Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration

We show how distributed control of reactive power can serve to regulate voltage and minimize resistive losses in a distribution circuit that includes a significant level of photovoltaic (PV) generation. To demonstrate the technique, we consider a radial distribution circuit with a single branch consisting of sequentially-arranged residential-scale loads that consume both real and reactive power. In parallel, some loads also have PV generation capability. We postulate that the inverters associated with each PV system are also capable of limited reactive power generation or consumption, and we seek to find the optimal dispatch of each inverter's reactive power to both maintain the voltage within an acceptable range and minimize the resistive losses over the entire circuit. We assume the complex impedance of the distribution circuit links and the instantaneous load and PV generation at each load are known. We compare the results of the optimal dispatch with a suboptimal local scheme that does not require any communication. On our model distribution circuit, we illustrate the feasibility of high levels of PV penetration and a significant (20% or higher) reduction in losses.Comment: 6 pages, 5 figures

Local Cyber-Physical Attack for Masking Line Outage and Topology Attack in Smart Grid

Malicious attacks in the power system can eventually result in a large-scale cascade failure if not attended on time. These attacks, which are traditionally classified into \emph{physical} and \emph{cyber attacks}, can be avoided by using the latest and advanced detection mechanisms. However, a new threat called \emph{cyber-physical attacks} which jointly target both the physical and cyber layers of the system to interfere the operations of the power grid is more malicious as compared with the traditional attacks. In this paper, we propose a new cyber-physical attack strategy where the transmission line is first physically disconnected, and then the line-outage event is masked, such that the control center is misled into detecting as an obvious line outage at a different position in the local area of the power system. Therefore, the topology information in the control center is interfered by our attack. We also propose a novel procedure for selecting vulnerable lines, and analyze the observability of our proposed framework. Our proposed method can effectively and continuously deceive the control center into detecting fake line-outage positions, and thereby increase the chance of cascade failure because the attention is given to the fake outage. The simulation results validate the efficiency of our proposed attack strategy.Comment: accepted by IEEE Transactions on Smart Grid. arXiv admin note: text overlap with arXiv:1708.0320

Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems, 15(1):15-27, March 2014. This is an extended version with Appendices VIII and IX that provide some mathematical preliminaries and proofs of the main result

Strengthening QC relaxations of optimal power flow problems by exploiting various coordinate changes

Motivated by the potential for improvements in electric power system economics, this dissertation studies the AC optimal power flow (AC OPF) problem. An AC OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. The difficulty of an AC OPF problem is strongly connected to its feasible space\u27s characteristics. This dissertation first investigates causes of nonconvexities in AC OPF problems. Understanding typical causes of nonconvexities is helpful for improving AC OPF solution methodologies. This dissertation next focuses on solution methods for AC OPF problems that are based on convex relaxations. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This dissertation proposes several improvements to strengthen QC relaxations of OPF problems. The first group of improvements provides tighter envelopes for the trigonometric functions and product terms in the power flow equations. Methods for obtaining tighter envelopes includes implementing Meyer and Floudas envelopes that yield the convex hull of trilinear monomials. Furthermore, by leveraging a representation of line admittances in polar form, this dissertation proposes tighter envelopes for the trigonometric terms. Another proposed improvement exploits the ability to rotate the base power used in the per unit normalization in order to facilitate the application of tighter trigonometric envelopes. The second group of improvements propose additional constraints based on new variables that represent voltage magnitude differences between connected buses. Using \u27bound tightening\u27 techniques, the bounds on the voltage magnitude difference variables can be significantly tighter than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can improve the QC relaxation --Abstract, page iv

Dispatching Stochastic Heterogeneous Resources Accounting for Grid and Battery Losses

We compute an optimal day-ahead dispatch plan for distribution networks with stochastic resources and batteries, while accounting for grid and battery losses. We formulate and solve a scenario-based AC Optimal Power Flow (OPF), which is by construction non-convex. We explain why the existing relaxation methods do not apply and we propose a novel iterative scheme, Corrected DistFlow (CoDistFlow), to solve the scenario-based AC OPF problem in radial networks. It uses a modified branch flow model for radial networks with angle relaxation that accounts for line shunt capacitances. At each step, it solves a convex problem based on a modified DistFlow OPF with correction terms for line losses and node voltages. Then, it updates the correction terms using the results of a full load flow. We prove that under a mild condition, a fixed point of CoDistFlow provides an exact solution to the full AC power flow equations. We propose treating battery losses similarly to grid losses by using a single-port electrical equivalent instead of battery efficiencies. We evaluate the performance of the proposed scheme in a simple and real electrical networks. We conclude that grid and battery losses affect the feasibility of the day-ahead dispatch plan and show how CoDistFlow can handle them correctly

Conic optimization of electric power systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 103-115).The electric power grid is recognized as an essential modern infrastructure that poses numerous canonical design and operational problems. Perhaps most critically, the inherently large scale of the power grid and similar systems necessitates fast algorithms. A particular complication distinguishing problems in power systems from those arising in other large infrastructures is the mathematical description of alternating current power flow: it is nonconvex, and thus excludes power systems from many frameworks benefiting from theoretically and practically efficient algorithms. However, advances over the past twenty years in optimization have led to broader classes possessing such algorithms, as well as procedures for transferring nonconvex problem to these classes. In this thesis, we approximate difficult problems in power systems with tractable, conic programs. First, we formulate a new type of NP-hard graph cut arising from undirected multicommodity flow networks. An eigenvalue bound in the form of the Cheeger inequality is proven, which serves as a starting point for deriving semidefinite relaxations. We next apply a lift-and-project type relaxation to transmission system planning. The approach unifies and improves upon existing models based on the DC power flow approximation, and yields new mixed-integer linear, second-order cone, and semidefinite models for the AC case. The AC models are particularly applicable to scenarios in which the DC approximation is not justified, such as the all-electric ship. Lastly, we consider distribution system reconfiguration. By making physically motivated simplifications to the DistFlow equations, we obtain mixed-integer quadratic, quadratically constrained, and second-order cone formulations, which are accurate and efficient enough for near-optimal, real-time application. We test each model on standard benchmark problems, as well as a new benchmark abstracted from a notional shipboard power system. The models accurately approximate the original formulations, while demonstrating the scalability required for application to realistic systems. Collectively, the models provide tangible new tradeoffs between computational efficiency and accuracy for fundamental problems in power systems.by Joshua Adam Taylor.Ph.D