For a hypothetical future power grid where production is dominated by variable renewable sources like PV and wind, the challenge of balancing supply and demand at all times is well know. Using again the ENTSO-E open-source data and Python linear programming solver, we extrapolate the grid level solar and wind forecast data to cover the entire yearly electricity demand while minimizing the sum of the absolute errors between supply and demand for all hours in a year.

In order to turn the problem of minimizing the sum of absolute values into a linear programming problem, we use the bounding technique presented in this tutorial.

Using for example the data for the German power grid from Spring 2022 to Spring 2023, the optimal generation mix according to the above criteria is about 75% wind and 25% PV (blue line). With this configuration about 80% of the annual supply & demand of 475 TWh would be matched at the hourly level, leaving a discrepancy of 20% or 107TWh to be equalized somehow.

For different time-scales, the diagram shows how much imbalance is left after if by some way we could equalize the imbalance up to some time-scale - for example 4 or 12 hours, days, weeks months etc. We can see for example that for the optimal mix, the greatest drop in unmatched imbalance is in between the order of days to weeks, which matches the cycles of the general weather situation in Europe which includes periods with more or less wind and more or less clouds and precipitations. The residual imbalance beyond the month timescale is less than 5% or 20TWh, which means that there is hardly a seasonal imbalance.

Compared to the optimal mix, a 100% PV generation would be much more imbalanced: 30% intra-day plus another 30% seasonal, which require equalization across more than a 3 months. A 100% Wind (optimal onshore & offshore mix) is much less volatile across hours of the day and generally follows the seasonality of demand (more demand & generation in winter).

The optimal mix and resulting imbalance is surprisingly similar across various European countries with different climatic conditions: from the north-sea cost of Netherland to the southern mediterranean Greece to to the semi-arid plains of Spain.

- Over-capacity with overproduction and curtailment
- Demand flexibility (shifting demand in time to match available supply)
- Storage
- Long-distance HVDC interconnects between regions with different weather pattern.
- Other intermittent energy sources which have low with wind or solar.
- Dispatchable renewable energy sources, e.g. hydro-electric.