Penetration Of Renewable Energy Resources Research Articles

Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty

The uncertainties resulting from the escalating penetration of renewable energy resources pose severe challenges to the efficient operation of modern power systems. Hydroelectricity is characterized by its flexibility, controllability, and reliability, and thus becomes one of the most ideal energy resources to hedge against such uncertainties. This paper studies the mid-term integrated generation and maintenance scheduling of a cascaded hydroelectric system (CHS) consisting of multiple cascaded reservoirs and hydroelectric units. To precisely describe the mid-term water regulation policies, the hydraulic coupling relationship and water-energy nexus of CHS are incorporated into the proposed optimization model. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization (MSO) approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of CHS. The proposed MSO model is formulated as a large-scale mixed-integer linear program that presents significant computational intractability. To address this issue, a tailored Benders decomposition algorithm is developed. Two real-world case studies are conducted to demonstrate the capability and characteristics of the proposed model and algorithm. The computational results show that the proposed MSO model can exploit the flexibility of hydroelectricity to efficiently respond to variable wind and solar power, and reserve water resources for the generation in peak months to reduce the consumption of fossil fuel. The proposed solution approach also exhibits promising computational efficiency when handling large-scale models.

Advancing Distance Relaying Reliability: S Transform Solution for Renewable Energy-Infused Smart Grid

Distance relaying is a crucial component in safeguarding transmission lines globally. However, the presence of Sub-Synchronous Resonance (SSR) introduces challenges, as oscillations in voltage and current magnitudes adversely affect the performance of conventional distance relays. Detecting faults accurately during these oscillations poses a significant challenge for traditional relaying mechanisms. This paper addresses the issue of SSR-induced maloperations in distance relays, particularly in the context of the increasing penetration of renewable energy resources in smart grids. The integration of wind power into the grid generates sub-synchronous oscillations, leading to protection issues. In response, a novel solution leveraging the S transform, a modern signal processing technique, is proposed to enhance the robustness of distance relaying under such challenging conditions. The developed algorithm is implemented in MATLAB and rigorously tested on the First Benchmark Model of sub-synchronous resonance. Simulation of the model is conducted in the PSCAD simulation software, and the results are thoroughly validated in MATLAB. The study demonstrates the efficacy of the S transform-based approach in accurately identifying faults and mitigating maloperations caused by SSR, thereby improving the reliability of distance relaying in smart grids with high renewable energy integration.

Distributed multi-horizon model predictive control for network of energy hubs

The increasing penetration of renewable energy resources has transformed the energy system from a traditional hierarchical energy delivery paradigm to a distributed structure. Local energy hubs activates synergies among energy carriers rendering flexibility to the system and gives rise to possible energy trading among networked local energy hubs. Joint operation of such hubs and peer-to-peer trading between them can improve energy efficiency and support the integration of renewable energy resources. However, for such complex systems involving multiple stakeholders, both computational tractability and privacy concerns need to be accounted for. In this work, a novel multi-horizon distributed MPC framework is introduced for the control of energy hub networks. The multi-horizon approach increases the prediction horizon for MPC without compromising the time discretization or making the problem computationally intractable. The distributed scheme is based on a consensus alternating direction method of multipliers algorithm. It combines the superior performance of the centralized approach with the privacy preservation of the decentralized approach. A benchmark three-hub network is used to investigate the performance of the proposed method in simulation and compare it to the decentralized, centralized and standard model predictive control (MPC) approaches. The results show superior performance of the distributed multi-horizon MPC in terms of total cost, computational time, and robustness to demand and prices variations. Finally, the performance was also experimentally validated in real time by implementing the controller on a real energy hub system.

Mitigation of total harmonic distortion and flicker emission in the presence of harmonic loads by optimal siting and sizing of wind turbines and energy storage systems

In distribution networks (DNs), there are significant technical challenges due to the high penetration of renewable energy resources (RERs), especially wind turbines (WTs) and the presence of non-linear electrical loads. One of the most important challenges is power quality. In such networks, to mitigate flicker emission produced by WTs and network voltage harmonics, it is necessary to solve the planning problems considering power quality objectives and standards. For this aim, this paper attempts to improve DN performance by optimal siting and sizing of WTs and energy storage systems (ESSs). In the planning problem, to take into account the power quality issue, flicker emission, total harmonic distortion (THD), and network voltage deviation (NVD) are included in the optimization problem. To effectively solve the planning problem, which is a non-linear and non-convex optimization problem, three variants of genetic algorithm (GA) are used. Simulation results indicate that optimal sizing and siting of WTs not only significantly improve the power quality issue but also improves the network performance.

Growing Importance of Micro-Meteorology in the New Power System: Review, Analysis and Case Study

With the increasing penetration of renewable energy resources, their variable, intermittent and unpredictable characteristics bring new challenges to the power system. These challenges require micro-meteorological data and techniques to provide more support for the power systems, including planning, dispatching, operation, and so on. This paper aims to provide readers with insights into the effects of micro-meteorology on power systems, as well as the actual improvement brought by micro-meteorology in some power system scenarios. This paper provides review including the relevant micro-meteorological techniques such asbservation, assimilation andumerical techniques, as well as artificial intelligence, presenting a relatively complete overview ofhe most recent and relevant micro-meteorology-related literature associated with power systems. The impact of micro-meteorology on power systemss analyzed inix different forms of power generationnd three typical scenariosf different stages in theower system, as well as integrated energy systemsnd disaster prevention and reduction. Finally, aase study in China is provided. This case takes wind power prediction as an example in aower system to compare the performance whenpplying micro-meteorological data or not. The experimental results demonstrated that using the micro-meteorological reanalysis dataset with high spatial–temporal resolution for wind power prediction performed better, verifying the improvement of micro-meteorology to theower system to some extent.

Optimal design and sizing of a hybrid energy system for water pumping applications

AbstractOne of the ways to increase the participation and penetration of renewable energy resources is to bring down the cost of these abundant resources for easy implementation and affordability. In this paper, a generalized reduced gradient (GRG) non‐linear optimization algorithm is implemented to solve a tri‐objective optimal design and sizing of a low‐cost hybrid mix consisting of a photovoltaic (PV) power plant, biomass power plant (BPP), and battery energy system for water pumping load applications in the University of Johannesburg, South Africa considering four different hybrids of biomass‐battery, PV‐battery, PV‐biomass, and PV‐biomass‐battery. The optimization model considers available energy and battery state of charge while minimizing least cost of energy (LCOE), carbon dioxide emission (tCO2eq), and loss of power supply probability (LPSP) including carbon tax incentive and penalty. The results when compared against particle swarm optimization (PSO) show the superiority of GRG over PSO with an optimal combination of PV‐biomass‐battery mix with optimal size of the PV power plant as 360.50 kW, the BPP 181.08 kW, and the battery size of 6,553.60 kWh giving a minimal optimal LCOE, CO2 emission and LPSP of 0.018 $/kWhr (with carbon tax), and 0.016 $/kWhr (without carbon tax), 28,067.73tCO2eq tCO2eq, and 1.7%, respectively. These values give a competitive advantage compared to the unit cost and values of CO2 emission and LPSP currently in the literature.

Deep Reinforcement Learning for Voltage Control and Renewable Accommodation Using Spatial-Temporal Graph Information

Renewable energy resources (RERs) have been increasingly integrated into distribution networks (DNs) for decarbonization. However, the variable nature of RERs introduces uncertainties to DNs, frequently resulting in voltage fluctuations that threaten system security and hamper the further adoption of RERs. To incentivize more RER penetration, we propose a deep reinforcement learning (DRL)-based strategy to dynamically balance the trade-off between voltage fluctuation control and renewable accommodation. To further extract multi-time-scale spatial-temporal (ST) graphical information of a DN, our strategy draws on a multi-grained attention-based spatial-temporal graph convolution network (MG-ASTGCN), consisting of ST attention mechanism and ST convolution to explore the node correlations in the spatial and temporal views. The continuous decision-making process of balancing such a trade-off can be modeled as a Markov decision process optimized by the deep deterministic policy gradient (DDPG) algorithm with the help of the derived ST information. We validate our strategy on the modified IEEE 33, 69, and 118-bus radial distribution systems, with outcomes significantly outperforming the optimization-based benchmarks. Simulations also reveal that our developed MG-ASTGCN can to a great extent accelerate the convergence speed of DDPG and improve its performance in stabilizing node voltage in an RER-rich DN. Moreover, our method improves the DN's robustness in the presence of generator failures.

Optimal siting and sizing of mobile-static storage mix in distribution systems with high renewable energy resources penetration

Optimal siting and sizing of mobile-static storage mix in distribution systems with high renewable energy resources penetration

Stochastic MPC based double-time-scale voltage regulation for unbalanced distribution networks with distributed generators

With the increasing penetration of renewable energy resources, the uncertainty of renewable energy resources output introduces challenges to voltage control in distribution networks (DNs). To solve these problems, this paper proposes a double-time-scale voltage control scheme for unbalanced DNs based on stochastic model predictive control (SMPC) to coordinate multiple voltage control devices. In fast-time-scale control, the active and reactive power outputs of distributed generators (DGs) are optimized to minimize voltage deviation, active power curtailment and reactive power fluctuation. In the slow-time-scale control, optimal tap changes of on-load tap changers (OLTC), step voltage regulators (SVR), and switched capacitor banks (CBs) are calculated to reduce voltage deviation and tap operations. Additionally, in the fast-time-scale control, the SMPC-based scheme adopts a scenario generation approach to represent the uncertainty of DG output. Considering the temporal correlation of the DG output, different prediction scenarios and scenario probabilities are obtained by the empirical cumulative distribution function fitted by the historical measurement data. In this paper, the effectiveness of the proposed double-time-scale voltage control scheme is verified by the unbalanced IEEE123 node system. The case study demonstrates that the proposed voltage scheme can effectively keep the three-phase voltages in unbalanced DN within the secure operation range and achieve better voltage profiles.

Analyses on the impact of consumers’ participation by demand response for flexibility procurement

Penetration of renewable energy resources is expected to increase further for a sustainable future. However, its intermittent nature creates differences between electricity supply and demand, endangering the stability of the power system. Demand-side management is becoming more crucial in maintaining the balance by procuring flexibility to the grid through demand response (DR) program by regulating the residential consumers’ distributed energy resources usage such as heat pump water heater, battery storage, etc. Coupled with economic incentives such as dynamic electricity pricing, cooperative consumers are also capable of reducing their energy costs. Although the potential of procuring flexibility through residential consumers is massive, the consumers are expected to participate in the DR program aggressively and consistently, which is practically impossible to expect of all consumers. This study presents a constructive DR model in procuring flexibility when viewed from a different angle, by considering the participation status of consumers (PSC). As PSC can depends on many different economical and psychological factors, there are complexities in modelizing it. In this study, two representative factors, achievable consumers’ cost reduction and response fatigue are considered. Those participating are given generous electricity rates to optimize their electricity usage while providing flexibility. By acknowledging different participation levels among consumers and offering generous electricity rates to participants, the program can enhance the overall success of renewable energy integration while fostering grid stability and cost savings. The simulation results further reveal the behavioral patterns of consumers within the DR program and their influence on other stakeholders involved in the initiative.

Cyber-secure energy and flexibility scheduling of interconnected local energy networks with introducing an XGBoost-assisted false data detection and correction method

The growing penetration of renewable energy resources (RERs) and the ever-increasing implementation of information and communication technologies in smart grids necessitate the utilization of fast and safe operation methods. These schemes should be able to cope with the intermittency of uncertain RERs and fully explore the capabilities of new technologies while considering the vulnerabilities as a result of digitalization. Here, the integrity of the energy and flexibility scheduling and trading heavily depends on the security of the cyber-physical system. Local energy networks (LENs) are introduced to easily incorporate and utilize distributed energy resources, improving electrical power reliability and efficiency. This study develops a cyber-secure energy and flexibility scheduling platform for interconnected local energy networks. Hence, it introduces a novel false data detection and correction method based on the XGBoost machine learning method and investigates the performance of the proposed algorithm in the context of an interconnected local energy network and the corresponding energy and flexibility transactions. In this regard, this paper initially presents a bilevel energy and flexibility scheduling problem for interconnected local energy networks (ILENs) considering cyber-attacks (BLEFSCAILEN), which tries to satisfy the energy and flexibility requirements of the ILEN guaranteeing a resilient decision against false data injection cyber-attacks. Within the proposed BLEFSCAILEN a bi-level multi-objective optimization problem is defined where the operator of ILEN optimizes both energy and flexibility trading among LENs in the upper level to maximize its revenue. In the proposed structure, the operator of each LEN is situated at the lower level and tries to minimize the scheduling cost and simultaneously maximize the local flexibility index. Furthermore, in order to evaluate and improve the proposed system’s cyber-security, a false data injection attack is constructed using the Gaussian probability distribution function. Herein, the scheduling of ILEN is optimized considering vulnerabilities of electricity consumption data as a consequence of cyber-attack. Finally, the novel XGBoost-assisted deviation bound-based false data detection/correction (XGBFDD) algorithm is suggested to mitigate the above-mentioned cyber-attack and attain near real-world conditions. Simulation results demonstrate that the proposed false data detection/correction strategy exhibits a maximum accuracy of 91.67 precent in mitigating the attack effects. This is because the acquired post-correction results exhibit minor deviations in comparison to the original optimization output that is calculated with the pre-attack consumption data.

Evaluating the impact of passenger electric vehicle adoption on high renewable resources electricity grid

A considerable amount of electricity is additionally demanded for Electric Vehicle (EV) charging due to rapid EV penetration. This study explores the impact of time of charging for different levels of passenger EV penetration on the electricity system using a case study electricity system with high penetration of renewable energy resources. A simulation approach is proposed to determine the new demand profile due to EV charging. Next, a Mixed Integer Linear Programming model is formulated considering the operation schedules of conventional power plants to mimic the real-time status of the electricity system. Finally, the developed approach considers the different possible interventions of actual EVs available in the market and tries to determine their impact in a renewable energy-dominated electricity system. The results from the study show that it is emission-friendly to encourage night charging rather than day charging for the considered renewable energy-dominated case study electricity system.

Techno-economic analysis of hybrid solar-biomass-wind for water pumping considering carbon tax and renewable energy rebate

There is a need for increased penetration of renewable energy resources (RES) in the energy mix of South Africa that is currently bedevilled by recurring load shedding thus affecting sustainable critical infrastructures such as water pumping and water use. This paper assesses the viability of three RES of solar, biomass, and wind for water pumping at two locations (University of Johannesburg, APK campus – L1 and Zuikerbosch pumping station – L2) in Johannesburg, South Africa by utilising daily data from 2003 to 2020. A detailed feasibility analysis of the three RES was conducted, after which a rebate-based novel model for reducing the unit cost with zero greenhouse gas (GHG) was implemented for solar PV. Key findings reveal that the power requirement in L1 and L2 booster stations are 91 kW and 71,331 kW, respectively while the produced power from a 350 W monocrystalline PV-module utilized is 0.103 kW in L1 and L2 using 882 and 692,534 modules. The biomass power of 47.68 GW in L1 and 99.42 GW in L2 was produced from an average amount of food waste estimate of 1641 and 1248,800 tonnes evaluated from 3729 and 2838,100 tonnes of putrescible waste using a population model. The power density results depict a very weak wind energy application capability in the two locations based on National Renewable Energy Laboratory indices after using 11 differently sized wind turbines in the two locations. Finally, the result from the rebated unit-cost model reveals that the unit cost of water dropped by 17.09$/kWhr from 0.33$/kWhr in L1 and 21.20$/kWhr from 0.66$/kWhr in L2 using the solar PV modules. The study aligns with similar study done in Qatar, and the Springer report on Energy Democracy Evaluation for 100% Renewable Energy Policies and Projects showing an increased penetration of affordable and carbon-free RES which will in turn reduce climate change effects globally.

Congestion management for coordinated electricity and gas grids in the presence of multi-energy hubs: A risk-based optimal scheduling

Due to the development of cost-effective and high-efficient infrastructures in electricity and natural gas carriers, the need for optimal operation of multi-carrier energy systems is essential. On the other side, with the increasing penetration of renewable energy resources (RERs), and power demand, the congestion management (CM) of power systems is turning out to be a significant challenge for system operators. Motivated by these, this paper focuses on the congestion management problem for a multi-energy hub (MEH) system incorporated by RERs, flexible energy resources (FERs), and different energy conversion technologies to supply electrical, heat, and cooling demands, aiming to minimize the total operating costs. In current practice, the steady-state Weymouth equation and AC-power flow method for natural gas and electricity networks are implemented to investigate the interdependency of power and gas networks. The renewable energy generation variations are mitigated by the scenario-based stochastic framework. Also, to manage the risk associated with random variables, the downside risk constraint (DRC) model is employed to analyze the changes in the expected cost per several values of the risk parameters. The numerical results demonstrate that the proposed model can significantly utilize the energy hub’s flexibility to alleviate gas and power congestion while decreasing the total operation cost.

The Role of Open-Source Software in the Energy Sector

Fast digitalization of the power grids and the adoption of innovative software solutions is key to a successful energy transition. In other sectors, such as telecommunication or cloud computing, open-source software has already proven capable of transforming entire industries, by speeding up development and lowering development costs while achieving high levels of stability, interoperability, and security. However, the energy sector has not yet embraced open-source software to the same level. We discuss how existing open-source software principles can be applied to the unique challenges of the energy sector during the transition towards higher penetration of renewable energy resources. To provide an overview of the current state of the open-source software landscape, we collected and analyzed 388 open-source projects, in terms of project activities, community composition, relevant licenses, and commonly used programming languages. One finding was that the majority of projects are currently driven by academic contributors, but that commercial players do also play a role, and we identify positive examples of collaboration between the two, mostly related to standardization.

Synergistic effect of complementary cleaner energy sources on controllable emission from hybrid power systems in optimal power flow framework

The increased penetration of renewable energy resources into the power system may make the system operation extremely vulnerable due to their inherent volatility and variability. Thus, optimum utilization of cleaner power generation into the power system without affecting the operational economy, voltage security and stability becomes a challenging issue. To minimize this adverse impact of intermittent renewable resources, hydro power sources may be considered as an effective option. Inclusion of hydro power may contribute towards optimal utilization of the abundant clean energy and enhance the capability to mitigate the volatile renewable power sources while forming a stable hybrid power system (HPS). In this context, an intelligent generation scheduling (IGS) mechanism is proposed to effectively mitigate these complex challenges. To further analyze these issues, multiple case studies under different operating conditions are carried out to portray the significance of incorporating the complementary behaviour of hydro-solar generation with thermal power generation facilities in environmental optimal power flow (EOPF) framework. Widely accepted IEEE 30 bus benchmark system is considered for the validation of results. Optimal operational paradigm (OOP) for the three different HPS configurations i.e. (1) Solar-Thermal (ST); (2) Hydro-Thermal (HT); and (3) Solar-Hydro-Thermal (SHT) is evaluated using Jaya algorithm (JA) while meeting the real time constraints. With the OOP, a comparative performance evaluation is carried out among different hybrid configurations in fulfilling the multiple objectives. Results show the supremacy of SHT configuration in minimizing the operating cost by 1.324×105 US$/y to 2.445×105 US$/y and emission up to 15.768 Tons/y compared to other configurations.

Efficient Red Kite Optimization Algorithm for Integrating the Renewable Sources and Electric Vehicle Fast Charging Stations in Radial Distribution Networks

The high penetration of renewable energy resources’ (RESs) and electric vehicles’ (EVs) demands to power systems can stress the network reliability due to their stochastic natures. This can reduce the power quality in addition to increasing the network power losses and voltage deviations. This problem can be solved by allocating RESs and EV fast charging stations (FCSs) in suitable locations on the grid. So, this paper proposes a new approach using the red kite optimization algorithm (ROA) for integrating RESs and FCSs to the distribution network through identifying their best sizes and locations. The fitness functions considered in this work are: reducing the network loss and minimizing the voltage violation for 24 h. Moreover, a new version of the multi-objective red kite optimization algorithm (MOROA) is proposed to achieve both considered fitness functions. The study is performed on two standard distribution networks of IEEE-33 bus and IEEE-69 bus. The proposed ROA is compared to dung beetle optimizer (DBO), African vultures optimization algorithm (AVOA), bald eagle search (BES) algorithm, bonobo optimizer (BO), grey wolf optimizer (GWO), multi-objective multi-verse optimizer (MOMVO), multi-objective grey wolf optimizer (MOGWO), and multi-objective artificial hummingbird algorithm (MOAHA). For the IEEE-33 bus network, the proposed ROA succeeded in reducing the power loss and voltage deviation by 58.24% and 90.47%, respectively, while in the IEEE-69 bus it minimized the power loss and voltage deviation by 68.39% and 93.22%, respectively. The fetched results proved the competence and robustness of the proposed ROA in solving the problem of integrating RESs and FCSs to the electrical networks.

Collaborative Optimization of Transmission and Distribution Considering Energy Storage Systems on Both Sides of Transmission and Distribution

With the high penetration of renewable energy resources, power systems are facing increasing challenges in terms of flexibility and regulation capability. To address these, energy storage systems (ESSs) have been deployed on both transmission systems and distribution systems. However, it is hard to coordinate these ESSs with a single centralized optimization, and the time-domain coupling constraints of ESSs lead to high optimization complexity and a time-consuming calculation process. In this regard, this paper proposes a hierarchical transmission and distribution systems coordinative optimization framework, considering the ESSs at both ends of the systems. The decoupling of the time-domain coupling constraints of ESSs is realized by the Lyapunov optimization. Furthermore, the decoupling mechanism is embedded in the iterative process of analytical target cascading (ATC). In addition, an ATC-based Lyapunov optimization (ATC-L) approach is proposed to solve the co-optimization problem of the operations of the transmission system with multiple connected distribution systems. Through a case study, it is verified that the proposed framework and the ATC-L approach can effectively reduce the system’s operational cost and improve the consumption rate of renewable energy.

Optimal battery energy storage system deployment from perspectives of private investors and system operators for enhancing power system reliability

Due to their intermittent nature, high penetration of renewable energy resources (RES) can deteriorate power system reliability. A battery energy storage system (BESS) offers an opportunity to reduce the uncertainty associated with RES and hence improve power system reliability. In the last decade, the cost of BESS has declined so its deployment has become increasingly feasible, but the decision ultimately depends on its Net-Benefit to the investor. Depending on the perspective of the investor, the deployment decision involves discovering the most optimal location, capacity, and technology of BESS. A sensitivity analysis based on the Z-bus matrix is used for selecting the optimal location. In this paper, from the narrow perspective of a private investor, the Net-Benefit function is the energy arbitrage value of BESS minus its overall cost. However, the system operator additionally values BESS because it enables more reliable system operation at reduced operating costs. After examining multiple power system reliability indices, the product of Expected Unserved Energy (EUE) and Value of Lost Load (VoLL) is incorporated into the Net-Benefit function of the system operator. MATPOWER Optimal Scheduling Tool (MOST) is used for testing the proposed Net-Benefit functions on a standard reliability test system (RTS) known as RTS-GMLC. Three diverse case studies are examined in three exploration phases; the first phase helps determine search space whereas the second one narrows it down and the third phase finds the optimal BESS solution. Presented research results demonstrate that, over a period of 15 years, optimal BESS deployment can offer as much as $M164.8 and $M33.6 Net-Benefits to the system operator and private investor respectively.

A Novel Adaptive Manta-Ray Foraging Optimization for Stochastic ORPD Considering Uncertainties of Wind Power and Load Demand

The optimal control of reactive powers in electrical systems can improve a system’s performance and security; this can be provided by the optimal reactive power dispatch (ORPD). Under the high penetration of renewable energy resources (RERs) such as wind turbines (WTs), the ORPD problem solution has become a challenging and complex task due to the fluctuations and uncertainties of generated power from WTs. In this regard, this paper solved the conventional ORPD and the stochastic ORPD (SORPD) at uncertainties of the generated power from WTs and the load demand. An Adaptive Manta-Ray Foraging Optimization (AMRFO) was presented based on three modifications, including the fitness distance balance selection (FDB), Quasi Oppositional based learning (QOBL), and an adaptive Levy Flight (ALF). The ORPD and SORPD were solved to reduce the power loss (PLoss) and the total expected PLoss (TEPL), the voltage deviations (VD) and the total expected VD (TEVD). The normal and Weibull probability density functions (PDFs), along with the scenario reduction method and the Monte Carlo simulation (MCS), were utilized for uncertainty representations. The performance and validity of the suggested AMRFO were compared to other optimizers, including SCSO, WOA, DO, AHA, and the conventional MRFO on the IEEE 30-bus system and standard benchmark functions. These simulation results confirm the supremacy of the suggested AMRFO for the ORPD and SORPD solution compared to the other reported techniques.