22-Mec-B3 Energy Conversion and Power Generation · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 16-Mec-B3 Energy Conversion and Power Generation, National Examinations, December 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 10–12, reference formulae and constants on pages 13–16, 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.
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.
Why storage is wanted at all. Electricity cannot be held in the network; generation must match demand instant by instant, and demand varies by a factor of two or more between the night minimum and the evening peak. Base-load plant — the nuclear station of Question 6 and the coal unit of Question 4 — is capital-intensive and thermally inflexible, and its unit cost falls with capacity factor, so it is worth running flat out. Storage resolves the conflict by absorbing surplus energy when the marginal cost of generation is low and returning it when the marginal cost is high, and its value has grown further as wind and solar have added variability on the supply side as well.
Method one: pumped hydroelectric storage. Here the energy is held as gravitational potential energy of water raised between two reservoirs at different elevations. Off peak, reversible pump-turbines driven as pumps lift water from the lower to the upper reservoir; at peak the same machines run as turbines and the water returns through them to generate. The quantity stored is $E=\rho\,V\,g\,H$, so a 10 million cubic metre upper reservoir at 300 m of head holds $$E=\frac{1000\times 10\times 10^{6}\times 9.81\times 300}{3.6\times 10^{12}} =8.2\ \text{GWh},$$ of which about 7.4 GWh is recoverable — enough to run a 1000 MW unit for seven hours. Pumped storage is the only technology deployed at that scale today, accounting for the overwhelming majority of the world's grid storage, and Canadian examples include the Sir Adam Beck facility at Niagara Falls.
Its limitations are geographic and environmental rather than technical. The site must offer two large reservoirs with a substantial head difference close together, which is rare and is often in terrain of high conservation or recreational value; the civil works are enormous and take several years to build; the upper reservoir's daily filling and drawdown causes shoreline erosion and disrupts aquatic habitat; and the energy stored is capped by reservoir volume, so the plant is characterised by both a power rating and a fixed number of hours of storage. Response is fast in generating mode — seconds from spinning reserve — but slower when starting from standstill in pumping mode. Efficiency is high: modern reversible Francis machines achieve about 90 per cent in each direction, so the round-trip figure is $0.90\times 0.90\simeq 0.81$, and with waterway and transformer losses real plants report 70 to 80 per cent.
Method two: compressed air energy storage. Here the energy is held as the internal energy and pressure of compressed air, usually in a solution-mined salt cavern or a depleted mine at 4 to 8 MPa. Off peak, a motor-driven compressor train charges the cavern; at peak the air is withdrawn, heated by burning natural gas in it and expanded through a turbine. Because the compression work has already been paid for, the expander delivers its full output without the compressor parasitic that consumes more than half a gas turbine's gross output — the back-work ratio of 0.552 computed in Question 1 — so about $1/(1-0.552)=2.2$ times as much electricity is produced per unit of gas as a simple-cycle machine would give. The commercial plants at Huntorf in Germany (290 MW) and McIntosh in Alabama (110 MW) have operated for decades.
The limitations begin with geology: a suitable airtight cavern of the right volume is as site-specific as a pumped-storage reservoir. Diabatic plants of the type built so far still consume fuel and emit carbon dioxide on discharge, which undermines the case for storing renewable energy; adiabatic designs that store the heat of compression in a solid or molten-salt thermal store and reuse it on expansion avoid the fuel but are still at demonstration scale. Cavern pressure falls as air is withdrawn unless a water compensation leg is used, so the machines must tolerate a sliding inlet pressure, and repeated pressure cycling raises long-term cavern-integrity questions. Efficiency is the weak point: the heat of compression is rejected to atmosphere in a diabatic plant, so the electricity-to-electricity round trip is only 40 to 55 per cent, though the effective figure improves to around 70 per cent when the fuel input is credited at the efficiency of the gas turbine it displaces. Adiabatic concepts target 65 to 70 per cent true round trip.
What decides economic viability. A storage plant earns nothing by making energy; it earns by moving energy in time, so the first determinant is the spread between off-peak and peak prices, and it must be wide enough to cover the round-trip loss. If the round-trip efficiency is $\eta_{rt}$, then breaking even on energy alone requires $$p_{peak}\ \ge\ \frac{p_{offpeak}}{\eta_{rt}} ,$$ so 81 per cent efficiency needs a peak price at least 1.23 times the off-peak price and a 45 per cent diabatic plant needs 2.2 times — which is exactly why the low-efficiency technology needs a fuel and capacity credit to be viable at all. The second determinant is utilisation: like the coal plant of Question 4 these are capital-dominated assets whose unit cost is dominated by an annual charge on a large capital sum, so the number of charge and discharge cycles achieved per year matters more than the efficiency. Third is the value of the services beyond arbitrage — capacity payments for firm peak availability, spinning reserve, black-start capability, frequency regulation and the deferral of transmission reinforcement — which in most markets now exceed the arbitrage revenue. Fourth are site cost and lead time, since the civil or geological works dominate the capital and permitting can take a decade. And fifth is the alternative: storage competes against simply building a flexible gas turbine, against demand response, and increasingly against lithium-ion batteries, which are far more expensive per kilowatt-hour of capacity but far cheaper per kilowatt and can be sited anywhere — so batteries take the short-duration, high-power services while pumped storage and compressed air remain the only economic options for shifting bulk energy over many hours.
