## 2 Black Start  
A restoration of the grid is a process necessary after a power outage has been experienced. The outage can be small and involve only a portion of the grid, as it most commonly happens, relying on the assistance of other neighbour systems. As stated in [4], these blackouts require a top-down restoration, where the tie lines that link the affected system and the support system are energized for delivering power to the affected transmission network. From there, power is delivered to the pertinent systems for bringing local generation online.  
Widespread power outages are a completely different story; a restoration after one of these events is far more complicated because it has to be done bottom-up, which means starting from generating units delivering power to other units in order to bring them back online to, as quickly as possible, restore the whole system. These kinds of system restorations are called black starts and, most commonly, they are composed of different recovery sequences that occur at the same time at different points of the grid in order to accelerate the process. When isolated parts of the grid are ready to be connected, they have to be synchronized to restore the original system.  
The process of restoring the portion of a power grid that has been affected by a power outage to its operating conditions, without relying on any external support from the unaffected parts of the grid, is called a black start [4]. Generally, any element of a grid that has been forced out of service can be put back online with the aid of external sources of power, but a black start restoration is notoriously more complicated than a conventional top-down startup, as the affected grid has to start by its own means.  
Black starts need generating units that can either start on their own or have the necessary systems for turning on their auxiliary loads (like motors, ventilating systems, pumps, etc.) [4]. These units are then used to supply power to adjacent distribution and transmission lines, and the transformers that are in between. Considering the outstanding characteristic of being able to start without off-site power, black start units mainly belong to four categories [9; 10]:  
* Hydroelectric units, which have fast response features.
* Diesel generators, which are useful, despite their small size, for supplying power for starting larger units.
* Aero-derivative gas turbine generators, thanks to their steep ramp rate, i.e., a fast increase in their power output.
* Larger gas turbines, even though they are not themselves capable of a black start, they can be coupled with diesel generators for this purpose.  
If a power system is not properly prepared against major outages, i.e., through black start capability, a large-scale fault can have catastrophic consequences. Studies have determined the possibility that if a fault occurred on strategic power plants, a global blackout would be imminent [32]. Massive blackouts, which occur when a fault has huge repercussions on the grid, have happened almost annually worldwide for the last two decades. As a result, the need for innovative applications and technical improvements of power grids will further increase [33].  
When a power system has several sources of black start that have already been identified and taking into account the behavior of the structure of the grid and its optimum conditions, the complete power network has to be divided into two or more subsystems for an independent recovery in this way, accelerating the restoring process until the network reaches synchronization after the delivery of stable power on each system after a period of time [34].