Comparative study of SBOAs on the tuning procedure of the designed SMPI controller for MIMO VSP/HVDC interconnected model

Elyas Rakhshani, Iman Mohammad Hosseini Naveh, Hasan Mehrjerdi

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
17 Downloads (Pure)


This paper presents a new application of advanced SMPI controller for a newly introduced interconnected dynamic system with VSP based HVDC links for frequency control problem. This work presents an outgrowth of analysis about the Swarm – Based Optimization Algorithms (SBOAs) in the tuning process of Multivariable Proportional – Integral (MPI) controller, which is called swarm – based MPI (SMPI). PSO, GOA and GWO algorithms are used for tuning process of the designed SMPI. The VSP based HVDC model is added for mitigation of system frequency dynamics with emulating virtual inertia. The proposed SMPI controller are designed for enhancing the dynamic performance of this system's states during contingencies and they are compared with the conventional designed MPI controller. Deviation characteristics of the step function in MIMO transfer function of the VSP based HVDC model is considered as the common performance index in the proposed algorithms. On the other hand, the role of the proposed SMPI controller is to stabilize such interconnected system while minimizing the associated cost function. Matlab simulations next to the performed Nyquist's stability anslysis demonstrate how the tuned SMPI can remarkably improve the frequency deviations and the damping of the inter-area oscillations excited during a fault. This enhancement is more obvious especially when SMPI controller for a VSP based virtual inertia emulation is tuned using GWO method.

Original languageEnglish
Article number106812
Pages (from-to)1-24
Number of pages24
JournalInternational Journal of Electrical Power and Energy Systems
Publication statusPublished - 2021


  • Frequency control
  • Inertia emulation
  • Optimal control
  • Swarm – Based MPI (SMPI) Controller
  • Swarm – Based Optimization Algorithms (SBOAs)
  • Virtual inertia


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