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This work considers the task of finding an ac-feasible operating point of a severely damaged transmission network while ensuring that a maximal amount of active power loads can be delivered. This AC maximal load delivery (AC-MLD) task is a nonconvex nonlinear optimization problem that is incredibly challenging to solve on large-scale transmission system data sets. This work demonstrates that convex relaxations of the AC-MLD problem provide a reliable and scalable method for finding high-quality bounds on the amount of active power that can be delivered in the AC-MLD problem. To demonstrate their effectiveness, the solution methods proposed in this work are rigorously evaluated on 1000 $N$ - $k$ scenarios on seven power networks ranging in size from 70 to 6000 buses. The most effective relaxation of the AC-MLD problem converges in less than 20 seconds on commodity computing hardware for all 7000 of the scenarios considered. [ABSTRACT FROM AUTHOR]

Severe geomagnetic disturbances (GMDs) increase the magnitude of the electric field on the Earth’s surface (E-field) and drive geomagnetically-induced currents (GICs) along the transmission lines in electric grids. These additional currents can pose severe risks, such as current distortions, transformer saturation and increased reactive power losses, each of which can lead to system unreliability. Several mitigation actions (e.g., changing grid topology) exist that can reduce the harmful GIC effects on the grids. Making such decisions can be challenging, however, because the magnitude and direction of the E-field are uncertain and non-stationary. In this paper, we model uncertain E-fields using the distributionally robust optimization (DRO) approach that determines optimal transmission grid operations such that the worst-case expectation of the system cost is minimized. We also capture the effect of GICs on the nonlinear AC power flow equations. For solution approaches, we develop an accelerated column-and-constraint generation (CCG) algorithm by exploiting a special structure of the support set of uncertain parameters representing the E-field. Extensive numerical experiments based on “epri-21” and “uiuc-150” systems, designed for GMD studies, demonstrate (i) the computational performance of the accelerated CCG algorithm, (ii) the superior performance of distributionally robust grid operations that satisfy nonlinear, nonconvex AC power flow equations and GIC constraints, in comparison with standard stochastic programming-based methods during the out-of-sample testing. [ABSTRACT FROM AUTHOR]

In recent years, there have been increasing concerns about how geomagnetic disturbances (GMDs) impact electrical power systems. Geomagnetically induced currents (GICs) can saturate transformers, induce hot spot heating, and increase reactive power losses. These effects can potentially cause catastrophic damage to transformers and severely impact the ability of a power system to deliver power. To address this problem, we develop a model of GIC impacts to power systems that includes 1) GIC thermal capacity of transformers as a function of normal alternating current (AC), and 2) reactive power losses as a function of GIC. We use this model to derive an optimization problem that protects power systems from GIC impacts through line switching, generator redispatch, and load shedding. We employ state-of-the-art convex relaxations of AC power flow equations to lower bound the objective. We demonstrate the approach on a modified RTS96 system and the UIUC 150-bus system and show that line switching is an effective means to mitigate GIC impacts. We also provide a sensitivity analysis of optimal switching decisions with respect to GMD direction. [ABSTRACT FROM PUBLISHER]

Energy supply in rural and off-grid communities has traditionally relied on diesel-based microgrids, due to limited access. But global environmental concerns are pushing for the transformation of these systems into renewable-based microgrids. This transition to more complex systems with a mix of dispatchable and nondispatchable resources requires new planning tools that ensure the security of supply. This paper presents a novel mixed-integer linear optimization model that determines optimal technology mix, size, placement, and associated dispatch for a multi-energy microgrid. The model satisfies microgrid's electrical and heat transfer network limitations by integrating linear power flow and heat transfer equations. It captures the efficiency gains from waste heat recovery through combined heat and power technologies, by modeling the interplay between electrical and heat sources. To ensure a secure design against generator outages, the optimization maintains sufficient reserve capacity in the system, which is dynamically allocated based on system operating conditions. Several case studies on an isolated microgrid model, developed based on a real microgrid in Alaska, illustrate how the proposed model works. The results show the effectiveness of the model and are used to discuss various aspects of the optimization solution. [ABSTRACT FROM PUBLISHER]

This paper introduces a statistical classifier that quickly locates line outages in a power system utilizing only time series phasor measurement data sampled during the system's transient response to the outage. The presented classifier is a linear multinomial regression model that is trained by solving a maximum likelihood optimization problem using synthetic data. The synthetic data is produced through dynamic simulations which are initialized by random samples of a forecast load/generation distribution. Real time computation of the proposed classifier is minimal and therefore the classifier is capable of locating a line outage before steady state is reached, allowing for quick corrective action in response to an outage. In addition, the output of the classifier fits into a statistical framework that is easily accessible. Specific line outages are identified as being difficult to localize and future improvements to the classifier are proposed. [ABSTRACT FROM PUBLISHER]