Scotland best for pumped-storage hydroelectricity energy economy

Scotland best for pumped-storage hydroelectricity energy economy

This is a statement of the obvious as far as Scottish electrical power-generation engineers and scientists are concerned I expect but I am making this statement anyway, not for the benefit of our scientists or engineers but to inform the political debate about the potential of the Scottish economy "after the North Sea oil runs out" because political debate involves mostly non-scientists and non-engineers who need to have such things explained to them.

The Scottish economy has a profitable living to make in future in the business of electrical energy import/export from/to English electrical power suppliers and perhaps even to countries further away one day.

The tried and tested engineering technology we Scots can use in future to make money is pumped-storage hydroelectricity.





In Scotland, the Cruachan Dam pumped-storage hydroelectric power station was first operational in 1966 and was built there to take advantage of Scotland's appropriate geography and available capital.

So Scotland has the appropriate geography for pumped-storage hydroelectric power and we have the capital particularly if we invest some of the taxes on North Sea oil before it all runs out and it is all spent.

Investment in wind-power energy generation is proceeding apace, in Scotland, in England, on and offshore, and that's very "green" and quite clever, though wind power is not as dependable as tidal power, but unless and until sufficient capacity to store energy becomes available to supply needs when the wind isn't blowing then conventional, and perhaps increasingly expensive, coal, gas or oil burning or nuclear energy power will still be needed to keep the lights on when the wind doesn't blow.

Scottish opportunity
Here is the opportunity for the Scottish economy in a future where wind-power generation is increasingly rampant: if we Scots build a large capacity of new pumped-storage hydroelectric power stations, not only can we supply all our own Scottish energy needs from "green" renewable energy schemes, but we could provide energy storage capacity for customers outside Scotland, particularly in England, who live in a land not so well endowed with appropriate geography for hydroelectric power.

In future, a Scotland with investment in a massive pumped-storage hydroelectric capacity could buy cheap English wind-power while the wind is blowing then sell the same energy back to English power suppliers, at a profit, when the wind isn't blowing and the English will pay more for energy.

So everyone wins, the energy is all green, the electricity supply is always available when it is needed and that is how the Scottish energy economy does very well after the North Sea oil runs out. 8)

So problem solved but not job done as yet. We Scots do actually need to get busy investing and building pumped-storage hydroelectric power generation and supply capacity in Scotland now.

You should be commended for taking interest in this form of power generation and I am sure you will make a good contribution to the discussions taking place about the dam but I am sorry to tell you how your plan is flawed.

The catchment area for the dam is the highest peaks facing towards the dam and this is the same in both yours and the official plan. This and the annual rainfall in the area sets the limit on how much water can be obtained within 1 year. You now divide this by 12 to find how much water per month is required for continuous generation. Now you look how much water falls in each individual month and look to store as much water as will be needed to supply the plant for the driest months, where you will have a deficit of water and this is the size of dam you need. Normally the dam will be a little bit larger than this to build in a margin of safety. The size of the dam has to be matched to the catchment area and the annual volume of water.

I don't know what the rainfall figures are for this area, but the original plan looks about right for the catchment area, using a rule of thumb view on it.

I notice that this new proposed dam feed into another dam, effectively increasing its capacity without threatening roads and villages in the area. I also notice that there are similar sites in the area where similar things could be done and no doubt similar plans have been made.

Thumbs up for looking for a better solution but as usual things get a little more complicated when you look in detail.

Take a look at the following page: The Josef Hasslberger page: Technology

See half way down in the "Calculation" section:

Basically in the example above: if you can get a stream which has a flow of 5 cubic meters per second. And increase the velocity to 25 m/sec (by narrowing the path the water takes and then through a funnel), you could produce over 1.5MW of power.

With no environmental destruction required...

Pumped-storage hydroelectricity

Thank you for your reply and for bumping this topic but I am pleased to tell you that you misunderstand. The plan is not flawed and I will explain.

It's a pumped-storage hydro dam scheme. The upper reservoir ("dam") is filled by pumping up water from a lower reservoir, lake or in this Scottish case, "loch".

You ought to educate yourself about pumped-storage hydro dams. I suggest this link.

The reason that additional pumped storage capacity is required is because of the increase in wind power generators means energy surpluses when the wind blows hard and deficits when the wind is calm - hence a need for much greater load balancing.

That'll be "Loch Lochy" which will serve as the lower reservoir for the pumped storage hydro scheme.

Yes they do. So I suggest that you look in more detail before assuming you know best.

Energy stored in a hydroelectric dam

The gravitational potential energy stored in a hydroelectric dam is

Energy = mass of water x acceleration of free fall due under gravity x height of the center of mass of the water above lower reservoir or turbine outlet.

E = m g h

For my proposed dam, those values would be about

m = 400 million Mega-grams = 4 x 10^11 Kgs (at most, an approximate figure)
g = 9.81 m/s^2 (assuming the standard gravity and local gravity won't be much different from that)
h = 569 metres (when then dam is full, by design)

So that works out to be
E = 2.2 x 10^15 Joules or 6.2 x 10^11 kW.hrs or 620 GigaWatt-hours

If you read the web page I linked to (The Josef Hasslberger page: Technology), you will understand the example. And why no dam is required, even for GigaWatt-hours of electricity.

Ahhh your proposal makes more sense now, Its a capacitor

Your dam would be for stored energy that was overcapacity that would not otherwise be used.

Although the efficiency is low, I don't agree with wikipedia, it does not matter because the input power is free.

Sorry I wasn't paying attention I jumped in based on a system I was working on for BP 20+ years ago, they wanted hydro electric power to drill for oil. I designed a 100Kw hydraulic drive system that gave constant power from a varying flow of water down a river. This was a cheaper alternative to a dam and also damming the area would prevent loggers from harvesting the trees in a vast area and the timber would have been lost. (amazon rain forest). We had to so a study to prove our system was better and so did the calculations for a dam. Our system was four huge pontoons with massive paddle wheels bigger than you get on a Mississippi paddle streamer, with a hydraulic drive to a generator on land.

This part of Scotland is a beautiful part of the world by the way, I have been there about 12 years ago, lovely people too.

Thank you for your interest my friend but in this case, a dam is required.

Right.

Well the efficiency is not too bad, Wikipedia say "70% to 87%" in practice.

So you get back most of the energy you put in.

That's not bad efficiency and the low cost of the raw materials which store the energy, low cost in Scotland anyway - water, concrete and hills - means it is easy to make an operating profit once you've invested enough to build the hydro scheme.

No need to apologise my friend. I am pleased that you bumped my topic!

Good thinking.

Although we have hills in Scotland people like to use them to walk in and to climb and enjoy in many other ways and so there is a duty on me to try to think of ways to use the least number of hills and the way to do that is to build bigger, higher dams in a few locations rather than many smaller lower dams all over the place.

You are very kind. To be honest I could do with more love from the Scots. For example, I am 51 and I have not found any women to bear my children in life even though I love women a lot, not just Scots women but all kinds of women, they don't seem to love me back, not much anyway.

In addition, I have been excluded from the local universities in Aberdeen. I have been arrested and tortured by the Queen's police and jailed for my outspoken nature and politics.

This is my website all about the politics of Scotland from my revolutionary republican perspective.

Peter Dow's Scottish National Standard Bearer website.

I would rather that non-Scots ask of or about the Scots - "how dare the Scots leave their beautiful country in the hands of that Queen whose state she is head of is mistreating that good Scotsman, Peter Dow, and other good Scots, so badly?"

I think sometimes the harsh truth is kinder in the long run.

I am not so complacent about the Scots. I call on our people to rise to a higher standard still, throw off the monarchy and establish a Scottish republic.

Meanwhile, I had better make sure that my hydro-dam scheme doesn't flood any Scots out of their homes or they will love me even less.

This is how I plan to keep people's feet and homes dry.

Loch Lochy and vicinity water flow control works

Here is an annotated satellite photograph of the land south from Coire Glas showing Loch Lochy, Loch Arkaig, the isthmus between the lochs, Mucomir where Loch Lochy empties into the River Spean before it flows on as the River Lochy, the Caledonian Canal and Fort William where the river flows into a sea loch.




Click to see larger image

New waterway

Loch Lochy is separated from a neighbouring loch, Loch Arkaig, by a 2 km wide isthmus, which I have identified on this map as "the Achnacarry Bunarkaig isthmus", after the local place names.

It ought to be quite straight forward to build a canal or culvert, to connect those two lochs. The idea is that the new waterway would be wide and deep enough, enough of a cross section area under water, perhaps hundreds of square metres, so as to allow free flow from one loch to the other, so as to equalise the surface elevations of the two lochs, so as to increase the effective surface area of Loch Lochy so as to decrease the depth changes to Loch Lochy when water flows in from the Coire Glas reservoir when it discharges water when supplying power.

Now, Loch Arkaig has a natural surface elevation of 43 metres and this would be lowered to that of Loch Lochy. The surface area of Loch Arkaig is given by wikipedia as 16 km^2 also, (though it looks to me somewhat smaller than Loch Lochy). In addition, partially draining Loch Arkaig to bring its level down to that of Loch Lochy will also reduce its surface area.

If say, the additional surface area of Loch Arkaig is about 10 km^2 added to Loch Lochy's 16 km^2 this would give an effective surface area of 26 km^2 and reduce the potential depth variation to

Potential depth variation of Loch Lochy + Loch Arkaig = 400 000 000 m^3 / 26 000 000 m^2 = 15.3 metres.

Without equalising the loch levels, the depth changes to Loch Lochy that would require to be managed may be potentially more like 25 metres than 15 metres. So the new waterway is an important part of the new water flow control works that Coire Glas/Dow requires to be constructed.

Additional Loch Lochy water level control measures

When the Coire Glas reservoir is full, then the water level of Loch Lochy should be prevented, by new water works - drains, dams, flood barriers etc. - from rising due to rainfall and natural flow into the loch above a safe level which allows for the reservoir to empty into the loch without overflowing and flooding.

The safe "upper-reservoir-full" loch level will likely turn out to be around about 15 metres below the maximum loch level.

The next diagram showing the new loch drain and the reservoir pump inlets indicates how this might be achieved.




Click to see larger image

The drain from Loch Lochy to the sea which goes underground from the 14 m elevation level in the loch would need capacity for the usual outflow from Loch Lochy which currently goes through the Mucomir hydroelectric station.

I have estimated the flow through Mucomir from its maximum power of 2MegaWatts and its head of 7m as somewhere near 0.2 Mega-cubic-metres-per-hour and compared that value using a spreadsheet I have written to predict the capacity of water flow through different sizes of drains using the empirical Manning formula and this is also useful for determining the appropriate size of the new water channel between the lochs.


Ease my quantity

To construct Coire Glas/Dow/600GW.Hrs/12GW may cost of the order of around £20 billion, but that would be my order of magnitude educated guess more than a professional cost estimate.

In other words, I'm only really confident at this early "vision" stage that the cost would be closer to £20 billion than it would be to £2 billion or to £200 billion but I'm not claiming to be able to quote an accurate cost estimate at this stage.

I have not itemised my costs - how much for land, how much for labour, how much for trucks, how much for diggers, how much for cement, how much to install the generators etc. and the SSE have not published itemised costs for theirs either so I can't calculate my costs in a proportion to the SSE's costs.

Although my version offers 600 GigaWatt-Hours energy and 12 GigaWatts power (or 20 times the capacity and performance) some of the items in my version would cost more than "in proportion", in other words more than 20 times the SSE's cost.

For example, the cost of my dam will be more like 27 times the cost of the SSE's dam. (3.44 times higher and thicker and 2.27 times longer).

For example, the cost of excavating 400 million tonnes of rock from the reservoir bed to increase the capacity of the reservoir to hold water (and energy) in my version won't be in proportion to the SSE costs for excavating their reservoir bed because, as far as I know, they don't plan to excavate their reservoir bed at all.

On the other hand, my land costs are about the same as the SSE's - much less than in proportion. I may well need to use more land to dispose of the additional excavated rock spoil but perhaps when that additional land has been landscaped over it could be resold?

So it depends how much the land is as a proportion of the SSE's costs. If land is a small part of their costs, if 20 similar sites to build on are just as cheap and easy to buy then my costs will be much more than proportional, since saving land won't save much money.

If land is scarce and valuable and the cost to purchase suitable land with a good chance to get permission to build on it is a significant proportion of the SSE's or anyone's costs to build 20 of their size of hydro dam schemes then my costs may be better than proportional. Sometimes securing suitable land for development can be very problematic, very expensive. Sometimes people won't sell their land. Sometimes the authorities won't agree that the land can be used in this way.

The SSE say that suitable sites for such pumped storage schemes are rare indeed, so land costs may be very significant and my scheme good value for money.

If indeed the cost of my scheme is somewhere around £20 billion it is likely to cost far more than the SSE or any electrical power supply company looking to their annual profits for the next few years could possibly afford.

Something like £20 billion I expect could only be found as a national public infrastructure project, spending government money, like the building of a large bridge or motorway would be.

A £20 billion government project would require Treasury approval, at least while Scotland is ruled as part of the UK.

I have suggested funding my much larger hydro dam scheme by re-allocating of some of the Bank of England's "Quantitative Easing" funds which amount to some £300 billion of new money printed with not much to show for it.

Geology of the Coire Glas site

Geology of the Coire Glas site
I have been able to extract this information from the British Geological Survey (BGS) Geology of Britain viewer, from the 1:50 000 scale map.




Click to see larger image

According to this map, the bedrock at the site which would be used to build the dam on top of and to extract rock from to create the tunnels for the underground complex seems to be a rock geologists call "psammite" which I understand to mean here "a metamorphic rock whose protolith was a sandstone".

What neither the map nor the "psammite" name is telling us is how fractured the psammite rock there is and therefore how strong and also how impermeable or otherwise to water this rock is likely to prove to be, both of which would be interesting for any engineers building a pumped-storage hydro dam scheme there to know.

What does look fairly obvious to me is that the superficial deposit of what the map calls "hummocky (moundy) glacial deposits - diamicton, sand and gravel" would not be strong enough, nor impermeable enough to build any dam on top of and at least along the line of the dam, this glacial deposit ought to be removed to get down to the bedrock within which to establish the foundations of the dam, although I would think that this glacial deposit might be made into aggregate to make the concrete for the dam by the sounds of it.

Dam foundations and height of the dam above the bedrock
The top of the Dow-Dam has an elevation of 780 metres by design.




Image also hosted here

The lowest elevation of the current ground surface of Coire Glas along the line of the proposed dam is 463 metres and subtracting 463 from 780 is how the initial value of 317 metres for the nominal height of the dam above the existing surface used in previous diagrams was arrived at.

However, the glacial deposit of as yet unknown thickness is to be removed before building the foundations of the dam within and upon the bedrock.

Although the lowest surface elevation along the line of the dam of the bedrock too is unknown a formula relating the Height of the Dam Above the Bedrock (HDAB) to the Glacial Deposit Depth (GDD) can be easily stated.

HDAB = 317 + GDD

Examples.

If the GDD turns out to be 13 metres then the dam will be 330 metres tall.
If the GDD turns out to be 83 metres then the dam will be 400 metres tall.




Image also hosted here

I propose that the height of the Dow-Dam be as tall above the bedrock as it needs to be to keep the top of the dam at an elevation of 780 metres no matter how deep the removed glacial deposit layer turns out to be.

My approach may well differ from the SSE's approach. The SSE have said that their dam will be "92 metres" high and they may stick to that without having any goal for the elevation of the top of their dam.

As the diagram indicates, I propose to secure the Dow-Dam to the bedrock by massive piles inserted and secured into shafts which would be drilled into the bedrock.

Spirit of Ireland, Seawater Pumped Storage Proposal, Shorter video - YouTube

Video which illustrates the principle of using wind turbines and pumped storage hydro dam schemes together.

"Dow" equation for the power and energy output of a wind farm

"Dow" equation for the power and energy output of a wind farm.

"The power and energy of a wind farm is proportional to (the square root of the wind farm area) times the rotor diameter".

In his book which was mentioned to me on another forum and so I had a look, David MacKay wrote that the power / energy of a wind farm was independent of rotor size which didn't seem right to me considering the trend to increasing wind turbine size.

Now I think the commercial wind-turbine manufacturing companies know better and very possibly someone else has derived this equation independently of me and long ago - in which case by all means step in and tell me whose equation this is.

Or if you've not see this wind farm power/energy equation before, then see if you can figure out my derivation!

No takers for the derivation challenge huh? OK then.

Derivation

Assume various simplifications like all turbine rotors are the same size and height, flat ground and a rotationally symmetrical wind turbine formation so that it doesn't matter what direction the wind is coming from.

Consider that an efficient wind farm will have taken a significant proportion of the theoretically usable power (at most the Betz Limit, 59.3%, apparently, but anyway assume a certain percent) of all the wind flowing at rotor height out by the time the wind passes the last turbine.

So assume the wind farm is efficient or at least that the power extracted is proportional to the energy of all the wind flowing through the wind farm at rotor height.

This defines a horizontal layer of wind which passes through the wind farm of depth the same as the rotor diameter. The width of this layer which flows through the wind farm is simply the width of the wind farm which is proportional to the square root of the wind farm area.

Wind farm turbine formations

Therefore the width or diameter of a rotationally symmetrical wind farm is a critically important factor and arranging the formation of wind turbines to maximise the diameter of the wind farm is important.

Consider two different rotationally symmetrical wind turbine formations, I have called the "Ring formation" and the "Compact formation".

Let n be the number of wind turbines in the wind farm
Let s be the spacing between the wind turbines

Ring formation




Larger image also hosted here

The circumference of the ring formation is simply n times s.

Circumference = n x s

The diameter of the ring formation is simply n times s divided by PI.

Diameter = n x s / PI

Compact formation




Larger image also hosted here

The area of the compact formation, for large n, is n times s squared. This is slightly too big an area for small n.

Area = n x s^2 (for large n)

The diameter of the compact formation, for large n, is 2 times s times the square root of n divided by PI. This is slightly too big a diameter for small n.

Diameter = 2 x s x SQRT(n/PI)

This is easily corrected for small n greater than 3 by adding a "compact area trim constant" (CATC) (which is a negative value so really it is a subtraction) to the s-multiplier factor.

The CATC is 4 divided by PI minus 2 times the square root of 4 divided by PI.

CATC = 4/PI - 2 x SQRT(4/PI) = - 0.9835

This CATC correction was selected to ensure that the compact formation diameter equation for n=4 evaluates to the same value as does the ring formation equation for n = 4, that being the largest n for which the ring and compact formations are indistinguishable.

The CATC works out to be minus 0.9835 which gives

Diameter = s x ( 2 x SQRT(n/PI) - 0.9835) (for n > 3)

Ratio of diameters




Larger image also hosted here

It is of interest to compare the two formations of wind farm for the same n and s.

The diameter of the ring formation is larger by the ratio of diameter formulas in which the spacing s drops out.

Ring formation diameter : Compact formation diameter

n/PI : 2 x SQRT (n/PI) - 0.9835

This ratio can be evaluated for any n > 3 and here are some ratios with the compact value of the ratio normalised to 100% so that the ring value of the ratio will give the ring formation diameter as a percentage of the equivalent compact formation diameter.

Here are some examples,

n = 4, 100 : 100
n = 10, 123 : 100
n = 18, 151 : 100
n = 40, 207 : 100
n =100, 309 : 100
n =180, 405 : 100
n =300, 514 : 100
n =500, 656 : 100

As we can see that for big wind farms, with more turbines, the ratio of diameters increases.

Since the Dow equation for the power and energy of a wind farm is proportional to the diameter of the wind farm then it predicts that the power and energy of the ring formation wind farms will be increased compared to the compact formation wind farms by the same ratio.

In other words, the Dow equation predicts, for example, that a 100 turbine wind farm in the ring formation generates 3 times more power and energy than they would in the compact formation, assuming the spacing is the same in each case.

Practical application when designing a wind farm

My recommendation would be to prefer to deploy wind turbines in a wind farm in the ring formation in preference to the compact formation all other things being equal.

The compact formation can be improved up to the performance of a ring formation by increasing the turbine spacing so that the circumference is as big as the ring but then if a greater turbine spacing is permitted then the ring formation may be allowed to get proportionally bigger as well keeping its advantage, assuming more area for a larger wind farm is available.

The ring formation may be best if there is a large obstacle which can be encircled by the ring, such as a town or lake where it would not be possible or cost effective to build turbines in the middle of it and so a compact formation with larger spacing may not be possible there.

Where it is not possible to install a complete ring formation then a partial ring formation shaped as an arc of a circle would do well also.

Reservoir bed drain

Reservoir bed drain

The high pressure of water which is deeper than 100 metres has the potential to induce seismic activity or earthquakes in susceptible rock in which a new reservoir has been constructed.

Coire Glas/SSE/92 m

Hopefully, reservoir induced seismicity was an issue considered by the SSE when selecting Coire Glas for their hydro dam project.

I am speculating that this issue may be why the SSE have limited their dam to a height and their reservoir to a depth of 92 metres?

I would note however that the pressure in the head race tunnels which supply water from the reservoir to the turbines would be proportional to their depth below the surface of the reservoir and this could be as much as 500 metres deep, so there would seem to be some potential for water to penetrate the bed rock from the high pressure water tunnels and induce seismic activity even in the SSE case.

This is an issue which ought to have been addressed in the many previous pumped-storage hydro scheme projects, most of which seem to have a difference in head of more than 100 metres.

Given that "understanding ... is very limited" according to Wikipedia, though, I do wonder if the reservoir induced seismicity issue has not always been properly addressed in all previous dam and reservoir construction schemes where the great depth of water and susceptible geology ought to make it a relevant concern?

Coire Glas/Dow/317+m

I am proposing measures to counter the reservoir induced seismicity effect in the case that the geology of Coire Glas is susceptible to it and in the general case.

I propose the construction of a large reservoir surface drain to cover the whole reservoir bed and the reservoir sides too to try to stop the penetration of water under high pressure into fractures in the bedrock and so thereby stop this high pressure water from widening and extending bedrock fractures.

To illustrate my "reservoir bed drain" concept, I have drawn a diagram comparing the usual no drain on the left, with my proposed reservoir bed drain on the right.





Image also hosted here.

So my idea is that the top layer of the bed drain is as impermeable as practical, using perhaps a layer of reinforced asphalt concrete.

In engineering practice I believe that impermeable reservoir bed layers have used clay or clay with asphalt or even rubberised asphalt mixed with sand.

My basic idea is to construct an impermeable layer and to use whatever material is best for that.

Then working downwards, the permeable drain layers are increasingly bigger loose particles, with sand at the 2nd top then beneath that grit, then gravel, then small stones and finally below all those a layer of large stones.

The higher layers support the top impermeable layer which is under high pressure from the reservoir water and the lower permeable layers provide many small channels for any (hopefully tiny amounts of) water which forces its way through the supposedly impermeable top layer to drain down the slope of the reservoir bed to the base of the dam and then out under the dam through drain-pipes built into the base of the dam.

The bottom layer is another impermeable layer to try to make doubly sure that the relatively low pressure water that gets into the drain will find its way out through the dam drain pipes by following the course of the drain.

These kinds of layers of different sized loose particles have previously been used to make simple narrow drains and impermeable layers have been added to reservoir beds before now but whether professional dam engineers have ever covered the entire reservoir bed and sides with one large drain I don't know. If not, this could be named the "Dow drain" solution to reservoir induced seismicity!

Why not add a simple impermeable layer to the reservoir bed?

I think the additional complexity and expense of a bed drain (and drains for the sides too) is better than simply adding an impermeable layer.

Consider the fault condition of the two possible solutions.

If a simple impermeable layer fails, if it cracks or ruptures or disintegrates under the pressure changes, how would anyone know? It may look fine but be leaking high pressure water into the bedrock and inducing seismicity which OK the engineers would notice any earthquakes but so would everyone else, the earthquakes could cause damage or loss of life and it could lead to a loss of confidence in the project and in the engineers who built it. They could go to jail!

If the top impermeable layer of the bed drain fails then there would be some water pouring out of the drainpipes through the base of the dam when at most it should only be a tiny trickle of water. So the engineers would know there was a problem with the bed drain and they'd know to drain the reservoir and fix or replace the top supposedly "impermeable" layer, fix the bed drain so that it operated as it should.

So failure with the bed drain is noticed right away and it is not a catastrophic failure. Whereas failure with the simple impermeable layer may not be noticed until a catastrophic earthquake happens.

So this is why I think the bed drain is worth the extra complexity and expense. It is a more fault tolerant engineering solution.