According to numerous articles, solar flares have done damage to the power grid on Earth in the past: http://science.nasa.gov/science-news/science-at-nasa/2008/06may_carringtonflare/
How bad can we expect a severe solar flare to impact the power grid / electronics? Would a bad flare also break electronics (e.g. computers), or "just" the power grid?
Is there anything that can be done to reduce the effects?
Space Weather is the field within heliophysics that tries to understand this Sun-Earth relationship. When a Solar Flare occurs multiple things may happen and how it interacts with the Earth and our technology depend on different factors.
The first effect, the X-ray radiation produced by an Solar Flare affects the ionosphere and therefore the radio communications. This effect is almost immediate and there's no way to attenuate or prevent it. We can forecast the likelihood of a flare to happen on the day but still we don't have the knowledge enough to exactly predict when it will happen. The radiation from the flare it takes around 8 minutes to get to Earth, and at the time we see it the radio communications have already been affected. This effects mostly to VLF bands.
After a solar flare high energetic particles and coronal mass ejection could be produced, these two events have different effects on Earth and whether interacts with Earth or not depends on where it happens on the Sun and the properties of the solar wind at that time. High energetic particles (also known as Solar Energetic Particle events - SEPs) could arrive around 30 minutes after the flare happened, and Coronal Mass Ejections (CMEs) between 2 or 3 days. These times depends on the properties of the events, not all are the same.
CMEs could be somehow predicted, and are these the ones that could affect, between others, the power grid. It won't affect your computer. The reason of why it affects the power grids is due to a induced electric current happened by the interaction of the CME's magnetic field produces in the Earth's magnetic field. The electric current finds it easier to travel through the power grid than through the Earth itself (the cables are better conductors). In simple words, when that happens the electric grid "thinks" that there is an increase of demand and tries to compensate it generating more electricity and that can burn them - as it happened in Canada in 1989.
To reduce it effects there are a lot of engineering work around these systems and I'm not an expert in such topic to be able to explain them properly. However, a warning to the power grids of a couple of days in advance helps. The difficult bit is how to be exact in the forecasting. CMEs sometime are deflected by the solar wind and just a flank of it "touches" the Earth, other times small ones get accelerated and have a larger impact than expected. So, to be able to reduce the effects we need to have a better understanding of their origin and surroundings, understand their physics and be able to model what they are doing. There are few models out there (e.g., CCMC) but at the moment we need to keep researching to improve these further.
Answering to "how bad" a solar storm (not just a flare) can affect Earth is hard to quantified, in UK it has been classified as one of the highest priority natural hazards in the National Risk Register, and similarly in other countries. An event like Carrington's (the one you linked) could have a lot of impact in our current technological civilization and it's been estimated in many years and trillions of US dollars to restore the damage (see Royal Academy of Engineer report on Space weather).
It would be good business for the news industry: sky lights, plane crashes, exploding grid transformers, city blackouts, satellite damage, long, electricity-carrying wires would spark, start fires and and send signals when they are switched off. Burning buildings, dead people, everything.
big flares occur about every 100 years. the last was the Carrington event in 1859. It triggering telegraph malfunctions (even giving operators electrical shocks) and caused some telegraph pylons to suddenly spark and catch fire.
A surge in solar wind can blow out power transformers by melting the coating that insulates copper windings and by melting the copper itself, especially in highly interconnected regions (i.e. the East Coast), transformer failures can trigger cascading effects, spreading power outages over wide areas.
a flash of light is seen from the sun 17 hours in advance of the magnetic storm, and sunspots are monitored for activity.
If a massive CME were spotted, 3-day forecasts give us some lead time: there are some measures electric utilities could take to protect their equipment, such as quickly disconnecting transformers. Polar flights, which travel at the highest altitudes, could be rerouted to avoid contact with damaging solar particles, and some satellites could be switched into a safe mode to minimize damage. Here on Earth, at the very least, we’d have some time to prepare for potential power blackouts and other problems.
Given the scope of our current technological infrastructure, it’s been estimated that the next Carrington-scale event (which happens roughly once every 100 years) will cause upwards of $2.6 trillion in damage across the globe, and require four to ten years for complete recovery.
Scientists studying tree rings found a sharp increase in the amount of radioactive carbon-14 recorded in the rings of ancient Japanese cedar trees between 774 and 775. Carbon-14 can be created by cosmic ray particles arriving from space, and the 774 incident could have been a solar flare.
there is a list of big solar storms here: https://en.wikipedia.org/wiki/List_of_solar_storms
Satellites have been damaged before. GPS has been effected before. Power grids surge during magnetic disturbances. Pipelines energize too. March 13 1989 was a whopper. There's a lot of reporting online of this event. Some papers are still being written on the event.
http://www.nasa.gov/topics/earth/features/sun_darkness.html
So if a bigger, say a magnitude more severe, take the above and extrapolate from there. With our greater dependence on satellites for military, commerce, and daily living, a major loss of connectivity would occur and may be prolonged if the satellites are damaged, and orbits disturbed by the solar wind. Power grids, electric rail service, all could be down for prolonged periods if transformers are overloaded.
Ionosphere could be reduced and that would impact life.
