Applying a splitting technique to estimate electrical grid reliability

Wadman, Wander; Crommelin, Daan; Frank, Jason

doi:10.1109/wsc.2013.6721452

Cited by 8 publications

(10 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then we use an IS distribution inspired by an approach developed by [1]. IS algorithms have also been used in [18], and [16] to solve a network operation problem with random inputs. While those two papers focus on the assessment of electrical constraints violation, we make use of IS to assess the solution of LP which involves optimization.…”

Section: )mentioning

confidence: 99%

Rare-Event Simulation for Distribution Networks

Blanchet

Nakayama

2019

Operations Research

View full text Add to dashboard Cite

We model equilibrium allocations in a distribution network as the solution of a linear program (LP) which minimizes the cost of unserved demands across nodes in the network. The constraints in the LP dictate that once a given node's supply is exhausted, its unserved demand is distributed among neighboring nodes. All nodes do the same and the resulting solution is the equilibrium allocation. Assuming that the demands are random (following a jointly Gaussian law), our goal is to study the probability that the optimal cost (i.e. the cost of unserved demands in equilibrium) exceeds a large threshold, which is a rare event. Our contribution is the development of importance sampling and conditional Monte Carlo algorithms for estimating this probability. We establish the asymptotic efficiency of our algorithms and also present numerical results which illustrate strong performance of our procedures.

show abstract

Section: )mentioning

confidence: 99%

Rare-Event Simulation for Distribution Networks

Blanchet

Nakayama

2019

Operations Research

View full text Add to dashboard Cite

show abstract

“…Consequently, in the near future, system operators will no longer be able to assume that the grid is static between control instants, and will have to set the operating point taking into account its variability in the short-term. This entails setting the operating point of the grid with stochastic guarantees on constraint satisfaction [5], [6]. In other words, the operating point must be set such that line constraint violation is a sufficiently rare event until the next control instant.…”

Section: Introductionmentioning

confidence: 99%

“…In an optimization framework, this leads to chance constraints which are hard to evaluate analytically. The analysis of such constraints, such as the probability of overheating or a blackout, has so far only been done using rare event simulation techniques [6]- [8]. Although detailed simulations can be more accurate, short-term planning requires tools that enable the grid operator to handle the stochastic constraints much faster.…”

Section: Introductionmentioning

confidence: 99%

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

Nesti

Nair

Zwart

2019

IEEE Trans. Control Netw. Syst.

View full text Add to dashboard Cite

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.

show abstract

“…Furthermore, our importance function is based on the asymptotic overload probability, and not on the proximity of the constraint state variable to its allowed maximum. In [Wadman et al, 2013] a splitting technique is applied to estimate various grid reliability indices. Although the current paper focuses on connection overload probabilities only, the large deviations approach enables accurate estimates even for high-dimensional state spaces (see Section 6.2) and in cases where the shortest path to the rare event is much less likely than the most likely path (see Section 6.4).…”

Section: Introductionmentioning

confidence: 99%

A Large-Deviation-Based Splitting Estimation of Power Flow Reliability

Wadman

Crommelin

Zwart

2016

ACM Trans. Model. Comput. Simul.

View full text Add to dashboard Cite

Given the continued integration of intermittent renewable generators in electrical power grids, connection overloads are of increasing concern for grid operators. The risk of an overload due to injection variability can be described mathematically as a barrier crossing probability of a function of a multidimensional stochastic process. Crude Monte Carlo is a wellknown technique to estimate probabilities, but it may be computationally too intensive in this case as typical modern power grids rarely exhibit connection overloads. In this paper we derive an approximate rate function for the overload probability using results from large deviations theory. Based on this large deviations approximation, we apply a rare event simulation technique called splitting to estimate overload probabilities more efficiently than Crude Monte Carlo simulation.We show on example power grids with up to eleven stochastic power injections that for a fixed accuracy Crude Monte Carlo would require tens to millions as many samples than the proposed splitting technique required. We investigate the balance between accuracy and workload of three splitting schemes, each based on a different approximation of the rate function. We justify the workload increase of large deviations based splitting compared to naive splitting -that is, splitting based on merely the Euclidean distance to the rare event set. For a fixed accuracy naive splitting requires over 60 times as much CPU time as large deviation based splitting, illustrating its computational advantage. In these examples naive splitting -unlike large deviations based splitting -requires even more CPU time than CMC simulation, illustrating its pitfall.

show abstract

Applying a splitting technique to estimate electrical grid reliability

Cited by 8 publications

References 10 publications

Rare-Event Simulation for Distribution Networks

Rare-Event Simulation for Distribution Networks

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

A Large-Deviation-Based Splitting Estimation of Power Flow Reliability

Contact Info

Product

Resources

About