Cliques in Power System Studies
Alireza Soroudi, PhD
Lead Data Scientist @ bluecrux || SMIEEE || Optimization expert || Healthcare management || Lab Digitalization || Power and Energy systems || Developer || Author / Speaker || (views are mine)
A?clique, in an?undirected power system (graph?G=(V,E))?is a subset of the?buses, such that every two distinct buses are connected.
The problem formulation is as follows:
Xi is a binary variable demonstrating if a node is selected to be in a clique or not. Eij represents the edge between node i and node j.
The pyomo code for finding the maximum clique?is as follows:
This code will provide one solution. How to find the next clique ?
The solution for different IEEE cases are obtained as follows (provided by Matpower).
IEEE 24 bus network, with 38 links. This network has only 1 clique. The maximum clique size in this graph is 3
IEEE 39 bus network, with 46 links.This network has only 1 clique. The maximum clique size in this graph is 3
The clique in a given power system provides some structural info for the system operator it basically shows which buses are well connected to each-other. If a contingency happens to a line in a clique then there is a parallel path to carry the power flow. Additionally, there will be a high correlation between the voltages of the nodes in a clique.
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Visiting researcher at University of Salerno
3 年MILP formulations are very powerful and expressive. Also very great heuristics to scale beyond the capacities of MILP solvers are available. For instance I and some colleagues tried a similar problem in 2019: "Dolatabadi, Mohammad, and Yaser Damchi. "Graph theory based heuristic approach for minimum break point set determination in large scale power systems."?IEEE Transactions on Power Delivery?34.3 (2019): 963-970."
Senior Algorithm Developer, Energy Exemplar||Ex-ExxonMobil, KPMG, Multiverse Computing||MSc (in Eng.), EE, IISc||BTech, ECE, NIT Durgapur||Optimization, ML||
3 年In one of my research works, we have explored a way to find all the maximum size cliques of a graph. We consider the one-hop neighbourhood graph at each node, then we use an algorithm proposed by Belachew and Gillis (very interesting paper: used symmetric rank-one non-negative matrix factorisation to find maximum clique). Though most of the time it returns a maximum clique, there is no guarantee (as this is a hard problem to solve). To ensure that we get the maximal clique, we further augmented few nodes in it (generally it was around 2-3 nodes as per our experiments) to ensure that the clique is the maximal clique. The link of the papers: https://ieeexplore.ieee.org/abstract/document/7979618 https://link.springer.com/article/10.1007%2Fs10957-016-1043-6
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3 年Another great one!
Ph.D- Head of Power Electrical Developing Advanced Research (PEDAR) Group. |Power Microgrids Control|SmartGrids|Machine Learning|EV Charging
3 年this is an excellent and professional achievement...I know the complexities of this work...congratulation dear soroudi