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László Garbai Department of Building Services and Process Engineering, Budapest University of Technology and Economics, Budapest, Hungary

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Andor Jasper Department of Building Services and Process Engineering, Budapest University of Technology and Economics, Budapest, Hungary

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Róbert Sánta Department of Mechanical Engineering and Material Sciences, Institute of Engineering Sciences, University of Dunaújváros, Táncsics Mihály 1/A, 2400 Dunaújváros, Hungary

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https://orcid.org/0000-0001-7559-2758
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Abstract

This study examines the economic optimisation of existing district heating systems. A new approach has been taken to solving a long-standing problem. The authors describe the input-output model of the system, the balance equations for the thermal equilibrium of the system, and the heat transfer system. From the balance equations of the series-connected system elements, the resultant heat transfer balance equation and the resultant power transmission equation are derived. In an example, the authors detailed how perturbations in some input variables can be corrected with other variables. The equations presented and the concepts introduced form absolutely new scientific results.

Abstract

This study examines the economic optimisation of existing district heating systems. A new approach has been taken to solving a long-standing problem. The authors describe the input-output model of the system, the balance equations for the thermal equilibrium of the system, and the heat transfer system. From the balance equations of the series-connected system elements, the resultant heat transfer balance equation and the resultant power transmission equation are derived. In an example, the authors detailed how perturbations in some input variables can be corrected with other variables. The equations presented and the concepts introduced form absolutely new scientific results.

1 Introduction

This study examines the economic optimisation of existing district heating systems. In the case of existing district heating systems, for the given pipe network and mechanical equipment, the task is to minimise the combined annual cost of system operation, circulation, and heat loss in line with the current consumer heating power needs. Therefore, the optimal flow and backward water temperatures and the circulated volume flow rate must be determined for the operating conditions examined.

1.1 Literature background

The economic optimisation of district heating systems has always been the focus of interest. There is a huge literature on the subject, and it is well known that the time to improve results is very fast as computing technology develops. In our papers, we therefore only provide a sketchy overview of the literature. The common feature of all the models developed was, that all consumers were condensed into the centre of gravity of the consumer circle. Then, based on the principle of one consumer, one heat source, the pumping cost and heat loss of the network were modelled at different primary forward and backward hot water temperatures. With these parameters, the resulting cost was calculated, and the lowest value was selected. The models provide information on optimal operating parameters. With the possibilities provided by today's computer technology, we now have a way to consider the operational possibilities of each consumer and calculate the flow pattern by taking actual geographical transport routes, pumping work, and heat loss into account in detail [1, 2].

Studies [3, 4] present the mathematical models and economic aspects used in the development of the software in addition to experiences of using already developed software. Module implementation is advantageous, as individual subsystems can be optimised separately. The system includes heat generating units and considers the effects of combined electricity production. In the case of combined production, it examines the use of pipes as thermal buffers during peak electricity consumption, but due to regulation difficulties, only the results of test calculations are being processed currently. The heat-generating units were tested at daily time intervals, which may not be appropriate at the annual level considering the time constant of extensive systems. In paper [5], a fully dynamic model of hydraulic transient and thermal dynamic processes is proposed, and the optimal spatial and temporal step sizes for the thermal dynamic model are selected. They validate your proposed fully dynamic model by comparing it with the widely used pseudo-dynamic model simulation in the simulation environment. In the paper [6], a PHLC minimization model for an existing DH system was constructed. A programme was designed to use MATLAB software to solve the optimisation model. The minimal PHLC is lower when regulating the main water mass flow rate (PMF) and the secondary water mass flow rate (SMF) simultaneously. The paper [7] outlines a methodological approach to determining optimal parameters for district heating systems with multiple heat sources. This approach uses a modified dynamic programming optimisation method, which allows for the determination of optimal parameters without decomposing the system into heat source service areas. A dynamic simulation tool is presented in this study [8] for assessing and optimising the performance of district heating and cooling systems. It considers factors such as building requirements, weather, energy costs, and more. The tool calculates fluid temperatures and simulates the pipeline network using plug-flow methodology. It also helps choose urban zones and optimises system design and operational parameters. By utilising a MatLab simulation model, the tool provides valuable design criteria and feasibility studies. A new thermo-hydraulic model for district heating system simulation is presented in [9]. The model simulates renewable networks with fluctuating energy profiles. Heat transmission over long pipes is modelled using a Lagrangian numerical approach. By avoiding numerical diffusion, this approach reduces computation time and improves result accuracy. A method for the simulation of district heating networks was shown by Zhao [10], in which the main characteristics of the network, e.g., the temperature differential, time constant, and heat output, are determined through the statistical processing of selected representative data. This method primarily enables the simulation of already extensive networks. The study [11] draws attention to problems arising from the complexity of district heating systems. Due to the extreme inhomogeneity of the plant optimisation model, several mathematical methods are recommended for these tasks simultaneously, such as discrete DP, Lagrange relaxation, and linear programming. The authors of the paper [12] propose two models for simulating large networks and analysing the optimal control strategy for a pumping system. The first model is a fluid dynamic model based on mass and momentum conservation equations, considering the network topology through a graph approach. The second model is a reduced model derived from the fluid dynamic model, using POD and RBF. POD is a reduction technique that reduces computational cost without losing important information, capturing the main features of the problem using fewer eigenfunctions. The paper [13] addresses the operation planning problem of a district heating and cooling plant. The problem is formulated as a multiobjective, nonlinear programming problem. To solve this problem, an interactive fuzzy satisficing method is proposed. Additionally, a particle swarm optimisation approach is introduced to find an approximate solution for the nonconvex problem with a large number of decision variables. The proposed method is evaluated using the operation planning problem of a real district heating and cooling plant to test its feasibility and effectiveness. Loewen et al. [14] presented the theoretical background of the pumping optimisation module of the software system. He only deals with control options and draws attention to the fact that, due to subsequent modifications of the planned hydraulic networks and load changes, the pumps never operate at the design point. The method compares the results of two network simulations based on a measurement result and a prescribed result. These can be traced back to a linear optimisation task. A polynomial approximation is used to model the characteristics of the pumps. Among the models mentioned above, the research of Szánthó [15] can be highlighted. This study [16] proposes a procedure to optimise the design of a DHN. The objective is to minimise pumping energy consumption and thermal energy losses while maximising annual revenue. District heating systems, with their high storage capability and dynamic thermal behaviour, can effectively support the operation of integrated energy systems with a significant share of renewable energy. However, current analysis methods for these systems are limited as they separate hydraulic and thermal equations, making it difficult to analyse the interactions within the integrated energy system. This paper [17] introduces a new method that combines hydraulic and dynamic thermal behaviour into a single-equation system. This coupled approach, using the Newton-Raphson power flow calculation, improves accuracy and allows for a more comprehensive analysis of the system's interdependencies. The study [18] aimed to create a solver algorithm specifically designed for DH networks, allowing for steady-state hydraulic analysis. The research objectives included developing an input/interface for representing the network in a mathematical form, creating an algorithm to model the network structure for steady-state hydraulic analysis, and developing a fast matrix-based solution algorithm for obtaining flow and pressure distribution in the DH network.

1.2 Research objectives

In our research, we determined the complex, systematic optimisation of the operation of existing district heating systems. Our goal is to determine the forward hot water temperature and circulated hot water volume flow for heat demands that occur stochastically as a function of the external temperature, with which the operating cost of the system is minimal. We achieve this objective by writing and solving an input-output model.

The power transmission coefficient − in a certain sense, the analogue of the heat transfer coefficient applied to complex wall structures − enables the calculation of variable operating modes with extreme simplicity, and it can be shown that with different input parameters, the heat output can be delivered to the heated space. In our research, we investigated how to maintain a constant internal air temperature. If we decrease the secondary system temperature drop, what are the suitable values of the secondary mass flow rate required so that we can correct the temperature decrease given the various external air temperatures.

2 Input-output model of the elements of district heating system

In our research, in association with the former literature, we examine two main elements of operating costs: the cost of heat loss and the cost of circulation. It is known that by increasing the temperature of incoming hot water, the volume flow of circulated hot water can be reduced. In this case, network heat loss increases, but the energy requirement and cost of circulation decrease. By reducing the flow temperature of hot water, the relationship is reversed.

It is evident that there is a minimum of costs, for which the forward hot water temperature and circulated hot water volume flow rate represent the optimal operating points of the system. To carry out the optimisation, one must have reliable knowledge of the system, the system data affecting the heat loss, and the circulation power requirement. Before carefully executing the optimisation, we must be able to solve the hydraulic problems known as base and inverse interpreted for the district heating system. Below, we define and analyse the base and inverse problems and their solutions. Again, we emphasise that both the implementation of the optimisation and the solution of the basic and inverse tasks that prepare them require the construction of an input-output model of the district heating system.

  • As defined in [1], for the base problem (or task), optimal forward characteristics (pump characteristics and operating point) are determined for known heat consumptions, consumption options, and network characteristics.

Part of this task is preparing the hydronic balancing plan for the network and determining the hydraulic endpoint, also known as the determining hydraulic circle.

  • As defined in [1], the goal of the inverse problem (or task) is to determine the flow pattern and resulting consumptions, as well as the consumption possibilities, for given feed- (pump characteristics) and network characteristics (resistance factors).

The inverse problem is actually a test for the network. By solving the problem, it can be analysed how the operating and working points of the heating centres change and comfort conditions for the consumers, especially internal temperatures, develop for different, methodically, consciously, or randomly changed feeding characteristics or feeding characteristics resulting from perturbances.

Through the solution of the base problem, also relying on the inverse task, the goal is to determine the optimal feed characteristics, which can be done with a systematic search-and-try algorithm or with a specifically intelligent algorithm, among which dynamic programming can be considered.

Solving both the base and the inverse problems means solving a system of simultaneous equations expressing the energy balance of the system elements. Both tasks examine the thermal balance of the system with different inputs and different outputs. The heat balance is presented for heating needs.

To perform the hydraulic base and inverse task, let us review the input-output models of the system elements (see Fig. 1) and how changing the operation of one element affects the operation of the subsequent element in the row.

Fig. 1.
Fig. 1.

Simplified input-output model of the district heating system [19]

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

2.1 Analysis of the heat balance of the district heating system

The model presented in Fig. 1 can be interpreted as a model with concentrated or distributed parameters. The balance equations of the energy model describe the balance of heating power from the central heating heat exchangers, the heat emitters of the living space, and the heat loss of the apartment. Basic equations for the heating powers can be written to check the heat balance of the district heating system:

Heat loss of an apartment:

Q˙=(kA)lak(tbtk)+nVρc(tbtk).

Performance of a heat emitter:

Q˙=(kA)rad(t2+t22tb).

Heat transfer by the heating system:

Q˙=m˙2c(t2t2).

Performance of the heat exchanger:

Q˙=(kA)HE(t1t2)(t1t1)ln(t1t2)(t1t1).

Heat transfer by the primary system:

Q˙=m˙1c(t1t1).

The Bošnjaković factor for countercurrent heat transfer:

ϕ(W˙1,W˙2)=t1t1t1t2.

In the actual calculations, we must consider the heat loss for heat transportation through pipelines.

2.2 Secondary water temperature as a function of outside temperature

The heat emitted by the radiator if the surface area of the radiator is known:
Q˙rad=kradArad(t2+t22tb)=kradAradt,
In this equation, Q˙rad and Arad is known, and Q˙rad is a function of the external (tk) temperature, because Q˙rad has to be equal to the heat load of the heated space, that is:
Q˙rad(tk)=(kA+nVρc)(tbtk).
The value of krad is a function of the average over-temperature of the radiator.
krad=k0tkM,M=0,25÷0,33
k0 = constant, its value depends on the type of radiator.
Q˙rad(tk)=k0AradΔtk1+M.
The average over-temperature of the radiator can be determined as a function of Q˙rad(tk),
Δtk=[Q˙rad(tk)k0Arad]11+M
and
t2+t22tb=[Q˙rad(tk)k0Arad]11+M.
If we consider
Q˙rad=m˙2c(t2t2)

We have two equations for the exact determination of t2 and t2.

From Eqs. (12) and (13), the temperatures of the flow and backward heating water are:
t2=tb+[Q˙rad(tk)k0Arad]11+M+Q˙rad(tk)2m˙2c,
t2=t2Q˙rad(tk)m˙2c.

To use Eqs. (14) and (15), we must make further assumptions, i.e.,

  1. -in the case of a constant secondary mass flow rate, we take the base value of the secondary circulated mass flow m˙2 expediently as the largest dimensioning value,
  2. -alternatively, we can take the value of t2 and t2 for the sizing (nominal) state tk=1215, with which we can calculate the secondary heating mass flow m˙2 to be circulated.

We must point out that the heat demand Q˙rad in the equations is random variable with a measurable uncertainty.

A density function, probability distribution, confidence level, and confidence band can be assigned to its values. This issue is analysed in detail in the literature [1]. The uncertainty of the secondary flow and backward water temperatures determined according to the above is reflected in the uncertainty of the external temperature tk.

2.3 Determining the temperature of the primary hot water as a function of the outside temperature, as well as the secondary flow and backward water temperatures

Performance of the heating heat exchanger:
Q˙heat=kAHEt1t2(t1**t2**)lnt1t2t1**t2.

Since Q˙heatQ˙rad(tk) is known, and t2 and t2 are also known based on the above, by solving (14), t1 and t1** are the only unknowns, the following two equations are available for determining them:

From the primary heat transportation equation
t1t1**=Q˙heat(tk)m˙1c,
and from Eq. (16)
lnt1t2t1**t2=kAHE[(t1t2)(t1**t2)]1Q˙heat(tk),
and with further rearrangement.
lnt1t2t1**t2=[kAHE(t1t1**)+kAHE(t2t2)]1Q˙heat(tk).

It is advisable to set the value of t1 and t1** to the nominal values and, with the help of Eq. (16) t2 and t2 - determine the size of the heating heat exchanger AHE .

Then, of course, m˙1 can also be determined from Eq. (17).

Knowing this, the values of primary hot water temperatures – t1 and t1** - are obtained by solving Eqs. (17) and (19) for states with lower heat demand.
t1**=Q˙heat(tk)m˙1c+t2ekAHEm˙1c+kAHEQ˙heat(tk)(t2t2)t2ekAHEm˙1c+kAHEQ˙heat(tk)(t2t2),
t1=t1**+Q˙heat(tk)m˙1c.

3 Connecting elements of the district heating system

The connection of the system components means the connection of the primary hydraulic system, the consumer heat center, the heating and domestic hot water heat exchanger, the secondary hydraulic system, the heat emitters, and the apartment as hydraulic and thermodynamic transfer members. Both the base and the inverse problems can be solved using the simultaneous equation system, described in Chapter 2.1.

3.1 Solving the base task

For a given room and external air temperatures, the appropriate radiator and heat exchanger working points can be calculated, and by solving the base problem, the primary and secondary circulation characteristics can be determined. In the basic task, by definition, the given known variables and unknowns can be chosen as follows:

Given variable tb.

Unknown variable m˙1,m˙2,W˙1,W˙2,t1,t1,t2,t2.

The solution process:

  • Heat demand Q˙ is determined with a set reliability level as a function of the room and external temperatures and calculated for the actual external temperature.

  • values of the primary circulated mass flow and heat capacity rate s m˙1,W˙1 for the optimal working point of the primary circulation pump or in its vicinity are used.

  • value of m˙2 the most efficient working point is selected on the curve of the circulation pump.

  • The Bošnjaković factor Φ(W˙1,W˙2) is calculated using the chosen values of heat capacity rates.

  • A value for the primary hot water temperature t1 is chosen.

  • The value of the primary backward water temperature t1 is determined.

  • The value of the secondary backward water temperature t2 is calculated.

In the base task, the optimisation of the operation can be defined, so the task is to realise the required internal temperature with circulation parameters, resulting in minimal cost of operation for a given period.

3.2 Solution for the inverse problem: derivation of the power transmission coefficient

In the inverse task, in addition to various input variables, we look for the resulting heat balance, the transferable heat output, the resulting internal air temperature, and the primary and secondary water temperatures coming from the heat exchangers. In the inverse problem, the primary and secondary characteristics entering the heat exchanger of the heat centre are given, as well as the external meteorological characteristics, primarily the external temperature: tk. In addition, the thermal technical parameters of the heat exchanger and the heat emitter are also known, of course. We are looking for the established thermal balance, primarily the resulting air temperature. The given and unknown variables can be defined as the following:

  • given variable: t1,m˙1,W˙1,m˙2,W˙2.

  • unknown variable: Q˙,tb,t2,t2,t1**.

The solution can be obtained in two ways. The problem is the logarithmic temperature difference tk for the heat exchanger, in which some of the variables are present in an implicit form. Therefore, solving the system of equations is only possible iteratively. In many cases, the logarithmic temperature difference can be well approximated by the arithmetic mean value, in which case the solution of the system of equations becomes less complicated. The solution of the system of equations expressed in both non-linear and linear forms is presented below in detail.

3.2.1 Solving the inverse problem based on the nonlinear heat exchanger equation

The basic equations to be used are the following.

Balance of primary and secondary system heat transfer:
m˙1c1(t1t1)=m˙2c2(t2t2).
The Bošnjaković factor:
t1t1t1t2=Φ(w˙1,w˙2).
The heat release of the heating heat exchanger and the heat emitter:
(kA)HE(t1t2)(t1t2)lnt1t2t1t2=(kA)rad(t2+t22tb).
The heat release of the heat emitter and the heat load of the apartment:
(kA)rad(t2+t22tb)=(kA)lak(tbtk).
For precise calculations, the ventilation heat loss must also be included in the apartment's heat balance.
((kA)lak+nVρc)(tbtk)
Equation obtained after derivation:
(kA)HEB(t2CD)lnt1t2t2E+F=(kA)rad(t2C+D2GH).
From this, the equation for t2 is:
2(kA)HEB(t2CD)lnt1t2t2E+F(kA)radCG+2HGCDC=t2.

3.2.2 Solving the inverse problem with linearization of the heat exchanger equation

A simple, explicit solution is obtained by linearizing the heat exchanger equation. For the solution, instead of the logarithmic mean temperature tk, we use the arithmetic mean temperature difference. The basic equations are presented below:

The heat transport of the primary system:
Q˙m˙1c1=t1t1.
Performance of the heating heat exchanger:
2Q˙(kA)HE=t1+t1(t2+t2).
Heating power of the heat emitter:
Q˙(kA)rad=t2+t22tb.
Heat loss of the apartment:
Q˙(kA)lak=tbtk.
From the addition of Eqs. (29) and (31):
Q˙m˙1c1+2Q˙(kA)HE=2t1(t2+t2).
From the addition of Eqs. (29) and (32):
Q˙(kA)rad+Q˙(kA)lak=t2+t22tk.
After rearranging:
Q˙m˙1c1+2Q˙(kA)HE+2Q˙(kA)rad+2Q˙(kA)lak=2t12tk.
Rearranging for Q˙:
Q˙=11m˙1c1+2(kA)HE+2(kA)rad+2(kA)lak(t1tk).

The above equation shows complete similarity with, for example, heat conduction and heat transfer taking place in a complex wall structure. Equation (36) will be referred to as the power transmission coefficient.

From the equation above, the power transmission coefficient is:
k=112m˙1c1+1(kA)HE+1(kA)rad+1(kA)lak.
With the Bošnjaković factor, omitting the derivation:
k=11(kA)rad+1(kA)lak+1m˙1cϕ12m˙2c.

Analysing the balance equations, we can notice that by introducing the Bošnjaković factor to the heat exchanger, the problem of calculating the mean temperature difference can be circumvented. As we know, the heat transfer coefficient of the radiator depends on the average temperature difference, which is expressed by Eq. (11).

By taking into account the temperature dependence of the heat transfer coefficient of the heat emitter, the power transmission coefficient is:
k=11(kA)lak+1m˙1cϕ+(1kA)11+MQ11+M112m˙2c.
According to the above, the power transmission coefficient can be interpreted separately for the primary system and separately for the secondary system. The heat transfer for the primary system only:
Q˙[12m˙1c+1(kA)HE+12m˙2c]=t1t2.
The heat transfer is exclusively for the secondary system:
Q˙[12m˙2c+1(kA)rad+1(kA)lak]=t2tk.

The Bošnjaković factor is used to connect linear and non-linear problem management. More precisely, we solve the non-linear problem at the same time since we can dispense with the use of the non-linear heat exchanger equation. It is emphasised that the above reasoning and derivations are based on the application and applicability of the laws of thermal conductivity and the so-called hydraulic Ohm's law. This proves that these are absolutely new research results.

4 Results. Application of the procedures

Equations (36)(41) are relationships that include all operating parameters of the district heating system and the effect of all intervening and controlling variables on the output variables. They can be used to determine the sensitivity of the system, namely how changes in the input variables affect the output variables. Another application of the presented procedures and equations is to see how the operating costs vary by scaling the spectrum of intervening variables, i.e., by calculating their set of values, and the smallest of these is obviously the optimal operating cost. In the following, the actual calculation of the cost optimum will be ignored, but a sensitivity analysis will be carried out for an average district heating system in Hungary, taking into account the heat demand of an average district heated apartment.

In the following, a calculation example is presented to show what happens in the unit apartment if we start to reduce the flow and backward temperature in the secondary system. What secondary mass flow rate is needed to compensate for the temperature drop?

In the case of a constant secondary mass flow rate, we can use the base value of the secondary circulated mass flow m˙2, for which the largest sizing value: m2=214,2kgh should be selected.

Input values for the simulation:

The heat demand of the apartment's secondary heating system is 5000W. The calculations are performed for external temperatures tk=15,10,5,0,5,10. The heat loss factor of the apartment: kAlak=143WK . Heat loss factor of the radiator: kArad=83WK. The internal air temperature is tb=20.

Figures 27 show the interrelated parameters that ensure the thermal balance of a family apartment depending on the external temperature while ensuring constant internal temperature of 20 °C.

Fig. 2.
Fig. 2.

The change in the mass flow of water as a function of the decrease in the temperature step if the external temperature: tK=15

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

Fig. 3.
Fig. 3.

The change in the mass flow of water as a function of the decrease in the temperature step if the external temperature: tK=10

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

Fig. 4.
Fig. 4.

The change in the mass flow of water as a function of the decrease in the temperature step if the external temperature: tK=5

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

Fig. 5.
Fig. 5.

The change in the mass flow of water as a function of the decrease in the temperature step if the external temperature: tK=0

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

Fig. 6.
Fig. 6.

The change in the mass flow of water as a function of the decrease in the temperature step if the external temperature: tK=5

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

Fig. 7.
Fig. 7.

The change in the mass flow of water as a function of the decrease in the temperature step if the external temperature tK=10

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00692

5 Conclusion

This study examines the economic optimisation of district heating systems. A new approach has been taken to solving a long-standing problem. From the balance equations of the series-connected system elements, the resultant heat transfer balance equation and the resultant power transmission equation are derived. With the help of the equations presented in this work, the heat balance of district heating systems can be comprehensively investigated with different combinations of input characteristics. The primary and secondary forward temperatures and circulated mass flow rates can be determined to maintain the specified internal temperature for different external temperatures and heating power requirements. It can be demonstrated that varied input parameters may be used to calculate variable operating modes with the power transmission coefficient Eq. (39) and provide the heat output to the heated area. This way, the resulting air temperature can also be calculated. The new Eq. (39) can be used to design all complex DHS, which ranges from 10 to 500 MW. The equations presented and the concepts introduced form absolutely new scientific results. The power transmission coefficient provides a kind of universality for connecting the operating states of the primary and secondary systems and for the simultaneous examination of the inverse and basic tasks. In the decentralised, complex optimisation model, this enables the simple calculation of the working points of the primary and secondary systems. This makes easy determination of the optimal system working point possible.

In our research, we defined the optimisation of operation, i.e., the task of determining the required internal temperature with which circulation parameters and, therefore, the cost of operation is minimal for a given period. The cost of operation is the combined cost of circulation and heat loss. A smaller mass flow reduces the cost of pumping, but the system must be operated at a higher temperature. This increases the cost of heat loss. With the help of the power transmission equation, the input and control parameters can be determined for each external temperature, at which point the operating cost reaches a minimum. No concrete cost optimisation was carried out, only a framework for the calculations was provided and an example was given to show how possible changes in the intervening characteristics or changes implemented can be corrected by specifying other characteristics.

Nomenclature

A [m2]

surface

c [kJ/kgK]

specific heat capacity

d [m]

diameter

k [W/m2K]

heat transfer coefficient

m˙ [kg s−1]

mass flow rate

Q˙ [W]

heat demand

R [K/W]

thermal resistance

t [°C]

temperature

V˙ [m3 s−1]

volumetric flow rate

n [1/h]

air change rate

W˙ [W/K]

heat capacity rate

K

cost

Greek symbols

ρ [kg m−3]

density

ϕ [-]

Bosnjakovic factor

τ [s]

time

Index

primary circuit

’’

secondary circuit

HE

heat exchanger

b

internal

k

external

lak

apartment

rad

radiator

heat

heating

v

backward

e

forward

p

primary

s

secondary

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    G. Barone, A. Buonomano, C. Forzano, and A. Palombo, “A novel dynamic simulation model for the thermo-economic analysis and optimisation of district heating systems,” Energy Convers. Manage., vol. 220, 2020, Art no. 113052. https://doi.org/10.1016/j.enconman.2020.113052.

    • Search Google Scholar
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    A. Dénarié, M. Aprile, and M. Motta, “Dynamical modelling and experimental validation of a fast and accurate district heating thermo-hydraulic modular simulation tool,” Energy, vol. 282, 2023, Art no. 128397.

    • Search Google Scholar
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    H. Zhao and J. Holst, “Study on a network aggregation model in DH systems,” Euroheat Power, vol. 27, pp. 3844, 1998.

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    D. Dobersek and D. Goricanec, “Optimisation of tree path pipe network with nonlinear optimization method,” Appl. Therm. Eng., vol. 29, pp. 15841591, 2008. http://doi.org/10.1016/j.applthermaleng.2008.07.017.

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    E. Guelpa, C. Toro, A. Sciacovelli, R. Melli, E. Sciubba, and V. Verda, “Optimal operation of large district heating networks through fast fluid-dynamic simulation,” Energy, Vol. 102, pp. 586595, 2016. http://doi.org/10.1016/j.energy.2016.02.058.

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    M. Sakawa and T. Matsui, “Fuzzy multi objective nonlinear operation planning in district heating and cooling plants,” Fuzzy Sets Syst., vol. 231, pp. 5869, 2013. https://doi.org/10.1016/j.fss.2011.10.020.

    • Search Google Scholar
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    M. A. Ancona, F. Melino, and A. Peretto, “An optimization procedure for district heating networks,” Energy Proced., vol. 61, pp. 278281, 2014. http://doi.org/10.1016/j.egypro.2014.11.1107.

    • Search Google Scholar
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    Z. Szánthó and B. Némethi, “Measurement study on demand of domestic hot water in residential buildings,” in 2nd IASME/WSEAS Int. Conf. on Energy & Environment, 2007, pp. 6873.

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    W. Wang, X. Cheng, and X. Liang, “Optimization modelling of district heating networks and calculation by the Newton method,” Appl. Therm. Eng., vol. 61, pp. 163170, 2013. http://doi.org/10.1016/j.applthermaleng.2013.07.025.

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    J. Danker and M. Wolter, “Improved quasi-steady-state power flow calculation for district heating systems: a coupled Newton-Raphson approach,” Appl. Energy, vol. 295, 2021, Art no. 116930. https://doi.org/10.1016/j.apenergy.2021.116930.

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    H. I. Tol, “Development of a physical hydraulic modelling tool for District Heating systems,” Energy Build., vol. 253, 2021, Art no. 111512. https://doi.org/10.1016/j.enbuild.2021.111512.

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    A. Jasper, Optimization of District Heating System Design and Operation (In Hungarian), PhD Dissertation, 2017.

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    L. Garbai, District Heating (In Hungarian), 2012, ISBN: 978-963-279-739-7.

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    L. Garbai, A. Jasper, and Z. Magyar, “Probability theory description of domestic hot water and heating demand,” Energy Build., vol. 75, pp. 483492, 2014. https://doi.org/10.1016/j.enbuild.2014.01.050.

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    R. Poggemann, “Anwender Erfahrungen mit einem neu entwickelten, EVD-Werkzeug zur Optimierung von Fernwarme Systemen,” Euroheat Power, vol. 27, pp. 6877, 1998.

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    G. Stock and A. Mertsch, “Betriebs Optimierung mit Bofist am Beispiel einer Fernwarme Verbundnetzes,” Euroheat Power, vol. 26, pp. 565572, 1997.

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    Y. Wang, X. Wang, L. Yheng, X. Gao, Y. Wang, S. You, H. Yhang, and S. Wei, “Thermo-hydraulic coupled analysis of long-distance district heating systems based on a fully-dynamic model,” Appl. Therm. Eng., vol. 222, 2023, Art no. 119912. https://doi.org/10.1016/j.applthermaleng.2022.119912.

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    P. Jie, N. Zhu, and D. Li, “Operation optimization of existing district heating systems,” Appl. Therm. Eng., vol. 78, pp. 278288, 2015. https://doi.org/10.1016/j.applthermaleng.2014.12.070.

    • Search Google Scholar
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  • [7]

    V. A. Stennikov, E. A. Barakhtenko, and D. A. Sokolov, “A methodological approach to the determination of optimal parameters of district heating systems with several heat sources,” Energy, vol. 185, pp. 350360, 2019. https://doi.org/10.1016/j.energy.2019.07.048.

    • Search Google Scholar
    • Export Citation
  • [8]

    G. Barone, A. Buonomano, C. Forzano, and A. Palombo, “A novel dynamic simulation model for the thermo-economic analysis and optimisation of district heating systems,” Energy Convers. Manage., vol. 220, 2020, Art no. 113052. https://doi.org/10.1016/j.enconman.2020.113052.

    • Search Google Scholar
    • Export Citation
  • [9]

    A. Dénarié, M. Aprile, and M. Motta, “Dynamical modelling and experimental validation of a fast and accurate district heating thermo-hydraulic modular simulation tool,” Energy, vol. 282, 2023, Art no. 128397.

    • Search Google Scholar
    • Export Citation
  • [10]

    H. Zhao and J. Holst, “Study on a network aggregation model in DH systems,” Euroheat Power, vol. 27, pp. 3844, 1998.

  • [11]

    D. Dobersek and D. Goricanec, “Optimisation of tree path pipe network with nonlinear optimization method,” Appl. Therm. Eng., vol. 29, pp. 15841591, 2008. http://doi.org/10.1016/j.applthermaleng.2008.07.017.

    • Search Google Scholar
    • Export Citation
  • [12]

    E. Guelpa, C. Toro, A. Sciacovelli, R. Melli, E. Sciubba, and V. Verda, “Optimal operation of large district heating networks through fast fluid-dynamic simulation,” Energy, Vol. 102, pp. 586595, 2016. http://doi.org/10.1016/j.energy.2016.02.058.

    • Search Google Scholar
    • Export Citation
  • [13]

    M. Sakawa and T. Matsui, “Fuzzy multi objective nonlinear operation planning in district heating and cooling plants,” Fuzzy Sets Syst., vol. 231, pp. 5869, 2013. https://doi.org/10.1016/j.fss.2011.10.020.

    • Search Google Scholar
    • Export Citation
  • [14]

    M. A. Ancona, F. Melino, and A. Peretto, “An optimization procedure for district heating networks,” Energy Proced., vol. 61, pp. 278281, 2014. http://doi.org/10.1016/j.egypro.2014.11.1107.

    • Search Google Scholar
    • Export Citation
  • [15]

    Z. Szánthó and B. Némethi, “Measurement study on demand of domestic hot water in residential buildings,” in 2nd IASME/WSEAS Int. Conf. on Energy & Environment, 2007, pp. 6873.

    • Search Google Scholar
    • Export Citation
  • [16]

    W. Wang, X. Cheng, and X. Liang, “Optimization modelling of district heating networks and calculation by the Newton method,” Appl. Therm. Eng., vol. 61, pp. 163170, 2013. http://doi.org/10.1016/j.applthermaleng.2013.07.025.

    • Search Google Scholar
    • Export Citation
  • [17]

    J. Danker and M. Wolter, “Improved quasi-steady-state power flow calculation for district heating systems: a coupled Newton-Raphson approach,” Appl. Energy, vol. 295, 2021, Art no. 116930. https://doi.org/10.1016/j.apenergy.2021.116930.

    • Search Google Scholar
    • Export Citation
  • [18]

    H. I. Tol, “Development of a physical hydraulic modelling tool for District Heating systems,” Energy Build., vol. 253, 2021, Art no. 111512. https://doi.org/10.1016/j.enbuild.2021.111512.

    • Search Google Scholar
    • Export Citation
  • [19]

    A. Jasper, Optimization of District Heating System Design and Operation (In Hungarian), PhD Dissertation, 2017.

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Senior editors

Editor-in-Chief: Ákos, LakatosUniversity of Debrecen, Hungary

Founder, former Editor-in-Chief (2011-2020): Ferenc Kalmár, University of Debrecen, Hungary

Founding Editor: György Csomós, University of Debrecen, Hungary

Associate Editor: Derek Clements Croome, University of Reading, UK

Associate Editor: Dezső Beke, University of Debrecen, Hungary

Editorial Board

  • Mohammad Nazir AHMAD, Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia

    Murat BAKIROV, Center for Materials and Lifetime Management Ltd., Moscow, Russia

    Nicolae BALC, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Umberto BERARDI, Toronto Metropolitan University, Toronto, Canada

    Ildikó BODNÁR, University of Debrecen, Debrecen, Hungary

    Sándor BODZÁS, University of Debrecen, Debrecen, Hungary

    Fatih Mehmet BOTSALI, Selçuk University, Konya, Turkey

    Samuel BRUNNER, Empa Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland

    István BUDAI, University of Debrecen, Debrecen, Hungary

    Constantin BUNGAU, University of Oradea, Oradea, Romania

    Shanshan CAI, Huazhong University of Science and Technology, Wuhan, China

    Michele De CARLI, University of Padua, Padua, Italy

    Robert CERNY, Czech Technical University in Prague, Prague, Czech Republic

    Erdem CUCE, Recep Tayyip Erdogan University, Rize, Turkey

    György CSOMÓS, University of Debrecen, Debrecen, Hungary

    Tamás CSOKNYAI, Budapest University of Technology and Economics, Budapest, Hungary

    Anna FORMICA, IASI National Research Council, Rome, Italy

    Alexandru GACSADI, University of Oradea, Oradea, Romania

    Eugen Ioan GERGELY, University of Oradea, Oradea, Romania

    Janez GRUM, University of Ljubljana, Ljubljana, Slovenia

    Géza HUSI, University of Debrecen, Debrecen, Hungary

    Ghaleb A. HUSSEINI, American University of Sharjah, Sharjah, United Arab Emirates

    Nikolay IVANOV, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Antal JÁRAI, Eötvös Loránd University, Budapest, Hungary

    Gudni JÓHANNESSON, The National Energy Authority of Iceland, Reykjavik, Iceland

    László KAJTÁR, Budapest University of Technology and Economics, Budapest, Hungary

    Ferenc KALMÁR, University of Debrecen, Debrecen, Hungary

    Tünde KALMÁR, University of Debrecen, Debrecen, Hungary

    Milos KALOUSEK, Brno University of Technology, Brno, Czech Republik

    Jan KOCI, Czech Technical University in Prague, Prague, Czech Republic

    Vaclav KOCI, Czech Technical University in Prague, Prague, Czech Republic

    Imre KOCSIS, University of Debrecen, Debrecen, Hungary

    Imre KOVÁCS, University of Debrecen, Debrecen, Hungary

    Angela Daniela LA ROSA, Norwegian University of Science and Technology, Trondheim, Norway

    Éva LOVRA, Univeqrsity of Debrecen, Debrecen, Hungary

    Elena LUCCHI, Eurac Research, Institute for Renewable Energy, Bolzano, Italy

    Tamás MANKOVITS, University of Debrecen, Debrecen, Hungary

    Igor MEDVED, Slovak Technical University in Bratislava, Bratislava, Slovakia

    Ligia MOGA, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Marco MOLINARI, Royal Institute of Technology, Stockholm, Sweden

    Henrieta MORAVCIKOVA, Slovak Academy of Sciences, Bratislava, Slovakia

    Phalguni MUKHOPHADYAYA, University of Victoria, Victoria, Canada

    Balázs NAGY, Budapest University of Technology and Economics, Budapest, Hungary

    Husam S. NAJM, Rutgers University, New Brunswick, USA

    Jozsef NYERS, Subotica Tech College of Applied Sciences, Subotica, Serbia

    Bjarne W. OLESEN, Technical University of Denmark, Lyngby, Denmark

    Stefan ONIGA, North University of Baia Mare, Baia Mare, Romania

    Joaquim Norberto PIRES, Universidade de Coimbra, Coimbra, Portugal

    László POKORÁDI, Óbuda University, Budapest, Hungary

    Roman RABENSEIFER, Slovak University of Technology in Bratislava, Bratislava, Slovak Republik

    Mohammad H. A. SALAH, Hashemite University, Zarqua, Jordan

    Dietrich SCHMIDT, Fraunhofer Institute for Wind Energy and Energy System Technology IWES, Kassel, Germany

    Lorand SZABÓ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Csaba SZÁSZ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Ioan SZÁVA, Transylvania University of Brasov, Brasov, Romania

    Péter SZEMES, University of Debrecen, Debrecen, Hungary

    Edit SZŰCS, University of Debrecen, Debrecen, Hungary

    Radu TARCA, University of Oradea, Oradea, Romania

    Zsolt TIBA, University of Debrecen, Debrecen, Hungary

    László TÓTH, University of Debrecen, Debrecen, Hungary

    László TÖRÖK, University of Debrecen, Debrecen, Hungary

    Anton TRNIK, Constantine the Philosopher University in Nitra, Nitra, Slovakia

    Ibrahim UZMAY, Erciyes University, Kayseri, Turkey

    Andrea VALLATI, Sapienza University, Rome, Italy

    Tibor VESSELÉNYI, University of Oradea, Oradea, Romania

    Nalinaksh S. VYAS, Indian Institute of Technology, Kanpur, India

    Deborah WHITE, The University of Adelaide, Adelaide, Australia

International Review of Applied Sciences and Engineering
Address of the institute: Faculty of Engineering, University of Debrecen
H-4028 Debrecen, Ótemető u. 2-4. Hungary
Email: irase@eng.unideb.hu

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2023  
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11
Scimago
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0.249
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Engineering (miscellaneous) (Q3)
Environmental Engineering (Q3)
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Management Science and Operations Research (Q4)
Materials Science (miscellaneous) (Q3)
Scopus  
Scopus
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Scopus
CIte Score Rank
Architecture (Q1)
General Engineering (Q2)
Materials Science (miscellaneous) (Q3)
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Management Science and Operations Research (Q3)
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Scopus
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0.751


International Review of Applied Sciences and Engineering
Publication Model Gold Open Access
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Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription Information Gold Open Access

International Review of Applied Sciences and Engineering
Language English
Size A4
Year of
Foundation
2010
Volumes
per Year
1
Issues
per Year
3
Founder Debreceni Egyetem
Founder's
Address
H-4032 Debrecen, Hungary Egyetem tér 1
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2062-0810 (Print)
ISSN 2063-4269 (Online)

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