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The maximum power flow for lossy transmission lines is derived using ABCD parameters in phasor form. These parameters create a matrix relationship between the sending-end and receiving-end voltages and currents, allowing the determination of the receiving-end current. This relationship facilitates calculating the complex power delivered to the receiving end, from which real and reactive power components are derived.
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A two-stage multi-objective optimization framework for coordinated EV charging scheduling and reactive power

Mohamed Sayed Badr1, H M Sharaf1, Ahmed M Zobaa2

  • 1Electrical Power Engineering Department Faculty of Engineering, Cairo University, Giza, 12613, Egypt.

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|April 15, 2026
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Summary
This summary is machine-generated.

Optimizing electric vehicle (EV) charging and reactive power dispatch significantly reduces grid losses and costs. This framework enhances power grid efficiency and user satisfaction with smart charging strategies.

Keywords:
EV charging patternsElectric vehiclesGrid metricsMulti-objective optimizationOzone layer depletionReactive power dispatch

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Area of Science:

  • Electrical Engineering
  • Power Systems
  • Sustainable Energy

Background:

  • Electric vehicles (EVs) offer environmental benefits but pose grid challenges due to uncoordinated charging.
  • Irregular EV charging patterns can lead to increased load variance, energy costs, and power losses.

Purpose of the Study:

  • To propose a two-stage framework for optimizing EV charging patterns and reactive power dispatch.
  • To minimize grid losses, energy costs, and voltage drops while maximizing voltage stability.
  • To analyze EV behavior under dynamic grid conditions.

Main Methods:

  • Developed day-ahead and real-time EV charging strategies.
  • Implemented optimal real-time reactive power dispatch using EV inverters.
  • Utilized multi-objective optimization with algorithms like particle swarm and slime mould optimization.
  • Tested on a 33-bus radial distribution system using MATLAB and MATPOWER.

Main Results:

  • Reduced daily active power losses from 4.04 MWh to 2.55 MWh (day-ahead) and 2.77 MWh (real-time).
  • Achieved EV charging cost savings of 28.63% (day-ahead) and 34.15% (real-time).
  • Maintained voltage profiles within acceptable limits (≥0.95 p.u.).

Conclusions:

  • The proposed framework effectively optimizes EV charging and reactive power dispatch.
  • Significant improvements in grid efficiency, cost reduction, and voltage stability were demonstrated.
  • The methodology enhances grid performance while ensuring customer satisfaction.