## 2 Material and Methods
### The Concept of the Pumped Thermal Energy Storage Unit for Trigeneration  
The present work outlines the idea of exploiting volatile electricity from renewables in order to convert it into three useful products that can be properly stored. Figure 1 demonstrates this idea with a simplistic depiction. The core of the system is a multi-stage heat pump that is fed by the ambient source and from cold input which is responsible for the cooling loads. The heat pump rejects heat to the medium temperature level, around 50 \({}^{\circ}\)C, in a heat storage system for space-heating purposes and/or domestic hot production. Furthermore, the heat pump is able to produce high heating temperatures, e.g., around 115 \({}^{\circ}\)C, for high-temperature storage. This high quantity can be used in an ORC for electricity recovery when there is a need. At this point, high-temperature thermal storage can also be used in alternative applications such as industrial processes (e.g., drying), but it is not in the scope of the present work which focuses on building applications. The storage of thermal/cold energy is a critical issue because it has to be both efficient and kept for significant time periods. Thus, this work suggests the use of latent storage systems. Evidence suggests that the use of ice storage is a cost-effective solution for cold storage at 0 \({}^{\circ}\)C. The other storage systems, medium and high-temperature levels, have to use phase change material (PCM) with melting temperature at 50 \({}^{\circ}\)C and at 115 \({}^{\circ}\)C, respectively. At this point, it is useful to highlight that the cold-storage temperature (0 \({}^{\circ}\)C) and the medium-storage temperature (50 \({}^{\circ}\)C) are fixed in this study, while the high-temperature level of the storage is variable. It is important to note that for the high temperature, the value of 115 \({}^{\circ}\)C is a typical choice in order to have high performance and not to face difficulties with the turbomachinery and other devices. The suggested unit is ideal for buildings and can be applied from low scale up to high scale. There is the scope to adjust the system capacity according to the building needs, plus this system with latent storage can be a compact design with the possibility of long-term storage for several weeks. The next step in this study is the description of the multi-stage heat pump, as well as the total configuration in detail. Figure 2 shows the total configuration, while Figure 3 describes the regenerative ORC. According to Figure 2, the suggested heat pump has three compressors and operates at four temperature levels: the low temperature (\(T_{low}\)), which is 5 K lower than cold storage; the (\(T_{in\text{-}am}\)), which is 5 K greater than the ambient temperature; the (\(T_{heat\text{,}m}\)), which is 5 K greater than the medium storage temperature; and the (\(T_{hunt\text{,}h}\)), which is 5 K greater than the high thermal storage temperature. These temperature differences of 5 K are selected as typical values for efficient and proper heat transfer. Figure 1: **A** general description of the “Power to XYZ” concept. Figure 3: The examined organic Rankine Cycle (ORC) with recuperator. Figure 2: Detailed description of the examined configuration of the pumped thermal energy storage system for trigeneration. The ambient source is used in order to counterbalance the system loads. Moreover, during the winter period there are no cooling needs, so the system can operate without the lower-stage compressor. In this scenario, the system operates as a cogeneration unit. Thus, at this point, it is important to separate the following operating scenarios:  
(A) Trigeneration operation: All the compressors are open and all the devices are used. (B) Cogeneration operation: The compressor (a) of the lowest stage is closed and there is no cold storage. In relation to the system description, it is worth noting that the working fluid is cyclopentane in both the heat pump and the ORC. This is a proper selection according to previous studies [8; 11].