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

Abstract

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 chance constraints which are computationally hard. In this paper we use large deviations techniques to study the probability of current and temperature overloads in a DC network 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 in power grids.

Large fluctuations in locational marginal prices

“…Proposition 4.1 allows us to approximate the probability of a price spike, for small ε, as Pfalse(ξε∈Yfalse)≈exp (−infbold-italicξ∈YIfalse(bold-italicξfalse)ε), as it is done in [21,22] in the context of studying the event of transmission line failures. Moreover, the minimizer of the optimization problem (4.2) corresponds to the most likely realization of uncontrollable generation that leads to the rare event.…”

“…Moreover, it would be of interest to study the sensitivity of the approximation in equation (4.10) with respect to the tuning parameter λ , which quantifies the conservatism in the choice of the line limits. This would allow us to extend the notion of safe capacity regions [21,39] in the context of energy prices. An alternative approach to deal with non-Gaussian fluctuations and more involved price spike structures could be to efficiently sample conditionally on a price spike to have occurred, a problem for which specific Markov chain Monte Carlo (MCMC) methods have been developed, e.g.…”

“…Large deviations techniques have been successfully used in queueing theory, telecommunication engineering, and finance [20]. In recent years, they have also been applied in the context of power systems in order to study transmission line failures [21,22] and statistical properties of blackouts [23,24].…”

REACT to Cyber Attacks on Power Grids

“…Vulnerability of power grids to failures and attacks was extensively studied [7,8,13,19,23,27,29,30]. In particular false data injection attacks on power grids and anomaly detection were studied using the DC power flows in [11,17,18,21,24,35].…”

Chance‐constrained optimal inflow control in hyperbolic supply systems with uncertain demand

“…This is also a popular choice to model demand in various fields (see, eg, Reference 25 in the context of electricity). In References 26,27, they use a multivariate Ornstein‐Uhlenbeck process from the supply‐side point of view. They model uncertain injections into the power network and assess the probability of outages.…”