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Thread: Large Scottish Pumped Storage Hydroelectric Reservoir and Dam (@ Coire Glas)

  1. #1 Large Scottish Pumped Storage Hydroelectric Reservoir and Dam (@ Coire Glas) 
    Forum Sophomore Peter Dow's Avatar
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    I am presenting here my vision for a large pumped storage hydroelectric 2-square kilometres surface-area reservoir and 300+ metre tall dam which I have designed for the Coire Glas site, Scotland.

    (View site using Google Earth where the convenient label is "Loch a' Choire Ghlais" - or, Loch a' Choire Ghlais - Google Maps)

    I was inspired to conceive and to publish my vision by learning of the Scottish and Southern Energy (SSE) proposal to build a smaller hydroelectric pumped-storage scheme at Coire Glas which has been presented to the Scottish government for public consultation.

    I have not long been aware of the SSE plan for the Coire Glas scheme, not being a follower of such matters routinely, but I was prompted by an earlier tangentially-related news story (about energy storage technology for renewable energy generators such as wind farms) to write to Members of the Scottish Parliament on the merits and urgency of new pumped storage hydroelectric power for Scotland on 14th February and a reply from Ian Anderson, the parliamentary manager for Dave Thomson MSP received the next day, the 15th February informed me about the SSE plan and Ian added "initially scoped at 600MW but, to quote SSE, could be bigger!"

    I replied to Ian "So the schemes proposed by the SSE are welcome and ought to be green-lighted and fast-tracked, but I am really proposing that Scots start thinking long term about an order of magnitude and more greater investment in pumped storage hydroelectric capacity than those SSE plans."

    So I had in mind "bigger would be better" but it was not until the next day on the 16th February when a news story informed me that the SSE plans had been submitted to the Scottish government for public consultation that I thought "this needs consideration now".

    So starting late on the night of the 17th, early 18th February and all through the weekend, I got busy, outlining my alternative vision for a far bigger dam and reservoir at the same location.

    So this is my vision as inspired by the SSE plan. If my vision is flawed then the fault is mine alone. If my vision is brilliant, then the brilliance too is mine.



    Image also hosted on postimage


    The black contour line at 550 metres elevation shows the outline of the SSE proposed reservoir of about 1 square kilometre surface-area and the grey thick line shows the position of the proposed SSE dam which would stand 92 metres tall and would be the tallest dam in Scotland and indeed Britain to date though it seems our dams are several times smaller than the tallest dams elsewhere in the world these days.

    Part of the red contour line at 775 metres elevation, where the red line surrounds a blue shaded area, blue representing water, shows the outline of my larger reservoir of about 2 square kilometres surface-area and the thicker brown line shows the position of my proposed dam which would stand 317 metres tall which would be one of the tallest man-made dams in the world.

    Cross section of the Dow-dam reservoir



    Cross section along the major diameter of the elliptical excavation of the reservoir bed


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    Excavated Reservoir Bed

    The green ellipse of major diameter of 1.5 kilometres and minor diameter of 1 kilometre represents an excavated reservoir bed, as flat and as horizontal as practical, at an elevation of 463 metres.

    Since an excavated reservoir bed is not, that I can see, part of the SSE plan, at any size, I will provide some more information about my vision for that now.

    The basic idea of excavating a flat or flattish reservoir bed is to increase the volume of the water stored in the reservoir because more water means more energy can be stored.

    Depending on the geology and strength of the rock of Coire Glas the walls of the reservoir bed perimeter could be as steep as vertical from the reservoir bed up to the natural elevation of the existing rock surface which would mean, presumably, blasting out rock to create a cliff which at places could be as much as about 290 metres tall.

    Near the dam, the reservoir bed perimeter wall would be only 40 metres or less tall. The further from the dam, the higher the wall will be and the more rock needs to be excavated.

    A vertical reservoir bed perimeter wall would be ideal to maximise reservoir volume wherever the geology provides a strong stone which can maintain a vertical wall face without collapse, a stone such as granite perhaps).

    Where the geology only provides a weaker stone then a sloping perimeter wall at a suitable angle of repose for reliable stability would be constructed.

    So the reservoir perimeter wall could be as sloped as shallow as 45 degrees from the natural elevation at the perimeter of the eclipse sloping down to the reservoir bed at 463 metres elevation in the case of the weakest and most prone to collapse kinds of stone.

    Exactly how strong the stone is at each location I guess we'll only find out absolutely for sure if and when engineers start blasting it and testing the revealed rock wall face for strength.

    The shape of the perimeter of the excavated reservoir bed is not absolutely critical. So long as it ends up as a stable wall or slope, however it is shaped by the blasting, it will be fine. There is no need to have stone masons chip the perimeter smooth and flat! The ellipse is simply the easiest approximate mathematical shape to describe and to draw. If the end result is not a perfect ellipse, don't worry, it will be fine!

    OK, well I guess that's the vision part over. The rest is fairly straight-forward engineering I hope. Oh, and there is always getting the permission and the funding to build it of course which is never easy for anything this big.

    OK, well if anyone has any questions or points to make about my vision or can say why they think the SSE plan is better than mine, or if you don't see why we need any pumped storage hydroelectric scheme at Coire Glas, whatever your point of view, if you have something to add in reply, please do.


    Last edited by Peter Dow; February 21st, 2012 at 08:44 PM.
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    Enhanced satellite photograph




    Image also hosted on PostImage.Org

    Cross section of the Dow-dam

    The Dow-dam would be more than 3 times higher than the proposed SSE-dam. In this diagram, a horizontal line one third of the way up the Dow-dam indicates the relative height of the SSE dam although it is not aligned with this cross-section.




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    Maps showing the line of cross-section viewed from each side




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    Some vision- what cost estimates for each version are available?
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    Maybe build something on the scale (and cost) of the SSG dam, providing for expansion to this ultimate DOW dam. Of course that's a redesigned and very overbuilt initial dam, but the cost could match the funds. And you'd get your DOW in time.
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    Quote Originally Posted by Arthur Angler View Post
    Some vision- what cost estimates for each version are available?
    Thank you for your question and sorry for not replying sooner. I forgot to order a notification watch for new replies.

    The SSE have provided a cost estimate of 800 million for their 30 GigaWatt-Hour energy store, 600 MegaWatts power version.

    BBC: SSE plans new 800m hydro electric storage scheme in Great Glen

    I've said maybe my version would cost of the order of around 20 billion, but that would be my order of magnitude educated guess more than a cost estimate.

    In other words, I'm only really confident 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 scare 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.
    Last edited by Peter Dow; March 4th, 2012 at 02:16 PM.
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    How much water flows into that coire? Just wonderong since from the map it looks like inflow comes from a few run-off streams. Is that sufficient to fill up the dam in a reasonable amount of time?

    I don't know anything about dams, so apologies in advance if this is a silly question.
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    Quote Originally Posted by Pong View Post
    Maybe build something on the scale (and cost) of the SSG dam, providing for expansion to this ultimate DOW dam. Of course that's a redesigned and very overbuilt initial dam, but the cost could match the funds. And you'd get your DOW in time.
    SSE, for "Scottish and Southern Energy". What does your "G" in SSG stand for, or is it just a typo?

    The time to build a major infrastructure project like my mega-dam is a time like now when the economy is weak, sluggish, with mass unemployment and in need of a stimulus, but the economy would do better in the long run with intelligent investment, rather than the Bank of England's brainless "Quantitative Easing".

    Better to build now when we have the slack in the economy to do it. If we leave it until years later, the dumb bankers may have started another housing price bubble and all the workers will be building luxury homes for bankers to spend their bonuses on and there will be no-one available to build energy storage schemes and so we'll be stuck with fossil fuel power when the wind is becalmed.

    Also the SSE are in no hurry to start building. So long as they are not building theirs, I'm going to argue that instead of waiting before the SSE builds there, we build mine now.

    My vision is not a proposal with financing secured that is ready to go and the immediate decision to be made is by the Scottish government which has to take a decision soon on an application to them by the SSE for permission to build on the Coire Glas site.

    This was my response to the Scottish government's public consultation as regards their decision.

    So what should the approach of ministers be to the SSE proposal which is on the table?

    I think turning the SSE's proposal down flat would send the wrong signal to the SSE.

    I think the SSE need praise and encouragement for their proposed hydro dam scheme at Coire Glas.

    I think the SSE's hydro dam would be better than no hydro dam scheme at all which is what there will be if no strategic investment is forthcoming from government for a much larger proposed hydro dam scheme.

    Since the SSE seem in no great hurry to build their hydro dam scheme at Coire Glas, if I was the minister what would I say, what would I decide?

    Something along these lines perhaps?





    "OK, the SSE proposal for a hydro dam scheme at Coire Glas has provisional approval - go ahead, as fast as you like.

    Meantime, noting the SSE's plans to delay construction, before the SSE has built your dam at Coire Glas, for so long as no bigger, better hydro dam scheme for Coire Glas comes forward with the financial backing to build it then the SSE may proceed with their proposed scheme at Coire Glas.

    However, we the Scottish government are keeping an open mind and keeping the options open for a bigger, better hydro-dam scheme at Coire Glas which the SSE or other interested parties can bring to the Scottish government for approval on any date before the SSE has built on the site."







    I certainly would not wish to delay the SSE building at Coire Glas but since they seem in no great hurry to build I think it wrong that the SSE should keep a veto on any bigger, better hydro dam scheme at Coire Glas going ahead meantime.

    I don't think Coire Glas should sit unused for years with a sign on it saying "reserved for the sole use of the SSE - everyone else hands off!". I think Coire Glas is too important a site, with too much potential to sit idle if something better is on offer sooner.
    Last edited by Peter Dow; March 6th, 2012 at 06:58 AM.
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    Quote Originally Posted by Zwirko View Post
    How much water flows into that coire? Just wonderong since from the map it looks like inflow comes from a few run-off streams. Is that sufficient to fill up the dam in a reasonable amount of time?

    I don't know anything about dams, so apologies in advance if this is a silly question.
    It's OK, even silly questions are usually better than no questions at all because it bumps the topic and helps keep the topic in view.

    This is a pumped storage hydroelectric dam scheme whose reservoir is filled, not by direct rain fall, nor streams, but by water pumped up from a lower reservoir, in this case "Loch Lochy".

    The volume of water held by the reservoir in my scheme when full will be about 400 million cubic metres.

    At full power (12 GigaWatts) the dam will empty in 50 hours and may take quite a lot longer than 50 hours to fill depending on the power and efficiency of the pumps, and the availability of cheap excess renewable power, such as on a very windy day, since the dam only gets filled up when there is excess power available.
    Last edited by Peter Dow; March 4th, 2012 at 03:42 PM.
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    Ah, so that's what "pumped storage" means. I really should have known that.


    I can't help but notice that the complete emptying of your dam in 50 hrs (400 million cubic meters) would substantially alter the volume of the loch (wikipedia tells me the volume of Loch Lochy is 1.1 km^3). Again, I don't know anything about pumped-storage, so I'm thinking about the operation of such a dam and wondering about what sorts of changes in water level would be observed when in operation. Emptying it one go would not be the standard way of operating the facility would it? Or would it?
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  11. #10 Options for draining Loch Lochy 
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    Quote Originally Posted by Zwirko View Post
    I can't help but notice that the complete emptying of your dam in 50 hrs (400 million cubic meters) would substantially alter the volume of the loch (wikipedia tells me the volume of Loch Lochy is 1.1 km^3).
    Indeed, 400 million cubic metres is 36% of 1.1 km^3 or 1100 million cubic metres.

    The Wikipedia entry for Loch Lochy may have to be updated to describe the effect of the large flows in and out of the loch. Updating the Wikipedia entry is the easy bit.

    Quote Originally Posted by Zwirko View Post
    Again, I don't know anything about pumped-storage, so I'm thinking about the operation of such a dam and wondering about what sorts of changes in water level would be observed when in operation.
    The observable effect is more to do with the surface area of Loch Lochy of 16 km^2 than the volume. A deeper loch with more volume but the same surface area would behave much the same.

    Consider the full upper reservoir volume distributed as the top layer of Loch Lochy, before being pumped up.

    For simplicity, neglecting that the loch shore is not a vertical cliff, the depth of water "off the top" from the loch required is

    Depth = Volume / Surface area = 400 000 000 m^3 / 16 000 000 m^2 = 25 metres.

    In reality, the sloping loch shore will mean that a greater depth than 25 metres "off the top" will be required to fill the upper reservoir.

    Likewise on the way down, there's 25 metres worth to distribute somehow.

    It's an issue which I have only recently started considering so I am thinking out loud here.

    There seem to be two broad options.

    Option 1.

    Let Loch Lochy drain 1/3rd empty, 2/3rds full and keep it that way when the upper reservoir is full so that the upper reservoir can empty out into the loch any time.

    Now, there's a problem with option 1 only if there's a lot of rain and the loch starts filling up from 2/3rds full to completely full naturally because then there'd be no room in the loch to dump another 25 metres worth so you'd need a new way to drain the loch to keep it down at 2/3rds full even when it rains.

    The existing out flow channels from the loch will probably be high and dry when the loch is only 2/3rds full so those existing channels cannot help to keep the loch drained at 2/3rds full, not without more work to make them at least as low as the loch 2/3rds full level all the way to the sea.

    Digging a 25+ m trench in the existing loch outflow channel and river to make it deeper would be one thing but then you have to stop the trench walls caving in, so it would need to be made wider or the walls reinforced.

    Or better than a trench might be an underground pipe or drain.

    Either way, trench or pipe, this outflow channel should be gated, be controllable like a floodgate so that you could drain or not drain according to whether you wanted to let the loch fill up because you needed more water to pump up to the upper reservoir.

    Otherwise not controlling the loch 2/3rds full drain with a gate means you might be faced with the situation of wanting to pump up to the upper reservoir from a loch which was only 2/3rds full and so you'd need your inlet to the pumps to be 25+ metres deeper than otherwise they'd have to be, 50 m or more deep and the loch is only about 70 metres deep on average anyway.

    Option 2.

    Let Loch Lochy drain 1/3rd empty, 2/3rds full temporarily when filling the upper reservoir but don't mind if Loch Lochy gets refilled naturally because you'd build if necessary additional outflow capacity to cope with the hydro dam reservoir unloading at its full rate.

    Right now, I have no idea how much can comfortably flow out now before the loch level starts rising but for Coire Glas/Dow we'd be talking 8 million cubic metres per hour flow from the upper reservoir at maximum. So I expect that would be a massive flow rate compared to what the loch outflow is able to cope with now.

    This is what the SSE plan for Coire Glas/SSE.

    4.2 Water Management

    4.2.1 Loch Lochy is currently controlled by SSE Generation Ltd at its existing hydroelectric powerstation at Mucomir (Gairlochy). Water is released from here through turbines to the River Spean and there are also floodgates to discharge larger flows as required.

    4.2.2 The operation of the Development would take priority over the operation of Mucomir Power Station, which would be managed to ensure that the operation of the Development was not constrained by Loch Lochy levels. Ultimately the total volume of water passed through the barrage in a year would remain unchanged.

    4.2.3 As part of the construction of the Development, Mucomir Power Station would be modified and a new operating regime determined with the aim to provide improved fish passage and flow management of the River Lochy downstream. This would include obtaining all necessary consents and relicensing. It is possible, although not guaranteed, that this modification may involve partially or completely decommissioning Mucomir as a power station and operating it solely as a regulating barrage and fish pass.

    4.2.4 Although the present maximum and minimum loch levels would not change, variations in Loch Lochy level between these limits could be expected to be more frequent.

    4.2.5 At the dam, a Q95 compensation flow would be released from the upper reservoir to maintain a constant flow from the upper reservoir down Allt a’ Choire Ghlais.
    Using Google image search turned up this photograph.



    Mucomir dam and hydro electric station

    Here's an aerial shot.


    Click for bigger image


    In the USA, they have these concrete flood control channels.


    What's the flow capacity of one of those?

    Perhaps widening and straightening the River Spean in this style to accommodate such additional flows would be required for an option 2 solution?

    Perhaps both options, perhaps a 3rd option. I'm still thinking about this.

    Quote Originally Posted by Zwirko View Post
    Emptying it one go would not be the standard way of operating the facility would it? Or would it?
    Well the concept here is that the reservoir would empty and supply its stored energy when there was a deficit of wind power.

    So it could be all in one go in a prolonged calm. So you'd need to design things so that the loch flows could cope with all 8 million cubic metres per hour emptying into the loch for 50 hours straight.
    Last edited by Peter Dow; March 6th, 2012 at 07:35 AM.
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    Quote Originally Posted by Peter Dow View Post
    I don't think Coire Glas should sit unused for years with a sign on it saying "reserved for the sole use of the SSE - everyone else hands off!". I think Coire Glas is too important a site, with too much potential to sit idle if something better is on offer sooner.
    I think you're right. That's why SSE should be compelled to provide that anything they build now may be expanded later. Expanded without service disruption. While the ultimate dam right now would be great, suppose the modest, original SSE plan gets started: then Scotland is stuck with an undersized dam for a century or more because it is inconvenient to demolish.
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    Peter,

    Have you looked at any possible impact on the Caledonian canal?

    I would also be interested in your thoughts regarding environmental impact. As I'm sure you are aware, addressing such concerns can form a substantial part of major proposals such as this.
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    Quote Originally Posted by Zwirko View Post
    Peter,

    Have you looked at any possible impact on the Caledonian canal?

    I would also be interested in your thoughts regarding environmental impact. As I'm sure you are aware, addressing such concerns can form a substantial part of major proposals such as this.
    I think it is safe to assume the environmentalists will oppose it, in spite of any alleged environmental benefits enumerated. This is a drearily familiar pattern of response. Excavation of a deeper basin would of course provide a convenient source of rock for the dam- forgive me for stating or restating the obvious, but best use of such material could be significant in terms of cost and time expenditure.
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    Quote Originally Posted by Peter Dow View Post
    Perhaps both options, perhaps a 3rd option. I'm still thinking about this.
    Here's my third option or 3rd additional measure since none of the options so far are mutually exclusive.

    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.




    Click to see larger image



    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 a few hundred 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.

    So this 3rd option, 3rd measure, looks like it would take care of 10 metres of the original 25 metre problem and leave less of an engineering task for option 1 and option 2 to deal with.
    Last edited by Peter Dow; March 7th, 2012 at 07:00 PM.
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    Quote Originally Posted by Pong View Post
    Quote Originally Posted by Peter Dow View Post
    I don't think Coire Glas should sit unused for years with a sign on it saying "reserved for the sole use of the SSE - everyone else hands off!". I think Coire Glas is too important a site, with too much potential to sit idle if something better is on offer sooner.
    I think you're right.
    Thanks.

    Quote Originally Posted by Pong View Post
    That's why SSE should be compelled to provide that anything they build now may be expanded later.
    Well rights for governments to make compulsory purchases of land for critical national developments, say to expand the size of a hydroelectric scheme are not rights "provided" by private companies. These are democratic rights intrinsic to a government and they always apply so it isn't something that a government has to state explicitly each and every time. It should be understood.

    What is good government is to make sure that investors get a good price for their investments if a need arises for a compulsory buy back. If a government treats investors badly then no-one else will invest.

    Quote Originally Posted by Pong View Post
    Expanded without service disruption.
    There is no practical way a hydroelectric scheme can be expanded "without service disruption". Realistically, there would have to be a long period of no-service from the site while it was upgraded. It may take even longer working around the first scheme than it would working on a green field site.

    Imagine for example, the additional difficulty of removing 400 million tonnes of excavated rock from the reservoir bed when there's a 92 metre dam blocking the exit from the reservoir! It's much easier to do all the excavation first, then build the dam.

    Quote Originally Posted by Pong View Post
    While the ultimate dam right now would be great,
    It would be great but it needs building and that is going to take some time to do, so "right now" is out.

    Quote Originally Posted by Pong View Post
    suppose the modest, original SSE plan gets started: then Scotland is stuck with an undersized dam for a century or more because it is inconvenient to demolish.
    Well unless an equally good site can be found and made available then at some point it probably will be more convenient to shut the SSE's scheme down and fill the gap in supply with fossil fuel generators until the new bigger, better scheme is completed.

    It's not the smart way to go - build too small then have to redo - but since when has business or government been smart?
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    Quote Originally Posted by Peter Dow View Post
    Quote Originally Posted by Pong View Post
    Expanded without service disruption.
    There is no practical way a hydroelectric scheme can be expanded "without service disruption". Realistically, there would have to be a long period of no-service from the site while it was upgraded. It may take even longer working around the first scheme than it would working on a green field site.
    Hypothetically, if your design was changed in height only - say to 100 meters - would it still work? Why would adding height to this stop operation?
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    Quote Originally Posted by Zwirko View Post
    Peter,

    Have you looked at any possible impact on the Caledonian canal?
    Not in any detail. If Loch Lochy varied from its present surface elevation down to say 15 metres lower then you'd probably need additional canal locks to get canal traffic down to the new lower loch levels. I don't see any major issues except for some interruption while the new locks are built.

    Then there is the prospect of a new waterway from Loch Lochy to Loch Arkaig to consider. It might be navigable most of the time enabling canal traffic to detour into Loch Arkaig to explore there if they wanted to but there is a catch.

    The new canal or culvert should be big enough to take canal traffic OK but this waterway may not always be navigable expect for fast traffic like speed boats because the currents through the new waterway when the hydroelectric turbines are running full power could well make it a one-way journey for most craft for a time.

    Since the turbines could be running continuously for 50 hours at full power an unsuspecting canal barge with a low power motor may find itself stranded in Loch Arkaig for a couple of days!

    Quote Originally Posted by Zwirko View Post
    I would also be interested in your thoughts regarding environmental impact. As I'm sure you are aware, addressing such concerns can form a substantial part of major proposals such as this.
    Well the SSE have considered environmental impacts so I'll deal only with the differences between my bigger scheme and their smaller scheme.

    Obviously my dam is bigger and will be more visible but I think that's OK. Dams are major national achievements and can serve as a tourist attraction. I think the impact of a dam will be positive for the local environment when completed.

    There would probably be more or bigger pylons to carry the additional electrical power. Some people won't like that so "don't look at the pylons which offend you then!" would be my reply!

    My bigger scheme would also have much more surplus excavated rock to dispose of than the SSE's scheme does.

    Local land could be bought and the surplus rock landscaped in and covered over with top soil, and returned to a natural state and possibly resold for other purposes.

    There are two broad options with the building of my scheme which needs 20 plus times more construction work compared to the SSE's scheme.

    One option would be to spend money 20+ times faster and get the construction job done in the same time. That means 20 times more intense building site activity and that will have a proportionate adverse impact but for the same time as with SSE. That would be my preferred way of doing it. Get it over and done with. It will be noisy, dusty, traffic in and out, and all the things you expect from a building site but soon it will be finished.

    The other option would be to spend money at the same rate as SSE but take 20+ times longer and have the same intensity of building site type activity and impact as with the SSE's construction plans but for 20+ times longer. I don't favour that option.

    It would be appropriate I think to compensate people who feel they need to go on a long holiday or even move house permanently to get away from the disruption while construction is going on. I think if people are being put out through no fault of their own then they deserve the help they need to put it right. I don't know if the SSE are planning to compensate people but I would hope anybody would.

    Then there is the bigger swings in the depth of Loch Lochy and the measures I have been thinking about to cope with that. So again there is some adverse impact while construction goes on but when completed it should be OK environmental impact wise.

    I know there are professionals who work in the area of environmental impact studies - in fact my brother works in that field. So I would expect a proper assessment of my much bigger scheme would have to be done before government approval could possibly be given. I can't expect to cover every issue at this early "vision" stage.
    Last edited by Peter Dow; March 6th, 2012 at 07:04 PM.
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    Quote Originally Posted by Arthur Angler View Post
    Quote Originally Posted by Zwirko View Post
    Peter,

    Have you looked at any possible impact on the Caledonian canal?

    I would also be interested in your thoughts regarding environmental impact. As I'm sure you are aware, addressing such concerns can form a substantial part of major proposals such as this.
    I think it is safe to assume the environmentalists will oppose it, in spite of any alleged environmental benefits enumerated. This is a drearily familiar pattern of response
    Some may oppose the SSE's scheme. More would oppose my bigger scheme for no other reason than because it's bigger. Hopefully more environmentalists will see the bigger picture and give the project serious consideration.

    Quote Originally Posted by Arthur Angler View Post
    Excavation of a deeper basin would of course provide a convenient source of rock for the dam- forgive me for stating or restating the obvious, but best use of such material could be significant in terms of cost and time expenditure.
    There's nothing to forgive. I am pleased that you have taken the time to reply.

    My plans calls for excavating the reservoir bed of about 138 million cubic metres of rock.

    In addition, by estimating in proportion to the SSE's estimate for excavated rock for their scheme's underground works, to deliver water to the turbine-pumps, to and from the loch and the upper reservoir, to provide operator and maintenance access to the turbine pumps and other control gear etc, my scheme requires also the excavation of 9 million cubic metres of rock for underground works.

    So in total maybe about 147 million cubic metres of rock would be excavated to construct Coire Glas/Dow.

    I estimate the Coire Glas/Dow dam may require 72 million cubic metres of reinforced concrete for its construction. About 50 million cubic metres of that will be construction aggregate and that can be manufactured by crushing some of the excavated rock, yes. I had thought of that.

    I think it may be best to bring the rock-crushing machines to the Coire Glas site rather than truck the excavated rock a long distance to the home of the rock-crushing machine and then have to truck the aggregate back again.

    This would still leave about 97 million cubic metres of excavated rock to dispose of in land-fill or maybe some of it will find a buyer - a construction supply business perhaps?
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    Quote Originally Posted by Pong View Post
    Quote Originally Posted by Peter Dow View Post
    Quote Originally Posted by Pong View Post
    Expanded without service disruption.
    There is no practical way a hydroelectric scheme can be expanded "without service disruption". Realistically, there would have to be a long period of no-service from the site while it was upgraded. It may take even longer working around the first scheme than it would working on a green field site.
    Hypothetically, if your design was changed in height only - say to 100 meters - would it still work?
    Well you can see from this diagram -



    - that if the dam was 100 metres high, which would be just above the hieght indicated for the SSE dam at 92 metres, then also the dam would be less long, maybe only 700 metres long instead of 1475 metres long.

    So you can't truly change the "height only". If you change the height then you automatically change the length.

    Also the thickness of a dam would usually be in proportion to its height, how tall it was. So a less tall dam wouldn't need to be so thick as a taller dam would have to be. You could build it as thick if you wanted to.

    Sure, you can say, "Right I'll make it more than three times thicker than it needs to be for its height because maybe one day I might want to build it taller" and sure, you could build it with the same thickness with that in mind if you had the money and that would no doubt mean there was less work to do if and when you came to build it taller.

    Now a less tall, less long dam would hold less water and therefore there would be less energy stored. So it would work but it would run out of energy sooner. Instead of supplying energy for 50 hours, at the same power, it might last for only 5 hours.

    Also with less energy available from a smaller dam, usually, you'd install fewer turbine-pumps and you wouldn't need to excavate so much underground tunnels and caverns to accommodate the fewer turbine-pumps. But if you really wanted to change nothing apart from the dam, you could install all the turbine-pumps I plan to install.

    And if you wanted to excavate the reservoir bed in the way I planned for the bigger dam I guess you could do that too even for the smaller dam.

    And if you wanted to do all the additional Loch Lochy and drainage water flow work that would be needed for a higher dam with more volume of water to deal with, that wouldn't be used at all because the smaller dam wouldn't be using so much water, sure, you could do all those addition jobs, if you really wanted to.

    Quote Originally Posted by Pong View Post
    Why would adding height to this stop operation?
    It may do, if you needed to add thickness on the water side of the dam below the full-water line. Then you'd need to drain the dam first.

    If you had carefully positioned the smaller dam so that you could build higher intelligently only by adding to the dry parts of the dam then I suppose you could.

    What you certainly could not do is to just build higher on the SSE dam while it was working and hope to get anything like my Coire Glas/Dow scheme which is far more than just a bigger dam than the SSE's.

    Why? Many reasons.

    The SSE dam is in a different position from my dam. See this diagram.



    I hope you can see that building my dam (brown thick line) on top of the SSE dam (grey line) would involve building part of my dam on the wet side of part of the SSE dam.

    But even if you drained the SSE reservoir to build my size of dam on top you still would not have my Coire Glas/Dow scheme because you would not have the additional turbine-pumps and underground works for them and neither would you have the excavated reservoir bed.

    Doing all that additional work would take 20+ times more work than it took to build the SSE dam, and likely it would take even longer than it would without the SSE dam there in the first place.

    Then there are the additional Loch Lochy flow works that are needed for my scheme that the SSE wouldn't have built.

    So simply building a bigger dam on top of the SSE's dam would leave you with a bigger dam and more water in it but with no good way to make proper use of the additional energy.

    Sure you'd have more energy but you could not deliver more power. So you could deliver a small amount of power for a long time but it would never be enough power to serve as a back up for all the wind power that was becalmed.

    Here is way to help you understand this.

    Coire Glas/Dow/600GW.Hrs/12GW is like a sports super-car, with the 12 GW turbine-pumps and 600GW.Hrs water reservoir to match, like the engine and petrol tank of a sports car.

    Coire Glas/SSE/30GW.Hrs/0.6GW is a like a moped with the 0.6GW turbine pumps and 30GW.Hrs water reservoir to match, like the engine and petrol tank of a moped.

    Just building a bigger dam on top of the SSE's dam might give you maybe Coire Glas/SSE+/300GW.Hrs/0.6GW or something like a moped with a petrol tank the size of a family car's bolted on but with the same wee engine.

    Sure you could go for miles and miles on a moped with a family car's petrol tank but at a very slow pace. If you want a family car then build a family car. If you want a sports car then build a sports car. But if you build a moped you are stuck with a moped unless you pull the whole thing to bits and start again.

    Really it is best to build Coire Glas pumped storage hydro dam scheme at the final size you want it from the very beginning.
    Last edited by Peter Dow; March 7th, 2012 at 08:26 AM.
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    Quote Originally Posted by Peter Dow View Post
    Potential depth variation of Loch Lochy + Loch Arkaig = 400 000 000 m^3 / 26 000 000 m^2 = 15.3 metres.

    So this 3rd option, 3rd measure, looks like it would take care of 10 metres of the original 25 metre problem and leave less of an engineering task for option 1 and option 2 to deal with.
    My next diagram is "Loch Lochy & Loch Arkaig surface elevation control".




    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.

    Quote Originally Posted by Peter Dow View Post
    What's the flow capacity of one of those?
    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.
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    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.
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    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.
    Last edited by Peter Dow; March 16th, 2012 at 11:36 PM.
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    Video which illustrates the principle of using wind turbines and pumped storage hydro dam schemes together.
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  25. #24 "Dow" equation for the power and energy output of a wind farm. 
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    "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!
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    That equation doesn't seem right to me. The power should be proportional to the wind farm area, not the square root thereof. If you had 2 wind farms that were far enough apart not to influence one another, then you should get twice the power of one wind farm, no? And if the turbines are influencing each other, that should be a function of the shape of the farm, not just the area.

    Also the rotor should catch an amount of wind proportional to the square of the diameter, or so I would think.
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    The power of a wind turbine is proportional to the rotor diameter squared (i.e proportional to the swept area). There is also a power coefficient that varies with wind speed so the relation with wind speed is not straightforward. Presumably the power of the wind farm would be the sum of the power of the individual turbines times a small derating factor for interference from upwind turbines, so roughly proportional to the wind farm area if uniform spacing is assumed.

    This paper gives the equation for a single turbine.

    http://www.raeng.org.uk/education/di...nd_Turbine.pdf
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    Quote Originally Posted by Harold14370 View Post
    That equation doesn't seem right to me. The power should be proportional to the wind farm area, not the square root thereof.
    Oh really?

    Quote Originally Posted by Harold14370 View Post
    If you had 2 wind farms that were far enough apart not to influence one another, then you should get twice the power of one wind farm, no?
    Right. But this equation, (or should I say "my" equation ) is for one wind farm where the individual turbines do influence each other. To assume they don't influence each other is the mistake David made when "experts" told him that wind turbines need to be at least 5 times the diameter apart to not influence each other whereas they'd need to be so far apart as to no longer be in the same wind farm.

    Quote Originally Posted by Harold14370 View Post
    And if the turbines are influencing each other, that should be a function of the shape of the farm, not just the area.
    OK but I am offering a first order approximate equation, not a precise equation for every possible wind farm shape and a result for every possible wind direction which would be so complex as to be of little practical use.

    We need a simple equation so then assume a simple rotationally-symmetrical wind farm area shape which gives the same power from no matter which direction the wind comes from. How about a circular or disc shape? Or a ring? Something like that.

    Quote Originally Posted by Harold14370 View Post
    Also the rotor should catch an amount of wind proportional to the square of the diameter, or so I would think.
    A single rotor would yes and we already have an equation for a single wind turbine in which indeed power is proportional to the rotor diameter squared.

    We need another equation for wind farms.
    Last edited by Peter Dow; March 23rd, 2012 at 12:23 AM.
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    Quote Originally Posted by Bunbury View Post
    The power of a wind turbine is proportional to the rotor diameter squared (i.e proportional to the swept area).
    Right but we are looking for an equation for the power of wind farm, not a single wind turbine.


    Quote Originally Posted by Bunbury View Post
    There is also a power coefficient that varies with wind speed so the relation with wind speed is not straightforward.
    The power co-efficient is 3. The specific kinetic energy is proportional to velocity squared and the mass flow is proportional to velocity. So the energy flow is proportional to velocity cubed and assume the wind turbine takes a proportion of that energy. Anyway I didn't mention the velocity cubed factor because we know that already. That's not disputed. That's a given. That's agreed.

    Quote Originally Posted by Bunbury View Post
    Presumably the power of the wind farm would be the sum of the power of the individual turbines times a small derating factor for interference from upwind turbines, so roughly proportional to the wind farm area if uniform spacing is assumed.
    No uniform spacing would not I think give you a uniform "derating factor" and neither would it be "small" so the velocity is quite different for every turbine which is downwind of another. Even if this factor of yours could be formulised, to apply it would depend, I presume, though it is your notion, on the number and spacing of the turbines? So the mathematical complexity is beginning to build with your approach.

    Ideally we want a simple equation which is independent of the number of turbines and their spacing and depends only on the assumption that the turbines are number enough and spaced closely enough to operate as a wind farm and not as independent isolated turbines.

    Better to 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.

    Quote Originally Posted by Bunbury View Post
    This paper gives the equation for a single turbine.

    http://www.raeng.org.uk/education/di...nd_Turbine.pdf
    Well no-one is questioning that. It doesn't give you the power of a wind farm though.
    Last edited by Peter Dow; March 23rd, 2012 at 12:42 AM.
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    Quote Originally Posted by Peter Dow View Post

    OK but I am offering a first order approximate equation, not a precise equation for every possible wind farm shape and a result for every possible wind direction which would be so complex as to be of little practical use.

    We need a simple equation so then assume a simple rotationally-symmetrical wind farm area shape which gives the same power from no matter which direction the wind comes from. How about a circular or disc shape? Or a ring? Something like that.
    Your approximation assumes that the power is proportional to the width of the circular wind farm (square root of the area). This would give zero credit for the turbines in the middle, no matter how large the farm is. Such being the case, a circular farm would be an extremely bad idea, when the wind is coming mostly from one prevailing direction.

    Do you have any data to show how accurate your approximation is? Why do we need a simple equation?
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    Double-post deleted
    Last edited by Peter Dow; March 24th, 2012 at 10:09 AM. Reason: Deleting since I seem to have double-posted the same post
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    Quote Originally Posted by Harold14370 View Post
    Quote Originally Posted by Peter Dow View Post

    OK but I am offering a first order approximate equation, not a precise equation for every possible wind farm shape and a result for every possible wind direction which would be so complex as to be of little practical use.

    We need a simple equation so then assume a simple rotationally-symmetrical wind farm area shape which gives the same power from no matter which direction the wind comes from. How about a circular or disc shape? Or a ring? Something like that.
    Your approximation assumes that the power is proportional to the width of the circular wind farm (square root of the area).
    Correct!

    It should be obvious to you now why my equation also says the power / energy is proportional to the rotor diameter. Is it?


    Quote Originally Posted by Harold14370 View Post
    This would give zero credit for the turbines in the middle, no matter how large the farm is.
    No it is crediting the entire width of the wind farm as being thick enough to take a proportional fraction of the energy of wind flow that is as wide as the wind farm.

    What the point you are close to making is that the wind path which passes through the middle is simply most likely to be over-supplied with turbines in its path, if turbines are arranged in a simple uniform turbine areal density, which is inefficient.

    With this uniform turbine density arrangement it is like trying to look through this glass of coke.



    The fact that the middle is especially dark doesn't cause the coke company to think that they are "not getting credit" for the colouring they are using in the coke which is in the middle of the glass. It simply is not possible for the coke company to selectively remove the colorant from the liquid in the middle of the glass and increase the efficiency of the use of their colorant. They are stuck with a uniform distribution but that's OK.

    However, it would indeed be possible to arrange the turbines in a rotationally symmetrical fashion which did not have turbines in the middle - a ring, torus or doughnut configuration perhaps, with a empty middle or centre.

    This reminds me somewhat of Wellington / Napoleonic / and earlier foot soldier arrangements. It did no good to have soldiers stuck in the middle of their own formations where they could not get a view of the enemy to use their line of fire weapons.

    One such formation the military used to counter attack from cavalry which could come from any direction was the "square".



    Quote Originally Posted by Harold14370 View Post
    Such being the case, a circular farm would be an extremely bad idea, when the wind is coming mostly from one prevailing direction.
    Well that's another point altogether. Sure you have wind farm with turbines in a long line, or two, three or more parallel lines square on to the prevailing wind. That'll be most efficient where the wind is strictly prevailing from one direction. (The armies from the above mentioned era also used straight line formations when the enemy was at a known direction.)

    I would point out that the direction of wind only has to rotate by 90 degrees and you are losing badly with a straight line formation. So where the wind varies significantly in direction I would not opt for a simple straight line formation.

    In the "long thin lines, prevailing wind" wind farm case you would need a different equation which specifically identified the width (or the "length" as it is more usually described in the case of a line) of the line as the factor of proportionality, rather than the square root of the area which is better for a rotationally symmetrical shape.

    Quote Originally Posted by Harold14370 View Post
    Do you have any data to show how accurate your approximation is?
    My point is that my approximation is a more useful equation than that in David MacKay's book in which he seemed to say that energy was independent of rotor size.

    The obvious data that I can see is the observable fact that wind farms use turbines with large rotors.

    For very widely spaced, isolated, non-wind-farm turbines, power and energy is proportional to rotor size squared times the number of turbines.

    For closely spaced turbines in a wind farm that is efficiently using wind farm area taking as much energy as possible from the wind as the area of land (or sea) used can achieve, then my equation says that the energy and power is proportional to the rotor size (not squared).

    To be efficient with turbines and wasteful of land (or sea) area then you spread turbines out, isolate them, and then the power and energy is proportional to a rotor size exponent of 2.

    To be efficient with land (or sea) area and wasteful of turbines then you pack turbines together to make a wind farm then the power and energy is proportional to a rotor size exponent of 1.

    For wind farms more loosely spaced, I would expect an exponent of rotor size between 1 and 2 depending on how loose the spacing is (and for both the square root of area / width and number of turbines to be factors).

    No I don't have empirical data to back that up. This is a theoretical postulation en passant.

    My topic is discussing pumped storage and David MacKay's book was mentioned in a similar topic in another forum and it seemed his "independent of the rotor diameter" equation needed improving upon and this is my "first order" equation.

    Quote Originally Posted by Harold14370 View Post
    Why do we need a simple equation?
    Well I presume those who want a wind farm need to think about what type and size of wind turbines to select and how to arrange them in a wind farm both in the case where there is one strongly prevailing wind direction and where the wind can come from a variety of directions.

    Realising that the efficiency is proportion to the width against the wind and the rotor diameter ought to help with the selection of turbines and how to arrange them.

    If you followed David MacKay and think rotor size doesn't matter you might buy many smaller, cheaper rotor turbines and miss out on wind energy farmed.

    Here's an idea for wind farms at sea.

    Have the wind turbines on individual floating platforms which can lift anchor and move to a straight-line formation to face square on to the prevailing wind! Not so easy to keep them wired up to the grid though.
    Last edited by Peter Dow; March 23rd, 2012 at 12:58 PM.
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    Quote Originally Posted by Peter Dow View Post
    Quote Originally Posted by Bunbury View Post
    The power of a wind turbine is proportional to the rotor diameter squared (i.e proportional to the swept area).
    Right but we are looking for an equation for the power of wind farm, not a single wind turbine.
    I am simply agreeing with you that Mr. MacKay is wrong.

    Quote Originally Posted by Bunbury View Post
    There is also a power coefficient that varies with wind speed so the relation with wind speed is not straightforward.
    The power co-efficient is 3.
    Not, I'm referring to the Betz factor which you mention below.

    Quote Originally Posted by Bunbury View Post
    Presumably the power of the wind farm would be the sum of the power of the individual turbines times a small derating factor for interference from upwind turbines, so roughly proportional to the wind farm area if uniform spacing is assumed.
    No uniform spacing would not I think give you a uniform "derating factor" and neither would it be "small" so the velocity is quite different for every turbine which is downwind of another. Even if this factor of yours could be formulised, to apply it would depend, I presume, though it is your notion, on the number and spacing of the turbines? So the mathematical complexity is beginning to build with your approach.
    This factor is not "mine" and it has been formularized which a quick google search will tell you. It is around 4-5% for typical layouts but obviously will vary.
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  34. #33 Wind farm turbine formations 
    Forum Sophomore Peter Dow's Avatar
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    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.
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    Last edited by Peter Dow; March 24th, 2012 at 11:51 PM.
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  35. #34 Reservoir bed drain 
    Forum Sophomore Peter Dow's Avatar
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    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.

    Quote Originally Posted by Wikipedia
    Wikipedia: Induced seismicity - Causes - Reservoirs.

    The mass of water in a reservoir alters the pressure in the rock below and through fissures in the rocks, lubricates the fault, which can trigger earthquakes.
    ...
    Unfortunately, understanding of reservoir induced seismic activity is very limited. However, it has been noted that seismicity appears to occur on dams with heights larger than 100 meters. The extra water pressure created by vast reservoirs is the most accepted explanation for the seismic activity.
    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.
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    Last edited by Peter Dow; March 30th, 2012 at 06:22 PM.
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