Articles for EEShttps://nowpublishers.com/feed/EESArticles for EEShttp://nowpublishers.com/article/Details/EES-012A Survey of Relaxations and Approximations of the Power Flow Equations<h3>Abstract</h3>The power flow equations relate the power injections and
voltages in an electric power system and are therefore key
to many power system optimization and control problems.
Research efforts have developed a wide variety of relaxations
and approximations of the power flow equations with a
range of capabilities and characteristics. This monograph
surveys relaxations and approximations of the power flow
equations, with a particular emphasis on recently proposed
formulations.<h3>Suggested Citation</h3>Daniel K. Molzahn and Ian A. Hiskens (2019), "A Survey of Relaxations and Approximations of the Power Flow Equations", Foundations and Trends® in Electric Energy Systems: Vol. 4: No. 1-2, pp 1-221. http://dx.doi.org/10.1561/3100000012Mon, 04 Feb 2019 00:00:00 +0100http://nowpublishers.com/article/Details/EES-015HELM: The Holomorphic
Embedding Load-Flow Method.
Foundations and Implementations<h3>Abstract</h3>The Holomorphic Embedding Load-Flow Method (HELM)
was recently introduced as a novel technique to constructively
solve the power flow equations in power networks,
based on advanced concepts from complex analysis, algebraic
curves, and modern techniques in approximation theory. In
contrast to traditional methods, which rely on numerical iterative
schemes whose convergence is often subject to varying
degrees of uncertainty, HELM’s results are always guaranteed
and unequivocal: if the power flow problem is feasible,
it constructs the most desirable solution; and conversely, if
the power flow problem is infeasible, it signals such condition
reliably. Additionally, the significance of HELM extends
beyond its utilitarian role as a reliable power flow solver,
since the theory backing this method is proving to be a
fertile ground for the development of new analysis tools for
power systems.
This work covers the HELM method from the ground up.
It revisits its theoretical foundations in detail, stressing the
importance of some key ideas grounded in the physics of
the problem. These provide the necessary intuition for the
mathematical developments to follow; in particular, for the
introduction of the holomorphic embedding as a way to
turn the original problem into the study of a plane algebraic
curve, where the branches represent the power flow
solutions. This is shown to be a natural way to characterize
the multiple solutions to the problem, answering some deep
practical questions such as: in the absence of information
about dynamic stability, which of the power flow solutions is
the most desirable one for the operation of a power system?
The formulations cover both traditional ac networks and
dc networks (which are gaining importance in microgrids,
spacecraft, and electric aircraft). Special attention is paid to
the analytic continuation of power series, in particular to the
calculation of Padé approximants. It also serves to introduce
the topic of higher order rational approximants, which allow
reproducing the nose points around voltage collapse with
better numerical stability than their Padé counterparts. An
interesting by-product of this theory, Sigma plots, is shown
to be a useful graphical tool for the quick visual assessment
and diagnosis of both feasible and unfeasible cases.
Controls, such as voltage regulation by generators, are first
incorporated into the method as algebraic equality constraints,
with no limits in the controlling variables. The
method also covers a formulation that allows for possible conflicts
between the specified controls, solving them optimally.
Also cover how to deal with control limits, without resorting
to control type-switching approaches, presenting a novel Lagrangian
formulation and using the Padé-Weierstrass (P-W)
HELM method, a special analytic continuation technique
that greatly increases the precision achievable with HELM.
<h3>Suggested Citation</h3>Antonio Trias (2018), "HELM: The Holomorphic
Embedding Load-Flow Method.
Foundations and Implementations", Foundations and Trends® in Electric Energy Systems: Vol. 3: No. 3-4, pp 140-370. http://dx.doi.org/10.1561/3100000015Wed, 19 Dec 2018 00:00:00 +0100http://nowpublishers.com/article/Details/EES-017Combinatorial Optimization of
Alternating Current
Electric Power Systems<h3>Abstract</h3>In the era of dynamic smart grid with fluctuating demands
and uncertain renewable energy supplies, it is crucial to
continuously optimize the operational cost and performance
of electric power grid, while maintaining its state within the
stable operating limits. Nonetheless, a major part of electric
power grid consists of alternating current (AC) electric
power systems, which exhibit complex behavior with nonlinear
operating constraints. The optimization of AC electric
power systems with dynamic demands and supplies is a very
challenging problem for electrical power engineers.
The hardness of optimization problems of AC electric power
systems stems from two issues: (1) non-convexity involving
complex-valued entities of electric power systems, and
(2) combinatorial constraints involving discrete control variables.
Without proper theoretical tools, heuristic methods
or general numerical solvers had been utilized traditionally
to tackle these problems, which do not provide theoretical
guarantees of the achieved solutions with respect to the
true optimal solutions. There have been recent advances in
applying convex relaxations to tackle non-convex problems
of AC electric power systems. On the other hand, discrete
combinatorial optimization is rooted in theoretical computer
science, which typically considers linear constraints, instead
of those non-linear constraints in AC electric power systems.
To bridge power systems engineering and theoretical computer
science, this monograph presents a comprehensive
study of combinatorial optimization of AC electric power
systems with (inelastic) discrete demands. The main idea
of this monograph is to draw on new extensions of discrete
combinatorial optimization with linear constraints,
like knapsack and unsplittable flow problems. We present
approximation algorithms and inapproximability results for
various settings from (1) basic single-capacitated AC electric
power systems, to (2) constant-sized AC electric grid
networks with power flows, and (3) scheduling of AC electric
power. This monograph aims to establish a foundation for
the inter-disciplinary problems of power systems engineering
and theoretical computer science.
<h3>Suggested Citation</h3>Sid Chi-Kin Chau, Khaled Elbassioni and Majid Khonji (2018), "Combinatorial Optimization of
Alternating Current
Electric Power Systems", Foundations and Trends® in Electric Energy Systems: Vol. 3: No. 1-2, pp 1-139. http://dx.doi.org/10.1561/3100000017Wed, 19 Dec 2018 00:00:00 +0100http://nowpublishers.com/article/Details/EES-018Distribution grids of the future:
Planning for flexibility to operate
under growing uncertainty<h3>Abstract</h3>In this paper optimal grid design problems are revisited in
view of the ongoing transformations in distribution systems.
The transformations are those caused by distributed generation,
changes in load use, and smart grid operation. These
transformations have an expressive impact on the way planning
must be carried out. Trends on grid design are advanced
to deal effectively with future problems of security of supply
in the context of advanced grid operation and demand
responsive resources as enabled by grid modernization technologies.
Formulations of key optimization problems in grid
design are provided together with the required modelling of
load behavior. Solution challenges for the key problems are
identified and the corresponding stochastic framework for
chronological simulation is advanced as favored by a plethora
of newly available load-data. Required developments in decision
support tools for planning the distribution grid of the
future are finally discussed.
<h3>Suggested Citation</h3>Pedro M. S. Carvalho, Luís A. F. M. Ferreira and Alexandre M. F. Dias (2018), "Distribution grids of the future:
Planning for flexibility to operate
under growing uncertainty", Foundations and Trends® in Electric Energy Systems: Vol. 2: No. 4, pp 324-415. http://dx.doi.org/10.1561/3100000018Wed, 19 Dec 2018 00:00:00 +0100http://nowpublishers.com/article/Details/EES-007Architecture and Economics for Grid Operation 3.0<h3>Abstract</h3>This monograph presents a possible research agenda for analytics
and control of a deep decarbonized electric grid with pervasive
data, interactive consumers, and power electronics interfaces. It
focuses on new lines of investigation that are driven by new
technological, economical, and policy factors. Conventional monitoring
and control of the power grid heavily depends upon the
physical principles of the underlying engineering systems. There
is however increasing complexity of the physical models compounded
by a lack of precise knowledge of their parameters, as
well as new uncertainties arising from behavioral, economic, and
environmental aspects. On the other hand there is increasing availability
of sensory data in the engineering and economic operations
and it becomes attractive to leverage such data to model, monitor,
analyze, and potentially close control loops over data.
The increasing deployment of large numbers of Phasor Measurement
Units (PMUs) provides the potential for providing timely
and actionable information about the transmission system. Chapter
2 examines a framework for drastically reducing the dimensionality
of the high volume streaming data, while preserving its
salient features for purposes such as event detection, classification
and visualization, and potentially even to close the loop around
the data. Driven by the deepening penetration of renewable energy
resources at both transmission and distribution levels, there
is an increasing need for utilizing power electronics interfaces
as intelligent devices to benefit the overall grid. Chapter 3 offers
a conceptual design and concrete examples of a qualitatively
different power grid stabilization mechanism in the context of
networked microgrids. Another major paradigm change in the
operation of the grid is that demand will have to be engaged much
more to balance the partially variable renewable energy supply,
which in turn requires greater understanding of human behavior
to economic variables such as price. Chapter 4 presents a possible
formulation to model the behavior of individual consumers in
future grid operations. Chapter 5 presents a proposed solution
to the problem of detecting attacks on the sensor measurements
in the grid, which has become a greater concern with increasing
reliance on sensor data transported over communication networks,
with both sensors and networks liable to malicious cyber-attacks.
The goal of this monograph is to design clean, affordable, reliable,
secure, and efficient electricity services. and to expand the horizon
of the state of the research in the electric energy systems, at a
critical time that is seeing the emergence of Grid 3.0. It is by no
means complete and aims to stimulate research by next generation
researchers.
<h3>Suggested Citation</h3>Le Xie, Meng Wu and P. R. Kumar (2018), "Architecture and Economics for Grid Operation 3.0", Foundations and Trends® in Electric Energy Systems: Vol. 2: No. 3, pp 198-323. http://dx.doi.org/10.1561/3100000007Wed, 19 Dec 2018 00:00:00 +0100http://nowpublishers.com/article/Details/EES-003Wide-area Oscillation Identification
and Damping Control in Power
Systems<h3>Abstract</h3>Low-frequency oscillation (LFO) is a phenomenon inherent
to power systems and should be carefully considered and
dampened to improve the dynamic stability of power systems.
With the development of wide area synchronous phasor
measurement technology, the measurement results of phasor
measurement units (PMUs) and wide-area measurement
system (WAMS) can be applied in system identification and
the wide area damping controller design to suppress LFO. In
this paper, the identification methods and controller design
methods of wide area damping control are reviewed. The
basic framework for the application of PMU/WAMS results
in power system identification and control is introduced first.
Both the output response identification and the input-output
identification are introduced in the identification section.
The offline controller design and adaptive controller design
methods are introduced. Practical cases in China Southern
Grid and China Central Grid are reviewed as engineering
application examples.
<h3>Suggested Citation</h3>Chao Lu, Jingyi Zhang, Xinran Zhang and Yi Zhao (2018), "Wide-area Oscillation Identification
and Damping Control in Power
Systems", Foundations and Trends® in Electric Energy Systems: Vol. 2: No. 2, pp 133-197. http://dx.doi.org/10.1561/3100000003Tue, 14 Aug 2018 00:00:00 +0200http://nowpublishers.com/article/Details/EES-016Sustainable Transportation with Electric Vehicles<h3>Abstract</h3>Electric vehicles are gaining more and more popularity due to low
oil dependency and low emission. Their deep penetration will significantly
benefit the environment, but meanwhile will cause two crucial
consequences. First, electric vehicles introduce heavy load impact into
the power grid by shifting energy demand from gasoline to electricity.
The surging load will compromise the grid’s reliability and jeopardize
its power supply quality. Second, charging stations become indispensable
infrastructure to support large deployment of electric vehicles. The
availability in public destinations comes with electric vehicles competing
for both power supply and service points of charging stations. The
competition degrades quality of service and thus can compromise the
original intent of advocating electric vehicles.
There are many research efforts addressing either of the two consequences
above. Different with them, we consider both and jointly study
quality of service for electric vehicle users and reliability of the power
grid. We review recent developments on this topic in this article. In
Chapter 1, we introduce the ecosystem of electric vehicles and discuss
motivations for managing charging load. This chapter further presents
a systematic solution framework for smart electric vehicle charging. The
following chapters then study each block of the framework. Specially, in
Chapter 2, we investigate charging rate control, which handles how to
allocate power supply to electric vehicles within a charging station. In
Chapter 3, we address electric vehicle demand response, which is how
to make electric vehicles follow the power supply of charging stations
and the power grid. In Chapter 4, we study electric vehicle scheduling,
which copes with how to schedule electric vehicles to multiple charging
points within a charging station. In Chapter 5, we discuss charging
demand balancing, which deals with how to balance electric vehicles
among multiple charging stations.
In these chapters, we first present deployable algorithms and mechanisms
that are designed for each framework blocks. Then, we evaluate
the proposed approaches by two complementary ways. One way is
leveraging theoretical analysis to demonstrate their performance guarantees,
while the other is using extensive simulations based on realistic
data traces and simulation tools. We also review studies that align
with the corresponding framework blocks and consider additional dimensions
and/or different optimization goals. Finally, in Chapter 6,
we conclude the article with summaries of main ideas discussed in the
previous chapters.
<h3>Suggested Citation</h3>Fanxin Kong and Xue Liu (2017), "Sustainable Transportation with Electric Vehicles", Foundations and Trends® in Electric Energy Systems: Vol. 2: No. 1, pp 1-132. http://dx.doi.org/10.1561/3100000016Mon, 18 Dec 2017 00:00:00 +0100http://nowpublishers.com/article/Details/EES-014Unit Commitment in Electric Energy Systems<h3>Abstract</h3>The unit commitment problem is a fundamental problem in the electric
power industry. The objective of unit commitment is to determine
an optimal schedule for each generating unit so that the demand for
electricity is met at minimum cost for the system as a whole. This
tutorial presents the most relevant mathematical optimization models
for the unit commitment problem. It is intended as a starting point for
learning about this important problem, and thus only the key technical
details are included. Likewise, we point out selected references instead
of providing a comprehensive literature review of the area.
<h3>Suggested Citation</h3>Miguel F. Anjos and Antonio J. Conejo (2017), "Unit Commitment in Electric Energy Systems", Foundations and Trends® in Electric Energy Systems: Vol. 1: No. 4, pp 220-310. http://dx.doi.org/10.1561/3100000014Mon, 18 Dec 2017 00:00:00 +0100http://nowpublishers.com/article/Details/EES-001Reliability Standards for the Operation and Planning of Future Electricity Networks<h3>Abstract</h3>Electricity networks, designed and operated in accordance
with the historic deterministic standards, have broadly
delivered secure and reliable supplies to customers. A key
issue regarding their evolution is how the operation and
planning standards should evolve to make efficient use of
the existing assets while taking advantage of emerging,
non-network (or non-wires) technologies. Deployment of
the smart grid will require fundamental changes in the
historical principles used for network security in order to
ensure that integration of low-carbon generation is undertaken
as efficiently as possible through the use of new
information and communication technology (ICT), and new
flexible network technologies that can maximize utilization
of existing electricity infrastructure. These new technologies
could reduce network redundancy in providing security of
supply by enabling the application of a range of advanced,
technically effective, and economically efficient corrective (or
post-fault) actions that can release latent network capacity of
the existing system. In this context, this paper demonstrates
that historical deterministic practices and standards, mostly
developed in the 1950s, should be reviewed in order to take
full advantage of new emerging technologies and facilitate
transition to a smart grid paradigm. This paper also demonstrates
that a probabilistic approach to developing future
efficient operating and design strategies enabled by new
technologies, will appropriately balance network investment
against non-network solutions while truly recognizing effects
of adverse weather, common-mode failures, high-impact
low-probability events, changing market prices for pre- and
post-contingency actions, equipment malfunctioning, etc.
This clearly requires explicit consideration of the likelihood
of various outages (beyond those considered in deterministic
studies) and quantification of their impacts on alternative
network operation and investment decisions, which
cannot be undertaken in a deterministic, “one size fits
all” framework. In this context, we developed advanced
optimization models aimed at determining operational and
design network decisions based on both deterministic and
probabilistic security principles. The proposed models can
recognize network constraints/congestion and various operational
measures (enabled by new technologies) composed of
preventive and corrective control actions such as operation
of special protection schemes, demand side response and
generation reserve utilization and commitment, considering
potential outages of network and generation facilities. The
probabilistic model proposed can also provide targeted levels
of reliability and limit exposure to severe low probability
events (mainly driven by natural hazards) through the use
of Conditional Value at Risk (CVaR) constraints, delivering
robust and resilient supplies to consumers at the minimum
cost. Through various case studies conducted on the Great
Britain (GB) power network, we set out the key questions
that need to be addressed in support of the change in
network reliability paradigm, provide an overview of the
key modelling approaches proposed for assessing the risk
profile of operation of future networks, propose a framework
for a fundamental review of the existing network security
standards, and set out challenges for assessing the reliability
and economics of the operation of future electricity network.
<h3>Suggested Citation</h3>Goran Strbac, Daniel Kirschen and Rodrigo Moreno (2016), "Reliability Standards for the Operation and Planning of Future Electricity Networks", Foundations and Trends® in Electric Energy Systems: Vol. 1: No. 3, pp 143-219. http://dx.doi.org/10.1561/3100000001Thu, 29 Dec 2016 00:00:00 +0100http://nowpublishers.com/article/Details/EES-002Toward a Unified Modeling and Control for Sustainable and Resilient Electric Energy Systems<h3>Abstract</h3>In this paper cyber role in social-ecological energy systems (SEES) is formalized by using the language of large-scale dynamical systems. The key notion of interaction variables is introduced in support of their modeling as multilayered dynamical systems. It is stressed that qualitatively different cyber designs are required for enabling performance of qualitatively different SEES architectures. In particular, it is proposed that composite control-based hierarchical control lends itself more naturally to supporting large-scale regulated monopolies, and that distributed multi-layered control with or without coordination is key to supporting SEES architectures comprising many decision makers. Today’s hierarchical control is described as a particular case of hierarchical composite control. Having these formulations may help bridge
R&D efforts across vastly multi-disciplinary communities working in the field of changing electric energy systems.
<h3>Suggested Citation</h3>Marija D. Ilic (2016), "Toward a Unified Modeling and Control for Sustainable and Resilient Electric Energy Systems", Foundations and Trends® in Electric Energy Systems: Vol. 1: No. 1-2, pp 1-141. http://dx.doi.org/10.1561/3100000002Thu, 22 Dec 2016 00:00:00 +0100