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Implementation of a novel enhanced hybrid multi-objective osprey optimization algorithm for off-grid hybrid system sizing

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Abstract

A novel enhanced hybrid multi-objective osprey optimization algorithm (EHMOOOA) is proposed in this research work. It is used here for the optimum sizing of an off-grid composite renewable energy sources-based framework comprising a photovoltaic (PV) system, wind turbine generators (WTs), and battery energy storage system (BESS). The system is modelled to supply the administrative block of Kalyani Government Engineering College, Kalyani, India. The novelties include the integration of the quasi-oppositional-based learning mechanism, composite solution-oriented differential evolution algorithm (CSODEA), and Brownian motion concept into the osprey optimization algorithm (OOA). The contribution lies in the development of two novel mutation mechanisms, three new scaling coefficients and advanced extraction strategies for the core vector and the primary predecessor solutions of the difference vectors. The final stage of the exploitation process presents a novel scheme for the location upgrade of the solutions employing Brownian motion. A mathematical configuration has been built to minimize three primary fitness functions: loss of power supply probability (LPSP), levelized cost of electrical energy (LCOE), and net present cost (NPC). For validation purposes, the performances of the proposed hybrid meta-heuristic algorithm are compared with five other powerful optimization algorithms. Eight standard CEC benchmark functions and three CEC2020 actual scenario-constrained optimization problem functions are employed here for the evaluation of the proposed algorithm. The suggested composite methodology yielded the lowest and optimum values of LCOE (0.3029 $/kWh), NPC (0.9184e+05 $), and LPSP (0.000541). The optimum contributions made by PV, WT, and BESS are 80.9%, 10%, and 9.1%, respectively. Validation of the suggested technique has been further carried out by conducting statistical performance analysis through standard deviations. The proposed technique yielded the lowest standard deviation values: 7.4330e\(-\)04 (LCOE), 376.8249 (NPC), and 1.9901e\(-\)06 (LPSP), respectively. Further, to validate the outcomes, the Shapiro-Wilk test is conducted, followed by the Welch-like ANOVA and Games-Howell post-hoc tests. Moreover, a sensitivity test is performed to evaluate the robustness of EHMOOOA.

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Data availability

No datasets were generated or analysed during the current study.

Abbreviations

\(P_{PV,yield}(t)\) :

Power generated by a PV panel element (Watts)

\(P_{PVrated}\) :

Rated power of the PV module (Watts)

\(DF_{PV}\) :

Derating factor of the PV module (%)

G(t):

Incident universal solar radiation on the PV panel (Watts/\(m^{2}\))

\(G_{std}\) :

Standard solar radiation (1000 Watts/\(m^{2}\))

\(\alpha _{PVmax}\) :

Topmost power temperature coefficient (1/°C)

\(T_{cell,PV}(t)\) :

PV panel cell temperature (°C)

\(T_{STC,PV}\) :

Cell temperature at conventional test states (25 °C)

\(T_{surr}(t)\) :

Surrounding temperature (°C)

\(T_{NO,PV}\) :

Cell temperature under usual operating conditions (°C)

\(P_{WT,yield}(t)\) :

Power yielded by a WT

\(W_{hub}(t)\) :

Wind speed (m/sec) at the hub height

\(W_{cin}\) :

Cut-in wind speed (m/sec)

\(W_{cout}\) :

Cut-out wind speed (m/sec)

\(W_{rat}\) :

Rated wind speed (m/sec)

\(P_{WTrat}\) :

Rated WT power

\(H_{hub}\) :

Hub height (m)

\(H_{anem}\) :

Anemometer height (m)

\(\kappa \) :

Power law exponent

\(W_{anem}\) :

Speed of wind (m/sec) at the anemometer height

\(C_{Ba}\) :

Battery framework power (Watts)

\(\beta \) :

Self-power release rate (%) of the battery

\(P_{surplus}\) :

Surplus power produced by the renewable energy sources (Watts)

\(\sigma _{charge}\) :

Charging efficiency (%)

\(P_{unserved}\) :

Unserved power (Watts)

\(\sigma _{discharge}\) :

Discharging efficiency (%)

\(N_{Ba}\) :

Number of storage batteries

\(N_{days}\) :

Number of autonomy days of the battery bank

\(E_{demand}\) :

Energy demand (kWh/day)

\(\sigma _{comb}\) :

Unified efficiency of the converter and battery (%)

\(Max_{dod}\) :

Maximum depth of discharge (%)

\(V_{Ba}\) :

Battery voltage (V)

\(R_{Ba}\) :

Nominal battery ampere-hour capacity (Ah)

\(P_{convert}(t)\) :

Power of the converter (Watts)

\(P_{topmost,load}(t)\) :

Topmost load demand (Watts)

\(\sigma _{inv}\) :

Inverter efficiency (%)

LCOE:

Levelized cost of electrical energy ($/kWh)

NPC:

Net present cost ($)

LPSP:

Loss of power supply probability

\(P_{yearly,gross}\) :

Gross yearly system price ($/year)

\(E_{supplied}\) :

Gross electrical demand supplied (kWh/year)

\(D_{R}\) :

Yearly existent discount rate (%)

CRF:

Capital recovery factor

\(P_{duration}\) :

Project duration (years)

LOLP:

Loss of load probability

\(UnP_{demand,hrs}\) :

Total number of hours for which the load could not be met

\(OS^{gen}_{i,j}\) :

The ith osprey with jth dimension

\(ub\,\text {and}\,lb\) :

The upper and lower bounds

\(r_{i,j}\) :

Random value between 0 and 1

\(EF^{gen}_{i}\) :

Evaluation function of the \(i{th}\) osprey

gen :

Generation count

\(OS^{{L1}^{gen}}_{i,j}\) :

New location of the \(i{th}\) osprey with \(j{th}\) dimension

\(CF_{i,j}\) :

Chosen prey concerning the \(i{th}\) osprey with \(j{th}\) i{th}j{th}dimension

\(R_{i,j}\) :

Random numbers ranging between 1 and 2

\(Zmin^{gen}_{i}\) :

Minimum \(i{th}\) vector

\(OS^{gen}_{OBL_{i,j}}\) :

The \(i{th}\) opposing solution with \(j{th}\) dimension

\(OS^{gen}_{QOBL_{i,j}}\) :

The \(i{th}\) quasi-opposite solution with \(j{th}\) dimension

\(Zupd^{gen}_{i}\) :

The \(i{th}\) updated vector

\(OS^{gen}_{V_{i}}\) :

The \(i{th}\) mutated vector

\(Z^{gen}_{upd,R_{1}}\) :

Randomly chosen solution

\(Z^{gen}_{upd,R_{2}}\) :

Randomly chosen solution

\(Z^{gen}_{upd,R_{3}}\) :

Randomly chosen solution

\(S_{F_{1}}\) :

First scaling coefficient

\(S_{F_{2}}\) :

Second scaling coefficient

\(S_{F_{3}}\) :

Third scaling coefficient

\(OS^{gen}_{U_{i,j}}\) :

The \(i{th}\) trial solution with \(j{th}\) dimension

CR :

Crossover rate

\(OS^{L2^{gen}}_{i,j}\) :

The new location of the \(i{th}\) osprey with \(j{th}\) dimension

\(EF_{count}\) :

The total count of the evaluation functions so far

\(EF_{count,max}\) :

The topmost limit of the count for the evaluation functions

maxgen :

Maximum limit of the generation count

r :

Brownian motion parameter

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  1. Joy Bandopadhyay

    Present address: Kalyani Government Engineering College, Kalyani, West Bengal, India

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  1. Department of Electrical Engineering, Kalyani Government Engineering College, West Bengal, Kalyani, India

    Joy Bandopadhyay & Provas Kumar Roy

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JB and PKR made substantial contributions to the conception or design of the work. JB and PKR drafted the work. JB and PKR agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

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Bandopadhyay, J., Roy, P.K. Implementation of a novel enhanced hybrid multi-objective osprey optimization algorithm for off-grid hybrid system sizing. Evol. Intel. 18, 103 (2025). https://doi.org/10.1007/s12065-025-01083-1

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