Carlos E. Murillo-Sánchez

Abstract: MATPOWER is an open-source Matlab-based power system simulation package that provides a high-level set of power flow, optimal power flow (OPF), and other tools targeted toward researchers, educators, and students. The OPF architecture is designed to be extensible, making it easy to add user-defined variables, costs, and constraints to the standard OPF problem. This paper presents the details of the network modeling and problem formulations used by MATPOWER, including its extensible OPF architecture. This structure is used internally to implement several extensions to the standard OPF problem, including piece-wise linear cost functions, dispatchable loads, generator capability curves, and branch angle difference limits. Simulation results are presented for a number of test cases comparing the performance of several available OPF solvers and demonstrating MATPOWER's ability to solve large-scale AC and DC OPF problems.

Abstract: The deregulated electricity market calls for robust optimal power flow (OPF) tools that can provide a) deterministic convergence; b) accurate computation of nodal prices; c) support of both smooth and nonsmooth costing of a variety of resources and services, such as real energy, reactive energy, voltages support, etc.; d) full active and reactive power flow modeling of large-scale systems; and e) satisfactory worst-case performance that meets the real-time dispatching requirement. Most prior research on OPF has focused on performance issues in the context of regulated systems, without giving much emphasis to requirements a)-c). This paper discusses the computational challenges brought up by the deregulation and attempts to address them through the introduction of new OPF formulations and algorithms. Trust-region- based augmented Lagrangian method (TRALM), step-controlled primal-dual interior point method (SCIPM), and constrained cost variable (CCV) OPF formulation are proposed. The new formulations and algorithms, along with several existing ones, are tested and compared using large-scale power system models.

Abstract: This paper describes the optimal power flow (OPF) architecture implemented in MATPOWER, an open-source Mat-lab power system simulation package. It utilizes an extensible architecture that allows the user to easily add new variables, constraints and costs to the standard OPF problem formulation while preserving the structure needed to use pre-compiled solvers. A software object is used to encapsulate the definition of the problem formulation, manage the corresponding named sets of variables, constraints and costs, and handle all of the tedious index maintenance tasks. The software design has the advantage of minimizing the coupling between variables, constraints and costs, making it possible, for example, to add variables to an existing model without having to explicitly modify existing constraints or costs to accommodate them. The example of adding joint co-optimization of reserves to the OPF, based on fixed zonal reserve requirements, is used to illustrate the capabilities of MATPOWER's extensible OPF architecture.

Abstract: This work presents a stochastic optimization framework for operations and planning of an electricity network as managed by an Independent System Operator. The objective is to maximize the total expected net benefits over the planning horizon, incorporating the costs and benefits of electricity consumption, generation, ancillary services, load-shedding, storage and load-shifting. The overall framework could be characterized as a secure, stochastic, combined unit commitment and AC optimal power flow problem, solving for an optimal state-dependent schedule over a pre-specified time horizon. Uncertainty is modeled to expose the scenarios that are critical for maintaining system security, while properly representing the stochastic cost. The optimal amount of locational reserves needed to cover a credible set of contingencies in each time period is determined, as well as load-following reserves required for ramping between time periods. The models for centrally-dispatched storage and time-flexible demands allow for optimal tradeoffs between arbitraging across time, mitigating uncertainty and covering contingencies. This paper details the proposed problem formulation and outlines potential approaches to solving it. An implementation based on a DC power flow model solves systems of modest size and can be used to demonstrate the value of the proposed stochastic framework.

Abstract: This paper describes the architecture and uses of an Internet-based software platform called PowerWeb. PowerWeb was designed and implemented as a simulation environment for evaluating various power exchange auction markets through experimental investigation. It is designed to host simulations of a competitive `day-ahead' electric energy market in which the participants interact by submitting bids or offers into a market via a web-based user interface. The PowerWeb environment is meant to be flexible so as to allow investigation of various market mechanisms. In this paper we describe its interactive, distributed and web-based character.

Abstract: MATPOWER is an open-source Matlab-based power system simulation package that provides a high-level set of power flow, optimal power flow (OPF), and other tools targeted toward researchers, educators, and students. The OPF architecture is designed to be extensible, making it easy to add user-defined variables, costs, and constraints to the standard OPF problem. This paper presents the details of the network modeling and problem formulations used by MATPOWER, including its extensible OPF architecture. This structure is used internally to implement several extensions to the standard OPF problem, including piece-wise linear cost functions, dispatchable loads, generator capability curves, and branch angle difference limits. Simulation results are presented for a number of test cases comparing the performance of several available OPF solvers and demonstrating MATPOWER's ability to solve large-scale AC and DC OPF problems.

Abstract: Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malignant attacks, and specific analysis tools as well as monitoring mechanisms need to be developed to enforce system security and reliability. This paper proposes a unified framework to analyze the resilience of cyber-physical systems against attacks cast by an omniscient adversary. We model cyber-physical systems as linear descriptor systems, and attacks as exogenous unknown inputs. Despite its simplicity, our model captures various real-world cyber-physical systems, and it includes and generalizes many prototypical attacks, including stealth, (dynamic) false-data injection and replay attacks. First, we characterize fundamental limitations of static, dynamic, and active monitors for attack detection and identification. Second, we provide constructive algebraic conditions to cast undetectable and unidentifiable attacks. Third, by using the system interconnection structure, we describe graph-theoretic conditions for the existence of undetectable and unidentifiable attacks. Finally, we validate our findings through some illustrative examples with different cyber-physical systems, such as a municipal water supply network and two electrical power grids.

Abstract: Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial control processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper: (i) we propose a mathematical framework for cyber-physical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (ii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

Abstract: The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this convex dual problem whenever the duality gap is zero. A necessary and sufficient condition is provided in this paper to guarantee the existence of no duality gap for the OPF problem. This condition is satisfied by the standard IEEE benchmark systems with 14, 30, 57, 118, and 300 buses as well as several randomly generated systems. Since this condition is hard to study, a sufficient zero-duality-gap condition is also derived. This sufficient condition holds for IEEE systems after small resistance (10-5 per unit) is added to every transformer that originally assumes zero resistance. We investigate this sufficient condition and justify that it holds widely in practice. The main underlying reason for the successful convexification of the OPF problem can be traced back to the modeling of transformers and transmission lines as well as the non-negativity of physical quantities such as resistance and inductance.

Abstract: The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.