Power systems — solar arrays (I-V curve, power tracking), batteries (DoD, cycles), RTG: Question bank

3.6.22 · D5 · Physics › Spacecraft Structures & Systems Engineering › Power systems — solar arrays (I-V curve, power tracking), ba

Yeh ek rapid-fire self-test hai un ideas ke liye jo Power Systems — Solar Arrays, Batteries, RTG mein hain. Har line ek prompt ::: answer reveal hai. Right-hand side cover karo, pehle apna answer socho, phir check karo. Goal arithmetic nahi hai — goal hai un conceptual mistakes ko pakadna jo real power-budget designs mein dooba deti hain.

Definition Symbol dictionary — pehle yeh padho

Neeche use hone wala har letter yahan fix hai taaki koi reveal naya symbol na introduce kare:

$V$ , $I$ — solar cell ki terminal voltage aur output current (I-V curve ke do axes).
$I_{sc}$ — short-circuit current: $V = 0$ par current (terminals shorted).
$V_{oc}$ — open-circuit voltage: $I = 0$ par voltage (no load).
$I_{L}$ — photocurrent: woh current jo light khud generate karti hai, roughly $\propto$ intensity.
$I_{0}$ — dark saturation current: junction ki chhoti si reverse leakage bina light ke.
$n$ — ideality factor ( $\approx 1$ – $2$ ), ek fudge number jo batata hai ki real diode textbook-perfect se kitna door hai.
$V_{T} = k_{B} T / q$ — thermal voltage ( $\approx 26$ mV at 300 K), temperature $T$ se set hone wala natural voltage scale.
$F F$ — fill factor, curve kitna "square" hai (questions mein defined hai).
$DoD$ — depth of discharge: battery ki capacity ka woh fraction (% mein) jo drain ho chuka hai.
$N$ — cycle life: kitne full charge/discharge cycles battery survive karti hai apni capacity ek chosen limit tak fade hone se pehle.

The single-diode picture (yeh pehle build karo phir answers do)

Figure — Power systems — solar arrays (I-V curve, power tracking), batteries (DoD, cycles), RTG

Formula

$V_{oc}$ derive karna — missing "why" WHAT: $V_{oc}$ woh voltage hai jab koi current bahar nahi jaata ( $I = 0$ ). WHY set $I = 0$ : open circuit ka matlab hai dono terminals kuch nahi touch kar rahe, toh koi charge bahar flow nahi kar sakta — cell voltage tab tak badhta hai jab tak diode exactly saara photocurrent wapas leak na kar de. Single-diode equation mein $I = 0$ daalo: $0 = I_{L} - I_{0} (e^{V_{oc} / n V_{T}} - 1) \Rightarrow e^{V_{oc} / n V_{T}} = \frac{I _{L}}{I _{0}} + 1$ Dono sides ka natural log lo (yahi woh tool hai jo exponential ko undo karta hai — yeh poochta hai "kaun sa exponent yeh deta hai?") aur $n V_{T}$ se multiply karo: $V_{oc} = n V_{T} ln (\frac{I _{L}}{I _{0}} + 1)$ WHAT IT MEANS: log yahi wajah hai ki zyada light sirf thodi extra voltage add karti hai — neeche figure mein amber curve dekho, jo intensity badhne par hard flatten ho jaati hai.

True or false — justify karo

Maximum power point (MPP) woh hai jahan output current sabse badi hoti hai

False — sabse badi current short-circuit current

I_{sc}

hai

V = 0

par, jahan power zero hai. MPP woh interior point hai jahan product

P = V I

peak karta hai, hamesha

V_{oc}

se neeche voltage par aur

I_{sc}

se neeche current par.

Sunlight double karna roughly open-circuit voltage

V_{oc}

bhi double kar deta hai

False —

I_{sc}

intensity ke saath nearly linearly scale karta hai, lekin

V_{oc} = n V_{T} ln (I_{L} / I_{0} + 1)

sirf intensity ke logarithm ke roop mein badhta hai, toh light double karne se sirf

\sim n V_{T} ln 2 \approx 27

mV per cell add hota hai.

Ek hotter solar cell zyada power produce karta hai

False — heat dark saturation current

I_{0}

ko badhata hai (yeh

T

ke saath exponentially climb karta hai), jo

V_{oc}

ko roughly

- 2.2

mV/°C per cell neeche kheenchta hai;

I_{sc}

mein chhota sa gain kabhi compensate nahi karta, toh hot cells power kho deti hain. Dekho Spacecraft Thermal Control.

Fill factor

F F

ek bahut achhe cell ke liye 1 se zyada ho sakta hai

False —

F F = P_{ma x} / (V_{oc} I_{sc})

actual MPP power ka ratio hai us rectangle

V_{oc} \times I_{sc}

se jo use bound karta hai, toh

F F < 1

hamesha; space-grade triple-junction cells

\sim 0.88

tak pohonchti hain lekin kabhi 1 nahi.

Agar tum array ko seedha battery se connect karo, toh woh automatically MPP par run karta hai

False — battery array ko apni terminal voltage (state-of-charge dependent) par pin kar deti hai, jo almost kabhi drifting

V_{m p}

ke equal nahi hoti; tumhe beech mein MPPT ke saath DC-DC converter chahiye. Dekho Power Electronics.

Battery ko 50% DoD tak do baar discharge karna 100% DoD ek baar ke barabar wear hai

False — cycle life DoD ke saath linearly se zyada tezi se girta hai (

N \propto DoD^{- k}

k \approx 1.5

–2), toh do shallow cycles ek deep cycle se gentler hain chahe move hua total charge same ho.

RTG ka electrical output radioactive half-life ko exactly track karta hai

False — thermal power isotope ki half-life ke saath decay karta hai, lekin electrical output zyada tezi se girta hai kyunki thermocouples khud degrade hote hain (sublimation, dopant diffusion), toh end-of-life electrical power half-life prediction se bhi kam hoti hai.

MPP par, incremental conductance

d I / d V

equals

- I / V

True —

P = V I

differentiate karke

d P / d V = 0

set karne se milta hai

I + V d I / d V = 0

, yaani

d I / d V = - I / V

; yahi exact equality hai jo incremental-conductance MPPT algorithm test karta hai.

Error pakdo

"Kyunki

I_{sc}

maximum current hai, array sabse efficient hai jab short-circuited ho."

Galat — short circuit par

V = 0

toh

P = V I = 0

; array wahan zero useful power deliver karta hai. Efficiency (power out per photon in) MPP par maximize hoti hai, maximum current par nahi.

"Single-diode equation kehta hai

I = I_{L} - I_{0} (e^{V / n V_{T}} - 1)

, toh

V = 0

par current

I_{L} - I_{0}

hai."

Exponential term

e^{0} - 1 = 0

hai, toh

V = 0

par

I = I_{L}

exactly hai, na ki

I_{L} - I_{0}

. Parenthesis ke andar

- 1

exist karta hai precisely taaki diode term zero bias par vanish ho jaye.

"Eclipse mein humein 290 Wh chahiye aur battery 560 Wh hold karti hai, toh 52% DoD theek hai aur battery forever chalti hai."

52% DoD lifetime-free nahi hai — har cycle phir bhi SEI layer grow karti hai aur capacity fade karti hai; "eclipse ke liye theek" ka sirf matlab hai ki energy fit hoti hai, jabki mission mein cycle count (LEO mein hazaaron orbits) real limit set karta hai.

"Lower sun angle

β

current aur voltage dono ko same fraction

cos β

se reduce karta hai."

Sirf intensity — aur isliye

I_{sc}

—

cos β

se scale karta hai;

V_{oc}

sirf

n V_{T} ln (cos β)

se drop karta hai, jo bahut chhota change hai. Dono ko

cos β

treat karna voltage loss ko badly overestimate karta hai. Dekho Orbital Mechanics (Keplerian).

"Perturb-and-Observe direction reverse karta hai jab bhi power drop ho, toh yeh hamesha exactly MPP par baithta hai."

Yeh MPP ke around hunt karta hai, har cycle mein ek step

Δ V

oscillate karta hai; yeh kabhi exactly peak par rest nahi karta, aur zyada bada

Δ V

wobble mein power waste karta hai jabki zyada chhota wala moving conditions ko zyada slowly track karta hai.

"Space mein radiation sirf

I_{L}

lower karta hai, toh purane panels sirf kam current banaate hain."

Radiation damage

I_{0}

bhi raise karta hai (zyada recombination centres), jo

V_{oc}

drop karta hai aur curve ke knee ko round off karta hai,

F F

bhi lower karta hai. Current aur voltage dono sides degrade hoti hain. Dekho Radiation Effects on Materials.

Why questions

I-V curve mein seedhi line ki jagah sharp "knee" kyun hoti hai?

Kyunki diode term

I_{0} e^{V / n V_{T}}

low voltage par negligible hai (flat, current-source region) lekin

V_{oc}

ke paas explode karta hai (steep, diode region); in dono regimes ke beech crossover curve ko bend karta hai, aur sharper knee ka matlab higher fill factor hai. Dekho Semiconductor Physics.

MPPT variable resistor ki jagah DC-DC converter kyun use karta hai?

Resistor mismatch ko sirf heat ke roop mein dissipate kar sakta hai, use waste karta hai; ek buck-boost converter array ki

(V_{m p}, I_{m p})

ko jo bhi

(V, I)

battery ko chahiye usme transform karta hai jabki power minus small switching losses conserve karta hai. Dekho Power Electronics.

Deep discharge shallow cycling se battery par zyada hard kyun hota hai?

Deeper discharge ka matlab electrodes par larger voltage swing hai, jo har cycle mein zyada electrolyte decomposition aur SEI growth drive karta hai; yeh irreversible side reactions lithium consume karti hain aur capacity fade karti hain, toh wear DoD ke saath super-linearly badhta hai.

Cycle-life exponent

k

1 ki jagah 1.5–2 ke around kyun hai?

Exponent 1 ka matlab hota ki wear purely charge moved ke proportional hai; mechanical aur chemical damage (electrode particle cracking, SEI regrowth on fresh surface, cathode metal dissolution) discharge depth se zyada tezi se scale karta hai kyunki deeper swings zyada fresh material expose karti hain aur larger strain per cycle, jo

k

ko 1 se upar push karta hai.

Deep-space missions ke liye solar arrays ki jagah RTGs kyun use hote hain?

Solar intensity Sun se

1/ r^{2}

se girta hai, toh Jupiter se aage flux practical arrays ke liye zyada kam ho jaata hai; RTG ka thermal output sirf radioactive decay par depend karta hai, Sun se distance se independent.

Diode exponential ke andar thermal voltage

V_{T} = k_{B} T / q

kyun appear karta hai?

Yeh natural voltage scale set karta hai iske liye ki thermally-agitated carriers junction barrier ko kitni aasaani se surmount karte hain; temperature

T

par Boltzmann factor

e^{q V / k_{B} T} = e^{V / V_{T}}

govern karta hai ki kitne carriers ke paas enough energy hai, jo exactly Shockley equation mein exponential hai. Dekho Thermodynamics & Heat Transfer.

Power budget mein beginning-of-life aur end-of-life array power separately kyun include karni chahiye?

Array mission ke dauran degrade hota hai (radiation, thermal cycling, micrometeoroids), toh sirf BOL power pe size karne se spacecraft ko saalon baad watts ki kami padti hai; tum array ko is tarah size karte ho ki degraded EOL power abhi bhi demand meet kare.

Edge cases

Full eclipse mein array output power kya hai?

Exactly zero — koi photon nahi matlab

I_{L} = 0

, toh source term vanish ho jaata hai aur cell sirf ek passive (thodi si leaky) diode ki tarah behave kar sakta hai; saari load power battery se aani chahiye.

Jis instant

V = V_{oc}

ho, cell se kitni power nikalta hai?

Zero — by definition open circuit par

I = 0

hai, toh

P = V I = 0

chahe voltage maximum par ho; useful power strictly dono axes ke beech rehti hai.

V_{oc}

ka kya hoga jab temperature absolute zero approach kare (ek limiting thought experiment)?

V_{T} = k_{B} T / q \to 0

aur

I_{0} \to 0

, toh

V_{oc} = n V_{T} ln (I_{L} / I_{0} + 1)

bandgap-limited maximum ki taraf tend karta hai; colder cells higher voltage deti hain, yahi wajah hai ki deep-space panels thande hone par "hot on volts" run kar sakti hain.

Agar DoD ko nearly 100% tak drive kiya jaaye, toh cycle-life formula kya predict karta hai aur yeh dangerous kyun hai?

N \propto DoD^{- k}

minimum possible cycles predict karta hai, aur near 100% real cells safe cutoff se neeche over-discharge ka risk leta hai, jisse copper dissolution aur permanent damage hota hai — isliye designers DoD ko 100% se well below cap karte hain.

MPPT kya karta hai jab illumination itna kam ho ki MPP power converter ki khud ki consumption se bhi kam ho?

Tracking pointless ho jaati hai — array apna khud ka control electronics bhi power nahi kar sakta, toh system battery power par fall back karta hai aur MPPT idle ya shut down ho sakta hai jab tak light wapas na aaye (e.g., eclipse exit karne par).

Agar series string mein ek single cell zero output ke liye shaded ho, toh string ka kya hota hai?

Shaded cell ek reverse-biased load ban jaati hai jo poori series current ko block karti hai aur overheat ho sakti hai (hot-spot); bypass diodes precisely isliye add ki jaati hain taaki current ek dead cell ke around route ho sake toh ek shadow poori string na kill kare.

Ek series string mein partial shading ke saath (kuch cells 50% par, kuch full sun par), string I-V ki kya shape hoti hai?

String current weakest cell se cap hoti hai, toh curve steps aur multiple local power humps develop karta hai — har shading level ke liye ek; ek naive MPPT ek lower local peak par lock ho sakta hai aur true global maximum miss kar sakta hai.

Parallel arrangement mein shading series case se kaise different hai?

Parallel strings voltage share karti hain lekin currents add karti hain, toh ek shaded string simply common voltage par kam current contribute karti hai — koi reverse-bias hot-spot issue force nahi karta, yahi wajah hai ki large arrays series (voltage ke liye) aur parallel (shade-tolerant current ke liye) mix karte hain.

Recall Quick self-audit

Is page ke teen "always true" anchors ko cover-and-recall karo. MPP voltage $V_{oc}$ ke relative ::: Hamesha strictly $V_{oc}$ se kam (interior maximum of $P = V I$ ). $V_{oc}$ light intensity ke saath kaise scale karta hai ::: Logarithmically, linearly nahi — sirf $I_{sc}$ linear hai. Fill factor range ::: Hamesha $0 < F F < 1$ ; higher matlab squarer, better curve.