Minimum Operating Cost Research Articles

Flexible resource allocation optimization model considering global K-means load clustering and renewable-energy consumption

Abstract Vigorously developing flexible resources in power systems will be the key to building a new power system and realizing energy transformation. The investment construction cost and operation cost of various flexible resources are different, and the adjustment ability is different in different timescales. Therefore, the optimization of complementary allocation of various resources needs to take into account the economy and adjustment ability of different resources. In this paper, the global K-means load clustering model is proposed and the 365-day net load is reduced to eight typical daily net loads by clustering. Secondly, a two-level optimization model of flexible resource complementary allocation considering wind power and photovoltaic consumption is constructed. The flexible resources involved include the flexible transformation of thermal power, hydropower, pumped storage, energy storage, and demand response. The upper-layer model optimizes the capacity allocation of various flexible resources with the minimum investment and construction cost as the goal and the lower layer optimizes the operating output of various units with the minimum operating cost as the goal. The results of the example analysis show that the flexible capacity of thermal power units has nothing to do with the abandonment rate of renewable energy. As the abandonment rate of renewable energy decreases, the optimal capacity of pumped storage, electrochemical energy storage, and hydropower units increases. When the power-abandonment rate of renewable energy is 5%, the optimal allocation capacity of thermal power flexibility transformation, pumped storage, electrochemical energy storage, hydropower unit, and adjustable load in Province A is 5313, 17 090, 5830, 72 113, and 4250 MW, respectively. Under the condition that the renewable-energy abandonment rate is 0, 5%, and 10% respectively, the configured capacity of pumped storage is 20 000, 17 090, and 14 847 MW, respectively.

Optimized energy management for interconnected networked microgrids: A hybrid NEGCN-PFOA approach with demand response and marginal pricing

This manuscript proposes a hybrid approach for operating cost reduction in networked microgrids. The proposed hybrid system is the combined performance of both the Neighbour Enhanced Graph Convolutional Networks (NEGCN) and the Piranha Foraging Optimization Algorithm (PFOA). Commonly it is named as NEGCN-PFOA technique. The primary goal of the proposed strategy is operating cost minimization in networked micro grids. The NEGCN is used for the demand prediction in networked microgrids and the PFOA is used for the operating cost optimization of networked microgrids. Moreover, the result of the system critic behaviour is researched, where the critic is a function of the control range. By then, the proposed method has been included in the working MATLAB platform, and its execution is calculated using the existing procedures. Compared to all current approaches, the proposed technique yields better outcomes like Deep Reinforcement Learning, Long Short-Term Memory and Deep Learning Artificial Neural Network. The proposed method is useful in reducing the operating cost in the networked micro grids. From the outcome, it is concluded that the proposed technique based costs is less contrasted with existing methods.

Optimal configuration of hydrogen storage capacity of hybrid microgrid considering peak regulation and frequency modulation requirements

This study proposes an innovative hydrogen storage capacity optimization configuration method that considers multiple demand factors, addressing the issue that traditional methods for optimizing hydrogen storage capacity in hybrid microgrids cannot simultaneously balance economic efficiency and grid connection quality. This method breaks through the traditional optimization framework and adopts a double-layer optimization model, combining the peak shaving operation cost of the hybrid microgrid with the interactive power deviation and power fluctuation penalty terms of the interconnection line during the frequency regulation stage, achieving dual optimization of economy and grid connection quality. Through precise mathematical modeling and efficient optimization algorithms, we have successfully obtained the minimum operating cost corresponding to the minimum power fluctuation, the minimum interconnection line interactive power deviation penalty term, and the optimal hydrogen storage capacity configuration scheme. Identify two typical days through cluster analysis. Option 1 (considering peak shaving, frequency regulation, and hydrogen electrolysis) has the lowest net load and a total operating cost of 3.0331 million yuan, which is better than Option 2 (3.0973 million yuan) and Option 3 (5.0398 million yuan). This plan effectively reduces wind and solar power waste, shortens the operating time of thermal power units, and demonstrates the rationality and economy of optimizing hydrogen storage capacity configuration.

Operational optimization of demand management strategy for hybrid power system based on battery capacity fading characteristics

In the hybrid power system (HPS), taking battery capacity fading characteristics and demand management strategy (DMS) into consideration, an operational optimization method is developed in this work. From the energy utilization and economic perspectives, the minimum total renewable energy curtailment rate (TCR), minimum total outsourced electricity (TOE) from the grid and minimum total operating cost (TOC) are respectively taken as the optimization objectives. The corresponding mathematical models of the proposed method are established, which feature mixed integer nonlinear programming (MINLP) ones. A case study of a solar-wind-biomass-battery HPS is adopted to verify and illustrate the application and effectiveness of this proposed method. Results show that the optimal operating schemes and the DMSs of the HPS based on battery capacity fading characteristics can be determined by minimizing the TCR, TOE and TOC. The target values of TOE and TOC of the HPS with adopting DMS are 15,995.3 kWh and 18,112.1 $, which are about 70 % these of the HPS without DMS. Furthermore, the relationships between battery capacity fading characteristics and DMS are comprehensively investigated in this operational optimization of the HPS. Finally, the effects of different battery types, outsourced electricity price changes on the operation of the HPS are analyzed and discussed. This work provides a valuable method for the operational optimization of the HPS.

Optimized removal of silica during manure treatment by electrocoagulation-flotation (EC-F) in view of fouling prevention of reverse osmosis membranes

Reverse osmosis (RO) membrane fouling threatens the performance of manure treatment. In this regard, silica is considered one of the most challenging inorganic foulants. Removing silica fouling from RO membranes is difficult, ultimately leading to performance deterioration, including reduced permeability and premature membrane failure. This study examines the removal of silica during manure treatment using a novel tubular electrocoagulation-flotation (EC-F) reactor with an Al electrode. The EC-F was positioned between an ultrafiltration and a RO membrane filtration system. The operational parameters—current density, electrolysis residence time, and initial pH—were optimized for maximum silica removal efficiency and minimum operational cost. At the optimum conditions (pH of 8.2, current density of 160 A/m2 and electrolysis residence time of 23 s), 88 % of silica (initial concentration of 104 mg/L) was removed. Subsequent membrane fouling assessment revealed that EC-F pretreatment decreased the fouling potential by 28 % (from 7.11 × 1016 to 5.10 × 1016 Pa·s/m2·t), indicating efficient foulant removal. SEM-EDX analysis of the membrane confirmed the lack of scale formation when using EC-F pretreated manure as a feed stream. This study demonstrates that the use of innovative EC-F pretreatment significantly reduces the operational expenditure (1.75 €/m3) compared to prior EC-F research for silica removal from manure, thereby reducing the fouling of RO membranes.

Energy management in integrated energy system with electric vehicles as mobile energy storage: An approach using bi-level deep reinforcement learning

The integrated energy system with electric vehicle charging station via vehicle-to-grid aims to offer a proactive solution for low-carbon development of both energy and transportation sectors. However, achieving optimal energy efficiency with minimal operational costs in such a complex system is challenging due to the high randomness of electric vehicle travel patterns. This work proposes a reinforcement learning-based energy management framework to optimize the coordinated scheduling of integrated energy and vehicle-to-grid. The problem is modeled as a Markov Decision Process and optimized using the bi-level soft actor-critic algorithm, where the upper-level agent supervises the scheduling of the integrated energy system, and lower-level agent sets the electric vehicles’ charging and discharging strategies based on upper-level decision. Numerical simulations demonstrated that by adopting a bi-level reinforcement learning approach, the proposed algorithm effectively enhances energy exchange between integrated energy and electric vehicle charging station, reducing operational costs by 8 % compared to other multi-agent algorithms. Furthermore, when compared to the Mixed-Integer Linear Programming model, the proposed algorithm achieves similar optimality with significantly less computation time, maintaining a margin of error of approximately 4 %. Additionally, integrating electric vehicles as mobile energy storage within this framework can lead to a further 10 % reduction in operating costs.

Multi-objective Bonobo optimisers of industrial low-density polyethylene reactor

Abstract A multi-objective optimization (MOO) technique to produce a low-density polyethylene (LDPE) is applied to address these two problems: increasing conversion and reducing operating cost (as the first optimization problem, P1) and increasing productivity and reducing operating cost (as the second optimization problem, P2). ASPEN Plus software was utilized for the model-based optimization by executing the MOO algorithm using the tubular reactor model. The multi-objective optimization of multi-objective Bonobo optimisers (MOBO-I, MOBO-II and MOBO-III) are utilised to solve the optimization problem. The performance matrices, including hypervolume, pure diversity, and distance, are used to decide on the best MOO method. An inequality constraint was introduced on the temperature of the reactor to prevent run-away. According to the findings of the study, the MOBO-II for Problems 1 and 2 was the most effective MOO strategy. The reason is that the solution set found represents the most accurate, diversified, and acceptable distribution points alongside the Pareto Front (PF) in terms of homogeneity. The minimum operating cost, the maximum conversion and productivity obtained by MOBO-II are Mil. RM/year 114.3, 31.45 %, Mil. RM/year 545.3, respectively.

Coordinated optimization of configuration and operation of a photovoltaic integrated building cooling system with electricity and ice storages under source-load uncertainties

Solar photovoltaic integration into buildings provides an effective and attractive method to decrease fossil energy consumption and reduce greenhouse gases emission. This study proposes a flexible photovoltaic integrated building cooling system with electricity and ice storages to address the challenges posed by the instability of solar energy and the integration and coordination of multiple components. Uncertainties in solar irradiance, ambient temperature, and cooling load are characterized using a scenario analysis method that combines Latin Hypercube Sampling and the K-Means++ algorithm. Then, aiming to achieve the minimal total cost, including investment, operational, and CO2 emission costs, a two-layer stochastic optimization model is developed to simultaneously determine the optimal capacities and operational strategies for each device. Genetic algorithm and mixed integer linear programming are, respectively, used to solve the two-layer optimization problem. The comparisons between optimum schemes with and without CO2 emission cost demonstrates that when the base chiller’s capacities are 1179 kW and 1081 kW in cases 1 and 2 respectively, it can independently meet 72.37 % and 61.27 % of the cooling load demand throughout the cooling season. In addition, the optimal capacity of photovoltaics, considering CO2 emission, increases by 109.7 %, and its penetration rate reaches 18.3 %, which is 9.7 % higher than the optimal scheme not considering CO2 emission. However, the annualized investment cost increases by 52.3 %. The developed methods provide effective tools for the system design and operation management of solar energy integrated building cooling system.

Towards optimal customized electricity pricing via iterative two-layer optimization for consumers and prosumers

Designing an electricity price mechanism that efficiently enables users to manage their self-production and consumption behavior to accommodate renewable energy and regulate peak load is a hard task with the emergence of prosumer with photovoltaic and energy storage. To address this issue, we propose an iterative two-layer optimization to investigate customized price of electricity for different types of users in the presence of photovoltaic uncertainty. By taking into account power flow restrictions, the model is used to explore the optimal time-of-use, demand, and on-grid prices for both electricity consumers and prosumers. The consumer and prosumer peak-flat-valley periods are initially divided in the upper layer. Then, a model for distribution system operator profit maximization is proposed to minimize operation cost, power loss, and peak–valley difference. A stochastic optimization model is presented in the lower layer for consumer and prosumer to hedge against the risk of uncertain photovoltaic with the aim of minimizing electricity tariff, demand tariff, and life cycle cost of energy storage. Numerical experiments conducted on modified 15-bus and 69-bus distribution systems with different types of users show the effectiveness of the iterative two-layer optimization for customized price of electricity in peak-shaving and valley-filling while ensuring the interests of distribution system operator and users. Results show that the total profit increases by more than 4% and the net load fluctuation variance reduces higher than 20% compared with the traditional pricing method.

An online cooperative control strategy for enhancing microgrid participation into electricity market

This paper develops a cooperative control methodology for the online energy management of grid-connected microgrids. The main aim of this methodology is to actively manage the active power outputs of all dispatchable energy sources available within the microgrid as well as the power exchanged with the utility grid so as to match the total load demand at the minimum operating cost. This implies to solve a constrained multi-objective dynamic optimization problem aimed at minimizing the total microgrid operating costs and ensuring the real-time balance within the microgrid in compliance with its technical-operational constraints. Lyapunov's theorem using sensitivity theory is adopted to solve this optimization.To test the performances of the proposed control methodology, several computer simulations corresponding to different operating scenarios have been conducted on the PrInCE Lab experimental microgrid built at the Polytechnic University of Bari.

A novel squirrel-cat optimization based optimal expansion planning for distribution system

AimIn recent years, renewable distributed generation (DG) has grown to deliver sustainable electricity with minimal environmental impact. However, renewable DG poses new provocation in the distribution system expansion planning problem (DSEP). To address those problems, this paper suggests a new mathematical model for distribution system expansion plans using a novel hybrid optimization strategy. MethodThe optimal expansion plan for the distribution system is achieved using the hybrid optimization model, named Squirrel Search Insisted Cat Swarm Optimization (SSI-CS) algorithm. The proposed hybrid optimization algorithm is developed with the incorporation of the characteristics features of Squirrel search optimization (SSA) algorithm and Cat Swarm Optimization (CSO) Algorithm to optimize the solar capacity, wind capacity and biomass capacity. This combination aims to strike a balance between global and local optimization, ultimately leading to better cost-effective results. The Distribution systems variables like DG type, size/capacity, location, real power, reactive power, and the solar and wind capacity during load demand uncertainty act as the input to the proposed hybrid optimization algorithm. The main objective of attaining minimal cost for the expansion plan of the distribution system is checked, and the cycle is repeated until obtaining the optimal solution (minimum cost). ResultThe experimental analysis using an IEEE-33 bus system with 5 system states is executed in MATLAB/Simulink. The suggested SSI-CS model attained a minimal operational cost of 7433.4 which better than GWO, SSA and CSO. ConclusionHence, the proposed SSI-CS shows promise as an efficient and effective approach for distribution system expansion planning.

تقييم أداء أنظمة ري مختلفة تعمل بالطاقة الشمسية وتأثيرها على إنتاجية الباقلاء (Vicia Faba…L)

An experiment was carried out at Al-Raed Research Station, which is located on the Baghdad-Anbar Road. It was conducted during the winter season of 2022-2023, in order to evaluate the performance of different solar irrigation systems and their effect on bean yield (Vicia faba… L). A randomized complete block design (RCBD) was used with three replications. The experiment consists of three factors. first factor was the solar panel type with two levels: mono-crystalline and poly-crystalline. Second factor was the irrigation system with two levels: drip and sprinkler irrigation system. The third factor was the distances between the sub-lines with three levels (40, 60, 80 cm). The results show that the monocrystalline achieved the best result by achieving the highest irrigation system efficiency (76.31%), and highest seeds yield total (6618 Kg/ha) with minimum operational costs (0.0252 $/KWh). The drip irrigation had the highest irrigation system efficiency (84.40%), and highest total seeds yield (6077 Kg/ha) with minimum operational costs (0.0340 $/ KWh). The distance (40cm) between the sublines had the highest irrigation system efficiency (76.83 %), with less operational costs (0.0398 $ / KWh).

Low-carbon operation of smart distribution grid based on life cycle assessment and ladder-type carbon trading

A large number of EVs are commonly added to peak loads without dispatch in the smart distribution grid system, and the grid system usually suffers from excessive carbon emission problems. This paper proposes an integrated approach to control the smart distribution grid system by utilizing life cycle assessment and the market mechanism. First, the system’s carbon emissions are estimated according to life cycle assessment and carbon flow theory. Then, a bi-level optimization strategy for a smart distribution grid is presented. The upper-layer operation object is the minimum comprehensive operation cost of the smart distribution grid, which is solved using an optimization algorithm. The lower-level optimization goal is to minimize the operating cost of electric vehicles, which is solved using the CPLEX toolkit. Our simulation results demonstrate that overall operating costs have been reduced by 71.11%, while SDG’s overall carbon emissions have been reduced by 49 kg. The low-carbon growth of the smart distribution grid may be successfully promoted by appropriate trading market scheduling and efficient low-carbon dispatching.

Intelligent Energy System and Power Metering Optimization Based on the Energy Plan Model

With the national carbon neutrality and carbon peaking policies proposed one after another, this paper proposes intelligent Energy system design and power metering based on the Energy Plan model. In this paper, the Energy PLAN model is proposed as the basic model for energy development planning during the 14th Five-Year Plan period, and the simulation calculation is carried out for the energy system in 2020. The research shows that there is a large gap between the peak and valley of power load, the peak time of power supply and demand does not match, and the response-ability of the energy supply department is poor. Thus, the problems to be solved in the development of energy are determined. In addition, the accuracy of the model is further verified by comparing the actual data with the simulation results of Energy PLAN, and the direction of energy structure reform is determined. By coupling the NSGA-II (Non-dominated Sorting Genetic Algorithms-II) algorithm with the development model, a dual-objective multi-time scale scheduling model is established, which aims at the minimum operating cost and the best energy and environmental benefit coefficient. Secondly, the proposed model is solved using the NSGA-II algorithm. In order to ensure the diversity of solutions and promote the Pareto front approach to the ideal Pareto front, the fuzzy dominance method is used to perform a fast non-dominated sorting of the population, and the maximum satisfaction method is used to select the Pareto optimal compromise solution. Example analysis shows that when the power demand level is L*-L*-L*, the power input under “H-M”, “M-L” and “H-L” scenarios is 106.02 × 103, 102.73 × 103 and 94.2 × 103 GWh, respectively. However, when the power demand level is H*-L*-L*, the power input is always 142.64 × 103 GWh. With the decrease in the transmission rate, the measurement data obtained by the user’s electric acquisition platform becomes less and less, and the performance of state estimation becomes worse. When λ=50%, the proposed model still maintains a high estimation accuracy.

Minimization of total operational cost & voltage deviation in grid-connected unbalanced MGs using optimization approach

Minimization of total operational cost & voltage deviation in grid-connected unbalanced MGs using optimization approach

Optimization of Triple Effect Vapour Absorption Refrigeration System: A Statistical Approach

Abstract The present manuscript optimized the First and Second Law performance of the triple effect vapour absorption refrigeration systems (TE-VARS) using statistical techniques like Taguchi, Taguchi-based GRA, and RSM-based GRA methods, which provide the most accurate and optimized results. Liquified pertrolium gas (LPG) and Compressed natural gas (CNG) are considered as the source of energy to operate TE-VARS, as the system requires significantly higher generator temperature. Also, volume flow rate of these gases along with the annual operating cost to drive the system have been presented. A thermodynamic model was first formulated using EES software for the computation of the coefficient of performance (COP) and exergetic efficiency (ECOP). The most influential parameters like temperature in the main generator, concentration and pressure at different components are studied and determined using ANOVA and Taguchi methods. The optimum parameters were determined based on the mean effect plot of S/N ratios for COP and ECOP. It has been found that the maximum COP and ECOP were calculated to be 1.915 and 0.15, respectively under the Taguchi method. Furthermore, Taguchi-GRA was used for the simultaneous optimization of the operating parameters and performance of the system. It is observed that the absorber temperature is the most influential parameter for affecting COP and ECOP. Moreover, a RSM-based GRA method was also applied and developed regression models that yield most optimum COP and ECOP as 1.963 and 0.1606, respectively. Comparison shows that the RSM-based GRA method provide the most optimum conditions, which is one of the key finding of the present study. Also, rate of exergy destruction at each component of TE-VARS has been plotted under optimized operating conditions. The optimum volume flow rate for LPG and CNG comes out to be 0.057 and 0.177 m3/s, while the minimum operating cost (yearly) are 299.827$ and 183.293$, respectively.

Optimization of multi-integrated energy microgrid scheduling under carbon trading mechanism

Abstract Realizing the power transaction and benefit distribution among multi-integrated energy microgrids with different interests in the system, a multi-microgrid cooperative operation optimization scheduling method under a carbon-trading mechanism is proposed. Considering the microgrid’s electric energy interaction, a model of multi-microgrid cooperation is established. The multi-microgrid cooperative game model is equivalently transformed into two sub-problems, multi-microgrid cooperative operation cost minimization and internal power transaction bargaining, and to solve the two sub-problems successively. The simulation results show that the method is valid.

Bi-objective optimization for last-mile routing of garbage trucks: Aesthetics and Public exposure.

In the area of Solid Waste Management, transportation of the collected waste is a critical aspect considering the substantial time spent by garbage trucks on public roads. Studies have reported that transporting garbage has challenges related to public exposure and aesthetics. This study presents a generalised bi-objective formulation for the optimal routing of garbage trucks from transfer stations to recycling sites/landfills considering the trade-off between public exposure and aesthetic loss and constraining the operating cost. The formulation uses the novel link capacity function to account for the delay at traffic signals and the mix of trucks and cars on link performance. The proposed formulation is solved using the weighted sum and ε-constraint methods and applied to a realistic case study of the City of Chicago, USA. The Pareto Front obtained for the bi-objective formulation offers diverse trade-off solutions catering to distinct performance metrics. The results highlight the disparity across the solutions; the solution (P0.95 on Pareto Front) for minimum operating cost (or travel time or distance travelled) is very different from the solution (P0.4 on Pareto Front) for aesthetic cost and public exposure. The parametric study indicated that a modest operating budget may suffice for achieving aesthetic benefits, but minimising public exposure requires a higher operating budget. Finally, the proposed framework is adaptable to address various challenges pertaining to waste transportation, thereby serving as a valuable tool for evaluating policies and practices geared towards sustainability objectives.

Day-ahead resilience-economic energy management and feeder reconfiguration of a CCHP-based microgrid, considering flexibility of supply

Many challenges have emerged due to the intense integration of renewables in the distribution system and the associated uncertainties in power generation. Consequently, local management strategies are developed at the distribution level, leading to the emergence of concepts such as microgrids. Microgrids include a variety of heating, cooling, and electrical resources and loads, and the operators' aim is to minimize operation and outage costs. Since significant distribution system outages are typically caused by events such as earthquakes, floods, and hurricanes, microgrid operators are compelled to improve resilience to ensure uninterrupted service during such conditions. A mixed-integer linear programming model is designed in this paper to optimize the energy management and structural configuration of microgrids. This optimization aims to enhance resilience cost, minimizing operation and capital costs as well as power loss and pollution. To achieve these goals, several tools are implemented including reconfiguration, storages, combined cooling, heat and power units, wind turbines, photovoltaic panels, as well as capacitors. Four case studies are defined to prove the developed model efficiency. The first case study focuses on energy management in the microgrid for operation cost minimization. The second case study emphasizes the improvement of resilience alongside energy management, aiming at minimizing costs and enhance resilience. In the third case, the microgrid's reconfiguration capability is also added to the second case. Therefore, this case aims to optimize both energy and structural management within the microgrid to simultaneously enhance resilience and minimize operational costs. Finally, in the fourth case, the problem is studied in a multi-objective approach. By comparing the results, the resilience impact on the operation of microgrids is elucidated. By considering the resilience concept in microgrid operation and based on the results of case 2, it is found that the operating costs are increased by an average of 10.38 %. However, because of reducing resilience costs by an average of 13.91 %, the total cost is reduced by an average of 5.93 % in case 2 compared to case 1. Furthermore, when comparing cases 2 and 3, the reconfiguration effect can be determined. It can be observed that the operating costs are decreased by an average of 4.5 %. Moreover, the resilience cost is decreased by an average of 1.61 %, resulting in an overall reduction of the total objective function by an average of 2.43 % in case 3 compared to case 2.

Multi-Regional Integrated Energy Economic Dispatch Considering Renewable Energy Uncertainty and Electric Vehicle Charging Demand Based on Dynamic Robust Optimization

Aiming at the problem of source-load uncertainty caused by the increasing penetration of renewable energy and the large-scale integration of electric vehicles (EVs) into modern power system, a robust optimal operation scheduling algorithm for regional integrated energy systems (RIESs) with such uncertain situations is urgently needed. Based on this background, aiming at the problem of the irregular charging demand of EV, this paper first proposes an EV charging demand model based on the trip chain theory. Secondly, a multi-RIES optimization operation model including a shared energy storage station (SESS) and integrated demand response (IDR) is established. Aiming at the uncertainty problem of renewable energy, this paper transforms this kind of problem into a dynamic robust optimization with time-varying parameters and proposes an improved robust optimization over time (ROOT) algorithm based on the scenario method and establishes an optimal scheduling mode with the minimum daily operation cost of a multi-regional integrated energy system. Finally, the proposed uncertainty analysis method is verified by an example of multi-RIES. The simulation results show that in the case of the improved ROOT proposed in this paper to solve the robust solution of renewable energy, compared with the traditional charging load demand that regards the EVs as a whole, the EV charging load demand based on the trip chain can reduce the cost of EV charging by 3.5% and the operating cost of the multi-RIES by 11.7%. With the increasing number of EVs, the choice of the starting point of the future EV trip chain is more variable, and the choice of charging methods is more abundant. Therefore, modeling the charging demand of EVs under more complex trip chains is the work that needs to be studied in the future.