## 4 Analysis and Interpretation of Results
### Dependence of the Occurrence of Negative Prices on RES Generation
#### 4.2.1 Germany: Quadratic Growth and Breaking Point--Figure 2  
An analysis of the relationship between aggregated hourly generation from renewable energy sources (wind and solar) and the occurrence of negative wholesale electricity prices on the daily market in Germany showed a systematic and non-linear dependence. Germany, as Europe's largest economy and at the same time one of the leaders in the integration of RES, provides a good case for analysing the impacts of high penetration of fluctuating sources in the electricity system. The resulting graph shows that at low levels of RES degeneration (up to about 60,000 MW), the incidence of negative prices is negligible, with values close to 0%. In this band, the market absorbs renewable production without a significant price response, indicating the presence of sufficient regulatory capacity, surplus exchange possibilities, or demand flexibility. After a threshold of about 65,000 MW is crossed, significant non-linearity occurs, with the proportion of hours with negative prices starting to increase sharply. This dynamic is even more pronounced in the 195,000 MW band, where the incidence of negative prices gradually approaches 100%. The resulting dependence is quadratic, with each additional increase in output associated with a disproportionately higher risk of negative prices. This non-linear nature suggests that the electricity system reaches a regulatory limit at a certain capacity band, after which it can no longer absorb excess generation without significant price distortions. The high incidence of negative prices for generation above 170,000 MW is likely due to a combination of several factors:  
1. Limited flexibility of basic resources (e.g., coal, nuclear)--shutdown of nuclear power plants. Negative prices mostly start to emerge in 2023.
2. Capacity limits on cross-border transmission lines that make it impossible to export surplus power.
3. Lack of demand response or absence of consumption systems for surplus (e.g., Power-to-X technologies).
4. Asymmetry between the geographical distribution of production and consumption, leading to internal transmission constraints (re-dispatch). Re-dispatch (or generation realignment) is a process used in the electricity industry to deal with situations where electricity cannot be transported from where it is generated to where it is consumed due to congestion on the transmission system.  
The results show that Germany is at a stage where the sheer amount of generation from RES is enough to create recurrent distortions in electricity prices. Negative prices lose the character of exceptional events and become a normal concomitant of surplus RES generation. In terms of methodology, this section demonstrates the effectiveness of the analysis to locate power bands with extreme occurrences of negative prices. In contrast to the average monthly or annual price analysis, this method allows a more precise identification of critical points of power stress.  
Germany is at an advanced stage of energy mix transformation, but the results of the analysis suggest that without adequate flexibility elements (storage, demand response, export capacity), the system will increasingly run into price anomalies. This trend may undermine Germany's investment strategy and market stability. The results thus point to the need for a redefinition of market rules and complementary mechanisms that will allow a high share of RES to be managed efficiently without disturbing the price equilibrium.