Nowadays, non-integer systems are a widely researched problem. One of the questions that is of great importance, is the use of mathematical theory of a non-integer order system to the description of supercapacitors (capacitors with very high capacitance). In the description of electronic systems built on a microscale, there are models with dis- tributed parameters of fractional derivatives, which can be successfully approximated by finite-dimensional structures, e.g, in the form of various types of ladder systems (chain). In this paper, we will analyze a ladder system of an RC type consisting of supercapacitors.

Electricity storage is one of the best-known methods of balancing the energy supply and demand at a given moment. The article presents an innovative solution for the construction of an electric energy storage device obtained from an innovative photovoltaic panel made of new dye-based photovoltaic modules and newly developed supercapacitors – which can be used as an emergency power source. In the paper, for the first time, we focused on the successful paring of new dye-sensitized solar cell (DSSC) with novel supercapacitors. In the first step, a microprocessor stand was constructed using Artificial Intelligence algorithms to control the parameters of the environment, as well as the solar charger composed of six DSSC cells with the dimensions of 100_100 mm and 126 CR2032 coin cells with a total capacitance of 60 F containing redox-active aqueous electrolyte. It was proven that the solar charger store enough energy to power, i.e. SOS transmitter or igniters, using a 5 V signal.

Energy storage systems (ESS) are indispensable in daily life and have two types that can offer high energy and high power density. Hybrid energy storage systems (HESS) are obtained by combining two or more energy storage units to benefit both types. Energy management systems (EMS) are essential in ensuring HESS's reliability, high performance, and efficiency. One of the most critical parameters for EMS is the battery state of health (SoH). Continuous monitoring of the SoH provides essential information regarding the system's status, detects unusual performance degradations and enables planned maintenance, prevents system failures, helps keep efficiency at a consistently high level, and helps ensure energy security by reducing downtime. The SoH parameter depends on parameters such as Depth of Discharge (DoD), charge and discharge rate (C-Rate), and temperature. Optimal values of these parameters directly affect the lifetime and operating performance of the battery. The proposed Adaptive Energy Management System (AEMS) uses the SoH parameter of the battery as the control input. It provides optimal control by dynamically updating the C-Rate and DoD parameters. In addition, the supercapacitor integrated into the system with filter-based power separation prevents deep discharge of the batteries. Under the proposed AEMS control, HESS has been observed to generate 6.31% more energy than a system relying solely on batteries. This beneficial relationship between supercapacitors and batteries efficiently managed by AEMS opens new possibilities for advanced energy management in applications ranging from electric vehicles to renewable energy storage systems.