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A comparison of aggregated models for simulation and operational optimisation of district heating networks
Energy Conversion and Management 45 (2004) 1119–1139 www.elsevier.com/locate/enconman
A comparison of aggregated models for simulation and operational optimisation of district heating networks Helge V. Larsen a b
a,*
, Benny Bøhm b, Michael Wigbels
c
Department of Systems Analysis, Risø National Laboratory, P.O. Box 49, DK-4000 Roskilde, Denmark Department of Mechanical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark c Fraunhofer Institute for Environmental, Safety and Energy Technology (UMSICHT), Osterfelder Strasse 3, 46047 Oberhausen, Germany Received 3 April 2003; accepted 2 August 2003
Abstract Work on aggregation of district heating networks has been in progress during the last decade. Two methods have independently been developed in Denmark and Germany. In this article, a comparison of the two methods is first presented. Next, the district heating system Ishoej near Copenhagen is used as a test case. For the 23 substations in Ishoej, heat loads and primary and secondary supply and return temperatures were available every 5 min for the period December 19–24, 2000. The accuracy of the aggregation models has been documented as the errors in heat production and in return temperature at the DH plant between the physical network and the aggregated model. Both the Danish and the German aggregation methods work well. It is concluded that the number of pipes can be reduced from 44 to three when using the Danish method of aggregation without significantly increasing the error in heat production or return temperature at the plant. In the case of the German method, the number of pipes should not be reduced much below 10 in the Ishoej case. 2003 Elsevier Ltd. All rights reserved. Keywords: District heating; Equivalent models; Aggregated models; Dynamic simulation; Operational optimisation
1. Introduction In 1996, the Danish Ministry of Energy initiated the research project ‘‘Equivalent models of district heating systems’’. The Department of Energy Engineering (presently Department of
*
Corresponding author. Tel.: +45-46-77-5114/5100; fax: +45-46-32-1999. E-mail address: [email protected] (H.V. Larsen).
0196-8904/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.08.006
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Mechanical Engineering) at the Technical University of Denmark (DTU), together with the Systems Analysis Department at Risø National Laboratory (Risø) performed the work. In the final report,[1], a method for aggregation of DH networks was developed with regard to simulation of the transient temperatures in DH networks and a subsequent calculation of the operational costs of running the DH system. This method of aggregation is, in the following, called ‘‘the Danish method’’. Operational data from two Danish DH systems were used to make the aggregated models and to test them by making an abrupt change in the supply temperature from the plant. The errors in the return temperature at the plant between simulations based on the real network and simulations based on the aggregated networks were used to verify the aggregation method. Some of the findings in [1] were referenced in [2]. In order to develop methods for structural simplification of complex DH network systems, a combined project has been conducted at the Fraunhofer Institute for Environmental, Safety and Energy Technology (UMSICHT) in Oberhausen together with the Technical University of Gdansk, Poland, the Gdansk district heating enterprise GPEC and the EVO Energy Supply Company of Oberhausen, Germany. The project has been sponsored within the German-Polish Research Network INCREASE by the German Federal Ministry of Education and Research (BMBF) and the Polish State Committee for Scientific Research (KBN). By application of the developed prototype the DH network can be highly aggregated and calculation times can be substantially reduced. In tests based on actual data from the district heating systems of Gdansk and Oberhausen, the automatic structure simplification has been proved. It was evaluated that an 85% saving of computational time for dynamic simulations compared with non-simplified networks is possible. This method of aggregation is, in the following, called ‘‘the German method’’. It is described in detail by Loewen [3], Loewen et al. [4] and Wigbels et al. [5]. In 1999, the IEA DHC programme (IEA District Heating and Cooling Programme of Research, Development and Demonstration on District Heating and Cooling, Including the Integration of CHP) initiated the research project ‘‘Simple Models for Operational Optimisation’’ to be conducted in 1999–2002 (Annex VI). The contractor was DTU with the subcontractors UMSICHT, Korea District Heating Corporation and the Technical Research Centre of Finland. Additional funding to the project was obtained from the Danish Ministry of Energy, enabling Risø to work as a subcontractor to DTU. Previous work has been summarised in a state of the art report by Park et al. [6]. In the IEA project, aggregated models developed through use of the Danish and German methods were further tested and compared, see [7]. Here the results for the DH system of Ishoej near Copenhagen are presented as a test case. This system has rather few connected loads (23) and a very high line heat demand. The special feature of the Ishoej system is that the data collection system enables information about instantaneous heat loads and return temperatures from the heat exchanger stations.
2. Comparison of aggregation methods and models The Danish and German methods are rather similar but with some important differences as shortly discussed below. Both methods are defined for a steady state situation, but nevertheless, they are, with good accuracy used for situations with time variations.
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Both methods have the same building blocks: • A model for changing a tree structure into a line structure. • A model for removing short branches. Moreover, the German method has a model for simplification of loops. 2.1. Changing a tree structure into a line structure This basic operation is illustrated in Fig. 1. Table 1 shows the variables conserved by the aggregation. 2.2. Removing short branches The German and Danish methods differ with respect to which sub-system is regarded. The German method removes a node, replacing two branches by one, whereas the Danish method removes a (short) branch, replacing three branches by two. This is shown in Fig. 2. Table 2 shows the variables conserved by the aggregation. Both methods consider a steady state situation, i.e. a situation with no time variations. In the Danish method, it is assumed that all (primary) return temperatures from the heat loads are equal. This leads to an aggregated grid with heat loss coefficients independent of temperatures. In contrast to this, in the German method it is assumed that the return temperatures
1 2 Original grid
A
B
Equivalent grid
Fig. 1. Changing tree structure into line structure.
Table 1 Comparison of aggregation methods of tree structures Pipe length Pipe inner diameter Water volume Delay Mass flow Heat load Heat loss from supply pipe Heat loss from return pipe Pressure drop a
German method conserves
Danish method conserves
LA+LB ¼ L2 No Yes Yes Yes Yes Noa Noa Yes
No DB ¼ D2 Yes Yes Yes Yes Yes Yes Not considered
The total heat balance of supply pipe and return pipe together is kept.
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2
Original grid Danish method: 1 2
A Equivalent grid
3
Original grid
A
B
Equivalent grid
Fig. 2. Removing a short branch.
Table 2 Comparison of aggregation methods of removing short branches Pipe length Pipe inner diameter Water volume Delay Mass flow Heat load Heat loss from supply pipe Heat loss from return pipe Pressure drop a
German method conserves
Danish method conserves
Yes No Yes Yes Yes Yes Noa Noa Yes
Yes No Yes Yes Yes Yes Yes Yes Not considered
The total heat balance of supply pipe and return pipe together is kept.
are constant in time. The heat loss coefficients are adjusted so that the heat balance of the supply pipe together with the corresponding return pipe and the connected consumer is kept. The two methods have different starting points in the development of aggregated grids. The German method conserves temperatures in all nodes (in the steady state situation). Since also volume and mass flow are conserved, this implies that heat losses from the physical and the aggregated grids are not exactly the same. This holds even in a steady state situation with the same temperature in all pipes. Heat loss coefficients found by the German method can be negative in situations where loops or branches are aggregated. For compatibility to different simulation platforms, it is possible to configure the algorithm so that the heat loss coefficients remain positive. In this case, higher variations between aggregated and not aggregated networks have to be accepted. However, the Danish method focuses on heat loss, which is conserved (in the steady state situation). Consequently, the node temperatures of the physical and aggregated grids are not exactly the same. Pressure drop in the pipes is not considered by the present Danish method, whereas the German method adjusts the surface roughness (major loss coefficient) or the additional resistance (minor loss coefficient) caused by elbows etc. for each pipe in the aggregated grid in order to preserve pressure in each node. A minor loss coefficient found by this method can be negative.
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Assuming that the software program used to simulate the operation of the aggregated grid can handle negative heat loss coefficients and negative minor loss coefficients, such values will not bring about any problems. During the aggregation, the Danish method keeps track of all physical loads and supplies information as to how each physical load is divided between the aggregated loads. At the moment, such information is not supplied by the German method that only gives data on the size of each aggregated load but not on the origin of this load. 2.3. Removing loops The German method can handle loops in two ways: • Transforming a loop into serial pipes. • Splitting a loop into two serial pipes and one branch. In the latter case, the heat balances of the loops can be kept for steady state simulations. For simplification of loops into serial pipes, small errors have to be accepted. It is up to the user which method he prefers. The former case leads to a faster simplification. To remove a loop, one has to identify a specific node where the mass flows (divided at the input into the loop) flow together again. Therefore, in situations when flows meet at another node (as can occur if the consumersÕ load varies in time), the simplification will give rise to some errors. Usually, these loops are only simplified if absolutely necessary. At the moment, the Danish method is not able to handle loops. 2.4. Model of consumers’ heating installation The German method uses a prescribed return temperature, which is a function of heat load (outdoor temperature) and supply temperature. The Danish method has a specific model for the heating installation that calculates the return temperature as a function of heat load, primary supply temperature, secondary temperatures and the heat transfer area (kA) of the heat exchanger (or radiator). Different types of heating installation models have been developed, but in this paper, it is assumed that all consumers are connected through plate heat exchangers. In the aggregation process, the Danish method traces the heat load and temperature time series from the real consumers to the aggregated consumers, whereupon a new kA-value is calculated for the aggregated consumer. 2.5. Structure of aggregated networks If applied straightforwardly, the Danish method will result in a line network. However, as previously documented in [1], DH networks could be aggregated in ways that preserve parts of the original tree structure. The German method can be applied in a similar way. Depending on the parameters controlling the aggregation process, the aggregated system could be a line network or a network with some
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parts of the tree and/or loop structure preserved. The difference in the aggregation philosophy has been exemplified in the Ishoej case study, cf. Section 3.4.2.
3. The Ishoej district heating system 3.1. The DH system Ishoej is a Copenhagen suburb located 17 km southwest of the city centre. The built up area consists mainly of blocks of flats, semi-detached houses, institutions and shopping centres. Many of the buildings were erected in the 1970s. The DH system was built in 1982. Today, some 8000 dwellings, five schools and the city centre with many shops and institutions are supplied by the DH system. All consumer installations are indirectly connected through 23 substations (each substation consists of one or two plate heat exchangers). The distribution network is shown in Fig. 3. It is made of preinsulated pipes, mostly with standard insulation thickness, and with pipe dimensions from 48 to 356 mm. The total length of the network is approximately 8.3 km. As all connected buildings are situated within a small area,
Fig. 3. The distribution network in Ishoej with 23 substations.
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the line heat demand is high, approximately 42 GJ/m, and the annual heat loss (from the primary network) is only approximately 3%. To begin with, heat was produced by three coal fired boilers, each with a nominal capacity of 17 MW, and by a smaller gas fired peak load boiler. Today, the Ishoej DH system is connected to the West Copenhagen Heating Transmission Company (VEKS). The boilers have been modified for bio fuel, and the plant can supply heat both locally and to the transmission grid. The Ishoej DH company has installed an advanced control and supervision system, which, among other tasks, stores data from the substations and the plant at five minute intervals. At a typical substation, the following data are available: • • • •
primary and secondary supply temperature, primary and secondary return temperature, pressures in the supply and return line, accumulated heat meter readings (energy and volume).
At the Ishoej plant, production by the boilers and the amount of heat delivered from the VEKS system are available as well as flow, temperature and pressure measurements. 3.2. The measurements In this work, 5 min interval data from December 19–24, 2000, are used. The heat loads at the substations were obtained by filtering the heat meter data. Heat production data at the Ishoej plant were obtained from VEKS. In this period, the boilers were used only a couple of hours. Manual reading of the heat meters had taken place on December 11 and 18, and the associated heat consumption is shown in Table 3. For those substations where no data were available, heat load series were constructed from other substations with data, taking into account the type of building (block of flats, school etc.) and the heat consumption according to Table 3. To distinguish between these two kinds of substations, substations with real measurements are called Vxx or Ixx, while substations with constructed time series are called Sxx. Despite the uncertainty associated with this way of generating the missing data, the result is quite good, as shown in Fig. 4. Here, the measured heat production at the Ishoej plant is compared with the sum of the heat loads in the substations. 3.3. The consumers Table 3 shows the heat consumption at the substations the week before the time series start, as well as the average heat load in the time series for the period December 19, 12:00–December 24, 24:00. To give an impression of the type of consumers in Ishoej, heat consumption and primary and secondary supply and return temperatures for some of the 23 substations are shown in Appendix A. Several interesting things are observed: the size and time variation of the heat loads are very different, varying from 8 kW to 6.7 MW on the average, cf. Table 3, and from almost constant consumption to substations with distinct time variations (night set back). Because of the Christmas holidays at the end of the period, the consumers behave very differently, as for instance, some of the institutions are closed for the holidays.
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Table 3 The substations in the Ishoej DH system Substation
Heat meters Dec. 11–18, 2000 (GJ)
V01 V02 S03 V04 V05 V61 V62 V07 V08 V09 S10 V11 V11A V12 S13 I13 V14 S15 S17 V18 S20 S39 I79
655 524 3191 1036 260 153 201 1245 849 94 144 22 35 142 130 4 188 132 47 16 53 251 104
Average load Dec. 19–24 (MW) 1.404 1.112 6.736 2.205 0.611 0.335 0.441 2.628 1.787 0.203 0.315 0.045 0.075 0.309 0.378 0.008 0.416 0.378 0.100 0.039 0.113 0.556 0.298
Total
Category Apartments Shopping centre Apartments Apartments Apartments Shopping centre Shopping centre Apartments Apartments Apartments Apartments Apartments Apartments Apartments Public school Kindergarten Public school Public school Youth hostel Church Institution Public school Technical school
20.491
Heat load in Ishoej Dec. 19-24, 2000 30 25
MW
20 15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes Buildings
Plant
Fig. 4. Measured heat production at the plant and the sum of the (filtered) heat loads in the substations.
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3.4. Modelling the Ishoej DH system In modelling the Ishoej system, the generated data set has been used as input files to a general simulation program. Time series for heat load as well as for secondary supply and return temperatures have been used for each substation. All substations were modelled as one plate heat exchanger, and kA values were estimated from the measured heat load and measured primary and secondary supply and return temperatures. 3.4.1. Physical grid The physical grid consists of 44 branches and 23 loads. 3.4.2. Aggregation Two methods, i.e. the Danish and the German methods, have been used to aggregate the physical grid. The Danish aggregation method is described in detail by Palsson et al. [1] and Larsen et al. [2]. Likewise, Loewen [3] and Loewen et al. [4] give a description of the German method. The aggregated systems are shown in Figs. 5 and 6 and described in detail in Appendix B. These aggregated systems all represent the physical system shown in Fig. 3.
D_23 D_5 D_2
Fig. 5. Aggregated networks in Ishoej. Danish models D_23, D_5 and D_2.
G_20
G_10
G_6
G_2
Fig. 6. Aggregated networks in Ishoej. German models G_20, G_10, G_6 and G_2.
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3.4.3. Simulations Time series covering the period from December 19, 2000 12:00 until December 24, 2000 24:00 with time steps of 5 min are used in the simulations of the various systems. For the aggregated systems, where substations have been combined, heat loads are not modelled in the same way for the Danish and for the German models. Weighted sums of measured time series (heat load and secondary supply and return temperatures) are used for the Danish aggregated substations. The German method of aggregation does not supply information about how to calculate time series for the aggregated loads using information about the individual physical loads. Instead the sum of all time series for physical heat loads is distributed between the aggregated loads, i.e. all aggregated loads are varying proportionally. For the secondary supply and return temperatures, the same constant values are used for all aggregated loads. These constant values are calculated as weighted averages of the measured time series. Regarding the supply temperature from the plant, two situations are considered: • The supply temperature is as measured (i.e. varying around 105 C). See Fig. 7. • The supply temperature is 100 C for a period, and then, it is suddenly increased to 110 C. 3.4.4. Results for the Danish method of aggregation Fig. 8 shows the amount of heat supplied by the DH plant for the physical system. The supply temperature is as measured. Fig. 9 gives the error in heat production for an aggregated system with 5 branches found by the Danish method (system D_5, see Fig. 5 and Appendix B). In Appendix C, more figures showing heat production as well as return temperature and flow at the plant can be found for aggregated systems D_23, D_5 and D_2.
Supply temperature from the plant 115 110
°C
105 100 95 90 85 0
1000
2000
3000
4000
5000
6000
7000
Minutes
Fig. 7. Measured supply temperature from the plant.
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Heat production 30 25
MW
20 15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes Phys
Fig. 8. Heat production supplied by the plant for the physical system. The measured time series is used as supply temperature from the plant.
Error in Heat production 1.0
MW
0.5
0.0
-0.5
-1.0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes D_5 - Phys
Fig. 9. Error in heat production for aggregated system D_5 as compared with the physical system. The measured time series is used as supply temperature from the plant.
3.4.5. Results for the German method of aggregation Fig. 10 shows the amount of heat supplied by the DH plant for the physical system when the supply temperature from the plant is 100 C and, then, suddenly increases to 110 C. Fig. 11 gives the error in heat production for an aggregated system with 6 branches found by the German method (system G_6, see Fig. 6 and Appendix B). The curve in Fig. 11 is much smoother than the corresponding curve in Fig. 9. The reason for this is that the supply temperature from the plant in Fig. 11 is constant (except for the step), whereas the supply temperature in Fig. 9 is a measured time series with variations, cf. Fig. 7.
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MW
20 15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes Phys
Fig. 10. Heat production supplied by the plant for the physical system. A step function is used as supply temperature from the plant.
Error in Heat production 0.5 0.0
MW
-0.5 -1.0 -1.5 -2.0 -2.5 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes G_6 - Phys
Fig. 11. Error in heat production for aggregated system G_6 as compared with the physical system. A step function is used as supply temperature from the plant.
3.4.6. Evaluation of aggregated models To assess the quality of a specific aggregated model, time series for the amount of heat supplied by the plant are found by simulating the aggregated system as well as the physical system. The standard deviation of the error between these two time series is then used as a criterion for the quality of the aggregation. Another criterion is also introduced. It is based on the standard deviation of the error between the return temperature to the plant calculated for the physical system and for the aggregated system.
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The following figures show how the standard deviation of error increases as the number of branches is reduced. The heat production at the plant is considered in the charts to the left, whereas the return temperature at the plant is considered in the charts to the right. Only models made by the Danish method of aggregation are considered here. German models will be dealt with below. For the physical system, all loads and secondary supply and return temperatures are represented by measured time series. For aggregated systems, however, time series for the loads and secondary temperatures are calculated as weighted averages of measured series. Regarding the supply temperature from the plant, two different situations are shown: • In Fig. 12, a measured time series is used as supply temperature from the plant (approximately 105 C). • In Fig. 13, a step function is used as supply temperature from the plant (step from 100 to 110 C). The definition of systems D_nn can be found in Appendix B. It is seen that the number of branches can be reduced to 3 without increasing the error too much. Model D_1, with only one branch and two loads, has a standard deviation of the error Standard deviation of return temperature difference at the plant 0.6 D_1
0.5
2.0
D_1
D_2
0.4 1.5
C
D_2 o
% of average heat production
Standard deviation of error in heat production at the plant 2.5
0.3
1.0
D_15
D_15
0.5
D_10
D_4
D_5
0.1 D_44
D_5
D_23 D_20
D_44
D_10
0.2
D_3
D_3 D_4
D_23 D_20
0.0 45
40
35
30
25
20
15
10
5
0.0 45
0
40
35
30
25
20
15
10
5
0
Number of branches
Number of branches
Fig. 12. Standard deviation of error. The measured time series is used as supply temperature from the plant.
Standard deviation of return temperature difference at the plant 0.6
2.0
0.5
D_1 D_2
0.4 1.5
D_1 oC
%of average heat production
Standard deviation of error in heat production at the plant 2.5
0.3
D_2
1.0
D_15
D_10
D_5
D_3 D_4
0.2 0.5
D_15
D_5
D_23 D_20
D_44
0.0 45
D_10
40
35
30
25
20
D_3
0.1 D_44
D_23
D_4
15
Number of branches
10
5
D_20
0
0.0 45
40
35
30
25
20
15
10
Number of branches
Fig. 13. Standard deviation of error. A step function is used as supply temperature from the plant.
5
0
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(defined on the basis of heat production at the plant) of approximately 2%, but the average error over the simulated time period is as small as 0.01%. At the moment, the German method of aggregation does not supply information about how the physical loads are divided among the aggregated loads. Therefore, the capability of such aggregated grids has to be tested with the following simpler load model: for the physical system, as well as for all aggregated systems, all load time series are modelled as fixed percentages of the time series for the total load. This means that all loads are varying proportionally and summing to the correct total load series. Secondary supply and return temperatures are constant and have the same values for all loads. These values are calculated as weighted averages of the measured temperature time series. Also, the Danish grids are tested with this simpler load model. Regarding the supply temperature from the plant, the same two situations as above are shown: • In Fig. 14, a measured time series is used as supply temperature from the plant (approximately 105 C). • In Fig. 15, a step function is used as supply temperature from the plant (step from 100 to 110 C).
Standard deviation of error in heat production at the plant
Standard deviation of error in return temperature at the plant 0.20 D_1
G_2
2.0 G_2
0.15
D_1
G_6 D_2
C
1.5 G_6
1.0
o
% of average heat production
2.5
0.10 D_2
G_10
G_10
D_3
G_20
0.05
0.5 D_23 D_20
D_15
D_44
0.0 45
35
30
25
20
15
D_3 D_23
D_4
D_10 D_5
40
G_20
10
D_20
D_15
D_10
15
10
D_4
D_44
5
0.00 45
0
D_5
40
35
Number of branches
30
25
20
5
0
Number of branches
Fig. 14. Standard deviation of error. The measured time series is used as supply temperature from the plant. A simple load model is used.
Standard deviation of error in return temperature at the plant 0.20 G_2
D_1
1.2
0.15
G_2
G_6
D_2
C
0.9 o
% of average heat production
Standard deviation of error in heat production at the plant 1.5
0.10
D_1
G_6
0.6
D_2
0.05
G_10
0.3 G_20
D_44
0.0 45
D_23
D_20
D_15
D_10
D_5
35
30
25
20
15
Number of branches
10
5
D_5
D_23 D_44
D_4
40
G_10
G_20
D_3
0
0.00 45
40
35
30
25
D_20
D_15
D_10
20
15
10
D_3 D_4
5
0
Number of branches
Fig. 15. Standard deviation of error. A step function is used as supply temperature from the plant. A simple load model is used.
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The definition of systems G_nn and D_nn can be found in Appendix B. From Figs. 12–15, it is seen that the number of branches can be reduced from 44 to three when using the Danish method of aggregation without significantly increasing the error in heat production or return temperature at the plant. When using the German method, the number of branches should not be reduced much below ten to guarantee a standard deviation below 0.3% for the error of heat production and 0.05 C for the error of the return temperature.
4. Discussion and conclusion In this paper two different ways of aggregating DH networks have been applied. Both the Danish and the German methods are systematic methods for changing the DH network and the heat loads (consumers) into a simpler system, which can be used for simulating and optimising the operational costs of the DH system. The goal of the present work has been to verify the aggregated models further. The DH system in Ishoej in Denmark has been used. The Ishoej DH company has supplied information from all 23 connected heat exchanger stations every 5 min. This facilitates the testing of aggregated network models in situations, that do not comply with the assumptions for making the models, i.e. all heat loads at the consumers should change in the same manner (time variation) and all return temperatures should be similar. In the work on the Ishoej DH system, 5 min values from December 19–24, 2000 are used. Because data were not available for all substations, a realistic data set had to be created from those heat exchanger stations where data existed. For the 23 substations in Ishoej, heat loads and primary and secondary supply and return temperatures were thus, available every 5 min. The accuracy of the aggregation models has been documented as the errors in heat production and in return temperature at the DH plant between the physical network and the aggregated model. Furthermore, a comparison has been made between the Danish and the German aggregation methods in the Ishoej case study. Both aggregation methods work well. The conclusion is that the number of pipes can be reduced from 44 to three when using the Danish method of aggregation without significantly increasing the error in heat production or return temperature at the plant. When using the German method, the number of pipes should not be reduced much below ten to guarantee the same errors in the case of the Ishoej DH system. The work on aggregated network models will hopefully be continued in future research projects. Some items that could be improved in the Danish and German methods appear from Tables 1 and 2. The Danish method, for instance, could be improved by the possibility of simplifying loops and conserving the pressure in the DH networks. Likewise, it would be an improvement to the German method if it were able to conserve heat loss and if it could supply information about how each physical load is divided between the aggregated loads. Some initial work has been done to improve the aggregation methods further by adjusting the parameters of the aggregated networks. One method is to minimise the squared sum of errors between the full network description and the aggregated model with respect to, for instance, the
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amount of heat stored in the network, the return temperature at the DH plant, or the pumping power. Further work is still required in this area. Finally, work is required to automate the aggregation process further, which today still requires decisions taken by an experienced researcher. Here, the goal is to make the process fully automatic or at least so simple that the operator can update the aggregated network when it is required, for instance, due to a changed load distribution or to an expansion of the DH network.
Acknowledgements We would like to thank the IEA District Heating and Cooling Programme of Research, Development and Demonstration on District Heating and Cooling, Including the Integration of CHP, Contract 524110/0010, project 2002:S1, and the Danish Ministry of Energy, J. no. 1373/010041, for funding the work. The support is gratefully acknowledged.
Appendix A. Heat loads in Ishoej DH system Figs. 16–19 show measured time series for primary and secondary supply and return temperatures as well as the load for 4 of the 23 consumers in Ishoej. The series cover the simulated period, i.e. from December 19, 2000 12:00 until December 24, 2000 24:00. The following symbols are used: • TS_Prim: Primary supply temperature. • TS_Sec: Secondary supply temperature. • TR_Prim: Primary return temperature.
24
100
20
80
16
60
12
40
8
20
4 0
0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Fig. 16. Measured time series for load L_S03.
Load [MW]
o
Temperature [ C]
Load L_S03 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
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2.4
100
2
80
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60
1.2
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20
0.4
Load [MW]
o
Temperature [ C]
Load L_V05 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
0
0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Fig. 17. Measured time series for load L_V05.
0.03
100
0.025
80
0.02
60
0.015
40
0.01
20
0.005
0 0
1000
2000
3000
4000
5000
6000
7000
Load [MW]
o
Temperature [ C]
Load L_I13 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
0
8000
Minutes
Fig. 18. Measured time series for load L_I13. Primary and secondary return temperatures are almost identical.
• TR_Sec: Secondary return temperature. • Load: Heat load. In Figs. 16–19, the five curves are positioned from the top and downwards according to the order in the list above. For those substations where no data were available, a heat load series was constructed from other substations with data, taking into account the type of building (block of flats, school etc.) and the heat consumption according to Table 3. To distinguish between these two kinds of substations, substations with real measurements are called Vxx or Ixx, while substations with simulated time series are called Sxx. Despite the uncertainty associated with this way of generating
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1.5
100
1.25
80
1
60
0.75
40
0.5
20
0.25
0 0
Load [MW]
o
Temperature [ C]
Load L_S15 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
0 1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Fig. 19. Measured time series for load L_S15.
the missing data, the result is quite good as shown in Fig. 4, where the measured heat production at the Ishoej plant is compared with the sum of the heat loads in the substations.
Appendix B. Network data for the Ishoej DH system B.1. Aggregation by the Danish method Table 4 lists the models generated by the Danish method. The model in a specific row of the table is made from the model in the preceeding row by a further aggregation. The physical grid is shown at the top of the table. A graphical representation of some of the grids is shown in Fig. 5. Table 4 Models generated by the Danish method Model
Number of branches
Number of loads
Description
Phys D_44
44 44
23 23
D_23
23
23
D_20 D_15 D_10 D_5 D_4 D_3 D_2 D_1
20 15 10 5 4 3 2 1
20 15 10 5 4 3 2 2
The physical system All branches in-line The number of branches is not reduced All branches with no load in-between are replaced by one branch Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed There is also a load at the plant
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B.2. Aggregation by the German method Table 5 lists the models generated by the German method. The physical grid is shown at the top of the table. A graphical representation of the grids is shown in Fig. 6.
Table 5 Models generated by the German method Model
Number of branches
Number of loads
Description
Phys
44
23
The physical system
G_20
20
18
Reduction of the physical system The tree structure is maintained
G_10
10
9
Further reduction The tree structure is maintained
G_6
6
5
Further reduction All branches in-line
G_2
2
2
Further reduction All branches in-line
Error in Heat production
Heat production
1.0
30 25
0.5
MW
MW
20 15
0.0
10 -0.5 5 -1.0
0 0
1000
2000
3000
4000
5000
6000
7000
8000
0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Minutes
D_23 - Phys
Phys
Error in Heat production
Error in Heat production
1.0
1.5 1.0
0.5
MW
MW
0.5 0.0
0.0 -0.5
-0.5 -1.0 -1.0
-1.5 0
1000
2000
3000
4000
Minutes D_5 - Phys
5000
6000
7000
8000
0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes D_2 - Phys
Fig. 20. Heat production. Aggregated systems D_23, D_5 and D_2 compared with the physical system.
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H.V. Larsen et al. / Energy Conversion and Management 45 (2004) 1119–1139 Return temperature difference at the plant
Return temperature at the plant 2.0
60
1.5
50
1.0
C
0.5
30
0.0
o
o
C
40
-0.5
20
-1.0 10 -1.5 0 0
1000
2000
3000
4000
5000
6000
7000
-2.0
8000
0
1000
2000
3000
Minutes Phys
6000
7000
8000
7000
8000
Return temperature difference at the plant 2.0
1.5
1.5
1.0
1.0
0.5
0.5
C
2.0
0.0
o
C
5000
D_23 - Phys
Return temperature difference at the plant
o
4000
Minutes
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5 -2.0
-2.0 0
1000
2000
3000
4000
5000
6000
7000
0
8000
1000
2000
3000
4000
5000
6000
Minutes
Minutes D_5 - Phys
D_2 - Phys
Fig. 21. Return temperature at the plant. Aggregated systems D_23, D_5 and D_2 compared with the physical system. Flow difference at the plant
Flow at the plant
5
140
4 120
3 2
80
kg/s
kg/s
100
1 0
60
-1
40
-2 -3
20
-4
0
-5 0
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6000
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D_23 - Phys
Phys
Flow difference at the plant
Flow difference at the plant 5
5
4
4
3
3
2
2
1
1
kg/s
kg/s
4000
Minutes
0
0
-1
-1
-2
-2
-3
-3
-4
-4 -5
-5 0
1000
2000
3000
4000
Minutes D_5 - Phys
5000
6000
7000
8000
0
1000
2000
3000
4000
5000
Minutes D_2 - Phys
Fig. 22. Flow from the plant. Aggregated systems D_23, D_5 and D_2 compared with the physical system.
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Appendix C. Time series for aggregated systems in Ishoej Time series for heat production and return temperature at the plant as well as flow from the plant are shown in Figs. 20–22. In each figure, the time series for the physical system is shown at the top chart. Below this, charts follow showing the difference between three aggregated systems and the physical one. Aggregated systems (D_23, D_5 and D_2) made by the Danish method of aggregation are considered. The supply temperature from the plant is as measured. For the physical system, all loads and secondary supply and return temperatures are represented by measured time series too. For aggregated systems, however, time series for loads and secondary temperatures are calculated as weighted averages of measured series.
References [1] P alsson H, Larsen HV, Bøhm B, Ravn HF, Zhou J. Equivalent models of district heating systems. Department of Energy Engineering, Technical University of Denmark and Systems Analysis Department, Risø National Laboratory; 1999. 179 pp. ISBN 87-7475-221-9. [2] Larsen HV, Palsson H, Bøhm B, Ravn HF. An aggregated dynamic simulation model of district heating networks. Energy Conversion and Management 2002;43(8):995–1019. [3] Loewen A. Entwicklung eines Verfahrens zur Aggregation komplexer Fernw€ armenetze. Dissertation, Universit€ at Dortmund. UMSICHT-Schriftenreihe Band 29. Fraunhofer IRB Verlag 2001. [4] Loewen A, Wigbels M, Althaus W, Augusiak A, Renski A. Structural simplification of complex DH-networks. Euroheat & Power 2001:46–50. [5] Wigbels M, Althaus W, Lucht M. Nonlinear Optimisation in CHP Applications, 2002. Available at:. [6] Park YS, Kim WT, Kim BK. State of the art report of Denmark, Germany and Finland. Simple Models for Operational Optimization. Korea District Heating Corporation, 2000. 294p. [7] Bøhm B, Ha S, Kim W, Kim B, Koljonen T, Larsen HV, et al. Simple models for operational optimisation, 2002. Report 2002: S1, 135 pp. ISBN 90 5748 021 2.
A comparison of aggregated models for simulation and operational optimisation of district heating networks Helge V. Larsen a b
a,*
, Benny Bøhm b, Michael Wigbels
c
Department of Systems Analysis, Risø National Laboratory, P.O. Box 49, DK-4000 Roskilde, Denmark Department of Mechanical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark c Fraunhofer Institute for Environmental, Safety and Energy Technology (UMSICHT), Osterfelder Strasse 3, 46047 Oberhausen, Germany Received 3 April 2003; accepted 2 August 2003
Abstract Work on aggregation of district heating networks has been in progress during the last decade. Two methods have independently been developed in Denmark and Germany. In this article, a comparison of the two methods is first presented. Next, the district heating system Ishoej near Copenhagen is used as a test case. For the 23 substations in Ishoej, heat loads and primary and secondary supply and return temperatures were available every 5 min for the period December 19–24, 2000. The accuracy of the aggregation models has been documented as the errors in heat production and in return temperature at the DH plant between the physical network and the aggregated model. Both the Danish and the German aggregation methods work well. It is concluded that the number of pipes can be reduced from 44 to three when using the Danish method of aggregation without significantly increasing the error in heat production or return temperature at the plant. In the case of the German method, the number of pipes should not be reduced much below 10 in the Ishoej case. 2003 Elsevier Ltd. All rights reserved. Keywords: District heating; Equivalent models; Aggregated models; Dynamic simulation; Operational optimisation
1. Introduction In 1996, the Danish Ministry of Energy initiated the research project ‘‘Equivalent models of district heating systems’’. The Department of Energy Engineering (presently Department of
*
Corresponding author. Tel.: +45-46-77-5114/5100; fax: +45-46-32-1999. E-mail address: [email protected] (H.V. Larsen).
0196-8904/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.08.006
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Mechanical Engineering) at the Technical University of Denmark (DTU), together with the Systems Analysis Department at Risø National Laboratory (Risø) performed the work. In the final report,[1], a method for aggregation of DH networks was developed with regard to simulation of the transient temperatures in DH networks and a subsequent calculation of the operational costs of running the DH system. This method of aggregation is, in the following, called ‘‘the Danish method’’. Operational data from two Danish DH systems were used to make the aggregated models and to test them by making an abrupt change in the supply temperature from the plant. The errors in the return temperature at the plant between simulations based on the real network and simulations based on the aggregated networks were used to verify the aggregation method. Some of the findings in [1] were referenced in [2]. In order to develop methods for structural simplification of complex DH network systems, a combined project has been conducted at the Fraunhofer Institute for Environmental, Safety and Energy Technology (UMSICHT) in Oberhausen together with the Technical University of Gdansk, Poland, the Gdansk district heating enterprise GPEC and the EVO Energy Supply Company of Oberhausen, Germany. The project has been sponsored within the German-Polish Research Network INCREASE by the German Federal Ministry of Education and Research (BMBF) and the Polish State Committee for Scientific Research (KBN). By application of the developed prototype the DH network can be highly aggregated and calculation times can be substantially reduced. In tests based on actual data from the district heating systems of Gdansk and Oberhausen, the automatic structure simplification has been proved. It was evaluated that an 85% saving of computational time for dynamic simulations compared with non-simplified networks is possible. This method of aggregation is, in the following, called ‘‘the German method’’. It is described in detail by Loewen [3], Loewen et al. [4] and Wigbels et al. [5]. In 1999, the IEA DHC programme (IEA District Heating and Cooling Programme of Research, Development and Demonstration on District Heating and Cooling, Including the Integration of CHP) initiated the research project ‘‘Simple Models for Operational Optimisation’’ to be conducted in 1999–2002 (Annex VI). The contractor was DTU with the subcontractors UMSICHT, Korea District Heating Corporation and the Technical Research Centre of Finland. Additional funding to the project was obtained from the Danish Ministry of Energy, enabling Risø to work as a subcontractor to DTU. Previous work has been summarised in a state of the art report by Park et al. [6]. In the IEA project, aggregated models developed through use of the Danish and German methods were further tested and compared, see [7]. Here the results for the DH system of Ishoej near Copenhagen are presented as a test case. This system has rather few connected loads (23) and a very high line heat demand. The special feature of the Ishoej system is that the data collection system enables information about instantaneous heat loads and return temperatures from the heat exchanger stations.
2. Comparison of aggregation methods and models The Danish and German methods are rather similar but with some important differences as shortly discussed below. Both methods are defined for a steady state situation, but nevertheless, they are, with good accuracy used for situations with time variations.
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Both methods have the same building blocks: • A model for changing a tree structure into a line structure. • A model for removing short branches. Moreover, the German method has a model for simplification of loops. 2.1. Changing a tree structure into a line structure This basic operation is illustrated in Fig. 1. Table 1 shows the variables conserved by the aggregation. 2.2. Removing short branches The German and Danish methods differ with respect to which sub-system is regarded. The German method removes a node, replacing two branches by one, whereas the Danish method removes a (short) branch, replacing three branches by two. This is shown in Fig. 2. Table 2 shows the variables conserved by the aggregation. Both methods consider a steady state situation, i.e. a situation with no time variations. In the Danish method, it is assumed that all (primary) return temperatures from the heat loads are equal. This leads to an aggregated grid with heat loss coefficients independent of temperatures. In contrast to this, in the German method it is assumed that the return temperatures
1 2 Original grid
A
B
Equivalent grid
Fig. 1. Changing tree structure into line structure.
Table 1 Comparison of aggregation methods of tree structures Pipe length Pipe inner diameter Water volume Delay Mass flow Heat load Heat loss from supply pipe Heat loss from return pipe Pressure drop a
German method conserves
Danish method conserves
LA+LB ¼ L2 No Yes Yes Yes Yes Noa Noa Yes
No DB ¼ D2 Yes Yes Yes Yes Yes Yes Not considered
The total heat balance of supply pipe and return pipe together is kept.
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2
Original grid Danish method: 1 2
A Equivalent grid
3
Original grid
A
B
Equivalent grid
Fig. 2. Removing a short branch.
Table 2 Comparison of aggregation methods of removing short branches Pipe length Pipe inner diameter Water volume Delay Mass flow Heat load Heat loss from supply pipe Heat loss from return pipe Pressure drop a
German method conserves
Danish method conserves
Yes No Yes Yes Yes Yes Noa Noa Yes
Yes No Yes Yes Yes Yes Yes Yes Not considered
The total heat balance of supply pipe and return pipe together is kept.
are constant in time. The heat loss coefficients are adjusted so that the heat balance of the supply pipe together with the corresponding return pipe and the connected consumer is kept. The two methods have different starting points in the development of aggregated grids. The German method conserves temperatures in all nodes (in the steady state situation). Since also volume and mass flow are conserved, this implies that heat losses from the physical and the aggregated grids are not exactly the same. This holds even in a steady state situation with the same temperature in all pipes. Heat loss coefficients found by the German method can be negative in situations where loops or branches are aggregated. For compatibility to different simulation platforms, it is possible to configure the algorithm so that the heat loss coefficients remain positive. In this case, higher variations between aggregated and not aggregated networks have to be accepted. However, the Danish method focuses on heat loss, which is conserved (in the steady state situation). Consequently, the node temperatures of the physical and aggregated grids are not exactly the same. Pressure drop in the pipes is not considered by the present Danish method, whereas the German method adjusts the surface roughness (major loss coefficient) or the additional resistance (minor loss coefficient) caused by elbows etc. for each pipe in the aggregated grid in order to preserve pressure in each node. A minor loss coefficient found by this method can be negative.
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Assuming that the software program used to simulate the operation of the aggregated grid can handle negative heat loss coefficients and negative minor loss coefficients, such values will not bring about any problems. During the aggregation, the Danish method keeps track of all physical loads and supplies information as to how each physical load is divided between the aggregated loads. At the moment, such information is not supplied by the German method that only gives data on the size of each aggregated load but not on the origin of this load. 2.3. Removing loops The German method can handle loops in two ways: • Transforming a loop into serial pipes. • Splitting a loop into two serial pipes and one branch. In the latter case, the heat balances of the loops can be kept for steady state simulations. For simplification of loops into serial pipes, small errors have to be accepted. It is up to the user which method he prefers. The former case leads to a faster simplification. To remove a loop, one has to identify a specific node where the mass flows (divided at the input into the loop) flow together again. Therefore, in situations when flows meet at another node (as can occur if the consumersÕ load varies in time), the simplification will give rise to some errors. Usually, these loops are only simplified if absolutely necessary. At the moment, the Danish method is not able to handle loops. 2.4. Model of consumers’ heating installation The German method uses a prescribed return temperature, which is a function of heat load (outdoor temperature) and supply temperature. The Danish method has a specific model for the heating installation that calculates the return temperature as a function of heat load, primary supply temperature, secondary temperatures and the heat transfer area (kA) of the heat exchanger (or radiator). Different types of heating installation models have been developed, but in this paper, it is assumed that all consumers are connected through plate heat exchangers. In the aggregation process, the Danish method traces the heat load and temperature time series from the real consumers to the aggregated consumers, whereupon a new kA-value is calculated for the aggregated consumer. 2.5. Structure of aggregated networks If applied straightforwardly, the Danish method will result in a line network. However, as previously documented in [1], DH networks could be aggregated in ways that preserve parts of the original tree structure. The German method can be applied in a similar way. Depending on the parameters controlling the aggregation process, the aggregated system could be a line network or a network with some
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parts of the tree and/or loop structure preserved. The difference in the aggregation philosophy has been exemplified in the Ishoej case study, cf. Section 3.4.2.
3. The Ishoej district heating system 3.1. The DH system Ishoej is a Copenhagen suburb located 17 km southwest of the city centre. The built up area consists mainly of blocks of flats, semi-detached houses, institutions and shopping centres. Many of the buildings were erected in the 1970s. The DH system was built in 1982. Today, some 8000 dwellings, five schools and the city centre with many shops and institutions are supplied by the DH system. All consumer installations are indirectly connected through 23 substations (each substation consists of one or two plate heat exchangers). The distribution network is shown in Fig. 3. It is made of preinsulated pipes, mostly with standard insulation thickness, and with pipe dimensions from 48 to 356 mm. The total length of the network is approximately 8.3 km. As all connected buildings are situated within a small area,
Fig. 3. The distribution network in Ishoej with 23 substations.
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the line heat demand is high, approximately 42 GJ/m, and the annual heat loss (from the primary network) is only approximately 3%. To begin with, heat was produced by three coal fired boilers, each with a nominal capacity of 17 MW, and by a smaller gas fired peak load boiler. Today, the Ishoej DH system is connected to the West Copenhagen Heating Transmission Company (VEKS). The boilers have been modified for bio fuel, and the plant can supply heat both locally and to the transmission grid. The Ishoej DH company has installed an advanced control and supervision system, which, among other tasks, stores data from the substations and the plant at five minute intervals. At a typical substation, the following data are available: • • • •
primary and secondary supply temperature, primary and secondary return temperature, pressures in the supply and return line, accumulated heat meter readings (energy and volume).
At the Ishoej plant, production by the boilers and the amount of heat delivered from the VEKS system are available as well as flow, temperature and pressure measurements. 3.2. The measurements In this work, 5 min interval data from December 19–24, 2000, are used. The heat loads at the substations were obtained by filtering the heat meter data. Heat production data at the Ishoej plant were obtained from VEKS. In this period, the boilers were used only a couple of hours. Manual reading of the heat meters had taken place on December 11 and 18, and the associated heat consumption is shown in Table 3. For those substations where no data were available, heat load series were constructed from other substations with data, taking into account the type of building (block of flats, school etc.) and the heat consumption according to Table 3. To distinguish between these two kinds of substations, substations with real measurements are called Vxx or Ixx, while substations with constructed time series are called Sxx. Despite the uncertainty associated with this way of generating the missing data, the result is quite good, as shown in Fig. 4. Here, the measured heat production at the Ishoej plant is compared with the sum of the heat loads in the substations. 3.3. The consumers Table 3 shows the heat consumption at the substations the week before the time series start, as well as the average heat load in the time series for the period December 19, 12:00–December 24, 24:00. To give an impression of the type of consumers in Ishoej, heat consumption and primary and secondary supply and return temperatures for some of the 23 substations are shown in Appendix A. Several interesting things are observed: the size and time variation of the heat loads are very different, varying from 8 kW to 6.7 MW on the average, cf. Table 3, and from almost constant consumption to substations with distinct time variations (night set back). Because of the Christmas holidays at the end of the period, the consumers behave very differently, as for instance, some of the institutions are closed for the holidays.
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Table 3 The substations in the Ishoej DH system Substation
Heat meters Dec. 11–18, 2000 (GJ)
V01 V02 S03 V04 V05 V61 V62 V07 V08 V09 S10 V11 V11A V12 S13 I13 V14 S15 S17 V18 S20 S39 I79
655 524 3191 1036 260 153 201 1245 849 94 144 22 35 142 130 4 188 132 47 16 53 251 104
Average load Dec. 19–24 (MW) 1.404 1.112 6.736 2.205 0.611 0.335 0.441 2.628 1.787 0.203 0.315 0.045 0.075 0.309 0.378 0.008 0.416 0.378 0.100 0.039 0.113 0.556 0.298
Total
Category Apartments Shopping centre Apartments Apartments Apartments Shopping centre Shopping centre Apartments Apartments Apartments Apartments Apartments Apartments Apartments Public school Kindergarten Public school Public school Youth hostel Church Institution Public school Technical school
20.491
Heat load in Ishoej Dec. 19-24, 2000 30 25
MW
20 15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes Buildings
Plant
Fig. 4. Measured heat production at the plant and the sum of the (filtered) heat loads in the substations.
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3.4. Modelling the Ishoej DH system In modelling the Ishoej system, the generated data set has been used as input files to a general simulation program. Time series for heat load as well as for secondary supply and return temperatures have been used for each substation. All substations were modelled as one plate heat exchanger, and kA values were estimated from the measured heat load and measured primary and secondary supply and return temperatures. 3.4.1. Physical grid The physical grid consists of 44 branches and 23 loads. 3.4.2. Aggregation Two methods, i.e. the Danish and the German methods, have been used to aggregate the physical grid. The Danish aggregation method is described in detail by Palsson et al. [1] and Larsen et al. [2]. Likewise, Loewen [3] and Loewen et al. [4] give a description of the German method. The aggregated systems are shown in Figs. 5 and 6 and described in detail in Appendix B. These aggregated systems all represent the physical system shown in Fig. 3.
D_23 D_5 D_2
Fig. 5. Aggregated networks in Ishoej. Danish models D_23, D_5 and D_2.
G_20
G_10
G_6
G_2
Fig. 6. Aggregated networks in Ishoej. German models G_20, G_10, G_6 and G_2.
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3.4.3. Simulations Time series covering the period from December 19, 2000 12:00 until December 24, 2000 24:00 with time steps of 5 min are used in the simulations of the various systems. For the aggregated systems, where substations have been combined, heat loads are not modelled in the same way for the Danish and for the German models. Weighted sums of measured time series (heat load and secondary supply and return temperatures) are used for the Danish aggregated substations. The German method of aggregation does not supply information about how to calculate time series for the aggregated loads using information about the individual physical loads. Instead the sum of all time series for physical heat loads is distributed between the aggregated loads, i.e. all aggregated loads are varying proportionally. For the secondary supply and return temperatures, the same constant values are used for all aggregated loads. These constant values are calculated as weighted averages of the measured time series. Regarding the supply temperature from the plant, two situations are considered: • The supply temperature is as measured (i.e. varying around 105 C). See Fig. 7. • The supply temperature is 100 C for a period, and then, it is suddenly increased to 110 C. 3.4.4. Results for the Danish method of aggregation Fig. 8 shows the amount of heat supplied by the DH plant for the physical system. The supply temperature is as measured. Fig. 9 gives the error in heat production for an aggregated system with 5 branches found by the Danish method (system D_5, see Fig. 5 and Appendix B). In Appendix C, more figures showing heat production as well as return temperature and flow at the plant can be found for aggregated systems D_23, D_5 and D_2.
Supply temperature from the plant 115 110
°C
105 100 95 90 85 0
1000
2000
3000
4000
5000
6000
7000
Minutes
Fig. 7. Measured supply temperature from the plant.
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Heat production 30 25
MW
20 15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes Phys
Fig. 8. Heat production supplied by the plant for the physical system. The measured time series is used as supply temperature from the plant.
Error in Heat production 1.0
MW
0.5
0.0
-0.5
-1.0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes D_5 - Phys
Fig. 9. Error in heat production for aggregated system D_5 as compared with the physical system. The measured time series is used as supply temperature from the plant.
3.4.5. Results for the German method of aggregation Fig. 10 shows the amount of heat supplied by the DH plant for the physical system when the supply temperature from the plant is 100 C and, then, suddenly increases to 110 C. Fig. 11 gives the error in heat production for an aggregated system with 6 branches found by the German method (system G_6, see Fig. 6 and Appendix B). The curve in Fig. 11 is much smoother than the corresponding curve in Fig. 9. The reason for this is that the supply temperature from the plant in Fig. 11 is constant (except for the step), whereas the supply temperature in Fig. 9 is a measured time series with variations, cf. Fig. 7.
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H.V. Larsen et al. / Energy Conversion and Management 45 (2004) 1119–1139 Heat production 30 25
MW
20 15 10 5 0 0
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2000
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4000
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Minutes Phys
Fig. 10. Heat production supplied by the plant for the physical system. A step function is used as supply temperature from the plant.
Error in Heat production 0.5 0.0
MW
-0.5 -1.0 -1.5 -2.0 -2.5 0
1000
2000
3000
4000
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6000
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8000
Minutes G_6 - Phys
Fig. 11. Error in heat production for aggregated system G_6 as compared with the physical system. A step function is used as supply temperature from the plant.
3.4.6. Evaluation of aggregated models To assess the quality of a specific aggregated model, time series for the amount of heat supplied by the plant are found by simulating the aggregated system as well as the physical system. The standard deviation of the error between these two time series is then used as a criterion for the quality of the aggregation. Another criterion is also introduced. It is based on the standard deviation of the error between the return temperature to the plant calculated for the physical system and for the aggregated system.
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The following figures show how the standard deviation of error increases as the number of branches is reduced. The heat production at the plant is considered in the charts to the left, whereas the return temperature at the plant is considered in the charts to the right. Only models made by the Danish method of aggregation are considered here. German models will be dealt with below. For the physical system, all loads and secondary supply and return temperatures are represented by measured time series. For aggregated systems, however, time series for the loads and secondary temperatures are calculated as weighted averages of measured series. Regarding the supply temperature from the plant, two different situations are shown: • In Fig. 12, a measured time series is used as supply temperature from the plant (approximately 105 C). • In Fig. 13, a step function is used as supply temperature from the plant (step from 100 to 110 C). The definition of systems D_nn can be found in Appendix B. It is seen that the number of branches can be reduced to 3 without increasing the error too much. Model D_1, with only one branch and two loads, has a standard deviation of the error Standard deviation of return temperature difference at the plant 0.6 D_1
0.5
2.0
D_1
D_2
0.4 1.5
C
D_2 o
% of average heat production
Standard deviation of error in heat production at the plant 2.5
0.3
1.0
D_15
D_15
0.5
D_10
D_4
D_5
0.1 D_44
D_5
D_23 D_20
D_44
D_10
0.2
D_3
D_3 D_4
D_23 D_20
0.0 45
40
35
30
25
20
15
10
5
0.0 45
0
40
35
30
25
20
15
10
5
0
Number of branches
Number of branches
Fig. 12. Standard deviation of error. The measured time series is used as supply temperature from the plant.
Standard deviation of return temperature difference at the plant 0.6
2.0
0.5
D_1 D_2
0.4 1.5
D_1 oC
%of average heat production
Standard deviation of error in heat production at the plant 2.5
0.3
D_2
1.0
D_15
D_10
D_5
D_3 D_4
0.2 0.5
D_15
D_5
D_23 D_20
D_44
0.0 45
D_10
40
35
30
25
20
D_3
0.1 D_44
D_23
D_4
15
Number of branches
10
5
D_20
0
0.0 45
40
35
30
25
20
15
10
Number of branches
Fig. 13. Standard deviation of error. A step function is used as supply temperature from the plant.
5
0
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H.V. Larsen et al. / Energy Conversion and Management 45 (2004) 1119–1139
(defined on the basis of heat production at the plant) of approximately 2%, but the average error over the simulated time period is as small as 0.01%. At the moment, the German method of aggregation does not supply information about how the physical loads are divided among the aggregated loads. Therefore, the capability of such aggregated grids has to be tested with the following simpler load model: for the physical system, as well as for all aggregated systems, all load time series are modelled as fixed percentages of the time series for the total load. This means that all loads are varying proportionally and summing to the correct total load series. Secondary supply and return temperatures are constant and have the same values for all loads. These values are calculated as weighted averages of the measured temperature time series. Also, the Danish grids are tested with this simpler load model. Regarding the supply temperature from the plant, the same two situations as above are shown: • In Fig. 14, a measured time series is used as supply temperature from the plant (approximately 105 C). • In Fig. 15, a step function is used as supply temperature from the plant (step from 100 to 110 C).
Standard deviation of error in heat production at the plant
Standard deviation of error in return temperature at the plant 0.20 D_1
G_2
2.0 G_2
0.15
D_1
G_6 D_2
C
1.5 G_6
1.0
o
% of average heat production
2.5
0.10 D_2
G_10
G_10
D_3
G_20
0.05
0.5 D_23 D_20
D_15
D_44
0.0 45
35
30
25
20
15
D_3 D_23
D_4
D_10 D_5
40
G_20
10
D_20
D_15
D_10
15
10
D_4
D_44
5
0.00 45
0
D_5
40
35
Number of branches
30
25
20
5
0
Number of branches
Fig. 14. Standard deviation of error. The measured time series is used as supply temperature from the plant. A simple load model is used.
Standard deviation of error in return temperature at the plant 0.20 G_2
D_1
1.2
0.15
G_2
G_6
D_2
C
0.9 o
% of average heat production
Standard deviation of error in heat production at the plant 1.5
0.10
D_1
G_6
0.6
D_2
0.05
G_10
0.3 G_20
D_44
0.0 45
D_23
D_20
D_15
D_10
D_5
35
30
25
20
15
Number of branches
10
5
D_5
D_23 D_44
D_4
40
G_10
G_20
D_3
0
0.00 45
40
35
30
25
D_20
D_15
D_10
20
15
10
D_3 D_4
5
0
Number of branches
Fig. 15. Standard deviation of error. A step function is used as supply temperature from the plant. A simple load model is used.
H.V. Larsen et al. / Energy Conversion and Management 45 (2004) 1119–1139
1133
The definition of systems G_nn and D_nn can be found in Appendix B. From Figs. 12–15, it is seen that the number of branches can be reduced from 44 to three when using the Danish method of aggregation without significantly increasing the error in heat production or return temperature at the plant. When using the German method, the number of branches should not be reduced much below ten to guarantee a standard deviation below 0.3% for the error of heat production and 0.05 C for the error of the return temperature.
4. Discussion and conclusion In this paper two different ways of aggregating DH networks have been applied. Both the Danish and the German methods are systematic methods for changing the DH network and the heat loads (consumers) into a simpler system, which can be used for simulating and optimising the operational costs of the DH system. The goal of the present work has been to verify the aggregated models further. The DH system in Ishoej in Denmark has been used. The Ishoej DH company has supplied information from all 23 connected heat exchanger stations every 5 min. This facilitates the testing of aggregated network models in situations, that do not comply with the assumptions for making the models, i.e. all heat loads at the consumers should change in the same manner (time variation) and all return temperatures should be similar. In the work on the Ishoej DH system, 5 min values from December 19–24, 2000 are used. Because data were not available for all substations, a realistic data set had to be created from those heat exchanger stations where data existed. For the 23 substations in Ishoej, heat loads and primary and secondary supply and return temperatures were thus, available every 5 min. The accuracy of the aggregation models has been documented as the errors in heat production and in return temperature at the DH plant between the physical network and the aggregated model. Furthermore, a comparison has been made between the Danish and the German aggregation methods in the Ishoej case study. Both aggregation methods work well. The conclusion is that the number of pipes can be reduced from 44 to three when using the Danish method of aggregation without significantly increasing the error in heat production or return temperature at the plant. When using the German method, the number of pipes should not be reduced much below ten to guarantee the same errors in the case of the Ishoej DH system. The work on aggregated network models will hopefully be continued in future research projects. Some items that could be improved in the Danish and German methods appear from Tables 1 and 2. The Danish method, for instance, could be improved by the possibility of simplifying loops and conserving the pressure in the DH networks. Likewise, it would be an improvement to the German method if it were able to conserve heat loss and if it could supply information about how each physical load is divided between the aggregated loads. Some initial work has been done to improve the aggregation methods further by adjusting the parameters of the aggregated networks. One method is to minimise the squared sum of errors between the full network description and the aggregated model with respect to, for instance, the
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amount of heat stored in the network, the return temperature at the DH plant, or the pumping power. Further work is still required in this area. Finally, work is required to automate the aggregation process further, which today still requires decisions taken by an experienced researcher. Here, the goal is to make the process fully automatic or at least so simple that the operator can update the aggregated network when it is required, for instance, due to a changed load distribution or to an expansion of the DH network.
Acknowledgements We would like to thank the IEA District Heating and Cooling Programme of Research, Development and Demonstration on District Heating and Cooling, Including the Integration of CHP, Contract 524110/0010, project 2002:S1, and the Danish Ministry of Energy, J. no. 1373/010041, for funding the work. The support is gratefully acknowledged.
Appendix A. Heat loads in Ishoej DH system Figs. 16–19 show measured time series for primary and secondary supply and return temperatures as well as the load for 4 of the 23 consumers in Ishoej. The series cover the simulated period, i.e. from December 19, 2000 12:00 until December 24, 2000 24:00. The following symbols are used: • TS_Prim: Primary supply temperature. • TS_Sec: Secondary supply temperature. • TR_Prim: Primary return temperature.
24
100
20
80
16
60
12
40
8
20
4 0
0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Fig. 16. Measured time series for load L_S03.
Load [MW]
o
Temperature [ C]
Load L_S03 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
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2.4
100
2
80
1.6
60
1.2
40
0.8
20
0.4
Load [MW]
o
Temperature [ C]
Load L_V05 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
0
0 0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Fig. 17. Measured time series for load L_V05.
0.03
100
0.025
80
0.02
60
0.015
40
0.01
20
0.005
0 0
1000
2000
3000
4000
5000
6000
7000
Load [MW]
o
Temperature [ C]
Load L_I13 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
0
8000
Minutes
Fig. 18. Measured time series for load L_I13. Primary and secondary return temperatures are almost identical.
• TR_Sec: Secondary return temperature. • Load: Heat load. In Figs. 16–19, the five curves are positioned from the top and downwards according to the order in the list above. For those substations where no data were available, a heat load series was constructed from other substations with data, taking into account the type of building (block of flats, school etc.) and the heat consumption according to Table 3. To distinguish between these two kinds of substations, substations with real measurements are called Vxx or Ixx, while substations with simulated time series are called Sxx. Despite the uncertainty associated with this way of generating
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1.5
100
1.25
80
1
60
0.75
40
0.5
20
0.25
0 0
Load [MW]
o
Temperature [ C]
Load L_S15 120
TS_Prim TS_Sec TR_Prim TR_Sec Load
0 1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Fig. 19. Measured time series for load L_S15.
the missing data, the result is quite good as shown in Fig. 4, where the measured heat production at the Ishoej plant is compared with the sum of the heat loads in the substations.
Appendix B. Network data for the Ishoej DH system B.1. Aggregation by the Danish method Table 4 lists the models generated by the Danish method. The model in a specific row of the table is made from the model in the preceeding row by a further aggregation. The physical grid is shown at the top of the table. A graphical representation of some of the grids is shown in Fig. 5. Table 4 Models generated by the Danish method Model
Number of branches
Number of loads
Description
Phys D_44
44 44
23 23
D_23
23
23
D_20 D_15 D_10 D_5 D_4 D_3 D_2 D_1
20 15 10 5 4 3 2 1
20 15 10 5 4 3 2 2
The physical system All branches in-line The number of branches is not reduced All branches with no load in-between are replaced by one branch Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed Short branches are removed There is also a load at the plant
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B.2. Aggregation by the German method Table 5 lists the models generated by the German method. The physical grid is shown at the top of the table. A graphical representation of the grids is shown in Fig. 6.
Table 5 Models generated by the German method Model
Number of branches
Number of loads
Description
Phys
44
23
The physical system
G_20
20
18
Reduction of the physical system The tree structure is maintained
G_10
10
9
Further reduction The tree structure is maintained
G_6
6
5
Further reduction All branches in-line
G_2
2
2
Further reduction All branches in-line
Error in Heat production
Heat production
1.0
30 25
0.5
MW
MW
20 15
0.0
10 -0.5 5 -1.0
0 0
1000
2000
3000
4000
5000
6000
7000
8000
0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes
Minutes
D_23 - Phys
Phys
Error in Heat production
Error in Heat production
1.0
1.5 1.0
0.5
MW
MW
0.5 0.0
0.0 -0.5
-0.5 -1.0 -1.0
-1.5 0
1000
2000
3000
4000
Minutes D_5 - Phys
5000
6000
7000
8000
0
1000
2000
3000
4000
5000
6000
7000
8000
Minutes D_2 - Phys
Fig. 20. Heat production. Aggregated systems D_23, D_5 and D_2 compared with the physical system.
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H.V. Larsen et al. / Energy Conversion and Management 45 (2004) 1119–1139 Return temperature difference at the plant
Return temperature at the plant 2.0
60
1.5
50
1.0
C
0.5
30
0.0
o
o
C
40
-0.5
20
-1.0 10 -1.5 0 0
1000
2000
3000
4000
5000
6000
7000
-2.0
8000
0
1000
2000
3000
Minutes Phys
6000
7000
8000
7000
8000
Return temperature difference at the plant 2.0
1.5
1.5
1.0
1.0
0.5
0.5
C
2.0
0.0
o
C
5000
D_23 - Phys
Return temperature difference at the plant
o
4000
Minutes
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5 -2.0
-2.0 0
1000
2000
3000
4000
5000
6000
7000
0
8000
1000
2000
3000
4000
5000
6000
Minutes
Minutes D_5 - Phys
D_2 - Phys
Fig. 21. Return temperature at the plant. Aggregated systems D_23, D_5 and D_2 compared with the physical system. Flow difference at the plant
Flow at the plant
5
140
4 120
3 2
80
kg/s
kg/s
100
1 0
60
-1
40
-2 -3
20
-4
0
-5 0
1000
2000
3000
4000
5000
6000
7000
8000
0
1000
2000
3000
Minutes
5000
6000
7000
8000
6000
7000
8000
D_23 - Phys
Phys
Flow difference at the plant
Flow difference at the plant 5
5
4
4
3
3
2
2
1
1
kg/s
kg/s
4000
Minutes
0
0
-1
-1
-2
-2
-3
-3
-4
-4 -5
-5 0
1000
2000
3000
4000
Minutes D_5 - Phys
5000
6000
7000
8000
0
1000
2000
3000
4000
5000
Minutes D_2 - Phys
Fig. 22. Flow from the plant. Aggregated systems D_23, D_5 and D_2 compared with the physical system.
H.V. Larsen et al. / Energy Conversion and Management 45 (2004) 1119–1139
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Appendix C. Time series for aggregated systems in Ishoej Time series for heat production and return temperature at the plant as well as flow from the plant are shown in Figs. 20–22. In each figure, the time series for the physical system is shown at the top chart. Below this, charts follow showing the difference between three aggregated systems and the physical one. Aggregated systems (D_23, D_5 and D_2) made by the Danish method of aggregation are considered. The supply temperature from the plant is as measured. For the physical system, all loads and secondary supply and return temperatures are represented by measured time series too. For aggregated systems, however, time series for loads and secondary temperatures are calculated as weighted averages of measured series.
References [1] P alsson H, Larsen HV, Bøhm B, Ravn HF, Zhou J. Equivalent models of district heating systems. Department of Energy Engineering, Technical University of Denmark and Systems Analysis Department, Risø National Laboratory; 1999. 179 pp. ISBN 87-7475-221-9. [2] Larsen HV, Palsson H, Bøhm B, Ravn HF. An aggregated dynamic simulation model of district heating networks. Energy Conversion and Management 2002;43(8):995–1019. [3] Loewen A. Entwicklung eines Verfahrens zur Aggregation komplexer Fernw€ armenetze. Dissertation, Universit€ at Dortmund. UMSICHT-Schriftenreihe Band 29. Fraunhofer IRB Verlag 2001. [4] Loewen A, Wigbels M, Althaus W, Augusiak A, Renski A. Structural simplification of complex DH-networks. Euroheat & Power 2001:46–50. [5] Wigbels M, Althaus W, Lucht M. Nonlinear Optimisation in CHP Applications, 2002. Available at: