Method for calculating the energy characteristics and solar battery parameters of high-voltage power supply systems

Introduction. Ensuring the long term of tOe spacecraft (SC) active li^ctimc (TAL) is Etc of prioritg ocien-fiflc, tenanicEl anti eaonomic iasks which solution demands a cemiggeOensroe fimOamrnfol approach during the drcrlopmrnf and creation oS sC' pupps funple tystems (PSS).

TOe msin primmy nufrgy source io SC PPB are solar boffrrirs (S>Itl dcsigncS ne the Sesis of Si or GaAs solar ealis -caning non-ltnear I-V a.nd V-W cSaracteristics with a proEouEene maeUeum oS the: genrcatrd pawoe, determined luc Ed oprraitng volOigr oanel fSat ijrsjg^eo lhp expediency at maesmum asraef poinl irackine (MPPT) mode of SB (n SSS cpylication [1-4]. Don to tie increase of oufpuf vof-ageof toe SGload power bus uptoOOO V, new frehniaat rcquerialhnk to t:Oie ways nf roOTdiEntion and srrciee conditions oh energy somnnn irc PSP have been coeated. tSis is dur to tPr snoiSilUI ito of rierttosistic dis-eOrogss PfOores ]эhoCэУCones chsCas aud eueseiit collec-fioEelemontsagtoeSB acS, as a)csult,-o theoosWfor the maximum locolaOSB apecci rcui t-iiCO voPage ogaration limifofion reachsd when thv SC Ineoes the erdO ohadow arras [5—7]. Applfcatias eg other eolar esПs tapns in PSS is posaibte m saee oh irasfuillty oh tSrei.r use caoUzed by means ae ashouiation eO hoE grpcraied bp SB sapacities durino TAL providing an energy balanca in PSS, raliacal disfribufion of enosgy -owc and prcaanlioit of PmS work rmrrnrEouoperaiion.

Toe dcyslopcd lechitisuc ggovfgrr due: rehuction in caCculaiion Оте nO p-wcr charofteristicc and the SB pa-romrfrrs aShigh-yo)tnge SC dSO wls irf is obtained by the drcoease in tOe nembee oO iterations dioeefls osoportisnal fo rhr uEEntity ar coиecitau factors t- hc calculetad. The frcgnrguc sac Pa caplied sshen oatcuiatino options of Oround End :зnbannn PSS wi-S vorious iaad curves End srrciee shndiiihne fon ths aursosr ag avalization oh energy floosie PSS rainicri redfsttibuiioncnУ im tmsaee its ECE and SB design reoeioements.

Mathematical model of solar battery. Tie OB elec-frio oareraftPhe dig'Sog SC oc-v-cc chonge significantly. TOe constdrraЫeanfluence on SBI-V and V-PV oharacter-isfire Sr rei-idcmd u>n< temprraiure did flluminniion. So, in low-orbo Sre the SB panek tcmpr-atiics ceangrs in the rohor from -9П to +80 9С, errrwitn tie SC can haer the seorptcorioblr load urcoc and thr siEitifiaane eemaer of shanow rorar on tdr orbif Thrrreorr for Vic oruofst plen-hiho oW Pg) iarger smiipmsnt ooeratisn it

TOe StB eisurint trnratnr^eп;, tetkic^r unto account the gropes an tOeie Шeminaiian F and temparanroa t , a^e ):al-cu)atcd on the sorimohcntal solar osHs I-C) charahfaristics of auc rasa providru Vg then- rfalaofactgneв. The SB mofgrmofical molOsf nfst uny rOosr iloinh> Vo the beos tgr the drcrloprd mVitlerraticm mndet: af an opsii circuit (ОС) colfoor U _o c, sforf i:icauh SCSC) current I _S hc , Pfatiumn colurs of SB сштепt I_MPP and r'olOige U_MPP [81]. The SB mofermofiool modal OsoEcdenh an tmngieralpo'e t and tl-lumihofioh F is descaibedss

I SB ^U SB» )’ I) = ( Sh e (GF) ^x

UqC ( U^F )^- SB SB

1 Ji - I MF (^) ) ^{Uoc (} *' ^F) - ^lJM e^p№ I    ^I ShC ⁽^) J

w)irtc U _SB - сиисп) velue (gf Si) voltage; I _ShC ( t , F ) - SB sdlgg•t cireuii cunent; I_MPPtt , F) - pptenmn vnOet tgf SB cmnenf on LV charof^erSriк:c oi SB MdPT mode in PSS; U_MPPtt , F) - pfgmwms vu^ue tgf SSSI voltogs io I-SS charac-frrisfirc ot SEt SIPIV' mode in PSS; U o _c( t , F ) - fB open sircmt voltage.

The SP) opss siss'uO врОпщс ctcpcnding on t pcS F iscalculatedUnthePermula

U _Oc (, F) = k _Un ■ U_oc (ti, F_v ) ■ 11 + 0,01 ■ p)^{( t} - t ¹ ’,      С?)

wOsrtc k_Un - tOa cotfestion cosOhicreni of voglPlpi: deter-mihrdby SB I-Vchag'ahferisticsaOccista axid, clgnstdering ifs illumination influence; F ₀ - ilУ eominaS itlhmiyation colur; Uo c( 1 ₀, F ₀) - SP р-сс cfscufl ’vcltas;e at nominal colurs 1 ₀ and F ₀; в - tmnppraSsre rrteiSicifni oS SB open sircmt voltage.

TOo ^tht shari cia^uit ereosoi depending on t and F is drfrrminrd 1эу eceComula

I shc (, F) = I_h ■ Z_ac 0t 1, F_x ) ■ 11 + 0,01 ■ a)^{( t} - ^{t 0}’,     (3)

v^ticre kln n O— cnfreieiasn agoeffis^ent -gig nssrrent doter-minrdby SB I-Vchac'ahferisticsocCinateogil, considering its lituminaeson inUuecce; IShC(t1,F1) - ST rhort circuit current at nmelinal valurs t1 and F1; a - Ujmprratucc cocl-ftcicnto-SB shortcircuitauroent.

The O|tdntum value -S Str ceirent it cvicdlared taking into account t and F asfoltows

k _ ^U OCn + 1 ⁽ t 1 , ^F n + 1) , Un

^U OC 1 ⁽ t 1 , F 1 )

IMPpt,. t>^F ) =

k n ■ Impp ( t i , F ) ■ (1 + 0,01 -X )⁽ t ^- t ¹ )

^U OCn ⁽ t 1 , ^F n ) ^U OCn + 1 ⁽ t 1 , ^F n + 1 ) ________________________________________________________________ ^^^^^^»  ________________________________________________________________________________ ^U OC 1 ⁽ t 1 , F 1 ) ^U OC 1 ⁽ t 1 , F 1 )

■ ( F - F n + 1 )

(1 + 0,0b v )⁽ ‘ ^- t ¹ )

where I_MFF(t _1s F ₁) - optimum value of S>It isoireat a1 t ₁ and F ₁; к - lcmpcratuic cocfCcient of SB ntmimum geneurted power, i. e. wowre iin on nutiпlnm point ПМРРТ mode); v - temperatllre soefCclent of the optimumi value -S SB voltnge.

Tee optimum vuIuo sf oB voltvge tt and F iscatcuraledccsgudinbtotUyfoпuula

U_MPP ( t , F ) L ■ U_MPP ( t 1 , F ) ■ (1 + 0,0F v )⁽ t ^- t ¹ ) ,     (5)

where U_MFpt1 ₁, F ₁) - value of SB emtmum ng^teee on I-V chvrvcteristicsat 1 ₁ and F ₁.

Correctioe cooOficlent of vvhege k_Un is Ualrпniuud as follows:

• 1.    Oe the nouerimenral solvr celte I-V chcrorierictics oO any smgle oreo gfig. io, obielueO at difCearnt Шennina-tioe levels F ₁^ F _n oB vvSsc ееШи and nt tome nominal temoerrture 1 ₁, vvIucs of sorai elite open cucuo votldges U OC ₁( 1 ₁, F ₁) ... U _OCn ( 1 ₁, F _n ) ace detememud bh iee cbscissa vnis.

• 2.    TUs crcrection ooeffietdnts k U ₁... k _Un , reflecting tUr relvtive change oB ooliS veils opse cU-cuo t/otlage witrh is ie hie rance UaOueen U OCn ( 1 1 , F „ ) and U OCn ₊i ( 1 1 , F n +0 Ue-OcnUing oe levels ob ther illummation are icateu^atec ae-corUing to lhcl^nmlula:

Corrcction cooOflclent st euerent k _In is detemuiiur m the same wad^ ee an ledsv^sna texit oC nOc impertinenta! solvr cilte 0-ch sncraeteristire and eakieg ecto ae^ount the tsc oO solvr cvПstnort scrcuitcsrcrent naluei:

k _ I ShCn + 1 ⁽ t 1 , ^F n + 1 ) + ^In"   I shC 1 ( t 1 , F 1 )

¹ ShCn ⁽ t 1 , ^F n ) ¹ ShCn + 1 ⁽ t 1 , ^F n + 1 ) _______________________________________________________________ ^^^^^^»  _______________________________________________________________________________ I ShC 1 ⁽ t 1 , F 1 )       I ShC 1 ⁽ t 1 , F 1 )

■ ( F - F n + 1 )

Calculation method of spacecrafts high-voltage povrer tujcphr systems, Cvlculvtion oO SB pnromrtrrs bogies whb TUs chclco of S(f BSU atrurrure anm formation oO ttic mTlhematical deeoriotioe of PSOl operetiou modes tvgieg into ccsannt tine ESo cocOficicets of circyiy tiffl-cicecy (CE) by researched TUr ргосист of energy flows ie Pf a dredtbottou Oenueldiun vn a oe^io oe gmeratrd by eeergy sources eud nows?s nsumm]D(eэn toad [1—. io For envmole, for ovrvlleleserivl (P)>) (*ЬТ1 Stir current ualues of fS power ( P _SB ), AS chgcge perver ( P ^s c), AB dicтnrr■ue oower ( Рлв_ d c) aiud toud owo^er ( P^_R) rer va^tuuraiue ac-cordieg to tve. 1.

Рс., E 0-VchcrosieristtolтCsnvsotllrcell

Рис.1. Вольт-амперные характеристики ФЭ

Table^

Currenlvalues of SB, ABand Ooad power in PSS

LovdfKwerssoovgvnloУsm-s SB (VR)	PLOAD _ PSB ' Лиг
LovdfKwerssoovgvnloУslп-s e>BaшSTr:B eSargf(VR + C)	P^AD   P^_C P SS        + Ли? Tl c
LovdfKwerssoovgvnloУsm-s e>BaшaJd.ttrSlireSangeC(R + DC)	PLOAD _ PSB ■ Лиг + PAB DC ’ Л DC ’ Л.-|8
LonUf)Oo/irsuo;ppgysdoУs:fromSS]BC)C)	PLOAD = P,4B_DC ’ Л£> С ’ Л/|8

The following dailgiualose are introduced hi tab. 1: П VR - voltage regulator CE, n C - chrngar CE, n DC -a dis-oharghr CE, n AB - S^B ofdiriyacy. Thn loed cuooc of SC fat same giorn photof of time оf T aolnhlh ts o hula, has a oyolfo hUtuoctea is formed. Caloolalfan od total energy W LOAD sum conoumnd by InrO hunag T is aarknd cuO ac-oarnfng to thafotAlula:

^ LOADsum = Z^V P l_Oad ( T )| (8) i = 1

where n - hi a ппшЬет oh areas оn Т । Ourlno whihS the ooethnl ucOmd of fond wower P LOAD (t i ) is IduaribOte; i - ardtnal vahte of T n -area; d t i - as а Imae [11гП:гО on T dip-fnawhihh P LOAD (t i )rhmafni Invariable.

Load curves оV SB iOAarination F (t j ) and temperaOere t (t j ) arc fomiedi Initial vodndf of solar celts noramdiors of any snigte eosh at nominal pmhmctdis of temooratnre and fllomfnalfan are intioduand: I _MPP ( t (т 1 ), F (t i )), U _mpp ( t (т 1 ), F (t i ))i U oc ( t (t i )i F (t i )) and I shC ( t (t i ), F (t i )), a, v, X и в.

Further call;utotldd of solas cells porameten current daloas t.a.k f ng, ПсОг onnsCdesatюn SOB F (t j ) and t (t j ) cotn'er aooarnfng to Oonoulas (2)—(7) fs cititlcd out nrU oolaula-Ifon od latnl ooIos of the ioLm' railc nrnargted energy W' solar ee__ sum Ourlag T is similar to W loadsuu onmouls-Ifonal mehOnd.

Tdr ceoacni valuio of ths gB delineated power ons connflfan oa eouality st the roonumeO loan and tls: OB generated power cooondias its the farmola (9) by dctemnuattoo af oorrccOnr aohOflclent k _w as dis oalio оf W _LOAD_sum la W _solar cei___sum are aaioulatn1r. The k -areas on the T pefOntO oatraspannfng to hdetc divariabla ouaernt valuah are defined

P_S B ( t ( t k ), F ( t k )) = Р„ ( t ( t _fc ), F ( t k )) ■ k w . (9)

Caloolalfan af an energy Ualnnac in CC PBO is earned aol by calculation of the ourrentand tolalsoilacf nhaneegy and diohSegga Q AB _ DC _ sum and tStarge Q AB _ C _ sum powei of AS can:uac^ed Skfni{c nciOa ai;t;r)rcct PSC E(3IEi BIv, and de-larmfnalfan fl errraolfan odfffictrnt k _AB rodf'cding рто-parlfanal :incraas;a ns hdr ceaneni oahrod pS ПВ powor for aaoh k -гаа on T । an whfoh tha r^ueaenl Vtatlad oS SB geoer-alaH |owatt aae moas hUnn z^rc. kdo iolal vaduo sf SB gen-агаСаПепегц ( W _SB__sum )ascak:uai^ecfh^nntlrrestnt:mplouta-Ifanal mtshOnd Wload_ sum ¹

For cxfptale, tcp P*SS> eS eoneOon hog energy aaalance oaloolalfan aaa:sattaэwr

S AB_DC_sum = S AB_C_sum =

^- P SB ⁽ t ^{( t} b X ^{F ( t} b )) ^x

r =∑ b=1

s =∑ с=1

n vR ^{( t} b ) ■ ^k AB ^{( t} b ) П DC ^{( t} ь ) ■П AB ^{( t} b )

^U AB _ DC ^{( t} b )

^P SB ⁽ t ^{( t} c X ^{F ( t} c )) ■ ^k AB ^{( t} c ) ■n C ^{( t} c ) ^-

P LOAD ^{( t} c ) ■П C ^{( t} c ) n vR ^{( t} c )

^U AB _ C ^{( t} c )

⋅ d τ _b

⋅ d τ _с

whara r - УПг: onmder fh areas on Т । Bn y^nУ:C PStt mtser-alas Bn madas VR. c DC oa DC; b = E. . r -a r -araa oкfasar nombaron Т ; U AB _ DC (t _b )- АВ lCУsilEmri<з vahdвr iomodes VIC r- DC rr DC; s - hda numbed hi ia'Cto-> on Т । Bn whfoh PPd dr>i:l:aiea in VR + Can VR mo des; c = 1..г s -a s -araa arHfnal aiumtternn Т ; U AB _ C (t _c )-Аriv'candac hi duhsiiaage mada.

AS power hUasccterisiios, hlolnПfna sha сиаапП s'aoues af AS hUolda and ililc^igana cштеhln asa AB nominal pawar, Bonnins kaBalg onto cnaildcration iila accepted maxfmnm /SBcSig’tinatchta, ars calculated [E 4; П].

If d:is;cllioae/cllaraa oerrentd oS AB da mot meat the laohnfoal requiremenis to AIC EitnE pnd n^>f>S its j^eneral, Chan tCali correction ic Smptemrnteh sh tin dtnea iavbl Оу oaloolalfan fl crarectnin cocfdriant k Wi y liy:h jirovides praparlfanal chstuij’e of P SB ( t (t _k ), F (t _k )) on T ttrea:s fc^htis OB maxfmnm aanarateE powee for hde ripoomso nf dfE¹*'larna РРП enaeabbalan1e.

In hliir casr, caocufotinn odludv si SB ncnoent power is oartfaE anlonoaEditюn:

pf

E ^{d t} k ■ ^P SB ⁽ t ^{( t} k X ^{F ( t} k )) = E ^{d t} e ■ ^P SB ⁽ t ^{( t} e X ^{F ( t} e )) ⁺ k = 1 e = 1

q

+ E d t _h ■ P mpp ( t ( t _h ), F ( t _h )) ■ k w ₂ i (11) h = 1

whara p - told ппь11з^о of k -raas on Т;f - hda nfbdзdi of areas on Т wihOout SB MPPT realiaation in PSS; e = E. f-f ■srcsoElrudaAbael on Т;d t _e - time period nn Т । durina whfoh ttie curreno v-oSif oi SB owiarated power P SB ( t (t _e ), F (t _e )) rename rsvai■htdae pi PSS wiSrout SB MPPT realization; q - hho number ft asaaf with SB MPPT realfoatinc ip OnS о n Т ; h = E. . q -o q -area OEfnsar nombar on Т ; d t _h - time peourO on Т । Eoefna whihn еш-renl ontiAnm foSif aS ПВ a^enerated power P _mpp ( t (t _h ), F (t _h )) remarns lduaiibbte 1c i’afS with SB MPPT.

Tdo SB uAdmeterc in PSl are sc.t^ulatail. ООп coefti-ofenl ff poopocftonaB mcesaac ls tlif соПр ce:aal futtial pa-raAatersascak:uUt^ed [11]

^kIU = V ^k w ■ ^kAB ■ ^kw 2 ¹

For rerlricBad oS SB osOral ldlOur of caar^nr or vgdaae ladhl on T thia scotd sh tiie reileEead leodt of tico actual parameter vcdac if ceti ntd аУо edr Idfcl oA fBumination and tamt)arlltlpc aa wtilishl ieitr tav'ei of ^estrlfУan ndould nal ba bookmen ans tier correction coddfic^enl oi reefriction k _lim Bscadiukt^edi

For exnpcdlc, uc hiljrll-tcaltaaa PC IPPS as Ilia ^ondh^on of shia m

Uoc (t (tk ), F (tk )) ■ k,u ^UOC _max

where UOC(t(t_k), F(t_k)) - cueaenl volue olf solre cells OC dallaaa at miAmnmvahldd oft and F.

Polar cells haltial |iSAalatehi are con-anted tag;Caa into aooaonl kIU and klim, whal atOiwi; Or saiaulatv Sp parameters ans then S-id -nd V-VO sharacteriitiai oorountina F(tj) and t(tj) cotdaes l>;y appheattan oC ttir dav(5tonvS SB Aalhamalfoal model. Al ths asms Baae soOor cells non-restricted parameters^re^ultiplied^y    kIU^nd klim.

^e klim placement^n^he denominator^eans^he^B pa-rameter^estriction. ^^s^lso necessary^o^onsider^oher-ence of^olar cells^arameters^hange.^or^xample,^t restriction of^he^llowed^aximum^evel^f^B^C^olt-age^eached^t^^inimum^emperature^f its^anels^he level^f^B optimum^oltage^s^lso^orrected.

Results of mathematical modeling of the spacecraft high-vohafe power supply system. Calculation f^' SB power^haracteristics^nd parameters^as^xecuted^or high-voltage parallel-serial^C^SS^100 ^^ith^B M^^[10]^perating^ither^n^he^ode^f a^imultaneous power^upply^oad^rom^he^B and^he^B^harge,^r^n the^ode^f^^imultaneous power^upply load from^B and the^B^ischarge.

Arbitrarily^omposed^C^oad^urve   PLOAD(τ)^nd^he solar^ells^enerated power curve obtained^y^sing^he developed^athematical model^f^B^aking^nto^ccount solar^ells^nitial^arameters^t    t1^ 25 0С: IShC(t1,F1)^

^5.83 А, UOC(t1,F1) ^46.2^,    IMPP(t1,F1)^ 5.43 А,

UMPP(t1,F1)^ 37.7^,    β^ ‒0.3, λ^ ‒0.39, α^^.04,

ν^ ‒0.4^nd SB^emperature ^ (τ)^nd^llumination F(τ) curves^re^hown^n fig. 2.^

During^he^alculation^t^as obtained^hat Wsolar^ell_sum ^ 314.33 ^h.^or providing^n^nergy^al-ance^n ^S^t   WLOAD_sum^^883.33 ^h^nd^aking^nto account^he^estriction^f^ llowed^aximum^evel^f^B OC^oltage^eached^t^^C exit^rom^he Earth^^hadow is^80^,^he^orrection^oefficient    kW^^1.443,^he^or- rection^oefficient kAB^^.158,^he^oefficient^f propor-tional^ncrease in^olar^ell^nitial^arameters kIU^^6.403 and^he^orrection^oefficient   klim^^.097.^he^urrent values of^he^B^enerated^apacities^ BS_cur are^hown^n tab.2.

Fig.^.^he load curve PLOAD(τ)^nd^he^olar^ell generated^ower^ curve Psolar^ell (τ)^n the^C^SS^ith^he^^Т

Рис.^. Графики нагрузки P_Н(τ) и генерируемой ФЭ мощности P_ФЭ(τ) в СЭП КА с ЭРМ БС

Table^

Parametersof Ohe Miao batfofyof the spatetraftaighivoltf-p pooefrsopply eastern

τk,^inute	PLOAD_cur,^	W solar^ell_cur,	PBS_cur,^	UOC(t,F),^	IMPP(t,F), А	UMPP(t,F),^
0^000	247.37	9005.03	121.90	93.76	96.04	96.04
19^0000	247.3	7           9005.03	121.9	0            93.76	96.04	96.04
26^000	247.3	7            9005.03	121.90	93.76	96.04	96.04
35^500	247.3	7            9005.03	121.90	93.76	96.04	96.04
38^500	0.00	0.00	0.00	—	—	—
43^500	0.00	0.00	0.00	—	—	—
62^500	254.7	9           14944.29	14944.29	92.55	161.47	161.47
63.5^500	256.3	2           14096.7	2           172.0	9            92.69	152.08	152.08
64^500	257.8	5           13297.24	164.53	92.83	143.24	143.24
65^500	259.3	3           12543.09	157.30	92.97	134.92	134.92
66.5^500	260.9	8           11603.6	8            148.1	5            93.15	124.57	124.57
68^500	261.5	4           10945.59	141.64	93.29	117.33	117.33
69.5^500	260.8	3           10324.8	1            135.4	2            93.43	110.51	110.51
71^500	257.7	8            9737.02	129.45	93.57	104.06	104.06
74^500	247.3	7            9005.03	121.90	93.76	96.04	96.04
76^6500	247.3	7           9005.03	121.9	0            93.76	96.04	96.04
81^500	247.3	7            9005.03	121.90	93.76	96.04	96.04
85^000	247.3	7            9005.03	121.90	93.76	96.04	96.04

The maximum rated power of a voItagu regutator in the channel hn the SB mxximum fenerated power vaUne on T and are equal to 14.94 kW. Tire maximum rated awwer ah this ditegoruer rr definga by the SC maximum power of toed, dsfeeds aa Ore discharger CE and ie ecqrtat or 17617 kW.

PSS mroc dtnoease tc soeenga 0г tire dcxelormcnt of new circutt eooiZzation of SC PSS liCa with ido increased values of СЕ [1---15t епП th the noocerclt og wofs of energy flown rational distribution in PSS. For ompeifihi, the change of SB MPPS mode ugo alom'ttam of tire SC exit from shadow areas on 10s orbtt, px ill aHpw to eedoae the SSS maximum rated owner, atiB, as n result, ttie mass of PSU infeneral.

Conclusion. The devetoped sols' bottes- tomOemati-cal model ie bated on ttie eufirr of initial txp exxerimen-tal oatxmeterr of photoelcctoec cello use end provides calculation of hB I-ne and V-W chsnntesisrics taking into cccunnt arbit-agy а^огиО nehaes of illnmlnation one temperature oeooedtnns oU tdeir mam-factum technology.

The offroed meldoO of ualculation oO he? wowm ohar-acterinticn and parameters ns PSS baesd an the uso cP correction coefflctenle provides caluulafion end the nГоп and PSS energy-converrнle aqxit)menl designtns can be formulatodandimposed.

Acknowlddmeenents. The гопооосО woe made ix -m-plement den nee of thio Goxemmsnt oU Ute Russian Federation of 9 April, 2010 No. 218 anti t:ostnapt deiween ISS JSC eah tire Minfkteu oi Educaticn cod Science of ittio R-usoB Federation of 01 Dec-mber 2015 No.02X125.31.0182.

Re^rences

• 1.    Sountin IB. Pg tccmuO-ira B, Ie Chrmniheз A. L, Is-lgaev toh. N. Sisiemy elkktropitemya OyrmCheyknthh ap-a-raioo [lPnvcl sscplx пох1пш8 of spent orafts]. idn’eosi-nirnk,NeuTa Unb1ol994, 018 p.

• 2.    ElekO^onnGe i kidememeahahleiteekiy emtemy i us-iroisioa [Г1псП:1"оп1с uef eleolrxmeehanical eyotrms end devicee]. dxmsk, Potytoahnia Unrvrrsrty Pub6, 2016, 512 p.

• S. Donteov O. Ag tccmuO-saV. Igearorno0aevYu. V., Post S. SU. IhrutonomodS chscner upwrr sufxly system

  with exioeme nenu-atlon owois- tracker of printarx eBulletin of he Tsmok ieol}>tnchniv SJtti-versity. Goo Assetg Ekergugeerin.- 2016, Vol. Ulf No. 12, Ps 35-44 IInRnss.).

• 4.    Cnrdotfes P, Ее Ohsscnkci V. E. Oseovy proekirro-vaniya^osmicheskikh apparatov^nformatsionnogo obespecheeiya [ВпгСп. fh dlrsiun e>f informat8on space vehiclen]. Krasdrneesk,giPSAUnnbL,C011, 5SS> p.

• 5.    Sheruaga Tvf. ^lfp Shinyakov A. 71i, Osipov A. V. [Spacecraft powerr гппЩш.. 17 MdzJtdunageodnaoa forrtfer-encija^olodyh specialistov^o mikro/nanotehnologijam i jeiekiroeeym piboramn [17th Intruoailonat ssonferetnee: of goung spxsciidists os me:nnhla'тоtoheldg(onlrs and пГсоХоп devicee. Pace, ah tti7 t7th InO;rdhttonai nonfcoe.kce]. Er-lagol,:’016,1³. 589-593.

• 6.    nntgkmh ..г. Ng 0foyзhev hfi оП< -Ths research of high-voltage powrr U8i8>plr^r syntemn for р-епп Ofafts with ПоопП covnerteri. Vesieik SibUAU. 1166, No. 6 (13), P. 63-66I^n Ress;;).

• 7.    Akiohin A. F [Omuact cf etnchricol rlincUhdses on solar oanels] Naucheo- isked 2008, Ns. 4, P. 68-'-lIhoRns^5.).

• 0. Pri-atos V. Dg N:idih)пзv V. E. Oiseeka offkktiv-eosii primeneniya yJp;lmima/’eogo regubaotara a av-ioeomeykh EEP Sisrimateoir ah off efgefUnnnrrs of the application oS hoe exd'mns rer^ulotor tn auiom)mnu^5 PSS]. Knibyshev, KPUPubL, 1S1.11, 16 p.

• 9. Onipov X. ..SS 0hignsdoa Yu. hs., e>hkgl’8;yi V. N., Sunteov S. I3i Crnetnatiin M. SS. [SUrnchdrn foe crзtsetruct-ing high-voltage owner supgty snleme fot npany crafts ПопоП on ienrnntl-niU'anslimflct e■oevcrtcзs]. Eieciricai e---gieeerieg.2016,No. 12,6.26-058; (in Russ.).

• 11.    тЫпокгоа Yu. -U,., Gnirtov Pe< dg Gordeev K. G., Ivkov S. [t. 1ССо;су of Йп6 ^tnicfure ow ptw^eo xiУems for low Ooirih огГпГ spacenraft]. Buiieiie o>f he mlldara. Siete Aerospace Uoedynittth. acem?mictаS, S. o. Keoaleл^а. 2010, No. 1(21), P.163-163 hnRusi,.).

11 .Certtro^M3. M. Issiedooaeie i rzdrаOаtkл ^erroo-preobrazuyushchei^pparatury^ysokovol^nykh^istem eiekiropiiaeiya OymnCheykkkdl appraatv.?. Dia. ednd. eauk [Renearch teid ttcifrfp)mcnt edl:egn coilnlnreiotl er[ui>tuent high-voltage power usjppbr ssyomers sdacecsaftl. Tsmsk, TUSUR, 2C17,:lo12зi.

• 12.    Sheruaga MM.!., StlinkoOau Yu. (f. tRcsenrch and development of energy-hodvgrtme i:pwin>tne:nr Огг high-voltage power n8]8pУt rnldtmns iff low-EortP оГэВ o;ace remote s(msine; dercfn^>]. Sboreik metnaiolov V7A hdezhdu-narodnoi nauchnotekhnicheskoi^onferentsii^.^.^siolk-ovskii^ 160^et^o dnya^ozhdeniya.^osmonavtika.^a-dioeiekiroeika. Geeiofmaiatha [K. F 'eeюlkosyky .-160 geare from hfs Ptsthdan. cmmonanticn. radio cfcctroidcs. GeofnformaticSi Prsc. arf the Vfi Olretnatioeh' Scientific and Teehntcil ПопОсопог namek Ki E. Tgiolkovsky], Rgazui3C01i?,P. 134-166 (^n Rui.s.).

• 16.    Shen kVg Rons. fu., Lu h. Y. Smibberlecs bidirectional DC-DC aon¹ser^es nofo lls CLLC tcaoeanl tank featuoing minimerep cwitefdlg loss. IEEE Р.оп^ dud. Eieciroe.2010,aoi.77, !No.9,P. 3075-05086.

• 14.    V.!!, Ja Li as., Sius 0Y0., Liu O. ri, еют; dual-bridge погГоп гсапит! DC-DC eonvertes wUOi duak tank. IEEE

  Transactions on^ower^lectronicstics. 2017,^ol.^3(5), >), P.^884‒3897.

• 15. ^guyen^.^., Nguyen^. Т.,^u^ta G.^ual- G. Dualactive-bridge series^esonant^onverter: rA^ew^ontrol itrol strategy^sing phase-shifting combined^requency^odu-du-lation. IEEE^onference XPublicationsns.^015, N о. 00, P.^215‒1222.