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District cooling network optimization with redundancy constraints in Singapore

District cooling network optimization with redundancy constraints in Singapore This study presents a mathematical optimization model for planning topology and capacity of a district cooling network. The model relies on a mixed-integer linear programming formulation to find the most economic network layout while satisfying redundancy criteria against unavailability of cooling stations. The simplicity of the formulation makes it easy to embed in other models or to extend it to other redundancy cases. The model is applied to a case study in the central business district of Singapore. Results show that district cooling is a profitable option for Singapore, especially due to its constant high cooling demand that is currently satisfied mainly through decentralized cooling units. This result generalizes to tropical cities world-wide with high cooling demand density. Keywords: District cooling, Mathematical optimization, Mixed-integer linear programming, Redundancy Introduction other areas of Singapore which comprise more residen- District cooling has been established in many countries. tial or industrial buildings. Due to the different type of Especially in bigger cities, it offers an energy efficient use of commercial buildings with the air conditioning run- alternative to individual generation of cooling power at ning all day long and amounting to approximately 50% the site of customers. Even in a city like Munich, Germany, of each building’s energy demand, the introduction of which is located in a temperate climate zone, several district cooling could lead to tremendous energy savings. district cooling systems have already been installed suc- Singapore already has a large underground district cool- cessfully and maintained. ing system in the Marina Bay. The system contains two In contrast to Munich, in Singapore, warm and humid plants with a maximum of 330MW of cooling power. weather prevails all year long, which results in much [1] According to the Singapore District Cooling Pte Ltd higher demand for cooling and dehumidification both (SDC), a subsidiary of Singapore Power, energy savings in residential and non-residential buildings. However, in amount to 40% which corresponds to the energy demand most buildings, cooling power is generated by using small of 24 000 three-room flats operated by Singapore’s Hous- chillers that use air for re-cooling which is very inefficient. ing Development Board (HDB). As a result, much electricity is used to operate the chillers. In this case study, we model a district cooling network State of projects for the central business district (CBD) of Singapore. We Over the last decades, district cooling networks have been present several cases and a comparison to conventional developed in several cities throughout Europe. Researches individual cooling. result in data shown in Table 1. Paris for example already Singapore’s CBD comprises mainly commercial build- started to supply in 1991 [2, 3]. Vienna has set the aim ings, e.g. shopping malls, hotels and office blocks, often of installing 200MW district cooling power until the with more than 50 floors. Thus, it stands in contrast to year 2020 ([4], p. 2). Stockholm has probably the biggest district cooling network today with a connected load of already 330MW, ranging from small (8kW) to large (7000kW) customers with an average load of about 500kW *Correspondence: johannes.dorfner@tum.de Technical University of Munich, Arcisstraße 21, 80333 München, Germany each [5]. Munich’s district cooling network [6] is con- Full list of author information is available at the end of the article stantly growing and they have installed different kinds of © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 2 of 13 Table 1 State of projects in European cities Khir [13] presents a mixed integer linear programming (MILP) model for designing district cooling system. It City Capacity Energy [Sources] (MW) (GWh/a) explicitly models flow rates, temperatures and pressures in a graph of arcs and nodes. Linearization of the physical Berlin [27] 44 constraints leads to a large amount of auxiliary variables. Helsinki [28, 29] 135 80 Both plant design and operation and network design can Munich downtown [6] 15 be optimized. However, to achieve a tractable problem Munich groundwater [6] 11.4 size, those two subproblems are solved separately. How- Munich M-Campus (mixed form) [6] 4.39 4.4 ever, this separation requires fixing the supply task. The paper also highlights the relationship with Steiner tree Paris [2] 290 420 problems. Stockholm [5] 330 460 Södermann [14] presents a similar MILP model for Vienna [30] 113.3 designing district cooling systems in urban areas. It uses a linearized cost function for sizing equipment (plants, pipes, storages). A small set of representative load periods (8 in the example study) approximate the annual cooling cooling in order to supply the best technology for each load duration curve. purpose. District heating State of research Due to the basic principle, district cooling and heating are This is a short summary of existing publications on dis- comparable types of supply. In both types, with few central trict cooling in Singapore, district cooling in general, generation plants heat or cold is generated which is mostly as well as similar or prominent approaches for district transferred to water. This tempered water is transported heating or more general multi-commodity district energy through pipes to customers buildings. Having transferred systems. the heat or cold to the buildings, the cooled or heated Cooling in Singapore water returns to the generation plants where the process Apart from the aforementioned existing district cool- starts from the beginning. The biggest difference between ing system [1], a recent study on Singapore [7] focused both are the technologies used in generation plants, which on comparing surface and subsurface cooling in tropical is not the focus of this article. Jamsek [15] presents a linear programming (LP) countries using an EnergyPlus model of a representa- approach for determining cost-minimal pipe topology and tive building. It concludes that an open-loop groundwater capacity configuration for a given structure and cost data. cooling system might be a better option for tropical cities A more conceptual, but worthwhile discussion of district like Singapore compared to conventional systems. The heating and cooling systems is given by Rezaie [16]. viability of district cooling in the CBD area of Singa- Udomsri [17] presents and compares the different pore has already been assessed in a working paper [8] by Singapore Power Ltd. options to combine centralized and decentralized heating and cooling. It points towards solutions that use decen- District cooling tralized, thermally driven chillers to produce cooling on- A thermal ice storage system and its influence on the site. This configuration can have advantages in regions cost-optimal design of district cooling distribution net- with both heating and cooling demands throughout the work is investigated [9] using non-linear optimization in year. two exemplary networks. It finds that ice storage can help Multi-commodity district energy system reduce the required pipe diameters. A TRNSYS model is A detailed model on combined energy system planning built to investigate a similar question [10] for a case study for electric, heating and cooling demand is presented by in Hong Kong; storage is not found to be an economically Chinese from 2008 [18]. It presents a MILP model. A case attractive option there. study in Udine, Italy, is performed with 7 nodes and 41 A genetic algorithm is used [11] to assess the opti- individually weighted time steps to represent the seasonal mum shares of five building types to form a cooling demand characteristics of a full year. load time series that is most suitable for district cool- A recent paper [19] investigates the case of combined ing. This approach was later embedded in an optimization district energy system for electricity, heating and cooling scheme for a development project in South East Kowloon, using a mixed integer linear optimization problem. Both Hong Kong. Another genetic algorithm was used by spatial (7 nodes) and temporal (2 days in 48 time steps) Feng and Long [12] to determine and compare piping resolution are low in the presented case study, but the layouts. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 3 of 13 non-linear performance of gas turbines is represented by To improve performance for large study regions, the a set of linearized constraints. model employs a linearized cost function for sizing the A broader review of computer models for renewable thermal pipe capacity. Depending on the parameteri- energy system analysis and optimization is provided by zation, one can either cautiously overestimate the real Connolly et al. [20]. Weber presents in her thesis [21] a estimated costs or try to fit as closely the observed cost comprehensive methodology to plan cost-optimal poly- function. In the latter case, one typically slightly underes- generation energy systems. timates the cost of medium capacities, while overestimat- ing the cost of small and large capacities. This work This paper presents the generalized version of a previ- Mathematical description ously published model developed for planning of district The presented model minimizes the total costs ζ of gen- heating distribution networks [22]. That model has then erating and distributing cooling through a district cooling been adapted for optimization of district cooling systems network. The key result is the size and topology of the and applied in a small case study for the city center of network, represented by the value of network capacity π ¯ Munich [23]. (vector of all individual arc capacities π ¯ ) in the optimal ij case: Model π ¯ = argmin ζ (1) This section describes a mathematical optimization π ¯ model to represent the planning task for a minimum cost Sets district cooling network. Its main input is a connected A district or city is represented as a graph of vertices and graph of street segments that represent the discrete possi- arcs. This graph is derived from the street network. It ble network parts. Each segment – called edge in the fol- should be derived in such a way to include all consider- lowing – has the attributes length and a cooling demand able locations for network pipes. The spatial resolution that may (but does not have to) be satisfied by the district can be chosen as fine as required. Here, it is on the level of cooling network. A subset of the graph’s vertices may pro- building blocks, i.e. a single street segment between two vide cooling at fixed specific costs, representing (possible) intersections. cooling stations. Let V be the set of vertices v , corresponding to connect- The model’s main contribution lies in a simple repre- ing or terminating points of the graph. Set A of arcs then sentation of redundancy constraints by means of artificial comprises ordered tuples of vertices a = (v , v ) with ij i j time steps (or periods) with pre-determined reduced i = j. A is symmetric, that means either both or none of availability of cooling stations. This technique can eas- the pair a and a are elements of A. For readability, the ij ji ily be embedded into other optimization models and subscript ◦ is used to denote any parameter or variable can increase the robustness of obtained solutions against that is defined over vertices v ∈ V , while ◦ is used to i ij equipment downtime due to outages or maintenance. denote a quantity defined over arcs a ∈ A. ij The set V ⊆ V defines so-called source vertices, which Overview represent locations of possible cooling sources. Usually, A brief conceptual overview on the model’s inputs the number of source vertices is low (≤ 10) compared to (parameters) and outputs (results) is given in Fig. 1. The thesizeofthe graph. presented optimization model, based on estimated (or The neighbor sets N of a vertex v are defined by the i i known) cooling demand and a graph of possible segments indices of all vertices that are connected to it by an arc: to construct a cooling network, derives the cost-optimal N = { k | a ∈ A }. i ki size and topology of such a network. The objective func- Time is represented by a set T of discrete time steps t, tion minimizes total costs (generation costs minus rev- which represent a small number of representative oper- enues), thus yielding the most profitable system design. ational situations. The minimum viable number of time steps is two: one for peak demand with a duration of one to several hours, a second for the average annual load with a duration of the remaining year. A more comprehensive choice are three to four time steps: The third can refer to the all-year base load, while the fourth can be used to rep- resent a common intermediate load level. Additional time steps need to be introduced if redundancy requirements Fig. 1 Optimization model overview. Inputs and outputs of the are to be stated. Refer to the discussion of the parameter presented mathematical optimization model availability below for more details. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 4 of 13 Parameters given in S$/(kW m), refers to the capacity-dependent cost The numerical given facts for this model are shown in component of building a pipe. Both values must be tai- Table 2. They are grouped by their defining domains. First lored to the study area to compensate for differences in are vertex parameters, then arc parameters, then con- cost structure and availability of different pipe sizes. The stant or global parameters, and finally time-dependent same is true for the operation & maintenance (OM) cost parameters. parameter c in S$/m. In contrast to the fixed investment om Vertices have a single parameter: their maximum power costterm,itisalsotobepaidforexistingpipes. Thecost max cool capacity Q . It is the thermal output power given in for providing cooling c here is dependent on the ver- i v kW for that location. All non-source vertices have this tex to allow for representing cheap surface water cooling parameter set to 0. in contrast to more expensive re-cooling options. Arcs have three main attributes: their length l (m), the The letter c and a subscript denote economic param- ij thermal peak demand d (kW) of their adjacent buildings eters. These are investment costs for building the pipe ij and g (binary), which states whether a pipe already exists network c and c , maintenance c , costs of provid- ij fix var om cool in this arc. ing c cooling, and revenue for delivering c cooling rev max As secondary parameter, C indicates the maximum to consumers. While c contains the size-independent fix ij thermal power capacity (kW) in an arc, which can be costs (mainly earth works), c contains costs that are var derived from the maximum available pipe diameter. For dependent on the thermal capacity (diameter) of the pipe. arcs with existing pipes (g = 1), this value should be set Time-dependent parameters s and w represent scal- ij t t according to the diameter of that existing pipe. As both ing factor (dimensionless) and weight or duration (h) of arcs a and a refer to the same street segment, parameter atimestep t. A value of s = 1 refers to peak demand, ij ji t values for both members are always identical. while smaller values correspond to moments of partial Global parameters are technical and economic parame- load. Together, these two parameters encode a discretized ters that refer to the district cooling system as a whole. annual load curve. Economic parameters are all costs and revenues. The Redundancy requirements can be stated in the model by investment costs are split into a fixed part c and a vari- setting the binary availability parameter y to value 0 in fix it able part c .The fixedpart, giveninS$/m,captures certaintimesteps for1,2, ... source vertices. If one time var all costs that are not dependent on the capacity of the step for each foreseen failure configuration is introduced, pipe to be built, mainly earth works. The variable part, a full n − 1, n − 2, ... failure safety (against cooling source outages) can be enforced in the produced solution. Clari- fication: in the conventional time steps discussed above in paragraph time step set, the value y = 1istobeset for Table 2 Optimization model parameters it all source vertices v ∈ V . i 0 Name Unit Description c S$/m Fixed investment costs fix Variables c S$/(kW m) Variable investment costs var The main optimization task is to find values for the binary c S$/(m a) Operation & maintenance costs om decision variable ξ . If its value is one, a pipe is built in the ij c S$/kWh Revenue for cooling street segment corresponding to the arc a . For each time rev ij fix step, the actual use of a given pipe is decided by setting w kW/m Fixed thermal losses the binary pipe usage decision variable ψ . If its value is var ijt w kW/(kW m) Variable thermal losses one, the pipe in arc a is used in direction from vertex v ij i b — Concurrence effect in to vertex v . Consequently, there must be a power flow π ijt q — Connect quota into the pipe. Simultaneously, a value ξ = 1 requires that ij u 1/a Annuity factor for investment costs the demand d of this arc has to be satisfied at all times. ij cool The power flow variable at the other end of the pipe is c S$/kWh Cooling costs at source vertices out called π . Its value is determined by the ingoing power max ijt Q kW Source vertex capacity flow minus losses and demand. l m Arc length ij Thenon-negativevariable ρ represents thermal power it d kW Arc peak demand ij output from a source vertex v ∈ V at time t in kW. It is i 0 g — Existence of a pipe (1=yes, 0=no) ij limited in value by the source vertex capacity parameter max max C kW Maximum pipe capacity Q and possibly by the availability parameter y .Table3 it ij i summarizes all model variables. The following line shows s 1 scaling factor their domains, on which they are defined: w h weight/duration y — availability (1=yes, 0=no) in out it ζ ∈ R ξ , ψ ∈{0, 1}¯ π , π , π , ρ ∈ R . ij ijt ij it ijt ijt 0 Dorfner et al. Future Cities and Environment (2017) 3:1 Page 5 of 13 Table 3 Optimization model variables linear approximation possibly over- and underestimates the cost of either small or large capacities. Depending on Name Unit Description the parameterization, one can either force an optimistic ζ S$ Total system cost (Inv, O&M, Rev, Gen) (by deliberate underestimation) or cautious (by deliberate ξ — Binary decision variable: 1 = build pipe ij overestimation) planning decision. The linear approxima- ψ — Binary decision variable: 1 = use pipe ijt tion exhibits unsteady jump from zero to the fixed cost π kW Thermal power flow capacity into arc a ij ij uc +c for any positive value of π ¯ for any non-existing fix om ij in (g = 0) pipe. The link between the binary decision vari- π kW Thermal power flow from v into arc a i ij ij ijt out able ξ and the continuous pipe capacity variable π ¯ is ij ij π kW Thermal power flow out of arc a into v ij j ijt enforced through Eqs. (8), (12), and (14) below. ρ kW Cooling in source vertex v it i These are the definitions for the four derived parame- ters used in the cost equation above. The division by value 2, common to all three arc parameters, compensates for Equations the double-representation of one street segment {v , v } as i j Equations fall into two categories: The first is the cost a pair two directed arcs a , a .Moreabout thisissuecan ij ji function whose value is to be minimized. The second are be found at the explanation of the symmetry constraints cool constraints that codify all the previously discussed rules in (15) and (16) below. The cooling cost parameter k is mathematical form. By that, they define the region of fea- divided by the concurrence effect parameter b to remove sible solutions, under which the solver selects a (close to) the load reduction effect that is introduced in Eq. 10. In cost optimal solution. other words, the power flow that needs to be satisfied The cost function value ζ is the sum of costs for pro- from a source vertex is lower by b than the energy flow viding cooling, minus revenue for that cooling. Network that needs to be delivered. The division by b removes that costs occur for building the network (annualized invest- difference in terms of costs. ment) and for operation & maintenance. The following fix ∀a ∈ A : k = c l u (1−g ) + c l /2(3) ij fix ij ij om ij derived parameters are introduced to shorten the def- ij var inition of the cost function whose definition is given ∀a ∈ A : k = c l u (1 − g ) /2(4) ij var ij ij ij fix var below: k (S$/a) and k (S$/(kW a)) cover network costs ij ij cool cool ∀v ∈ V : k = c /b (5) i i cool (investment, O&M). k (S$/kWh) represents cooling ij cool ∀a ∈ A : r = c d q/2(6) cool ij rev ij ij generation costs, while r (S$/h) represents revenue for ij provided cooling. With these, the cost function is equal to The constraints formalize all physical laws and technical rules that need to be satisfied by a feasible solution. The fix var cool ζ = k ξ + k π + k w ρ ij ij t it ij ij i first constraint concerns energy conservation in vertices a ∈A v ∈V ij i v , with respect to its neighbors N : i i t∈T cool in out − r s w ξ.(2) ∀v ∈ V , t ∈ T : π − π ≤ ρ (7) t t ij ij i it int nit a ∈A n∈N ij i t∈T This inequality is thus a relaxed version of the law of The first summand forms a piece-wise linear function energy conservation. Relaxed, because it allows for power that is depicted in Fig. 2. The plot also depicts that the to vanish at any vertex. As power does not come for free, any solution returned by the solver will satisfy this con- straint to equality. For all non-source vertices (i.e. ρ = it 0), the difference between outgoing and incoming power must be smaller than or equal to zero. In source vertices, a positive difference may remain when it is met by an equal amount of input power ρ into the network at that vertex. it Demand satisfaction is the main arc constraint.Itcreates thelogical connectionbetween thediscretepipeusage decision ψ and the demand satisfaction. Like the cost ijt equation, it relies on two derived parameters x and y . ij ijt This constraint is also graphically explained in Fig. 3. Fig. 2 MILP pipe investment cost function. Investment and operation in out ∀a ∈ A, t ∈ T : x π − π = y ψ (8) ij ij ijt ijt & maintenance costs for a single arc a over thepipecapacity π ¯ ijt ijt ij ij (thick, blue). The curved line (thin, green) indicates a representative var Parameter x refers to losses w that are proportional ij possible real non-linear cost function to the amount of power flow into the arc a . Parameter ij Dorfner et al. Future Cities and Environment (2017) 3:1 Page 6 of 13 Pipe capacity is a technical constraint that limits the power flow through a pipe by the built capacity. This is accomplished by first limiting the ingoing power flow into in apipe π by the built pipe capacity π ¯ . The second con- ij ijt straint is required to set the pipe usage decision variable ψ . Its value is forced to 1 if a flow in direction from ijt v to v at time step t is required. The reason for this i j seemingly artificial constraint is explained in the following constraint. in in ∀a ∈ A, t ∈ T : π ≤ π (11) Fig. 3 Sankey diagram of Eq. (8). Ingoing cooling power flow π from ij ij ijt ijt vertex v is reduced by variable losses (1 − x ), fixed losses and cooling i ij in max ∀a ∈ A, t ∈ T : π ≤ ψ C (12) out ij ijt ijt ij demand (y ) before leaving to vertex v as power flow π ijt j ijt in Unidirectionality of the power flow π is required, as ijt otherwise the solver would happily use a pipe’s capacity in fix y refers to fixed thermal losses w that only depend ijt both directions simultaneously, which would not be phys- on the pipe length, not on the power flow, and the time- ically possible. Therefore, the pipe usage decision variable dependent demand d · s that is further reduced by the ij t ψ may only have the value 1 in one direction at any given ijt concurrence effect b and the connect quota parameter q. time step t. This way, the direction of flow may change In notation: between time steps, but any given pipe may only be used var in one direction at a given time. ∀a ∈ A: x = 1 − l w (9) ij ij ij fix ∀a ∈ A, t ∈ T : y = bq d s + l w (10) ∀a ∈ A, t ∈ T : ψ + ψ ≤ 1 (13) ij ijt ij t ij ij ijt jit Fig. 4 Study region within Singapore. The green outline shows the location of the CBD study region within the extent of Singapore. It covers the Marina Bay and follows Orchard Road to the north west Dorfner et al. Future Cities and Environment (2017) 3:1 Page 7 of 13 Table 4 Total floor area and cooling peak load by building type Build capacity limits the pipe capacity variables to the maximum available diameter, whose capacity in kW is Building type Peak load Floor area max represented by parameter C . At the same time, this 2 3 2 ij (W/m)(10 m ) constraint sets the value of the building decision variable Civic & community institution 112.5 529 ξ , if a non-zero pipe capacity π ¯ is needed. ij ij Commercial 112.5 6685 max ∀a ∈ A: π ≤ ξ C (14) ij ij ij ij Commercial & residential 100 1021 Educational institution 112.5 175 Symmetry of building decision are two constraints that Health & medical care 125 40 enforce that the mathematically independent arcs a and ij a must have identical variable values for their pipe capac- Hotel 112.5 1605 ji ity π ¯ and building decision ξ . This way, a pipe can then ij ij Open space 0 22 be used in both directions at different time steps. Park 0 58 Place of worship 0 137 ∀a ∈ A: ξ = ξ (15) ij ij ji Reserve site 0 157 ∀a ∈ A: π = π (16) ij ij ji Residential 112.5 717 Use if built is the last piece in the puzzle to link the Residential/commercial (1st storey) 112.5 357 building decision ξ to the pipe usage decision ψ .Up ij ijt Sports & recreation 75 15 to this point, nothing in the formulation requires that the Transport facilities 0 29 cooling demand of a customer is satisfied at all times.This Utility 0 43 constraint enforces exactly that, by requiring that the sum of ψ + ψ is greater or equal to 1, if a pipe is built along ijt jit that arc. Otherwise, the condition should not be enforced. This is done by calculating the expression (ξ + ξ )/2. It ij ji is equal to 1 if ξ = 1, as Eq. (15) requires ξ = ξ . ij ij ji Equations 2 to (18) together define a linear mixed- Otherwise, its value is equal to 0. In other words: if an integer program, whose optimal solution is the desired arc is has a pipe, its demand must always be satisfied by a vector of pipe capacities π ¯ , accompanied by optimal power flow from any of its two sides. cooling power flows. ∀a ∈ A, t ∈ T : ψ + ψ ≥ (ξ + ξ )/2 (17) ij ijt jit ij ji Case study Source vertices is the last constraint. It limits the source The presented model is applied on a potential supply area vertex power flow ρ by its maximum allowed capacity it in the central business district of Singapore, as shown in max Q . The availability parameter y usually has value 1, it i Fig. 4. The first part describes how the input parame- except for special time steps in which the source vertex v ters were derived. Then the assumptions for a sensitiv- is made unavailable by setting y = 0: it ity analysis against conventional per-building cooling are described. max ∀v ∈ V , t ∈ T : ρ ≤ y Q (18) i it it Table 5 Parameter values in case study Name Value Unit c 7000 S$/m fix c 8e-4 S$/(m kW) var c 80 S$/(m a) om c 0.14 S$/kWh rev fix w 0.01 kW/m var w 1e-8 kW/(kW m) b 0.9 — q 1.0 — Fig. 5 Annual load duration curve. Estimated duration curve (thin, green) and its discretization to 8 steps (thick, blue)asusedbythe u 0.091 1/a optimization model. Step lengths correspond to time step weight w cool and the relative load value to s c 0.03 or 0.07 S$/kWh i Dorfner et al. Future Cities and Environment (2017) 3:1 Page 8 of 13 Load profile estimation To record and to utilize the optimization potential of Due to lack of access to a load profile from Singapore, a this expanding system, in a detail data analysis a question known cooling load from Munich was extrapolated based amongst others was examined on which factors the cus- on weather data in Singapore. tomers cooling demand is depending. Furthermore the The district cooling system of Munich has mostly collected data serve as basis for the evaluation of the cool- non-residential customers like shopping malls, offices, ing demand in other cities like Singapore. Based on a congress centers and smaller retail trades. Its usage type period of two years up to 2015 the influence of tempera- composition is therefore rather similar to Singapore’s ture, humidity, insolation and the customer behavior itself CBD. However, the buildings are much smaller and thus was analyzed. have a different surface to volume ratio and surface mate- The strongest influence on the cooling demand is the rials than the much higher buildings in Singapore’s CBD. temperature. The humidity plays a subordinated role in Fig. 6 Demand and cooling stations. Location of cooling demand (color and line thickness of edges) and cooling stations (triangles). Large triangles (at vertices 57, 110, 154) correspond to cheap surface water cooling, while small triangles assume more expensive air re-cooling Dorfner et al. Future Cities and Environment (2017) 3:1 Page 9 of 13 Munich (but not in Singapore), cause of the temperate cli- areasandofficesaswellasthehighlyvolatiletemperature mate zone and the previous low dehumidification in the profile of a day, the cooling demand is five times higher comfort zones. To count in this factor to the further cus- during the day than at night or on a holiday. This charac- tomer and grid extension, the enthalpy of the outside air, teristic day-night cycle are also recorded in other Central as an index for the heat input to the buildings, is used as European cities ([24], pp. 8, 80). leading control parameter. The insolation has no consid- Using the high cooling demand during the business erable influence on the customers’ requirements because hours and the enthalpy dependence, a trend was generated of the good insulation of the rather new buildings and the for the customers’ requirements. This trend line is com- shading situation in the densely built city center. bined with the climate records of Singapore to create an The second strongest influence factor on the cooling approximated annual load duration curve, shown in Fig. 5. demand of the Munich costumers are the business hours. To reduce the temporal resolution for the optimization Due to the simultaneous public traffic in the shopping model to manageable sizes, this curve is discretized to 8 Fig. 7 Cost-optimal network layout. Line thickness corresponds to thermal capacity π ¯ (kW) of each pipe ij Dorfner et al. Future Cities and Environment (2017) 3:1 Page 10 of 13 individually weighted time steps, also shown. One 24 h PengKee [8]. Building or area types with small total area long time step represents peak demand, while the other 7 were ignored. With those assumptions, a total summed steps have durations ranging from 390 h to 2006 h. peak cooling demand of 1241MW exists in the case study area. Annual cooling demand Cooling demand is estimated based on previous work Input data conducted by Böhme et al. [25]. There, a geographic The street graph is derived from OpenStreetMap data dataset of buildings with gross floor area and usage type [26], processed using previously described [22] pre- was prepared. The total floor area by building type (e.g. processing steps using polygon skeletonization for simpli- residential, commercial, ...) is summarized in Table 4. fying the dense street network. It also states the assumed design cooling loads, based Cost data (given in S$) and technical parameters for this on a mean design load of 112.5kW/m ,estimatedfrom case study are summarized in Table 5. Pipe investment Fig. 8 Cost-optimal power flow during peak load. All three surface water cooling station operate at maximum capacity (150 MW each) Dorfner et al. Future Cities and Environment (2017) 3:1 Page 11 of 13 costs of 7000 S$/m are the main cost driver on the supply cost of 0.03 S$/kWh. The other six cooling stations have side. This value is scaled to one year with an annuity factor higher costs of 0.07 S$/kWh. (1 + i) · i Scenarios u = (19) Base case (1 + i) − 1 The base case is designed to show today’s demand situ- ation. In this scenario, the size and layout of a profitable with interest rate i = 6.5% and depreciation duration district cooling network is to be determined. n = 20a, yielding a value of 0.091. Operation & mainte- nance are relatively cheap with annual 80 S$/m. Cooling In the base case, a revenue of 0.14 S$/kWh is assumed. A cost depends on the location of the cooling station. The sensitivity analysis with reduced revenues in steps of 0.02 large triangles in Fig. 6 show stations with access to surface S$/kWh is also conducted to determine how sensitive the water, which allows cheap re-cooling with an assumed optimal network size is on the price for cooling. Fig. 9 Power flow during outage of cooling station at vertex 57. In this situation, the large pipe capacities south of vertex 13 are needed to transmit backup cooling power from the western three cooling stations to the central bay area Dorfner et al. Future Cities and Environment (2017) 3:1 Page 12 of 13 Growing demand In order to assess how the total cooling costs (genera- tion and distribution) are affected by a possible demand growth in the study area, additional load is introduced in the edge (54, 114) in the south-eastern corner. It’s value is changed from 0MW to 200MW with steps of 50 MW. As this step creates more load than the existing cooling stations could satisfy while satisfying the redun- dancy constraint, all cooling stations’ capacity is increased by 50%. Results Base case Fig. 10 Specific cooling costs for growing demand with original 0.03 and 0.07 S$/kWh cooling stations. Cost increase is caused by higher The resulting network for the base case is shown in utilization of expensive cooling stations Fig. 7. It shows a district cooling network that satisfies almost all (1240MW of 1241MW) cooling demand. In other words: under the presented cost assumptions and a cooling revenue of 0.14 S$/kWh, district cooling is an Discussion and future research economically viable strategy. A sensitivity check with a District cooling can be an attractive option for cities with reduced cooling revenue of 0.10 S$/kWh still leads to an constant high cooling load, compared to less efficient dis- almost full saturation of 1237 MW supplied demand. The tributed cooling. The high demand density of Singapore’s unsatisfied demands are mainly short, isolated edges with CBD makes it a very well suited candidate. Direct access low demand (≤ 3MW) that cannot offset the network to surface and seawater provides enough cooling poten- investment cost. Only when revenue is further reduced, tial to satisfy a significant fraction of the present cooling between 0.08 and 0.06 S$/kWh, the optimal network loads. drops from satisfying 1200 MW to 0 MW. This value As Singapore is planning to establish further dense com- range thus can be taken as a lower bound for profitabil- mercial areas similar to the CBD with many office blocks, ity of a district cooling system (under the given cost e.g. in Jurong, more regions will become suitable candi- assumptions). dates for district cooling. Moreover, the potential of dis- Figures 8 and 9 compare the cooling power flow in two trict cooling could also be evaluated for densely populated of the 18 time steps considered for designing the net- residential areas, e.g. Bukit Panjang or Punggol. work capacities in Fig. 7. The first situation shows the The redundancy requirements on cooling stations could cost-optimal cooling power flow when all cooling stations need refinement, possibly by relaxing the full (n-1) capa- are operational. The three cheap cooling stations (57, 110, bility for the whole system to only certain areas. An 154) are delivering their full capacity of 150 MW each, extension could introduce the same requirement not only while several of the other stations only run in partial load. to cooling station, but also to crucial parts of the network. The second situation in Fig. 9 shows how the redundancy requirement leads to the consideration of very different Acknowledgements flow situations. Here, cooling station 13 now runs at full We express our gratitude to the Singapore Land Authority for supporting us capacity and satisfies the middle of the study area. with geospatial data. This work was financially supported by the Singapore National Research Foundation under its Campus for Research Excellence And Technological Growing demand Enterprise (CREATE) programme. This work was supported by the German The resulting cooling cost for gradually increasing the Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open Access Publishing Program. demand in edge (54, 114) for each case is shown in Fig. 10. The cooling cost here is calculated by dividing total costs Availability of data and materials for generation and network by the amount of provided The optimization model’s implementation is available under the GPL 3.0 cooling (in kWh). Cost for cooling grows slightly – along license at https://github.com/tum-ens/dhmin. The model input data is available under the CC-BY license via doi:10.6084/m9.figshare.3582456. with demand – from approximately 0.045 S$/kWh to 0.048 S$/kWh in the case of additional 200MW peak cool- Authors’ contributions ing demand. This increase is caused by a higher utilization JD developed and applied the optimization model to the case study. PK lead of the more expensive 0.07 S$/kWh cooling stations. The his expertise in planning district cooling networks to provide input data and scenario definitions. MD contributed the method for deriving the annual load specific network costs actually exhibit a minor reduc- duration curve. TM provided data for the case study region and vetted model tion as demand grows, but this effect is negligibly small results against local experience. All authors collaborated for writing the article. here. All authors have read and approved the final submitted manuscript. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 13 of 13 Competing interests 20. Connolly D, Lund H, Mathiesen BV, Leahy M (2010) A review of computer The authors declare that they have no competing interests. tools for analysing the integration of renewable energy into various energy systems. Appl Energy 87(4):1059–1082. Author details doi:10.1016/j.apenergy.2009.09.026 Technical University of Munich, Arcisstraße 21, 80333 München, Germany. 21. Weber CI (2008) Multi-objective design and optimization of district energy Stadtwerke München, Emmy-Noether-Straße 2, 80992 München, Germany. systems including polygeneration energy conversion technologies. PhD 3 4 SWM Infrastruktur, Emmy-Noether-Straße 2, 80992 München, Germany. TUM thesis, École Polytechnique Fédérale de Lausanne, Bucharest (Romania) CREATE, 1 CREATE Way, #10-02 CREATE Tower, 138602 Singapore, Singapore. 22. Dorfner J, Hamacher T (2014) Large-scale district heating network optimization. IEEE Trans Smart Grid 5(4):1884–1891. Received: 2 September 2016 Accepted: 7 December 2016 doi:10.1109/TSG.2013.2295856 23. Krystallas P, Dorfner J (2014) Expansion planning for district cooling networks using mathematical optimization:38–42. EuroHeat Power Int 3: 24. Urbaneck T (2012) Kältespeicher: Grundlagen, Technik, Anwendung. 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Rezaie B, Rosen MA (2012) District heating and cooling: Review of Submit your manuscript to a technology and potential enhancements. Appl Energy 93:2–10. journal and benefi t from: doi:10.1016/j.apenergy.2011.04.020 17. Udomsri S, Bales C, Martin AR, Martin V (2012) Decentralized cooling in 7 Convenient online submission district heating network: System simulation and parametric study. Appl 7 Rigorous peer review Energy 92:175–184. doi:10.1016/j.apenergy.2011.10.009 7 Immediate publication on acceptance 18. Chinese D (2008) Optimal size and layout planning for district heating and cooling networks with distributed generation options. Int J Energy 7 Open access: articles freely available online Sector Manag 2(3):385–419. doi:10.1108/17506220810892946 7 High visibility within the fi eld 19. Ameri M, Besharati Z (2016) Optimal design and operation of district 7 Retaining the copyright to your article heating and cooling networks with cchp systems in a residential complex. Energy Buildings 110:135–148. doi:10.1016/j.enbuild.2015.10.050 Submit your next manuscript at 7 springeropen.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Future Cities and Environment Springer Journals

District cooling network optimization with redundancy constraints in Singapore

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Copyright © 2017 by The Author(s)
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Energy; Energy Efficiency; Renewable and Green Energy; Energy Technology; Landscape/Regional and Urban Planning
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10.1186/s40984-016-0024-0
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Abstract

This study presents a mathematical optimization model for planning topology and capacity of a district cooling network. The model relies on a mixed-integer linear programming formulation to find the most economic network layout while satisfying redundancy criteria against unavailability of cooling stations. The simplicity of the formulation makes it easy to embed in other models or to extend it to other redundancy cases. The model is applied to a case study in the central business district of Singapore. Results show that district cooling is a profitable option for Singapore, especially due to its constant high cooling demand that is currently satisfied mainly through decentralized cooling units. This result generalizes to tropical cities world-wide with high cooling demand density. Keywords: District cooling, Mathematical optimization, Mixed-integer linear programming, Redundancy Introduction other areas of Singapore which comprise more residen- District cooling has been established in many countries. tial or industrial buildings. Due to the different type of Especially in bigger cities, it offers an energy efficient use of commercial buildings with the air conditioning run- alternative to individual generation of cooling power at ning all day long and amounting to approximately 50% the site of customers. Even in a city like Munich, Germany, of each building’s energy demand, the introduction of which is located in a temperate climate zone, several district cooling could lead to tremendous energy savings. district cooling systems have already been installed suc- Singapore already has a large underground district cool- cessfully and maintained. ing system in the Marina Bay. The system contains two In contrast to Munich, in Singapore, warm and humid plants with a maximum of 330MW of cooling power. weather prevails all year long, which results in much [1] According to the Singapore District Cooling Pte Ltd higher demand for cooling and dehumidification both (SDC), a subsidiary of Singapore Power, energy savings in residential and non-residential buildings. However, in amount to 40% which corresponds to the energy demand most buildings, cooling power is generated by using small of 24 000 three-room flats operated by Singapore’s Hous- chillers that use air for re-cooling which is very inefficient. ing Development Board (HDB). As a result, much electricity is used to operate the chillers. In this case study, we model a district cooling network State of projects for the central business district (CBD) of Singapore. We Over the last decades, district cooling networks have been present several cases and a comparison to conventional developed in several cities throughout Europe. Researches individual cooling. result in data shown in Table 1. Paris for example already Singapore’s CBD comprises mainly commercial build- started to supply in 1991 [2, 3]. Vienna has set the aim ings, e.g. shopping malls, hotels and office blocks, often of installing 200MW district cooling power until the with more than 50 floors. Thus, it stands in contrast to year 2020 ([4], p. 2). Stockholm has probably the biggest district cooling network today with a connected load of already 330MW, ranging from small (8kW) to large (7000kW) customers with an average load of about 500kW *Correspondence: johannes.dorfner@tum.de Technical University of Munich, Arcisstraße 21, 80333 München, Germany each [5]. Munich’s district cooling network [6] is con- Full list of author information is available at the end of the article stantly growing and they have installed different kinds of © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 2 of 13 Table 1 State of projects in European cities Khir [13] presents a mixed integer linear programming (MILP) model for designing district cooling system. It City Capacity Energy [Sources] (MW) (GWh/a) explicitly models flow rates, temperatures and pressures in a graph of arcs and nodes. Linearization of the physical Berlin [27] 44 constraints leads to a large amount of auxiliary variables. Helsinki [28, 29] 135 80 Both plant design and operation and network design can Munich downtown [6] 15 be optimized. However, to achieve a tractable problem Munich groundwater [6] 11.4 size, those two subproblems are solved separately. How- Munich M-Campus (mixed form) [6] 4.39 4.4 ever, this separation requires fixing the supply task. The paper also highlights the relationship with Steiner tree Paris [2] 290 420 problems. Stockholm [5] 330 460 Södermann [14] presents a similar MILP model for Vienna [30] 113.3 designing district cooling systems in urban areas. It uses a linearized cost function for sizing equipment (plants, pipes, storages). A small set of representative load periods (8 in the example study) approximate the annual cooling cooling in order to supply the best technology for each load duration curve. purpose. District heating State of research Due to the basic principle, district cooling and heating are This is a short summary of existing publications on dis- comparable types of supply. In both types, with few central trict cooling in Singapore, district cooling in general, generation plants heat or cold is generated which is mostly as well as similar or prominent approaches for district transferred to water. This tempered water is transported heating or more general multi-commodity district energy through pipes to customers buildings. Having transferred systems. the heat or cold to the buildings, the cooled or heated Cooling in Singapore water returns to the generation plants where the process Apart from the aforementioned existing district cool- starts from the beginning. The biggest difference between ing system [1], a recent study on Singapore [7] focused both are the technologies used in generation plants, which on comparing surface and subsurface cooling in tropical is not the focus of this article. Jamsek [15] presents a linear programming (LP) countries using an EnergyPlus model of a representa- approach for determining cost-minimal pipe topology and tive building. It concludes that an open-loop groundwater capacity configuration for a given structure and cost data. cooling system might be a better option for tropical cities A more conceptual, but worthwhile discussion of district like Singapore compared to conventional systems. The heating and cooling systems is given by Rezaie [16]. viability of district cooling in the CBD area of Singa- Udomsri [17] presents and compares the different pore has already been assessed in a working paper [8] by Singapore Power Ltd. options to combine centralized and decentralized heating and cooling. It points towards solutions that use decen- District cooling tralized, thermally driven chillers to produce cooling on- A thermal ice storage system and its influence on the site. This configuration can have advantages in regions cost-optimal design of district cooling distribution net- with both heating and cooling demands throughout the work is investigated [9] using non-linear optimization in year. two exemplary networks. It finds that ice storage can help Multi-commodity district energy system reduce the required pipe diameters. A TRNSYS model is A detailed model on combined energy system planning built to investigate a similar question [10] for a case study for electric, heating and cooling demand is presented by in Hong Kong; storage is not found to be an economically Chinese from 2008 [18]. It presents a MILP model. A case attractive option there. study in Udine, Italy, is performed with 7 nodes and 41 A genetic algorithm is used [11] to assess the opti- individually weighted time steps to represent the seasonal mum shares of five building types to form a cooling demand characteristics of a full year. load time series that is most suitable for district cool- A recent paper [19] investigates the case of combined ing. This approach was later embedded in an optimization district energy system for electricity, heating and cooling scheme for a development project in South East Kowloon, using a mixed integer linear optimization problem. Both Hong Kong. Another genetic algorithm was used by spatial (7 nodes) and temporal (2 days in 48 time steps) Feng and Long [12] to determine and compare piping resolution are low in the presented case study, but the layouts. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 3 of 13 non-linear performance of gas turbines is represented by To improve performance for large study regions, the a set of linearized constraints. model employs a linearized cost function for sizing the A broader review of computer models for renewable thermal pipe capacity. Depending on the parameteri- energy system analysis and optimization is provided by zation, one can either cautiously overestimate the real Connolly et al. [20]. Weber presents in her thesis [21] a estimated costs or try to fit as closely the observed cost comprehensive methodology to plan cost-optimal poly- function. In the latter case, one typically slightly underes- generation energy systems. timates the cost of medium capacities, while overestimat- ing the cost of small and large capacities. This work This paper presents the generalized version of a previ- Mathematical description ously published model developed for planning of district The presented model minimizes the total costs ζ of gen- heating distribution networks [22]. That model has then erating and distributing cooling through a district cooling been adapted for optimization of district cooling systems network. The key result is the size and topology of the and applied in a small case study for the city center of network, represented by the value of network capacity π ¯ Munich [23]. (vector of all individual arc capacities π ¯ ) in the optimal ij case: Model π ¯ = argmin ζ (1) This section describes a mathematical optimization π ¯ model to represent the planning task for a minimum cost Sets district cooling network. Its main input is a connected A district or city is represented as a graph of vertices and graph of street segments that represent the discrete possi- arcs. This graph is derived from the street network. It ble network parts. Each segment – called edge in the fol- should be derived in such a way to include all consider- lowing – has the attributes length and a cooling demand able locations for network pipes. The spatial resolution that may (but does not have to) be satisfied by the district can be chosen as fine as required. Here, it is on the level of cooling network. A subset of the graph’s vertices may pro- building blocks, i.e. a single street segment between two vide cooling at fixed specific costs, representing (possible) intersections. cooling stations. Let V be the set of vertices v , corresponding to connect- The model’s main contribution lies in a simple repre- ing or terminating points of the graph. Set A of arcs then sentation of redundancy constraints by means of artificial comprises ordered tuples of vertices a = (v , v ) with ij i j time steps (or periods) with pre-determined reduced i = j. A is symmetric, that means either both or none of availability of cooling stations. This technique can eas- the pair a and a are elements of A. For readability, the ij ji ily be embedded into other optimization models and subscript ◦ is used to denote any parameter or variable can increase the robustness of obtained solutions against that is defined over vertices v ∈ V , while ◦ is used to i ij equipment downtime due to outages or maintenance. denote a quantity defined over arcs a ∈ A. ij The set V ⊆ V defines so-called source vertices, which Overview represent locations of possible cooling sources. Usually, A brief conceptual overview on the model’s inputs the number of source vertices is low (≤ 10) compared to (parameters) and outputs (results) is given in Fig. 1. The thesizeofthe graph. presented optimization model, based on estimated (or The neighbor sets N of a vertex v are defined by the i i known) cooling demand and a graph of possible segments indices of all vertices that are connected to it by an arc: to construct a cooling network, derives the cost-optimal N = { k | a ∈ A }. i ki size and topology of such a network. The objective func- Time is represented by a set T of discrete time steps t, tion minimizes total costs (generation costs minus rev- which represent a small number of representative oper- enues), thus yielding the most profitable system design. ational situations. The minimum viable number of time steps is two: one for peak demand with a duration of one to several hours, a second for the average annual load with a duration of the remaining year. A more comprehensive choice are three to four time steps: The third can refer to the all-year base load, while the fourth can be used to rep- resent a common intermediate load level. Additional time steps need to be introduced if redundancy requirements Fig. 1 Optimization model overview. Inputs and outputs of the are to be stated. Refer to the discussion of the parameter presented mathematical optimization model availability below for more details. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 4 of 13 Parameters given in S$/(kW m), refers to the capacity-dependent cost The numerical given facts for this model are shown in component of building a pipe. Both values must be tai- Table 2. They are grouped by their defining domains. First lored to the study area to compensate for differences in are vertex parameters, then arc parameters, then con- cost structure and availability of different pipe sizes. The stant or global parameters, and finally time-dependent same is true for the operation & maintenance (OM) cost parameters. parameter c in S$/m. In contrast to the fixed investment om Vertices have a single parameter: their maximum power costterm,itisalsotobepaidforexistingpipes. Thecost max cool capacity Q . It is the thermal output power given in for providing cooling c here is dependent on the ver- i v kW for that location. All non-source vertices have this tex to allow for representing cheap surface water cooling parameter set to 0. in contrast to more expensive re-cooling options. Arcs have three main attributes: their length l (m), the The letter c and a subscript denote economic param- ij thermal peak demand d (kW) of their adjacent buildings eters. These are investment costs for building the pipe ij and g (binary), which states whether a pipe already exists network c and c , maintenance c , costs of provid- ij fix var om cool in this arc. ing c cooling, and revenue for delivering c cooling rev max As secondary parameter, C indicates the maximum to consumers. While c contains the size-independent fix ij thermal power capacity (kW) in an arc, which can be costs (mainly earth works), c contains costs that are var derived from the maximum available pipe diameter. For dependent on the thermal capacity (diameter) of the pipe. arcs with existing pipes (g = 1), this value should be set Time-dependent parameters s and w represent scal- ij t t according to the diameter of that existing pipe. As both ing factor (dimensionless) and weight or duration (h) of arcs a and a refer to the same street segment, parameter atimestep t. A value of s = 1 refers to peak demand, ij ji t values for both members are always identical. while smaller values correspond to moments of partial Global parameters are technical and economic parame- load. Together, these two parameters encode a discretized ters that refer to the district cooling system as a whole. annual load curve. Economic parameters are all costs and revenues. The Redundancy requirements can be stated in the model by investment costs are split into a fixed part c and a vari- setting the binary availability parameter y to value 0 in fix it able part c .The fixedpart, giveninS$/m,captures certaintimesteps for1,2, ... source vertices. If one time var all costs that are not dependent on the capacity of the step for each foreseen failure configuration is introduced, pipe to be built, mainly earth works. The variable part, a full n − 1, n − 2, ... failure safety (against cooling source outages) can be enforced in the produced solution. Clari- fication: in the conventional time steps discussed above in paragraph time step set, the value y = 1istobeset for Table 2 Optimization model parameters it all source vertices v ∈ V . i 0 Name Unit Description c S$/m Fixed investment costs fix Variables c S$/(kW m) Variable investment costs var The main optimization task is to find values for the binary c S$/(m a) Operation & maintenance costs om decision variable ξ . If its value is one, a pipe is built in the ij c S$/kWh Revenue for cooling street segment corresponding to the arc a . For each time rev ij fix step, the actual use of a given pipe is decided by setting w kW/m Fixed thermal losses the binary pipe usage decision variable ψ . If its value is var ijt w kW/(kW m) Variable thermal losses one, the pipe in arc a is used in direction from vertex v ij i b — Concurrence effect in to vertex v . Consequently, there must be a power flow π ijt q — Connect quota into the pipe. Simultaneously, a value ξ = 1 requires that ij u 1/a Annuity factor for investment costs the demand d of this arc has to be satisfied at all times. ij cool The power flow variable at the other end of the pipe is c S$/kWh Cooling costs at source vertices out called π . Its value is determined by the ingoing power max ijt Q kW Source vertex capacity flow minus losses and demand. l m Arc length ij Thenon-negativevariable ρ represents thermal power it d kW Arc peak demand ij output from a source vertex v ∈ V at time t in kW. It is i 0 g — Existence of a pipe (1=yes, 0=no) ij limited in value by the source vertex capacity parameter max max C kW Maximum pipe capacity Q and possibly by the availability parameter y .Table3 it ij i summarizes all model variables. The following line shows s 1 scaling factor their domains, on which they are defined: w h weight/duration y — availability (1=yes, 0=no) in out it ζ ∈ R ξ , ψ ∈{0, 1}¯ π , π , π , ρ ∈ R . ij ijt ij it ijt ijt 0 Dorfner et al. Future Cities and Environment (2017) 3:1 Page 5 of 13 Table 3 Optimization model variables linear approximation possibly over- and underestimates the cost of either small or large capacities. Depending on Name Unit Description the parameterization, one can either force an optimistic ζ S$ Total system cost (Inv, O&M, Rev, Gen) (by deliberate underestimation) or cautious (by deliberate ξ — Binary decision variable: 1 = build pipe ij overestimation) planning decision. The linear approxima- ψ — Binary decision variable: 1 = use pipe ijt tion exhibits unsteady jump from zero to the fixed cost π kW Thermal power flow capacity into arc a ij ij uc +c for any positive value of π ¯ for any non-existing fix om ij in (g = 0) pipe. The link between the binary decision vari- π kW Thermal power flow from v into arc a i ij ij ijt out able ξ and the continuous pipe capacity variable π ¯ is ij ij π kW Thermal power flow out of arc a into v ij j ijt enforced through Eqs. (8), (12), and (14) below. ρ kW Cooling in source vertex v it i These are the definitions for the four derived parame- ters used in the cost equation above. The division by value 2, common to all three arc parameters, compensates for Equations the double-representation of one street segment {v , v } as i j Equations fall into two categories: The first is the cost a pair two directed arcs a , a .Moreabout thisissuecan ij ji function whose value is to be minimized. The second are be found at the explanation of the symmetry constraints cool constraints that codify all the previously discussed rules in (15) and (16) below. The cooling cost parameter k is mathematical form. By that, they define the region of fea- divided by the concurrence effect parameter b to remove sible solutions, under which the solver selects a (close to) the load reduction effect that is introduced in Eq. 10. In cost optimal solution. other words, the power flow that needs to be satisfied The cost function value ζ is the sum of costs for pro- from a source vertex is lower by b than the energy flow viding cooling, minus revenue for that cooling. Network that needs to be delivered. The division by b removes that costs occur for building the network (annualized invest- difference in terms of costs. ment) and for operation & maintenance. The following fix ∀a ∈ A : k = c l u (1−g ) + c l /2(3) ij fix ij ij om ij derived parameters are introduced to shorten the def- ij var inition of the cost function whose definition is given ∀a ∈ A : k = c l u (1 − g ) /2(4) ij var ij ij ij fix var below: k (S$/a) and k (S$/(kW a)) cover network costs ij ij cool cool ∀v ∈ V : k = c /b (5) i i cool (investment, O&M). k (S$/kWh) represents cooling ij cool ∀a ∈ A : r = c d q/2(6) cool ij rev ij ij generation costs, while r (S$/h) represents revenue for ij provided cooling. With these, the cost function is equal to The constraints formalize all physical laws and technical rules that need to be satisfied by a feasible solution. The fix var cool ζ = k ξ + k π + k w ρ ij ij t it ij ij i first constraint concerns energy conservation in vertices a ∈A v ∈V ij i v , with respect to its neighbors N : i i t∈T cool in out − r s w ξ.(2) ∀v ∈ V , t ∈ T : π − π ≤ ρ (7) t t ij ij i it int nit a ∈A n∈N ij i t∈T This inequality is thus a relaxed version of the law of The first summand forms a piece-wise linear function energy conservation. Relaxed, because it allows for power that is depicted in Fig. 2. The plot also depicts that the to vanish at any vertex. As power does not come for free, any solution returned by the solver will satisfy this con- straint to equality. For all non-source vertices (i.e. ρ = it 0), the difference between outgoing and incoming power must be smaller than or equal to zero. In source vertices, a positive difference may remain when it is met by an equal amount of input power ρ into the network at that vertex. it Demand satisfaction is the main arc constraint.Itcreates thelogical connectionbetween thediscretepipeusage decision ψ and the demand satisfaction. Like the cost ijt equation, it relies on two derived parameters x and y . ij ijt This constraint is also graphically explained in Fig. 3. Fig. 2 MILP pipe investment cost function. Investment and operation in out ∀a ∈ A, t ∈ T : x π − π = y ψ (8) ij ij ijt ijt & maintenance costs for a single arc a over thepipecapacity π ¯ ijt ijt ij ij (thick, blue). The curved line (thin, green) indicates a representative var Parameter x refers to losses w that are proportional ij possible real non-linear cost function to the amount of power flow into the arc a . Parameter ij Dorfner et al. Future Cities and Environment (2017) 3:1 Page 6 of 13 Pipe capacity is a technical constraint that limits the power flow through a pipe by the built capacity. This is accomplished by first limiting the ingoing power flow into in apipe π by the built pipe capacity π ¯ . The second con- ij ijt straint is required to set the pipe usage decision variable ψ . Its value is forced to 1 if a flow in direction from ijt v to v at time step t is required. The reason for this i j seemingly artificial constraint is explained in the following constraint. in in ∀a ∈ A, t ∈ T : π ≤ π (11) Fig. 3 Sankey diagram of Eq. (8). Ingoing cooling power flow π from ij ij ijt ijt vertex v is reduced by variable losses (1 − x ), fixed losses and cooling i ij in max ∀a ∈ A, t ∈ T : π ≤ ψ C (12) out ij ijt ijt ij demand (y ) before leaving to vertex v as power flow π ijt j ijt in Unidirectionality of the power flow π is required, as ijt otherwise the solver would happily use a pipe’s capacity in fix y refers to fixed thermal losses w that only depend ijt both directions simultaneously, which would not be phys- on the pipe length, not on the power flow, and the time- ically possible. Therefore, the pipe usage decision variable dependent demand d · s that is further reduced by the ij t ψ may only have the value 1 in one direction at any given ijt concurrence effect b and the connect quota parameter q. time step t. This way, the direction of flow may change In notation: between time steps, but any given pipe may only be used var in one direction at a given time. ∀a ∈ A: x = 1 − l w (9) ij ij ij fix ∀a ∈ A, t ∈ T : y = bq d s + l w (10) ∀a ∈ A, t ∈ T : ψ + ψ ≤ 1 (13) ij ijt ij t ij ij ijt jit Fig. 4 Study region within Singapore. The green outline shows the location of the CBD study region within the extent of Singapore. It covers the Marina Bay and follows Orchard Road to the north west Dorfner et al. Future Cities and Environment (2017) 3:1 Page 7 of 13 Table 4 Total floor area and cooling peak load by building type Build capacity limits the pipe capacity variables to the maximum available diameter, whose capacity in kW is Building type Peak load Floor area max represented by parameter C . At the same time, this 2 3 2 ij (W/m)(10 m ) constraint sets the value of the building decision variable Civic & community institution 112.5 529 ξ , if a non-zero pipe capacity π ¯ is needed. ij ij Commercial 112.5 6685 max ∀a ∈ A: π ≤ ξ C (14) ij ij ij ij Commercial & residential 100 1021 Educational institution 112.5 175 Symmetry of building decision are two constraints that Health & medical care 125 40 enforce that the mathematically independent arcs a and ij a must have identical variable values for their pipe capac- Hotel 112.5 1605 ji ity π ¯ and building decision ξ . This way, a pipe can then ij ij Open space 0 22 be used in both directions at different time steps. Park 0 58 Place of worship 0 137 ∀a ∈ A: ξ = ξ (15) ij ij ji Reserve site 0 157 ∀a ∈ A: π = π (16) ij ij ji Residential 112.5 717 Use if built is the last piece in the puzzle to link the Residential/commercial (1st storey) 112.5 357 building decision ξ to the pipe usage decision ψ .Up ij ijt Sports & recreation 75 15 to this point, nothing in the formulation requires that the Transport facilities 0 29 cooling demand of a customer is satisfied at all times.This Utility 0 43 constraint enforces exactly that, by requiring that the sum of ψ + ψ is greater or equal to 1, if a pipe is built along ijt jit that arc. Otherwise, the condition should not be enforced. This is done by calculating the expression (ξ + ξ )/2. It ij ji is equal to 1 if ξ = 1, as Eq. (15) requires ξ = ξ . ij ij ji Equations 2 to (18) together define a linear mixed- Otherwise, its value is equal to 0. In other words: if an integer program, whose optimal solution is the desired arc is has a pipe, its demand must always be satisfied by a vector of pipe capacities π ¯ , accompanied by optimal power flow from any of its two sides. cooling power flows. ∀a ∈ A, t ∈ T : ψ + ψ ≥ (ξ + ξ )/2 (17) ij ijt jit ij ji Case study Source vertices is the last constraint. It limits the source The presented model is applied on a potential supply area vertex power flow ρ by its maximum allowed capacity it in the central business district of Singapore, as shown in max Q . The availability parameter y usually has value 1, it i Fig. 4. The first part describes how the input parame- except for special time steps in which the source vertex v ters were derived. Then the assumptions for a sensitiv- is made unavailable by setting y = 0: it ity analysis against conventional per-building cooling are described. max ∀v ∈ V , t ∈ T : ρ ≤ y Q (18) i it it Table 5 Parameter values in case study Name Value Unit c 7000 S$/m fix c 8e-4 S$/(m kW) var c 80 S$/(m a) om c 0.14 S$/kWh rev fix w 0.01 kW/m var w 1e-8 kW/(kW m) b 0.9 — q 1.0 — Fig. 5 Annual load duration curve. Estimated duration curve (thin, green) and its discretization to 8 steps (thick, blue)asusedbythe u 0.091 1/a optimization model. Step lengths correspond to time step weight w cool and the relative load value to s c 0.03 or 0.07 S$/kWh i Dorfner et al. Future Cities and Environment (2017) 3:1 Page 8 of 13 Load profile estimation To record and to utilize the optimization potential of Due to lack of access to a load profile from Singapore, a this expanding system, in a detail data analysis a question known cooling load from Munich was extrapolated based amongst others was examined on which factors the cus- on weather data in Singapore. tomers cooling demand is depending. Furthermore the The district cooling system of Munich has mostly collected data serve as basis for the evaluation of the cool- non-residential customers like shopping malls, offices, ing demand in other cities like Singapore. Based on a congress centers and smaller retail trades. Its usage type period of two years up to 2015 the influence of tempera- composition is therefore rather similar to Singapore’s ture, humidity, insolation and the customer behavior itself CBD. However, the buildings are much smaller and thus was analyzed. have a different surface to volume ratio and surface mate- The strongest influence on the cooling demand is the rials than the much higher buildings in Singapore’s CBD. temperature. The humidity plays a subordinated role in Fig. 6 Demand and cooling stations. Location of cooling demand (color and line thickness of edges) and cooling stations (triangles). Large triangles (at vertices 57, 110, 154) correspond to cheap surface water cooling, while small triangles assume more expensive air re-cooling Dorfner et al. Future Cities and Environment (2017) 3:1 Page 9 of 13 Munich (but not in Singapore), cause of the temperate cli- areasandofficesaswellasthehighlyvolatiletemperature mate zone and the previous low dehumidification in the profile of a day, the cooling demand is five times higher comfort zones. To count in this factor to the further cus- during the day than at night or on a holiday. This charac- tomer and grid extension, the enthalpy of the outside air, teristic day-night cycle are also recorded in other Central as an index for the heat input to the buildings, is used as European cities ([24], pp. 8, 80). leading control parameter. The insolation has no consid- Using the high cooling demand during the business erable influence on the customers’ requirements because hours and the enthalpy dependence, a trend was generated of the good insulation of the rather new buildings and the for the customers’ requirements. This trend line is com- shading situation in the densely built city center. bined with the climate records of Singapore to create an The second strongest influence factor on the cooling approximated annual load duration curve, shown in Fig. 5. demand of the Munich costumers are the business hours. To reduce the temporal resolution for the optimization Due to the simultaneous public traffic in the shopping model to manageable sizes, this curve is discretized to 8 Fig. 7 Cost-optimal network layout. Line thickness corresponds to thermal capacity π ¯ (kW) of each pipe ij Dorfner et al. Future Cities and Environment (2017) 3:1 Page 10 of 13 individually weighted time steps, also shown. One 24 h PengKee [8]. Building or area types with small total area long time step represents peak demand, while the other 7 were ignored. With those assumptions, a total summed steps have durations ranging from 390 h to 2006 h. peak cooling demand of 1241MW exists in the case study area. Annual cooling demand Cooling demand is estimated based on previous work Input data conducted by Böhme et al. [25]. There, a geographic The street graph is derived from OpenStreetMap data dataset of buildings with gross floor area and usage type [26], processed using previously described [22] pre- was prepared. The total floor area by building type (e.g. processing steps using polygon skeletonization for simpli- residential, commercial, ...) is summarized in Table 4. fying the dense street network. It also states the assumed design cooling loads, based Cost data (given in S$) and technical parameters for this on a mean design load of 112.5kW/m ,estimatedfrom case study are summarized in Table 5. Pipe investment Fig. 8 Cost-optimal power flow during peak load. All three surface water cooling station operate at maximum capacity (150 MW each) Dorfner et al. Future Cities and Environment (2017) 3:1 Page 11 of 13 costs of 7000 S$/m are the main cost driver on the supply cost of 0.03 S$/kWh. The other six cooling stations have side. This value is scaled to one year with an annuity factor higher costs of 0.07 S$/kWh. (1 + i) · i Scenarios u = (19) Base case (1 + i) − 1 The base case is designed to show today’s demand situ- ation. In this scenario, the size and layout of a profitable with interest rate i = 6.5% and depreciation duration district cooling network is to be determined. n = 20a, yielding a value of 0.091. Operation & mainte- nance are relatively cheap with annual 80 S$/m. Cooling In the base case, a revenue of 0.14 S$/kWh is assumed. A cost depends on the location of the cooling station. The sensitivity analysis with reduced revenues in steps of 0.02 large triangles in Fig. 6 show stations with access to surface S$/kWh is also conducted to determine how sensitive the water, which allows cheap re-cooling with an assumed optimal network size is on the price for cooling. Fig. 9 Power flow during outage of cooling station at vertex 57. In this situation, the large pipe capacities south of vertex 13 are needed to transmit backup cooling power from the western three cooling stations to the central bay area Dorfner et al. Future Cities and Environment (2017) 3:1 Page 12 of 13 Growing demand In order to assess how the total cooling costs (genera- tion and distribution) are affected by a possible demand growth in the study area, additional load is introduced in the edge (54, 114) in the south-eastern corner. It’s value is changed from 0MW to 200MW with steps of 50 MW. As this step creates more load than the existing cooling stations could satisfy while satisfying the redun- dancy constraint, all cooling stations’ capacity is increased by 50%. Results Base case Fig. 10 Specific cooling costs for growing demand with original 0.03 and 0.07 S$/kWh cooling stations. Cost increase is caused by higher The resulting network for the base case is shown in utilization of expensive cooling stations Fig. 7. It shows a district cooling network that satisfies almost all (1240MW of 1241MW) cooling demand. In other words: under the presented cost assumptions and a cooling revenue of 0.14 S$/kWh, district cooling is an Discussion and future research economically viable strategy. A sensitivity check with a District cooling can be an attractive option for cities with reduced cooling revenue of 0.10 S$/kWh still leads to an constant high cooling load, compared to less efficient dis- almost full saturation of 1237 MW supplied demand. The tributed cooling. The high demand density of Singapore’s unsatisfied demands are mainly short, isolated edges with CBD makes it a very well suited candidate. Direct access low demand (≤ 3MW) that cannot offset the network to surface and seawater provides enough cooling poten- investment cost. Only when revenue is further reduced, tial to satisfy a significant fraction of the present cooling between 0.08 and 0.06 S$/kWh, the optimal network loads. drops from satisfying 1200 MW to 0 MW. This value As Singapore is planning to establish further dense com- range thus can be taken as a lower bound for profitabil- mercial areas similar to the CBD with many office blocks, ity of a district cooling system (under the given cost e.g. in Jurong, more regions will become suitable candi- assumptions). dates for district cooling. Moreover, the potential of dis- Figures 8 and 9 compare the cooling power flow in two trict cooling could also be evaluated for densely populated of the 18 time steps considered for designing the net- residential areas, e.g. Bukit Panjang or Punggol. work capacities in Fig. 7. The first situation shows the The redundancy requirements on cooling stations could cost-optimal cooling power flow when all cooling stations need refinement, possibly by relaxing the full (n-1) capa- are operational. The three cheap cooling stations (57, 110, bility for the whole system to only certain areas. An 154) are delivering their full capacity of 150 MW each, extension could introduce the same requirement not only while several of the other stations only run in partial load. to cooling station, but also to crucial parts of the network. The second situation in Fig. 9 shows how the redundancy requirement leads to the consideration of very different Acknowledgements flow situations. Here, cooling station 13 now runs at full We express our gratitude to the Singapore Land Authority for supporting us capacity and satisfies the middle of the study area. with geospatial data. This work was financially supported by the Singapore National Research Foundation under its Campus for Research Excellence And Technological Growing demand Enterprise (CREATE) programme. This work was supported by the German The resulting cooling cost for gradually increasing the Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open Access Publishing Program. demand in edge (54, 114) for each case is shown in Fig. 10. The cooling cost here is calculated by dividing total costs Availability of data and materials for generation and network by the amount of provided The optimization model’s implementation is available under the GPL 3.0 cooling (in kWh). Cost for cooling grows slightly – along license at https://github.com/tum-ens/dhmin. The model input data is available under the CC-BY license via doi:10.6084/m9.figshare.3582456. with demand – from approximately 0.045 S$/kWh to 0.048 S$/kWh in the case of additional 200MW peak cool- Authors’ contributions ing demand. This increase is caused by a higher utilization JD developed and applied the optimization model to the case study. PK lead of the more expensive 0.07 S$/kWh cooling stations. The his expertise in planning district cooling networks to provide input data and scenario definitions. MD contributed the method for deriving the annual load specific network costs actually exhibit a minor reduc- duration curve. TM provided data for the case study region and vetted model tion as demand grows, but this effect is negligibly small results against local experience. All authors collaborated for writing the article. here. All authors have read and approved the final submitted manuscript. Dorfner et al. Future Cities and Environment (2017) 3:1 Page 13 of 13 Competing interests 20. Connolly D, Lund H, Mathiesen BV, Leahy M (2010) A review of computer The authors declare that they have no competing interests. tools for analysing the integration of renewable energy into various energy systems. Appl Energy 87(4):1059–1082. 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