## 2 Our Proposed Solution  
A rule-based expert system (RBES) is an artificial intelligence component that uses knowledge-based rules to perform an activity [39]. Their design is similar to an advanced computer program that tries to mimic the capabilities of a human expert collecting knowledge sources used to perform an objective in a particular domain [36; 39]. Thus, knowledge is taken from the human expert and converted into a production rule set that represents the domain knowledge. The basic structure of a RBES contains the following main components: knowledge base module, inference engine, decision-making module, explanation facilities, and user interface. The characteristics of the main components (see Figure 2) included in the proposed RBES used in the voltage control from the active LVEDNs are described in the following. The knowledge database of the proposed expert system has two partitions: the rule base and the database. The rule base stores the rules and facts. The database is divided into two partitions (static and dynamic) and is associated with recording the immutable facts. The static partition of the database contains information on the features of the active LVEDNs regarding:  
* Line sections characterized by the input and end nodes, type (aerial/underground), cross-sections of the phase, and neutral conductors;
* MV/LV distribution transformers from the EDSs characterized by rated power, performance standards identified through the commissioning year, tap changer type (NLTC/OLTC), and tap positions;
* Reactive power compensation devices identified through the installed capacity, type (capacitor banks or static reactive (VAR) compensator), and their locations;  
Figure 2: The structure of the proposed RBES used in the voltage control from the active LVEDNs. * Energy storage systems identified through the installed capacity and their locations;
* End-users characterized by type (single-phase/1-P or three-phase/3-P), the location in the AEDNs (the connection pillars), the connection phase (for 1-P end-users);
* Energy generation systems installed to the prosumers characterized by the installed capacity. The RBES uses the data communication between the smart meters installed at all end-users and the data concentrator installed in the MV/LV EDS. These data form the dynamic database of the RBES, together with the outcomes of the steady-state calculations, represented by the values of the voltage from the nodes:  
* Upper and lower allowable limits of the voltages imposed by the quality power standards;
* Information from the smart metering system associated with the injected/requested powers by the end-users (prosumers/consumers) at the fixed time slots (depending on setting the sampling step of the smart meters), the annual energy production/consumption. The nodal voltages, power flows, and power losses resulting from the steady-state calculations are performed with a performance algorithm developed by [PERSON] and [PERSON] in [40]. The algorithm is characterized by a fast convergence with a reduced calculation time. Three stages characterize its internal structure:  
* The first stage involves online work, uploading the data from the SMS database, which contains the production and consumption profiles of the prosumers and consumers integrated in the LVEDN. * The second stage corresponds to the fast recognition of the topology associated with the LVEDN using a structure vector-based method. The data are uploaded from the network topology database. * The third stage focuses on the steady-state calculations using an improved variant of the forward/backward sweep algorithm determining the power/energy losses in four-wire LVEDNs regardless of the operating regimes (balanced and unbalanced). It uploads the topology of the AEDNs identified through the data recorded in the static database at the request of the inference engine. The inference engine accesses the data and, using the rule-based motivation, decides whether to modify the tap position of OLTC.