Abstract-In this paper, uncertainties from wind power in-feed are taken into account in a DC security-constrained optimal power flow (SCOPF) by formulating probabilistic constraints. The deviations from the wind power forecast are represented as Gaussian random variables and an analytical reformulation of the constraints is proposed, which is exact for the Gaussian distribution. The resulting formulation has the same computational complexity as the deterministic problem. Furthermore, a valuation framework to assess the cost of securing the system against fluctuations in wind power in-feed is proposed. The applicability of the method and the valuation framework is demonstrated on the IEEE RTS96 system. We show that the probabilistic formulation leads to lower probability of thermal overloads, and that it is less costly to secure the system against uncertain in-feed than to secure the system against failures in most cases.
Abstract-Higher shares of electricity generation from renewable energy sources and market liberalization is increasing uncertainty in power systems operation. At the same time, operation is becoming more flexible with improved control systems and new technology such as phase shifting transformers (PSTs) and high voltage direct current connections (HVDC). Previous studies have shown that the use of corrective control in response to outages contributes to a reduction in operating cost, while maintaining N-1 security. In this work, we propose a method to extend the use of corrective control of PSTs and HVDCs to react to uncertainty. We characterize the uncertainty as continuous random variables, and define the corrective control actions through affine control policies. This allows us to efficiently model control reactions to a large number of uncertainty sources. The control policies are then included in a chance constrained optimal power flow formulation, which guarantees that the system constraints are enforced with a desired probability. By applying an analytical reformulation of the chance constraints, we obtain a second-order cone problem for which we develop an efficient solution algorithm. In a case study for the IEEE 118 bus system, we show that corrective control for uncertainty leads to a decrease in operational cost, while maintaining system security. Further, we demonstrate the scalability of the method by solving the problem for the IEEE 300 bus and the Polish system test cases.
Using a simple quantum master equation approach, we calculate the full counting statistics of a single-electron transistor strongly coupled to vibrations. The full counting statistics contains both the statistics of integrated particle and energy currents associated with the transferred electrons and phonons. A universal as well as an effective fluctuation theorem are derived for the general case where the various reservoir temperatures and chemical potentials are different. The first relates to the entropy production generated in the junction, while the second reveals internal information of the system. The model recovers the Franck-Condon blockade, and potential applications to noninvasive molecular spectroscopy are discussed.
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