**1. Introduction**

The gradual depletion of fossil fuels has driven research into renewable resources [1]. Many countries have made progress in promoting renewables within their energy mix, but obstacles remain, and further efforts are needed. Making a renewable system reliable over time requires provision from storage systems to avoid gaps in energy supply [2]. Energy storage is a key determinant in the energy transition process. Energy storage systems provide greater accessibility to renewable energy sources in the power grid, ensuring both energy savings and reduced impact on the environment [3,4], while reducing the gap between energy supply and demand [5]. The advantages offered by storage systems include increased stabilization of energy supply that can cope with high- and low-demand scenarios, relief of consumer bills by reducing and shifting peak electricity demand, and improved grid resilience [6].

The energy stored can be generated from a system (active storage) or can be stored passively in materials exploiting climatic fluctuations. In the latter case, some materials can store the solar energy directly in the building's walls using a sensible or latent process, i.e., with traditional or phase-change materials (PCMs) [7]. By the same principle, thermal solar energy can be stored in tanks integrated with PCMs to decrease the tank discharge time [8].

The classification of active storage systems can be made by considering the form of secondary energy in which the primary energy is stored.

**Citation:** Congedo, P.M.; Baglivo, C.; Panico, S.; Mazzeo, D.; Matera, N. Optimization of Micro-CAES and TES Systems for Trigeneration. *Energies* **2022**, *15*, 6232. https:// doi.org/10.3390/en15176232

Academic Editors: Alon Kuperman and Alessandro Lampasi

Received: 14 July 2022 Accepted: 24 August 2022 Published: 26 August 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In electrical energy storage systems (EESSs), electrical energy is converted into other types of potential energy, such as chemical, mechanical, elastic, and magnetic energy. Among them are the following:


Although the importance of storage systems for energy efficiency is widely recognized, the range of energy storage techniques for microscale applications is very limited, and some mechanical and thermal energy storage systems include those that are applied in the high-power generation sector. In addition to being expensive [11], storage systems are often oversized [12], and their disposal and average lifespan are also challenging [13].

Electrochemical storage is currently the state of the art for small-scale energy storage. However, batteries are not yet considered to be a fully mature technology either technically or economically. The most promising technology—namely, the lithium-ion battery—depends on a strategic material that has limited uptake and is currently not recycled for economic reasons. However, in addition to cost reduction, technological improvements will also need to address increasing the specific energy and lifetime of storage batteries.

CAES technology enables the trigeneration of electrical, thermal, and cooling energy in the energy release process. Specifically, trigeneration systems simultaneously provide heat, power, and cooling using a single fuel source. Compared with conventional systems, cogeneration and trigeneration systems reduce fossil fuel demand and grid losses [14].

The trigeneration system of electrical, thermal, and refrigeration energy allows excess energy to be stored in the form of compressed air and thermal heat, and enables refrigeration energy to be produced through the direct expansion of compressed air. Modeling of compressed-air energy storage systems considering network-specific requirements has shown that optimal design leads to improved functionality and an overall reduction in system costs [15]. CAES systems provide several advantages over other storage systems, including high power and energy capacity, long service life, rapid response, and relatively low capital and maintenance costs [16].

CAES can be integrated with renewable energy systems, such as wind and solar power. This allows excess energy from renewable sources to be stored, effectively addressing the fluctuation of renewable sources (i.e., avoiding curtailment) [17]. Several articles in the literature have provided an overview of CAES in terms of scale, fuel utilization, and integration with other technologies (e.g., smart grid and energy internet), emphasizing its potential applications [18,19]. Wang et al. presented a discussion of the challenges and prospects of using CAES systems [20]. CAES is considered to be the most cost-effective technology, as well as being excellent for its scalability and ease of implementation when used on a utility scale [21].

Today, CAES is mainly used on a large scale (i.e., macro-CAES)—compressed air is stored, during the hours when the cost of energy is lowest, inside hermetically sealed underground cavities and at pressures generally around 70–100 bar; the same high-pressure gas is used in traditional turbo gas systems, or for pneumatic drives in production lines for a wide variety of needs and for automation in general. These systems have a good energy density—typically around 2–3 kWh/m<sup>3</sup> of storage, which is almost 10 times higher than the energy density of mechanical gravity storage used in hydroelectric power plants.

A potentially viable alternative to electrochemical systems for small-scale storage is micro-CAES. Among the main advantages of micro-CAES coupled with TES (thermal energy storage) is the possibility of recovering waste energy to make the micro electric generation system more competitive. The heat developed during the compression phase can be used for residential heating and/or domestic hot water production, while the expanding cold air can be used for space cooling.

The potential advantages of micro-CAES systems are as follows:


Applications of small-scale CAES systems are not currently widespread. One reason that residential micro-trigeneration and trigeneration have received much less attention than large-scale systems is that small-scale applications provide a cooling load through a reverse Rankine cycle that requires high capital cost components, such as absorption chillers and boilers, to cool the load [22].

Cogeneration and trigeneration systems can operate more efficiently if electricity and heat production are decoupled using thermal energy storage, where unneeded heat is stored during the production period [23]. Achieving a highly feasible CAES system enables the design of a flexible energy system characterized by the optimal use of fluctuating renewable energy sources [24]. Different numerical and thermodynamic analyses have been conducted in the literature to highlight and evaluate the applicability of CAES systems [25,26]. Solutions to improve CAES systems' performance have been proposed as a result of optimization analyses [27]. Luo et al. [28] proposed a modeling and simulation tool for A-CAES (adiabatic compressed-air energy storage) system optimization to identify heat exchange and thermal storage units with suitable capacity and performance for air compression/expansion units, and then analyze system efficiency and identify potential improvement strategies.

Considering that the above, energy storage techniques for microscale applications are still very limited—especially micro-CAES applications. This study proposes an optimization of mechanical and thermal storage systems for small-scale trigeneration. The objectives are to identify solutions that are economical (e.g., components with affordable costs, technologies easily available on the market, and minimal maintenance) and adaptable to the spaces generally available in the residential area.

The present work is an extension of previous works [29,30]; the system is designed for a single-family residential building equipped with a photovoltaic system with a rated power of 3 kW.

First, this paper presents the case study to which the optimization for a mechanical and thermal storage system for small-scale trigeneration is applied. The purpose of the optimization was to improve the efficiency of the micro-CAES + TES system, along with attempting to simplify the structure as much as possible to make it economical and suitable for residential spaces. Finally, a comparison with the use of battery storage systems was conducted.

#### **2. The Case Study: Micro-CAES for Trigeneration**

The micro-CAES + TES system is designed for a single-family residential building equipped with a photovoltaic system with a nominal power of 3 kW. The average electricity demand of a family can be estimated at about 3000 kWh/year which, divided daily, becomes about 8.2 kWh/day. Assuming that at least 50% of household consumption takes place in the evening or at night when the photovoltaic system does not produce energy, about 4 kWh/day must be accumulated to have a good margin of autonomy from the grid. Therefore, on a typical day, the photovoltaic system can produce for immediate daytime consumption, or alternatively for night-time consumption by loading the mechanical storage system so that it can be discharged for the night.

The operation, as in any other storage technology, is divided into two phases deferred in time according to the time-shifting of the electricity demand of domestic users—a charging phase of the CAES's compressed air tank, with electricity absorption to the compressor, followed by a discharge phase of the same CAES tank with electricity generation to the expander. During the charging phase, the CAES system accumulates photovoltaic electrical energy in the form of energy elastic mechanics in the storage tank. At the same time, the HTTES (high-temperature thermal energy storage) system is also charged with the heat transfer fluid which, moving in a specially designed secondary circuit, recovers the thermal waste from the compression. During the discharge phase, the elastic energy is again converted into electrical energy using a turbine connected to the alternator. At the same time, the LTTES (low-temperature thermal energy storage) system is charged through the expanded cold air that cools the heat transfer fluid, which moves in its secondary circuit (distinct from that of the HTTES system). The heat developed during the compression phase can be used for residential heating and/or domestic hot water production, while the expanded cold air can be used for room cooling.

The problem is initially analyzed from a thermodynamic point of view. When filling the storage tank, the compressor sucks in atmospheric air and processes it to raise the storage pressure from the minimum operating value to the maximum. This process is non-stationary, and the type of compressor chosen must have suitable characteristics to keep the processed flow rate as constant as possible as the compression ratio varies. From this point of view, the best-performing compressors are the alternatives, which also offer a wide pressure range, long life, easy maintenance, and high reliability.

The choice of the type of expander, on the other hand, falls on the pneumatic reed motor as a technology widely used on the market and at affordable prices. It is chosen to power a motor with a nominal power of 5 kW with compressed air at 5 bar, obtaining a mechanical power of 3.85 kW on the shaft.

In this study, the aim was to optimize a micro-CAES system powered by a photovoltaic solar system with a nominal power of 3 kW for a domestic user, to which an electrical power of 3 kW was allocated through a pneumatic reed motor powered constantly at 5 bar. The CAES was combined with a high-temperature TES system for the recovery of thermal compression waste, which took place through a reciprocating volumetric compressor, and a low-temperature TES system for the recovery of the cooling capacity of the expanded air.

#### **3. Optimization Setup**

The goal of optimization is to maximize efficiency measures for mechanical and thermal storage. The charging and discharging processes of the micro-CAES were analyzed from a thermodynamic point of view to obtain the equations governing the problem in a previous study [29]. These equations were implemented in MATLAB and optimized with modeFRONTIER software.

Figure 1 shows the workflow of the optimization problem carried out in modeFRON-TIER. The inputs, outputs, and constraints applied to the optimization model are described in detail in the following paragraphs (Sections 3.1 and 3.2).

**Figure 1.** Workflow of the optimization problem on modeFRONTIER.

In the workflow, the first set of DOE (design of experiments) is a random sequence. The chosen NSGA-II (non-dominated sorting genetic algorithm II) optimization algorithm

is an evolutionary algorithm suitable for solving optimization problems with multiple objectives [31,32].

#### *3.1. Inputs*

The thermodynamic equations were implemented in the MATLAB environment. Several operational coefficients and parameters were established in the preliminary analysis, as shown in Table 1.

**Table 1.** Thermodynamic coefficients and parameters that are not subject to optimization.


The optimization analysis was based on the variation, within a fixed range, of the parameters shown in Table 2. By simulating the variables in appropriate ranges, it is possible to obtain, among all possible combinations, those that optimize the predetermined objectives.

**Table 2.** Input variables.


For the maximum compression ratio (*βmax* ) the lower limit of 10 was chosen, since for pressures below 10 bar the air compression has insignificant temperature variations, which would not justify the installation of the HTTES system. The upper limit, on the other hand, was taken to be 35, because the datasheets of manufacturers of reciprocating compressors show that with a maximum installed motor power of 3 kW (equal to the nominal power of the photovoltaic system) it is possible to compress air up to a maximum of 35 bar. The storage volume of the compressed air (*VS*) had an upper limit of 10 m<sup>3</sup> for space and cost reasons. Finally, the duration of the charging phase of the CAES (*tc*) must be consistent with the hours during which the solar photovoltaic system can operate during the day; for this reason, the upper limit of 5 h was set. The possible values assigned to each input variable result in up to 300 different experiments to be conducted.
