Efficient Computation of Minimal Wind-Power Deviations That Induce Temporal Line Overloading

The paper develops an optimization method for assessing transmission network vulnerability to small changes in generation (as caused, for example, by wind forecast inaccuracy). The method computes the smallest deviation (in a weighted 2-norm sense) from the nominal generation pattern that would drive a particular line to a specified temperature, over a given time horizon. The 2-norm weighting matrix provides a means of capturing spatial and temporal coupling between generation sites and time intervals. The temperature constraint is second-order in voltage angle differences. The problem is therefore a quadratically-constrained quadratic program (QCQP). Solving the QCQP for each line in the network yields a set of candidate generation deviation patterns which may then be sorted to determine the lines that are most vulnerable to overloading. The paper develops a computationally efficient algorithm for solving this QCQP. An example explores line-overload vulnerability due to changes in wind patterns. Numerical results emphasize the framework’s ability to incorporate evolving ambient and system conditions, as well as computational scaling properties.

I. Introduction

Wind-induced network congestion is becoming more common as wind develops into a major transmission-scale energy source [1]–[3]. Increasing wind generation accentuates the challenges posed by forecast inaccuracy [4], raising the possibility that even small deviations from a forecast may compound across multiple wind-farms to overload transmission lines. Operators need to know which lines are most vulnerable to such overloading events. This paper proposes a computationally efficient (though approximate) algorithm which quickly identifies and ranks deviations from the forecast wind-power generation pattern that would induce unacceptably high line flows.¹

This algorithm can also be used to compute efficient re-dispatch patterns that return an overloaded line back to its operational limit.