Power system restoration after blackouts plays a key role in minimizing economic and social losses. Natural disasters, equipment failures, human errors and cyber or physical attacks can cause total or partial blackouts in power systems. Following a blackout, most of generating units cannot be restarted and need to be energized from the grid or other resources. Black start units are those with capability of being restarted without relying on any other resources. They can energize transmission system and provide cranking power to restart non-black start units. Therefore, it is of great importance where to install black start units in a power system. Planning of black start power plants which are needed to participate in power system restoration is independent system operator's responsibility. Due to the energy transition and increasing the role of wind farms and batteries in power systems, the impact of such resources should also be considered in power system restoration and its black start capability. In recent years numerous researches have been conducted on power system restoration; nevertheless, most of these are focused on the operation of power system during restoration process. On the other hand, those which are about planning and allocation of black start units are limited and the impact of wind farms and batteries are not taken into account. In this thesis, wind farms and batteries are considered in the planning of black start units to avoid non-optimal decisions. The objective of the model includes maximizing total generation capability (minimizing unavailable power plants), maximizing energization of transmission system and minimizing unserved load in the restoration process. The constraints of this model consist of initial conditions of power system, energization constraints of transmission lines and buses, power plants operation and start-up constraints, black start power plant installation constraints, power flow constraints including active and reactive power and constraints of wind farms and batteries. The approach is a static power system restoration. Therefore, dynamic and stability aspects and transients during power system restoration are not considered. It should be noted that financial aspects relating type and size of black start power plants are not included and are treated as predetermined. The developed model is formulated as a stochastic mixed-integer linear optimization problem. IEEE 39-bus network is used to eva‎luate the model and optimization is performed using GAMS software. By solving the problem, best location for installing black start power plant, optimal start-up sequence of power plants as well as optimal sequence for energizing transmission lines and buses are identified and the restored loads at each step of restoration is optimized. The results show that in power systems with high penetration of wind energy or batteries, reaching to non-optimal decisions is possible if these resources are not considered in planning of the black start resources.

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