# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
###### Abstract  
The improvement of efficiency in new and existing buildings is one of the key aspects in achieving the climate change targets promoted by international regulatory and technical bodies, and among the measures that deserve renewed attention is the balancing of hydronic systems. However, the balancing procedures currently applied have not been updated for decades and are still largely unimplemented, as they are mainly based on cumbersome and iterative procedures. This paper deals with the proposal and advanced adaptation of a non-iterative balancing method previously developed for air systems, known as the progressive flow method (PFM). The application to water systems of the PFM's concepts includes some aspects of an existing empirical method called the compensated method (CM) and overcomes its main limitations; moreover, the original PFM has been radically rethought in its implementation aspects, taking advantage of the tightness of water distribution systems, minimising instrumentation and the number of measurement operations, to definitively overcome the iterative nature of the currently applied methods. Experimental validation was carried out. Compared with a standard method, the enhanced PFM reduced the number of measurements by 48% and the number of balancing operations by 41%, achieving final flow rates within tolerances and the same configuration of balancing devices. hydronic systems balancing; progressive flow method; compensated method; commissioning; energy efficiency +
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do not generally require balancing ([PERSON] et al. 2002 [3]), many applications still need balancing; radiators systems equipped with thermostatic valves need pre-balancing to handle start-up transients ([PERSON] et al. 2017 [4], [PERSON] et al. 2017 [5]), while a number of systems serving on/off zones designed to operate at constant flow rates need balancing of local terminals. In addition, even in situations where the desired performance is achieved, balancing hydronic systems is also a viable solution for pursuing significant reductions in consumption. A study by [PERSON] et al. 2022 [6] concerning underfloor heating systems for low-energy apartments in Copenhagen, Denmark, presented the development and application of gray-box modelling aimed at continuous commissioning and highlighted how poor balancing and set-up were the decisive causes of gaps between assumed and actual consumption. In cases of retrofitting existing multi-unit residential buildings, a more economically viable strategy than installing individual thermostatic radiators valves (TRV) is to define grouping strategies whereby a variable number of suites can be controlled through a single valve. These strategies were investigated by [PERSON] et al. in 2020 [7] and applied to post-war buildings in Toronto, Canada; in the case study, 14% reduction in space-heating energy consumption and 10 years payback time were achieved, compared with 17,8 years for the solution with individual TRV. In any case, the possibility of control for large groups of apartments is based on the premise of hydronic balancing between all radiators belonging to the same group. In 2024 [PERSON] et al. [8] reported numerical evaluations supplemented by case studies regarding the lifecycle cost of plants evaluated over periods as long as 50 years. The evaluation also confirmed the importance of balancing to maximize the benefits of an optimized distribution layout (direct vs. reverse return). In all cases, balancing was indicated as fundamental, indicating LCC variations between unbalanced and balanced systems that could reach values between 30% and 50%. Among the most recent applications, the issue of balancing is strategic in the field of district heating systems (DHSs), where it has been verified that the problem of poor flow control is one of the main causes of high temperature returns and degradation of the energy performance of distribution systems and thermal generation units ([PERSON] et al. 2011 [9], [PERSON] et al. 2017 [10]). In particular, [PERSON] et al.