Using national power grid data from the ENTSO-E transparency platform, some very rough and hand-wavy cost assumptions and a standard Python LP solver, we can do a back of the envelope estimation of what it would take to satisfy todays electricity needs of some European countries using an extrapolation of their current solar and wind production in combination with a fictitious storage pool.

Linear Programming is a very common optimisation technique used in operations research and economic modelling which can be applied as long as a problem can be expressed as minimisation of a linear cost function und the constraint of a series of linear inequalities.

For the storage system, we are assuming a combination of "short duration storage" (SDS) inspired by current lithium-ion battery storage plants and "long duration storage" (LDS) inspired by a hydrogen based storage plant consisting of electrolyzers to convert electricity into hydrogen, storage in underground caverns and conversion back into electricity using conventional combined-cycle gas turbine plants. The cost assumptions for this configuration are taken from this paper, which also helped to inspire and validate the formulation of the LP model - which is described in more detail in this following post. The capital costs are annualised using a 3% interest rates and added to the annual operating cost estimates.

For the cost of solar and wind generation, we are using a LCOE cost estimates in Euro per MWh from Wikipedia, which are based on this 2021 report. Given the wide range of values, we are using rough median values of 55, 60 and 90 Euro/MWh for solar, onshore wind and offshore wind respectively.

As an example for the hourly load and generation profiles, we are using the Netherlands, which has significant production forecast data for all the 3 types of renewable sources we are considering: solar, onshore wind and offshore wind.

We are running the LP model for different target levels of coverage or system availability factors for this fictitious production system. This represents the ability to satisfy 80 to 100% of the demand from solar, wind & storage alone, using the actual load & generation data from spring 2022 to spring 2023. A coverage factor of 80% implies that the simulated system would only satisfy 80% of the load, with the remaining 20% coming from other sources - import or other sources of generation.

80% | 90% | 95% | 100% | |
---|---|---|---|---|

Load (total / avg / peak) | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW |

Generation (total / avg / peak) | 87.2TWh / 10.0GW / 36.8GW | 101.0TWh / 11.5GW / 42.5GW | 108.1TWh / 12.4GW / 45.6GW | 116.4TWh / 13.3GW / 48.9GW |

Generation PV / ONW / OFFW | 43.1% / 56.9% / 0.0% | 40.8% / 59.2% / 0.0% | 41.3% / 58.7% / 0.0% | 39.4% / 60.6% / 0.0% |

Annual Cost / Cost per MWh | 5.8B€ / 73.2 €/MWh | 6.9B€ / 77.4 €/MWh | 7.6B€ / 80.2 €/MWh | 8.5B€ / 85.3 €/MWh |

System Efficiency | 91.4% | 88.8% | 87.5% | 85.5% |

Surplus | 1.7% | 1.6% | 1.5% | 1.5% |

Storage contribution | 16.4TWh (16.5%) | 22.3TWh (22.4%) | 25.9TWh (26.0%) | 28.2TWh (28.4%) |

SDS Power | 8.2GW | 8.9GW | 9.4GW | 7.6GW |

SDS Capacity / Duration | 44.3GWh / 5.4h | 48.9GWh / 5.5h | 51.4GWh / 5.4h | 39.9GWh / 5.2h |

SDS contribution | 9.8TWh (9.8%) | 10.9TWh (11.0%) | 11.8TWh (11.8%) | 9.5TWh (9.5%) |

LDS Power (charge/ discharge) | 6.6GW / 1.5GW | 9.4GW / 3.5GW | 11.0GW / 4.4GW | 14.1GW / 11.0GW |

LDS Capacity / Duration | 1273.2GWh / 855h | 2310.2GWh / 662h | 3767.8GWh / 847h | 5489.6GWh / 500h |

LDS contribution | 6.7TWh (6.7%) | 11.4TWh (11.4%) | 14.2TWh (14.2%) | 18.8TWh (18.9%) |

The resulting optimal allocation of annual cost into the choices of resources is as follows, resulting in an average per MWh production cost between 73 and 85 Euro per MWh depending on the achieved coverage/availability:

The resulting system is surprisingly well-balanced, with an energy generation surplus (curtailment or export) of only 1.5-2%. While solar is slightly cheaper than wind per MWh generated, the optimisation seems to favor wind due to a more even match of supply and demand, reducing the need for even more expensive storage. Offshore wind is excluded from most solutions, presumably due to being more expensive than onshore wind and not offering a sufficiently complementary production profile.80% | 90% | 95% | 100% | |
---|---|---|---|---|

Load (total / avg / peak) | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW |

Generation (total / avg / peak) | 94.0TWh / 10.7GW / 39.9GW | 111.2TWh / 12.7GW / 47.2GW | 124.4TWh / 14.2GW / 52.2GW | 126.5TWh / 14.5GW / 52.2GW |

Generation PV / ONW / OFFW | 45.6% / 54.4% / 0.0% | 45.2% / 54.8% / 0.0% | 39.4% / 60.6% / 0.0% | 30.4% / 69.6% / 0.0% |

Annual Cost / Cost per MWh | 6.4B€ / 80.8 €/MWh | 8.0B€ / 89.7 €/MWh | 9.2B€ / 96.8 €/MWh | 12.2B€ / 122.4 €/MWh |

System Efficiency | 84.7% | 80.6% | 76.0% | 78.7% |

Surplus | 6.3% | 9.7% | 13.7% | 8.7% |

Storage contribution | 14.1TWh (14.1%) | 19.6TWh (19.7%) | 20.6TWh (20.7%) | 24.1TWh (24.2%) |

SDS Power | 3.3GW | 5.7GW | 4.5GW | 4.2GW |

SDS Capacity / Duration | 12.4GWh / 3.8h | 24.3GWh / 4.3h | 17.1GWh / 3.8h | 13.3GWh / 3.1h |

SDS contribution | 3.3TWh (3.3%) | 6.0TWh (6.0%) | 4.2TWh (4.2%) | 3.2TWh (3.3%) |

LDS Power (charge/ discharge) | 11.8GW / 4.3GW | 13.6GW / 6.1GW | 15.2GW / 8.1GW | 13.5GW / 12.9GW |

LDS Capacity / Duration | 298.9GWh / 69h | 620.6GWh / 101h | 996.8GWh / 123h | 4322.8GWh / 335h |

LDS contribution | 10.8TWh (10.8%) | 13.6TWh (13.7%) | 16.4TWh (16.5%) | 20.8TWh (20.9%) |

80% | 90% | 95% | 100% | |
---|---|---|---|---|

Load (total / avg / peak) | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW | 99.6TWh / 11GW / 17.7GW |

Generation (total / avg / peak) | 95.8TWh / 10.9GW / 58.9GW | 110.7TWh / 12.7GW / 68.1GW | 118.7TWh / 13.6GW / 73.0GW | 125.9TWh / 14.4GW / 77.4GW |

Generation PV / ONW / OFFW | 100.0% / 0.0% / 0.0% | 100.0% / 0.0% / 0.0% | 100.0% / 0.0% / 0.0% | 100.0% / 0.0% / 0.0% |

Annual Cost / Cost per MWh | 7.9B€ / 99.7 €/MWh | 9.8B€ / 109.0 €/MWh | 10.8B€ / 113.9 €/MWh | 11.9B€ / 119.2 €/MWh |

System Efficiency | 83.2% | 80.9% | 79.7% | 79.1% |

Surplus | 3.9% | 3.3% | 3.0% | 2.9% |

Storage contribution | 41.6TWh (41.8%) | 50.2TWh (50.5%) | 57.1TWh (57.3%) | 59.7TWh (60.0%) |

SDS Power | 22.8GW | 24.2GW | 24.9GW | 26.3GW |

SDS Capacity / Duration | 121.5GWh / 5.3h | 124.8GWh / 5.2h | 126.6GWh / 5.1h | 133.2GWh / 5.1h |

SDS contribution | 29.1TWh (29.3%) | 31.3TWh (31.5%) | 34.5TWh (34.7%) | 34.3TWh (34.4%) |

LDS Power (charge/ discharge) | 14.8GW / 2.7GW | 21.4GW / 5.4GW | 24.9GW / 6.3GW | 27.3GW / 10.7GW |

LDS Capacity / Duration | 11486.5GWh / 4202h | 19563.6GWh / 3625h | 24419.0GWh / 3858h | 28878.8GWh / 2710h |

LDS contribution | 12.5TWh (12.5%) | 18.9TWh (19.0%) | 22.5TWh (22.6%) | 25.4TWh (25.5%) |

For the purpose of this analysis, we are looking at the load and generation capacity of a national power grid in aggregate, completely ignoring the internal capacity constraints of the distribution network. Given that in our retail electricity prices, distribution cost accounts for nearly two thirds of the price should serve as an indication of how flawed this assumption is. It is also not clear to what degree a distributed system where many different stakeholders held together by regulation and market designs, could approximate a globally optimal solution.