To evaluate the HC model concerning the results and its effects on simulation performance, a demonstration network is modeled and simulated in Dymola using the models of the in-house
DHNSim library. The simulations are run with the same network and heat load data for different HC model configurations to investigate their effects on simulation results and performance. Additionally, simulations are also performed with the two open-loop demand models from
AixLib.Fluid.DistrictHeatingCooling (
VarTSupplyDp and
VarTSupplyDpBypass, constant return temperature) and the most simple configuration of DisHeatLib.Demand.Demand (constant return temperature, linearized flow characteristic in the flow unit). For the latter, it was a difficult task to obtain stable operation of the HCs due to oscillations in the internal control loops.
Table 1 shows an overview on the simulation runs and their specifications.
4.1. Demonstration Network
The basic demonstration network is a fictional, simple DHN with one supply unit and six HCs. The pipe network consists of 17 pairs of pipes (supply and return line), including house lead-in pipes, and contains one loop to introduce a certain degree of complexity (the loop results in a non-linear system of equations for the mass flows and pressures). The pipe closing the loop (DN 50) is split into two parts to obtain a temperature value in the middle of the pipe for analysis. To analyze the effect of different network sizes, this basic layout (“small”) is repeated three times (“medium”) and nine times (“large”), branching off after the first network pipe. The layout and the main parameters are depicted in
Figure 4.
The HCs are simulated with six real, measured heat load profiles from an existing DHN with a resolution of 15 min. For the “medium” and “large” simulations, the profiles are reused with random variations (normal distribution, standard deviation 10%) so that the peaks and valleys do not perfectly coincide. The heat load profiles consist of exemplary periods for high load, medium load, low load (each three days) and an undersupply situation (two days with a temporary drop of supply line temperature to 50 °C). The supply line temperature at the supply unit is set via a temperature curve between 70 and 80 °C, apart from the undersupply situation, where the actual measured supply temperatures are used. During the simulation, these values are interpolated using smooth splines with Modelica.Blocks.Sources.CombiTimeTable.
The heat load profiles, being real measurement data, show higher dynamics (frequent peaks and valleys) than common synthetic heat load profiles. This is most pronounced during the medium- and low-load periods at HC 5 and HC 6, which show frequent switching between zero and substantial load values. Furthermore, most of the load profiles include periods with zero load for some hours. Thus, these heat load profiles are challenging yet realistic examples of heat load profiles that may be used in the simulation of DHNs.
4.2. Evaluation of Simulation Results and Performance
To check whether the demonstration network is configured realistically, some general indicators are estimated from the results of the main simulation run (low load = winter, medium load = spring and autumn, high load = summer). For the basic small demonstration network and the main simulation run, the estimation yields a total annual heat demand of 3.2 GWh/a, relative heat losses of 12% and a relative hydraulic energy for the circulation of 0.22%. Given the route length of 2.2 km, the linear heat density is 1.3 MWh/(m·a). The mass flow weighted mean temperatures at the supply unit are 72 °C in the supply line and 48 °C in the return line. These values are considered plausible for a medium-sized DHN with network temperatures as low as possible while still supplying old buildings and preparation of domestic hot water.
4.2.1. Comparison of General Simulation Results
In general, the simulation results of the different HC models should be similar. In the following, the results are compared to the main simulation run and major differences are reported and explained.
The total heat from the supply unit does not differ by more than 3% compared to the main result for all models and periods, which indicates a good agreement of the models.
During the low-load period, it makes a major difference whether the HC model includes a bypass. Compared to main, models without bypass (noBypass, AixLib and DisHeatLib) result in about 9% less heat losses, because the network is not kept hot and lower return temperatures occur. Furthermore, they yield a 20 to 30% higher maximum heat flow due to mass flow peaks after the supply line temperature cools down. In addition, the maximum pressure difference at the supply unit is 13 to 19% lower due to lesser mass flow in the network. Accordingly, the total hydraulic energy at supply unit is about 30% lesser than with bypasses in this period.
Furthermore, during the low-load period, AixLibBypass has 7% less heat losses than main, as the constant bypass flows are not sufficient to keep the network hot (but also should not be tuned to the necessary value, because too much load would be omitted then).
In the undersupply period, the AixLib models have 13% lower maximum pressure differences, as they assume a constant minimum temperature difference (set to 5 K in this case), while DHNSim models set mass flows to a maximum allowed value. Furthermore, the hydraulic energy is 20 to 30% lesser without bypasses (noBypass, DisHeatLib) and 56% lesser for the AixLib models due to lower mass flows in both cases.
Another difference is that the maximum differential pressure at the supply unit is 19% higher for the
AixLib models during the high-load period due to a single, probably faulty, data point in the heat load profile of HC 4 (critical path), with a prescribed heat flow of 35 kW (although rated to 17.5 kW). The
DHNSim models limit the mass flow according to Equation (
2) (here with
), which limits the heat load in this case to 18 kW.
4.2.2. Effect of Mass Flow Time Constant and Load Correction
The comparison of the heat and mass flows at HC 6 for simulation runs
main,
fastDynamics and
corrLoad in
Figure 5 demonstrates that a heat load peak and bypass operation changes due to different values of the time constant and the optional correction of deviations of the actual heat load from the prescribed value.
The time constant delays and slightly reduces the heat load peak compared to the input signal due to the added dynamics. The smaller the value of tau_m_flow, the more immediate the reaction of the HC model to the input signal. Depending on the goals and available input data, the user of the model chooses a sensible value for tau_m_flow. For input time series at a resolution of 15 min to 1 h, a value of 180 s has proven to be suitable in previous simulation studies.
In contrast, with load correction, the heat load peak is increased, because during the rising slope the actual heat load is below the prescribed value, so the model increases the heat flow over the prescribed value to equalize this deficit. During the falling slope, the heat load is reduced faster with load correction than without once the previous deficit is equalized.
Figure 5 also shows that
tau_m_flow has an impact on bypass operation. After 130 h, the heat flow signal, and subsequently that of the mass flow, drops to zero. However, after a short zero-flow period, the supply line temperature (not shown for clarity) drops below the set point of the bypass, causing it to increase the mass flow. The bypass in
fastDynamics reacts first because the zero flow starts earlier so the cooled house lead-in pipe becomes flushed earlier than in
main. The slower dynamics in
main finally cause a slightly higher peak mass flow, because the bypass mass flow depends on the temperature reaching the HC, which is lower the longer the water cools down. However, both configurations maintain the required supply line temperature at the HC. The bypass in
corrLoad behaves similarly to
main.
The other evaluated HC models show different behavior concerning dynamics as shown in
Figure 6. In general, course and magnitude of the mass flow peak are similar to those of the
main model. The
AixLib model reacts immediately to the prescribed heat flow signal and follows it strictly during the heat flow peak. This leads to an immediate and steep rise of mass flow with a minor intermediate peak which results from the fact that once the house lead-in pipe is flushed, the supply temperature rises and the mass flow can be reduced to meet the heat load. In contrast, the
DisHeatLib model shows a delayed answer, but then an even steeper rise of mass flow. The intermediate mass flow peak occurs a little later but similarly to
AixLib. On the falling slope, the
DisHeatLib model slowly approaches (but never reaches) zero mass flow. This behavior results from the model implementation with a control loop for the load mass flow.
4.2.3. Bypass Behavior
Bypasses are intended to maintain a small mass flow through HCs during zero-load periods so that the supply line temperature does not drop too much.
Figure 7 shows the results for temperatures and mass flows at HC 6 during a period without heat load for
main and
noBypass. In
main, the bypass starts to operate once the supply line temperature approaches 65 °C. The mass flow shows an decreasing oscillation, which is caused by the interplay of the thermostatic control approach and the delay due to the dwell time of the water in the house lead-in pipe. As long as the bypass operates and the heat load is zero, the return line temperature equals the supply line temperature. The bypass successfully maintains the required temperature of about 65 °C. Once the heat load rises (at 133.5 h), the return temperature smoothly drops.
In contrast, in noBypass, the mass flow is zero during the period without heat load and the supply line temperature continuously drops. As a consequence, a mass flow peak occurs afterwards until the supply line temperature rises, causing steep slopes of mass flow and temperature. Nevertheless, the implementation of the HC is robust also without bypass due to the limited dynamics and maximum value of mass flow and its reduction if the differential pressure is too low. This prevents the HC model from imposing excessively high mass flows after zero-flow periods which might cause simulation failure.
For the demonstration network,
noBypass implementation requires substantially less time to compute (see
Section 4.2.7), which indicates that the reduced effort (no calculation of bypass mass flow) outweighs the computational effort to simulate the higher dynamics after zero-flow periods. In the end, it is up to the user whether a bypass is included, depending on whether it is intended and realistic to have it.
In general, the proposed bypasses work as intended. In the main simulation run, only HC 6 has supply line temperatures below 64 °C in the three-day low-load period, totaling 1 h, affecting a heat consumption of 9 kWh. In contrast, without a bypass, at all HCs supply line temperatures below 64 °C occur, with the strongest effect at HC 6 during the low-load period for 30 h and 300 kWh.
Figure 8 shows a comparison of the simulation results from
main to the other HC models. In general, a major difference between models with and without bypass can be observed.
AixLibBypass maintains a constant minimum mass flow. If tuned properly, this approach succeeds in maintaining a sufficient supply line temperature. However, the bypass is active irrespective of the supply line temperature, whenever the load mass flow reaches the set point, as can be seen at 134.5 h. The implementation of the return line temperature is not robust (switches at an undetermined time instant, here 131.7 h) and causes abrupt changes. The bypass implementation of AixLibBypass does not reduce the duration of temperature undersupply significantly for two reasons. First, bypass operation does not depend on temperature but on heat load, so that in some periods the bypass does not act, although the supply line temperature is low. Second, and more importantly, it is not possible to tune the bypasses of critical consumers to a value that always maintains the supply line temperature, because it is chosen to limit the maximum allowed bypass mass flow to 10% of nominal mass flow, as too much heat load is omitted otherwise.
The two other models without bypass,
AixLib and
DisHeatLib, produce results that are very similar to those from
noBypass (shown in
Figure 7). During the zero-flow period, the supply line temperature constantly drops. Once the heat load is above zero, the mass flow rises. Both models show a strong and short peak of mass flow, which results from the cooled water in the house lead-in pipe. However, as
DisHeatLib reacts with a certain delay, its mass flow peak is later and higher compared to
AixLib.
4.2.4. Load Hysteresis
The hysteresis feature explained in
Section 3.2 affects the behavior of the HC model when the prescribed load value is close to zero.
Figure 9 shows an example for HC 3, comparing the results for heat and mass flows from
main and
hysteresis. In the period, two very low heat load peaks occur. The first (210.5–212 h) reaches values above the hysteresis thresholds. While the
main result shows a smooth rise of heat flow following the set-point,
hysteresis has zero heat flow until the threshold is reached (right before 211 h), followed by a steep rise of heat flow until the required values is reached. At the falling slope, the heat flow suddenly falls to zero once the switch-off threshold of the hysteresis is crossed (at 211.7 h). The second heat load peak (212–213 h) never crosses the switch-on threshold, so it is completely ignored in
hysteresis. The mass flows are very similar, as they are dominated by the bypass mass flow that is similar for both results.
This example shows that the hysteresis approach may avoid the calculation of negligible heat flows. However, it imposes additional computational effort due to the events that are triggered whenever thresholds are crossed and the steep slopes that occur right after every switching.
4.2.5. Undersupply
The proposed HC model is designed to provide plausible results during undersupply situations (excessively low supply temperature and/or differential pressure).
Figure 10 shows the simulation results in such a period for
main and
corrLoad at HC 4, which is at the end of the critical path. The supply line temperature (upper graph) falls steadily and approaches the return line temperature, and as a consequence, the proposed HC model increases the mass flow (lower graph) to reach the needed heat flow.
In main, the first phase of undersupply starts at about 281 h when the mass flow reaches its maximum (first vertical dotted line). From this point onward, the set-point heat flow is not covered. The second phase, starting after 282 h, is marked by insufficient differential pressure. Due to the enormous increase in mass flows in the network, pressure losses in the pipes rise, causing high differential pressures to be provided by the heat supply unit. At a certain point, the upper limit of differential pressure is reached so that the required minimum differential pressure at the HC (here 0.6 bar) is no longer maintained. As a consequence, the load model reduces the mass flow. Finally, after 284 h (third dotted line), the supply line temperature even drops below the set-point return temperature, so the heat flow is zero and the return line temperature equals the supply line temperature. Once the supply line temperature rises substantially at 287 h, the required differential pressure is restored and the HC returns to normal operation.
The model configuration corrLoad behaves similarly to main during the undersupply period (its densely dotted line is hidden behind the solid line of main). However, right after reestablishing a sufficient supply line temperature, the load correction comes into action causing a major load peak of 14 kW which lasts about 3 h until the heat load that was not covered is balanced. The load correction works properly for all loads, with deviations between set point and actual heat consumption below 0.1% for all HCs in the undersupply period. In contrast, other models result in substantial deviations of up to −15% for the proposed HC model without load correction and up to −25% for DisHeatLib (note that the actual undersupply lasts for only 6 hours in the two-day simulation period).
Figure 11 shows the simulation results from
main in comparison to
AixLib and
DisHeatLib.
DisHeatLib behaves similarly to
main, as the flow unit in the model limits the mass flow to a maximum value according to the available pressure difference. The parameterization is derived from nominal values and results in rather low maximum mass flows and more undersupply than
main. In addition, oscillations of the mass flow control system can be seen, especially right after the undersupply period.
The AixLib model, however, deals with the situation differently. The model assumes a minimum temperature difference between flow and supply line (here 5 K) that is used whenever the supply line temperature is low. This implementation leads to smaller mass flows compared to the proposed HC model and lets the model follow the set-point heat flow, so no undersupply occurs. However, the return temperature drops to 45 °C, and might even drop further, which is unrealistic if the secondary return temperature of the actual HC is higher than that.
4.2.6. Comparison with Measurement Data from an Existing DHN
To further evaluate the plausibility of the HC model, measurement data from an existing DHN were used. A major difference to the presented HC model is that the return temperatures are not constant but change over time. This is a major weakness of the proposed model and the HC models from other libraries, and this limits the comparability between measurement and simulation.
Unfortunately, the data are only available as instantaneous values every 15 min, so the analysis of processes below that time step is not possible. Thus, an evaluation of the time constant was not possible. However, it is known from practice that the actuators of valves have runtimes of about 30 s to a few minutes; therefore, a time constant in that range is plausible.
The hysteresis feature is not intended to be physical; it rather represents an idea to improve the simulation time with very little deviation from the original time series. Thus, a comparison to measurement data is not suitable.
Bypass behavior does not necessarily require an actual bypass component. The measurement data indicate that HCs with instantaneous hot water preparation act like thermostatic bypasses at zero load because the substation maintains a small mass flow to keep the domestic hot water heat exchanger hot so that hot water preparation can start immediately when water is tapped.
Figure 12 shows an exemplary period. Note that the secondary
y-axis ranges only from 0 to 0.25, so the small values for heat and mass flow are visible.
After a short heat load peak (corresponding to a tapping event) at 21:00 h, the mass flow and heat load are zero. Then, the supply line temperature drops and the mass flow starts to rise again. For the next 8 h, the substation shows the bypass behavior maintaining a temperature of about 55 °C, with a small mass flow, almost no cooling of the water and a negligible heat flow. The behavior is similar to a thermostatic valve, meaning that the more the supply line temperature drop, the greater the mass flow. This behavior shows great similarity to the results from
main (see
Figure 7).
For the undersupply behavior, appropriate measurement data are available to demonstrate that the behavior of the proposed HC model can be found in the real world.
Figure 13 shows the measurement data of one HC that experiences the supply line temperature drop that was simulated as well. Due to the intermittent nature of this HCs heat load profile, the evaluation is only meaningful starting from 1:00 h in this case. From that moment on, it can be seen that the HC draws a high mass flow from the network but is not able to extract heat from it (supply and return line temperatures are almost equal). As the supply line temperature drops further, other HCs in the network increase their mass flow, so the differential pressure at this HC is reduced, and in consequence, the mass flow is reduced.
In contrast to the simulation, from 5:00 to 6:15, the mass flow is on a higher level again. This effect can be observed at all HCs that increased their mass flow drastically due to insufficient supply temperature. Most probably, the differential pressure in the network increased during that period by manually setting the pump speed to a maximum to try to overcome the undersupply situation.
Once the supply line temperature is restored to a sufficient value at 7:30, the HC has a short but massive heat load peak and draws a high mass flow until its heat demand is fulfilled. Then, its mass flow and heat load is zero again, so the water in the house lead-in pipe cools down.
All in all, the undersupply behavior is very similar to that of the proposed HC model with almost no extraction of heat, a high mass flow that drops as the differential pressure is reduced and a sharp heat load peak after the undersupply situation (see
Figure 10).
4.2.7. Simulation Performance
For a profound analysis of the influence of the different implementations of HC models and network sizes on simulation performance, the CPU time for integration is evaluated (best of three runs, integration algorithm Dassl, tolerance 1 × 10−4, on a machine with CPU Intel i5-4300U @ 4x1.9 GHz, RAM 8 GB).
Figure 14 shows the CPU time relative to the
main model.
OnePipe requires only a small fraction of CPU time compared to
main, which proves that the HC model itself does not require much computational effort. However, the implementation of the HC model causes major variations in CPU time for the same network, with an increasing importance for larger models (more than a factor of five between
noBypass and
corrLoad for the large model). The models with open-loop design and without bypass (
noBypass and
AixLib) have the lowest and very similar CPU times. The proposed model
main is the fastest with a bypass.
FastDynamics lead to a minor increase in CPU time.
DisHeatLib requires 33 to 40% and
AixLibBypass 55 to 60% more computational effort. The implementation of
hysteresis causes the long CPU times, especially for the large network. The use of the load correction in
corrLoad leads to the longest CPU times (100 to 150% longer than
main).
The absolute values (indicated in
Figure 14 as well) show that CPU time scales non-linearly with model size, reaching about 850 s (
main) for the large demonstration network. Assuming a linear dependence on simulated time, an annual simulation of the large network takes about 8 hours, which is acceptable but substantial, which stresses the importance of a careful design of the HC models.
Table 2 offers an overview on all simulation runs for the large DHN with their CPU time alongside selected model properties and simulation characteristics that help identify causes for differences in simulation performance.
The results reveal that the number of result points has a direct and almost linear impact on CPU time. A simple linear fit of CPU time as a function of the number of result points yields a high coefficient of determination of 0.70.
Figure 15 shows both measured and fitted CPU times for the large model. The deviations of the real measured CPU times from the fit may be caused by various factors that cannot be clearly identified due to the complexity of the computations. Some of these factors are the number of state events that occur, the number of Jacobian evaluations, the complexity of the resulting equation systems and the number of variables and states to be computed.
AixLib and the proposed HC model without bypass, noBypass, are much faster than expected from the fit and have a low number of state events and Jacobian evaluations. DisHeatLib, on the other hand, has a 30% higher CPU time measured than that according to the fit. As the model does not have an increased number of state events or Jacobian evaluations, this increase can be attributed to the fact that this HC model does not follow the open-loop design which leads to solving complex systems of equations. Model hysteresis triggers by far the most events and thus has high CPU times. Similarly, corrLoad has a strongly increased CPU time that may be caused by the high number of Jacobian evaluations and a slightly increased number of states and variables to be calculated. Therefore, hysteresis and load correction should be used with care as these features may substantially increase the simulation time. Finally, AixLibBypass has a much shorter simulation time than expected from the fit, which cannot be attributed to any of the analyzed properties.
4.3. Limitations of the Proposed HC Model
Naturally, the simplified implementation of the HC model results in a number of limitations which are discussed in this section.
First, the simulation needs an external heat load profile which might either be derived from measured data or be generated artificially. However measurement data are only available for existing HCs and usually have limited quality (potential issues concerning accuracy, data availability for all HCs, gaps in the time series). In contrast, artificial heat load profiles can be generated with good accuracy for space heating loads, but they usually represent a smoothed profile for a whole district and ignore specifics of single HCs (e.g., dimensioning of components, optional night-time setback, user behavior). For domestic hot water, it is even more difficult to obtain suitable heat load profiles. Its characteristics are highly dependent on user behavior (tapping events) as well as the hydraulics (direct preparation or storage, circulation). Thus, providing valid heat load profiles is a tricky task which is left to the user of the proposed HC model.
Second, it may be a limitation that the model does not provide an option to change parameters during the simulation. In reality, set points in a controller, such as the temperature that a bypass maintains, may change during the course of the day or the year via schedules or at an unpredictable point of time, when users change these values.
Third, despite its ability to react plausibly to changing pressure and temperature conditions in the DHN, the HC model is simple and shows idealized behavior. An example is the undersupply model which assumes that the heat load is zero once the temperature in the supply line is as low as the prescribed return line temperature. This is not exactly true, as a HC still extracts heat to some extent during undersupply (see
Figure 13). Thus, the results from undersupply simulations somewhat differ from real scenarios. Nevertheless, we believe that the HC model is accurate enough concerning undersupply to draw general conclusions whether undersupply may occur and which HC would be affected to what extent.
Finally, and by far the most importantly, in our opinion, there exists limitation in the model since it uses a set point for the return temperature or the temperature difference (either constant or from an input time series) for heat extraction from the mass flow. Thus, the model is not able to reflect the dependence of the return temperature on the flow temperature or other influences such as current heat load value or type (space heating or domestic hot water) or the time of the day (e.g., important when the space heating controller includes a night-time setback). Providing an input time series for the return temperature is difficult, because either measured data must exist or detailed simulations of the building and its heat distribution system must be performed. Therefore, usually, users are left with using a constant return temperature, which is certainly not very realistic throughout the course of a year. Thus, there is a need for robust validated models for the return temperature depending on supply temperature, current heat load and other relevant factors, all of which are simple enough to be included in simplified HC models.