Socio-Economic Planning Sciences xxx (2016) 1e21
Contents lists available at ScienceDirect
Socio-Economic Planning Sciences
journal homepage: www.elsevier.com/locate/seps
An agent-based modeling optimization approach for understanding
behavior of engineered complex adaptive systems
Moeed Haghnevis a, *, Ronald G. Askin a, Dieter Armbruster b
a
b
School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ 85287-8809, USA
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 February 2015
Received in revised form
17 April 2016
Accepted 19 April 2016
Available online xxx
The objective of this study is to present a formal agent-based modeling (ABM) platform that enables
managers to predict and partially control patterns of behaviors in certain engineered complex adaptive
systems (ECASs). The approach integrates social networks, social science, complex systems, and diffusion
theory into a consumer-based optimization and agent-based modeling (ABM) platform. Demonstrated
on the U.S. electricity markets, ABM is integrated with normative and subjective decision behavior
recommended by the U.S. Department of Energy (DOE) and Federal Energy Regulatory Commission
(FERC). Furthermore, the modeling and solution methodology address shortcomings in previous ABM
and Transactive Energy (TE) approaches and advances our ability to model and understand ECAS behaviors through computational intelligence. The mathematical approach is a non-convex consumerbased optimization model that is integrated with an ABM in a game environment.
© 2016 Elsevier Ltd. All rights reserved.
Keywords:
Agent-based modeling and simulation
Complex adaptive systems
Non-linear complexity
US electricity markets
Demand response
Transactive energy
1. Introduction and literature review
Today's engineered complex adaptive systems (ECASs) are
composed of many autonomous and heterogeneous components
with myriad interrelationships. ECASs exhibit the inherent behaviors of natural complex adaptive systems (CASs) but are designed
for expressed purposes and include intrinsic design parameters and
operational controls that can influence behavior. Nonetheless,
autonomous agents interact with limited environmental information and without central control [5,76]. ECASs evolve to adapt to
unforeseen dynamic conditions. Their highly dynamic and nonlinear behaviors make them difficult to fully understand and thus
to effectively design, operate, and maintain. The self-organizing
components readjust themselves continuously and emerge new
behaviors through interaction with other components and their
environment. The individual agents adjust their decisions to optimize their objective functions but they may not be fully rational or
knowledgeable and may have latent objectives and influences.
Emergence in behaviors may also result from social network influences. This micro optimized emergence in the lower level causes
* Corresponding author.
E-mail addresses: [email protected] (M. Haghnevis), ron.askin@asu.
edu (R.G. Askin), [email protected] (D. Armbruster).
optimized evolution in the higher level of the system. Our objective
is to develop a descriptive platform and modeling approach that
can be customized to understand the behavior of ECASs. In
particular, we use the U.S. Electricity Markets as a target application
in which complex social dynamics and engineered infrastructure
interact to complicate complete understanding and ability to achieve societal goals.
The U.S. Electricity Markets behave as an ECAS (see Section 1.3
for references). Government and service providers desire to use
price-based incentives to impact demand and achieve efficiency,
reliability and sustainability. Most Demand Response (DR) programs have focused on large industries and business sectors (they
mainly consider passive energy efficiency more than active DR
options). Moving forward there is the potential to utilize smart
technologies to include smaller consumers. Traditional studies
focus on rational choice of economical drivers ignoring behavioral
factors that may determine individual consumer demand elasticity
to financial incentives. The current lack of supporting technology
and knowledge of consumer behavior provide challenges for
developing effective broad price-based DR programs. Challenges
and needs to implement DR in accordance with Federal Energy
Regulatory Commission (FERC) Order 745, March 2011 and Sections
1252(e)/(f) of the US Energy Policy Act of 2005 motivate this
research and are considered in the modeling approach.
http://dx.doi.org/10.1016/j.seps.2016.04.003
0038-0121/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Haghnevis M, et al., An agent-based modeling optimization approach for understanding behavior of
engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
In our study an ECAS evolves on the basis of embedded behavior
rules related to non-convex consumer-based optimization. A
modeling approach is developed for general study of ECASs,
behavioral-based demand response in the US power markets is
used to demonstrate its applicability. Economic incentives motivate
local consumers to adjust their pattern of demand usage. To study
and analyze ECAS Refs. [48,49] defined emergence as “the capability
of components of a system to do something or present a new
behavior in interaction, and dependent to other components that
they are unable to do or present individually”, evolution as “a process of resilience and agility in the whole system”, and adaptation as
“the ability to learn and adjust to a new environment to promote
their survival”. We will explain how to study these hallmarks of
CASs in our agent-based simulation for Demand Response complex
systems. Our research builds upon previous modeling approaches
to resolve weaknesses of the current models (see comprehensive
survey studies for agent-based electricity market models, tools, and
simulation by Refs. [84,94,97]. We employ consumer interoperability in a social layer whereas previous research studied economic
models in a business layer.
The key contributions of this study are:
! Developing a descriptive platform and integrated optimization
and agent based simulation modeling approach that enables
study of ECASs,
! Demonstrated application of the platform and modeling
approach to understanding consumer social interactions in
electricity demand response,
! Guidelines for improving effectiveness of economic incentives
and targeted education in social networks,
! Understanding effects of the social network topologies for
cascading behaviors.
The reminder of Section 1 provides background on electricity
markets and ECASs and discusses the motivations of this study.
Section 2 explains our integrated approach. Properties of the agents
and their decision diagram are defined in Section 3.1. We depict the
layers of the environment in Section 3.2. Section 4.1 details the logic
of agent-based process and presents mathematical equations and
definitions for the agent-based engine. Also, in Section 4.2 all decision variables and rules (defined in the previous sections) are
integrated into an agent-based optimization model. Sections 5 and
6 show the simulation results. We define required variables to run
the model and we analyze different scenarios. Various examples
demonstrate the validity of our method in each section.
1.1. Motivation to study the US power system as an ECAS
The US electricity power system is one of the most complex
systems ever invented [7]. The physical network consists of
approximately 450,000 miles of high voltage lines and 146 Million
ultimate customers [38,39]. Demand (nearly 3725 Billion Kilowatthours (kWh) in 2013) is increasing (expected to increase by 28
percent from 2011 to 2040) requiring capacity expansion, that
along with its spatial-temporal stochasticity, stretches distribution
constraints and impacts electricity markets. Additional features
that motivate examining the US power system as an ECAS include:
! Emerging technologies (e.g. time-based pricing, smart meters,
and home-based solar systems) serve to add a decentralized
consumer-interactive role to the traditionally producercontrolled systems,
! The diversity of people, their interdependencies (human decisions based on other consumers), and their willingness to
cooperate,
! Time dependency of the network topologies [20], and
! Scale-free or single-scale feature of these networks - their node
degree distribution follows a power-law or Gaussian distribution [85].
The US Federal Energy Regulatory Commission (FERC) formed
Independent System Operators (ISOs) and Regional Transmission
Organizations (RTOs) based on the Wholesale Power Market Platform [41] to coordinate, control, and monitor the operations of the
US wholesale electrical systems. These entities manage electricity
generation and transmission across geographic regions and balance
supply and demand. ISOs/RTOs serve two-thirds of electricity
consumers in the US based on Locational Marginal Price (LMP). This
structure increases the complexity of the US wholesale electricity
markets. As an illustration, Fig. 1 provides the LMP contour map of
the Midcontinent Independent System Operators [72]. There is a
huge gap between LMP values for two neighborhoods A and B
(from "40USD in Point A to þ150USD in Point B). This pattern may
change totally in the next 5 min Fig. 2 depicts the LMP maps in
different time intervals on Nov 23, 2015 (Fig. 2(a)e(d) show variation in short time intervals (15 min)).
Demand Response is defined by Ref. [37] as ”changes in electric
usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or
to incentive payments designed to induce lower electricity use at
times of high wholesale market prices or when system reliability is
jeopardized”. Pursuant to the Sections 1252 (e) and (f) of the US
Energy Policy Act of 2005 (EPACT), the U.S. Department of Energy
(DOE) has provided a report to Congress that identifies and quantifies DR benefits and makes recommendations for achieving them.
The report shows that actual peak demand reduction was only
9,000 MW in 2004 while the potential demand response was
20,500 MW [37]. FERC issued Order 745 in 2011 to meet the
Congressional direction and remove barriers to the participation of
DR in organized wholesale electricity markets [42]. A list of questions that DR studies strive to answer includes:
! When (what day) is the best time to trigger a demand response
event?
! What is the event window (start and finish time)?
! How much trigger is required?
! What type of events (rewards, penalties, larger and discrete,
smaller and continuous) are more effective and efficient?
! Who are the event recipients? What is the schedule to receive
their triggers?
! What percent of the recipients may answer to the triggers?
What is their outcome (e.g. total saving)?
Electric power is generated from multiple sources of energy
(coal, hydro, wind, solar, natural gas). Sources vary with respect to
flexibility, startup times and operating costs thus increasing the
complexity of dispatching and pricing electricity. Studies on
behavior of consumers for the PJM Interconnection Regional
Transmission Organization [88] show that small shifts in peak demand would have a large effect on savings (a 1% shift in peak demand would result in savings of $1.27 billion at the system). Largescale social science field experiments by Ref. [11]; academic studies
by Ref. [4]; and testimony by American Council for an EnergyEfficient Economy to Congress [2] suggest that social and behavioral programs can increase the efficiency of load management
programs.
In the current electricity markets, demand response programs
are managed by separate organizations (such as ISOs, utilities,
aggregators, and retailers) that operate almost independently [45].
Due to the amount of new demands and challenges of customer
Please cite this article in press as: Haghnevis M, et al., An agent-based modeling optimization approach for understanding behavior of
engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003
M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
3
Fig. 1. LMP contour map of the Midcontinent ISO.
controls, it is nearly impossible for utilities and independent system operators (ISOs) to manage and monitor the new complex
system [8,89]. Moreover, Prosumers (i.e., consumers who also
produce their own power from a range of different onsite generators) can significantly increase the complexity of the system [8].
Transactive energy (TE) is a relatively new concept (the first TE
conference was held in 2013 in Portland, Oregon) that proposes a
new approach to solve these complexities [1,45,90]. GridWise Architecture Council (GWAC), Transactive Energy Association (TEA),
the Smart Grid Interoperability Panel (SGIP), and Pacific Northwest
National Laboratory (PNNL) have discussed the concepts and
standards of TE [45,69,70,78]. Ref. [45] defines TE as ”A system of
economic and control mechanisms that allows the dynamic balance of supply and demand across the entire electrical infrastructure using value as a key operational parameter”. TE facilitates
collaboration and encourages cooperation between all elements of
the power system. It tries to manage the electric power system via
market-based incentives by taking advantages of two-way communications and intelligent communicating devices [45]. It is not
clear what differentiates TE from smart Grid. While some experts
believe that it just a Smart Grid application [8]; TE is an extension of
the electricity markets to the end-use customers and the next step
in development of demand response” [1]. Moreover, in TE concepts
residential customers will have energy management systems (or a
third party assistance) to make decision and create value [8]. TE
plays a significant integrating role by providing communication
capabilities between demand response programs [45].
Our model enables us to improve the ability of regulators and
consumers to communicate and optimize consumption. We
consider a technology-enabled system with smart meters and appliances where consumers can control their demand at all times in
response to incentives (dynamic pricing). As electricity consumption is inelastic in short time frames, social education mechanisms
are included to increase the effect of economic incentives. Our
reward approach attempts to improve the effectiveness of triggers
to motivate consumers to shift their demand. We show that
combining social drives with economical incentives enables us to
reduce and control the huge gap between potential load management and actual DR. We propose a more complex, less idealized
multi-layered adaptive approach to show influences of combined
social-economical incentives on behavioral-based DR programs.
We seek to understand how to change consumption patterns of
end-users and load aggregators to level demand by providing
economical incentives and exploiting social networks.
1.2. Engineered complex systems and complex adaptive systems
Complex systems are classified by Ref. [67]. Four reports of the
Defense R&D Canada-Valcartier [32e34] and Ref. [35] present a
comprehensive survey to the study of complexity theory, chaos and
complex systems. Mathematical modeling of CASs is fragmented
and inapplicable because engineers and mathematicians focus on
purposes and outcomes while complex systems are strongly characterized by emergence in behaviors of components and evolution
in behaviors of a system. Refs. [13,14] mathematically studied the
structure of complex systems and the interdependence of components. Difficulties in understanding emergence, abstract theoretical
concepts, and incomplete applicable frameworks continue to present challenges in the study of CASs [36]. Despite this Ref. [77]
shows that simple rules between components can describe an
organized agent.
We are concerned with the interplay between the physical
electricity generation and distribution network and the consumer
social network. Ref. [6] studied structural properties of the electric
power grid of Southern California and Ref. [91] considered the
complex network of the New York electric power grid. Ref. [10]
modeled evolutionary structure of population and components in
social networks. Ref. [54] showed emergence of cooperative
behavior by combining social network dynamics and stochastic
learning. We are interested in how external control parameters can
impact the behavior of the autonomous agents in the network and
how that then translates into system behavior. Ref. [61] classified
three developed approaches to mimic human complex decision
behaviors. Refs. [59,60] employed engineering methodologies to
represent such systems in complex environments. Ref. [62]
considered information cascades in large social networks and
investigate a large person-to-person recommendation network.
Ref. [58] discussed probabilistic and game-theoretic models for
flow of information or influence through social networks. Our study
discusses the complex structure and behavior of a human decision
Please cite this article in press as: Haghnevis M, et al., An agent-based modeling optimization approach for understanding behavior of
engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
Fig. 2. Variation of LMP map of Midcontinent ISO by time.
network itself and how components cooperate as a result of their
connections through a network and in relationship with their
environment. We include human decision making and show how
our proposed framework encapsulates the previous models.
1.3. Agent-based modeling of engineered complex adaptive systems
Usually, game theoretical modelers only consider a limited
number of components with often unrealistic assumptions. Traditional equilibrium models disregard strategic behaviors and
learning of components [94]. Weaknesses of traditional modeling
methods make agent-based modeling and simulation useful tools
to study and analyze systems that exhibit emergent phenomena,
nonlinear dynamics, and path-dependent behavior [27,65,66,86].
Recently, ABMs have been used to study the impact of new
electricity technologies. Ref. [51] consider performance of a new
technology versus an old technology and study the effects of a
specific spatial externality (fashion effect). They analyzed the dynamics of technology diffusion among bounded rational agents
with uncertainty by using ABM. An ABM for a market game is
presented by Ref. [96] to evaluate the effects of government strategies on promoting new electricity technologies in complex
systems involving human behavior. Ref. [9] used ABM to control
consumer demands by supporting interaction between consumers
in a diffusion mechanism. In another approach, advantages and
disadvantages of optimization models and ABM for technological
change in different energy systems is compared in Ref. [64].
The impact of the structure of a social network on the spread of
innovations has been an actively researched issue. Ref. [73]
considered competing alternatives when an agent adapts to a
new behavior based on its neighbors. In their model the payoff for
agents increases with the number of neighbors who adopt the same
choice. Ref. [47] used dynamic pricing in modeling diffusion of innovations in a social network. Ref. [18] analyzed network topologies and communication links between innovator and follower
market segments in the diffusion process. Ref. [80] compared
agent-based and differential equation models and analyzed the
effect of individual heterogeneity and network topologies in the
dynamics of diffusion. Refs. [56,57] studied spread of an innovation
or behavior based on word-of-mouth recommendations in social
networks.
Agent-based modeling of complex adaptive electricity systems
has been attempted by several countries and US national laboratories. Refs. [22e26] analyzed market power and price-formation of
Please cite this article in press as: Haghnevis M, et al., An agent-based modeling optimization approach for understanding behavior of
engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003
M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
utilities and generators in the UK. Ref. [12] created a multi-agent
model for the UK electricity generation market. In Germany Ref.
[19] studied bidding strategies, and an agent-based German electricity market is presented by Ref. [83]. Refs. [46] and [28] presented an agent-based model for the complex adaptive system of
interactions between human behaviors in markets, infrastructures
and environment of Australia's national electricity market by using
the National Electricity Market Simulator (NEMSIM). In the US, the
Agent-Based Modeling of Electricity Systems (AMES) is designed
for computational study of wholesale power market [63,92].
Argonne National Laboratory developed the Electricity Market
Complex Adaptive System (EMCAS) to analyze the possible impacts
on the power system of various events [31,75]. Sandia National
Laboratories presented the Aspen-EE (Electricity Enhancement) to
simulate the effects of market decisions in the electric system on
critical infrastructures of the US economy [16]. Honeywell Technology Center (HTC) constructed the Simulator for Electric Power
Industry Agents (SEPIA) [95]. Pacific Northwest National Laboratory
also studied power systems as complex adaptive systems [29].
These studies however have not considered social interactions or
subjective behavior of consumers.
2. Multi-layered integrated approach
We propose a methodology that advances our ability to model
and understand engineered complex adaptive system behaviors
through computational intelligence. The development of this
methodology has significant intrinsic merit as it will explore
fundamental issues in multi-layered ECASs and presents new
optimization actions. This ABM presents a platform and toolkit that
creates a dynamic laboratory to study properties and behavior of
consumer social interactions in the US Electricity Market demand
response (DR) as an ECAS. This paper does not propose a specific
power system platform for DR but studies the social interaction
effects of complex adaptive consumers in electricity usage patterns.
The concept of DR is used to define a value mechanism in the multiobjective optimization model and justify incentive/reward
5
functions for agents to cooperate and change their behavior. We
acknowledge that the modeling framework in this paper provides a
first step. The goal of this paper is to provide a framework rather
than a specific solution for any particular grid. Undoubtedly operators would need to consider their constraints in setting the incentives. Our framework provides a mechanism for those operators
to model the DR of a set of proposed incentives.
We integrate concepts from social networks (e.g. friendship,
scale-free and single-scale networks), social science (e.g. opinion
exchange, media impact, and irrationality), complexity theory (e.g
emergent behavior and adaptation), diffusion theory (e.g. adaptability and innovativeness), and decision theory (e.g. utility) to
build our comprehensive ABM. This model enables us to integrate
optimization rules and build a comprehensive social layer to
analyze and simulate details of social behaviors in ECASs. We justify
our model by illustrating its applicability on the US power system.
In this study, a multi-layer descriptive modeling approach
(Fig. 3) composed of conceptual behavior and fundamental entity
aspects is considered as the whole system structure. This approach
integrates layers by cross-layer effects, effect of stochastic events
(e.g. system failure and extreme weather condition), and rules of
standards and procedures. Usually, physical layer(s) model networks, their characteristics, and physical components [50]. In this
layer effects of topology and structure of networks have been
studied in the past by Refs. [18,47,73]. Decision/control layer(s)
represent different business strategies, optimization models and
rules for decision makers (e.g. regulators). Those models are used
for short-term, mid-term, or long-term analysis. Previous modeling
approaches such as AMES [63,92] are useful for modeling behaviors
of this layer. Some models (e.g. EMCAS by Ref. [31] presents a more
comprehensive view on different layers.
The GridWise Transactive Energy framework [45] depicts three
layers of interoperability: physical (or cyber-physical) at the lower
levels, information interoperability in the mid-levels, and business
models (market structures, regulation, and policy) in the upperlevels. One of the significant principles of Transactive Energy systems is to implement some form of highly coordinated self-
Fig. 3. Integration of the structural entity model.
Please cite this article in press as: Haghnevis M, et al., An agent-based modeling optimization approach for understanding behavior of
engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
optimization [45]. Our proposed framework goes further than the
current TE and other ABM studies as follows:
1. The TE framework suggests a likelihood of increasing interactions as social networks [45], but it does not define a social
network in the TE framework. This paper considers the interactions between agents via a social network,
2. One of the most important TE challenges is to move from current centralized control systems to more distributed systems.
”Distributed computing or control exists when the decentralized elements (that independently operate) explicitly cooperate
to solve a common problem” [45]. This study proposes a
mathematical model to examine the imputed cooperation of
agents,
3. We need multi-objective optimizations to align the TE value
discovery mechanism (an attribute of TE that stablishes the
economic or engineering value) of utilities, customers, and other
operators [45]. In this study, a value-based optimization model
is implemented to examine the cooperation, satisfaction,
desirability, and other properties of the system components,
4. In TE concept, a free flow of information between parties allows
them to enter into exchanges. In this concept Interoperability
(an attribute of TE) is defined as enabled transaction through the
exchange of information between transacting parties [8]. This
study applies an explicit mathematical method to measure the
interoperability and interrelationships,
5. Assigning value to the normal residential customers is tricky.
Their values are usually defined through their choices and based
on qualitative measures such as value comfort and satisfaction.
In this study, the proposed dissatisfaction concept enables us to
calculate and incorporate the non-economic aspects of values to
the model.
In this study, Social/Swarm Layers(s) include the interrelationship between agents and their effects on each other. Also behavioral
properties and attributes of decision makers are considered in this
layer (see Section 3.2).
To show cascading of decisions from Decision/Control Layer(s)
to Physical Layer(s), we detail the Social/Swarm Layer(s). This
integration helps us depict emergence in behavioral patterns in the
lower level of the system and their effects on evolution in the
higher levels (e.g. predict the result of dynamic pricing and prizes in
future). Moreover, we formulate a consumer-based optimization
model and integrate it with the agent-based model. Then we
include effects of externalities and subjective behaviors in the integrated agent-based optimization model. We study the effect
strategies have on the decision/control and social/swarm layers.
Useful managerial insights are derived from executing the model.
Electricity regulators adjust service attributes (e.g. price and
reward functions) in response to demand fluctuations to motivate
the consumer agent to cooperate in balancing workload. Consumer
agents make decisions to maximize their quantitative and qualitative utilities. They change consumption patterns in response to
incentives and to social education provided by the regulators. Based
on the individual and total patterns of the electricity consumption,
agents may receive individual and cooperation rewards. Moreover,
they may have dissatisfaction to change their behavior (Section 4.1
presents details for calculating utilities, rewards, and dissatisfaction). We study cooperativeness or competition in the consumers
game environment by embedding a non-convex consumer-based
optimization model with the agent-based simulation (see Section
4.2). We study the behavior of consumers under different control
and incentive strategies. Then, we include intrinsic environment
and control factors to the model dynamics.
Instead of reducing nonlinear systems to a set of causal variables
and error terms, our ABM shows how complex adaptive outcomes
flow from simple phenomena and depend on the way that agents
are interconnected. Rather than aggregating outcomes to find a
total equilibrium, our ABM presents the evolution of outcomes as
the result of the efforts of agents to achieve better fitness. This
method allows the study and analysis of the complexities arising
from individual actions and interactions that exist in the real world
by bottom-up iterative design methodologies. Applying this integrated agent-based optimization model has the following benefits
for the US power system and may lead to a reduction in investment
on the power grid infrastructure:
! Motivates consumers to balance the total workload by providing
incentives and social education,
! Encourages agents to cooperate with the grid regulators in high
stress times and environments by communicating energy
information,
! Increases the grid's security and reliability by analyzing its
behavior during accidents or system faults,
! Allows studying complex system response to dynamic pricing
and other control strategies,
! Predicts and controls emergent behavior of the agents and
system evolution by mathematical modeling in respect to economic incentives and social interactions.
3. Agent-based structure
This section presents an overview of agents' properties and their
environment. We present more details and mathematical modeling
of the framework in Section 4. Outcomes of running the simulation
are discussed in Section 5.
3.1. Decision makers/agents
1- Pattern of Consumption: Consider System m (e.g. a power
system) comprised of a large number of components (e.g. consumer agents). We study the individual electricity consumption
C(w) of these agents which changes dynamically during a period of
length w0. For example, C(w),0 $ w $ 24, is the profile of daily
consumptions when w0 ¼ 24 hours. We assume there are q,
q ¼ 1,…,T equal discrete periods and that Cq(w) may differ at each
period. As an illustration, to show consumption of electricity for a
year, w covers the 24 h of consumption at each day while
q ¼ 1,…,365. Behaviors of components are grouped into classes
based on similar consumption pattern. Assume there are n defined
classes of patterns and each component follows one pattern at
period q. We use Xiq ; i ¼ 1; …; n to show the number of components
P q
that follow class i. Here, Q q ¼
Xi is the total number of compoi C q ðwÞ presents a profile of daily
nents in the system at period q.
i
consumption at period q for consumer that follows pattern i (Ciq ðwÞ
is the consumption of electricity at time w for pattern i in period q).
2- Properties of Agents: Agents have the capability to present
new behaviors by interaction and dependent to other agents. They
can switch to new patterns and change their attributes based on
their current properties and neighborhood relationships. We
represent the influence on an agent from another agent by interoperability (will be defined mathematically in the next section). We
initiate a social network of consumer agents where Xi(0) is the
initial size of the population for each pattern and the population of
each pattern (Xi;i ¼ 1,…,n) can grow with growth rate, bi, exponentially. Agents may switch from one pattern to another based on
the attributes of the patterns (namely; price, convenience, and
glamour) or through influences of these in their social network.
Price defines the total cost of consumption in a 24 h cycle time for
Please cite this article in press as: Haghnevis M, et al., An agent-based modeling optimization approach for understanding behavior of
engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
the related pattern. Convenience shows how fast and easy consumers can make a decision to switch to this pattern. Glamour
shows the effects of advertisement or other fashion attributes of the
patterns. These micro interrelationships make new networks and
update the structure of the population in the macro level of the
system.
2- Influences on Agent Decisions: Fig. 4 shows how agents are
influenced in the system. Ovals present uncertain variables. Rectangles show the variables that the agents have the power to modify
or select. Hexagons are measurable outcomes. Arcs denote direct
influences. Dashed arcs indicate there are some influences; however, the values can be calculated from other variables with direct
influences. Agents consume electricity based on the environment
conditions (e.g. seasonal weather conditions and time of the day)
and consumption attributes (e.g. price of electricity consumption
and advertisements). This consumption shapes their pattern of
P
behaviors. The entropy of the system, E ¼ " Pi log2 Pi , is defined
by the frequency of these patterns and the interrelationships between the agents (i.e. emergent behavior of agents, interoperabilities, and willingness to effect or follow each other). This
entropy of the patterns in a system, yields the dis-uniformity (Eq.
(4)) of the whole system. Cooperation reward (Eq. (15)) can be
measured based on the regulator's decisions. Consumers measure
their profit (Eq. (14)) on the bases of the cooperation reward, their
individual rewards, their dissatisfaction, and qualitative utilities.
Individual rewards (Eq. (16)) and dissatisfaction (Eq. (17)) are
calculated based on the patterns of individual behavior. Qualitative
utilities (Eq. (13)) are functions of the consumption attributes. This
total profit leads agents to change their consumption in the cooperative game model to adapt to the new environment.
We can characterize the agents as follows (they will be discussed and defined by details in the next sections):
! Each agent runs a pattern that has three attributes (price, convenience, and glamour),
! Agents connect to each other based on a complex network,
! An agent has desirability coefficients and importance weights
for each attribute,
Consump on
a ributes
Regulator’s
decisions
Qualita ve
values
Interoperability
between the agents
! Agents belong to interoperability classes based on their node
degrees,
! An agent (partially or fully) optimizes its profits based on optimization rules in cooperation with other agents,
3.2. Environment/patches
Fig. 5(a)e(c) present an overview of a three-layer image of our
modeling study. The Decision/Control Layer (Fig. 5(a)) includes
strategies (e.g. dynamic pricing), optimizing (e.g. maximum profits
and peak reduction), plans (e.g. new generators), investments
(transmission and distribution infrastructure), and information
sharing (e.g. communicate energy information). In the US energy
system Independent System Operators (ISOs) and Regional Transmission Organizations (RTOs) work in this layer of the complex
system.
The Social/Swarm Layer (Fig. 5(b)) considers interrelationships
between agents and preferences. We can consider bounded rationality for agents and externalities (e.g. fashion effects) in this layer.
Non-physical attributes of agents (e.g. glamour) and their utility
function can be studied and analyzed here. We will discuss how the
behavior of agents as a group emerges in this layer and converges to
a steady pattern. Learning algorithms (e.g. reinforcement learning)
and adaptation scenarios can be considered in this layer.
The Physical Layer (Fig. 5(c)) includes features, mechanism of
components of the system, and their physical network. In the energy system example this layer includes generators (e.g. main power plant, wind forms, solar panels, and small generators),
distributors and transmission, and consumers (e.g. homes, businesses, and industries). The topology of networks is considered in
this layer.
This paper focuses on the social layer and does not focus on a
specific architecture or a detailed physical layer. Similarly, the TE
framework is not suggested as an architecture or the standards for
TE [8]. These works should be done by a team of expert power
system architects to represent the design of a specific case of a
power system. For more information review the ABM and TE
Environment
condi ons
Agent
consump ons
Individual
Rewards
Pa erns of
behaviors
Dissa sfac on
Dis-uniformity
of the system
Entropy of
the system
Coopera on
Rewards
Consumer
profit
Fig. 4. Influence diagram.
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
Fig. 5. Structural entity framework.
examples in the literature review of Sections 1.1, 1.3, and 2. Fig. 5(c)
is a high level conceptual depiction of the physical layer and does
not intend to detail any mesh or radial power grid. As described in
this paper the model does not explicitly account for transmission
constraints and would be appropriate within a tightly coupled
physical subnetwork without tight transmission constraints connecting different regions. We assume a significant body of consumers with usage flexibility but established patterns. For
justification and supportive examples of electricity usage patterns
based on different segmenting classes see Refs. [21,44,55,79]. The
presence of smart meters and incentives, both economic and
emotional, enable consumer choice on consumption patterns.
Future extensions can incorporate physical layer constraints into
the optimization model. Conceptually this would not present a
problem but it would significantly increase computational requirements. This is expanded in outlining the future research in
Section 7 by incorporating vertical interactions in Fig. 3 between
the physical and social layers.
The Social/Swarm layer helps us to cascade effects of the Decision/Control layer(s) to the Physical layer(s) by modeling the
emergence and adaptation of the whole swarm. The topology of
connectedness and protocols for interaction in the network are
important properties of the network for our study. The topology of
interactions defines who is, or could be, connected to whom. The
protocols of interactions are the mechanisms of the dynamics of the
interactions. Both specify the local information accessible to an
agent. The structure of the network (e.g. scale-free or singleescale
properties) helps us to calculate the class of interoperability for
each agent and find its influencer nodes. We assign the class of an
agent based on the size of the network and the degree of the node
(see the next section for mathematical details). Also, we consider
the pattern of behavior for each consumer. The distribution of
patterns of behaviors and the way the agents are seeded with
patterns are important. We present the value of interoperability
between two agents as the weights of the edges. In summary, three
parts of the network are used in our agent-based modeling (they
are mathematically defined in the next section):
1 Patterns of nodes (consumer agents),
2 Degree of agents that is related to the structure of the network,
3 Weights of edges that show the interoperability of agents.
The social network G between agents with preferential attachment and growth can be represented by a scale-free network
[47,73,87,91]. jEðGÞj is the set of links in the social network G. The
nodes of the network depict autonomous consumer agents while
the edges symbolize the influences or interoperability between the
agents. The node degree distribution of the network follows a power law i.e., the probability a node has k edges is ck"l where, c is a
normalization constant and l defines the shape of the distribution
[3,15]. We will relax this assumption to study single-scale behavior
of a Gaussian network later. The size of the network may grow by
period while its scale-free/single-scale characteristic remains valid.
4. Agent-based optimization engine
This section presents the detail procedure of decision rules to
show how agents optimize their actions and change their
behaviors.
4.1. Process Overview and scheduling
Fig. 6 shows the logical flowchart of the agent-based process
and its scheduling. The flowchart includes three main sections:
setup, switch, and optimize.Switch and optimize together regulate
the dynamic behavior of the network initialized in setup.
1- Setup section initiates the scale-free network of interrelated
consumers and seeds them with the patterns of consumption. Assume initially that agents are independent (this assumption will be
relaxed later to induce complex behavior). Population of pattern i
(Xi;i ¼ 1,…,n) changes exponentially (Eq. (1)) with growth rate bi at
period q, q ¼ 1,…,T. We need this equation to setup the initial social
network and its growth rule. We will incorporate the complex topology of the influences and switching rules later in this section.
Complex Entropy of the system is analyzed in Section 6. Note a
complex system is comprised of a large number of components, so
Xi is integer (with a good approximation) in all periods.
ðqþ1Þ
Xi
q
q
(1)
¼ bi $Xi þ Xi :
Note that generally bi can be negative or positive. For pattern
P
probability Pi ¼ Xi = Xi the growth of entropy follows Eq. (2).
E
ðqþ1Þ
q
"E ¼
n
X
i¼1
bi Pi
n
X
i¼1
!
Pi log2 Pi " log2 Pi :
(2)
Here, at each time increment, new agents create 9 connections
with previous agents based on the scale-free property where 9 is a
random number between 1 and 9max . Here 9max defines the max link
generation. We assign desirability coefficients and attribute weights
to the agents that will be used to compute optimization decisions
(to be formally defined later).
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Start
Set the agent popula on and the scale-free network
Seed the popula on with the pa ern ra os
Assign desirability coefficients and a ribute
weights to each agent
Setup
Grow the network based on the
fitness rates
Update dis-uniformity and Entropy of the system
Increment the me period
Find the interoperability class of agents
based on the network protocol
Switch
Compute the interrela onship of
agents based on interoperabili es
Find the agent with first/second
highest interrela onship
Switch to the agent with
first/second highest
interrela onship
Calculate the agent u li es based on the
desirabili es
Y
New π >
Old π
Calculate the agent dissa sfac ons based on
difference of new and switch pa erns
Op mize
N
Compute the coopera ve reward based on the
system dis-uniformity and individual agent
rewards based each agent dis-uniformity changes
Calculate the value for the total reward π
Fig. 6. Logical flow chart for scheduling of the process overview.
We measure the agents' level of cooperation by the disuniformity of aggregated pattern consumption at period q. The
dis-uniformity of pattern i is shown in Eq. (3). Recall Ciq ðwÞ is the
consumption of electricity at time w for pattern i in period q. Let
Rw
Ciq ¼ 0 0 Ciq ðwÞdw=w0 be the daily time average consumption of
pattern i at period q. The dis-uniformity of pattern i in period q is:
q
Di ¼
Zw0 !
0
q
q
Ci ðwÞ " Ci
"2
dw;
i ¼ 1; …; n;
q ¼ 1; …; T:
(3)
The dis-uniformity of a patterns is the mean square deviation
between the current state of an agent and the goal state (the
average daily consumption) (see Refs. [48,49] for detailed discussion on its relations to the entropy).
To establish a value mechanism to motivate the decision makers
(consumer agents) to cooperate and achieve in such a way that the
aggregate consumption in each period is uniform over time, we
seek to minimize the total dis-uniformity, Eq. (4). This mechanism
helps us on better load management and peak reduction. The other
possible values based on the attributes of a consumption pattern,
agent preferences, satisfactions, and comfort will be added to a
multi-objective optimization model later in this paper. Used to
address ”what if” scenarios, the model allows predictability of demand response which in turn can facilitated determining resource
adequacy.
0
Zw0 B
B
q
D ¼
B
@
0
Pn
i¼1
!
" 12
Ciq ðwÞ " Ciq Xiq C
C
Pn
C dw:
q
A
i¼1 Xi
(4)
The total Dis-uniformity, Eq. (4), could be reduced by incentives
that change one or more profiles or rearrange probability of
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patterns. We will show interactions between agents and their
interoperability effects on dis-uniformity of the system.
2- Switching section defines a set of rules for finding a switching
target based on interoperability of agents. We define four sets of
classified interoperability for the social layer population on the
basis of the network protocol. This classification shows the agent's
ability to connect and effect each other where, dy shows the class of
P
agent y; y ¼ 1; …; ni¼1 Xi . Influencers(INF) have the highest number
of connection links (interoperability). They maintain central positions in the social network and their numbers are small. Based on
behavioral profiles, we classify agents by type INF, EF, LF, and ISL.
Early Followers(EF) are more localized and have less interoperability
compared to the influencers. Late Followers(LF) are classified between the Early Followers and Isolated categories. Isolated(ISL) have
low interoperability. They do not have a big influence on other
individuals and are insensitive to others. The idea of this classification is similar to the term innovativeness categories in diffusion
theory by Ref. [81]. However, innovativeness categories consider
speed of adaptation while we consider influences and interoperability in a network.
The network node degree distribution follows a scale-free power-law and the node degrees depend on the network size. To
measure the interoperability classification based on this protocol
we need to linearize the power-law functions. We use Eq. (5) as the
linearization function and Eq. (7) shows how the power-law functions are linearized for each classification.
#
$
(5)
Lin ady ; bdy ¼ ady $lnðjEðGÞjÞ " bdy ;
where,
dy 2fINF; EF; LF; ISOg;
aINF > aEF > aLF > aISO ;
bINF > bEF > bLF > bISO ;
(6)
and, jE(G)j shows the number of links in the social network G (total
number of interoperability links). All agents follow a similar
network topology in the network G. Degy is the degree of agent y in
the network i.e. the number of interoperability connections that
each consumer makes in the system.
8
INF;
>
>
<
EF;
dy ¼
LF;
>
>
:
ISL;
if Degy ( LinðaINF ; bINF Þ;
if LinðaEF ; bEF Þ $ Degy < LinðaINF ; bINF Þ;
if LinðaLF ; bLF Þ $ Degy < LinðaEF ; bEF Þ;
o:w:
(7)
In summary, to classify the agents we chose a and b. Then the
size of the network and the degree of the node determine the agent
classes. We will use these classes to assign interoperability between
agents and calculate their interrelationship.
For agent y consider all other agents that are connected to y. The
influence on agent y from agent z is based partly on the classes of
the two agents. Let Idc d represent interoperability between classes of
y z
agents. Here, Idcy dz is a monotonic function of the influence that an
agent of Class dz has on an agent of Class dy. Interoperability is a
positive number with maximum of one where, Idcy dz ¼ 0 shows
autonomic (independent) class of agents and Idc d ¼ 1 when they
y z
Table 1
Interoperability between consumer agents.
Idcy dz
INF
EF
LF
ISL
INF
EF
LF
ISL
0.8
0.6
0.4
0.3
0.6
0.5
0.3
0.2
0.4
0.3
0.2
0.1
0.3
0.2
0.1
0.001
follow each other (identical). Table 1 shows an example of an
interoperability classification matrix. Section 5 provides justification for values in this table.
Self-preferenceqyz, lets agents vary their individual interoperability i.e. it lets two agents have different interoperability with a
specific agent even if all three of them are in the same set of classification. The interoperability matrix defines a maximum possible
value for all pairs of classification sets and 0.5 $ qyz $ 1 may vary
this value to half of its maximum. qyz ¼ 1 shows agent y does not
have any self-preference and follows the interoperability matrix.
Note if qyz ¼ 0, the model will be modified to a system without the
P
network. To simplify the formulation we use qydz ¼ z2dz qyz =Xz2dz ,
average self-preference, in Eq. (8). For example, assume consumer 1
has two neighbors (consumers 2 and 3) and all three of them are
INF. Based on Table 1, consumer 1 can have maximum interoperability 0.8 with both neighbors. However she/he may has less willingness to be affected by consumer 3. Then consumer 1 reduces its
interoperability to 0.4 by selecting self-preference equal to 0.5 (See
more examples in Fig. 7(a) and (b)).
The interrelationship <, between agents will be assigned based
on the interoperability, Ic, matrix and their classification. Let Xdzi be
the number of connected agents (neighbors) to agent y in class dz
with pattern i. To calculate interrelationship of agent y with its
neighbors in pattern i we used Eq. (8),
<yi ¼
P
c
dz qydz $Idy dz $Xdzi
P P
dz
i Xdzi
;
i ¼ 1; …; n; y ¼ 1; …; Q ;
(8)
where, Idcy dz is the interoperability of the agent in class dy with agent
in class dz where dz2{INF, EF, LF, ISO}.
Each period, such as a day, agents potentially react to stimuli and
may change their patterns. To select an appropriate pattern as a
switching target, we use Eq. (9) or Eq. (10) allowing the agent to
consider the strongest or top two alternatives held by connected
q
agents where, switchy is the pattern that agent y chooses as the
switching target at period q. The agents have two ways to select
their target. Eq. (9) lets an agent compare its objective with the
objective of its highest weighted interrelationship neighbor. Here
the switching target of agent y is the pattern of an interconnected
agent with the highest interrelationship in its neighborhood. The
decision to switch requires overcoming the inertia of the current
set point. To consider the agent tendency to stay in her current
pattern, we define an awareness-threshold Yy that must be overcome to switch. Thus, <yi ¼ <0yi þ Yy =Total Neighbors if
i ¼ Pattern(y), where <0yi is her current interrelationship.
switchqy ¼ argi fmaxð<yi Þg;
ci:
(9)
To avoid similar patterns when the agent with the highest
interrelationship has the same pattern with the target, we may use
Eq. (10) to let agents look at the second highest interrelationship.
q
switchy ¼ argi fmaxð<yi Þg;
cisPatternðyÞ:
(10)
Example 1: Fig. 7(a) presents an example for calculating interrelationships. Assume consumer y is an agent trying to decide
whether to switch her consumption pattern. Agent y is an influencer agent, INF and six other agents are connected to this agent.
Two of them follow pattern i (1 EF, 1 LF), three of them follow
pattern j (1 INF, 1 EF, 1 LF), and one of them follows pattern k (INF) at
this time. Assume the awareness-threshold Yy ¼ 0 and the agent y
does not have any self-preference i.e., qyz ¼ 1. Then
<yi ¼ 0:6 þ 0:4=6 ¼ 0:17,
<yj ¼ 0:6 þ 0:4 þ 0:8=6 ¼ 0:3,
and
<yk ¼ 0:8=6 ¼ 0:13. Hence, if agent y has the pattern j the switching
q
q
target switchy ¼ i from Eq. (10) and switchy ¼ j otherwise.
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Fig. 7. Calculating the interrelationship.
Example 2: Fig. 7(b) continues Example 1 by adding a selfpreference to the agent y for one of its neighbors (underlined
number in the arc). This means agent y prefers to weigh the
interoperability of the EF class of pattern i by half (qyi ¼ 0.5). We
calculate <yi ¼ 0:5 ) 0:6 þ 0:4=6 ¼ 0:12 changing switchqy ¼ k if we
use Eq. (10) and Pattern(y) ¼ j.
Note the ordering of influence does not matter as the agents
influence each other and make decisions at the same time (same
iteration) then change their behavior in the next iteration. This
ability is built into the agent-based model.
3- Optimizing section: once a target pattern is defined, the agent
has to decide whether to keep her current pattern or to switch
based on the patterns' utility functions, rewards, and dissatisfactions. The total utility value of a pattern is a weighted average of the
desirability score Uys that is a number between 0 and 1 for each
attribute [74]. Recall that the attributes are price, convenience, and
glamour. Here, Uys shows the desirability score of agent y for
attribute s. When the agents target the maximum value of an
attribute (e.g. glamour), to calculate the desirability, we use Eq. (11)
where y shows the value of the attribute and L and U are its lower
and upper bound in Fig. 8(a). We apply Eq. (12) when the target is a
minimum value, Fig. 8(b) (e.g. time to make decisions or cost of
changing behaviors). The Desirability coefficient gys, parameterize
the desirability score Uys. Desirability functions showing (g < 0)
characterizes risk-averse agents and (g > 0) characterizes riskseeking agents if the agent targets a maximum and vice versa if
the agent targets a minimum.
!
"
8
ys " Ls
>
1
"
exp
g
*
>
ys U " L
>
>
s
s
<
;
gy s Þ
1
"
expð
Uys ¼
>
>
>
>
ys " Ls
:
;
Us " L s
if gys s0; y ¼ 1;…;Q ;s ¼ 1;2;3;
if gys ¼ 0; y ¼ 1;…;Q ;s ¼ 1;2;3:
(11)
!
"
8
Us " y s
>
1
"
exp
g
*
>
y
s
>
Us " L s
>
<
; if gys s0; y ¼ 1; …; Q ; s ¼ 1; 2; 3;
1 " expðgys Þ
Uys ¼
>
>
>
>
Us " y s
:
;
if gys ¼ 0; y ¼ 1; …; Q ; s ¼ 1; 2; 3:
Us " L s
(12)
The Utility Value Uy, is the weighted average of the desirability
scores of its pattern attributes. Agents can assign their own
importance weight Wys, to different attributes to have individual
value functions (Eq. (13)).
Uy ¼
P
s Wys Uys
P
;
s Wys
y ¼ 1; …; Q ; s ¼ 1; 2; 3:
(13)
Agents receive two types of rewards when they switch to new
Fig. 8. Desirability functions.
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b is a function of the total dispatterns. The Cooperation reward R,
uniformity. An agent may receive this reward without any
switching when their current pattern cooperates with others to
reduce the dis-uniformity i.e. cooperation reward will be payed by
the central authority to all agents based on the total dis-uniformity
that they create. The Individual reward Ry, reflects the controllers
individual rewards to the agent based on the contribution of the
agent pattern to the central objectives. An agent will receive more
individual reward when they choose to change their pattern of
behavior in the way that minimizes their dis-uniformity. Dissatisfaction 4, is the only variable that has a negative effect on the decisions. Dissatisfaction will be measured based on the amount of
difference between new and old pattern of each agent. The more
each agent changes its pattern the more dissatisfaction with its
decision (see Section 4.2 for the formulations).
At the end of each period the pattern of the agents are updated
as follows:
1. In a growing network (dbi > 1), the new network expands from
the old one,
2. Agent classes are redefined based on the network topology,
3. Interrelationships are updated,
4. A target pattern will be selected based on the chosen switching
rule,
5. The agent applies a decision rule based on value of perceived
choices.
4.2. Decision rules
In the previous section we described how an agent determines
the utility value of a possible switching target. A consumer-based
optimization will be executed in order to determine if switching
actually occurs. Decision makers (consumer agents) desire to
maximize their total reward py. The total reward is a
b the individual reward
normalized sum of the cooperation reward R,
Ry, the utility value Uy, and dissatisfaction 4 of the agents. The
consumer-based optimization compares the anticipated total
q
q
reward pqþ1
y ðCy ðwÞ; Cswitch ðwÞÞ with the reward obtained
q
q
pqþ1
If
continuing
the
current
pattern,
y ðCy ðwÞ; Cy ðwÞÞ.
%
&
#
$
qþ1
q
q
qþ1
q
q
py
Cy ðwÞ; Cswitch ðwÞ =py
Cy ðwÞ; Cy ðwÞ > switching threshold
Y0 y , the agent switches her pattern to the pattern given by the
possible switch in the period q þ 1. A general model for agent y at
period q would be,
q
b þ kr Rqy þ ku Uyq " k4 4q ;
pqy ¼ kbr R
to be a logarithmic function of the differences between current
and
previous
pattern
of
consumption
behavior,
'
R w0 '' q
'
q
q
q
f2 ðCy ðwÞ; Cswitch ðwÞÞ ¼ lnð 0 'Cy ðwÞ " Cswitch ðwÞ'dwÞ=l2 . The value
of l2 will be assigned later in this study. Note that this presents the
agents decision model. Above this sits the master problem of the
controlling entity who sets prices and rewards in order to induce
desired behavior (consumption).
4.3. Termination rules
The simulation continues the flow described in Fig. 6 until one of
the following termination rules apply:
! The patterns do not change any more,
! A maximal period (simulation time) has been reached.
5. Agent-based simulation and specifying the parameters
Here is an example to show how our integrated Agent-based
optimization model simulates and analyzes the emergent
behavior of consumption patterns. This study enables the electricity regulators to examine the effect of social interaction topologies with more realistic cognitive behaviors and improves the
efficiency and effectiveness of demand response and peak reduction programs via behavioral-based incentives (e.g. social education
and advertisement).
To illustrate the dynamic behavior of our system we assume
three patterns of consumption (see Refs. [21,44,52,53,55,79] for
justification and examples). Fig. 9 shows the behavior of those
patterns in 24 h.
Table 2 presents the variables for running the model. Convenience varies between 2 and 5 indicating relative time or effort
required to change to a pattern. Glamour is a qualitative variable
with higher values implying more fashionable or advertised
patterns.
Consumers are autonomous and receive gy, Wy, and qydz identically from sampling random Normal and Uniform distributions
ignoring negative samples. To classify the consumer agents based
on their interrelationships, we set aINF ¼ 4.5, aEF ¼ 2.5, aLF ¼ 1.5,
bINF ¼ 17, bEF ¼ 9, and bLF ¼ 5. Moreover, we
DðtÞ
Dy ðtÞ
assume
f0 ðDq Þ ¼ 100e 10 ,
f00 ðDqy Þ ¼ 100e 10 ,
and
'
'
R
'
'
w0 q
q
q"1
q
f2 ðCy ðwÞ; Cy ðwÞÞ ¼ lnð 0 'Cy ðwÞ " Cswitch ðwÞ'dwÞ=2. These pa-
rameters are defined to provide proper scaling and their impetus
discussed in previous sections.
(14)
7
where, Uyq is defined by Eq (13) and
b ¼ f ðDq Þ;
R
0
# $
Rqy ¼ f00 Dqy ;
6
cq;
(15)
cy; q;
(16)
%
&
q
q
q
4y ¼ f2 Cy ðwÞ; Cswitch ðwÞ ;
cy; q; w:
(17)
The maximization is to be taken relative to the decision that
agent y can make in period q. To be specific, we choose the coopb q a decreasing exponential function of the total
eration reward R
q
dis-uniformity (defined in Eq. (4)) at period q, f0 ðDq Þ ¼ l0 eD l00 , and
q
the individual rewards Ry a decreasing exponential function of the
individual dis-uniformity (Eq. (3)) of each agent at period q,
q
f00 ðDqy Þ ¼ l00 eDy l000 . Values of l0, l00, l00 , and l000 are constants and
q
will be assigned later in this study. We choose the dissatisfaction 4y
Consump on(KW)
q
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
w
i
j
k
Fig. 9. Patterns of consumption.
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
Table 2
State variables for running the simulation.
Parameter
Variable
Initial Population
Initial patterns
Growth rate
Max link generation
Price
Convenience
Glamour
Desirability coefficient
Attribute weight
Average self-preference
*
P
y ¼ 1; …; i Xi
P
Xi = i Xi ; i ¼ 1; 2; 3
bi, i ¼ 1,2,3
9max
S1
S2
S3
gys
Wy
qydz
Range
Units
Default
Area*
100- inf
0 to 1
0 to 1
1 to 10
3e8
2e5
1e10
~ Normal (0, 4)
~ Normal (1, 0.2)
~ Uniform (0.5, 1)
# of consumers
% of total population
% of pattern population
number
Currency (cents/KWh)
Qualitative
Qualitative
N/A
N/A
N/A
500
0.15,0.65,0.20
0, 0, 0
1
5, 5, 5
4, 4, 4
3, 3, 3
N/A
N/A
N/A
E
E
E
E
C
C
C
A
A
A
Here E, C, and A stand for Environment, Consumption and Agents respectively.
To define interoperability between agents we use the results of
empirical studies on spread of happiness [43], dynamics of smoking
[30], and formal/informal influence in adoption [93]. Refs. [43] and
[30] classify individuals in large social networks based on their
influence and study probability of changing behaviors (smoking
habits and happiness) in agents when their connected agents adopt
to a new behavior. Based on both studies we conclude that the
probability to influence a participant in the same class is approximately 505%, 35%, 25%, and 10% for the classes of close friend,
friend, spouse, and colleague receptively [93]. showed that authority structure like the one between managers and workers will
add to or subtract to the influences determined in the previous
studies. Based on these studies we choose the interoperability between the two classes of agents as shown in Table 3. These interoperabilities are selected for consistency with the finding of the
three mentioned comprehensive studies but are not uniquely
determined.
6. Analyzing behaviors
We study the behavior of the integrated agent-based optimization system under a variety of different circumstances. We
examine how the agents' tendency to stay on their own pattern
(awareness-threshold) effects the distribution of entropy of the
system. We define a baseline awareness-threshold based on previous studies. Then we show how the regulators can improve the
effect of a social network. Also we build more realistic results by
considering limited rationality in cognitive capabilities of agents.
Finally, we show the effect of saturated friendship behavior in the
system.
6.1. The effect of the awareness-threshold
To study behavior of the system we run the model with the
default values in Table 2 while we modify the awareness-threshold
Y from 0.00 to 0.32 in 0.02 increments (for larger thresholds the
system does not converge in 400 time periods). Fig. 10 shows the
results of 300 runs. This figure shows the distribution of the time to
converge as a function of awareness-threshold Y. This time is
defined as the time when the entropy of the system is less than
0.3364 i.e. when at least 95% of agents converge to a pattern (here is
Table 3
Measuring the interoperabilities.
Icdydz
INF
EF
LF
ISL
INF
EF
LF
ISL
0.79
0.65
0.41
0.28
0.4
0.51
0.35
0.2
0.1
0.25
0.29
0.15
0.002
0.03
0.06
0.1
Pattern i).
Fig. 11 depicts a vertical slice from Fig. 10. We see how the distribution of convergence to pattern i shifts from left to right by
increasing the awareness-threshold Y. The convergence time increases by increasing the awareness-threshold i.e. the agents have
more tendency to stay in their current pattern and converge slower.
Fig. 12 compares the average entropy of systems with different
awareness-thresholds. Larger awareness-thresholds cause higher
entropy in the system because the system converges slower and
has more agent diversity by period. For very large awarenessthresholds (e.g. 0.3), the system does not converge in 400 periods. At the beginning of the simulation, the entropy may increase
because the agents may start to switch from a high populated
pattern to a low populated one. These results match with Theorem
II and Corollary II in Ref. [49] where pattern i positively dominates
patterns j and k (iej and iek). Here, the objective is to minimize
the total dis-uniformity in time (DY) so based on Theorem II.1 entropy is increasing in time (E[) as long as E<"log2Pi and based on
Theorem II.2 entropy is decreasing in time (EY) when E>"log2Pi.
For more details and proofs see Ref. [49].
6.2. Establishing a BaseLine
As a baseline we use the current system that has small interaction (almost zero) and we intend to increase the interactions.
Interoperability in our system shows improving the interaction due
to control decisions. It has been observed that only 5% of end users
are currently empowered to react to the real-time or day-ahead
locational marginal price (LMP) and participate in DR Programs
[40]. In order to calibrate our agent-based simulations, we will
determine an awareness-threshold that generates a change in
pattern over time that is as close as possible to a simulation without
a network and 5% participation rate. We quantify the closeness of
two simulations by registering the average percentage of populað1Þ
ð2Þ
tion Piq and Piq of pattern i in the system as function of time
period q. The difference H (Eq. (18)) is the absolute sum of difference pattern over time:
H¼
'
X X'' ð1Þ
ð2Þ '
'Piq " Piq '
i
q
i ¼ 1; 2; 3;
q ¼ 1; …; 400:
(18)
Fig. 13 shows the total difference H between an agent-based
simulation without network (5% participation) and an agentbased simulation with a social network as a function of the
awareness-thresholds.
Based on Fig. 13 awareness-threshold between 0.08 and 014
yields the most similar behavior with current systems without
networks. For example Fig. 14 compares the emergence in the
pattern of behavior in the first ten runs for awarenessthreshold ¼ 0.1 and 0.3. The system converges after 160 time
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
450
400
350
Time Period
300
Min
10%
250
1st Qua
200
Median
3rd Qua
150
90%
100
Max
50
0
0.32
0.3
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Awareness-Threshold
Fig. 10. Convergence of the entropy.
Fig. 11. Distribution of Convergence to Pattern i.
periods in Fig. 14(a) when the threshold ¼ 0.1 and it does not
converge when threshold ¼ 0.3, Fig. 14 (b).
6.3. Improving effect of the network
A well designed social network can increase the number of
friendships and/or decrease awareness-threshold of agents (i.e.
decrease the tendency to stay in their initial behavior). Here we
show the behavior of the system when we increase max link generation 9max . Fig. 15 compares the results of networks with 9max ¼ 1
and 9max ¼ 3 (i.e. average link generation equal to 2) when
awareness-threshold is equal to 0.1. This figure shows how the
social network increases the effects of economical incentives. 1st
quarter, median, and third quarter in the network with 9max ¼ 3 are
three time faster than 9max ¼ 1. Both systems may converge after
400 time periods in some cases, however, 90% of the times the
higher link generation converges at least 20% faster. Fig. 15(b)
shows how the distribution of convergence shifts to left (i.e. converges faster).
We checked the behavior of the topology of the network by
logelog plots [6,71]. Fig. 16 compares the scale-free behavior of the
network for 9max ¼ 1 and 9max ¼ 3 and depicts the scale-free metric
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
1.306998
1.332431
1.354272
1.372586
1.388672
1.402339
1.415224
1.426525
1.436724
1.446221
1.454407
1.46199
1 46199
1.468582
on the social/swarm layer by incorporating them into the agent
decisions and study their effect on objectives and control strategies.
Considering irrationality helps us to create more realistic cases. We
propose discrete choice models (Eq. (19)) based on the total reward
p and the interoperability classification to study the behavior of
irrational agents. We consider two types of irrationality (namely:
Irr-I and Irr-II). The probability that agent y does not switch to the
new pattern even if the p value of the new pattern is higher than
the p value of the old pattern (i.e. Irr-I) is given by,
Th=0
Th=0.1
Th=0.2
Th=0.3
1
21
41
61
81
101
01
121
21
141
41
161
61
181
81
201
01
221
21
241
41
261
61
281
81
301
01
321
21
341
41
361
61
381
81
401
01
Entropyy
02058
1.8 1.387334
26618
1.6 1.433907
21885 1.463869
1.4
05751 1.485003
1.2
486321 1.50028
4672491 1.510736
0.8 1.517728
44456
0.6 1.521325
420105
39821
0.4 1.522141
0.3364
74004
0.2 1.52085
348360 1.518426
22206 1.515625
1 515625
298723 1.511883
Proby ¼
Time Period
expðkI *pNew Þ
expðkI *pNew Þ þ expðkI *pOld Þ
(19)
where, pNew and pOld are the new and old values for the total reward
Fig. 12. Convergence of the average entropies.
0.9
0.8
0.7
TTotal difference H
0.6
Min
10%
0.5
1st Qua
0.4
Median
3 d Qua
3rd
Q
0.3
90%
0.2
Max
0.1
0
0.32
0.3
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Awareness-Threshold
Fig. 13. Total difference with and without a social network.
Fig. 14. Comparison of Awareness-Threshold ¼ 0.1 and 0.3.
l increases from 1.47 to 1.81 when we increased 9max . This shows
how regulators can improve the convergence time by sharing information between agents or by encouraging them to increase their
friendships via social electricity networks.
6.4. Externalities and irrationality
Characteristics of agents (such as irrationality) and the effects of
externalities (such as a fashion effect) are not considered in most of
the previous studies that modeled electricity consumptions as a
complex adaptive system. We analyze the impact of these factors
of agent and kI shows the sensitivity of the agents to differences
between the p values (the higher the kI, the more sensitive). The
probability that agent y switches to a new pattern even if the p
values do not satisfy the switching threshold (i.e. Irr-II) can be
measured by similar formulation with a new sensitivity factor kII.
Fig. 17 compares behaviors of completely rational agents
(Irr ¼ 0) with strongly irrational/non-sensitive agents
(kI ¼ 0.1;kII ¼ 0.1) and weak irrational/sensitive agents
(kI ¼ 1;kII ¼ 1) scenarios. The weak irrational scenario does not
converge to any pattern. The strongly irrational scenario converges
with an almost similar temporal distribution to rational agents.
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
Fig. 15. Comparison of 9max ¼ 1 and.9max ¼ 3
1
0.5
0
P
Probability
-0.5
0
0.5
1
1.5
-1
y = -1.8061x + 0.4304
-1.5
2
ρ_max=1
ρ max=3
ρ_max
3
-2
-2.5
y = -1.4698x - 0.4154
-3
-3.5
Node Degree
Fig. 17. Effects of irrationality.
Fig. 16. The scale-free metric of the network.
However, this simulation of the system does not converge to a
pattern of low dis-uniformity but it converges to the pattern that
had the highest initial population.
Consumers with the same patterns may create a community in
the network. These communities can become dominant and
restrict the influence of other patterns even if they have higher p
values. Generally we can observe that sometimes the system does
not evolve to the situations with lower dis-uniformity. This results
from the effect of emergent behavior of consumers in interrelationship with each other in the network.
6.5. Effects of saturated interrelationships
Recent studies show the degree distribution for friendship in
growing networks may not be scale-free in the long run [87]. The
tail decays faster than power-law with increasing size of links and
can converge to a Gaussian distribution. Here, when an agent has
more than a critical number of links, new edges cannot connect to
it. To create this environment (see Section 3.2) we group agents to
active or inactive. All new agents are created active. An agent becomes inactive when it reaches a maximum number of links.
Inactive agents cannot receive new links. This constraint leads to a
single-scale network where the degree of nodes follows a truncated
Gaussian distribution.
We study the effect of saturation by comparing Gaussian Distribution (with a maximum number of 4 friends/influencer) to an
unbounded scale-free network (power-law distribution) in Fig. 18.
This shows regulators should try to avoid Gaussian distribution
node degrees by motivating agents to not saturate their friendships.
From Fig. 18(b), we note the convergence of entropy occurs faster in
mose cases in scale-free networks. However, the scale-free network
has a longer right tail and in some cases never converges.
6.6. Significant factors
To examine importance and effect of the parameters of the social network on the system outputs, we design two full factorial
experiments. We study the system responses by pqy (the average
total rewards of agents), Dq (the total dis-uniformity of the system),
and Eq (the entropy of the system). An Exponential Weighted
Moving Average (EWMA) with discount factor equal to 0.005 is
used for weighting the data points at older periods where the
number of periods q ¼ 1 to 400. We study effect of the social
network size by considering two levels (200 and 1000) for the
initial population. To study the impact of group vs. individual rewards for minimizing dis-uniformity, we examine two levels for the
weight of individual dis-uniformities (kr ¼ kbr and kr ¼ 2kbr ). Also,
we vary attributes of pattern i from a normal utility (Price ¼ 5,
Convenience ¼ 4, Glamour ¼ 3) to a weak utility (Price ¼ 8,
Convenience ¼ 3, Glamour ¼ 2). The P-values of experimental results for the 23 full factorial experiment with 30 replications are
presented in Table 4. The results are created by MiniTab and 0.000
means the P-value is less than 0.05. Note that the normality test for
residuals was not convincing. We tried several transformations for
responses (e.g. Box-Cox power including square root and Log). A
logistic
transformation,
Log[(Response
"
minResponse)/
(maxRresponse " Response)], improved the results of the normality
test.
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
Fig. 18. Effect of saturated friendship on the topology of the network.
Table 4
P
Estimated effects and coefficients of
Xi , Kr, and U.
Table 5
Estimated effects and coefficients of topology and max link generation.
Response
P reward
P dis-uniformity
P entropy
Response
P reward
P dis-uniformity
P entropy
Constant
Population
Kr
Utility
Population ) Kr
Population ) Utility
Kr ) Utility
Population ) Kr ) Utility
0.000
0.268
0.000
0.000
0.169
0.534
0.004
0.260
0.000
0.677
0.447
0.003
0.205
0.709
0.004
0.262
0.000
0.174
0.018
0.000
0.174
0.728
0.000
0.096
Constant
Topology
Link Generation
Topology ) Link Generation
0.000
0.000
0.002
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.121
0.000
P
Fig. 19(a), (b), and (c) depict the effect of
Xi, Kr, and U on the
responses. The results show that the population size is not a significant factor for the defined responses of the system; however,
the utility and the weight of individual dis-uniformities should be
considered as significant factors. Kr has the largest significant effect
and U has the second largest significant effect on the total rewards
pqy . Effect of U and interaction effect of U and kr on the total disuniformity Dq and entropy Eq are significant.
In another experiment we study the topology of the network by
using the similar responses and leveling the node degree distribution to scale-free and single-scale. Also, we consider two levels
for the max link generation (9max ¼ 1 and 9max ¼ 6). The P-values of
experimental results for the 22 full factorial experiment are presented in Table 5.
Fig. 20(a), (b), and (c) depict the effect of topology and max link
generation on the responses. The results show that all of them are
significant factors. Topology, max link generation, and their interaction have almost a similar size of effect on the total rewards pqy
and the total dis-uniformity Dq. Topology has a slightly larger effect
in comparison to max link generation. Likewise, max link generation has a smaller effect on entropy in comparison to topology of
the network and the interaction effect of max link generation and
topology.
6.7. Effect of social education
Social education refers to activities by super agents that influence an individual's behavior to effect a specific pattern. To study
effects of social education we consider a super influencer agent (e.g.
a utility company or celebrity) which follows a specific pattern (e.g.
pattern i). This super influencer agent is connected to h percent of
other agents randomly and uses the interoperability and interrelationship rules similar to other agents. However, this agent never
switches its pattern. Social educations and advertisements can increase the percentage of the agents who get influenced by the super
influencer (i.e. larger h). Fig. 21 compares the convergence time of
the system based on h. The figure shows even if only 20% of agents
are connected to the super influencer agent, there is a huge
improvement in the convergence time. Moreover, it reduces the
Fig. 19. Pareto chart and normal probability plot for experiment 1.
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M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
Fig. 20. Pareto chart and normal probability plot for experiment 2.
h ¼ 20%. This figure shows if we only facilitate the interoperability
of influencer agents by 5%, the maximum convergence time
decrease significantly. This strategy increases the system predictability but does not change the other parameters of the convergence distribution (e.g. min and median). Based on Figs. 21 and 22
managers and decision makers can invest on facilitating the interoperability of utility companies or celebrities on the society instead
of trying to connect more agents to the super influencer in the
network. However, first we need 20 to 40 percent of agents to get
connected to the super influencer.
Fig. 21. Effects of percentage of influenced agents, h
right tail of the distribution of convergence significantly (all agents
converges before 350 time periods) i.e. the system is more predictable and has less fluctuation. Note that we run the simulation
for 400 time periods and if the agents do not converge before 400
periods their convergence time will be presented in time
period ¼ 400. The figure also shows a significant improvement on
the distribution of convergence specially its right tail, if we
encourage another 20% of agents to connect to super influencer (i.e.
h ¼ 40 in comparison to h ¼ 20). The size of this effect decays for
larger h’s.
Another impact of social education or advertisements can
improve the interoperability between the agents. Fig. 22 shows
how investment on improving the effects of influencer agent on
other classes (i.e. the first column in Table 3) changes the convergence time of the system. Here, we assume social investments
improve these effects by 5%, 10%, 15%, and 20% for a fixed amount of
Fig. 22. Effects of improving intolerability of Influencers with other classes.
7. Framework notation and limitations
This study examines how consumption behavior is diffused in a
population. Managerial insights about the qualities that make the
diffusion successful are offered by this study. Also the importance
of social networks and peer to peer conversations are examined
here. The S-shape convergence in the pattern of behavior and bellshape curves of frequency of convergence depict the similarity of
the behavior of our ECAS and Bass Diffusion Model [17,68]. A
comprehensive discussion on comparison of CASs and diffusion
models is presented by Ref. [82]. Table 6 summarizes the notation
used throughout the paper.
Previous field experiments and theoretical studies addressed
the importance of social interactions in electricity end-used load
management (see cited references in Section 1.1 and Section 2),
however, the authors of this paper could not find concrete
evidence-based studies that examine effects of social networks on
the power systems. This study assumes a scale-free social network
between electricity users that is the most common characteristic of
other social networks. This assumption is relaxed in Section 6.5 to
study single-scale behavior of a Gaussian network. Section 6 analyzes the behavior of the social network under variety of different
circumstances such as irrationality, saturated friendships, and social education.
In this paper, conceptual inclusion of a social network of heterogeneous consumers with cognitive decision making capabilities
(goal directed and adaptive agents) permits our attentions to the
possibility of complex adaptive unintended or unforeseen consequences from the viewpoint of electricity market operators. The
limitations of this study provide a high-level direction for future
researches as follows:
1. Empirical validation of the framework with the real-world
electricity markets data could lead to precise specifications,
2. Information technology (cyber-physical) constraints could be
incorporated in the social layer interoperabilities,
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19
Table 6
List of notation.
Notation
Description
Ciq ðwÞ
Xiq
The consumption of electricity at time w for pattern i in period q
Pi
Qq
bi
Eq
9
q
Ci
Dqi
Dq
dy
jEðGÞj
Degy
a,b
Idc d
y z
qyz
Xdzi
<y i
Yy
Uy s
gys
Uy
Wys
b
R
The number of components that follow pattern i
The probability of pattern i
The total number of components in the system in period q
Growth rate of population of pattern i
Entropy of the system in period q
The number of connections that new agents create with previous agents at each interval
The daily time average consumption of pattern i in period q
The dis-uniformity of pattern i in period q
The total Dis-uniformity of the system in period q
P
The class of agent y; y ¼ 1; …; ni¼1 Xi
The number of links in the social network G (total number of interoperability links)
The degree of agent y in the network i.e. the number of interoperability connections
Parameters of linearization the function
Interoperability of the agent in class dy with agent in class dz
Self-preference, lets agents vary their individual interoperability
The number of connected agents (neighbors) to agent y in class dz with pattern i
Interrelationship of agent y with its neighbors in pattern i
Awareness-threshold of agent y, that must be overcome to switch
The desirability score of agent y for attribute s
Desirability coefficient, parameterize the desirability score Uys
Utility Value for agent y
Importance weight of agent y for attribute s
Cooperation reward
Ry
Individual reward of agent y
Dissatisfaction of agent y in period q
l
Constant parameters for reward functions
Weighting factors for reward functions
Total reward of agent y
The number of agents connected to a supper agent in social education
The absolute sum of difference pattern over time
Attributes: Price, Convenience, Glamour
Two types of irrationality
4qy
k
py
h
H
S1,2,3
Irr-I, Irr-II
3. Different biding and auctions strategies in an electricity market
and their effects in the vertical interactions of the social and
decision layers could be tested in the framework,
4. DR implementation issues and practical DR initiative concerns
in electricity markets (contracts, offers, and other market activities) could be added to the modeling constraints,
5. Architectural and topological constraints of an electricity power
grid could be considered in a detailed physical layer and its
vertical interactions with the social layer (this paper only
examined the horizontal interaction of the social network in
Fig. 3). These vertical interactions can be considered by:
! effects on the social network structure (e.g., two or more
islands that are connected with one or few influencers or
other class of interoperability),
! effects on interoperability or interrelationships (e.g., physical
constraints can change the interrelationships in different
parts of the network),
! additional constraints on friendships (e.g., disable relationships or increase the tendency to make a relation in some
parts of the network),
! a social network that has different characteristics (e.g., growth
rate and link generations) in different geographical locations
because of physical structures.
8. Conclusion
This study takes a mathematical and computational approach to
a socio-technical model combining social behavior, economics and
technology. The complex engineered system is modeled as consisting of a social layer of agents and a decision layer of external
incentives and agent optimization. System behavior emerges and
the system evolves dynamically through consumer agent decisions.
The modeling and solution methodology address shortcomings in
previous approaches and advances our ability to model and understand ECAS behaviors through computational intelligence. The
specific model used facilitates reduction of electricity consumption
variability referred to as dis-uniformity.
Unlike traditional stochastic learning methods that are based on
limited memory of past experiences and utility optimization
models that are built by rationality and decision theory, our
approach combines both backward and forward looking perspectives. This combination enables us to invest individuals with more
concrete cognitive capabilities. This ABM agents are adaptive (can
learn based on social education), goal-directed (adjust themselves
or their interactions based on a goal), and heterogeneous (their
attributes and behaviors may vary and change dynamically).
Moreover, complex behaviors such as altruistic versus selfish and
cooperation versus competition can be studied by our approach.
Within the electricity context, we develop methods to enable
changing consumption patterns of end-users and load aggregators
through incentives and social education. We have advanced understanding of the interaction between social behaviors and
economical incentives for load management and impacting peak
demand. Furthermore, we have provided a toolkit for regulators
and managers to help predict behaviors and trajectories of the
ECASs based on the status of variables. This enables finding more
effective and efficient strategies to change behavior. This framework can be extended to other ECASs.
Finally, we build a baseline to study emergence behavior of
electricity consumers. This study shows how the social network
topology impacts consumer behavior patterns. Load aggregators
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20
M. Haghnevis et al. / Socio-Economic Planning Sciences xxx (2016) 1e21
and system operators can apply this study to examine the value of
investments in education and smart technology vs. capacity. We
also show how the degree of irrationality in micro level of a system
affects the convergence in macro level.
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