CC BY
144
UDC 620.92
Doi: 10.31772/2587-6066-2018-19-4-651-657
For citation: Chernaya M. M. [Method for calculating the energy characteristics and solar battery parameters of high-voltage power supply systems]. Siberian Journal of Science and Technology. 2018, Vol. 19, No. 4, P. 651-657. Doi: 10.31772/2587-6066-2018-19-4-651-657
Для цитирования: Черная М. М. Методика расчета энергетических характеристик и параметров солнечных батарей высоковольтных систем электропитания космических аппаратов // Сибирский журнал науки и технологий. 2018. Т. 19, № 4. С. 651-657. Doi: 10.31772/2587-6066-2018-19-4-651-657
METHOD FOR CALCULATING THE ENERGY CHARACTERISTICS AND SOLAR BATTERY PARAMETERS OF HIGH-VOLTAGE POWER SUPPLY SYSTEMS
M. M. Chernaya
Tomsk State University of Control System and Radio Electronics 40, Lenina Av., Tomsk, 634050, Russian Federation E-mail: cmm91@inbox.ru
One of the main tasks arising in power supply systems (PSS) of spacecraft (SC) design is the determination of rational structure in terms ofproviding consumers with electricity of the required quality. At the same time, a reasonable consumption of power generated by solar batteries (SB) and accumulator batteries (AB) should be realized in PSS. The choice of the PSS structure is based on the calculation and comparative analysis of PSS options, taking into account the adopted system performance criteria, the main ones being the energy and weight-dimension characteristics. For this purpose, the process of energy flows distribution in the PSS by forming a mathematical description of the PSS operating modes is carried out. In order to obtain the graphs of the SB generated power and to calculate SB parameters during the service life, a mathematical model of the SB based on the use of initial and experimental parameters of its photovoltaic elements of any area was developed. The SB model provides the required accuracy of I-V and V-W characteristics calculation for any given values of illumination and temperature.
In the article the method for calculating the energy characteristics of PSS and SB parameters taking into account the possibility of its limitation at the maximum or minimum level was described. It is shown that the method allows to determine the ways of rational redistribution of energy flows in the systems being designed to improve its weight-dimension characteristics by reducing the maximum design power of energy-converting equipment (ECE), which is achieved by forming a rational logic for applying the SB maximum power point tracking mode, in particular, when the spacecraft leaves the Earth's shadow. Energy balance in PSS is provided by applying correction coefficients. The calculation results obtained by the method are the basis for requirements for ECE and SB design in PSS and can be used by developers and manufacturers of onboard and ground PSS.
Keywords: spacecraft, power supply system, mathematical model of the solar battery, energy characteristics, maximum power point tracking mode.
МЕТОДИКА РАСЧЕТА ЭНЕРГЕТИЧЕСКИХ ХАРАКТЕРИСТИК И ПАРАМЕТРОВ СОЛНЕЧНЫХ БАТАРЕЙ ВЫСОКОВОЛЬТНЫХ СИСТЕМ ЭЛЕКТРОПИТАНИЯ
КОСМИЧЕСКИХ АППАРАТОВ
М. М. Черная
Томский государственный университет систем управления и радиоэлектроники Российская Федерация, 634050, г. Томск, просп. Ленина, 40 Е-mail: cmm91@inbox.ru
Одной из основных задач проектирования систем электропитания (СЭП) космических аппаратов (КА) является определение их рациональной с точки зрения обеспечения потребителей электроэнергией заданного качества структуры. При этом в системе должно быть реализовано обоснованное потребление генерируемых солнечными (БС) и аккумуляторными батареями мощностей. Выбор структуры СЭП основывается на проведении расчета и сопоставительного анализа их альтернативных вариантов с учетом принятых критериев эффективности системы, основными из которых являются энергетические и габаритно-массовые характеристики СЭП. Для этого проводится исследование процессов распределения потоков энергии в системе путем формирования математического описания режимов работы СЭП. С целью получения графиков ге-
нерируемой БС мощности и для расчета ее параметров в течение срока эксплуатации разработана математическая модель БС, которая основана на использовании основных и экспериментальных параметров их фотоэлектрических элементов любой площади. Модель БС обеспечивает требуемую точность расчета вольт-амперных и вольт-ваттных характеристик для любых заданных значений температуры и освещенности. Описана методика расчета энергетических характеристик СЭП и параметров БС с учетом возможности их ограничения по максимальному либо минимальному уровню. Показано, что методика позволяет определять пути рационального перераспределения потоков энергии в системах с целью улучшения их габаритно-массовых характеристик за счет уменьшения максимальной расчётной мощности их энергопреобразующей аппаратуры (ЭПА), что достигается путем формирования рационального алгоритма применения режима экстремального регулирования мощности БС, в частности, при выходе КА из тени Земли. Энергобаланс в СЭП при этом обеспечивается за счет применения поправочных коэффициентов. Полученные по методике результаты являются основой ряда требований по проектированию ЭПА и БС в СЭП и могут быть использованы разработчиками и производителями бортовых и наземных СЭП.
Ключевые слова: космический аппарат, система электропитания, математическая модель солнечной батареи, энергетические характеристики, экстремальное регулирование мощности.
Introduction. Ensuring the long term of the spacecraft (SC) active lifetime (TAL) is one of priority scientific, technical and economic tasks which solution demands a comprehensive fundamental approach during the development and creation of SC power supply systems (PSS).
The main primary energy source in SC PSS are solar batteries (SB) designed on the basis of Si or GaAs solar cells having non-linear I-V and V-W characteristics with a pronounced maximum of the generated power, determined by an operating voltage level that proves the expediency of maximum power point tracking (MPPT) mode of SB in PSS application [1—4]. Due to the increase of output voltage of the SC load power bus up to 100 V, new technical requirements to the ways of coordination and service conditions of energy sources in PSS have been created. This is due to the possibility of electrostatic discharges between photodiodes chains and current collection elements of the SB and, as a result, to the need for the maximum level of SB open circuit (OC) voltage operation limitation reached when the SC leaves the orbit shadow areas [5-7]. Application of other solar cells types in PSS is possible in case of feasibility of their use realized by means of calculation of the generated by SB capacities during TAL providing an energy balance in PSS, rational distribution of energy flows and prevention of PSS work emergency operation.
The developed technique provides the reduction in calculation time of power characteristics and the SB parameters of high-voltage SC PSS which is obtained by the decrease in the number of iterations directly proportional to the quantity of correction factors to be calculated. The technique can be applied when calculating options of ground and onboard PSS with various load curves and service conditions for the purpose of realization of energy flows in PSS rational redistribution and to impose its ECE and SB design requirements.
Mathematical model of solar battery. The SB electric parameters during SC service change significantly. The considerable influence on SB I-V and V-W characteristics is rendered by temperature and illumination. So, in low-orbit SC the SB panels temperature changes in the range from -90 to +80 0C, herewith the SC can have the
sharp-variable load curve and the significant number of shadow areas on the orbit. Therefore for the correct planning of PSS target equipment operation it is expedient to carry out the calculation of SB generated power in all operating modes of SC PSS during TAL.
The SB current parameters, taking into account the graphs of their illumination F and temperature t, are calculated on the experimental solar cells I-V characteristics of any area provided by their manufacturers. The SB mathematical model set by three points is the basis for the developed mathematical model: of an open circuit (OC) voltage UOc, short circuit (ShC) current Ishc, optimum values of SB current Impp and voltage UMPP [8]. The SB mathematical model depending on temperature t and illumination F is described as
Isb (Usb , t, F ) = IShc (t, F ) x
1 -
1 -
Impp (t, F ) Л Ishc (t, F )
Uoc (t,fyunb Uoc (t,f)-Umpp (t,f)
(1)
where USB - current value of SB voltage; IShC(t,F) -SB short circuit current; IMPP(t,F) - optimum value of SB current on I-V characteristics at SB MPPT mode in PSS; UMPP(t,F) - optimum value of SB voltage on I-V characteristics at SB MPPT mode in PSS; UOc(t,F) - SB open circuit voltage.
The SB open circuit voltage depending on t and F is calculated by the formula
Uoc (t, F) = kun • Uoc (A, F ) • (1 + 0,01- P)
(t-t1)
(2)
where kUn - the correction coefficient of voltage determined by SB I-V characteristics abscissa axis, considering its illumination influence; Fi - SB nominal illumination value; UOC(ti,Fi) - SB open circuit voltage at nominal values ti and Fi; p - temperature coefficient of SB open circuit voltage.
The SB short circuit current depending on t and F is determined by the formula
Ishc (t, F ) = kM • Iskc (t1, F1) • (1 + 0,01-a)'
(t-<1)
(3)
where kIn - the correction coefficient on current determined by SB I-V characteristics ordinate axis, considering
its illumination influence; IShC(ti,Fi) - SB short circuit current at nominal values ti and a - temperature coefficient of SB short circuit current.
The optimum value of SB current is calculated taking into account t and F as follows
,(f,F ) =
MP ft, F) • (1+0,01-X)
(t -<i)
(1 + 0,01 -v)
(t-ti)
(4)
Umpp (t, F ) = kUn-Umpp (ti, F1) • (1 + 0,01-v)
(t-ti)
(5)
k — UOCn+1 (t1, Fn+1 )
^Un ~ '
Un UOC1(t1, F1)
f Uocn(A,Fn) - UQcn+i(ti,Fn+1) '
Uqc1 (t1, F1) U
QC1 (t1, F) Fn - Fn1
•( F-Fn+1)
(6)
where IMPP(ti,Fi) - optimum value of SB current at ti and Fi; I - temperature coefficient of SB maximum generated power, i. e. power in an optimum point (MPPT mode); v - temperature coefficient of the optimum value of SB voltage.
The optimum value of SB voltage taking into account t and F is calculated according to the formula
where UMPP(ti,Fi) - value of SB optimum voltage on I-V characteristics at ti and Fi.
Correction coefficient of voltage kUn is determined as follows:
1. On the experimental solar cells I-V characteristics of any single area (fig. i), obtained at different illumination levels Fi...Fn of solar cells and at some nominal temperature t1, values of solar cells open circuit voltages UoC1(t1,F1) ... UOcn(t1,Fn) are determined by the abscissa axis.
2. The correction coefficients kU1...kUn, reflecting the relative change of solar cells open circuit voltage which is in the range between Uocn(ti,Fn) and Uocn+i(ti,Fn+i) depending on levels of their illumination are calculated according to the formula:
Correction coefficient of current kIn is determined in the same way by an abscissa axis of the experimental solar cells I-V characteristics and taking into account the use of solar cells short circuit current values:
k _ 1ShCn+1 (t1, Fn+1) +
FhC1 (t1, F1)
1ShCn (t1, Fn ) _ 1 ShCn+1 (t1, Fn+1 ) ^ 1 ShC1 ft, F1) ShC1 ft, F)
Fn _Fn„
( F -Fn+1)
(7)
Calculation method of spacecrafts high-voltage power supply systems. Calculation of SB parameters begins with the choice of SC PSS structure and formation of the mathematical description of PSS operation modes taking into account the ECE coefficients of energy efficiency (CE) by researching the processes of energy flows in PSS distribution depending on a ratio of generated by energy sources and power consumption load [9-ii]. For example, for parallel-serial (PS) PSS the current values of SB power (РSB), AB charge power (РAB_C), AB discharge power ^^d) and load power are calculated according to tab. i.
Voltage of solar cell. V Uoc\ Fig. 1. I-V characteristics of the solar cell Рис. 1. Вольт-амперные характеристики ФЭ
Current values of SB, AB and load power in PSS
Table 1
Load power supply mode from SB (VR) plqad — psb ' лук
Load power supply mode from SB and AB charge (VR + C) d plqad , pab_c rsb ~ 1 лук Лс
Load power supply mode from SB and AB discharge (VR + DC) plqad — psb ' лук + pab_dc ' '4dc ' лав
Load power supply mode from AB (DC) plqad — pab_dc ' лdc ' лм
The following designations are introduced in tab. 1: nvR - voltage regulator CE, nC - charger CE, nDC - discharger CE, nAs - AB efficiency. The load curve of SC for some given period of time of T which, as a rule, has a cyclic character is formed. Calculation of total energy WLOADjsum consumed by load during T is carried out according to the formula:
W
= S dXi ■ PLOAD (Xi ):
(8)
where n - the number of areas on T, during which the current value of load power PLOAD(x) is invariable; i -ordinal value of T n-area; dxt - is a time period on T during which PLOAD(xi) remains invariable.
Load curves of SB illumination F(x,) and temperature t(Tj) are formed. Initial values of solar cells parameters of any single area at nominal parameters of temperature and illumination are introduced: IMpp(t(x1), F(ii)), UMPP (t(ii), F(ii)), Uoc(t(Ti), F(ii)) and Ishc(t(ii), Ffa)), a, v, 1 u p.
Further calculation of solar cells parameters current values taking into consideration SB F(x,) and t(x,) curves according to formulas (2)-(7) is carried out and calculation of total value of the solar cells generated energy Wsoiar ceii sum during T is similar to WLOAD_sum computational method.
The current values of the SB generated power on condition of equality of the consumed load and the SB generated power according to the formula (9) by determination of correction coefficient kW as the ratio of WLOAD_sum to Wsolar c.llsum are calculated. The k-areas on the T period corresponding to their invariable current values are defined
PSB (t (xk ), F (Tt )) = Psolar cell (t (Tt ), F (Tt )) • kw
(9)
=s
Qa
PLOAD (Xb )
= Qa
- PSb (t (x, ), F (x, ))>
4dc (Xb ) -4ab (Xb )
,, 4VR (Xb ) • kAB (Xb )
_4dc (Xb ) -4ab (Tb )
,(4 )
• d x.
=z
Psb (t (Xc ), F (Xc )) • kAB (Xc ) •Лс (Xc ) -
- PLOAD (xc ) •Лс (Xc ) _nvR (Xc )
U a
:(Xc )
-• d x.
(10)
where r - the number of areas on T, in which PSS operates in modes VR + DC or DC; b = 1.. .r - r-area ordinal number on T; UAB DC(xb) - AB discharge voltage in modes VR + DC or DC; s - the number of areas on T, in which PSS operates in VR + C or VR modes; c = 1... s - s-area ordinal number on T; Uab c(tc) - AB voltage in the charge mode.
AB power characteristics, including the current values of AB charge and discharge currents and AB nominal power, counted taking into consideration the accepted maximum AB charge depth, are calculated [1; 4; 11].
If discharge/charge currents of AB do not meet the technical requirements to AB, ECE and PSS in general, then their correction is implemented at the given level by calculation of correction coefficient kW2 which provides proportional change of PSB(t(xk),F(xk)) on T areas with SB maximum generated power for the purpose of providing PSS energy balance.
In this case, calculation values of SB current power is carried out on condition:
X d xk • PSB (t (xk ), F ^ )) = £ dxe • PSb (t (t. ), F (t. )) +
Sd xh
• Pmpp (t (Xh ), F (xh )) • kw
(11)
Calculation of an energy balance in SC PSS is carried out by calculation of the current and total values of energy and discharge QAB_Dc_sum and charge QAB_c_sum power of AB calculated taking into account PSS ECE CE, and determination of correction coefficient kAB providing proportional increase in the current values of SB power for each k-rea on T, on which the current values of SB generated power are more than zero. The total value of SB generated energy (WSB_sum) is calculated similarly to computational method WLOAD_sum.
For example, for PSS PS equation for energy balance calculation is as follows
where p - total number of k-reas on T; f - the number of areas on T without SB MPPT realization in PSS; . = 1.. f -f-area ordinal number on T; dx. - time period on T, during which the current value of SB generated power PSB(t(x.),F(x.)) remains invariable in PSS without SB MPPT realization; q - the number of areas with SB MPPT realization in PSS on T; h = 1.q - q-area ordinal number on T; dxh - time period on T, during which current optimum value of SB generated power PMPP(t(xh),F(xh)) remains invariable in PSS with SB MPPT.
The SB parameters in PSS are calculated. The coefficient of proportional increase in the solar cells initial parameters is calculated [11]
ku \lkw ' kAB ' kw 2 .
(12)
For restriction of SB actual value of current or voltage level on T the value of the restricted level of the actual parameter value is set, and also the level of illumination and temperature at which this level of restriction should not be broken and the correction coefficient of restriction klim is calculated.
For example, in high-voltage SC PSS on the condition of the maximum SB OC voltage level UOC_max restriction the coefficient of restriction kiim is calculated as:
klim ~
Uoc (t (Xk ), F (Xk )) • k„
UOC max
(13)
where UOC(t(xk), F(xk)) - current value of solar cells OC voltage at minimum values of t and F.
Solar cells initial parameters are corrected taking into account kIU and kUm, what allows to calculate SB parameters and their I-V and V-W characteristics accounting F(xj) and t(Xj) curves by application of the developed SB mathematical model. At the same time solar cells
i=1
+
h=1
i=1
с=1
non-restricted parameters are multiplied by kIUr and kUm. The klim placement in the denominator means the SB parameter restriction. It is also necessary to consider coherence of solar cells parameters change. For example, at restriction of the allowed maximum level of SB OC voltage reached at a minimum temperature of its panels the level of SB optimum voltage is also corrected.
Results of mathematical modeling of the spacecraft high-voltage power supply system. Calculation of SB power characteristics and parameters was executed for high-voltage parallel-serial SC PSS (100 V) with SB MPPT [10] operating either in the mode of a simultaneous power supply load from the SB and the AB charge, or in the mode of a simultaneous power supply load from SB and the AB discharge.
Arbitrarily composed SC load curve PLoad(t) and the solar cells generated power curve obtained by using the
developed mathematical model of SB taking into account solar cells initial parameters at t1 = 25 0C: Ishc(ti,Fi) = = 5.83 A, Uoc(ti,Fi) = 46.2 V, Iupp(ti,Fi) = 5.43 A, UMPP(t1,F1) = 37.7 V, P = -0.3, 1 = -0.39, a = 0.04, v = -0.4 and SB temperature t(x) and illumination F(t) curves are shown in fig. 2.
During the calculation it was obtained that Wsoiar ceii sum = 314.33 W-h. For providing an energy balance in PSS at WLOAD_sum = 9883.33 W-h and taking into account the restriction of allowed maximum level of SB OC voltage reached at a SC exit from the Earth's shadow is 180 V, the correction coefficient kW = 31.443, the correction coefficient kAB = 1.158, the coefficient of proportional increase in solar cell initial parameters kIU = 36.403 and the correction coefficient kUm = 2.097. The current values of the SB generated capacities PBS cur are shown in tab. 2.
Fig. 2. The load curve PlOad(t) and the solar cell generated power curve Psoiar cell(T) in the SC PSS with the MPPT
Рис. 2. Графики нагрузки РН(т) и генерируемой ФЭ мощности РФЭ(т) в СЭП КА с ЭРМ БС
Table 2
Parameters of the solar battery of the spacecraft high-voltage power supply system
% minute PbOAD cun W Psolar cell cur, ^^ PESCU^ W Uoc(tF), V W*F), А Umff( F V
0 4000 247.37 9005.03 121.90 93.76 96.04
19 10000 247.37 9005.03 121.90 93.76 96.04
26 4000 247.37 9005.03 121.90 93.76 96.04
35 5500 247.37 9005.03 121.90 93.76 96.04
38 5500 0.00 0.00 - - -
43 6500 0.00 0.00 - - -
62 6500 254.79 14944.29 180 92.55 161.47
63.5 6500 256.32 14096.72 172.09 92.69 152.08
64 6500 257.85 13297.24 164.53 92.83 143.24
65 6500 259.33 12543.09 157.30 92.97 134.92
66.5 6500 260.98 11603.68 148.15 93.15 124.57
68 6500 261.54 10945.59 141.64 93.29 117.33
69.5 6500 260.83 10324.81 135.42 93.43 110.51
71 6500 257.78 9737.02 129.45 93.57 104.06
74 6500 247.37 9005.03 121.90 93.76 96.04
76 16500 247.37 9005.03 121.90 93.76 96.04
81 6500 247.37 9005.03 121.90 93.76 96.04
85 4000 247.37 9005.03 121.90 93.76 96.04
The maximum rated power of a voltage regulator in the channel of energy transformation from the SB and an AB charger are defined by the SB maximum generated power value on T and are equal to 14.94 kW. The maximum rated power of the discharger is defined by the SC maximum power of load, depends on the discharger CE and is equal to 17.37 kW.
PSS mass decrease is reached by the development of new circuit realization of SC PSS ECE with the increased values of CE [12-15] and by the research of ways of energy flows rational distribution in PSS. For example, the change of SB MPPT mode use algorithm at the SC exit from shadow areas on the orbit, will allow to reduce the ECE maximum rated power, and, as a result, the mass of PSS in general.
Conclusion. The developed solar battery mathematical model is based on the values of initial and experimental parameters of photoelectric cells use and provides calculation of SB I-V and V-W characteristics taking into account arbitrary assigned values of illumination and temperature regardless of their manufacture technology.
The offered method of calculation of SB power characteristics and parameters in PSS based on the use of correction coefficients provides calculation and the possibility of energy flows redistribution in the system for the purpose of PSS weight-dimension characteristics decrease, and allows to obtain SB initial parameters, on condition of ensuring an energy balance in PSS, accounting the given service conditions and load curves of the SC. Based on calculation results, carried out according to the developed technique, the requirements for solar batteries and PSS energy-converting equipment designing can be formulated and imposed.
The developed method of SB initial parameters calculation allows defining the requirements to their design in PSS taking into consideration the limitation of the actual values of SB currents and/or voltage maximum or minimum level.
Acknowledgements. The research was made to implement decree of the Government of the Russian Federation of 9 April, 2010 No. 218 and contract between IS S JSC and the Ministry of Education and Science of the Russian Federation of 01 December 2015 No. 02.G25.31.0182.
Благодарности. Работа выполнена в рамках реализации Постановления Правительства РФ № 218 от 09.04.2010 г. и договора между АО «ИСС» и Мин-обрнауки РФ от 01.12.2015 г. № 02.G25.31.0182.
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© Chernaya М. М., 2018
