This study presents a mathematical optimization model for planning topology and capacity of a district cooling network. The model relies on a mixedinteger 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 worldwide with high cooling demand density.
District cooling has been established in many countries. Especially in bigger cities, it offers an energy efficient alternative to individual generation of cooling power at the site of customers. Even in a city like Munich, Germany, which is located in a temperate climate zone, several district cooling systems have already been installed successfully and maintained.
In contrast to Munich, in Singapore, warm and humid weather prevails all year long, which results in much higher demand for cooling and dehumidification both in residential and nonresidential buildings. However, in most buildings, cooling power is generated by using small chillers that use air for recooling which is very inefficient. As a result, much electricity is used to operate the chillers. In this case study, we model a district cooling network for the central business district (CBD) of Singapore. We present several cases and a comparison to conventional individual cooling.
Singapore’s CBD comprises mainly commercial buildings, e.g. shopping malls, hotels and office blocks, often with more than 50 floors. Thus, it stands in contrast to other areas of Singapore which comprise more residential or industrial buildings. Due to the different type of use of commercial buildings with the air conditioning running all day long and amounting to approximately 50% of each building’s energy demand, the introduction of district cooling could lead to tremendous energy savings.
Singapore already has a large underground district cooling system in the Marina Bay.
The system contains two plants with a maximum of 330MW of cooling power. [
Over the last decades, district cooling networks have been developed in several
cities throughout Europe. Researches result in data shown in Table
State of projects in European cities
City  Capacity  Energy  

[Sources]  (MW)  (GWh/a)  
Berlin  [ 
44  
Helsinki  [ 
135  80 
Munich downtown  [ 
15  
Munich groundwater  [ 
11.4  
Munich MCampus (mixed form)  [ 
4.39  4.4 
Paris  [ 
290  420 
Stockholm  [ 
330  460 
Vienna  [ 
113.3 
This is a short summary of existing publications on district cooling in Singapore, district cooling in general, as well as similar or prominent approaches for district heating or more general multicommodity district energy systems.
Apart from the aforementioned existing district cooling system [
A thermal ice storage system and its influence on the costoptimal design of
district cooling distribution network is investigated [
A genetic algorithm is used [
Khir [
Södermann [
Due to the basic principle, district cooling and heating are comparable types of supply. In both types, with few central generation plants heat or cold is generated which is mostly transferred to water. This tempered water is transported through pipes to customers buildings. Having transferred the heat or cold to the buildings, the cooled or heated water returns to the generation plants where the process starts from the beginning. The biggest difference between both are the technologies used in generation plants, which is not the focus of this article.
Jamsek [
Udomsri [
A detailed model on combined energy system planning for electric, heating and
cooling demand is presented by Chinese from 2008 [
A recent paper [
A broader review of computer models for renewable energy system analysis and
optimization is provided by Connolly et al. [
This paper presents the generalized version of a previously published model
developed for planning of district heating distribution networks [
This section describes a mathematical optimization model to represent the planning
task for a minimum cost district cooling network. Its main input is a connected
graph of street segments that represent the discrete possible network parts. Each
segment – called
The model’s main contribution lies in a simple representation of redundancy constraints by means of artificial time steps (or periods) with predetermined reduced availability of cooling stations. This technique can easily be embedded into other optimization models and can increase the robustness of obtained solutions against equipment downtime due to outages or maintenance.
A brief conceptual overview on the model’s inputs (parameters) and outputs
(results) is given in Fig.
Optimization model overview. Inputs and outputs of the presented mathematical optimization model
To improve performance for large study regions, the model employs a linearized cost function for sizing the thermal pipe capacity. Depending on the parameterization, one can either cautiously overestimate the real estimated costs or try to fit as closely the observed cost function. In the latter case, one typically slightly underestimates the cost of medium capacities, while overestimating the cost of small and large capacities.
The presented model minimizes the total costs
A district or city is represented as a graph of vertices and arcs. This graph is derived from the street network. It should be derived in such a way to include all considerable locations for network pipes. The spatial resolution can be chosen as fine as required. Here, it is on the level of building blocks, i.e. a single street segment between two intersections.
Let
The set
The neighbor sets
Time is represented by a set
The numerical given facts for this model are shown in Table
Optimization model parameters
Name  Unit  Description 

S$/m  Fixed investment costs  
S$/(kW m)  Variable investment costs  
S$/(m a)  Operation & maintenance costs  
S$/kWh  
kW/m  Fixed thermal losses  
kW/(kW m)  Variable thermal losses  
—  Concurrence effect  
—  Connect quota  
1/a  Annuity factor for investment costs  
S$/kWh  Cooling costs at source vertices  
kW  Source vertex capacity  
m  Arc length  
kW  Arc peak demand  
—  Existence of a pipe (1=yes, 0=no)  
kW  Maximum pipe capacity  
1  scaling factor  
h  weight/duration  
—  availability (1=yes, 0=no) 
As secondary parameter,
Economic parameters are all costs and revenues. The investment costs are
split into a fixed part
The letter
Redundancy requirements can be stated in the model by setting the binary
availability parameter
The main optimization task is to find values for the
The nonnegative variable
Optimization model variables
Name  Unit  Description 

S$  Total system cost (Inv, O&M, Rev, Gen)  
—  Binary decision variable: 1 = build pipe  
—  Binary decision variable: 1 = use pipe  
kW  Thermal power flow capacity into arc


kW  Thermal power flow from


kW  Thermal power flow out of arc


kW  Cooling in source vertex

Equations fall into two categories: The first is the cost function whose value is to be minimized. The second are constraints that codify all the previously discussed rules in mathematical form. By that, they define the region of feasible solutions, under which the solver selects a (close to) cost optimal solution.
The
The first summand forms a piecewise linear function that is depicted in Fig.
MILP pipe investment cost function. Investment and operation
& maintenance costs for a single arc
These are the definitions for the four derived parameters used in the cost
equation above. The division by value 2, common to all three arc parameters,
compensates for the doublerepresentation of one street segment
{
The
This inequality is thus a relaxed version of the law of energy conservation.
Relaxed, because it allows for power to vanish at any vertex. As power does
not come for free, any solution returned by the solver will satisfy this
constraint to equality. For all nonsource vertices (i.e.
Sankey diagram of Eq. (
Parameter
Equations
The presented model is applied on a potential supply area in the central business
district of Singapore, as shown in Fig.
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
Due to lack of access to a load profile from Singapore, a known cooling load from Munich was extrapolated based on weather data in Singapore.
The district cooling system of Munich has mostly nonresidential customers like shopping malls, offices, congress centers and smaller retail trades. Its usage type composition is therefore rather similar to Singapore’s CBD. However, the buildings are much smaller and thus have a different surface to volume ratio and surface materials than the much higher buildings in Singapore’s CBD.
To record and to utilize the optimization potential of this expanding system, in a detail data analysis a question amongst others was examined on which factors the customers cooling demand is depending. Furthermore the collected data serve as basis for the evaluation of the cooling demand in other cities like Singapore. Based on a period of two years up to 2015 the influence of temperature, humidity, insolation and the customer behavior itself was analyzed.
The strongest influence on the cooling demand is the temperature. The humidity plays a subordinated role in Munich (but not in Singapore), cause of the temperate climate zone and the previous low dehumidification in the comfort zones. To count in this factor to the further customer and grid extension, the enthalpy of the outside air, as an index for the heat input to the buildings, is used as leading control parameter. The insolation has no considerable influence on the customers’ requirements because of the good insulation of the rather new buildings and the shading situation in the densely built city center.
The second strongest influence factor on the cooling demand of the Munich
costumers are the business hours. Due to the simultaneous public traffic in the
shopping areas and offices as well as the highly volatile temperature profile of
a day, the cooling demand is five times higher during the day than at night or
on a holiday. This characteristic daynight cycle are also recorded in other
Central European cities ([
Using the high cooling demand during the business hours and the enthalpy
dependence, a trend was generated for the customers’ requirements. This trend
line is combined with the climate records of Singapore to create an approximated
annual load duration curve, shown in Fig.
Annual load duration curve. Estimated duration curve (
To reduce the temporal resolution for the optimization model to manageable sizes, this curve is discretized to 8 individually weighted time steps, also shown. One 24 h long time step represents peak demand, while the other 7 steps have durations ranging from 390 h to 2006 h.
Cooling demand is estimated based on previous work conducted by Böhme et al.
[
Total floor area and cooling peak load by building type
Building type  Peak load  Floor area 

(W/m^{2})  (10^{3} m^{2})  
Civic & community institution  112.5  529 
Commercial  112.5  6685 
Commercial & residential  100  1021 
Educational institution  112.5  175 
Health & medical care  125  40 
Hotel  112.5  1605 
Open space  0  22 
Park  0  58 
Place of worship  0  137 
Reserve site  0  157 
Residential  112.5  717 
Residential/commercial (1st storey)  112.5  357 
Sports & recreation  75  15 
Transport facilities  0  29 
Utility  0  43 
The street graph is derived from OpenStreetMap data [
Cost data (given in S$) and technical parameters for this case study are
summarized in Table
Parameter values in case study
Name  Value  Unit 

7000  S$/m  
8e4  S$/(m kW)  
80  S$/(m a)  
0.14  S$/kWh  
0.01  kW/m  
1e8  kW/(kW m)  
0.9  —  
1.0  —  
0.091  1/a  
0.03 or 0.07  S$/kWh 
with interest rate
Demand and cooling stations. Location of cooling demand (color and
line thickness of edges) and cooling stations
(
The base case is designed to show today’s demand situation. In this scenario, the size and layout of a profitable district cooling network is to be determined.
In the base case, a revenue of 0.14 S$/kWh is assumed. A sensitivity analysis with reduced revenues in steps of 0.02 S$/kWh is also conducted to determine how sensitive the optimal network size is on the price for cooling.
In order to assess how the total cooling costs (generation and distribution) are affected by a possible demand growth in the study area, additional load is introduced in the edge (54, 114) in the southeastern corner. It’s value is changed from 0MW to 200MW with steps of 50 MW. As this step creates more load than the existing cooling stations could satisfy while satisfying the redundancy constraint, all cooling stations’ capacity is increased by 50%.
The resulting network for the base case is shown in Fig.
Costoptimal network layout. Line thickness corresponds to
thermal capacity
Figures
Costoptimal power flow during peak load. All three surface water cooling station operate at maximum capacity (150 MW each)
Power flow during outage of cooling station at vertex 57. In this situation, the large pipe capacities south of vertex 13 are needed to transmit backup cooling power from the western three cooling stations to the central bay area
The resulting cooling cost for gradually increasing the demand in edge (54,
114) for each case is shown in Fig.
Specific cooling costs for growing demand with original 0.03 and 0.07 S$/kWh cooling stations. Cost increase is caused by higher utilization of expensive cooling stations
District cooling can be an attractive option for cities with constant high cooling load, compared to less efficient distributed cooling. The high demand density of Singapore’s CBD makes it a very well suited candidate. Direct access to surface and seawater provides enough cooling potential to satisfy a significant fraction of the present cooling loads.
As Singapore is planning to establish further dense commercial areas similar to the CBD with many office blocks, e.g. in Jurong, more regions will become suitable candidates for district cooling. Moreover, the potential of district cooling could also be evaluated for densely populated residential areas, e.g. Bukit Panjang or Punggol.
The redundancy requirements on cooling stations could need refinement, possibly by relaxing the full (n1) capability for the whole system to only certain areas. An extension could introduce the same requirement not only to cooling station, but also to crucial parts of the network.
We express our gratitude to the Singapore Land Authority for supporting us with geospatial data.
This work was financially supported by the Singapore National Research Foundation under its Campus for Research Excellence And Technological Enterprise (CREATE) programme. This work was supported by the German Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open Access Publishing Program.
The optimization model’s implementation is available under the GPL 3.0 license at
JD developed and applied the optimization model to the case study. PK lead his expertise in planning district cooling networks to provide input data and scenario definitions. MD contributed the method for deriving the annual load duration curve. TM provided data for the case study region and vetted model results against local experience. All authors collaborated for writing the article. All authors have read and approved the final submitted manuscript.
The authors declare that they have no competing interests.