Optimal Scheduling Research Articles

Study on two‐stage optimal scheduling of DC distribution networks considering flexible load response

AbstractDue to the aim of developing sustainable energy systems, promoting the large‐scale accommodation of distributed renewable energy sources (DRESs) and flexible loads in DC distribution networks (DCDNs) is significant. The uncertainty of DRESs and the insufficient use of flexible loads pose a considerable challenge to the economical and safe operation of DCDNs. To address the challenge, this paper puts forward a two‐stage optimal scheduling model for the DCDNs considering flexible load response. The proposed model realises joint economic optimisation and reactive power optimisation, which is solved by the hybrid NSGAII‐MOPSO algorithm and the CPLEX. The performance of the proposed model in the modified Institute of Electrical and Electronics Engineers 33‐node system with the DCDNs is validated under different scenarios. The hybrid NSGAII‐MOPSO performs better in obtaining the Pareto front than the NSGA‐II and MOPSO individually. Compared to the traditional scheduling model, the proposed model can realise the power coordination of the flexible loads and energy storage systems to reduce the negative impact of uncertainty of DRESs while decreasing operating costs and carbon emissions by 3.94% and 36.4%. In addition, the proposed model can alleviate the network losses and ensure the node voltage for the DCDNs. Hence, the efficiency of the proposed model has been confirmed.

Truck Transportation Scheduling for a New Transport Mode of Battery-Swapping Trucks in Open-Pit Mines

To address the scheduling challenges associated with the increasing deployment of battery-swapping trucks in open-pit mines, this study proposes a multi-objective scheduling optimization model. This model accounts for the unique characteristics of battery-swapping trucks by incorporating constraints related to battery swapping alerts, the selection of battery-swapping stations, and the impact of ambient temperature on battery capacity. The primary objective is to minimize the total haulage cost and total waiting time. Both a genetic algorithm and an adaptive genetic algorithm are applied to solve the proposed multi-objective scheduling optimization model. The aim is to identify an optimal scheduling solution without violating any model constraints. Results demonstrate that both the basic genetic algorithm and the adaptive genetic algorithm effectively achieve truck transportation scheduling. However, the adaptive genetic algorithm surpasses the basic genetic algorithm, reducing the total transportation costs by 5.6% and total waiting time by 17.4%. It also reduces the number of battery swaps and transportation distance by 15.8% and 1.2%, respectively. The proposed multi-objective scheduling optimization model successfully minimizes the waiting time and transportation costs of battery-swapping trucks while ensuring the completion of production tasks. This approach provides valuable technical support for improving the production and transportation efficiency of open-pit mining operations.

Multi‐timescale optimal scheduling of microgrids for generating new energy output scenarios based on correction error sampling intervals

AbstractMicrogrid can realize energy saving and emission reduction and multi‐energy complementation, but the fluctuation of renewable energy output and the error of day‐ahead scheduling will threaten the stability of microgrid operation. For this reason, this article proposes a microgrid multi‐timescale optimal scheduling method based on new energy output scenario generation. First, the microgrid framework of this article is introduced, and an energy cycle emission reduction model taking into account electricity‐to‐gas conversion is designed; second, a new energy prediction error model is established based on the prediction box and Gaussian hybrid model, and the scenario of wind and photovoltaic power generation is generated by correcting the sampling intervals for error sampling; and then, based on the day‐ahead scheduling plan, an intraday cooling, heating and electricity two‐layer rolling optimization model is established to correct the day‐ahead scenario. Finally, the example analysis shows that the cyclic emission reduction model can realize the recycling of resources, reduce the fuel cost and carbon emission, and the generation of scenarios for wind power can smooth out the fluctuation of new energy power, which, together with the intra‐day two‐layer rolling optimization, can reduce the day‐ahead scheduling error and improve the stability of microgrid operation.

Optimization of emission scheduling in microgrids with electric vehicle integration

In the context of the continuous development of new energy vehicles, an increasing number of electric vehicles (EVs) are being integrated into microgrids, which impacts the operation of microgrids. It is necessary to analyze the emission scheduling of microgrids connected with EVs to ensure the smooth and reliable operation of microgrids with EV integration. This paper aims to realize optimal microgrid scheduling. This article took the case of EV connection with microgrids through orderly charging and discharging. Firstly, mathematical models for each output unit in the microgrid were established. Then, aiming to minimize both the operational cost and pollution emission treatment cost of the microgrid, an emission dispatch optimization model was developed. The whale optimization algorithm (WOA) was chosen as the solving algorithm, and an improved WOA (IWOA) was obtained by optimizing the original WOA in terms of population initialization and position updating parameters. An example analysis revealed that the IWOA demonstrated superior optimization performance compared to other optimization algorithms. In the scenario of orderly charging and discharging, the EVs discharged during peak hours and charged during off-peak hours to balance the microgrid load. The operating cost obtained through the IWOA was 967.25 yuan, and the pollution emission treatment cost was 241.52 yuan, resulting in a total cost of 1208.77 yuan. These results confirm the reliability of the proposed IWOA in solving the model and its applicability in optimizing microgrids with EV integration.

Energy-efficient time and cost constraint scheduling algorithm using improved multi-objective differential evolution in fog computing

The recent surge in Internet of Things (IoT) applications and smart devices has led to a substantial rise in the data generation. One of the major issues involved is to meet strict quality of service (QoS) requirements for computing these applications in terms of execution time, cost and in an energy-efficient manner. To extract useful information, fast processing and analysis of data is needed. Consequently, moving all the data to centralized cloud data centers would lead to high processing times, increased cost and energy consumption and more bandwidth usage; thus, processing of applications with strict latency requirements becomes challenging. The addition of fog layer between cloud and IoT devices has provided promising solutions to such issues. However, efficient employment of computing resources in the hybrid infrastructure of fog and cloud nodes is of great significance and demands an optimal scheduling strategy. Toward this direction, a novel Pareto-based algorithm in fog computing, namely energy-efficient time and cost (ETC) constraint scheduling algorithm, is introduced in this paper for scheduling workflow applications. ETC attempts to optimize monetary cost along with time and energy objectives. Improved multi-objective differential evolution (I-MODE) meta-heuristic is introduced and incorporated with deadline-aware stepwise frequency scaling approach that is based on our previously proposed energy makespan multi-objective optimization (EM-MOO) algorithm. Synthetic and real-world application workflows are used to conduct evaluation of the proposed work with existing well-known algorithms from the literature. The experimental results for synthetic workflows reveal that the proposed algorithm lessens energy utilization by 14–21%, execution time by almost 25% and cost consumption by 22–27%, while for real-world application workflows, energy consumption is reduced by 12–24%, execution time by 14–16% and cost consumption by 23–29%.

Capacity Optimization of Wind–Solar–Storage Multi-Power Microgrid Based on Two-Layer Model and an Improved Snake Optimization Algorithm

A two-layer optimization model and an improved snake optimization algorithm (ISOA) are proposed to solve the capacity optimization problem of wind–solar–storage multi-power microgrids in the whole life cycle. In the upper optimization model, the wind–solar–storage capacity optimization model is established. It takes wind–solar power supply and storage capacity as decision variables and the construction cost of the whole life cycle as the objective function. At the lower level, the optimal scheduling model is established, considering the output characteristics of various types of power supplies and energy storage, microgrid sales, and purchases of power as constraints. At the same time, the model considers constraints, such as the power balance, the operating state of the energy storage system, the power sales and purchases, and the network fluctuations, to ensure the system operates efficiently. Taking a microgrid in South China as an application scenario, the model is solved and the optimal capacity allocation scheme of the microgrid is obtained. Meanwhile, the demand response mechanism and the influence of planning years are introduced to further optimize the configuration scheme, and the impact of different rigid–flexible load ratios and various planning horizons on microgrid capacity optimization is analyzed, respectively, by a numerical example. The comparison shows that the ISOA has better optimization performance in solving the proposed two-layer model.

Low-Carbon Optimization Scheduling of Integrated Energy Systems Based on Bilateral Demand Response and Two-Level Stackelberg Game

In the context of low-carbon energy transformation, fully utilizing the integrated demand response (IDR) resources on the load side can improve the operational flexibility and economy of the integrated energy system (IES). However, establishing a reasonable trading mechanism to enhance users’ participation in IDR has become a key issue that IES urgently needs to solve. To this end, this paper first establishes an IES model that includes electricity, heat, and gas. To reduce carbon emissions, a ladder-type carbon trading mechanism is introduced while adding low-carbon technologies such as carbon capture devices and power-to-gas conversion. Secondly, a bilateral IDR mechanism centered on the load aggregator (LA) is proposed, and a multi-agent operation model including IES, LA, and users is established. The IDR subsidy price is dynamically determined through a two-level Stackelberg game model involving IES, LA, and users. Then, through KKT conditions and the Big M method, the two-level game model is turned into an IES-LA game model, which is solved using a combination of the White Shark Optimization method and the Gurobi solver. The final simulation results show that the scheduling model can fully reflect the time value of IDR resources, and the IES cost is decreased by USD 152.22, while LA and user benefits are increased by USD 54.61 and USD 31.85. Meanwhile, the ladder-type carbon trading mechanism and low-carbon technology have effectively achieved low-carbon operation of the system.

Zero-carbon-oriented optimal power scheduling of electric vehicles considering V2G response

Abstract This paper presents an electric vehicle (EV) optimization scheduling method that incorporates vehicle-to-grid (V2G) responses within the framework of a carbon market. Initially, the method characterizes the grid-connected and off-grid operational states of EVs. These states are represented by three types of probability density functions derived from historical data. Subsequently, a V2G response model is formulated based on consumer psychology theory. The approach then integrates the impact of carbon trading on the charging and discharging schedules of EVs, aiming to minimize carbon trading costs. The resulting optimization scheduling model is solved using the CPLEX solver.

On Optimal Scheduling

We consider a decision-maker sequentially choosing among alternatives when periodic payoffs depend on both chosen and unchosen alternatives in that period. We show that when flow payoffs are the sum or product of payoffs from chosen and unchosen alternatives, the optimal policy is an index policy. We characterize key properties of the optimal dynamics and present an algorithm for computing the indices explicitly. Furthermore, we use the results to generalize Weitzman’s (1979) classic “Pandora’s boxes” problem to allow for complementarities. We illustrate the framework’s usefulness through applications, including decision problems with disappearing alternatives, repeated bargaining, dynamic supervision, and dynamic occupational choice. (JEL C78, D82, M11)

Optimal scheduling of distributed generation in smart microgrids: A comprehensive model and efficient algorithm

Abstract This study proposes an optimal scheduling model for distributed generation (DG) within smart microgrids, incorporating various distributed energy resources (DERs) such as photovoltaic panels, wind turbines, biomass generators, and energy storage systems. To address the complexities of the scheduling problem, we design a hybrid optimization algorithm combining Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). This hybrid algorithm leverages the global search capabilities of GA and the local search efficiency of PSO to achieve robust and efficient convergence to near-optimal solutions. A comprehensive case study based on a real-world smart microgrid system demonstrates the effectiveness of the proposed model and algorithm. The results indicate significant reductions in total operational costs, enhanced renewable energy utilization, reduced grid dependency, and improved system reliability. This research highlights the potential for broader implementation of the model, contributing to the advancement of smart grid technologies and the transition towards sustainable energy systems.

Muti‐units day‐ahead scheduling involving the pumped storages and considering deep‐load regulation

AbstractThis paper presents a day‐ahead scheduling for multi‐energy entities. The deep load regulation involving pumped storages, which refers to deep peak regulation, is adopted to address the impact of wind power and photovoltaic (PV) uncertainties, thereby improving the economic efficiencies of day‐ahead dispatching. And the impact of different peak valley electricity price differences on the peak shaving effectiveness of pumped storage energy was studied. Firstly, the multi‐scenario random programming method is applied to solve the prediction uncertainties of wind power and PV output in the day‐ahead. Subsequently, the multi‐scenario set of day‐ahead wind power and PV output and the load forecasting curve are considered. A pumped storage scheduling model is then established integrating the hydropower, thermal power and pumped storage. The optimal generation scheduling of pumped storage and thermal units is determined by minimizing load fluctuations and peak shaving costs. Finally, a local power grid in the Hunan province of China is selected for verification. It is shown that the proposed model can effectively accommodate the fluctuation of renewable energy output, reduce the peak regulating pressure of thermal units, and improve the operational economy of the power system.

Research on solving multi-preference intelligent scheduling problem based on improved genetic algorithm

Abstract. The paper will use the improved genetic algorithm that adds Gaussian perturbation based on the standard deviation of the population fitness and increases the variance probability operation to optimize the traditional genetic algorithm, and after iterating until the optimal scheduling strategy is found, we combine this algorithm with a mathematical model, and adopt a variety of variations to improve the efficiency of the algorithm. Among them, we take into account the customer flow, area of the store, employee work preference and other related factors to maximize its adaptability. We use real store employee data for simulation example experimental evidence, and compared with other algorithms, the results show that the study of the scheduling optimization ideas and algorithms are practical and feasible.

Probing an LSTM-PPO-Based reinforcement learning algorithm to solve dynamic job shop scheduling problem

With the growth of personalized demand and the continuous improvement in social productivity, the large-scale and few-variety centralized production model is gradually transitioning towards a personalized model of small batches and multiple varieties, which makes the manufacturing process of the job shop increasingly complex. Furthermore, disruptive events such as machinery failures and rush orders in the job shop increase the uncertainty and variability of the production environment. Traditional scheduling methods are usually based on fixed rules and heuristic algorithms, which are difficult to adapt to constantly changing production environments and demands. This may lead to inaccurate scheduling decisions and hinder the optimal allocation of job shop resources. To solve the dynamic job shop scheduling problem (JSP) more effectively, this paper proposes a Reinforcement Learning (RL) optimization algorithm integrating long short-term memory (LSTM) neural network and proximal policy optimization (PPO). It can dynamically adjust scheduling strategies according to the changing production environment, achieving comprehensive status awareness of the job shop environment to make optimal scheduling decisions. First, a state-aware network framework based on LSTM-PPO is proposed to achieve real-time perception of job shop state changes. Then, the state and action space of the job shop are described within the context of the state-aware network framework. Finally, an experimental environment is established to verify the algorithm’s effectiveness. Training the LSTM-PPO algorithm makes it feasible to achieve better performance than other scheduling methods. By comparing the initial planning time with the actual completion time of the rescheduling decision under different dynamic disturbances, the efficiency of the proposed algorithm is verified for the dynamic JSP

Optimal Configuration of Electricity-Heat Integrated Energy Storage Supplier and Multi-Microgrid System Scheduling Strategy Considering Demand Response

Shared energy storage system provides an attractive solution to the high configuration cost and low utilization rate of multi-microgrid energy storage system. In this paper, an electricity-heat integrated energy storage supplier (EHIESS) containing electricity and heat storage devices is proposed to provide shared energy storage services for multi-microgrid system in order to realize mutual profits for different subjects. To this end, electric boiler (EB) is introduced into EHIESS to realize the electricity-heat coupling of EHIESS and improve the energy utilization rate of electricity and heat storage equipment. Secondly, due to the problem of the uncertainty in user-side operation of multi-microgrid system, a price-based demand response (DR) mechanism is proposed to further optimize the resource allocation of shared electricity and heat energy storage devices. On this basis, a bi-level optimization model considering the capacity configuration of EHIESS and the optimal scheduling of multi-microgrid system is proposed, with the objectives of maximizing the profits of energy storage suppliers in upper-level and minimizing the operation costs of the multi-microgrid system in lower-level, and solved based on the Karush-Kuhn-Tucker (KKT) condition and Big-M method. The simulation results show that in case of demand response, the total operation cost of multi-microgrid system and the total operation profit of EHIESS are 51,687.73 and 11,983.88 CNY, respectively; and the corresponding electricity storage unit capacity is 9730.80 kWh. The proposed model realizes the mutual profits of EHIESS and multi-microgrid system.

Two-Stage Optimal Scheduling Strategy of Microgrid Distribution Network Considering Multi-Source Agricultural Load Aggregation

With the proposed “double carbon” target for the power system, large-scale distributed energy access poses a major challenge to the way the distribution grid operates. The rural distribution network (DN) will transform into a new local power system primarily driven by distributed renewable energy sources and energy storage, while also being interconnected with the larger power grid. The development of the rural DN will heavily rely on the construction and efficient planning of the microgrid (MG) within the agricultural park. Based on this, this paper proposes a two-stage optimal scheduling model and solution strategy for the microgrid distribution network with multi-source agricultural load aggregation. First, in the first stage, considering the flexible agricultural load and the market time-of-use electricity price, the economic optimization is realized by optimizing the operation of the schedulable resources of the park. The linear model in this stage is solved by the Lingo algorithm with fast solution speed and high accuracy. In the second stage, the power interaction between the MG and the DN in the agricultural park is considered. By optimising the output of the reactive power compensation device, the operating state of the DN is optimised. At this stage, the non-linear and convex optimization problems are solved by the particle swarm optimization algorithm. Finally, the example analysis shows that the proposed method can effectively improve the feasible region of safe operation of the distribution network in rural areas and improve the operating income of a multi-source agricultural load aggregation agricultural park.

Optimized Noise Suppression for Quantum Circuits

Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on noise characterization, mitigation, and suppression. Crucially, these methods must also be efficient in terms of their classical and quantum overhead. Here, we efficiently characterize and mitigate crosstalk noise, which is a severe error source in, for example, cross-resonance based superconducting quantum processors. For crosstalk characterization, we develop a simplified measurement experiment. Furthermore, we analyze the problem of optimal experiment scheduling and solve it for common hardware architectures. After characterization, we mitigate noise in quantum circuits by a noise-aware qubit routing algorithm. Our integer programming algorithm extends previous work on optimized qubit routing by swap insertion. We incorporate the measured crosstalk errors in addition to other, more easily accessible noise data in the objective function. Furthermore, we strengthen the underlying integer linear model by proving a convex hull result about an associated class of polytopes, which has applications beyond this work. We evaluate the proposed method by characterizing crosstalk noise for two chips with up to 127 qubits and leverage the resulting data to improve the approximation ratio of the Quantum Approximate Optimization Algorithm by up to 10% compared with other established noise-aware routing methods. Our work clearly demonstrates the gains of including noise data when mapping abstract quantum circuits to hardware native ones. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue on Quantum Computing. Funding: This work was supported by Bavarian state government; Bayerische Staatsministerium für Wirtschaft, Landesentwicklung und Energie. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0551 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0551 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Long-Term Optimal Scheduling of Hydro-Photovoltaic Hybrid Systems Considering Short-Term Operation Performance

Integrating photovoltaic power stations into large-capacity hydropower stations is an efficient and promising method for regulating large-scale photovoltaic power generation. However, constrained by the time step length, traditional long-term scheduling of hydro-PV hybrid systems does not adequately consider short-term operational performance indicators, resulting in sub-optimal scheduling plans that fail to coordinate the consumption of photovoltaic power and the utilization of water resources in the basin. To address this, this study established a long-term optimal scheduling model for hydro-PV hybrid systems. This model overcomes the limitation of the time step length in long-term scheduling by incorporating long-term power generation goals and short-term operation performance targets into the long-term optimal scheduling process based on scheduling auxiliary functions. In case studies, the optimised model balanced the long-term power-generation goals and short-term operational performance targets by redistributing energy across different periods. Compared to optimization models that did not consider short-term operation performance, in a typical normal year, the model effectively reduced the electricity curtailment volume (28.54%) and power shortage volume (10.91%) of the hybrid system while increasing on-grid electricity (0.03%). Similar improvements were observed in wet and dry years. These findings provide decision support for hydropower scheduling in the context of large-scale photovoltaic power integration.

Optimal scheduling of virtual power plants with reversible solid oxide cells in the electricity market

Virtual power plants (VPP) can act as an independent entity to aggregate different distributed resources to participate in the electricity market, which is an inevitable trend in building green and low-carbon power systems. To investigate the beneficial effect of bi-directional electric-hydrogen conversion on market trading and optimal scheduling of VPP, this paper presents an optimal scheduling method for VPP with reversible solid oxide cells (RSOC) in the electricity market. Firstly, according to the Butler-Volmer equation and Faraday law, the relationship between the hydrogen flow rate and the electric power is established, and the equivalent physical models of the two RSOC working modes are developed based on the relationship. Then, the optimal scheduling model of the VPP participating in the energy and reserve joint market is proposed based on the two-stage robust optimization theory. The system operator reserve demand is used to describe the uncertainty of the transactions between VPP and reserve market. Finally, the column and constraint generation (C&CG) algorithm is used to solve the two-stage robust scheduling model. The simulation results show that RSOC can effectively promote renewable energy consumption and improve the VPP operating profit. Where, the operating profit can be increased by 46.5 % and the wind power consumption rate can be increased by 3.4 %, compared with the non-hydrogen VPP. Furthermore, compared with the traditional conversion equipment, RSOC can increase the VPP operating profit by 2.3 % and the wind power consumption rate by 1.85 %.

Fuel Cell-Based Distributed Robust Optimal Scheduling for Combined Heat and Power Supply

At present, the safe operation of integrated energy systems is significantly affected by the considerable uncertainty inherent to wind and photovoltaic power generation. Based on this, this paper proposes an optimal scheduling model for integrated electricity, heat, and hydrogen-based energy systems on distributed robust optimization (DRO). Firstly, a combined heat and power microgrid system considering hydrogen energy systems was constructed based on the thermoelectric cogeneration characteristics of fuel cells and electrolyzers. Then, a data-driven two-stage distribution robust optimization scheduling model is built by combining typical historical data of wind power output, photovoltaic power output, and load. The results show that the distributed robust method reduces the running cost by 6% compared to the deterministic method. The proposed method and model are capable of meeting the demand for thermoelectric loads within the microgrid in a more cost-effective manner, thereby achieving stable and independent operation of the system.

Integrated market scheduling with flexibility options

This work presents a generic optimization framework using advanced mixed-integer programming techniques to integrate day-ahead and balancing markets with distributed energy resources such as storage, electric vehicles, demand response, and Transmission and Distribution System Operators' coordination schemes. The day-ahead model determines optimal initial energy scheduling, while the balancing model optimizes energy and reserve products for three market designs with varying Transmission and Distribution System Operators’ coordination. The framework is applied to the interconnected Greek-Bulgarian-Romanian power system, considering 2030 installed capacities.The model outputs illustrate market coupling scenarios among Romania, Bulgaria, and Greece, highlighting clear price signals and distributed energy resources flexibility. Results reveal the significance of a diverse energy mix for energy security and show that Transmission and Distribution System Operators’ coordination significantly influences ancillary service prices, with reductions of up to 80 % in certain scenarios. Net demand values determine electricity flow direction. Flexibility providers like storage can cover up to 100 % of the upward congestion management requirements and 11 % of upward balancing energy, helping smooth energy allocation from intermittent renewables. The impact of electric vehicle penetration on generation scheduling is minimal. The proposed model offers valuable insights for system operators, market participants, and policymakers, enabling them to provide accurate price signals and optimize resource allocation.The integrated day-ahead and balancing market models support efficient renewable energy integration, emissions reduction, enhanced grid stability, and investment in low-carbon technologies. This aligns with the United Nations Framework Convention on Climate Change goals, contributing to the development of sustainable and resilient energy systems.