Thank you again
I'll try to explain in details how N1 works.
Actually the network N1 is just connected with N2. the connections are 3, in 3 different points with different measured values of head. 2 of them are completly free, even without a CV valve, and serve the biggest part of N1: so head in N1 completly depends on N2 demands and head; the other one conncetion between N1 and N2 is controlled by a CV valve, but in facts it's always closed because of bigger head in N1 in the point of connection. N1 is also connected to another network ( called N4 and not modeled) with a partialized valve which limits the flow in about 5 l/s (in order not to create pressure deficiencies in N4) and this connection serves a little part of N1.
With this actual conncetions, network N1 has some head deficiencies both in winter and in summer at the rush hours, because the N1 pipes have small diameters and many headlosses. So we thought we could connect N1 with the near network N3 (this network is completly modeled and calibrated), which can serve a part of N1 (with max 8,5 l/s). This new connection actually does not exists, i'm designing it with a new pipe. The pressure this new pipe can guarantee is about 5 meters bigger than the actual pressure in N1 at the point where the new connection should be realized. This estimate comes from the difference between the calculated value of pressure in the point of connection between N1 and N3 taken from N3 model simulating a 8,5 l/s new demand for N1, and the real measured pressure in N1 at the point of this new connection.
Then i've made a new model which includes both N1 and N3, with the new pipe which should connect the two networks.
In order to prevent N3 tank to get empty, we decided to limit the flow between N3 and N1 with the FCV valve I was talking about. To limit the headloss in the FCV valve the builder suggested me a model of valve with just 3 meters headloss when the flow is limited in 8,5 l/s. As i keep the same actual head boundary conditions for N1, the N1-N3 model gives me a 6 meters headloss in the FCV valve and gives me not satisfying pressure results and underestimates the pressure in FCV controlled part of N1 (less than 3 meters accurancy is important for me to justify the new pipe in project). For this reason i thought i could make some iterative little changes (max 2-3 meters) in the other head boundary condition (with N2 and N4) in order to have new balances of N1, till the headloss in the FCV centers about 3 meters (the real headloss). Of course i can't say that new boundary conditions i've found are the perfect ones, but the system works, and the results now are satisfying.
As you can understand, it's hard to optimize this problem, and obviously the best solution can't prescind the model of N2 and N4 too.
But i can't do that: N1 and N3 belong to a municipality, N2 and N4 belong to a different one...the problem has too many variables and i think that i can't model 4 networks (even with a simplified model) just to design one new pipe...i add that N2 is much bigger than the other netwoks (50,000 people for N2 vs about 10,000 for each other one)...it's too expensive for me!!!
For this reason i think the solution i've found can be enough for me.
The problem is not simple, what do you think?
Thank you for your attention!
Max