Exploring the impact space of different technologies using a
portfolio constraint based approach for multi-objective
optimization of integrated urban energy systems
Rui Jinga,b,1, Kamal Kuriyanb,1, Qingyuan Kongb, Zhihui Zhanga,
Nilay Shahb, Ning Lia, Yingru Zhaoa,*
a College of Energy, Xiamen University, Xiamen, China
b Department of Chemical Engineering, Imperial College London,
London, UK
Abstract
Optimization-based modelling provides valuable guidance for
designing integrated urban energy systems. However, modelers have
to make certain assumptions and they may lack awareness of
realistic conditions such as decision-makers’ preferences on
certain technology, which can easily lead the obtained optimal
solution to be invalid. Therefore, instead of focusing on one
“fragile” optimal solution, this paper provides a systematic
overview of the contribution each technology can bring to the whole
system design so as to achieve the optimum. To achieve this, a
portfolio constraint based approach is proposed, which is inspired
by the modelling to generate alternatives (MGA) method as well as
the eps-constraint method for multi-objective optimization. By
varying the threshold values of portfolio constraints, a series of
solutions can be gathered as an “impact space” representing the
economic and environmental contributions of each technology for the
whole system design. A practical Fitting of Ellipses method is
further applied to quantify the size of the impact space. Through
observing the formation of the impact space, more valuable insights
on system design can be obtained.
The proposed approach is applied to a case study of an urban
district in Shanghai, China, where a generalized urban energy
system model involving commonly used energy supply technologies is
established. Various technologies and design options lead to
significantly different impact spaces, where CHP is found to have
the largest impact on system design. Overall, instead of merely
providing decision-maker a very specific solution, this paper
introduces a new approach to evaluate multiple technologies when
designing integrated urban energy systems.
Keywords: impact space; modelling to generate alternatives;
eps-constraint; portfolio constraint; integrated urban energy
system; multi-objective optimization.
______________________________________________
1 The first and second authors make equally contribution to this
work.
One first author E-mail address: [email protected] (R
Jing).
* Corresponding author. Tel.: +86 592 5952781; Fax: +86 592
2188053.
E-mail address: [email protected] (Y. Zhao).
Nomenclature
Abbreviations
ATC
annual total cost
δ
network/grid connection status
AB
absorption chiller
γ
energy transfer direction
CAPEX
capital cost
Subscripts/superscript
CHP
combined heating and power
ac
absorption chiller
CRF
capital recovery factor
b
boiler
EC
electric chiller
cap
capital cost
FC
fuel cost
cha
heat storage charge
GC
grid cost
cool
cooling energy
MC
maintenance cost
c-dem
cooling energy demand
MILP
Mixed Integer Linear Programming
cf
cooling flow among buildings
MGA
Modelling to generate alternatives
c-pipe
cooling pipework
MOPSO
Multi-objective Particle Swarm Optimization
disc
heat storage discharge
MOO
multi-objective optimization
ec
electrical chiller
MST
minimum spanning tree
h
hour
NSGA-II
Non-sorted Genetic Algorithm
heat
heating energy
PV
photovoltaic
hf
heat flow among buildings
SRI
solar radiation index
hp
heat pump
DC
district cooling
h-dem
heating demand
DH
district heating
h-pipe
heating pipework
Symbols
i
building index
C
cost
im
electricity import
CAP
installed capacity
in-st
in storage
DX
distance between buildings
j
building index
E
electrical power
maint
maintenance cost
Q
thermal energy
n
project life
Greek symbols
NG
natural gas
η
efficiency
r
interest rate
ψ
emission factor
re
heat recovered
χ
start limit
s
season
β
on/off status
t
each technology
α
storage charge/discharge status
Graphical Abstract
Highlights
- Define and explore the impact space for urban integrated
energy systems design
- Propose the portfolio constraint method and combine with
multi-objective optimization
- Quantify the size of impact space for all commonly used
technologies by fitted ellipse
- Analyze the formation process of impact space via a real-world
case study
- Provide high-level suggestions for decision-makers instead of
a specific optimal solution
1 Introduction
Integrated energy systems are a promising solution for
energizing urban areas urban areas in an efficient and low-cost
manner [1]. The design of such systems is complex since multiple
highly integrated energy sectors are involved [2]. Thanks to
improvements in mathematical optimization and computational
capability, the problem can be formulated and solved as an
optimization model. The modelevaluates the possible design and
dispatch of integrated energy systems based on certain assumptions
on input parameters. Deterministic models in which all input
parameters are pre-determinedhave been widely studied, see e.g., Li
et al. [3], Wang et al. [4], and Wu et al. [5].
1.1 Review of approaches to modelling with uncertainty
Different sources of uncertainties exist in the evaluation of
future scenarios and correponding approaches have been developed to
address these. The two main categories of methods are reviewed
below.
1.1.1 Modelling with parametric uncertainty
Much research addresses parametric uncertainty which considers
factors such as variations in future energy prices, the stochastic
nature of renewables and fluctuating energy demand. Zheng et al.
[6] utilized Monte Carlo simulation to convert a stochastic problem
into a deterministic problem, so as to analyze the sensitivity of
demand to project cost when planning a solar-biomass micro-grid
with demand response capability. Hocine et al. [7] proposed a
multi-segment fuzzy goal programming approach to address high
levels of uncertainty when making decisions during optimization of
renewable energy portfolios in Italy. The results indicated that
such an approach can provide better and more suitable solutions
than other approaches. Majewski et al. [8] proposed a two-stage
robust approach to deal with uncertainties when designing a
distributed urban energy system. Through the proposed approach, the
optimal designed system’s energy supply security can be ensured
with minimum additional cost.
Mavromatidis et al. [9] clarified the concept of global
sensitivity when planning distributed energy systems. A two-step
approach combining the Morris method and the Sobol method was used
to investigate the parametric sensitivity of various kinds of
parameters. The results indicated that demand profiles and energy
prices are the most significant parameters in terms of the impact
on the whole project. After that, they further proposed a two-stage
stochastic approach to account for uncertain parameters [10]. The
difference between sensitivity analysis and stochastic programming
is clarified, where sensitivity analysis is an posterio approach
and stochastic programming is an prior approach considering the
uncertainty during the model establishment. An instructive review
was presented [11] to summarize the procedure of dealing with
uncertain parameters.
Based on this research, Yue et al. [12] further reviewed the
approaches to deal with parametric uncertainty in energy system
optimization models. Four kinds of approaches, i.e., Monte Carlo
analysis, stochastic programming, robust optimization, and
modelling to generate alternatives were summarized and compared,
which provides clear guidance for the use of these methods. The
former three methods are proven efficient approaches to deal with
parametric uncertainty, while the modelling to generate
alternatives (MGA) method has been utilized to address another
category of uncertainty, which is called structural uncertainty
[13].
1.1.2 Modelling with structural uncertainty
Structural uncertainty has received less attention with limited
previous research, particularly in the integrated urban energy
system community. The reason for such uncertainty lies in the fact
that modellers can never foresee and model all practical conditions
by constraints, e.g., the decision-makers’ preference for a certain
technology. Therefore, even though the obtained solution is
optimal, it is only valid for the specific model and the results
may become invalid due to slight changes in practical situations
[14]. Therefore, the “Modelling to generate alternatives (MGA)”
approach was proposed by Brill et al. to deal with un-modelled
uncertainties, i.e., structural uncertainty, in public-sector
planning [15, 16]. The MGA concept was introduced to the long-term
energy-economics planning field by DeCarolis [17]. The
Hop-Skip-Jump method for MGA [18] is used to generate the
near-optimal decision space comprising a series of energy solutions
that are maximally different in the decision space but perform well
in the objective space.
Voll and co-workers [19] developed a framework for the
optimization of distributed energy systems, and subsequently
proposed a method to generate alternative solutions in conjunction
with this framework. The near-optimal” solution space identified by
iteratively adding integer cut constraints [20]. Based on the
occurrence frequency of each technology during the iteration, the
“must-haves” and “must-avoids” solutions are presented, which
provides valuable insight to the problem. Hennen et al. [21]
further developed methods to analyze the impact of both technology
type and capacity. The correlation between the capacities of
different technologies such as CHP and boiler are visualized by
plotting colored matrix. This research highlights the importance of
coupling visualization and analysis methods with methods for
generating alternative solutions. Through observation on the
“persistence” of certain technologies in the solution space as well
as the difference among obtained solutions, relevant suggestions
can be provided to decision-makers.
1.2 Motivation and contribution
Based on the above research background, urban energy systems
models are widely developed in an environment of uncertainty, which
can easily lead to the obtained solution being invalid. So far,
although a significant amount of effort has been spent to seek the
global optimum solution with parameter uncertainties, e.g., by Qu
et al. [22], and Mazzeo et al. [23], relevant research gaps still
exist.
(1) Modelers may not be aware of all practical considerations
such as the decision-makers’ preferences, which may lead to optimal
“knife-edge” solutions with limited practical significance. Limited
research has been done to tackle the unforeseen structural
uncertainties in urban energy systems models.
(2) There is a lack of a systematic approach to understanding
the individual contribution of each technology to the whole system
for multiple objectives. As focusing on one specific solution may
be invalid, a new systematic method for evaluation of system design
is required.
To fill these gaps, this paper proposes a new approach for
evaluation of system design by generating alternative solutions to
optimisation problems which is similar to the eps-constraint method
for solving multi-objective optimisation problems, and can easily
be integrated into existing formulations for solving these
problems. This approach allows the modeller to explore the solution
space and quantify the impacts of individual technologies within an
integrated system. While this provides a useful perspective to the
modeller in itself, as a by-product, the method also generates a
familyof technology specific solutions that are dominated by the
Pareto front. Each member of the family shows the best possible
approach to the overall Pareto front that can be achieved for a
specified band of the technology’s penetration level within the
overall technology mix. The segments of these curves that are close
to the pareto front form a solution space analogous to the
near-optimal space identified by the methods in the previous
section for models with a single objective.
Overall, instead of presenting a specific optimal solution to
decision-makers, this paper aims to provide high-level insights on
integrated urban energy systems design through identifying the
contribution of various technologies for the whole system. By
integration with a multi-objective approach, the impact of each
technology on both cost and emission objectives may be
investigated. The results should be more robust and provide more
insight to the decision-makers or engineers.
The novelty of the present study is as follows:
a) Introduce the structural uncertainty concept to urban energy
system modelling and addressing this by providing a systematic
overview of alternative solutions to decision-makers instead of
focusing on only a single optimal solution.
b) Propose a portfolio constraint based approach and combine
this with methods for multi-objective optimization to investigate
the impact space of different technologies on the whole system’s
design.
The rest of the paper is organized as follows: Section 2
describes the problem. Section 3 introduces the methodology.
Section 4 presents a case study. Section 5 discusses the obtained
results. Section 6 makes some conclusions. The detailed model
formulations are given in the supplementary material.
2 Problem description
The objective of urban integrated energy system optimization is
to find the best technology portfolio among various available
technologies and the corresponding design and dispatch strategy.
Thus, the problem is similar to the idea of optimizing an
investment portfolio. A conceptual illustration of the problem is
presented in Fig. 1, where the pie chart represents the technology
portfolio, and each selected technology has its own optimal
dispatch strategy to fulfill buildings’ cooling/heating/electricity
demand. Through the optimized network, energy can be transferred
among buildings to achieve cheaper or lower environmental impact
design solutions. The entire problem is generally formulated as
follows,
(1)
where f1(x) to fn(x) represent different objectives, among which
the most commonly considered are cost and emissions [24]; the
objectives are constrained by both inequality constraints and
equality constraints. For an optimization problem of integrated
urban energy systems, the inequality constraints including the grid
exchange, devices’ operation, and the network flows; while the
energy balances, as well as energy conversions, are equality
constraints.
Fig 1. Problem illustration of urban integrated energy system
optimization
When establishing the model, all decisions are assumed to be
perfectly rational over the entire time-horizon [14]. With the help
of optimization, the selected technical portfolio is optimum.
However, the model is set within an uncertain environment, e.g. the
modeler can never cover all practical constraints or the
decision-makers’ preference for a certain technology. these
constraints may come from local industrial needs, which may lead to
slightly different solutions from the theoretically optimal
solution. This phenomenon is defined as structural uncertainty,
which may make the obtained optimal solution invalid with limited
practical significance [20]. Therefore, instead of focusing on the
optimal solution, it would be of interest to explore alternative
solutions and quantify the impact of each technology on the whole
system design.
To do this, a portfolio constraint based approach, which is
inspired by the modelling to generate alternatives (MGA) approach,
is proposed and further combined with a multi-objective
optimization method as described in the next section.
3 Methodology
Before introducing details of the proposed approach, the
definition of impact space needs to be clarified.
3.1 Impact space
The “impact” in this study is defined as the amount of economic
and environmental benefits an individual technology can bring to
the whole system. In other words, how close to the optimal
objective (i.e., least cost or emissions) value a whole system can
approach with no/partial/full availability of a certain technology
(by adding portfolio constraint).
As shown in Fig. 2, the blue Pareto frontier is the “baseline”
condition with no extra constraints on the availability of any
technology. Each technology’s contribution to achieving this
baseline condition (i.e., non-dominated cost or emissions) is
represented by examples of three different technologies’ impact
spaces. The impact space is determined by gathering a series of
Pareto optimal solutions with different degrees of availability for
a certain technology.
Each technology’s impact space may take on a different shape and
size as the contribution of each technology for the whole system is
different. For a given technology the projection of the impact
space onto a particular objective function axis, say emissions,
represents the range of objective values over which the technology
may have an impact. The actual impact on the emissions objective
for a given cost value can be quantified by the length of the
segment parallel to that axis that is contained within the impact
space, extending from the pareto front to the furthest point on
that segment that is contained in the impact space. This will vary
according to the position of this segment on the perpendicular
axis, representing the cost objective. Similarly, the projection of
the impact space on to the cost axis represents the range of cost
values over which that technology may have an impact. The average
emissions impact within this cost range may be quantified by the
area of the impact space scaled by the length of the cost range.
Conversely, the average impact of the technology on cost may be
quantified by the area of the impact space scaled by the length of
the emissions range. Consequently, the area of the impact space may
be taken to be a measure of the overall impact of the technology on
both cost and emissions.
The relative impact values of different technologies may be
interpreted as an indicator of their importance in the system
design and more attention should be given to technologies with
higher impact values. In this paper an estimate of the size of the
impact space for a technology is obtained by fitting an ellipse to
the family of pareto solutions generated for that technology by
varying the thresholds of the portfolio constraints. Hence, the
size of the impact space fitted by the ellipse can be utilized to
represent the economic and environmental contribution of each
technology for the whole system’s design. Additionally, it is
noteworthy that the impact space is a problem-oriented term. The
reason why solutions in the impact space are dominated by the
baseline solution lies in adding different degrees of portfolio
constraints.
Fig 2. Illustration the concept of impact space and
corresponding formation process
3.2 Multi-objective optimization
An important issue for designing urban energy systems is the
comprehensive consideration from different perspectives, which is
generally formulated by multiple objectives. Multi-objective
optimization (MOO) is an efficient tool to deal with multiple
objectives [25]. By generating the Pareto frontier, the trade-offs
among conflictive objectives can be visuailized clearly. Several
approaches based on different theories exist, e.g, ε-constraint
[26], weighted-sum [27], goal programming [28], lexicographic order
approach [29], Non-sorted Genetic Algorithm (NSGA-II) [30], and
Multi-objective Particle Swarm Optimization (MOPSO) algorithm [31].
In this case, the ε-constraint approach is selected as an example
for the ease of reformulating the model, and further combined with
the addition of portfolio constraint approach to solve the problem.
Taking the bi-objective minimization problem of the present study
as an example, the ε-constraint approach keeps f1(x) as the
objective function and converts f2(x) to a constraint by
introducing a parameter ε. Thus, a single-objective function can be
obtained [32]:
(2)
By minimizing f1(x) and f2(x) individually, the minimum f2min(x)
and maximum f2max(x) values of f2(x) can be obtained. Then, for
each point N+1, the value of ε can be calculated by , where N is
the number of user-defined intervals between the minimum and
maximum values of f2(x), μ=0,…,N [33]. Increasing the value of N
will lead to more solutions to cover the Pareto frontier, while the
computational cost increases accordingly. Notice that the present
study only utilizes ε-constraint approach to deal with multiple
objectives, while not aiming to innovate in multi-objective
optimization. More details on the ε-constraint approach are
presented in Ref. [34-36].3.3 Modelling to generate
alternatives
Before describing the proposed portfolio constraint method, it
is worth mentioning one of the inspirations of the present study,
i.e., the Modelling to Generate Alternatives (MGA) approach. The
Hop-Skip-Jump formulation of the MGA approach is shown in Eq. 3,
taking the cost objective function as an example,
(3)
where p is a specific objective constructed by summation over
the set of binary variables (βt), whose value equals 1 in the
previous solutions; βt is the decision variable for including
technology t in the portfolio (i.e., 1 means included, 0 means
excluded); C* is the global optimal value of objective for the
original problem (i.e., cost); Cj is the optimal cost for the jth
run of MGA iteration, slack is a percentage to relax the original
cost objective’s optimal value.
Within Hop-Skip-Jump MGA based methods for generating
alternative solutions, a new “dummy” objective is constructed, and
the original cost objective is converted to a constraint with a
specified amount of slack. The core concept of this method is to
diversify the technology portfolio by generating maximally
different alternative solutions that yield an objective function
value that is bounded with respect to the original solution.
3.4 Proposed portfolio constraint approach
The present study adds the portfolio constraint to the orignial
model to investigate the contribution of one technology to the
whole system design. It not only considers the “kicking out”
situation similar to MGA method but also sets a series of portfolio
constraints on certain technology’s investment against the whole
project’s capital cost. Two conditions exist as derived in Eq. 4,
where condition (1) forcibly excludes a certain technology from the
portfolio by introducing a binary yt,i and setting it to 0 for all
buildings (M). While in condition (2), if a certain technology is
selected in the portfolio (yt,i = 1), then the capital cost of this
technology is restricted as a percentage of the whole project’s
total investment by setting a threshold (λ). The reason for setting
a threshold on the capital cost lies in the fact that the
decision-makers tend to care about the investment most. The
constraints from the original model take effect along with the
proposed portfolio constraints in two conditions.
(4)
where subscript i denotes the building index, and t is the
technology index; CAPcost is the investment cost, y is a binary
variable representing the existence of certain technology in the
portfolio (yt,i = 1 exists, yt,i = 0 not).
The proposed approach is similar to the eps-constraint method in
adding new constraints to re-configure the problem. However, the
eps-constraint method acts upon objective functions, while
portfolio constraint method deals with decision variables (i.e.,
system design variables). Compared to the Hop-Skip-Jump MGA method,
both methods aim to generate different model-based solutions, but
the proposed approach leaves the objective function unmodified, and
there is no need need to add integer cuts as in some of the other
methods. Thus, the proposed approach can be easily integrated into
multi-objective formulation based on the eps-constraint method.
The detailed procedure of the portfolio constraint method is
presented in Fig. 3. Each principal procedure is outlined by grey
boxes, and two modules are defined, namely an ε-constraint module
and a portfolio constraint module.
(1) Step 1, the whole procedure starts with solving the original
model by calling the ε-constraint module, from which a baseline
optimal solution can be obtained. Since no extra constraints are
applied, the corresponding Pareto frontier is expected to achieve
the best performance as marked in red, which is located at the
nearest bottom-left corner in the illustrative impact space
figure.
(2) Step 2, each technology from the optimal portfolio is
processed in turn via sub-step 2.1 and 2.2. In Step 2.1, the
technology is excluded from the portfolio, the constrained Pareto
frontier (in purple) is expected dominated by the baseline one.
Then, in Step 2.2, the portfolio constraint module is called
iteratively, followed by calling ε-constraint module. By updating
the threshold value (λ) in Eq. (4), a series of constrained Pareto
frontiers are expected as marked in orange. The iteration of λ
value stops when no more optimal solutions can be discovered.
(3) Step 3, based on all obtained Pareto solutions for one
technology, the Direct Least Squares Fitting of Ellipses algorithm
is applied [37] via MATLAB [38], which provides the best fitting
ellipse for all Pareto points allowing a certain amount of points
out of the fitted ellipse. Hence, the impact space of one
technology can be calculated by the area of the fitted ellipse. A
larger fitted ellipse area indicates the technology has a larger
impact on project design. All areas of the fitted ellipse can be
further normalized based on the largest one for comparison
purpose.
Fig 3. Outline of the combined portfolio constraint and
ε-constraint approach
As displayed by the illustrative impact space in Fig. 2 and 3,
plotting an impact space starts from the baseline optimal solutions
(obtained by Step 1). Then, due to additional portfolio
constraints, all optimal solutions obtained in Step 2 are expected
to be dominated by the baseline optimal solutions. Hence, the whole
procedure looks like starting from Pareto optimal solutions, then
going backward to the “sub-optimal” objective space. This is
opposite to the multi-objective problem-solving process by
meta-heuristic approaches, e.g., NSGA-II, in which the sub-optimal
solutions are updated iteratively approaching to the Pareto front.
Therefore, the “portfolio constraint” and “impact space” have their
own problem-oriented meanings.
It is noteworthy to explicate the rules of setting threshold
value (λ) as illustrated in Fig. 4. Obviously, the value of λ
should be within 0% -- 100%. Each technology has an inherent
optimal value for the investment share (in red), which can be
calculated during Step 1 as the baseline. Then, the λ value should
be set to “oversize” intentionally (in blue), i.e., be larger than
its inherent optimal value. Then, the next λ value can be further
increased until it reaches the stopping criteria (in green). As
long as these selection rules are satisfied, the interval of λ
value can be user-defined. Additionally, the number of intervals
(N) during ε-constraint approach is user-defined as well, two
practical recommendations for interval selections for λ and ε
values are as follows for ease of comparison different technologies
in one system,
(1) Each technology has its own inherent optimal value of λ, it
is difficult to define the best number of intervals for λ value.
Nevertheless, the number of intervals for λ value could be
consistent for all investigated technologies, in other words,
generating impact spaces of different technologies with a similar
quantity of Pareto points.
(2) In Step 2.2, during each run of updating λ value, the number
of intervals for ε value should maintain similar.
Fig 4. Selection of threshold value (λ)
Overall, the impact space and its formation process can be
obtained through the proposed portfolio constraint method. The size
of the impact space represents one technology’s impact on the whole
system’s design.
4 Case study
To verify the proposed combined portfolio constraint and MOO
approach, a case study at a commercial district in Shanghai, China
is conducted. There are 9 different commercial buildings in the
district as shown in Fig. 5. All buildings are assumed connected
with the national grid from an energy security perspective. Each
building can build its own energy system and can be connected with
neighboring buildings. Possible cooling and heating network
availabilities are mapped out by blue and red dash lines,
respectively.
Fig 5. Overview of the case study with 9 buildings in a
network
Each category of the buildings has different hourly demand
profiles; the aggregated energy profiles over the 24-hour
time-horizon for different seasons are presented in Fig. 6. it is
assumed that cooling demand only exists in summer and space heating
demand is only required in winter. During the transition season,
only hotels need domestic hot water.
Fig 6. Demand profiles of the case study
Considering the fact that electric chiller and gas boiler are
two proven mature and essential technologies, this paper focuses on
investigating the impact of CHP, absorption chiller, PV panel,
battery, and thermal storage. In addition, considering
decision-makers’ possible preference of establishing an energy
network, a scenario with a network connecting of all buildings is
also investigated. All investigated scenarios are illustrated in
Fig. 7, where the original optimal solution is considered as the
baseline for comparison purposes.
Fig 7. Scenario tree for the case study
5 Results and discussion
The entire problem is formulated as a Mixed Integer Linear
Programming (MILP) model built in GAMS [39], calling the CPLEX
solver [40] with 8*12 – Core Xeon X5675 clusters with 48GB RAM. The
model has roughly 85,000 variables in total (including 13,000
binary variables) and 105,000 equations, the model solving time for
each run varies from 2 minutes to 16 minutes with an average of 5
minutes. The optimality gap is set to 0.5%, and all other settings
remain at default values. The following sub-sections analyze the
impact of each technology in detail.
5.1 Impact of combined heating and power (CHP) unit
CHP is one of the key technologies among urban integrated energy
system’s portfolio since it can be used for generating electricity
and heating simultaneously. Fig. 8 presents the impact of CHP as a
series of Pareto frontiers when cost and emission objectives are
considered. Four thresholds are applied, which limits the CHP
investment cost by 0%, <10%, 10%~25%, 25%~50%, 50%~75% of the
overall investment, respectively. Due to the extra constraints on
CHP capacity, the system performance (cost and emission) is not as
good as the baseline optimal solution, as expected.
It is seen from Fig. 8 that when CHP is “excluded” from the
portfolio (CHP=0%), the system design has a limited range of
optimal solutions, and the environmental performance in terms of
carbon emissions is much worse than the baseline optimal solution
as most of the electricity has to be imported from the utility grid
with a higher emission factor value. With different stages of
threshold limits on CHP investment, the system performance improves
gradually towards the baseline optimal as shown by the green, red
and purple Pareto frontiers, respectively. When the investment on
CHP is allowed to be within 50%~75% of overall capital cost, the
obtained solutions are very close to the baseline optimum (in
blue). However, due to the threshold, the system design can only
vary within a small range of cost, which is not as broad as the
baseline optimal condition (in orange).
Fig 8. Impact space of CHP with different threshold values, ACE
– Annualized Carbon Emissions (103 ton), ATC – Annualized Total
Cost (106 US$)
5.2 Impact of absorption chiller
The impact space for absorption chiller is displayed in Fig. 9,
where four threshold values are applied to limit the investment
cost on absorption chillers by 0%, 0%~5%, 5%~10%, and 10%~15% of
the project total investment, respectively. The results indicate
that 5%~10% is the best threshold, where the system can achieve as
good performance as the baseline optimal condition in a certain
range, while the system performance drops when other thresholds
applied. Meanwhile, it is interesting to observe that the
performance for 0%~5% threshold condition (in green) is worse than
the 0% threshold condition (in purple). Then, the performance
improves significantly (in blue) when 5%~10% threshold is adopted.
Afterward, the performance drops again when 10%~15% is applied.
This non-monotonic behavior during the formation of impact space is
significantly different from that of CHP, the underlying reasons
will be discussed in Section 5.6.2.
Fig 9. Impact space of absorption chiller with different
threshold values
5.3 Impact of photovoltaic panels
As for the photovoltaic (PV) panels, considering the physical
limits of available space for installation, three thresholds are
applied, i.e., no installation, install 50% of available space (250
m2 each building), and full installation (500 m2 each
building).
The results are presented in Fig. 10, where all scenarios can
achieve a similar optimal cost objective. With the emission
criteria becoming stringent, a significant difference between each
scenario can be noticed. When comparing the “half-install” and
“not-install” scenarios, it is interesting that the “not-install”
scenario (yellow) incurs even less overall cost than the
“half-install” scenario (green) to achieve a similar level of
emissions. This phenomenon indicates that although PV is one
well-known low-emission technology, alternative cheaper designs
still exist to achieve similar emissions due to the complexity of
an urban energy system with a highly integrated network.
In general, compared to the impact of CHP and absorption
chiller, PV panels present a lower impact on the whole system’s
design due to the fact that the available installation space within
the urban scale is already limited practically.
Fig 10. Impact space of PV panels with different threshold
values
5.4 Energy storage technologies comparison
The impact of different energy storage technologies, i.e.,
battery and thermal (cooling) storage, are compared as displayed in
Fig. 11. Both storage technologies are investigated by setting 4
thresholds, i.e., 0%, 0%~5%, 5%~10%, 10%~25%, 25%~50% of the whole
project’s investment, respectively. Generally speaking, the battery
brings more benefits to the whole system than the cooling storage,
as shown by the more widespread set of Pareto frontiers in Fig.
11(a) than that of Fig. 11(b).
Focusing on Fig. 11(a), when the investment in battery storage
is less than 10%, the system can achieve similar cost and emissions
compared to the baseline. When the investment in battery storage
increases to more than 10%, the system performance drops
significantly, and it becomes even worse when more than 25% of the
investment is spent in battery storage. If the battery storage is
“excluded” from the portfolio, the system can achieve similar
low-cost designs compared to the baseline optimal condition as
shown in black, but the solution distribution is narrower than the
condition with 0%~5% or 5%~10% thresholds. Therefore, the best
investment proportion for battery storage is less than 10% of the
overall investment in this case.
As for the cooling storage shown in Fig. 11(b), the impact of
cooling storage is weaker than battery storage generally. No
investment or 5% investment on cooling storage does not have a
significant difference as shown in grey and purple, respectively.
Meanwhile, the investment should be lower than 10% of the overall
investment, otherwise a very limited number of solutions are
available, with only one solution available when the investment
threshold is 10%~25% (red), and no solution is found if cooling
storage accounts for 25%~50% of whole project investment.
The underlying reason why it is more valuable to store
electricity than cooling is that electricity has higher an energy
grade than urban-level thermal energy. However, this observation is
based on the comprehensive effects of both economic and emission
parameters, which are specific to this case.
Fig 11. Impact space of battery storage (a) and cooling storage
(b) with different threshold values
5.5 Network topology comparison
In this case, a compulsive networking scenario is also
investigated, considering that the decision-maker may prefer
establishing an energy network instead of multiple distributed
systems in one district. Therefore, assuming each building is one
node on the map, based on the geographical information of each
node, the minimum spanning tree (MST) algorithm is applied to
generate an all-connected network as displayed in Fig. 12 [41].
Based on a mandatory network as input, the corresponding Pareto
frontier is further plotted in Fig. 13.
Fig 12. Generating a mandatory network by MST approach
As shown in Fig. 13, the mandatory network scenario achieves
slightly worse performance both economically and environmentally
compared to the baseline condition. The reason is analyzed as shown
in Fig. 14.
Fig 13. Impact space of compulsory networking
Seen in Fig. 14, compared to the baseline optimum, the mandatory
network solution has several features: (1) Install similar capacity
of PV panels; (2) Install lower capacity of CHP, heat pump,
absorption chiller and two kinds of energy storage technologies;
(3) Install larger capacity of electric chiller and boiler; (4)
Install both longer cooling and heating networks; and (5) Purchase
more electricity from the grid and feed-back to grid more. Among
these features, (2), (3) and (5) lead to higher emissions, and (4)
results in a higher cost than the baseline condition. Therefore,
the mandatory network scenario incurs more cost and has higher
emissions than the baseline condition. In addition, the
pre-optimized network design by the MST algorithm with minimum
distance turns out not the best network topology. Other factors
such as the demand complementarity effect need to be considered as
well.
Fig 14. Comparison of mandatory network scenario and baseline
optimum scenario; (a) comparison of installed capacity in the unit
of kW, subscript of e, c, h denotes electricity, cooling, and
heating respectively; (b) optimized network design for mandatory
network scenario where solid lines are mandatory pipelines and dash
lines are additional pipelines based on the optimization result;
(c) optimal network design for baseline optimal solution where
solid lines are optimal pipework design.
5.6 Discussion
Based on the obtained impact space of various technologies as
presented in the above section, this section discusses two
interesting observations.
5.6.1 Quantifying impact space
Obviously, the size of the impact space differs for various
technologies. To simplify the estimation of the size of the impact
space while taking into account the complex geometry resulting from
the interaction of multiple factors during the formation process, a
practical method to quantify the impact space is proposed, i.e.,
the area of a fitted ellipse. By plotting Pareto solutions of all
technologies as two-dimensional scatters together in one figure as
shown in Fig. 15, the size of impact space can be quantified and
compared directly.
Fig 15. Visualized impact space for different technologies
Since two axes in Fig. 15 could have different numerical scales
and units, for the convenience of comparison, all obtained ellipses
are normalized according to the largest one (i.e., CHP in blue).
Table 1 lists the normalized area of fitted ellipses for different
scenarios.
Table 1. Normalized size of different scenarios’ impact
space
Scenarios/Technologies
Normalized area of the fitted ellipse
CHP
1.00
PV panel
0.40
Mandatory network
0.19
Absorption chiller
0.18
Battery storage
0.11
Cooling storage
0.06
As shown in Fig. 15 and Table 1, CHP has the biggest impact
within the portfolio, PV panels rank in second place while cooling
storage brings the least amount of benefit to system design.
Meanwhile, absorption chillers, battery storage, and mandatory
network have moderate impacts on the cost and emissions of the
whole system. Therefore, when designing an integrated urban energy
system in the locality of interest, more focus should be spent on
CHP technology. In contrast, installing cooling storage will not
make a great difference to the whole system based on the present
case study. As discussed in the previous sections further insight
may be gained by analyzing the formation of the impact space at
different threshold levels for the individual technologies.
5.6.2 Formation of impact space
Another interesting observation comes from the formation of
impact space for different technologies. For CHP (recalling Fig.
8), the formation starting from applying a 0% threshold, i.e.,
“exclude” CHP from the portfolio, the corresponding solutions are
the farthest from the baseline optimum. Then, with the threshold
value increases, the obtained solutions move closer to the baseline
optimum gradually until almost overlapping with the baseline
optimum. At that point, the corresponding threshold value, i.e.,
50%~75%, represents the ideal investment proportion for CHP. If the
threshold value keeps increasing, the system performance is
expected to be worse as the threshold value is beyond the ideal
proportion and other technologies’ investment portions will be
affected.
This phenomenon is verified when evaluating the impact space of
absorption chillers (recalling Fig. 9). Starting from the condition
that absorption chiller is excluded from the portfolio, the system
performance gap between the baseline optimal and obtained Pareto
frontier exists. Then, with a threshold increase, absorption
chiller reaches its own ideal proportion, i.e., 10% of total
investment, where the corresponding solutions are the closest to
the baseline optimum. When the threshold keeps increasing, the
system performance drops as expected.
Meanwhile, it is also interesting that the process of
approaching the ideal proportion shows a positive correlation with
increments to the threshold starting from the 0% threshold for CHP
(recalling Fig. 8). However, that is not always the case. For
absorption chiller (recalling Fig. 9), compared to the 0% threshold
condition, the system achieves even worse performance for 0%~5%
threshold condition. Once the threshold is set to 5%~10%, the
Pareto frontier returns to a very close position to the baseline
optimal solution. After that, the system achieves worse objective
values again when the threshold is set to 10%~15%. This observation
indicates that the formation of impact space may not be a monotonic
process with the increment of the threshold. Taking absorption
chiller as an example to further analyze this phenomenon, Fig. 16
presents the system configuration comparison of 0%~5%, 5%~10% and
10%~15% conditions with similar emission level.
Comparing 5%~10% (in blue) and 10%~15% (in orange) conditions,
the results show that both the length of networks, amount of
electricity bought/sold to the grid, and installed capacities of
various technologies are similar, except for the difference in
installed capacity of absorption chillers due to the threshold
value. Due to the larger installed capacity of absorption chillers,
more capital cost is spent. However, the average load factor of the
absorption chiller does not improve accordingly, which means
although a larger capacity is installed, they are not
well-utilized. The Load Factor is defined as actual output (i.e.,
cooling) by absorption chillers in all buildings divided by the
total of maximum output. In this way, the absorption chiller’s load
factor for 0%~5% (in grey) condition is expected to be even higher,
i.e., 77%, compared to that of 41% and 27% achieved by the 5%~10%
condition (in blue) and 10%~15% condition (in orange),
respectively. In this condition, the absorption chiller capacity is
limited to a lower level compared to other two conditions, a larger
capacity of electrical chiller has to be installed accordingly with
more electricity purchased from the grid. Meanwhile, in order to
maintain a similar level of emissions as the other two conditions,
larger capacities of battery storage and cooling storage are
installed correspondingly. All these factors make the 0%~5%
condition a more expensive one. Similar phenomena can be found when
evaluating the PV panel’s impact space formation as displayed in
Fig. 10, where no installation can achieve better performance than
50% installation. However, since the constraints on PV panels
(i.e., no installations and half installations) lead to two
completely different network designs, system designs, and dispatch
strategies, no distinct clue can be found to explain this
observation. It is the result of the comprehensive effects of
case-specific economic and emission parameters. Overall, the
formation processes of impact spaces for different technologies
could be different, which reminds system designers to be cautious
about the sizing of one technology – improper sizing of a
technology could increase the capital cost while not bringing any
benefit.
Fig 16. System configuration comparison for Absorption chiller
with different thresholds
In general, instead of focusing on one baseline optimal
solution, the economic and environmental benefits that commonly
used technologies can bring to the whole urban energy system
design, i.e., impact space, are quantified through the proposed
“portfolio constraint” method. Different technologies offer
significantly different amounts of impact on system design. Each of
them has an inherent best investment proportion specific to the
case. When all technologies reach corresponding ideal proportions
simultaneously, the whole system achieves the baseline optimum.
Otherwise, the obtained Pareto frontiers are somewhat away from the
baseline optimum, which forms the impact space. Through observing
the formation of the impact space, it may be seen that certain
technologies will not be well-utilized and make no contribution to
reducing cost or emissions, sometimes it would be better to simply
exclude them from the portfolio.
6 Conclusion
Inspired by the modelling to generate alternatives method and
eps-constraint method, this paper proposes a portfolio constraint
approach to quantify benefits that commonly used technologies can
bring to the whole urban energy system design. Through tuning the
threshold value of portfolio constraint, as well as combined with
the eps-constraint multi-objective optimization method, the
economic and environmental benefits of individual technology for
the whole system are plotted as families of Pareto optimal
solutions, and further defined as the impact space. The size of the
impact space is estimated as the area of fitted ellipses. The
formation process of the impact space is further analyzed
in-depth.
The results obtained can guide the decision-makers from a
systematic perspective while not simply presenting a specific and
brittle optimal solution, which makes the outcome more robust when
encountering unpredicted uncertainties. Through a case study, the
proposed approach is illustrated, and several interesting
conclusions can be drawn from both case specific and generalized
standpoints.
Specific conclusions
Based on the present case study,
(1) According to the size of the fitted ellipses, CHP has the
most significant impact on overall economic and environmental
performance; PV panels, absorption chillers, battery storage, and
mandatory network options have moderate impacts on system
performance; while cooling storage brings the least cost and
emission reduction benefit to the system design.
(2) Considering energy storage technology, batteries tend to
have a larger impact on system performance than thermal (cooling)
storage. Meanwhile, more than 50% of the overall capital is
recommended to be spent on CHP, and the recommended proportions are
less than 10% for both battery and cooling storage.
Generalized suggestions
(1) Each technology has an inherent best investment ratio for a
specific case. When all technologies achieve ideal proportions
simultaneously, the whole system achieves the baseline optimum. If
that cannot happen due to unpredicted or practical concerns, the
decision-maker should prioritize the technology with the largest
impact.
(2) The decision-maker should be cautious of preferences for
certain technologies. Instead of improper investment in certain
technology which may not well-utilized, it may be better not to
invest in it at all.
(3) Connecting several nodes together as an energy network could
be preferred by the decision maker. But the design needs to
consider not only the overall shortest distance but also other
factors, e.g., the demand complementarity between each
building.
Finally, it is noteworthy that the size and formation of the
impact space are specific to different cases. More importantly, the
proposed approach and metrics can provide valuable insights to the
decision makers of urban energy system when evaluating multiple
technologies, especially when these technologies are new and the
relative importance of them is not clear.
Acknowledgment
The research has received support from the National Natural
Science Foundation of China under grant No. 51876181. The authors
are also grateful to the fund of the China Scholarship Council with
grant No. 201806310046.
24
Reference
[1] Gabrielli P, Gazzani M, Martelli E, Mazzotti M. Optimal
design of multi-energy systems with seasonal storage. Applied
Energy. 2018;219:408-24.
[2] Liu Z, Chen Y, Zhuo R, Jia H. Energy storage capacity
optimization for autonomy microgrid considering CHP and EV
scheduling. Applied Energy. 2018;210:1113-25.
[3] Li L, Liu P, Li Z, Wang X. A multi-objective optimization
approach for selection of energy storage systems. Computers &
Chemical Engineering. 2018;115:213-25.
[4] Wang L, Jing ZX, Zheng JH, Wu QH, Wei F. Decentralized
optimization of coordinated electrical and thermal generations in
hierarchical integrated energy systems considering competitive
individuals. Energy. 2018;158:607-22.
[5] Wu C, Gu W, Xu Y, Jiang P, Lu S, Zhao B. Bi-level
optimization model for integrated energy system considering the
thermal comfort of heat customers. Applied Energy.
2018;232:607-16.
[6] Zheng Y, Jenkins BM, Kornbluth K, Kendall A, Træholt C.
Optimization of a biomass-integrated renewable energy microgrid
with demand side management under uncertainty. Applied Energy.
2018;230:836-44.
[7] Hocine A, Kouaissah N, Bettahar S, Benbouziane M. Optimizing
renewable energy portfolios under uncertainty: A multi-segment
fuzzy goal programming approach. Renewable Energy.
2018;129:540-52.
[8] Majewski DE, Lampe M, Voll P, Bardow A. TRusT: A Two-stage
Robustness Trade-off approach for the design of decentralized
energy supply systems. Energy. 2017;118:590-9.
[9] Mavromatidis G, Orehounig K, Carmeliet J. Uncertainty and
global sensitivity analysis for the optimal design of distributed
energy systems. Applied Energy. 2018;214:219-38.
[10] Mavromatidis G, Orehounig K, Carmeliet J. Comparison of
alternative decision-making criteria in a two-stage stochastic
program for the design of distributed energy systems under
uncertainty. Energy. 2018;156:709-24.
[11] Mavromatidis G, Orehounig K, Carmeliet J. A review of
uncertainty characterisation approaches for the optimal design of
distributed energy systems. Renewable and Sustainable Energy
Reviews. 2018;88:258-77.
[12] Yue X, Pye S, DeCarolis J, Li FGN, Rogan F, Gallachóir BÓ.
A review of approaches to uncertainty assessment in energy system
optimization models. Energy Strategy Reviews. 2018;21:204-17.
[13] DeCarolis JF, Babaee S, Li B, Kanungo S. Modelling to
generate alternatives with an energy system optimization model.
Environmental Modelling & Software. 2016;79:300-10.
[14] Heuberger CF, Staffell I, Shah N, Mac Dowell N. Impact of
myopic decision-making and disruptive events in power systems
planning. Nature Energy. 2018;3:634-40.
[15] Brill, E.D. The use of optimization models in public-sector
planning. Management Science. 1979;25:413–422.
[16] Brill, E.D., Chang, S.Y., Hopkins, L.D.. Modeling to
generate alternatives: the HSJ approach and an illustration using a
problem in land use planning. Management Science.
1982;28:221–235.
[17] DeCarolis JF. Using modeling to generate alternatives (MGA)
to expand our thinking on energy futures. Energy Economics.
2011;33:145-52.
[18] Brill, E.D., Flach, J.M., Hopkins, L.D., Ranjithan, S. MGA:
a decision support system for complex, incompletely defined
problems. IEEE Transactions on Systems, Man, and Cybernetics.
1990;20:745–757.
[19] Voll P, Klaffke C, Hennen M, Bardow A. Automated
superstructure-based synthesis and optimization of distributed
energy supply systems. Energy. 2013;50:374-88.
[20] Voll P, Jennings M, Hennen M, Shah N, Bardow A. The optimum
is not enough: A near-optimal solution paradigm for energy systems
synthesis. Energy. 2015;82:446-56.
[21] Hennen M, Lampe M, Voll P, Bardow A. SPREAD – Exploring the
decision space in energy systems synthesis. Computers &
Chemical Engineering. 2017;106:297-308.
[22] Qu K, Yu T, Zhang X, Li H. Homogenized adjacent points
method: A novel Pareto optimizer for linearized multi-objective
optimal energy flow of integrated electricity and gas system.
Applied Energy. 2019;233-234:338-51.
[23] Mazzeo D, Oliveti G, Baglivo C, Congedo PM. Energy
reliability-constrained method for the multi-objective optimization
of a photovoltaic-wind hybrid system with battery storage. Energy.
2018;156:688-708.
[24] Hennen M, Postels S, Voll P, Lampe M, Bardow A.
Multi-objective synthesis of energy systems: Efficient
identification of design trade-offs. Computers & Chemical
Engineering. 2017;97:283-93.
[25] kianmehr E, Nikkhah S, Rabiee A. Multi-objective stochastic
model for joint optimal allocation of DG units and network
reconfiguration from DG owner’s and DisCo’s perspectives. Renewable
Energy. 2019;132:471-85.
[26] Jing R, Wang M, Liang H, Wang X, Li N, Shah N, et al.
Multi-objective optimization of a neighborhood-level urban energy
network: Considering Game-theory inspired multi-benefit allocation
constraints. Applied Energy. 2018;231:534-48.
[27] Majidi M, Nojavan S, Nourani Esfetanaj N, Najafi-Ghalelou
A, Zare K. A multi-objective model for optimal operation of a
battery/PV/fuel cell/grid hybrid energy system using weighted sum
technique and fuzzy satisfying approach considering responsible
load management. Solar Energy. 2017;144:79-89.
[28] Ju L, Tan Z, Li H, Tan Q, Yu X, Song X. Multi-objective
operation optimization and evaluation model for CCHP and renewable
energy based hybrid energy system driven by distributed energy
resources in China. Energy. 2016;111:322-40.
[29] Liu S, Papageorgiou LG. Multiobjective optimisation of
production, distribution and capacity planning of global supply
chains in the process industry. Omega. 2013;41:369-82.
[30] Saber H, Moeini-Aghtaie M, Ehsan M. Developing a
multi-objective framework for expansion planning studies of
distributed energy storage systems (DESSs). Energy.
2018;157:1079-89.
[31] Lu X, Zhou K, Yang S. Multi-objective optimal dispatch of
microgrid containing electric vehicles. Journal of Cleaner
Production. 2017;165:1572-81.
[32] Mavrotas G, Florios K. An improved version of the augmented
ε-constraint method (AUGMECON2) for finding the exact pareto set in
multi-objective integer programming problems. Applied Mathematics
and Computation. 2013;219:9652-69.
[33] Zhang D, Evangelisti S, Lettieri P, Papageorgiou LG.
Optimal design of CHP-based microgrids: Multiobjective optimisation
and life cycle assessment. Energy. 2015;85:181-93.
[34] Fazlollahi S, Mandel P, Becker G, Maréchal F. Methods for
multi-objective investment and operating optimization of complex
energy systems. Energy. 2012;45:12-22.
[35] Si F, Wang J, Han Y, Zhao Q, Han P, Li Y. Cost-efficient
multi-energy management with flexible complementarity strategy for
energy internet. Applied Energy. 2018;231:803-15.
[36] Schütze O, Hernández C, Talbi EG, Sun JQ, Naranjani Y,
Xiong FR. Archivers for the representation of the set of
approximate solutions for MOPs. Journal of Heuristics.
2018;25:71-105.
[37] Andrew W. Fitzgibbon, Maurizio Pilu and Robert B. Fisher.
Direct Least Squares Fitting of Ellipses. 1996.
[38] MathWorks Corporation. MATLAB R2018b.
https://www.mathworks.com [Access: 2018/12/01].
[39] GAMS Development Corp. https://www.gams.com/ [Access:
2018/12/01].
[40] IBM ILOG CPLEX.
https://www.ibm.com/analytics/cplex-optimizer [Access:
2018/12/01].
[41] Unternährer J, Moret S, Joost S, Maréchal F. Spatial
clustering for district heating integration in urban energy
systems: Application to geothermal energy. Applied Energy.
2017;190:749-63.
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Fittingε-constraintsmoduleε-constraintsmodulePortfolio constraints
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original modelPortfolio constraint moduleInputOutputNo opti.
solution?StopNoYesProcedureCalling moduleCalling moduleOutput to
figure
0%Optimal value (baseline)Interval of λNo solution
found(stopping criteria)100%λOversize
0200400600800100012000200400600800100012001400143258976Sever
ColdColdHot-Summer-Cold-WinterTemperateHot-Summer-Warm-Winter-100101318252830SummerWinterClimate
zones℃metersmetersAll buildings are
Grid-connectedHotelExhibitionOfficeShopping centerCooling network
potentialHeating network potential
0123456h1h3h5h7h9h11h13h15h17h19h21h23Electrical demand
(MW)B9B8B7B6B5B4B3B2B1Total00.10.20.30.40.50.60.70.80.9h1h3h5h7h9h11h13h15h17h19h21h23Heating
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–(d) x-axis: 24 hours (c) Transition
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(MW)B9B8B7B6B5B4B3B2B1Total(b) Summer cooling(d) Winter heating
Scenario treeBatteryvs. Thermal storagevs. Network Distributed3
stagesof λPV4 stagesof λCHP4 stagesof
λchillerAbsorptionBaselineconditionwith no extra constraints
3.13.64.14.65.15.66.111131517(106) ATC(103ton)
ACECHP=0%CHP=10%CHP=25%CHP=50%CHP=75%Pareto frontier
approximationComputedsolutionsBaseline
3.13.43.744.34.64.91112131415(106) ATC(103ton)
ACEAB=0%AB=5%AB=10%AB=25%AB=15%BaselinePareto frontier
approximationComputedsolutions
33.33.63.94.24.54.8111213141516(106) ATC(103ton) ACEPV=0
m^2PV=250 m^2PV=500 m^2BaselinePareto frontier
approximationComputedsolutions
33.33.63.94.24.54.8111213141516(106) ATC(103ton)
ACEBattery=0%Battery=5%Battery=10%Battery=25%Battery=50%(a)BaselinePareto
frontier
approximationComputedsolutions33.33.63.94.24.54.81112131415(106)
ATC(103ton)
ACECool_ST=0%Cool_ST=5%Cool_ST=10%Cool_ST=25%Cool_ST=50%(b)BaselinePareto
frontier approximationComputedsolutions
0200400600800100012000200400600800100012001400143258976metersmetersMinimum
Spanning Tree (MST) network design
33.23.43.63.844.24.44.61112131415(106) ATC(103ton) ACECompulsive
networkMandatory networkBaselinePareto frontier
approximationComputedsolutions
- 4,000 8,000 12,000 16,000 20,000PV (kW_e)CHP (kW_e)Boiler
(kW_h)Heat pump (kW_h)Ele_chiller (kW_c)Ab_chiller (kW_c)Battery
(kW_e)Cool_storage (kW_c)Installed
capacityCom_networkGlobal_opti0246Cool_networklength
(km)Heat_networklength (km)051015Ele_sell (GWh)Ele_buy
(GWh)0200400600800100012000200400600800100012001400143258976metersmeters0200400600800100012000200400600800100012001400143258976metersmeters(a)(b)(c)Man_network
Near-optimal decision spacePV panelCHPCooling storageAbsorption
chillerBatteryCompulsory
network33.544.555.566.5711121314151617(106) ATC(103ton)
ACEABCHPPVBatteryCool_STCom_Network
- 5,000 10,000 15,000 20,000 25,000PV (kW_e)CHP (kW_e)Boiler
(kW_h)Heat pump (kW_h)Ele_chiller (kW_c)Ab_chiller (kW_c)Battery
(kW_e)Cool_storage (kW_c)Installed
capacityAB0~5AB10~15AB5~100112Cool_networklength
(km)Heat_networklength (km)05101520Ele_sell (GWh)Ele_buy (GWh)Load
factorAB10~15: 27%AB5~10: 41%AB0~5: 77%
f2 min costf1min emissionPareto frontierDifferent technologies’
impact spacesObjective space(fragile)(solid)
12
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