Post-contingency states representation and redispatch for restoration in power systems operation
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In this treatise, we will present a dynamic version of the Security Constrained Optimal Power Flow (SCOPF) problem, the "Look Ahead Security Constrained Optimal Power Flow" (LASCOPF) problem with post-contingency states representation and redispatch scheme for restoration to normal operation, following an outage represented in the mathematical formulation. We will also propose a distributed algorithm to solve the OPF, SCOPF, and LASCOPF problems. The objective of the problem is to minimize the cost of operation, over a number of dispatch intervals and across all contingency scenarios subject to the constraints of the network. It is, therefore, a large optimization problem, requiring an effective distributed solution method. As one of the means to address this challenge, we will be extending the Proximal Message Passing (PMP) algorithmic framework, which is based on another algorithm, called Alternating Direction Method of Multipliers (ADMM) and combine it with the Auxiliary Problem Principle (APP). The resulting algorithm, which we hereafter will call Auxiliary Proximal Message Passing (APMP) is extremely scalable with respect to both network size and the number of scenarios. We implement a look-ahead contingency planning, representing the post-contingency states of the system ahead of time, in a Receding Horizon Control (RHC) or, Model Predictive Control (MPC) type of formulation. One goal of this work is to particularly focus our attention on the trajectories of post-contingency line temperature rise, line MW flow rise, and line current rise and try to limit them through our proposed method. We also investigate how to reduce the computational burden. The reason for paying particular attention to line temperature rise and limiting the same, is the intention of the present scheme to make the most use of the existing transmission capability, without costly transmission upgrades. The means of attaining that goal is to make use of short term thermal overload rating and dynamic thermal limit, and in the event of an actual outage, modifying the dispatch in such a way, that the flows on the remaining lines can be brought back to within allowed values in a given time interval. We demonstrate the effectiveness of our distributed method with a series of numerical simulations based on some simple systems and the IEEE test systems. Finally, we conclude, with a suggestion to some possible future research directions.
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