### Location

The map shows how and where the biggest-ever pumped-storage hydro-scheme could be built – Strathdearn in the Scottish Highlands.

### Energy storage capacity

The scheme requires a massive dam about 300 metres high and 2,000 metres long to impound about 4.4 billion metres-cubed of water in the upper glen of the River Findhorn. The surface elevation of the reservoir so impounded would be as much as 650 metres when full and the surface area would be as much as 40 square-kilometres.

The maximum potential energy which could be stored by such a scheme is colossal – about **6800 Gigawatt-hours** – or **283 Gigawatt-days** – enough capacity to balance and back-up the intermittent renewable energy generators such as wind and solar power now in use for the whole of Europe!

Transmission losses

Most of Europe is within 3,000 km of Strathdearn meaning that one-way transmission losses to or from anywhere in Europe could be as low as 10.5% using existing high-voltage (800 kV), direct current (HVDC) electric power transmission system.

In theory, transmission power losses are inversely proportional to the voltage-squared so it is possible that if and when even higher voltage than 800 kV transmission technology were to be developed, transmission losses could be reduced still further.

Transmitting power at **800 kV** to and from a well-designed efficient pumped-storage hydro-scheme, **two-way transmission losses** are

- at distances of
**2000 km to 3000 km**,**from 14% to 21%**and represent the single most significant loss factor, indicating that 800 kV is an inappropriately low transmission voltage for service at this distance – 800 kV at this distance is not recommended but possible meantime if and while no better option is available - at distances of
**1000 km to 2000 km**,**from 7% to 14%**and so the losses at the pumped-storage hydro scheme itself are likely to be the single most significant loss factor – 800 kV at this distance is not ideal, may be practical but reconsider if and when there are any better options - at distances of
**less than 1000 km**,**less than 7%**and so losses are acceptable – 800 kV at this distance is ideal and recommended for full service life for Scotland, England, Wales, Ireland, southern Norway, Denmark, north-west Germany, Netherlands, Belgium and northern France.

### Power

There would need to be two pumping and turbine generating stations at different locations – one by the sea at Inverness which pumps sea-water uphill via pressurised pipes to 300 metres of elevation to a water well head which feeds an unpressurised canal in which water flows to and from the other pumping and turbine generating station at the base of the dam which pumps water up into the reservoir impounded by the dam.

To fill or empty the reservoir in a day would require a flow rate of 51,000 metres-cubed per second, the equivalent of the discharge flow from the Congo River, only surpassed by the Amazon!

The power capacity emptying at such a flow rate could be equally colossal. When nearly empty and powering only the lower turbines by the sea, then about 132 GW could be produced. When nearly full and the upper turbines at the base of the dam fully powered too then about 264 GW could be produced.

Modelling of a wind turbine power and pumped-storage hydro system recommends –

**store energy capacity = 1.5 days x peak demand power**

suggesting that a store energy capacity of 283 GW-days would be sufficient to serve a **peak demand power** of 283 / 1.5 = ** 189 GW**, though this could only be produced from reservoir heads of at least 430 metres, at least 8% of energy capacity, assuming a flow rate of 51,000 m^{3}/s. To supply 189 GW from the lowest operational head of 300 metres would require increasing the flow capacity to 73,000 m^{3}/s.

This represents many times more power and energy-storage capacity than is needed to serve all of Britain’s electrical grid storage needs for backing-up and balancing intermittent renewable-energy electricity generators, such as wind turbines and solar photo-voltaic arrays for the foreseeable future, opening up the possibility to provide grid energy storage services to Europe as well.

### Canal

The empirical Manning formula relates the properties, such as volume rate, gradient, velocity and depth of a one-directional steady-state water flow in a canal.

For 2-way flow, the canal must support the gradient in both directions and contain the stationary water at a height to allow for efficient starting and stopping of the flow.

The “2-way Power Canal” diagram charts from a spreadsheet model for a 51,000 m^{3}/s flow how the** width of the water surface** in a 45-degree V-shaped canal varies with the designed maximum flow velocity. The lines graphed are

**Moving width**– from simple geometry, for a constant volume flow, the faster the flow velocity, the narrower the water surface width**Static width**– the width of the surface of the stationary water with enough height and gravitational potential energy to convert to the kinetic energy of the flow velocity**30km 2-way wider by**– using the Manning formula, the hydraulic slope can be calculated and therefore how much higher and deeper the water must begin at one end of a 30km long canal to have sufficient depth at the end of the canal and therefore by how much wider the canal must be**Canal width**– adding the 30km-2-way-wider-by value to the static-width determines the maximum design width of the water surface.

The equation thus derived,

#### y = 2 √ ( 51000/x) + 0.1529 x^{2} + x^{8/3}/40

*where y is the maximum surface water width in the canal and x is the designed maximum flow velocity*

predicts a minimum value for the canal width of about 170 metres (plus whatever additional above the waterline freeboard width is added to complete the design of the canal), containing up to 216 million cubic-metres of water, at a design maximum flow velocity between 10 and 11 metres per second, similar to the velocity of the 2-way flow of the fastest tidal race in the world at Saltstraumen, Norway.

Video of the tidal race at Saltstraumen

Guinness World Records states that the widest canal in the world is the Cape Cod Canal which is “only” 165 metres wide.

The construction of the Panama Canal required the excavation of a total of 205 million cubic-metres of material but the Strathdearn Power Canal would need more excavating and construction work than Panama did.

So the Strathdearn Power Canal, too, would be the biggest ever!

#### Canal efficiency

To improve the power canal’s energy efficiency requires designing for a **slower** maximum flow velocity which requires a **wider** moving and static width of the water surface to maintain the maximum volume flow rate which –

**increases**the canal’s construction costs**decreases**the canal flow’s hydraulic slope**decreases**the canal’s 2-way hydraulic head height loss, at most equal to the*30km-2-way-wider-by***decreases**the canal’s energy loss**increases**the canal’s energy efficiency

So a wider canal would be more expensive to build but would be more energy efficient in use, saving energy costs over the longer term. A wider canal also allows for a higher flow rate. For example, 62,000 m^{3}/s – which could be useful to power 159 GW when the reservoir was running low, assuming additional turbines were installed for such a purpose – would require a minimum canal width of 182 metres.

For a **minimum** canal width of **170 metres** and a flow rate of 51,000 m^{3}/s, implying a maximum flow velocity of 9.8 m/s, the *30km-2-way-wider-by * is 11 metres so the maximum 2-way hydraulic head height loss as a proportion of the reservoir operational head heights from 300 to 625 metres would represent an energy loss from 11/625 = 1.8% to 11/300 = 3.7%, averaging presumably somewhere around 11/462 = 2.4%, estimating the power canal to be about **97.6%** efficient when operated at full power and even more efficient at reduced power. The follow table indicates how energy efficiency increases with canal width.

**Table of canal efficiency for a flow rate of 51,000 m ^{3}/s**

Width (m) | 2-way head loss (m) | Energy loss | Efficiency |
---|---|---|---|

170 | 11.1 | 2.4% | 97.6% |

180 | 5.1 | 1.1% | 98.9% |

190 | 3.3 | 0.72% | 99.3% |

200 | 2.3 | 0.51% | 99.5% |

210 | 1.7 | 0.37% | 99.6% |

220 | 1.3 | 0.28% | 99.7% |

230 | 1.0 | 0.22% | 99.8% |

#### Canal lining and boulder trap

To maximise the water flow velocity, canals are lined to slow erosion. Concrete is one lining material often used to allow for the highest water flow velocities, though engineering guidelines commonly recommend designing for significantly slower maximum flow velocities than 10 m/s, even with concrete lining.

Water flowing at 10 m/s has the power to drag large – in excess of 10 tonnes – boulders along the bottom of a canal with the potential of eroding even concrete, so I suggest that the bottom 6 metres width of the lining, (3 m either side of the corner of the V) may be specially armoured with an even tougher lining material than concrete and/or include bottom transverse barriers of 2 metres depth to impede the flow along the corner of the V and trap boulders, smaller stones and gravel, in which case the water flow is more precisely modelled for Manning formula calculations as a trapezoidal canal with a bed width equal to the 4 metre width of the top of bottom transverse barrier (“boulder trap”) and a 2-metre smaller depth from the top of the boulder trap to the water surface.

### Main Dam

The image shows the location of the main dam at latitude 57°15’16.2″N, decimal 57.254501°, longitude 4°05’25.8″W, decimal -4.090506°.

Assuming the dam would be twice as wide as its height below the dam top elevation of 650 metres, the superficial volume is estimated at 80 million cubic metres, not including the subterranean dam foundations which would be built on the bedrock after clearing away the fluvial sediment.

### Geology

The image shows an extract from the British Geological Survey’s bedrock map overlaid upon my plan for the Strathdearn Pumped-storage hydro scheme. Readers are referred to the BGS’s Geology of Britain viewer for details.