## 1 Introduction  
Distributed energy resources (DERs) have experienced a massive and generally uncontrolled growth in the last few decades, especially low-size photovoltaic (PV) power plants installed by residential users and directly connected to distribution networks [1; 2]. If, on the one hand, this enables a less dependence on fossil fuels, increasing environmental and energy sustainability of modern power systems, on the other hand it causes several issues to power system management [3; 4]; this historically relies on a hierarchical and concentrated structure, namely few and big thermal power plants connected to the transmission networks, while most of the users draw energy at the distribution level. Consequently, a significant amount of PV energy injected by a multitude of prosumers may have a negative impact on voltage/frequency regulation and power quality due to intermittency and unpredictability of PV production [5; 6; 7]. In this scenario, energy storage systems (ESSs) play a fundament role in the transition from actual to modern power systems as ESSs can cope with the randomness of renewable energy sources [4; 8; 9; 10]. In particular, ESS can provide several power and energy services depending on its size and inherent features (dynamic response, rated power and energy, calendar and cycle life, etc.). Electrochemical batteries are surely the most popular solutions for residential prosumers, as proved by a number of ESSs already on the market [11; 12]; batteries guarantee adequate power and energy performance, flexible power to capacity ratio, low maintenance, small dimensions and weights, and good modularity [13]. On the other hand, batteries suffer from relatively low cycling capability and aging effects, which may significantly reduce their expected lifetime depending on their usage and environmental conditions [14]. Increased cycling capability can be assured by supercapacitors [15], which, however, are characterized by a very weak energy density, making them suitable for uninterruptible power supplies and, generally speaking, for power services mostly [16]. A viable alternative to both batteries and supercapacitors is represented by flywheel ESSs (FESSs) [17; 18; 19; 20; 21; 22]; these devices are generally characterized by a high power density, superior to that of electrochemical batteries and comparable to that of supercapacitors, and by a fair energy density, less than batteries but much greater than supercapacitors [19; 23]. Furthermore, FESSs are characterized by a very long lifetime and cycling capability (several hundreds of thousands of cycles compared to the few thousands of batteries), and they are maintenance free and environmental-friendly [4; 19; 20]. On the other hand, FESSs are technologically complex, namely they are made up of several mechanical, electromagnetic and electronic components (electrical machine, power electronic converters, sensors, bearings, etc. ), thus requiring expert knowledge in different fields to be designed and manufactured appropriately [22; 24; 25], this, along with high capital cost, represents the main drawbacks that is still preventing FESS to be widespread, especially for low-medium size applications [20; 22]. FESSs can be classified in accordance with different criteria, among which the most popular concerns their speed range [20; 26]. In this regard, low-speed FESSs rotate up to approximately 10 k rpm, and they are made of steel, which is inexpensive but gives them a significant weight. Consequently, this kind of FESS is generally heavy and bulky, making it suitable for large scale stationary applications, such as underground FESS banks devoted to primary-secondary frequency regulation [20]. Differently, high-speed FESSs have a much wider speed range (up to hundreds k rpm), thus they are able to store as much energy as low-speed FESSs, but with a significant weight reduction. As a result, high-speed FESSs are more suited for small-scale stationary and vehicular applications, such as small power plants and buses [20].