الفهرس 
Graph Theory
Optimal Network Reconfiguration in Active Distribution Networks with Soft Open PointsOnly 14 pages are availabe for public view
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Abstract
Optimization of electrical network parameters has been of great importance to cope with the new challenges in the modern power grids. Accordingly, various optimization techniques/strategies were employed to coverup these needs. Hence, various single, multi-objective, bi-level, tri-level, and other optimization formulations were done to get a near-global solution to the optimization problem. In this thesis, various optimization formulations were conducted to achieve a better objective function for several purposes.
Recently, in modern distribution grids, the high penetration of distributed generation (DG) units poses new challenges, including power loss increase, harmonic distortion aggregation, equipment overloads, and voltage quality problems in the planning and operation of power distribution systems. Thus, there is significant room for improvement. New perceptions are therefore needed to face these challenges, cope with future advances to realize resilient electrical distribution systems with a high penetration of renewables and guarantee reliable and efficient network performance. Transmission and distribution network operators struggle to identify the sources of network losses, utilize appropriate solutions to ensure reduced losses, operational costs, and emissions while keeping future energy losses as low as possible through proper planning of distribution systems with low carbon technologies using various optimization formulations. Various strategies were employed to increase the hosting capacity (HC) of distribution networks to accommodate more DGs. These strategies include network reinforcement, power quality (PQ) improvement, optimizing tab changers, distribution network reconfiguration (DNR), soft open points (SOPs), and others. These strategies have guaranteed a promising ability to minimize power losses and total annual costs while increasing DGs penetration and dealing with operational issues like reverse power, line thermal, and voltage limits. In this thesis, the main aim is to investigate both DNR and SOPs for maximizing DGs penetration from the operational and planning perspectives via choosing the proper mathematical optimization formulations, applying new graph theoretic mathematical algorithms to optimize networks’ topology efficiently and also choosing the best solution using multi-criteria decision-making mathematical algorithms.
from the operational perspective, DNR can provide resiliency for the distribution systems by relocating the distribution systems’ tie-lines. As a result, many research works have employed DNR to maximize DGs penetration and decrease power losses. In this thesis, we proposed two DNR mathematical algorithms based on graph theory. The first DNR methodology succeeded in guiding heuristic/metaheuristic randomness towards finding the distribution system’s optimal radial configurations. The second one succeeded in obtaining a global/near-global structure of large distribution systems up to the 4400-node distribution system by checking different possibilities to exchange the existing tie-lines’ status with their neighboring sectionalized status lines using a new index called weighted voltage deviation index. It was figured out that the graph-theoretic mathematical approach has outperformed against the heuristic and metaheuristic optimization algorithms.
Further, simultaneous DNR and DGs penetration were assessed using single and multi-objective optimization approaches. Two objectives are simultaneously minimized, including power loss minimization and fast voltage stability for multiple penetrations of DGs based smart inverters, which provides both active and reactive power supply regularly.
Finally, SOPs are placed instead of tie-lines to provide meshed networks’ benefits by transferring apparent powers between the connected feeders. Both single and multi-objective formulations are proposed to step on the effectiveness of SOPs placement. from the single objective viewpoint, various scenarios were deployed for power loss minimization by allocating lossless/lossy SOPs with/without DNR, and also with/without DGs based smart inverters penetration. It was concluded that simultaneous DNR, and SOPs, and DGs placement succeeded in obtaining the maximum reduced power losses among the proposed scenarios. from the multi-objective viewpoint, three objectives were optimized simultaneously for an SOP placement instead of a certain tie-line in an original Egyptian distribution feeder (i.e., 59-node distribution feeder), and the presence of three DGs penetrations.
from the HC maximization perspective, a multi-objective bilevel optimization approach is formulated, including HC maximization and the total annual cost with/without load uncertainty consideration to step on the real benefits from applying DNR and SOPs’ placements. The optimal solution is chosen based on a mathematical decision-making algorithm called TOPSIS. Case studies are conducted on the 59- and 83-node real distribution networks. Finally, a multi-objective bilevel formulation is developed to maximize the HC of the allocated wind turbines, photovoltaic DGs, and the power loss reduction of five distribution networks using DNR. Various uncertainties were considered, including solar irradiance, wind speed, and load uncertainties. The optimal solution was chosen using TOPSIS. Also, sensitivity indices were used to measure the studied distribution networks’ performance, including the 16-, 59-, 69-, 83-, 415-, and 880-node distribution networks.