How do I simulate a simple (circular & continuous) district heating network?

[TheNeedForSleep]

Hello :)
Im currently trying to setup a simple pandapipes net.

Why?
I have the data of a real existing district heating network. I created a RL model that optimizes the heat production. I cant evaluate the model in the live system.
Im trying to simulate a small part of the real existing district heating network to generate optimal heat production data for verification and non-optimal data for training.
I then want to use the data to evaluate the RL model.

But I already fail on an minimal example.

Ive found the following example but it has fixed pressure and temperature: https://github.com/e2nIEE/pandapipes/blob/develop/tutorials/circular_flow_in_a_district_heating_grid.ipynb
See test setup: "const mass flow pump with fixed temp and pressure"

Current Setup

This is my current minimal example setup:

import pandapipes as pp

pn_bar = 5
tfluid_k = 273.15+60
ambient_temp = 273.15+10
alpha_w_per_m2k = 10

net = pp.create_empty_network(fluid="water")

geodata = [(0,0),(0,10),(3,10),(5,10),(8,10),(8,0),(7,0),(5,0),(4,0),(2,0)]
junctions = pp.create_junctions(net,10,pn_bar,tfluid_k, geodata=geodata)

pipes = [(0,1),(1,2),(3,4),(4,5),(5,6),(7,8),(9,0)]
for pipe_from, pipe_to in pipes:
    length_m = ((geodata[pipe_from][0]-geodata[pipe_to][0])**2+(geodata[pipe_from][1]-geodata[pipe_to][1])**2)**0.5
    length_km=length_m/1000
    pp.create_pipe_from_parameters(net,pipe_from,pipe_to,length_km,0.05,sections=int(length_m),text_k=ambient_temp,alpha_w_per_m2k=alpha_w_per_m2k)

pp.create_heat_exchanger(net,junctions[2],junctions[3],0.05,qext_w=50_000,name="consumer")
pp.create_heat_exchanger(net,junctions[8],junctions[9],0.05,qext_w=-50_000, name='producer')

Test setups

regular pump

If i now add a "regular" pump between junction 6 & 7 and run the simulation I get the following error:

# add pump before simulation
pp.create_pump(net,junctions[6],junctions[7],std_type=std_type)
...
# run simulation
pp.pipeflow(net,fluid='water',iters=100_000,mode='all',ambient_temp=ambient_temp)

Maximum number of iterations reached but hydraulics solver did not converge.

which is apparently a FloatingPointError: invalid value encountered in double_scalars if we set np.seterr('raise')

const mass flow pump with fixed temp and pressure

pp.create_circ_pump_const_mass_flow(net,junctions[7],junctions[6],pn_bar,flow_kg_per_s,273.15+60,type="pt)

Resulting in:

While this converges the water will flow into the pump with 57.1°C and flow out with fixed 60°C. This is not the behaviour i want.

const mass flow pump with non fixed pressure and/or temperature

Will all fail.

regular pump + ext grid

## add external source
def add_external_source(connection_j):
    ext_src_j = pp.create_junction(net,pn_bar,tfluid_k,name='ext_src_j',geodata=(5,5))
    pp.create_ext_grid(net,ext_src_j,pn_bar,tfluid_k)
    pp.create_pipe_from_parameters(net,ext_src_j,connection_j,0.001,diameter_m=0.05)

Adding an external source with fixed temperature and pressure combined with the regular pump approach converges to

This seemingly works. No water actually flows from the external grid into the network as shown by the flow values in blue.
Putting in and extracting an equal amount of energy converges to the ambient temp of 10°C.

Confirming convergence to ambient temp with:regular pump + ext grid + heat exchanger set to 0W

const mass flow pump with non fixed temp and non fixed pressure + ext grid

Does not work

 warn("Matrix is exactly singular", MatrixRankWarning)
Maximum number of iterations reached but heat transfer solver did not converge.

ValueError: could not broadcast input array from shape (0,) into shape (1,)

Questions:

• How do I create a network that is "prefilled" with water? That I do not need to add an external grid to "fill" the network. I tried to add the type of fluid everywhere i could. Or am I misunderstanding the way pandapipes works?
• Why does a "regular" pump work but no const mass flow pump with non fixed values in the previous test setups? I just want the water to circle at a given rate.

I also noted that:

• The regular pump and the const mass flow pump seem to have different flow directions

[TheNeedForSleep]

An important prerequisite to finding a good solution of the pipeflow is that all nodes and branches included in the internal structure are connected to different components and finally have a connection to some external grid that presets a fixed pressure or temperature level. -https://pandapipes.readthedocs.io/en/latest/pipeflow/pipeflow_procedure.html#connectivity-check

From this sentence I conclude that the solver can only find a solution if both the pressure and the flow are fixed at one point in the network.

Adding an external grid with a lower pressure somewhat replicates my desired behavior given that the flow is exactly at 0.

Im wondering why this would work?

PS: This converges to ambient temp if both heat exchangers are set to 0W.