## 1 Introduction  
The 28 th Meeting of the Parties to the Montreal Protocol adopted the Kigali Amendment on hydrofluorocarbons (HFC), now included in the Montreal Protocol [1]. This historic agreement aims to reduce the use and production of HFC worldwide, with the goal being to reduce HFC emissions by over 80 billion tonnes of carbon dioxide equivalent (CO\({}_{2,e}\)) by 2050. Kigali Amendment has fixed a phase-down schedule based on overall CO\({}_{2,e}\) emissions, which is thus dependent on the GWP of each substance. This agreement follows the same action line as the F-Gas Regulation adopted in Europe [2], which has limited the GWP value of the substances that could be used in different refrigeration applications according to different time lines. Referring to commercial refrigeration, the most important restrictions and limitations are: a GWP limit of 2500 for stationary equipment from 2020 on and the limit of GWP of 150 for multipack centralised refrigeration systems with rated capacity of more than 40 kW from 2022 on, except for the primary circuits of cascade systems, which GWP limit has been fixed in 1500. Another important aspect is the recharge limit with refrigerant of GWP higher than 2500, which has been fixed at 40 tonnes CO\({}_{2,e}\) (10.15 kg of R-404A, 10.03 kg of R-507A). Those restrictions and agreements are facilitating the transition towards more environmentally friendly solutions based on natural working fluids [3] and the development of more efficient refrigeration solutions [4]. We focus on centralized commercial refrigeration systems with multiplexed direct expansion systems as they make the largest direct contribution to global warming because of their large refrigerant charge (300 to 3000 kg [5]) and high annual leakage rate (between 15% and 25% [6]). In addition, most of them still rely on high GWP refrigerants, such as R-404A (GWP = 3922), R-507A (GWP = 3985) and R-134a (GWP = 1430). According to [PERSON] [7], [PERSON] [8] and [PERSON] [9], the use of indirect systems instead of direct expansion systems can reduce the total refrigerant charge by approximately 90%. The indirect configuration avoids refrigerant leakage through the distribution lines and services and reduces the overall annual leakage ratio since the refrigerant is contained inside the machinery room. However, indirect systems usually introduce an increment in the energy consumption of the system, caused by the extra temperature difference in the additional heat exchanger between the refrigerant and the secondary fluid and the energy consumption of the secondary pump. Nonetheless, this last effect could be minimized by a correct design of the indirect system, since by introducing a secondary loop the large pressure drops of the refrigerant through the distribution lines are avoided. Several researchers analysed through simulation the performance of indirect systems regarding multiplexed direct expansion systems. [PERSON] et al. [10] simulated, using field data, a French supermarket of 10,000 m\({}^{2}\) sales area with an R-404A primary system and propylene-glycol/water for MT and Tyfoxit for LT against a parallel R-404A multiplexed direct expansion system. They pointed out that the introduction of the secondary loops introduced 6 K at MT and 7 K at LT evaporating temperature drops, which resulted in a 33.7% increase in the system energy consumption regarding the direct expansion system. For this system, the refrigerant charge reduction was 56%. [PERSON] [11] contrasted an R22 multiplexed direct expansion system with an indirect ammonia-HFE 7100 indirect system, quantifying the reduction in energy consumption at 15%. Recently, [PERSON] [12], also simulating using field data, contrasted a multiplexed R-404A direct expansion system of a 2700 m\({}^{2}\) supermarket against a similar system using indirect loops, with propylene-glycol/water at 35% vol. for MT and with CO\({}_{2}\) for the LT.