Cross-Gramian Model Reduction Approach for Tuning Power System Stabilizers in Large Power Networks

Sudipta Ghosh, Younes J. Isbeih, Mohamed Shawky El Moursi, Ehab F. El-Saadany

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Poorly damped inter-area modes of oscillations represent a major concern to power system operation since they detain the power transfer capability of transmission networks. This situation becomes more stringent as the tie-lines are heavily stressed and/or large amounts of renewable energy resources are installed. To overcome this issue, a detailed mathematical model is proposed in this paper to reduce the linearized model of a large power system using the cross-Gramian technique. The presented approach divides the system into a study area which contains one generation unit with installed power system stabilizer (PSS) and an external one which comprises the rest of generation units in the system. Model order reduction is only applied to the external area with the objective of maintaining the characteristics of the original model. Meanwhile, the dynamics of the study area are preserved to provide the required damping through the designed PSS. In addition, an online tuning methodology is also presented to provide robust damping performance in response to changes in the system operating conditions. The deployed cross-Gramian model order reduction alleviates the computational burden and time associated with the online PSS tuning when original power system models are used. The effectiveness of the proposed approach is tested using the New-England 39-bus system in addition to another practical system which resembles the Northern Regional Power Grid India test system.

Original languageBritish English
Article number8744409
Pages (from-to)1911-1922
Number of pages12
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - May 2020


  • cross gramian (CG)
  • Low frequency oscillation (LFO)
  • model order reduction (MOR)
  • power system stabilizer (PSS)


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