## 1 Introduction  
The European Union (EU) is planning its green transition largely on the basis of renewable energy [1]. Given that aluminium smelting contributes significantly to greenhouse gas emissions, there is a focused effort to reduce its carbon footprint [2, 3], improve sustainability [4], and meet the European Union's environmental targets [5]. One of the EU's fundamental objectives is to generate electricity through the use of PV (photovoltaic) systems. However, due to the dependence of their operation on light conditions and, consequently, the weather and other environmental factors (such as shadows from surrounding buildings, the angle of incidence of the sun's rays, and the position of the sun), they are not able to ensure constant production. Thus, the planned increase in electricity production from PV systems also leads directly to a significant increase in grid disturbances [6], requiring an appropriate upgrade of system services to ensure the smooth transmission of electricity and to enable the safe and reliable operation of the system. Demand-side management has been identified as a key strategy to address the variability of renewable energy sources [7], where large industrial consumers play a significant role in balancing supply and demand. To this end, the transmission system operator must ensure an adequate level of system services at all times. System service providers are the electricity generators and, in the process of automatic frequency restoration, also major customers, who can increase or decrease their consumption sufficiently quickly to contribute to balancing. A large aluminium smelter is able to provide automatic frequency restoration services [8] through the provision of the energy flexibility services concept, which, in some literature, is referred to as a virtual battery [9]. This concept is gaining traction as a means to manage the intermittent production of renewable energy sources. [PERSON] [10] assessed the theoretical demand response potential in Europe, highlighting the significant flexibility that industrial processes can offer to the energy system. Similarly, [PERSON] and [PERSON] [11] analysed the potential of demand-side management in energy-intensive industries, demonstrating how industries like aluminium smelting can adjust their electricity consumption in response to market prices. Such energy flexibility allows for fast adjustment and dispatch and offers regulation in case of energy shortages in the electricity distribution system. While a traditional battery balances by transmitting stored energy, energy flexibility services provide variability in consumption. In the case of peaks, the smelting process allows for a few hours of increased output and, thus, higher load. While the prices of regular battery systems are very high [12; 13] and their performance decreases with ageing [14], aluminium smelting can provide system services to the same or a greater extent at a significantly lower cost. It should be noted, however, that for traditional aluminium smelter technology, the aluminium smelting must be profitable, even without the provision of energy flexibility services, to be able to take advantage of this concept, as most of the day, it still needs to run at the same high power consumption level to smell aluminium. The reason for this is that, traditionally, smelting cannot be stopped and restarted at will every day. In recent years, new technological and methodological developments have emerged [9; 15; 16; 17; 18] that allow for flexible energy consumption, which allows such an aluminium smelter to modulate their power consumption according to the availability and price of electricity [9]. Such an approach to minimise electricity cost through demand-side management in combination with the smart grid concept [19; 20; 21; 22] is economically profitable, especially for large electricity consumers [23; 24]. The concept of using aluminium smelting to provide energy flexibility services to balance the electricity grid has been explored by several researchers.