This study explores microgrids as small, independent electrical systems that reduce emissions, lower costs, and improve the efficiency and reliability of renewable energy sources (RES). It focuses on solving the optimal power flow (OPF) problem in isolated microgrids to minimize production costs, integrating variable RES like solar photovoltaic systems and wind turbines with a stable small hydropower plant. A novel physics-based Flow Direction Algorithm (FDA), inspired by the D8 hydrological model, is introduced, offering superior precision compared to bio-inspired metaheuristics. The FDA balances global and local search for accurate solutions. Monte Carlo simulation models uncertainties in wind speeds and solar irradiance. Validated on IEEE 33-bus, 69-bus, and 15-bus systems, the FDA outperforms algorithms like Whale Optimization, Ant Lion, Dung Beetle, and Walrus Optimization in efficiency and reliability, advancing microgrid performance.
AbdelazizMMAFaragHEEl-SaadanyEF, et al. (2013) A novel and generalized three-phase power flow algorithm for islanded microgrids using a Newton Trust Region method. IEEE Transactions on Power Systems28(1): 190–201.
2.
AbediniMMoradiMHHosseinianSM (2016) Optimal management of microgrids including renewable energy scources using GPSO-GM algorithm. Renewable Energy90: 430–439.
3.
AlayandeASOlowolajuJTOkakwuIK (2019) Solving optimal generation dispatch problem in power networks through pso and lambda iteration techniques. Nigerian Journal of Technology38(1): 165.
4.
AlvarezWSLópezJCLiedererFW, et al. (2024) Dynamic security constrained AC optimal power flow for microgrids. Electric Power Systems Research236: 110927.
5.
BanerjiASenDBeraAK, et al. (2013) Microgrid: a review. In: 2013 IEEE Global Humanitarian Technology Conference: South Asia Satellite (GHTC-SAS), August 2013. IEEE, 27–35.
6.
BasuM (2023a) Dynamic optimal power flow for grid-connected multi-microgrid system considering outage of energy sources. In: Electric Power Components and Systems. Taylor and Francis Ltd.
7.
BasuM (2023b) Dynamic optimal power flow for isolated microgrid incorporating renewable energy sources. Energy264: 126065.
8.
CagnanoACaldarulo BugliariADe TuglieE (2018) A cooperative control for the reserve management of isolated microgrids. Applied Energy218: 256–265.
9.
ContaxisGCDelkisCKorresG (1986) Decoupled optimal load flow using linear or quadratic programming. IEEE Power Engineering Review1(2): 1–7.
10.
Dall’AneseEZhuHGiannakisGB (2013) Distributed optimal power flow for smart microgrids. IEEE Transactions on Smart Grid4(3): 1464–1475.
11.
DasDKothariDPKalamA (1995) Simple and efficient method for load flow solution of radial distribution networks. International Journal of Electrical Power & Energy Systems17(5): 335–346.
12.
DiazGGomez-AleixandreJCotoJ (2016) Direct backward/forward sweep Algorithm for solving load power flows in AC droop-regulated microgrids. IEEE Transactions on Smart Grid7(5): 2208–2217.
13.
DineshMSDineshMSSinghA, et al. (2014) Voltage stability analysis of radial distribution networks. In: Institute of Engineers at Jamshedpur, Jamshedpur, 2014.
14.
Garcés-RuizAGil-GonzálezWMontoyaOD (2025) Quasi-dynamic optimal power sharing in isolated DC microgrids. Electric Power Systems Research239: 111222.
15.
HameedFAl HosaniMZeineldinHH (2019) A modified backward/forward sweep load flow method for islanded radial microgrids. IEEE Transactions on Smart Grid10(1): 910–918.
16.
HassanMHKamelSAlateeqA, et al. (2024) Optimal power flow in hybrid Wind-PV-V2G systems with dynamic load demand using a hybrid MRFO-AHA algorithm. In: IEEE Access. Institute of Electrical and Electronics Engineers Inc.
17.
HauWSasakiHKubokawaJ, et al. (2000) Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming. IEEE Transactions on Power Systems15(1): 396–403.
18.
HeYWuHDingM, et al. (2023) Reduction method for multi-period time series scenarios of wind power. Electric Power Systems Research214: 108813.
19.
HetzerJYuDCBhattaraiK (2008) An economic dispatch model incorporating wind power. IEEE Transactions on Energy Conversion23(2): 603–611.
20.
JadhavSK (2018) Optimal power flow in wind farm microgrid using dynamic programming. In: 2018 International Conference on Emerging Trends and Innovations in Engineering and Technological Research (ICETIETR), pp. 1–4. IEEE.
21.
KamhMZIravaniR (2010) Unbalanced model and power-flow analysis of microgrids and active distribution systems. IEEE Transactions on Power Delivery25(4): 2851–2858.
22.
KaramiHAnarakiMVFarzinS, et al. (2021) Flow Direction Algorithm (FDA): a novel optimization approach for solving optimization problems. Computers & Industrial Engineering156: 107224.
23.
KumarVSharmaRNSikarwarSK (2018) Multi-Area Economic Dispatch Using Dynamically Controlled Particle Swarm Optimization. Advances in Energy and Power Systems: Select Proceedings of ICAEDC 2017. Singapore: Springer, 151–163.
24.
LaraJDOlivaresDECanizaresCA (2019) Robust energy management of isolated microgrids. IEEE Systems Journal13(1): 680–691.
25.
LevronYGuerreroJMBeckY (2013) Optimal power flow in microgrids with energy storage. IEEE Transactions on Power Systems28(3): 3226–3234.
26.
LiF-FQiuJ (2016) Multi-objective optimization for integrated hydro–photovoltaic power system. Applied Energy167: 377–384.
27.
LiangR-HLiaoJ-H (2007) A fuzzy-optimization approach for generation scheduling with wind and solar energy systems. IEEE Transactions on Power Systems22(4): 1665–1674.
28.
MaheshwariASoodYR (2022) Solution approach for optimal power flow considering wind turbine and environmental emissions. Wind Engineering46(2): 480–502.
29.
MaheshwariASoodYRJaiswalS (2023) Flow direction algorithm-based optimal power flow analysis in the presence of stochastic renewable energy sources. Electric Power Systems Research216: 109087.
30.
MohamedA-AAMohamedYSEl-GaafaryAAM, et al. (2017) Optimal power flow using moth swarm algorithm. Electric Power Systems Research142: 190–206.
31.
MoradiMHReza TousiSMAbediniM (2014) Multi-objective PFDE algorithm for solving the optimal siting and sizing problem of multiple DG sources. International Journal of Electrical Power & Energy Systems56: 117–126.
32.
MoradiMHAbediniMHosseinianSM (2016) Optimal operation of autonomous microgrid using HS–GA. International Journal of Electrical Power & Energy Systems77: 210–220.
33.
MumtazFSyedMHAlHM, et al. (2016) A novel approach to solve power flow for islanded microgrids using modified Newton Raphson with droop control of DG. IEEE Transactions on Sustainable Energy7(2): 493–503.
34.
NguyenTT (2019) A high performance social spider optimization algorithm for optimal power flow solution with single objective optimization. Energy171: 218–240.
35.
NikkhajoeiHIravaniR (2007) Steady-state model and power flow analysis of electronically-coupled distributed resource units. In: 2007 IEEE Power Engineering Society General Meeting. IEEE, 1.
36.
OlivaresDECanizaresCAKazeraniM (2014) A centralized energy management system for isolated microgrids. IEEE Transactions on Smart Grid5(4): 1864–1875.
37.
OlofssonMAnderssonGSoderL (1995) Linear programming based optimal power flow using second order sensitivities. IEEE Transactions on Power Systems10(3): 1691–1697.
38.
PandeyMKMahiaRN (2023) Hybrid LQR control optimized with PSO and TLBO algorithms for single area load frequency control incorporating renewable energy systems. In: Proceedings of IEEE International Conference on Modelling, Simulation and Intelligent Computing, MoSICom 2023. Institute of Electrical and Electronics Engineers Inc, Vol. 2023, 581–586.
39.
PandeyMKMahiaRNTiwariS, et al. (2025) Robust and metaheuristic load frequency control techniques for renewable energy-based power system: comprehensive review and comparative analysis. International Journal of Ambient Energy46(1): 2474150.
40.
Power Generation Operation and Control3rd edition By WoodAJWollenbergBFShebleGB (n.d.).
41.
RajHJaiswalS (2024) Economic load dispatch in microgrid using whale optimization algorithm. In: 2024 IEEE 5th India Council International Subsections Conference (INDISCON). IEEE, 1–6.
42.
RajHJaiswalSGuptaPP, et al. (2025) Optimal security-constrained scheduling of a renewable energy-based multi-microgrid with compressed air energy storage and demand response. Sustainable Energy, Grids and Networks44: 101959.
43.
RajwarKDeepKDasS (2023) An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artificial Intelligence Review56(11): 13187–13257.
44.
Renewable Energy Agency I (2018) Global energy transformation: a roadmap to 2050. https://www.irena.org
45.
Rezaei AdaryaniMKaramiA (2013) Artificial bee colony algorithm for solving multi-objective optimal power flow problem. International Journal of Electrical Power & Energy Systems53: 219–230.
46.
RoyPKPaulC (2015) Optimal power flow using krill herd algorithm. International Transactions on Electrical Energy Systems25(8): 1397–1419.
47.
ShahbazitabarMAbdiH (2018) A novel priority-based stochastic unit commitment considering renewable energy sources and parking lot cooperation. Energy161: 308–324.
48.
ShiWXieXChuC-C, et al. (2015) Distributed optimal energy management in microgrids. IEEE Transactions on Smart Grid6(3): 1137–1146.
49.
SubramonyVADoollaSChandorkarM (2017) Microgrids in India: possibilities and challenges. IEEE Electrification Magazine5(2): 47–55.
50.
TrojovskýPDehghaniM (2023) A new bio-inspired metaheuristic algorithm for solving optimization problems based on walruses behavior. Scientific Reports13(1): 8775.
51.
VergaraPPLopezJCRiderMJ, et al. (2019a) Optimal operation of unbalanced three-phase islanded droop-based microgrids. IEEE Transactions on Smart Grid10(1): 928–940.
52.
VergaraPPReyJMLopezJC, et al. (2019b) A generalized model for the optimal operation of microgrids in grid-connected and islanded droop-based mode. IEEE Transactions on Smart Grid10(5): 5032–5045.
53.
XueJShenB (2023) Dung beetle optimizer: a new meta-heuristic algorithm for global optimization. The Journal of Supercomputing79(7): 7305–7336.
