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Improved spectral clustering for multi-objective controlled islanding of power grid

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Abstract

We propose a two-step algorithm for optimal controlled islanding that partitions a power grid into islands of limited volume while optimizing several criteria: maximizing generator coherency inside islands, minimizing power flow disruption due to teared lines, and minimizing load shedding. Several spectral clusterings strategies are used in the first step to lower the problem dimension (taking into account coherency and disruption only), and CPLEX tools for the mixed-integer quadratic problem are employed in the second step to choose a balanced partition of the aggregated grid that minimizes a combination of coherency, disruption and load shedding. A greedy heuristics efficiently limits search space by generating the starting solution for the exact algorithm. Dimension of the second-step problem depends only on the desired number of islands K instead of the dimension of the original grid. The algorithm is tested on the standard systems with 118, 2383, and 9241 nodes showing high quality of partitions and competitive computation time.

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Notes

  1. Alternatively, the minimum K-cut problem is to minimize the total weight of edges, which, if removed, break the graph into K connected components. These two definitions are, in fact, equivalent.

  2. For further acceleration of calculations the problem in hand can be reduced to the mixed-integer linear problem (MILP) with the techniques described in [20, 42] but in the present article this possibility is not studied in detail.

  3. To some extent these starting conditions can be interpreted as a situation in contingency case after the load shedding program run to balance demands and available generation/transmission capacities. It is assumed that these efforts where not enough to stabilize the system, and the controlled islanding is performed.

  4. Some analysis of different islanding performance metrics can be found in [37].

  5. Correlation is equal to 0.89 for SMALL system and 0.78 for MEDIUM system.

  6. Training and testing sets were obtained with halfway random sampling.

  7. Distinct to SMALL system, the definition of MEDIUM system includes realistic real power flow constraints for transmission lines, which results in better prediction accuracy.

  8. This result is valid for the fixed weights of performance metrics: \(\alpha _C=\alpha _D=\alpha _S=1\). Having the weights changed, the leading strategies can also change (see the analysis in Sect. 6.3).

  9. cplexmiqp routine of CPLEX 12.6.2.0 was used to solve MIQP; tests were run on Intel Core i-5 3337U CPU 1.8 GHz.

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Acknowledgements

The first author would like to thank support from Russian Foundation for Basic Research (Project 16-37-60102).

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Correspondence to Mikhail Goubko.

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Goubko, M., Ginz, V. Improved spectral clustering for multi-objective controlled islanding of power grid. Energy Syst 10, 59–94 (2019). https://doi.org/10.1007/s12667-017-0240-1

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