# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
## 2 Material and Methods
### Non-Iterative Methods
#### 2.2.1 Description of the Compensated Method  
The method is based on (i) the availability of calibrated balancing valves (CBVs) at each terminal and (ii) the presence of a branch CBV, named \"partner valve\". Specifically, the method has been developed exploiting the features of CBVs: these devices are manual modulating valves provided with pressure taps and whose flow coefficient value at every knob position can be obtained from the manufacturer's data sheets. Such devices offer the advantage of acting as a flow rate meter and as a balancing device at the same time. The CM procedure requires the availability of two pressure gauges to obtain simultaneous flow-rate measurements at specific CBVs. The basic idea is that it is possible to balance the terminals sequentially and one at a time by acting on its valve, without affecting the flow conditions of the previously balanced terminals: this requires following a specific order and at the same time acting on a branch valve named the \"partner valve\" to supply the circuit with a compensation flow. With reference to Figure 1, a branch with multiple users to be balanced can be considered and the following steps carried out:  
Terminal 1 is considered the farthest terminal (on the right in the upper figure). A manometer is connected to the CBV valve _BV-1_ for flow measurement, and the valve is then opened to the maximum (consistent with the minimum pressure drop required for reliable measurement; 3 kPa at nominal flow rate is the value recommended by the authors of the method). The nominal flow rate value at this terminal is reached through adjusting the partner valve. From this point on, that value is considered as the'reference', and it is constantly monitored and kept constant via continuous adjustment of the partner valve. The operator moves to the very next terminal (Terminal 2 on the lower figure), connects the second manometer to the pressure taps of the valve _BV-2_, and acts on that valve to obtain the nominal flow rate. Any action causes a flow change in the reference valve, which has to be continuously compensated by modulating the partner valve. The balancing of Terminal 2 is completed when both the design flow rates occur simultaneously. The method  
Figure 1: Compensated method procedure performed by an operator; different levels of gray indicate sequential operations, darker means more recent. continues with the third user _BV-3_ (still keeping the reference value on the farthest _BV-1_), and so on until all users have been balanced to each other. The method does not show any criticalities if the farthest terminal is also the unfavored terminal (referred to as the \"index\" in the CM procedure), but this may not always be true: when it happens that, even having fully opened the valve of the new terminal, its design flow rate value is not reached (while the reference flow rate is maintained at its nominal value), this means that the new terminal just considered is disadvantaged compared to the reference one, and it will therefore be necessary to go back and act on the terminals already considered. In this case, the enforcement of an iterative sub-procedure can be avoided thanks only to the full exploitation of the specific features of the calibrated balancing devices, and the method indicates a series of additional operations involving measurements, calculation, and full re-balancing of the whole branch from the beginning. Any time a newly considered terminal behaves as the new most disadvantaged, the whole sub-procedure must be repeated for each of them. In the case of systems consisting of multiple branches, each branch can be balanced independently and, lastly, the branches are balanced among themselves; this requires only a main partner valve (or providing the same feature by acting on the pump velocity) and the consideration of the branches in the same sequence as before for the terminals. Even in this case, the procedure proceeds cleanly only if the farthest branch turns out to be the most disadvantaged one.