Backup power

We are fortunate in the UK that most of our power distribution is underground. This means that power cuts are very rare. I can remember maybe one in the last 10 years.

However, with the move towards greater electrification of modern life, and the various power cuts that have occurred recently, I have thought about getting some sort of backup power setup.

The variety of options can be confusing, so I've been learning, and am making a note here for others.

Safety

First things first.
The main risks here are electric shocks and fire. Overcharging or damaging a battery, or pushing or pulling too many amps into/out can cause heat and fire.

Electricity is dangerous.
Your heart works with small electrical impulses. A very small number of amps can kill you, if it travels across your heart.
The danger varies with several things - current, resistance, time, and location of the electricity flow. The Electrical injury Wiki page has a chart halfway down the page showing the danger of amps over time. 1 Amp can easily kill you if it goes through your heart.
Watch out for your amps
Make sure that all your equipment is rated for the right number of amps. Don't, for instance, try and pull 200 Amps from a 30 AH battery. Similarly, don't use cables that can't support the current.

Amps/Watts

With power solutions, you'll see Amps mentioned a lot. In general, the higher the amperage, the more it will cost. Batteries, chargers, solar panels, even cables - will cost more for higher Amps, but will charge more quickly/be able to provide more power for longer.
In 12V systems (which is what I will be talking about here), 1A is 12W (Watts = Volts x Amps).
For comparison with the mains, in the UK we have 240V, 13A supplies. This means that each socket can provide 3120 W (which is why we can have 3 KW electric kettles to make our tea quickly)

Battery

This is the main part of your backup power set-up. Batteries are measured in Amp-hours (AH).

To judge the size of battery you might need, this table shows the charging/discharge times for a 100 AH battery at varying currents/watts at 12V.

Amps (Watts)	Hours
1 (12 W)	100
2 (24 W)	50
5 (60 W)	20
10 (120 W)	10
20 (240 W)	5
50 (600 W)	2
100 (1200 W)	1

Batteries are scary. They're essentially little bombs containing a lot of power, often containing nasty chemicals. Lithium for example catches on fire on exposure to the air, and water makes a lithium fire worse. Lithium fires are also extremely hot.
Luckily, the technology has evolved so that the newer types are much safer.

Car batteries (lead-acid) are not good batteries. They contain acid (nasty), lead (toxic, heavy), and are designed for short sharp bursts of power (starting a car) rather than providing low levels of constant power (e.g. for running equipment). Also, charging lead-acid batteries produces flammable, explosive hydrogen gas (which isn't a problem when you are driving your car, but would be if you were charging it indoors). There are sealed lead-acid batteries which get round the problems of acid spillage and hydrogen generation, but they still aren't good batteries for the other reasons mentioned

Lithium ion batteries (such as are used in phones) are very good, but are expensive for the power they provide, and also don't like being left charged, or charged up and down a lot.

The best type of battery right now is a LiFePo4 battery - Lithium Iron Phosphate. It has a nice trade off between capacity, weight, safety, lifespan and cost.
TLDR; Buy a LiFePo4 battery with the amount of AH that you think suits your needs. An example is this 100AH 12V LiFePo4 battery

Charging

Batteries are not much use unless they're charged. You have a couple of choices.
The first is charging from the mains, and the second is charging from solar.

Charging from the mains

Charging from the mains is easier and cheaper, but of course, if the power goes out before you've charged the battery, or you use all the battery before the power returns, then you are out of luck.
There are a couple of things to consider.
Batteries don't have some magical way of stopping accepting charging when they are full. You need a charger which knows how much charge the battery needs, and stops providing it when it reaches the limit. If you have a dumb charger, and leave it connected, the battery will overcharge, be damaged, and finally catch fire. You don't want this.
Chargers are rated in Amps. The higher the rated Amps, the faster you can charge your battery. A 10A charger will take 10 hours to charge a 100 AH battery. This might be fine for you, or you might want a higher power one that will charge faster.
TLDR; You want a smart LiFePo4 battery charger.
An example of a mains charger is this 10A 12V smart battery charger

Charging from solar panels

This is where it gets a little more complicated, and my knowledge isn't very good.
Solar panels work best in bright sunlight, but will still work in grey/overcast conditions, just not providing as much power.
The brightness of the sunlight, the number of panels, and the efficiency, and power rating of the panels will dictate how much power you can produce from the sun.

Solar panels

Do you want portable solar panels, or non-portable ones?
Do you want a single higher rate panel, or more lower rated panels? Multiple panels can be wired in parallel.
Once you have decided this, pick your panels. The higher wattage (amps) ones will of course cost more.
TLDR; This is a portable 130W solar panel

Charge controllers

Even if the panels produce 12V, for reasons I don't fully understand, you can't just connect them to your battery, and have them charge. You need a charging controller.
There are two kinds - PWM (Pulse-width modulation) and MPPT (Maximum power point tracking).
It seems that PWM controllers are cheaper than MPPT, and are fine for smaller setups. I imagine that the rapid switching on and off could cause RFI, so if that's an issue for you, you might want to go for an MPPT controller.
TLDR; Get a charge controller to be able to connect your solar panels to charge your battery. An example is this PWM solar charge controller

Using your charged battery

240V

If you want to be able to run mains-powered devices, you will need an 12V inverter. These convert 12V DC power into 220V AC power. As with everything, these will be rated in terms of power (amps or watts). You will need to buy one sufficiently powerful enough to be able to supply whatever 240V appliance you are running.
TLDR; Buy an inverter if you want to be able to run 240V equipment. An example is this 2000W inverter

12V

If you only want to use your battery for 12V usage, you're pretty much good to go. You can connect your 12V device straight to your battery. If you want to use multiple devices at the same time, you can buy "distribution panels" which allow multiple 12V devices to be plugged in to the battery at the same time.

Connectors and cables

Finally, don't forget cables and connectors. No good having the equipment if you can't join it up together.
Running too much current (Amps) through a cable will cause it to get warm, melt and maybe catch fire. Make sure you have cables sufficiently highly rated to support the amount of power you are producing or using.

The amateur radio community have standardised on Anderson powerpoles for connecting 12V equipment up. This could be an option if you have multiple devices, and want easy ways of connecting them to your batteries.