Coupling load-following control with OPF

Mohammadhafez Bazrafshan, Nikolaos Gatsis, Ahmad F. Taha, Joshua A. Taylor

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper, the optimal power flow (OPF) problem is augmented to account for the costs associated with the load-following control of a power network. Load-following control costs are expressed through the linear quadratic regulator (LQR). The power network is described by a set of nonlinear differential algebraic equations (DAEs). By linearizing the DAEs around a known equilibrium, a linearized OPF that accounts for steady-state operational constraints is formulated first. This linearized OPF is then augmented by a set of linear matrix inequalities that are algebraically equivalent to the implementation of an LQR controller. The resulting formulation, termed LQR-OPF, is a semidefinite program which furnishes optimal steady-state setpoints and an optimal feedback law to steer the system to the new steady state with minimum load-following control costs. Numerical tests demonstrate that the setpoints computed by LQR-OPF result in lower overall costs and frequency deviations compared to the setpoints of a scheme where OPF and load-following control are considered separately.

Original languageEnglish (US)
Article number8281533
Pages (from-to)2495-2506
Number of pages12
JournalIEEE Transactions on Smart Grid
Issue number3
StatePublished - May 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Computer Science


  • Optimal power flow
  • linear quadratic regulator
  • load-following control
  • semidefinite programming


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