# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
###### Abstract
showed in a 2016 [11] paper how demand-driven heat-delivery logic made possible through good balancing at the user level, introduced in the form of pre-set thermostatic valves combined with automatic balancing valves, was able to stabilize the temperatures of the dwellings served and optimize the operation of the primary distribution network with a reduction in pumping consumption (42.8% in the case analyzed) and a substantial reduction in thermal losses (17%). A similar analysis conducted by [PERSON] et al. in 2017 [12] showed that energy consumption could be reduced by up to 30% through balancing. [PERSON] et al. in 2018 [13] determined how balancing was a crucial requirement for low-temperature DHSs, by analyzing the effects of imbalance in four different control scenarios. The results showed that energy consumption was significant in all cases analyzed. [PERSON] et al. in 2023 [14] reported on the problems of poor balancing in DHSs and the difficulty of performing balancing via traditional methods; they proposed a method to regulate the hydraulic balance of the network by managing the opening of automatic valves with an NSGA-II (non-dominated sorting genetic algorithm II) as a function of heat demand. In the field of solar thermal collectors, the issue of balancing water circuits is of great importance; [PERSON] et al. in 2016 [15] produced a model for studying the flow distribution within collectors, reiterating that good balancing is especially important with regard to the optimized management of low-flow operation achievable by applying variable speed pump technology ([PERSON] et al. 2019 [16]). In addition, flow rate control has been found to be critical in a number of emerging applications linked to new technologies promoted by energy transition policies, such as battery power systems used in the hybrid powertrain sector; these storage systems need thermal uniformity guaranteed by water cooling circuits whose balancing requirements are often affected by the presence of invasive flow meters characterized by non-negligible drop losses ([PERSON] et al. 2023 [17]). While on the one hand, the need for balancing continues to exist, on the other hand, HVAC systems balancing is an often-neglected issue because of its inherent difficulties and time-consuming procedures; this frequently leads to badly balanced or completely unbalanced systems. This is also due to the fact that for heating terminals, the change in flow rate does not equate to an equivalent change in power output. This is due to the typical behaviour of any exchanger, where a reduction/increase of the flow rate is always associated with an increase/reduction of \(\Delta T\); [PERSON] et al. (2014) [18] modelled the dependence between the deviation of the user flow rate from the design value and variations in room temperature for different types of radiators, showing, for example, that for some terminal types, a variation of flow rate in the range between \(-15\%\) and \(+25\%\) resulted in room temperature variations of less than \(1\)\({}^{\circ}\)C. Since poor balancing does not directly impact performance, in these cases, it is often disregarded. In other types of application, such as in cases of radiant floor heating and cooling systems mostly characterized by a number of parallel circuits working under constant flow conditions, [PERSON] et al. (2008) [19] showed that such systems are very sensitive to flow variations and highlighted the need for a proper balancing of user sub-systems based on TRNSYS simulations. In 2020 [PERSON] et al. [20] investigated the relationship between issues related to maintaining comfortable environmental conditions and energy consumption in existing buildings and identified how balancing could be considered the most cost-effective and most decisive intervention; they analyzed a series of buildings in Geneva, Switzerland, and verified possible savings between 2% and 14%.