An Optimization Framework for Resilience-based Power Grid Restoration



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Power outage is a terrible consequence of an extreme event that affects a wide range of consumers including homes, hospitals, and commercial industries. An extreme event such as a hurricane, windstorm or earthquake can disrupt power grids located in open areas. In a power grid, transmission lines are the most vulnerable equipment and their damage usually results in a cascading failure of the whole network. Although a power system should be strengthened in advance to withstand these events, having a plan to restore the failed power grid is essential. Emergency generation units play an important role in a restoration process; these pre-located units are called black start (BS) units. The restoration process with BS units is conducted through a parallel restoration over independent sections within a network. Appropriate sectionalization provides a more resilient power system against a long outage. Assessing and optimizing the resilience of a power system could improve the quality of the restoration process. To achieve this resilient power system, a mathematical model is presented to maximize the system’s resiliency while planning a restoration process. The system resiliency is measured through an innovative resilience vector. As a result, the restoration would be performed quickly to satisfy all critical demands. The model is a mixed integer programming (MIP), which is decomposed to a bi-level model where it can be solved in the lower complexity. Rather than the bi-level programming, a mathematical programming with equilibrium constraints (MPEC) approach is applied to solve the model. The comparison between the results of both methods demonstrates the high efficiency of bi-level programming solution methodology in a large-scale case. A pre-emptive goal programming (PEP) method also supports the solution methodologies to take care of multiple terms with different scales and priorities in the objective function of the model. The model is analyzed by 6- and 118-bus IEEE standard test systems. Sectionalization of a transmission network has a close association with partitioning a graph (i.e., the lines are considered as edges and grid buses are the same as graph nodes). The graph partitioning problem (GPP) is formulated as a MIP model to minimize the amount of dis-joint edges so that well connected sections can be formed. Therefore, the proposed restoration model is combined with the GPP model. In this order, the sectionalization constraints are replaced with GPP constraints while the GPP objective is added to the model’s objective. The new GPP-based restoration model is examined for both 6- and 118-bus case studies and the results are compared with the first sectionalization approach. The analysis of advantages and disadvantages for the first and second restoration models is currently under work. Both proposed deterministic models are solved under the assumption of a given status for the transmission network after disruption; however, it is rarely possible to have a precise prediction on the post-status of a transmission network following an extreme weather. Hence, the post-status of transmission lines can be considered as a source of uncertainty. In this study, a robust optimization model is provided to take care of this uncertainty. The proposed robust model is a scenario-based model of the GPP-based model. These scenarios are prepared based on simulated hurricane wind speeds and the fragility profile of transmission lines. Furthermore, the worst-case model against all realization of the grid post-status is provided. The result on 118-bus test system gives a reliable solution for all realization of the scenarios with a narrow band in objectives performance measures. Dealing with large network-structured systems such as a power system is difficult. For this reason, a parallel processing is recommended by partitioning the network; which can facilitate the process by reducing the size of the target network at each moment. The common partitioning criterion is modularity while considering another metric beside it is beneficial to the result. The final chapter of the dissertation addresses the undirected network partitioning challenges in the vulnerability of the partitions via maximization of edge-connectivity and modularity. The edge-connectivity is a graph metric, which represents the robustness of the sub-networks and its optimization, enhance the robustness of the partitions. The problem is formulated as a bi-objective maximization model. The results on multiple random test cases of different sizes are analyzed to demonstrate the model’s performance.



Optimization, Resilience, Power systems, Network Partitioning, Robust optimization