1,721,037 research outputs found
Approximating the parameter-space stability boundary considering post-contingency corrective controls
No full textLately, much work in the area of voltage stability assessment has been focused on finding post-contingency corrective controls. In this article a contribution to this area will be presented where we investigate the surface of maximal loadability while allowing for post-contingency corrective controls. This objective is different from the usual, where the aim is to include the post-contingency controls in a security-constrained optimal power flow. Our aim is rather to find approximations of the post-contingency stability boundary, in pre-contingency parameter space, while including the possibility for post-contingency corrective controls. These approximations can then be used in, for example, a chance-constrained optimal power flow routine. (C) 2014 Elsevier B.V. All rights reserved
Sequential Systems of Reflected Backward Stochastic Differential Equations with Application to Impulse Control
No full textWe consider a system of finite horizon, sequentially interconnected, obliquely reflected backward stochastic differential equations (RBSDEs) with stochastic Lipschitz coefficients. We show existence of solutions to our system of RBSDEs by applying a Picard iteration approach. Uniqueness then follows by relating the limit to an auxiliary impulse control problem. Moreover, we show that the solution to our system of RBSDEs is connected to weak solutions of a stochastic differential game where one player implements an impulse control while the opponent plays a continuous control that enters the drift term. As all our arguments are probabilistic and hence hold in a non-markovian framework, we are able to consider the setting where the underlying uncertainty in the game stems from an impulsively and continuously controlled path-dependent stochastic differential equation driven by Brownian motion
Optimal stopping of BSDEs with constrained jumps and related zero-sum games
No full textIn this paper, we introduce a non-linear Snell envelope which at each time represents the maximal value that can be achieved by stopping a BSDE with constrained jumps. We establish the existence of the Snell envelope by employing a penalization technique and the primary challenge we encounter is demonstrating the regularity of the limit for the scheme. Additionally, we relate the Snell envelope to a finite horizon, zero-sum stochastic differential game, where one player controls a path-dependent stochastic system by invoking impulses, while the opponent is given the opportunity to stop the game prematurely. Importantly, by developing new techniques within the realm of control randomization, we demonstrate that the value of the game exists and is precisely characterized by our non-linear Snell envelope
Zero-sum stochastic differential games of impulse versus continuous control by FBSDEs
No full textWe consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of "backward semigroups" we first prove the dynamic programming principle (DPP) for a truncated version of the problem in a straightforward manner. Relying on a uniform convergence argument then enables us to show the DPP for the general setting. Our approach avoids technical constraints imposed in previous works dealing with the same problem and, more importantly, allows us to consider impulse costs that depend on the present value of the state process in addition to unbounded coefficients. Using the dynamic programming principle we deduce that the upper and lower value functions are both solutions (in viscosity sense) to the same Hamilton-Jacobi-Bellman-Isaacs obstacle problem. By showing uniqueness of solutions to this partial differential inequality we conclude that the game has a value.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).</p
Approximating the Loadability Surface in the Presence of SNB-SLL Corner Points
No full textPower system voltage security assessment is generally applied by considering the power system loadability surface. For a large power system, the loadability surface is a complicated hyper-surface in parameter space, and local approximations are a necessity for any analysis. Unfortunately, inequality constraints due to for example generator overexitation limiters, and higher codimension bifurcations, makes the loadability surface non-smooth. One situation that is particularly difficult to handle is when a saddle-node bifurcation surface intersects a switching loadability limit surface. In this article we intend to investigate how several local approximations can be combined to obtain an adequate approximation of the loadability surface near such intersections
Stochastic optimal power flow by multi-variate Edgeworth expansions
No full textStochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only steady-state variable limits have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. Recently an extension of the stochastic optimal power flow formulation that included constraints for voltage stability as well as small-signal stability was proposed. This was done by approximating the voltage stability and small-signal stability constraint boundaries with second order approximations in parameter space. In this article an alternative solution method to this problem will be proposed. The new improved solution method, which is based on Edgeworth series expansions, is both more efficient and accurate. We also give details on convexity of the problem and discuss some computational issues. (C) 2013 Elsevier B.V. All rights reserved
A note on reflected BSDEs in infinite horizon with stochastic Lipschitz coefficients [Elektronisk resurs]
No full textWe consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon RBSDEs to the setting where the driver has a stochastic Lipschitz coefficient. As an application, we consider robust optimal stopping problems for functional stochastic differential equations (FSDEs) where the driver has linear growth.</p
Optimal stopping of BSDEs with constrained jumps and related double obstacle PDEs
No full textWe consider partial differential equations (PDEs) characterized by an upper barrier that depends on the solution itself and a fixed lower barrier, while accommodating a non-local driver. First, we show a Feynman–Kac representation for the PDE when the driver is local. Specifically, we relate the non-linear Snell envelope, arising from an optimal stopping problem—where the underlying process is the first component in the solution to a stopped backward stochastic differential equation (BSDE) with jumps and a constraint on the jumps process—to a viscosity solution for the PDE. Leveraging this Feynman–Kac representation, we subsequently prove existence and uniqueness of viscosity solutions in the non-local setting by employing a contraction argument. This approach also introduces a novel form of non-linear Snell envelope and expands the probabilistic representation theory for PDEs.
A Note on Reflected BSDEs in Infinite Horizon with Stochastic Lipschitz Coefficients
Get PDFWe consider an infinite horizon, obliquely reflected backward stochastic
differential equation (RBSDE). The main contribution of the present work is
that we generalize previous results on infinite horizon reflected BSDEs to the
setting where the driver has a stochastic Lipschitz coefficient. As an
application we consider robust optimal stopping problems for functional
stochastic differential equations (FSDEs) where the driver has linear growth
Probabilistic representation of viscosity solutions to quasi-variational inequalities with non-local drivers
No full textWe consider quasi-variational inequalities (QVIs) with general non-local drivers and related systems of reflected backward stochastic differential equations (BSDEs) in a Brownian filtration. We show existence and uniqueness of viscosity solutions to the QVIs by first considering the standard (local) setting and then applying a contraction argument. In addition, the contraction argument yields existence and uniqueness of solutions to the related systems of reflected BSDEs and extends the theory of probabilistic representations of PDEs in terms of BSDEs to our specific setting
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