Meshed District Heating Networks in nPro

Why meshed networks need a different design approach

In a tree-shaped network, the flow rate in each pipe follows directly from the node balance: each pipe carries exactly the load of the buildings downstream of it. Pipe sizing, diversity factor and pressure losses can therefore be calculated pipe by pipe.

In a loop, some buildings are supplied from two sides. Physically, the flow splits so that the pressure loss is the same on both paths around the loop (loop rule). However, this split is only known once the diameters have been fixed. For the design, this results in a circular problem: the diameters are to be derived from the flows, but the flows only follow from the diameters. nPro solves this in several consecutive steps.

nPro detects loops automatically from the drawn network geometry. Rings do not have to be marked manually.

Overview: The calculation chain in nPro

In tree-shaped networks, step 1 is omitted because the flows are unambiguous. All other steps are the same for tree-shaped and meshed networks.

Step 1: Cost-optimal flow distribution

For meshed networks, nPro first solves a linear optimization problem. The objective function is the annual cost of the pipes. As constraints, the load balance must be satisfied at every node, and each pipe can carry at most the load of its nominal diameter. The optimization thus determines both the nominal diameter of each pipe and the share of each building supplied via each path (e.g. 63 % from the north, 37 % from the south).

The optimization only balances loads. It does not consider pressure losses or the loop rule. The resulting split is cost-optimal, but not necessarily the split that physically occurs during operation. This is why a hydraulic check follows in step 3.

Manually specified diameters are taken into account in the optimization as fixed capacities, and the remaining pipes are sized around them. If the capacity of a fixed pipe is insufficient, nPro displays a notice that the pipe is undersized.

Step 2: Pipe sizing with diversity factor

With the shares from the optimization, it is known for each pipe which buildings it supplies and to what extent. From here on, pipe sizing works the same way as in a tree-shaped network:

• The static load of a pipe results from the proportional connection capacities of the buildings (heating load and instantaneous domestic hot water load).
• The dynamic load is the maximum of the hourly load profile in the pipe over the year.
• The diversity factor is calculated from the number of buildings supplied. In loops, this number is fractional because buildings are assigned proportionally (e.g. 9.2 buildings).

The design load of a pipe is the maximum of the dynamic and the static load, taking the diversity factor into account. This determines the design flow rate, the nominal diameter and the design pressure loss.

Step 3: Hydraulic network calculation (simulation)

In the next step, nPro performs a hydraulic calculation of the network. A Newton method solves the node and loop rules simultaneously for all loops in the network. The result is the physical flow distribution that occurs with the selected nominal diameters. Pipe friction is calculated depending on the flow regime (laminar or turbulent according to Colebrook); fittings and pipe installations are taken into account via a surcharge on the pipe pressure loss (default assumption 25 %).

The simulation is calculated for the hour with the highest heat demand of all buildings. In networks with feed-in (prosumers, decentralized generators), a summer time step is added as soon as a surplus occurs at the energy hub.

An important difference between optimization and physics: an undersized ring pipe is not bypassed in the hydraulics but overloaded. The water does not take the path intended by the optimization, but the path on which the pressure losses on both sides of the loop are equal. Such pipes stand out on the simulation map due to a high pressure gradient (Pa/m).

Step 4: Node pressures and critical point

For pump sizing, nPro needs the pressure at every node in the supply and return lines. From this, the available differential pressure at each building is derived. The building with the lowest available differential pressure is the critical point. Exactly the pressure loss of the building substation is available there (default assumption 30 kPa).

nPro calculates two pressure fields:

• Design: node pressures from the pressure losses of the pipe sizing (step 2), with the flow directions from the hydraulic calculation.
• Simulation: node pressures from the pressure losses of the hydraulic network calculation (step 3).

In a tree-shaped network, the design pressure field is exactly determined. In a loop, however, the pressure losses around the loop must add up to zero. Because the design values stem from different points in time and different diversity factors, this is usually not exactly the case. nPro then solves the system of equations in the least-squares sense and distributes the discrepancy among the pipes of the loop. The size of this loop discrepancy relative to the pressure loss up to the critical point is a good indicator of how reliable the design pressure field is in a meshed network. The simulation pressure field, on the other hand, is always physically consistent, but only represents the peak hour (without short-term domestic hot water peaks).

Supply and return are treated as separate networks that are coupled via the building substations and the energy hub. How the absolute pressures are derived from these pressure fields, taking into account pressure maintenance, geodetic heights and minimum pressure, is described in the article on pressure calculation in district heating networks.

Step 5: Pump sizing in meshed networks

The pump head of the main pump is the sum of the pressure loss of the pipes up to the critical point (supply and return, incl. fittings), the pressure loss of the building substation and the pressure loss of the energy hub (default assumption 20 kPa). What matters is which pressure field these values come from. nPro selects a governing state according to the rules in Table 2.

The simulation is scaled up via the ratio of the flow rates in the energy hub pipe: Δp = Δp_Sim · (V̇_Design / V̇_Sim)^1.8. This preserves the physically correct flow distribution of the simulation while raising the pump head to the design case including domestic hot water peaks.

Pump head, critical point, available differential pressures at the buildings and the pressure diagram always come from the same governing state, so that all values are consistent with each other. The pump flow rate comes from the pipe sizing of the energy hub pipe (only in the pumping direction). The pump electricity demand results from the pump head, the annual circulated volume and a capacity-dependent pump efficiency, assuming a constant pump head over the year [1].

Notice “Meshed network: pump sizing based on simulation”

nPro displays this notice when the water flow in the ring pipes is distributed significantly differently in the simulation than assumed in the design. Pump head, critical point, differential pressures at the buildings and pressure diagrams are then based on the (scaled) simulation. The design pressure losses on the map no longer add up to the pump head, and the unscaled values on the simulation map are also lower than in the pressure diagram.

Loops with prosumers and multiple feed-in points

If prosumers (e.g. waste heat) or secondary energy hubs feed into the network, the flow direction can reverse over the course of the year. In the case of a relevant surplus, the optimization considers two design points in time: the winter peak and the point in time with the largest surplus. The nominal diameters of the main pipes are then chosen to cover both points in time. In this case, there is no longer a unique assignment of buildings to pipes, so nPro takes the nominal diameters directly from the optimization and resizes the house connection pipes according to their static load.

In this case, pump sizing is based entirely on the simulation, since pump head and flow rate should come from a consistent operating point. Feed-in pumps are additionally checked for the summer time step, because each pump has its own most unfavorable point in time: for heated buildings it is the winter peak, for feed-in points often the summer.

Decentralized pumping concept (5GDHC networks)

In the decentralized pumping concept, as is common in 5GDHC networks, there is no network pump. Each building station pumps against the differential pressure at its node. The selection of the pressure field follows the same principles as in the central pumping concept, with two differences: the threshold for the loop discrepancy is stricter, because errors in the pressure field directly affect each individual building pump, and the simulation is only scaled upwards. Each station is only sized for the states in which it is actually in operation.

Results

The same results are available for meshed networks as for tree-shaped networks:

• Flow rates and flow directions in all pipe sections, for both design and simulation
• Temperature profiles in supply and return
• Pressure profiles and absolute pressures throughout the network, including a pressure diagram to the critical point
• Nominal diameters, utilization and capacity reserves per pipe section
• Pump head, flow rate and electricity demand of the pumps as well as the available differential pressure at each building

The results can be visualized on the map and exported as an Excel file or a GIS and CAD file.

Frequently asked questions

Do all pipes in a loop have the same nominal diameter?

No. Each pipe receives the nominal diameter resulting from the optimization and the subsequent pipe sizing. As a result, the pipes on the two paths of a loop can differ in size, which is usually considerably cheaper than a uniform nominal diameter for the entire ring. If you want to size individual sections larger on purpose, e.g. for future extensions, you can specify the nominal diameter manually.

Why do the pressure losses on the map not add up to the pump head?

The map always shows the two raw states, design and simulation. If the loop discrepancy is large, the pump is based on the scaled simulation, which is not displayed as a separate map. In tree-shaped networks and consistent loops, on the other hand, the governing state matches one of the two maps.

Why is the simulation usually lower than the design?

The design accounts for short-term domestic hot water peaks via the static load, while the simulation uses the highest hourly load. In networks without pronounced domestic hot water peaks, the simulation can also be slightly higher than the design. In this case, nPro uses the higher value so that the pump is not undersized.

Does closing a ring automatically reduce the pump head?

Not necessarily. An additional connection reduces the total pressure losses in the network, but not necessarily the pressure loss to each individual building [2]. In addition, when a ring is closed, the optimization resizes all pipes and often selects smaller nominal diameters on both paths. A meshed network can therefore have a higher pump head than the corresponding tree-shaped network, at lower pipe costs. For comparing variants, flow rate and pump electricity demand are better suited than the pump head. Variants are only strictly comparable with fixed diameters.

Why is no mean pressure gradient given for meshed networks?

In a loop, several paths with the same pressure loss but different lengths lead to the critical point. The path length, and thus the mean pressure gradient, is not uniquely defined. The maximum pressure gradient of individual pipes on the simulation map is more meaningful.

Which path is shown in the pressure diagram?

The pressure diagram shows a path from the energy hub to the critical point in the flow direction, on which overloaded ring pipes become visible as a steep section.

How can I influence the flow distribution in the ring?

By manually specifying nominal diameters. The optimization then sizes the remaining pipes around the specified ones, and the simulation shows how the flow is actually distributed with these nominal diameters.

Is the hydraulic calculation based on Hardy Cross?

nPro uses a Newton method that solves the node and loop rules for all loops simultaneously. The result corresponds to that of the classic Hardy Cross method [3], which corrects the loops one after the other, but converges considerably faster for several coupled loops.

Limitations of the approach

The hydraulic network calculation is performed for individual governing time steps (winter peak and, if applicable, summer) and not for all 8,760 hours of the year. The diversity factor that is applied individually to each pipe in pipe sizing can only be approximated in a single hydraulic state. The pump electricity demand is calculated with a constant pump head and is therefore rather conservative for pumps with differential pressure control at the critical point. Transient effects such as pressure surges are not considered.

References