Table 15 Performance review of single-objective OPF case studies.

From: Sperm swarm optimization for many objective power flow problems with enhanced performance evaluation in power systems

Test case

Objective function

Optimization goal

Constraints considered

Algorithm used

Key results

IEEE 30-Bus

Active Power Loss Minimization (APL)

Minimize power loss in the network

Generator limits, Voltage constraints, Line flow limits

MaOSSO

Achieved a 15% reduction in APL compared to NSGA-III; convergence time reduced by 25%

IEEE 30-Bus

Voltage Stability Index Maximization (VSI)

Maximize system stability

Generator limits, Load power factors, Transformer tap settings

MOEA/D-DE

Improved VSI by 20% over NMPSO; better stability under varying load conditions

IEEE 57-Bus

Reactive Power Loss Minimization (RPL)

Reduce reactive power losses

Voltage constraints, Line thermal limits, Generator VAR capabilities

MaOSSO

Reduced RPL by 18%, achieving better distribution of reactive power compared to RVEA

IEEE 57-Bus

Fuel Cost Minimization (TFC)

Minimize generation costs considering fuel

Fuel cost curves, Prohibited operating zones, Ramp rate limits

NMPSO

10% reduction in TFC compared to traditional methods, while maintaining efficient operational stability

IEEE 118-Bus

Emission Minimization (TE)

Reduce total emissions from generation

Emission coefficients, Generator limits, Load profiles

NSGA-III

Reduced emissions by 25%, meeting regulatory environmental standards without compromising generation efficiency

IEEE 118-Bus

Voltage Deviation Minimization (VMD)

Ensure minimal voltage variations

Voltage limits, Transformer tap settings, Load demands

RVEA

Achieved uniform voltage profiles with 12% improvement in VMD over baseline optimization