Extreme hydroelectricity on the Danube

When it comes to discharge, one the largest rivers (if not the largest river) in Europe is the Danube. This river, too, passes through a convenient gorge at the Iron Gate, in which the border between Serbia and Romania lies. This fact has not been lost on these two countries, and they have indeed build not just one, but two hydroelectric power installations: Iron Gate I and II. These two stations have a peak capacity of somewhat above 2 GW, and an average capacity of much less than that.

Hey, sure, two power stations is nice, but guys, show some ambition! Here is how:

Again, the GTOPO30 data set is our friend. The critical region on the Danube's watershed is the Moravian Gate, which lies here in the saddle between the Sudetes range and the Carpathian mountains, at 310 meters above sea level. Going any higher than that would cause the lake to spill over into southern Poland, and from there into the Baltic sea. Putting the lake surface at an conservative 300 meters above sea level, we obtain the following, huge, Lake Danube:

Yes, Hungary has transformed into a lake, but as said before: this is purely a technical exercise.

Now, as before, we need our two key parameters: the average discharge at the dam, and the maximum drop height. The average discharge at the Iron Gate is large, at 5600 cubic meters per second, as can be seen on page 540 of this article. The Danube flows at some 50 meters above sea level there, allowing for a full 250 meter drop. Calculating the average power output yields:

P = ρhrgk = 1000 * 250 * 5600 * 9.81 * 0.5 = 6.87 GW.

On a yearly basis, this would yield 59.6 TWh, or 2.15e+17 Joule. This is a lot more than our previous attempts: this installation could cover 2.15% of Europe's electrical power.

Extreme hydroelectricity on the Rhine

I closed my last post with the question "can we do better?". Well, at least we can try, by using one of the other major rivers in Europe: the Rhine. The Rhine passes through a convenient gorge between Bingen and Bonn.

Almost any place in that gorge is suitable for a dam, so I planned one about in the middle near Kamp-Bornhofen. Now, we need to ask the same question as before; how high can be make the reservoir? Using the same procedure on the GTOPO30 data set shows that the critical point on the Rhine's watershed lies in the saddle between the Taunus range and the Vogelsberg, or right about here. GTOPO30 suggests that a waterlevel of 210 meters above sea level would leave some 5-10 meters of headroom.

Now, filling up the lake to 210 meters above sea level floods the entire middle Rhine valley, and even partly extends into the Elzas in France:

So how much power do we get from this? One can find here that just below Mainz (or just above the Rhine gorge), the average discharge is 1620 cubic meters per second. Wikipedia tells us that the Rhine flows at 69 meters above sea level in Kamp-Bornhofen, which gives us a 210 - 69 = 141 meter drop. Using the same calculation as before, this yields:

P = ρhrgk = 1000 * 141 * 1620 * 9.81 * 0.5 = 1.12 GW

This is already better than our previous installation. Over the course of a full year, this would give us 9.82 TWh of electrical energy, or about 3.54e+16 Joules. This would cover 0.35% of Europe's needs.

But we can do better. Check in later!

Extreme hydroelectricity on the Rhône

Hydroelectricity is -at least at the plant itself- a clean and renewable form of electricity generation; it is driven by the water cycle, which in itself is a manifestation of solar energy.

The main mechanism by which a hydroelectric power plant generates energy is by converting the water's potential gravitational energy (dictated by the surface-level difference above and below the dam) into kinetic energy of the turbines, and from there into electrical energy. The electrically generated power can thus be calculated in a rather simple manner:

P = ρhrgk, where:

• P is Power in watts,
• ρ is the density of water (~1000 kg/m3),
• h is height in meters,
• r is flow rate in cubic meters per second,
• g is acceleration due to gravity of 9.8 m/s2,
• k is a coefficient of efficiency ranging from 0 to 1.

It is clear that ρ and g are constants, and that -for any sufficiently large-scale system- k will not be too changeable either. So, basically, if we wish to generate a lot of power, we need a high drop and a high flow rate. This leaves of with the task of choosing a large river on which we can generate a high drop by building a large dam. Obviously, the further downstream we can build the dam, the larger our catchment basin becomes, and the higher the flow rate.

Now, Europe does not have very-high flow-rate rivers compared to, e.g., South America, Asia, or Africa, but Europe does have three relatively-high flow-rate rivers where a natural canyon downstream can be used to create a high drop. These are: The Rhône, the Rhine, and the Danube.

In this post, I will describe a totally ridiculous-scale hydroelectricity project on the Rhône. This project could never ever be executed, due to social, ecological, and economical constraints, but that does not stop me from assessing how much electrical energy we could generate in the extreme case (yes, this blog has "extreme" in its title!).

Some 60 km South of the French city of Lyon, the Rhône passes Saint Vallier, where an Eastern outcropping of the Massiv Central and a Western outcropping of the Alps creates a canyon. Here, a dam can be erected.

As we determined earlier, we now have a high-flow-rate spot, but we need a high drop, too. So how high can we go here? In order to find out, I downloaded the freely-available GTOPO30 digital elevation model, which contains elevation data for the entire world at 120x120 points per square degree. Using Octave, I generated contour lines at increasing elevations until the reservoir lake spilled over the lowest point of the water shed between the Rhône catchment basin and an other catchment basin.

As it turns out, the lowest point on the basin's water shed is that between the Rhône basin and the Loire catchment basin, in the Canal du Centre at 298 meters above sea level, around here. This means that if we leave a precautionary 8-meter head room, we can raise the lake surface to 290 meters above sea level. This creates "Lac du Rhône", which has a considerable size:

In fact, this reservoir utterly dwarfs Lake Geneva, which creates the small trouble of forcing millions of people to move, etc. However, from a purely technical point of view, it is possible. Now, let's find out how much power we get out of this setup.

In Saint-Vallier, the Rhone flows at 131 meters above sea level. This means that is we raise the water in the reservoir to 290 meters above sea level, we have a drop of h = 159 meters. The next unknown is the flow rate. This site on Rhone flow rates lists an annual average of 1100 m3/s at Ternay, which is just a bit upstream from our dam, and -just like our dam- upstream from the confluence with the rather large Isere.

The final unknown is the efficiency of the generators. I have not found solid data, but it seems that 0.5 is a safe bet.

Using these figures gets us:

P = ρhrgk = 1000 * 161 * 1100 * 9.81 * 0.5 = 868.6 MW

This would be an average over the year. Using the maximum flow rate of ~2700 m3/s would give us a peak power output of 2.132 GW. Over the course of a year (on average, 8766 hours), the average power output would get us 7.61 TWh, or 2.74e+16 Joules.

Putting that into perspective, that would be 0.27% of the EU27 electricity usage... pretty sobering, isn't it?

Now, the question is, can we do better than this?

Hey, I am an engineer; of course we can do better than this! See you next time...

How much electricity do we use? (Europe / EU27)

In this first post, I will provide the one thing that takes emotions out of debates: numbers. Hard and cool numbers.

If one wishes to assess the effectiveness of electricity-generation methods, one first has to know how much electrical energy is needed in the first place. This is post, I will focus on the EU27 . The EU fortunately is very willing to openly share its statistics on many things, which means that numbers are readily available. Lots of tables can be found here, where the table on

final energy consumption of electricity is most interesting for our purposes.

In short, the EU27 has an annual energy consumption of slightly less than 246 million toe (2008), which (taken one of the various definitions, as 42 GJ per toe), pretty much comes down to 1e+19 Joules. This amount of course is not evenly distributed over the year, and there is also a large variation depending on the time of day. The total gross electricity generation in the EU27 is 3.37 TWh (2008), which comes down to about 1.2e+19 Joules. The ~20% difference between net consumption and gross production can be attributed to energy use by the plants themselves, and transport losses. At any rate, it is the gross number that we need to produce to cover Europe's electricity needs.

The electricity is currently generated by the following methods (2008):

• Nuclear: 937236 TWh (27.8% of total)
• Natural gas: 774773 TWh (23.0% of total)
• Hard coal: 534035 TWh (15.8% of total)
• Hydroelectricity: 359185 TWh (10.6% of total)
• Wind: 118733 TWh (3.5% of total)
• Petroleum products: 104498 TWh (3.1% of total)

This sums up to 83.8%, or almost exactly 1e+19 Joules. This means that either the remaining 16.2% is not listed, or the figures in the above list are -by accident- net numbers. However, the statistics pages state that they are gross numbers, so I assume that the 16.2% of smaller electricity-generating methods was simply not included.

At any rate, if we wish to make an order-of-magnitude estimation of what we can achieve with electricity-generating methods, we can very well live with a 1e+19 Joule consumption.

Why this blog?

The development of our civilization, as well as the trend to cut emissions, leads to an electrification of our societies. That -in itself- is a good thing, but unfortunately the political debate around energy/electricity generation by conventional or renewable means is conducted in a very emotional manner.

Although I am all for alternative methods of generating electricity, the methods in question need to be able to supply electricity in sufficient amounts, and reliably. I feel that especially the emotional debate around some renewable energy methods forgets these two absolutely necessary conditions.

Therefore, in this blog, I will try to assess some energy generations methods to find out whether they -even when taken to the Extreme- will be able to provide enough electricity for our needs.