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Optimal operation of transmission power networks by using improved stochastic fractal search algorithm

  • Thang Trung NguyenEmail author
  • Thuan Thanh Nguyen
  • Minh Quan Duong
  • Anh Tuan Doan
Original Article
  • 17 Downloads

Abstract

This paper presents the application of an improved stochastic fractal search algorithm (ISFSA) for optimizing five single objectives of optimal power flow (OPF) problem and satisfying all constraints consisting of operating limits of electric components, power balance and load voltage magnitude limits. The proposed ISFSA is formed by implementing three improvements on the conventional stochastic fractal search algorithm (SFSA). The first improvement cancels one ineffective formula but keeps another one in diffusion process. The second improvement selects some worst solutions in the first update and some best solutions in the second update for producing new solutions. In the third improvement, a proposed technique is applied for carrying out the update processes. Comparisons of obtained results from three standard IEEE power systems indicate that the proposed method is superior to SFSA in terms of optimal solution quality, execution speed as well as success rate. The performance comparisons with other existing methods available in previous studies also lead to the conclusions that the proposed method can reach lower generation fuel cost, smaller total power losses, less amount of emission, better voltage profile and faster execution process. As a result, it can be recommended that the proposed ISFSA should be used for OPF problem in high-voltage power system field.

Keywords

Stochastic fractal search Diffusion process Update process Optimal power flow Objective function Operating limitations 

List of symbols

\(F_{i}\)

Fuel cost function of the ith thermal unit

\(\phi_{i} ,\phi_{j}\)

Phase angles of voltage at the ith bus and the jth bus

\(a_{fi} ,b_{fi} ,c_{fi} ,d_{fi} ,e_{fi}\)

Fuel cost coefficients of the ith thermal unit

\(a_{fim} ,b_{fim} ,c_{fim}\)

Fuel cost coefficients of the fuel type m of the ith thermal unit

\(a_{ei} ,b_{ei} ,c_{ei} ,d_{ei} ,e_{ei}\)

Emission function coefficients of the ith thermal unit

\(FF_{s,j}\)

Fitness function of new solution s at the jth diffusion

\(FF_{s}^{new}\)

Fitness function of the new solution s

\(FF_{s}\)

Fitness function of the sth retained solution

\(FF_{average}\)

Average fitness function of the whole population

\(G_{ij} ,B_{ij}\)

Conductance and susceptance of a branch connecting the ith bus and the jth bus

\(K_{1} ,K_{2} ,K_{3} ,K_{4} ,K_{5}\)

Penalty factors

\(N_{fs}\)

Number of fuel sources

NVPZi

Number of violated power zones of the ith thermal unit

\(N_{bus}\)

Number of buses in considered system

\(N_{lb}\)

Number of load buses

\(N_{tb}\)

Number of transformer buses

\(N_{cb}\)

Number of compensator buses

\(N_{tl}\)

Number of transmission lines in the considered power system

\(N_{di}\)

Maximum number of diffusion

\(N_{ps}\)

Population size

\(P_{i}^{\hbox{min} } ,P_{i}^{\hbox{max} }\)

Lower and upper limitations of real power of the ith thermal unit

\(P_{i}\)

Real power output of the ith thermal unit

\(P_{im}^{\hbox{min} } ,P_{im}^{\hbox{max} }\)

Lowest and the highest generations of the ith thermal unit corresponding to the mth fuel type

\(P_{loadi} ,Q_{loadi}\)

Real and unreal power of load at the ith bus

\(P_{{i,VPZ_{j} }}^{\hbox{min} } ,P_{{i,VPZ_{j} }}^{\hbox{max} }\)

Lower and upper bounds of the jth violated power zone of the ith thermal unit

\(Q_{sci}^{\hbox{min} } ,Q_{sci}^{\hbox{max} }\)

Minimum and maximum reactive power output of the capacitor banks at the ith bus

\(Q_{i}^{\hbox{min} } ,Q_{i}^{\hbox{max} }\)

Lower and upper limitations of reactive power of the ith thermal unit

\(Q_{i} ,V_{i}\)

Currently working unreal power and voltage magnitude of the ith thermal unit

\(rand_{s,j}\)

Random number for the solution s at the jth diffusion

\(S_{br}^{\hbox{max} }\)

Maximum apparent power flow of the brth transmission line

\(Sol_{s,j}^{new}\)

The sth new solution at the jth diffusion

\(T_{i}^{\hbox{min} } ,T_{i}^{\hbox{max} }\)

Minimum and maximum setting of tap changer at the ith bus

\(V_{i}^{\hbox{min} } ,V_{i}^{\hbox{max} }\)

Lower and upper limitations of voltage magnitude of the ith thermal unit

VPZj

The jth violated power zone

\(V_{li}^{\hbox{min} } ,V_{li}^{\hbox{max} }\)

Lower and upper bounds of operation voltage of the ith bus

Iter, NIt

Current iteration and the maximum number of iterations

Pros

Ratio of rank of the sth solution to population size

Ncv

Number of control variables

βs, εs

Random number within 0 and 1 for the sth solution

ε

Random number within 0 and 1

Abbreviations

EIL

Emission improvement level

FC

Fuel cost

FCIL

Fuel cost improvement level

OPF

Optimal power flow

TPL

Total power losses

TPLIL

Total power loss improvement level

VD

Voltage deviation

VDIL

Voltage deviation improvement level

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest with other individuals or particles.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Power System Optimization Research Group, Faculty of Electrical and Electronics EngineeringTon Duc Thang UniversityHo Chi Minh CityViet Nam
  2. 2.Faculty of Electrical Engineering TechnologyIndustrial University of Ho Chi Minh CityHo Chi Minh CityViet Nam
  3. 3.Faculty of Electrical EngineeringThe University of DaNang, University of Science and TechnologyDaNang CityViet Nam

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