Exercises: 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.

List the common energy supplies that reach a home (electricity, gas, etc.) and explain which meter measures the consumption of each and in which unit it is billed.

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.

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.

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.

Agreed power capacity is the maximum power you can use at the same time at home. Explain what happens if you plug in appliances that exceed it (the circuit breaker trips and power is cut) and how the situation is resolved.

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

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.

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 $220\ \text{V}$.

An electricity bill usually includes a standing charge (for the agreed power capacity, even if not used) and an energy usage charge (for the $\text{kW} \cdot \text{h}$ consumed). Explain what each term pays for and analyse what would happen to the bill of a home that contracts a high power capacity but uses very little energy.

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.

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.

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.

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).

Solar energy is cheap but intermittent; gas is expensive but available on demand. Explain what renewable intermittency is and three ways to manage it in the electrical system (pumped-storage reservoirs, batteries, cross-border interconnectors).

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.

Observe the following data from the hourly price curve of the wholesale electricity market on a sunny spring day in Spain: from 02:00 to 06:00 h the average price is $0{,}07\ \text{€/kW}\cdot\text{h}$; between 11:00 and 16:00 h the price plummets to $0{,}00\ \text{€/kW}\cdot\text{h}$ (with hours of negative prices); and between 20:00 and 23:00 h it skyrockets to $0{,}17\ \text{€/kW}\cdot\text{h}$.

(a) Technically justify the emergence of this "duck curve", relating the supply of generation technologies in the mix (non-dispatchable renewables, hydroelectric, combined cycle gas) and demand in each time slot.

(b) A user states: "It is best to schedule the electric water heater ($1{,}5\ \text{kW}$, $3\ \text{h}$ per day) and the slow charging of the electric car ($3{,}7\ \text{kW}$, $4\ \text{h}$) in the early morning, because historically it has always been the cheapest slot." Refute their statement with calculations by comparing the cost of energy consumed in both options, and determine what contracted power limit they must watch out for if they decide to concentrate these consumptions during the minimum price hours.

An isolated rural accommodation located $1{,}8\ \text{km}$ from the nearest electricity distribution grid point requires an electricity and energy supply for heating, domestic hot water (DHW), and cooking. The overhead electrical grid connection quoted by the distributor has a cost of $28\ \text{€/m}$ plus $6500\ \text{€}$ for the transformer substation.

(a) Evaluate the economic feasibility of connecting to the grid versus off-grid solutions.

(b) Powering the heating and DHW exclusively with photovoltaic panels and batteries is ruled out. Technically justify why this option would lead to unfeasible oversizing in winter, analyzing the seasonal correlation between solar resource and thermal demand, as well as the low energy density of electrochemical storage.

(c) Design and justify the most efficient and reliable energy combination for this case (distributing loads between a photovoltaic system with storage, a biomass/pellet boiler, liquefied petroleum gas, and an auxiliary emergency generator set).

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.

A single-family home with a single-phase supply ($230\ \text{V}$) has a contracted power capacity of $6{,}90\ \text{kW}$ and pays an excessive fixed charge. The owner wants to reduce it to $3{,}45\ \text{kW}$ or $4{,}60\ \text{kW}$. The following appliances commonly run at the same time in the house:

• Induction hob (two active zones): $2800\ \text{W}$

• Electric oven: $2200\ \text{W}$

• Washing machine (water heating phase): $1900\ \text{W}$

• Electric water heater: $1500\ \text{W}$

• Refrigerator and permanent standby loads: $350\ \text{W}$

• Heat pump: $1400\ \text{W}$

(a) Calculate the total installed power. If a theoretical diversity factor $K_s = 0{,}6$ is applied, what power demand would result? Explain why blindly relying on this average factor causes nuisance tripping of the power control switch (ICP).

(b) Knowing that digital smart meters apply a thermal trip curve (they can tolerate $10\ \%$ overloads for several hours and $30\ \%$ for approximately $15$ minutes), evaluate with reasoning whether it would be viable to contract $3{,}45\ \text{kW}$ or whether it is technically safer to choose $4{,}60\ \text{kW}$, establishing an appliance usage management protocol to prevent tripping.

The National Integrated Energy and Climate Plan (PNIEC) outlines the phased shutdown of the nuclear fleet in Spain between 2027 and 2035 to transition to a predominantly renewable system.

(a) From an electrical grid engineering perspective, explain why nuclear power plants operate in continuous baseload mode and analyze the technical drawbacks posed by their low flexibility (slow power ramp rates) in a system with massive volumes of intermittent renewable generation during hours of high solar radiation or wind.

(b) If $7000\ \text{MW}$ of firm nuclear capacity is decommissioned, justify technically why it is not sufficient to simply replace it with $7000\ \text{MW}$ of solar PV or wind capacity. In your answer, use the concepts of capacity factor (or plant factor), dispatchability of generation, and the need for spinning reserve in the grid.

(c) Evaluate the technological trade-off between the long-term management and deep geological confinement of high-level radioactive waste (CTS/DGR) versus the dependence on critical raw materials (lithium, cobalt, rare earths) required for alternative seasonal storage.

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 standalone solar photovoltaic system at $24\ \text{V}$ (direct current) is being designed to power a monitoring station and technical shelter with the following alternating current ($230\ \text{V}$) loads:

• Technical refrigerator/freezer: average operating power of $80\ \text{W}$, with a duty cycle of $40\ \%$ of the time over the $24\ \text{h}$ of the day.

• Lighting: $4$ LED luminaires of $15\ \text{W}$ for $5\ \text{h/day}$.

• Telecommunications transmitter and sensors: $45\ \text{W}$ for $24\ \text{h/day}$.

• Tools and auxiliary instrumentation: $600\ \text{W}$ for $30\ \text{min/day}$.

The $24\ \text{V DC} \to 230\ \text{V AC}$ inverter has an average efficiency of $90\ \%$, and wiring and connection losses are estimated at $5\ \%$.

(a) Calculate the required daily useful energy in alternating current ($E_{\text{AC}}$ in $\text{W}\cdot\text{h/day}$) and the total daily energy that the battery bank must supply to the inverter input ($E_{\text{DC}}$).

(b) Lithium iron phosphate (LiFePO4) $24\ \text{V}$ batteries are selected, with a maximum recommended depth of discharge ($DOD$) of $85\ \%$ and a coulombic efficiency of $96\ \%$. Calculate the required nominal capacity ($C_n$ in $\text{A}\cdot\text{h}$) to provide $2$ full days of autonomy without solar radiation.

(c) If the system is located where the worst-case month (December) yields $2{,}5\ \text{PSH}$ (peak sun hours) and the overall PV generator efficiency (temperature, dust, MPPT charge controller) is $0{,}82$, determine the total peak power ($P_{\text{pico}}$ in $\text{Wp}$) required to replenish daily consumption during this critical month, as well as the minimum number of $450\ \text{Wp}$ panels needed.