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Decision support system for design of long distance heat transportation system
Accepted Manuscript
Decision Support System for Design of Long Distance Heat Transportation System Piotr Hirsch , Michał Grochowski , Kazimierz Duzinkiewicz PII: DOI: Reference:
S0378-7788(17)32874-8 10.1016/j.enbuild.2018.05.010 ENB 8551
To appear in:
Energy & Buildings
Received date: Revised date: Accepted date:
24 August 2017 12 April 2018 7 May 2018
Please cite this article as: Piotr Hirsch , Michał Grochowski , Kazimierz Duzinkiewicz , Decision Support System for Design of Long Distance Heat Transportation System, Energy & Buildings (2018), doi: 10.1016/j.enbuild.2018.05.010
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Decision Support System for Design of Long Distance Heat Transportation System
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Piotr Hirsch1,*, Michał Grochowski1 and Kazimierz Duzinkiewicz1 1
Gdansk University of Technology, Faculty of Electrical and Control Engineering, Narutowicza 11/12, 80-233 Gdansk, Poland
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Abstract. District Heating (DH) systems are commonly supplied using local heat sources. Nowadays, modern insulation materials allow for effective and economically viable heat transportation over long distances (over 20 km). The paper proposes a Decision Support System (DSS) for optimized selection of design and operating parameters of a long distance Heat Transportation System (HTS). The method allows for evaluation of feasibility and effectiveness of heat transportation from the considered heat sources to the given DH area. The optimized selection is formulated as the multicriteria decision-making problem. The constraints for this problem include a static HTS model, allowing considerations of the system life cycle, as well as time variability and spatial topology. Thereby, the variation of heat demand and ground temperature within the DH area, the insulation and pipe aging, as well as the terrain elevation profile are taken into account in the decision-making process. The HTS construction costs, the operating costs (pumping power), and the heat loss are considered as objective functions, while such parameters as: inner pipeline diameter, insulation thickness, temperature and pressure profiles, as well as pumping station locations are optimized during the decision-making process. Moreover, variants of pipe laying e.g. one pipeline with a larger diameter, or two parallel pipelines with smaller diameters might be considered during the optimization. The analyzed optimization problem is multicriteria, hybrid and nonlinear. The genetic solver has been proposed to solve it.
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1. Introduction
Space heating is a major component of overall heat consumption in Europe. At the same time, heating uses up to 80% of total energy consumed in residential houses [1]. The district Heating (DH) is an attractive solution for space heating, especially when it is supplied by a Combined Heat and Power (CHP) plant [2–4]. Recovering the heat from any kind of a thermal power plant increases the plant energy efficiency and is an effective method for cutting carbon emissions. Several studies have shown that conventional CHP plants are
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Corresponding author: [email protected]
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highly attractive from the economic and environmental perspective [5–7], however the DH area has to be situated close to the plant site. Another important Heat Source (HS) for DH supply temperature [K] Nomenclature heating water flow velocity [m/s] Abbreviations pumping power [W] CHP Combined Heat and Power decision vector DH District Heating design vector DSS Decision Support System simulation vector HS Heat Source loss/drop of heat, temperature or pressure, also variable for HTS Heat Transportation System discretization steps LHTD Long Horizon Time Discretization NPP Nuclear Power Plant insulation thickness [m] SHTD Short Horizon Time Discretization heat exchanger efficiency pump efficiency Parameters and variables insulation thermal conductivity construction costs [m.u.] [W/(m∙K)] pumping station construction costs inner pipe roughness [mm] [m.u.] pipeline inner diameter [m] L HTS length [km] LHTD intervals number HTS Life cycle [years] SHTD sub-models number heating water mass flow [kg/s] ̇ base spatial discretization nodes Subscripts number A annual computational spatial discretization DHe DH side heat exchanger nodes number HSe HS side heat exchanger parallel pipelines number base spatial discretization index active pipelines computational spatial discretization index heat price [m.u./GJ] electricity price [m.u./MWh] LHTD interval index pressure [Pa] SHTD sub-models index pressure gain [Pa] parallel pipeline index linear pressure losses [Pa] base spatial discretization step [m] nominal pressure [Pa] max maximum value of the variable elevation difference pressure [Pa] TL total ̇ transported heat per second [W] pipeline direction index ̇ heat transportation limit [W] computational spatial discretization step [m] common ratio temperature [K] LHTD time step [years] return temperature [K] SHTD time step [days] systems can be a CHP Nuclear Power Plant (NPP) [8]. Although the CHP NPP can be a source of carbon-free heat for residential and industrial use [9], it is seldom considered as a viable HS for DH [10–12]. The main obstacle in nuclear heat utilization is the necessity of long distance heat transportation, as NPPs are most often located far from dense urban areas. However, there are some examples of supplying nuclear heat to DH networks, one of the most notable is located in Switzerland, Beznau. In this system, the peak load reaches 80 MW and the length of the main transport line is 35 km [13]. Modernization of conventional and nuclear power plants, either already built or just planned to operate in a partial cogeneration mode, requires large capital investments. A significant part of these costs is associated with the need to construct the Heat
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Transportation System (HTS) between the HS and potential DH areas. The considered distance may even reach over 100 km, with several GWs of transported heat. Therefore, it is crucial to evaluate the overall technic feasibility and economic effectiveness of the long distance HTS, as part of the whole cogeneration project evaluation. The cogeneration project is understood here as modernization of a thermal power plant to work in partial cogeneration mode. This paper proposes a method to evaluate the optimized cogeneration project in the part concerning heat transportation. Giving an opinion on the cost effectiveness of the long distance heat transportation is a decision which ends the properly constructed and carried out decision-making process. The complexity of this task justifies designing and utilization of an advanced computer-aided tool, such as the Decision Support System (DSS). The basic components of the proposed DSS are: the subsystem of decision models (mathematical programming models) and the tools used to solve these models – the solvers. To determine DSS’s functionality for the efficiency analysis of a HTS project, a preliminary analysis was carried out [3]. This analysis, which can be described as a feasibility study, allowed for determining the decision area. Consequently, the HTS evaluation requires analyzing: parameters of the HTS (number of pipelines, inner pipeline diameter, insulation thickness etc.); the working fluid pumping strategy (number of pumping stations, working fluid flow rate, supply and return temperatures etc.). These two analyzes should be conducted simultaneously because the result of one analysis influences the result of the other. In [3,14] desired characteristics of the HTS efficiency analysis method are discussed. The method should utilize optimization techniques to find the design which minimizes the construction costs, the operating costs (pumping power), and the heat loss. Therefore, the considered optimization problem is multicriteria. The design variables that need to be taken under consideration include: the number of pipelines, inner pipeline diameter, insulation thickness, supply and return temperatures, and the number of pumping stations. These variables can be represented as integers or real numbers, as a result of which the optimization problem becomes hybrid. Furthermore, the HTS performance changes over the time due to energy market shifts and pipe and insulation aging processes. Therefore, a decision was made to analyze the HTS over the presumed system lifetime. Other important conditions that affect the HTS efficiency are: the heat demand and its annual variability, the terrain profile, as well as the annual air and ground temperature distribution. An assessment of the long distance HTS can be performed by using various subcriteria, heading ultimately to the techno-economic evaluation. Two specific layers of the efficiency analysis can be named, which are: the layer of goods and services, and the layer of the value of technical and technological design solutions. Taking into account the set of criteria considered in this study, the construction costs fall under the first layer, while the transport efficiency, represented by the energy used for working fluid pumping, and the thermal efficiency, indicated by the heat loss during transportation, belong to the second efficiency analysis layer. For the decision support purpose, an optimizing model for the decision problem and a solver to the optimization problem need to be developed. The technical insights on the long distance heat transportation can be derived from earlier publications on the subject. However, there are not many instances of such systems. The long distance HTS was analyzed as part of the planned Loviisa 3 CHP NPP in Finland [15,16]. The project assumed the 77 km HTS which was expected to transport 1000 MW of heat. The inner pipeline diameter was specified to be 1200 mm. The supply temperature was assumed equal to 120 C and the return temperature - to 54 C, with the resulting mass flow rate of 3580 kg/s. The overall heat loss was estimated as 11 MW, meaning that the heat loss ratio was 1.1%. In [2,17] the 110 km long 3000 MW HTS was evaluated. In that
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case, two main lines, each transporting 1500 MW, were considered. The inner pipeline diameter of 2000 mm with insulation thickness of 300 mm was selected for the supply temperature of 120 C. The authors report the pressure drop of 0.16 bar/km and less than 2% of heat loss during the transportation. A concept of two phase thermochemical process for heat transportation from Bugey NPP to Lyon area (35 km) is analyzed in [18]. In [19], a concept of long distance heat transportation based on absorption heat exchangers is presented. The authors considered low-grade waste heat transportation over distances of up to 100 km. Different approaches to design optimization of various elements of the long distance HTS have been presented in a number of scientific papers. A methodology for technoeconomic analysis of a CHP NPP was presented in [4]. The authors considered modification of condensing-extraction turbine systems which was necessary to improve heat production and transportation parameters in order to evaluate the technological feasibility and profitability of the nuclear cogeneration plant. In [2] the supply temperature and the pipeline diameter were chosen separately. Firstly, the optimal temperature range was established, followed by arbitrary temperature selection from that range. Then the minimum of the estimated cost of thermal energy as the function of pipeline diameter was found. In many cases, both the aim and methods of optimization of long distance fuel transportation systems are similar to those applied for the considered HTS, which justifies taking advantage of authors’ experience. In [20] the problem of natural gas transportation via pipeline systems is overviewed. The system design (pipeline length and diameter, compressor station locations) and operation (operating costs of compressors) are commonly subjected to optimization. The population based optimization techniques, such as evolutionary and genetic algorithms, are effectively utilized to solve the design and operation optimization problems in long distance fuel transportation [21] because of their ease and flexibility in solving hybrid, multicriteria and constrained optimization problems. DH networks are often subject to detailed analysis in order to find optimal pipes sizing [22] or to minimize the heat loss [23,24]. Similar approaches can be utilized for DH supply systems which are expected to transport the heat from the HS to the DH area over long distances. The novelty of the approach presented in this paper is, besides taking into account the time and spatial structure of the problem, the possibility of evaluation and decision making on the pipe-lying strategy. This will allow the decision-maker to find optimal values of the number, design and operation of multiple pipelines working in parallel. Moreover, the HTS decision model, built for the purpose of design and operation optimization, has been improved in terms of computational complexity by applying an additional spatial discretization method. Due to the improved computing performance, the genetic solver could be effectively applied for mixed-integer solutions.
2. Decision model for optimization-based efficiency analysis 2.1. Assumptions The decision model for the HTS optimization-based efficiency analysis consists of the mathematical model of objectives and constraints, and optimization problem formulation. Preconditions and necessary inputs for optimization are specified as follows: The HTS should be analyzed within a certain timeframe and based on the annual costs. This leads to the analysis conducted for the presumed project lifetime, with the primary time base of one year. The length of the HTS project life cycle is assumed to be equal to the HS lifetime, designated by .
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Locations of the HS and the DH area are known. This leads to conclusions that the route of the HTS is known and, as a result, the terrain elevation profile of the HTS is known as well. The sample terrain elevation profile is shown in Fig. 1.
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Fig. 1. The sample HTS terrain elevation profile
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The knowledge of the HTS route leads to further considerations: since the historic data on air temperatures on the HTS route are known, there is a possibility to determine the ground temperatures in the corresponding period. It is convenient to use temperature profiles in the form of structured graphs when formulating the optimization problem (Fig. 2.). The air and/or ground temperatures are assumed to be the same along the whole HTS route.
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Annual heat demand of the DH area is given in the form of structured graph
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Fig. 3. Sample structured graphs of annual heat demand of the DH area, a) long period of high and more balanced heat demand ̇ , b) significant step changes in heat demand ̇ , as a result of heating season changes, is the short horizon time discretization index
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In addition, a number of case study dependent parameters, such as insulation, thermal conductivity, or nominal pipeline pressure, need to be specified. A detailed list of case study parameters is presented in the case study discussion. Furthermore, for the purpose of decision model formulation, the following assumptions concerning HTS operation are considered: the heat delivered to the DH is equal to the heat demand; the outlet and inlet temperatures of the HS heat exchanger are the supply and return temperatures, respectively; the pumping station pressure gains are constant and independent of the heating water flow rate. Further assumptions for the decision model computation are: only steady states are considered, minor pressure losses are neglected.
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2.2. Time and spatial discretization
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The evaluation of the HTS design and operation over its life cycle has to take into account time variability of HTS operation conditions and parameters. The time-variant processes affecting the HTS occur on significantly different time scales. The pipeline and insulation aging are examples of processes with time constants of several years. It is convenient to approximate the impact of these processes as fixed over some intervals. This approach leads to Long Horizon Time Discretization (LHTD) of the HTS life cycle , with time step, into intervals indexed by . As a result, for selected parameters such as: pipeline roughness, thermal conductivity, and the price of heat and electricity, it is possible to acquire different constant values for each life cycle interval. Depending on the decision maker’s needs and knowledge, the LHTD time step can be either fixed or variable. The HTS is also subjected to significant annual variability due to annual heat demand and ground temperature changes. To deal with these conditions, the Short Horizon Time Discretization (SHTD) is proposed. The SHTD time base is one year, which is divided with the variable time step into intervals indexed by , in accordance to the discretized, structured graph of annual heat demand (see Fig. 3). As a result, sub-models are created for each LHTD interval. Each sub-model corresponds to a different heat demand level (different part of the year) and is characterized by different flows and temperatures.
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Although the duration of each LHTD interval may be decades, its parameters are assumed constant over that period and, consequently, it may be covered by only one set of sub-models, the results of which are multiplied according to the LHTD time step. According to the HTS topology scheme shown in Fig. 4, the HTS is a network composed of links, base nodes, and computational nodes. The links are pipeline sections, pipeline sections with pumping stations, or heat exchangers. The base and computational nodes are allocated according to the applied spatial discretization methods. Spatial discretization is introduced to deal with the HTS spatiality and the resultant terrain elevation profile impact on the nodal pressure and on the pumping stations localization (see Fig. 1). The base discretization is characterized by a small, fixed step, which ensures high accuracy of the thermal mathematical model due to temperature approximations over short pipeline sections. As a consequence of base discretization, the HTS of length [km] is discretized with the step [m], resulting in base nodes in each direction, indexed by . In order to reduce the computational complexity of the mathematical model, the computational discretization is proposed and applied. This method allows to reduce the number of nodes without accuracy deterioration. The terrain elevation profile, given with the base resolution is chosen as the basis of computational discretization, with the computational nodes being allocated at points of terrain profile change, as shown in Fig. 5. Therefore, the HTS is discretized with the variable step [m] which is an integer multiplicity of the , resulting in nodes in each direction, indexed by . In both discretization methods, the supply and return pipeline directions are denoted with the second subscript . The parallel pipelines are indexed with .
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Fig. 4. Scheme of HTS topology
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2.3. Mathematical models
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The mathematical model formulation utilizes reduced notation for conciseness. The nodal variables (describing a quantity at each node) have the subscripts , meaning respectively: the node number (either base or computational), the supply/return line, the SHTD interval, the LHTD interval, and the pipeline. In reduced notation, unless necessary, only the subscript is listed while the subscript is completely omitted until the criteria are formulated.
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2.3.1. Thermal mathematical model
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The main purpose of the thermal model is to calculate the heat loss during transportation. This quantity must be taken into account to ensure that the delivered heat equals the heat demand, which is one of the main assumptions. Considering the pipeline section of length [m], diameter [m], external insulation thickness of [m], and thermal conductivity W/(m∙K)], in which the superheated water at temperature of [K] is flowing (Fig. 6), the ̇ linear heat loss can be calculated as: ̇
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and can vary from 100 meters up to several kilometers. The loss of heat translates in direct proportional manner into the temperature loss: ̇ (2) ̇ where is the specific water heat capacity [J/(kg∙K)] at 100˚C, and ̇ is the heating water mass flow [kg/s] at a given time step. Assuming the absence of heating water phase change in the heat exchanger and the heat exchanger efficiency , the heating water mass flow can be calculated from the amount of the exchanged heat and the temperature drop on the heat exchanger. This applies for both DH and HS side heat exchangers: ̇ ̇ (3) ̇
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In Eq. (3), ̇ is the heat delivered to the DH network per second [W], with the temperature drop of [K]. Similarly, ̇ is the heat absorbed from the HS per second [W] at temperature drop [K] (time discretization indexes are omitted). The heat delivered to the DH network is equal to the heat demand and is known at any time, while the amount of heat needed from HS has to be calculated as the sum of the total heat lost in transportation in both directions and the heat delivered. The same applies to temperatures: is equal to the difference between the supply and return temperatures, which are inputs to the model, while has to be calculated using Eqs. (1-3).
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Fig. 6. Scheme of pipeline section with associated variables and parameters
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The proposed thermal model is characterized by dense base nodalization, which is required because of the temperature approximation accuracy. At the same time, the terrain elevation profile based spatial computational discretization is much sparser. It can be shown that the thermal model can be calculated only at the computational nodes, without the need to compute all the base nodes in between. Considering the heat loss ratio in two successive pipeline sections, as shown in Eq. (1): ̇ ̇ | ̇ ̇ ̇ ( ) (4) ̇ ⁄ ̇ it can be observed that the successive heat loss ratio values are constant and lower than 1 at any given time step. The same applies to the temperature loss ratio, as these two quantities ⁄ are proportional. It can be seen that also equals . Therefore, the heat or temperature loss at any base pipeline section can be found from the geometric sequences: ̇ ̇ . By applying geometric series, the heat rate and the temperature at any base pipeline section can be calculated:
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As the computational nodes are allocated at the integer multiplicity of the base discretization step , the base thermal model (Eqs. (1-6)) can be modified, allowing high accuracy calculations of the heating water temperature and the heat rate, while utilizing reduced nodalization: ̇ (7) ̇ ̇ (8)
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The hydraulic model is the base for calculating the number of the required pumping stations and their locations, as well as the electrical power used for pumping. Since the supply and return lines of the considered HTS are buried in a single trench, the terrain elevation has no impact on the number of pumping stations, as its impact on the pressure profile cancels out. However, the terrain has still a strong impact on pumping station locations. The pressure drop between consecutive base nodes [Pa] is affected by: the linear pressure loss [Pa] (minor pressure losses are neglected), the elevation difference pressure [Pa], and the possible pressure gain [Pa] due to pumping station
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allocation at the inlet node. As a consequence of the assumed fixed pipeline diameter and closed HTS structure (without branching nodes), the flow velocity is the same for each node at any given time step. Thus, the linear pressure loss over the pipeline section is constant for any given time step and can be described by the Darcy-Weisbach equation: (10)
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where is the density of water [kg/m3], is the heating water flow velocity [m/s], calculated from the mass flow rate, and is the Darcy-Weisbach friction coefficient, which for the fully turbulent flow (Reynolds number>4000) and the inner pipe roughness of [mm] can be calculated as shown in [2]. The overall pressure drop between consecutive base nodes is defined as follows: (11) where ( ), is the HTS elevation head [m] and is the Earth gravity 2 constant [m/s ]. As for the thermal model, the hydraulic model base nodalization can be reduced without accuracy deterioration, thus decreasing computational burden. Due to constant linear pressure loss over the pipeline section, the linear pressure loss between any two nodes can
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be found by applying arithmetic series. The elevation difference pressure between any two nodes and the corresponding pressure gain are also available. Assuming that the pressure at the first node is equal to the nominal pressure [Pa], set by the main pumping station, the pressure at any computational node can be obtained from Eq. (12). (
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where is introduced from Eq. (9). The pumping stations can be allocated according to a simple rule: add a pumping station whenever the nodal pressure decrease is below the safety limit. The pressure gain of a single pumping station can also be fixed and be the same for each station. 2.3.3. Pipe-laying strategy
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The same amount of heat can be transported using different pipe-laying strategies. Depending on the peak value and annual variation of heat demand, it may be cost-effective to use a single, large diameter pipeline or a number of smaller pipelines. The decision regarding the pipe-laying strategy should be a result of optimization. Therefore, the decision model is extended, allowing parallel pipelines with independent variables and parameters, except for the supply and return temperatures. The number of actually used pipelines is determined indirectly, as the optimizer choses the limit value of the maximum heat that can be transported by a single pipeline ̇ per second [W]. Based on that limit and the heat demand at a given time step, the number of active pipelines is specified using Eq. (13). The peak heat demand requires most pipelines, each contributing to the overall construction costs, including separate pumping stations for each pipeline. At a given time step, an arbitrary number of pipelines can be utilized, simultaneously or alternately, depending on the current heat demand. ̇ (13) ⌈ ⌉ ̇
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To prevent the possibility of the number of active pipelines exceeding the number of allowed pipelines , the lower bound on ̇ is specified: ̇ ̇ (14)
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2.4. Optimization problem formulation As a result of time discretization, a number of sub-models are established. Each sub-model is described by a set of variables. Some of these variables are the same for each sub-model (i.e. inner pipeline diameters, insulation thickness, supply and return temperatures), while other, such as nodal pressure or temperature, are independent. While all variables together constitute the decision space , the former are more important for the decision-making process. Therefore, categorization of the decision space is proposed, in which the variables shared by the sub-models are called the design vector, denoted , while the remaining variables compose the simulation vector . According to this categorization, the decision [ ] . A detailed form of the design vector is shown in space is represented as Eq. (15).
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The inner pipeline diameter and the insulation thickness are integer variables. These variables can be modified in order to represent indexes of either pipeline diameters or insulation thicknesses selected from the appropriate series. The decision variables are subjected to a set of nonlinear equality constraints that constitute the mathematical model. Furthermore, the upper and lower bounds, as well as the inequality constraints , can be considered on the decision space due to technological and operational limitations. The range of considered supply temperatures and the maximal heating water flow velocity can be examples of such constraints. The HTS design and operation is assessed taking into account its technical and economic value. The technical value can be represented by terms of thermal and transport efficiency. One way to assess the thermal efficiency of the HTS is to estimate its life cycle heat loss in transportation. It can be done by calculating firstly the heat loss of each suḃ ̇ model for each pipeline [W] (Eq. (16)), followed by the annual heat loss [GJ/year] (Eq. (17)) and the total heat loss Δ [GJ] in transportation (Eq. (18)).
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where: is the unit conversion coefficient, is the time step of interval [years], and is the time step of sub-model [days]. The transport efficiency can be represented by the amount of energy used for heating water pumping. First, the pumping power of each sub-model for each pipeline [W] is found using Eq. (19). Then, the annual pumping energy [MWh/year] is calculated using Eq. (20), finally the total pumping energy [MWh] is obtained from (Eq. (21)):
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The economic value of the HTS is estimated using the empirical construction cost function: ∑
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where is the overall HTS construction cost [m.u.], is the pipeline material and labor costs of each active pipeline as a function of pipeline diameter, and is the cost of pumping station construction [m.u.]. The subscript means the maximum value of the variable in the range of all intervals and sub-models. The objective functions Eqs. (16-22) [ ] , can be represented as the objective vector leading to general optimization problem formulation: s.t.
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The optimization problem is multicriteria, nonlinear, and hybrid, as a result of simultaneous occurrence of integer (e.g. inner pipeline diameter) and continuous (e.g. water temperature) decision variables. The combination of these properties makes the problem difficult to solve. In an attempt to simplify the optimization problem, the weighted-sum scalarization method is proposed. Eq. (18) is multiplied by heat and Eq. (21) by electricity prices, thus allowing summation of the objective functions. The resultant optimization problem, with integer values of pipeline diameters and insulation thickness and real values of other decision variables, is solved using a genetic algorithm solver. One of the genetic algorithm steps is the HTS design evaluation. Due to time and spatial discretization, and the multiple pipeline option, it is a complicated process. The results for all sub-models, intervals, and pipelines have to be merged in order to calculate the fitness function. The flowchart of the HTS design evaluation procedure is shown in Fig. 7. In this case the sequential method presented in [3] is applied to compute the temperature, heat and pressure profiles. This procedure is represented as the “Mass flow estimation loop” block. Due to the structure of the decision model, all sub-models, intervals and pipelines are independent of each other. Consequently, all instances of each loop can be computed in parallel, which greatly increases the computing performance. Respective results are merged in three-stage aggregation, described by Eqs. (16-22).
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For each of the 𝜏𝐿 LHTD intervals
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Total heat loss (18) and total pumping power (21), construction costs (22) Fig. 7. The HTS design evaluation flowchart
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4. Case Study The presented methodology has been verified and analyzed based on the case study of a 40 km HTS. The NPP, located by Lake Żarnowiec, Northern Poland, was assumed to be the intended heat source, while the main heat customer would be the city of Gdynia and its surroundings. The knowledge of NPP and DH locations allows specifying the terrain elevation profile (Fig. 8a.), the annual ground temperature, and the DH heat demand (Fig. 8b.). b)
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[ ] [ ] ] [ The and variables represent the indexes of insulation thickness series [ ] [m]. The lower bound on ̇ is a result of Eq. (14). The pipeline construction cost estimation function is specified by Eq. (25). The insulation thickness of 0.1 m decreases its outcome by 15%, while the 0.3 m case increases it by 15%. (25) The case study parameters are shown in Table 1. The number and length of SHTD intervals can be read from Fig. 8b. Three LHTD intervals of 20 years each are considered, allowing the variability of certain parameters: pipe roughness, insulation thermal conductivity, and heat and electricity prices. Due to the HTS length and the base spatial discretization step, there are 401 base nodes. The appliance of computational discretization resulted in only 22 computational nodes, while all calculations are still done with the accuracy of 100-meter base step.
Table 1. Case study parameters Parameter
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Number of computational nodes Number of possible pipelines Pipe roughness Insulation thermal conductivity Nominal pressure Minimal supply line pressure Minimal return line pressure Pump pressure gain Heat price Electricity price Pumping station cost Pump efficiency Heat exchanger efficiency
Nc Np [mm] λis [W/(m∙K)] Pnm [MPa] Pmin S [MPa] Pmin R [MPa] Pg [MPa] ph [€/GJ] pe [€/MWh] cps [M€]
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60 [20, 20, 20] 3 [25, 30, 35, 90, 45, 18, 122] 7 40 100 401 [7,3,10,17,11,10,4,10,10,14,6, 23,16,19,19,31,11,17,22,67,73] 22 2 [0.1, 0.15, 0.2] [0.02, 0.03, 0.05] 1.5 0.24 0.05 1 [12, 18, 24] [60, 64, 68] 3.5 0.75 1
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HTS life cycle LHTD time step Number of LHTD intervals SHTD time step Number of sub-models HTS length Spatial discretization base step Number of base nodes Spatial discretization computational step
The results of the optimization procedure for the analyzed case study are presented in Table 2.
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Design variables: Symbol 80% Heat 100% Heat 120% Heat Demand Demand Demand 1 1 1
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Table 2. Optimization results
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Inner pipeline 1 diameter [m] 0.606 Inner pipeline 2 diameter [m] Pipeline 1 insulation [m] 0.3 Pipeline 2 insulation [m] Supply temperature TS [K] 393.15 Return temperature TR [K] 323.15 Heat transportation limit Q̇ 220 [MW] Number of pumping 6 stations Objective functions [M€]: Construction costs CC 171.97 Heat loss costs ΔQ’TL 68.56 Pumping energy costs W’TL 38.99 Total costs J 279.53 Selected operation variables: Flow velocity [m/s] 2.49 Pressure drop per 1 km [bar/km] 0.75 ̇ Heat loss per 1 km [MW/km] 0.054 ̇ Supply line heat loss 2.17 [MW] ̇ Return line heat loss 0.90 [MW] Heat loss rate [%] 1.53
0.659 0.3 393.15 323.15 250 6
0.707 0.3 393.15 323.15 300 6
195.22 72.91 48.89 317.03
217.79 76.83 58.33 352.95
2.62 0.75 0.058 2.3 0.95 1.3
2.73 0.75 0.061 2.43 1 1.14
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Three cases of heat demand are considered: 80%, 100% and 120% of the DH heat demand shown in Fig. 8b. Each time, the maximum heat that can be transported by single pipeline is equal to the peak heat demand, therefore only one of the two possible pipelines is active. The supply and return temperatures are on the upper and lower bounds, respectively, which means that the temperature difference is always maximized. It can be observed that the benefits of thicker insulation outweigh the 15% construction costs increase for each of the heat demand cases. The heat loss costs Δ [M€] and the pumping energy costs [M€] result from total heat loss and total pumping energy weighting by corresponding prices.
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The pressure profile and the pumping station locations for the case of 100% heat demand are shown in Fig. 9. The pumping stations located on the supply line are marked by blue dots, while those on the return line by green, and the main pumping station by black. Significant impact of the terrain elevation profile on the pressure profile can be observed. The cross-section of the objective function and its components is shown in Fig. 10. All design variables except the inner diameter of pipeline 1 are fixed, and pipeline 2 is inactive. The objective function is non-convex due to the number of pumping stations. x 106
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The impact of variations of selected parameters on the optimization results is presented in Table 3. The HTS life cycle and electricity price are considered. In the case of [ ]. For years, three LHTD intervals are considered, with the time step: years, there are two LHTD intervals, each spanning 10 years. The impact of insulation and pipe aging processes on optimal inner pipeline diameter and insulation thickness can be observed. In the case of shorter life cycle, the pipe roughness is smaller, which results in smaller inner pipeline diameter. Similarly, the overall smaller insulation thermal conductivity resulted in lower insulation thickness. The total costs for the case of years have decreased by almost 38% in comparison to the base case (60 years), while the operation time is shorter by roughly 67%. The temperature difference is still maximized and again, there is only one active pipeline. The variation of electricity price, which is applied to each LHTD interval, shows the trade-off between the inner pipeline diameter and the number of pumping stations. Table 3. Impact of variations of selected parameters on the optimization results Symbol
Design variables: LC = 20 LC = 40 years years 1
Inner pipeline 1 diameter [m] Inner pipeline 2 diameter [m] Pipeline 1 insulation [m] Pipeline 2 insulation [m] Supply temperature TS [K] Return temperature TR [K] Heat transportation limit Q̇ [MW] Number of pumping stations
0.634 0.1 393.15 323.15 250 7
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140% electricity price
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0.641 0.2 393.15 323.15 250 7
0.659 0.3 393.15 323.15 250 6
0.624 0.3 393.15 323.15 250 8
0.683 0.3 393.15 323.15 250 5
195.22 72.91 48.89 317.03
186.67 70.06 38.92 295.65
202.82 74.86 56.88 334.56
Objective functions [M€]: 145.00 168.96 33.87 54.54 19.13 36.67 198.00 260.17
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5. Conclusions
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The proposed method to optimize HTS efficiency can be utilized as part of the decision support system for evaluation of projects associated with heat transportation. An example of such a project is the Combined Heat and Power NPP, where part of the technical and economic feasibility assessment task concerns a high-power, long distance HTS. With the appliance of the proposed DSS, the optimal design and operation strategy of the HTS can be found with respect to construction costs, and thermal and transport efficiency, while being subject to a number of operation and technological constraints resulting from the mathematical model and governing equations. Additional constraints can be imposed by the decision-maker to ensure specific HTS operation, i.e. heating water flow velocity or heat loss over the pipeline section. An important feature of the proposed method is the ability to evaluate projects in long term or in particular, over the project life cycle. Long Horizon Time Discretization allows consideration of pipe and insulation aging phenomena, as well as heat and electricity prices
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changes. At the same time, conditions of the time scale of a month or even days are still taken into account due to Short Horizon Time Discretization. In addition, the proposed method takes into account the spatial topology of the HTS to evaluate the terrain elevation impact on the nodal pressure and localizations of pumping stations. The decision model formulation allows the user to investigate different pipe-lying strategies. Depending on the case study and decision-maker’s preferences, the solver determines whether one bigger or several smaller pipelines are more cost effective. As a result, a set of integer design variables is found by solving the optimization problem for each pipeline inner diameter, insulation thickness, number of pumping stations, as well as for two real variables: supply and return temperatures. Moreover, all of the simulation variables, such as nodal pressure or temperature, are calculated and stored, thus making a basis for further HTS safety analyzes.
Acknowledgements
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The research work was done under the grant 8902/E-359/M/2016 entitled “Young Researcher Support Program” and financed by the Polish Ministry for Science and Higher Education. The authors wish to express their thanks for support.
References
[4]
[5]
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[3]
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[2]
Connolly D. Heat Roadmap Europe: Quantitative comparison between the electricity, heating, and cooling sectors for different European countries. Energy 2017;139:580– 93. doi:10.1016/j.energy.2017.07.037. Safa H. Heat recovery from nuclear power plants. International Journal of Electrical Power & Energy Systems 2012;42:553–9. doi:10.1016/j.ijepes.2012.04.052. Hirsch P, Duzinkiewicz K, Grochowski M, Piotrowski R. Two-phase optimizing approach to design assessments of long distance heat transportation for CHP systems. Applied Energy 2016;182:164–76. doi:10.1016/j.apenergy.2016.08.107. Jaskólski M, Reński A, Minkiewicz T. Thermodynamic and economic analysis of nuclear power unit operating in partial cogeneration mode to produce electricity and district heat. Energy 2017. doi:10.1016/j.energy.2017.04.144. Colmenar-Santos A, Rosales-Asensio E, Borge-Diez D, Collado-Fernández E. Evaluation of the cost of using power plant reject heat in low-temperature district heating and cooling networks. Applied Energy 2016;162:892–907. doi:10.1016/j.apenergy.2015.10.161. Lund H, Möller B, Mathiesen BV, Dyrelund A. The role of district heating in future renewable energy systems. Energy 2010;35:1381–90. doi:10.1016/j.energy.2009.11.023. Leurent M, Da Costa P, Rämä M, Persson U, Jasserand F. Cost-benefit analysis of district heating systems using heat from nuclear plants in seven European countries. Energy 2018;149:454–72. doi:10.1016/j.energy.2018.01.149. Locatelli G, Fiordaliso A, Boarin S, Ricotti ME. Cogeneration: An option to facilitate load following in Small Modular Reactors. Progress in Nuclear Energy 2017;97:153– 61. doi:10.1016/j.pnucene.2016.12.012. Leurent M, Jasserand F, Locatelli G, Palm J, Rämä M, Trianni A. Driving forces and obstacles to nuclear cogeneration in Europe: Lessons learnt from Finland. Energy Policy 2017;107:138–50. doi:10.1016/j.enpol.2017.04.025.
CE
[1]
[7]
[8]
[9]
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PT
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[10] Tokimatsu K, Konishi S, Ishihara K, Tezuka T, Yasuoka R, Nishio M. Role of innovative technologies under the global zero emissions scenarios. Applied Energy 2016;162:1483–93. doi:10.1016/j.apenergy.2015.02.051. [11] Persson U, Möller B, Werner S. Heat Roadmap Europe: Identifying strategic heat synergy regions. Energy Policy 2014;74:663–81. doi:10.1016/j.enpol.2014.07.015. [12] Puchalski B, Rutkowski TA, Duzinkiewicz K. Nodal models of Pressurized Water Reactor core for control purposes – A comparison study. Nuclear Engineering and Design 2017;322:444–63. doi:10.1016/j.nucengdes.2017.07.005. [13] Minkiewicz T, Reński A. The Possibility to use a Nuclear Power Plant as a Source of Electrical Energy and Heat. Acta Energetica 2014:114–8. doi:10.12736/issn.23003022.2014310. [14] Hirsch P, Grochowski M, Duzinkiewicz K. Pipeline system for heat transportation from nuclear power plant - An optimizing approach, IEEE; 2015, p. 1044–9. doi:10.1109/MMAR.2015.7284023. [15] Paananen M, Henttonen T. Investigations of a long-distance 1000 MW heat transport system with apros simulation software, Espoo, Finland: 2009. [16] Bergroth N. Large-Scale Combined Heat and Power (CHP) Generation at Loviisa Nuclear Power Plant Unit 3. Proceedings of the 8th Conference on Nuclear Option in Countries with Small and Medium Electricity Grids Dubrovnik, Croatia, 16–20 May 2010. [17] Jasserand F, Devezeaux de Lavergne J-G. Initial economic appraisal of nuclear district heating in France. EPJ Nuclear Sciences & Technologies 2016;2:39. doi:10.1051/epjn/2016028. [18] Le Pierrès N, Luo L, Berthiaud J, Mazet N. Heat transportation from the Bugey power plant. International Journal of Energy Research 2009;33:135–43. doi:10.1002/er.1429. [19] Xie X, Jiang Y. Absorption heat exchangers for long-distance heat transportation. Energy 2017;141:2242–50. doi:10.1016/j.energy.2017.11.145. [20] Ríos-Mercado RZ, Borraz-Sánchez C. Optimization problems in natural gas transportation systems: A state-of-the-art review. Applied Energy 2015;147:536–55. doi:10.1016/j.apenergy.2015.03.017. [21] Wang Y, Tian C-H, Yan J, Huang J. A survey on oil / gas pipeline optimization: Problems, methods and challenges, Suzhou: IEEE; 2012, p. 150–5. doi:10.1109/SOLI.2012.6273521. [22] Asim T, Mishra R, Kollar LE, Pradhan SR. Optimal sizing and life-cycle cost modelling of pipelines transporting multi-sized solid–liquid mixtures. International Journal of Pressure Vessels and Piping 2014;113:40–8. doi:10.1016/j.ijpvp.2013.11.003. [23] Dalla Rosa A, Li H, Svendsen S. Method for optimal design of pipes for low-energy district heating, with focus on heat losses. Energy 2011;36:2407–18. doi:10.1016/j.energy.2011.01.024. [24] Başoğul Y, Keçebaş A. Economic and environmental impacts of insulation in district heating pipelines. Energy 2011;36:6156–64. doi:10.1016/j.energy.2011.07.049.
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Decision Support System for Design of Long Distance Heat Transportation System Piotr Hirsch , Michał Grochowski , Kazimierz Duzinkiewicz PII: DOI: Reference:
S0378-7788(17)32874-8 10.1016/j.enbuild.2018.05.010 ENB 8551
To appear in:
Energy & Buildings
Received date: Revised date: Accepted date:
24 August 2017 12 April 2018 7 May 2018
Please cite this article as: Piotr Hirsch , Michał Grochowski , Kazimierz Duzinkiewicz , Decision Support System for Design of Long Distance Heat Transportation System, Energy & Buildings (2018), doi: 10.1016/j.enbuild.2018.05.010
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Decision Support System for Design of Long Distance Heat Transportation System
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Piotr Hirsch1,*, Michał Grochowski1 and Kazimierz Duzinkiewicz1 1
Gdansk University of Technology, Faculty of Electrical and Control Engineering, Narutowicza 11/12, 80-233 Gdansk, Poland
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Abstract. District Heating (DH) systems are commonly supplied using local heat sources. Nowadays, modern insulation materials allow for effective and economically viable heat transportation over long distances (over 20 km). The paper proposes a Decision Support System (DSS) for optimized selection of design and operating parameters of a long distance Heat Transportation System (HTS). The method allows for evaluation of feasibility and effectiveness of heat transportation from the considered heat sources to the given DH area. The optimized selection is formulated as the multicriteria decision-making problem. The constraints for this problem include a static HTS model, allowing considerations of the system life cycle, as well as time variability and spatial topology. Thereby, the variation of heat demand and ground temperature within the DH area, the insulation and pipe aging, as well as the terrain elevation profile are taken into account in the decision-making process. The HTS construction costs, the operating costs (pumping power), and the heat loss are considered as objective functions, while such parameters as: inner pipeline diameter, insulation thickness, temperature and pressure profiles, as well as pumping station locations are optimized during the decision-making process. Moreover, variants of pipe laying e.g. one pipeline with a larger diameter, or two parallel pipelines with smaller diameters might be considered during the optimization. The analyzed optimization problem is multicriteria, hybrid and nonlinear. The genetic solver has been proposed to solve it.
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1. Introduction
Space heating is a major component of overall heat consumption in Europe. At the same time, heating uses up to 80% of total energy consumed in residential houses [1]. The district Heating (DH) is an attractive solution for space heating, especially when it is supplied by a Combined Heat and Power (CHP) plant [2–4]. Recovering the heat from any kind of a thermal power plant increases the plant energy efficiency and is an effective method for cutting carbon emissions. Several studies have shown that conventional CHP plants are
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Corresponding author: [email protected]
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highly attractive from the economic and environmental perspective [5–7], however the DH area has to be situated close to the plant site. Another important Heat Source (HS) for DH supply temperature [K] Nomenclature heating water flow velocity [m/s] Abbreviations pumping power [W] CHP Combined Heat and Power decision vector DH District Heating design vector DSS Decision Support System simulation vector HS Heat Source loss/drop of heat, temperature or pressure, also variable for HTS Heat Transportation System discretization steps LHTD Long Horizon Time Discretization NPP Nuclear Power Plant insulation thickness [m] SHTD Short Horizon Time Discretization heat exchanger efficiency pump efficiency Parameters and variables insulation thermal conductivity construction costs [m.u.] [W/(m∙K)] pumping station construction costs inner pipe roughness [mm] [m.u.] pipeline inner diameter [m] L HTS length [km] LHTD intervals number HTS Life cycle [years] SHTD sub-models number heating water mass flow [kg/s] ̇ base spatial discretization nodes Subscripts number A annual computational spatial discretization DHe DH side heat exchanger nodes number HSe HS side heat exchanger parallel pipelines number base spatial discretization index active pipelines computational spatial discretization index heat price [m.u./GJ] electricity price [m.u./MWh] LHTD interval index pressure [Pa] SHTD sub-models index pressure gain [Pa] parallel pipeline index linear pressure losses [Pa] base spatial discretization step [m] nominal pressure [Pa] max maximum value of the variable elevation difference pressure [Pa] TL total ̇ transported heat per second [W] pipeline direction index ̇ heat transportation limit [W] computational spatial discretization step [m] common ratio temperature [K] LHTD time step [years] return temperature [K] SHTD time step [days] systems can be a CHP Nuclear Power Plant (NPP) [8]. Although the CHP NPP can be a source of carbon-free heat for residential and industrial use [9], it is seldom considered as a viable HS for DH [10–12]. The main obstacle in nuclear heat utilization is the necessity of long distance heat transportation, as NPPs are most often located far from dense urban areas. However, there are some examples of supplying nuclear heat to DH networks, one of the most notable is located in Switzerland, Beznau. In this system, the peak load reaches 80 MW and the length of the main transport line is 35 km [13]. Modernization of conventional and nuclear power plants, either already built or just planned to operate in a partial cogeneration mode, requires large capital investments. A significant part of these costs is associated with the need to construct the Heat
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Transportation System (HTS) between the HS and potential DH areas. The considered distance may even reach over 100 km, with several GWs of transported heat. Therefore, it is crucial to evaluate the overall technic feasibility and economic effectiveness of the long distance HTS, as part of the whole cogeneration project evaluation. The cogeneration project is understood here as modernization of a thermal power plant to work in partial cogeneration mode. This paper proposes a method to evaluate the optimized cogeneration project in the part concerning heat transportation. Giving an opinion on the cost effectiveness of the long distance heat transportation is a decision which ends the properly constructed and carried out decision-making process. The complexity of this task justifies designing and utilization of an advanced computer-aided tool, such as the Decision Support System (DSS). The basic components of the proposed DSS are: the subsystem of decision models (mathematical programming models) and the tools used to solve these models – the solvers. To determine DSS’s functionality for the efficiency analysis of a HTS project, a preliminary analysis was carried out [3]. This analysis, which can be described as a feasibility study, allowed for determining the decision area. Consequently, the HTS evaluation requires analyzing: parameters of the HTS (number of pipelines, inner pipeline diameter, insulation thickness etc.); the working fluid pumping strategy (number of pumping stations, working fluid flow rate, supply and return temperatures etc.). These two analyzes should be conducted simultaneously because the result of one analysis influences the result of the other. In [3,14] desired characteristics of the HTS efficiency analysis method are discussed. The method should utilize optimization techniques to find the design which minimizes the construction costs, the operating costs (pumping power), and the heat loss. Therefore, the considered optimization problem is multicriteria. The design variables that need to be taken under consideration include: the number of pipelines, inner pipeline diameter, insulation thickness, supply and return temperatures, and the number of pumping stations. These variables can be represented as integers or real numbers, as a result of which the optimization problem becomes hybrid. Furthermore, the HTS performance changes over the time due to energy market shifts and pipe and insulation aging processes. Therefore, a decision was made to analyze the HTS over the presumed system lifetime. Other important conditions that affect the HTS efficiency are: the heat demand and its annual variability, the terrain profile, as well as the annual air and ground temperature distribution. An assessment of the long distance HTS can be performed by using various subcriteria, heading ultimately to the techno-economic evaluation. Two specific layers of the efficiency analysis can be named, which are: the layer of goods and services, and the layer of the value of technical and technological design solutions. Taking into account the set of criteria considered in this study, the construction costs fall under the first layer, while the transport efficiency, represented by the energy used for working fluid pumping, and the thermal efficiency, indicated by the heat loss during transportation, belong to the second efficiency analysis layer. For the decision support purpose, an optimizing model for the decision problem and a solver to the optimization problem need to be developed. The technical insights on the long distance heat transportation can be derived from earlier publications on the subject. However, there are not many instances of such systems. The long distance HTS was analyzed as part of the planned Loviisa 3 CHP NPP in Finland [15,16]. The project assumed the 77 km HTS which was expected to transport 1000 MW of heat. The inner pipeline diameter was specified to be 1200 mm. The supply temperature was assumed equal to 120 C and the return temperature - to 54 C, with the resulting mass flow rate of 3580 kg/s. The overall heat loss was estimated as 11 MW, meaning that the heat loss ratio was 1.1%. In [2,17] the 110 km long 3000 MW HTS was evaluated. In that
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case, two main lines, each transporting 1500 MW, were considered. The inner pipeline diameter of 2000 mm with insulation thickness of 300 mm was selected for the supply temperature of 120 C. The authors report the pressure drop of 0.16 bar/km and less than 2% of heat loss during the transportation. A concept of two phase thermochemical process for heat transportation from Bugey NPP to Lyon area (35 km) is analyzed in [18]. In [19], a concept of long distance heat transportation based on absorption heat exchangers is presented. The authors considered low-grade waste heat transportation over distances of up to 100 km. Different approaches to design optimization of various elements of the long distance HTS have been presented in a number of scientific papers. A methodology for technoeconomic analysis of a CHP NPP was presented in [4]. The authors considered modification of condensing-extraction turbine systems which was necessary to improve heat production and transportation parameters in order to evaluate the technological feasibility and profitability of the nuclear cogeneration plant. In [2] the supply temperature and the pipeline diameter were chosen separately. Firstly, the optimal temperature range was established, followed by arbitrary temperature selection from that range. Then the minimum of the estimated cost of thermal energy as the function of pipeline diameter was found. In many cases, both the aim and methods of optimization of long distance fuel transportation systems are similar to those applied for the considered HTS, which justifies taking advantage of authors’ experience. In [20] the problem of natural gas transportation via pipeline systems is overviewed. The system design (pipeline length and diameter, compressor station locations) and operation (operating costs of compressors) are commonly subjected to optimization. The population based optimization techniques, such as evolutionary and genetic algorithms, are effectively utilized to solve the design and operation optimization problems in long distance fuel transportation [21] because of their ease and flexibility in solving hybrid, multicriteria and constrained optimization problems. DH networks are often subject to detailed analysis in order to find optimal pipes sizing [22] or to minimize the heat loss [23,24]. Similar approaches can be utilized for DH supply systems which are expected to transport the heat from the HS to the DH area over long distances. The novelty of the approach presented in this paper is, besides taking into account the time and spatial structure of the problem, the possibility of evaluation and decision making on the pipe-lying strategy. This will allow the decision-maker to find optimal values of the number, design and operation of multiple pipelines working in parallel. Moreover, the HTS decision model, built for the purpose of design and operation optimization, has been improved in terms of computational complexity by applying an additional spatial discretization method. Due to the improved computing performance, the genetic solver could be effectively applied for mixed-integer solutions.
2. Decision model for optimization-based efficiency analysis 2.1. Assumptions The decision model for the HTS optimization-based efficiency analysis consists of the mathematical model of objectives and constraints, and optimization problem formulation. Preconditions and necessary inputs for optimization are specified as follows: The HTS should be analyzed within a certain timeframe and based on the annual costs. This leads to the analysis conducted for the presumed project lifetime, with the primary time base of one year. The length of the HTS project life cycle is assumed to be equal to the HS lifetime, designated by .
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Locations of the HS and the DH area are known. This leads to conclusions that the route of the HTS is known and, as a result, the terrain elevation profile of the HTS is known as well. The sample terrain elevation profile is shown in Fig. 1.
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Fig. 1. The sample HTS terrain elevation profile
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The knowledge of the HTS route leads to further considerations: since the historic data on air temperatures on the HTS route are known, there is a possibility to determine the ground temperatures in the corresponding period. It is convenient to use temperature profiles in the form of structured graphs when formulating the optimization problem (Fig. 2.). The air and/or ground temperatures are assumed to be the same along the whole HTS route.
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Annual heat demand of the DH area is given in the form of structured graph
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In addition, a number of case study dependent parameters, such as insulation, thermal conductivity, or nominal pipeline pressure, need to be specified. A detailed list of case study parameters is presented in the case study discussion. Furthermore, for the purpose of decision model formulation, the following assumptions concerning HTS operation are considered: the heat delivered to the DH is equal to the heat demand; the outlet and inlet temperatures of the HS heat exchanger are the supply and return temperatures, respectively; the pumping station pressure gains are constant and independent of the heating water flow rate. Further assumptions for the decision model computation are: only steady states are considered, minor pressure losses are neglected.
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2.2. Time and spatial discretization
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The evaluation of the HTS design and operation over its life cycle has to take into account time variability of HTS operation conditions and parameters. The time-variant processes affecting the HTS occur on significantly different time scales. The pipeline and insulation aging are examples of processes with time constants of several years. It is convenient to approximate the impact of these processes as fixed over some intervals. This approach leads to Long Horizon Time Discretization (LHTD) of the HTS life cycle , with time step, into intervals indexed by . As a result, for selected parameters such as: pipeline roughness, thermal conductivity, and the price of heat and electricity, it is possible to acquire different constant values for each life cycle interval. Depending on the decision maker’s needs and knowledge, the LHTD time step can be either fixed or variable. The HTS is also subjected to significant annual variability due to annual heat demand and ground temperature changes. To deal with these conditions, the Short Horizon Time Discretization (SHTD) is proposed. The SHTD time base is one year, which is divided with the variable time step into intervals indexed by , in accordance to the discretized, structured graph of annual heat demand (see Fig. 3). As a result, sub-models are created for each LHTD interval. Each sub-model corresponds to a different heat demand level (different part of the year) and is characterized by different flows and temperatures.
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Although the duration of each LHTD interval may be decades, its parameters are assumed constant over that period and, consequently, it may be covered by only one set of sub-models, the results of which are multiplied according to the LHTD time step. According to the HTS topology scheme shown in Fig. 4, the HTS is a network composed of links, base nodes, and computational nodes. The links are pipeline sections, pipeline sections with pumping stations, or heat exchangers. The base and computational nodes are allocated according to the applied spatial discretization methods. Spatial discretization is introduced to deal with the HTS spatiality and the resultant terrain elevation profile impact on the nodal pressure and on the pumping stations localization (see Fig. 1). The base discretization is characterized by a small, fixed step, which ensures high accuracy of the thermal mathematical model due to temperature approximations over short pipeline sections. As a consequence of base discretization, the HTS of length [km] is discretized with the step [m], resulting in base nodes in each direction, indexed by . In order to reduce the computational complexity of the mathematical model, the computational discretization is proposed and applied. This method allows to reduce the number of nodes without accuracy deterioration. The terrain elevation profile, given with the base resolution is chosen as the basis of computational discretization, with the computational nodes being allocated at points of terrain profile change, as shown in Fig. 5. Therefore, the HTS is discretized with the variable step [m] which is an integer multiplicity of the , resulting in nodes in each direction, indexed by . In both discretization methods, the supply and return pipeline directions are denoted with the second subscript . The parallel pipelines are indexed with .
Supply lines
Computational nodes 1,1 Δlc,1 lb
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Heat Source side heat exchanger (HSe)
Nc,2
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Return lines
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1,1 2,1 Base nodes
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District Heating network side heat exchanger (DHe) Pipeline section i Δlc,i ic,2
ic+1,2 ib+2,2
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ib,2
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Fig. 4. Scheme of HTS topology
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7 Computational nodes 1 2 3 4
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Δlc,7 8
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Terrian elevation profile [m]
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Fig. 5. Scheme of spatial discretization
2.3. Mathematical models
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The mathematical model formulation utilizes reduced notation for conciseness. The nodal variables (describing a quantity at each node) have the subscripts , meaning respectively: the node number (either base or computational), the supply/return line, the SHTD interval, the LHTD interval, and the pipeline. In reduced notation, unless necessary, only the subscript is listed while the subscript is completely omitted until the criteria are formulated.
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2.3.1. Thermal mathematical model
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The main purpose of the thermal model is to calculate the heat loss during transportation. This quantity must be taken into account to ensure that the delivered heat equals the heat demand, which is one of the main assumptions. Considering the pipeline section of length [m], diameter [m], external insulation thickness of [m], and thermal conductivity W/(m∙K)], in which the superheated water at temperature of [K] is flowing (Fig. 6), the ̇ linear heat loss can be calculated as: ̇
̇
̇
(
)
(1) ⁄ where ̇ is the heat transfer rate at given base pipeline section [W] and is the ground temperature [K]. Note that the insulation thermal conductivity and the ground temperature in (1) are discretized according to LHTD and SHTD, respectively. Another important feature of the presented linear heat loss model is the approximation of superheated water temperature over the section with , which is the inlet temperature to the section. Different approximation methods, such as inlet-outlet average or logarithmic mean can also be utilized, however if the section length is small enough, the outcome differences are negligible. The exact value of ‘small enough’ section length is dependent on the case study
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and can vary from 100 meters up to several kilometers. The loss of heat translates in direct proportional manner into the temperature loss: ̇ (2) ̇ where is the specific water heat capacity [J/(kg∙K)] at 100˚C, and ̇ is the heating water mass flow [kg/s] at a given time step. Assuming the absence of heating water phase change in the heat exchanger and the heat exchanger efficiency , the heating water mass flow can be calculated from the amount of the exchanged heat and the temperature drop on the heat exchanger. This applies for both DH and HS side heat exchangers: ̇ ̇ (3) ̇
Tg
Ti 1 Q i 1 Pi 1
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In Eq. (3), ̇ is the heat delivered to the DH network per second [W], with the temperature drop of [K]. Similarly, ̇ is the heat absorbed from the HS per second [W] at temperature drop [K] (time discretization indexes are omitted). The heat delivered to the DH network is equal to the heat demand and is known at any time, while the amount of heat needed from HS has to be calculated as the sum of the total heat lost in transportation in both directions and the heat delivered. The same applies to temperatures: is equal to the difference between the supply and return temperatures, which are inputs to the model, while has to be calculated using Eqs. (1-3).
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Fig. 6. Scheme of pipeline section with associated variables and parameters
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The proposed thermal model is characterized by dense base nodalization, which is required because of the temperature approximation accuracy. At the same time, the terrain elevation profile based spatial computational discretization is much sparser. It can be shown that the thermal model can be calculated only at the computational nodes, without the need to compute all the base nodes in between. Considering the heat loss ratio in two successive pipeline sections, as shown in Eq. (1): ̇ ̇ | ̇ ̇ ̇ ( ) (4) ̇ ⁄ ̇ it can be observed that the successive heat loss ratio values are constant and lower than 1 at any given time step. The same applies to the temperature loss ratio, as these two quantities ⁄ are proportional. It can be seen that also equals . Therefore, the heat or temperature loss at any base pipeline section can be found from the geometric sequences: ̇ ̇ . By applying geometric series, the heat rate and the temperature at any base pipeline section can be calculated:
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̇
̇ ̇
(5) (6)
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As the computational nodes are allocated at the integer multiplicity of the base discretization step , the base thermal model (Eqs. (1-6)) can be modified, allowing high accuracy calculations of the heating water temperature and the heat rate, while utilizing reduced nodalization: ̇ (7) ̇ ̇ (8)
∑
(9)
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̇ and The first node is the same for both spatial discretization methods, therefore ̇ . The heat and temperature losses at the first pipeline section ̇ and are calculated from Eqs. (1) and (2), respectively. The reduced thermal model can be solved either as the system of equations, or by using sequential procedure as described in [3]. 2.3.2. Hydraulic mathematical model
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The hydraulic model is the base for calculating the number of the required pumping stations and their locations, as well as the electrical power used for pumping. Since the supply and return lines of the considered HTS are buried in a single trench, the terrain elevation has no impact on the number of pumping stations, as its impact on the pressure profile cancels out. However, the terrain has still a strong impact on pumping station locations. The pressure drop between consecutive base nodes [Pa] is affected by: the linear pressure loss [Pa] (minor pressure losses are neglected), the elevation difference pressure [Pa], and the possible pressure gain [Pa] due to pumping station
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allocation at the inlet node. As a consequence of the assumed fixed pipeline diameter and closed HTS structure (without branching nodes), the flow velocity is the same for each node at any given time step. Thus, the linear pressure loss over the pipeline section is constant for any given time step and can be described by the Darcy-Weisbach equation: (10)
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where is the density of water [kg/m3], is the heating water flow velocity [m/s], calculated from the mass flow rate, and is the Darcy-Weisbach friction coefficient, which for the fully turbulent flow (Reynolds number>4000) and the inner pipe roughness of [mm] can be calculated as shown in [2]. The overall pressure drop between consecutive base nodes is defined as follows: (11) where ( ), is the HTS elevation head [m] and is the Earth gravity 2 constant [m/s ]. As for the thermal model, the hydraulic model base nodalization can be reduced without accuracy deterioration, thus decreasing computational burden. Due to constant linear pressure loss over the pipeline section, the linear pressure loss between any two nodes can
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be found by applying arithmetic series. The elevation difference pressure between any two nodes and the corresponding pressure gain are also available. Assuming that the pressure at the first node is equal to the nominal pressure [Pa], set by the main pumping station, the pressure at any computational node can be obtained from Eq. (12). (
)
∑
(12)
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where is introduced from Eq. (9). The pumping stations can be allocated according to a simple rule: add a pumping station whenever the nodal pressure decrease is below the safety limit. The pressure gain of a single pumping station can also be fixed and be the same for each station. 2.3.3. Pipe-laying strategy
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The same amount of heat can be transported using different pipe-laying strategies. Depending on the peak value and annual variation of heat demand, it may be cost-effective to use a single, large diameter pipeline or a number of smaller pipelines. The decision regarding the pipe-laying strategy should be a result of optimization. Therefore, the decision model is extended, allowing parallel pipelines with independent variables and parameters, except for the supply and return temperatures. The number of actually used pipelines is determined indirectly, as the optimizer choses the limit value of the maximum heat that can be transported by a single pipeline ̇ per second [W]. Based on that limit and the heat demand at a given time step, the number of active pipelines is specified using Eq. (13). The peak heat demand requires most pipelines, each contributing to the overall construction costs, including separate pumping stations for each pipeline. At a given time step, an arbitrary number of pipelines can be utilized, simultaneously or alternately, depending on the current heat demand. ̇ (13) ⌈ ⌉ ̇
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To prevent the possibility of the number of active pipelines exceeding the number of allowed pipelines , the lower bound on ̇ is specified: ̇ ̇ (14)
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2.4. Optimization problem formulation As a result of time discretization, a number of sub-models are established. Each sub-model is described by a set of variables. Some of these variables are the same for each sub-model (i.e. inner pipeline diameters, insulation thickness, supply and return temperatures), while other, such as nodal pressure or temperature, are independent. While all variables together constitute the decision space , the former are more important for the decision-making process. Therefore, categorization of the decision space is proposed, in which the variables shared by the sub-models are called the design vector, denoted , while the remaining variables compose the simulation vector . According to this categorization, the decision [ ] . A detailed form of the design vector is shown in space is represented as Eq. (15).
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[
|
̇
|
]
(15)
∑ [ ̇ ̇
̇
∑[
̇
]
̇
̇
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(16)
(17)
]
(18)
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The inner pipeline diameter and the insulation thickness are integer variables. These variables can be modified in order to represent indexes of either pipeline diameters or insulation thicknesses selected from the appropriate series. The decision variables are subjected to a set of nonlinear equality constraints that constitute the mathematical model. Furthermore, the upper and lower bounds, as well as the inequality constraints , can be considered on the decision space due to technological and operational limitations. The range of considered supply temperatures and the maximal heating water flow velocity can be examples of such constraints. The HTS design and operation is assessed taking into account its technical and economic value. The technical value can be represented by terms of thermal and transport efficiency. One way to assess the thermal efficiency of the HTS is to estimate its life cycle heat loss in transportation. It can be done by calculating firstly the heat loss of each suḃ ̇ model for each pipeline [W] (Eq. (16)), followed by the annual heat loss [GJ/year] (Eq. (17)) and the total heat loss Δ [GJ] in transportation (Eq. (18)).
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where: is the unit conversion coefficient, is the time step of interval [years], and is the time step of sub-model [days]. The transport efficiency can be represented by the amount of energy used for heating water pumping. First, the pumping power of each sub-model for each pipeline [W] is found using Eq. (19). Then, the annual pumping energy [MWh/year] is calculated using Eq. (20), finally the total pumping energy [MWh] is obtained from (Eq. (21)):
where
∑ [(
)
∑[
∑[ is the unit conversion coefficient,
̇
]
]
(19)
(20)
]
(21)
is the pump efficiency,
is the
number of pumping stations set for the given sub-model and pipeline, is the pressure added by the pump station [MPa], is the pressure added by the main pump station [Pa] and ̇
is the volumetric flow rate [m3/s].
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The economic value of the HTS is estimated using the empirical construction cost function: ∑
∑
(22)
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where is the overall HTS construction cost [m.u.], is the pipeline material and labor costs of each active pipeline as a function of pipeline diameter, and is the cost of pumping station construction [m.u.]. The subscript means the maximum value of the variable in the range of all intervals and sub-models. The objective functions Eqs. (16-22) [ ] , can be represented as the objective vector leading to general optimization problem formulation: s.t.
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3. Solver
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The optimization problem is multicriteria, nonlinear, and hybrid, as a result of simultaneous occurrence of integer (e.g. inner pipeline diameter) and continuous (e.g. water temperature) decision variables. The combination of these properties makes the problem difficult to solve. In an attempt to simplify the optimization problem, the weighted-sum scalarization method is proposed. Eq. (18) is multiplied by heat and Eq. (21) by electricity prices, thus allowing summation of the objective functions. The resultant optimization problem, with integer values of pipeline diameters and insulation thickness and real values of other decision variables, is solved using a genetic algorithm solver. One of the genetic algorithm steps is the HTS design evaluation. Due to time and spatial discretization, and the multiple pipeline option, it is a complicated process. The results for all sub-models, intervals, and pipelines have to be merged in order to calculate the fitness function. The flowchart of the HTS design evaluation procedure is shown in Fig. 7. In this case the sequential method presented in [3] is applied to compute the temperature, heat and pressure profiles. This procedure is represented as the “Mass flow estimation loop” block. Due to the structure of the decision model, all sub-models, intervals and pipelines are independent of each other. Consequently, all instances of each loop can be computed in parallel, which greatly increases the computing performance. Respective results are merged in three-stage aggregation, described by Eqs. (16-22).
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For each of the 𝜏𝐿 LHTD intervals
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For each of the 𝜏𝑆 SHTD sub-models
For each of the Np pipelines
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Initial mass flow estimation
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Linear pressure loss
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Pressure profile
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Pumping stations
Heat loss (16) and pumping power (19)
Annual heat loss (17) and annual pumping energy (20)
Total heat loss (18) and total pumping power (21), construction costs (22) Fig. 7. The HTS design evaluation flowchart
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4. Case Study The presented methodology has been verified and analyzed based on the case study of a 40 km HTS. The NPP, located by Lake Żarnowiec, Northern Poland, was assumed to be the intended heat source, while the main heat customer would be the city of Gdynia and its surroundings. The knowledge of NPP and DH locations allows specifying the terrain elevation profile (Fig. 8a.), the annual ground temperature, and the DH heat demand (Fig. 8b.). b)
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Days
Distance [km]
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Fig. 8. a) The case study terrain elevation profile, b) structured graph of annual ground temperature and heat demand
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A maximum of two possible pipelines was assumed, resulting in the decision vector size of 7. The lower and upper bounds were specified:
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(24)
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[ ] [ ] ] [ The and variables represent the indexes of insulation thickness series [ ] [m]. The lower bound on ̇ is a result of Eq. (14). The pipeline construction cost estimation function is specified by Eq. (25). The insulation thickness of 0.1 m decreases its outcome by 15%, while the 0.3 m case increases it by 15%. (25) The case study parameters are shown in Table 1. The number and length of SHTD intervals can be read from Fig. 8b. Three LHTD intervals of 20 years each are considered, allowing the variability of certain parameters: pipe roughness, insulation thermal conductivity, and heat and electricity prices. Due to the HTS length and the base spatial discretization step, there are 401 base nodes. The appliance of computational discretization resulted in only 22 computational nodes, while all calculations are still done with the accuracy of 100-meter base step.
Table 1. Case study parameters Parameter
Symbol
Value
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LC [years] ΔτL [years]
Number of computational nodes Number of possible pipelines Pipe roughness Insulation thermal conductivity Nominal pressure Minimal supply line pressure Minimal return line pressure Pump pressure gain Heat price Electricity price Pumping station cost Pump efficiency Heat exchanger efficiency
Nc Np [mm] λis [W/(m∙K)] Pnm [MPa] Pmin S [MPa] Pmin R [MPa] Pg [MPa] ph [€/GJ] pe [€/MWh] cps [M€]
[days]
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L [km] lb [m] Nb Δlc,i [100 m]
60 [20, 20, 20] 3 [25, 30, 35, 90, 45, 18, 122] 7 40 100 401 [7,3,10,17,11,10,4,10,10,14,6, 23,16,19,19,31,11,17,22,67,73] 22 2 [0.1, 0.15, 0.2] [0.02, 0.03, 0.05] 1.5 0.24 0.05 1 [12, 18, 24] [60, 64, 68] 3.5 0.75 1
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HTS life cycle LHTD time step Number of LHTD intervals SHTD time step Number of sub-models HTS length Spatial discretization base step Number of base nodes Spatial discretization computational step
The results of the optimization procedure for the analyzed case study are presented in Table 2.
Variable
Design variables: Symbol 80% Heat 100% Heat 120% Heat Demand Demand Demand 1 1 1
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Table 2. Optimization results
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Inner pipeline 1 diameter [m] 0.606 Inner pipeline 2 diameter [m] Pipeline 1 insulation [m] 0.3 Pipeline 2 insulation [m] Supply temperature TS [K] 393.15 Return temperature TR [K] 323.15 Heat transportation limit Q̇ 220 [MW] Number of pumping 6 stations Objective functions [M€]: Construction costs CC 171.97 Heat loss costs ΔQ’TL 68.56 Pumping energy costs W’TL 38.99 Total costs J 279.53 Selected operation variables: Flow velocity [m/s] 2.49 Pressure drop per 1 km [bar/km] 0.75 ̇ Heat loss per 1 km [MW/km] 0.054 ̇ Supply line heat loss 2.17 [MW] ̇ Return line heat loss 0.90 [MW] Heat loss rate [%] 1.53
0.659 0.3 393.15 323.15 250 6
0.707 0.3 393.15 323.15 300 6
195.22 72.91 48.89 317.03
217.79 76.83 58.33 352.95
2.62 0.75 0.058 2.3 0.95 1.3
2.73 0.75 0.061 2.43 1 1.14
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Three cases of heat demand are considered: 80%, 100% and 120% of the DH heat demand shown in Fig. 8b. Each time, the maximum heat that can be transported by single pipeline is equal to the peak heat demand, therefore only one of the two possible pipelines is active. The supply and return temperatures are on the upper and lower bounds, respectively, which means that the temperature difference is always maximized. It can be observed that the benefits of thicker insulation outweigh the 15% construction costs increase for each of the heat demand cases. The heat loss costs Δ [M€] and the pumping energy costs [M€] result from total heat loss and total pumping energy weighting by corresponding prices.
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The pressure profile and the pumping station locations for the case of 100% heat demand are shown in Fig. 9. The pumping stations located on the supply line are marked by blue dots, while those on the return line by green, and the main pumping station by black. Significant impact of the terrain elevation profile on the pressure profile can be observed. The cross-section of the objective function and its components is shown in Fig. 10. All design variables except the inner diameter of pipeline 1 are fixed, and pipeline 2 is inactive. The objective function is non-convex due to the number of pumping stations. x 106
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Fig. 9. Pressure profile with marked pumping station locations
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Objective function J [M€]
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Q' T L W' T L
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100 325
50
315 600
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640 660 680 Inner pipeline 1 diameter [m]
700
Objective function components [M€]
200 J C' c
0 720
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=0.3 m
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The impact of variations of selected parameters on the optimization results is presented in Table 3. The HTS life cycle and electricity price are considered. In the case of [ ]. For years, three LHTD intervals are considered, with the time step: years, there are two LHTD intervals, each spanning 10 years. The impact of insulation and pipe aging processes on optimal inner pipeline diameter and insulation thickness can be observed. In the case of shorter life cycle, the pipe roughness is smaller, which results in smaller inner pipeline diameter. Similarly, the overall smaller insulation thermal conductivity resulted in lower insulation thickness. The total costs for the case of years have decreased by almost 38% in comparison to the base case (60 years), while the operation time is shorter by roughly 67%. The temperature difference is still maximized and again, there is only one active pipeline. The variation of electricity price, which is applied to each LHTD interval, shows the trade-off between the inner pipeline diameter and the number of pumping stations. Table 3. Impact of variations of selected parameters on the optimization results Symbol
Design variables: LC = 20 LC = 40 years years 1
Inner pipeline 1 diameter [m] Inner pipeline 2 diameter [m] Pipeline 1 insulation [m] Pipeline 2 insulation [m] Supply temperature TS [K] Return temperature TR [K] Heat transportation limit Q̇ [MW] Number of pumping stations
0.634 0.1 393.15 323.15 250 7
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140% electricity price
1
1
1
1
0.641 0.2 393.15 323.15 250 7
0.659 0.3 393.15 323.15 250 6
0.624 0.3 393.15 323.15 250 8
0.683 0.3 393.15 323.15 250 5
195.22 72.91 48.89 317.03
186.67 70.06 38.92 295.65
202.82 74.86 56.88 334.56
Objective functions [M€]: 145.00 168.96 33.87 54.54 19.13 36.67 198.00 260.17
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Construction costs Heat loss costs Pumping energy costs Total costs
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60% electricity price
Base case
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Variable
5. Conclusions
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The proposed method to optimize HTS efficiency can be utilized as part of the decision support system for evaluation of projects associated with heat transportation. An example of such a project is the Combined Heat and Power NPP, where part of the technical and economic feasibility assessment task concerns a high-power, long distance HTS. With the appliance of the proposed DSS, the optimal design and operation strategy of the HTS can be found with respect to construction costs, and thermal and transport efficiency, while being subject to a number of operation and technological constraints resulting from the mathematical model and governing equations. Additional constraints can be imposed by the decision-maker to ensure specific HTS operation, i.e. heating water flow velocity or heat loss over the pipeline section. An important feature of the proposed method is the ability to evaluate projects in long term or in particular, over the project life cycle. Long Horizon Time Discretization allows consideration of pipe and insulation aging phenomena, as well as heat and electricity prices
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changes. At the same time, conditions of the time scale of a month or even days are still taken into account due to Short Horizon Time Discretization. In addition, the proposed method takes into account the spatial topology of the HTS to evaluate the terrain elevation impact on the nodal pressure and localizations of pumping stations. The decision model formulation allows the user to investigate different pipe-lying strategies. Depending on the case study and decision-maker’s preferences, the solver determines whether one bigger or several smaller pipelines are more cost effective. As a result, a set of integer design variables is found by solving the optimization problem for each pipeline inner diameter, insulation thickness, number of pumping stations, as well as for two real variables: supply and return temperatures. Moreover, all of the simulation variables, such as nodal pressure or temperature, are calculated and stored, thus making a basis for further HTS safety analyzes.
Acknowledgements
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The research work was done under the grant 8902/E-359/M/2016 entitled “Young Researcher Support Program” and financed by the Polish Ministry for Science and Higher Education. The authors wish to express their thanks for support.
References
[4]
[5]
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Connolly D. Heat Roadmap Europe: Quantitative comparison between the electricity, heating, and cooling sectors for different European countries. Energy 2017;139:580– 93. doi:10.1016/j.energy.2017.07.037. Safa H. Heat recovery from nuclear power plants. International Journal of Electrical Power & Energy Systems 2012;42:553–9. doi:10.1016/j.ijepes.2012.04.052. Hirsch P, Duzinkiewicz K, Grochowski M, Piotrowski R. Two-phase optimizing approach to design assessments of long distance heat transportation for CHP systems. Applied Energy 2016;182:164–76. doi:10.1016/j.apenergy.2016.08.107. Jaskólski M, Reński A, Minkiewicz T. Thermodynamic and economic analysis of nuclear power unit operating in partial cogeneration mode to produce electricity and district heat. Energy 2017. doi:10.1016/j.energy.2017.04.144. Colmenar-Santos A, Rosales-Asensio E, Borge-Diez D, Collado-Fernández E. Evaluation of the cost of using power plant reject heat in low-temperature district heating and cooling networks. Applied Energy 2016;162:892–907. doi:10.1016/j.apenergy.2015.10.161. Lund H, Möller B, Mathiesen BV, Dyrelund A. The role of district heating in future renewable energy systems. Energy 2010;35:1381–90. doi:10.1016/j.energy.2009.11.023. Leurent M, Da Costa P, Rämä M, Persson U, Jasserand F. Cost-benefit analysis of district heating systems using heat from nuclear plants in seven European countries. Energy 2018;149:454–72. doi:10.1016/j.energy.2018.01.149. Locatelli G, Fiordaliso A, Boarin S, Ricotti ME. Cogeneration: An option to facilitate load following in Small Modular Reactors. Progress in Nuclear Energy 2017;97:153– 61. doi:10.1016/j.pnucene.2016.12.012. Leurent M, Jasserand F, Locatelli G, Palm J, Rämä M, Trianni A. Driving forces and obstacles to nuclear cogeneration in Europe: Lessons learnt from Finland. Energy Policy 2017;107:138–50. doi:10.1016/j.enpol.2017.04.025.
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[10] Tokimatsu K, Konishi S, Ishihara K, Tezuka T, Yasuoka R, Nishio M. Role of innovative technologies under the global zero emissions scenarios. Applied Energy 2016;162:1483–93. doi:10.1016/j.apenergy.2015.02.051. [11] Persson U, Möller B, Werner S. Heat Roadmap Europe: Identifying strategic heat synergy regions. Energy Policy 2014;74:663–81. doi:10.1016/j.enpol.2014.07.015. [12] Puchalski B, Rutkowski TA, Duzinkiewicz K. Nodal models of Pressurized Water Reactor core for control purposes – A comparison study. Nuclear Engineering and Design 2017;322:444–63. doi:10.1016/j.nucengdes.2017.07.005. [13] Minkiewicz T, Reński A. The Possibility to use a Nuclear Power Plant as a Source of Electrical Energy and Heat. Acta Energetica 2014:114–8. doi:10.12736/issn.23003022.2014310. [14] Hirsch P, Grochowski M, Duzinkiewicz K. Pipeline system for heat transportation from nuclear power plant - An optimizing approach, IEEE; 2015, p. 1044–9. doi:10.1109/MMAR.2015.7284023. [15] Paananen M, Henttonen T. Investigations of a long-distance 1000 MW heat transport system with apros simulation software, Espoo, Finland: 2009. [16] Bergroth N. Large-Scale Combined Heat and Power (CHP) Generation at Loviisa Nuclear Power Plant Unit 3. Proceedings of the 8th Conference on Nuclear Option in Countries with Small and Medium Electricity Grids Dubrovnik, Croatia, 16–20 May 2010. [17] Jasserand F, Devezeaux de Lavergne J-G. Initial economic appraisal of nuclear district heating in France. EPJ Nuclear Sciences & Technologies 2016;2:39. doi:10.1051/epjn/2016028. [18] Le Pierrès N, Luo L, Berthiaud J, Mazet N. Heat transportation from the Bugey power plant. International Journal of Energy Research 2009;33:135–43. doi:10.1002/er.1429. [19] Xie X, Jiang Y. Absorption heat exchangers for long-distance heat transportation. Energy 2017;141:2242–50. doi:10.1016/j.energy.2017.11.145. [20] Ríos-Mercado RZ, Borraz-Sánchez C. Optimization problems in natural gas transportation systems: A state-of-the-art review. Applied Energy 2015;147:536–55. doi:10.1016/j.apenergy.2015.03.017. [21] Wang Y, Tian C-H, Yan J, Huang J. A survey on oil / gas pipeline optimization: Problems, methods and challenges, Suzhou: IEEE; 2012, p. 150–5. doi:10.1109/SOLI.2012.6273521. [22] Asim T, Mishra R, Kollar LE, Pradhan SR. Optimal sizing and life-cycle cost modelling of pipelines transporting multi-sized solid–liquid mixtures. International Journal of Pressure Vessels and Piping 2014;113:40–8. doi:10.1016/j.ijpvp.2013.11.003. [23] Dalla Rosa A, Li H, Svendsen S. Method for optimal design of pipes for low-energy district heating, with focus on heat losses. Energy 2011;36:2407–18. doi:10.1016/j.energy.2011.01.024. [24] Başoğul Y, Keçebaş A. Economic and environmental impacts of insulation in district heating pipelines. Energy 2011;36:6156–64. doi:10.1016/j.energy.2011.07.049.
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