# A Literature Review of Energy Justice

Weihang Ren  Department of Industrial and Systems Engineering, University of
Florida, Gainesville, FL, USA  Yongpei Guan  Department of Industrial and
Systems Engineering, University of Florida, Gainesville, FL, USA  Feng Qiu
Energy Systems Division, Argonne National Laboratory, Lemont, IL, USA
<EMAIL_ADDRESS>Todd Levin  Energy Systems Division, Argonne National
Laboratory, Lemont, IL, USA  Miguel Heleno  Lawrence Berkeley National Lab

###### Abstract

Energy justice, at the intersection of energy and societal ethics, studies the
origins, quantification, and resolution of persistent and potential inequities
within the energy sector, serving as a foundational pillar for societal
harmony. In this review, we overview the historical and modern definitions of
energy equity and frameworks of energy justice. We highlight the tools adopted
to measure equity in the energy context, unveiling multifaceted inequities
that permeate global energy landscapes. We discuss the limitations of
prevalent metrics such as the Gini coefficient and Generalized Entropy Indices
in the evaluation of energy justice concerns. Finally, we analyze publications
that examined current practices and proposed improving methods towards a more
equitable energy market for the society from policy, planning, and operation
perspectives.

Keywords— energy justice, energy equity, energy burden, inequality

In the last three decades, energy justice has emerged as a subject of
considerable discourse among research communities and policy makers. Energy
justice refers to the fair distribution of benefits and burdens associated
with energy production, distribution, and consumption. It encompasses the idea
that all individuals, regardless of socioeconomic status, race, or geographic
location, should have equal access to the benefits of clean and affordable
energy, as well as a fair share of the costs and risks associated with energy
development. The understanding, definition, measurements, priorities on energy
justice are also evolving, especially in recent years as renewable penetration
and electric vehicle adaption surge, power market reform continues, and new
business models emerge. These latest development in energy sector, plus
significant disruptions by recent pandemics and extreme weather events, have
created more challenges for energy justice. In a significant stride towards
this goal, the 2021 Biden administration’s Justice40 Initiative [1] aims to
deliver at least $40\%$ of the overall benefits of relevant federal
investments in climate and clean energy to disadvantaged communities. Notably,
the number of publications on energy justice during 2019-2021 (1003) exceeds
the total number of publications in the previous three decades (879) [2], as
shown in Figure 1. To better understand and address energy justice in this
complex and dynamic environment, in this review, we delve into the historical
evolution of energy justice and equity definitions and summarize prevalent
metrics employed to reveal the various forms of energy inequities around the
world, highlighting efforts in policies, grid planning, and operations that
dedicated to ushering justice into energy systems.

Figure 1: Annual number of publications on “energy justice” from 1992 to 2021,
counted by [2].

##  1 Energy Justice and Equity in Government Definitions

Qiu: please comment

Energy justice and energy equity are crucial concepts affecting society in
many ways. Before delving into the broad academic research on them, we start
with the government definitions that reflect the comprehensive ideas behind
these terms.

###  1.1 Energy Justice

As energy is an indispensable branch of the environment, there was no formal
government definition of energy justice alone in the 20th century, instead,
the energy justice concept was covered under the umbrella of environmental
justice. The latter was provided in 1994 during President Clinton’s
administration and defined as “identifying and addressing, as appropriate,
disproportionately high and adverse human health or environmental effects of
its programs, policies, and activities on minority populations and low-income
populations” [3]. Based on this definition, energy justice could be
interpreted as applying justice principles to the health and environmental
consequences of energy programs, energy policies, and energy activities on
minority and low-income populations.

As renewable energy increasingly penetrates into the power grid, the energy
price gets more volatile, among others, and accordingly, disproportionately
distributed benefits from renewable energy broaden the coverage of energy
justice. The economic consequence has thus stood out in the government
definitions. In 2019, the US Department of Energy (DOE) defined energy justice
as “the goal of achieving equity in both the social and economic participation
in the energy system, while also remediating social, economic, and health
burdens on those disproportionately harmed by the energy system” [4]. As
compared to the 1994 interpretation, this definition specifically highlights a
new dimension of achieving equity (with the definition below in Section 1.2)
in both the social and economic participation in the energy system, besides
health and environmental concerns.

Most recently, along this direction, a guideline regarding a quantitative
measure has been introduced in 2021 by President Biden’s Administration to
characterize justice. It is called Justice40 Initiative, which guides certain
Federal investments intending to direct 40 percent of the overall benefits in
climate and clean energy to disadvantaged communities [1]. The “disadvantaged
communities” are specifically identified by DOE through 36 indicators covering
fossil dependence, energy burden, environmental and climate hazards, and
vulnerability (socioeconomic, housing burden, transportation burdens, etc.)
[5]. This guideline delineates a quantifiable goal and adds more dimensions by
not limiting the subject to specific injustice matters.

###  1.2 Energy Equity

As mentioned in Section 1.1, energy equity is a term associated with energy
justice. While energy justice sets goals of justice in energy systems as
mentioned above, energy equity provides means to achieve these goals, such as
through energy accessibility, participation in energy programs, and fair
treatment of all individuals.

The definition of energy equity evolves from a simple concept to specified
implementable policies. The earliest government definition of energy equity
dates back to 2015 when the United Nations (UN) advocated equality and non-
discrimination in energy usage in its Sustainable Development Goals (SDGs) and
envisaged a world where “the needs of the most vulnerable are met.”
Specifically, SDG 7 aimed to provide all people with affordable, reliable,
sustainable, and modern energy by 2030 [6]. It defines energy equity as
unlocking access to energy for everyone to realize the goal of energy justice.

To achieve this, the main focus should be empowering people who are most
vulnerable to access energy. Accordingly, DOE launched the Equity in Energy
initiative in 2020. It aims to “expand the inclusion and participation of
individuals in underserved communities, such as minorities, women, veterans,
and formerly incarcerated persons, in all the programs of the DOE and the
private energy sector [7].” This initiative focuses on the underserved
communities out of all populations, which are usually the most vulnerable
groups, gathering the resources where they are needed the most.

Lately, the “equity” and “underserved communities” have been specified by the
US government in 2021, to enrich the coverage of energy equity to better carry
out policies. The government defined “equity” as “the consistent and
systematic fair, just, and impartial treatment of all individuals, including
individuals who belong to underserved communities that have been denied such
treatment, such as Black, Latino, and Indigenous and Native American persons,
Asian Americans and Pacific Islanders and other persons of color; members of
religious minorities; lesbian, gay, bisexual, transgender, and queer (LGBTQ+)
persons; persons with disabilities; persons who live in rural areas; and
persons otherwise adversely affected by persistent poverty or inequality.” It
further defined “underserved communities” as “populations sharing a particular
characteristic, as well as geographic communities, that have been
systematically denied a full opportunity to participate in aspects of
economic, social, and civic life, as exemplified by the list in the preceding
definition of ‘equity’”[8]. This definition provides a detailed guideline for
society to actually implement energy equity policies to achieve justice. In
addition, this state-of-the-art categorization of the underserved communities
highlights the modern focus of the energy equity programs.

At the end of this section, we summarize the timeline and evolution process of
energy justice and energy equity government definitions in Table 1.

Table 1: Summary of government definitions on energy justice and energy equity Concept | Institute | Time |  Subject |  Target
---|---|---|---|---
Environmental Justice [3] | White House | 1994 |  Health or environmental effects |  Minority and low-income populations
Energy Equality [6] | UN | 2015 |  Access to energy |  All individuals
Energy Justice [4] | DOE | 2019 |  Participation in the energy system; burdens |  Those disproportionately harmed by the energy system
Equity in Energy [7] | DOE | 2020 |  Inclusion and participation in energy programs |  Underserved communities
Equity [8] | White House | 2021 |  Consistent and systematic treatment |  All individuals; underserved communities
Justice40 [1] | White House | 2021 |  Federal investments |  Disadvantaged communities

##  2 Energy Justice and Equity in Literature

The energy fairness issues have been studied in the academic domain earlier
than the government definitions were provided. As compared to high-level
conceptual governmental definitions, energy justice and energy equity in the
academic domain focuses on establishing detailed analytical frameworks and
quantitative methods on injustice, unfair, or disproportionate issues. More
specifically, the lens of energy justice in literature analyzes justice issues
from three or more dimensions emphasizing various aspects of justice, such as
the distribution of resources, the decision-making procedure, and the
recognition of injustice. The concept of energy equity is further specified by
measuring the severity of the sufferings resulting from energy injustice,
covering common types of unfair treatment in energy-related areas. It is
worthwhile mentioning here that different concepts, such as energy democracy,
have been proposed in the literature to promote individual’s participation in
decision-making processes relating to the energy systems, and eventually are
included in the energy justice framework [9].

###  2.1 Energy Justice

As a conceptual notion derived from justice, energy justice in literature can
be summarized as a framework for analyzing the fair and impartial
accessibility and opportunity for all individuals involved in the energy
systems. This analytical framework mainly consists of three core tenets:
distributional justice, procedural justice, and recognition justice [10, 11,
12].

Distributional justice initially addressed the locational disparities of
benefits or burdens related to energy [10]. The purpose of the distributional
justice is to identify and avoid situations where some populations carry a
disproportionate share of the burdens or lack access to benefits. This concept
has been extended in [11] from across geographic locations to across
populations, because the locational difference can be seen as a character
within a community, among other characteristics. It is worth noting that,
while the unfair distributions across locations and economic statuses have
been studied, the unequal treatments across gender, race, and other
characteristics still require more attention [13].

Procedural justice is concerned with who has access to energy decision-making
processes. It aims for equitable energy procedures by encouraging the
inclusiveness of persons involved at all levels. Three mechanisms to
facilitate inclusion for procedural justice were proposed, namely, local
knowledge mobilization, full information disclosure, and equal institutional
representation [10]. Especially, overlooking indigenous knowledge in energy
decision-making can be detrimental to the local community [14].

Recognition justice calls for efforts to identify individuals affected by
energy injustices. While some publications include it as part of procedural
justice given its fair representation feature [12], many take it as a separate
tenet because it recognized energy injustice from more perspectives than the
coverage of procedural justice, such as historical energy inequalities [11].
Failure to recognize injustice situations postpones the realization of energy
justice. Three main categories of misrecognition are cultural domination, non-
recognition, and disrespect [15].

Some researchers add a fourth dimension to the framework: restorative justice,
which describes the remediation of a perceived energy injustice [12]. As a
concept primarily used in criminal law, restorative justice can be applied to
each phase of the energy life-cycle to repair the harm caused by injustice
[16].

By utilizing this framework, researchers can analyze and uncover existing
energy injustice related issues. For example, one study applied the framework
to explore urban residential energy consumption for heating and discovered the
significance of spatial, racial, and socioeconomic factors in the unjust
distribution of energy efficiency in Detroit, Michigan [17]. In another study,
the framework was used to survey and categorize energy equity metrics (with
the details to be described in the following section), such that the focus of
each metric in terms of energy justice dimensions is identified, which helps
facilitate interactions among metric users [18]. Moreover, researchers have
utilized energy justice to investigate specific issues in energy policy,
planning, and operations, including energy transitions [19, 11], community
energy initiatives [12], gas policy and planning [20], power plant pollution
[21], energy storage [22], and electricity tariff designs [23]. Finally, as a
by-product, researchers surveyed energy programs across the US and identified
253 energy justice programs in total, with 83% of them being run by nonprofit
organizations, indicating less effective actions from governments (less than
17%) [24].

###  2.2 Energy Equity

Within the framework of energy justice, “energy equity” serves as an
comprehensive term encompassing various forms of inequities experienced by
individuals and communities as a whole. To gauge the extent of inequity within
energy-related situations, “energy equity” can be further divided into
distinct categories, such as energy poverty, energy burden, and energy
insecurity. Some publications have previously used these notions
interchangeably [17, 25, 26], but recent studies have increasingly emphasized
their unique angles in characterizing situations that challenge the notion of
energy equity.

Tarekegne et al. [27] summarized four primary categories within the realm of
energy inequity: energy poverty, energy burden, energy insecurity, and energy
vulnerability. While the boundaries of each category do not have a universal
consensus in research [28], a rigorous delineation of these concepts holds
significant importance. Such a classification not only standardizes research
within the field of energy justice but also facilitates the identification of
those who are disproportionately affected. By dissecting and distinguishing
these categories based on demographic and energy-related indicators [29], this
approach enhances our understanding of energy inequities.

In this section, we aim to categorize and present the prevalent definitions,
status quo, and challenges associated with these equity angles. It is
important to note that our focus here is on these inequity terms within the
context of households, they shall not to be confused with the same words in
other contexts, such as “energy burden” in the context of energy generation
systems [30] or “energy insecurity” for a nation [31].

####  2.2.1 Energy poverty

Energy poverty, defined as inadequate access to modern energy services, stems
from various causes, including a lack of energy infrastructure and utility
disconnections due to the inability to pay the energy bills [26]. For
instance, in Africa, the persistence of energy poverty is exacerbated by the
high costs associated with extending power grids, while in South American
urban communities, where the grid exists, unpaid utility bills pose
significant challenges [19]. Energy poverty extends beyond electricity; it
encompasses inadequate access to cooking and heating fuels, transportation
gas, and other essential daily energy needs, making its eradication a complex
endeavor.

The consequences of energy poverty are far-reaching, including social
exclusion, material deprivation, and poor health resulting from the lack of
access to essential lighting, cooling, or heating services [32]. Additionally,
gender and ethnicity disparities play a substantial role in perpetuating
energy poverty, further exacerbating the imbalance in access to energy
resources [33, 34, 35]. As an intersection of poverty and the energy system,
energy poverty contradicts the fundamental goal of energy equity, resulting in
unequal access to vital energy resources.

Alarmingly, as of 2021, approximately 770 million people worldwide still lack
access to electricity, with the majority residing in Africa and developing
Asian countries [36]. Coronavirus Disease 2019 (COVID-19) disrupted the steady
progress towards universal access to electricity and clean cooking. In
response, researchers and policymakers have been actively addressing these
challenges through initiatives such as rural electrification [37] and revising
energy pricing strategies [38] to promote greater accessibility among
marginalized communities.

####  2.2.2 Energy insecurity

Energy insecurity is defined as the inability to adequately meet household
energy needs [27]. It is worth clarifying that energy insecurity is a term
often applied in the studies for developed countries, in contrast to “energy
poverty” which is more commonly used in discussions of less developed regions
[39]. Interestingly, some studies in developed countries use “energy poverty”
interchangeably with “energy insecurity” [40].

The notion of energy insecurity can be traced back to “fuel poverty.” Boardman
[41] first used “fuel poverty” to describe the homes that could not afford
adequate warmth. This concept invoked rigorous studies on fuel pricing and
energy efficiency in the United Kingdom (UK) and Northern Europe. Unlike
“energy poverty,” people who suffer from fuel poverty have access to the
required energy service but struggle with affordability.

Households often experience energy insecurity issues as a result of extreme
heat or cold-related events. Yoon and Hernández [42], through a thematic
analysis of US news media articles from 1980 to 2019, shed light on
geographical distinction in energy insecurity risks. They found that Southern
states were the predominant victims of extreme heat, whereas Midwestern and
Northeastern states had more coverage of extreme cold-related issues. The
authors emphasized that income and wealth inequalities within states played a
significant role in shaping the disproportionate impact of extreme
temperatures on various demographic groups.

However, Baker et al. [43] warned that ethnicity disparities in energy
insecurity were often more severe than the disparities based on socioeconomic
levels. Memmott et al. [44] further showed that households at or below $200\%$
of the federal poverty line, as well as Black and Hispanic households, were
more likely to experience energy insecurity.

A critical issue highlighted by Bednar and Reames [45] is that, despite its
prevalence, the United States has not formally recognized energy insecurity as
a distinct problem from general poverty at the federal level, limiting
effective responses. They argued for a shift in current metrics, which
primarily focus on resource distribution, toward metrics that prioritize
improving household well-being and reducing overall energy insecurity. In this
regard, Cong et al. [46] developed a novel energy insecurity metric known as
the “energy equity gap.” This metric is calculated based on the difference in
the inflection temperatures between low and high-income groups, with
inflection temperature defined as the outdoor temperature at which a household
begins to use its cooling system. Figure 2 illustrates the disparities in
inflection temperatures. The figure on the left compares the median inflection
temperature for each ethnicity over a span of 4 years. The figure on the right
presents the ”Energy Equity Gap” within each ethnicity over the same period,
where each data point represents the difference in inflection temperatures
between low- and high-income populations for a given ethnicity. The figure
shows increasing Energy Equity Gaps for all four races from 2017 to 2019. It
is evident that the Black population experienced both the highest overall
inflection temperature and the most significant energy equity gap during the
years 2015-2019.

Figure 2: Inter- and Intra-group Comparison of the Inflection Temperature
[46]. Left: Median inflection temperature shows disparities across ethnicity.
Right: The energy equity gap illustrates the difference in energy consumption
behavior between high and low-income groups within each group.

Recent publications have also examined the disproportionate impact of the
pandemic on energy insecurity. Lou et al. [47] analyzed the percentage changes
in hourly electricity consumption resulting from measures took against
COVID-19 and found an increasing trend in energy insecurity among ethnic-
minority households and low-income households.

####  2.2.3 Energy burden

Energy burden measures the percent of a household’s income spent to cover
energy cost [48]. This financially induced definition implies low
affordability of energy for low-income families. When the energy burden
surpasses a certain threshold, it can push a family into a state of energy
insecurity. In many studies, $6\%$ has become a widely used threshold, based
on the idea that families can reasonably allocate up to $30\%$ of their income
on shelter costs, with energy bills usually accounting for $20\%$ of that
expenditure [49].

Scheier and Kittner [40] highlighted a lag in energy burden studies in the US
due to the absence of more modern metrics. The energy burden formula results
in long tail of households with very low incomes and fails to capture zero
income and negative energy cost scenarios. To address this gap, they
introduced the Household Net Energy Return ($N_{h}$), defined as:

$N_{h}=(G-S)/S,$ (1)

where $G$ represents the gross income for a household and $S$ denotes their
spending on energy. With the established threshold for energy burden at
$S/G=6\%$, the energy insecurity line for $N_{h}$ is approximately $16$. In
practical terms, this means that a household earning less than $$16$ for each
dollar spent on energy will be considered energy insecure (or “energy poor” in
the developed country context). This is shown as the horizontal red dotted
line in Figure 3a, where horizontal axis shows the proportion of households
and vertical axis shows the Net Energy Return. The black curve in Figure 3a
shows the distribution of $N_{h}$ across all population.

It is crucial to emphasize that, despite the financial nature of the notion of
energy burden, the income gap is not the only aspect that needs to be
addressed. Some other important household characteristics are shown in Figure
3c-f, including primary heating fuel type, housing type, household race, and
education. As Executive Order 13985 [8] advocated, all underserved communities
who have been denied opportunities to the modern energy services are worth
further attention from researchers and policy-makers. Consequently, there is a
growing need to establish effective and tailored metrics to facilitate the
recognition and support of energy-burdened families.

Figure 3: The Distribution of $N_{h}$s Across Different Household
Characteristics [40]. Subfigure a shows the overall distribution. Subfigures
b-f show the difference among groups of households with different
characteristics.

Bird and Hernández [50] estimated potential annual savings ranging from $\$4$
billion to $\$11$ billion by addressing the energy burdens for the poorest
renters in the United States. To facilitate the recognition and assisting
process for energy burdened families, the U.S. DOE developed the Low-income
Energy Affordability Data (LEAD) Tool [51]. This tool provides census-tract
level data on low-income household populations and their associated energy use
characteristics.

####  2.2.4 Energy vulnerability

Energy vulnerability, a lesser-explored aspect of energy equity, describes the
propensity of a household to suffer from a lack of adequate energy services
due to advert event or change [27]. Households facing severe energy
vulnerability may in turn experience high energy burden, energy insecurity, or
even energy poverty in the foreseeable future. This vulnerability often arises
from mismatches between the supply and demand of the energy, influenced by a
multitude of factors. These factors include risks associated with weather and
climate, which are common causes of changes in energy demand and setbacks in
energy generation and transmission. Additionally, trade patterns and
geopolitical concerns can cause volatile energy price [36].

Recent studies show that the transition and development in energy grid can
affect households’ energy supply unintentionally. Carley et al. [52] provided
a framework for understanding energy vulnerability from energy transitions
across three dimensions: exposure to risk, sensitivity to the impacts of these
risks, and adaptive capacity to attenuate, cope with, or mitigate the negative
effects. To quantify vulnerability, the authors proposed a Vulnerability score
$V$ based on this framework, calculated as follows:

$V=\sum_{p=1}^{P}\left(1/I\sum_{i=1}^{I}E_{i}\left(\sum_{j=1}^{J}S_{j}\right)_{i}-1/I\sum_{i=1}^{I}E_{i}\left(\sum_{k=1}^{K}A_{k}\right)_{i}\right),$
(2)

where $p$ is each policy (risk) under consideration, $E_{i}$ measures the
exposure of type $i$ associated with a policy, $S_{j}$ and $A_{k}$ evaluate
the sensitivity of type $j$ and adaptive capacity of type $k$ for a type of
exposure respectively. A higher vulnerability score indicates less resilience
to the risk for a community. In Figure 4, the authors demonstrated significant
geographic variation in energy vulnerability by 2013.

Figure 4: Vulnerability Score Mmap Based on the US Renewable Portfolio
Standard (RPS) Example with Price Effect Exposure for 2014 [52]. RPS policies
require that a specified percentage of the electricity utilities sell comes
from renewable resources thus influencing the energy price. Native American
territories are not assigned a vulnerability score as they are exempt from RPS
requirements. Each colored range of the vulnerability score has the same
number of observations.

Numerous publications have attempted to enhance energy resilience through
initiatives related to housing and energy supply infrastructure [53],
vulnerability indices [54], and trading policies [55]. While efforts to
improve energy resilience benefit those directly involved, it is important to
acknowledge that the unequal distribution of energy vulnerability across the
population remains a significant concern. Factors influencing energy
vulnerability are expected to exacerbate such injustices.

Chen et al. [56] addressed disproportionate impacts of disasters and pandemics
from both micro-level (socio-demographic and household factors) and macro-
level (quality of energy and infrastructure) perspectives. They discussed the
applications of mathematical and statistical models to understand and predict
the outcomes of disasters, further highlighting the multifaceted nature of
energy vulnerability within communities.

####  2.2.5 Beyond existing categories

While these four energy equity categories provide valuable building blocks for
studying energy inequity situations based on the accessibility and
affordability of energy resources to households and communities, they fall
short in capturing the full spectrum of energy equity issues. More
perspectives must be explored to more precisely and effectively address energy
justice.

A crucial aspect often overlooked is the differentiation of energy resources
and energy services. Various energy types and evolving energy services have
distinct impacts on consumer behaviors and priorities. For instance, the
utility bills associated with electricity used for cooking may differ
significantly from those used for charging electric vehicles. These nuances
are not given sufficient attention in current energy equity discussions.

Moreover, the portray of “underserved communities” and “disadvantaged
communities” based solely on income, race, and location is limited. Ivanova
and Middlemiss [57] highlighted that households with disabled members often
earn less and consume $10\%$ less than other households in the European Union
(EU), making them more susceptible energy poverty. Baker et al. [43] made a
critical distinction between marginalized communities and low-income
neighborhoods, emphasizing that marginalized populations are often
underrepresented in decision-making processes related to energy justice.
Raising the voices of underrepresented population can introduce greater
diversity into studies and help overcome the inertia within traditional
frameworks. Pinpoint the target persons and communities who have suffered from
energy injustice can enhance the recognition process and improve the
effectiveness of assistance programs.

Furthermore, despite of the innovative scores we have reviewed earlier, there
remain energy equity issues that lack a satisfying quantitative measure.
Additionally, special attention should be given to the localization of energy
metrics derived from foreign research. When translating energy metrics across
countries, these methods often necessitate the normalization of various
variables among different types of data, which can be a complex and
challenging endeavor [40]. This highlights the need for further research and
the development of more adaptable and context-specific metrics to address
energy justice on a global scale.

##  3 Measures for Equity

While many methods were applied to recognize and correct energy inequities,
such as regression models [39, 57, 26, 58], net energy analysis [40], along
with various data mappings and visualizations [59, 60, 61], there are well-
established equity measuring tools from economics and network communications
being widely adopted in energy equity studies. The most popular instruments
are the Gini coefficient and generalized entropy indices. In this section, we
introduce the definition of each measurement, present their applications in
energy equity, and analyze the shortcomings of these tools.

###  3.1 Definition of Gini Coefficient

Gini coefficients have been widely used in economics to estimate income
inequality as an indicator of social welfare [62] thanks to its simple
mathematical formulation and instinctive graphical interpretation of
inequality. The Gini coefficient quantifies the inequality as the difference
between an ideal situation of equality where everyone has the same shares of a
resource and the actual distribution of the resource. It ranges from $0$ to
$1$ with value $0$ denoting the perfect equality while value $1$ denoting the
maximum inequality, where only one person possesses all the resources.

There are two mathematical expressions of the Gini coefficient. For the first
one, it is used to measure the variability of any statistical distribution. As
proposed by Gini [63], it is represented as the average absolute difference
between pairs of observations $x,y$ divided by twice the mean $\mu$ , i.e.,

$G=\mathrm{E}(|x-y|)/(2\mu).$ (3)

For the second one, it can be regarded as a summary statistic of the Lorenz
Curve for a resource [64]. More specifically, as shown in Figure 5, in which
the $x$ axis represents the cumulative share of components $F(i)$ and the $y$
axis represents the cumulative share of attribute value $L(i)$, where $i$ is
the index of population group, the Lorenz curve specifies the cumulative
amount of the resource that belongs to the lowest $100i$-th percentile of the
population. If it is perfect equality, the Lorenz curve converges towards the
diagonal line (red line in the figure) from the origin $(0,0)$ to the upper
right corner $(1,1)$, corresponding to a uniform distribution, which indicates
that everyone receives the same amount of the resource. The general Lorenz
curve can be represented as the black line in the figure, corresponding to the
actual distribution of the resource. This black line splits the lower triangle
into two areas $A$ and $B$, in which $A$ is the area between the egalitarian
line and the general Lorenz curve, representing the gap between the actual
allocation and the uniform distribution, and $B$ is the area below the Lorenz
curve. Based on this, the Gini coefficient is defined as the ratio of $A$ to
$A+B$, i.e.,

$G=A/(A+B).$ (4)

Because $A+B=1/2$ and it is easy to obtain $B$, we can rewrite the above
formula (4) for the discrete case as

$G=2A=1-2B=1-\sum_{i=1}^{N}(F_{i}-F_{i-1})(L_{i}+L_{i-1}),$ (5)

where $F_{i}$ is the cumulative proportion of the population up to group $i$
(with $F_{0}=0$), in which the population groups are non-decreasingly ordered,
and $L_{i}$ is the cumulative proportion of the resource possessed by
population groups up to group $i$ (with $L_{0}=0$). In the less used
continuous case, area $B$ can be measured by integration. Because the area
under the equality line is constant, the further the Lorenz curve is away from
the diagonal line, the higher the Gini coefficient gets, and the more severe
inequality underlies. Yitzhaki and Schechtman [62] pointed out that the second
definition can be applied to both discrete and continuous distributions while
the first definition is only valid for the continuous case. Furthermore,
different shapes of Lorenz curves may result in the same Gini coefficient
value. In this case, the Gini coefficient ignores the structural difference
among various inequalities. Therefore, when comparing similar Gini
coefficients, a graphical representation based on the Lorenz curve is more
precise in explaining the inequality structure.

Figure 5: The Lorenz Curve for the Gini Coefficient [65].

###  3.2 Application of Gini Coefficient in Energy Equity

To quantify the equity issues in energy production, access, and consumption
among different population groups, an increasing number of researchers have
turned to Gini coefficients. Gini coefficient has been used to identify the
distribution of energy among population groups [66] before the concept of
energy justice was involved.

The first notable literature of Gini coefficient application in the context of
energy justice focused on power consumption inequality [67]. In this work, the
authors revealed the significant disparities across nations, using the intra-
country distribution of residential electricity consumption with the Lorenz
curves for five countries. By the comparison of Gini coefficients, they
highlighted the stark contrast between Norway, where $38\%$ of the population
used half of the residential electricity (Gini coefficient of 0.61), and
Kenya, where $6\%$ of the households consumed half of its electricity (Gini
coefficient of 0.87). Following this landmark study, many papers have employed
the Gini coefficient to assess the energy consumption inequality.

Some publications utilizing Gini Coefficient of energy consumption focused on
one country. In Brazil, the decreasing of the Gini Coefficient after the
expansion of access to electricity endorses the effectiveness of rural
electrification in terms of energy equity [68]. In China, the fossil energy
consumption were getting more equitable among provinces from 1997 to 2013 [69]
while a reversal relationship between the Gini ratio and urbanization level
indicates more energy equality among buildings in more developed provinces
[70]. In rural China, two major energy types contributing to the overall
energy inequality were biomass ($61.4\%$) and electricity ($12.1\%$) [71]. In
both urban and rural India, equity in energy consumption was improved over
1987-2012 [72]. In the U.S., little inequality in residential energy
consumption was seen during 1990-2015 while the energy poverty rate increased
from $15.7\%$ in 1990 to $22.6\%$ in 2015 [73].

Some publications took a global perspective. While global inequality in energy
consumption has been decreasing [74], more prominent inequalities were evident
across countries in specific energy services, including renewable energy [75],
air transport energy [76], and solid fuels [77].

Beyond energy consumption, various Gini coefficients related to other energy
equity have been explored, including carbon emission [78, 79, 80], energy
services [81], photovoltaic solar installation [82], energy supply [83, 84],
energy system’s reliability [85, 86], energy technology [87], and global
energy trade [88].

In addition to depicting the static status of energy equity at a time point,
the Gini coefficient can be further integrated into decision-making process
for dynamic analyses of energy equity. This integration allows for monitoring
changes in Gini coefficients related to a specific energy topic, thus
demonstrating the positive impact on energy equity resulting from proposed
frameworks or models. For instance, one study adopted the efficiency-fairness
trade-off curve for evaluating the electricity pricing scheme, where fairness
is measured by the Gini Coefficient [89]. Another research compared the Gini
coefficients of natural gas consumption for actual and simulated data to
support the proposed tariff scheme over the existing one [90]. The Gini
coefficient was also employed to measure the regional equity as the result of
their decentralized renewable electricity generation allocation that balanced
cost-efficiency and energy equity [91]. Humfrey et al. [92] monitored the
resulting Gini coefficient of $\mathrm{CO_{2}}$ emission from the proposed
dynamic charging system integrated with renewable energy to ensure a fair
impact on user experience.

Moreover, the Gini coefficient can be set as part of the objective to be
optimized for the consideration of energy equity. For instance, one study
introduced preference for equality measured by the Gini coefficient in their
generation expansion planning model for people with limited electricity
infrastructure to appraise the trade-offs between energy inequality and total
electricity consumption [93]. Ma et al. [94] included minimizing the Gini
coefficient of coal production capacity in their coal capacity allocation
model to balance efficiency and equity. Sasse and Trutnevyte [60] modeled the
regional equality of the impacts from energy transition using Gini coefficient
and discussed the trade-offs among minimizing system costs, maximizing
regional equality, and maximizing renewable electricity generation. Levinson
and Silva [95] constructed a cost redistribution model for electricity pricing
based on the Gini coefficients of electricity bills for each electricity
utility in the US which shifted more costs in utilities with higher Ginis.

Publications also pointed out caveats of the Gini method when applied in
energy equity studies. Considering the financial origin of the Gini
coefficient, Jacobson et al. [67] emphasized the difference between income and
energy data when applying the Lorenz curve. The authors stated two
requirements when quantifying energy as a reasonable attribute for the Gini
coefficient: (i) roughly constant overall energy efficiency among consumers,
and (ii) approximately consistent marginal utility from the energy for each
consumer. In other words, all individuals should produce similar result with
the same level of energy usage and all individuals should have similar
improvement with one unit of extra energy. Otherwise, the Gini coefficient may
lose reliability when an equal amount of energy generates distinct levels of
utility for different users. Shu and Xiong [96] validated the continuous Gini
coefficient method for the fat-tailed data of China’s inter-regional energy
consumption.

###  3.3 Analysis of the Gini Coefficient for Energy Equity

In this section, we summarize the energy equity applications of Gini
coefficient based on the attribute values and population group criteria and
reveal weak points in current studies in addressing modern concept of energy
equity.

Table 2 and Figure 6 provide a summary of the attribute values used in the 33
publications discussed above. As can be seen, a large majority of the
publications focused on energy consumption ($39\%$). Compared to other data,
energy consumption data is more accessible, accurate and relatively more
stable with regard to energy-based inequality [71]. As shown in publications,
inequality of energy consumption exists from emerging markets to developed
area, from past to present.

Table 2: Publications on Energy Equity Using Gini Coefficient by Attribute Value Attribute value |  Publications
---|---
Energy consumption |  [67, 68, 70, 74, 71, 72, 69, 75, 90, 76, 93, 77, 73]
Energy supply |  [91, 94, 83, 84, 88]
Energy expenditure |  [81, 72, 76, 95]
Pollution emission |  [78, 74, 79, 96, 92, 80]
Other |  [89, 82, 85, 86, 87]
Figure 6: Attribute Values of Publications on Energy Equity with Gini
Coefficient

However, consumption alone cannot depict the whole picture of the energy
equity issues. Besides energy consumption revealing inequality in energy
poverty, energy expenditure sheds light on energy accessibility and burden
[73], and energy production and supply affects the energy security and
diversification [83].

In addition to the general energy consumption data, researchers also have
studied inequalities in terms of specific energy types and energy usages,
revealing greater inequalities in less accessible energy sources (e.g.,
liquefied petroleum gas and biomass) and more expensive applications (e.g.,
space cooling and air transportation) [71, 76].

Most studies show energy inequality measured by direct data, while some recent
publications utilize constructed indicators as attribute values for the Gini
coefficient calculation. For example, Wang et al. [73] focused on the
residential energy burden, defined as the ratio of the energy expenditure to
the household income.

Finally, we report literature on energy equity based on the population group
criterion. Table 3 and Figure 7 outline comparison scopes that have been
published using Gini method. Almost all Gini coefficients were calculated
based on the population data grouped by region except for Zhang and Wang [86],
who used a GDP-based Gini. Hence, most of the publications focused on regional
gaps ($78.3\%$), either concentrated on one country, or investigated multiple
countries at the same time. In the latter case, regional inequalities can be
evaluated in two ways. Some studied global allocation of the energy by
plotting multiple countries on the same Lorenz curve [78, 82, 75, 97, 76, 84,
77] while some displayed Lorenz curves for each country and compared the
structural difference among their inequalities [67, 72, 83, 98, 86].

Table 3: Literature on Energy Equity using Gini Coefficient by Comparison Focus Comparison focus |  Literature
---|---
Region |
\- One country |  [68, 70, 81, 79, 91, 69, 96, 82, 94, 86]
\- Multiple countries |  [67, 78, 74, 75, 97, 83, 84, 77]
Economic status |  [72, 76, 86]
Race |  [98, 73]
Figure 7: Comparison Scopes of Literature on Energy Equity with Gini
Coefficient

Recent publications shifted their comparison scope from geography to other
features, such as economic status and race. To evaluate disparities across
prosperity levels, Zhang and Wang [86] established Lorenz curves based on GDP
standards, and Ranjan and Singh [72] and Zhang and Wang [86] compared
inequalities in rural and urban parts of a country. To study racial
inequalities, Tong et al. [98] represented each block of a city by its racial
minority percentage, while Wang et al. [73] used household data categorized by
ethnic group. There are two approaches to investigate inequalities among
communities considering features, including region, race, gender, sexuality,
and disability. One is using feature-based data, whose components can be
divided into groups based on the characteristics of interest. The other one is
using region-based data, where we can extract the feature for each region by
quantifying its composition structure and distinguish the groups by regional
difference.

###  3.4 Limitation of Gini Coefficient

However, energy equality is not the same as energy justice. Despite wide
applications, the Gini coefficient suffers from reductiveness that impedes the
progress of solving energy injustices. It describes the state of inequality in
a number while often ignoring the structure of the inequality which can be the
center of today’s energy issues. Hence, two very different Lorenz curves may
produce the same value of the Gini index even though the actual distributions
vary. For example, based on the data from the World Bank, in 2015, Greece and
Thailand have the same Gini index of income ($0.36$) but the ratio of the
income share held by the richest $10\%$ to the income share held by the
poorest $10\%$ in Greece is $13.8$ while that in Thailand is $8.9$ [99].

Furthermore, a situation with a certain amount of population inaccessible to
the resource may still exhibit a good Gini coefficient as long as the resource
is more equally distributed among the rest of the population albeit the people
who suffer most are usually the focus of social problems. Graphically, this
scenario can be represented as the lower end of a Lorenz curve staying at $0$
for some population shares. For example, consider two communities, A and B,
with the same $100$ individuals who divide $100$ units of energy in total.
Twenty people in community A are allocated $0$ energy resource while the rest
of the community divides the energy equally. In community B, half of the
population divides $25$ units of energy evenly while the other half consumes
the rest $75$ units of the energy uniformly. As shown in Figure 8, community A
has a Gini coefficient of $0.2$ and community B has $0.25$. Because community
A has a lower Gini value, we may conclude A is a better community regarding
the equity in energy consumption. However, there is a $20\%$ population have
no access to the energy in A while everyone in B has a similar amount of
energy. The underserved people in community A are the focus of Executive Order
1398 signed by President Biden. Hence, this limitation makes the Gini
coefficient ineffective in addressing the energy inequity issues for
underserved communities.

Figure 8: Lorenz Curve of Energy Distribution. The diagonal line denotes the
perfect equality. The Gini coefficient of community A is $0.2$ and the Gini
coefficient of community B is $0.25$.

Moreover, the underserved community remains on the frontier that suffers from
fatal impacts of energy inequity. In reality, lack of access to energy
services costs lives. An average of 702 heat-related deaths occurred in the US
each year from 2004 to 2018 [100], the key driver of which is inaccessibility
to the cooling service [101, 102]. In 2020, there were more than 20 million
American families owed about $\$23$ billion in utility bills in total [103].
Therefore, failure to address the structural characteristics of the observed
inequality when applying the Gini method can lead to ineffective or even false
results.

###  3.5 Generalized Entropy Indices

Besides Gini Coefficient, inequality measures derived from the Generalized
Entropy (GE) are another group of popular indices for evaluating income
inequality. First used in thermodynamics, Entropy was introduced to
information theory by Shannon as the information of a random variable [104].
Generalized Entropy is defined as [105]

$GE(\alpha)=\left[1/n\sum_{i=1}^{n}(q_{i}/p_{i})^{\alpha}-1\right]/(\alpha^{2}-\alpha),$
(6)

where $q_{i}=L_{i}-L_{i-1}$ denotes the resource share in group $i$ and
$p_{i}=F_{i}-F_{i-1}$ denotes the population share in group $i$ with $L_{i}$
and $F_{i}$ defined the same as in (5), and $\alpha$ is a non-negative
sensitivity parameter. Some literature adapts a formulation replacing $p_{i}$
with $\bar{q}_{i}$, the mean of $q_{i}$. It is an equivalent expression when
individuals are grouped evenly. GE indices vary from $0$ to infinity with $0$
denoting the ideal egalitarian state of equal allocation and higher values
meaning more severe inequality. The parameter $\alpha$ indicates the weight on
the higher and lower ends of the distribution. Low values for $\alpha$ make GE
more sensitive to changes in the lower tail, while higher values emphasize the
population with more resources.

Theil’s $T$ [106] and Theil’s $L$ [107] are two commonly used Entropy indices.
Taking the limits of (6) when $\alpha$ goes to $1$ or $0$ gives Theil’s $T$
(see (7)) or $L$(see (8)), which are given by

$T=\sum_{i=1}^{n}q_{i}\ln(q_{i}/p_{i}),$ (7)
$L=\sum_{i=1}^{n}p_{i}\ln(p_{i}/q_{i}).$ (8)

Theil’s $L$ sometimes may be referred to as the mean log deviation measure. It
is worth noting that the specification of $\alpha$ affects the configuration
of the $GE(\alpha)$ index, making it hard for comparison between studies [99].

While this class of equity measures is more complicated and graphically lacks
intuitive representation, they are helpful for decomposing inequalities for
in-depth analysis, which is hard to accomplish with the Gini coefficient. If
we arrange the groups into different categories, then inequalities measured by
Theil indices can be decomposed into the “within-category” component and the
“between-category” component. Depending on the categorizing criterion (e.g.,
region, GDP, education, or gender), decomposition can be helpful in policy-
making and planning [108].

Atkinson index (see (9)), another income inequality measure, is also related
to GE. Similar to GE measures, it can determine which end of the distribution
contributed more to the observed inequality. The Atkinson index ranges from
$0$ to $1$ with $0$ representing ideal equality. It is defined as

$A=\begin{cases}1-\left[1/n\sum_{i=1}^{n}(q_{i}/p_{i})^{1-\epsilon}\right]^{1/(1-\epsilon)},&\epsilon\neq
1,\\\ 1-\left(\Pi_{i=1}^{n}q_{i}^{(1/n)}\right)/p_{i},&\epsilon=1.\end{cases}$
(9)

where $\epsilon$ is an inequality aversion parameter [109]. When $\epsilon$
goes to infinity, i.e., infinite aversion to inequality, the marginal welfare
from the resource to the “poorest” individual is infinitely higher than any
“richer” individual. In this case, the Atkinson index is more sensitive to
changes at the lower end of the distribution. Atkinson index is ordinally
equivalent to GE measures when $\alpha=1-\epsilon$.

###  3.6 Application of GE Measures

Alcantara and Duro [110] first proposed to apply Theil’s $L$ and its
decomposition to assessing energy intensity inequalities across Organization
for Economic Co-operation and Development (OECD) countries during 1971-1999.
Energy intensity, or reciprocal of energy efficiency, is the amount of energy
used to produce a certain level of output. A downward trend was found with a
$64\%$ decrease in the Theil index. The authors divided OECD countries into
$4$ groups by geographical neighborhood and concluded that between-group
inequality was the main contributor to the whole inequality. Feng et al. [111]
observed narrowing gaps in China’s regional disparities of energy intensity
since 2004 over the period from 1985 to 2010. By decomposing Theil’s $T$, they
also found the intra-regional component account for more inequality than the
inter-regional component.

Many studies employed GE indices for measuring carbon emission inequalities.
Padilla and Duro [112] investigated the evolution of $\mathrm{CO_{2}}$
emission inequalities in EU during 1990-2009 with Theil’s $L$. The reduction
in inequality was mostly justified by the reduction in inequality between the
groups of countries. The authors discussed the policy implications of the
decomposition result and foresaw fewer countries with conflicting interests in
future environmental agreements if the reduction of between-group inequality
continued. Bianco et al. [113] spotted a stable trend in the disparities of
carbon emission in the EU during 2008-2016 using the Theil index. For the
decomposition analysis, they found higher between-group inequality when
countries were grouped by geographic criterion, while both components
presented similar results when grouped by GDP level. Pakrooh et al. [114]
presented a similar research method in understanding the provincial
inequalities of $\mathrm{CO_{2}}$ emission in Iran’s agriculture sector. They
suggested GDP based grouping criterion over the population criterion when
focusing on inter-province differences because the former had a lower within-
group contribution towards the total inequality.

GE measures also have been chosen for evaluating energy consumption equities,
sometimes accompanied by the Gini method. Yao et al. [115] utilized the Theil
index to analyze inter- and intra-regional disparities of energy consumption
in five energy sources from an environmental quality perspective. Based on 57
countries’ data over the period 1995-2018, they depicted the evolution of
inequalities between geographical groups for each energy source, including
oil, coal, natural gas, hydroelectricity, and renewable energy. Bianco et al.
[116] conducted Theil approach on energy consumption in five countries of the
Eurasian Economic Union during 2000-2017, revealing decreasing GDP-related
inequality and increasing population-related inequality. Through decomposition
and grouping of countries by GDP level, The authors found between-group
inequality as the dominant factor. Dwi Cahyani et al. [117] found declined
electricity usage inequality among 33 provinces in Indonesia using Theil’ $T$,
$L$, and Gini index. Still, they raised concern about energy poverty for the
low-income population. Ma et al. [118] observed more equality of energy
consumption in China using a survey data of 1010 Chinese households in 2019,
compared with the values of Gini and Theil indices from previous studies. The
result endorsed the government’s promotion of energy reform.

Atkinson index can be found in energy equity analysis, as a complementary
method to the Gini coefficient and GE measures for the robustness of the
result. Sáez and [119] evaluated gross inland energy consumption in the EU
during 2005-2014 using Gini, GE, and Atkinson indices. The author maintained
no preference among the three measures since they gave the same decreasing
trend of inequality, which was explained more by inter-group inequality in the
decomposition of the Theil index. Takada et al. [120] illustrated global
inequalities of energy consumption efficiency from 1980 to 2015 with 41
countries using Lorenz curves, Theil index, and Atkinson index. Countries with
higher energy use exhibited more equality than ones with lower energy
consumption. They considered GE indices as a better measurement than the Gini
index when aiming for greater sensitivity at the lower or upper ends of the
distribution. Setyawan [121] also applied these three inequality measures to
energy usage in Indonesia, arriving at the same result that the level of
disparities decreased from 2010 to 2015.

###  3.7 Other Equity Measures

There are other equity measures deployed in energy-related studies, including
variance-based methods and fairness indices that are commonly employed in
communication networks.

Two basic statistics, standard deviation and coefficient of variation, have
been applied and compared as fairness indices for different power systems
[85]. Standard deviation, or the square root of the variance, measures the
amount of dispersion of observations to its mean. The coefficient of variation
is the ratio of standard deviation to the mean. What makes the coefficient of
variation particularly valuable is its ability to be decomposed into “between-
entity” and “within-entity” components. Moreover, it provides information
about each user’s position regarding the equitable situation, a characteristic
that can be challenging to ascertain using the Gini coefficient. Their case
studies showed that both the coefficient of variation and Gini index generally
yielded similar trends in terms of equality assessment.

Studies in the field of telecommunication have attempted to measure fairness
while developing products and providing services. Quality of Service (QoS) and
Quality of Experience (QoE) are the main fairness indicators [122]. QoS and
QoE consider fairness based on service and user experience. Specifically, QoS
measures the overall performance of a service which depends on the fulfillment
of the user’s need. Jain’s index ($J$) is the most often used metric for QoS
fairness [123] and can be formulated as

$J=1/(1+c^{2}),$ (10)

where $c=\sigma/\mu$ is the coefficient of variation of QoS value. It ranges
from $0$ to $1$ and reaches $1$ when the standard deviation is $0$, i.e., same
QoS across all entities.

QoE measures “the degree of delight or annoyance of the user of an application
or service” [124]. Fairness index $F$ is often used to evaluate the equity of
QoE values among surveyed users. It is defined as

$F=1-\sigma/\sigma_{\max}=1-2\sigma/(H-L),$ (11)

where $\sigma$ is observed standard deviation of the surveyed QoE values,
$\sigma_{\max}$ is the maximum possible standard deviation. $\sigma_{\max}$ is
calculated by the difference between $H$ and $L$, which are upper bound and
lower bound of the QoE value. By normalizing the standard deviation, index $F$
transforms the $\sigma$ of QoE to interval $[0,1]$ and attains the end point
at minimum or maximum standard deviation.

Several publications have employed these indices to guide equitable decision-
making in various energy-related contexts. Jain’s index was utilized along
with the Gini coefficient as fairness indicators in an electricity pricing
scheme, which aimed to maximize social welfare while enhancing fairness [89].
Another study [122] assessed community fairness in their decentralized
electricity market design, where prosumers (consumers who also produce power)
share energy with the community. They evaluated fairness using Jain’s index
for QoS and the $F$ index for QoE. In their framework, QoS represented the
energy allocated to each individual, while QoE denoted the perceived price of
energy.

These fairness indices have also found application in the field of electrical
vehicles (EVs) research. A fair charging mechanism for electrical vehicles,
based on a queuing system, was proposed [124]. The study defined three QoS and
two QoE criteria for the proposed charging service and calculated their
fairness with $F$ index. Through the integration of these metrics, their
weighted fair queuing approach demonstrated superior performance in terms of
QoS results and fairness level. Another study on EV charging established a
transactive energy framework for the real-time coordination of EVs with
voltage control [125]. They measured the fairness among EV owners regarding
energy trading volume (QoS) and their satisfaction (QoE) using Jain’s and $F$
indices, respectively.

##  4 Studies on Improving Energy Justice and Equity

Recognizing various inequity issues and employing equity measurement tools are
crucial steps in bringing the issue of energy justice to the forefront.
However, it is equally urgent to take action to improve the current state of
energy equity. Advancing energy justice involves three primary aspects:
implementing policies to assist disadvantaged communities, incorporating
equity considerations into power system planning, and ensuring that energy
operations are conducted with a focus on equity. In this section, we will
highlight recent efforts aimed at improving energy equity from the
perspectives of policy, planning, and operations.

###  4.1 Policy

Policies aimed at addressing energy equity have faced a range of challenges
and shortcomings. One crucial issue is the potential for policies to
prioritize economic stimulation and overlook structural disparities. For
example, the UK’s fracking policy for shale gas shifted focus from protecting
local communities to favoring pro-industry benefits, resulting in distributive
injustices [20]. To address this, experts suggest applying procedural justice
through the energy justice framework to empower communities in decision-making
processes. Another study found that, while the primary goal within certain
clean energy programs was to benefit low-income groups, Hispanic population
was in a disadvantaged position in terms of the amount of funding received
[126]. This highlights the importance of ensuring that energy policies do not
inadvertently perpetuate inequities among different demographic groups.

In the US, various low-income energy programs have been implemented,
encompassing energy bill assistance, financial incentives, energy information,
and regulations [25]. Yet, decades of weatherization and bill-payment programs
failed to reduce energy insecurity for low-income households, particularly in
rural areas, minority communities, and households with children and elderly
residents [127]. Short-term energy bill assistance programs, like the Low-
Income Home Energy Assistance Program (LIHEAP), often fail to address the
enduring and structurally racialized consequences of energy insecurity.
Advocates propose redirecting more funding toward long-term solutions, such as
Weatherization Assistance Program (WAP), which focuses on weatherization and
energy efficiency for low-income households. Data from 2013 showed
approximately $80\%$ of low-income energy funding went to bill assistance only
while $14\%$ to energy efficiency [25]. To boost the benefits of
weatherization for renters, an on-bill financing policy with split incentives
has been proposed [50]. This policy reduces utility costs for renters while
optimizing the energy efficiency of the building for the landlord and
relieving the energy burden for low-income tenants.

Eligibility criteria for energy assistance programs, particularly those
assessing a household’s assets, can have negative consequences. A research
found that asset tests reduced program participation, disproportionately
affecting the lowest-income families and increasing overall administrative
costs [128]. In their estimation, removing asset tests could have enabled
LIHEAP to assist an additional 9097 households in 2014. However, as of 2023,
assets tests are still required for LIHEAP participants, albeit with varying
definitions and thresholds by state
111https://liheapch.acf.hhs.gov/tables/assets.htm.

The Biden-Harris Administration has taken steps to enhance federal programs,
including LIHEAP, WAP, and clean energy programs targeting disadvantaged
communities, with the goal of lowering energy burdens, increasing access to
clean energy, and modernizing the grid [129]. Despite the promising
developments, further research is needed to evaluate the effectiveness of
these policies and identify any unintended consequences.

Equity challenges also arise in policies not explicitly targeting the low-
income population. Government and utility programs promoting residential
rooftop solar power, EVs, and home energy storage often remain inaccessible to
low-income households. While residential rooftop solar is promising to play a
significant role in changing US electric grid in the coming decades, high
adoption costs have led to disparities in installation rates across
demographics and regions [130]. To address these inequities, there is a
growing focus on ensuring that low- and moderate-income (LMI) residents
benefit from solar power. Initiatives like the State Energy Strategies project
aim to expand the adoption of solar photovoltaic (PV) technology among LMI
residents and communities, with the goal of benefiting at least 15,000 LMI
households [131].

Policies that subsidize EVs to promote them as a clean alternative mode of
transportation have also faced equity challenges. An equity analysis of the
California Clean Vehicle Rebate Project discovered that, while the share of
rebates distributed to low-income groups and disadvantaged communities
increased over time, high-income buyers received a substantial share of
rebates [132]. They emphasized the need for more equitable incentive policies
that take into account underserved individuals and communities.

Energy storage systems represent another promising technology for promoting
affordable and sustainable energy. It has been deployed to support grid
reliability and renewable resource integration. Researchers have highlighted
the equity aspects of assistance programs and policies related energy storage
systems. It is important for government agencies to enact incentive programs
that prioritize the preferences of affected communities as sites for emerging
energy technologies. Programs like the California Energy Storage Initiative
(SB 700) aim to integrate revenue-generating energy storage systems in low-
income and underserved communities, ensuring that these communities benefit
from the advantage of this technology [22]. Similarly, the Oakland Clean
Energy Initiative (OCEI) seeks to replace legacy fossil fuel power plants,
which are often located in disadvantaged communities, with clean energy
storage deployment [133]. These initiatives demonstrate a commitment to both
sustainable energy and energy justice by addressing historical disparities in
energy access and environmental impacts.

###  4.2 Planning

The design and construction of power systems are substantial for every
country, but the challenges and forms of inequity they face can vary based on
their development status.

In less developed countries, bringing utility service to rural areas is a
critical step in improving energy accessibility and combating energy poverty.
Unfortunately, progress in rural electrification has often been slow, leading
to a widening energy gap between rural and urban regions [134]. A
comprehensive review of $170$ papers on rural electrification revealed a lack
of equity discussions in the literature [37]. This gap had two main aspects.
First, while many models aimed to provide affordable energy through power
system planning in alignment with aforementioned SDG 7, only one paper
incorporated energy equity as an optimization objective [135]. This particular
study focused on minimizing the electrification inequality by reducing the
maximum absolute discrepancy between urban and rural electrification rates and
minimizing the maximum disparity of total electrification between any two
regions in Uganda. Second, the review found an imbalance in the regional
coverage of rural electrification literature, with only $15\%$ of articles
focusing on countries with less than $50\%$ electrification rate. Many
countries with very low access rates to energy, including Chad, Burundi, South
Sudan, and Malawi, were not adequately studied. Furthermore, the review
highlighted that current multi-objective frameworks often suffered from
conflicting objectives, making it challenging to fully address energy equity
goals related to accessibility. Lastly, the authors criticized current
mathematical models for their simplicity and their lack of alignment with
real-world scenarios. As a response, a recent study on power system expansion
planning in sub-Saharan Africa [136] developed a mathematical model that
sought to ensure equal electrification for all urban and rural regions across
the country.

In emerging economies, the challenge lies in balancing economic growth with
transitioning to low-emission energy systems. Nock et al. [93] highlighted the
oversight of significant budget constraints faced by many developing nations
in previous literature on generation expansions. Their optimization model
considered per-capita energy consumption as the objective, parameterized by
stakeholders’ preference for equality. The study discovered that a strong
preference for equality led to lower overall electricity consumption but
higher electrification costs due to increased investment in transmission
infrastructure. Conversely, indifference to equality resulted in higher
overall consumption levels in urban areas but lower electrification costs.

In many developed countries, renewable energy development has taken center
stage. Consequently, the discussions about the equitable allocation of
renewable power plants have become increasingly important [36]. A study in
Germany defined equity, in this context, as the equal distribution of the
negative environmental impacts associated with renewable electricity
production across all individuals [137]. These impacts are quantified based on
the ratio of generated renewable electricity to the renewable energy potential
for each state, weighted by the state’s population size. However, the pursuit
of equity often comes into conflict with efficiency. An efficient planning
approach for energy generations, focused on cost minimization, typically
follows energy harvesting conditions, such as placing wind turbines in windy
northern regions and photovoltaic power plants in sunny southern areas. In
contrast, equity considerations advocate for a more even and mixed allocation
of renewable power plants, which may undermine overall efficiency. Given the
significant costs associated with reallocating existing renewable power
plants, there is a pressing need for more research to address the trade-off
between efficiency and equity. In Switzerland, researchers quantified this
trade-off by examining the balance between regional equity and the total
generation cost [91]. They found that $50\%$ increase in equity led to an
$18\%$ increase in cost, highlighting the challenges of achieving both equity
and cost-efficiency simultaneously. Another intriguing study in Switzerland
used a unique approach to elicit citizen preferences for future electricity
generation allocation [138]. Participants engaged in a serious board game that
allowed them to make choices regarding the allocation of new generation
plants. The results showed that participants consistently favored the
efficiency strategy, where new plants were concentrated in the areas that
could produce the most electricity, over the strategy of regional equity,
which involved an equal distribution of new generation plants across all Swiss
regions. This preference for efficiency underscores the complex decisions that
policymakers face when balancing energy transition goals with equity
considerations.

Around the world, the rising popularity of EVs has drawn attention to the
equitable concerns for EV charging, which is becoming an an increasingly
important energy service. Disparities in access to charging facilities has
been recognized, particularly in California, where data shows that Black and
Hispanic majority neighborhoods have approximately half the access to charging
compared to other areas [139]. To address these disparities and guide the
planning process, a comprehensive four-stage framework has been proposed for
analyzing the spatial equity of urban EV charging station distribution [140].
This framework leverages widely accepted statistical methods for evaluating
spatial autocorrelation, Global Moran’s $I$, and its decomposition, known as
Local Moran’s $I$. By employing these techniques, the framework can detect
significant spatial patterns of residential accessibility, identify spatial
clusters of charging stations, and pinpoint outliers in charging station
planning. Meanwhile, a machine learning approach has been developed to
optimize the placement of EV charging station while considering spatial
disparities [141]. Using Random Forest algorithm, this model predicted the
future charging station density in Orange County, California, achieving an
impressive accuracy of $94.9\%$. The analysis incorporates a wide range of
factors, such as vehicle ownership rates, population density, the percentage
of minority populations, education levels, and household income. By assessing
access equity based on these multifaceted factors, grid planners gain the
capability to identify disadvantaged communities with limited accessibility to
charging stations. This approach empowers decision-makers to implement
targeted investments that can rectify these disparities.

###  4.3 Operation

In contrast to planning, operational changes in the power system have a more
immediate and tangible impact on consumers. As a result, numerous publications
have focused on achieving energy equity by modifying the mechanisms of power
system operations, with particular attention to system reliability,
electricity pricing, and the integration of emerging technologies.

In the realm of power system operations, decisions can significantly affect
the energy provision and system reliability for individual end-users. This
raises important equity concerns for those affected by these decisions. A
research [85] introduced a set of fairness ratios to assess the distribution
of reliability among end-users based on the energy demand and various
reliability indicators, such as load curtailment, total interruption duration,
and interruption cost. The authors injected these ratios into equity measures,
including the Gini coefficient and variance-based methods, to assess the
impact of reliability on consumers. This approach enables the evaluation of
operational decisions in the power system, based on customized equity
requirements, ensuring that the distribution of reliability aligns with
fairness principles.

Another essential component of power system operations is tariff design. It
plays a pivotal role in recovering utility costs while simultaneously
addressing multiple objectives, including equity and fairness [38]. The common
equity considerations in tariff designs are allocative equity, distributional
equity, and transitional equity [142]. First, an allocatively equitable tariff
charges customers at the same location and time the same marginal rate for
electricity consumption. This approach minimizes the impact of one customer’s
actions on another, aligning with principles of “distributional justice”.
Second, distributional equity requires a tariff design to address the
equitable access to electricity services for vulnerable customers, as
identified by local standards. For instance, lifeline rates and energy
affordability policies have been proposed to subsidize electricity consumption
for low-income households [143, 49]. Besides, a justice-aware tariff model has
been introduced to account for socio-economic and demographic profiles to
create an equitable locational hourly tariff [23]. Third, transitional equity
considers the fair impact on customers when transitioning to new tariff
structures. These considerations range from Pareto criteria to Kaldor-Hicks
criteria, with the former emphasizing that at least one customer benefits from
the transition and no one loses, while the latter favors the transition that
improves overall net welfare [142]. Transitioning to more economically
efficient tariffs has been observed to lead to bill increases for low-income
customers in some cases. Simple adjustments to tariff designs, such as
discounted fix charges for low-income customers, can help mitigate these
disparities [144].

The surge in Distributed Energy Resources (DERs), including PV panels and
small wind turbines, has introduced additional complexities into electricity
tariff designs. DERs are small-scale electricity generation modules that can
be integrated into the power grid, providing significant advantages to
retailers and consumers by reducing cost and emission and increasing power
reliability. Traditional tariff structures have been found to perform poorly
with DERs, potentially leading to substantial wealth transfers from other
consumers to DERs owners [145, 38]. One of the primary equity concerns
surrounding DERs pricing is affordability. The cost structures associated with
DERs and the corresponding tariffs must consider the financial accessibility
of these technologies to a broad range of consumers. There are also concerns
related to regional disparities, as different geographic areas may have
varying levels of DER adoption due to factors such as climate and local
policies. Ensuring that DER tariffs are equitable across regions is a
significant challenge.

In addition to DERs, increasing use of EV charging overlays equity concerns
for the current tariff structure as it alters the usual power grid demands. A
case study conducted in Great Britain found that as EV penetration increases,
the distribution tariffs decrease for all customer groups, regardless of
whether they own an EV. In contrast, the proliferation of PV panels escalates
these tariffs [146]. Besides, to address equity concerns related to EV
charging, an EV ranking mechanism is designed to allocate energy to EVs based
on the demand urgency and fairness, which fairness being quantified by Jain’s
index [147].

The massive adoption of DERs has given rise to the development of new energy
communities, consisting of both consumers and prosumers (consumers who also
produce energy) within the same neighborhood. These communities present
significant opportunities to alleviate energy poverty, boost social inclusion,
promote energy-saving measures, and transit to more sustainable and
environmentally friendly energy sources [148]. Real-world examples of energy
communities, such as the city of Kingston, New York, illustrate the potential
of community-based transitions to lift energy burdens off of vulnerable
residents while going green, with an aim for $100\%$ power consumption with
renewable sources by 2050 [48]. In the context of these decentralized energy
markets, it is necessary to address energy justice. From the operational
perspective, a study [122] demonstrates a fair energy community model that
reflects the true preference of consumers while protecting their privacy. In
this optimization model, the goals of the community manager, including
preserving fairness, were realized by integrating energy importing and
exporting, penalties, and geographical preferences into the optimization
objective. Another study on energy community system factorized a fairness
index into their optimization model, allowing for equitable allocation of
benefits and the prevention of penalties based on each member’s contribution
to the community [148]. By considering both benefits and penalties, their
approach compensates for individuals who may be suffering from disadvantages,
ensuring a more consistent distribution of benefits to all users. Furthermore,
a recent study emphasizes the importance of the energy justice when
considering prosumers in optimal retail tariff design [149]. They proposed a
quantitative measure for energy equity as minimizing the difference of energy
burdens between consumer and prosumer. Their energy market equilibrium models
and analyses suggest that providing direct financial compensation to low-
income households would be more economically efficient than subsidizing their
utility rates.

Despite these advancements in modeling and equity considerations on the
operations level, there remain challenges in developing more detailed and
nuanced equity mechanisms, especially for underserved individuals within
energy communities. The challenge also extends to other emerging energy
markets, including peer-to-peer and hybrid market organizations. Achieving
energy justice within these contexts requires ongoing research and innovation
to develop equitable solutions that benefit all.

Figure 9 summarizes the publications on improving energy justice and equity by
solution level and equity focus. We can find that past studies on policy
advancement emphasized the disparities across races while studies on power
system planning focused on rural-urban inequalities and methods to improve
equity by upgrading utility operations mainly attempted to compensate for the
income gaps. Meanwhile, disabled households started to gain attention from
researchers [130]. However, communities who suffer from energy inequities due
to their religion or sexuality remain to be recognized and helped in the
future.

Figure 9: Heat map of publications on promoting energy equity by category and
equity focus. Each literature is categorized into one or more tiles of the
heat map based on its equity focus. White tiles have no publications
identified by authors. Top bar plot displays the total count of unique
publications for each equity focus. Right bar plot shows the total count of
unique publications by solution level.

##  5 Challenges and Perspectives

Energy equity is a common goal people have been striving for but various
limiting factors reside in the way to achieve it. In this section, we analyze
the limitations of current methods and summarize key open gaps from equity
awareness and study participation to modeling drawbacks and technology
difficulties.

Publications on identifying and quantifying energy equity issues revealed
various forms of inequity from the perspective of energy. While energy
poverty, insecurity, and burden are becoming more and more visible and
important, energy vulnerability deserves more attention as it offers a new
perspective to characterize energy equity as dynamic states integrating
external impacts and internal household characteristics, highlighting the
factors that influence the likelihood of becoming energy poor [45].
Furthermore, it helps level up energy gaps to explore the drivers of energy
inequities, determine reasonable and clear energy inequity reduction
objectives, and investigate and evaluate the effectiveness of existing and
future policies and programs.

As we analyzed in measuring and improving energy justice and equity sections,
the majority of literature focused on disparities across geography or income
levels while overlooking those otherwise historically and systemically
marginalized. These communities form the center of the modern definition of
energy equity but can fall through the policy cracks of economic-based poverty
metrics or broad geographical assistance programs. For example, disabled
people are especially disadvantaged in terms of energy and may become further
underserved without more recognition [57].

However, the lack of relative, comprehensive, and high-resolution data remains
a major challenge for the recognition and awareness of energy equity.
Expressed needs for important data sets include in-door temperature [46],
energy affordability indicators [45], and the cost of generation and
transmission infrastructure in less developed countries [93, 136]. Lack of
data not only leads to inaccurate quantification of energy inequity but also
influences policy designs. The availability of collected data significantly
influenced the design and implementation of energy assistance policies and
programs for different states [131].

Besides, there are limitations in the current process of data collecting, such
as single time frame and financially focused survey. Periodic evaluation
benefits the policy-maker and researcher through a record of the effectiveness
of deployed responses to understand how the landscape of certain issues has
changed and how the problem of energy poverty has evolved [45]. Beyond
financial data, figuring out the strategies employed in underserved
communities to cope with energy inequity will establish a behavioral benchmark
and reveal the unintentional effects of new policies. For example, consumer
behaviors during times of crisis exhibit more risky sides, which could lead to
severe adverse effects on health and well-being [44].

Some methods and models require upgrading to overcome their limitations or to
address the emerging equity. While Gini Coefficient is widely applied in
measuring energy equities around the world, it reduces the complex social
issues to a number and may cause an improper representation of inequalities.
In searching for a better way to bring electricity to rural areas, existing
tools only consider an economic objective. However, other criteria such as
reliability, equity, various environmental impacts, food security, and gender
equality may create trade-offs with financial objectives. Especially, the
efficiency-equity trade-off has been identified and quantified in generation
expansion problems but lacks a solution to resolve the conflicting objectives.
In addition, current planning methods dealing with energy equity only consider
the particular equity between urban and rural areas or across all individuals,
ignoring the needs of otherwise underserved communities.

Implementation is another challenge faced by proposed models. These models
usually require some linearization assumptions, which may not adequately
reflect the complex nature of the systems. While some problems can be more
realistically modeled using dynamic programming or non-linear programming
techniques, which may not need such assumptions, only a few studies in rural
electrification literature utilize these methods [37].

Last but not least, complicated technologies of renewable energy slows down
the execution of equity-promoting policies and models, even when there is
strong commitment from a state agency to advance them. The energy technologies
restrict their accessibility and discourage the financial-focus assistance
programs to advance energy equity. It may cause delayed participation for a
community and further exacerbate disparity gaps relative to other communities
that have gained access earlier [59]. Hence, more careful evaluations of
energy assistance efforts to bring timely and equitable access to mitigate
energy inequities are needed.

## References

  * [1] “Exec. Order No. 14008, 86 Fed. Reg. 7619 (February 1, 2021)”
  * [2] Yu Qian, Zeshui Xu, Xunjie Gou and Marinko Škare “A survey on energy justice: a critical review of the literature” In _Economic Research-Ekonomska Istraživanja_ 36.3 Taylor & Francis, 2023, pp. 2155860
  * [3] “Exec. Order No. 12898, 59 Fed. Reg. 7629 (February 16, 1994)”
  * [4] United States Department of Energy “How energy justice, presidential initiatives, and executive orders shape equity at DOE”, 2022 URL: https://www.energy.gov/diversity/articles/how-energy-justice-presidential-initiatives-and-executive-orders-shape-equity
  * [5] United States Department of Energy “Justice40 initiative”, 2022 URL: https://www.energy.gov/diversity/justice40-initiative
  * [6] United Nations Department of Economic and Social Affairs “Transforming our world: The 2030 agenda for sustainable development”, 2015
  * [7] United States Department of Energy “Equity in energy”, 2021 URL: https://www.energy.gov/diversity/equity-energytm
  * [8] “Exec. Order No. 13985, 86 Fed. Reg. 7009 (January 25, 2021)”
  * [9] Sufyan Droubi, Raphael J Heffron and Darren McCauley “A critical review of energy democracy: A failure to deliver justice?” In _Energy Research & Social Science_ 86 Elsevier, 2022, pp. 102444
  * [10] Kirsten Jenkins et al. “Energy justice: a conceptual review” In _Energy Research & Social Science_ 11 Elsevier, 2016, pp. 174–182
  * [11] Sanya Carley and David M Konisky “The justice and equity implications of the clean energy transition” In _Nature Energy_ 5.8 Nature Publishing Group, 2020, pp. 569–577
  * [12] Natascha Bommel and Johanna I Höffken “Energy justice within, between and beyond European community energy initiatives: A review” In _Energy Research & Social Science_ 79 Elsevier, 2021, pp. 102157
  * [13] Clare EB Cannon and Eric K Chu “Gender, sexuality, and feminist critiques in energy research: a review and call for transversal thinking” In _Energy Research & Social Science_ 75 Elsevier, 2021, pp. 102005
  * [14] D McCauley, RWM Rehner and M Pavlenko “Assessing the justice implications of energy infrastructural development in the Arctic” In _Delivering Energy Law and Policy in the EU and US_ Edinburgh University Press, 2015
  * [15] Nancy Fraser “Social justice in the age of identity politics: redistribution, recognition, and participation” In _Culture and Economy after the Cultural Turn_ 1 Sage London, 1999, pp. 25–52
  * [16] Raphael J Heffron and Darren McCauley “The concept of energy justice across the disciplines” In _Energy Policy_ 105 Elsevier, 2017, pp. 658–667
  * [17] Tony Gerard Reames “Targeting energy justice: exploring spatial, racial/ethnic and socioeconomic disparities in urban residential heating energy efficiency” In _Energy Policy_ 97 Elsevier, 2016, pp. 549–558
  * [18] Jay Barlow, Rebecca Tapio and Bethel Tarekegne “Advancing the state of energy equity metrics” In _The Electricity Journal_ 35.10 Elsevier, 2022, pp. 107208
  * [19] Erin Baker et al. “Who is marginalized in energy justice? Amplifying community leader perspectives of energy transitions in Ghana” In _Energy Research & Social Science_ 73 Elsevier, 2021, pp. 101933
  * [20] Matthew Cotton “Fair fracking? Ethics and environmental justice in United Kingdom shale gas policy and planning” In _Local Environment_ 22.2 Taylor & Francis, 2017, pp. 185–202
  * [21] Nathan Frischkorn and Samuel Waxman “Power and pollution: approaching coal-fired power plants and renewable energy through a racial justice lens” In _Chicago-Kent Journal of Environmental and Energy Law_ 10, 2020, pp. 1
  * [22] Bethel Tarekegne, Rebecca O’Neil and Jeremy Twitchell “Energy storage as an equity asset” In _Current Sustainable/Renewable Energy Reports_ 8.3 Springer, 2021, pp. 149–155
  * [23] Hafiz Anwar Ullah Khan, Burcin Unel and Yury Dvorkin “Electricity tariff design via lens of energy justice” In _arXiv preprint arXiv:2110.10122_ , 2021
  * [24] Sanya Carley, Caroline Engle and David M Konisky “An analysis of energy justice programs across the United States” In _Energy Policy_ 152 Elsevier, 2021, pp. 112219
  * [25] Marilyn A Brown et al. “High energy burden and low-income energy affordability: conclusions from a literature review” In _Progress in Energy_ 2.4 IOP Publishing, 2020, pp. 042003
  * [26] Benjamin Goldstein, Tony G Reames and Joshua P Newell “Racial inequity in household energy efficiency and carbon emissions in the United States: An emissions paradox” In _Energy Research & Social Science_ 84 Elsevier, 2022, pp. 102365
  * [27] Bethel W Tarekegne, Barbara GR Pennell, Danielle C Preziuso and Rebecca S O’Neil “Review of energy equity metrics”, 2021
  * [28] Lin Qin, Weida Chen and Licheng Sun “Impact of energy poverty on household quality of life – based on Chinese household survey panel data” In _Journal of Cleaner Production_ Elsevier, 2022, pp. 132943
  * [29] Diana Hernández “Sacrifice along the energy continuum: a call for energy justice” In _Environmental Justice_ 8.4 Mary Ann Liebert, Inc. 140 Huguenot Street, 3rd Floor New Rochelle, NY 10801 USA, 2015, pp. 151–156
  * [30] Giyong Park and Hana Kim “Water conservation and regional equity: An Energy–Water nexus perspective on how Seoul’s efforts relieve energy burdens on electricity-producing areas” In _Journal of Cleaner Production_ 305 Elsevier, 2021, pp. 127222
  * [31] Adam Mayer “Fossil fuel dependence and energy insecurity” In _Energy, Sustainability and Society_ 12.1 BioMed Central, 2022, pp. 1–13
  * [32] Anthony Hilbert and Marion Werner “Turn up the heat! Contesting energy poverty in Buffalo, NY” In _Geoforum_ 74 Elsevier, 2016, pp. 222–232
  * [33] Meital Rosenberg, Daniel Erian Armanios, Michaël Aklin and Paulina Jaramillo “Evidence of gender inequality in energy use from a mixed-methods study in India” In _Nature Sustainability_ 3.2 Nature Publishing Group, 2020, pp. 110–118
  * [34] Nikki Luke “Powering racial capitalism: Electricity, rate-making, and the uneven energy geographies of Atlanta” In _Environment and Planning E: Nature and Space_ SAGE Publications Sage UK: London, England, 2021, pp. 25148486211016736
  * [35] Saul Ngarava et al. “Gender and ethnic disparities in energy poverty: the case of South Africa” In _Energy Policy_ 161, 2022, pp. 112755 DOI: https://doi.org/10.1016/j.enpol.2021.112755
  * [36] International Energy Agency “World Energy Outlook 2021” Paris: International Energy Agency, 2021 URL: https://www.iea.org/reports/world-energy-outlook-2021
  * [37] Beste Akbas, Ayse Selin Kocaman, Destenie Nock and Philipp A. Trotter “Rural electrification: an overview of optimization methods” In _Renewable and Sustainable Energy Reviews_ 156, 2022, pp. 111935 DOI: https://doi.org/10.1016/j.rser.2021.111935
  * [38] Mohammad Ansarin, Yashar Ghiassi-Farrokhfal, Wolfgang Ketter and John Collins “A review of equity in electricity tariffs in the renewable energy era” In _Renewable and Sustainable Energy Reviews_ 161 Elsevier, 2022, pp. 112333
  * [39] Tanga McDaniel Mohr “Fuel poverty in the US: evidence using the 2009 residential energy consumption survey” In _Energy Economics_ 74 Elsevier, 2018, pp. 360–369
  * [40] Eric Scheier and Noah Kittner “A measurement strategy to address disparities across household energy burdens” In _Nature Communications_ 13.1 Nature Publishing Group, 2022, pp. 1–11
  * [41] Brenda Boardman “Fuel Poverty: from Cold Homes to Affordable Warmth” Pinter Pub Limited, 1991
  * [42] Liv Yoon and Diana Hernández “Energy, energy, read all about it: a thematic analysis of energy insecurity in the US mainstream media from 1980 to 2019” In _Energy Research & Social Science_ 74 Elsevier, 2021, pp. 101972
  * [43] Erin Baker, Anna P Goldstein and Inês ML Azevedo “A perspective on equity implications of net zero energy systems” In _Energy and Climate Change_ 2 Elsevier, 2021, pp. 100047
  * [44] Trevor Memmott, Sanya Carley, Michelle Graff and David M Konisky “Sociodemographic disparities in energy insecurity among low-income households before and during the COVID-19 pandemic” In _Nature Energy_ 6.2 Nature Publishing Group, 2021, pp. 186–193
  * [45] Dominic J Bednar and Tony G Reames “Recognition of and response to energy poverty in the United States” In _Nature Energy_ 5.6 Nature Publishing Group, 2020, pp. 432–439
  * [46] Shuchen Cong, Destenie Nock, Yueming Lucy Qiu and Bo Xing “Unveiling hidden energy poverty using the energy equity gap” In _Nature Communications_ 13.1 Nature Publishing Group, 2022, pp. 1–12
  * [47] Jiehong Lou et al. “Inequitable and heterogeneous impacts on electricity consumption from COVID-19 mitigation measures” In _Iscience_ 24.11 Elsevier, 2021, pp. 103231
  * [48] Megan Day and Katherine Richardson “Equitable clean energy transitions for small communities: NREL supports Kingston, New York, in building a community-first approach to 100% renewable energy”, 2020
  * [49] NYC Mayor’s Office of Sustainability and Mayor’s Office for Economic Opportunity “Understanding and alleviating energy cost burden in New York City”, 2019 URL: https://www1.nyc.gov/assets/sustainability/downloads/pdf/publications/EnergyCost.pdf
  * [50] Stephen Bird and Diana Hernández “Policy options for the split incentive: increasing energy efficiency for low-income renters” In _Energy policy_ 48 Elsevier, 2012, pp. 506–514
  * [51] Ookie Ma et al. “Low-income energy affordability data (LEAD) tool methodology”, 2019
  * [52] Sanya Carley, Tom P Evans, Michelle Graff and David M Konisky “A framework for evaluating geographic disparities in energy transition vulnerability” In _Nature Energy_ 3.8 Nature Publishing Group, 2018, pp. 621–627
  * [53] Alexandra Maxim and Emily Grubert “Anticipating climate-related changes to residential energy burden in the United States: advance planning for equity and resilience” In _Environmental Justice_ 15.3 Mary Ann Liebert, Inc., publishers 140 Huguenot Street, 3rd Floor, 2022, pp. 139–148
  * [54] Andrea Gatto and Francesco Busato “Energy vulnerability around the world: The global energy vulnerability index (GEVI)” In _Journal of Cleaner Production_ 253 Elsevier, 2020, pp. 118691
  * [55] Yuling Pan and Feng Dong “Design of energy use rights trading policy from the perspective of energy vulnerability” In _Energy Policy_ 160 Elsevier, 2022, pp. 112668
  * [56] Chien-fei Chen et al. “Extreme events, energy security and equality through micro-and macro-levels: Concepts, challenges and methods” In _Energy Research & Social Science_ 85 Elsevier, 2022, pp. 102401
  * [57] Diana Ivanova and Lucie Middlemiss “Characterizing the energy use of disabled people in the European Union towards inclusion in the energy transition” In _Nature Energy_ 6.12 Nature Publishing Group, 2021, pp. 1188–1197
  * [58] Andrew Adewale Alola “The nexus of renewable energy equity and agricultural commodities in the United States: Evidence of regime-switching and price bubbles” In _Energy_ 239 Elsevier, 2022, pp. 122377
  * [59] Deborah A Sunter, Sergio Castellanos and Daniel M Kammen “Disparities in rooftop photovoltaics deployment in the United States by race and ethnicity” In _Nature Sustainability_ 2.1 Nature Publishing Group, 2019, pp. 71–76
  * [60] Jan-Philipp Sasse and Evelina Trutnevyte “Regional impacts of electricity system transition in Central Europe until 2035” In _Nature Communications_ 11.1 Nature Publishing Group, 2020, pp. 1–14
  * [61] Anna M Brockway, Jennifer Conde and Duncan Callaway “Inequitable access to distributed energy resources due to grid infrastructure limits in California” In _Nature Energy_ 6.9 Nature Publishing Group, 2021, pp. 892–903
  * [62] Shlomo Yitzhaki and Edna Schechtman “The Gini Methodology: a Primer on a Statistical Methodology” Springer, 2013, pp. 249–408
  * [63] Corrado Gini “Variabilitá E Mutabilitá: Contributo Allo Studio Delle Distribuzioni E Delle Relazioni Statistiche.[fasc. I.]” Tipogr. di P. Cuppini, 1912
  * [64] Robert Dorfman “A formula for the Gini coefficient” In _The Review of Economics and Statistics_ JSTOR, 1979, pp. 146–149
  * [65] Björn Lechthaler, Christoph Pauly and Frank Mücklich “Objective homogeneity quantification of a periodic surface using the Gini coefficient” In _Scientific Reports_ 10.1 Nature Publishing Group, 2020, pp. 1–17
  * [66] Y. Saboohi “An evaluation of the impact of reducing energy subsidies on living expenses of households” In _Energy Policy_ 29.3, 2001, pp. 245–252 DOI: https://doi.org/10.1016/S0301-4215(00)00116-6
  * [67] Arne Jacobson, Anita D Milman and Daniel M Kammen “Letting the (energy) Gini out of the bottle: Lorenz curves of cumulative electricity consumption and Gini coefficients as metrics of energy distribution and equity” In _Energy Policy_ 33.14 Elsevier, 2005, pp. 1825–1832
  * [68] Marcio Giannini Pereira, Marcos Aurélio Vasconcelos Freitas and Neilton Fidelis Silva “The challenge of energy poverty: Brazilian case study” In _Energy Policy_ 39.1 Elsevier, 2011, pp. 167–175
  * [69] Jiandong Chen et al. “Regional differences in China’s fossil energy consumption: an analysis for the period 1997–2013” In _Journal of Cleaner Production_ 142 Elsevier, 2017, pp. 578–588
  * [70] He Xiao, Qingpeng Wei and Yi Jiang “The reality and statistical distribution of energy consumption in office buildings in China” In _Energy and Buildings_ 50 Elsevier, 2012, pp. 259–265
  * [71] Shimei Wu, Xinye Zheng and Chu Wei “Measurement of inequality using household energy consumption data in rural China” In _Nature Energy_ 2.10 Nature Publishing Group, 2017, pp. 795–803
  * [72] Rahul Ranjan and Sudershan Singh “Energy deprivation of Indian households: evidence from NSSO data”, 2017 URL: https://mpra.ub.uni-muenchen.de/83566/
  * [73] Qiang Wang, Mei-Po Kwan, Jie Fan and Jian Lin “Racial disparities in energy poverty in the United States” In _Renewable and Sustainable Energy Reviews_ 137 Elsevier, 2021, pp. 110620
  * [74] Scott Lawrence, Qin Liu and Victor M Yakovenko “Global inequality in energy consumption from 1980 to 2010” In _Entropy_ 15.12 MDPI, 2013, pp. 5565–5579
  * [75] Cuncun Duan and Bin Chen “Analysis of global energy consumption inequality by using Lorenz curve” In _Energy Procedia_ 152 Elsevier, 2018, pp. 750–755
  * [76] Yannick Oswald, Anne Owen and Julia K Steinberger “Large inequality in international and intranational energy footprints between income groups and across consumption categories” In _Nature Energy_ 5.3 Nature Publishing Group, 2020, pp. 231–239
  * [77] Tomasz Rokicki et al. “Changes in energy consumption in agriculture in the EU countries” In _Energies_ 14.6 Multidisciplinary Digital Publishing Institute, 2021, pp. 1570
  * [78] Fei Teng, Jiankun He, Xunzhang Pan and Chi Zhang “Metric of carbon equity: carbon Gini index based on historical cumulative emission per capita” In _Advances in Climate Change Research_ 2.3 Elsevier, 2011, pp. 134–140
  * [79] Jiandong Chen, Shulei Cheng and Malin Song “Decomposing inequality in energy-related CO2 emissions by source and source increment: The roles of production and residential consumption” In _Energy Policy_ 107 Elsevier, 2017, pp. 698–710
  * [80] Yi Yang and Mingdong Fan “Analysis of the spatial-temporal differences and fairness of the regional energy ecological footprint of the Silk Road Economic Belt (China Section)” In _Journal of Cleaner Production_ 215 Elsevier, 2019, pp. 1246–1261
  * [81] Peter Alstone, Dimitry Gershenson and Daniel M Kammen “Decentralized energy systems for clean electricity access” In _Nature Climate Change_ 5.4 Nature Publishing Group, 2015, pp. 305–314
  * [82] Jacqueline Hettel Tidwell, Abraham Tidwell and Steffan Nelson “Surveying the solar power gap: assessing the spatial distribution of emerging photovoltaic solar adoption in the State of Georgia, USA” In _Sustainability_ 10.11 Multidisciplinary Digital Publishing Institute, 2018, pp. 4117
  * [83] Tomasz Rokicki and Aleksandra Perkowska “Changes in energy supplies in the countries of the Visegrad Group” In _Sustainability_ 12.19 Multidisciplinary Digital Publishing Institute, 2020, pp. 7916
  * [84] Tomasz Rokicki and Aleksandra Perkowska “Diversity and changes in the energy balance in EU countries” In _Energies_ 14.4 Multidisciplinary Digital Publishing Institute, 2021, pp. 1098
  * [85] Evelyn Heylen et al. “Fairness and inequality in power system reliability: summarizing indices” In _Electric Power Systems Research_ 168 Elsevier, 2019, pp. 313–323
  * [86] Boyan Zhang and Mingming Wang “How will the improvements of electricity supply quality in poor regions reduce the regional economic gaps? A case study of china” In _Energies_ 14.12 Multidisciplinary Digital Publishing Institute, 2021, pp. 3456
  * [87] Toshiyuki Sueyoshi, Jingjing Qu, Aijun Li and Xiaohong Liu “A new approach for evaluating technology inequality and diffusion barriers: The concept of efficiency Gini coefficient and its application in Chinese provinces” In _Energy_ 235 Elsevier, 2021, pp. 121256
  * [88] Hao Li, Xianmei Liu, Song Wang and Zhaohua Wang “Impacts of international trade on global inequality of energy and water use” In _Journal of Environmental Management_ 315 Elsevier, 2022, pp. 115156
  * [89] Xu Sun “Advances in Electric Power Systems: Robustness, Adaptability, and Fairness”, 2011
  * [90] Shipei Zeng, Zhan-Ming Chen, Ahmed Alsaedi and Tasawar Hayat “Price elasticity, block tariffs, and equity of natural gas demand in China: Investigation based on household-level survey data” In _Journal of Cleaner Production_ 179 Elsevier, 2018, pp. 441–449
  * [91] Jan-Philipp Sasse and Evelina Trutnevyte “Distributional trade-offs between regionally equitable and cost-efficient allocation of renewable electricity generation” In _Applied Energy_ 254 Elsevier, 2019, pp. 113724
  * [92] Harry Humfrey, Hongjian Sun and Jing Jiang “Dynamic charging of electric vehicles integrating renewable energy: a multi-objective optimisation problem” In _IET Smart Grid_ 2.2 IET, 2019, pp. 250–259
  * [93] Destenie Nock, Todd Levin and Erin Baker “Changing the policy paradigm: a benefit maximization approach to electricity planning in developing countries” In _Applied Energy_ 264 Elsevier, 2020, pp. 114583
  * [94] Gang Ma, Xu Li and Jianping Zheng “Efficiency and equity in regional coal de-capacity allocation in China: a multiple objective programming model based on Gini coefficient and Data Envelopment Analysis” In _Resources Policy_ 66 Elsevier, 2020, pp. 101621
  * [95] Arik Levinson and Emilson Silva “The electric gini: income redistribution through energy prices” In _American Economic Journal: Economic Policy_ 14.2, 2022, pp. 341–65
  * [96] Hui Shu and Pingping Xiong “The Gini coefficient structure and its application for the evaluation of regional balance development in China” In _Journal of Cleaner Production_ 199 Elsevier, 2018, pp. 668–686
  * [97] Julius Alexander McGee and Patrick Trent Greiner “Renewable energy injustice: the socio-environmental implications of renewable energy consumption” In _Energy Research & Social Science_ 56 Elsevier, 2019, pp. 101214
  * [98] Kangkang Tong et al. “Measuring social equity in urban energy use and interventions using fine-scale data” In _Proceedings of the National Academy of Sciences_ 118.24 National Acad Sciences, 2021
  * [99] Thitithep Sitthiyot and Kanyarat Holasut “A simple method for measuring inequality” In _Palgrave Communications_ 6.1 Palgrave, 2020, pp. 1–9
  * [100] Ambarish Vaidyanathan, Josephine Malilay, Paul Schramm and Shubhayu Saha “Heat-related deaths-united states, 2004–2018” In _Morbidity and Mortality Weekly Report_ 69.24 Centers for Disease ControlPrevention, 2020, pp. 729
  * [101] Jacqueline E Cardoza et al. “Heat-related illness is associated with lack of air conditioning and pre-existing health problems in Detroit, Michigan, USA: a community-based participatory co-analysis of survey data” In _International Journal of Environmental Research and Public Health_ 17.16 MDPI, 2020, pp. 5704
  * [102] Suzy Khimm and Joshua Eaton “As deadly heat waves spread, access to air conditioning becomes a lifesaving question” In _NBC News_ , 2021 URL: https://www.nbcnews.com/news/us-news/deadly-heat-waves-spread-access-air-conditioning-becomes-lifesaving-question-n1277213
  * [103] Mark Wolfe “Opinion: struggling us families face a wave of power shutoffs if congress doesn’t act” In _Cable News Network_ , 2022 URL: https://www.cnn.com/2022/04/28/perspectives/utility-bills-power-shutoffs/index.html
  * [104] José M Amigó, Sámuel G Balogh and Sergio Hernández “A brief review of generalized entropies” In _Entropy_ 20.11 MDPI, 2018, pp. 813
  * [105] Nicholas Rohde “Lorenz curves and generalised entropy inequality measures” In _Modeling Income Distributions and Lorenz Curves_ Springer, 2008, pp. 271–283
  * [106] Henri Theil “Economics and information theory” North Holland, 1967
  * [107] Henri Theil “World income inequality and its components” In _Economics Letters_ 2.1 Elsevier, 1979, pp. 99–102
  * [108] Jonathan Haughton and Shahidur R Khandker “Handbook on Poverty + Inequality” World Bank Publications, 2009
  * [109] Frank A. Cowell “Measuring Inequality” Oxford University Press, 1995
  * [110] Vicent Alcantara and Juan Antonio Duro “Inequality of energy intensities across OECD countries: a note” In _Energy Policy_ 32.11 Elsevier, 2004, pp. 1257–1260
  * [111] Chao Feng, Bin Lu and Zhiqiang Xu “A weighted Gini coefficient and Theil index-based approach for estimating the spatial disparity in energy efficiency in China” In _International Journal of Global Energy Issues_ 39.1-2 Inderscience Publishers (IEL), 2016, pp. 4–17
  * [112] Emilio Padilla and Juan Antonio Duro “Explanatory factors of CO2 per capita emission inequality in the European Union” In _Energy Policy_ 62 Elsevier, 2013, pp. 1320–1328
  * [113] Vincenzo Bianco, Furio Cascetta, Alfonso Marino and Sergio Nardini “Understanding energy consumption and carbon emissions in Europe: a focus on inequality issues” In _Energy_ 170 Elsevier, 2019, pp. 120–130
  * [114] Parisa Pakrooh et al. “Focus on the provincial inequalities in energy consumption and CO2 emissions of Iran’s agriculture sector” In _Science of the Total Environment_ 715 Elsevier, 2020, pp. 137029
  * [115] Xing Yao et al. “Inequalities by energy sources: an assessment of environmental quality” In _PLoS One_ 15.3 Public Library of Science San Francisco, CA USA, 2020, pp. e0230503
  * [116] V Bianco, L Proskuryakova and A Starodubtseva “Energy inequality in the Eurasian Economic Union” In _Renewable and Sustainable Energy Reviews_ 146 Elsevier, 2021, pp. 111155
  * [117] Ambarsari Dwi Cahyani, Nachrowi Djalal Nachrowi, Djoni Hartono and Diah Widyawati “Modern residential energy inequalities in Indonesia: spatial and income analyses” In _Energy Sources, Part B: Economics, Planning, and Policy_ 15.6 Taylor & Francis, 2020, pp. 329–350
  * [118] Shaoyue Ma et al. “Energy consumption inequality decrease with energy consumption increase: Evidence from rural China at micro scale” In _Energy Policy_ 159 Elsevier, 2021, pp. 112638
  * [119] Marta Pascual Sáez, David Cantarero-Prieto and Jose R Pires Manso “Gross inland energy consumption inequality in Europe: an empirical approach” In _Revista de economía mundial_ , 2018
  * [120] Hellinton H Takada, Celma O Ribeiro, Oswaldo LV Costa and Julio M Stern “Gini and entropy-based spread indexes for primary energy consumption efficiency and CO2 emission” In _Energies_ 13.18 MDPI, 2020, pp. 4938
  * [121] Dhani Setyawan “Energy efficiency development in Indonesia: An empirical analysis of energy intensity inequality” In _International Journal of Energy Economics and Policy_ , 2020
  * [122] Fabio Moret and Pierre Pinson “Energy collectives: a community and fairness based approach to future electricity markets” In _IEEE Transactions on Power Systems_ 34.5, 2019, pp. 3994–4004 DOI: 10.1109/TPWRS.2018.2808961
  * [123] Tobias Hoßfeld, Lea Skorin-Kapov, Poul E Heegaard and Martin Varela “Definition of QoE fairness in shared systems” In _IEEE Communications Letters_ 21.1 IEEE, 2016, pp. 184–187
  * [124] Dominik Danner and Hermann Meer “Quality of service and fairness for electric vehicle charging as a service” In _Energy Informatics_ 4.3 Springer, 2021, pp. 1–20
  * [125] Md Murshadul Hoque et al. “Transactive coordination of electric vehicles with voltage control in distribution networks” In _IEEE Transactions on Sustainable Energy_ 13.1 IEEE, 2021, pp. 391–402
  * [126] Shan Zhou and Douglas S Noonan “Justice implications of clean energy policies and programs in the United States: A theoretical and empirical exploration” In _Sustainability_ 11.3 MDPI, 2019, pp. 807
  * [127] Jamal Lewis, Diana Hernández and Arline T Geronimus “Energy efficiency as energy justice: Addressing racial inequities through investments in people and places” In _Energy efficiency_ 13.3 Springer, 2020, pp. 419–432
  * [128] Michelle Graff and Maureen Pirog “Red tape is not so hot: Asset tests impact participation in the Low-Income Home Energy Assistance Program” In _Energy Policy_ 129 Elsevier, 2019, pp. 749–764
  * [129] The White House “Fact sheet: A year advancing environmental justice”, 2022 URL: https://www.whitehouse.gov/briefing-room/statements-releases/2022/01/26/fact-sheet-a-year-advancing-environmental-justice/
  * [130] Naı̈m R Darghouth, Eric O’Shaughnessy, Sydney Forrester and Galen Barbose “Characterizing local rooftop solar adoption inequity in the US” In _Environmental Research Letters_ 17.3 IOP Publishing, 2022, pp. 034028
  * [131] Warren Leon and Abbe Ramanan “State strategies to bring solar to low-and moderate-income communities”, 2021
  * [132] Shuocheng Guo and Eleftheria Kontou “Disparities and equity issues in electric vehicles rebate allocation” In _Energy Policy_ 154 Elsevier, 2021, pp. 112291
  * [133] Will McNamara et al. “Seeking energy equity through energy storage” In _The Electricity Journal_ 35.1 Elsevier, 2022, pp. 107063
  * [134] Pedro Ciller and Sara Lumbreras “Electricity for all: the contribution of large-scale planning tools to the energy-access problem” In _Renewable and Sustainable Energy Reviews_ 120, 2020, pp. 109624 DOI: https://doi.org/10.1016/j.rser.2019.109624
  * [135] Philipp A. Trotter, Nathanial J. Cooper and Peter R. Wilson “A multi-criteria, long-term energy planning optimisation model with integrated on-grid and off-grid electrification - the case of Uganda” In _Applied Energy_ 243, 2019, pp. 288–312 DOI: https://doi.org/10.1016/j.apenergy.2019.03.178
  * [136] Amelia Musselman et al. “The impact of development priorities on power system expansion planning in sub-Saharan Africa” In _Energy Systems_ 13.2 Springer, 2022, pp. 461–492
  * [137] Martin Drechsler et al. “Efficient and equitable spatial allocation of renewable power plants at the country scale” In _Nature Energy_ 2.9 Nature Publishing Group, 2017, pp. 1–9
  * [138] Franziska Steinberger, Tobias Minder and Evelina Trutnevyte “Efficiency versus equity in spatial siting of electricity generation: citizen preferences in a serious board game in Switzerland” In _Energies_ 13.18 MDPI, 2020, pp. 4961
  * [139] Chih-Wei Hsu and Kevin Fingerman “Public electric vehicle charger access disparities across race and income in California” In _Transport Policy_ 100, 2021, pp. 59–67 DOI: https://doi.org/10.1016/j.tranpol.2020.10.003
  * [140] Guijun Li, Tanxiaosi Luo and Yanqiu Song “Spatial equity analysis of urban public services for electric vehicle charging-Implications of Chinese cities” In _Sustainable Cities and Society_ 76 Elsevier, 2022, pp. 103519
  * [141] Avipsa Roy and Mankin Law “Examining spatial disparities in electric vehicle charging station placements using machine learning” In _Sustainable Cities and Society_ Elsevier, 2022, pp. 103978
  * [142] Scott Burger, Ian Schneider, Audun Botterud and Ignacio Pérez-Arriaga “Fair, equitable, and efficient tariffs in the presence of distributed energy resources” In _Consumer, Prosumer, Prosumager: How Service Innovations will Disrupt the Utility Business Model_ Academic Press, 2019, pp. 155
  * [143] ISAAC N Iwuagwu “Electricity pricing in less developed countries: incorporating economic efficiency and equity objectives” In _Nigerian Journal of Technology_ 20.1, 2001, pp. 11–18
  * [144] Scott P Burger et al. “The efficiency and distributional effects of alternative residential electricity rate designs” In _The Energy Journal_ 41.1 International Association for Energy Economics, 2020
  * [145] Mohammad Ansarin, Yashar Ghiassi-Farrokhfal, Wolfgang Ketter and John Collins “The economic consequences of electricity tariff design in a renewable energy era” In _Applied Energy_ 275 Elsevier, 2020, pp. 115317
  * [146] Sinan Küfeoğlu and Michael G Pollitt “The impact of PVs and EVs on domestic electricity network charges: A case study from Great Britain” In _Energy Policy_ 127 Elsevier, 2019, pp. 412–424
  * [147] Akhtar Hussain and Petr Musilek “Fairness and utilitarianism in allocating energy to EVs during power contingencies using modified division rules” In _IEEE Transactions on Sustainable Energy_ IEEE, 2022
  * [148] Valeria Casalicchio, Giampaolo Manzolini, Matteo Giacomo Prina and David Moser “From investment optimization to fair benefit distribution in renewable energy community modelling” In _Applied Energy_ 310, 2022, pp. 118447 DOI: https://doi.org/10.1016/j.apenergy.2021.118447
  * [149] Yihsu Chen, Andrew L Liu, Makoto Tanaka and Ryuta Takashima “Optimal retail tariff sesign with prosumers: pursuing equity at the expenses of economic efficiencies?” In _IEEE Transactions on Energy Markets, Policy and Regulation_ IEEE, 2023