Available via license: CC BY 4.0
Content may be subject to copyright.
Citation: Howard, D.A.; Jørgensen,
B.N.; Ma, Z. Multi-Method
Simulation and Multi-Objective
Optimization for
Energy-Flexibility-Potential
Assessment of Food-Production
Process Cooling. Energies 2023,16,
1514. https://doi.org/10.3390/
en16031514
Academic Editors: Rodolfo Haber,
Bartłomiej Gładysz and
Krzysztof Ejsmont
Received: 30 November 2022
Revised: 21 January 2023
Accepted: 1 February 2023
Published: 3 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Multi-Method Simulation and Multi-Objective Optimization
for Energy-Flexibility-Potential Assessment of Food-Production
Process Cooling
Daniel Anthony Howard * , Bo Nørregaard Jørgensen and Zheng Ma *
SDU Center for Energy Informatics, The Maersk Mc-Kinney Moller Institute, University of Southern Denmark,
5230 Odense, Denmark
*Correspondence: danho@mmmi.sdu.dk (D.A.H.); zma@mmmi.sdu.dk (Z.M.)
Abstract:
Process cooling for food production is an energy-intensive industry with complex inter-
actions and restrictions that complicate the ability to utilize energy-flexibility due to unforeseen
consequences in production. Therefore, methods for assessing the potential flexibility in individual
facilities to enable the active participation of process-cooling facilities in the electricity system are
essential, but not yet well discussed in the literature. Therefore, this paper introduces an assessment
method based on multi-method simulation and multi-objective optimization for investigating energy
flexibility in process cooling, with a case study of a Danish process-cooling facility for canned-meat
food production. Multi-method simulation is used in this paper: multi-agent-based simulation to
investigate individual entities within the process-cooling system and the system’s behavior; discrete-
event simulation to explore the entire process-cooling flow; and system dynamics to capture the
thermophysical properties of the refrigeration unit and states of the refrigerated environment. A
simulation library is developed, and is able to represent a generic production-flow of the canned-food
process cooling. A data-driven symbolic-regression approach determines the complex logic of individ-
ual agents. Using a binary tuple-matrix for refrigeration-schedule optimization, the refrigeration-cycle
operation is determined, based on weather forecasts, electricity price, and electricity CO
2
emissions
without violating individual room-temperature limits. The simulation results of one-week’s pro-
duction in October 2020 show that 32% of energy costs can be saved and 822 kg of CO
2
emissions
can be reduced. The results thereby show the energy-flexibility potential in the process-cooling
facilities, with the benefit of overall production cost and CO2emissions reduction; at the same time,
the production quality and throughput are not influenced.
Keywords:
industrial-energy flexibility; agent-based modeling; simulation; process cooling;
multi-objective optimization
1. Introduction
The need to reduce the environmental impact of industries and prepare industries for
the intermittent behavior of the increasingly renewable future-energy-system necessitates
disruptive approaches for transitioning the industry to become increasingly flexible [
1
].
The typical energy-flexibility approaches considered in industries include the introduction
of carbon pricing and time-of-use-based electricity pricing [
2
]. The industrial facilities can
reduce the overall operation costs while aiding in electricity-system balancing through the
flexible operation of the industrial units in combination with time-of-use-based electricity
pricing. The facility flexibility can be derived from the production process units within the
facility, providing an instantaneous response. The flexibility can also be derived through
flexible control of the production environment, which can be curtailed based on the thermal
inertia of the system.
Due to the electricity consumption and thermal inertia, refrigeration and cooling pro-
cesses and ventilation units have been identified as end-use applications with significant
Energies 2023,16, 1514. https://doi.org/10.3390/en16031514 https://www.mdpi.com/journal/energies
Energies 2023,16, 1514 2 of 27
flexibility potential [
3
]. One of the industrial sectors with a substantial use of refrigeration
and cooling processes is the meat industry [
4
]. An example of a meat production facility
is the production of canned meat that can be used for long-term storage. However, there
is still hesitance among industrial consumers to provide energy flexibility, due to uncer-
tainties surrounding energy potential, production implications, and economic influence.
For instance, in Denmark, the meat industry constitutes 2% of the annual electricity con-
sumption, and can hence provide substantial flexibility. Within the Danish meat industry,
specific steps of the meat-processing stage are subject to legislation that hinders flexible
consumption by ensuring food safety and spoilage. Therefore, the primary refrigeration
and cooling for flexible operation are found in the meat-production facilities that produce
consumer products from the meat cuttings.
However, process cooling for food production is an energy-intensive industry with
complex interactions and restrictions that complicates the ability to utilize energy flexibility,
due to unforeseen consequences to production. Meanwhile, introducing energy flexibility
to industrial facilities has been coupled with several barriers that hinder participation
in energy-flexibility programs, e.g., a lack of understanding of the consequences flexible
operation may induce on production [
5
,
6
]. These barriers within the industrial-process
operations are complicated, due to complex system-interactions [
7
]. Furthermore, research
has mainly focused on single-process evaluation of flexibility potentials that do not ade-
quately consider up- and downstream propagation of production decisions [
8
]. Moreover,
little literature has focused on the energy-flexibility potential in the meat-canning process.
Methods for assessing the potential flexibility in individual facilities which can enable the
active participation of process-cooling facilities in the electricity system are essential, but
not yet well discussed in the literature.
Therefore, this paper introduces a simulation-based assessment method for investi-
gating energy flexibility in process cooling with a case study of a Danish process-cooling
facility for canned-meat food production. Multi-method simulation is used in this paper:
multi-agent-based simulation to investigate individual entities within the process-cooling
system and the system’s behavior; discrete-event simulation to explore the entire process-
cooling flow; and system dynamics to capture thermophysical properties of the refrigeration
unit and states of the refrigerated environment. Furthermore, a multi-method simulation
library is developed in this paper with the OptQuest optimization engine for accessing
energy-flexibility potential in the case study.
The rest of this paper is structured as follows: firstly, a literature review is presented,
examining the current literature on energy flexibility in process-cooling facilities. Secondly,
the applied methods, the agent-based modeling and multi-objective optimization approach,
are introduced. The simulation-development section outlines the simulation architecture
and agent communication. Subsequently, the individua- agent logics are outlined, covering
the production environment, meat product, process-flow agents, and the refrigeration unit.
Together with the refrigeration unit, the schedule-optimization explanation is provided.
The scenario-design section introduces the scenarios conducted to verify and validate the
designed agents. Based on the developed simulation-solution, three scenarios are presented;
the scenarios are presented to verify and test the developed solution. The case-study section
outlines the case study used for testing the scenarios with the specific agent-population
sizes. Subsequently, in the results section, the resulting operation based on the case study
is presented, emphasizing the refrigeration-cycle performance for three scenarios. Lastly,
the results and limitations are discussed, before the conclusion section.
2. Literature Review
Industries have high demand-response potential due to high baseloads, less coordina-
tion effort, and energy-management systems already in place [
9
]. For instance, in Denmark
industries consume 26.3% of the Danish end-user electricity consumption [
10
], and the
amount of flexible electricity consumption within Danish manufacturing companies is
equivalent to 380 MW [11].
Energies 2023,16, 1514 3 of 27
Implicit demand-response entails the industrial company reacting to market-price
signals, e.g., from Nord Pool Spot Market, and thereby adapting the electricity-consumption
behavior to lower operating-costs. In practical terms, this incites the industrial companies
to allocate their bulk production of goods to hours where the day-ahead electricity price is
low, to benefit from arbitrage. In addition to implicit demand-response, it is also possible
for the industrial company to participate in explicit demand-response. Explicit demand-
response is dispatchable and tradable flexibility [
12
]. A third-party, e.g., an aggregator,
often facilitates explicit demand-response. Explicit demand-response is often divided into
programs based on the capacity and response times of the actors.
Refrigeration and cooling represent most of the electricity consumption in the food-
processing industry where, on average, approximately 50% of the electricity consumption
is used for cooling and refrigeration [
4
]. The food processing can be subdivided into
processing and production. The processing stage uses the most electricity. Some food, e.g.,
meat, requires fast freezing-speed to avoid spoilage [
3
]. Therefore, the electricity used for
freezing tunnels is considered inflexible. The electricity usage related to the storage cooling
that keeps the food under acceptable conditions between process steps can be considered
for energy-load deviations and flexibility.
There is large energy-flexibility potential for ventilation, refrigeration, and cooling.
For instance, according to [
3
], cooling processes could be used for load shifting for multiple
hours and for around 50%, equivalent to 1513 TJ, of electricity consumption. However,
process-production systems often involve complex systems and processes that are chal-
lenging to model and describe, and often operate based on extensive tacit knowledge [
7
].
For instance, ref. [
13
] examines the meat-production process, and presents the initial pro-
cessing of different meat types (cattle, pork, poultry) and the energy usage associated with
production across European countries. Similarly, in [
14
], the saving potential in the food
industry for Latvia and Kazakhstan are compared, comparing the potentials for shifting for
cooling and ventilation.
Process cooling has previously been examined for its ability to provide flexibility in the
electricity market. Ref. [
15
] examines the potential for demand response through fan-speed
variations in the drying chambers and cooling interruption in the drying chamber, and
shows a 6.65% reduction in total cost of electricity. Ref. [
16
] evaluates the effects of demand
response in a refrigerated room, and shows that utilizing demand response once per day
yielded a core-temperature increase of the stored product of 1.1
◦
C after three days. Ref. [
17
]
reviews the economic and environmental impact of the meat industry’s participation in
energy flexibility, and shows that the meat industry can save between 3 and 5% on annual
CO
2
emissions by participating in demand response and 5–6% on the overall electricity cost.
Ref. [
18
] examines a frozen-food manufacturing plant for load balancing in the processes
of cooking, deep freezing, and cold warehouse, and finds that the facility can provide
balancing for the local power system. Ref. [
19
] examines the potential for HVAC systems
to provide demand response in industrial facilities with high thermal-inertia, and finds a
potential saving of 15.23% to 17.33%.
Furthermore, ref. [
20
] proposes a multi-criteria evaluation framework for mapping
various industrial processes to the feasibility of electricity-market participation. The study
considers a cooling process for food storage, which has fewer barriers in capacity-based
reserve markets. However, the study also remarks on the need to consider the facility’s
flexibility and the interactions of the industrial processes with other processes along the
production chain. Ref. [
21
] finds that an industrial-scale bakery with a glycol coolant-
system (that cools the bread-dough mixers and the fermentation room) can respond to
electricity system changes.
Process cooling has also been considered extensively in combination with various types
of thermal-energy-storage technologies. In [
22
], slurry-ice thermal storage is proposed for
the process cooling of cheese production, to aid in reducing the cost of energy costs. In [
23
]
a site-specific feasibility study is performed to investigate the potential for aquifer thermal
Energies 2023,16, 1514 4 of 27
energy storage. In [
24
], an HVAC chiller is examined in conjunction with an ice-storage
system in a supermarket, and is investigated for the potential to provide ancillary services.
However, industries’ active participation in implicit demand-response schemes is
associated with various barriers. In the process-cooling facilities, the primary barriers
and concerns regarding implicit demand-response participation are linked to the quality
constraints of the product. As described in [
8
], there is a need for to quantify the implications
for a production process in terms of up- and downstream propagation that may be incurred
due to a flexible operation. In [
5
], barriers to demand-response programs are examined in
which the most frequent barriers are related to technical uncertainty in terms of damage
to the product; however, economic considerations such as idle labor and unpredictability
are mentioned. Similar findings are presented in [
6
], with the addition of research that
can identify portfolios of demand-response measures that can be executed with minimal
impact on the production.
Furthermore, the demand-response potential for a process-cooling facility involv-
ing food will often be subject to food-temperature restrictions. Ref. [
25
] introduces a
supermarket-food-temperature estimation approach for a portion of ground beef. The
estimation approach is a time-constant approach for determining the temperature increase
over time, and the result shows that the food can reach its maximum allowable temperature
within 150 min. The shift in refrigeration load under consideration of the food temperature
has also been discussed in [26,27].
Moreover, there are often limitations from a legal standpoint regarding how much
temperatures can vary in the cooling process. The cooling processes are often subject to
some leeway regarding temperature setpoints. Ref. [
28
] finds that varying temperatures do
not affect the food products significantly, enabling the potential for flexible operation.
Several studies have used optimization to effectively utilize energy flexibility. For
instance, ref. [
29
] applies a linear program for optimizing a food-dehydration process using
a drum dryer. Ref. [
30
] applies a mixed-integer linear program across seven production lines
to optimize the food-production scheduling with the consideration of multiple factors for
each production line, e.g., energy consumption, productivity, and labor costs. Ref. [
31
] uses
a mixed-integer nonlinear program for optimal chiller-loading to improve the operation of a
large-scale process-cooling facility, and an 8.57% energy saving is achieved. The study also
considers variable electricity price and shows a potential economic saving of approximately
42.2%. Using an optimization-based framework examines the potential for chiller plants to
provide demand response through load curtailment [
32
]. Ref. [
33
] investigates the potential
for a large constant-speed centrifugal chiller to provide grid-frequency regulation, and
finds 5–7.5% regulation-capacity potential by using a model-predictive-control strategy.
However, as the optimization methods do not consider the internal-production-process
flow and optimization, start conditions may change before an optimal solution has been
found in a dynamic production system. Simulation methods can solve the above issues
and can capture the inherent uncertainty in production processes [
8
,
34
]. Some previous
research has applied agent-based simulation to the food industry. For instance, [
35
] uses
agent-based simulation to examine the beef-cattle supply chain. Ref. [
36
] introduces agent-
based modeling in the meat industry as a control layer in production. Ref. [
37
] utilizes
agent-based modeling for brewery-fermentation optimization. Furthermore, to efficiently
examine the potential for implicit demand-response in a canned-meat production facility,
the applied methods should be able to address all aspects of the facility sufficiently.
Based on the reviewed literature, it was found that limited literature has discussed
the energy-flexibility potential in the meat-canning process. Furthermore the literature
has emphasized single-process evaluation of flexibility potentials that do not adequately
consider up- and downstream propagation of production decisions. Therefore, the novelty
value of this paper is to introduce a simulation-based assessment method for investigating
energy flexibility in process cooling, using a case study of a Danish process-cooling facility
for canned-meat food production. The importance of the findings proposed in this paper is
Energies 2023,16, 1514 5 of 27
their contribution to the enablement of increasingly flexible behavior in industries using
process cooling.
3. Methodology
A multi-method simulation is used in this paper to capture the canned-meat process-
cooling facility. The multi-methods include multi-agent-based simulation to investigate
individual entities within the process-cooling system and the system’s behavior; discrete-
event simulation to explore the entire process-cooling flow; system dynamics to capture
the thermophysical properties of the refrigeration unit and states of the refrigerated en-
vironment. Based on the developed simulation-model, multi-objective optimization is
used to examine the refrigeration unit’s response to various operation schedules, including
time-of-use electricity price and carbon emissions. Machine learning is used to establish
the relationship between the facility cooling-temperature and electricity-consumption. In
combination, the methods provide an adequate description of the canned-meat system for
examining the energy-flexibility potential.
3.1. Multi-Method Simulation
Multi-method simulation enables the use of different modeling paradigms in order
to capture the underlying behavior as accurately as possible. The primary modeling-
approaches are discrete-event, system-dynamics, and agent-based modeling. The simula-
tion platform, AnyLogic, is chosen in this paper, due to its multi-method modeling and
simulation support.
Discrete-event models the system as a sequence of discrete events occurring at specified
time points and changing the system’s state. Discrete-event modeling considers the system
as a process with several sequential steps triggered as discrete events. The transition of
products between processes can often be described using discrete-event, where products
are transitioning between stages at specified times. Previous research has also utilized
discrete events for production systems [38].
System dynamics represents the system using stocks and flows to model the behavior
of systems over time. System dynamics can involve feedback loops, and is often used to
represent continuous-time systems. System dynamics has seen application in adoption
theory for examining the adoption of technologies in populations. Furthermore, system
dynamics has previously been used for the mathematical modeling of cooling systems [
39
].
Agent-based modeling and simulation can facilitate the investigation of complex sys-
tems by focusing on the individual-agent behavior [
40
–
42
]. Agent-based modeling allows
for the modeling of each entity in the system as an autonomous agent that encapsulates each
separate agent’s internal behavior and logic. Using multiple interacting intelligent-agents,
a multi-agent system can be developed in which the system’s behavior becomes a result of
emergent phenomena. Agent-based modeling, furthermore, allows for the establishing of
generic software agents that can be instantiated with parameters corresponding to their
domain, thereby providing reusability across a single domain.
Agent-based modeling and simulation have applications in several industrial do-
mains, including meat-processing facilities [
35
,
36
]. In a study from 2021, a fillet and nugget
processing line is presented, using agent-based modeling for describing the system com-
ponents using generic agents [
36
]. Another agent-based model in [
35
] presents beef-cattle
production and transportation simulation in southwest Kansas. Furthermore, there are
applications of agent-based modeling and simulation for reducing the overall CO
2
impact
of industrial production facilities [43].
3.2. Multi-Objective Optimization
Previous work has considered various types of optimization approaches including
mixed-integer linear programming (MILP), as covered in [
26
,
30
,
44
]. However, as described
in [
45
], linear programming is limited by the need for structured and well-defined problems
which may compromise real-system representation and the ability to provide quality
Energies 2023,16, 1514 6 of 27
solutions. Many real-life complex systems include multiple objectives which may be
conflicting. Multi-objective optimization has been used in previous work, e.g., [
29
], where
it was used to optimize food dehydration while also maximizing energy-efficiency.
Multi-objective optimization presents an ideal solution for considering the conflicting
and complex objectives and variables found in an industrial facility, and has previously
been discussed as a favorable solution in industrial food-processing [
46
,
47
]. In order
to solve the multi-objective optimization problem, various techniques can be used; the
literature presents a wide array of methods and metaheuristics including genetic algorithms,
tabu search, scatter search, neural networks, simulated annealing, and multi-variate linear
regression, etc. It has been shown that the use of search-based metaheuristics based on
scatter search and tabu search can outperform, e.g., genetic algorithms [48].
Therefore, the optimization in this paper is realized with the OptQuest optimization
software engine, a search-based algorithm based on scatter search and tabu search [
48
].
Furthermore, OptQuest simulation engine has shown better performance compared with
other optimization engines [
48
,
49
]. Moreover, the OptQuest optimization engine is also
embedded in the simulation platform, AnyLogic, which allow the realization of both
multi-method simulation and optimization. Anylogic was chosen based on an extensive
simulation-software comparison conducted in [
50
]. As only the simulation tools Enterprise
Dynamics, Pedestrian Dynamics, and AnyLogic supported the requirement for multi-
method modeling, these were chosen for further examination. As Pedestrian Dynamics
emphasizes the simulation of crowd management, the tool falls outside the scope of
simulation for this paper. Comparing the specifications for Enterprise Dynamics and
AnyLogic, it was evident that only AnyLogic supported multi-method modeling within
one model, which led to the selection of AnyLogic as the simulation tool.
4. Simulation Development
The developed simulation represents the chosen canned-meat production, which can
be used for examining the potential for energy flexibility. Canned-meat production consists
of several facility-specific process steps. While in production, the meat is contained in
various cold-storage areas collectively controlled by one or multiple refrigeration units.
Facility resources can be required for operating the processes, e.g., personnel for operating
machinery or forklifts for transporting goods.
An overview of the simulation architecture is shown in Figure 1. The top-level process-
cooling agent represents the given facility. Each facility may have multiple rooms or storage
areas with various temperature-requirements and profiles. It is important to note that the
primary production-flow is modeled and matched with the given cooling-environment.
Energies 2023, 16, x FOR PEER REVIEW 7 of 28
Figure 1. The simulation architecture.
The process cooling is a placeholder for all the environments in the different rooms
across the entirety of the facility. Several processes and conveyor blocks are associated
with each environment that receives its temperature data. The user controls the associated
processes and conveyor blocks. The environment is not required to contain any blocks.
All the environments are connected to the centrally controlled refrigeration unit. The in-
door temperature is determined based on the refrigeration unit’s electricity consumption
and current outdoor temperature. As seen from Figure 1, there is a continuous flow of
products between processes and conveyors, and the processes and conveyors are subject
to the environment in which they reside. Thereby, the environment will continuously no-
tify its observers of any state changes. Using an observer pattern enables a dynamic num-
ber of observers within the environment subjects. Similarly, the environments observe the
refrigeration unit and the internal-state changes in response to the refrigeration-unit input
are determined by the individual environments. The communication of the developed
simulation follows the sequence diagram, which is shown in Figure 2, and the refrigera-
tion unit determines the state of the refrigerated rooms. The state of the refrigerated room
subsequently propagates into the agents contained in the environment.
Figure 2. Sequence diagram showing primary-agent communication and interaction.
Figure 1. The simulation architecture.
Energies 2023,16, 1514 7 of 27
The process cooling is a placeholder for all the environments in the different rooms
across the entirety of the facility. Several processes and conveyor blocks are associated
with each environment that receives its temperature data. The user controls the associated
processes and conveyor blocks. The environment is not required to contain any blocks. All
the environments are connected to the centrally controlled refrigeration unit. The indoor
temperature is determined based on the refrigeration unit’s electricity consumption and
current outdoor temperature. As seen from Figure 1, there is a continuous flow of products
between processes and conveyors, and the processes and conveyors are subject to the
environment in which they reside. Thereby, the environment will continuously notify its
observers of any state changes. Using an observer pattern enables a dynamic number
of observers within the environment subjects. Similarly, the environments observe the
refrigeration unit and the internal-state changes in response to the refrigeration-unit input
are determined by the individual environments. The communication of the developed
simulation follows the sequence diagram, which is shown in Figure 2, and the refrigeration
unit determines the state of the refrigerated rooms. The state of the refrigerated room
subsequently propagates into the agents contained in the environment.
Energies 2023, 16, x FOR PEER REVIEW 7 of 28
Figure 1. The simulation architecture.
The process cooling is a placeholder for all the environments in the different rooms
across the entirety of the facility. Several processes and conveyor blocks are associated
with each environment that receives its temperature data. The user controls the associated
processes and conveyor blocks. The environment is not required to contain any blocks.
All the environments are connected to the centrally controlled refrigeration unit. The in-
door temperature is determined based on the refrigeration unit’s electricity consumption
and current outdoor temperature. As seen from Figure 1, there is a continuous flow of
products between processes and conveyors, and the processes and conveyors are subject
to the environment in which they reside. Thereby, the environment will continuously no-
tify its observers of any state changes. Using an observer pattern enables a dynamic num-
ber of observers within the environment subjects. Similarly, the environments observe the
refrigeration unit and the internal-state changes in response to the refrigeration-unit input
are determined by the individual environments. The communication of the developed
simulation follows the sequence diagram, which is shown in Figure 2, and the refrigera-
tion unit determines the state of the refrigerated rooms. The state of the refrigerated room
subsequently propagates into the agents contained in the environment.
Figure 2. Sequence diagram showing primary-agent communication and interaction.
Figure 2. Sequence diagram showing primary-agent communication and interaction.
In Figure 2, the adjustment of the refrigeration unit is started from the top-level indus-
trial facility. The refrigeration adjustment can happen at specified intervals. Once the signal
for refrigeration-unit control is sent, the refrigeration unit will collect the temperatures of
the rooms and the current outdoor temperature, which will determine the refrigeration
power-consumption for the forthcoming hour. The refrigeration power is published to
the cooling environments, which adjust their temperature based on the supplied cooling
power and the current outdoor temperature. Once the temperature adjustment has been
completed, the alarm setpoint is checked, and if the temperature has been above the alarm
setpoint for more than the specified alarm-delay-time, the specific cooling-environment
will trigger an alarm at the top-level facility agent.
Subsequently, the state of the cooling environment is published to all the environment
listeners. The environment listeners consist mainly of process-type agents that will pass
the state information to agents currently contained in the process, i.e., the meat-product
containers and meat products. The meat agent will adjust its temperature based on the
Energies 2023,16, 1514 8 of 27
environment state received, which in turn updates the thermophysical properties of the
meat for future state-changes.
As shown in Figure 2, the agent-based system follows an observer-based design
pattern. The use of an observer design-pattern enables system flexibility and reusability.
An event-driven system furthermore complements the domain-specific use of observer
responses to a subject, e.g., cooling-environment state changes are reflected in all agents cur-
rently residing in the specific environment that implements the required listener-interface.
An overview of the individual agents developed for the process-cooling facility and
their functionality can be seen in Table 1:
Table 1. Developed canned-meat-production facility agents.
Agent Description Parameter Input
Facility
The top-level facility agent in which
all other agents reside. Represents
the physical facility.
•Longitude
•Latitude
•Price area
Refrigeration
unit
The refrigeration unit that supplies
the facility sub-sections with
cooling, to enable correct
temperature levels.
•Cooling environments
•Operating schedule d
•Power function
•Power capacity
•Outdoor weather d
Cooling
environment
A delimited area of the facility that
has a desired temperature and an
alarm installed, with limits for
allowable temperature.
•Outdoor weather d
•Reciprocal time
constants
•Alarm temperature limit
•Alarm delay
Curing
station
The curing station takes the
received cuttings and distributes
them in containers, based on a
prescribed recipe.
•Delay
•Power consumption
•Resource requirements
•Maximum capacity
Cold-
storage room
The cold-storage room contains the
containers with collections of meat
cuttings that are stored until they
are required in production.
•Delay
•Power consumption
•Resource requirements
•Maximum capacity
Conveyor
The conveyors are used for
transporting the meat containers
throughout the facility.
•Start point
•End point
•Length
•Speed
•Power consumption
Meat
grinder
The meat grinder represents a
mixing station in which multiple
containers with meat cuttings are
inputted and ground to a mince.
•Delay
•Power consumption
•Resource requirements
•Maximum capacity
Filling
machine
The filling machine takes mince
prepared by the meat grinder and
fills the cans with it.
•Delay
•Power consumption
•Resource requirements
•Maximum capacity
Energies 2023,16, 1514 9 of 27
Table 1. Cont.
Agent Description Parameter Input
Cooker
The cooker takes the filled cans and
cooks them, in order to sterilize and
prolong the shelf-life of the product.
•Delay
•Power consumption
•Resource requirements
•Maximum capacity
Packing
station
The finished cans are sent to the
packing station, where they are
prepared for shipping.
•Delay
•Power consumption
•Resource requirements
•Maximum capacity
Staff
The staff operate the machinery and
are subject to schedules and breaks
during a workday.
•Shift schedule
•Employment contract
•Certifications
Meat The meat in the facility, with a
given composition and weight.
•Composition
•Weight
ddynamic parameter, changes during simulation runtime.
The primary parameters that are modified during simulation are those of the operating
schedule of the refrigeration unit, which propagate to the cooling environments. The state
of the cooling environments will determine the temperature of the meat. The temperature
estimation of the meat is, in this case, dependent on the composition. There are four
primary agents in the simulation: production environment, meat product, process agent,
and refrigeration unit.
4.1. Production Environment
The production-environment agent was created as a placeholder for the facility’s
environment in a specific room. A central parameter to be estimated for the operation of the
process cooling is the room temperature. The temperature is considered a main decision
parameter, as the correct temperature ensures the quality of the products. The literature’s
general approach to cooling-load estimation is centered around Newton’s cooling law [
51
].
Cengel states that the temperatures evolve according to an exponential curve [52]
T(t)−T∞
Ti−T∞=e−b·t(1)
where T(t) is the temperature at the next time step, T
i
is the internal temperature at the
current time step, and T
∞
is the surrounding temperature. The temperature is assumed to
be uniform, and the reciprocal time constant is defined as:
b=h·As
ρ·V·Cp(2)
where
h
is the overall heat-transfer-coefficient,
As
is the surface area,
ρ
is the density,
V
the volume, and
Cp
is the specific heat under constant pressure [
52
]. The reciprocal-time-
constant parameter,
b
, can be estimated based on the temperature segments found in
collected data, similar to the approach presented by Herten et al. [
51
]. The reciprocal time
constant is used to ensure that the temperature development does not exceed the observed
maximum hourly change.
The production-environment agent adheres to the company’s temperature setpoints
and restrictions. The state-chart representation of alarm behavior is shown in Figure 3.
Energies 2023,16, 1514 10 of 27
Energies 2023, 16, x FOR PEER REVIEW 10 of 28
where T(t) is the temperature at the next time step, T
i
is the internal temperature at the
current time step, and T
∞
is the surrounding temperature. The temperature is assumed to
be uniform, and the reciprocal time constant is defined as:
𝑏= ·
··
, (2)
where ℎ is the overall heat-transfer-coefficient, 𝐴 is the surface area, 𝜌 is the density,
𝑉 the volume, and 𝐶 is the specific heat under constant pressure [52]. The reciprocal-
time-constant parameter, 𝑏, can be estimated based on the temperature segments found
in collected data, similar to the approach presented by Herten et al. [51]. The reciprocal
time constant is used to ensure that the temperature development does not exceed the
observed maximum hourly change.
The production-environment agent adheres to the company’s temperature setpoints
and restrictions. The state-chart representation of alarm behavior is shown in Figure 3.
Figure 3. Production-environment alarm logic.
The production-environment agent will initially start with the alarm off. It will start
the alarm timer if the temperature is above the setpoint. If the temperature is not reduced
before the alarm timer runs out, the alarm is triggered, and a warning message will be
issued. Alternatively, the temperature can become too low, damaging the products and
directly triggering an alarm. In terms of optimization, an alarm trigger corresponds to an
infeasible run. The temperature within the compartment is updated continuously. The
compartment-environment temperature is determined based on Equations (1) and (2).
4.2. Meat Product
Limited information was obtained about the meat within the production flow. How-
ever, based on an example provided by [3] and the ASHRAE chapter on the food-temper-
ature thermal properties, modeling of the individual meat products could be performed
[53,54]. The temperature modeling of the meat was carried out using Newton’s law of
cooling, previously presented in (1). As surface temperature is used for the rules on the
hygiene of food of animal origin, a uniform-temperature estimation is assumed to be suf-
ficient [55]. The thermophysical properties of meat are highly dependent on the product’s
composition. It is assumed that the pork meat adheres to the composition found in the
shoulder of the pig. The composition is outlined in Table 2.
Figure 3. Production-environment alarm logic.
The production-environment agent will initially start with the alarm off. It will start
the alarm timer if the temperature is above the setpoint. If the temperature is not reduced
before the alarm timer runs out, the alarm is triggered, and a warning message will be
issued. Alternatively, the temperature can become too low, damaging the products and
directly triggering an alarm. In terms of optimization, an alarm trigger corresponds to an
infeasible run. The temperature within the compartment is updated continuously. The
compartment-environment temperature is determined based on Equations (1) and (2).
4.2. Meat Product
Limited information was obtained about the meat within the production flow. How-
ever, based on an example provided by [
3
] and the ASHRAE chapter on the food-temperature
thermal properties, modeling of the individual meat products could be performed [
53
,
54
].
The temperature modeling of the meat was carried out using Newton’s law of cooling,
previously presented in (1). As surface temperature is used for the rules on the hygiene of
food of animal origin, a uniform-temperature estimation is assumed to be sufficient [
55
].
The thermophysical properties of meat are highly dependent on the product’s composition.
It is assumed that the pork meat adheres to the composition found in the shoulder of the
pig. The composition is outlined in Table 2.
Table 2. Meat-agent composition.
Property Value
Mass [kg] 30
Moisture content 72.63
Protein [%] 19.55
Fat [%] 7.14
Carbohydrate [%] 0.0
Fiber [%] 0.0
Ash [%] 1.02
The meat’s thermal properties were regularly evaluated based on the above composi-
tion and the thermal-property model for food components presented in [
5
]. The density of
the meat is calculated according to (3):
ρ=(1−ε)
∑xi
ρi
(3)
Energies 2023,16, 1514 11 of 27
The porosity,
ε
, of the meat is zero, as no granularity is present, and
xi
and
ρi
are the
mass fractions and density of the meat constituent, respectively. In a similar way to the
density, the specific heat of the meat is modeled according to its constituents, as seen in (4).
Cp=∑Cp,i·xi(4)
The heat transfer coefficient of the meat was modeled based on the experimental
findings presented by [
56
], which were extended to be described using the regression
model seen in (5):
h(v) = −1.4869v2+14.105v+3.1676 (5)
where
v
describes the air velocity. It is assumed that the meat was always kept above its
initial freezing-point, for modeling the thermal properties. Falling below the initial freezing-
point will lead to significant changes in the thermal properties and potential damage to
the product. The initial freezing-point for a pork shoulder is
−
2.2
◦
C, significantly below
the compartments’ storage temperature. Within the production-flow simulation, the meat-
product agent adheres to the production environment associated with the process in which
it currently resides.
4.3. Process-Flow Agents
The process agent refers to the fundamental process logic inherited by any specific
process agent used for the simulation. The process agents represent the subprocesses shown
in Figure 4, which the product agent will pass through during its lifetime in production.
The flowcharts used for specific agents within the simulation can be seen in Figure 4.
Energies 2023, 16, x FOR PEER REVIEW 12 of 28
Cold Storage
Meat Grinder
Filling Machine
Hydrostatic
Cooker
Figure 4. Process-flow agents.
The meat-product agent will be inserted into the process block through the enter
block. After entering the block, the product will go through the process steps in the spe-
cific agent before exiting the next step in production or finishing the production. All the
process blocks were modeled based on the above concept. The cold storage had to be
slightly altered to include a rack system for storage. For raw-material storage, the prod-
ucts are transferred to a storage rack, where they will stay for a specified time before being
picked automatically and continuing production. The rack-store delay may be case-spe-
cific, as the meat is retrieved based on its usage in a required recipe. The current imple-
mentation delays all the products for the same duration of time. The meat grinder will
wait for a specified amount of meat agent to enter the process; once the amount is satisfied,
the products are batched into one new meat agent which is delayed, based on the grinder
setting. The filling machine will take two inputs of a container, i.e., a can and a containable
entity, i.e., meat, and will add the meat to the can, which can be delayed for a set period.
The hydrostatic cooker will take the filled-can agents and delay them for a period corre-
sponding to the cooking time.
4.4. Refrigeration Unit
The refrigeration-unit agent represents the facility’s control and operation of the re-
frigeration unit. The state-chart logic used for the agent can be seen in Figure 5.
Figure 4. Process-flow agents.
The meat-product agent will be inserted into the process block through the enter block.
After entering the block, the product will go through the process steps in the specific agent
before exiting the next step in production or finishing the production. All the process
blocks were modeled based on the above concept. The cold storage had to be slightly
altered to include a rack system for storage. For raw-material storage, the products are
transferred to a storage rack, where they will stay for a specified time before being picked
Energies 2023,16, 1514 12 of 27
automatically and continuing production. The rack-store delay may be case-specific, as the
meat is retrieved based on its usage in a required recipe. The current implementation delays
all the products for the same duration of time. The meat grinder will wait for a specified
amount of meat agent to enter the process; once the amount is satisfied, the products are
batched into one new meat agent which is delayed, based on the grinder setting. The filling
machine will take two inputs of a container, i.e., a can and a containable entity, i.e., meat,
and will add the meat to the can, which can be delayed for a set period. The hydrostatic
cooker will take the filled-can agents and delay them for a period corresponding to the
cooking time.
4.4. Refrigeration Unit
The refrigeration-unit agent represents the facility’s control and operation of the
refrigeration unit. The state-chart logic used for the agent can be seen in Figure 5.
Energies 2023, 16, x FOR PEER REVIEW 12 of 28
Cold Storage
Meat Grinder
Filling Machine
Hydrostatic
Cooker
Figure 4. Process-flow agents.
The meat-product agent will be inserted into the process block through the enter
block. After entering the block, the product will go through the process steps in the spe-
cific agent before exiting the next step in production or finishing the production. All the
process blocks were modeled based on the above concept. The cold storage had to be
slightly altered to include a rack system for storage. For raw-material storage, the prod-
ucts are transferred to a storage rack, where they will stay for a specified time before being
picked automatically and continuing production. The rack-store delay may be case-spe-
cific, as the meat is retrieved based on its usage in a required recipe. The current imple-
mentation delays all the products for the same duration of time. The meat grinder will
wait for a specified amount of meat agent to enter the process; once the amount is satisfied,
the products are batched into one new meat agent which is delayed, based on the grinder
setting. The filling machine will take two inputs of a container, i.e., a can and a containable
entity, i.e., meat, and will add the meat to the can, which can be delayed for a set period.
The hydrostatic cooker will take the filled-can agents and delay them for a period corre-
sponding to the cooking time.
4.4. Refrigeration Unit
The refrigeration-unit agent represents the facility’s control and operation of the re-
frigeration unit. The state-chart logic used for the agent can be seen in Figure 5.
Figure 5. Refrigeration-unit operating modes.
The refrigeration unit responds to an inputted operation schedule. The initial state of
the refrigeration unit is chosen based on the initial schedule, through the branch shown in
Figure 4. The ON or OFF states do not represent the refrigeration unit being entirely on or
off. The states correspond to an increase or decrease in power consumption, as it is currently
enforced that the refrigeration unit should run all the time, and the capacity is adjusted.
The refrigeration unit’s primary power-consumption is attributed to the compressors that
adjust the inputted work, based on the refrigeration load. As modeling the correct behavior
of the refrigeration unit poses a significant challenge, with underlying assumptions that
can be challenging to address, a data-driven modeling approach is applied.
Symbolic regression has been identified as a promising solution for obtaining explana-
tory models without imposing any a priori assumptions [
57
]. Symbolic regression has
seen development using both genetic programming and simulated annealing; however, as
shown in [
58
], symbolic regression using simulated annealing generally outperforms sym-
bolic regression based on genetic programming. The performance was further underlined in
another study comparing state-of-the-art symbolic-regression tools; the study showed that
the software TuringBot, based on simulated annealing, outperformed its counterparts, Eu-
reqa and AI Feynman, discovering target equations faster and with fewer data points [
59
].
Symbolic regression was enabled through TuringBot to establish the refrigeration-unit
electricity consumption under various conditions. Therefore, TuringBot was used to de-
velop a refrigeration-unit power function, relating the individual room-cooling-load to the
refrigeration-unit electricity consumption.
Multi-Objective Optimization of Refrigeration-Operation Schedule
Enabled by the OptQuest optimization engine, multi-objective optimization was used
to select the refrigeration-unit-operation schedule. The objectives used for the multi-
objective optimization are stated below (6):
minimize CO2emissions
minimize Electricity cos t (6)
Energies 2023,16, 1514 13 of 27
The minimization is subject to operational constraints of the refrigeration unit. Fur-
thermore, the problem is constrained by the number of cooling-system alarms being equal
to zero. The optimization was performed in incremental steps for the simulation. Each
simulation step corresponded to the optimization horizon. A sequence diagram providing
an overview of the multi-objective optimization utilization can be seen in Figure 6.
Energies 2023, 16, x FOR PEER REVIEW 14 of 28
Figure 6. Sequence diagram showing the multi-objective optimization-simulation interaction.
As seen from the sequence diagram presented in Figure 6, the optimization is started
by generating all possible operation schedules. Using the developed simulation, the oper-
ational schedule performance is tested under the outlined constraints. Once an optimized
schedule has been identified, it is used to for simulating the forthcoming 24 hours in the
simulation before the optimization procedure is repeated. As the simulation-optimization
engine does not support schedule optimization, an alternative approach is used for select-
ing the appropriate schedule. A discrete schedule contains a finite number of possible
combinations and a finite number of possible states. Therefore, the possible schedules can
be constructed as arrays of states from the current timestamp, n, until the desired planning
horizon, m, i.e., the number of future timesteps considered.
𝑠𝑡𝑎𝑡𝑒…𝑠𝑡𝑎𝑡𝑒
, (7)
The possible schedules can be collected in an array with a length corresponding to
the number of possible permutations. The possible permutations are derived from the
number of possible states, s.
Each possible schedule is linked to the resulting operation’s associated electricity
price, carbon dioxide emission, and facility operation. The simulation-optimization en-
gine can subsequently use an index list referring to all possible permutations, where each
index holds a unique combination of states. Based on the index list, the simulation envi-
ronment can be used as a testbed for examining the impact of a specific operation sched-
ule.
Assuming that the scheduling is carried out on an hourly basis and that the state of
the refrigeration cycle is operated in an ON/OFF manner, inferring two states, the total
number of operational possibilities can be expressed as (8) [60]
𝑠, (8)
where m represents the scheduling horizon and (8) represents the total number of permu-
tations with repetition allowed. It is essential to include repetitions, as the system’s current
state will influence its future states, due to changing temperatures. Each operational pos-
sibility can be expressed as a binary number with a number of bits corresponding to the
scheduling horizon. In this case, zeros correspond to OFF, and a one in the system is ON.
Generating all possible schedules hence presents a matrix of size (𝑠𝑚), in which each
row represents a possible operational schedule. Based on the possible operational
Figure 6. Sequence diagram showing the multi-objective optimization-simulation interaction.
As seen from the sequence diagram presented in Figure 6, the optimization is started
by generating all possible operation schedules. Using the developed simulation, the opera-
tional schedule performance is tested under the outlined constraints. Once an optimized
schedule has been identified, it is used to for simulating the forthcoming 24 h in the sim-
ulation before the optimization procedure is repeated. As the simulation-optimization
engine does not support schedule optimization, an alternative approach is used for se-
lecting the appropriate schedule. A discrete schedule contains a finite number of possible
combinations and a finite number of possible states. Therefore, the possible schedules can
be constructed as arrays of states from the current timestamp, n, until the desired planning
horizon, m, i.e., the number of future timesteps considered.
staten. . . staten+m(7)
The possible schedules can be collected in an array with a length corresponding to the
number of possible permutations. The possible permutations are derived from the number
of possible states, s.
Each possible schedule is linked to the resulting operation’s associated electricity price,
carbon dioxide emission, and facility operation. The simulation-optimization engine can
subsequently use an index list referring to all possible permutations, where each index
holds a unique combination of states. Based on the index list, the simulation environment
can be used as a testbed for examining the impact of a specific operation schedule.
Assuming that the scheduling is carried out on an hourly basis and that the state of
the refrigeration cycle is operated in an ON/OFF manner, inferring two states, the total
number of operational possibilities can be expressed as (8) [60]
Energies 2023,16, 1514 14 of 27
sm, (8)
where mrepresents the scheduling horizon and (8) represents the total number of per-
mutations with repetition allowed. It is essential to include repetitions, as the system’s
current state will influence its future states, due to changing temperatures. Each operational
possibility can be expressed as a binary number with a number of bits corresponding to
the scheduling horizon. In this case, zeros correspond to OFF, and a one in the system is
ON. Generating all possible schedules hence presents a matrix of size
(sm×m)
, in which
each row represents a possible operational schedule. Based on the possible operational
schedules, the objective functions are optimized under the previously outlined constraints.
The scheduling is carried out on an hourly basis, in order to coincide with the electricity
spot-prices which are supplied on an hourly basis. As the scheduling is carried out hourly,
it is hence assumed that the refrigeration operation is varied on an hourly basis. The
room-temperature development could be simulated in response to each binary string’s
composition. As the optimization is carried out room-wise, each room’s preferred schedule
may vary, based on the parameters and constraints; i.e., one room may increase in temper-
ature more rapidly than another. Therefore, the optimization was carried out using the
temperature development for all rooms, and only solutions that adhere to all the individual
room constraints were considered for use. The approach was deemed necessary because
the refrigeration unit is centrally controlled, and any operational change will affect all
connected rooms.
The schedule was optimized using the CO
2
emissions and electricity spot-price. The
Danish transmission system operator, Energinet, supplies a forecast of the electricity spot-
price for the next 24 h and for the forthcoming 9 h for CO
2
emissions [
61
]. Note that for
the forecasted CO
2
emission, Energinet ensures a minimum of 9 h of prognosis, but can
include more hours. The energy-system forecasts were combined with a weather forecast to
correspond to the scheduling horizon. The electricity price and CO
2
emissions associated
with the operation were calculated as shown in (9) and (10).
Electricity cos t =∑m
i=nPconsumption,i·Ecost,i(9)
where
Pconsumption,i
, is the electricity consumption in the hour i, and
Ecost,i
, is the cost of
electricity in the hour i. Similarly, the CO2emissions are calculated as:
CO2emissions =∑m
i=nPconsumption,i·Eemissions,i(10)
where Eemissions,i, refers to the amount of CO2emission per consumed electricity-unit.
5. Scenario Design
Three scenarios are designed to examine the canned-meat process-cooling operation. A
baseline scenario for simulation-model verification and two optimization scenarios examine
the facility’s impact and potential for energy flexibility. All the scenarios were simulated
within the period of 5–12 October 2020, which was the period with available data. The
simulation was conducted with hourly timesteps.
5.1. Baseline Scenario
The purpose of the baseline scenario is to verify that the developed agent-based
simulation model can correctly capture the observed operation of the facility. The process-
cooling operation in the base scenario is based on historical data. The corresponding
historical electricity spot-market-prices and the measured outdoor-weather conditions are
collected. The expected results for the baseline scenario are to verify comparable behavior
and electricity consumption of the refrigeration-unit agent, i.e., observe similar overall
electricity consumption for the facility and simulation model. Furthermore, the production-
process agents should be able to represent the various production stages and cover the
Energies 2023,16, 1514 15 of 27
production flow from initialization to completion. The results are expected to verify the
established agent-architecture and communication presented in Figures 1and 2.
5.2. Carbon Dioxide-Based Optimization Scenario
The carbon dioxide-based optimization scenario aims to validate the ability to adjust
refrigeration load based on the current carbon dioxide emissions associated with electricity
consumption in order to reduce the facility’s overall carbon footprint.
The optimization is performed daily, using the forecast of the carbon-dioxide emissions
provided by the Danish transmission system operator. A 9-hour forecast is used to schedule
the refrigeration-unit operation. The carbon-dioxide-based optimization scenario seeks to
examine the potential for the meat-canning industry to partake in the flexible operation of
their refrigeration cycle without sacrificing operational security. The optimization is based
on the OptQuest optimization engine using a binary tuple-matrix for examining various
opportunities for flexible operation. In each case, the optimization is examined for viability,
based on whether any alarms were triggered in operation, inferring an infeasible run. The
feasible run with the lowest associated-carbon-emissions was selected.
The expected result of the carbon dioxide-based optimization scenario is to investi-
gate the potential for carbon-dioxide-emission saving. through flexible refrigeration-load
operation. The investigation is subject to the consideration of room-temperature-setpoint
requirements for food safety. Thereby, the investigation provides an estimation of the
potential within the operational constraints of the facility.
5.3. Electricity-Spot-Price-Based Optimization Scenario
The electricity-spot-price-based optimization scenario aims to validate the ability to
adjust refrigeration load based on the spot-market electricity price associated with the
electricity consumption for reducing the facility’s overall electricity cost. The optimization
is performed similarly to the carbon-dioxide-based optimization scenario, but the feasible
run with the lowest-associated electricity price was selected.
The expected result of the electricity-spot-price-based optimization scenario is to
investigate the potential for electricity-cost savings through a flexible refrigeration-load
operation. The investigation is subject to the consideration of room-temperature-setpoint
requirements for food safety. Thereby, the investigation provides an estimation of the
potential within the operational constraints of the facility.
6. Case Study
The case study process-cooling is located in Denmark, primarily produces canned
meat, and has a small production line for sausages. In this case study, the primary produc-
tion line of canned meat is examined, and some aspects of the temperature development for
other facility parts are also included. The production facility is divided into several rooms
that represent a specified space. The specific rooms may be physically interconnected or
separate. An overview of the facility layout is shown in Figure 7.
As shown in Figure 7, meat cuttings are first received in the raw-materials section,
room 1071. Subsequently, the meat is transported to the curing station; the meat is placed in
containers, each of approximately 30 kg, with a distribution of cuttings matching the specific
recipe. After being placed into containers, the containers are transported by conveyor to the
storage room, and stay there for a prolonged time, in room 1060. Once ready, the containers
adhering to the same recipe are transported by conveyor to a selected mincing-and-mixing
machine. Each mincing-and-mixing machine marks the beginning of a factory line. The
facility has a total of 7 lines for producing canned meat. After mincing and mixing, the
minced meat is filled into cans and sealed. Once the cans are sealed, they are transported
to the cooking station, where the meat is cooked within the can. The cooking station is the
final step before the cans are ready to be packed and shipped to customers. The primary
canned-meat production process can be represented by the flowchart seen in Figure 8.
Energies 2023,16, 1514 16 of 27
Energies 2023, 16, x FOR PEER REVIEW 17 of 28
Figure 7. An overview of the case-study-facility layout.
As shown in Figure 7, meat cuttings are first received in the raw-materials section,
room 1071. Subsequently, the meat is transported to the curing station; the meat is placed
in containers, each of approximately 30 kg, with a distribution of cuttings matching the
specific recipe. After being placed into containers, the containers are transported by con-
veyor to the storage room, and stay there for a prolonged time, in room 1060. Once ready,
the containers adhering to the same recipe are transported by conveyor to a selected minc-
ing-and-mixing machine. Each mincing-and-mixing machine marks the beginning of a
factory line. The facility has a total of 7 lines for producing canned meat. After mincing
and mixing, the minced meat is filled into cans and sealed. Once the cans are sealed, they
are transported to the cooking station, where the meat is cooked within the can. The cook-
ing station is the final step before the cans are ready to be packed and shipped to custom-
ers. The primary canned-meat production process can be represented by the flowchart
seen in Figure 8.
Figure 8. Case-study canning process.
Figure 7. An overview of the case-study-facility layout.
Energies 2023, 16, x FOR PEER REVIEW 17 of 28
Figure 7. An overview of the case-study-facility layout.
As shown in Figure 7, meat cuttings are first received in the raw-materials section,
room 1071. Subsequently, the meat is transported to the curing station; the meat is placed
in containers, each of approximately 30 kg, with a distribution of cuttings matching the
specific recipe. After being placed into containers, the containers are transported by con-
veyor to the storage room, and stay there for a prolonged time, in room 1060. Once ready,
the containers adhering to the same recipe are transported by conveyor to a selected minc-
ing-and-mixing machine. Each mincing-and-mixing machine marks the beginning of a
factory line. The facility has a total of 7 lines for producing canned meat. After mincing
and mixing, the minced meat is filled into cans and sealed. Once the cans are sealed, they
are transported to the cooking station, where the meat is cooked within the can. The cook-
ing station is the final step before the cans are ready to be packed and shipped to custom-
ers. The primary canned-meat production process can be represented by the flowchart
seen in Figure 8.
Figure 8. Case-study canning process.
Figure 8. Case-study canning process.
Consumer requirements, food-safety law, and regulations partially specify the room-
temperature requirements. The temperature of each room within the production flow is
monitored. The restrictions and setpoints of the different rooms are shown in Table 3. The
temperature setpoint is the temperature at which the room should be maintained. The
alarm setpoint is the maximum temperature allowed to trigger the alarm delay. If the
temperature stays above the alarm setpoint for the alarm-delay duration, the alarm will
trigger, leading to food spoilage and economic loss for the company.
Energies 2023,16, 1514 17 of 27
Table 3. Facility room-temperature constraints.
Room Temperature
Setpoint [◦C]
Alarm
Setpoint [◦C]
Alarm Delay
[hours]
1001 3 4 2
1030 5 6 2
1060 2 3 6
1071 2 3 3
1193 5 6 2
1200 4 5 2
1220 2 3 5
A central refrigeration-unit refrigerates the facility to maintain the required tempera-
ture within the individual rooms. The refrigeration unit comprises several components,
and it is operated using five compressors and three condensers with individual fans and
pumps. Each condenser operates with two fans and a pump that sprays water for increasing
heat-transfer. The refrigeration cycle uses ammonia and has three tanks to store cooled
ammonia temporarily. The cooled ammonia is utilized through heat exchangers; the heat is
exchanged into glycol, used as the medium for refrigerating the facility. The refrigeration
unit’s power consumption can be divided based on the components shown in Table 4.
Table 4. Refrigeration units and power consumption.
Type Unit n Power Consumption
[kW]
Compressor GSV-185 3 270
Compressor SMC-8-180 2 183
Condenser VXC 680 3 38.4
The refrigeration unit is continuously operating, and the electricity consumption is
regulated based on the cooling demand. The compressors are turned on hierarchically once
the current compressor(s) is insufficient to meet the cooling demand.
The examined facility provided several datasets for production and refrigeration;
an overview of the available data can be seen in Table 5. Besides the facility-specific
data obtained from the company, several external-data sources were integrated into the
simulation. The data were retrieved using the associated APIs. All the data were extracted
based on the Unix timestamp of the simulation or the correlated UTC timestamp, to ensure
the correct model time and data match. Currently, the Danish Meteorological Institute
API is only used to retrieve the temperature; however, it is also possible to extract other
parameters, e.g., wind speed, wind direction, and humidity, which can also be influential.
All the Danish transmission system APIs were sorted based on data from DK1. If the
simulation model is used for future projects in other physical locations than DK1, this
should be adjusted. Note that the CO2emissions in DK1 and DK2 are not differentiated.
Table 5. Data Overview.
Description Source Description
Room temperatures Facility The hourly individual room
temperatures.
Outdoor-facility
temperatures Facility The temperature measured outside
the facility.
Energies 2023,16, 1514 18 of 27
Table 5. Cont.
Description Source Description
Compressor capacities Facility The installed capacities for all
compressors at the facility.
Condenser capacities Facility The installed capacities for all
condensers at the facility.
Refrigeration-unit power Facility
The power consumption of the
individual components within the
refrigeration unit, as well as the
combined power-consumption.
Room alarm-setpoints Facility
The specified setpoints for alarm
temperatures and delays across all
rooms in the facility.
Facility layout Facility The physical layout of the facility.
Outdoor temperature Danish Meteorological
Institute
The outdoor temperature measured
at the closest weather-station.
CO2emissions Danish TSO The actualized CO2-emissions
associated with the electricity mix.
CO2-emissions prognosis Danish TSO The expected CO2emissions
associated with the electricity mix.
Electricity-system spot price
Danish TSO
The actualized electricity spot-prices
in the DK1 synchronous area of
Denmark.
Electricity-system spot-price
prognosis Danish TSO
The expected electricity spot-prices in
the DK1 synchronous area of
Denmark.
7. Results
The three designed-scenarios are conducted to test the operation and performance of
the developed simulation and the impact on the facility’s operation regarding monetary
expenses and carbon dioxide emissions.
7.1. Baseline Scenario
In the baseline scenario, the simulation realization of the production-process flow
agents can be seen in Figure 9. As seen from Figure 8, the facility uses a single curing and
cold-storage room to prepare the meat for further processing. After the cold-storage room,
the meat is transported to a specified meat-grinder with seven production-lines available.
Once the meat has been processed in one of the meat grinders, it is transferred to the filling
machines, where it is canned. The cans are transported to a hydrostatic cooker used for
boiling meat in the can for preservation. Once the hydrostatic cooking is completed, the
cans are transferred to the packing station, where they are prepared for shipping.
An overview of the agent populations contained in the facility simulation model can
be seen in Table 6.
A key component for establishing the refrigeration-unit agent is to provide a rela-
tionship between the electricity consumption and the cooling-load required. Examining
the workload as a function of the internal- and external-temperature difference reveals a
correlation between the temperature difference and the compressor workload. Applying
symbolic regression, with a Pareto split between training and test data, resulted in a func-
tion that could be used to model the refrigeration cycle’s power-consumption dependency
on the room-temperature difference.
Energies 2023,16, 1514 19 of 27
Energies 2023, 16, x FOR PEER REVIEW 20 of 28
Figure 9. Developed process-flow for the canned-meat production process.
An overview of the agent populations contained in the facility simulation model can
be seen in Table 6.
Table 6. Agent population-sizes for case study.
Agent Population Size
Facility 1
Refrigeration unit 1
Cooling environment 7
Curing station 1
Cold-storage room 1
Conveyor 11
Meat grinder 7
Filling machine 7
Cooker 1
Packing station 1
Staff Dynamic
Meat Dynamic
Can Dynamic
A key component for establishing the refrigeration-unit agent is to provide a rela-
tionship between the electricity consumption and the cooling-load required. Examining
the workload as a function of the internal- and external-temperature difference reveals a
correlation between the temperature difference and the compressor workload. Applying
symbolic regression, with a Pareto split between training and test data, resulted in a func-
tion that could be used to model the refrigeration cycle’s power-consumption dependency
on the room-temperature difference.
The developed refrigeration-unit power function can be seen in (11), with an RMS of
26.7 kWh.
Figure 9. Developed process-flow for the canned-meat production process.
Table 6. Agent population-sizes for case study.
Agent Population Size
Facility 1
Refrigeration unit 1
Cooling environment 7
Curing station 1
Cold-storage room 1
Conveyor 11
Meat grinder 7
Filling machine 7
Cooker 1
Packing station 1
Staff Dynamic
Meat Dynamic
Can Dynamic
The developed refrigeration-unit power function can be seen in (11), with an RMS of
26.7 kWh.
P(Toutdoor,∆T1193,∆T1060 ,∆T1071,∆T1200,∆T1030 )=168.085
+tan(0.19167 ·∆T1071 −∆T1193)−((2.10042/ cos(∆T1193))
+(−59.3594 ·sin(1.70687 ·(∆T1030 −∆T1193 ))))
+0.288334 ·tan(Toutdoor +0.0526233)−tan(∆T1200 +0.0638923)
+((−12.0232 +(∆T1060 −∆T1200 )) ·∆T1060 )
(11)
As shown in (11), the power consumption of the refrigeration unit relies on the
temperature difference between several of the rooms in the facility and the current outdoor
temperature. A plotting of the obtained function together with the observed refrigeration-
unit power is shown in Figure 10.
Energies 2023,16, 1514 20 of 27
Energies 2023, 16, x FOR PEER REVIEW 21 of 28
𝑃(𝑇
,ΔT
,ΔT
,ΔT
,ΔT
,ΔT
) = 168.085 + tan(0.19167 ⋅
ΔT
−ΔT
) − ((2.10042/cos(ΔT
)) + (−59.3594 ⋅ sin(1.70687 ⋅
(ΔT
−ΔT
)))) + 0.288334 ⋅ tan(𝑇 + 0.0526233) − tan(ΔT
+
0.0638923) + ((−12.0232 + (ΔT
−ΔT
)) ⋅ ΔT
),
(11)
As shown in (11), the power consumption of the refrigeration unit relies on the tem-
perature difference between several of the rooms in the facility and the current outdoor
temperature. A plotting of the obtained function together with the observed refrigeration-
unit power is shown in Figure 10.
Figure 10. Prediction of refrigeration-unit power consumption.
Figure 10 shows that there are spikes in temperatures at certain times, probably due
to some internal processes or a change of shift, etc. Furthermore, the refrigeration-unit
usage of storage tanks is also expected to skew the regression. The overall behavior of the
refrigeration unit could be successfully captured, based on the symbolic-regression model
implemented into the simulation model.
The reciprocal time constant was estimated for temperature-increasing and temper-
ature-decreasing segments to examine the room responses to cooling or heating. The tem-
perature increases and decreases of segments were done for each room as the reciprocal
time constant is influenced by physical constraints and boundaries associated with the
individual compartments. The temperature-decreasing segments were included as a ref-
erence point for modeling the temperature decrease over time governed by the system
constraints. Exponential regression was used for determining the reciprocal time constant;
the regression coefficients for all the segments within a room were averaged to obtain one
room’s overall coefficient. The obtained constants can be seen in Table 7.
Table 7. Determined reciprocal-time-constants for each room.
Room Reciprocal Time Constant
Temperature Increasing
Reciprocal Time Constant
Temperature Decreasing
1001 0.05935 −0.08202
1030 0.02308 −0.04952
1060 0.09375 −0.07786
1071 0.007737 −0.01180
Figure 10. Prediction of refrigeration-unit power consumption.
Figure 10 shows that there are spikes in temperatures at certain times, probably due
to some internal processes or a change of shift, etc. Furthermore, the refrigeration-unit
usage of storage tanks is also expected to skew the regression. The overall behavior of the
refrigeration unit could be successfully captured, based on the symbolic-regression model
implemented into the simulation model.
The reciprocal time constant was estimated for temperature-increasing and temperature-
decreasing segments to examine the room responses to cooling or heating. The temperature
increases and decreases of segments were done for each room as the reciprocal time con-
stant is influenced by physical constraints and boundaries associated with the individual
compartments. The temperature-decreasing segments were included as a reference point for
modeling the temperature decrease over time governed by the system constraints. Exponential
regression was used for determining the reciprocal time constant; the regression coefficients
for all the segments within a room were averaged to obtain one room’s overall coefficient. The
obtained constants can be seen in Table 7.
Table 7. Determined reciprocal-time-constants for each room.
Room Reciprocal Time Constant
Temperature Increasing
Reciprocal Time Constant
Temperature Decreasing
1001 0.05935 −0.08202
1030 0.02308 −0.04952
1060 0.09375 −0.07786
1071 0.007737 −0.01180
1193 0.03434 −0.04436
1200 0.007226 −0.007870
1220 0.09031 −0.13350
Initially, the process-cooling facility’s current operation was simulated as a reference
point for changes and future simulations. The current operation was evaluated based on the
company’s actual data and the approximated values obtained through
Equation (8)
. The
following scenario will calculate electricity consumption based on the symbolic regression
function. The calculated electricity price for all scenarios is the electricity price excluding
tax, etc. The resulting baseline results can be seen in Table 8.
Energies 2023,16, 1514 21 of 27
Table 8. Baseline-operation results.
Scenario Electricity
Consumption [kWh]
Total Electricity Cost
[DKK]
Total CO2Emissions
[kg]
Actual
consumption 38,829.89 8276.048 2781.5
Simulated
consumption 38,829.93 8284.093 2799.5
7.2. Carbon-Dioxide-Based Optimization Scenario
Based on the CO
2
prognosis and the optimization approach described earlier, the
schedule was adjusted to minimize CO
2
emissions associated with electricity consumption.
The results can be seen in Table 9. The carbon-dioxide-based scenario sought to reduce
the overall consumption of CO
2
. It was possible to achieve significant reductions with
associated reductions in total electricity costs.
Table 9. Carbon-dioxide-based optimization results.
Scenario Electricity
Consumption [kWh]
Total Electricity Cost
[DKK]
Total CO2Emissions
[kg]
CO2-based Operation 28,983.12 5738.2 1976.85
7.3. Electricity-Spot-Price-Based Optimization Scenario
The schedule was adjusted, based on the spot-price forecast and the optimization
approach described earlier, to minimize the electricity-consumption price. The results
using a 9-h forecast can be seen in Table 10. Table 10 shows that the total electricity
price was reduced by 2648 DKK. It could be observed that optimizing solely in terms of
electricity price provides improved economic-gain over CO
2
-based scheduling. The choice
of scheduling objective is based on the criteria the company emphasizes.
Table 10. Price-based optimization results.
Scenario Electricity
Consumption [kWh]
Total Electricity Cost
[DKK]
Total CO2Emissions
[kg]
Price-based
Operation 30,808.77 5636.45 2116.31
8. Discussion
Three scenarios cover the baseline operation and flexible operation based on electricity
price and carbon dioxide emissions, respectively. The baseline scenario verifies the system’s
ability to reflect the case study. Simulating during 5–12 October 2020 shows consistency
between the historical and simulated electricity-consumption, with an absolute error of
0.04 kWh. The flexible-operation scenarios show that the refrigeration load can be shifted
without violating room-temperature constraints, and could save the company approxi-
mately 32% on electricity costs and 30% on associated carbon dioxide emissions. Similarly,
previous research examining energy-cost saving has reported potential from 5% to upwards
of 70% [15,37,62,63].
As in results shown in Tables 8–10, the facility can adjust its load to take advantage
of the electricity-market conditions and forecasts. It is possible to reduce the facility’s
electricity costs and CO
2
emissions. The current price optimization is the implicit demand-
response that reacts to the electricity-market-price signals. However, electricity-market
participation through explicit demand-response is expected to provide a more significant
monetary benefit. Currently, the energy flexibility is fully based on the refrigeration unit
within the facility. However, some flexibility may also be available in the operations through
Energies 2023,16, 1514 22 of 27
adequate planning. A comparison of the three scenarios and the actual consumption is
shown in Table 11. The simulated and actual consumption are comparable, indicating that
the developed simulation-model can capture the underlying system. The savings can be
realized effectively, and there are differences depending on the emphasis, i.e., wanting to
save more on the electricity price or CO2, even though both operations induce savings.
Table 11. Comparison of scenario results.
Scenario Consumption
[kWh]
Total
Electricity
Cost [DKK]
Total CO2
Emissions
[kg]
2030 CO2
Taxation
[DKK]
Total Cost
[DKK]
Actual
consumption 38,829.9 8276.1 2781.5 2086.1 10,362.2
Simulated
consumption 38,829.9 8284.1 2799.5 2099.6 10,383.7
CO2-based
Operation 28,983.1 5738.2 1976.9 1482.6 7220.8
Price-based
Operation 30,808.8 5636.5 2116.3 1587.2 7223.7
It should be noted that the Danish government has agreed to introduce carbon taxation
from 2030 on 750 DKK/tonne of emitted CO
2
[
64
]. As shown in Table 11, accounting for
the taxation in the overall evaluation of the results would effectively make the operating
cost of the CO
2
-based operation marginally cheaper, indicating that industrial facilities
should consider this when considering a flexible operation.
The relationship between electricity price and carbon intensity has been shown to
follow a positive relationship [
65
,
66
]. Therefore, optimizing toward either electricity cost or
carbon intensity is likely to entail cost savings, which can also be observed from the results
in Table 11.
The observed savings resulting from the multi-objective optimization should be consid-
ered in response to the facility not utilizing their underlying leeway allowing temperature
intervals. The difference in energy consumption results from operating the refrigeration
unit closest to the temperature limits. The difference in CO
2
emissions is a result of
the variability of the emissions associated with electricity consumption at various hours.
Therefore, savings can be observed as a combination of the refrigeration unit operating
less and becoming flexible. The saving should also be considered in response to uncer-
tain room-temperature behavior. Generally, including sensor data in the production-flow
model could increase the resolution of the simulation. Integrating IoT devices within the
production-flow simulation allows new opportunities to be tested in a risk-free environ-
ment. Furthermore, this would allow AI-driven solutions to further the operation and
achieve optimal refrigeration-load scheduling. Currently, the temperature estimation of
the compartments is carried out based on the data analysis. As [
51
] noted, adjacent cold
stores influence each other in terms of refrigeration load, and this could hence be included
in further investigation. In the process-cooling field, the application of reciprocal time
constants, e.g., [
25
,
51
], are used to investigate the cooling-room-response over time. How-
ever, approaches using deep-learning artificial-neural-network models for predicting the
room temperature may provide improved approximations over time [
67
]. Other rooms and
food-temperature-estimation approaches include model-based estimations using Kalman
Filtering, as presented in [
68
]. In this paper, reciprocal time constants were used for esti-
mating the temperature response of the individual rooms, based on data provided for the
case study.
Previous research has shown the ability to use various machine-learning approaches
to examine the curtailment period for energy flexibility. Hoang et al. [
67
] presented LSTM
RNN models for predicting power and temperature variations. Similarly, Herten et al. [
51
]
introduced least-squares support-vector regression and Gaussian processes for accurately
Energies 2023,16, 1514 23 of 27
predicting the time to reach a specified boundary-condition. This paper introduces the use
of a symbolic-regression method, which enables the possibility of visual inspection of the
provided function and ease of integrating the function into the simulation environment. In
addition, this paper considers the underlying production-process flow in combination with
load curtailment for implicit demand-response.
This paper utilizes agent-based modeling to promote the reusability of the agents
across the domain, similar to [
42
]. As shown in the sequence diagram presented in Figure 2,
the agent communication follows an event-driven observer pattern. Through the generic-
agent interfaces, the agent behavior in response to, e.g., the refrigeration cooling-load, can
be altered to utilize other methods or customized to the specific case study.
Most previous research applies optimization approaches to address the production
process and energy cost [
29
,
30
,
69
]. However, using optimization alone is challenging for
capturing underlying uncertainties in production processes, verification issues, and long
runtimes [
8
,
34
]. The multi-method-simulation and optimization approach in this paper can
capture underlying uncertainties in production processes and improve the performance of
the energy-flexibility-potential assessment.
9. Conclusions
Process cooling for food production is an energy-intensive industry with complex
interactions and restrictions that complicates the ability to utilize energy flexibility, due to
unforeseen consequences in production. Therefore, methods for assessing the potential flex-
ibility in individual facilities to enable the active participation of process-cooling facilities in
the electricity system are essential but not yet well discussed in the literature. Therefore, this
paper applies multi-method simulation and multi-objective optimization for investigating
energy flexibility in process cooling with a case study of a Danish process-cooling facility
for canned-meat food production.
The multi-method simulation with multi-agent based discrete-event and system
dynamic-simulations have been developed for the canned meat production-flow. The
developed simulation-model is centered around a data-driven approach with the inte-
gration of external-data sources. Furthermore, a simulation architecture is proposed,
and the architecture provides a foundation for simulating production-flows in varying
process-cooling facilities. Several generic agents are designed to interact in the simula-
tion environment. The core agents are a production-environment agent representing the
physical environment within the different rooms; a meat-product agent that was processed
throughout the facility; a process agent which is used to represent the different processes
that the product goes through; and a refrigeration-unit agent to control the cooling load of
the production environments, centrally. Using the developed simulation, multi-objective
optimization was used to select a refrigeration-unit load schedule to minimize overall
electricity cost and CO2emissions.
Three scenarios are designed and tested in the paper. The baseline scenario shows
that the current operation could be captured using the developed agents. Building on
the verified simulation-model, the decoupled operation could be examined for flexibility
potentials using multi-objective optimization. The results show potential for the examined
process-cooling facility to adjust its load based on electricity-market signals, to reduce
the overall electricity cost and CO
2
emissions. For one week (in October 2020), 32% of
electricity costs and 822 kg of CO2can be saved.
Furthermore, this paper proposes a domain-specific multi-method simulation and
optimization approach for accessing energy-flexibility potential in industrial processes.
The application to the process-cooling industry shows that this approach can not only
decode the uncertainties in production processes, but also provide a holistic perspective on
energy-flexibility potential. A simulation library is developed, and is able to represent a
generic production-flow of the canned-food process cooling. This library allows building
case-based simulations with pre-built facility components. Furthermore, various external
Energies 2023,16, 1514 24 of 27
factors, e.g., changed weather conditions, external electricity-market signals, etc., are also
included in the library.
The food-process-cooling industry can use the proposed method to examine the
energy-flexibility potential in the production-flows, ensuring the energy flexibility does
not compromise the quality or food-safety requirements. Furthermore, the multi-method
simulation and optimization can be modified to represent multiple facilities for examining
the flexibility potential across an entire electricity end-user segment. Moreover, the method
can be used by the distribution- and transmission-system operators to identify flexible and
available loads within their electricity system.
This paper only considers implicit demand-response as a means of energy flexibility,
due to the increased resistance towards explicit demand-response in the industry, due to
the potential loss of control. The economic potential in explicit demand-response may be
higher and recommended for examination in future research. Furthermore, the seasonal
variance might influence the maximum curtailment in the facility, but only one week’s data
is obtained in this paper. Therefore, a longer period should be examined to obtain a holistic
understanding of the energy-flexibility potential. Furthermore, it would be beneficial
to implement a sensitivity analysis to examine the impact of different cooling systems.
Moreover, the general agent-based production-process flow could be extended to other food
industries, e.g., breweries, to examine if any flexibility potential could be available during
the food-processing stages. Furthermore, machine-learning methods might be useful for
improving agent behaviors; the temperature development especially within the rooms
could be improved. The optimization could be improved by expanding the optimization
criteria to consider health and quality indicators, as well as additional key performance-
indicators in the food industry. Lastly, the analysis should be extended to consider the
entire supply chain, considering all stages for the manufacturers and consumers.
Author Contributions:
Conceptualization, Z.M. and B.N.J.; methodology, D.A.H.; software, D.A.H.;
validation, D.A.H., Z.M. and B.N.J.; formal analysis, D.A.H.; investigation, D.A.H.; resources, B.N.J.;
data curation, D.A.H.; writing—original draft preparation, D.A.H.; writing—review and editing,
D.A.H., Z.M. and B.N.J.; visualization, D.A.H.; supervision, Z.M. and B.N.J.; project administration,
Z.M. and B.N.J.; funding acquisition, Z.M. and B.N.J. All authors have read and agreed to the
published version of the manuscript.
Funding:
This paper is part of the IEA-IETS Annex XVIII: Digitization, artificial intelligence and
related technologies for energy efficiency and reduction of greenhouse gas emissions in industry
project, funded by EUDP (project number: 134-21010).
Data Availability Statement:
Restrictions apply to the availability of these data. Data were obtained
from Danish Crown and are available from the authors with the permission of Danish Crown.
Acknowledgments:
The authors would like to thank the project partners for providing data
and information.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. International Energy Agency. Tracking Industry 2021; IEA: Paris, France, 2021.
2.
Khan, I. Importance of GHG emissions assessment in the electricity grid expansion towards a low-carbon future: A time-varying
carbon intensity approach. J. Clean. Prod. 2018,196, 1587–1599. [CrossRef]
3.
Energianalyse, E. Kortlægning af Potentialet for Fleksibelt Elforbrug i Industri, Handel og Service. 2011. Available online:
https://www.ea-energianalyse.dk/da/projekter/1128-kortlaegning-af-potentialet-for-fleksibelt-elforbrug-i-industri-handel-
og-service/ (accessed on 31 January 2023).
4.
Energistyrelsen. Kortlægning af Energiforbrug i Virksomheder. 2015. Available online: https://ens.dk/sites/ens.dk/files/
Energibesparelser/kortlaegning_af_energiforbrug_i_virksomheder.pdf (accessed on 31 January 2023).
5.
Lashmar, N.; Wade, B.; Molyneaux, L.; Ashworth, P. Motivations, barriers, and enablers for demand response programs: A
commercial and industrial consumer perspective. Energy Res. Soc. Sci. 2022,90, 102667. [CrossRef]
Energies 2023,16, 1514 25 of 27
6.
McKane, A.; Piette, M.; Faulkner, D.; Ghatikar, R.; Radspieler, A., Jr.; Adesola, B.; Murtishaw, S.; Kiliccote, S. Opportunities,
Barriers and Actions for Industrial Demand Response in California. 2008. Available online: https://eta-publications.lbl.gov/
sites/default/files/lbnl-1335e.pdf (accessed on 31 January 2023).
7.
Perno, M.; Hvam, L.; Haug, A. Implementation of digital twins in the process industry: A systematic literature review of enablers
and barriers. Comput. Ind. 2022,134, 103558. [CrossRef]
8.
Howard, D.A.; Ma, Z.; Jørgensen, B.N. Evaluation of Industrial Energy Flexibility Potential: A Scoping Review. In Proceedings of
the 2021 22nd IEEE International Conference on Industrial Technology (ICIT), Valencia, Spain, 10–12 March 2021; pp. 1074–1079.
9. Müller, T.; Möst, D. Demand Response Potential: Available when Needed? Energy Policy 2018,115, 181–198. [CrossRef]
10.
Energistyrelsen. Energistatistik 2020. 2020. Available online: https://ens.dk/sites/ens.dk/files/Statistik/energy_statistics_2020
.pdf (accessed on 31 January 2023).
11.
Petersen, T. Afrapportering af “Fleksibelt Elforbrug”. 2012. Available online: https://www.teknologisk.dk/_/media/49776_
FlexEl-slutrapport.pdf (accessed on 31 January 2023).
12.
Coalition, S.E.D. Explicit and Implicit Demand-Side Flexibility; Smart Energy Demand Coalition: Brussels, Belgium, 2016; Available
online: https://www.smarten.eu/wp-content/uploads/2016/09/SEDC-Position-paper-Explicit-and- Implicit-DR-September-
2016.pdf (accessed on 31 January 2023).
13.
Ramirez, C.; Patel, M.; Blok, K. How much energy to process one pound of meat? A comparison of energy use and specific energy
consumption in the meat industry of four European countries. Energy 2006,31, 2047–2063. [CrossRef]
14.
Khabdullin, A.; Khabdullina, Z.; Khabdullin, A.; Khabdullina, G.; Lauka, D.; Blumberga, D. Analysis of Industrial Electricity
Consumption Flexibility. Assessment of Saving Potential in Latvia and Kazakhstan. Energy Procedia
2017
,113, 450–453. [CrossRef]
15.
Alcazar-Ortega, M.; Escrivá, G.; Alvarez, C.; Domijan, A. Active Demand Response Strategies to Improve Energy Efficiency in
the Meat Industry. 2011. Available online: https://ep.liu.se/en/conference-article.aspx?series=ecp&issue=57&Article_No=30
(accessed on 31 January 2023).
16.
Akerma, M.; Hoang, H.-M.; Leducq, D.; Delahaye, A. Experimental characterization of demand response in a refrigerated cold
room. Int. J. Refrig. 2020,113, 256–265. [CrossRef]
17.
Alcázar-Ortega, M.; Álvarez-Bel, C.; Domijan, A.; Escrivá-Escrivá, G. Economic and environmental evaluation of customers’
flexibility participating in operation markets: Application to the meat industry. Energy 2012,41, 368–379. [CrossRef]
18.
Naegler, T.; Simon, S. Potential for residual load balancing of a frozen food manufacturing plant—A heuristic approach. Sustain.
Energy Technol. Assess. 2018,28, 43–53. [CrossRef]
19.
Mohammad, N.; Rahman, A. Transactive control of industrial heating–ventilation–air-conditioning units in cold-storage ware-
houses for demand response. Sustain. Energy Grids Netw. 2019,18, 100201. [CrossRef]
20.
Fatras, N.; Ma, Z.; Jørgensen, B.N. Process-to-market matrix mapping: A multi-criteria evaluation framework for industrial
processes’ electricity market participation feasibility. Appl. Energy 2022,313, 118829. [CrossRef]
21.
Westberg, B.; Machalek, D.; Denton, S.; Sellers, D.; Powell, K. Proactive Automation of a Batch Manufacturer in a Smart Grid
Environment. 2019, Volume 2. Available online: https://www.researchgate.net/publication/325791155_Proactive_Automation_
of_a_Batch_Manufacturer_in_a_Smart_Grid_Environment (accessed on 31 January 2023).
22.
Gladis, S.P. Slurry Ice Thermal Energy Storage for Cheese Process Cooling. 1997, pp. 725–729. Available online: http://www.
icesynergy.com/L3-8-PDFlibrary/Ice- SlurryTES-Cheese.pdf (accessed on 31 January 2023).
23.
Brown, D.R. Site-Specific Investigations of Aquifer Thermal Energy Storage for Space and Process Cooling. In Proceedings of the
Intersociety Energy Conversion Engineering Conference, Boston, MA, USA, 4–9 August 1991; pp. 155–160.
24.
Rahnama, S.; Green, T.; Lyhne, C.H.; Bendtsen, J.D. Industrial Demand Management Providing Ancillary Services to the
Distribution Grid: Experimental Verification. IEEE Trans. Control. Syst. Technol. 2017,25, 485–495. [CrossRef]
25.
Pedersen, R.; Schwensen, J.; Biegel, B.; Green, T.; Stoustrup, J. Improving Demand Response Potential of a Supermarket
Refrigeration System: A Food Temperature Estimation Approach. IEEE Trans. Control. Syst. Technol.
2017
,25, 855–863. [CrossRef]
26.
Hovgaard, T.G.; Larsen, L.F.S.; Skovrup, M.J.; Jørgensen, J.B. Optimal energy consumption in refrigeration systems-modelling
and non-convex optimisation. Can. J. Chem. Eng. 2012,90, 1426–1433. [CrossRef]
27. Hovgaard, T.G.; Larsen, L.F.S.; Edlund, K.; Jørgensen, J.B. Model predictive control technologies for efficient and flexible power
consumption in refrigeration systems. Energy 2012,44, 105–116. [CrossRef]
28.
Gormley, R.; Walshe, T.; Hussey, K.; Butler, F. The Effect of Fluctuating vs. Constant Frozen Storage Temperature Regimes on
Some Quality Parameters of Selected Food Products. LWT Food Sci. Technol. 2002,35, 190–200. [CrossRef]
29.
Almena, A.; Goode, K.R.; Bakalis, S.; Fryer, P.J.; Lopez-Quiroga, E. Optimising food dehydration processes: Energy-efficient
drum-dryer operation. Energy Procedia 2019,161, 174–181. [CrossRef]
30.
Angizeh, F.; Montero, H.; Vedpathak, A.; Parvania, M. Optimal production scheduling for smart manufacturers with application
to food production planning. Comput. Electr. Eng. 2020,84, 106609. [CrossRef]
31.
Kapoor, K.; Powell, K.; Cole, W.; Kim, J.; Edgar, T. Improved Large-Scale Process Cooling Operation through Energy Optimization.
Processes 2013,1, 312–329. [CrossRef]
32.
Campos, G.; Liu, Y.; El-Farra, N.H.; Palazoglu, A. Optimal Day-Ahead Load Curtailment for Central Chiller Plants. In Computer
Aided Chemical Engineering; Elsevier: Amsterdam, The Netherlands, 2021; Volume 50, pp. 1809–1814.
33.
Shan, K.; Wang, S.; Zhuang, C. Controlling a large constant speed centrifugal chiller to provide grid frequency regulation: A
validation based on onsite tests. Appl. Energy 2021,300, 117359. [CrossRef]
Energies 2023,16, 1514 26 of 27
34.
Bank, L.; Rösch, M.; Unterberger, E.; Roth, S.; Rohrer, A.; Köberlein, J.; Braunreuther, S.; Schilp, J. Comparison of Simulation-based
and Optimization-based Energy Flexible Production Planning. Procedia CIRP 2019,81, 294–299. [CrossRef]
35.
Yang, Q.; Gruenbacher, D.; Heier Stamm, J.L.; Brase, G.L.; DeLoach, S.A.; Amrine, D.E.; Scoglio, C. Developing an agent-based
model to simulate the beef cattle production and transportation in southwest Kansas. Phys. A Stat. Mech. Its Appl.
2019
,
526, 120856. [CrossRef]
36.
Paape, N.; van Eekelen, J.A.W.M.; Reniers, M.A. Design of meat processing systems with agent-based production control.
IFAC-PapersOnLine 2021,54, 1112–1117. [CrossRef]
37.
Howard, D.; Ma, Z.; Engvang, J.; Hagenau, M.; Jørgensen, K.; Olesen, J.; Jørgensen, B. Optimization of Energy Flexibility in
Cooling Process for Brewery Fermentation with Multi-Agent Simulation. In 6th IEEJ International Workshop on Sensing, Actuation,
Motion Control, and Optimization; Shibaura Institute of Technology: Tokyo, Japan, 2020.
38.
Hübl, A.; Altendorfer, K.; Jodlbauer, H.; Gansterer, M.; Hartl, R. Flexible Model for Analyzing Production Systems with Discrete Event
Simulation; IEEE: New York, NY, USA, 2011.
39.
Cipollone, R.; Villante, C. A System Approach to Mathematical Modeling of Cooling System Dynamics. 2003. Available
online: https://www.researchgate.net/publication/235248931_A_system_approach_to_mathematical_modeling_of_cooling_
system_dynamics (accessed on 31 January 2023).
40.
Ma, Z.; Schultz, M.; Christensen, K.; Værbak, M.; Demazeau, Y.; Jørgensen, B. The Application of Ontologies in Multi-Agent
Systems in the Energy Sector: A Scoping Review. Energies 2019,12, 3200. [CrossRef]
41.
Vrabiˇc, R.; Erkoyuncu, J.A.; Farsi, M.; Ariansyah, D. An intelligent agent-based architecture for resilient digital twins in
manufacturing. CIRP Ann. 2021,70, 349–352. [CrossRef]
42.
Værbak, M.; Ma, Z.; Demazeau, Y.; Jørgensen, B.N. A generic agent-based framework for modeling business ecosystems: A case
study of electric vehicle home charging. Energy Inform. 2021,4, 28. [CrossRef]
43.
Christensen, K.; Ma, Z.; Demazeau, Y.; Jørgensen, B. Agent-Based Modeling for Optimizing CO
2
Reduction in Commercial Greenhouse
Production with the Implicit Demand Response; IEEJ: Tokyo, Japan, 2020.
44.
Diekerhof, M.; Hecker, S.; Monti, A. Modeling and Optimization of Industrial Compressed-Air Energy Systems for Demand Response;
IEEE: New York, NY, USA, 2016; pp. 1–6.
45.
Laguna, M. OptQuest Optimization of Complex Systems. 2011. Available online: https://opttek.com/sites/default/files/pdfs/
OptQuest-Optimization%20of%20Complex%20Systems.pdf (accessed on 31 January 2023).
46.
Abakarov, A.; Sushkov, Y.; Mascheroni, R.H. A multi-criteria optimization and decision-making approach for improvement of
food engineering processes. Int. J. Food Stud. 2013,2, 1–21. [CrossRef]
47.
Madoumier, M.; Trystram, G.; Sébastian, P.; Collignan, A. Towards a holistic approach for multi-objective optimization of food
processes: A critical review. Trends Food Sci. Technol. 2019,86, 1–15. [CrossRef]
48.
Jafferali, M.; Venkateshwaran, J.; Son, Y.-J. Performance comparison of search-based simulation optimisation algorithms for
operations scheduling. Int. J. Simul. Process Model. 2005,1, 58. [CrossRef]
49.
Eskandari, H.; Mahmoodi, E.; Fallah, H.; Geiger, C. Performance Analysis of Commercial Simulation-based Optimization
Packages: OptQuest and Wittness Optimizer. In Proceeding of the Winter Simulation Conference, Phoenix, AZ, USA, 11–14
December 2011; pp. 2358–2368.
50.
ORMS Today 2021 Simulation Software Survey Results. Available online: https://pubsonline.informs.org/magazine/orms-
today/2021-simulation-software-survey (accessed on 17 January 2023).
51.
Herten, J.V.D.; Depuydt, F.; Baets, L.D.; Deschrijver, D.; Strobbe, M.; Develder, C.; Dhaene, T.; Bruneliere, R.; Rombouts, J.
Energy flexibility assessment of an industrial coldstore process. In Proceedings of the 2016 IEEE International Energy Conference
(ENERGYCON), Bremen, Germany, 4–8 April 2016; pp. 1–6.
52. Cengel, Y.A. Heat and Mass Transfer: A Practical Approach, 3rd ed.; McGraw-Hill: Blacklick, OH, USA, 2006.
53.
Sweat, V.E. Thermal Properties of Food. 2006. Available online: https://www.cae.tntech.edu/~{}jbiernacki/CHE%204410%20201
6/Thermal%20Properties%20of%20Foods.pdf (accessed on 31 January 2023).
54.
Tuan Pham, Q.; Trujillo, F.J.; Davey, L.M.; McPhail, N. Cooling curves for the preliminary design of beef chillers. Int. J. Refrig.
2009,32, 1944–1953. [CrossRef]
55.
EUR-Lex Regulation (EC) No 853/2004 of the European Parliament and of the Council of 29 April 2004 Laying Down Specific
Hygiene Rules for Food of Animal Origin. Available online: http://data.europa.eu/eli/reg/2004/853/2022-12-08 (accessed on
16 January 2023).
56.
Radford, R.D.; Herbert, L.S.; Lovett, D.A. Chilling of meat—A mathematical model for heat and mass transfer. In Proceedings of
the Joint Meeting of Commissions C2, D1, D2, D3 & E1, International Institute of Refrigeration, Australian National Committee,
Melbourne, VIC, Australia, 6–10 September 1976; p. 8.
57.
Mridula, M.R.; Nair, A.S.; Kumar, K.S. Genetic programming based models in plant tissue culture: An addendum to traditional
statistical approach. PLoS Comput. Biol. 2018,14, e1005976. [CrossRef]
58.
Kantor, D.; Zuben, F.J.V.; Franca, F.O.D. Simulated annealing for symbolic regression. In Proceedings of the Genetic and
Evolutionary Computation Conference, Online, 10–14 July 2021; Association for Computing Machinery: Lille, France, 2021;
pp. 592–599.
59.
Ashok, D.; Scott, J.; Wetzel, S.J.; Panju, M.; Ganesh, V. Logic Guided Genetic Algorithms. In Proceedings of the AAAI Conference
on Artificial Intelligence, New York, NY, USA, 7–12 February 2020.
Energies 2023,16, 1514 27 of 27
60.
Haldar, A.; Mahadevan, S. Probability, Reliability, and Statistical Methods in Engineering Design, 1st ed.; Wiley: Hoboken, NJ,
USA, 1999.
61.
Energinet; Energidataportal. Available online: https://energinet.dk/El/Data-om-energisystemet/EnergiDataPortal (accessed on
14 December 2022).
62.
von Hayn, A.; Moske, J.; Aselmann, P.; Weigold, M. Demand side management in the cooling supply of brewing processes.
Procedia CIRP 2022,105, 146–151. [CrossRef]
63.
Schulze, C.; Plank, M.; Linzbach, J.; Herrmann, C.; Thiede, S. Energy flexible management of industrial technical building services:
A synergetic data-driven and simulation approach for cooling towers. Procedia CIRP 2019,81, 775–780. [CrossRef]
64.
Ministry of Finance Regeringen Indgår Bred Aftale om en Ambitiøs Grøn Skattereform. Available online: https://fm.dk/
nyheder/nyhedsarkiv/2022/juni/regeringen-indgaar-bred-aftale-om- en-ambitioes-groen-skattereform/#:~{}:text=ton%20
udledt%20CO2%20i%202030,i%202030%20for%20virksomheder%20indenfor (accessed on 29 November 2022).
65.
Ding, D. The impacts of carbon pricing on the electricity market in Japan. In Humanities and Social Sciences Communications;
Nature: London, UK, 2022; p. 9.
66.
Stoll, P.; Brandt, N.; Nordström, L. Including dynamic CO
2
intensity with demand response. Energy Policy
2014
,65, 490–500.
[CrossRef]
67.
Hoang, H.M.; Akerma, M.; Mellouli, N.; Montagner, A.L.; Leducq, D.; Delahaye, A. Development of deep learning artificial
neural networks models to predict temperature and power demand variation for demand response application in cold storage.
Int. J. Refrig. 2021,131, 857–873. [CrossRef]
68.
O’Neill, Z.; Narayanan, S. Model-based estimation of cold room temperatures in a supermarket refrigeration system. Appl. Therm.
Eng. 2014,73, 819–830. [CrossRef]
69.
Gong, X.; Liu, Y.; Lohse, N.; De Pessemier, T.; Martens, L.; Joseph, W. Energy-and Labor-Aware Production Scheduling for
Industrial Demand Response Using Adaptive Multiobjective Memetic Algorithm. IEEE Trans. Ind. Inform.
2019
,15, 942–953.
[CrossRef]
Disclaimer/Publisher’s Note:
The statements, opinions and data contained in all publications are solely those of the individual
author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to
people or property resulting from any ideas, methods, instructions or products referred to in the content.
