Real-time Energy Price Research Articles

Optimization and energy management strategies, challenges, advances, and prospects in electric vehicles and their charging infrastructures: A comprehensive review

Electric vehicles (EVs) are at the forefront of global efforts to reduce greenhouse gas emissions and transition to sustainable energy systems. This review comprehensively examines the optimization and energy management strategies for EVs and their charging infrastructure, focusing on technological advancements, persistent challenges, and future prospects. By the end of 2023, the number of electric cars on the road globally reached 40 million, with 14 million new registrations recorded in 2023 alone—95% of which were in China, Europe, and the United States. Governments across the globe have introduced incentives and policies to promote EV adoption, and by 2030, EVs are expected to comprise a significant portion of light-duty vehicles in major regions. Despite these encouraging developments, challenges such as range anxiety, the relatively low energy density of 200–300 Wh/kg in Li-ion batteries (compared to 13,000 Wh/kg for petroleum), and insufficient public charging infrastructure remain key barriers to widespread EV adoption. This review also explores the critical role of smart grid technologies, vehicle-to-grid (V2G) systems, and renewable energy integration in supporting the growing EV market. V2G technologies are projected to enhance grid stability by 20–30% and reduce operational costs by 10–15% through load balancing and real-time energy price forecasting. By thoroughly analyzing optimization techniques such as load balancing, dynamic scheduling, and real-time energy management, this paper offers a roadmap for researchers, policymakers, and industry stakeholders to accelerate the integration of EVs into global energy systems and enhance sustainability in urban transportation networks.

Optimal Energy Management of EVs at Workplaces and Residential Buildings Using Heuristic Graph-Search Algorithm

As the adoption of electric vehicles (EVs) continues to rise, efficient scheduling methods that minimize operational costs are critical. This paper introduces a novel EV scheduling method utilizing a heuristic graph-search algorithm for cost minimization due to its admissible nature. The approach optimizes EV charging and discharging schedules by considering real-time energy prices and battery degradation costs. The method is tested on systems with solar generation, electric loads, and EVs featuring vehicle-to-grid (V2G) connections. Various charging rates, such as standard, fast, and supercharging, along with uncertainties in EV arrival and departure times, are factored into the analysis. Results from various case studies demonstrate that the proposed method outperforms popular heuristic optimization techniques, such as particle swarm optimization and genetic algorithms, by 3–5% for different real-time energy prices. Additionally, the method’s effectiveness in reducing operational costs for workplace EVs is confirmed through extensive case studies under varying uncertain conditions. Finally, the system is implemented on a digital real-time simulator with DNP3 communication, where real-time results align closely with offline simulations, confirming the algorithm’s efficacy for real-world applications.

Optimal control algorithms for Gabon’s Smart Grid: Enhancing efficiency and sustainability

The adoption of smart grid technologies offers Gabon several opportunities to enhance energy efficiency and sustainability. This study investigates the use of optimum control algorithms to increase grid stability and enhance the utilization of renewable energy sources. Mathematical models and simulations are used to assess genetic algorithms in light of Gabon's unique energy situation. Systems known as electrical smart grids supply electricity to users directly from power plants in an effort to reduce costs, cut down on blackouts, and improve energy efficiency. Smart grids, or SGs, are well-known pieces of equipment because of their amazing capabilities, which include bi-directional communication, stability, power failure detection, and interconnectivity with appliances for monitoring. Many modern data and security management systems, including modeling, monitoring, optimization, and/or artificial intelligence, lead to SGs. Energy was once cheap, easily managed, and dependent only on fundamental elements. Demand has significantly increased as a result of the current circumstances, which has also increased Gabon's electricity expenses, the likelihood of a contingency, and the complexity of the electrical network. In Gabon, smart grids have shown to be the most practical and clever way to lessen these problems in recent years. An electrical network with information technology integrated is called a smart grid. According to this study, using genetic algorithms in a smart grid could lower Gabon's overall electricity prices. In order to meet demand, the proposed approach makes use of off-grid battery banks and renewable energy sources. The goal of GA optimization is the short-term time averaged power cost; factors that affect this include grid energy to satisfy load, battery discharge, and other factors. MATLAB software is used to solve the optimization problem over a 24-hour period of renewable input, real-time energy pricing, and load. The results are presented.

Crafting a decentralized framework for energy sharing among smart homes in a peer-to-peer market

In this paper, a new framework for the participation of smart homes in the peer-to-peer energy market is presented, in which smart homes share their surplus energy with each other to maintain the balance between generation and demand through bilateral trading. The seller smart homes, players who always sell their excess energy to the buyer smart homes in the peer-to-peer market, are equipped with distributed energy resources including electric vehicles, power-only units, and uncontrollable loads. The buyer smart homes always interact with sellers as energy consumers to supply their flexible loads. The presence of battery energy storage systems in the model of these players, as well as active participation in load response programs, increases the flexibility and profit obtained from energy transactions. All players regardless of their role in the peer-to-peer market, have bilateral trading with the retail market considering real-time energy pricing rates to gain more profit. A fully decentralized method called the Fast Alternating Direction Method of multipliers (FADMM) is used to clear the developed market. To prove the effectiveness of the proposed framework, numerical studies are considered for the energy transactions of several smart homes with each other and with the retail market.

Fuzzy-based smart energy management system for residential buildings in Saudi Arabia: A comparative study

Considering Saudi Arabia's strategy entails economic diversification and a reduction in dependency on oil, a change towards sustainable and efficient energy management practices is required. Effective energy management is critical for optimising energy consumption, lowering costs, and reducing the environmental footprint. Traditional energy management systems are frequently built on rule-based or deterministic techniques that fail to address the complexity and uncertainty inherent in home energy usage patterns and user behaviours. Fuzzy logic-based solutions have emerged in recent years, holding enormous promise for domestic energy management. Fuzzy logic excels at dealing with imprecise and uncertain input, making it ideal for modelling human-centric systems such as domestic energy management. This study presents a cutting-edge fuzzy-based smart energy management system adapted to Saudi residential buildings. Using fuzzy logic approaches, the system intends to optimize energy usage, reduce peak demand, and improve energy efficiency. It automatically adjusts energy-consuming devices such as air conditioning, lights, and appliances depending on user preferences, occupancy patterns, as well as real-time energy prices using fuzzy decision-making algorithms. The research not only substantiates the success of this strategy through a comparative study, but it also highlights its prospective benefits for Saudi Arabian residential constructions. It also covers the obstacles and potential research possibilities for adopting fuzzy-based smart energy management systems, exposing a promising road towards a more sustainable and safe energy future. The study's findings underscore the superiority of the comparative study alternative, revealing it as the most effective means to evaluate the fuzzy-based system's performance and unique advantages in relation to other established energy management approaches.

Optimal operation of coordinated multi-carrier energy hubs for integrated electricity and gas networks

"In the field of energy supply, coordinated multi-carrier systems, which include natural gas and electric energy, offer unique opportunities to enhance energy efficiency and flexibility. Nevertheless, the interdependence between electricity and natural gas networks poses various challenges related to the flow of electricity and gas in feeders, pipes, and connection points. To address these challenges, the concept of an energy hub emerges as an essential component in multi-carrier energy systems, serving as a connection point between the electricity grid and gas grids. This study introduces an optimal operation method for coordinating gas and electricity distribution networks through interconnected energy hubs. The infrastructure of the proposed energy hub comprises a combined heat and power unit, a boiler, an electric energy storage system, a heat pump, and a gas-burning unit, effectively meeting heating and electrical load requirements. The model formulation follows a stochastic approach based on a two-stage scenario. Considering uncertainties related to wind energy, electric load, and real-time energy prices, the primary objective of this study is to minimize the total operating cost of the energy system. The optimization problem is solved using Wall's optimization algorithm. To meet its energy requirements, the integrated energy system presented in this paper actively participates in the real and daily electric energy markets, as well as the natural gas market, providing the necessary energy resources. Additionally, the model incorporates realistic descriptions of electric power and gas flow in feeders and gas pipelines, considering AC load distribution and the Weymouth equation. With consideration of connectivity constraints, the proposed model offers a comprehensive representation of the integrated electricity and gas networks. The simulations conducted on the integrated energy system, comprising a 33-bus electric network and a 6-node gas network with interconnected energy hubs, highlight a remarkable 12 % decrease in electricity purchase costs and a substantial 18 % reduction in natural gas procurement expenses, underscoring the cost-efficiency and effectiveness of the stochastic planning approach.

Regional revenues of solar and wind generation in Texas

Effective regulatory policies, ample renewable energy potential, and a favorable business climate have led to a boom in wind farms and solar energy projects in Texas. Using a large sample of 15-min data for the six-year period of 2016–2021, we analyze per MWh revenues from solar generation and wind generation in the renewable regions of the Electric Reliability Council of Texas (ERCOT). We find that average regional revenues from variable renewable energy (VRE) for the daytime hours of 07:00–19:00 exceed the average levelized price of recently signed solar and wind power purchase agreements (PPAs), although average regional revenues for wind generation for the nighttime hours of 19:00–07:00 were lower than recent PPA prices. Moreover, VRE's 15-min regional revenues move with ERCOT's cap on the real-time market's energy price offers, regulatory price adder, daily wholesale natural gas price, 15-min nuclear energy generation, 15-min system load, 15-min regional solar energy and 15-min regional wind energy. While continued VRE development may suppress wholesale market prices, continued growth in electricity demand and increasing natural gas prices provide offsetting effects. Nevertheless, new policies are under development to mitigate the adverse effects of further VRE development on grid reliability and generation investment incentive.

Information Gap Decision Theory-Based Risk-Averse Scheduling of a Combined Heat and Power Hybrid Energy System

This research investigates the optimal management of electric and heat energies in a hybrid energy system (HES). In the studied HES, a pair of photovoltaic and battery storage devices is used to supply the electricity demand, and a boiler system to supply the heat demand directly. In addition, a modified cycle power plant acted as a combined heat and power (CHP) unit to increase the generation capacity and supply reliability. The HES is also able to connect to the electric grid to exchange power according to real-time energy prices. The uncertainty of renewable generation, demand levels, and energy prices challenge the decision-making process. To deal with the uncertainty of these overlapping parameters, a comprehensive information-gap decision theory (IGDT) approach is proposed in this paper that, despite other works, considers the uncertainties in an integrated framework and derives risk-averse and risk seeker strategies in different steps. The problem is modeled as mixed-integer linear programming and solved using the GAMS optimization package. Concerning simulation results, from the viewpoint of a risk-seeking decision maker, the increment of the uncertainty degree by 10.906% results in a reduced operating cost of 8.6%. From the viewpoint of a risk-averse decision maker, the increment of the uncertainty degree by 10.208% results in 8.6% more operating cost.

A mixed conditional value-at-risk/information gap decision theory framework for optimal participation of a multi-energy distribution system in multiple energy markets

This study provides a unique risk-based hybrid two-stage operational model for a coordinated power and gas distribution system that enables it to engage optimally in the electricity, gas, and thermal markets in order to serve electricity, gas, and heat demands. The suggested hybrid model enables the integrated energy distribution system (IEDS) operator to apply several risk-averse methods concurrently, based on the nature of the uncertainties and the availability of data for unknown parameters. The conditional value-at-risk-based stochastic programming (CVaR-SP) technique is utilized to cover the uncertainty in wind speed, vehicle behavior in a parking lot, day-ahead energy prices, and multi-energy demands. Furthermore, the infromation gap decision theory (IGDT) model is used to control uncertainty in real-time energy prices without requiring the use of a probability distribution function or the creation of scenarios. To provide a high-flexibility structure to meet a variety of demands, the IEDS is outfitted with some local energy resources, including a gas-fired power-only unit, a gas-fired combined heat and power plant, a wind turbine, a gas boiler, an electric vehicle parking lot (EVPL), multi-energy storages (MESs), and integrated demand response (IDR). According to the numerical data, the IEDS operator can lower the risk level by 2% while raising the operating cost by 1.3%. Furthermore, the simultaneous use of MESs, EVPL in vehicle-to-grid mode, and IDR reduce operating costs by up to 17.5%.

Day-ahead self-scheduling from risk-averse microgrid operators to provide reserves and flexible ramping ancillary services

In this paper, a new decision-making framework is proposed for the day-ahead self-scheduling problem of microgrids, in which the microgrid operator (MGO) can provide ancillary services for both the independent system operator (ISO) and the distribution system operator (DSO). The MGO provides the reserve and flexible ramping product (FRP) services for the ISO through participating in the corresponding markets. Also, the MGO reschedules its resources to provide the requested services for the DSO. To model the uncertain behavior of the renewable energy resource, demand, and real-time energy price, the MGO problem is modeled as a two-stage stochastic model. Then, the uncertainties of the reserve and the FRP deployment in real-time operation are modeled using the information gap decision theory approach. The results show the effects of the different strategies in scheduling the local resources adopted by the MGO to participate in the energy and ancillary service markets. In the risk-based model proposed for the MGO, increasing the risk parameter decreases the capacity of the provided reserve and ramp-up FRP while it increases the energy sold to the day-ahead energy market.

Optimising Building-to-Building and Building-for-Grid Services Under Uncertainty: A Robust Rolling Horizon Approach

Energy systems are undergoing radical changes that have resulted in buildings being regarded as proactive players with the potential to contribute positively to energy networks. This study investigates the role of active buildings (ABs) as prosumers in energy systems by introducing a building-to-building (B2B) strategy for energy exchange between residential units, as well as a building-for-grid (B4G) model by exploiting the demand flexibility of residential microgrids (RMGs). The mid-market rate mechanism is adopted to produce local market price signals at RMG level. A robust rolling horizon controller is developed for real-time energy management of a community of ABs. This control philosophy can improve the robustness of the RMG in face of real-time weather and energy price prediction errors. The proposed method is a multi-level optimisation which pursues multiple goals while making a trade-off between operational cost and occupant comfort. Finally, the repercussions of COVID-19 induced power consumption resulting from changing lifestyle and building occupancy profile is analysed by the proposed method as a case study. The results show that the proposed B2B and B4G strategy can reduce energy bills by 18.45%, while notable robust real-time control and computational efficiencies are achieved when benchmarked against conventional methods.

Economic real-time energy trading services for electric vehicles with uncertain mobility demand

Real-time energy trading services have recently been proposed to facilitate the transition from vehicles with combustion engines to e-vehicles. Such services involve e-vehicle owners and a provider of energy trading skills, where the latter manages e-vehicle (dis-)charging at real-time energy prices. We propose and evaluate a data-driven optimization approach for the operational management of services that address e-vehicle owners with uncertain mobility demand and with a solar generator. We formulate the management problem as a sequential decision problem, and propose to solve it by integrating a lookahead policy with a safety energy buffering approach. We study by computer simulation the economic sustainability and the practical viability of the services under different degrees of mobility demand uncertainty, and for different e-vehicle owner types. We assess the negative impact of the uncertainty on both financial value and mobility demand satisfaction of the services. We show that our optimization approach with time-dependent energy buffering enables high mobility demand satisfaction while achieving, even in the case of extreme mobility demand uncertainty, on average at least 92% of the financial value that can be achieved under quasi-deterministic mobility demand. We show that combining our approach with departure time flexibility is sufficient to reach perfect mobility demand satisfaction and a further increase of the financial value.

Energy trading efficiency in the US Midcontinent electricity markets

Efficient trading under wholesale market competition reduces an electric grid’s energy costs for meeting time- and location-dependent demands. We analyse energy trading efficiency by estimating three newly developed sets of energy price difference regressions interconnected by their common root of energy price level regressions. Using a sample of ~ 0.6 million hourly observations for 01/01/2014 to 10/31/2020, our estimation documents energy trading efficiency of the 10 local resource zones across 15 American states administered by the Midcontinent Independent System Operator (MISO). We find MISO’s zonal energy markets integrated across space (zone j vs. zone k for j ≠ k) and time (day-ahead market vs. real-time market). However, these markets exhibit inter-day energy prices differences that move with the fundamental drivers (e.g., day-ahead forecasts for natural gas price and zonal wind generation) of day-ahead energy prices and their forecast errors. Inter-zonal day-ahead energy price differences move with the fundamental drivers and their zonal variations. Inter-zonal real-time energy price differences increase with inter-zonal day-ahead energy price differences and depend on zonal variations of the fundamental drivers’ forecast errors. Our empirics yield two important policy implications. First, enhancing inter-day trading efficiency requires accuracy improvements in (a) day-ahead forecasts for natural gas price, zonal load levels, and zonal wind generation, and (b) day-ahead scheduling of zonal nuclear and must-run generation. Second, improving inter-zonal trading efficiency requires mitigating inter-zonal transmission congestion via transmission capacity expansion, generation investment and demand reduction in a load pocket, and virtual bidding for inter-zonal energy price differences.

Optimal Planning Design of a District-Level Integrated Energy System Considering the Impacts of Multi-Dimensional Uncertainties: A Multi-Objective Interval Optimization Method

Improving the utilization efficiency of renewable energy sources (RES) is an important task for the development of an integrated energy system (IES). To address this challenge, this paper proposes a novel multi-objective interval optimization framework for the energy hub (EH) planning problem from the perspective of the source load synergy, while considering the impacts of both supply- and demand-side uncertainties. For this aim, based on an in-depth analysis of the adjustable characteristics of various loads in EH and their effect on RES absorption, an interval model is first established to describe the responsiveness of users’ load demand to real-time energy price variations and its associated uncertainties. In view of the natural contradiction between the system’s economic and environmental benefits, a multi-objective interval optimization model for the EH planning problem is developed, wherein the minimization of the system’s economic costs and the maximization of the RES utilization rate are considered as the dual objectives to be optimized simultaneously. Moreover, this study takes into account the uncertainties of RES availability and demand-side behaviors by using interval numbers and properly considering their impacts in the context of long-term planning. According to the features of the proposed model, the interval order relation and possible degree method are jointly used to transform the model into a deterministic optimization problem first, and then an improved non-dominant sorting genetic algorithm is used to derive the optimal solution to the problem. The results show that the proposed method can effectively improve the economy of EH and the utilization efficiency of RES and flexibly meet different planning requirements, giving better engineering practicability.

Machine learning and price-based load scheduling for an optimal IoT control in the smart and frugal home

We pose and study a scheduling problem for an electric load to develop an Internet of Things (IoT) control system for power appliances, which takes advantage of real-time dynamic energy pricing. Using historical pricing data from a large U.S. power supplier, we study and compare several dynamic scheduling policies, which can be implemented in a smart home to activate a major appliance (dishwasher, washing machine, clothes dryer) at an optimal time of the day, to minimize electricity costs. We formulate our scheduling task as a supervised machine learning classification problem which activates the load during one of two preferred time bins. The features used in the machine learning problem are hourly market, spot and day-ahead prices along with delayed label of the prior day. We find that boosting tree-based algorithms outperform any other classification approach with measurable reduction of energy costs over certain types of naive and static policies. We observe that the delayed label has most predictive power across features, followed, on average, by spot, hourly market, and day-ahead energy prices. We further discuss implementation issues using a micro controller system coupled with cloud-based serverless computing and dynamic data storage. Our test system includes an interactive voice interface via an intelligent personal assistant.

Assessing the performance of uncertainty-aware transactive controls for building thermal energy storage systems

Energy storage systems provide a wide range of technological approaches to manage the balance between energy supply and demand in the electric grid. With the increasing uncertainty and variability that comes with wide-spread adoption of grid-scale and behind-the-meter renewable energy, it is imperative to develop stochastic operational planning and control approaches that can account for uncertainty in future conditions. Although, coordination of multiple thermal energy storage resources can support the transition to low carbon energy by enabling valuable system flexibility, few stochastic planning and control approaches have been developed for coordinating building-level thermal energy storage resources. In addition, there is also a need to analyze the potential benefits of an aggregator-level stochastic control framework versus applying stochastic planning and controls at each building individually. This work addresses these needs by developing an uncertainty-aware transactive control (UA-Tx) framework for an aggregator to coordinate the thermal energy storage (TES) assets of multiple buildings. A two-stage stochastic optimization framework is formulated for day-ahead energy procurement that considers uncertainty in building occupancy patterns, weather conditions, and real-time energy prices of the following day. In the second stage, possible recourse decisions through modifying TES operation are also considered. The dispatch of TES operational strategies is implemented through transactive controls, which use market mechanisms and customer preferences to achieve changes in building demand. During real-time operation, a local demand response aggregator determines the transactive clearing prices to dispatch the flexibility enabled by TES. Simulation case studies were conducted to demonstrate the capabilities of the uncertainty-aware aggregator control framework compared to the performance of applying intelligent controllers at each individual building. Up to 3.7% energy cost savings were observed for buildings under the UA-Tx aggregator control framework. Other potential benefits of the control approach are also discussed, along with anticipated future extensions.

QoS and power network stability aware simultaneous optimization of data center revenue and expenses

Data center profits are directly impacted by electric power consumption, which in turn has critical environmental implications. Geo distributed data centers maximize profits by optimizing resource allocation and leveraging diverse power tariffs available in a deregulated market. However, a power network state apathetic profit maximization can destabilize the grid and hamper a data center's sustainability goals. In this paper, we formulate the data center profit maximization as a constrained optimization problem. We then propose a multi-level algorithm where the lower level scheme is based on evolutionary optimization. The algorithm simultaneously optimizes revenue and expenses while preserving QoS and power network stability. The proposed approach considers real-time demand-based energy price variations to orchestrate request routing and resource allocation. The approach is suitable for heterogeneous and homogeneous data center architectures. The proposed scheme is also thermal-aware and considers both computing and cooling consumption. Simulation results show that the proposed technique is effective; it achieves a higher profit over a broad range of price variations and data center utilization levels.

Development of Home Energy Management Scheme for a Smart Grid Community

The steady increase in energy demand for residential consumers requires an efficient energy management scheme. Utility organizations encourage household applicants to engage in residential energy management (REM) system. The utility’s primary goal is to reduce system peak load demand while consumer intends to reduce electricity bills. The benefits of REM can be enhanced with renewable energy sources (RESs), backup battery storage system (BBSS), and optimal power-sharing strategies. This paper aims to reduce energy usages and monetary cost for smart grid communities with an efficient home energy management scheme (HEMS). Normally, the residential consumer deals with numerous smart home appliances that have various operating time priorities depending on consumer preferences. In this paper, a cost-efficient power-sharing technique is developed which works based on priorities of appliances’ operating time. The home appliances are sorted on priority basis and the BBSS are charged and discharged based on the energy availability within the smart grid communities and real time energy pricing. The benefits of optimal power-sharing techniques with the RESs and BBSS are analyzed by taking three different scenarios which are simulated by C++ software package. Extensive case studies are carried out to validate the effectiveness of the proposed energy management scheme. It is demonstrated that the proposed method can save energy and reduce electricity cost up to 35% and 45% compared to the existing methods.

Advanced bidding strategy for participation of energy storage systems in joint energy and flexible ramping product market

Recently, power system operators have initiated procurement of a new service in electricity markets named flexible ramping product (FRP). With the main goal of enhancing the grid flexibility, this product can provide a remarkable opportunity for an enhanced short-term profitability. Energy storage systems (ESSs) with high ramping capability can leverage their profitability when properly participating in this market. This study introduces a stochastic optimisation framework for participation of ESSs in the FRP market. The proposed model formulates the optimal bidding strategy of ESSs considering the real-time energy, flexible ramp-up and ramp-down marginal price signals and the associated uncertainties. In addition, as the market participants cannot directly submit bids for the FRP, the corresponding energy bidding adjustments required to award the proper FRP amounts are elaborated. The mathematical model is linearised and its application in real-time market is investigated. The proposed framework is numerically analysed through which its effectiveness on enhancing the ESS profitability in the real-time electricity markets is verified.

A risk-constrained decision support tool for EV aggregators participating in energy and frequency regulation markets

The growing trend of electric vehicles (EVs) in recent years has led to the emergence of EV aggregators in electricity markets. Generally, the main goal of an EV aggregator is to buy electricity from the wholesale market in a cost-effective manner while satisfying the charging requirements of EV owners. Accordingly, this paper presents a decision support tool for EV aggregators which enables them to determine the optimal bidding strategy to effectively participate in the day-ahead and real-time energy, and frequency regulation markets. Indeed, the aggregator mainly obtains profit by selling energy during the high-price hours (via vehicle-to-grid (V2G) capability) and providing primary frequency regulation service to the system operator. The proposed approach is based on a two-stage stochastic programming method, where risk aversion is modeled through the conditional value-at-risk (CVaR). The underlying uncertainties including the real-time energy prices, real-time regulation service deployments, and the uncertainties associated with the EV owners (i.e., arrival time, departure time, and initial battery state-of-charge (SOC)) are modeled as stochastic processes that are represented by different sets of scenarios. The cardinality of the combined scenario set is reduced using backward probability distance algorithm to make the resulting mixed-integer linear programming (MILP) problem tractable in large-scale and real-world cases. Extensive numerical analysis with one thousand EVs and real-world market data are conducted to validate the efficiency of the proposed approach in terms of solution optimality, robustness, and computation efficiency.