Solar, Wind & Storage - optimal resource allocation

As wind and solar are reaching a double-digit share of production in many power grids, the focus is increasingly shifting towards adding storage. Large consumers like Google are pushing their suppliers towards  providing low carbon energy 24/7 all year round. The same goal is also captured well by the catchy new term of "Grüne Grundlast" (green baseload) , despite being slightly misleading as the goal should not be constant production when nobody needs it, but production which matches the load at all times.

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.

For the storage model, the battery based SDS is very efficient (>90% round-trip efficiency) with expensive storage cost but a lower additional per power capacity cost compared to hydrogen LDS which requires very expensive conversion equipment. For the optimal solution overall storage need is driving the dimensioning of the LDS system while the SDS systems seems to mostly serve to supplement peak power capacity as illustrated by a energy flow graph for a few days in April 2022 in the simulated model:

Despite the much lower efficiency, the H2 storage system is also used heavily for short-term intraday turnarounds, where one might have expected the more efficient battery SDS to do most of the heavy lifting. The resulting optimal SDS storage capacity remains relatively small about 5.5 hours only. In a way it seems that the SDS battery system mostly acts as a short-term power-capacity booster to better absorb the sharp solar peaks. The model has no penalty term for ramping, turnaround or usage based degradation, leading to some arbitrary oscillations which likely would be discouraged in a real system.

The model seems to be mostly driven by a trade-off between low solar & wind productions costs and low hydrogen storage cost while minimising the need for  expensive power capacity to transfer between the two. The low energy efficiency of the H2 storage system does not seem to matter much, if the alternative would be more overproduction and curtailment. Or in other words, the optimal configuration is determined by the needs for the worst-case situation and for all the other times, efficiency matters very little. While 5.5 TWh of H2 storage might seem like a lot, this report claims an existing potential of over 140 TWh H2 underground storage for the Netherlands, mostly in the form depleted natural gas fields.

By increasing storage capacity cost 2x for batteries and 10x for H2 storage, we can see the optimal allocation shifting towards more overproduction and curtailment. Also there is a significant jump in cost & storage investments necessary to meet the last 5% of demand all the time.

	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%)

To create another extreme scenario, we can peg the production from wind at zero only allowing generation from solar, which generally is the most unevenly distributed both across the day and across the seasons, resulting in a much higher storage requirement:

	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%)

Because the model is only based on a single year, long-term variability and rare, extreme weather events are not taken into account. However, the biggest weakness of any such model is the sensitivity to assumptions. Even changing them within a reasonable range, can change the resulting configuration significantly.

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.

We could also argue that modelling today's electricity demand is not as relevant for the future, given the planned electrification of sectors which use fossil fuels to day like transportation, building heat or industrial processes. While we expect the demand to increase significantly, the vast majority of this new demand is also flexible in the order of hours or days, as the needed energy can be buffered more cheaply in the form of heat or stored in generously sized car batteries - as we discussed in this previous post. In other words, the future demand profile will likely to be more closely matched in time to the availability of renewable energy.

Yet even this very basic back of the envelope analysis shows that with an optimal mix of today's technologies, a 100% renewable grid would be possible for an average generation cost that is less than any fossil fuel source (assuming carbon emission certificates close to 100 Euro). The key would be to deploy as much of storage technology with the cheapest cost of storage (likely H2 - regardless of efficiency or power capacity cost) and complement some of the peak power capacity needs with faster but much smaller storage (likely lithium-ion or similar battery technologies).