22-Mec-B3 Energy Conversion and Power Generation · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 16-Mec-B3 Energy Conversion and Power Generation, National Examinations, May 2018. Three hours, closed book. Two sections: Section A is calculative (Questions 1–5) and Section B is descriptive (Questions 6–8). Candidates answer four questions from Section A and two from Section B; six questions of 10 marks each constitute a complete paper (60 marks). Reference data for individual questions are bound in as attachments on pages 9–15, reference formulae and constants on pages 16–19, and Granet & Bluestein steam tables are supplied. All eight questions are solved below, because the set is a study resource rather than a timed attempt.
Reference texts.
Wherever the paper's own attachments carry a value that duplicates a computed result — the Koeberg terminal temperature difference and back pressure on page 10, the gas-turbine output quoted in the preamble to Question 2, the published rating of the Oconee unit — that printed value is used as an independent check and the agreement is quoted in the answer.
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.
Assumptions stated. Each of the four sources is one quarter of the system maximum capacity, so each block is 25 % of the vertical scale. The load curve reads from a minimum of about 46 % of capacity at 04:00 to a peak of about 92 % between 18:00 and 19:00, and the daily load factor is therefore about 0.75. All plant is assumed available — no unit is on outage — and the pumped storage round-trip efficiency is taken as 75 %, so about 1.33 kWh must be pumped for every kilowatt hour generated. Because the upper reservoir is not on a river, every drop generated must first have been pumped: the scheme is an energy store, not an energy source, and its daily generation is limited by what the system can afford to pump the previous night.
Nuclear: flat base load. A nuclear unit has a very high capital cost and a very low fuel cost, so every hour it spends below full output is money thrown away; it is also the least manoeuvrable plant on the system, with xenon poisoning making a return to power after a deep load reduction slow and awkward. It is therefore run flat out at 25 % of system capacity for all twenty-four hours. This is only possible because the night minimum, 46 %, is comfortably above the nuclear block; had the valley fallen below 25 % the station would have had to be part-loaded or the surplus absorbed by pumping.
Coal: base load with limited two-shifting. Coal is the next cheapest to run and the next least flexible: a large drum boiler needs hours to start from cold and its thermal stresses limit both ramp rate and the number of starts its life can stand. The second quarter of capacity is therefore also carried as base load, taking the combined thermal block to 50 % of capacity, which still sits under the night minimum. If the system had a deeper valley, the correct response would be to reduce coal units to their minimum stable generation, typically 40 % to 50 % of unit rating, rather than to shut them down overnight.
Gas: mid-merit, load following. Gas turbines and combined-cycle units start in minutes, ramp quickly and tolerate frequent cycling, at the price of the most expensive fuel on the system. They are therefore the load-following plant: they pick up the whole of the morning rise from 06:00, follow the daytime plateau, and carry the shoulder of the evening peak, being backed off again overnight. In the shading above, the gas block fills the gap between the 50 % thermal base and the load curve, up to the 75 % line that represents its own full output.
Pumped storage: peaking and night pumping. The hydro plant is reserved for the sharp evening peak above 75 % of capacity, roughly 17:00 to 21:00, where it can be brought from standstill to full load in a couple of minutes and where it displaces the most expensive gas generation of the day. The energy required is the area of the load curve above the 75 % line, which reads from the diagram as about 60 per cent-hours of capacity. Allowing for the round-trip efficiency, roughly 80 per cent-hours must be pumped back, and the only period when there is spare cheap capacity to do it is the night valley between about 23:00 and 05:00, shown hatched. Pumping in those hours has a second benefit: it lifts the night trough, which keeps the coal and nuclear units nearer full load and improves their efficiency and their emissions per unit sent out.
Reserve and the isolated-system constraint. Because the utility has no interconnection, it must carry its own spinning reserve. The schedule above leaves the gas plant part-loaded for most of the day and the hydro machines idle in the pond, which between them provide fast reserve against the loss of the largest unit — here the nuclear station, which is a quarter of the system and therefore the credible worst contingency. That single fact is the strongest argument for keeping the pumped storage reservoir full at the end of each daily cycle rather than exhausting it on the peak: on an isolated system the store is as valuable as reserve as it is as energy.
