%
\marginfig{
\begin{center}
%
%\lowres{\epsfxsize=53mm\epsfbox{../../images/Nant_y_Moch_dam_04_AndrewDixonS.eps}}%
%{\epsfxsize=53mm\epsfbox{../../images/Nant_y_Moch_dam_04_AndrewDixon.eps}}\\
{\epsfxsize=53mm\epsfbox{../../images/nant-y-moch3.jpg.eps}}\\
\end{center}
\caption[a]{\ind{Nant-y-Moch} \ind{dam}, part of a 55\,MW
hydroelectric scheme in \ind{Wales}. Photo
by
% Andrew Dixon and
Dave Newbould, \myurlb{www.origins-photography.co.uk}{http://www.origins-photography.co.uk}.}
%% permission granted for web version but not for printed Wed 22/8/07
}
\index{hydroelectricity}\index{water power}\index{electricity!hydroelectric}%
% \ind\index{water power} is
% already being exploited nearly fully in the UK.
To make {hydroelectric power}, you need altitude,
and you need rainfall.
Let's estimate the total energy of all the rain
as it runs down to sea-level.
% (Bear in mind, in fact,
% that much of this water evaporates again.)
For this hydroelectric forecast, I'll divide Britain into two:
the lower, dryer bits, which I'll call ``the \ind{lowlands};'' and the
higher, wetter bits, which I'll call ``the \ind{highlands}.''
% -- understood to include places like
% the \ind{Lake District}, the \ind{Pennines}, and \ind{Wales}.
I'll choose \ind{Bedford} and \ind{Kinlochewe} as my representatives of these
two regions.
% \medskip \par
%\marginfig{
%\begin{center}
%\mbox{\epsfig{file=../../images/PUBLICDOMAIN/maps/bedford.eps,angle=270}}
%\medskip \\
%\end{center}
%}%
Let's do the lowlands first.\index{Britain!rainfall}\index{England, rainfall}\index{highlands!rainfall}\index{lowlands!rainfall}
%
% \section{England}
To estimate the gravitational power of lowland rain,
we multiply the\nlabel{prainf}
% rate of
\ind{rainfall} in \ind{Bedford} (584\,\mm\ per year)\
%\marginfig{
%\begin{center}
%\mbox{\epsfig{file=../../images/PUBLICDOMAIN/maps/rain.eps,angle=270}}\\
%\end{center}
%}
by the density of water (1000\,kg/m$^3$), the strength of gravity
(10\,m/s$^2$) and
the typical lowland altitude above the sea (say $100\,\m$).
The power per unit area works out to
0.02\,\Wmm.\index{power density!hydroelectricity}
That's the power per unit area of land on which rain falls.
%## pop area(sq.km) - country (2002)
%49561800 130423 380 England that is 2173 each
%2918700 20779 140 Wales 350 each
%5054800 78789 64 Scotland 1313 each
%## 59553800 244820 243 United Kingdom 4080 each
When we multiply this by the area per person (2700\,m$^2$,
% was 2200 then 2500
if the lowlands
% England and Wales
are equally shared between all 60 million Brits),
we find an average raw power
of about 1\,kWh per day per person.
% 50W = 1.25 kWh/d
This is the absolute upper limit for lowland hydroelectric power,
if every
river were dammed and every drop perfectly exploited.
Realistically, we will only ever dam rivers with substantial
height drops, with catchment areas much smaller than the whole country.
Much of the water evaporates before it gets anywhere near a turbine,
and no hydroelectric system exploits the full potential energy of the water.
We thus arrive at a firm conclusion about lowland water power.
People may enjoy making
``run-of-the-river'' hydro and other small-scale
hydroelectric schemes, but such lowland facilities can never deliver
more than 1\,kWh per day per person.
% (Bear in mind
% that the current
\begin{figure}[hbtp]
\figuremarginb{
\begin{center}
\mbox{\epsfbox{metapost/heights.21}}
\end{center}
}{
\noindent%
\raisebox{10.4cm}[0cm]{\epsfig{file=../../images/PUBLICDOMAIN/maps/bedford.eps,angle=270}}%
\par
\caption[a]{%
Altitudes of land in Britain.
The rectangles show how much land area there is
at each height.\index{heights}\index{Britain!heights}\index{area}\index{data!height}
}
}
\end{figure}
%%% Let's turn to
%\section{Scotland}
Let's turn to the highlands.
\ind{Kinlochewe} is a rainier spot:
it gets 2278\,\mm\ per year, four times more than Bedford.
The height drops there are bigger too -- large areas of land
are above 300\,\m.\index{Britain!rainfall}\index{Scotland!rainfall}
So overall a twelve-fold increase in power per square metre
is plausible for mountainous regions. The raw power per unit area is roughly\index{power density!highland hydroelectricity}\index{hydroelectricity!highland}\index{highland hydroelectricity}
$0.24\,\Wmm$.\nlabel{pLochSloy}
%%
%% typical figure 3,000 mm per year in the western Highlands
%% \tinyurl{2rqloc}{http://www.metoffice.gov.uk/climate/uk/location/scotland/index.html}
%%
%% The Lake District is the wettest part, with average annual totals exceeding 2,000 mm (this is comparable with that in the western Highlands of Scotland). The Pennines and the moors of south-west England are almost as wet. However, all of East Anglia, much of the Midlands, eastern and north-eastern England, and parts of the south-east receive less than 700 mm a year.
%%
If the highlands
generously share their hydro-power with the rest of the \UK\
(at 1300\,m$^2$ area per person),
we find an upper limit of about 7\,kWh per day per person.
As in the lowlands, this is the upper limit on raw power if
evaporation were outlawed and every drop were perfectly exploited.
What should we estimate is the plausible practical limit?
Let's guess 20\% of this -- 1.4\,kWh per day, and round it up a little to allow
for production in the lowlands: \OliveGreen{1.5\,kWh per day}.%
\amarginfig{b}{
% \begin{figure}
% \begin{center}
\mbox{\epsfbox{metapost/stacks.28}}
% \end{center}
% }{
\caption[a]{Hydroelectricity.}
}
%% (which is about 1\% of UK electrical power)
The actual power from hydroelectricity in the UK today
is\label{pHydro} 0.2\,kWh/d per person,
so this 1.5\,kWh/d per person would require a seven-fold increase
in hydroelectric power.
% Realistically, I don't imagine that Britain will ever get more than
% 0.6\,kWh/d/person from hydro.
%And from (what document? DTI?)
%the DTI's estimates, the hydro resource of the UK is 40 TWh/y.
%Which is 1.8\,kWh per day per person.
% \end{figure}
\small
\section*{Notes and further reading}
\beforenotelist
\begin{notelist}
% RESTORE ME IN 2nd EDITION!!!! ***
% \item[page no.] % ***
\item[\npageref{prainf}] {\nqs{Rainfall}} statistics are from the BBC weather centre.
\item[\npageref{pLochSloy}]
{\nqs{The raw power per unit area [of Highland rain] is roughly
$0.24\,\Wmm$.}}
We can check this estimate against the actual power per unit area of
the {Loch Sloy hydro-electric scheme}, completed in 1950 \citep{LochSloy}.
The catchment area of \ind{Loch Sloy} is\index{power density!hydroelectricity}
% 32\, sq mi
about 83\,km$^2$; the rainfall there is
% 115 inches per year
about 2900\,mm per year (a bit higher than the 2278\,mm/y of Kinlochewe);
and the
% annual electricity output was predicted to be 130\,GWh per year,
% (In fact in 2006 it produced 142\,GWh.)
electricity output in 2006 was 142\,GWh per year,
which corresponds to a power density of
% (130 (GWh / year)) / (32 (sq miles)) = 0.178938344 W / (m ** 2)
% (142 (GWh / year)) / (32 (sq miles)) = 0.1954 W / (m ** 2)
\pdcol{0.2\,\W\ per m$^2$} of catchment area.
Loch Sloy's surface area is about 1.5\,km$^2$, so
% , in case it's of interest, we can also work out the power density of the
the hydroelectric facility itself
% (130 (GWh / year)) / (1.5 (sq km)) = 9.88689457 W / (m ** 2)
% (142 (GWh / year)) / (1.5 (sq km)) = 10.8 W / (m ** 2)
% In our calculation we used TIGC = 152.5MW
% And Annual Output = 141.885 GWh
has a
per unit lake area of \pdcol{11\,\Wmm}.
So the hillsides, aqueducts, and tunnels bringing water to Loch Sloy
act like a 55-fold power concentrator.%
\amarginfig{b}{
\begin{center}
\begin{tabular}{@{}c@{}}
\lowres{\mbox{\epsfxsize=51mm\epsfig{file=../../images/DinorwigWheelS.jpg.eps,angle=270,width=53mm}}}
{\mbox{\epsfxsize=51mm\epsfig{file=../../images/DinorwigWheel.jpg.eps,angle=270,width=53mm}}}
\end{tabular}
\end{center}
\caption[a]{
% An 80\,horsepower (60\,kW) waterwheel
A 60\,kW \ind{waterwheel}.
% in \ind{Dinorwig}, North \ind{Wales}.
}\label{fig.bigWheel}
}
\item[\npageref{pHydro}]
{\nqs{The actual power from hydroelectricity in the UK today
is 0.2\,kWh per day per person.}}
% ,\label{pHydro}
%The actual generation of hydroelectricity in the UK
% in 2006 was 0.17\,kWh/d/person.}}
% page 130
Source: \citet{Dukes07}.
% , actual production of hydroelectricity in 2006 was:
In 2006,
large-scale hydro produced 3515\,GWh (from plant with a
capacity of 1.37\,GW);
small-scale hydro, 212\,GWh (0.01\,kWh/d/p) (from a capacity of 153\,MW).
% (3515+212)*1e6 / 60e6 / 365.25
% Source: BP statistical review of world energy.
% 1.7 million {\tonne}s of oil equivalent
% is 7.65\,\TWhe/y,
% which is 0.35\,\kWhe/day/person.
% (1\,M {\tonne}s of oil produces about 4.5\,TWhe\ in a modern power station.)
% This multiplier is not standard, sadly.
% In DUKES the standard multiplier is
% 1\,TWh of electricity = 0.086\,Mtoe.
% This means 1\,Mtoe = 11.6\,TWhe.
In 1943, when the growth
of hydroelectricity was in full swing,
the North of Scotland Hydroelectricity Board's engineers estimated
that the Highlands of Scotland could produce
% 6273\,GWh per year in 102 facilities.
6.3\,TWh per year in 102 facilities -- that would correspond to
0.3\,kWh/d per person in the UK \citep{LochSloy}.
%6273e6 / 365.25 / 60e6
%ans = 0.28624
%
% at the time they were already building facilities for 3 TWh per year
% http://www.reuters.com/article/pressRelease/idUS104835+07-Jan-2008+RNS20080107
Glendoe, the first new large-scale hydroelectric project in the UK
since 1957, will add capacity of 100\,MW
and is expected to deliver 180\,GWh per year.
% roughly 8% increase
Glendoe's catchment area is 75\,km$^2$, so its power density works out to
\pdcol{0.27\,\W\ per m$^2$} of catchment area.
\ind{Glendoe} has been billed as ``big enough to
power\index{myth!hydroelectricity}
% every home in a city the size of
Glasgow.''
% I bet that people get the impression from this that
% Glendoe will provide enough electricity ``to
% power \ind{Glasgow}.'' But this is a long way from the truth.
But if we share its 180\,GWh per year across the population of \ind{Glasgow}
(616\,000 people), we get only 0.8\,kWh/d per person. That is just
% 4.32 or 4.44
5\% of the average electricity consumption of 17\,kWh/d
per person.
% Total production 406,000 GWh 2006 including imports and pumped s.
% 18.5kWh/d/p. If omit pumped st get 18.3. Good I like 18.
% losses are 30.9. If we omit them too then we get 17kWh/d/p.
% Losses are 7.7%. 8% good enough.
% Final consumption 342,781 15.6 16kWh/d/p
% that figure omits ``energy industry use'', ``elec gen''...
% Rainfall is 2000 mm/y
% head is 630-21.4 m
% Can reach full output in 30 seconds.
%
% glendoe expected to deliver 180GWh per year
% 11.5 million cubic metres of water from a catchment area of75 square kilometres
% 180 GWh per year / 75 square kilometres in W/m**2
% 0.27379 W / (m ** 2)
The 20-fold exaggeration is achieved by focusing on Glendoe's {\em{peak}\/}
output rather than its {\em{average}}, which is 5 times smaller;
% which is factor of 5
and by discussing ``homes'' rather
than the total electrical power of Glasgow (see \pref{pHOME}).
\end{notelist}
\normalsize
%Rarely it reaches 1.9.
%Let's say 2? (Converted on the basis of thermal equivalence
%assuming 38\% conversion efficiency in a modern thermal power station)
%(cf total UK consumption was 227 million {\tonne}s of oil equivalent)
%(1M {\tonne}s of oil produces about 4.5TWh of elec in a modern power station)
%% (700/6e9/365) * 4.5e9
% example of tiny hydro scheme:
% http://news.bbc.co.uk/1/hi/scotland/tayside_and_central/7347001.stm
% The 1.4 megawatt Innerhadden Burn project will be two kilometres south east of Kinloch Rannoch.
% biggest capacity facilities in UK:
% Fasnakyle 69MW (affric)
% lochay 47MW (breadalbane)
% luichart 34MW (conon)
% glenmoriston 37MW (great glen)
% shin 19MW
% Sloy 153MW (sloy/awe)
% The calculated annual LF output for Loch Sloy Hydro for 2006 is 10.62%.
% 365 * 24 * 0.1062 * 0.153 GW
% 142.337736 GWh
% from Jim Oswald et al
% clachan 40MW
% tummel errochty 75MW
% clunie 61MW
% rannoch 44MW
% tongland 33MW
% SSE output from hydro: 2007/08 was 3,518GWh
% run of the river schemes are all sub 3MW (peak)
% glendoe expected to deliver 180GWh per year
% 11.5 million cubic metres of water from a catchment area of75 square kilometres
% 180GWh per year / 75 square kilometres in W/m**2
% 0.27379 W / (m ** 2)
% source:
% http://miranda.hemscott.com/ir/sse/ar2008/download/pdf/ar2008.pdf
% SSE 2008 Annual Report and Accounts
% it cost 140 million
% from http://www.ref.org.uk/Pages/4/uk_renewable_energy_data.html
%
% http://www.arrocharheritage.com/LochSloyHydroElectricScheme.htm
% % in 1935 they already planned
% to make Sloy reversible (pumped storage)
% this page shows the catchment area
% estimated output of Sloy:
% 130 GWh per year.
% natural catchment area: 6.5 sq mi;
% Increased to 27.5 sq mi, then
% to 32 sq mi by diversions
% This increased output by 15 GWh per y.
% the dam raised the level of
% loch sloy by 155 feet; it is 1160 ft
% long and 160 ft high.
% loch sloy stores 1200 M cu ft,
% equivalent to 20 GWh.
% each inch of rain yields 1.3GWh, assuming the reservoir is at 910 feet
% above turbines (ie full).
% 130MW of francis turbines and an extra 0.45MW pelton set.
% The Board's engineers estimated in 1943
% that the rivers and lochs of the
% Highlands could produce 6273 GWh
% per year, and the North of Scotland Hydro
% -Electric Board's development programme
% visualized the construction of 102 HE
% schemes.
% 19 schemes with capacity of 630MW
% and annual output of 1600 GWh have been
% promoted.
%
% Morar has a catchment area of 65 sq mi,
% rainfall 100 in per year.
% this is great!
% http://www.arrocharheritage.com/LochSloyHydroElectricScheme.htm
% Loch Morar could be raised 8 feet.
% Head is 16 feet at present.
% Lochalsh: head is 490ft. 1MW
% there could be 2nd dam.
% is linked to Storrs Lochs hydro station in Skye
% Tummel-Garry scheme to produce 300GWh/y
% (Extension of rannoch scheme from 1930s)
% Catchment area 706 sq mi
% Errochty reservoir is at 1100 ft above sea level
% aqueduct from rivers Bruar and Garry
% Clunie station 61MW. started 1950
% Mullardoch-Fasnakyle-Affric,
% catchment area 124 sq mi, 223 GWh/y
% 66MW
% Conon, Loch Fannich. output expected (includes loch Maree)
% 437GWh/y.
% Glascarnoch-Luichart-Torr Achilty sceme
% 60MW, estd output 280GWh/y.
% Grudie Bridge, 24MW, 83 GWh/y.
% Glen Shira, 100 GWh/y - planned to
% have pumped storage
% Cowal: 14 GWh/y
% Gairloch
% Glen Garry : 145GWh/y.
% Glen Morriston: 214GWh/y.
% Gaur scheme - 17GWh/y
% Lawers: 1362ft head, power station at Killin end of
% Loch Tay (top loch called Lochan-na-Lairige)
% 71 GWh
% List of schemes under construction
% Schemes promoted but not yet started
% biggest ones are Glascarnoch (112), Luichart (124), Quoich (63GWh),
% Invergarry (82GWh), Invermoriston (75GWh), Lawers (71GWh)
% the lists show catchment areas and heads and rainfalls
% SCHEMES UNDER SURVEY
% Lyon-Lochay 195GWh/y, Lednock-Earn 87;
% Shin: 164;
% further schemes: 883 GWh
% Total: 409MW and 1436GWh under survey.
%
% http://rls.org.uk/database/record.php?usi=000-000-001-499-L
% Al smelting started at Foyers
% 1896
% 1903-1907 Kinlochleven Blackwater Dam
% Hydro building for the public started in 1927.
% Really got going (under Tom JOhnston) in 1943.
% Cruachan 1967 in side a cavern
% conon built 1946-61
% from 1945 to 1970, homes connected went from 0% to 90%