Agricultural Engineering · Energy, Structures & Environment · also Renewable Energy, Renewable Power Sources, Solar Energy Engineering, Wind Energy Engineering
Solar thermal, solar PV, wind and micro-hydro for farms, from sun geometry to sizing a solar pump.
In the exams: GATE AG Section 3 (solar PV in 5 of 8, wind in 5 of 8 papers 2019–26); ICAR AIEEA-PG Unit V; ICAR AICE subject 42 Units 4, 5 and 7; NCEES PE energy sources
Renewable energy sources, as taught in agricultural engineering, are the energy flows that nature replenishes on a human time scale — sunlight, wind and falling water — and the machines that turn them into heat, electricity and shaft work on farms and in rural industries. This subject covers solar thermal devices (collectors, dryers, cookers, water heaters and stills), solar photovoltaics from the physics of the cell to the sizing of a solar pump, wind turbines and water-pumping windmills, micro-hydro plants, and the storage that lets an intermittent source meet a steady load. Biomass and biofuels have their own subject.
Farms use energy in awkward places: a tube well far from a reliable grid, a dryer needed exactly at harvest, a diesel pump burning fuel whose price the farmer cannot control. Solar pumps, dryers, small wind and micro-hydro are now ordinary engineering choices that an agricultural engineer must size, test and judge on cost.
India's GATE Agricultural Engineering paper asks short numerical questions on the PV fill factor, module efficiency, power in the wind and the Betz limit; ICAR's AIEEA-PG covers solar and wind energy under Unit V; ICAR's AICE-JRF/SRF paper goes deeper; licensure exams such as the Philippine ABE board and the NCEES PE Agricultural and Biological Engineering exam expect a candidate to size a PV array or a solar pump and to compare energy options on cost. Nearly every question reduces to a handful of equations used with careful units.
Energy is the capacity to do work, measured in joules (J). Power is the rate of energy flow, measured in watts (W, joules per second). The distinction matters in every calculation in this subject: a solar module is rated in watts, but a farmer pays for, and a crop needs, energy delivered over time, usually counted in kilowatt-hours (1 kWh = 3.6 MJ). Solar radiation is reported both as irradiance, an instantaneous power per unit area (W/m²), and as irradiation or insolation, the energy per unit area over an hour or a day (MJ/m² or kWh/m²). Large statistics use the tonne of oil equivalent (1 toe = 41.868 GJ, IEA convention).
Primary energy is energy as found in nature; final energy is what reaches the user (electricity, diesel, hot water); useful energy does the task (water lifted, grain dried). Efficiencies in a chain multiply: a 20% efficient PV module feeding a 90% controller and a 45% efficient motor-pump set delivers only about 8% of the incident solar energy as hydraulic energy.
Conventional sources (coal, oil, gas, uranium) are stocks, used faster than they form; renewable sources (sun, wind, hydropower, biomass, geothermal, tides) are flows. Solar and wind are intermittent, of low energy density, and capital-heavy with zero fuel cost; these three facts shape every design decision in this manual.
Fossil fuels still supply the large majority of the world's primary energy — roughly four-fifths in recent International Energy Agency statistics — but solar PV and wind have been the fastest-growing sources of new electricity capacity for more than a decade, because their costs fell steeply. Hydropower remains the largest renewable source of electricity worldwide. Shares, capacities and targets change every year; take them from the latest IEA, IRENA or national-ministry report.
Countries organise renewable energy policy differently. India has a Ministry of New and Renewable Energy (MNRE), which runs programmes such as PM-KUSUM for solar pumps and solarisation of agricultural feeders, and a stated national goal of 500 GW of non-fossil electricity capacity by 2030. Elsewhere feed-in tariffs, auctions, net metering, capital subsidies or tax credits are used; the mechanism decides whether a farm system sells power, replaces purchased power or stands alone. Know the tools in outline, not rates that will be out of date by the exam.
Energy enters agriculture directly, as diesel for tractors and pumps and electricity for pumps, dryers, cold stores and processing, and indirectly, as the energy used to make fertiliser, pesticides and machinery. Irrigation pumping is the largest direct electrical use on farms in much of South Asia; drying, cold storage and milling follow.
Water pumping suits solar PV well: the load is flexible within the day, water can be stored in a tank or the soil instead of electricity in batteries, and demand peaks in the dry, sunny season. Drying suits solar thermal collectors because it needs low-temperature heat (typically 40–70 °C for most crops). Remote lighting and fencing suit small PV or wind with batteries; hilly regions with perennial streams suit micro-hydro.
Energy auditing compares energy input with output using equivalents from a stated, cited table (they vary by source and country). An audit is the natural first step before any renewable project: reducing waste (a badly matched pump, a leaking pipeline) is almost always cheaper than generating new energy.
The earth's axis is tilted about 23.45° to the plane of its orbit, so the angle between the sun's rays and the equatorial plane — the solar declination δ — swings from +23.45° at the June solstice to −23.45° at the December solstice, passing zero at the equinoxes. The usual textbook approximation (Cooper's equation) is δ = 23.45 sin[360(284 + n)/365] degrees, where n is the day of the year (n = 1 on 1 January). For n = 172 (21 June) it gives +23.45°; for n = 355 it gives −23.45°. Declination is positive when the sun is north of the equator.
The hour angle ω measures the sun's position east or west of the local meridian: the earth turns 360° in 24 hours, so ω changes by 15° per hour, ω = 15(ts − 12), with ts in solar hours. It is zero at solar noon, negative in the morning and positive in the afternoon (the common convention; some books reverse it).
Solar time is not clock time. Local apparent (solar) time = standard time ± 4(Lst − Lloc) + E, in minutes, where Lst is the longitude of the standard meridian, Lloc the local longitude, and E the equation of time, a correction of up to about a quarter of an hour caused by the eccentricity of the orbit and the tilt of the axis. In the eastern hemisphere the longitude term is subtracted when the site lies west of the standard meridian; for India, with a standard meridian of 82.5° E, a site at 77.2° E has solar time about 21 minutes behind Indian Standard Time before E is applied.
For a site of latitude φ (positive north), the zenith angle θz between the sun's rays and the vertical is given by cos θz = sin φ sin δ + cos φ cos δ cos ω. The solar altitude α is its complement, α = 90° − θz. At solar noon ω = 0 and the expression reduces to θz = |φ − δ|, so the noon altitude is 90° − |φ − δ|. At 28.6° N on the June solstice (δ = 23.45°) the noon altitude is about 84.9°; a common mistake is to add φ and δ, which gives 38° and puts the midsummer sun absurdly low.
The solar azimuth angle γs gives the sun's compass direction, measured from south in most solar-engineering texts (zero due south, east negative, west positive) and from north in navigation and many software packages.
Setting cos θz = 0 gives the sunset hour angle, ωs = cos⁻¹(−tan φ tan δ), and the day length N = 2ωs/15 hours. At 30° N on the June solstice ωs is about 104.5° and the day length about 13.9 hours. Day length is 12 hours at the equator all year and everywhere at the equinoxes. Air mass m, the relative path length of the beam through the atmosphere, is approximately 1/cos θz for zenith angles up to about 70°; m = 1 with the sun overhead, and the standard spectrum for rating PV modules is air mass 1.5, which corresponds to a zenith angle of about 48°.
The angle of incidence θ between the beam and a surface normal depends on latitude, declination, hour angle, tilt β and surface azimuth. For the common case of a surface facing due south in the northern hemisphere (or due north in the southern), the equation simplifies because the surface is parallel to a horizontal surface at latitude (φ − β): cos θ = sin(φ − β) sin δ + cos(φ − β) cos δ cos ω. At noon this gives θ = |φ − β − δ|.
The beam tilt factor Rb is the ratio of beam radiation on the tilted surface to that on a horizontal surface, Rb = cos θ / cos θz. On a winter noon at 30° N with δ = −20°, a surface tilted at 40° gets θ = 10° and θz = 50°, so Rb = cos 10° / cos 50° ≈ 1.53: the tilted collector receives about half as much beam energy again as a horizontal one.
Rules of thumb follow from the geometry. A fixed collector used all year is tilted at about the latitude; one used mainly in winter at about latitude + 10–15°; one used mainly in summer at about latitude − 10–15°. These are starting points; local cloud, diffuse fraction and load profile shift the optimum. Single- and two-axis trackers keep θ small and raise collected beam energy at the cost of moving parts.
The solar constant is the irradiance on a surface normal to the sun's rays just outside the atmosphere at the mean sun–earth distance. Most agricultural-engineering texts use 1367 W/m², the World Meteorological Organization value adopted in 1981; older books use 1353 W/m², and more recent satellite measurements give about 1361 W/m². Because the orbit is slightly elliptical, the extraterrestrial normal irradiance varies through the year as I0n = Isc[1 + 0.033 cos(360n/365)], about 3.3% above the mean in early January and 3.3% below in early July.
Passing through the atmosphere, radiation is absorbed (by ozone, water vapour, carbon dioxide) and scattered (by air molecules and aerosols). What reaches the ground arrives as beam (direct) radiation from the sun's disc and diffuse radiation from the rest of the sky. Their sum on a horizontal surface is global radiation. Clear-sky noon global irradiance is typically near 1000 W/m²; on overcast days nearly all is diffuse.
The daily extraterrestrial radiation on a horizontal surface, H0, is found by integrating the instantaneous value from sunrise to sunset: H0 = (24 × 3600/π) Isc [1 + 0.033 cos(360n/365)] [cos φ cos δ sin ωs + (π ωs/180) sin φ sin δ]. It depends only on latitude and date (tabulated in FAO Paper 56). The clearness index KT = H/H0 compares what actually arrived with what arrived at the top of the atmosphere.
A pyranometer measures global radiation on a plane from the whole hemisphere of sky. The common type has a thermopile under one or two glass domes: blackened hot junctions heat up in sunlight relative to cold junctions, producing a small voltage proportional to irradiance. With a sensitivity of, say, 10 µV per W/m², an output of 8.5 mV means 850 W/m². Pyranometers are graded by ISO 9060 into classes (the 2018 edition names them A, B and C, replacing the older 'secondary standard', 'first class' and 'second class'). Cheaper silicon-cell pyranometers respond to only part of the spectrum and are less accurate.
With a shadow band a pyranometer measures diffuse only. A pyrheliometer measures beam (direct normal) radiation: it is a tube with a small aperture angle (about 5° in modern instruments) pointed at the sun by a tracker. Global, beam and diffuse are linked by G = Gb cos θz + Gd, which is used to cross-check the three instruments.
The Campbell–Stokes sunshine recorder uses a glass sphere to focus the sun onto a card, which is scorched when the sun is bright enough; the length of the burn trace gives the hours of bright sunshine n. The World Meteorological Organization defines sunshine duration as the time during which direct normal irradiance exceeds 120 W/m².
Where radiation is not measured, the Ångström–Prescott relation estimates daily global radiation from sunshine hours: H/H0 = a + b(n/N), where n is the measured bright-sunshine hours and N the day length. The constants depend on climate and are fitted to local data; FAO Paper 56 recommends a = 0.25 and b = 0.50 when no local calibration exists. With H0 = 35 MJ/m² per day and n/N = 0.7, H ≈ 35 × (0.25 + 0.35) = 21 MJ/m² per day. Satellite datasets such as NASA POWER give daily radiation anywhere, with some error against ground data.
Design needs radiation on the tilted collector, not on the horizontal. The isotropic-sky model of Liu and Jordan adds three parts: beam, HbRb; diffuse from an isotropic sky, Hd(1 + cos β)/2; and ground-reflected, ρg H(1 − cos β)/2, where ρg is the ground reflectance (albedo), commonly taken as about 0.2 for ordinary ground and much higher for fresh snow. The diffuse part must first be separated from measured global using an empirical correlation of the diffuse fraction with KT. Anisotropic models (Hay–Davies, Perez) are more accurate and used in simulation software.
For PV and solar pump sizing, daily insolation in kWh/m² is numerically equal to peak sun hours (PSH): the number of hours of 1000 W/m² that would deliver the same energy. A site with 5.5 kWh/m² per day on the array plane has 5.5 PSH. Converting between units, 1 kWh/m² = 3.6 MJ/m², so 18 MJ/m² per day is 5 PSH.
A flat-plate collector heats water, antifreeze or air to moderate temperatures (losses grow large above about 80–100 °C). It uses beam and diffuse radiation, needs no tracking, and is the workhorse of water heating and crop drying. Its parts are a transparent cover (usually low-iron toughened glass), an absorber plate with a black coating, fluid passages (tubes bonded to the plate in a liquid collector; ducts or channels in an air heater), back and edge insulation, and a weather-tight casing.
The cover transmits short-wave sunlight but blocks long-wave emission from the absorber and suppresses convection. The absorber should have a high solar absorptance α and, ideally, a low thermal emittance ε. Ordinary black paint has both near 0.9. A selective surface (black chrome, black nickel, sputtered cermets) keeps α above about 0.9 while cutting ε to about 0.1 or lower. Evacuated-tube collectors remove the air around the absorber, nearly eliminating convective loss, for higher temperatures or cold climates.
The transmittance–absorptance product (τα) is the fraction of incident radiation absorbed by the plate. With τ = 0.88 and α = 0.95 it is about 0.84.
The steady-state energy balance of a collector is: useful gain = absorbed solar − heat lost. Per unit area the absorbed flux is S = (τα)G, and the loss is UL(Tp − Ta), where UL is the overall loss coefficient (W/m²K) and Tp the mean plate temperature. Plate temperature is hard to measure, so the equation is rewritten using the fluid inlet temperature Ti through the heat removal factor FR (the ratio of actual useful gain to the gain if the whole plate were at the inlet temperature): Qu = Ac FR [S − UL(Ti − Ta)]. This is the Hottel–Whillier–Bliss equation. FR is less than one; it rises with fluid flow rate and with good thermal contact between plate and tubes (captured by the collector efficiency factor F′ and the fin efficiency).
Instantaneous efficiency is η = Qu/(Ac G) = FR(τα) − FR UL (Ti − Ta)/G. Plotted against the reduced temperature (Ti − Ta)/G, this is a straight line. The intercept FR(τα) is the optical efficiency — the efficiency when the collector runs at ambient temperature and has no losses. The slope is −FR UL. For a collector with FR(τα) = 0.75 and FR UL = 5 W/m²K, running with inlet 20 K above ambient at 800 W/m², η = 0.75 − 5 × 20/800 = 0.625.
When no fluid is drawn off, useful gain is zero and the plate reaches its stagnation temperature, found by setting η = 0: Ti − Ta = FR(τα)G/(FR UL). For the collector above at 800 W/m² that is 120 K above ambient, a useful check on material and safety limits.
In a test, efficiency is found from the fluid side: Qu = ṁ cp (To − Ti). A water flow of 0.02 kg/s heated by 10 K (cp = 4186 J/kg K) gives 837 W; on a 2 m² collector at 700 W/m² this is an efficiency of about 60%.
Collectors are tested to standards such as ISO 9806 (international), ASHRAE 93 (United States) and, in India, the Bureau of Indian Standards specification for flat-plate collectors (IS 12933). The steady-state test runs the collector at several inlet temperatures near solar noon under clear sky, measures flow rate, inlet and outlet temperatures, irradiance and ambient temperature, and fits the efficiency line; a time-constant test and an incidence-angle-modifier test complete the characterisation. Modern reports often fit a second-order curve in the mean fluid temperature Tm; check whether a line uses inlet or mean temperature before comparing collectors.
The overall loss coefficient UL is the sum of top, bottom and edge coefficients. Top loss dominates and depends on covers, emittance, wind and plate temperature; bottom loss ≈ insulation conductivity / thickness. A collector is most efficient when its fluid is coldest, so stratified tanks should return their coldest water; selective surfaces pay only well above ambient, and a single-glazed black collector suits low-temperature duties such as drying air. Air heaters have lower plate-to-air heat transfer, hence lower FR, improved with fins or roughened plates.
A flat-plate collector loses heat from the same area that absorbs sunlight, so its efficiency falls rapidly as temperature rises. A concentrating collector gathers sunlight over a large aperture and focuses it onto a small receiver; since heat loss scales with receiver area, higher temperatures become possible with acceptable efficiency. The geometric concentration ratio C is the aperture area divided by the receiver (absorber) area. For a parabolic trough of aperture width 2 m focusing onto a tube of 5 cm outer diameter, the absorber area per metre is πD = 0.157 m², so C = 2/0.157 ≈ 12.7; dividing by the diameter alone (giving 40) is a common error.
The sun is not a point: its disc subtends a half-angle of about 0.27°. This sets thermodynamic upper limits to concentration: about 1/sin θs ≈ 215 for a line-focus (two-dimensional) concentrator and 1/sin² θs ≈ 46,000 for a point-focus (three-dimensional) concentrator. Real devices achieve far less because of mirror errors and tracking errors. Concentrators focus only beam radiation. A low-concentration compound parabolic concentrator (CPC) with a wide acceptance angle can collect some diffuse radiation and may need only seasonal adjustment; higher concentrations need continuous tracking.
The gain is paid for in optics. Optical efficiency is the product of mirror reflectance, intercept factor (fraction of reflected rays hitting the receiver), transmittance and absorptance; dust cuts it quickly. Concentrators therefore suit clear, sunny sites with high direct normal irradiance and are poor in hazy or cloudy climates where the diffuse fraction is large.
Line-focus concentrators include the parabolic trough, a curved mirror that focuses onto an evacuated receiver tube along its focal line and tracks the sun about one axis; the linear Fresnel reflector, which uses rows of nearly flat mirror strips to approximate a trough; and the CPC. Point-focus concentrators include the paraboloidal dish, which tracks on two axes and focuses onto a receiver at its focal point, and the central receiver (solar tower), where a field of individually tracking mirrors called heliostats focuses onto a receiver on a tower. Troughs typically run at a few hundred degrees Celsius; dishes and towers reach much higher temperatures.
Concentrated solar power stations use troughs or towers to raise steam, often with molten-salt storage; in agro-industry concentrators supply process steam, for example for dairy cleaning and pasteurisation. The Scheffler reflector, a paraboloid section rotating about an axis parallel to the earth's so that its focus stays fixed in a kitchen, is widely used for community cooking in India. For drying and water heating a non-concentrating collector is almost always the right choice.
Open sun drying on the ground is the oldest and cheapest method, but produce is exposed to rain, dust, birds, insects and uneven, sometimes excessive heating, and quality suffers. A solar dryer encloses the crop and raises air temperature to speed moisture removal. Direct (cabinet) dryers expose the crop to sunlight through a transparent cover; the crop itself absorbs radiation. Indirect dryers heat air in a separate collector and pass it through a drying chamber where the crop is shaded, which protects colour and vitamins in fruits and vegetables. Mixed-mode dryers combine the two. Natural-convection dryers rely on buoyancy through a chimney; forced-convection dryers use a fan, often PV-powered, giving better control. Greenhouse and tunnel dryers handle bulk batches.
Sizing starts from the water to be removed. For a product of initial mass Wi dried from wet-basis moisture Mi to Mf, the water removed is Wi(Mi − Mf)/(1 − Mf): 100 kg at 80% wb dried to 10% wb loses 77.8 kg of water, not 70 kg. The heat needed is roughly the water removed times the latent heat of vaporisation (about 2.4 MJ/kg at drying temperatures; bound water needs more). The collector area follows from area = energy needed / (drying efficiency × daily insolation × drying days). Drying efficiencies of simple solar dryers are low and vary widely with design and load, so a measured value for the dryer type is used.
The box-type solar cooker is an insulated box with a blackened tray, a double-glazed lid and usually one reflector mirror; pots are painted black. It reaches roughly 100–140 °C on a clear day, enough to boil, bake and slow-cook, and needs little attention, but cooking is slow. The dish (parabolic) cooker concentrates sunlight onto the pot bottom, reaches frying temperatures and cooks fast but needs frequent re-aiming and care to avoid eye glare.
Box cookers are tested by thermal figures of merit (the Mullick method, adopted in the Indian standard IS 13429). The first figure of merit, F1 = (Tps − Tas)/Hs, is measured with the cooker empty at stagnation: Tps is the stagnation plate temperature, Tas the ambient temperature and Hs the insolation on a horizontal surface at that time. With Tps = 120 °C, Tas = 30 °C and Hs = 900 W/m², F1 = 0.10 °C m²/W. F1 reflects the optical efficiency divided by the heat loss coefficient — a higher F1 means a better-insulated, better-glazed cooker. The second figure of merit, F2, is measured with a water load and reflects heat transfer to the pot.
Domestic and farm solar water heaters use flat-plate or evacuated-tube collectors with an insulated storage tank. In a thermosiphon (natural circulation) system the tank sits above the collector: water heated in the collector becomes less dense and rises to the tank while cooler water from the bottom of the tank sinks to the collector inlet, with no pump. Forced-circulation systems use a pump controlled by a differential thermostat and allow the tank to be placed anywhere. In frost-prone areas an antifreeze loop with a heat exchanger, or a drain-back design, prevents freezing.
The load sets the size. To heat 100 litres of water from 20 °C to 60 °C needs 100 × 4.186 × 40 ≈ 16.7 MJ. With a daily insolation on the collector of 18 MJ/m² and a daily system efficiency of 50%, the collector area is 16.7/(0.5 × 18) ≈ 1.9 m². Dairies and food processors use it for cleaning water and boiler feed pre-heating.
A basin-type solar still is a shallow blackened tray of saline or brackish water under a sloping glass cover. Sunlight heats the water, which evaporates; vapour condenses on the cooler underside of the glass, runs down to a collecting channel, and is drawn off as distilled water. Salts remain in the basin, which must be flushed periodically. The daily output per unit area is approximately the still efficiency times daily insolation divided by the latent heat of vaporisation. With efficiency 35%, insolation 20 MJ/m² per day and latent heat 2.35 MJ/kg, output is about 3.0 kg/m² per day — in the range of 2–3 litres per square metre that simple basin stills commonly give on clear tropical days. So 30 litres of drinking water per day needs about 10 m² of basin.
Output rises with shallower water depth, better insulation, a cover angle close to the local latitude for year-round use and good sealing against vapour leaks.
A photovoltaic (PV) cell converts light directly into electricity. It is a semiconductor p–n junction: a thin n-type layer (doped with a group V element such as phosphorus, giving free electrons) on p-type material (doped with a group III element such as boron, giving holes). At the junction, diffusion of carriers sets up a depletion region with a built-in electric field. A photon with energy greater than the band gap Eg can lift an electron from the valence band to the conduction band, creating an electron–hole pair; if the pair is generated within or near the depletion region, the field separates it, and the separated charges drive current through an external load.
Photon energy E = hc/λ, conveniently E (eV) = 1240/λ (nm). Crystalline silicon has Eg ≈ 1.12 eV, so photons with wavelength longer than about 1100 nm pass through unused; photons with much more energy than the gap waste the excess as heat. These two losses set a theoretical ceiling for a single-junction cell, the Shockley–Queisser limit, of about 33% under the standard solar spectrum. Other absorbers include GaAs (Eg ≈ 1.42 eV), thin-film CdTe and CIGS, amorphous silicon and perovskites; multi-junction cells stack band gaps to beat the limit.
Commercial modules are mostly crystalline silicon; use the datasheet efficiency, which changes with each product generation.
An illuminated cell behaves like a current source (the light-generated current IL) in parallel with a diode, with a series resistance Rs and a shunt resistance Rsh. The single-diode model is I = IL − I0[exp(q(V + IRs)/(nkT)) − 1] − (V + IRs)/Rsh, where I0 is the diode saturation current, n the ideality factor (1 to 2), k Boltzmann's constant, T the absolute cell temperature and q the electron charge. The thermal voltage kT/q is about 25.9 mV at 300 K.
Three points define the curve. At short circuit (V = 0) the current is Isc ≈ IL, proportional to irradiance. At open circuit (I = 0), for an ideal cell, Voc = (nkT/q) ln(IL/I0 + 1): for IL = 3 A and I0 = 10⁻⁹ A at 300 K this gives about 0.56 V. Voc rises only logarithmically with irradiance. Between them lies the maximum power point (Vmp, Imp), where the product V × I is greatest.
Temperature affects the curve strongly. As the cell warms, Voc falls — by about 2 mV per °C per silicon cell — while Isc rises slightly, so power falls. Crystalline silicon modules typically lose about 0.3–0.5% of maximum power per °C above 25 °C; the datasheet gives the exact coefficient. Cell temperature in the field is estimated from the nominal operating cell temperature (NOCT, measured at 800 W/m², 20 °C ambient and 1 m/s wind): Tc = Ta + (NOCT − 20)G/800; a module with NOCT 45 °C in 35 °C air at 1000 W/m² runs at about 66 °C, and a 250 W module with a −0.4%/°C coefficient then delivers about 209 W.
Modules are rated at standard test conditions (STC): 1000 W/m², cell temperature 25 °C and air mass 1.5 spectrum. Cells are connected in series to raise voltage (36 cells of 0.6 V give an open-circuit voltage of about 21.6 V) and strings in parallel to raise current. Bypass diodes across groups of cells stop a shaded cell from being driven into reverse bias and overheating (a hot spot); blocking diodes stop reverse current into a string or from a battery at night.
The fill factor measures how 'square' the I-V curve is: FF = (Vmp × Imp)/(Voc × Isc). A module with Vmp = 17.2 V, Imp = 4.65 A, Voc = 21.6 V and Isc = 5.0 A has Pmax = 80.0 W and FF = 80.0/108 = 0.74. Good crystalline silicon modules have fill factors of roughly 0.7–0.8 or a little higher; series resistance and low shunt resistance reduce it. Conversion efficiency is η = Pmax/(G × A): the 80 W module with an area of 0.65 m² at 1000 W/m² is 12.3% efficient.
A load connected directly to a module operates where the load line crosses the I-V curve, which is usually not the maximum power point, and the maximum power point moves with irradiance and temperature. A maximum power point tracker (MPPT) is a DC–DC converter (or the front end of an inverter or pump drive) that continuously adjusts the operating voltage so the array works at its maximum power point. Common algorithms are perturb and observe (change the voltage a little, keep going in the direction that raises power) and incremental conductance, which uses the fact that at the maximum power point dP/dV = 0, which is equivalent to dI/dV = −I/V. Simpler methods set the voltage at a fixed fraction of Voc or the current at a fixed fraction of Isc. Partial shading creates several local peaks, needing a periodic global sweep.
A pulse-width-modulation (PWM) charge controller simply connects the array to the battery, forcing the array to operate near battery voltage; it is cheap and adequate when module and battery voltages match. An MPPT controller can take a higher-voltage array and convert the power down to battery voltage, harvesting more energy, especially in cold weather and with long cable runs.
A grid-connected (on-grid) PV system feeds its output through an inverter into the utility network. It usually has no battery: the grid absorbs surpluses and supplies deficits. Grid-tied inverters must disconnect when the grid fails (anti-islanding), so an ordinary on-grid system gives no power in an outage. Metering arrangements differ: under net metering the meter runs backwards when the system exports and the customer pays for net consumption; under gross metering (feed-in tariff) all generation is sold at a set price and all consumption bought separately. The arrangement and its prices come from the national regulator and change over time.
An off-grid (stand-alone) system has an array, a charge controller, a battery bank, and an inverter if AC loads are served. A hybrid system adds a diesel generator, wind turbine or grid backup. Directly coupled systems (array to DC pump, no battery) are the simplest.
Losses come from temperature, dust (soiling), module mismatch, cable resistance, inverter conversion, shading and ageing (degradation, commonly taken as around half a per cent to one per cent per year for crystalline silicon).
Annual energy from a grid-connected array is estimated as E = P × PSH × 365 × PR, where P is the array rating at STC (kWp), PSH the average daily peak sun hours on the array plane and PR the performance ratio, the fraction of ideal output that actually reaches the grid after all losses. PR is commonly about 0.75–0.85. A 5 kWp system at a site with 5.0 PSH and PR 0.75 gives about 6,840 kWh per year.
The capacity utilisation factor (CUF), or capacity factor, is actual annual energy divided by the energy the plant would give running at rated power all year: CUF = E/(P × 8760). For the system above, CUF = 6,840/(5 × 8760) ≈ 15.6%. Fixed-tilt PV plants in sunny regions commonly report capacity factors in the mid-teens to low twenties per cent; trackers raise it.
Designers often install somewhat more DC array than inverter AC rating (DC/AC ratio above one), accepting a little midday clipping. The string voltage must stay within the inverter's MPPT voltage window at the hottest and the coldest expected cell temperatures: Voc rises in cold weather and must not exceed the inverter's maximum input voltage.
Off-grid sizing begins with a load table: each appliance's power, hours of use per day and the resulting daily energy in watt-hours. The total daily energy, divided by the product of the component efficiencies (inverter, battery round trip, wiring), gives the energy the array must deliver. Array size in watts-peak = daily energy required / (PSH × derating factor), where the derating factor combines temperature, soiling and mismatch losses. For a load of 3 kWh per day, 5 PSH and an overall derating of 0.7, the array needs about 860 Wp. Use the PSH of the worst month the system must serve, not the annual average.
Battery capacity in ampere-hours = (daily energy × days of autonomy)/(allowable depth of discharge × system voltage), sometimes also divided by battery and temperature efficiency factors. For 3 kWh per day, 2 days of autonomy, a 50% allowable depth of discharge (typical for lead-acid to preserve cycle life) and a 24 V system, the bank needs 500 Ah. Forgetting the depth of discharge gives 250 Ah and a bank that dies in months. Lithium iron phosphate batteries tolerate much deeper discharge, commonly 80% or more, so the same duty needs fewer ampere-hours.
The charge controller is rated above array short-circuit current (a margin of about 1.25 is common) and the inverter for simultaneous loads plus motor-starting surge. System voltage rises (12, 24, 48 V) with load to keep currents manageable.
A solar pumping system has a PV array, a controller (with MPPT and, for AC motors, a variable-frequency drive), a motor–pump set and usually a water storage tank instead of a battery. Pumps are surface (centrifugal, for suction lifts within about 6–7 m in practice) or submersible (multistage centrifugal or helical-rotor positive displacement, for boreholes). Motors are DC (often brushless permanent-magnet) or AC induction on a drive. Centrifugal pumps suit high flow at low to moderate head; positive displacement pumps suit low flow at high head and keep good efficiency at low speed, which matters in morning and evening sun.
Sizing follows the hydraulic energy. Daily hydraulic energy = ρgVH, where V is the daily water volume and H the total dynamic head (static lift plus drawdown plus friction and minor losses). For 50 m³ per day at 30 m, the hydraulic energy is 1000 × 9.81 × 50 × 30 = 14.7 MJ, or 4.09 kWh. Dividing by the subsystem efficiency (motor-pump-controller, perhaps 40% for a small system) gives the electrical energy, 10.2 kWh, and dividing by PSH (say 5) gives an array of about 2.0 kWp, before temperature and soiling derating. A quick rule is: array Wp ≈ 2.725 × V(m³/day) × H(m) / (PSH × ηsubsystem), since 1 m³ lifted 1 m needs 2.725 Wh.
Output peaks at noon, so drip irrigation with a tank matches well. Size for the critical month. Free pumping energy risks groundwater over-extraction; letting farmers sell surplus solar power to the grid gives an incentive to save water.
Agri-voltaics (agrivoltaics) is the use of the same land for crop or livestock production and PV generation. Modules are elevated above crops, set in rows with crops between, mounted vertically as bifacial fences, or placed over grazed pasture. It rests on light saturation: many crops cannot use full midday sun, and partial shade can cut leaf temperature and water stress.
The standard measure is the land equivalent ratio (LER), borrowed from intercropping: LER = (crop yield under the agri-voltaic system / crop yield on an equal area of open field) + (electricity from the agri-voltaic system / electricity from an equal area of ground-mounted PV). If a system gives 80% of the open-field crop yield and 70% of the electricity of a conventional solar farm on the same area, LER = 1.5: one hectare does the work of one and a half hectares used separately. An LER above one means the combined system uses land more efficiently.
Design variables are module height (clearance for machinery, typically several metres for elevated systems), row spacing and the ground coverage ratio (module area divided by ground area), module orientation, and crop choice. Shade-tolerant crops such as leafy vegetables, some herbs and some fruits respond well; sun-demanding crops can lose substantial yield. Shading benefits are larger in hot, dry regions. Structures cost more than ground-mounted PV, and land-use rules differ by country.
The kinetic energy of air moving at speed V through an area A normal to the flow arrives at a rate P = ½ρAV³ (mass flow ρAV times ½V²). Doubling wind speed multiplies power by eight; a 20% higher wind speed gives 73% more power. For a rotor of 10 m diameter (A = 78.5 m²) at 8 m/s with ρ = 1.225 kg/m³, the power in the wind is about 24.6 kW. Air density ρ = p/(RT), R = 287 J/kg K, is 1.225 kg/m³ at sea level and 15 °C and falls with altitude and temperature.
Wind speed rises with height because of friction at the ground. The power law V2/V1 = (h2/h1)^α with α ≈ 1/7 for open, flat terrain is the usual textbook model; α is larger over rough terrain such as forests and towns. Raising a hub from 10 m to 50 m in open terrain raises mean speed by about 26% and power by about 99% — the reason turbine towers are tall.
Wind speed varies continuously, and because power follows the cube, the mean of the cubes is larger than the cube of the mean. The statistical distribution of hourly wind speed is usually fitted with a Weibull distribution of shape factor k and scale factor c; with k = 2 it becomes the Rayleigh distribution, used when only the mean speed is known. For a Rayleigh distribution the mean power density is 6/π ≈ 1.91 times ½ρV̄³ (1.91 is the energy pattern factor).
A turbine cannot stop the air completely — the air must leave to make room for more. Actuator-disc (momentum) theory treats the rotor as a disc that slows the wind from V1 far upstream to V2 far downstream. The axial induction factor a is the fractional slowing at the disc, where the velocity is V1(1 − a); far downstream it is V1(1 − 2a). The power coefficient, the fraction of wind power extracted, is Cp = 4a(1 − a)². Setting dCp/da = 0 gives a = 1/3: the air at the rotor is slowed to two-thirds, and far downstream to one-third, of the free-stream speed. The maximum is Cp = 16/27 ≈ 0.593. This is the Betz limit, and it holds for any open rotor, independent of design.
Real rotors fall short because of wake rotation, tip losses and blade drag. Good modern three-bladed turbines reach peak rotor power coefficients of roughly 0.45–0.5; the gearbox, generator and converter losses reduce the overall electrical figure further. Traditional multi-blade water-pumping windmills reach roughly 0.3 at their best. Useful power is P = Cp × ½ρAV³ × ηmechanical × ηelectrical. For the 10 m rotor at 8 m/s with Cp = 0.4, shaft power is about 9.9 kW.
Horizontal-axis wind turbines (HAWT) dominate electricity generation. Their blades are aerofoils driven mainly by lift, and they must be yawed to face the wind. Vertical-axis turbines accept wind from any direction: the Darrieus type uses lift on curved or straight blades, while the Savonius type is a drag machine of two or more half-cylinders with high starting torque but a low power coefficient. The tip speed ratio, λ = ωR/V = πDN/(60V), compares blade-tip speed with wind speed. High-solidity rotors (many blades covering much of the swept area, as in American multi-blade windmills) run at low λ, around 1, and give high starting torque — ideal for a reciprocating pump that must start under load. Low-solidity three-bladed rotors run at λ of about 6–8, with low torque and high speed, suiting generators.
A turbine's power curve shows output versus wind speed: nothing below the cut-in speed, a steep rise to the rated power at the rated speed, a flat region where output is held at rated power by pitch or stall control, and shutdown at the cut-out speed to protect the machine in storms. The capacity factor = annual energy/(rated power × 8760 h). Onshore wind farms commonly report about 20–40%. A 250 kW turbine giving 547,500 kWh per year has a capacity factor of 25%.
Water-pumping windmills drive a reciprocating (piston) pump through a crank and pump rod. Pump and rotor match well only near the design speed; above it, the windmill furls (turns out of the wind) by a tail vane mechanism to protect itself. Delivered water is Q = P/(ρgH), where P is rotor power times the pump and transmission efficiency. A 3 m multi-blade windmill with Cp 0.3 in a 4 m/s wind, and 60% pump-transmission efficiency, lifting against 10 m head delivers about 1.8 m³ per hour. Turbine design classes are set by IEC 61400-1.
Hydropower output is P = ρgQHη, where Q is flow (m³/s), H is net head (m) and η the overall efficiency of turbine, drive and generator. A flow of 0.1 m³/s through a net head of 20 m with 60% overall efficiency gives about 11.8 kW. Size classes are not universal: a common convention calls plants up to 100 kW micro-hydro and those from about 100 kW to 1 MW mini-hydro (India's MNRE puts the mini limit at 2 MW), with 'small hydro' extending to 10 MW or 25 MW depending on the country.
Most micro-hydro schemes are run-of-river: a low weir diverts part of the stream into an intake with a trash rack, a headrace channel carries water along the contour at a gentle slope to a forebay (a settling tank), and a penstock pipe drops the water steeply to the powerhouse. A tailrace returns the water to the stream. Gross head is the vertical drop from forebay water level to turbine (or tailwater); net head subtracts friction and fitting losses in the penstock, which designers commonly try to keep to around a tenth of the gross head by choosing the pipe diameter economically.
Flow is measured by the bucket method for very small streams, by a temporary weir or notch, by velocity–area methods (a current meter, or floats whose surface speed is multiplied by a correction factor, often about 0.8, to give mean velocity), or by salt dilution. Design flow is chosen from a flow-duration curve (percentage of time a flow is equalled or exceeded); a smaller design flow gives higher load factor, a larger one more wet-season energy.
Impulse turbines convert all the head to velocity in a nozzle before the jet strikes the runner in air: the Pelton wheel (buckets split by a central ridge) suits high head and low flow; the Turgo and the crossflow (Banki–Michell) turbine suit medium heads, and the crossflow is widely built in small workshops for micro-hydro. Reaction turbines run full of water with pressure falling across the runner: the Francis turbine suits medium heads and the propeller and Kaplan (with adjustable blades) suit low heads and large flows. The specific speed, Ns = N√P / H^(5/4), groups turbines: it is lowest for Pelton, intermediate for Francis and highest for propeller and Kaplan machines. Numerical ranges depend on the units used for P (kW or metric horsepower), so always check the units of any table. Pumps run in reverse (pump-as-turbine) are a cheap option for steady small flows.
A stand-alone micro-hydro generator must hold frequency steady as village load changes. Instead of a mechanical governor adjusting water flow, most small plants run the turbine at full flow and use an electronic load controller (ELC), which diverts surplus power to a ballast (dump) load such as a water or air heater so that the total electrical load, and hence speed and frequency, stays constant.
Traditional Himalayan water mills (gharats) grind grain by direct drive; improved mills add better runners and generators. Micro-hydro runs day and night with long life and low running cost; its limits are seasonal flow, costly civil works, sediment and floods, and water-rights rules that differ by country.
Storage moves energy from times of surplus to times of need and smooths short fluctuations. Batteries are rated in ampere-hours at a stated discharge rate; stored energy is voltage times capacity, so a 12 V, 150 Ah battery holds 1.8 kWh nominal, of which only 0.9 kWh is usable at 50% depth of discharge (DoD). The C-rate expresses current relative to capacity: discharging a 100 Ah battery at C/10 means 10 A for about 10 hours. Lead-acid capacity falls at high rates (Peukert effect) and in cold.
Lead-acid batteries (flooded or valve-regulated sealed types, 2 V nominal per cell) are cheap, recyclable and familiar, but heavy, sensitive to deep discharge and partial charge, and have round-trip efficiencies around 75–85%. Lithium-ion batteries, especially the lithium iron phosphate chemistry favoured for stationary storage (3.2 V nominal per cell), accept deeper discharge, give many more cycles, have round-trip efficiencies above 90% and need a battery management system to protect each cell. Cycle life of every chemistry falls as depth of discharge rises, so the design DoD is an economic choice between capacity bought and years of life.
Pumped hydro is by far the largest bulk storage worldwide; compressed air and hydrogen are others. Pumped hydro stores E = ρgVhη: 1000 m³ raised 50 m holds 136 kWh, of which about 100 kWh returns at 75% round-trip efficiency. On a farm the cheapest storage is often a water tank or a precooled cold store.
Solar thermal systems store heat. Sensible-heat storage raises the temperature of a material: Q = mcpΔT. Water has a high specific heat (4.186 kJ/kg K) and is the usual medium for liquid systems; 1 m³ of water heated through 40 K stores about 167 MJ, or 46.5 kWh. Rock beds and gravel store heat from air collectors in dryers and buildings. Latent-heat storage uses phase-change materials (PCMs) such as paraffin wax or salt hydrates that melt near the working temperature, storing much more heat per unit mass over a narrow temperature range; they are used to extend drying into the evening and to hold solar cooker temperatures. Thermochemical storage is mostly at pilot scale.
Renewable systems exchange fuel cost for capital cost, so their economics depend on the cost of money and the life of the equipment. Simple payback period = initial investment / annual net savings: a system costing 300,000 currency units that saves 60,000 per year pays back in 5 years. It ignores the time value of money and is a screening tool only.
Discounted methods treat money properly. The present worth of a future amount F after n years at discount rate i is F/(1 + i)ⁿ. Net present value (NPV) sums the present worth of all savings minus all costs over the project life; a positive NPV means the project earns more than the discount rate. The internal rate of return is the discount rate that makes NPV zero. The capital recovery factor, CRF = i(1 + i)ⁿ/[(1 + i)ⁿ − 1], converts a present capital cost into an equal annual payment; at 10% over 20 years CRF ≈ 0.1175.
The levelised cost of energy (LCOE) is the constant price per kWh that recovers all costs over the life: LCOE = (CRF × capital cost + annual O&M) / annual energy. A system costing 1,000,000 with annual O&M of 10,000 and annual output of 15,000 kWh has LCOE ≈ (117,460 + 10,000)/15,000 ≈ 8.5 per kWh at 10% over 20 years. LCOE is compared with the grid tariff or diesel cost per kWh, then tested for sensitivity to discount rate, resource and subsidy.
Energy payback time is a different measure: the years a system must run to generate the energy used to make it. For modern PV it is a small fraction of system life.
Learn the few equations that carry most marks until they are automatic: declination and hour angle, noon altitude, Rb, the Hottel–Whillier–Bliss efficiency line, FF and module efficiency, Voc from the diode equation, ½ρAV³ with Cp and the Betz limit, tip speed ratio, ρgQH for pumps and hydro, PV and battery sizing, and CRF. For each, write the units beside every symbol and practise the classic slips: using radius as diameter, forgetting depth of discharge, using 70 kg instead of 77.8 kg of water removed, taking absorber tube area as its diameter. Know the instruments, the collector and dryer types, and the turbine types by head and solidity. Be able to explain in words why each formula has the form it has.
A practising engineer uses this subject to design and verify real systems: sizing a solar pump for a borewell from the crop water requirement, total dynamic head and critical-month insolation; checking a vendor's PV array and controller against the pump curve; sizing a solar dryer for a farmer-producer organisation's chilli or turmeric harvest; setting out a small off-grid system for a dairy chilling unit; or assessing a stream for micro-hydro with a bucket or float test. Typical decisions are array size versus tank size, DC or AC pump, lead-acid or lithium storage, fixed tilt or tracking, and whether a subsidy's equipment rules fit the site. Field tasks include commissioning tests, reading I-V curves to find shaded or faulty strings, and training operators to clean modules.
After 25 years an engineer manages programmes and portfolios rather than single systems: specifying tenders for thousands of solar pumps with performance guarantees, setting minimum water output per kWp and test protocols, deciding feeder-level solarisation versus individual pumps, planning agri-voltaic pilots with agronomists, and auditing the energy and groundwater outcomes of subsidy schemes. Judgement lies in the trade-offs a textbook does not settle: over-extraction risk from free solar pumping, after-sales service in remote districts, grid-integration limits on rural feeders, and the life-cycle cost of batteries. Such an engineer also writes the design norms and checklists that younger engineers follow, and must keep them aligned with national standards as they are revised.
A researcher with long field experience works where the standard equations stop: validating tilted-surface and satellite radiation models against ground data in hazy or dusty climates; modelling the coupled crop–microclimate–PV system in agri-voltaics and measuring real land equivalent ratios over several seasons; developing MPPT and pump-drive control for partial shading and variable head; designing low-cost thermal storage with phase-change materials for dryers; and studying degradation of modules and batteries in hot, humid farm conditions. Such work also covers the political economy of energy–water–food linkages, such as how pricing solar electricity changes groundwater use, and techno-economic and life-cycle assessment to guide policy. Rigorous uncertainty analysis and openly published field data are expected.
This manual gives no current installed capacities, tariffs, subsidy rates or national targets beyond one widely reported Indian goal, because they change every year; take them from IEA, IRENA or the national ministry. Numerical ranges for turbine specific speed are not tabulated because they depend on the unit system, and grade thresholds for solar cooker figures of merit in IS 13429 are not quoted. Detailed collector heat-transfer analysis (fin efficiency, Klein's top-loss equation, F′ and FR derivations), diffuse-fraction correlations, blade-element momentum theory, wind turbine structural design, grid codes, and detailed electrical protection design are described in outline only. Biomass, biogas, gasification and liquid biofuels are covered in the separate Bio-energy Systems subject, and psychrometry for dryers in the post-harvest subjects.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions. Every numerical answer was computed by script and the working is shown in the explanation.
These notes are free to read here, with no account.
What the Laisha app adds:
Free for ten days, then a subscription. We would rather write that here than have you find it later.