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A novel artificial electric field strategy for economic load dispatch problem with renewable penetration

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Abstract

This article presents an innovative method to address the economic load dispatch (ELD) problem in power systems incorporating renewable energy sources within thermal units. Employing the 2-m point estimation technique for determining renewable energy output power, the proposed approach effectively addresses challenges associated with renewable-based ELD by utilizing the artificial electric field method. Inspired by the electrostatic force principle among charged particles, this approach guides particles toward optimal solutions within the search space. Validation on power systems featuring 3, 5, 6, 15, and 40 units demonstrates superior performance compared to established algorithms, confirmed by the Wilcoxon signed-rank test. The research contributes to the advancement of sustainable and efficient power systems.

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Abbreviations

\(\textrm{a}_{\textrm{i}}\),\(\textrm{b}_{\textrm{i}}, \textrm{c}_{\textrm{i}}\),\(\textrm{e}_{\textrm{i}}\), \(\textrm{f}_{\textrm{i}}\) :

Cost variable of the \(\textrm{i}_{\textrm{th}}\) thermal unit

\(\textrm{N}\) :

Count of connected generators

\(\textrm{Ti}\) :

Generated power of \(\textrm{i\;th}\) thermal generator in MW

\(\textrm{W}_{\textrm{p}}, \textrm{S}_{\textrm{p}}\) :

Generated power of wind-solar in MW

\(\textrm{C}_{\textrm{w}}\) :

Cost variable of wind in $/h

\(\textrm{N}_{\textrm{W}}, \textrm{N}_{\textrm{s}}\) :

Count of wind and solar unit

Bidl:

Bid price of \(\textrm{l\;th}\) solar unit

TL:

Transmission loss

TD:

Power requirement

\(\textrm{B}_{\textrm{ij}}, \textrm{B}_{0\textrm{i}}, \textrm{B}_{00}\) :

Loss matrix

\(\textrm{T}_{\textrm{imin}}, \textrm{T}_{\textrm{imax}}\) :

Boundary limit Minimum-maximum power \(\textrm{i\;th}\) unit

\(\textrm{S}_{\textrm{hp}}, \textrm{S}_{\textrm{cp}}\) :

Weibull variables

\(\textrm{v, v}_{\textrm{r}}\) :

Instant and rated haste of wind unit

\(\textrm{v}_{\textrm{in}}, \textrm{v}_{\textrm{out}}\) :

Cut in–cut out the haste of wind unit

\(\textrm{W}_{\textrm{p}}, \textrm{W}_{\textrm{pt}}\) :

Instant and rated power of wind unit

\(\upomega , \uppsi\) :

Beta variables

\(\Gamma\) :

Gamma objectives

\(\textrm{S}_{\mathrm{rad(t)}}\) :

Cellular solar radiation at time t

\(\textrm{S}_{\textrm{rad,stc}}\) :

Solar radiation in normal circumstances

\(\textrm{S}_{\textrm{P,stc}}\) :

Solar power in normal circumstances

\(\upgamma\) :

Temperature variable in %/°\(\hbox {C}\)

Tcell:

The degree of heat in a solar cell

\(\textrm{T}_{\textrm{cell,stc}}\) :

The solar cell’s temperature under the usual test conditions

NOT:

The cell’s typical operating temperature

\(\textrm{N}_{\textrm{sc}}, \textrm{N}_{\textrm{pc}}\) :

Number of solar cells in series and parallel

\(\upmu , \upsigma\) :

The average and standard deviation

\(\textrm{I}_{\textrm{k}}\) :

Input constant

\(\textrm{S}_{\textrm{e}}\) :

Total electricity production, including solar and wind

\(\textrm{z}_{\textrm{l}}\) :

Uncertainty in the input variable

\(\mathrm{Qi(t)}, \mathrm{Qj(t)}\) :

Charges of \(\textrm{i\;th}\) and \(\textrm{j\;th}\) fleck

K(t):

Coulomb’s variable

E:

Modestly positive constant

\(\textrm{R}_{\textrm{ij(t)}}\) :

The distance in Euclid between two particles

\(\upalpha\), K0 :

Parameter and starting point

\(\textrm{F}_{\textrm{i}}, \textrm{M}_{\textrm{i}}\) :

Force and mass of the \(\textrm{i\;th}\) particle

\(\textrm{V}_{\textrm{i}}, \textrm{X}_{\textrm{i}}\) :

Particle’s location and speed

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Authors and Affiliations

  1. Institute of Technology, Nirma University, Ahmedabad, Gujarat, 382481, India

    Diwakar Verma, Jatin Soni & Kuntal Bhattacharjee

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  1. Diwakar Verma
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  2. Jatin Soni
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  3. Kuntal Bhattacharjee
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Contributions

Diwakar Verma: Methodology, software, writing original Draft, data curation, conceptualization, investigation, validation, resources, project administration, format analysis, visualization, supervision. Jatin Soni: Writing original Draft, data curation, conceptualization, investigation, validation, format analysis, visualization, supervision. Kuntal Bhattacharjee: Investigation, validation, format analysis, visualization, supervision.

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Correspondence to Jatin Soni.

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Verma, D., Soni, J. & Bhattacharjee, K. A novel artificial electric field strategy for economic load dispatch problem with renewable penetration. Evol. Intel. (2024). https://doi.org/10.1007/s12065-024-00946-3

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