Page - 209 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 594 2. Whenthe totalpowerPofagroupofhouses isaboveagiventhresholdofXwatts, theEVsare requestedtodecrease their total charging in thenext time intervalbyΔ=P−X inawaythat keeps the individual localpowerprofilesasflataspossible for their remainingchargingwindow. 3. When the total power P of a group of houses is below a given threshold of Y watts (e.g., PVproductionpeak), the EVs are requested to increase their total charging in the next time intervalbyΔ=Y−P inawaythatkeeps the individual localpowerprofilesasflataspossible for their remainingchargingwindow. This approach,which is detailed below, has several important advantages. By startingwith flatprofilesonhouse level in thefirst step, the individualpeak loads,andwith it theprobabilityof overloadingthenetwork,decreases. Furthermore,flatteningthehouseloadincreasesself-consumption of locallygeneratedelectricity (e.g.,PV),hasapositive impactonthevoltage,avoidsoverloadingthe grid,anddecreases losses (as isdemonstrated inSection6). Whenthere is still apeakconsumptionfor thegroupofhouses (e.g., in theevening), thesecond stepof theproposedapproachcoordinates thechargingwhileavoidingnewlocalpeaks. Toquantify these localpeaks,weuseacost function Cˆn(δ) thatexpresseshowmuchchangingthepower for the upcominginterval fromxn,m toxn,m+δ influences theflatnessof theentirepowerprofile forhouse n (i.e., also considering impact on the future). This functionaidsuswithfinding theEVs that can contribute toobtaininga totalpowerdifferencewithminimal impact to the localflatness, andthus preventingproblems in the future.Morespecifically,ourobjective is toobtaina totalpowerdifference Δ for thegroupofhouses in thenext time interval,while retaining theflatnessof thepowerprofilesof individualhousesasmuchaspossible. This isexpressedmathematicallyas: Problem2. min δ1,...,δN f( δ)= N ∑ n=1 Cˆn(δn), subject to g( δ)= N ∑ n=1 δn=Δ, where f and g are introduced for reference in the later results. To ease the presentation, maximal charging powers are not considered in this formulation. However, to solve Problem 2 with additionalmaximal chargingpower constraints, we just can solve Problem2 (without these constraints)andfixanyviolationsusingaPeggingMethod; see [22] foradiscussionofsuchmethods. Beforewe can solve this problem,wefirst need a formal description of Cˆn(δn). These costs dependonthecharging level tobeattained in thecharging intervals (i.e., thefill levelZn), and the uncontrollable loads in theother intervals. Thesubsetof intervalswherecharginguptoZ takesplace isdenotedbyIn⊆{1,. . . ,M}, i.e.,In contains the intervalswhere pn,m−qn,m<Zn. Let In= |In| denote thenumberof such intervals (excluding thefirst interval). Using thisnotation, thecosts for housen canbedeterminedas functionofZn (note thatC(Z)nowreceiveda subscript to indicate thehouse): Cn(Zn)= ∑ m∈In Z2n+ ∑ m∈{1,...,M}\In (pn,m−qn,m)2 = InZ2n+ ∑ m∈{1,...,M}\In (pn,m−qn,m)2. Intuitively, thismeans that the incurred costs are the costs of chargingup toZn in the active intervalsIn (first term), andthecostsof the intervalswherenocharging takesplace (secondterm). Wenotice that, forpracticaldata, (see thediscussion in thenextsection) In rarelychangeswithδand 209