Exercises: Domestic installations and efficiency in the home

Explain what the main distribution board (consumer unit) of a home is, where it is usually located and what two functions it performs (distributing electricity and providing protection).

Circuit breakers (MCBs) and residual current devices (RCDs) are located in the consumer unit. Explain what each one protects: one protects the installation and appliances, and the other protects people.

The electrical installation is divided into circuits (lighting, sockets, kitchen...). Explain what a circuit inside a home is and give two advantages of keeping them separate.

The figure shows a domestic consumer unit through which electricity enters and flows out to the home's circuits, with an element marked with ?. State what this element is, explain when it trips, and what or whom it protects.

Describe the path of water inside a house from the mains supply (the main inlet) to a hot water tap, naming the main stopcock and the water heater or boiler.

Name the three common indoor climate control systems in a home (heating, air conditioning and ventilation) and explain in one sentence what each contributes to comfort.

Explain what home automation (domotics) is and name three specific smart home applications that help save energy at home, stating what each one saves.

Explain what the main electrical switch and the main water stopcock are, and reason why the whole family should know where they are located (think of a water leak or an electrical fault).

When plugging in a faulty appliance, the RCD trips and the whole house loses power. Explain what the RCD detected, what steps you would take to safely reset the installation, and why this switch must never be bypassed.

A circuit breaker trips when more current flows through its circuit than permitted; an RCD trips when it detects a current leak. Provide a specific scenario for each trip and explain what each one protects.

The diagram shows the floor plan of a house with the circuits running from the consumer unit to the rooms, with a circuit marked with ?. Identify which circuit each line corresponds to and reason why the kitchen usually has its own dedicated circuit.

A family installs a programmable thermostat, occupancy sensors in the hallway, and timer control on the water heater. Explain how each of these three smart home measures saves energy.

In the diagram of a house's plumbing system, the following appear in order: mains supply, main stopcock, water heater, and two branch pipes (cold water and hot water) leading to the bathroom and kitchen. Explain what each component does and reason why the hot water branch leaves after the water heater and not before.

An oven rated at $3.000\ \text{W}$ and a dishwasher rated at $2.200\ \text{W}$ operate simultaneously in the kitchen. Calculate the total current flowing through the circuit using $I = \frac{P}{V}$ (mains supply voltage is $230\ \text{V}$) and reason why this circuit uses a circuit breaker with a higher amp rating than the lighting circuit.

Occupancy sensors turn on the hallway light only when someone is present. A $10\ \text{W}$ LED bulb goes from being on for 5 hours a day to just 1 hour. Calculate the annual energy savings in $\text{kWh}$ and comment on which rooms you would NOT install an occupancy sensor in, giving your reasons.

Compare an instantaneous water heater with a storage water heater: how each heats water, when each system is preferable (occasional use versus multiple consecutive showers), and what keeping hot water stored 24 hours a day implies for energy consumption.

In the electrical panel shown in the figure, a user notices that the $25\ \text{A}$ miniature circuit breaker (MCB) for the kitchen trips frequently when preparing food while the washing machine is running. A neighbour advises: "Replace that breaker with a $32\ \text{A}$ or $40\ \text{A}$ one; that way it won't trip again and you'll be able to turn on all three appliances at the same time".

1. a) Verify quantitatively whether the $25\ \text{A}$ breaker will trip when the oven ($3.000\ \text{W}$), the washing machine ($2.200\ \text{W}$), and the microwave ($800\ \text{W}$) are running simultaneously at a voltage of $230\ \text{V}$ ($P = V \cdot I$).
2. b) Technically refute the neighbour's advice: predict what will happen in the electrical installation's conductors if the MCB is replaced with one of a higher rating without changing the cable cross-section, justifying it using Joule heating and the risk of fire according to the REBT.
3. c) Propose a standard technical solution (circuit distribution according to the REBT) and a rational usage guideline that prevents tripping without the need for construction work.

Design the home automation control system for HVAC (reversible heat pump) and motorized blinds in a penthouse in Madrid with a large south-facing window, subject to a time-of-use electricity tariff (cheap off-peak hours from 00:00 to 08:00; expensive peak hours from 10:00 to 14:00 and from 18:00 to 22:00).

1. a) Write the logic control rules table for winter and for summer, indicating in each case: input sensors (indoor temperature, outdoor solar radiation, tariff schedule), the logical condition, and the actuators' action (raise/lower blind, HVAC mode and setpoint temperature).
2. b) Justify how your design takes advantage of the building's thermal inertia and passive solar gains to minimize consumption during peak hours without compromising the occupants' comfort.

During the renovation of an old home that lacks a residual current device (RCD) and earthing in the sockets, an amateur installer claims: "If we install new, properly rated $16\ \text{A}$ miniature circuit breakers on each circuit, people will be fully protected against any electrical contact with the metal casing of a faulty washing machine".

1. a) Technically refute this claim: if the phase wire comes into direct contact with the metal casing and a barefoot person touches it (approximate body resistance $R = 1.500\ \Omega$ at $230\ \text{V}$), calculate the current that will flow through their body. Compare this value with the ventricular fibrillation threshold ($30\ \text{mA}$) and with the minimum current that trips the $16\ \text{A}$ circuit breaker.
2. b) Explain the physical operating principle of the residual current device (RCD) and justify why it is the only device capable of protecting life in this scenario, whether earthing is present or not.

A detached house in a cold zone consumes $12.000\ \text{kWh}$ of thermal energy annually to maintain heating at $23\ ^\circ\text{C}$ during winter, with an average energy cost of $0,15\ \text{€/kWh}$. The family is evaluating two independent saving options:

• Option A (Active management): Lower the thermostat to $20\ ^\circ\text{C}$ (an estimated energy saving of $7\ \%$ per degree reduced) and install a zone-programmable modulating thermostat (an investment of $420\ \text{€}$, which saves an additional $8\ \%$ on top of the already reduced consumption).

• Option B (Passive insulation): Replace windows with triple-glazed models featuring thermal break (an investment of $4.800\ \text{€}$, which reduces the home's overall thermal losses by $25\ \%$ while keeping the thermostat at $23\ ^\circ\text{C}$).

1. a) Calculate the annual energy savings (in kWh) and the annual financial savings (in euros) provided by each of the two options.
2. b) Calculate the payback period (simple payback in years) for both options.
3. c) Technically justify which of the two measures you would recommend implementing first and evaluate the feasibility of combining them.

In a detached house with a garden and underfloor heating, the main water meter registers an anomalous continuous flow rate of $15\ \text{l/h}$ overnight without any tap being open, but no visible damp patches can be seen on the walls.

1. a) Design a sequential diagnostic protocol to pinpoint which subsystem the leak is located in (indoor domestic cold/hot water network, closed heating circuit, or buried garden irrigation branch), specifying which shut-off valves to close and which pressure gauges or meters to check at each step.
2. b) Design the control algorithm for a smart home automation system equipped with an electronic flow meter at the service connection and a main shut-off solenoid valve. Define the logical conditions (instantaneous flow rate, accumulated volume, and continuous duration) for the system to accurately distinguish between normal use (shower, washing machine filling), a slow drip/hidden leak, and a catastrophic pipe burst, acting autonomously without triggering false cut-offs.

In a living room wall socket (C2 circuit protected by a $16\ \text{A}$ MCB and standard $2,5\ \text{mm}^2$ wiring), a commercial power strip is connected with its own reduced cross-section cable ($1\ \text{mm}^2$) and a maximum permissible power specified by the manufacturer of $2.300\ \text{W}$ ($10\ \text{A}$). An oil radiator rated at $2.000\ \text{W}$, a ceramic fan heater rated at $1.500\ \text{W}$, and a television rated at $150\ \text{W}$ are plugged into it simultaneously at a voltage of $230\ \text{V}$.

1. a) Calculate the total current demanded by the appliances operating simultaneously and compare it with the allowable limits of the power strip, the socket branch line, and the panel's circuit breaker.
2. b) Justify using Joule's law ($P = I^2 \cdot R$) why there is a severe risk of fire even before the electrical panel's circuit breaker trips, identifying precisely which element of the installation will fail thermally first.
3. c) An occupant proposes replacing the panel's $16\ \text{A}$ circuit breaker with a $25\ \text{A}$ one "so that it won't trip when using both heaters". Explain the hazard that this modification introduces to the installation embedded in the wall.

A 6-storey residential building has a centralised one-pipe heating system without individual regulation. During the winter, the homes on the lower floors barely reach $17\ ^\circ\text{C}$ (residents use backup electric heaters), while on the 6th floor the thermometers read $26\ ^\circ\text{C}$ and users open the windows to avoid overheating. The community's gas expenditure amounts to $36.000\ \text{€}$ per year.

The community is debating two renovation proposals:

• Proposal A: Replace the current community boiler with high-efficiency air-source heat pump equipment, keeping the current hydraulic distribution intact (investment: $52.000\ \text{€}$; estimated reduction in energy consumption of $30\ \%$).

• Proposal B: Hydraulic balancing of risers and installation of valves with thermostatic heads and electronic heat cost allocators on each radiator in all homes (investment: $14.500\ \text{€}$; estimated savings from eliminating overheating and individual control: $22\ \%$).

1. a) Explain the physical and thermal principle that causes the temperature imbalance between the lower and upper floors in this type of installation.
2. b) Critically evaluate why Proposal A is technically deficient to solve the building's underlying problem, despite offering a higher percentage of energy savings.
3. c) Calculate the payback period for both proposals and write a prioritised and justified technical recommendation for the residents' meeting.

To manage the climate control of two homes with different construction characteristics whose occupants work rotating and unpredictable shifts, the installation of a 'smart' home automation thermostat with geolocation is analysed, which turns off the heating when leaving home and turns it back on 30 minutes before arriving:

• Home A: Heating via sheet steel radiators and a condensing boiler (low thermal inertia: heating/cooling time on the order of 20 to 30 minutes).

• Home B: Heating via geothermal underfloor heating (high thermal inertia: response time to change room temperature of 4 to 6 hours).

1. a) Reasonably predict the indoor thermal behaviour and the impact on energy efficiency of the geolocated thermostat in each of the two homes. Justify why the system is ideal for Home A but a failure in terms of comfort and consumption in Home B.
2. b) Design the optimal control strategy for Home B (setpoint temperature when present and away, hysteresis band, and weather compensation via an outdoor sensor) to maximise savings without compromising habitability in the face of unforeseen schedules.