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Chapter 4 Photovoltaic–Battery System 4.1 Introduction Photovoltaic conversion of the sun’s energy is the most common source of electrical power in space. An array of photovoltaic cells powers the load and charges a battery during sunlight. The battery powers the load during an eclipse. If the solar array, the battery and the load were operated at the same constant voltage, no voltage regulator would be needed. All the equipment could be wired to the same bus. However, the solar array output voltage is higher at the beginning of life, and when the array is cold for several minutes after each eclipse. Also, the battery has a lower voltage during discharge than during charge. Since the system is required to provide power to the load at a voltage regulated within specified limits, a voltage regulator is always needed to match voltages of various power components during the entire orbit period. The photovoltaic power system, therefore, primarily consists of a solar array, a rechargeable battery, and a power regulator which regulates power flow between various components to control the bus voltage. Other components such as various sensors are also required to make the array and the battery work together. The total power system is thus coordinated internally as well as externally through interfaces with other systems of the spacecraft. The top-level performance characteristics of the basic PV–battery system are described in this chapter, leaving the component level details for later chapters. 4.1.1 Solar Array The solar array is made of numerous PV cells stacked in series–parallel connections to obtain the desired voltage and current from the assembly. It converts the incident photon energy into d.c. voltage, which drives current through the external load circuit. The solar array works more like a constant current source over its normal operating range. Its terminal voltage versus current characteristic, referred to as the IV curve, is shown in Figure 4.1. The end of life (EOL) curve must meet the performance requirement. The characteristic curve changes significantly with temperature and the radiation dose of charged particles as shown in the figure. The power, being the product of the voltage and current, varies as in Figure 4.2. The

Spacecraft Power Systems: Chapter 4. Photovoltaic Battery System

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Page 1: Spacecraft Power Systems: Chapter 4. Photovoltaic Battery System

Chapter 4Photovoltaic–Battery System

4.1 Introduction

Photovoltaic conversion of the sun’s energy is the most common source ofelectrical power in space. An array of photovoltaic cells powers the loadand charges a battery during sunlight. The battery powers the load duringan eclipse. If the solar array, the battery and the load were operated at thesame constant voltage, no voltage regulator would be needed. All theequipment could be wired to the same bus. However, the solar array outputvoltage is higher at the beginning of life, and when the array is cold forseveral minutes after each eclipse. Also, the battery has a lower voltageduring discharge than during charge. Since the system is required toprovide power to the load at a voltage regulated within specified limits, avoltage regulator is always needed to match voltages of various powercomponents during the entire orbit period.

The photovoltaic power system, therefore, primarily consists of a solararray, a rechargeable battery, and a power regulator which regulates powerflow between various components to control the bus voltage. Othercomponents such as various sensors are also required to make the arrayand the battery work together. The total power system is thus coordinatedinternally as well as externally through interfaces with other systems of thespacecraft. The top-level performance characteristics of the basic PV–batterysystem are described in this chapter, leaving the component level details forlater chapters.

4.1.1 Solar Array

The solar array is made of numerous PV cells stacked in series–parallelconnections to obtain the desired voltage and current from the assembly. Itconverts the incident photon energy into d.c. voltage, which drives currentthrough the external load circuit. The solar array works more like a constantcurrent source over its normal operating range. Its terminal voltage versuscurrent characteristic, referred to as the I–V curve, is shown in Figure 4.1.The end of life (EOL) curve must meet the performance requirement. Thecharacteristic curve changes significantly with temperature and theradiation dose of charged particles as shown in the figure. The power,being the product of the voltage and current, varies as in Figure 4.2. The

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power output of an array is maximum at the knee-point voltage. The systemproduces less power when operating at any other voltage. Also, the poweroutput gradually degrades with accumulated radiation dose. At the end oflife, the array generates less power than at the beginning of life.

4.1.2 Battery

The battery is made of rechargeable electrochemical cells connected in aseries–parallel combination to obtain the desired voltage and current. Itsterminal voltage depends primarily on the state of charge (SOC), and tosome extent on the operating temperature. The battery charge is measuredin terms of the ampere-hours stored between the positive and negativeplates. The voltage is highest when the battery is fully charged, and thelowest when it is fully discharged. Since the battery works more like aconstant voltage source over the normal operating range, its terminalcharacteristic is generally expressed in terms of the battery voltage versusthe state of charge. Figure 4.3 depicts the voltage of one fully charged cell asit discharges and then gets recharged. The voltage scale in the figure

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FIGURE 4.1 Current versus voltage characteristics of a photovoltaic cell.

FIGURE 4.2 Power versus voltage characteristics of a photovoltaic cell.

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represents both the NiCd and the NiH2 cells. The battery voltage dropssignificantly with increasing discharge, and then rises during charge. Theaverage voltage during charge is higher than that during discharge.

4.1.3 Power Regulation

Power regulation is primarily accomplished by battery charge anddischarge converters, a shunt dissipator, and a mode controller thatresponds to the bus voltage error signal. The shunt dissipator is necessaryto control the bus voltage during sunlight as described hereafter. The solararray (source) and the constant power load have their own I–V character-istics as shown in Figure 4.4. The system can operate at either of the twointersection points A or B. However, point A is inherently unstable becausethe load slope is less than the source slope. Point B, on the other hand, isinherently stable. Without a shunt control, the system would operate atpoint B, producing a lower power. With shunts designed to regulate the

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FIGURE 4.3 Battery cell voltage versus state of charge in one complete cycle.

FIGURE 4.4 Stability of operating point and shunt control during sunlight.

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sunlight voltage at say 35V; the system will pull back from point B to pointC by shunting the excess current to the ground. The shunt current in thisoperating mode would be Ishunt, the difference between the source current atD and the load current at C.

The mode controller sets the system’s operating mode in response to theerror signal, which is the difference between the actual bus voltage and thereference voltage representing the required bus voltage. Depending on theerror signal value and its polarity (positive or negative), the mode controllersends a control signal to either the shunt regulator, or the battery chargeregulator, or to the battery discharge regulator (Figure 4.5). One of thesethree sub-regulators, in turn, maintains the bus voltage within the specifiedlimits. Details of the next level of the mode controller during the batterydischarge regulation are shown in Figure 4.6.

External interfaces of the power system with other systems of thespacecraft are mission specific, and difficult to describe in general.However, Figure 4.7 depicts key external interfaces in a typical commu-nications satellite.

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FIGURE 4.5 Mode controller error signal routing concept.

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4.2 Power System Architectures

The solar array, battery, and the shunt characteristics described above,along with the load voltage requirement, are extremely important inselecting the power system architecture that is most suitable for the mission.The mission-imposed or self-derived requirements on the power systemalso have bearings on the architecture selection. The PV–battery system isconfigured in one of the following architectures that would optimize thesystem performance for a given mission.

4.2.1 Direct Energy Transfer

Direct energy transfer (DET), in which the solar power is transferred to theloads with no series component in between. The necessary exceptions are:(1) the slip rings to provide a rotary joint between the Earth-facing

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FIGURE 4.6 Mode controller error signal to battery discharge regulator.

FIGURE 4.7 External electrical interfaces in a typical power system.

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spacecraft body and the sun-facing solar array, and (2) the powerdistribution unit consisting of load switching relays and fuses to protectthe power system from faults in the load circuits. The DET can be furthersubdivided into two classes: (1) the fully regulated bus, and (2) the sunlightregulated bus. The components and operation of these two busses aresimilar, except that the latter has no battery discharge converter in thepower regulator unit (PRU).

4.2.2 Peak Power Tracker

Peak power tracker (PPT), in which the solar array output voltage is alwaysset at the value which results in the maximum power transfer from thearray to the load. A series power converter between the array and the loadmatches the load voltage requirement and the array output voltage. For thisarchitecture to be cost effective, the power loss in the PPT converter must beless than the gain in operating the system at the peak power point all thetime.

4.3 Fully Regulated Bus

In a fully regulated direct energy transfer bus, commonly known as theregulated bus, the bus voltage is controlled within a few percent during theentire orbit period. The typical bus voltage variation is �2 to 5% of thenominal voltage. The architecture of this bus is shown in Figure 4.8. It hasthe following components.

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FIGURE 4.8 Fully regulated direct energy transfer architecture.

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4.3.1 Solar Array

The solar array (SA) is an array of PV cells that convert sunlight intoelectricity. The large array is generally divided into many parallel circuits(strings), each with isolation diodes so that a failed string would not drawpower from the healthy ones. The ungrounded end of each section andindividual string is isolated from the main bus and battery by diodes. Thesediodes may be located inside the PRU for protection, or on the back of thesolar array exposed to the environment. In one case, the slip rings areinvolved, but not in the other. The electrostatic discharge induced transientvoltage suppressing snubber capacitors may be located inside or outside.The array negative terminal is usually grounded. If the positive weregrounded, the power system would work just as well, except that we mustuse p–n–p semiconductors instead of traditional n–p–n devices in the PRU.The power converter design would change accordingly. One advantage ofthe positive ground is that the structure becomes negatively charged, andattracts atomic oxygen ions at lower speed, causing less sputtering of theanodized aluminum commonly used in the spacecraft structure. The busdiodes pair d(2), typically Schottky diodes, prevents loss of the bus voltagein case the battery charger gets an internal fault, which may clear after sometime. Such diodes — appropriately called the DET diodes — have beenused in many defense meteorological satellites (DMSs). They are notabsolutely needed, and would reduce efficiency. In its absence, adequatefusing should be used to protect the bus from faults in a battery charger.The current required to clear a charger fault would come from the solararray whether or not d(2) is present.

4.3.2 Solar Array Drive

The solar array drive (SAD) consists of slip rings, a motor, and motor driveelectronics. It continuously orients the solar array to face the sun forgenerating the maximum possible power during the entire sunlight periodof the orbit.

4.3.3 Shunt Dissipator

During sunlight, particularly in the beginning of life, this componentdissipates power that is unwanted after meeting the load power and thebattery charge power requirements.

4.3.4 Battery

The battery stores energy in an electrochemical form to supply power to theloads during eclipse periods over the entire mission life. NiCd secondarybatteries were extensively used in satellites until the mid 1980’s. In the

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newer designs, however, they have been replaced by NiH2 for betterperformance and lower mass.

4.3.5 Power Regulator Unit

The power regulator unit (PRU) provides an interface between the solararray bus and the battery. The battery voltage varies widely with the cellvoltage varying from 1.0V when fully discharged to 1.55V when fullycharged. The discharge converter in the PRU boosts the battery voltage tothe bus voltage during an eclipse and the charge converter bucks the arrayvoltage to the battery voltage during sunlight. For GEO missions, the chargeconverter rating is much smaller than the discharge converter rating. Insuch situations, designing the charge and discharge converters separatelywould be beneficial, as their individual designs can be better tuned to theirown ratings and requirements. For LEO missions, on the other hand, a bi-directional converter may be beneficial, as the charge converter and thedischarge converter ratings are comparable. The following approximationsmay help trading various options in conceptual designs. A 1-kW batterydischarge converter may weigh 2 to 3 kg. A 1-kW PRU designed to operatebetween –25 and 60 �C with a reliability of 0.99975 may weigh 6 to 7 kgincluding the battery charge converter and dedicated support electronics.

4.3.6 Power Distribution Unit

The power distribution unit (PDU) ensures that all loads, except critical andessential loads, are powered through switches and fuses. The fuses are notto protect the loads as much as to protect the power system from faults inthe user equipment.

4.3.7 Bus Voltage Controller

The bus voltage controller consists of the bus voltage sensor, the referencevoltage and the error signal amplifier. The amplified error signal output ofthe bus controller enters the mode controller, which in turn sends commandsignals needed to regulate the bus voltage within required limits.

4.3.8 Mode Controller

The mode controller automatically changes the EPS mode in response to theerror signal as follows. The mode selector switch is typically a magneticlatching relay.

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4.3.8.1 Shunt mode

During sunlight, if the solar power exceeds the load and battery chargerequirements, the mode controller turns on the shunts to dissipate excesspower, else the bus voltage will rise above the allowable limit. During thismode, the battery is charged at full, partial or trickle charge rate, asrequired.

4.3.8.2 Charge cut-back mode

When the battery is approaching full charge, the charge rate is cut back tocontrol the battery temperature. This mode includes trickle charge ratewhen the battery reaches a 100% state of charge. The charge cut-back modeis also activated in case the solar power exceeds the load requirement, butnot enough to supply the required charge current to the battery. In such acase, the battery charge power is cut back to the level that will maintain thebus voltage within the allowable limits.

4.3.8.3 Discharge mode

In the absence of solar power during an eclipse, the battery is discharged tomaintain the bus voltage. The battery voltage falls with the decreasing stateof charge. The discharge converter, therefore, must increase the boost ratioaccordingly. The PRU does this automatically by increasing the duty ratioof the discharge converter as the battery voltage decays.

4.3.8.4 PRU bypass mode

In case a fault occurs in any of the loads, the fuse must be blown as quicklyas possible in order to minimize the bus voltage decay. The delay in PRUcontrol loop response and the additional impedance introduced by the PRUwould significantly extend the fuse blow time. To circumvent this, thebattery is instantly connected to the bus by the bypass diode quad d(4),which quickly delivers the battery energy to the fuse in case of a fault, andblocks power flow to the battery at all other times.

4.3.9 Battery Bus

The battery bus is essentially a tap point directly off the battery. During thelaunch and ascent phases of the mission, the PV array is not deployed, andthe battery meets all the energy needs. For example, all electro-explosivedevices (EEDs) for deployment are powered directly from the battery busfor high reliability and low bus impedance (as there is nothing between thepower source and the load).

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4.3.10 Power and Energy Management Software

Although the power and energy management software (PEM) is part of thesoftware system, it is dedicated to the EPS performance, health monitoring,control, and protection. In case of emergencies, or during planned missionoperations, PEMS sheds loads in a preset sequence if and when the batterystate of charge cannot support all loads. The battery telemetry consists ofthe battery voltage, current, temperature, individual cell voltages and theinternal pressures of selected cells. Some of these telemetry readings also goto PEMS.

4.3.11 Loads

The term load includes all loads, i.e., the payloads (transmitters, receivers,science instruments, etc.) as well as the bus system loads. Most loads insatellites are constant power loads. Some loads may have a low duty ratio.For all loads, the orbit average power requirement is taken into account insizing the PV array and the battery.

4.3.12 Ground Power Cord

To preserve the battery power during pre-launch testing and final checksbefore lift-off, the on-board system uses external ground power via anumbilical cord. To further preserve the battery, power transfer is scheduledas late as possible in the countdown.

4.4 Bus Voltage Control

The regulated bus in normal operation maintains the bus voltage betweenthe specified upper limit and the lower limit. The mode control scheme forGPS IIR type 28-V regulated MEO bus with about 1000W load, may be setup as follows:

Shunt mode regulates the bus voltage by using a shunt dissipator. In thismode, the batteries are fully charged and the solar array powergeneration exceeds the spacecraft’s needs, so the excess current fromthe solar array is shunted. This mode is established when the shuntdrive voltage signal is greater than 2.5V d.c. and the battery chargecurrents are not responsive to the shunt drive voltage.

Battery charge control mode regulates the bus voltage using the batterychargers as linear shunting circuits. In this mode, the batteries arecharged and the spacecraft loads are met by the solar array. If thesolar array power capability is only slightly above the system load,the battery charge current must be limited. This mode is established

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when the shunt drive voltage is 1.0 to 2.5V d.c. and the battery chargecurrent is linearly responsive to the shunt drive voltage and isbetween 0 and 3.6 A.

Discharge mode regulates the bus by the battery discharge converter. Inthis mode, solar array current is not adequate for spacecraft busloads, so the batteries are in discharge to provide the power neededfor the bus. The solar array power capability is less than the bus loaddemand. This mode is established when the shunt drive voltage isless than 1.0V d.c.

Reference and error amplifiers measure the difference between the 28-Vvolt bus and reference voltage. Depending on the magnitude and sign of theerror signal, signals are sent to activate the shunt dissipators, the batterycharge controllers or the battery discharge controllers. These modes aremutually exclusive and easily identified by monitoring the shunt drivevoltage telemetry signal. The PRU performance is significantly different foreach mode but varies only slightly for various input conditions within eachmode.

In another example, in an EOS-AM type fully regulated 120-V LEO buswith a 3000-W load, the bus voltage is regulated within �5V to remainbetween 115 and 125V as shown in Figure 4.9. This regulation band isfurther subdivided into five sub-bands. The voltage control is implementedusing a mode controller, which places the power system in one of thefollowing operating modes:

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FIGURE 4.9 Bus voltage versus operating mode bands in a 120 � 5-V regulated bus.

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� Discharge mode when the bus voltage falls below the specified limit(point a)

� Dead band (do nothing band) when the voltage is between the dead-band limits (a and b)

� Charge mode when the bus voltage rises above the dead-band limit(point b)

� Shunt mode when the battery is fully charged and solar array outputpower exceeds the load power requirement (point c)

As a refinement, the control scheme may have two dead bands betweenthe charge mode and the shunt mode, one for placing the battery in highcharge rate, and the other for a low charge rate, as shown between the 122and 124-V bands in Figure 4.9.

The bus voltage is regulated at a specified bus sense point, generallydefined inside the power regulator unit. For dynamic stability of thefeedback control loop, the mode controller amplifier provides a minimumphase margin of 45� and gain margin of 10 dB. The bus is generallydesigned to accommodate payload shedding in case the bus voltage dropsto 90–95%, and is capable of powering the essential spacecraft functions to75–80% of the nominal bus voltage.

4.5 Control Circuit

The control circuit may be analog, digital or a hybrid, as described below.

4.5.1 Analog Control

Analog control has been used in spacecraft for decades. A fully analogcontrol loop for the main bus voltage regulator gives much better dynamicresponse to the power bus transients. The bandwidth of this control loop iskept high to optimize the bus regulation while reducing the noise.

4.5.2 Digital Control

Digital control is an alternative to the traditional analog control. A digitalshunt regulator uses relatively small shunt dissipators to provide smallsignal control of the bus. As the analog shunt approaches its limit, it wouldclock up/down counter, which controls the number of shunt switches inuse. While it may present challenges with respect to dynamic response ofthe system controller, it offers flexibility in tailoring the system to multiplemissions. For example, by simply changing the gain constant in thesoftware table, one can adjust the system’s transient response. One canalso incorporate a number of different battery charge regimes, and thenadjust the charge rate in orbit with single command from the ground. This

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arrangement is adaptable to a variable number of solar array segments andto a number of array configurations. The result is more flexibility in usingstandard modules of the solar array and the battery, which translates intocost reduction.

4.5.3 Analog–Digital Hybrid Control

In a hybrid control scheme, a high bandwidth analog control loop for themain bus voltage regulator assures better dynamic response to the powerbus transients while keeping the EMI low. The digital control loop is usedfor managing the lower functions where a low bandwidth is acceptable. Afield programmable gate array (FPGA) may be used to command solararray shunts on and off the bus and for commanding the battery chargestates. The FPGA samples the power system parameters, calculates theaverages and monitors large rate changes in order to make adjustmentsneeded in the solar array shunts and battery charge state. Such a hybridcontrol system results in good bus transient response with flexibility,reprogramming capability, bandwidth, and design simplicity.

4.6 Sun-Regulated Bus

If the design objective is to minimize complexity, an obvious approach is todistribute power from both sources — the solar array and the battery —directly to the load. Although such a direct energy transfer bus is sometimesknown as unregulated bus, the bus voltage is regulated by shunt controlduring sunlight, and is unregulated only during an eclipse. For this reason,such a bus is also known as the partially regulated bus, sunlight regulatedbus, or sun-regulated bus. Typical sun-regulated bus architecture is depictedin Figure 4.10. The difference in the sun-regulated bus and the fullyregulated bus is only in the PRU. The sun-regulated bus has the usualbattery charge regulator to regulate the battery charge rate during sunlightas commanded, but does not have the battery discharge converter. Instead,the battery discharges directly to the bus during eclipse through diode ‘d’,which is not called the ‘bypass diode’ any more, but is now called the‘battery discharge diode’. It only allows discharge from the battery, butblocks any uncontrolled charge current coming directly to the battery,leaving the charging function to the charge regulator. Thus, the battery isdisconnected from the bus during sunlight when the shunt controller isregulating the bus voltage. This architecture would be most beneficial inmultiple battery systems in GEO where the sunlight duration is long andthe eclipse is short.

In this architecture, the voltage regulation during sunlight is achieved byshunt control circuits. Since the battery is directly connected to the buswithout a discharge converter in between, the bus voltage is the same as the

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battery voltage. Therefore, the bus voltage falls as the battery dischargesduring eclipse, and rises as it gets recharged during sunlight. The busvoltage variations are the same as the battery voltage. A nominal 28-V busvoltage typically varies from 22 to 35V during the orbit period. In theabsence of shunt regulation, the solar array output voltage would settle atthe naturally stable operating point B in Figure 4.4, which would be toohigh particularly in the beginning of life and for several minutes after eacheclipse when the array is cold. The maximum to minimum bus voltage ratiowithout the shunt control may approach 3 in some cases during missionlife, versus about half as much with the shunt control.

The mode controller controls the battery charger and the shunts asneeded. The power and energy management software maintains the energybalance. Non-critical loads are powered through switches and fuses.

4.7 Fully Regulated Versus Sun-Regulated Bus

Power system design must give equal importance to conditioning anddistributing power from both the solar array during sunlight and from thebattery during eclipse. This poses a difficult design problem since bothpower sources have fundamentally different characteristics. The solar arrayis inherently a constant current source whose output voltage is limited bythe forward junction voltage of the PV cell. On the other hand, the battery isinherently a constant voltage source of low internal resistance giving adischarge voltage regulation of about 10%. It has high current and powercapability and its size is determined by the energy requirement duringeclipse. However, the fully regulated bus finds application in spacecrafthaving the load power requirements above 3 kW, typically in GEO. The

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FIGURE 4.10 Sun-regulated direct energy transfer architecture.

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sun-regulated bus, on the other hand, finds applications mostly in satelliteshaving the load power requirement of less than a couple of kilowatts,typically in LEO.

The sun-regulated bus is simple and hence more reliable. However, theequipment connected to the bus must be designed to operate over widevariations in voltage up to �25% around the nominal value. Some loads,such as traveling wave tube amplifiers (TWTAs) may accept suchvariations, but most others require a voltage regulator at the point wherethe power is distributed to the equipment. The sun-regulated bus saves thecost and the power loss in the battery discharge converter. However, thepower loss in a battery discharge converter in the regulated bus and thebattery bypass diode in the sun-regulated bus compensate each other.

The fully regulated bus offers certain advantages at the cost of complexityand potentially lower reliability. Low system impedance can cause voltagevariations due to cross-coupling between items of equipment. This mayincrease the electromagnetic interference particularly in the time divisionmultiple access (TDMA) mode. However, the advantages of a fullyregulated bus are as follows:

� Low battery mass and cost, as it allows use of fewer higher capacitybattery cells.

� Low solar array mass and cost due to not having a battery latch-upproblem, which requires over-sizing the array as described in Chapter13. The saving is typically 7 to 10%, and can be as high as 15 to 20% insome cases.

� Lighter power distribution harness mass, since the main bus works at aconstant voltage. In contrast, the sun-regulated bus requires heavierwires to carry high current at the lowest voltage level at the end ofeclipse.

� Lightweight load power converters, since they are supplied withconstant voltage input.

In the sun-regulated bus, if the battery latch-up occurs at the eclipse exit, theresulting bus current can be in theory 60% higher than that in the fullyregulated bus. However, due to the reduced thermal load in eclipses andthe availability of charge power, latch-up in equinox is not a design driver.Summer solstice is more critical period, when the bus latches onto a fullycharged battery, limiting the array over-sizing to 10 to 15%. The over-sizingcan be further reduced by temporarily reducing the heater load.

The harness connecting two pieces of equipment is usually designed tolimit the voltage drop under maximum load current. The specifiedallowable voltage drop primarily depends on the bus voltage, and can befrom 100 to 500mV in a 28-V bus, and 1 to 2V in a 120-V bus. The sun-regulated bus requires thicker conductors to limit the voltage drop at high

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current at the end of eclipse. For a 5-kW load power capability, the powerdistribution harness, including the metallic cable shield and variousconnectors, could weigh approximately 20 to 30 kg in a sun-regulated busand 15 to 20 kg in a fully regulated bus.

The load power conditioner (LPC) provides interface between the EPSbus and the radio frequency (RF) amplifier of the communication loads. Theoutput ratings of LPC vary in the 50 to 500-W range. Generally, it has a pre-regulator and a switch mode converter if the bus is sun-regulated, or alinear regulator with fully regulated bus. The LPC efficiency ranges from 90to 98% depending on the design. However, for comparable power ratings,its efficiency is about 2% higher for a fully regulated bus than that for a sun-regulated bus, and the LPC mass is lower by 2 to 4 g/W of output.

A fully regulated bus in general provides straightforward power systemspecifications, simple design interface, in-orbit operating flexibility, auton-omous overload and eclipse entry control, and simple testing at the userend. At power levels above a few kilowatts, it also provides high efficiency,low mass and low overall cost at the power system level and/or the satellitelevel. On the other hand, it needs a battery discharge converter. This can beexpensive, as each item of equipment has some base cost associated withthe design, documentation, manufacture, quality control, and testing.

The fully regulated bus also offers great flexibility in battery cell selection.Fewer high capacity cells can be selected, since the battery voltage can beany value within the charge and discharge converter duty ratio limit, Thisgenerally reduces the battery cost and footprint by selecting one of thestandard ampere-hour capacity cells to match the exact requirement of thebus. On the other hand, the required cell ampere-hour rating in a sun-regulated bus may fall between two standard capacity cells, forcing thedesign engineer to select the higher capacity cell, costing more in mass andmoney.

4.8 Peak Power Tracking Bus

The solar array generates more power at higher voltage at the beginning oflife and when cold coming out of an eclipse. The maximum power can beextracted only if the bus voltage is varied with years in service and withtemperature. However, the load must be supplied power at the samevoltage, generally lower than the maximum power producing voltage of thesolar array. A suitable switching regulator between the solar array and theload, as shown in Figure 4.11, remedies this disparity between themaximum power producing voltage and the constant load voltage. Theseries regulator input voltage is then maintained at the maximum powerproducing level by the peak power tracker, and the output voltage isstepped down to the constant load voltage by varying the duty ratio asrequired. The peak power tracking is activated only when the battery needs

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charging or the load demand exceeds the solar array output. Otherwise, theexcess power is left on the array raising the array temperature. The batteryrelay is opened up when the battery is fully charged.

The peak power tracking (PPT) electronic controller senses the maximumpower point in one of the following ways:

� The solar array output power — the product of voltage and current —is continually computed and fed to the peak power tracker. The arrayoperating voltage is changed until the peak is detected.

� As seen in Chapter 8, the bus dynamic and static (a.c. and d.c.)impedances are equal in magnitude at the peak power point. A ripple isinjected into the solar array bus, and the dynamic impedance dV/dIand the static impedance V/I are continuously measured. The busvoltage is adjusted such that both impedances are equal.

� The ratio of the Vmp to the Voc for any solar array is approximatelyconstant, say K (typically 0.70 to 0.75). The Voc of a solar cell couponmaintained in the same environment as the main array is continuouslymonitored. The operating voltage of the main array is then adjusted toK�Voc to extract the maximum power.

� The inner voltage control loop regulates the solar array output voltageto the reference value from the PPT controller. By changing thisreference value at regular intervals, the PPT controller moves theoperating point of the solar array. In each time interval, the PPTcontroller calculates the solar array power slope by multiplying thesensed solar array voltage and current. If this power slope is positive,the PPT controller increases the reference value until the sensed powerslope is negative, and vice versa. Thus, the operating point of the solararray is located near the peak power point where the power slope iszero. The algorithm can be written as

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FIGURE 4.11 Peak power tracking architecture for a mission with wide variations in solarflux and temperature.

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Vref ðn þ 1Þ ¼ Vref ðnÞ þ K�P

�Vð4:1Þ

where K is a suitable constant. The peak power voltage thus derived isfed to the series switching regulator, which then converts the arrayvoltage to the load voltage. Figure 4.12 shows a complete PPTassembly.

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FIGURE 4.12 Power regulator unit with peak power tracker.(Source: Dornier Satellitensysteme Gmbh, Daimler-Benz Aerospace. With permission.)

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The peak power tracking architecture is particularly useful in thefollowing applications, where the additional weight, power loss, and costof adding such an assembly can be justified:

� Small satellites having no pointing gimbals, such that the solar array isnot always oriented towards the sun

� Satellites having the solar radiation and array temperature varying overa wide range, indirectly varying the array voltage

In low Earth orbit, where the battery must be charged in a short period.The PPT allows maximum power to be captured for several minutes aftereach eclipse when the array is cold. Architecture without the PPT feature,such as a DET bus, would waste a significant amount of power as shown inFigure 4.13. If a DET system were designed to deliver the required power atone-half the illumination at EOL, the power waste would be CD watts atEOL full sun, BD watts at BOL full sun, and AD watts at EOL full sun on acold array. The PPT design eliminates this waste by utilizing all the powerthat can be generated.

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FIGURE 4.13 Power wasted in direct energy transfer architecture in certain conditions.

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The main advantages of the peak power tracking are that it maximizesthe solar array output power all the time, and it does not require the shuntregulator and the battery charge regulator. On the other hand, it results inpoor system efficiency due to power loss in the peak power trackingconverter. Moreover, since this loss is dissipated inside the spacecraft body,it negatively impacts the thermal system.

The PPT can have three configurations: series, parallel, and series–parallel, as shown in Figure 4.14.1 The series–parallel configuration yieldsbetter system efficiency because the input and the output power conversionis processed by a single converter for all operating modes, as seen in Table4.1.

A PPT algorithm has been developed2 and tested using only the solararray voltage information, giving the tracking control without using currentsensors. This results in low ripple current, hence lighter bus filtercapacitors.

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FIGURE 4.14 Battery charge and discharge options in peak power tracking architecture.

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4.9 Architecture Trades

A primary criterion of choosing between alternative architectures is theoverall mass, efficiency and cost of the system. Table 4.2 summarizes thetrades between various architectures with their best applications. The finalselection of the architecture depends on the mission specific details.However, past experience indicates that peak power tracking architecture

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Table 4.1 Operating modes of series–parallel battery dischargeregulators in the PPT system

Mode Series regulator Battery charger Battery discharger

Eclipse Off Off Regulated busPPT discharge(partial sun)

PPT Off Regulates bus

PPT charge(full sun)

Regulates bus PPT Off

Trickle charge Regulated bus Trickle charge Off

Table 4.2 Pros and cons of various architectures and their best applications

System Sun regulated Fully regulated Peak power tracking

Pros High power transferefficiency from solararray and battery toload.

Fewer power systemcomponents.

Well regulatedinput voltage toall loads.

Simpler, lighterand moreefficiency loadconverters.

No need for shuntregulator and batterycharge regulator.a

Makes the maximum useof the incident solarenergy.

Cons More complex loadconverters.

Battery latch-upconcern.

Larger solar array.

Needs morepowerconverters.

Series power lossbetween batteryand load.

Lower efficiency than DETat EOL in many cases.

More heat dissipationinside the spacecraft body.

Bestapplication inmissions withthese features

Small load variations.

Small variations inillumination for mostof the sun period.

Loads requiringclose regulation.

Large solar arrayoutput voltagevariations.

Large variation in solararray input energy(illumination) throughoutthe mission.

aTrue for a single battery bus with the battery connected directly to the bus. For a multiplebattery system, or a fully regulated bus, each battery must have its own charger for effectivebattery charge management.

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is generally advantageous for small satellites in low or irregular orbitshaving a power requirement of less than 500W. Between 1000 and 3000W,the sun-regulated direct energy transfer architecture would most probablybe advantageous. For power levels exceeding 5000W, the regulated directenergy transfer architecture is generally found advantageous. Although theregulated bus requires additional equipment, the added mass is compen-sated by the elimination of converters and regulators in the loads.Moreover, decoupling the battery design from the solar array voltage,and operating the system at a constant voltage optimizes the operatingpoint of the solar array. The battery voltage is then chosen to optimize thenumber of battery cells in the most economical capacity.

The PPT architecture is more suitable for LEO satellites having relativelyshort periods of sunlight. It is also attractive for missions with largevariations in solar flux, solar array temperature, and sun angle in satelliteswith no sun tracking gimbals. It makes the best use of the solar array all thetime in such missions.

In addition to the DET and PPT architectures described above, somespacecraft use hybrid architecture, such as two power busses, one regulatedand the other sun-regulated. Charging the battery from a dedicated solararray section rather than from the main bus is another possibility.

The architectures of some of the spacecraft busses flying at present aredescribed in the next sections.

4.10 The International Space Station 160- to 120-V Bus

The International Space Station is truly the largest and most complex spacestructure ever built, with 16 international partners. The complete assemblyshown in Figure 4.15 weighs one million pounds and the total interior spaceof its six laboratories equals two Boeing 747 aircraft. It is taller than a 30-story building and wider than the length of a football field. The attitude iscontrolled within 1� stabilized at a rate less than 0.1�/s. It is in 335 to 500-kmlow Earth, 51.6� inclined orbit with a 90-min orbit period and 35-mineclipse. The experiments planned for its on-board laboratories are targetedto enhance our understanding in:

� The Earth, by viewing 75% of its surface

� Long term exposure of micro-gravity on humans

� Producing new medicines and materials

Like any other large space programs, such as the manned landing on Moon,the engineering and technology spin-offs on our everyday lives on Earth arethe side benefits.

The ISS power system generates 105 kW using a solar array with an areaof nearly 1 acre. The loads are powered during an eclipse by thirty-eight

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81-Ah NiH2 batteries3 via bi-directional battery charge–discharge units(BDCUs), autonomously controlled by the bus voltage set point. It has twointerconnected power systems; the 160/120-V US built system, and 120/28-V dual voltage Russian built system to power the US, European, andJapanese modules. The two systems are generally independent, but areinterconnected via d.c. converters to allow bi-directional transfer of power.Figure 4.16 is the functional block diagram of the US system, including theconverter at the interface with the Russian power source. The US systemis described below.3

The solar array is made of four modules (wings) for a total of 76 kWpower under nominal conditions, and more during favorable conditions.Each wing consists of two thin blankets held under tension on each side of acentral collapsible mast. The entire assembly turns on a � gimbal, whichprovides one axis of rotation for sun pointing. A second orthogonal axisrotation is provided at the � gimbal, where the entire solar array connects tothe rest of the truss structure of the station. The 76 kW from the US systemadded to the 29 kW from the Russian system makes the 105 kW capability ofthe complete station assembly. Each of the four solar modules is made in 82strings of eighty 8� 8 cm PV cells and coverglass for protection againstspace charged particles. The PV cells are crystalline silicon with 14.5% EOLefficiency over a 15-year life. The module printed circuit is Kapton/copper/Kapton laminate welded to each cell to provide a series interconnection for

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FIGURE 4.15 International Space Station with solar array and other modules in view.(Source: NASA.)

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the assembly. Parallel bypass diodes are used every eight cells for reliabilityin case of cell damage and to avoid reverse current heating duringprolonged shadows. Sequential shunt units (SSUs) on the solar arraysoperate at 20-kHz switching frequency.

The seasonal sun-pointing is done by � gimbals and the orbit sun-following by � drive and roll rings. For currents of the space stationmagnitudes, the roll rings provide superior power transfer performanceover the slip rings with rubbing contacts, as described further in Chapter22.

The solar array output voltage is 160V, which is the highest voltage thatcan be practically used in a low Earth (high plasma) orbit in view ofpotential plasma arcing and/or leakage current concerns. The 160V isstepped down to 120V using d.c.–d.c. converter units (DDCUs), each ratedat 4.25 kW, for utilization inside the user modules. The DDCUs provide150% current limiting capability and 20 dB isolation between the generationpoint and the distribution points for personnel safety.

The solar array area and the operating voltage are greater than in anyother spacecraft flown before. Therefore, the nature of the single pointground on the ISS in high plasma in LEO poses an arcing problem. Topreclude such arcing, a device called the plasma contactor located on the

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FIGURE 4.16 International Space Station single channel power flow diagram.(From E.B. Gietl et al. NASA Report No. 210209, 2000.)

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truss creates a plume of ionized xenon gas, which acts as a conductivebridge between the station and the plasma. It protects the array and otherconductive surfaces of the station from arcing, pitting, and erosion.

The battery is made of 48 battery packs, each with thirty-eight 81-AhIPV NiH2 cells, designed for 5 years (40,000 charge/discharge cycles) at35% depth of discharge (DOD), although the actual operational DOD isaround 15%. With two packs connected in series, the battery voltagevaries between 95 and 115V. Battery replacements are planned every 5years to assure the power margin. With 15 years life of the station, thebattery replacements every 5 years constitute significant recurring cost.The maximum charge rate is 50A, which tapers down to 40, 27, 10 and5A, and finally to 1A trickle charge rate. No bypass diodes are used ineither direction, but the cells are closely matched. An open cell will losethe entire battery string. The operating temperature is in the range of 0 to10 �C.

The switching and fault protection is achieved by solid-state remotepower controllers (RPCs) in six ratings from 3.5 to 65A in both currentlimiting and non-current limiting designs. The RPCs trip at different setpoints of over-current, over-voltage, and under-voltage to isolate faults asclose as possible to the faulted equipment. The solid state power controllers(SSPCs) provide switching and protection. They reset automatically forcritical loads and remain tripped for non-critical loads. The upstreamcoordinated fault protection in the 160-V segment is achieved by largermain bus switching units (MBSUs) containing a remote bus isolator (RBI).The RBIs are essentially large relays capable of interrupting up to 350A ofd.c. fault current.

The power system stability is also a serious concern because the loads onthe station are constantly changing as new scientific experiments arebrought on board. As a result, the output impedance of the DDCUs and theinput characteristic of the loads have been specified to ensure stability withany combination of the expected loads. The stability criteria under suchdiverse load combinations are discussed in Chapter 14.

A hierarchy of redundant computers linked via the MIL-STD-1553 buscontrols the ISS power system. The computers autonomously control manyfunctions such as sun tracking, battery energy storage, and thermal control.The power flow balance between major segments of the station iscoordinated by the on-board command and control systems, which alsoprovide interface control between the segments.

Future plans for new technology developments on the ISS that are relatedto the electrical power systems include: (1) replacing the silicon solar cellswith GaAs panels to increase conversion efficiency, (2) using high dischargecycle NiH2 batteries, and (3) using flywheel energy storage to significantlyincrease the specific energy.

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4.11 Large Communications Satellite Buses

In view of reducing cost and delivery time, all prime manufacturers havedeveloped standards busses, which can meet various power requirementswithout making many changes. The standard bus, however, has a degree offlexibility to tweek a little if and when needed to meet a customer’sspecifications. A few such standard busses presently available for commu-nication satellites are briefly described below.

4.11.1 100-V Bus

A standard fully regulated DET bus operating at 100V d.c. is offered byBoeing Satellite Systems under the trade name BSS-702TM. Its power systemarchitecture is shown in Figure 4.17.4 The BSS-702 bus is a dual voltage bus,primary 100V d.c. for high power equipment and secondary 30V d.c. forlow power component. It uses a NiH2 battery and silicon triple junctionsolar cells. A xenon electric ion-propulsion system is used for N–S stationkeeping, which is powered from the 100-V bus.

After each discharge of the battery, the basic function of any batterycharge management is to return the battery to the highest achievable SOCwith the minimum amount of overcharge. In the BSS-702 bus, this isachieved by performing the following health monitoring and maintenancefunctions:

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FIGURE 4.17 Fully regulated 100-V bus architecture.(From R. Hill, Proc. 36th IECEC, ASME, p. AT-59, 2001. With permission.)

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� Monitor and process the battery voltage, current, temperature, andpressure sensor readings.

� Control over-temperature to prevent inadvertent overcharge.

� Autonomously control the charge rate by switching between high, low,and trickle charge rates as needed in different seasons.

� Adjust battery bias to account for voltage degradation in NiCd andpressure growth in NiH2 cells.

� Detect and report low SOC conditions.

Each battery is built in multiple packs to distribute the mass and heat asneeded to balance the spacecraft layout. Each pack has redundant heaters,reconditioning circuit health sensors, and cell bypass diodes in case of cellfailure. The sensor monitors the cell voltage, pressure, temperature, andbypass and reconditioning circuit status telemetry. The cells are 5.5-inchdiameter NiH2 and are stacked vertically with the electrodes on twoseparate sides.

The solar array panel tracks the sun in one axis only, so the seasonalvariations in power generation can be more than 10% over the year. Theoriginal solar array design was a concentrator type with channeled solarreflector panels along both sides of the wing with GaInP2/GaAs/Ge PVcells mounted on a graphite face sheet on an aluminum honeycombsubstrate. After suspecting some plume related problems, the array wasreplaced with a traditional flat panel array.

Loads are either unfused, fuse protected, or switched by relay ortransistor, depending on the current magnitude and the nature of the load.

4.11.2 70-V Bus

A standard fully regulated DET bus operating at 70V is offered byLockheed Martin Space Systems under trade name A2100TM. Of the 16commercial satellites contracted in 2002 and the first half of 2003, five werefor A2100. It is available up to 15-kW power level, scalable up to 20 kWusing multi-junction GaAs PV cells. The power system architecture isshown in Figure 4.18.5 The solar array is made of flat panels with Si, GaAsor multi-junction PV cells as needed for the required power level. The PVcell coverglass is coated with indium tin oxide (ITO) to eliminate arcing dueto electrostatic discharge (ESD). The honeycomb substrate with a graphiteepoxy composite face sheet saves mass over that with aluminum. Thebooms and yokes are made from aluminum or graphite. One solar arraydrive (SAD) per solar array wing with redundant motor winding provides alarge torque margin in case jerking is needed. Power slip rings and signalslip rings are in separate sections.

The batteries are made of NiH2 cells assembled in two batteries for therequired energy storage. The battery power converters in the PRU can be

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directional (buck and boost separately), or bi-directional if it is beneficial.The charge converters have multiple charge rates. The batteries havemultiple heater control zones for maintaining desired temperature withredundant temperature and pressure sensors. For open cell protection, athermally activated switch is preferred over the bypass diode, as the formerresults in lower loss of power. Reconditioning is considered unnecessary forthe NiH2 batteries. However, if required by the specifications, resistancesare connected across the entire battery, or across a battery section, or acrosseach cell. In the first option, which is the most mass effective, two parallelresistors are first commanded across the battery. As the battery voltageapproaches 1.0 per cell, the discharge rate is cut back by commanding oneof the resistors off to avoid cell voltage reversal. The charge rate is also cutback in case of any peaking power on the bus sensed by a voltage dip.

The battery nominally operates between –5 and 0 �C during the chargeperiod. However, its temperature rises to about 20 �C at the end of thelongest eclipse. The allowable cell-to-cell and battery-to-battery gradientsare 5 to 10 �C. Locating the battery outside the spacecraft body can beadvantageous in maintaining the 0 to 5 �C temperatures during the chargeperiods. The MEP is the module-enabling plug for the battery. The electro-explosive devices (EEDs) for deployment are powered directly from thebattery at the 22nd cell tapping, and are protected by fuses in the EEDenable plugs.

The main power bus assembly provides the load distribution, currentsensors, voltage sensors, and bus filter. The fuse box houses protective fuses

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FIGURE 4.18 Fully regulated 70-V bus architecture.(From A.A. Salim, Proc. 35th IECEC, AIAA, p. 2809, 2000. With permission.)

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and also load power switches for controlling the bus load when needed.The transient over-voltage and under-voltage following a large load step,such as turning on an arc jet (>4 kW total), is individually analyzed toensure meeting the bus ripples requirement.

In the A2100 bus, the energy balance is managed by controlling twobatteries independently in the following steps:

� Using the current telemetry, determine the total battery charge anddischarge current

� Determine the cell voltage and pressure

� Compute the state of charge

� Control the battery charge rate

� If the battery temperature exceeds a set limit, reduce the charge rate

� Shed load if the battery discharge falls below the set level

� Provide for parallel or sequential battery charge

� Prevent the disconnection of all battery power converters

� Provide ground override capability

The bus under-voltage protection under a set limit is provided bycommanding and latching the payload power converter off. The shadedloads can be turned on only by a ground command.

A shunt is connected across each solar circuit. The shunt switch is eithercompletely turned on or off. The on-switch shunts the power to the ground,while the off-switch feeds the power to the bus. The desired bus regulationwith fine resolution is maintained by using one active shunt. Suchconfiguration also minimizes the bus voltage ripple.

4.11.3 Under-50-V Buses

British Aerospace’s standard 42.5-V fully regulated and 28 to 42.5-V sun-regulated busses have been used on many small satellites. US manufac-turers, on the other hand, offer 28-V fully regulated and 22 to 35-Vsun-regulated busses for small satellites requiring load power under acouple of kilowatts. One such bus offered by Daimler-Benz Aerospace isdepicted in Figure 4.19.

4.12 Small Satellite Bus

The following power system features are typical in small satellites:

� A solar array covering a wide range of solar flux and temperature withwide swings in the I–V characteristics.

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atteryS

ystem87

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FIGURE 4.19 Sun-regulated low voltage bus architecture. (Source: Dornier Satellitensysteme Gmbh, Daimler-Benz Aerospace. With permission.)

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� Peak power tracking architecture and no sun-tracking gimbals.

� Body mounted solar array or three to four flat panels on 1 to 2 mmaluminum substrate with insulation and optimized coverglass. Or,flexible solar array with cloth-type substrate weighting about 5% of therigid substrate.

� One battery, if permissible; otherwise two; NiCd or NiH2; both to havea reliable flight history.

Early small satellites were spin stabilized, with their drum-like bodycovered with PV cells all around. Such configuration used the cellsineffectively; because it uses less than one third of the PV cells for powergeneration at any given time. Today’s spacecraft have 3-axis active attitudecontrol with solar cells installed on flat panels pointed normally to the sun.

The PPT is more suitable for being one common architecture for anumber of small satellites for a variety of missions. The design can bemodular and adaptable without component redesign, thus being costeffective. The power control unit maximizes the energy delivered to the busby driving the solar arrays to operate at their maximum power point over awide range of temperature, sun inclination, and illumination intensity. Thetracker system, in addition to its flexibility, does not dissipate powerassociated with the shunt regulation inside the spacecraft. It adjusts theoperating point of the solar array as needed, thereby leaving the excesspower on the array.

A PPT bus that has flown successfully had the following design features,which can be easily changed to accommodate other missions.

The solar array continuously tracked the sun using a solar array drive.The PV cell could be either 8 mil or 2 mil thick silicon or 5.5 mil thick GaAs.The NiH2 battery used 22 cells. The maximum battery DOD for LEO wasnominally 30% and 35% with one cell failed. For GEO, it was nominally 70%and 75% with one cell that failed. The charge/discharge ratio wasmaintained at 1.05 for LEO and 1.2 for GEO.

The peak power tracker received telemetry from the battery chargecontrol loop, which varied the modulation of the control signal operatingthe tracker in each PRU.

The PRU worked as the interface between the solar array and the bus,designed to deliver the total power generated by the solar array to thespacecraft bus. It contained a peak power tracker comprised of a buckregulator with pulse width modulation (PWM) control and the requiredbattery voltage–temperature (V–T) control. After receiving the batterytelemetry and comparing with the selected V–T charge curve, the PRUvaried the duty ratio of the buck converter. This changes the solar arrayoperating point thus reducing the power to the bus. All power regulationfunctions were monitored and controlled within the PRU, including thebattery charge control. Separate PRUs were used for each wing if more than

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one solar array wing under different operating conditions were needed forsome satellites in the standard product line. This ensures that the EPSdesign remained modular to accommodate all possible mission scenarioswith little or no design changes.

4.13 Micro-Satellite Bus

Very small satellites with load power requirements in watts can use simpleand lean architecture shown in Figure 4.20. The solar array, the battery, andthe loads are permanently connected in parallel. The battery feeds to theloads automatically during an eclipse, and recharges itself during sunlightby imposing its drained voltage on the bus. Once fully charged, the batteryvoltage is relatively constant, and the battery works as the buffer. Anyexcess current is absorbed by the shunt resistance connected in parallel withthe battery by means of a switch.

Two simple architectures for satellites that require power only duringsunlight are shown in Figure 4.21(a) and (b). The shunt voltage regulatormakes the power source behave like a current source. On the other hand,the series regulator makes the source behave like a voltage source. Thedisadvantage of the series approach is that, without the shunt regulator, thesolar array output voltage in a typical GEO satellite would exceed 150% ofits EOL voltage. For a few minutes after exiting the eclipse, the cold arraycan produce as much as 300% of the nominal bus voltage.

Low voltages (7 to 15V) have been considered for satellites with load intens of watts. However, such low voltage is likely to end up in high costbecause it requires components other than standard 28-V class components.For example, ST5 spacecraft designed by NASA GSFC6 for a few watts loadused a battery dominated low voltage bus depicted in Figure 4.22. Tominimize the number of components for high reliability and low mass, itused a body mounted solar array with triple-junction cells, one lithium-ionbattery, and simple power electronics. The electronics that traditionally

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FIGURE 4.20 Simple power system for a micro-satellite.

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FIGURE 4.21 Micro-satellite power system with shunt regulator and series regulator.

FIGURE 4.22 Micro-satellite power system with no regulator.

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provide the solar array regulation and battery charge control areeliminated. Low loss diodes are used in series with a solar array for faultisolation. The bus voltage is the same as the battery voltage, which mayvary from 2.7 to 4.0 V per cell. The design can be modular in that for ahigher power microsat, two modules can be connected in series as shown inthe figure.

References

1. Cho, Y.J. and Cho, B.H., ‘‘A novel battery charge–discharge of theregulated peak power tracking systems,’’ in Proceedings of the 34thIntersociety Energy Conversion Engineering Conference, SAE, 1999, PaperNo. 01-2445.

2. Veerachary, M., Senjyu, T., and Uezato, K., ‘‘Voltage-based maximumpower point tracking control of PV system,’’ IEEE Transactions on Aerospaceand Electronics Systems, 38(1), 262–267, 2002.

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