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Aerospace 2018, 5, 123 16 of 21 Aerospace 2018, 5, x FOR PEER REVIEW 16 of 21 solvedforallthetimeinstantsoftheflight.tfTinheevaluationoftheelectricalbehaviorisassuredbythe ∫ Ibatt (t) solutionofthefollowingmathemSaotCicatlm=o−deladopteddt forthecalculationoftheelectricalparameters: () tQb 0 Qb t0P (t) ele . (9) (t) tfin V =n d bSatotC(t) d R I+ (t)−. (9) out,batt s 0I (t) 1 b batt SoC(t)=− dt VI t = n [d SoC(t) + d ] − R I obuatt,tba(tt) s 0 1 b batt ηnV I (t) = gPelep(t)out,batt batt ηgnpVout,batt In tthemooddeel,l,itiitsiasssausmsuemdetdhathbaotthboththe cthapeacaitpaancietasnacneds tahnedpathraesiptiacriansdituictiandcuesctoafntcheesboaftttehrye cbealtltearrye cnelgl leacretedn.egTlehcetegdl.obTahleefgfilocibeanlcyeffηicietankceys ηing ttoakaecscoiunntot alclctohuentefafilclietnhceiesffoicfiethneciesleoctfritchael g peloewcterric-tarlainpocwomerp-tornaeintsc(oemlepctornicemntosto(re,lpecotwriecr mcoontvoerr,tepros)w. Ceroncsoidnevreirntgeras)c.onCsotannstidtemrinpgeratucroenfostraanltl theme dpevraicteusre(infocrluadlilntghethdeebvaitctesri(eisn)calundiangquthasei-bcaotntsetraienst)aanngdularqsupaeseid-cofntshtaenptraonpgelulelarrs,sipt eisedpoosfsitbhle tporoapsseullmeres,tihtaisttphoesgsilbolbeatloeaffisscuiemnecythisatcothnestgalnotb.aTlheeffitcwieonvcyariisacbolenss,tdanta.nTdhedt,waorevmareiabsulerse,dd0inanVdoldts1, 01 arnedmareeasruerlaetdedintVo othltes,dainscdharegereclautrevdetofttheedcieslclhs.arIgt eisciumrvpeoortfatnhtetcoenllos.teIttihsaitmthpeorttoatnatl tporonpotuelstihoant pthoewteorta(wl phircohpiuslsthioensupmowoefrth(ewthiecrhmiasltehnegisnuemanodfetlheecttrhicemrmoatolrepnogwiner)ainsdfixeeledctarnicdmeqoutaolrtopothweetro)taisl pfioxwederanredqueiqruedalbtyotthestoatnadlaprodwaeircraeqftuwirietdhtbhyetmheaxsitmanudmartdakaeir-ocrffafwtewigithttahnedmfoarxtihmeucmontsaidke-roefdf wfliegihgth. tHaencde,ftohre athdejuncoctniosindoerfebdattfelirgiehst,.anHdenocfet,hetheelecatrdijcupnocwtioenr-troafinb,adteteterirems,inaensda roedf utchteioneloefctrhiec paoywloear-dtranind, pdaestesremngineresnaumrebdeurcst.ion of the payload and passenger numbers. 5.2. Solutions of the Optimization Problem 5.2. Solutions of the Optimization Problem The optimization problems (4)–(6) have been solved using a random search method. This choice The optimization problems (4)–(6) have been solved using a random search method. This choice is due to the fact that two of the three independent variables must be integer numbers. The iterative is due to the fact that two of the three independent variables must be integer numbers. The iterative procedure adopted is depicted in Figure 20. procedure adopted is depicted in Figure 20. Figure 20. Random search algorithm adopted for the solution of the optimization problem. Considering a set of n , n , and D , generated as a random uniform distribution, Considering a set of npp, ns,sand DDCD,mCax,,magxenerated as a random uniform distribution, the the mathematical model (6) is solved. If the constraints (5) are satisfied, the sets (n , n , D ) mathematical model (6) is solved. If the constraints (5) are satisfied, the sets (np, ns, DpDC,msax) bDecCo,maxe become feasible solutions for the problem, and the value of the objective function is stored. If the value feasible solutions for the problem, and the value of the objective function is stored. If the value of the of the objective function at kth iteration is less than the value at (k − 1)th iteration, a new optimal objective function at kth iteration is less than the value at (k − 1)th iteration, a new optimal solution is 6 solution is found. If the total number of iterations reaches the value k (in our case,6 2 × 10 ), the last found. If the total number of iterations reaches the value kmax (in omuarx case, 2 × 10 ), the last stored solution becomes the optimal solution. stored solution becomes the optimal solution. 6. Simulation Results The solution of the previous problem is carried out using MATLAB. In order to obtain the best solution for the considered hybrid propulsion system, different numerical simulations are reported.PDF Image | Turboprop Hybrid Electric Propulsion System
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