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An Improved Tent Map-Adaptive Chaotic Particle Swarm Optimization (ITM-CPSO)-Based Novel Approach Toward Security Constraint Optimal Congestion Management

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Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

The introduction of deregulation into the electric utility industry has led to the transmission dispatch and congestion problem becoming more severe and complex to manage. This paper presents the implementation of an improved tent map-embedded chaotic particle swarm optimization (ITM-CPSO) algorithm to the nonlinear congestion management cost problem. To prevent the particle swarm optimization (PSO) plugging into the local minima with low convergence rate at later stages of iterations in case of nonlinear problems, a novel approach comprising a combination of PSO with tent map-adaptive chaotic particle swarm optimization has been implemented on nonlinear congestion management cost problem in this work. ITM-CPSO is a hybrid evolutionary algorithm, whose search procedure performs within a normalized plane of search space for all the chosen optimization variables for population-based procedures. The dual and full benefits of the characteristics of chaotic variables (i.e., periodicity and randomness) and tent map (i.e., more flat distribution than logistic maps) have been taken while formulating the congestion management cost problem. Further, to preserve the diversity of the proposed algorithm the inequality constraints have been handled by constraint prior optimal dominance method which is more efficient than the traditional penalty function method. Main contributions of the paper are twofold: Firstly, participating generators are selected using power flow tracing algorithm which is superior than sensitivity-based approach stated in the literature and secondly the implementation of proposed algorithm to the nonlinear congestion management cost problem further minimizes deviations of the rescheduled generator outputs from the scheduled levels as well as reduces the overall load shedding amount and cost. The simulation results of proposed algorithm are compared with those using classical PSO, random search method, simulated annealing, flower pollination algorithm, symbiotic organism search, firefly algorithm and ant lion optimizer for various line outage cases of IEEE-30, IEEE-57 and IEEE-118 bus system to prove the quality of results in terms of number of participating generators for rescheduling process and overall congestion management cost to relieve congestion.

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Abbreviations

\(C_{{g_{i} }} \left( {\Delta P_{{g_{i} }} } \right)\) :

Incremental or decremented bid submitted by ith generator or generator company (GENCO) at which they are willing to adjust their real power outputs to relieve the congestion

\(\Delta P_{{g_{i} }}\) :

Active power adjustment of generator i

\(N_{\text{pg}}\) :

Number of participating generators

\(N_{\text{g}}\) :

Number of generators

\(N_{\text{s}}\) :

Number of load buses selected for load shedding

\(C_{j}^{\text{bid}} (\Delta P_{D}^{j} )\) :

Load shedding bids submitted by jth load or DISCO willing to shed the load

\(P_{gi}^{0}\) :

Active Power generated by the ith as determined by the system operator

\(P_{gi}^{\text{resh}}\) :

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

\(i\) :

Participating generator

\(k\) :

Non-participating generator

\(P_{Dm}^{0}\) :

Active power consumed by the mthload determined by the system operator

\(Nd\) :

Number of loads

\(m\) :

Individual load at each bus

\(P_{L}\) :

Active power loss

\(P_{i}\) :

Real power of the ith bus

\(Q_{i}\) :

Reactive power of the ith bus

\(G_{ij}\) :

Conductance of the transmission line between i and j buses

\(B_{ij}\) :

Susceptance of the transmission line between i and j buses

\(\theta_{ij}\) :

Angle between i and j buses

\(V_{i}\) :

Voltage magnitude at ith bus

\(N_{B - 1}\) :

Number of buses except slack bus

\(S_{L\hbox{max} }\) :

Maximum line limit of the line

\(S_{L}\) :

MVA power flow in the line

\(N_{PQ}\) :

Number of PQ buses

\(V_{Li}\) :

Load bus voltage of bus i

\(V_{Li,\hbox{min} }\) and \(V_{Li,\hbox{max} }\) :

Minimum and maximum values of voltages

\(P_{Gi,\hbox{min} }\) and \(P_{Gi,\hbox{max} }\) :

Minimum and maximum real power generation limits of PV buses, respectively

\(P_{gi}^{\hbox{max} }\) :

Maximum limit of the ith generator

\(P_{gi}^{\hbox{min} }\) :

Minimum limit of the ith generator

\(N_{\text{PQ}}\) :

Number of PQ buses

\(V_{Li}\) :

Load bus voltage of bus i

\(V_{Li,\hbox{min} }\) and \(V_{Li,\hbox{max} }\) :

Minimum and maximum values of load bus voltages, respectively

\(S_{Lpq}\) :

Apparent power flow in the line p–q

\(S_{Lpq,\hbox{max} }\) :

Maximum MVA limit of the line p–q

\(P_{DLi,\hbox{min} }\), \(P_{DLi,\hbox{max} }\) :

Minimum and maximum values of the load bus powers, respectively

\(P_{ij}\) :

Real power flow in the line i–j

\(P_{ij}^{\hbox{max} }\) :

Maximum flow of the line i–j

\(X\) :

Line reactance

\(P_{j}^{{}}\) :

Real power at receiving end

\(Q_{j}^{{}}\) :

Reactive power at receiving end

\(V_{i}\) :

Sending end voltage

\(N_{\text{sv}}\) :

Number of specified inequality constraints on state variables

\({\text{CF}}_{i - j,k}^{G}\) :

Generation contribution factor, which is the flow in the line i–j due to kth generator

\(V_{i}^{k + 1}\) :

Velocity of the ith particle at k + 1th iteration

\(V_{i}^{k}\) :

Velocity of the ith particle at kth iteration

\(P_{i}^{k}\) :

Position of the ith particle at kth iteration

\(P_{i}^{k + 1}\) :

Position of the ith particle at k + 1th iteration

\(rand_{1}\), \(rand_{2}\) :

Random values between 0 and 1

\(w\) :

Inertia weight

\(w_{\hbox{max} }\) :

Initial value of the inertia weight, which is 0.9

\(w_{\hbox{min} }\) :

Final value of the inertia weight, which is 0.4

\(iter_{\hbox{max} }\) :

Maximum number of iterations allowed

\(rand_{1} ,rand_{2} ,C_{r}\) :

Deterministic displaying chaotic dynamics

\(\lambda\) :

Driving parameter which controls the behavior of chaotic sequence and 0 ≤ λ ≤ 4

\(C_{r} x_{i}^{k}\) :

ith chaotic variable for kth iteration, which has been distributed in range [0, 1]

\(\mu_{S}\) :

Sensitivity index

\(\mu_{cL}\) :

Load curtailment index

\(\mu_{IC}\) :

Incentive cost index

\(\omega_{L}\) :

Overall index

\(\Delta P_{Dj}\) :

Amount of load shedding at jth bus

\({\text{RGC}}_{i}\) :

Rescheduling cost of generator i

TGR:

Total generation rescheduled

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Acknowledgements

We are thankful to Thapar University, Patiala, for granting ‘TEQIP-Centre of excellence’ financial assistance to carry out this research.

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Authors and Affiliations

  1. Department of Electrical and Instrumentation Engineering, Thapar University, Patiala, Punjab, 147003, India

    Indu Batra & Smarajit Ghosh

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  1. Indu Batra
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  2. Smarajit Ghosh
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Correspondence to Indu Batra.

Appendix

Appendix

See Tables 16, 17, 18, 19 and 20.

Table 16 Price bids submitted by GENCOs and DISCOs for IEEE 30-bus test system
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Table 17 Price bids submitted by GENCOs for IEEE 57/modified IEEE 57 bus system
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Table 18 Load shedding bids submitted by GENCOs for IEEE 57 bus system
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Table 19 Price bids submitted by GENCOs for modified IEEE 30 bus system
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Table 20 Price bids submitted by GENCOs for IEEE 118 bus system
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Batra, I., Ghosh, S. An Improved Tent Map-Adaptive Chaotic Particle Swarm Optimization (ITM-CPSO)-Based Novel Approach Toward Security Constraint Optimal Congestion Management. Iran J Sci Technol Trans Electr Eng 42, 261–289 (2018). https://doi.org/10.1007/s40998-018-0072-6

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