Dynamic Model of Battery Energy Storage Systems through Assessment of their State-of-Charge
Presenter: Nada abdelfattah (Montana State University)
Abstract:
In the last decades, the need and the importance of the energy storage has been increased by the large penetration of distributed generation and renewable energy resources. Moreover, Electric vehicles introduced a revolution in transportation system which pushed the research into better ways of managing the available energy at the vehicle level. Stationary energy storage systems are required for the new available renewable energy resources. Therefore, a considerable amount of research is being devoted to the battery management system device which plays a central role in improving the reliability of a battery back. Among all different types of battery technologies, Lithium-ion battery is the most promising technology for portable devices, and vehicular applications power system applications due to their superior properties including long lifespan, high energy density, and low self-discharge. State of charge (SoC) is an indication of how much energy is left at the system. Accurate estimation of SoC is complicated because it is affected by many factors as temperature, capacity, and internal resistance. However, failure in estimating accurate SoC results in under/overcharging situations, which leads to irreversible damage of the battery. This research is using the nonlinear model, which is a series of three electric dipoles, together with a procedure for parameters estimation relying on voltage measures and a given current profile to estimate the SoC for Li-ion battery. The assessment of the parameters of the model will be performed by using experimental tests characterized by different sub-phases: constant charging, constant discharging, and relaxation phases. A set of tests will be performed to find the relationship between the initial SoC and Voc and consequently pulsed charging tests will be performed to obtain parameters. The experimental results will be used to optimize the parameters of the model via Matlab. In this respect, it can be concluded that the proposed battery model represents an adequate extension of the classical electrical circuit ones with a minimal computational overhead.
Differentially Private Distributed Optimal Power Flow
Presenter: Vladimir Dvorkin (Georgia Institute of Technology)
Abstract:
A common belief is that distributed dispatch algorithms enable privacy preservation for power system agents: each agent optimizes its local optimization by means of primal-dual communication without disclosing its sensitive data, e.g., load. However, sensitive information can be inferred by a potential adversary from responses of agents to communication signals over iterations. To ensure information integrity, this paper leverages the concept of differential privacy to develop privacy-preserving distributed algorithms for optimal power flow (OPF) problem. We first distribute the OPF problem using consensus alternating direction method of multipliers (ADMM), and then introduce two methods to provide differential privacy: dual and primal variable perturbations. The perturbations are random and drawn from a carefully parameterized Laplace distribution, such that inferring agent data from primal-dual communication conforms to random guessing. The main benefit is that the privacy of each agent can be quantified and provably guaranteed up to user-specified privacy parameters. Moreover, unlike common differentially private algorithms, there is no privacy loss accumulated across ADMM iterations. A series of numerical experiments across NESTA testbeds supports our theoretical findings.
A Transient Stability Certificate for Power Networks
Presenter: Amin Gholami (Georgia Institute of Technology)
Abstract:
Transient stability is the ability of a power system to remain in synchronism when subjected to large contingencies such as faults, loss of system components, and severe fluctuations in generation or load. Despite extensive studies, several basic questions on transient stability in power systems have still remained unanswered. In particular, when is a power system with nontrivial transfer conductances stable? What is the relation between the underlying graph of a power system with the stability of its equilibrium points? In this work, we address the foregoing questions. Moreover, we develop sufficient conditions for the asymptotic stability of the equilibrium points in power networks. Our findings provide new insights into the dynamic behavior and oscillatory solutions of power systems.
Indirect mechanism design for efficient and stable renewable energy aggregation
Presenter: Hossein Khazaei (Stony Brook University)
Abstract:
Mechanism design is studied for aggregating renewable power producers (RPPs) in a two-settlement power market. Employing an indirect mechanism design framework, a payoff allocation mechanism (PAM) is derived from the competitive equilibrium (CE) of a specially formulated market with transferrable payoff. Given the designed mechanism, the strategic behaviors of the participating RPPs entail a non-cooperative game: It is proven that a unique pure Nash equilibrium (NE) exists among the RPPs, for which a closed-form expression is found. Moreover, it is proven that the designed mechanism achieves a number of key desirable properties at the NE: these include efficiency (i.e., an ideal “Price of Anarchy” of one), stability (i.e., “in the core” from a coalitional game theoretic perspective), and no collusion. In addition, it is shown that a set of desirable “ex-post” properties are also achieved by the designed mechanism. Extensive simulations are conducted and corroborate the theoretical results.
Two and Three Stage Scenario Based Optimization for Wind and Storage Expansion
Presenter: Michael Kratochvil (University of Iowa)
Abstract:
With costs of large scale wind and storage devices decreasing, there is an increasing need to bring these technologies onto the power grid. The Expansion Problem (EP) is an attempt to determine the optimal location and capacity of these items onto an existing power network. With the choice to expand on the network as the first stage, a long term period of simulated power system operations in subsequent stages, this becomes a multi-stage optimization problem. In this poster, a continuous linear cost function in the first stage, and a direct current optimal power flow (DCOPF) problem being solved in subsequent problem, (EP) has an inherent block-angular linear structure, which is exploited through the Julia package StructJuMP and is solved using the Progressive Hedging algorithm. Preliminary results from a two-stage deterministic and three-stage stochastic (with renewable energy outputs considered random) are presented and future research is discussed.
Impacts of Transmission Switching on Zonal Markets
Presenter: Quentin Lete (Université catholique de Louvain)
Abstract:
Day-ahead electricity market design has been a long-lasting debate among European power system economists. A central question in this debate asks whether the zonal design should be abandoned in favor of a nodal design, common to many markets around the world.
This question is for instance raised in some recent research that highlights the inefficiencies with respect to unit commitment of Flow Based Market Coupling (FBMC), the market coupling mechanism currently used in the Central Western Europe (CWE) system.
The assessment of short-term operational efficiency hinges on the degree of operational flexibility that is afforded to the system operator. A recurrent argument in favor of the zonal design is that its efficiency can be significantly improved by considering the possibility to actively configure the network using active network management measures, such as transmission switching. Our interest in this research is to provide a quantitative framework for substantiating this argument.
In this research, we show how the day-ahead problem with switching can be formulated as an adaptive robust optimization problem with mixed integer recourse and present a algorithm for solving the adversarial max-min problem with interdiction game structure.
We apply the model on a realistic instance of the Central Western European system and comment on the impacts of both proactive and reactive transmission switching on the operating costs of the system.
Solving Power Flow Equations Using A Weighted Nuclear Norm
Presenter: Li-Hsiang Lin (Georgia Institute of Technology)
Abstract:
This study presents a novel method of solving the nonlinear power flow equations that are rooted in an alternating current (AC) power system. To recover the power flow state (PFS) matrix, it is known that solving the corresponding system of nonlinear power flow equations can be formulated as a semi-definite programming (SDP) problem with a rank-1 constraint. The associated numerical problem is computationally challenging and intrinsically NP-hard. To obtain a rank-1 solution in the semi-definite programming problem, convex regularization is often used. In this paper, we explore a novel non-convex weighted nuclear norm regularization approach. Comparing to existing regularization approaches, the proposed weighted nuclear norm approach can converge faster to a rank-1 solution. We propose an algorithm with a convergence guarantee. Numerical study shows that our proposed method can better recover the rank-1 solution in comparison with the existing methods, as our method improves both the robustness and the accuracy. We also provide an accelerated algorithm, which is especially useful when the number of buses is large. We test the proposed method for a 2383-bus system and obtain the state-of-the-art result.
Algebraic Methods in Power Engineering
Presenter: Julia Lindberg (University of Wisconsin-Madison)
Abstract:
The operating points of an n-node power network are real solutions of the power flow equations, a system of 2n − 2 quadratic polynomials in 2n − 2 variables. Our work aims to find the distribution of the number of real solutions, which is important in determining the stability of the network. We use techniques from computational algebraic geometry to find families of graphs for which the number of nontrivial operating points equals the number of real solutions of a single polynomial. We use this polynomial to dramatically speed up computations of distributions. This allows us to visualize regions with a fixed number of real solutions, finding that some cluster around hyperplanes.
PowerModelsRestoration.jl
Presenter: Noah Rhodes (University of Wisconsin-Madison)
Abstract:
With the escalating frequency of extreme grid disturbances, such as natural disasters, comes an increasing need for efficient recovery plans. Algorithms for optimal power restoration play an important role in developing such plans, but also give rise to challenging mixed-integer nonlinear optimization problems, where tractable solution methods are not yet available. To assist in research on such solution methods, this work proposes PowerModelsRestoration, a flexible, open-source software framework for rapidly designing and testing power restoration algorithms. PowerModelsRestoration constructs a mathematical modeling layer for formalizing core restoration tasks that can be combined to develop complex workflows and high performance heuristics. The efficacy of the proposed framework is demonstrated by proof-of-concept studies on three established cases from the literature; the results demonstrate that PowerModelsRestoration reproduces the established literature, and extends those methods to nonlinear models, which have not been previously considered.
Distributed Restoration for Integrated Transmission and Distribution Systems with DERs
Presenter: Reza Roofegari nejad (University of Central Florida)
Abstract:
A resilient power system is capable of providing fast and efficient recovery from outages caused by natural or man-made attacks. After a major blackout, transmission and distribution system operators (TSOs and DSOs) coordinate to restore the system in a timely and reliable manner. However, these two systems are usually operated separately without considering the capabilities and limitations of each individual network, or their mutual impacts. This could prolong the restoration process and lead to unpractical outcomes. Therefore, a distributed strategy for integrated transmission and distribution systems restoration (ITDSR) has been developed in this paper. Based on the alternating direction method of multipliers (ADMM), the distributed algorithm is able to provide the coordinated restoration for both TSOs and DSOs by sharing limited information of boundary buses in an iterative procedure. The ADMM-ITDSR model includes a convex AC power flow model and the three-phase unbalanced branch flow model. The ITDSR strategy coordinates the operation of distributed energy resources in terms of serving high priority loads across different networks. The effectiveness and advantage of developed models and algorithms are validated and demonstrated through testing of the integrated IEEE test cases, such as 14-bus transmission with 13-node distribution systems, and 39-bus transmission with 123-node distribution systems.
Variable Frequency AC OPF
Presenter: David Sehloff (University of Wisconsin-Madison)
Abstract:
In traditional power system operations, a standard system-wide frequency is imperative. However, advances in power electronics now enable networks with areas operating at distinct frequencies. This has advantages for the controllability of the system as well as power transfer under thermal and transient stability limits. A multi-area model with controllable frequencies and inter-area power transfer is developed, and the benefits of this increased controllability are demonstrated in case studies based on the IEEE 14 bus and 39 bus networks.
A convergent distributed algorithm for nonconvex optimization with applications in optimal power scheduling
Presenter: Kaizhao Sun (Georgia Institute of Technology)
Abstract:
Motivated by the problem of coordination between ISO markets, we study distributed optimization algorithms for the AC optimal power flow problem. We first give an overview of the field of distributed optimization with an emphasis on applications to OPF, and identify two crucial conditions for the convergence of nonconvex ADMM. Then we propose distributed algorithms for solving the nonconvex version of the AC OPF problems with provable convergence guarantees. Numerical results show promising performance.
Distributionally Robust Transmission Expansion Planning: a Multi-scale Uncertainty Approach
Presenter: Alexandre Velloso (PUC-Rio / Georgia Institute of Technology)
Abstract:
We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long- and short-term uncertainties on the system demand and renewable generation. On the long-term level, as it is customary in industry applications, the deep uncertainties arising from social and economic transformations, political and environmental issues, and technology disruptions are addressed by long-term scenarios devised by experts. The system planner is then allowed to consider exogenous long-term scenarios containing partial information about the random parameters, namely, the average and the support set. For each constructed long-term scenario, a conditional ambiguity set is used to model the incomplete knowledge about the probability distribution of the uncertain parameters in the short-term. Consequently, the mathematical problem is formulated as a DRO model with multiple conditional ambiguity sets. The resulting infinite-dimensional problem is recast as an exact, although very large, finite-deterministic mixed-integer linear programming problem. To circumvent scalability issues, we propose a new enhanced-column-and-constraint-generation (ECCG) decomposition approach with an additional Dantzig–Wolfe procedure. In comparison to existing methods, ECCG leads to a better representation of the recourse function and, consequently, tighter bounds. Numerical experiments based on the benchmark IEEE 118-bus system are reported to corroborate the effectiveness of the method.
A New Semidefinite Programming Algorithm for Power Flow Analysis and Robust State Estimation
Presenter: Chuanping Yu (Georgia Institute of Technology)
Abstract:
This paper proposes a new semidefinite programming algorithm to solve both power flow analysis and robust state estimation problem. We first show that both of the two types of problems are on the complex domain and can be reformulated as nonconvex semidefinite programming problems on the real domain. Existing literatures mostly focus on convex relaxation to overcome the NP-hardness, where additional knowledge of the true solutions are often required, which are in practice unable to obtain. In this paper, rather than convex relaxation, we propose a new semidefinite programming algorithm to further formulate the semidefinite programming problem into a sequence optimization problem which solves two convex problems alternatively. Convergence analysis provides the conditions under which the equivalency holds between the original problem and the newly proposed sequence optimization problem. Numerical results on the 4-bus, 9-bus, and the 118-bus power flow systems demonstrate the performance of our new algorithm for both the power flow analysis and the robust state estimation.
Quickest detection of cascading failure
Presenter: Rui Zhang (Georgia Institute of Technology)
Abstract:
We consider online detection of cascading failure in the networks using sequential data. Our goal is to detect the failure as quickly as possible after it occurs. To achieve this goal, we propose a temporal diffusion network model to capture the dynamic of the potential change, which will help us to capture the change as quickly as possible since its onset. Under this model, the hazard rate of a node increases as the number of failure neighbors increases. Once the failure affects a node, the distribution of the measurement changes from pre-change distribution to an unknown post-change distribution. We develop a sequential generalized likelihood ratio statistics, which performs joint detection and estimation in detecting the change. Numerical experiments show that our method outperforms the existed methods.