Electricity generation

Almost all power stations share three elements. Match each one with its function: (1) turbine, (2) alternator, and (3) transformer, with: (a) converts rotational motion into electrical energy; (b) receives the force of water, steam, or wind and converts it into rotation; (c) steps up the voltage to transmit energy with fewer losses.

Describe the chain of energy transformations in a coal or gas thermal power station, from fuel to the electricity grid: chemical energy, thermal energy of the steam, mechanical energy of the turbine, and electrical energy.

Order the stages of a biomass thermal power plant, which are given out of order: (a) the high-pressure steam drives the turbine; (b) the transformer steps up the voltage; (c) the boiler burns the fuel and heats the water; (d) the alternator generates electricity. Write the complete sequence and name the form of energy at the beginning and end of each stage.

In a nuclear power station, heat is obtained from the fission of uranium atoms, without combustion. Explain what its process has in common with that of a thermal power station (everything that happens after high-pressure steam is generated) and what is different (how the heat is obtained and what waste is produced).

A thermal power plant receives $1.000\ \text{MW}$ in the form of heat from the fuel and delivers $380\ \text{MW}$ of electrical energy. (a) Calculate its efficiency, $\eta = \frac{P_{electrica}}{P_{termica}} \cdot 100$. (b) Explain where most of the lost energy goes (heat transferred to the cooling water and to the atmosphere) and why those cooling towers are so visible.

The figure shows the basic operating diagram of a nuclear power plant.

During an energy audit, the following plant data are recorded: thermal power released in the reactor = $3.000\ \text{MW}_t$; net electrical power injected into the grid = $1.020\ \text{MW}_e$.

(a) A popular science article claims that the equipment marked with "?" performs very poorly because it "wastes almost two thirds of the energy produced by the reactor". Refute this statement technically: identify the actual function of "?", its typical electromechanical efficiency, and explain in which component of the closed circuit (missing from the block diagram) most of that energy is actually rejected, and by which physical law this is unavoidable.

(b) During a heatwave, the temperature of the river cooling the external circuit rises from $18\ ^\circ\text{C}$ to $29\ ^\circ\text{C}$. Predict with reasoning how this warming will affect the maximum theoretical thermal efficiency (Carnot cycle) of the plant and the electrical power it can deliver.

(c) If the nuclear reactor were replaced by a coal-fired or natural gas boiler while maintaining the same thermal input power, explain why a gas-fired thermal power plant can achieve higher overall efficiencies ($> 50\,\%$) than a nuclear plant ($33\,\%\text{-}35\,\%$), taking into account the temperature and pressure limits of steam in both types of reactor/boiler.

Explain what form of energy a reservoir hydroelectric power station uses (the potential energy of water stored at height) and write its chain of transformations up to the electrical grid, pointing out which component converts each form of energy into the next.

A wind turbine uses the kinetic energy of the wind. Write its chain of energy transformations and reason why, unlike a thermal power station, it requires neither a boiler nor steam: the wind directly turns the rotor.

The figure shows the diagram of a reservoir hydroelectric power plant, with an element marked with a question mark, as shown in the figure.

(a) Identify the element marked with the question mark and explain what energy conversion it performs. (b) Write the complete chain of transformations of the plant, from the stored water to the power line. (c) Reason which two factors the power output of the plant depends on (the head height and the water flow rate).

Explain the difference between a photovoltaic solar plant (panels convert light directly into electricity) and a solar thermal power plant (mirrors concentrate sunlight to heat a fluid and drive a turbine). Which of the two is more similar in its process to a conventional thermal power station?

A $400\ \text{W}$ photovoltaic panel receives the equivalent of $5\ \text{h}$ of peak sun per day. (a) Calculate the energy it generates per day, $E = P \cdot t$, in $\text{kW} \cdot \text{h}$. (b) Calculate how many panels would be needed to cover $10\ \text{kW} \cdot \text{h}$ per day. (c) Reason why the calculation uses 'peak sun hours' and not the total hours of daylight.

The figure shows the diagram of a central receiver solar thermal tower power plant.

(a) A designer proposes replacing the thermal receiver, turbine, and equipment “?” with a conventional high-power photovoltaic panel placed at the top of the tower to generate electricity directly and eliminate the thermal loop. Justify two physical and technological limitations (related to temperature and irradiance concentration) explaining why this approach would destroy or severely degrade the silicon cells.

(b) The tower receiver receives a net concentrated radiant power of $90\ \text{MW}_t$. Molten salts with a specific heat capacity $c = 1{,}55\ \text{kJ/(kg}\cdot\text{K)}$ are used as the heat transfer fluid. If the salts enter at $290\ ^\circ\text{C}$ and must exit at $565\ ^\circ\text{C}$, calculate the mass flow rate ($q_m$, in $\text{kg/s}$) that the pump must circulate through the receiver.

(c) The plant has two molten-salt thermal storage tanks with a usable capacity of $6.000\ \text{t}$. Knowing that the efficiency of the power block (turbine + alternator “?”) is $38\,\%$, calculate how many hours the plant can operate at its rated power of $45\ \text{MW}_e$ during the night using exclusively the thermal energy stored between $565\ ^\circ\text{C}$ and $290\ ^\circ\text{C}$.

Nuclear and thermal power are said to be 'baseload' energies and wind power is 'variable'. Explain what it means for a power plant to be dispatchable (it can decide when to generate) as opposed to variable (it depends on the wind or the sun) and reason why an electrical grid needs a combination of both types.

The table shows the expected average electricity demand profile in an isolated system during a winter day:

The grid operator has the following generation fleet available:

• Nuclear: $10.000\ \text{MW}$ installed (variable cost $14\ \text{€/MWh}$; start-up time over 24 hours; zero flexibility to modulate power rapidly).

• Combined-cycle gas turbines: $14.000\ \text{MW}$ installed (variable cost $68\ \text{€/MWh}$; start-up in $1\text{-}2\ \text{h}$).

• Reservoir hydroelectric plants: $6.000\ \text{MW}$ maximum turbining capacity (stored energy in water limited to a maximum of $24.000\ \text{MWh}$ per day; start-up under 3 minutes).

• Pumped-storage plant: pumping capacity $2.500\ \text{MW}$ and round-trip storage cycle efficiency of $72\,\%$.

(a) Design the hourly dispatch plan for each time slot (specifying how much power each technology should provide), minimising the total economic cost while respecting the water availability and flexibility limits of each plant.

(b) Demonstrate with an economic balance whether it is cost-effective to use the pumped-storage plant during the early morning to turbine that water during the evening peak, replacing natural gas.

(c) At 15:00, demand unexpectedly rises by $2.000\ \text{MW}$ in under 5 minutes. Justify which technology must immediately take on this power step and why it is not technically feasible to assign it to the nuclear power plant.

A power plant generates an active power of $150\ \text{MW}$ that must be supplied to a distribution center located $90\ \text{km}$ away. The transmission line is a two-wire line, and each of the two conductors has a linear ohmic resistance of $0{,}075\ \Omega/\text{km}$ (total round-trip resistance: $R_T = 2 \cdot 90 \cdot 0{,}075 = 13{,}5\ \Omega$). Assume a unity power factor ($\cos \varphi = 1$).

(a) If you tried to transmit this power directly at the output voltage of the plant's alternators, $V_1 = 15\ \text{kV}$:

1. Calculate the current that would have to flow through the line ($I_1 = P / V_1$).

2. Calculate the power that would be dissipated by the Joule effect ($P_{\text{pérdidas}} = I_1^2 \cdot R_T$).

3. Physically interpret the result obtained and justify why it is impossible to carry out transmission at that voltage.

(b) To solve the problem, a step-up transformer substation is installed to raise the line voltage to $V_2 = 400\ \text{kV}$:

1. Calculate the new current ($I_2$) and the power dissipated by the Joule effect in the line.

2. Determine the percentage of power lost in transmission relative to the injected power.

3. Calculate the voltage drop along the line ($\Delta V = I_2 \cdot R_T$) and the actual voltage arriving at the receiving substation.

(c) A student suggests: “To reduce losses even further, we should always transmit at voltages of around $1.500\ \text{kV}$ or higher on all transmission and distribution lines”. Technically refute their proposal by analyzing the dielectric breakdown limits of air (corona effect), the costs and footprint/volume of insulators and transformers, and the required safety clearances.