Equilibrium Optimizer: Insights, Balance, Diversity for Renewable Energy Resources Based Optimal Power Flow with Multiple Scenarios

ABSTRACT

Today, along with renewable energy sources such as wind generation units and solar photovoltaic systems, the power grid consists of traditional generating units. An approach for solving single-objective optimal power flow problems with the combination of renewable energy resources (RER-OPF) solar and wind power with conventional coal-based power stations is recommended in the proposed paper. In the proposed work, functions of lognormal and Weibull probability distribution are used, respectively, to forecast solar and wind outcomes. The objective feature includes the underestimation service charge and the standby charge for overestimating unusual non-conventional power generation. The quantitative and comparative results show that Equilibrium optimizer (EO) outperforms compare to Harris Hawks Optimizer (HHO), Grey Wolf Optimizer (GWO), Ions Motion Optimizer (IMO) and Success-History based Adaptive Differential Evolution (SHADE), which are all well-known optimization algorithms for solving RER-OPF problem. The EO optimizer provides the optimum value of each objective function and has merits in solving IEEE-30 bus-based RER-OPF problem, according to several evaluation criteria such as best value statistical criterion.

Graphical Abstract

KEYWORDS:

• Wind units
• meta-heuristics
• optimal power flow
• solar pv energy
• stochastic
• probability density function

List of Nomenclature

Optimal Power Flow

TGThermal Generator

WGWind Generator

PVPhoto Voltaic

ISOIndependent System Operator

PDFProbability Density Function

FCFuel Cost

VPEValve Point Effect

MFMultiple Fuel

POZProhibited Operating Zone

EOEquilibrium Optimizer

HHOHarris Hawks Optimization

GWOGrey Wolf Optimization

IMAIon Motion Algorithm

SHADESuccess-History based Adaptive Differential Evolution

RERRenewable Energy Resources

TFCTotal Fuel Cost

TETotal Emission

APLActive Power Loss

VDVoltage Deviation

VSIVoltage Stability Index

TctaxTotal Carbon Tax

$P_{TGi}$Power output of $i^{th}$ thermal unit

$P_{ws,j}$Scheduled power from $j^{th}$ wind power unit

$P_{ss,k}$Scheduled power from $k^{th}$ solar PV unit

$P_{wav,j}$Actual available power from $j^{th}$wind power unit

$P_{sav,k}$Actual available power from $k^{th}$solar PV unit

$g_j$Direct cost coefficient for $j^{th}$wind power unit

$h_k$Direct cost coefficient for $k^{th}$solar PV unit

$K_{Rw,j}$Reserve cost coefficient for overestimation of wind power from $j^{th}$unit

$K_{Pw,j}$Penalty cost coefficient for underestimation of wind power from $j^{th}$unit

$K_{Rs,k}$Reserve cost coefficient for overestimation of solar power from $k^{th}$unit

$K_{Ps,k}$Penalty cost coefficient for underestimation of solar power from $k^{th}$unit

$C_{tax}$Carbon tax in $/Tonne

$G$Solar irradiance in $\mathrm{W}/{\mathrm{m}}^2$

$f_v\left(v\right)$Probability of wind speed $v$ m/s

$f_G\left(G\right)$Probability of solar irradiance $G\mathrm{W}/{\mathrm{m}}^2$

$p_{wr}$The rated power output of a wind turbine

$P_{sr}$The rated power output of the solar PV plant

$c,k$Weibull PDF scale and shape parameters respectively

$\mu ,\sigma$Lognormal PDF mean and standard deviation respectively

$P_{loss}$Real power loss in the grid

Disclosure of Potential Conflicts of Interest

No potential conflict of interest was reported by the author(s).