A hybrid solution approach consisting of both robust optimization and stochastic programming is developed to solve the DSAO model. A novel robust optimization-based Defender-Sequential-Attacker-Operator (DSAO) model is developed, which considers game-theoretic interactions between different agents (the defender, attacker and operator), selection of attacking targets, as well as the probabilities of attacks and correlations between attacks. the defender chooses the critical branches to harden for the purpose of minimizing the expected damage second, the attacker may launch multiple attacks to disrupt the branches aiming to maximize the damage third, following each of the attacks, the operator performs the optimal power re-dispatch to minimize the load shedding. The problem formulation involves a multi-stage decision process: first. In this paper, the defense strategy of the transmission system in case of multi-period attacks considering uncertainties is investigated. The power system is under increasing threat of terrorist attacks, and it is important to develop efficient methods to improve the power system resiliency for defending against the attacks. Numerical results show the effectiveness of the proposed methodology. The original trilevel program is first transformed into an equivalent bilevel program, which is subsequently solved by an efficient implicit enumeration algorithm. We propose a novel two-stage solution approach that attains optimality with moderate computational effort. Finally, in the lower level, the system operator minimizes the damage caused by the outages selected by the disruptive agent by means of an optimal operation of the power system. In the middle level, the disruptive agent determines the set of out-of-service components so that the damage in the system is maximized. In the upper level, the system planner identifies the components to be defended or hardened in order to reduce the damage associated with plausible outages. This planning problem is characterized by a defender-attacker-defender model which is formulated as a trilevel programming problem. This paper addresses the allocation of defensive or hardening resources in an electric power grid to mitigate the vulnerability against multiple contingencies. Although the proposed decomposition approach cannot guarantee global optimality, a high level picture of how the network can be planned reliably and economically considering CVSR is achieved.
Moreover, the appropriately allocated CVSRs add flexibility to the TEP problem and allow reduced planning costs. The detailed simulation results on the IEEE 24-bus and a more practical Polish 2383-bus system demonstrate the effectiveness of the approach. To reduce the computational burden for a practical large scale system, a decomposition approach is proposed. The nonlinear part of the power flow introduced by the variable reactance is linearized by a reformulation technique. The multistage TEP with the CVSR considering the N - 1 security constraints is formulated as a mixed integer linear programming model. However, the cost of the CVSR is about one tenth of a similar rated FACTS device which potentially allows large numbers of devices to be installed. The CVSR is a FACTS-like device which has the capability of controlling the overall impedance of the transmission line.
#Grid defense series
This paper introduces a Continuously Variable Series Reactor (CVSR) to the transmission expansion planning (TEP) problem.
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