"Electric cars do not burn more often than conventional vehicles"

No, they're not. Before a new model of electric vehicle may enter the market, the manufacturers have to meet strict safety requirements or they wouldn’t obtain approval. In our experience, electric cars catch fire with the same frequency as cars with conventional engine. As part of a study, we observed the fire properties of an electric car in a tunnel – we did not identify any higher hazard potential here either.

There are three possible causes:

1. First, the battery can be damaged by a blow or impact, for example in an accident, in which case the membranes in a battery cell can become damaged, leading to an undesired chemical reaction in the cell. If this process is not stopped, one cell can "infect" the next and in this way trigger a chain reaction. This phenomenon is known as "thermal overrun". It results in overheating and then fire.
2. Secondly, the battery could have a production error, as in the well-known case of burning smartphones.
3. Third reason: If a car is already burning, the battery will at some point also catch fire. Theoretically, overcharging could also occur at the charging station if the charging protection fails. I am not familiar with any case where this happened in practice. Overall, it is relatively improbable that a battery catches fire. It is also installed at the possibly safest part of the vehicle. But what is really dangerous: If an underground garage is flooded and a car happens to be connected to a charging station there. You can imagine the situation as if you had an enormous hairdryer in an enormous bath tub, which can cause a fatal electric shock.

The normal rules of behavior also apply to the driver of an electric vehicle: Get out carefully, secure the accident location and call the emergency services – 117 for the police or 118 for the fire department. If there is an accident on the highway, get behind the crash barrier and, if possible, put on a reflective vest. If your car starts to give off smoke, you should likewise quickly drive to the right side of the road and park your car at a distance to any combustible material You do not need to worry about getting an electric shock from your electric car. The vehicles are designed to ensure they are not dangerous after an accident. But do not touch any parts lying around, especially if they are orange, because these could be live.

If an electric car is really on fire, we put it out quite conventionally with water. If the battery package catches fire, it usually does not reach the interior of the battery. Some years ago, several electrical vehicles were built with a so-called "fireman access" to permit the battery to be flooded. The formula E racers still have this. But we can also restrict thermal overrun from outside with enough water. Whether the battery is then completely discharged, is unknown – and as a result, the cars could definitely start burning again later. Consequently, the big towing companies in Switzerland have acquired containers in which electric cars can be deposited. The vehicle is monitored with sensors or thermal imaging cameras in the container until it can be safely disposed of. 

If your car suffered a violent impact, you should take it to the garage and have the battery package checked. This is because you cannot rule out something having been damaged that sooner or later might trigger a fire, for example, during the next charging process. Otherwise, I would recommend you treat the technology – as in all vehicles – with proper respect. But you do not need to be afraid.