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Uncertainty-based dynamic economic dispatch for diverse load and wind profiles using a novel hybrid algorithm

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Abstract

Optimal scheduling of the conventional generating units for five dynamic test systems is percolated in this paper. When the valve point loading effect (VPE) is present, the system's fitness function becomes non-convex and nonlinear. This paper compares and contrasts among three types of wind profile formulations, namely linear, quadratic and cubic, which are used to calculate wind power from hourly wind speed to find the profile with the greatest penetration of wind power. Thereafter, the wind profiles in turns for the five test systems are used to execute dynamic economic dispatch. The optimization tool of the study was a unique hybrid algorithm created by combining the properties of the recently developed crow search algorithm (CSA) and JAYA. Results infer that maximum level of wind penetration was attained by linear wind profile and a fuel cost reduction of 8% was realized upon incorporation of the same. Also owing to its high penetration level, the least generation cost was obtained with linear wind profile when compared to quadratic and cubic ones. Furthermore, numerical results also claims that proposed hybrid CSAJAYA approach consistently yielded better quality solutions within minimum execution time without being affected by the dimension of the problem, thereby outperforming a long list of algorithms implemented for the study.

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Data availability

Data will be available by the authors upon reasonable request.

Abbreviations

AP:

Awareness probability

CSA:

Crow search algorithm

CSAJAYA:

Hybrid crow search algorithm–jaya algorithm

CSASCA:

Crow search algorithm–sine–cosine algorithm

DE:

Differential evolution

DER:

Distributed energy resources

DG:

Distributed generator

ELD:

Economic load dispatch

GWO:

Grey wolf optimizer

JAYA:

Jaya algorithm

MAE:

Mean absolute error

MGWO-SCA-CSA:

Modified grey wolf optimizer–sine–cosine algorithm–crow search algorithm

Pop_Size:

Population size

PSO:

Particle swarm optimization

RE:

Relative error

RES:

Renewable energy sources

RMSE:

Root mean square error

SCA:

Sine–cosine algorithm

SD:

Standard deviation

SOS:

Symbiotic organisms search

TLBO:

Teaching–learning-based optimization

UP:

Utilization percentage

WOA:

Whale optimization algorithm

WOASCA:

Whale optimization algorithm—sine–cosine algorithm

VPE:

Valve point effect

a, b, c :

Cost coefficients of DG unit

A, B, C :

Constraints of quadratic wind profile

d, e :

Coefficients of valve point loading effect

D t :

Load demand at time t

FFV ii :

Fitness function value at iith trial

FFV min :

Minimum value of fitness function

\(\overline{FFV }\) :

Mean value of fitness function

fl :

Flight length of the crow

f t v :

Weibull distribution function

i :

Indices of DG units

ii :

Index of trial

iter/max_iter :

Current iteration/Maximum number of iterations

j :

Indices of wind units

k t , c t :

Shape parameter and scale parameter at tth time interval.

n :

Total number of DG units

NOT :

Number of trials

P i :

Power output of ith unit

P i,max P i,min :

Minimum and maximum limit of ith unit

P j w,t :

Wind power of jth wind unit at time t

P j w − r :

Rated power of jth wind unit

P RES,t :

RES power output at time tth hour

Rand 1, Rand 2 , Rand i, Rand j , c ’ , c” :

Random numbers used in algorithms

t :

Indices of time intervals

v i j , v o j , v r j :

Cut-in, cutout and rated wind speed of jth unit

v t p :

Wind speed at tth hour.

σ t v , μ t v :

Mean and standard deviation of wind speed at time t

References

  • Alham, M. H., Elshahed, M., Ibrahim, D. K., El Din, E., & El Zahab, A. (2016). A dynamic economic emission dispatch considering wind power uncertainty incorporating energy storage system and demand side management. Renewable Energy, 96, 800–811.

    Google Scholar 

  • Askarzadeh, A. (2016). A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm. Computers and Structures, 169, 1–12.

    Google Scholar 

  • Attaviriyanupap, P., Kita, H., Tanaka, E., & Hasegawa, J. (2002). A hybrid EP and SQP for dynamic economic dispatch with nonsmooth fuel cost function. IEEE Transactions on Power Systems, 17(2), 411–416.

    Google Scholar 

  • Azizipanah-Abarghooee, R. (2013). A new hybrid bacterial foraging and simplified swarm optimization algorithm for practical optimal dynamic load dispatch. International Journal of Electrical Power & Energy Systems, 49, 414–429.

    Google Scholar 

  • Billinton, R., Chowdhury, A.A. (1992). Incorporation of wind energy conversion systems in conventional generating capacity adequacy assessment. In IEE Proceedings C (Generation, Transmission and Distribution), vol. 139, no. 1, pp. 47–56. IET Digital Library, 1992.

  • Bora, T. C., Mariani, V. C., dos Santos, L., & Coelho. (2019). Multi-objective optimization of the environmental-economic dispatch with reinforcement learning based on non-dominated sorting genetic algorithm. Applied Thermal Engineering, 146, 688–700.

    Google Scholar 

  • Chauhan, G., Anjali, J., Neelam, V. (2017). Solving economic dispatch problem using MiPower by lambda iteration method. In 2017 1st International Conference on Intelligent Systems and Information Management (ICISIM), pp. 95–99. IEEE, 2017.

  • Dai, W., Yang, Z., Juan, Y., Cui, W., Li, W., Li, J., & Liu, H. (2021). Economic dispatch of interconnected networks considering hidden flexibility. Energy, 223, 120054.

    Google Scholar 

  • Daniel, L., Chaturvedi, K. T., & Kolhe, M. L. (2018). Dynamic economic load dispatch using Levenberg Marquardt algorithm. Energy Procedia, 144, 95–103. https://doi.org/10.1016/j.egypro.2018.06.013

    Article  Google Scholar 

  • Daryani, N., & Zare, K. (2018). Multiobjective power and emission dispatch using modified group search optimization method. Ain Shams Engineering Journal, 9(3), 319–328.

    Google Scholar 

  • Devarapalli, R., Venkateswara Rao, B., Dey, B., Vinod Kumar, K., Malik, H., García Márquez, F.P. (2021). An approach to solve OPF problems using a novel hybrid whale and sine cosine optimization algorithm. Journal of Intelligent & Fuzzy Systems Preprint, 1–11.

  • Dey, B., Biplab, B. (2018). Dynamic economic and emission dispatch of large scale renewable integrated microgrids for varying loads and seasons. In 2018 2nd International Conference on Power, Energy and Environment: Towards Smart Technology (ICEPE), pp. 1–6. IEEE, 2018.

  • Dey, B., Shyamal Krishna, R., Biplab, B. (2018). Neighborhood based differential evolution technique to perform dynamic economic load dispatch on microgrid with renewables. In 2018 4th International Conference on Recent Advances in Information Technology (RAIT), pp. 1–6. IEEE, 2018.

  • Dey, B., & Bhattacharyya, B. (2019). Dynamic cost analysis of a grid connected microgrid using neighborhood based differential evolution technique. International Transactions on Electrical Energy Systems, 29(1), e2665.

    Google Scholar 

  • Dey, B., & Bhattacharyya, B. (2021). Comparison of various electricity market pricing strategies to reduce generation cost of a microgrid system using hybrid WOA-SCA. Evolutionary Intelligence. https://doi.org/10.1007/s12065-021-00569-y

    Article  Google Scholar 

  • Dey, B., Bhattacharyya, B., & Devarapalli, R. (2021a). A novel hybrid algorithm for solving emerging electricity market pricing problem of microgrid. International Journal of Intelligent Systems, 36(2), 919–961.

    Google Scholar 

  • Dey, B., Bhattacharyya, B., & Márquez, F. P. G. (2021). A hybrid optimization-based approach to solve environment constrained economic dispatch problem on microgrid system. Journal of Cleaner Production, 307, 127196.

    CAS  Google Scholar 

  • Dey, B., Bhattacharyya, B., Srivastava, A., & Shivam, K. (2020a). Solving energy management of renewable integrated microgrid systems using crow search algorithm. Soft Computing, 24(14), 10433–10454.

    Google Scholar 

  • Dey, B., Márquez, F. P. G., & Basak, S. K. (2020). Smart energy management of residential microgrid system by a novel hybrid mgwoscacsa algorithm. Energies, 13(13), 3500.

    Google Scholar 

  • Dey, B., Raj, S., Mahapatra, S., & Márquez, F. P. G. (2022). Optimal scheduling of distributed energy resources in microgrid systems based on electricity market pricing strategies by a novel hybrid optimization technique. International Journal of Electrical Power & Energy Systems, 134, 107419.

    Google Scholar 

  • Dey, B., Roy, S. K., & Bhattacharyya, B. (2019). Solving multi-objective economic emission dispatch of a renewable integrated microgrid using latest bio-inspired algorithms. Engineering Science and Technology, an International Journal, 22(1), 55–66.

    Google Scholar 

  • Diljinder, S., & Dhillon, J. S. (2019). Ameliorated grey wolf optimization for economic load dispatch problem. Energy, 169, 398–419. https://doi.org/10.1016/j.energy.2018.11.034

    Article  Google Scholar 

  • Elattar, E. E. (2018). Modified harmony search algorithm for combined economic emission dispatch of microgrid incorporating renewable sources. Energy, 159, 496–507. https://doi.org/10.1016/j.energy.2018.06.137

    Article  Google Scholar 

  • Elsayed, W. T., Hegazy, Y. G., Bendary, F. M., & El-Bages, M. S. (2016). Modified social spider algorithm for solving the economic dispatch problem. Engineering Science and Technology, an International Journal, 19(4), 1672–1681.

    Google Scholar 

  • Dey, B., Sourav, B., Biplab, B. (2021). A comparative analysis between price‐penalty factor method and fractional programming method for combined economic emission dispatch problem using novel hybrid CSA‐JAYA algorithm. IET Smart Grid (2021)

  • Ganjefar, S., & Tofighi, M. (2011). Dynamic economic dispatch solution using an improved genetic algorithm with non-stationary penalty functions. European Transactions on Electrical Power, 21(3), 1480–1492.

    Google Scholar 

  • Hazra, S., & Roy, P. K. (2019). Quasi-oppositional chemical reaction optimization for combined economic emission dispatch in power system considering wind power uncertainties. Renewable energy focus, 31, 45–62.

    Google Scholar 

  • Jadoun, V. K., Pandey, V. C., Gupta, N., Niazi, K. R., & Swarnkar, A. (2018). Integration of renewable energy sources in dynamic economic load dispatch problem using an improved fireworks algorithm. IET renewable power generation, 12(9), 1004–1011.

    Google Scholar 

  • Jiang, S., Zhang, C., Wenjin, W., & Chen, S. (2019). Combined economic and emission dispatch problem of wind-thermal power system using gravitational particle swarm optimization algorithm. Mathematical Problems in Engineering, 2019, 1–19. https://doi.org/10.1155/2019/5679361

    Article  Google Scholar 

  • Karmakar, N., & Bhattacharyya, B. (2020). Optimal reactive power planning in power transmission system considering FACTS devices and implementing hybrid optimisation approach. IET Generation, Transmission and Distribution, 14(25), 6294–6305.

    Google Scholar 

  • Kennedy, J., Russell, E. (1995). Particle swarm optimization. In Proceedings of ICNN'95-international conference on neural networks, vol. 4, pp. 1942–1948. IEEE, 1995.

  • Khalilpourazari, S., & Pasandideh, S. H. R. (2020). Sine–cosine crow search algorithm: Theory and applications. Neural Computing and Applications, 32(12), 7725–7742.

    Google Scholar 

  • Lahon, R., & Gupta, C. P. (2018). Risk-based coalition of cooperative microgrids in electricity market environment. IET Generation, Transmission and Distribution, 12(13), 3230–3241.

    Google Scholar 

  • Liu, Y., & Nair, N.-K. (2015). A two-stage stochastic dynamic economic dispatch model considering wind uncertainty. IEEE Transactions on Sustainable Energy, 7(2), 819–829.

    Google Scholar 

  • Lokeshgupta, B., & Sivasubramani, S. (2018). Multi-objective dynamic economic and emission dispatch with demand side management. International Journal of Electrical Power & Energy Systems, 97, 334–343.

    Google Scholar 

  • Lu, X., Zhou, K., & Yang, S. (2017). Multi-objective optimal dispatch of microgrid containing electric vehicles. Journal of Cleaner Production, 165, 1572–1581.

    Google Scholar 

  • Lu, X., Zhou, K., Yang, S., & Liu, H. (2018). Multi-objective optimal load dispatch of microgrid with stochastic access of electric vehicles. Journal of Cleaner Production, 195, 187–199.

    Google Scholar 

  • Ma, H., Yang, Z., You, P., & Fei, M. (2017). Multi-objective biogeography-based optimization for dynamic economic emission load dispatch considering plug-in electric vehicles charging. Energy, 135, 101–111.

    Google Scholar 

  • Mandal, S., & Mandal, K. K. (2020). Optimal energy management of microgrids under environmental constraints using chaos enhanced differential evolution. Renewable Energy Focus, 34, 129–141.

    Google Scholar 

  • Maulik, A., & Das, D. (2017). Optimal operation of microgrid using four different optimization techniques. Sustainable Energy Technologies and Assessments, 21, 100–120.

    Google Scholar 

  • Mirjalili, S. (2016). SCA: A sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96, 120–133.

    Google Scholar 

  • Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  • Mohit, K., & Dhillon, J. S. (2018). Hybrid artificial algae algorithm for economic load dispatch. Applied Soft Computing, 71, 89–109.

    Google Scholar 

  • Nayak, A., Avirup, M., & Debapriya, D. (2021). An integrated optimal operating strategy for a grid-connected AC microgrid under load and renewable generation uncertainty considering demand response. Sustainable Energy Technologies and Assessments, 45, 101169.

    Google Scholar 

  • Padhi, S., Panigrahi, B. P., & Dash, D. (2020). Solving dynamic economic emission dispatch problem with uncertainty of wind and load using whale optimization algorithm. Journal of The Institution of Engineers (India): Series B, 101(1), 65–78.

    Google Scholar 

  • Partha, K., & Chanda, C. K. (2015). Optimal mix of solar and wind distributed generations considering performance improvement of electrical distribution network. Renewable Energy, 75, 173–186.

    Google Scholar 

  • Pasandideh, S.H.R., Soheyl K (2018) Sine cosine crow search algorithm: a powerful hybrid meta heuristic for global optimization. arXiv preprint https://arxiv.org/abs/1801.08485

  • Qiao, B., & Liu, J. (2020). Multi-objective dynamic economic emission dispatch based on electric vehicles and wind power integrated system using differential evolution algorithm. Renewable Energy, 154, 316–336.

    Google Scholar 

  • Qu, B.-Y., Zhu, Y. S., Jiao, Y. C., Wu, M. Y., Suganthan, P. N., & Liang, J. J. (2018). A survey on multi-objective evolutionary algorithms for the solution of the environmental/economic dispatch problems. Swarm and Evolutionary Computation, 38, 1–11.

    Google Scholar 

  • Rabiee, A., Sadeghi, M., & Aghaei, J. (2018). Modified imperialist competitive algorithm for environmental constrained energy management of microgrids. Journal of Cleaner Production, 202, 273–292.

    Google Scholar 

  • Rao, R. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations, 7(1), 19–34.

    Google Scholar 

  • Rao, R. V., Savsani, V. J., & Vakharia, D. P. (2011). Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-Aided Design, 43(3), 303–315. https://doi.org/10.1016/j.cad.2010.12.015

    Article  Google Scholar 

  • Roy, S. (2018). The maximum likelihood optima for an economic load dispatch in presence of demand and generation variability. Energy, 147, 915–923.

    Google Scholar 

  • Shrivastava, A., Saksham, N. (2017). Cost economic power dispatch analysis and solution using optimization technique:“CEPD model solution”. In 2017 International Conference on Intelligent Sustainable Systems (ICISS), pp. 1106–1111. IEEE, 2017.

  • Sun, Y., & Wang, Z. (2017). Improved particle swarm optimization based dynamic economic dispatch of power system. Procedia Manufacturing, 7, 297–302.

    Google Scholar 

  • Tabar, V. S., Jirdehi, M. A., & Hemmati, R. (2018). Sustainable planning of hybrid microgrid towards minimizing environmental pollution, operational cost and frequency fluctuations. Journal of cleaner production, 203, 1187–1200.

    Google Scholar 

  • Toopshekan, A., Yousefi, H., & Astaraei, F. R. (2020). Technical, economic, and performance analysis of a hybrid energy system using a novel dispatch strategy. Energy, 213, 118850.

    Google Scholar 

  • Trivedi, I. N., Dhaval, K. T., Ayman, E., Pradeep, J. (2015). A multiple environment dispatch problem solution using ant colony optimization for micro-grids. In 2015 International Conference on Power and Advanced Control Engineering (ICPACE), pp. 109–115. IEEE, 2015.

  • Trivedi, I. N., Jangir, P., Bhoye, M., & Jangir, N. (2018). An economic load dispatch and multiple environmental dispatch problem solution with microgrids using interior search algorithm. Neural Computing and Applications, 30(7), 2173–2189.

    Google Scholar 

  • Victoire, T. A. A., & Jeyakumar, A. E. (2005). Reserve constrained dynamic dispatch of units with valve-point effects. IEEE Transactions on Power Systems, 20(3), 1273–1282. https://doi.org/10.1109/TPWRS.2005.851958

    Article  Google Scholar 

  • Wu, K., Li, Q., Chen, Z., Lin, J., Yi, Y., & Chen, M. (2021). Distributed optimization method with weighted gradients for economic dispatch problem of multi-microgrid systems. Energy, 222, 119898.

    Google Scholar 

  • Xie, M., Xiong, J., Ke, S., & Liu, M. (2016). Two-stage compensation algorithm for dynamic economic dispatching considering copula correlation of multiwind farms generation. IEEE Transactions on Sustainable Energy, 8(2), 763–771.

    Google Scholar 

  • Xu, B., Zhong, P.-a, Zhao, Y.-f, Zhu, Y.-Z., & Zhang, G.-q. (2014). Comparison between dynamic programming and genetic algorithm for hydro unit economic load dispatch. Water Science and Engineering, 7(4), 420–432.

    Google Scholar 

  • Yin, N., Abbassi, R., Jerbi, H., Rezvani, A., & Müller, M. (2021). A day-ahead joint energy management and battery sizing framework based on θ-modified krill herd algorithm for a renewable energy-integrated microgrid. Journal of Cleaner Production, 282, 124435.

    Google Scholar 

  • Yuan, X., Anjun, Su., Yuan, Y., Nie, H., & Wang, L. (2009). An improved PSO for dynamic load dispatch of generators with valve-point effects. Energy, 34(1), 67–74.

    Google Scholar 

  • Yuan, X., Wang, L., Yuan, Y., Zhang, Y., Cao, Bo., & Yang, Bo. (2008). A modified differential evolution approach for dynamic economic dispatch with valve-point effects. Energy Conversion and Management, 49(12), 3447–3453.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, India

    Sourav Basak, Bishwajit Dey & Biplab Bhattacharyya

  2. Department of Electrical and Electronics Engineering, Gandhi Institute of Engineering and Technology, Gunupur, Odisha, India

    Bishwajit Dey

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  1. Sourav Basak
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Appendix

Appendix

See Tables 11, 12, 13 and 14.

Table 11 Generator cost coefficients of the test systems
Full size table
Table 12 Algorithms implemented and their tuning parameters
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Table 13 Fixed dimensional multimodal Benchmark function
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Table 14 Values of fixed dimensional multimodal Benchmark function
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Realization of the proposed algorithm on the benchmark functions: Any metaheuristic algorithm is inherently stochastic in obtaining the optimal solution for the given problem, which means that the performance varies over different runs. To comment on the suitability and effectiveness of the proposed algorithm, it has been undergone for realization on the set of certain benchmark functions. Here, for the proposed CSAJAYA method, the authors have used a set of six benchmark functions that are mostly used by various researchers. Table 13 lists the formula, dimensions and variable limits for unimodal, multimodal and fixed dimensional multimodal benchmark functions, respectively. All of these functions were evaluated using CSA, JAYA and proposed hybrid CSAJAYA for 30 individual trials. The best values, worst values, their average and standard deviation after 30 runs are listed in Table 14. Figure

Fig. 24
figure 24

Benchmark functions for CSA, JAYA and CSAJAYA

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24 displays the parameter space of the proposed algorithm, convergence characteristics with the proposed algorithms and box plot after 30 runs of the six benchmark functions.

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Basak, S., Dey, B. & Bhattacharyya, B. Uncertainty-based dynamic economic dispatch for diverse load and wind profiles using a novel hybrid algorithm. Environ Dev Sustain 25, 4723–4763 (2023). https://doi.org/10.1007/s10668-022-02218-5

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