% of the original capacity. This lifetime is con-verted into a number of cycles the battery can charge and dis-charge. And finally, the total opportunity cost and total capacitydegradation costs are divided by the number of operating cyclesto find Copp and Cdgdn.

All the necessary parameters (including cost, and amount ofenergy from all the vehicles that discharge at a particular hour),are calculated to find the total cost of energy from the vehicles,Vc(t) as follows:

VcðtÞ ¼XNGV�DschðtÞ

s¼1

EsðtÞpsðtÞ ð9Þ

B. Variation in per cycle charging/discharging cost and analysis of thevehicle-to-grid economics

The cost of capacity degradation and consequently of per cycledischarging, changes according to the variation of the vehicle price,type of vehicle, and rate of discharge. Further, the cost of energysold to the grid depends on the variation in the amount of energyactually sold, as this is directly related to the depth-of-discharge(DOD), which ultimately affects the rate of capacity degradation

per cycle. From previous research [7], we can relate the DOD tothe cost per cycling of a battery. A DOD corresponding to dischargecycles of either less/more than that specified, require an adjust-ment factor of more/less than unity, respectively. The capacity deg-radation cost then becomes a direct product of the cost and theadjustment factor.

C. Proposed optimization model considering cost of vehicle energy

Wind and solar energy are emission free and their operatingcosts are negligible. Fuel cost of a conventional thermal generatoris expressed as a quadratic function of the unit’s generated poweras follows:

FCiðPiðtÞÞ ¼ ai þ biPiðtÞ þ ciP2i ðtÞ ð10Þ

where ai, bi and ci are positive fuel cost coefficients of unit i.Emissions cost is expressed as another quadratic function of the

unit’s generated power as follows:

ECiðPiðtÞÞ ¼ ai þ biPiðtÞ þ ciP2i ðtÞ ð11Þ

where ai, bi and ci are emission coefficients of unit i.With GVs as sources, the load balance equation is:

XN

i¼1

PiðtÞ þ PpvðtÞ þXNGV�DschðtÞ

j¼1

fPv jðWpre �WdepÞ þ PwindðtÞ

¼ DðtÞ þ Losses ð12Þ

With GVs either acting as a load or providing storage capacity, theload balance equation becomes:

XN

i¼1

PiðtÞ þ PpvðtÞ þ PwindðtÞ ¼ DðtÞ þ Losses

þXNGV�DschðtÞ

j¼1

fPvjðWdep �WpreÞ ð13Þ

Load balance equations with adequate spinning reserves are givenby Eqs. (2) and (3), where NGV(t) is replaced by NGV-Dsch(t). Each ther-mal generator has its own generation range, represented as:

Pmini 6 PiðtÞ 6 Pmax

i ð14Þ

where Pimax and Pi

min are the maximum and minimum generationlimits of the i th unit.

Charging/discharging up to certain maximum/minimum levelsis ensured to prevent battery failure, and is given by:

WminPvj 6 PvjðtÞ 6 WmaxPvj ð15Þ

where Wmin and Wmax are the minimum and maximum levels ofcharge respectively, of the individual vehicles. Vehicles that havebeen registered for charging/discharging from/to the grid NGV

max,can take part during a predefined scheduling period; and are givenby:

XH

t¼1

NGV ðtÞ ¼ NmaxGV ð16Þ

Minimizing generation cost, emissions cost, and cost of buyingenergy from the vehicles are considered to be the primary objec-tives of the smart grid; and load balance, reserve, power generationlimit, and charging/discharging limits are considered to be theconstraints.

The objective function for cost-emission optimization, includingthe cost for vehicle energy, is therefore:

minXN

i¼1

XH

t¼1

½wcðFCiðPiðtÞÞÞ þweðwiECiðPiðtÞÞÞ� þ VcðtÞ !

ð17Þ

U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024 1021

Optimizing fuel and emissions cost

An efficient optimization method is required to minimize fueland emissions cost in a system consisting of thermal generators,RESs, and GVs. Particle swarm optimization (PSO) [14] is used inthis study to schedule the power intelligently. PSO provides a pop-ulation based search procedure- where each individual called aparticle, is represented by its position (state) and velocity, and par-ticles move around in a multidimensional search space. Each par-ticle adjusts its position according to both its own experience,and its neighboring particles’ experience, making use of the bestpositions discovered by itself and its neighbors.

In PSO, the velocity and position of each particle is calculatediteratively as follows:

vpqðkþ 1Þ ¼ ½vpqðkÞ þ c1r1ðpbestpqðkÞ � xpqðkÞÞþ c2r2ðgbestqðkÞ

� xpqðkÞÞ� 1þ�RangeMaxIte

ðIte� 1Þ� �

ð18Þ

xpqðkþ 1Þ ¼ xpqðkÞ þ vpqðkþ 1Þ ð19Þ

where velocity v, position x, accelerating parameters c1 and c2, ran-dom numbers r1 and r2, particle number p, problem dimension q,and iteration index k, are standard terms of PSO [15]. The flowchartfor the minimization of fuel and emissions cost with RESs and GVsin a smart grid, using our proposed models is given in Fig. 3. If athour t, the schedule is; [P1(t), P2(t),. . ., PN(t), NGV(t), Ppv(t), Pwind(t)]T,then power supplied to/from vehicles is fNGV(t)Pvi (Wpre � Wdep).The sign of this expression will indicate whether it is a load orsource; and the rest of the load demand, given by the expression;[D(t) + fNGV(t)Pvi (Wpre � Wdep) � Ppv(t) � Pwind(t)] will be met fromthe conventional thermal units.

Fig. 3. Flowchart for fuel and emissions cost minimization with RESs and GVs in thesmart grid using proposed models.

Results and discussion

The system described in this study includes thermal generators,RESs, and GVs in the smart grid environment. An on-board GVinterface system and the parking station computer system commu-nicate with all registered vehicles for collecting information on thevehicles’ battery condition. This is how the owners will know thecurrent rate of capacity degradation, and are able to decide if dis-charging will make revenue for them. GVs that discharge to thegrid are eligible for charging at a subsidized rate for a period deter-mined by the operator. An independent system operator (ISO) of a6-unit system with 50,000 registered GVs has been simulated inthis study. Unit characteristics taken from [16], and emission coef-ficients taken from [6] are given below in Tables 1 and 2. For GVs,the following parameter values were considered: vehicle batterycapacity S = 15 kW, H = 24 h, minimum Wdep = 40%, and f = 85%.For PSO, swarm size = 50, iterations = 1000, c1 = c2 = 2, Range = 0.5,wi = 25 $/ton, and wc = we = 1.

GVs arrive at parking stations randomly, so the number of GVsavailable may not meet the real-time requirement of the grid. Plan-ning is thus necessary to provide a match between the number ofGVs and the real-time demand. An availability planning model [17]does this matching by scheduling the GVs to discharge to the gridonly when the grid needs them the most. The availability planningmodel provides a distribution of number of GVs that will dischargeenergy to the grid at different times throughout the peak periods.

To reflect the real-time mobility of the vehicles during the 24 hdaily cycle, a mobility factor, m, which is a measure of the percentageof vehicles that are on the road (not at the parking station) at a cer-tain period, has been considered [17]. In the availability planningmodel we divide the 50,000 registered vehicles into a group of20,000 and a group of 30,000 for the two peak periods, pk1 (9 am–4 pm) and pk2 (4 pm–11 pm), respectively. We have set the mobilityfactors m1 and m2 as 0.2 and 0.3, corresponding to pk1 and pk2,respectively. We also assumed that around 0.2% of the GVs wouldnot show up at all, giving us the proposed availability planningVdisch for each of the 24 h of the day: Vdisch = [00000000163362176545654562176336374412856716171612856441-210]. All GVs are assumed to be charged during each 24-h period,and thus the total energy required to charge them is distributed overthe hours when the demand is close to the base load demand. Econ-omy of the charging load distribution over individual hours isdependent on the load demand, RESs generation, time-of-use pric-ing, generator parameters, and balance between cost and emissions.An intelligent coordination of all these factors has been performed,which gives us the following daily distribution of GV charging,where Vchrg = [20668133336666000000000000016670000010006666].

To study the effect of the proposed cost models with respect tocost and emissions reduction, these two models have been incor-porated in the economic load dispatch (ELD) problem. PSO wasused to minimize fuel and emissions costs for the economic dis-patch. For RESs, solar insolation data, wind speed data, and gener-ated power, and demand data over the 24-h period have beentaken from [6]. The time-of-use pricing of energy (in $/MW h) for

Table 1Generating unit capacity and coefficients.

Unit Pmin (MW) Pmax (MW) a ($) b ($/MW) c ($/MW2)

1 100 500 240 7.0 0.00702 50 200 200 10.0 0.00953 80 300 220 8.5 0.00904 50 150 200 11.0 0.00905 50 200 220 10.5 0.00806 50 120 190 12.0 0.0075

0 5 10 15 20 250

1000

2000

3000

4000

5000

6000

7000

8000

Time of a day (Hour)

GV

s di

char

ging

for

diffe

rent

ran

ge o

f wei

ghts

(N

o.)

Expected to discharge

For range of weights (0.25-0.35, 0.8-0.9)For range of weights (0.25-0.35, 0.9-1.0)

For range of weights (0.30-0.40, 0.8-0.9)

For range of weights (0.25-0.40, 0.8-1.0)

For range of weights (0.30-0.40, 0.9-1.0)

Fig. 6. Number of discharging GVs at loss at different hours in a day for differentranges of weight factors (wopp, wdgdn) described in (8).

1 2 3 4 5 60

10

20

30

40

50

60

Combination of weight factors

Per

cent

age

of G

Vs

at lo

ss (

%)

Bar 1 - For weights (0.35, 0.95)Bar 2 - For weights (0.35, 1.00)Bar 3 - For weights (0.40, 0.90)Bar 4 - For weights (0.40, 1.00)Bar 5 - For weights (0.45, 0.90)Bar 6 - For weights (0.45, 0.95)

Fig. 5. Percentage of discharging GVs at loss at different hours in a day for differentweight factors (wopp, wdgdn) described in (8), corresponding to Fig. 4.

Table 2Generator emissions coefficients.

Unit a (ton/h) b (ton/MW h) c (ton/MW2 h)

1 10.33908 �0.24444 0.003122 32.00006 �0.38132 0.003443 32.00006 �0.38132 0.003444 30.03910 �0.40695 0.005095 32.00006 �0.38132 0.003446 30.03910 �0.40695 0.00509

1022 U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024

a typical day is as follows [18]: from hours 7 to 17, price is 320.30;from hours 18 to 23, price is 332.00; and during all other hours,price is 145.90.

For calculating per cycle charging-discharging costs, the oppor-tunity cost has been taken from the $800–$1200 per kW h range[12,13] (assuming a cycling capacity of around 4000 cycles). Capac-ity degradation cost is measured throughout the entire life of a bat-tery until it is suitable for discharging to the grid. By taking batterycosts from [12,13], capacity degradation cost for a 4000 cycle bat-tery can be taken as $6000–$8000 throughout its dischargingcapacity lifetime. A random distribution of these costs has beenconsidered, within the specified range, for all 50,000 vehicles.

Owners are free to choose the weighting factors in (8) that bestrepresent the cost of their vehicle’s energy. Although vehicles dis-charge to supply the grid, they also discharge while being drivenfor everyday purposes, which accounts for a significant portion ofthe various cost items. Depending upon the situation, capacity deg-radation costs may account fully for each discharge cycle. A rangeof different weighting factors have been studied. From this study,the gross numbers of vehicles experiencing a loss, and the percent-age with respect to the available vehicles have been calculated asshown in Figs. 4 and 5.

Figs. 4 and 5 show that up to a 52.47% of vehicles can be in a losscondition, depending on the specific choices made by each owner.Even with a grid-friendly weight factor selection, which is unlikelyto happen from the owners’ perspective, at least 4.76% of the vehi-cles would be operating at loss.

To reflect the differences in weighting factor selection from dif-ferent GV owners, the calculations have been performed againallowing the weighting factors to vary randomly within a certainrange, and illustrated in Figs. 6 and 7. Figs. 6 and 7 show that eventhough different GV owners select a variety of weighting factorsfrom within a given range, up to a 36.30% of vehicles can still beoperating at a loss.

1 2 3 4 50

5

10

15

20

25

30

35

40

Combination of range of weight factors

Per

cent

age

of G

Vs

at lo

ss (

%)

Bar 1-Range of weights (0.25-0.35, 0.8-0.9)Bar 2-Range of weights (0.25-0.35, 0.9-1.0)Bar 3-Range of weights (0.30-0.40, 0.8-0.9)Bar 4-Range of weights (0.25-0.40, 0.8-1.0)Bar 5-Range of weights (0.30-0.40, 0.9-1.0)

Fig. 7. Percentage of discharging GVs at loss at different hours in a day for differentranges of weight factors (wopp, wdgdn) in (8), corresponding to Fig. 6.

0 5 10 15 20 250

1000

2000

3000

4000

5000

6000

7000

8000

Time of a day (Hour)

GV

s di

scha

rgin

g fo

r diff

eren

t wei

ghts

(No.

)

Expected to dischargeFor weights (0.35, 0.95)For weights (0.35, 1.00)For weights (0.40, 0.90)For weights (0.40, 1.00)For weights (0.45, 0.90)For weights (0.45, 0.95)

Fig. 4. Number of discharging GVs at loss at different hours in a day for differentweight factors (wopp, wdgdn) described in (8).

Table 3PSO results with vehicle energy and costs considered with no price-check.

Time(H)

Unit 1(MW)

Unit 2(MW)

Unit 3(MW)

Unit 4(MW)

Unit 5(MW)

Unit 6(MW)

Solar(MW)

Wind(MW)

Vehicles(MW)

Demand(MW)

Loss(MW)

Total cost($)

1 170.45 152.41 160.38 104.90 149.80 101.68 0.00 10.54 �131.76 700.00 18.40 17967.962 168.57 150.84 158.78 103.79 148.22 100.55 0.00 22.27 �85.00 750.00 18.02 17707.783 180.40 161.13 169.10 110.89 158.37 107.67 0.00 25.50 �42.5 850.00 20.56 19420.214 192.98 172.08 180.08 118.48 169.12 115.21 0.00 25.50 0 950.00 23.45 21362.125 204.41 182.05 189.89 125.38 178.87 120.00 0.00 25.50 0 1000.00 26.11 23158.926 231.45 200.00 213.21 141.58 200.00 120.00 0.00 25.50 0 1100.00 31.74 27092.557 255.29 200.00 233.61 150.00 200.00 120.00 0.09 25.50 0 1150.00 34.49 29286.398 273.87 200.00 249.47 150.00 200.00 120.00 17.46 25.50 0 1200.00 36.30 30849.989 323.11 200.00 291.20 150.00 200.00 120.00 31.45 25.50 +0.1020 1300.00 41.36 35524.1410 412.60 200.00 300.00 150.00 200.00 120.00 36.01 25.50 +2.1420 1400.00 46.25 42317.3611 450.69 200.00 300.00 150.00 200.00 120.00 38.06 25.50 +13.8720 1450.00 48.13 48783.0712 483.57 200.00 300.00 150.00 200.00 120.00 35.93 25.50 +34.7820 1500.00 49.78 57904.8413 377.49 200.00 300.00 150.00 200.00 120.00 36.78 25.50 +34.7820 1400.00 44.56 50047.0914 315.50 200.00 284.77 150.00 200.00 120.00 31.59 24.82 +13.8720 1300.00 40.55 39027.9315 279.80 200.00 254.51 150.00 200.00 120.00 9.70 20.74 +2.1420 1200.00 36.89 32034.2616 216.45 192.46 200.30 132.58 189.16 120.00 12.92 14.62 +0.2359 1050.00 28.73 25050.5917 206.38 183.74 191.61 126.57 180.54 120.00 0.00 25.50 �7.8157 1000.00 26.53 24321.1018 227.15 200.00 209.51 138.98 198.18 120.00 0.00 19.04 +18.2070 1100.00 31.07 32248.9119 257.80 200.00 235.79 150.00 200.00 120.00 0.00 25.50 +45.6514 1200.00 34.74 43644.5920 412.58 200.00 300.00 150.00 200.00 120.00 0.00 18.02 +45.6514 1400.00 46.25 55803.8221 330.81 200.00 297.67 150.00 200.00 120.00 0.00 25.50 +18.2070 1300.00 42.19 41926.7922 232.00 200.00 213.69 141.90 200.00 120.00 0.00 21.42 +2.8114 1100.00 31.81 28017.3523 189.01 168.64 176.51 116.10 165.69 112.80 0.00 0.00 �6.2411 900.00 22.51 20772.6824 174.46 156.00 163.98 107.34 153.32 104.12 0.00 2.55 �42.50 800.00 19.27 18552.13

Total Cost (Fuel, Emission and Vehicle Energy) = $782822.56

Table 4PSO results with vehicle energy and costs considered with price-check.

Time(H)

Unit 1(MW)

Unit 2(MW)

Unit 3(MW)

Unit 4(MW)

Unit 5(MW)

Unit 6(MW)

Solar(MW)

Wind(MW)

Vehicles(MW)

Demand(MW)

Loss(MW)

Total cost($)

1 170.45 152.41 160.38 104.90 149.80 101.68 0.00 10.54 �131.76 700.00 18.40 17967.962 168.57 150.84 158.78 103.79 148.22 100.55 0.00 22.27 �85.00 750.00 18.02 17707.783 180.40 161.13 169.10 110.89 158.37 107.67 0.00 25.50 �42.5 850.00 20.56 19420.214 192.98 172.08 180.08 118.48 169.12 115.21 0.00 25.50 0 950.00 23.45 21362.125 204.41 182.05 189.89 125.38 178.87 120.00 0.00 25.50 0 1000.00 26.11 23158.926 231.45 200.00 213.21 141.58 200.00 120.00 0.00 25.50 0 1100.00 31.74 27092.557 255.29 200.00 233.61 150.00 200.00 120.00 0.09 25.50 0 1150.00 34.49 29286.398 273.87 200.00 249.47 150.00 200.00 120.00 17.46 25.50 0 1200.00 36.30 30849.989 323.13 200.00 291.21 150.00 200.00 120.00 31.45 25.50 +0.0765 1300.00 41.36 35517.7310 413.65 200.00 300.00 150.00 200.00 120.00 36.01 25.50 +1.1411 1400.00 46.30 42081.9211 457.20 200.00 300.00 150.00 200.00 120.00 38.06 25.50 +7.6946 1450.00 48.45 47375.6112 500.00 200.00 300.00 150.00 200.00 120.00 35.93 25.50 +18.4429 1500.00 50.62 54302.5013 394.13 200.00 300.00 150.00 200.00 120.00 36.78 25.50 +18.9401 1400.00 45.35 46242.3114 319.00 200.00 287.73 150.00 200.00 120.00 31.59 24.82 +7.7775 1300.00 40.92 37488.7315 280.34 200.00 254.99 150.00 200.00 120.00 9.70 20.74 +1.1730 1200.00 36.95 31783.0116 216.46 192.50 200.34 132.60 189.17 120.00 12.92 14.62 +0.1339 1050.00 28.74 25022.9717 206.70 184.00 191.86 126.72 180.86 120.00 0.00 25.50 �9.0461 1000.00 25.50 23985.6918 228.79 200.00 210.94 139.95 199.60 120.00 0.00 19.04 +13.0560 1100.00 31.38 30864.9019 265.27 200.00 242.13 150.00 200.00 120.00 0.00 25.50 +32.5571 1200.00 35.46 40205.6620 452.85 200.00 300.00 150.00 200.00 120.00 0.00 18.02 +33.0289 1400.00 46.90 52848.4721 333.81 200.00 300.00 150.00 200.00 120.00 0.00 25.50 +13.1899 1300.00 42.50 40673.3422 232.29 200.00 213.96 142.08 200.00 120.00 0.00 21.42 +2.1038 1100.00 31.85 27827.7623 189.00 168.64 176.48 116.10 165.68 112.86 0.00 0.00 �6.2539 900.00 22.51 20769.1624 174.46 156.00 163.98 107.34 153.32 104.12 0.00 2.55 �42.50 800.00 19.27 18552.13

Total Cost (Fuel, Emission and Vehicle Energy) = $762387.67

U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024 1023

Resource scheduling has been performed with vehicles assources, storages, and loads. Results for cost and emissions reduc-tion in a smart grid system, incorporating the proposed availabilityplanning model and the battery capacity degradation model, withreal-world costing for wind, solar, and GVs are shown in Tables 3and 4. As a likely real-world scenario, weighting factors represent-ing the fourth bar in the bar chart of Fig. 7 have been taken to selectthe number of discharging vehicles. Table 3 represents the eco-nomic load dispatch for a conventional smart grid model, and theplanned availability distribution. Table 4 represents the same

scenario for weighting factors of (0.25–0.40, 0.8–1.0) that leadsto 35.85% of discharging vehicles operating at a loss, and hencebeing restricted from discharging.

As a result, 35.85% of the expected discharging vehicles have beensaved from operating at a loss. The GV discharging distribution inthis case is V = [00000000121791207289329711220184212482048510751812069330190]. Signs for the GV energy in Tables3 and 4 represent GVs as source (+) and load (�).

It is evident from Tables 3 and 4 that fuel and emissions costshave been reduced with our proposed models. As a considerable

Table 5Overall benefits of using our proposed models.

Items With conventionalmodel

With our proposedmodel

GVs at loss Up to 52% Close to noneExpected GV

participation rateAs low as 48% Close to 100%

Total cost More LessPotential for RESs

integrationLess due to participationrate

More

Basis of dischargingdecision

Non-transparent Transparent andobjective

1024 U.K. Debnath et al. / Electrical Power and Energy Systems 64 (2015) 1017–1024

amount of power has been supplied from the vehicles, utilizationof more renewable sources has been and would be possible, if itwere available. Similar results with other combination of weight-ing factors justify the benefits of using our proposed models.

A summary of the benefits of using our models are given inTable 5.

For an ISO implementing V2G, total storage capacity potentiallyavailable from the GVs is dependent on the number of participatingGVs and the effective discharging capacity of the GV batteries. Ourproposed system model maintains the owners’ confidence in theirvehicles’ operating conditions, as well as maintaining revenue out-comes against battery wear. At the same time, owners have thefreedom to stop discharging to the grid should they be concernedthat they are not earning any revenue, which would help providean incentive to participate and remain in the grid discharge pro-gram. Because the individual owners are convinced of their revenueoutcomes, the system operator can in turn be confident of the avail-ability of a considerable number of GVs for discharge. As a result,both the vehicle owners and the system operator have their ownfreedom to choose any combination of buying and selling energyto/from the grid. Providing such a flexible arrangement will encour-age more owners to participate in the grid discharge program,which is imperative if the GV integration is to be a success.

In an effort to compare the approach taken by other researchappearing in literature [19,20], especially for what concerns theinclusion of degradation costs into the optimization models, ourresults show that we have taken a different approach to the inclu-sion of degradation costs into the optimization model. While thementioned research [19,20] use the capacity degradation costs tocompare the effectiveness of their proposed models, our researchdemonstrates how to calculate the degradation cost, why is itimportant to include it in the optimization model and how thevehicle owners can save themselves from revenue losses from dis-charging to the grid. Moreover, our research deals with the funda-mental issue of decision making as to whether or not a vehicle willdischarge at the grid operator’s request.

Conclusion

Using GV batteries as energy storage units for dealing with thevariable RESs and loads in the smart grid environment has been anundesirable option for each individual operator. The low participa-tion rate in the V2G discharge program has been a major impedi-ment to the successful implementation of this concept. The mainobstacles being the owners’ anxiety about battery lifetime, andconcern over the ultimate benefit arising from using GVs as energystorage units. In this paper, we have proposed a model that consid-ers the issues associated with battery degradation and relevantcosts, and have provided the owners of the GVs with a transparent

tool for estimating the real-time cost of discharging to the grid,eradicating concerns that they will incur a loss over the long run.We have also proposed an economic load dispatch model thatincludes the cost of using GV energy in the objective function,along with the fuel and emissions cost of the thermal sources.Our proposed models will save discharging vehicles from experi-encing a loss, which is expected to significantly increase V2G par-ticipation rate, to integrate more RESs, and ensure improved levelsof sustainability. In addition, the models provide an assurance tothe operators that GV energy is available, enabling them to dealwith more variable generations and loads, and to maintain eco-nomic load dispatch with GVs.

Acknowledgement

This work is supported by a Commonwealth of AustraliaScholarship.

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