Scottish Scientist

Modelling of wind and pumped-storage power

Graph 1. June 2014. Demand 6GW, Wind 33GW, Pumped-storage 160GWh
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This Scottish scientist produced a spreadsheet model of an electricity generating system composed primarily of wind turbines backed up with pumped-storage hydro-electricity schemes. Such modelling can predict how much wind power and pumped-storage energy capacity should be installed for satisfactory renewables-only generation.

The spreadsheet line graph above plots power & energy variables for the time-line modelled –

The time-line graphs data for the grid in Scotland, normalised in proportion to wind power and demand data for June 2014, as downloaded from the Gridwatch Database of the U.K. National Grid Status Website.

Modelling assumptions for this graph –

I used estimated relative costs of wind turbines versus pumped-storage hydro to arrive at a optimal minimum cost balance –

I conclude that such models will help to take the guesswork and uncertainty out of renewable-energy electricity system design!

Graph 2. January 2014. Demand 6GW, Wind 33GW, Pumped-storage 160GWh

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Graph 3. April 2015. Demand 52.5GW, Wind 290GW, Pumped-storage 1,400GWh

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The next power grid and energy storage timelines illustrate that when the system is under-powered, for the very low wind conditions over Britain in the period September 2014, with an annual maximum wind power of only 5.5 x peak demand power and storage energy of only 1.11 days x peak demand, the energy store runs out, the reservoir(s) drain dry and the system requires to import energy to meet demand.

Graph 4. September 2014. Demand 52.5GW, Wind 290GW, Pumped-storage 1,400GWh

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With the recommended

the system has enough wind power and energy storage to cope with the very low wind conditions of September 2014.

Graph 5. September 2014. Demand 52.5GW, Wind 370GW, Pumped-storage 1,900GWh

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Note that in Graph 5, the maximum pump power is equal to peak demand and therefore cannot exploit all of the available wind power on Sep/7 18: to 23: hours and similarly on Sep/14, forcing the system to export precious power in a week when wind power was in short supply.

This suggests that increasing the installed maximum pump power from a nominal 100% up to at least 115% and perhaps as much as 145% of peak demand power could somewhat more efficiently take advantage of a few gusty hours on low wind days assuming that the power line transmission capacity between the wind generators and the pumps exceeds peak demand and that the water flow rates could increase by the appropriate percentage too.

Back-up Generators

A similar system but including back-up generators (such as biomass power stations) was modelled.

Graph 6. Peak Demand (52,500 MW), Store – 1.1 days x peak demand (1,385 GWh), Wind – 5.5 x peak demand (288,600 MW), Back-up – 0.15 x peak demand ( 7,900 MW)

The system modelled in graph 6 differs from that in graph 4 with the addition of back-up generators with a power capacity of 15% of peak demand which power up when the energy store drops to 75% of maximum capacity, thereby successfully avoiding the need for imports even during the extreme low wind weather event of September 2014.

Graphs 7 to 12 give further examples of many possible system configurations.

Graph 7. Peak Demand (52,500 MW), Store – 0.8 days x peak demand (1008 GWh), Wind – 4 x peak demand (210,000 MW), Back-up – 0.3 x peak demand ( 15,700 MW)
Graph 8 Peak Demand (52,500 MW), Store – 0.7 days x peak demand (882 GWh),
Wind 3.3 x peak demand (173,200 MW), Back-up 0.35 x peak demand ( 18,400 MW)
Graph 9. Peak Demand (52,500 MW), Store  0.6 days x peak demand (756 GWh),  Wind 2.7 x peak demand (141,700 MW), Back-up 0.4 x peak demand ( 21,000 MW)
Graph 10. Peak Demand (52,500 MW), Store – 0.4 days x peak demand (504 GWh), Wind – 1.9 x peak demand (99,750 MW), Back-up – 0.47 x peak demand ( 24,675 MW)
Graph 11. Peak Demand (52,500 MW), Store – 0.3 days x peak demand (378 GWh), Wind – 1.5 x peak demand (78,700 MW), Back-up – 0.51 x peak demand ( 26,775 MW)
Graph 12. Peak Demand (52,500 MW), Store – 0.21 days x peak demand (265 GWh), Wind – 1 x peak demand (52,500 MW), Back-up – 0.56 x peak demand ( 29,400 MW)

Table of wind, pumped-storage & back-up factors
The factors in the table are peak demand power multipliers. Each row triplet describes a possible system configuration for 24/7/52 reliable 100% renewable energy generation.

Wind power Storage days Back-up
7 1.5 0
5.5 1.1 0.15
4 0.8 0.3
3.3 0.7 0.35
2.7 0.6 0.4
1.9 0.4 0.47
1.5 0.3 0.51
1 0.21 0.56

Wind, storage and back-up system designer

Wind farm on-site energy storage

This simple modelling glosses over how wind power surpluses can be “exported” or from where power deficiencies can be “imported” to meet demand?

Wind farms could “export” their power generation surpluses no further than to on-site energy storage facilities and “import” power from those stores to meet demand at times of low wind.

A more complex computer model which includes on-site energy stores would be useful to research in future work.

A footnote on the limitations of spreadsheets with large data-sets.

The Gridwatch data consists of 1 row of data every 5 minutes of time recording, 12 data rows an hour, 288 a day, 2016 a week, 26208 a quarter and 104832 for a full year. The data as downloaded also comes with a number of erroneous data values that must be painstakingly weeded out.

Microsoft Works Spreadsheet cannot read in a quarter of a year of data because it does not allow more than 16,384 rows. Excel on a PC may do but since I don’t buy Excel and the free online version doesn’t seem to read .csv files, I gave up with Excel.

Google Sheets free online I managed to use to read up to 3 months of data though I found it became sluggish and buggy with 25,000 rows in a sheet with multiple columns with complex formulas but I got the results I wanted with perseverance. Google Sheets could not handle a year of data rows though.

Example Spreadsheet Model produced using Google Sheets

Download Spreadsheet model .xlsx file

Download the spreadsheet model file from the above link.