Robust Scheduling Model Research Articles

Risk-Averse Scheduling of Combined Heat and Power-Based Microgrids in Presence of Uncertain Distributed Energy Resources

In this paper, a robust scheduling model is proposed for combined heat and power (CHP)-based microgrids using information gap decision theory (IGDT). The microgrid under study consists of conventional power generation as well as boiler units, fuel cells, CHPs, wind turbines, solar PVs, heat storage units, and battery energy storage systems (BESS) as the set of distributed energy resources (DERs). Additionally, a demand response program (DRP) model is considered which has a successful performance in the microgrid hourly scheduling. One of the goals of CHP-based microgrid scheduling is to provide both thermal and electrical energy demands of the consumers. Additionally, the other objective is to benefit from the revenues obtained by selling the surplus electricity to the main grid during the high energy price intervals or purchasing it from the grid when the price of electricity is low at the electric market. Hence, in this paper, a robust scheduling approach is developed with the aim of maximizing the total profit of different energy suppliers in the entire scheduling horizon. The employed IGDT technique aims to handle the impact of uncertainties in the power output of wind and solar PV units on the overall profit.

Robust day-ahead coordinated scheduling of multi-energy systems with integrated heat-electricity demand response and high penetration of renewable energy

As fossil fuels dry up and the proportion of renewable energy increases, multi-energy system (MES) becomes an effective way to realize renewable energy accommodation. High penetration of renewable energy brings challenges to the operation of power system, such as frequent curtailment of wind and the uncertainty of renewable energy threaten the security of the system. This paper proposes a two-stage robust scheduling model of MES considering integrated heat-electricity demand response (DR) to derive robust operation decisions. The proposed robust model minimizes the operation costs under base-case scenario, while guaranteeing all operation constraints are met in any scenarios. Power-to-Gas (P2G) equipment which converts surplus wind and photovoltaic generation into natural gas is included to effectively reduce curtailment of renewable generation. Furthermore, integrated heat-electricity DR, fully utilizing the couplings among various systems, is proposed to decrease operation costs and enhance system security against uncertainties. Column-and-Constraint Generation (CCG) method is used to effectively solve the proposed robust model. Numerical results in MATLAB indicate that robust optimization ensures secure operation of the system, and the integrated heat-electricity DR could promote the accommodation of renewable energy as well as enhance economic benefits and robustness of the system.

Robust scheduling for multiple agile Earth observation satellites under cloud coverage uncertainty

Agile satellites are the next generation of Earth observation satellites (EOSs) because they can rotate on three axes while EOSs cannot. Due to this improvement, agile EOS scheduling has attracted much attention. Meanwhile, the influence of cloud coverage for EOS is inevitable for most satellites equipped with optical remote sensing instruments, causing a significant impact on the quality of the images obtained, which therefore impacts on practical satellite scheduling. To deal with the agile satellite scheduling problem under cloud coverage uncertainty, we introduce the concept of budgeted uncertainty set and establish a linearized robust scheduling model, where the budget value should be determined by the satellite operation cost and the conservative degree. Then the original problem is transformed into a master problem and multiple pricing problems based on the column generation. Considering the enormous number of variables introduced by the dual transformation in the robust model, we propose a hybrid heuristic including column generation and simulated annealing. Finally, extensive simulation experiments are conducted to verify the effectiveness and efficiency of the proposed method.

Distributed robust synergistic scheduling of electricity, natural gas, heating and cooling systems via alternating direction method of multipliers

Due to the development of multi-energy conversion technologies and the higher public awareness of the sustainability, the energy system has begun a transition toward the energy hub (EH) based integrated energy system (IES). This paper proposes a distributed robust synergistic scheduling method for multi-EH-based IES coupled with electricity, natural gas, heating and cooling, to minimize the operating cost of the IES while considering the uncertainties of renewable generations (RGs) and multi-energy load demands. The nonconvexity of energy network constraints, uncertainties in multiple EHs as well as limitation of information exchange lead to significant challenges for IES scheduling. To deal these issues, the original robust scheduling model of IES is first reformulated as a mixed integer second-order cone programming (MISOCP) by convex relaxation method. Furthermore, to improve the economy and flexibility of robust scheduling solution, a light robust model is developed to address the multiple uncertainties from EHs. Finally, a consensus-based alternating direction method of multipliers (ADMM) approach is developed to tackle the robust scheduling model in MISOCP form, where EH operators parallelly solve their respective EH subproblems with limited information exchange, and subsequently the EH subproblem in MISOCP form is solved by a nonconvex ADMM (NC-ADMM) approach to guarantee the convergence of the consensus-based ADMM. Simulation results in a three-EH IES are presented to illustrate the effectiveness of proposed method for optimal synergy of multiple EHs with uncertainties.

Two-stage optimal robust scheduling of hybrid energy system considering the demand response programs

This paper proposes a two-stage robust scheduling model for the optimal operation of the solar-wind-hydropower-thermal-pumped storage (SWHTP) system considering both energy and reserve markets in the competitive environment. Day-ahead energy costs are intended in the first stage of the proposed model while the second stage considers the worst-case energy dispatch costs. Optimal scheduling of the reserve and energy markets is conducted to ensure the energy balance in the presence of the stochastic producers. Uncertainty modeling is also carried out by considering the worst occurrence of wind speed using the robust optimization method. Moreover, the demand response program’s capability is used due to the flexibility of some loads. The modified IEEE 5-bus and 24-bus test systems are selected for analyzing the effectiveness of the proposed model. Simulation results proved the success of the proposed model in meeting the electricity demand with minimum energy costs and maximum usage of the clean energy resource’s potential. Given the numerical results, increasing 27.04% in the amount of operation costs considering the worst occurrence of the wind speed concludes that enhancing the robustness of the system in the presence of uncertainties will increase the total costs of the system. Moreover, applying the demand response program for improving the flexibility of the system has been led to 7.48% increment in the system revenue, which indicates that the effective usage of the shiftable and curtailable features of the elastic loads can improve the reliability of continuous energy supply along with total energy costs in the deregulated environment.

Distributionally Robust Scheduling of Integrated Gas-Electricity Systems With Demand Response

This paper proposes a distributionally robust scheduling model for the integrated gas-electricity system (IGES) with electricity and gas load uncertainties, and further studies the impact of integrated gas-electricity demand response (DR) on energy market clearing, as well as locational marginal electricity and gas prices (LMEPs and LMGPs). The proposed model maximizes the base-case system social welfare (i.e., revenue from price-sensitive DR loads minus energy production cost) minus the worst-case expected load shedding cost. Price-based gas-electricity DRs are formulated via price-sensitive demand bidding curves while considering DR participation levels and energy curtailment limits. By linearizing nonlinear Weymouth gas flow equations via Taylor series expansion and further approximating recourse decisions as affine functions of uncertainty parameters, the formulation is cast into a mixed-integer linear programming problem to enhance computational tractability. Case studies illustrate effectiveness of the proposed model for ensuring system security against uncertainties, avoiding potential transmission congestions, and increasing financial stability of DR providers.

Min–max regret criterion-based robust model for the permutation flow-shop scheduling problem

ABSTRACTThis article studies the permutation flow-shop scheduling problem (PFSP) with interval production time. A min–max regret criterion-based robust scheduling model is established by taking both the robustness of total completion time and the tardiness of production into consideration simultaneously. To decrease the infinite number of scenarios to a limited level, a directed graph tool is applied to conduct worst case scenario analysis. In addition, since the PFSP is proved to be NP hard, a genetic algorithm is implemented to solve this robust scheduling model. Experimental simulation results verify the effectiveness and efficiency of this model. Moreover, it could cover the drawback of the traditional uncertain scheduling models, which consider only the robustness of total completion time. This could help manufacturing enterprises to increase time delivery capability so as to enhance downstream customers’ satisfaction.

A multi-objective robust scheduling model and solution algorithm for a novel virtual power plant connected with power-to-gas and gas storage tank considering uncertainty and demand response

Power-to-gas (P2G) provides a new means for accommodating abandoned new energy that will support the optimal operation of virtual power plants (VPPs) in the future. In this study, a novel structure of a P2G-based virtual power plant (GVPP) is designed. A flexible risk aversion model for GVPP operation is proposed with two objectives—maximum operation profit and minimum operation risk. In the model, the conditional value at risk method and robust optimization theory are utilized to reflect uncertainty risks. To solve the multi-objective model, a solution algorithm was constructed for iteratively obtaining the optimal weight coefficient for transforming the multi-objective model into a single-objective model based on a payoff table and a rough set method. Four simulation cases were set for comparative analysis based on a nine-node energy hub system. The results show the following outcomes: (1) GVPP realizes the complementary utilization of distributed energy and forms a power-gas-power recycling mode, (2) the proposed model can provide an effective decision-making tool for different risk-attitude decision makers by setting a reasonable confidence level and robust coefficient, (3) P2G and price-based demand response (PBDR) improve the grid-connected space of clean energy, in particular, PBDR improves the flexibility of system operation and reduces operation risk, and (4) if the maximum emission trade allowance (META) is considered, P2G preferentially converts carbon dioxide into methane when the META is lower, while clean energy is preferentially used to satisfy load demand and the methane produced by P2G can be sold to the natural gas network when the META is higher. Overall, the proposed optimal decision model achieves the maximum utilization of clean energy to obtain higher economic benefits while rationally controlling operation risks; hence, providing reliable support for decision makers.

Data‐driven multi‐time scale robust scheduling framework of hydrothermal power system considering cascade hydropower station and wind penetration

A data-driven multi-time scale robust scheduling model for a wind–hydro–thermal power system is presented in this study, according to the characteristic that wind power prediction accuracy increases with the decrease of the time scale. In day-ahead scheduling, a generation plan is formulated with the target of minimising the total operating cost, and a data-driven robust optimisation method based on the robust kernel density estimation (RKDE) is employed to deal with the uncertainty of wind power. That is, the distributional information of wind power is extracted by the RKDE from the big data, then the distributional information is incorporated into a data-driven uncertainty set, and finally, a robust optimisation model is formed. During the intraday scheduling stage, the objective is to minimise the total water spillage in cascade hydropower stations and the adjustment cost of thermal units, and the task is to readjust the outputs of units based on the base outputs obtained by the day-ahead scheduling, combined with the rolling forecast data of wind power and load. The real-time scheduling is aimed at satisfying the power balance with minimum power adjustment. Finally, a test system is carried out to verify the efficiency and practicability of the proposed framework.

Multi-Objective Robust Scheduling Optimization Model of Wind, Photovoltaic Power, and BESS Based on the Pareto Principle

With the increasing proportion of distributed power supplies connected to the power grid, the application of a battery energy storage system (BESS) to a power system leads to new ideas of effectively solving the problem of distributed power grid connections. There is obvious uncertainty involved in distributed power output, and these uncertainties must be considered when optimizing the scheduling of virtual power plants. In this context, scene simulation technology was used to manage the uncertainty of wind power and photovoltaic output, forming a classic scenario. In this study, to reduce the influence of the uncertainty of wind and photovoltaic power output on the stable operation of the system, the time-of-use (TOU) prices and BESS were incorporated into the optimal scheduling problem that is inherent in wind and photovoltaic power. First, this study used the golden section method to simulate the wind and photovoltaic power output; second, the day-ahead wind and photovoltaic power output were used as the random variables; third, a wind and photovoltaic power BESS robust scheduling model that considers the TOU price was constructed. Finally, this paper presents the Institute of Electrical and Electronics Engineers (IEEE) 30 bus system in an example simulation, where the solution set is based on the Pareto principle, and the global optimal solution can be obtained by the robust optimization model. The results show that the cooperation between the TOU price and BESS can counteract wind and photovoltaic power uncertainties, improve system efficiency, and reduce the coal consumption of the system. The example analysis proves that the proposed model is practical and effective. By accounting for the influence of uncertainty of the optimal scheduling model, the actual operating cost can be reduced, and the robustness of the optimization strategy can be improved.

A two-stage assignment strategy for the robust scheduling of dual-resource constrained stochastic job shop scheduling problems

Abstract This paper addresses the job shop scheduling problems with stochastic processing times (SJSSP) under machine-worker dual-resource constraints. Considering the difference in worker’s proficiency level, a robust scheduling approach is adopted. And then the machine-worker dual-resource constrained robust scheduling model of SJSSP based on the expected scenario of processing times (DR-SJSSP-EPS) is formulated. In view of the requirements of DR-SJSSP-ESP for the rational assignment of the workers, we propose a two-stage assignment strategy (TSAS), which can decrease the random disturbance of the processing times as well as its impact on the scheduling performance. Furthermore, a multi-objective hybrid estimation of distribution algorithm (MO-HEDA) is employed to solve the DR-SJSSP-ESP. At last, the effectiveness of the proposed method to solve the DR-SJSSP-ESP in the job shop manufacturing system is verified according to the simulation results.

Robust resource-constrained max-NPV project scheduling with stochastic activity duration

This study investigates the robust resource-constrained max-NPV project problem with stochastic activity duration. First, the project net present value (NPV) and the expected penalty cost are proposed to measure quality robustness and solution robustness from the perspective of discounted cash flows, respectively. Then, a composite robust scheduling model is proposed in the presence of activity duration variability and a two-stage algorithm that integrates simulated annealing and tabu search is developed to deal with the problem. Finally, an extensive computational experiment demonstrates the superiority of the combination between quality robustness and solution robustness as well as the effectiveness of the proposed two-stage algorithm for generating project schedules compared with three other algorithms, namely simulated annealing, tabu search, and multi-start iterative improvement method. Computational results indicate that the proactive project schedules with composite robustness not only can effectively protect the payment plan from disruptions through allocating appropriate time buffers, but also can achieve a remarkable performance with respect to the project NPV.

A Robust Scheduling Optimization Method for Flight Deck Operations of Aircraft Carrier With Ternary Interval Durations

The sortie and recovery operations of the carrier-based aircraft fleet are carried out in a cyclic mode, and there are uncertainties during the flight deck operations, which is the main factor that influences the sustainability of cyclic operations. The robust scheduling problem for flight deck operations (RSPFDO) with uncertain duration is studied in this paper. First, the robust scheduling model of flight deck operations with ternary interval durations is established. In this model, the precedence and resource constraints including personnel, equipment, workstation space, and supply resource are taken into account, and the uncertain duration is modeled as a ternary interval number. Second, to make a proactive plan, serial schedule generation scheme is used to generate baseline schedules, and a robust personnel allocation scheme is designed. In terms of executing schedules, a pre-constrained scheduling policy is proposed to evaluate the ternary interval of makespan. Third, a double-population and self-adaptive differential evolution (DSDE) algorithm is presented to optimize the robust plan, which is embedded in a population-based double justification scheme, self-adaptive selection of mutation and crossover factors, and a chaotic catastrophe operator based on the scouts mode of artificial bee colony algorithm. The validity of the established model and the superiority of the DSDE algorithm are verified by simulations with mission cases and algorithm comparison. The results demonstrate that the proposed robust scheduling method can effectively improve the robustness of the flight deck operations.

Multiobjective Robust Scheduling for Smart Distribution Grids: Considering Renewable Energy and Demand Response Uncertainty

The fluctuating nature of renewable energy is a key factor that limits large-scale integration with the power grid. In this paper, a new method of utilizing multitype demand response (DR) resources to smooth fluctuations in renewable energy on different timescales is proposed. A multiobjective robust scheduling model considering renewable energy and DR uncertainties is established using this method. First, the robust optimization theory is introduced, and uncertainties in renewable energy and multitype DR resources are described in the form of robust intervals on multiple timescales. Then, the multiobjective scheduling model is constructed with the objective of obtaining the lowest operating cost and the highest renewable energy utilization rate, while considering renewable energy integration constraints, DR output constraints, and system power balance constraints. Finally, according to the model characteristics, the uncertainty problem is transformed into a deterministic problem by using a robust counterpart transformation, and a nondominated set genetic algorithm-II is used to solve the deterministic problem. A case study is presented to verify the effectiveness of the proposed scheduling model and solution method. The calculation results show that multitype DR resources can effectively smooth fluctuations in renewable energy, and the proposed robust scheduling method can increase the robustness of the scheduling plan.

A bi-level stochastic scheduling optimization model for a virtual power plant connected to a wind–photovoltaic–energy storage system considering the uncertainty and demand response

To reduce the uncertain influence of wind power and solar photovoltaic power on virtual power plant (VPP) operation, robust optimization theory (ROT) is introduced to build a stochastic scheduling model for VPP considering the uncertainty, price-based demand response (PBDR) and incentive-based demand response (IBDR). First, the VPP components are described including the wind power plant (WPP), photovoltaic generators (PV), convention gas turbine (CGT), energy storage systems (ESSs) and demand resource providers (DRPs). Then, a scenario generation and reduction frame is proposed for analyzing and simulating output stochastics based on the interval method and the Kantorovich distance. Second, a bi-level robust scheduling model is proposed with a double robust coefficient for WPP and PV. In the upper layer model, the maximum VPP operation income is taken as the optimization objective for building the scheduling model with the day-ahead prediction output of WPP and PV. In the lower layer model, the day-ahead scheduling scheme is revised with the actual output of the WPP and PV under the objectives of the minimum system net load and the minimum system operation cost. Finally, the independent micro-grid in a coastal island in eastern China is used for the simulation analysis. The results illustrate that the model can overcome the influence of uncertainty on VPP operations and reduce the system power shortage cost by connecting the day-ahead scheduling with the real-time scheduling. ROT could provide a flexible decision tool for decision makers, effectively addressing system uncertainties. ESSs could replace CGT to provide backup service for the WPP and PV, to smooth the VPP output curve and to improve the WPP and PV grid connection by its charging–discharging characteristics. Meanwhile, IBDR and PBDR could smooth the load curve to the maximum extent, link the generation side with the demand side to minimize abandoned power value and reach the optimum benefit of VPP operation.

Robust scheduling of a two-stage hybrid flow shop with uncertain interval processing times

This paper studies the makespan minimisation scheduling problem in a two-stage hybrid flow shop. The first stage has one machine and the second stage has m identical parallel machines. Neither the processing time nor probability distribution of the processing time of each job is uncertain. We propose a robust (min–max regret) scheduling model. To solve the robust scheduling problem, which is NP-hard, we first derive some properties of the worst-case scenario for a given schedule. We then propose both exact and heuristic algorithms to solve this problem. In addition, computational experiments are conducted to evaluate the performance of the proposed algorithms.

Robust Scheduling for Wind Integrated Energy Systems Considering Gas Pipeline and Power Transmission N-1 Contingencies

The security of natural gas network and the wind power uncertainty bring new challenges for power system operation. This letter develops a robust scheduling model for wind-integrated energy systems with the considerations of both gas pipeline and power transmission N –1 contingencies. The proposed method is robust against wind power uncertainty to ensure that the system can sustain possible N –1 contingency event of gas pipeline or power transmission line. Case studies demonstrate the effectiveness of the proposed model.

Self-balancing robust scheduling with flexible batch loads for energy intensive corporate microgrid

With the development of microgrid technology, for an energy intensive corporate such as an iron and steel plant energy consumptions and costs can be saved significantly by achieving the balance between self-generation and consumption. In this paper, we present a self-balancing and robust scheduling model with flexible batch loads for an energy intensive corporate. The model is a multi-level optimization model with the objective to minimize the unbalance cost in the worst case. Load following properties are given to determine whether the uncertain loads can be followed or not, and the self-balancing capability of an energy intensive corporate is analyzed. The problem is equivalently converted from the multi-level model to a single-level optimization model with a set of constraints. In this way, the iteration between the outer and inner level can be avoided. Case study based on an energy intensive corporate microgrid is tested and the results show that the unbalance cost can be significantly reduced by using the robust self-balancing model. In addition, compared the approach method with iterative solving method, computational efficiency can be improved and local optimum can be avoided.

Energy and reserve scheduling under correlated nodal demand uncertainty: An adjustable robust optimization approach

This paper presents a nonparametric approach based on adjustable robust optimization to consider correlated nodal demand uncertainty in a joint energy and reserve scheduling model with security constraints. In this model, up- and down-spinning reserves provided by generators are endogenously defined as a result of the optimization problem. Adjustable robust optimization is used to characterize the worst-case load variation under a given user-defined uncertainty set. This paper differs from recent previous work in two respects: (i) nonparametric correlations between nodal demands are accounted for in the uncertainty set and (ii) based on the binary expansion linearization approach, a mixed-integer linear model is provided for the optimization related to the worst-case demand. The resulting problem is formulated as a trilevel program and solved by means of Benders decomposition. Empirical results suggest that the effect of nodal correlations can be effectively captured by the robust scheduling model.

Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach

We address short‐term batch process scheduling problems contaminated with uncertainty in the data. The mixed integer linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998; 37(11):4341–4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp‐MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4184–4211, 2013