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Arabian Journal for Science and Engineering

, Volume 44, Issue 8, pp 6861–6886 | Cite as

A Novel Approach of Congestion Management in Deregulated Power System Using an Advanced and Intelligently Trained Twin Extremity Chaotic Map Adaptive Particle Swarm Optimization Algorithm

  • Indu BatraEmail author
  • Smarajit Ghosh
Research Article - Electrical Engineering

Abstract

This paper addresses the implementation of an advanced twin extremity chaotic map adaptive particle swarm optimization (TECM-PSO) algorithm to the nonlinear congestion management cost problem in deregulated power system. The goal of proposed approach is twofold: firstly, to identify accurate number of participating generators for rescheduling process using a robust upstream real capacity tracing method requiring less information of generator units, and secondly, to achieve minimum possible rescheduled generation cost function using TECM-PSO algorithm while alleviating all the line overloads. Further to preserve the diversity of the algorithm and to increase its near-global searching capability, the incursion of dynamic constraint handling has also been done in the algorithm to retrieve the feasible solutions in the search space. The objective function is solved for near-global optima by step-by-step execution of the proposed algorithm. Twin extremity chaotic maps have been generated by updating the equations governing the PSO algorithm in order to prevent the particle swarm optimization plugging into local minima with less convergence rate at later stages of iterations. The feasibility of the proposed algorithm is validated on various line outage cases of both the small and large test systems, namely modified IEEE 30-, IEEE 57- and IEEE 118-bus systems. Simulation results show a considerable reduction in net rescheduled generation cost, power losses and rescheduled generation amount, ensuring more secure and reliable operation of power system.

Keywords

Nonlinear congestion cost management Upstream real capacity tracing method Generator rescheduling Twin extremity chaotic map adaptive particle swarm optimization Rescheduled generation cost function 

Abbreviations

TECM-PSO

Twin extremity chaotic map adaptive particle swarm optimization

URCT

Upstream real capacity tracing

RPCF

Real power contribution factor

CM

Congestion management

CV

Cumulative violation

MFE

Main function evaluation

AF

Auxiliary function

RGC

Rescheduled generation cost

NGR

Net generation rescheduled

RGCF

Rescheduled generation cost function

CMR

Convergence mobility rate

Decision Variables

\(\hbox {TECM}r\)

Twin extremity chaotic mapped sequence

\(\hbox {TECM}r^{0}\)

Initial value of twin extremity chaotic mapped sequence

\(C_\mathrm{g}^+ \)

Incremental price bids submitted by generators at which they are willing to adjust their real power outputs in $/MWh

\(C_\mathrm{g}^- \)

Decremented price bids submitted by generators at which they are willing to adjust their real power outputs in $/MWh

Npg

Number of participating generators which are decided using upstream real capacity tracing algorithm (described in “Appendix A1”)

\(\Delta P_\mathrm{GK}\)

Change in the real power adjustment at bus k in MW.

i

Participating generator

\(P_{{\mathrm{g}}_{i}}^0 \)

Active power generated by the ith generator as determined by the system operator in MW

\(\Delta P_{{\mathrm{g}_i}}\)

Change in real power by the ith generator in MW

\(P_{{\mathrm{g}_{i}}}^\mathrm{resh}\)

Active power generated by the ith generator after the process of rescheduling in MW

j

Non-participating generator

\(P_{{\hbox {D}_{m}}}^0\)

Active power consumed by the mth load determined by the system operator in MW

Nd

Number of loads

m

Individual load at each bus

\(P_\mathrm{L}\)

Active power loss in MW

\(V_{{i_\mathrm{D}}} ^{k+1}\)

Updated velocity of the ith particle

\(V_{{i_\mathrm{D}}} ^{k}\)

Old velocity of the ith particle

\(P_{{i_\mathrm{D}}} ^{k+1}\)

Updated position of the ith particle

\(P_{{i_\mathrm{D}}} ^{k}\)

Old position of the ith particle

Constant Variables

\(c_1\)

Cognitive accélération coefficient

\(c_2 \)

Social accélération coefficient

\(r_i\)

Random numbers between 0 and 1. \(i=1,2\)

w

Inertia weight

\(w_{\max } \)

Maximum inertia weight

\(w_{\min } \)

Minimum inertia weight

k

Current iteration

\(k_{\max } \)

Maximum number of iterations

\(N_\mathrm{PQ} \)

Number of PQ buses

\(N_\mathrm{PV} \)

Number of PV buses

\(S_{\mathrm{L}_{\max }} \)

Maximum line limit of the line in MVA

\(S_\mathrm{L} \)

MVA power flow in the line

\(G_{ij} \)

Conductance of the transmission line between i and j buses

\(B_{ij}\)

Susceptance of the transmission line between i and j buses

\(P_i\)

Real power of the ith bus in MW

\(Q_i\)

Reactive power of the ith bus in MVAR

\(V_i\)

Voltage magnitude at ith bus

\(N_{B-1} \)

Number of buses except slack bus

\(V_{{\mathrm{G}_{i,\mathrm{min}}} } \) and \(V_{{\mathrm{G}_{i,\mathrm{max}}} } \)

Minimum and maximum voltage limits, respectively, of PV buses

\(V_{{\hbox {L}_{i}}}\)

Load bus voltage of ith bus

\(V_{{\mathrm{L}_{i, \mathrm{min}}} } \) and \(V_{{\mathrm{L}_{i, \mathrm{max}}} } \)

Minimum and maximum values of voltages of the ith bus, respectively

\(Q_{{\mathrm{G}_{i,\min }}} \) and \(Q_{{\mathrm{G}_{i,\max }}} \)

Minimum and maximum reactive power generation limits in MVAR

\(P_{{\mathrm{G}_{i,\mathrm{min}}} } \) and \(P_{{\mathrm{G}_{i, \mathrm{max}}} } \)

Minimum and maximum real power generation limits of PV buses in MW

\(x_{\mathrm{best},d}^k \)

Best individual in the kth iteration for dth dimension

\({{\overline{x}}} _{{\mathrm{best},d} }\)

Mean value of the best individuals

Greek Symbols

\(\lambda \)

Lyapunov exponent

\(\theta _{ij} \)

Angle between i and j buses

\(\eta \)

Number of iterations for which stopping criterion applies

\(\in \)

Standard deviation threshold for which stopping criterion applies

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Notes

Acknowledgements

We are highly thankful to Thapar University, Patiala, to Grant TEQIP-II (Center of Excellence) financial assistance to carry out this research.

Compliance with ethical standards

Conflict of interest

We have no conflict of interest with any of the ethical statements.

Supplementary material

13369_2018_3675_MOESM1_ESM.doc (522 kb)
Supplementary material 1 (doc 521 KB)

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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Electrical and Instrumentation EngineeringT.I.E.T.PatialaIndia

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