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

Frequency violations from random disturbances: an MCMC approach

The frequency stability of power systems is increasingly challenged by various types of disturbance. In particular, the increasing penetration of renewable energy sources is increasing the variability of power generation while reducing system inertia against disturbances. In this paper we explore how this could give rise to rate of change of frequency (RoCoF) violations. Correlated and non -Gaussian power disturbances, such as may arise from renewable generation, have been shown to be significant in power system security analysis. We therefore introduce ghost sampling which, given any unconditional distribution of disturbances, efficiently produces samples conditional on a violation occurring. Our goal is to address questions such as “which generator is most likely to be disconnected due to a RoCoF violation?” or “what is the probability of having simultaneous RoCoF violations, given that a violation occurs?

Frequency violations from random disturbances: an MCMC approach

The frequency stability of power systems is increasingly challenged by various types of disturbances. In particular, the increasing penetration of renewable energy sources is increasing the variability of power generation and at the same time reducing system inertia against disturbances. In this paper we are particularly interested in understanding how rate of change of frequency (RoCoF) violations could arise from unusually large power disturbances. We devise a novel specialization, named ghost sampling, of the Metropolis-Hastings Markov Chain Monte Carlo method that is tailored to efficiently sample rare power disturbances leading to nodal frequency violations. Generating a representative random sample addresses important statistical questions such as "which generator is most likely to be disconnected due to a RoCoF violation?" or "what is the probability of having simultaneous RoCoF violations, given that a violation occurs?" Our method can perform conditional sampling from any joint distribution of power disturbances including, for instance, correlated and non-Gaussian disturbances, features which have both been recently shown to be significant in security analyses

Short and long-term wind turbine power output prediction

In the wind energy industry, it is of great importance to develop models that accurately forecast the power output of a wind turbine, as such predictions are used for wind farm location assessment or power pricing and bidding, monitoring, and preventive maintenance. As a first step, and following the guidelines of the existing literature, we use the supervisory control and data acquisition (SCADA) data to model the wind turbine power curve (WTPC). We explore various parametric and non-parametric approaches for the modeling of the WTPC, such as parametric logistic functions, and non-parametric piecewise linear, polynomial, or cubic spline interpolation functions. We demonstrate that all aforementioned classes of models are rich enough (with respect to their relative complexity) to accurately model the WTPC, as their mean squared error (MSE) is close to the MSE lower bound calculated from the historical data. We further enhance the accuracy of our proposed model, by incorporating additional environmental factors that affect the power output, such as the ambient temperature, and the wind direction. However, all aforementioned models, when it comes to forecasting, seem to have an intrinsic limitation, due to their inability to capture the inherent auto-correlation of the data. To avoid this conundrum, we show that adding a properly scaled ARMA modeling layer increases short-term prediction performance, while keeping the long-term prediction capability of the model

Large Fluctuations in Locational Marginal Prices

This paper investigates large fluctuations of Locational Marginal Prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form ℙ(LMP∉∏ni=1[α−i,α+i]), where LMP is the vector of LMPs at the n power grid nodes, and α−,α+∈ℝn are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply-demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modeling uncontrollable renewable generation. We utilize techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations and are validated numerically on the IEEE 14-bus test case

Frequency violations from random disturbances: an MCMC approach

The frequency stability of power systems is increasingly challenged by various types of disturbance. In particular, the increasing penetration of renewable energy sources is increasing the variability of power generation while reducing system inertia against disturbances. In this paper we explore how this could give rise to rate of change of frequency (RoCoF) violations. Correlated and non -Gaussian power disturbances, such as may arise from renewable generation, have been shown to be significant in power system security analysis. We therefore introduce ghost sampling which, given any unconditional distribution of disturbances, efficiently produces samples conditional on a violation occurring. Our goal is to address questions such as “which generator is most likely to be disconnected due to a RoCoF violation?” or “what is the probability of having simultaneous RoCoF violations, given that a violation occurs?

Line failure probability bounds for power grids

\u3cp\u3eWe 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.\u3c/p\u3

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