## 2 State of the Art  
The energy network falls into the section of critical infrastructure. The entire grid has many levels of control and management, according to the technological domain (e.g., transmission grid, distribution grid, demand side) [10; 11; 12]. Complex optimization tasks, including Unit Commitment and Economic Dispatch (ED), are solved during the operational planning of system elements. The complexity of discrete optimization related to Unit Commitment (i.e., curse of dimensionality) prevents its real-time solution. Therefore, these complex optimization tasks (Unit Commitment complemented by ED) are usually solved in advance [11; 12]. Short-term operational planning is solved on the day-ahead time horizon in the case of distribution grids. This task uses statistical methods and models to estimate and forecast this value for a given time frame [13]. The Unit Commitment problem optimizes an activation or deactivation of selected controllable assets (e.g., generators) [14]. On the other hand, the EDP is continuously solved in real-time to manage system disturbances and system state deviations from the expectation when unit commitment has been calculated. The EDP defines operational set points for committed controllable assets (e.g., generators, energy storage) according to the energy needs (i.e., balance) of the energy system, considered optimization constraints and selected control policy. Minimizing operational costs of technology asset groups is often the primary goal [15; 16; 17]. There are several ways to solve EDP. Article [18] presents a review of methods that were used around 1990. These are mainly centralized solution methods, which include, for example, the Lambda-iteration method or genetic programming [19; 20]. Other applicable methods are based on particle swarm optimization or evolutionary programming [21; 22; 23]. Over the years, efforts have been made to replace these methods with decentralized methods. The inclination towards decentralized methods is mainly thanks to the progress of multi-agent systems theory and technological progress [10; 24]. Many consensus-based algorithms are used for a distributed way of solving [8; 9; 25]. Furthermore, there is also an effort to incorporate renewable sources, mainly from replacing conventional sources to reduce emissions [26; 27]. These goals also lead to advancing the technical possibilities of renewable power plants. This development led to the need to manage them across the entire energy network [28]. In order to make greater use of energy from renewable sources, they are often extended by BESS [29; 30; 31]. BESSs can provide stored energy to the grid but also take it from the grid [30; 32]. Due to the growing number of electric cars, the energy network needs to account for them [33]. The next step is the integration of charging stations [34]. This fact leads to the need to ensure stability and cover the required load in the case of networks that consist of different generators, renewables, and BESS. It is also essential that the distributed methods are applicable even for a large number of considered agents [35]. Paper [36] demonstrates the suitability of distributed algorithms even for many agents, specifically for thousands of generators. Electricity prices change during the day, so it is necessary to adapt to them [37; 38]. Mostly, the price is set using an auction-based system, which can be on a different time horizon in Europe; it is usually a 15-min trading interval [39; 40]. In order to build such power plants, which will have the lowest possible costs, it is necessary to consider changes in energy prices as well as other costs associated with the operation of generators and the entire energy network. It can sometimes be advantageous for BESS to buy energy at lower prices, then sell it and feed it back into the grid once the price rises. None of the previously described works represented uncertainties or time delays in the communication network. In realistic cases, however, the communication network is never ideal [41].