Table 1 Overview of metaheuristic-based model reduction methods for power systems.

From: Constrained search space selection based optimization approach for enhanced reduced order approximation of interconnected power system models

Reduction algorithm

Initial search space selection

Coefficients optimized

Total decision variables

Preserves stability

Attain zero steady-state error.

Algorithm applied to

System reduced to

Numerator/

Denominator

Metaheuristic search-based methodologies for optimization of ROM numerator coefficients with compact initial search space selection

BTM PSO29

Compact

Numerator

k

Yes

Yes

9th order boiler system, 10th order MIMO SMIB power system

3rd, 4th order

PAM BBBCA 27

Compact

Numerator

k

Not always

Not always

4th order SISO Power system

2nd order

Metaheuristic search-based methodologies for optimization of ROM numerator coefficients with random initial search space selection

TMM BBBCA54,55

Random

Numerator

k

Not always

Not always

10th order MIMO SMIB power system

3rd order

DPR FFA56

Random

Numerator

k + 1

Yes

Not always

10th order MIMO SMIB power system

4th order

Metaheuristic search-based methodologies for optimization of ROM denominator coefficients

PSO DE IMPPA15

Random

Denominator

k + 1

Not always

Yes

7th order two-area thermal–thermal (non

reheated) MIMO power system

3rd order

EDE IMPPA17

Random

Denominator

k + 1

Not always

Yes

10th order MIMO SMIB power system

3rd order

Metaheuristic search-based methodologies for optimization of ROM numerator and denominator coefficients with initial compact search space selection

BTM MFO30,31

Compact

Numerator &

Denominator

2k + 1

Not always

Yes

7th order two-area thermal–thermal (non

reheated) MIMO power system

3rd order

Metaheuristic search-based methodologies for optimization of ROM numerator and denominator coefficients with initial random search space selection

PIV-GWO21

Random

Numerator &

Denominator

2k + 1

Not always

Yes

19th order TI FO power system

2nd order

Modified SPBO20

Random

Numerator &

Denominator

2k + 1

Not always

Not always

South Iran’s power grid, 24th order Biomass gasifier model

2nd order

SPBO57

Random

Numerator &

Denominator

2k + 1

Not always

Not always

8th -order proton exchange membrane fuel cell system

2nd order

GWO58

Random

Numerator &

Denominator

2k + 1

Not always

Not always

4th order heavy-duty gas turbine

2nd order

R GWO43

Random

Numerator &

Denominator

2k + 1

Not always

Not always

9th order boiler system

3rd order

HHO59

Random

Numerator &

Denominator

2k + 1

Not always

Not always

12th order three area interconnected wind turbines

2nd order

  1. Balanced truncation method (BTM), Pade approximation method (PAM), big bang big crunch algorithm (BBBCA), time moment matching (TMM), dominant pole retention (DPR), firefly algorithm (FFA), Slime mold optimization (SMO), enhanced DE (EDE), moth flame optimization (MFO), proximity index value (PIV), student psychology-based optimization (SPBO), modified SPBO, Harris Hawkes optimization (HHO).