Energy systems and markets

Classify these energy sources as renewable or non-renewable, briefly justifying each case: (a) solar, (b) coal, (c) wind, (d) natural gas, (e) hydroelectric, and (f) nuclear.

Explain the difference between primary energy (the source as obtained: sun, gas, uranium) and final energy (the energy you use: electricity at the socket, petrol at the pump), with an example of converting one into the other.

Name three renewable energy sources and write which natural phenomenon each one uses (solar radiation, wind, dammed or flowing water).

Explain with a household example the difference between power (measured in $\text{kW}$) and energy (measured in $\text{kW} \cdot \text{h}$): use the example of a $2000\ \text{W}$ oven switched on for half an hour to illustrate both quantities.

The electricity bill charges for $\text{kW} \cdot \text{h}$. Explain what $1\ \text{kW} \cdot \text{h}$ represents using an example (a $1000\ \text{W}$ appliance running for one hour) and why it is a unit of energy and not of power.

A house has an agreed power capacity of $4{,}4\ \text{kW}$. Calculate whether the oven ($2\ \text{kW}$), washing machine ($2\ \text{kW}$), and ceramic hob ($1\ \text{kW}$) can operate at the same time by adding their power ratings, and explain two practical choices that would prevent exceeding the limit without changing tariff.

The smart electricity meter measures and communicates consumption. Explain what it measures exactly, how often it sends data to the utility company, and one advantage it has over the traditional meter.

The figure shows the chain that carries electricity from where it is generated to a house, but one of the stages is covered with a question mark, as shown in the figure.

Indicate which stage is missing from the chain, explain what happens during it, and reason why that stage is carried out at very high voltages instead of directly at $220\ \text{V}$.

Between the power station and your home there are several transformers. Explain what a transformer does, why voltage is stepped up for transmission and stepped down for consumption (in relation to line losses), and where you have seen transformers in your town or city (substations, distribution kiosks, poles).

A country's 'energy mix' is the breakdown of sources used to generate its electricity. Analyse why this distribution matters so much in three areas: dependence on other countries, price stability, and greenhouse gas emissions, giving an example of a source in each argument.

Time-of-use tariffs divide the day into periods with different prices. Explain how this works, which household appliances should be programmed during off-peak hours (electric water heater, washing machine, dishwasher), and why these appliances can wait while others cannot.

In the day-ahead wholesale electricity market (OMIE), the hourly generation bids arranged by merit order for a specific hour are:

• Nuclear power: $6500\ \text{MW}$ bid at $0\ \text{€/MW}\cdot\text{h}$

• Wind and solar: $11\ 500\ \text{MW}$ bid at $0\ \text{€/MW}\cdot\text{h}$

• Dispatchable hydro: $3000\ \text{MW}$ bid at $48\ \text{€/MW}\cdot\text{h}$

• Combined cycle gas turbine (CCGT) plants: $7000\ \text{MW}$ bid at $95\ \text{€/MW}\cdot\text{h}$

(a) Scenario 1: Hourly demand is $19\ 000\ \text{MW}$. Determine the marginal technology that clears the market, the resulting hourly price ($P_{\text{pool}}$), and the total revenue received by generators in that hour.

(b) Scenario 2: During a heatwave, widespread air conditioning use drives demand up to $22\ 500\ \text{MW}$, and the heat reduces wind output, bringing the combined solar/wind capacity to $7500\ \text{MW}$. Determine the new marginal clearing price and calculate the percentage increase in the price of a $\text{MW}\cdot\text{h}$.

(c) Explain the concept of «inframarginal rents» (or windfall profits) based on the results above, and discuss the technical and market impact of replacing the marginalist system with a Contract for Difference (CfD) auction model.

A bill has a standing charge of $10\ \text{€}$ and a consumption of $250\ \text{kW} \cdot \text{h}$ at $0{,}18\ \text{€}$ per $\text{kW} \cdot \text{h}$. (a) Calculate the total amount excluding tax. (b) Calculate what percentage of the total corresponds to consumption and what percentage to the standing charge. (c) Reason who is affected more by a high standing charge: someone who consumes a lot or someone who consumes very little.

A user states on a forum: "I'm going to install $5\ \text{kWp}$ of photovoltaic panels on the roof of my house without batteries. My home consumes $4800\ \text{kW}\cdot\text{h}$ per year and the installation will produce about $7000\ \text{kW}\cdot\text{h}$ annually. Therefore, thanks to surplus compensation on the bill, my electricity bill will drop to zero euros every month." They only occupy the home in the evenings and nights.

(a) Technically refute their claim by explaining the legal limits of simplified surplus compensation in Spain (energy term limit at €0, inability to compensate for power tolls and taxes) and the problem of the time mismatch between the solar generation curve and the residential consumption curve.

(b) If the energy drawn from the grid costs $0{,}18\ \text{€/kW}\cdot\text{h}$ and the energy retailer compensates injected surpluses at only $0{,}05\ \text{€/kW}\cdot\text{h}$, quantitatively demonstrate why excessive oversizing without storage or load shifting drastically reduces the marginal profitability of each additional panel.

(c) Justify which user profile (a single-family home with daytime remote work versus an apartment block unoccupied during the day) would make better use of the investment without resorting to batteries.

A household consumes $4200\ \text{kW}\cdot\text{h}$ per year, $45\ \%$ of which is concentrated during the central hours of daytime solar radiation and $55\ \%$ during nighttime or twilight hours. A rooftop photovoltaic self-consumption system is planned for a location with an average solar irradiation of $1650\ \text{h}$ of peak sun hours (PSH) per year and an overall system performance ratio ($PR$) estimated at $0{,}80$.

(a) Calculate the peak power ($P_{\text{pico}}$ in $\text{kWp}$) required for the annual photovoltaic production to exactly match the household's daytime consumption ($1890\ \text{kW}\cdot\text{h}$).

(b) Assuming that $80\ \%$ of that produced energy is directly self-consumed and the remaining $20\ \%$ is injected into the grid as surplus compensated at $0{,}06\ \text{€/kW}\cdot\text{h}$, while energy consumed from the grid costs $0{,}19\ \text{€/kW}\cdot\text{h}$, calculate the total financial savings achieved in the first year.

(c) If the turnkey cost of the installation is $1200\ \text{€/kWp}$ installed and the local council grants a property tax (IBI) rebate of $200\ \text{€/year}$ for 4 years, determine the simple payback period of the investment.