# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
## 6 Conclusions  
The proposed method was investigated, taking into account that there are many existing and new applications for which balancing is required. Traditional methods present the problems of being iterative and requiring direct or indirect terminal flow measurement systems. The compensated method, which was proposed in the 1990s to overcome the problem of iterativity, also has some drawbacks such as the need to install calibrated balancing valves with flow measurement features on all terminals, and it does not fully address some situations that can be faced during balancing and that require going back in operations. The proposed method, referred to as PFM and derived from previous studies on the balancing of air systems, is presented from a theoretical perspective and declined for application with reference to the main architectures of water systems; the method has been optimized by appropriately exploiting the tightness characteristic of hydronic networks, making it possible to propose a procedure that does not involve terminal flow measurements but only \(\Delta P\) measurements across the farthest terminals, which are used as a reference, and a single centralized flow measurement point. The flow rate detection equipment, consisting of multiple instruments placed in parallel and activated as required, can be used to apply the procedure to all sections of even complex plants according to a logic of scalability that guarantees adequate resolution and measuring range. The measuring tool can be placed in series with the pump during TAB operations and removed after finishing, to be reused on similar installations. The procedure was tested experimentally in comparison with a standard method (ratio method). The results were validated and both applied methods led to a result within the accepted tolerance of 10% in terms of flow rate and to a comparable configuration of the balancing device. Finally, savings were quantified not only in terms of the number of flow meters required, but also the numbers of measuring and balancing operations required, which in the case analyzed were reduced by 48% and 41%, respectively. The research developed in the field of balancing water systems offers interesting insights. In particular, these include developments in the application of general balancing concepts to the field of flow control in variable flow systems and a possible rethinking of the dynamic control modes currently adopted. Conceptualization, F.P. ; Methodology, F.P. ; Software, F.P. ; Validation, F.P. ; Formal analysis, L.P.M.C. ; Investigation, F.P. ; Resources, L.P.M.C. and F.R. ; Data curation, F.P. ; Writing  
1. Preliminary setup. All the valves are fully opened, and the pump is adjusted so that the total flow rate results to be slightly (normally about 10%) greater than the design value. 2. Testing. At this working condition, each terminal flow rate is measured and the ratio \(\dot{Q}_{M}/\dot{Q}_{N}\) between actual and nominal flow rate is calculated for each terminal; referring to the ratio values, all the terminals belonging to each branch are sorted in ascending order from the most advantaged (or \"favoured\") to the most disadvantaged (or \"unfavoured\"). 3. Balancing. Considering one branch at a time, all the terminals are considered in pairs, starting from the two most disadvantaged and acting on the less disadvantaged's valve to achieve the same rate ratio of the other, according to the accepted tolerance. This process is iterative, since every action on a valve has the effect to change the flow rate of all the other terminals so that the operator is supposed to move back and forth between the two users, checking every time the actual ratio. When they result to be balanced, the third terminal in the ranking is taken into account and brought to the same ratio of the previously balanced pair (i.e., considering it in a pair with the original MD), thus proceeding to the next and going in this way up to the last one, which is also the one that was originally the most favored.