Distributed Grid restoration based on graph theory

TL;DR

This paper proposes a unique approach to the restoration of smart grids under attack by impostors or due to natural calamities via optimal islanding of the grid with primary generators and distributed generators into sub-grids minimizing the amount of load shed which needs to be incurred and at the same time minimizing the number of switching operations via graph theory.

Abstract

With the emergence of smart grids as the primary means of distribution across wide areas, the importance of improving its resilience to faults and mishaps is increasing. The reliability of a distribution system depends upon its tolerance to attacks and the efficiency of restoration after an attack occurs. This paper proposes a unique approach to the restoration of smart grids under attack by impostors or due to natural calamities via optimal islanding of the grid with primary generators and distributed generators(DGs) into sub-grids minimizing the amount of load shed which needs to be incurred and at the same time minimizing the number of switching operations via graph theory. The minimum load which needs to be shed is computed in the first stage followed by selecting the nodes whose load needs to be shed to achieve such a configuration and then finally deriving the sequence of switching operations required to achieve the configuration. The proposed method is tested against standard IEEE 37-bus and a 1069-bus grid system and the minimum load shed along with the sequencing steps to optimal configuration and time to achieve such a configuration are presented which demonstrates the effectiveness of the method when compared to the existing methods in the field. Moreover, the proposed algorithm can be easily modified to incorporate any other constraints which might arise due to any operational configuration of the grid.

Figures (6)

• Figure 1: A sample grid is shown in (A). The feeders 702-713 and 730-709 are under attack. After the attack, the grid becomes disconnected as shown in (B). It is divided into 3 connected components, some with a power deficit and others with a surplus. The auxiliary graph $G_a$ is formed in (C) as shown. Since this is the optimal set of tie lines to be connected, the nodes whose load needs to be shed are searched for as shown in (D). This is the final grid configuration after islanding and reconfiguration.
• Figure 2: The figure gives a brief representation of the algorithm presented in the paper.
• Figure 3: The figure shows a simplified representation of the 1069-node grid system. This configuration is used with four taxonomy feeders and interconnected by seven tie lines. Moreover, DGs are placed randomly in the grid.
• Figure 4: The figure shows a simplified representation of the IEEE-37 node system. The configuration is modified by introducing tie lines in the existing grid.
• Figure 5: This graph presents the load shed pre and post restoration as given by \ref{['tab3']} for the IEEE-37 node system. The horizontal axis represents the number of attacks whereas the vertical axis corresponds to the amount of load shed.