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This is a disaster for renewable energy and should be reported as such. The costs of such unreliable power are enormous. Such naive reporting does the world no favors.
Actually it is good for renewables industry as a whole as it provides business case for storage technologies which is lagging a bit behind.
Oh, wait, some engineer was cheating with the reporting software... :D
If customers are getting paid to use electricity, is it legal for them to just send it to a ground wire the whole time rates are negative to get paid as much as possible?
I doubt the power producers care what happens to the power since they just need to get rid of it. Given the rarity of these events and the cost of building something that can dissipate large amounts of energy very quickly I don't think it would be worth building infrastructure to do so. If it were, the power producers could just build their own.
At the powers involved you might melt quite a bit of the ground :). But some heating plants for centralized house heating do have electric water heaters, which are used, as soon as the electricity spot price goes below a certain number - the rest of the time they heat with gas.

These spikes would go mostly away, if more coal plants get replaced by gas plants which can be switched off very quickly. I guess, as soon as there are more of those days, this shift is getting financially attractive.

Electricity doesn't work that way. To a first approximation, shorting something out actually uses no power, as there is no resistance/voltage drop. In reality, there is some resistance which takes the energy, and thus dissipates heat (in the scenario you're envisioning, likely the wires for a short time). Dissipating that heat is going to be your problem to overcome.
Isn't Sunday family day, culturally? At least when I visited last year, businesses were closed and there were many more families outside walking/biking/etc than on Saturday.

You'd have to pay me to use the power, too, if I would rather be outside in this perfect weather.

We're also having a RIDICULOUSLY hot may, with 27°C being my apartment's temperature for the past 4 or 5 days straight, with windows open and no heating on.
It's only been 11 days into May, the cold change is about to happen. And just two weeks ago, it was snowing.
Marginal return. Include infrastructure investments required to build it all, and they're all probably still deep in the red?
Let me illustrate: an Uber driver may make money on a given day, if the cost of ownership of the car is not included. Payback period is a term used to describe the time needed at a profitable level to pay for the purchase/installation of a system. While its a good thing to see money coming in for your energy system, that means little in terms of the purchase decision.
The problem is storage.. what to do.. what do do with all this .. freeze the pumped water storage to horizontal glaciers?
Pump water uphill into a hydro dam is the typical case, I think.
Melt very large vats of aluminium and then use that molten aluminium to boil water later on to drive some turbines.

Pump water uphill into a reservoir or series or reservoirs.

Produce hydrogen gas by electrolysis and sell it to fuel cell people.

Charge very large arrays of batteries.

I dunno.

Unless there is some process I haven't heard of, one of those is not like the others.
Pumping water uphill is already in common use. Here are a couple of other ideas:

Use electric cargo trains to carry many loads of gravel from the bottom of a mountain to the top. Dump the gravel out into a huge pile. Later, load the gravel back in the trains and regenerative brake all the way back down the mountain.

Cut a large-diameter shaft into bedrock. Using the rubble from the excavation of the shaft as aggregate, pour a very heavy concrete piston that fits in the shaft. Pump water into the bottom to lift the piston, discharge pressurized water through turbines later.

Compress air and put it in old natural gas wells. Discharge pressurized air through turbines later.

Use a large heat pump to warm depleted uranium or similarly dense material in a large vacuum flask. Run the heat pump backwards (like a steam engine) later.

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Is Agora Energiewende still counting ethanol as "renewable"? Any article about German energy that doesn't mention the country is following the same disastrous path (of fulfilling new energy demands, caused by the loss of nuclear, by moving the energy sector inefficiently to agriculture) that the US took in the Bush years is negligent.
Real time prices go negative in U.S. energy markets as well. Usually during off peak hours with a high percentage of wind generation in the zone.

Look at the North Zone of New York, it spent a good chunk of Sunday negative: http://mis.nyiso.com/public/csv/realtime/20160508realtime_zo...

Use the LMP column(Locational Marginal Price)

It should be noted that most energy is purchased in the day ahead market, which I can't recall seeing negative - although maybe in Texas (ERCOT).

The provider will need to buy back the energy in at the realtime price if they are not generating. But I am not sure about the market rules for negative prices.

You can get negative day-ahead prices quite frequently due to congestion depending on what lines, generators, transformers, etc are out.
So many of these articles (and HN comments too) seem to regard negative prices as a terrible no-no.

I don't see why paying electricity users to timeshift is worse than paying for storage facilities.

I bet most of the German metal industry has already tweaked its production facilities to be able to ramp higher and lower on short order, while keeping weekly production stable. Good thing too IMO.

That should be the goal of these "po public utilities". The public pays the upfront cost and assumes the risk of I stalling and maintaining these new systems. The should be able to relish in the benefits when those costs are overcome.
Question: Why do they have to pay to put energy into the grid? If there's too much energy being generated, is there not a way to release that energy? Who gets paid, the consumer, or the local utilities? This sounds more like good energy conservation, than what will actually happen when Germany's nuclear plants go offline.