Power Scheduling of Coupled System of Electrical Spring and Flexible-Renewable Virtual Power Plant based on Energy Market Model

Document Type : Research article

Authors

1 Department of electrical engineering, Ha.C., Islamic Azad University, Hamedan, Iran

2 Department of Electrical Engineering, Ayatollah Boroujerdi University, Boroujerd, Iran

3 Electrical Engineering; Bu-Ali Sina University, Hamedan, Iran

10.61882/jgeri.2026.2085200.1104
Abstract
This study investigates the operation of a flexible-renewable virtual power plant (VPP) integrated with electrical spring (ES) devices within a smart distribution network. The proposed framework jointly addresses the technical and economic objectives of the distribution system operator (DSO) while enabling the VPP’s optimal participation in the wholesale energy market. A bi-level optimization structure is adopted: the upper-level problem focuses on minimizing active power losses via an AC optimal power flow (AC-OPF) formulation, whereas the lower-level problem maximizes the VPP’s revenue from energy market transactions. Operational constraints include detailed modeling of electrical spring behavior and the VPP’s internal components. The bi-level problem is transformed into a single-level equivalent using the Karush–Kuhn–Tucker (KKT) optimality conditions. The key innovations of this work are threefold: (i) the formulation of an electrical-spring-based virtual power plant model, (ii) the integration of multiple technical–economic indices into the optimization framework, and (iii) the employment of flexible resources for system-level energy management. Simulation results validate the proposed scheme’s efficacy in improving both network technical performance and VPP profitability. Compared with conventional load flow analyses, the proposed strategy improves network operational metrics by approximately 37% to 66.7% through intelligent dispatch and voltage regulation enabled by virtual power plant control.

Keywords



Articles in Press, Accepted Manuscript
Available Online from 19 June 2026

  • Receive Date 11 February 2026
  • Revise Date 04 June 2026
  • Accept Date 19 June 2026
  • Publish Date 19 June 2026