Parabolic Trough Solar Plant

From sunlight to a hot oil loop

A parabolic trough focuses direct normal irradiance (DNI) onto an absorber tube at the focal line, z = x2/(4f), with f = 1.71 m and a 5.77 m aperture. The troughs lie north-south and rotate east-west to follow the sun. The sun's incidence angle on the aperture is cosθ = √(cos2θz + cos2δ sin2ω) (declination δ, hour angle ω), and at solar noon this reduces to cos(φ - δ), which the numerical checks verify. Clear-sky DNI uses a Meinel/Hottel-type atmosphere with airmass, I = 1.353 e0 [(1 - 0.14 h) 0.7AM0.678 + 0.14 h] and is reduced by haze, clouds and mirror cleanliness.

Optical and thermal efficiency

Optical efficiency is η0 K(θ) with the incidence-angle modifier K = cosθ + 0.000884 θ/cosθ - 5.369e-5 θ2/cosθ (LS-2 type collector, θ in degrees), an end-loss factor 1 - f tanθ/L and low-sun shading. The receiver loses heat as q = 0.141 ΔT + 6.48e-9 ΔT4 W per metre (Dudley et al., LS-2), which is why hotter outlet temperatures cost efficiency. Along a 600 m loop the oil follows dT/dx = (qabs - qloss(T)) / (m cp(T)) with cp = 1.498 + 0.002414 T kJ/kg/K (synthetic-oil type). The controller sets the flow per loop (3 to 12 kg/s) to hold the outlet at the setpoint; if even the minimum flow overheats the oil, mirrors are defocused. Above 15 m/s wind the collectors stow face-down.

Molten-salt storage and dispatch

Surplus heat charges a two-tank system: salt at 292 C is heated to 386 C and held in the hot tank. The energy per kilogram is cp (386 - 292) = 143 kJ/kg with cp = 1.443 + 0.000172 T, so a 7.5-hour 50 MWe store holds about 19 000 tonnes. Three dispatch strategies are offered: solar-first (run whenever heat exists, store surplus), evening peak (store by day, full power 17-24 h) and constant output. The 50 MWe steam block has efficiency 0.385 (0.82 + 0.18 L) and a minimum load of 25 %, derated slightly for hot air. Parasitics (pumps, trace heating, fans) are subtracted to give net power.

Honest simplifications

Each of the 14 rows in the 3D view stands for a group of loops and is drawn shorter than a real 600 m loop. One lumped loop is solved and scaled by the loop count; the oil thermal inertia is a 150 s lag; tank temperatures are constant; heat-exchanger approach temperatures, start-up and warm-up energy, freeze protection, row-to-row shading and the circumsolar radiation are ignored; the block efficiency is a simple load curve. Clear-sky DNI is smooth, clouds are only a slider and an optional 20-minute event. The model resembles a 50 MWe Andasol-type plant for teaching and is not based on any plant's measured data.