Department of Architecture and Civil Engineering Division of Building services engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2020 Master’s Thesis 2020:ACEX60 Optimization modeling of the district cooling system in Gothenburg Master’s Thesis in Sustainable Energy Systems SHRAVAN KUMAR ii iii MASTER’S THESIS 2020:ACEX60 Master’s Thesis in Sustainable Energy Systems Supervisors: Maria Jangsten and Torbjörn Lindholm Examiner: Jan-Olof Dalenbäck Department of Architecture and Civil Engineering Division of Building services engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2020 iv Optimization modeling of district cooling system in Gothenburg SHRAVAN KUMAR © SHRAVAN KUMAR, 2020 Supervisors: Maria Jangsten and Torbjörn Lindholm, Division of Building services engineering Examiner: Jan-Olof Dalenbäck, Division of Building services engineering Master’s thesis 2020:ACEX60 Department of Architecture and Civil Engineering Division of Building services engineering Chalmers University of Technology SE-412 96 Gothenburg, Sweden Telephone: + 46 31-772 1000 v Optimization modeling of the district cooling system in Gothenburg SHRAVAN KUMAR Department of Architecture and Civil Engineering Division of Building services engineering Chalmers University of Technology Abstract Göteborg Energi is the sole provider of district cooling in the Gothenburg. The district cooling system (DCS) is currently expanding. The installed capacity in 2030 will be double the current capacity. Besides, a thermal energy storage (TES) in the form of a tank that stores cold water will be installed in the system by 2024. The impact of future investments on the operation of the system must be investigated. Further, the district cooling network is also modeled and an effective method to model the district cooling network into a numerical model is developed. To evaluate the effect of the different investments and the interaction of the cooling system with the heating and electricity sectors, an optimization study through the software GAMS has been conducted in this thesis. The model has been formulated as a mixed integer optimization problem. Models and cases were created to examine different scenarios. Model 1 dealt with the optimization of the chilled water generation in the DCS. Further, three different cases are setup within model 1 to analyze different scenarios. Case 2018 compared the optimal operation of the district cooling system to a hypothetical best alternative case of having chillers in individual buildings. The impact of the thermal energy storage on the system was investigated in case 2024. In case 2030, different scenarios were considered to evaluate the impact of the developments in the heating and electricity systems on the operation of DCS. In model 2, the chilled water generation and distribution are optimized together. Like model 1, model 2 also consists of different cases to investigate different scenarios. Case 2018 compared different methods of effectively modeling the network in numerical models. The two methods considered in this case are the ‘Fixed pumping parameter’ method and the ‘Linked cost functions’ method. In case 2024, the impact of the tank was investigated when modeled along with the network. The optimization was performed on an hourly basis and the prices of heat were obtained from a corresponding model of the DHS. The electricity price profiles were obtained either from spot market prices or from modeled future prices. It was found from model 1 that the district cooling system was more economical and environment friendly that the hypothetical best-case alternative of a conventional cooling system. The results from model 1 also showed that the installation of the TES in the system helps achieve significant savings in the system. The major result from ‘model 1 - case 2030’ was that future investments in the district cooling system depend largely on the developments in the electricity system. From model 2, it was concluded that the linked cost functions method has a more detailed representation of the network and is a more effective method to model the network. Lastly, in ‘model 2 – case 2024’, it was seen that the optimal operation of the TES depended on the control strategy of the TES and the location of the chillers. Keywords: District cooling, optimization modeling, network modeling, thermal energy storage. vi Acknowledgment I would like to thank my supervisor at Chalmers University of Technology, Maria Jangsten for making this study possible and for her great support with material and inspiration. Her inputs throughout the thesis have been very important. I am also grateful to her for generously dedicating time to answer my questions. I wish also to thank my supervisor Torbjörn Lindholm for dedicating time to answer my questions and for his support during the thesis. I would also like to express my gratitude to my examiner Jan-Olof Dalenbäck for his guidance. I also thank Anders Strand at Göteborg Energi for making this study possible and for supporting me throughout the thesis with data and valuable discussions. I am also grateful to Marc Thevenot, Jan Ahlgren, Paul Leinberg, and Per Gustafsson at Göteborg Energi for their valuable inputs. I Would also like to thank everyone at the division of building services engineering at Chalmers for making the last one year fun and enjoyable. My thanks also go out to Dmytro Romanchenko, Viktor Walter, and Karl Vilén at the division of energy technology at Chalmers for their valuable support and input. Shravan Kumar, Gothenburg, June 2020 vii Contents Abstract ................................................................................................................................................... v Acknowledgment ................................................................................................................................... vi Contents………………………………………………………………………………………… … vii Abbreviations and Symbols .................................................................................................................... x Chapter 1: INTRODUCTION ................................................................................................................. 1 1.1 Purpose .................................................................................................................................... 2 1.2 Research questions .................................................................................................................. 2 1.3 Scope ............................................................................................................................................. 3 1.4 Limitations and delimitations........................................................................................................ 3 Chapter 2: Background ........................................................................................................................... 4 2.1 District Cooling System ................................................................................................................ 4 2.2 The DCS in Gothenburg ............................................................................................................... 4 2.3 The district cooling network ......................................................................................................... 5 2.3 Operation of the DCS in Gothenburg ........................................................................................... 6 2.4 Investment plans for Future DCS in Gothenburg ......................................................................... 7 2.5 DHS in Gothenburg ...................................................................................................................... 9 2.5.1 The heat demand .................................................................................................................. 10 2.6 Thermal energy storage ............................................................................................................... 11 2.6.1 Thermal energy storage in a chilled water storage tank ....................................................... 12 2.7 Literature review ......................................................................................................................... 14 Chapter 3: Method ................................................................................................................................ 17 3.1 Description of the DCS in Model 1 ............................................................................................ 17 3.1.1 Objective function ................................................................................................................ 18 3.1.2 Demand-Supply balance constraint ..................................................................................... 18 3.1.3 Ramp up and Ramp down constraint ................................................................................... 18 3.1.4 Minimum up and down time constraints .............................................................................. 19 3.2 Description of the District cooling network model: Model 2 ..................................................... 19 3.2.1 Radial network ..................................................................................................................... 19 3.2.2 Linked cost functions ........................................................................................................... 22 3.2.1 Objective function ................................................................................................................ 24 3.2.2 Demand-Supply balance constraint ..................................................................................... 24 3.2.3 Capacity and ramping constraints ........................................................................................ 24 3.2.4 Pipe constraints .................................................................................................................... 24 Chapter 4: Assumptions and Input data ................................................................................................ 26 4.1 Assumptions ................................................................................................................................ 26 viii 4.2 Input Data.................................................................................................................................... 27 4.2.1 Fuel prices ............................................................................................................................ 27 4.2.2 COP of electric chillers ........................................................................................................ 28 4.3 Demand data ............................................................................................................................... 29 Chapter 5: Model Implementation ........................................................................................................ 31 5.1 Model 1 ....................................................................................................................................... 31 5.1.1 Case 2018 ................................................................................................................................. 31 Scenario 1 ...................................................................................................................................... 31 Scenario 2 ...................................................................................................................................... 32 5.1.2 Case 2024 ................................................................................................................................. 33 Cooling demand in 2024 ............................................................................................................... 33 Scenario 3 ...................................................................................................................................... 34 Scenario 4 ...................................................................................................................................... 34 5.1.3 Case 2030 ................................................................................................................................. 35 Cooling demand in 2030 ............................................................................................................... 35 Developments in the DHS............................................................................................................. 35 The electricity system in 2030 ...................................................................................................... 37 DCS in 2030 .................................................................................................................................. 38 5.2 Model 2 ....................................................................................................................................... 39 5.2.1 Case 2018 ................................................................................................................................. 39 Method 1: Model based on fixed pumping cost parameter ........................................................... 39 Method 2: Model based on linked cost functions ......................................................................... 40 5.2.2 Case 2024 ................................................................................................................................. 41 Model with DCS, network and thermal energy storage ................................................................ 41 Chapter 6: Results ................................................................................................................................. 44 6.1 Model 1 - Case 2018 ................................................................................................................... 44 6.1.1 Scenario 1 ............................................................................................................................. 44 6.2.1 Scenario 2 ............................................................................................................................. 47 6.1.3 District cooling vs Individual Chillers ................................................................................. 48 6.2 Model 1- Case 2024 .................................................................................................................... 49 6.2.1 Scenario 3 ............................................................................................................................. 49 6.2.2 Scenario 4 ............................................................................................................................. 50 6.2.3 Impact of the thermal energy storage ................................................................................... 53 6.3 Model 1- Case 2030 .................................................................................................................... 54 6.3.1 Results for scenarios with No coll electricity prices ............................................................ 55 6.3.2 Results for scenarios with Coll electricity prices ................................................................. 57 6.3.3 Performance of the DCS ...................................................................................................... 58 ix 6.4 Model 2- Case 2018 .................................................................................................................... 61 Model based on fixed pumping cost parameter ............................................................................ 61 Model based on linked cost functions ........................................................................................... 62 Comparison of the two models ..................................................................................................... 66 6.5 Model 2 - Case 2024 ................................................................................................................... 67 Model with DCS, network and thermal energy storage ................................................................ 67 6.6 Sensitivity analysis ...................................................................................................................... 71 6.6.1 Model 1 - Case 2018 ............................................................................................................ 71 6.6.2 Model 1 – Case 2024 ........................................................................................................... 73 6.6.3 Model 1- Case 2030 ............................................................................................................. 75 6.6.4 Model 2 – Case 2018 ........................................................................................................... 77 6.6.5 Model 2- Case 2024 ............................................................................................................. 77 Chapter 7: Discussions .......................................................................................................................... 79 7.1 Advantages and disadvantages of the model .............................................................................. 80 7.2 Perfect foresight .......................................................................................................................... 81 7.3 Cooling demand and weather ...................................................................................................... 81 7.4 Input data and assumptions ......................................................................................................... 81 7.5 Network related uncertainties ..................................................................................................... 82 7.6 Future work ................................................................................................................................. 82 Chapter 8: Conclusion ........................................................................................................................... 84 Bibliography ......................................................................................................................................... 86 Appendix ............................................................................................................................................... 89 x Abbreviations and Symbols Abbreviations DC District cooling DCS District cooling system CHP Combined Heat and Power COP Coefficient of Performance SES Seasonal Thermal Energy Storage DH District Heating DHS DHS GAMS General Algebraic Modeling System LP Linear Programming MILP Mixed Integer Linear Programming TES Thermal Energy Storage Symbols T Temperature [°C] ΔT Temperature difference [°C] E Energy [MWh] P Chilled water generation unit α Power to Heat ratio [-] V Volume [m3] C Cost [MSEK] q Chilled water generation [MWh] Q Storage charge or discharge [MW] η Efficiency [-] Cp Specific heat capacity [kJ/kg] 𝜌 Density [kg/m3] ΔP Pressure drop [KPa] v Velocity [ms-1] g Acceleration due to gravity [ms-2] Q̇ Flow [m3/h] A Area [m2] l Length[m] d Diameter[m] f Friction coefficient [-] K Loss coefficient [-] k Roughness coefficient [m] Re Reynolds number [-] ν Kinematic viscosity [m2/s] Pp Pumping power [KW] 𝐸𝑙𝑡Electricity prices [SEK/MWh] xi VC variable cost [SEK/MWh] SC Startup cost [SEK] D Cooling demand [MWh] RU Ramp up [MW] RD Ramp down [MW] On binary variable to indicate the status of a unit [-] tsh Shut down time [hours] tst Start up time [hours] chr Plant charge [MW] dis Cluster discharge [MW] char Total charge [MW] disc Total discharge [MW] t Time Variable [hour] 1 Chapter 1: Introduction The greatest challenge faced by the world right now is global warming. To limit the rise of temperatures around the globe, it is crucial to reduce emissions arising from the use of fossil fuels across various sectors. Reducing energy consumption is an effective approach to reduce emissions. Energy use in buildings accounts for about 37 % of the total primary energy use. About half of the energy consumption in buildings is for space heating and cooling. Space cooling in buildings can be provided by installing chillers, air conditioners or heat pumps in each building or by district cooling (DC). The use of district cooling can reduce the total energy consumption compared to inbuilding installations, by increasing chilled water generation efficiency in centralized plants and make more use of renewable energy. [1] The future of the District Cooling Systems (DCSs) can be described as a smart DCS with an optimal interaction with the electricity grid and the DHS (DHS). With the increasing share of variable renewable electricity in the energy system, there is a need for flexibility in the system. There are several methods to add flexibility, such as combining different systems, adding storage in the system and increasing supply and demand flexibility. [2] In the city of Gothenburg, the utility company Göteborg Energi is the sole provider of district cooling. The chilled water for cooling is generated from three different methods: free cooling from the river, absorption chillers, and electric chillers. In the year 2018, the installed capacity of chillers is 54.5 MW. By the year 2030, Göteborg Energi plans to increase the installed capacity up to 132.5 MW. Also, Göteborg Energi plans to invest in a Thermal Energy Storage (TES) in the form of a tank that can store chilled water. [3] In 2018, about 50% of the chilled water generation is from electric chillers. Electric chillers are the expensive peak load generation in the DC system. With an expansion of the system, the chilled water generation costs will also continue to increase. The DCS in Gothenburg continues to use electricity to run electric chillers to meet peak demand. The electricity consumption from the chillers leads to a large additional demand in the electricity system and can potentially stress the electricity grid. It is to be examined, whether the DCS relieves or burdens the electricity grid as compared to using individual chillers. Thus, the effectiveness of a DC system must be analyzed. This is done by comparing the optimal operation of the DC system with a hypothetical best alternative case of using individual chillers to meet the cooling demand. The usage of TES in the system can replace the expensive peak load generation and hence reduce the chiller running costs [4]. Also, the thermal energy storage in the system can help reduce variations in the cooling demand and hence increase the efficiency of the chillers [5]. The performance of the thermal energy storage will depend on several factors in a DCS: temperature, demand for cooling, electricity prices, the constraints from the network, and prices of heat. Thus, the impact of having a TES in the DCS is to be examined. Further, the performance of DCS in Gothenburg is dependent on the electricity system and the DHSs. The changes in the future electricity and DHS could thus have a significant impact on future investments in the DCS. Thus, the operation of future DCS must be examined. Besides, the impact of the changes in the electricity and the DHS on the operation of the DCS should also be analyzed. 2 A major problem in most models of the district cooling system is the representation of the DC network in the model. A physically-based model can indicate the effects of the district cooling network well, but it is computationally expensive to run optimization programs for large time periods in physical models [6]. Whereas, in a numerical model, the topology of the network is not represented accurately. Thus, for optimization modeling, an effective method must be devised to model the network accurately in numerical models. 1.1 Purpose The purpose of this thesis is to evaluate the optimal operation of the DCS and the DC network in Gothenburg and investigate the impact of future investments in the system. Further, the thesis also explores different methods of modeling the network and integrating the network into numerical models of the DCS. The evaluation will be performed by creating different optimization models of the DCS. These models will represent different scenarios where the effect of installing thermal energy storage is studied and various methods of including the network in the optimization model are examined and compared. The optimizations shall yield the total yearly chiller running costs as well as the hourly marginal price for generating chilled water and the hourly chilled water generation from the chillers. Also, the effects that differing electricity prices will have on the DCS are studied. The effect of the corresponding developments in the DHS is also examined. 1.2 Research questions This thesis aims at answering the following questions. • How effective is the DCS compared to a case of having individual chillers in buildings? • What is the optimal functioning of the DCS and how different is it from the practical operation ? • What impact does a TES have on the DCS and how does it affect the chilled water generation from different chillers? • How is the performance of the DCS in 2030 and what are potential investments in the system? • How will different development scenarios in the electricity and the DHS affect the performance of the DCS in 2030? • How does the inclusion of the DC network affect the results of the model? • What are the different possible methods to effectively model the network in a numerical model? 3 1.3 Scope The scope of modeling in this thesis will include a model of the DCS in Gothenburg. The model consists of the various chiller units in the DCS, the TES, and the network of the DCS. The main aim of the model is to optimize the chilled water generation and the chiller water distribution. The thesis also covers the alternative case of having conventional cooling systems and provides a comparison between the DCS and the conventional cooling system. Further, in the framework of the thesis, different methods are devised for modeling the district cooling network in numerical models. Within the scope of this thesis, both current and future DCS systems are modeled. The current district cooling system is the DCS in 2018 and the future DCSs are the systems in 2024 and 2030. 1.4 Limitations and delimitations The prices of heat and electricity must be input to the model as fuel price. The price of electricity is retrieved from an external source and is not modeled internally. The prices of heat are obtained by running a corresponding model of the DHS in Gothenburg. The district heating network of Gothenburg is connected to several other neighboring district heating networks and district heat can be exported and imported between these networks. In this thesis, only the heat load in the Gothenburg network is modeled and no import or export is considered. It will be assumed that there are no feedback effects between the DCS, the DHS, and the electricity system. In other words, the use of electricity and heat in the DCS (electric and absorption chillers) will not affect the price of electricity and heat. In reality, the demand for electricity in the DC system will have some effect on the price of electricity and heat, but since the studied system is relatively small, the effects can be neglected. The constraints in model 1 are limited to those concerned with the running of the chillers. The constraints due to the network such as congestions are not included in the optimization in model 1. Model 1 only deals with the generation of chilled water to meet the cooling demand but does not include the distribution of the chilled water. Whereas, model 2 includes the constraints in the network and the pumping cost. Thus, the model 2 includes both the generation and distribution of chilled water. No installation costs or fixed costs will be considered when performing the optimizations. The only costs that are considered are the running costs, pumping costs, and startup costs of the chillers. The running costs of the chillers are just the cost of electricity and heat required to run the chillers. The costs of operating the condenser pumps and cooling towers are also excluded from the model. 4 Chapter 2: Background The main aim of this thesis is the optimization of the DCS in Gothenburg and analyzing the impact of investments in the future DCS. Therefore, it is important to provide some background about the system for a better understanding of the results. This chapter explains DCS in general, the current DCS in Gothenburg, and the district cooling network. Future investments in the system such as the TES are also presented. 2.1 District Cooling System The DCS is a setup where cooling energy is centrally generated and is supplied to end-users using water or another secondary fluid as an energy carrier and thus increasing economy of scale. DCSs deliver chilled water or a secondary fluid to consumers in a more efficient, reliable, and environmentally friendly way than the inbuilding air conditioners. The DCS has higher energy efficiency and lower emissions as compared to chillers or air conditioners used individually. [7] At the same time, the DCS involves large investment and operating costs. Also, there are significant energy losses when transporting water in the pipes in the district cooling network. Thus, a high load density is necessary to cover the large capital costs which are about 50 % of the total cost of the system. This makes DC systems more attractive in urban areas with a large population density and high-density buildings with large thermal loads. [8] A DCS can consist of different chilled water generation units such as absorption chillers, electric chillers, and free cooling. Thus, the fuels used in the DCS are heat and electricity. District cooling is a relatively new technology and very few statistics have been collected on the subject. However, statistics show that there is a sharp increase in the use of district cooling due to its positive effects on both the environment and the economy. [1] 2.2 The DCS in Gothenburg The DCS in Gothenburg supplies cold water through pipes for space cooling. The DC system in Gothenburg generates chilled water from absorption chillers, free cooling sources from the river, and electric chillers. In Gothenburg, the cooling demand during the winters is satisfied using the cooling from the river. The river water is used to cool the return water from the buildings in heat exchangers. The usage of the river for cooling is limited by a constraint on the cooling production corresponding to a withdrawal of 16 000 m3/h (4.44 m3/s) at a temperature rise of 10◦C [9]. This makes the DCS in Gothenburg quite different from other systems. The cooling obtained from the river is referred to as “Free Cooling” in this thesis. In addition to the free cooling, Göteborg Energi operates electric and absorption chillers to meet the cooling demand during the warmer periods of the year. The electric chillers use electricity as fuel while the absorption chillers use both electricity and the heat from the DHS. The chilled water generation systems and their technical details are specified in Table 1 [3]. 5 Table 1: Chilled water generation units in 2018 Type of unit Unit Capacity [MW] Primary Fuel Absorption chillers Rosenlund 22 DH and electricity Svenska Massan 3.4 DH and electricity Gullbergsvass 3 DH and electricity Odin 2 DH and electricity Ceres 1 DH and electricity Arkaden 1.1 DH and electricity Electric chiller Rosenlund 10 Electricity Svenska Massan 1.2 Electricity Gullbergsvass 1.25 Electricity Odin 2.2 Electricity Ceres 0.6 Electricity Arkaden 4.25 Electricity Sahlgrenska 2.5 Electricity 2.3 The district cooling network The district cooling network consists of pipes that are used to supply the chilled water from the district cooling plants to the demand sites. The network consists of pipes of varying diameters. The pipes are dimensioned based on the maximum flow through the pipes. The dimensioning of pipes is discussed later. The pipes in the network are mostly made of plastic i.e. SDR 11 and SDR17. Besides, in some parts of the network, stainless steel pipes are also used. The DC network is shown in Figure 1. The red dots in Figure 1 indicate the location of the chiller units connected to the network. The blue dots indicate the chiller units which are cooling islands. The cooling islands are usually chillers that are installed on the building sites and are used to meet the cooling demand at these buildings. The network consists of a main pipe which has a diameter of 630 mm. 6 Figure 1: DC network [10] 2.3 Operation of the DCS in Gothenburg The operation of the Gothenburg DCS is governed by a few different factors, namely the river temperature, the availability of excess heat in the DHS, and the cooling demand. The river water is used to provide cooling as long as the river temperature is below 6◦C. Therefore, the river water is used for cooling during the winter months i.e. from December to February. During spring and autumn, a combi operation between the chillers and free cooling exists. During this period, the river water temperature is greater than 6◦C but less than the return water temperature. The combi operation first uses the river water to cool the return water, as long as the temperature difference is less than the permissible value in the heat exchanger. The chillers are then used to further cool down the water to the supply temperature. In summer, when there is a high demand for cooling, the absorption and electric chillers are run. The absorption chillers use heat as fuel. This heat is obtained from the DHS. In the summers, there is excess heat available in the DHS since the demand for heat is low. The excess heat arises from the industrial waste heat from the refineries and waste incineration. This excess heat is used in the absorption chillers. This excess heat is available to the DCS at zero cost. Hence, absorption chillers have very low running costs in the summer. The system is run based on merit order and the absorption chillers form the baseload. The electric chillers are used as peak load technology and are used to meet the peaks in the demand in summer. The operation of the system is shown in Figure 2. 7 Figure 2: Distribution of district cooling production in Gothenburg [11] 2.4 Investment plans for Future DCS in Gothenburg Since this thesis deals with modeling the future DCS in 2024 and 2030, it is important to state the reason for choosing these two years. As discussed earlier, Göteborg Energi plans to install thermal energy storage in the DCS in the form of a tank that stores cold water. It is planned to invest in the thermal energy storage by 2024. Hence, this year was chosen to analyze the immediate impact that the storage will have on the DCS. Also, the current investment plans for the DCS consist of the addition of capacity until the year 2030. There will be investments in the system after 2030. But it is not in the scope of this thesis to consider the investments after 2030. Hence it is important to analyze the optimal operation of the system in 2030. Also, the effectiveness of the thermal energy storage in 2030 is to be examined [3]. The plans for the DCS in Gothenburg mostly involve the expansion of the network for increasing the number of connected customers and hence investments in chilled water generation capacity. The existing absorption chillers have a functional issue described by Göteborg Energi as the “ΔT (temperature difference) problem”. The change in temperature of the warm water in the absorption chiller is not high enough for it to be returned to the district heating network. However, to maintain the mass balance in the system, the water must be returned to the DHS. Hence, this leads to larger flows in the DHS causing increased costs. Thus, no plans to install new absorption chillers in the system exist as of now [3]. The installed capacity is thus increased by installing electric chillers and thermal energy storage. Installing heat pumps instead of electric chillers are also being considered, but this thesis does not consider heat pumps. Tables 2 and 3 show the list of chillers in the year 2024 and the year 2030 [12]. 8 Table 2: Chilled water generation units in 2024 DCS in 2024 Type of unit Unit Capacity [MW] Primary Fuel Absorption chillers Rosenlund 22 Heat and electricity Svenska Massan 3.4 Heat and electricity Gullbergsvass 3 Heat and electricity Odin 2 Heat and electricity Ceres 1 Heat and electricity Arkaden 1.1 Heat and electricity Electric chillers Rosenlund 30 Electricity Svenska Massan 1.2 Electricity Gullbergsvass 8.25 Electricity Odin 2.2 Electricity Ceres 6.6 Electricity Arkaden 4.25 Electricity Sahlgrenska 2.5 Electricity TES Chilled water tank 30 n/a Table 3: Chilled water generation units in 2030 DCS in 2030 Type of unit Unit Capacity [MW] Primary Fuel Absorption chillers Rosenlund 22 Heat and electricity Svenska Massan 3.4 Heat and electricity Gullbergsvass 3 Heat and electricity Odin 2 Heat and electricity Ceres 1 Heat and electricity Arkaden 1.1 Heat and electricity Electric chillers Rosenlund 60 Electricity Svenska Massan 11.2 Electricity Gullbergsvass 8.25 Electricity Odin 2.2 Electricity Ceres 6.6 Electricity Arkaden 4.25 Electricity Sahlgrenska 2.5 Electricity Almedal 5 Electricity TES Chilled water tank 30 n/a The capacity of the thermal energy storage which has been specified as 30 MW indicates the discharging capacity of the tank. The storage capacity of the tank in terms of energy is 200 MWh. The charging capacity of the tank is not limited since the charging capacity depends on the network and the pumping capacity. [3] 9 2.5 DHS in Gothenburg The DCS is linked with the DHS by the use of heat in the absorption chillers. The heat from the DHS is used as fuel in the absorption chillers and hence, the prices of heat must be input to the model of the DCS. Unlike electricity prices, the prices of heat for 2018 are not readily available. The prices of heat are determined from an optimization model of the DHS. Similarly, for the models which represent the future DCSs, the prices of heat are obtained from corresponding models of the DHS. Thus, it is important to describe the DHS in Gothenburg and how it is modeled. The DHS is built and operated by Göteborg Energi. The basic concept of district heating is to make use of local fuel or heat source, that otherwise would be wasted, to satisfy the local heating demand. The DHS in Gothenburg has a large input of heat from the refineries and waste fired units. The heat from the refineries and incineration of waste constitutes a large part of the total heat in the system. The heat from these sources is referred to as industrial waste heat in this report. This industrial waste heat is available to Göteborg Energi at a very low cost and hence, it is optimal to maximize the use of industrial waste heat in the DHS. [13] In addition to a supply of industrial waste heat, the system operates two large combined heat and power (CHP) plants, Sävenäsverket and Ryaverket. The CHP units are used to cover the baseload. These CHP units also produce electricity according to their respective power to heat ratios (α values). The generated electricity is sold to a spot market and hence additional income is generated. Also, two large heat pumps are operated. The heat pumps use cleaned sewage water as their cold sides. Göteborg Energi also operates a large number of small-scale heat generation plants as back-up and to cover peak loads. These plants are all boilers that are denoted as heat-only boilers (HOB), which simply means that they do not generate any electricity. All the heat generation facilities and their technical specifications in the current DHS are presented in Table 4. [13] The DHS in Gothenburg is moving towards a cleaner production of heat. This means that the use of fossil fuels in the system is to be reduced. Göteborg Energi has plans to move to a fossil- free heat generation by the year 2030 [12]. The generation mix on the future models of the system is based on these plans. The major investments in the system are a thermal energy storage in the form of an accumulator tank and a new biofuel-powered combined heat and power plant. Also, plants that utilize biofuels are prioritized to a greater extent over plants based on fossil fuels. Thus, most plants that run on fossil fuels are either phased out or they are converted to biofuel-powered plants. The generation mix considered for future models is presented in the appendix. 10 Table 4: Heat production units Type of unit Unit Capacity [MW] Primary Fuel Excess heat Renova 185 Municipal waste Preem 60 Industrial excess ST1 85 Industrial excess CHPs and HPs Sävenäs CHP 110 Wood chips/Natural gas Rya CHP 295 Natural gas Högsbo CHP 85 Natural gas Heat pumps Rya HP 1-2 60 Electricity Rya HP 3-4 100 Electricity Heat only boilers Rya HOB1 50 Wood pellets Rya HOB2 50 Wood pellets Sävenäs HOB1 90 Natural gas Sävenäs HOB2 60 Bio-oil Angered HOB1 35 Bio-oil Angered HOB2 35 Bio-oil Angered HOB3 35 Bio-oil Rosenlund HOB1 140 Bunker oil Rosenlund HOB2 140 Bunker oil Rosenlund HOB3 140 Bunker oil Rosenlund HOB4 140 Natural gas Tynnered HOB 20 Fuel oil 2.5.1 The heat demand The heat demand is the most important input into the model. The heat demand for the year 2018 is determined by looking at heat generation data from various units. The hourly production data is summed up to calculate the demand in the year 2018. For the models representing the future DHS, the demand in the corresponding years must be projected. The demand in a future DHS in the year 2030 is estimated using the method developed by Holm and Ottoson [13]. The demand for heat is reduced by the increased efficiency measures in the buildings, whereas, the demand will increase with an increase in the number of connections to the DHS. A study conducted to determine the future district heating demand in Gothenburg regions showed that the demand for heat will stay constant or increase by a very small level of about 2% [14]. This study claims that the increased demand from the new connections will balance out the reduction in demand due to the efficiency measures. Despite the total annual demand remaining almost constant, the profile of the demand curve changes to a significant extent. This is because, the space heating demand in the winter is reduced to a large extent due to the increasing efficiency measures, whereas in the warmer periods where the hot water demand is greater than the space heating demand, the total demand is increased as the new connections to the system lead to an increase in the total demand. Hence, the demand profile of the future DHS is different from the present demand profile. This is a key aspect of demand projection [13]. 11 2.6 Thermal energy storage The future energy system, including electricity, heating, and cooling sectors is transforming into a system with more intermittencies than the current system. The intermittencies stem from an increased share of variable renewable energy in the system in the form of solar and wind energy. The DCS is directly affected by these developments in the electricity system as electricity is used in both electric and absorption chillers. During hours when the share of generation from the variable renewables is very low in the system, expensive peak power plants fired by fossil fuels must be operated to meet the electricity demand. This is neither economically nor environmentally optimal. During such hours, the electricity prices are at the highest. To prevent such large variations in the system, various measures are being discussed. Installing a thermal energy storage (TES) in the system in one such measure. The TES can be used to store energy during peak demand hours and hence reduce electricity consumption during high electricity price hours. Besides, the TES can help make use of the waste heat available in the summer to run the absorption chillers at peak capacity and store the generated chilled water. The stored energy can be discharged to meet peak demands in the system. Figure 3: Cooling demand in the last week of July 2018 The cooling demand in a DCS can fluctuate heavily between different hours of the day. Figure 3 shows the cooling demand in DCS in Gothenburg in the last week of July 2018. The diurnal variation in the demand is as high as 25 MW. To meet the varying demand many starts, and stops are required which may reduce the lifetime of the chiller and reduce its efficiency. This problem can be solved by using a TES. The storage can then be charged during low demand hours and the discharge from the storage can be used to meet the peak demands. The high diurnal variation in cooling loads during warm summer days gives a high incentive for TES in DCSs. Also, the storage can help reduce the total installed capacity of chillers substantially. The storage will then reduce the investment cost and the operating cost for chillers installed for the total peak capacity [15]. 0 5 10 15 20 25 30 35 40 1 6 1 1 1 6 2 1 2 6 3 1 3 6 4 1 4 6 5 1 5 6 6 1 6 6 7 1 7 6 8 1 8 6 9 1 9 6 1 0 1 1 0 6 1 1 1 1 1 6 1 2 1 1 2 6 1 3 1 1 3 6 1 4 1 1 4 6 1 5 1 1 5 6 1 6 1 1 6 6 C o o lin g d em an d ( M W h ) Hours Cooling demand 12 TES can be classified into two broad categories, short-term storage, and long-term storage. Examples of short-term TES are rock and earth beds, cold water tanks, and phase changing materials. The short-term storages are most suited for handling diurnal variations. On the other hand, long term TES is suited to handle seasonal variations in the demand. Examples of long- term cold storages are aquifer thermal energy storage, borehole thermal energy storage, and cavern thermal energy storage [4]. 2.6.1 Thermal energy storage in a chilled water storage tank The most common type of short-term thermal energy storage in a DCS is a tank that stores chilled water. The supply and return lines of the network are directly connected to the tank. The chilled water from the chillers is pumped into the tank during low demand hours. The stored chilled water is then discharged during high demand hours to complement the chillers to meet the demand. Tanks are typically constructed of steel or pre-stressed concrete. The ambient temperature is typically higher than the temperature of the water in the cold storage tanks and heat load from the environment can be a major cause of inefficient operation of the system. Thus, tank surfaces are properly insulated including a high-integrity exterior vapor barrier to prevent the chilled- water from unwanted warming and to minimize ingress of moisture and condensation into the insulation layer [16]. The loss of energy from a chilled water tank depends on the temperature of the stored water and the ambient temperature. The relationship between the two temperatures is defined in equation 2.1 [17] 𝑄𝑙𝑜𝑠𝑠 = 𝑇𝑤𝑎𝑡𝑒𝑟 − 𝑇𝑜𝑢𝑡𝑑𝑜𝑜𝑟 ℎ𝑡𝑎𝑛𝑘 2.1 Here, 𝑇𝑤𝑎𝑡𝑒𝑟 is the temperature of the water inside the tank and 𝑇𝑜𝑢𝑡𝑑𝑜𝑜𝑟 is the temperature of the surroundings. ℎ𝑡𝑎𝑛𝑘 is the heat transfer coefficient of the tank wall. The calculation of the ℎ𝑡𝑎𝑛𝑘 includes several uncertainties as ℎ𝑡𝑎𝑛𝑘 is the total heat transfer coefficient of the tank wall material, the insulation, and the convection on the inside and the outside of the tank. Generally, the energy loss from a chilled water storage tank per day is between 2-5% of the stored energy. The active volume in a water accumulator tank required for a given amount of energy to be stored can be calculated according to equation 2.2. 𝑉𝑇𝑎𝑛𝑘 = 𝐸𝑇𝑎𝑛𝑘 𝐶𝑝,𝑤𝑎𝑡𝑒𝑟 ∗ 𝜌𝑤𝑎𝑡𝑒𝑟∗ ∆𝑇𝑤𝑎𝑡𝑒𝑟 2.2 Where 𝐸𝑇𝑎𝑛𝑘 is the amount of energy (in Joules), 𝜌𝑤𝑎𝑡𝑒𝑟 is the density of water and 𝐶𝑝,𝑤𝑎𝑡𝑒𝑟 is the heat capacity of water per kg. ∆𝑇𝑤𝑎𝑡𝑒𝑟 is the temperature difference between the supply and return water in the system. The lowest temperature in the tank would be equal to the district cooling supply. The active temperature difference in a DCS is between 10-12◦C. The actual volume of the tank might be larger than the volume calculated from equation 2.2 due to increase in volume from construction and operational purposes [17]. The capital cost of a chilled water storage tank consists of the cost of construction the tank, installation costs, and the cost of connecting the tank to the network. Based on previously 13 installed thermal energy storage tanks in Sweden, an expression for an estimation of the construction and installation costs of an accumulator tank is made [18]. The construction costs are calculated by 𝐶𝑡𝑎𝑛𝑘 = 1.55 ∗ 107 ∗ ln(𝑉𝑡𝑎𝑛𝑘) − 1.39 ∗ 108 2.3 Where Ctank is the cost of constructing the tank in SEK and VTank is the actual volume of the tank in m3. The installation costs can be approximated as below 𝐶𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑎𝑡𝑖𝑜𝑛 = 157 ∗ 𝑉𝑇𝑎𝑛𝑘 + 6 000 000 2.4 Where Cinstallation is the installation costs in SEK. The costs for connecting the tank to the network are hard to generalize as it varies in each case based on the network and the tank. The costs presented above can be used to approximate the investment costs of the tank. The tank has a technical lifetime of 25-30 years [19]. 14 2.7 Literature review Various previous studies focusing on the modeling of district cooling and DHSs have been conducted. These studies deal with the simulation of the system operation, the best design of generating plants, or on optimal capacity and utilization of a thermal storage. The optimization models of the DHS are considered since they are quite similar to the DCS models. Romanchenko et al. [18] developed an optimization model that investigated the characteristics of interaction between DHSs and the electricity system, and how this interaction changed when moving from present to future electricity price curves. A mixed-integer linear programming model was developed in GAMS to study optimal operating strategies for DHSs. The model minimized the total cost of heat generation for a given DHS. Further developing this model, the impact of the implementation of thermal energy storage on the operation cost of the system, dispatch of various heat generation units, and environmental impact in a future DHS in Gothenburg were investigated by Holm et al [13]. This study made use of an optimization model in GAMS to determine the optimal functioning of a future DHS with and without thermal energy storage and hence evaluating the impact of the addition of storage into the system. A few other models have analyzed the district energy system as a whole and looked at the dynamic optimization of the network. In contrast to the models above, Schweiger et al. [20] set up a thermo-hydraulic model of the district energy system to represent a framework for on-grid simulations, dynamic simulations, and optimization. The framework is based on the modeling language Modelica and the scripting language Python. This paper presented the continuous dynamic optimization of a DHS in a virtual city district. The network is first represented on a modeling tool and the optimizations conducted using a mixed-integer approach. An integrated energy model including electricity, district heating, and DCS was set up by Dominkovic et al. [21] to investigate the impact of District Energy Share in Cities on the Optimal Storage Sizing. A linear continuous optimization was built using the Matlab interface and Gurobi optimization solver. This paper also compared the socio-economic costs in the systems with and without storage. Also, the effectiveness of having storages in different systems was analyzed. Söderman et al. [22] developed an investment model for optimization of the design and operation of a district cooling network. A Mixed Integer Linear Programming model was developed for the design optimization of a DC network in an urban region. The cooling demand profile from the year 2006 was used as input. A predicted future demand profile with an additional number of new potential consumers for the year 2020 was also used. The impact of a thermal energy storage in the system was also analyzed. This model optimizes both the structure of the DCS and its operation. Also, a thermo-hydraulic modeling approach is used for determining the optimal operation. This presents the most comprehensive model of a DCS and hence this model is chosen as a base for further modeling. But since this is an investment model, only the part which deals with the optimization of the operation is considered. The model is further presented in the next section. Gang et al. [23] compared the operation of the DCS and the conventional cooling system. The DCS was designed, and the operation of the system was simulated using TRNSYS. The main aim of this study was to quantitatively assess the performance of the DCS in a new development area in Hong Kong. In this model the cooling demand in the buildings and installed capacity of the cooling systems is included. The performance of DCS is compared with the conventional cooling system i.e. individual in-building cooling systems with chillers installed at the demand site. The major conclusion from this study was that the district cooling system was more 15 beneficial economically and used about 15 % less electricity than the conventional cooling system. Further, the DCS provided higher savings during the cold months when the operating load was less than 50 %. This was due to the higher efficiency of the chillers in the DCS Jungbauer et al. [24] compared the operation of the conventional cooling systems and the district cooling systems in Europe. This paper uses a three-step method to create parameters for comparing DCS with the conventional cooling system. In the first step, practical measurements are made to compare the practical and theoretical energy efficiency ratios of the chillers. In the second step, a primary energy factor is calculated for the district cooling system. The primary energy factor is a measure of the efficiency of the DCS. In the third step, the PEF of the DCS is compared with the EER of the conventional cooling system. It was concluded that the district cooling system is better because of better utilization of locally available resources and a combination of different cooling sources. Zhang et al. [25] analyzed the impact of the installation of the thermal energy storage in a DCS in hot summer and cold winter areas in China. The analysis method is based on measured data, which is obtained by long term monitoring and on-site measurements of the cooling season. The main aim was to investigate the operation modes of the DCS and determine the change in the energy efficiency of the system when the TES is installed. The chillers operate at partial load for a large proportion of the cooling time which reduces the energy efficiency of the system. Thus, the TES was installed in the system to increase energy efficiency. Söderman et al. [26] developed a model for the structural and optimization of distributed energy systems. In this model, production, and consumption of electrical power and heat, power transmissions, transport of fuels to the production plants, transport of water, in the district heating pipelines and storage of heat are considered. This is similar to the model described in [22]. Additionally, in this model, the storage of heat in the pipelines is considered. A part of the model developed in this study is also used as a base for formulating models in this thesis. Schwan et al. [27] illustrated a new approach to use Modelica to evaluate the dynamic behavior of district heating grids. The simulation approach presented can simulate thermo-hydraulics of a district heating grid. This approach simplifies the grid into a radial network and considers the pressure drops in the pipes to evaluate the dynamics of the system. Similar methods have been used in this thesis to compute the pumping costs. Damien et al. [5] built a simulation model for DCS using the object-oriented language Modelica. The model consists of a cooling production plant, a network of pipes, and 6 substations. The approach is used to study interactions between substation cooling demand and cooling production plant efficiency. A simplified model of substations with ideal control and a performance-based model of electric chiller considering variable evaporator entering conditions were developed. These models are used to evaluate alternate control strategies for substations. This study describes the use of Modelica for building a physically-based model of a DCS. Sandou et al. [28] developed an optimization model for DHSs. A global modeling approach has been described in this paper, where individual models of various components of the DHS such as boilers, pipes, heat exchangers, etc. were brought together into a single model of the system. The model has been simulated under different scenarios and was used to design new DHSs. 16 Oppelt et al. [29] presented a dynamic thermo-hydraulic model ISENA in their paper. ISENA can be applied for design and operational simulation of the district cooling network. The network-based model consists of a two-part model, a quasistatic hydraulic model, and a transient thermal model. The two-part model is based on tracking the transport of water through the whole network (Lagrangian method). Sameti et al. [6] described different types of optimization problems, constraints, and techniques as well as the optimization tools used in district energy systems. This paper examines existing optimization models, the objective functions in these models, the tools used, and gives a review of these models and tools. Different software, solvers, and tools used for building and running the optimization algorithms are compared and their applicability to specific scenarios are defined. A major conclusion is that most models suffer from a very long computational time when large networks are considered and thus, a special tool is required for the model to be applicable in larger districts. Khir et al. [30] investigated the optimal design and operation of a DCS so that the total investment and operational costs are minimized. The model optimizes chiller capacities, network layout and pipe diameters, storage tank capacity, and the district cooling production. The mixed-integer programming (MIP) models, developed in the study model the structural aspects and the pressure and temperature demands. Schweiger et al. [31] presented a novel framework for representing and simplifying on-grid energy systems as well as for dynamic thermo-hydraulic simulation and optimization of district heating and cooling systems. The framework built consists of a physical model in Modelica coupled with a MIQCP based optimization algorithm. 17 Chapter 3: Method This thesis deals with the modeling of the district cooling systems. The main aim of modeling is to determine the optimal functioning of the DCS and the impact of various future investments. To evaluate the different situations that could arise in the district cooling system in Gothenburg, an optimization model has been used. The optimization model uses hourly data regarding cooling demand, electricity prices, and heating prices and shows how the DC system is operated. Different models and cases are set up to investigate different scenarios. • Model 1: DCS model excluding the network. ➢ Case 2018: DCS vs Individual chillers in 2018 ➢ Case 2024: DCS in 2024 with the inclusion of TES ➢ Case 2030: DCS in 2030 with corresponding developments in electricity and DHS • Model 2: DCS and DC network model. ➢ Case 2018: Comparison of methods for modeling of network ➢ Case 2024: DCS and network in 2024 with the inclusion of TES These models can thus be a pre-study to investigate the operation of the DCS in the future and the impact of investments in the DCS. The prices of heat must be input to the model of the DCS. The prices of heat are obtained for each case from a corresponding model of the DHS. The DHS is modeled similar to the DCS. Like the DCS, the DHS is operated based on merit order. Hence, the dispatch of power plants is based on their running costs. Since the only output expected from these models is the prices of heat, the model only provides a basic representation of the district heating, and a few technical details such as variable α values of the CHP plants are not included in the model. 3.1 Description of the DCS in Model 1 This DCS is modeled in the linear program solver software GAMS (General algebraic modeling software). A mixed-integer linear program is created, which solves an optimization problem. The objective of the optimization is to reduce the yearly total chiller running costs. The model has an hourly resolution, which means that data about the demand for heat, cost of electricity, and outdoor temperature is available for every hour of the year. Given this information, the model decides the heat generation dispatch in each hour that gives the lowest total system cost over the entire year. The various constraints and equations of the model are explained further [32]. GAMS (The General Algebraic Modeling System) is a modeling system that is constructed specifically for modeling linear, non-linear, and mixed-integer optimization problems. GAMS handles an optimization process from the stage of a defined mathematical model of a real-life problem to the stage of solution evaluation. Many solvers are connected to GAMS such as CPLEX, MINOS, CONOPT, and SCIP. In this thesis project, the CPLEX solver is used. For problems with integer variables as in this thesis, CPLEX uses a branch and cut algorithm which solves a series of Linear programming (LP) problems, subproblems. Because a single mixed- integer problem generates many subproblems, even small mixed-integer problems can be very computationally intensive and require significant amounts of physical memory [33]. 18 3.1.1 Objective function In an optimization model, the objective function can be described as the main goal of the model. To obtain an optimal result from the model, the objective function must be controlled. The models in this thesis deal with the economic optimization of the DCS. Therefore, in the models described in this thesis, the main aim of the optimization is to reduce the cost. The objective of the optimization is to minimize the yearly chilled water generation cost which is calculated according to Equation 3.1. The cost function consists of several different terms i.e. fuel costs, start-up, and shut-down costs, fixed and variable running costs, and taxes. The startup and the shut-down costs are included as a constant value. The running cost in each hour is summed up over the total number of hours in a year to get the yearly chilled water generation cost. 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = ∑ ∑ [𝑞(𝑝, 𝑡) × 𝑉𝐶𝑝] + 𝑝 𝑡 1 𝑆𝐶𝑝,𝑡 3.1 3.1.2 Demand-Supply balance constraint A constraint is an equation that describes the various boundaries of the system in the model. The constraints can also be used to describe the operation of the system. The demand-supply balance constraint describes the basic operation of the district cooling system. This constraint is binding in the model. i.e. this constraint has a direct effect on the decision variable which is the chilled water generation from each chiller. The major constraint of the model is the balance constraint. The demand for cooling must be satisfied in each hour of the year. This ensures that the sum of chilled water outputs from all the chillers is equal to or greater than the total demand. This constraint thus directly affects the dispatch of the chillers in each hour. This constraint is mathematically represented in equation 3.2. ∑ 𝑞[𝑝, 𝑡]𝑝 ≥ 𝐷𝑡 3.2 3.1.3 Ramp up and Ramp down constraint Ramp up and ramp down constraints limit the maximum increase and decrease in chilled water generation from a given chiller at any given hour. Equations 3.3 and 3.4 show how ramp-up and ramp-down rates affect the chilled water generation at the next hour to be within the limits. 𝑞(𝑝, 𝑡) ≤ 𝑞(𝑝, 𝑡 − 1) + 𝑅𝑈(𝑝) 3.3 𝑞(𝑝, 𝑡) ≥ 𝑞(𝑝, 𝑡 − 1) − 𝑅𝐷(𝑝) 3.4 The difference between the amount of chilled water generated at hour t and the hour (t-1) should be less than or equal to the ramp-up rate if the production level is increased, and the difference between the chilled water generated at the hour (t-1) and the hour t should be less than or equal to the ramp down rate if the production level is decreased. This has been described numerically in equations 3.3 and 3.4. 19 3.1.4 Minimum up and down time constraints Minimum on time constraints are assigned to prevent a chiller to be turned off before it has been run at least as long as its “minimum on time”. Similarly, minimum off-time constraints are defined to prevent a chiller to be switched on before it has been off at least for the “minimum off-time”. Minimum on time constraints are defined by Equation 3.5 [34]. 𝑜𝑛(𝑝, 𝑡 − 1) − 𝑜𝑛(𝑝, 𝑡) ≤ 1 − ∑ 𝑜𝑛(𝑝, 𝑡) 𝑡+𝑡𝑠𝑡 𝑡 3.5 Minimum off time constraints are defined by Equations 3.6 [34]. 𝑜𝑛(𝑝, 𝑡) − 𝑜𝑛(𝑝, 𝑡 − 1) ≤ ∑ 1 − 𝑜𝑛(𝑝, 𝑡) 𝑡+𝑡𝑠ℎ 𝑡 3.6 The above two constraints are based on the binary variable on(p,t). This variable describes whether a certain chiller is generating chilled water during an hour. The variable takes a value of 0 or 1. When on(p,t) is 0, then the chilled water generation is 0, i.e. the chiller is not turned on, whereas if it takes a value of 1, the chiller is turned on and there is some chilled water generation from the chillers. 3.2 Description of the District cooling network model: Model 2 The model which includes district cooling network is built on the previous model of the DCS. This model is hereafter referred to as the network model. This model consists of additional constraints that describe the network. The district cooling network is a complex network that consists of a large number of buildings and district cooling plants. The pipes in the network connect the plants to the demand. A method must be developed to include the network into the model both in terms of constraints and costs. The network is first simplified into a simpler form called the radial network. Based on their location, the buildings are grouped into demand clusters. These demand clusters are included in the radial network. The radial network and the demand clusters are then used to develop the ‘linked cot functions’ which are used to link each chiller to every demand. This is further explained below. 3.2.1 Radial network A district cooling network can be constructed as a radial, ring, or mesh system. Radial networks are the simplest form of a district cooling network in which a large main pipeline feeds several distribution pipelines, forming individual branches. In these branches, the pressure of the main pipe is distributed homogeneously over all distribution pipes. The complex and big network must first be represented in the simplest possible form i.e. a radial network. However, due to restrictions in time, it was very difficult to model the entire DCS. Therefore, a part of the network was first chosen. While making this choice, a few major factors considered were • An accurate representation of the whole network. • Must consist of both electric and absorption chillers in equal capacities. • Must cover a significant portion of the network and the demand. Taking to account the above, it was decided to take the district cooling network in the center of the city as a representative network for modeling. This network consists of the chiller units in Table 5. 20 Table 5: Chilled water generation units in the chosen central network Type of unit Unit Capacity [MW] Primary Fuel Absorption chillers Rosenlund 22 DH and electricity Svenska Massan 3.4 DH and electricity Gullbergsvass 3 DH and electricity Odin 2 DH and electricity Arkaden 1.1 DH and electricity Electric chiller Rosenlund 10 Electricity Svenska Massan 1.2 Electricity Gullbergsvass 1.25 Electricity Odin 2.2 Electricity Arkaden 4.25 Electricity The chosen central network is shown in Figure 4. This network accounts for a total of 65 % of the total demand (excluding cooling islands) in the system. However, the installed capacity in this network is about 92.4 % of the total installed capacity (excluding cooling islands). However, the main aim of this study is to investigate methods by which the network can be integrated into the model. Dimensioning of the system for the peak demand is not the most important aspect of this model. Hence, this mismatch in the share of the total demand and the share of total installed capacity can be overlooked. Figure 4: Chosen central network [10] The network shown in Figure 4 is then simplified into a radial network, by creating the different demand clusters. 7 demand clusters were created based on their location with respect to the different chiller units. The demand clusters are shown in Figure 5. 21 Figure 5: Demand clusters [10] The demand clusters, along with the pipes and the chiller units are used to make the radial network as shown in Figure 6. Figure 6: Radial network Main pipe 22 In Figure 6, RS, AR, SVM, GU, and OD denote the chiller units in Rosenlund, Arkaden, Svenska Massan, Gullbergsvass, and Odinsplatsen, respectively. The developed radial network is used to develop the linked cost functions as explained below. Flow and temperature difference The data regarding the temperature difference is obtained from a physically-based model of the Gothenburg DCS. This model is built and run by Göteborg Energi. In this model, the average temperature difference between the supply and return temperatures at all the customers is 6.64◦C. The same value is used for temperature difference in the models in this thesis [35]. From this value, the flow is calculated using equation 3.12. 3.2.2 Linked cost functions The linked cost functions as specified earlier are developed to link each chiller to every demand cluster. The linked cost function gives the pumping power needed in kW to pump water from chiller A to demand cluster B. This can then be used to calculate the pumping cost required to pump water from chiller A to demand cluster B. Since the pumping cost is dependent on flow, the linked cost functions are developed as a function of flow. The cost functions are developed based on the pressure drop in the pipes [36]. The pressure drops are obtained by using equations 3.6 to 3.12. ∆𝑃 = 𝐾 ∗ 9.81 ∗ 𝑣2 2𝑔 𝑣 = Q̇ 𝐴 𝐾 = 𝑓 ∗ 𝑙 𝐷 𝑓 = 0.25 [log { 𝑘 3.7 ∗ 𝑑 + 5.74 𝑅𝑒0.9}]2 𝑅𝑒 = 𝑣 ∗ 𝑑 ν 3.6 3.7 3.8 3.9 3.10 3.11 23 𝑃𝑝 = 𝑄 ∗ ∆𝑃 𝜂 The flows for calculating the pressure drops are obtained from the demand as below. Q̇ = 𝑄ℎ𝑒𝑎𝑡 𝑐𝑝∗ 𝜌∗𝛥𝑇 The maximum and minimum flow from a chiller to a demand cluster is determined by the demand and the capacity of the chiller. Thus, a set of data points within this range of flows is used to plot a function of the pumping power based on the above equations. The data points in the range of the flow are chosen linearly with the equal difference between each data point. Also, mean, median, mode, the maximum and minimum values are also included in the set of points used to calculate the pumping power. An example of the calculated linked cost function between Rosenlund and C1 is shown in Figure 7. Figure 7: Linked cost function The Figure 7 shows the linked cost function between Rosenlund and C1. As shown in the graph, here the function which defines the pumping power is non-linear and hence has to be linearized. When linearizing, the accuracy to which the function can represent the curve is lost. The linearized linked cost function is shown in Figure 8. The coefficient of determination (R²) is 1 in this case, which means that there is a negligible variance when the cubic polynomial is used. Figure 8: Linearized linked cost function y = 144402x3 + 4198.4x2 - 52.694x + 0.1268 R² = 1 0 50 100 150 200 250 300 0 0.02 0.04 0.06 0.08 0.1 0.12 P u m p in g p o w er ( K W ) Flow (m3/s) Pumping power y = 1808.3x - 18.113 R² = 0.8778 0 50 100 150 200 250 300 0 0.02 0.04 0.06 0.08 0.1 0.12 P u m p in g p o w er ( K W ) Flow (m3/s) Pumping power 3.12 24 When using the linear polynomial to represent the function, the variance is much higher, and the R² is 0.88. There is an inaccuracy in the linked cost function when represented as a linear function. But most of the linked costs function used for modeling have an R² value of above 0.7 and thus, the cost linear cost function is able to represent the actual curve to an acceptable accuracy. 3.2.3 Objective function The objective of the optimization is to minimize the yearly running cost of the district cooling network which is calculated according to Equation below. The cost function consists of several different terms i.e. fuel costs, start-up, and shut-down costs, fixed and variable running costs, and taxes. The startup and the shut-down cost are included as a constant value. The pumping costs are also included in the model as a representative of network operation costs. 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = ∑ ∑ 𝑐 ∑ {[𝑞(𝑝, 𝑐, 𝑡) × 𝑉𝐶𝑝] + [𝑃𝑝(𝑝, 𝑐, 𝑡) × 𝐸𝑙𝑡] 𝑝 𝑡 1 + 𝑆𝐶𝑝,𝑡} 3.13 3.2.4 Demand-Supply balance constraint The demand-supply constraint in this model includes an additional index in terms of the cluster. Since the demand is split into different clusters, it is required to provide separate constraints for each demand. Thus, the demand at each cluster must be met during every hour. ∑ 𝑞[𝑝, 𝑐, 𝑡]𝑝 ≥ 𝐷𝑐,𝑡 3.14 3.2.5 Capacity and ramping constraints The chilled water generation from the chillers must be restricted in the model to their peak capacity. Since the chilled water generation is indexed over both the plant and the cluster, the capacity constraint for this model must be defined differently. ∑ 𝑞[𝑝, 𝑐, 𝑡]𝑐 ≤ 𝐶𝑎𝑝𝑝 3.15 The ramping constraints are defined similarly ∑ 𝑞(𝑝, 𝑐, 𝑡)𝑐 ≤ ∑ 𝑞(𝑝, 𝑐, 𝑡 − 1)𝑐 + 𝑅𝑈(𝑝) 3.16 ∑ 𝑞(𝑝, 𝑐, 𝑡)𝑐 ≥ ∑ 𝑞(𝑝, 𝑐, 𝑡 − 1)𝑐 − 𝑅𝐷(𝑝) 3.17 The minimum off-time and minimum on-time constraints are defined as done previously. 3.2.6 Pipe constraints The constraints related to the pipes must also be included in the model in order to completely represent the network in the model. The main constraint in the pipes is the maximum possible flow in the pipes. This is defined by the dimensioning pressure drop in the pipes, which is 1.5 bar per km length of the pipe [35] The maximum flow is calculated for this value of pressure drop using Equations 3.6 to 3.10. The flow constraints in the pipes are defined by dividing the network into various pipe segments based on the diameters of the pipes. This is shown in the Appendix. The constraints are then defined based on the possible flows in these pipe segments. When the pipe segment connects the main pipe to the demand, then the flow through that pipe is equal to the demand flow. Whereas, when the pipe connects a demand cluster and a chiller unit to the main pipe, then the flow in the pipe is then equal to the sum of the demand flow and the generation flow from the chiller. Thus, the constraints for each pipe segment are defined similarly. 25 Another constraint included in the models is regarding the two chillers pumping the chilled water in opposite directions to each other. This is not possible in reality and hence must be defined in the model. This is defined by using binary variables. A binary variable called on(plant,t,cluster) is created to identify whether there is a flow of water from a plant to a cluster at a given hour. This variable has a value of 1 when there is flow and 0 when there is no flow. An obvious example of the above situation is pumping water from a chiller at one end of the network to another end i.e. Rosenlund to c7 and Odinsplatsen to c1. For this example, the constraint is defined as below on(Rosenlund,t,c1) + on(odinsplatsen,t,c7) ≤ 1 3.12 This constraint ensures that only one of the binary variables can have a value of 1 during a given hour t, thus eliminating opposite flows in the model. 26 Chapter 4: Assumptions and Input data To evaluate the developed optimization model, a large amount of data must be gathered and processed. Certain assumptions are made wherever necessary. This chapter explains the various assumptions and the simplifications made in the optimization model. Also, this chapter provides a description of the data used, how this data was obtained, processed, and transformed to reflect the actual system as closely as possible. 4.1 Assumptions Appropriate assumptions and simplification are made in cases where there is a lack of proper data or when specific information is not available. The assumptions are made such that they can be reliable enough to represent reality as accurately as possible. Therefore, the model has various assumptions related to the DCS’s functioning, the chillers, and the input data. The first assumption is related to the heat gains along the pipes in the distribution network. The data concerning chilled water generation from each chiller was not available. This made it hard to calculate the heat losses directly despite the data from the demand side being available. For model 1, the losses in the network were assumed to be negligible. After looking at the results, this assumption did not seem reasonable and hence it was decided to modify this assumption for further modeling. Hence, in model 2, the heat gains in the network are considered to be 2% and are included as a percentage of the hourly demand. This assumption was made based on [37]. The objective function of all the optimization in model 1, is to minimize the annual running costs of the chillers. But the running costs here consist only of the costs of fuels i.e. heat and electricity costs for running the chillers. The objective function in model 1 does not include the pumping costs in the network. Also, the costs of electricity for running the condenser pumps are excluded from the objective function. Whereas, in model 2 when the network is modeled, the pumping costs are included as a representative of the network operation costs. But, as in model 1, the costs associated with the condenser pumps and the cooling towers are excluded in model 2. The network-based models in model 2 do not consider the dynamics of the system. The model is built assuming that each chiller has a separate pipe connecting to each demand, which is not the case in reality. Although the constraints have been imposed on the maximum flows in the pipes, the dynamic effects of the network such as the fluid junctions, pressure drops in loops, etc. have been excluded while calculating the pumping costs. Besides, the pressure drops considered are only those due to the pipes. The pressure drops from the valves, substations, etc. have been excluded in this study. These are the major assumptions made in setting up the model. Other assumptions have also been made in processing the input data and while setting up the different scenarios. These are scenario specific assumptions and are explained further when each scenario is described in chapter 5. 27 4.2 Input Data In this section, the technical and economic data of the various chillers is presented. Also, the method of obtaining and processing various input data such as demand and fuel prices is explained. The DCS in Gothenburg consists of absorption chillers, electric chillers, and free cooling from the river. The technical details of the various chillers are presented in Table 6. Table 6: Technical details of units in DCS Type of unit Unit Name Primary Fuel COPelectricity COPheat Minimum up time (Hours) Minimum Output (MW) Absorption chillers Rosenlund Heat and electricity 20 0.7 4 0 Svenska Massan Heat and electricity 20 0.7 4 0 Gullbergsvass Heat and electricity 20 0.7 4 0 Odin Heat and electricity 20 0.7 4 0 Ceres Heat and electricity 20 0.7 4 0 Arkaden Heat and electricity 20 0.7 4 0 Electric chillers Rosenlund Electricity Variable N/A 0 2 Svenska Massan Electricity Variable N/A 0 0.24 Gullbergsvass Electricity Variable N/A 0 0.25 Odin Electricity Variable N/A 0 0.44 Ceres Electricity Variable N/A 0 0.12 Arkaden Electricity Variable N/A 0 0.85 Sahlgrenska Electricity Variable N/A 0 0.5 4.2.1 Fuel prices As seen in Table 6, there are two major fuels in the DCS, heat from the DHS, and electricity. The electricity prices from the spot market were considered in this thesis. The prices for electricity were taken from the nordpool website [38]. In reality, there are some taxes and grid connection fees that are added to the spot market prices. Since, here there is a comparison between two scenarios and two methods, the taxes and the grid connection fees have not been included. Therefore, it is assumed that the spot market prices are the electricity prices paid by Göteborg Energi to run the chillers. The prices for heat are obtained by running an optimization model of the DHS. This model is based on a previous model of the DHS developed to study the impact of thermal energy storage in the system [13]. An assumption has been about the prices of heat from the DHS. The absorption chillers use both electricity and district heating as input fuels. The absorption chillers are run only during the periods when excess heat is present in the district heating network. The marginal cost of heat output from this model is used as heating price input. If the heat demand is lower than the total amount of waste heat coming from the industries, then there is said to be excess heat in the system. According to Göteborg Energi, this excess heat is available to the DCS at zero price. Hence, in hours when there is excess heat in the system, the price of heat is set to zero. 28 4.2.2 COP of electric chillers The COP of electric chillers varies based on the load on the chiller. The COP varies based on the load as shown in Figure 9. Figure 9: Variation of COP of electric chillers with load The relationship between the COP and the load on the chillers is non-linear and hence, it cannot be represented in a linear program that is used to construct the model. In addition, since the COP will be used to calculate the running costs of the chillers, it must be a constant value. Therefore, a constant value must be assigned to the COP value, the ESEER (European seasonal energy efficiency ratio) is used. The ESEER value is calculated using the equation below [39]. ESEER = COPA × WCA + COPB × WCB + COPC × WCC + COPD × WCD Here A, B, C, and D represent the various load condition of the chillers. WC is the weighting coefficient for that load condition. Table 7: Loading conditions of the electric chiller Condition Load Ratio % Weighting coefficient A 100 0.03 B 75 0.33 C 50 0.41 D 25 0.23 Loss of accuracy of results obtained by the program runs with constant COP can be assumed to be insignificant, since the operation of the chillers is modeled over the entire year. Moreover, since the thesis aims to compare different modeled scenarios, efficiency can be assumed as a constant value without diminishing the accuracy of results. The issue of variable efficiencies occurs only in the case of electric chillers since the absorption chillers have a constant efficiency irrespective of the load on the chiller. 0 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 C O P Percentage of loading COP of electric chillers 29 4.3 Demand data The cooling demand is input exogenously to the model. This data must be obtained at an hourly resolution, which means that the demand in MWh for each hour of the year is to be determined. The cooling demand for each hour is obtained by measuring the hourly consumed cooling energy from the substations in each connected building. The total hourly cooling demand is obtained by summing up all the hourly consumed cooling energy from each building. The cooling demand is the most vital parameter in the optimization model because the demand- supply balance constraint must be satisfied in each hour and hence decides the dispatch of the chillers. Also, the demand curve created here will be used to make a projection for future demand in further modeling. Hence, the demand considered here must be an accurate representation of the cooling demand in any year. Hence, the demand data from two years, 2017 and 2018 were considered. The year 2017 was a cold year with a lesser than average cooling demand. Thus, this demand had more dense regions in the average cooling demand and lesser peaks. This is shown in Figure 10. Figure 10: Cooling demand in 2017 The year 2018 was a warm year with a higher than average cooling demand. Thus, the demand curve in 2018 had more demand peaks as shown in Figure 11. Figure 11: Cooling demand in 2018 0 10 20 30 40 50 60 1 2 4 5 4 8 9 7 3 3 9 7 7 1 2 2 1 1 4 6 5 1 7 0 9 1 9 5 3 2 1 9 7 2 4 4 1 2 6 8 5 2 9 2 9 3 1 7 3 3 4 1 7 3 6 6 1 3 9 0 5 4 1 4 9 4 3 9 3 4 6 3 7 4 8 8 1 5 1 2 5 5 3 6 9 5 6 1 3 5 8 5 7 6 1 0 1 6 3 4 5 6 5 8 9 6 8 3 3 7 0 7 7 7 3 2 1 7 5 6 5 7 8 0 9 8 0 5 3 8 2 9 7 8 5 4 1C o o lin g d em an d ( M W h ) Hours Cooling demand in 2017 0 10 20 30 40 50 60 1 2 5 9 5 1 7 7 7 5 1 0 3 3 1 2 9 1 1 5 4 9 1 8 0 7 2 0 6 5 2 3 2 3 2 5 8 1 2 8 3 9 3 0 9 7 3 3 5 5 3 6 1 3 3 8 7 1 4 1 2 9 4 3 8 7 4 6 4 5 4 9 0 3 5 1 6 1 5 4 1 9 5 6 7 7 5 9 3 5 6 1 9 3 6 4 5 1 6 7 0 9 6 9 6 7 7 2 2 5 7 4 8 3 7 7 4 1 7 9 9 9 8 2 5 7 8 5 1 5 C o o lin g d em an d ( M W h ) Hours Cooling demand in 2018 30 Since, there were two demand profiles considered, these have to be further processed to create an average demand. The peaks in the demand are pivotal to design and dimension the capacity of the DCS. The main aim of the optimization model was to determine the optimal functioning of the DCS, hence the dense regions in the average demand is more important than the peaks. Thus, the peaks in the demand were not added to the average demand. Instead, an arithmetic average of the demands in 2017 and 2018 was calculated. This demand will be referred to as “Average Demand” from here on. Figure 12: Comparison of the demands Figure 12 shows the average demand with the demands in 2017 and 2018. The average demand profiles have points both above and below the other demands at different hours in the year. Table 8 shows the variation of the average demand. The total demand in 2018 was higher than that in average demand case and in 2017. The peak production from the chillers in 2018 is much higher than in the average demand case and in 2017. But, the peak production in the average case is very close to the peak in 2017. This shows that the peak demands in the two years do not occur at the same hours. Hence, this average demand is an accurate representation of the demand in the dense average regions in the profile and thus, the demand in an average year. 0 10 20 30 40 50 60 1 2 4 5 4 8 9 7 3 3 9 7 7 1 2 2 1 1 4 6 5 1 7 0 9 1 9 5 3 2 1 9 7 2 4 4 1 2 6 8 5 2 9 2 9 3 1 7 3 3 4 1 7 3 6 6 1 3 9 0 5 4 1 4 9 4 3 9 3 4 6 3 7 4 8 8 1 5 1 2 5 5 3 6 9 5 6 1 3 5 8 5 7 6 1 0 1 6 3 4 5 6 5 8 9 6 8 3 3 7 0 7 7 7 3 2 1 7 5 6 5 7 8 0 9 8 0 5 3 8 2 9 7 8 5 4 1 C o o lin g d em an d ( M W h ) Hours Demand Demand 2017 Demand 2018 Average demand Table 9 : Variation in demand Table 8 : Comparison of the demands 31 Chapter 5: Model Implementation The modeling in this thesis is split into two models. The models are based on the scope of modeling and the main aim of the models. In model 1, the scope of modeling is limited to the DCS i.e. the network is not included in these models. Further, different scenarios are investigated in this case. In model 2, the main aim is to develop methods to accurately model the network in numerical optimization algorithms. Further, different scenarios are set-up to analyze different situations. This chapter explain in detail the models, cases and the scenarios. 5.1 Model 1 Figure 13 shows the different cases and scenarios in model 1. Figure 13: Cases and models 5.1.1 Case 2018 The first case in this thesis presents a comparison between the DCS and a hypothetical case in which individual chillers are used to meet the entire cooling demand. Two different models are set up for each scenario in this case. An optimization model of the DCS in 2018 is used to determine the optimal operation of the system. Scenario 1 This is a model of the DCS in the year 2018. The main aim of this model is to determine the optimal functioning of the DCS in terms of the dispatch of the chillers. The system consists of electric chillers, absorption chillers, and free cooling from the river. The average demand which was described in the previous section is used as input to the model. The free cooling from the river is included in the system by revising the demand. The free cooling from the river is used to meet the cooling demand during the winter. Hence, it is assumed that the free cooling Model 1 Case 2018 Scenario 1 : DCS Scenario 2 : Individual chillers Case 2024 Scenario 3: DCS without TES Scenario 4 : DCS with TES Case 2030 DCS with SES in DH DCS without SES in DH 32 satisfies the cooling demand entirely from December to February. This assumption is made by looking at the chilled water generation from the chillers and the temperature of the river. To include this into the model, the hourly demand is made zero in hours between December and February. Also, the free cooling from the river is not included as a chilled water generation technology in the model. This ensures that chillers do not have to operate during the winter and the free cooling is not available during the months after the winter. During the combi-operation period, the chiller and free cooling are used together to meet the demand. During this period, a net demand is calculated. The net demand is given by the equation below. Net demand = Actual demand – Free cooling from the river This net demand is included in the model and hence, the chillers are run to satisfy this demand. Thus, the free cooling from the river is included in the optimization model through the demand profile which is input exogenously. Scenario 2 A hypothetical case of using individual chillers to meet the entire cooling demand is represented in this model. This model is referred to as “Individual chillers” in this thesis. Since it is a hypothetical case, the model has many inherent assumptions which are explained in this section. Firstly, the demand for each individual chiller is determined. There is a total of about 150 substations in the network. Since including each of those demands in the model can be very time consuming and make the model computationally complex, it was decided to group these demands into clusters. The main parameter that was used to make these clusters is the location of the buildings. It is assumed that the buildings which are located close to each other have a common chiller to meet the demand. The demand for this chiller is then determined by summing up the hourly cooling energy consumption from the substations. The chiller is dimensioned with an oversizing of 20% on the highest hourly demand. The buildings were grouped into 60 clusters [40]. It is assumed that only electric chillers are used in the buildings and no absorption chillers are considered. Another assumption is that there is no free cooling from the river. Although, it was decided that the river water could be used in water-cooled condensers in buildings that are located close to the river. Buildings that are located farther from the river have air-cooled condensers. Further, an additional assumption is made that the buildings do not have air-based free cooling in the winters i.e. cooling by using outdoor air in the ventilation system in the winter. Thus, in this scenario, it is assumed that the chillers must be run to meet the cooling demand even during the winter. The COP for the chillers was obtained from “Daikin Chiller catalogs” based on the installed capacity of the chiller and the type of condenser [41]. The demand of a cluster is coupled with the respective chiller by the equations in the model. Since each demand can be met only by the corresponding chiller, this is a simulation model where the main aim would be to calculate the total cost of running the chillers. The technical data of the chillers are presented in the appendix. 33 5.1.2 Case 2024 This case investigates the impact of the thermal energy storage in the DCS in Gothenburg. A tank that stores cold water is to be installed in the system. The main aim is to determine the impact of the thermal energy storage on the system. Hence, two models are set up, one with a thermal energy storage and one without. The prices of heat are obtained by running a model of the DHS in the year 2024. The main reason for installing the thermal energy storage in the system is to reduce the usage of the electric chillers during the summer. Göteborg Energi wants to operate absorption chillers at peak capacity and store the generated cold water in the tank. This is because a large amount of waste heat is available from the DHS free of cost. Thus, when the absorption chillers are run at peak capacity, a large amount of chilled water can be generated at very low costs and hence reduce the running costs of the system significantly. The stored cold water can then be discharged from the tank to meet the peak demand. Hence, the absorption chillers and the discharge from the tank can be used to meet the demand, and therefore, the