Master GreenBee : Integrated RE(Equation Sheet)

Solar cells: Structure, role of the different layers (absorbers, selective layers, contacts,..)
 Semiconductors, p-type, N-type,
 Origin of the BSF and FSF (PN junction, N+N and P+P junctions),
 Current voltage of P-N junction in the dark,
 Absorption of light in SC, Absorption depth and thickness of the absorber
 Number of photons absorbed/unit surface/unit time, and maximum current density,
 recombination, life time and diffusing length
 I-V characteristics of Solar cell under light: parameters, Isc, Voc, Vmpp, Impp, Pmpp, efficiency,
 Effect of irradiance and temperature. Temperature coefficients of Voc, P, I…
 Technologies: generations, architectures: PERC, PERL, PERT, TOPCON, Bifacial, HIT, Back contact..)

PV modules: Why modules? Number of cells, type of connection, Currents and voltages, by-pass diodes and role,
 STC conditions, NOCT conditions,
𝐺𝑔𝛽
 Cell temperature: 𝑇𝑐 = 𝑇𝑎 + (𝑁𝑂𝐶𝑇 − 20)
𝐺𝑁𝑂𝐶𝑇
 Types (semi-transparent, flexible, thin films, bifacial, CPV, BIPV), STC parameters..
Solar field: types (fixed, tracking), distances between rows, protection of strings (fuse), type of installation south facing, east-
west

PV Power Production(simple model: can also use I-V curve)

𝐺𝑔𝛽
 DC power produced by PV array (or solar cell): 𝑃𝐷𝐶 (𝑇, 𝐺) = 𝜂𝑟 ∗ 𝑃𝑐 ∗ , 𝐺𝑔𝛽 =POA Irradiance, Pc=peak power
𝐺𝑟𝑒𝑓
 𝜂𝑟 = 𝑘 𝑇 ∗ 𝑘𝑔 : relative efficiency (relative to STC: 𝜂𝑟 = 𝜂𝑖 /𝜂𝑆𝑇𝐶 )
 𝑘 𝑇 = [1 + 𝛼𝑝 (𝑇𝑐 − 𝑇𝑟𝑒𝑓 )](temperature)
 kg product of other factors reducing efficiency (IAM, soiling, mismatch, tolerance,……)
𝐺𝑔𝛽
 𝑇𝑐 = 𝑇𝑎 + (𝑁𝑂𝐶𝑇 − 20)
𝐺𝑁𝑂𝐶𝑇
𝐺𝑔𝛽
 𝑃𝐴𝐶 (𝑇, 𝐺) = 𝜂𝐴𝐶 𝑃𝐷𝐶 (𝑇, 𝐺) = 𝜂𝐴𝐶 𝜂𝑟 ∗ 𝑃𝑐 ∗ ,
𝐺𝑟𝑒𝑓

Bifacial
𝑃𝑚𝑎𝑥,𝑟
 Bifacially factor: 𝜑𝑝max = Equivalent irradiance: 𝐺𝐸 = 𝐺𝑓 + 𝜑𝐺𝑟
𝑃𝑚𝑎𝑥, 𝑓
Concentration (CPV)
 𝑃𝐷𝐶 (𝐶) = 𝑃𝐷𝐶 (𝐶 = 1) ∗ C*(1+ 𝑛𝑉𝑇 ln(𝐶) /𝑉𝑜𝑐), VT=kT/q, n ideality factor, C concentration factor

Estimating PV Energy Production (daily) Performance indicators PV plant (for a given period):
𝐻𝑔𝛽/ 𝐻𝑔𝛽
 DC production: 𝐸𝐷𝐶/𝑗 = 𝜂𝑅 ∗ 𝑃𝐶 ∗  Reference yield: 𝑌𝑅 =
𝐺𝑆𝑇𝐶 𝐺𝑆𝑇𝐶
𝐸𝐷𝐶
 Relative energy efficiency: 𝜂𝑅 = 𝑘𝑔 ∗ 𝐾𝑇  Array yield: 𝑌𝐴 = = 𝜂𝑅 𝑌𝑅
𝑃𝑐
𝐻𝑔𝛽/𝑗
 AC production: 𝐸𝐴𝐶/𝑗 = 𝜂𝐴𝐶 𝜂𝑅 ∗ 𝑃𝐶 ∗  Final yield: 𝑌𝐹 =
𝐸𝐴𝐶
= 𝜂𝐴𝐶 𝜂𝑅 𝑌𝑅
𝐺𝑆𝑇𝐶 𝑃𝑐
 AC efficiency:  = *(1-AC losses/100)  Performance ratio : 𝑃𝑅 =
𝑌𝐹
= 𝜂𝐴𝐶 𝜂𝑅 =
𝜂𝑠𝑦𝑠𝑃𝑉
AC o
𝑌𝑅 𝜂𝑆𝑇𝐶

Inverters: types, characteristics, difference between off-grid and on-grid inverters

Compatibility rules (inverter) (see specs of other devices to be connected)
𝑈𝑀𝑃𝑃𝑇,min 𝑈𝑀𝑃𝑃𝑇,𝑚𝑎𝑥
 𝑁𝑠,𝑚𝑖𝑛 = 𝐸 + ( ) 𝑁𝑠,𝑚𝑎𝑥 = 𝐸 − ( )(number of panels in a string)
0.85∗𝑉𝑚𝑝𝑝 1.25∗𝑉𝑚𝑝𝑝
𝑰𝒎𝒂𝒙
 𝑵𝒑 = 𝑬 ( ), (number of strings in //); Imax: max current /MPPT input
𝟏.𝟐𝟓∗𝑰𝒄𝒄
 0.9< Pc/PAC-nom< 1.2 (choose DC/AC >=1.1) peak power of the PV field connected to the inverter)

On-grid and off grid systems, Topologies of standalone system

BOS
Battery bank sizing:
Sizing battery for a given DC energy needs BEJ/day and Nj days of autonomy
 Cn= Nj*BEJ/(b DOD Vs ) avec (n =24*Nj)
 Vs system Voltage, DOD : depth of discharge, b : battery efficiency (include charge controller efficiency)
Sizing battery and PV for a given DC consumption during the day: Ej and at Night En (obtained from the load curve)
 Daily DC PV production Epv= Ej +En/b+((Ej + En)/ b)*Na)/Nr
 Battery bank Capacity : Es=(En+((Ej + En))*Na/ (b *DOD)=C*Vs
 b=roundtrip efficiency of the battery system (battery and charge controller)
 Accurate sizing requires optimization of LPSP(loss of load probability) and costs
 Master GreenBee : Integrated RE(Equation Sheet)

Transmission, reflection and absorption of light

1 1 tan2 (𝜃′−𝜃) sin2 (𝜃′−𝜃) 𝑛2 −𝑛1 2
Reflection at an interface, incidence angle  : 𝑅(𝜃) = (𝑅∥ + 𝑅⊥ ) = ( + ) , 𝑅(𝜃 = 0) = ( )
2 2 tan2 (𝜃′+𝜃) sin2 (𝜃′+𝜃) 𝑛2 +𝑛1
Law of refraction : 𝑛1 sin(𝜃) = 𝑛2 sin( 𝜃′) (n1=1 for air and n2=n for glass
(Spectral) Transmittance, réflectance, absorptance, emissivity (meaning)

Transmission  of slab of thickness d (ex. Glass), including multiple refelxion

𝑑
1−𝑅 1
𝜏 ≈ 𝜏𝑎 , , 𝜏𝑎 = 𝑒 −𝛼𝑎(𝑐𝑜𝑠𝜃) (a=1 for non-absrbing glass), 𝜏 = (𝜏⊥ + 𝜏// )
1+𝑅 2
Consequence : transmission of glass depends on incidence angle (effect more pronounced for  >=50°)  efficency of PV, solar thermal
(IAM) as well solar gains vary with the indence angle (

Characteristics of glasses/windows
Solar transmittance Tsol, Visible Transmittance TV, UV transmittance, IR-transmission??(Greenhouse effect), Color Rendering index, Solar
Heat Gain Coefficient, SHGC= e + qi =eg +Nig , Heat loss coefficient of glass (Ug) and of the window Uw, double glazing..
Solar gain control
 Internal or external shading solutions
 Absorbing (tinted), reflecting glasses, low-e coatings, double/triple glazing
 Smart windows/glasses: Electrochromic, Suspended Particle Devices SPD, liquid crystals; photochromic,
thermochormic
 Heat reflectors
Solar Thermal
Flat plate collector
 Useful power transferred to the fluid: 𝑄̇𝑢 = 𝐴𝐹𝑅 [(𝜏𝛼)𝐺 − 𝑈𝐿 (𝑇𝑓,𝑖 − 𝑇𝑎 )] = 𝐴[(𝜏𝛼)𝐺 − 𝑈𝐿 (𝑇𝑝 − 𝑇𝑎 )] =
𝑚̇𝑐𝑝 [𝑇𝑓,𝑜 − 𝑇𝑓,𝑖 ] = 𝜂𝐴𝐺
 G=POA Irradiance, 𝜂 collector efficiency, useful Power, FR=heat removal factor, Tfj=inlet fluid temperature, Ta
ambient temperature, Tfo : fluid outlet temperature, Tp : absorber mean temperature, UL overall loss factor of
collector, (𝜏𝛼) absorbance-transmittance product: optical efficiency 𝜂𝑜 (can also include IAM)
Concentrators
𝑄̇𝑢 = 𝐹𝑅 [𝐴𝑜 (𝜂𝑜 )𝐺𝑏 − 𝐴𝑟 𝑈𝐿 (𝑇𝑓,𝑖 − 𝑇𝑎 )] = [𝐴𝑜 𝜂𝑜 𝐺𝑏 − 𝐴𝑟 𝑈𝐿 (𝑇𝑝 − 𝑇𝑎 )] = 𝑚̇𝑐𝑝 [𝑇𝑓,𝑜 − 𝑇𝑓,𝑖 ] = 𝜂𝐴𝑜 𝐺𝑏
 Ar: receiver surface area, Ao aperture area, C=Ao/Ar : centration factor (take into consideration: reflection of
mirror𝜌, intecepation factor𝛾, ..in the optical efficiency 𝜂𝑜 = 𝜌𝛾 𝜏𝛼 also include the IAM..Gb: beam Irradiance.
𝑑(𝑇𝑠 )
Energy balance of the storage (no stratification): 𝑐𝑝 𝑉𝑠𝑡 = 𝑞𝑠 − 𝑞𝑠𝑡_𝑙𝑜𝑠𝑠 − 𝑞𝑠𝑡𝐿_𝑛𝑒𝑡
𝑑𝑡
 𝑞𝑠𝑡_𝑙𝑜𝑠𝑠 = 𝐴𝑠𝑡 𝑈𝐿𝑠𝑡 [ (𝑇𝑠 − 𝑇𝑒𝑛𝑣 )] (Losses of the reservoir,
+
 𝑞𝐿𝑠𝑡_𝑛𝑒𝑡 = 𝑚𝑠𝑡
̇ 𝑐𝑝 [ (𝑇𝑠 − 𝑇𝑅 ) ], 𝑞𝑠 = 𝐴𝑐 𝐹𝑅 [𝐺𝑡 (𝜏𝛼) − 𝑈𝐿 (𝑇𝑠 − 𝑇𝑎 ) ]

𝑄 𝑄
 SF = 𝐿𝑠 =1− 𝑎𝑢𝑥
𝑄 𝑄
𝐿 𝐿
Biomass: Definitions, valorization (combustion, pyrolysis, gasification, methanation..), efficiency of boilers, air-fuel ratio
Geothermal: Definitions, evolution of the soil temperature with depth, passive and active techniques, air-sol exchangers,
Canadian Wells,

Wind energy: Wind power, conversion chain, efficiency, types of wind turbine, wind speed measurements, effect of
height, classes, frequencies, Weillbul distribution, average speed, electric Powers vs wind speed characteristics,
evaluation of the energy production of wind turbine, Wind energy systems