Exercises: Sustainable consumption and energy saving

The energy label on household appliances rates them with letters from A to G. Explain what information this label provides and why a class A appliance can end up being cheaper than a class G appliance even if it costs more to buy.

Propose three simple actions to save energy in a home (lighting, heating/air conditioning, appliance use, etc.) and explain for each one why it saves energy and which quantity is reduced (power, operating time, losses, etc.).

Explain what standby power consumption is in appliances, why it is sometimes called 'phantom load', and describe two practical ways to eliminate it at home without giving up using the appliances.

An electricity bill does not charge for 'watts' but for '$\text{kW} \cdot \text{h}$'. Explain with an example the difference between the power rating of an appliance and the energy it consumes (a $800\ \text{W}$ microwave used for 15 minutes versus a $10\ \text{W}$ light turned on all day).

Appliances that produce heat are the biggest energy consumers. Name three typical 'power guzzlers' in a home (oven, electric heating, hot water heater, tumble dryer) and explain why electrical heating elements consume so much energy.

Many household appliances have an "eco" programme. Explain what this programme usually changes (lower temperature, longer duration, less water) and why it saves energy even though it takes longer to finish.

An appliance on standby consumes between $1\ \text{W}$ and $5\ \text{W}$ without doing anything useful. Explain how it is possible for it to consume energy while "turned off" (plugged-in power supply, indicator lights, waiting for the remote control signal) and how this power consumption can be eliminated completely.

Insulation is the primary measure for energy savings in heating and air conditioning. Explain what insulating a home means and name two areas through which the most heat escapes in winter (windows and shutter boxes, roof, exterior walls), giving a simple measure for each.

An incandescent light bulb of $60\ \text{W}$ is replaced with an LED bulb of $9\ \text{W}$ that provides the same amount of light, used for $5\ \text{h}$ a day for $30$ days. (a) Calculate the monthly energy consumed by each, in $\text{kW} \cdot \text{h}$ ($E = P \cdot t$). (b) Calculate the monthly savings in euros if the price is $0{,}20\ \text{€}$ per $\text{kW} \cdot \text{h}$. (c) Comment on why the savings from LED bulbs are so significant when there is barely any noticeable difference in lighting.

The figure compares the monthly electricity consumption of several household appliances, as shown in the figure.

(a) Read the monthly consumption of each appliance from the graph. (b) Calculate how much energy the fridge consumes in a full year. (c) The fridge consumes a lot of energy even though its power rating is modest, whereas the oven is very powerful but consumes less per month: explain this apparent contradiction and reason which two appliances energy-saving efforts should be focused on.

Propose a short "audit" of phantom energy consumption (standby power) in your home: how you would locate the appliances that consume the most on standby (observation, plug-in energy monitor, meter), which appliances you suspect would top the list, and what specific measures you would implement after measuring.

An electric water heater of $1500\ \text{W}$ operates for $3\ \text{h}$ a day. (a) Calculate its monthly consumption in $\text{kW} \cdot \text{h}$ (30 days). (b) Calculate its monthly cost at $0{,}20\ \text{€}$ per $\text{kW} \cdot \text{h}$. (c) Calculate the monthly savings if usage is reduced to $2\ \text{h}$ per day and comment on how this reduction can be achieved (timer, lower setpoint temperature).

A tumble dryer of $2500\ \text{W}$ is used for $1\ \text{h}$ per load, 12 times a month. (a) Calculate its monthly consumption and cost at $0{,}20\ \text{€}$ per $\text{kW} \cdot \text{h}$. (b) Compare this with hanging out clothes to dry (almost zero energy cost) and reason in which situations using the tumble dryer is justified (damp winter, lack of space, allergies) even if it costs money.

The energy label of one washing machine indicates $220\ \text{kW} \cdot \text{h}$ per year and another indicates $160\ \text{kW} \cdot \text{h}$. (a) Calculate the annual cost of each at $0{,}20\ \text{€}$ per $\text{kW} \cdot \text{h}$. (b) Calculate the savings over a 10-year lifespan. (c) Reason how you would use these figures alongside the purchase price to choose between the two.

It is estimated that every degree lower in the heating setpoint saves around $7\ \%$ in energy. If a family spends $100\ \text{€}$ a month on heating, calculate the approximate monthly savings of lowering the thermostat from $22\ ^\circ\text{C}$ to $20\ ^\circ\text{C}$ and comment on what comfort measures offset those two degrees (warm clothing, blankets, draught excluders).

"Leaving the mobile phone charger plugged in uses a huge amount of energy." Put this into context with numbers: an idle charger consumes between $0{,}1\ \text{W}$ and $0{,}5\ \text{W}$. Calculate the annual cost in the worst-case scenario at $0{,}20\ \text{€}$ per $\text{kW} \cdot \text{h}$ (a year has $8760\ \text{h}$) and conclude where energy-saving efforts should be directed (heating appliances, standby of many appliances simultaneously) as opposed to actions with minimal impact.

A user claims: “My 10-year-old refrigerator still works perfectly, but it consumes $380\ \text{kW} \cdot \text{h}/\text{año}$. I am going to throw it away today to buy a class A one ($130\ \text{kW} \cdot \text{h}/\text{año}$, $600\ \text{€}$) because that way I will save money and immediately reduce my ecological footprint”. You have the following technical data: the cost of electricity is $0{,}22\ \text{€}/(\text{kW} \cdot \text{h})$, the estimated lifespan of the new refrigerator is 10 years, and manufacturing, transporting, and recycling a new refrigerator involves an embodied energy footprint equivalent to $1\,100\ \text{kW} \cdot \text{h}$ of primary energy. (a) Quantitatively demonstrate whether the user's economic claim is correct or incorrect by calculating the payback period of the investment and the net financial balance at the end of the lifespan. (b) Determine from which year the overall energy balance (manufacturing plus accumulated operation) begins to favor replacement. (c) As a future technologist, write a reasoned recommendation: is it advisable to replace it right now or wait until it breaks down? Justify the concept of ecological payback versus voluntary obsolescence.

A family lives in a $90\ \text{m}^2$ flat in a cold climate zone. Their annual consumption is $8\,500\ \text{kW} \cdot \text{h}$ for Joule-effect electric heating, $2\,400\ \text{kW} \cdot \text{h}$ for domestic hot water (electric water heater), and $2\,800\ \text{kW} \cdot \text{h}$ for appliances and lighting, paying for electricity at $0{,}20\ \text{€}/(\text{kW} \cdot \text{h})$. They have a fixed budget of $3\,000\ \text{€}$ for immediate renovations and must choose between three options that are mutually exclusive due to the budget:

1. Replace all lighting with LEDs and appliances with class A units (investment: $2\,200\ \text{€}$; estimated savings: $25\ \%$ of that category).

2. Insulate the false ceiling and roller shutter boxes, and install weatherstripping and low-emissivity films on windows (investment: $1\,800\ \text{€}$; estimated reduction of $20\ \%$ in heating thermal demand).

3. Replace the electric water heater with an aerothermal heat pump for DHW (investment: $2\,400\ \text{€}$; seasonal average efficiency $\text{COP} = 3{,}0$).

(a) Calculate the annual energy savings (in $\text{kW} \cdot \text{h}$) and financial savings (in euros) for each of the three options.

(b) Determine the payback period of the investment for each option and technically justify which one should be implemented first with the available budget.

(c) Explain why taking action on passive demand (thermal insulation) is usually considered technically prioritary compared to replacing active generation systems.

A town hall subsidises the replacement of old air conditioning units (seasonal efficiency $\text{EER} = 2{,}0$, average electrical input power $1{,}5\ \text{kW}$) with new high-efficiency inverter units ($\text{EER} = 4{,}0$). It was estimated that each family used the old unit for $200\ \text{h}$ per summer. Following the campaign, a field study reveals that the average summer electricity consumption per household only decreased from $300\ \text{kW} \cdot \text{h}$ to $225\ \text{kW} \cdot \text{h}$, well below the savings predicted by the municipal technicians.

(a) Calculate the electrical consumption that the technicians had predicted for the new units, assuming exactly the same cooling thermal energy delivered and the same $200\ \text{h}$ of operation.

(b) Quantitatively demonstrate the existence of the rebound effect by calculating how many actual operating hours the new units were run for and what percentage of the theoretical potential savings has been lost due to the change in habits ("rebound rate").

(c) Justify what socio-technological or user perception factor causes this deviation, and propose two measures (one technical measure based on automation/smart home systems and one economic measure) to prevent the efficiency gain from being diluted.

A school intends to replace 120 fluorescent light fixtures with $2 \times 36\ \text{W}$ tubes (conventional electromagnetic ballast) with $40\ \text{W}$ LED panels. The caretaker states: "The power savings will be exactly $(72 - 40)\ \text{W} = 32\ \text{W}$ per fixture, and since the LEDs have $\cos \varphi = 0{,}95$ compared to $\cos \varphi = 0{,}50$ for the uncompensated tubes, we will also halve the active energy billed on the meter." The lights operate $1\,200\ \text{h}$ per year, each ballast dissipates an additional $9\ \text{W}$ of constant thermal losses, and the cost of active $\text{kW} \cdot \text{h}$ is $0{,}18\ \text{€}$.

(a) Refute the caretaker's claim about the meter and the power factor using technical arguments: what does the active energy meter measure, and what electrical quantity is actually reduced by improving $\cos \varphi$?

(b) Calculate the real active power demanded by each fluorescent fixture (tubes plus ballast) and determine the school's total real annual energy savings (in $\text{kW} \cdot \text{h}$) and financial savings after switching to LEDs.

(c) If each LED panel costs $25\ \text{€}$ installed, calculate the simple payback period. Predict what will happen to the building's thermal demand in winter and in summer due to the reduction in waste heat dissipated by the fixtures (thermal interaction effect).

An energy audit in a detached house over one month records the following electricity consumptions: heat pump heating $210\ \text{kW} \cdot \text{h}$, water heater $135\ \text{kW} \cdot \text{h}$, refrigerator $45\ \text{kW} \cdot \text{h}$, ceramic hob $40\ \text{kW} \cdot \text{h}$, standby power consumption $20\ \text{kW} \cdot \text{h}$, and lighting $15\ \text{kW} \cdot \text{h}$. The family proposes focusing all their efforts on completely eliminating standby consumption and replacing all light bulbs with ultra-low-energy models, claiming that "this will drastically cut their bill".

(a) Critically analyse the family's claim: calculate the maximum percentage of the total monthly consumption represented jointly by standby power and lighting, and demonstrate why this approach suffers from the scale fallacy when compared to a Pareto analysis (80/20 rule).

(b) The $100\ \text{l}$ electric water heater keeps the water at $65\ ^\circ\text{C}$ continuously, recording static thermal losses through insulation of $1{,}2\ \text{kW} \cdot \text{h}/\text{day}$. Design two technical interventions on the water heater (one involving timer/thermostatic regulation and another on flow consumption) and quantify the percentage savings and savings in $\text{kW} \cdot \text{h}$ that would be achieved in this category.

(c) Technically justify why a $15\ \%$ reduction in the two main thermal categories generates a much greater economic and environmental impact than eliminating $100\ \%$ of the minor categories.

When analysing the hourly load curve of the digital meter in a detached house during a week when the owners were away travelling, a constant baseline active power (base load or phantom load) of $120\ \text{W}$ is observed, with cyclical peaks of $180\ \text{W}$ lasting $20\ \text{minutes}$ every hour due to the refrigerator compressor. The energy charge is billed at $0{,}22\ \text{€}/(\text{kW} \cdot \text{h})$.

(a) Quantitatively break down the consumption: calculate the energy consumed over a 30-day month attributable exclusively to the cycling of the refrigerator, and that attributable to the rest of the permanent residual consumption (phantom loads).

(b) The owners want to install a home automation system for general disconnection using contactors in the electrical panel to disconnect secondary circuits during extended absences. Identify which circuits must mandatory remain under continuous power and which ones can be disconnected without risk to the home.

(c) If the home automation system reduces the non-refrigeration permanent phantom load from $120\ \text{W}$ to just $15\ \text{W}$, has an installation cost of $150\ \text{€}$, and an internal power self-consumption of $2\ \text{W}$, calculate how many days of absence per year would be required to amortise the system over a period of 3 years.

A small technical office replaces its old climate control and lighting systems with top-rated energy efficiency equipment. However, during the first few months, the electricity bill barely decreased: users kept the thermostat at $19\ ^\circ\text{C}$ in summer and at $24\ ^\circ\text{C}$ in winter, and fixtures remained switched on for hours in unoccupied offices and meeting rooms under the premise that "since they are low-consumption LEDs, the expense is negligible".

(a) Mathematically model the thermal impact: knowing that for each degree the thermostat setpoint deviates from the standard comfort temperature ($26\ ^\circ\text{C}$ in summer and $21\ ^\circ\text{C}$ in winter, according to RITE), the heat pump's consumption varies by approximately $7\ \%$, calculate the percentage extra cost resulting solely from improper setpoint habits in summer and winter.

(b) Design a technical solution based on automation and control (PIR occupancy/light sensors, smart thermostats locked by software with deadband, and centralised scheduling) to correct the problem without relying on individual user willingness.

(c) Technically justify why in energy engineering passive automation (systems that operate autonomously) is prioritised over awareness campaigns to neutralise the rebound effect.

A Technology student uses a plug-in power meter during a home energy audit. After measuring several appliances, they obtain the following nameplate and measurement records:

• Microwave: rated power $1\,200\ \text{W}$; daily operating time $15\ \text{min}$; power factor $\cos \varphi = 0{,}92$.

• Fridge-freezer: compressor rated power $120\ \text{W}$; recorded cumulative active energy after $24\ \text{h} = 0{,}84\ \text{kW} \cdot \text{h}$; $\cos \varphi = 0{,}78$.

• TV + soundbar in standby mode: measured active power $15\ \text{W}$; standby time $20\ \text{h}/\text{day}$; $\cos \varphi = 0{,}42$.

• Desktop computer: power supply rated power $650\ \text{W}$; average actual power recorded during use $130\ \text{W}$; daily use $5\ \text{h}$; $\cos \varphi = 0{,}98$.

The student concludes: "The microwave consumes the most energy because it has the highest rated power ($1\,200\ \text{W}$), while the refrigerator barely has any impact since it has a motor of only $120\ \text{W}$."

(a) Quantitatively refute the student's conclusion by calculating the daily and monthly (30 days) energy consumption in $\text{kW} \cdot \text{h}$ of each of the four appliances from the recorded data.

(b) Interpret the refrigerator's record: why does the energy consumed in $24\ \text{h}$ ($0{,}84\ \text{kW} \cdot \text{h}$) not match the direct product of its rated power and time ($120\ \text{W} \times 24\ \text{h} = 2{,}88\ \text{kW} \cdot \text{h}$)? Calculate the compressor duty cycle.

(c) Analyze the value of $\cos \varphi = 0{,}42$ recorded in standby: why would a basic meter that only multiplies current by voltage ($V \times I$) vastly overestimate the actual billed consumption? Explain the difference between apparent power and active power in electronic loads.

Unit Challenge. Energy audit and optimization of your home utility bill. Become the energy manager of your home by analyzing the impact of the electricity market on daily habits.

1. System data: Check the percentage of renewable generation for the day on Red Eléctrica de España (REE, e·sios website or RedOS app) and record the regulated $PVPC$ price (e.g., $0,15$ €/kWh) during peak and off-peak hours.

2. Home audit: Review your home's electricity bill (contracted power in kW) and record the nominal power and estimated daily usage time of $3$ significant appliances (washing machine, oven, refrigerator, or climate control).

3. Simulation in LibreOffice Calc: Design a spreadsheet that determines the current weekly energy cost compared to an optimized scenario (shifting consumption to off-peak hours and adjusting the contracted power by $0,5$ kW). Generate a cost comparison graph.

4. Technical proposal: Write a brief report with three reasoned measures to improve efficiency, reduce the bill, and promote sustainable consumption at home.

Assessment criteria:

• Rigor in obtaining and recording real data from REE and the domestic installation.

• Technical accuracy in the formulas, units, and charts implemented in LibreOffice Calc.

• Feasibility and justification of the proposed energy-saving and sustainability measures.