Temperature Overloads in Power Grids Under Uncertainty: a Large Deviations Approach

The advent of renewable energy has huge implications for the design and control of power grids. Due to increasing supply-side uncertainty, traditional reliability constraints such as strict bounds on current, voltage and temperature in a transmission line have to be replaced by computationally demanding chance constraints. In this paper we use large deviations techniques to study the probability of current and temperature overloads in power grids with stochastic power injections, and develop corresponding safe capacity regions. In particular, we characterize the set of admissible power injections such that the probability of overloading of any line over a given time interval stays below a fixed target. We show how enforcing (stochastic) constraints on temperature, rather than on current, results in a less conservative approach and can thus lead to capacity gains.Comment: 12 pages (10 pages + 2 pages appendix), 2 figures. Revised version with extended numerical sectio

A Holistic Approach to Forecasting Wholesale Energy Market Prices

Electricity market price predictions enable energy market participants to shape their consumption or supply while meeting their economic and environmental objectives. By utilizing the basic properties of the supply-demand matching process performed by grid operators, known as Optimal Power Flow (OPF), we develop a methodology to recover energy market's structure and predict the resulting nodal prices by using only publicly available data, specifically grid-wide generation type mix, system load, and historical prices. Our methodology uses the latest advancements in statistical learning to cope with high dimensional and sparse real power grid topologies, as well as scarce, public market data, while exploiting structural characteristics of the underlying OPF mechanism. Rigorous validations using the Southwest Power Pool (SPP) market data reveal a strong correlation between the grid level mix and corresponding market prices, resulting in accurate day-ahead predictions of real time prices. The proposed approach demonstrates remarkable proximity to the state-of-the-art industry benchmark while assuming a fully decentralized, market-participant perspective. Finally, we recognize the limitations of the proposed and other evaluated methodologies in predicting large price spike values.Comment: 14 pages, 14 figures. Accepted for publication in IEEE Transactions on Power System

Numerical methods for computing the steady-state distribution of a G-network.

G-networks are a class of queueing networks introduced by E. Gelembe in 1989, which are characterized by the presence of positive and negative customers. Negative customers have the capability to destroy a positive customer present in a queue, thus reducing the workload. Under ergodicity condition the steady-state distribution of the network is given as the product of the marginal distributions of each queue, but unlike classical queueing network the equation yelding the steady-state distribution are non-linear. In this thesis we develeop two new numerical methods for the computation of the steady-state distribution. Rewriting the problem as a fixed point matrix equation, we study a fixed point iteration and a Newton-Raphson iteration. We prove that both the methods converge, with linear and quadratic rate respectively, choosing the starting value in a neighbourhood of the fixed point. We then compare these methods with an existing algorithm develped by Fourneau, concluding that the Newton-Raphson iteration is preferable for moderate-sized G-networks

Emergence of scale-free blackout sizes in power grids

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.Comment: 27 pages (6 pages + 21 pages with supplemental material). Accepted for publication in Physical Review Letter

A holistic approach to forecasting wholesale energy market prices

Electricity market price predictions enable energy market participants to shape their consumption or supply while meeting their economic and environmental objectives. By utilizing the basic properties of the supply-demand matching process performed by grid operators, known as Optimal Power Flow (OPF), we develop a methodology to recover energy market's structure and predict th

Line failure probability bounds for power grids

We develop upper bounds for line failure probabilities in power grids, under the DC approximation and assuming Gaussian noise for the power injections. Our upper bounds are explicit, and lead to characterization of safe operational capacity regions that are convex and polyhedral, making our tools compatible with existing planning methods. Our probabilistic bounds are derived through the use of powerful concentration inequalities

On the solution of a rational matrix equation arising in G-networks

We consider the problem of solving a rational matrix equation arising in the solution of G-networks. We propose and analyze two numerical methods: a fixed point iteration and the Newton–Raphson method. The fixed point iteration is shown to be globally convergent with linear convergence rate, while the Newton method is shown to have a local convergence, with quadratic convergence rate. Numerical experiments show the effectiveness of the proposed methods

Line failure probability bounds for power grids

We develop upper bounds for line failure probabilities in power grids, under the DC approximation and assuming Gaussian noise for the power injections. Our upper bounds are explicit, and lead to characterization of safe operational capacity regions that are convex and polyhedral, making our tools compatible with existing planning methods. Our probabilistic bounds are derived through the use of powerful concentration inequalities