# Development and Application of a Novel Non-Iterative Balancing Method for Hydronic Systems
## 3 Theory and Calculations
### PFM Balancing Procedure  
On the basis of the theoretical elements outlined above, a procedure was developed and is here proposed as a PFM procedure. Figure 8 shows the case of a system in direct return configuration, with a single branch and \(n\) terminals, each with a balancing device. If the designer has determined that the most disadvantaged terminal is not the farthest (e.g., the MD terminal is Terminal 2 as shown in Figure 8), a line valve may be provided (shown in grey), as discussed above. The balancing procedure involves the monitoring of the pressure across the last terminal on the right (the farthest) and the flow rate measurements at the control point placed after the pump, represented by a rotameter. The pump is driven at variable speed and is suitable for inclusion in an automatic control loop when required. The procedure has been designed as follows:  
Preliminary Setup. All the balancing valves shall be closed with only the exception of the one serving the farthest, which has to be fully open. In case of presence of line valves, they must be fully opened as well. For stability of pump operating at low flow rates, it may be appropriate to provide a modulating bypass across the circulator. First step. (Figure 9). Measuring the flow rate at the control point (represented by the 'watching eye' icon), the pump velocity is varied until the flow rate measured by the rotameter reaches the design value of the \(n\)-terminal \(\dot{Q}_{n}\). Second step. (Figure 10). An automatic control loop is implemented to keep unchanged the flow rate at the \(n\)-terminal acting on the pump velocity. In order to do that, a probe is connected to the pressure taps across the terminal and the actual value is taken as reference. Then, a controller is electrically connected to the probe and to the inverter. The set on the loop controller is \(\Delta P_{set}=\Delta P_{reference}\). Figure 8: Representation of the system to be balanced, balancing devices, and required measuring points/instruments. Figure 9: First step of PFM procedure; tuning flow rate of the farthest terminal by adjusting pump velocity. Third step (balancing). The operator acts on terminal balancing devices or on line valves. Each user is balanced, starting from \((n-1)\) and moving backwards (Figure 10) to the first terminal of the branch. At each new path considered, the gradual opening of the valve causes a reduction in the reference pressure, which is immediately compensated by the loop control. In most cases, the terminal that has just been opened, compared with that previously activated, is not disadvantaged; the valve is throttled to a opening position lower than 100% and the correct balancing position is detected. When a disadvantaged terminal (e.g., Terminal 2 in Figure 10) is encountered, the total opening of the terminal is not sufficient to guarantee the desired flow rate through the user, so the operator moves to act on the line valve according to the theory. Then, the procedure continues as planned to the next terminal. If the system is multi-branch, each branch is assumed to be equipped with a balancing device. After balancing the terminals belonging to each branch, the next step is to achieve balance between different branches, following the same strategy as before: starting with all branches closed, first open the reference branch completely, bring it to nominal flow rate conditions acting on upstream components (e.g., on the pump), set the reference pressure loop control, and progressively open all the other branches in sequence, as described previously. Again, the application of the PFM in direct return systems requires the presence of line valves downstream of the disadvantaged branch if this is not also the farthest. Fourth step (adjustment). According to the procedure, the pump speed is continuously adjusted through the reference pressure control following the previous steps, so that each terminal is brought to and maintained at its nominal flow rate.