Question 6 of 8: Solar energy

Question 6: Solar energy (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Descriptive answers are expected in essay form with sketches, at roughly one page for every five marks. Part (a) is answered for the central-receiver system, the option the sketch below illustrates.

(a) Central-receiver system with heliostats

A central-receiver, or power-tower, plant concentrates sunlight optically before it is converted to heat, so that heat can be collected at a temperature high enough to run a conventional steam cycle. The collecting element is a field of heliostats: individually steerable mirrors, typically 100 to 150 square metres each, mounted on two-axis drives that track the sun continuously and reflect the direct beam onto a fixed aiming point at the top of a tower 100 to 200 metres high. Several thousand heliostats are arranged around the tower, densely to the north of it in the northern hemisphere and more sparsely at the edges of the field where the incidence angles and the shading between neighbouring mirrors become unfavourable. Because each mirror tracks independently, the field achieves a geometric concentration ratio of several hundred to one, far beyond anything a single-axis line-focus collector can reach.

The receiver at the aiming point is the heat exchanger of the plant. In the external-tube design it is a cylindrical or cavity array of thin-walled tubes coated black, through which the heat-transfer fluid is pumped at high velocity to keep the tube metal below its creep limit despite incident fluxes of several hundred kilowatts per square metre. The working fluid may be water, in which case the receiver is a once-through boiler, but the dominant modern choice is a molten nitrate salt (a sodium and potassium nitrate eutectic) circulated between a cold tank at about 290 °C and a hot tank at about 565 °C. Salt is used because it is liquid over that entire range at atmospheric pressure, has a volumetric heat capacity comparable with water, and can therefore be stored: several hours of full-load thermal storage in two atmospheric tanks lets the plant generate after sunset and ride through cloud transients, which is the single most valuable feature of the configuration.

The flow diagram is otherwise that of a conventional plant. Hot salt is drawn from the hot tank through a steam generator train — preheater, evaporator, superheater and, in the larger plants, a reheater — raising steam at roughly 12 MPa and 550 °C. The steam expands through a condensing turbine coupled to a synchronous generator, and heat is rejected at the condenser to wet cooling towers or, at desert sites where water is scarce, to air-cooled condensers. Condensate is returned by the feed pumps, and the cooled salt returns to the cold tank to be pumped back up the tower. Heat is therefore received only at the receiver, power is produced only at the turbine-generator, and heat is rejected only at the condenser.

The overall efficiency at optimal radiation is the product of a chain of losses. The heliostat field delivers perhaps 55 to 65 per cent of the incident direct-normal energy to the receiver aperture once mirror reflectivity, cosine losses, blocking, shading, atmospheric attenuation and spillage are counted; the receiver itself loses 10 to 15 per cent by re-radiation and convection from a surface at 565 °C, so it returns about 85 to 90 per cent of what reaches it; and the steam cycle converts 40 to 43 per cent of the collected heat to electricity, with a further 8 to 10 per cent of gross output consumed by the heliostat drives, salt pumps and cooling system. Multiplying these gives a peak solar-to-electric efficiency of roughly 20 to 23 per cent at design-point irradiance, falling to an annual average nearer 15 per cent once off-design hours, start-up and cloud are included. That peak figure is markedly better than a trough plant, which is limited by its 390 °C oil to about 14 to 16 per cent, and it is the direct consequence of the higher concentration ratio the tower geometry permits.

(b) Photovoltaic generating system

A photovoltaic plant converts sunlight directly to direct-current electricity with no working fluid, no moving parts in the conversion step and no heat engine in the chain. The conversion element is a semiconductor diode operated in the fourth quadrant. In a crystalline silicon cell a thin, heavily doped n-type emitter is diffused into a p-type wafer, creating a p-n junction a fraction of a micrometre below the front surface. Diffusion of majority carriers across that junction leaves behind a depleted layer of fixed ionised dopant atoms, and the resulting space-charge region carries a built-in electric field of the order of 0.7 volts.

When a photon whose energy exceeds the silicon band gap of 1.12 electron-volts is absorbed, it promotes an electron from the valence band to the conduction band, creating an electron-hole pair. If that pair is generated within a diffusion length of the junction, the built-in field sweeps the electron toward the n-side and the hole toward the p-side before they can recombine. Charge therefore accumulates on the two contacts and a current flows when an external circuit is connected: the front contact is a fine grid of screen-printed silver fingers and busbars, narrow enough to shade only a few per cent of the surface, and the rear contact is a full-area aluminium layer. Photons below the band gap pass through without contributing at all, and those well above it give up their excess energy as heat within picoseconds; these two mechanisms alone place a theoretical ceiling of about 33 per cent on a single-junction cell, the Shockley-Queisser limit.

One cell of any area produces only about 0.5 to 0.6 volts at maximum power, so the system is built up by aggregation. Sixty to seventy-two cells are connected in series and laminated between glass and a polymer backsheet to form a module rated at 30 to 45 volts and 350 to 550 watts. Modules are wired in series into strings of typically 15 to 30 to reach 600 to 1500 volts direct current, which is the practical limit set by insulation and by electrical safety codes, and strings are paralleled through combiner boxes with string fuses and blocking or bypass diodes to build the array current. Series connection thus raises voltage and parallel connection raises current, and the two together let an arbitrarily large plant be assembled from a half-volt building block; the penalty is that a series string is limited by its worst cell, which is why bypass diodes are fitted across each sub-string to prevent a shaded cell from being driven into reverse breakdown.

The balance of system converts that array output into grid-quality power. A maximum-power-point tracker continuously adjusts the operating voltage to sit at the knee of the current-voltage curve as irradiance and cell temperature change; a grid-tie inverter synthesises three-phase alternating current at the required frequency and power factor, with anti-islanding protection and, in modern grid codes, fault ride-through and reactive support; and a transformer raises the output to distribution or transmission voltage. Overall efficiency at optimal radiation is the module efficiency, 18 to 22 per cent for mainstream crystalline silicon at standard test conditions, reduced by the cell temperature coefficient of roughly −0.35 per cent per kelvin (a cell at 55 °C loses about 10 per cent of its rated output), by 2 to 3 per cent of direct-current wiring and mismatch loss, by 2 to 3 per cent inverter loss, and by soiling. The net alternating-current efficiency of a well-designed plant at full sun is therefore about 15 to 19 per cent — comparable with a solar-thermal tower on a peak basis, though without any inherent storage, which is why photovoltaic plants are increasingly paired with batteries where firm capacity is needed.