A Two-Stage Scenario-Based Robust Optimization Model and a Column-Row Generation Method for Integrated Aircraft Maintenance-Routing and Crew Rostering

Motivated by a critical issue of airline planning process,this paper addresses a new two-stage scenario-based robust optimization in operational airline planning to cope with uncertainty and possible flight disruptions.Following the route network scheme and generated flight timetables,aircraft maintenance routing and crew scheduling are critical factors in airline planning and operations cost management.This study considers the simultaneous assignment of aircraft fleet and crew to the scheduled flight while satisfying a set of operational constraints,rules,and regulations.Considering multiple locations for airline maintenance and crew bases,we solve the problem of integrated Aircraft Maintenance Routing and Crew Rostering(AMRCR)to achieve the minimum airline cost.One real challenge to the efficiency of the planning results is the possible disruptions in the initial scheduled flights.Due to the fact that disruption scenarios are expressed discretely with a specified probability,and we provide adjustable decisions under disruption to deal with this disruption risk,we provide a Two-Stage Scenario-Based Robust Optimization(TSRO)model.In this model,here-and-now or first-stage variables are the initial resource assignment.Furthermore,to adapt itself to different disruption scenarios,the model considers some adjustable variables,such as the decision to cancel the flight in case of disruption,as wait-and-see or second-stage variables.Considering the complexity of integrated models,and the scenario-based decomposable structure of the TRSO model to solve it with better computational performance,we apply the column and row generation(CRG)method that iteratively considers the disruption scenarios.The numerical results confirm the applicability of the proposed TSRO model in providing the AMRCR problem with an integrated and robust solution with an acceptable level of computational tractability.To evaluate the proposed TSRO model,which solves the AMRCR problem in an integrated and robust manner,five Key Performance Indicators(KPIs)like Number of delayed/canceled flights,Average delay time,and Average profit are taken into account.As key results driven by conducting a case study,we show the proposed TSRO model has substantially improved the solutions at all indicators compared with those of the sequential/non-integrated and nominal/non-robust models.The simulated instances used to assess the performance of the proposed model and CRG method reveal that both CPLEX and the CRG method exhibit comparable and nearly optimal performance for small-scale problems.However,for large-scale instances the proposed TSRO model falls short in terms of computational efficiency.Conversely,the proposed CRG method is capable of significantly reducing computational time and the optimality gap to an acceptable level.

An Optimal Dynamic Generation Scheduling for a Wind-Thermal Power System

In this paper, a dynamic generation scheduling model is formulated, aiming at minimizing the costs of power generation and taking into account the constraints of thermal power units and spinning reserve in wind power integrated systems. A dynamic solving method blended with particle swarm optimization algorithm is proposed. In this method, the solution space of the states of unit commitment is created and will be updated when the status of unit commitment changes in a period to meet the spinning reserve demand. The thermal unit operation constrains are inspected in adjacent time intervals to ensure all the states in the solution space effective. The particle swarm algorithm is applied in the procedure to optimize the load distribution of each unit commitment state. A case study in a simulation system is finally given to verify the feasibility and effectiveness of this dynamic optimization algorithm.

Short-term power generation scheduling rules for cascade hydropower stations based on hybrid algorithm

Power generation dispatching is a large complex system problem with multi-dimensional and nonlinear characteristics. A mathematical model was established based on the principle of reservoir operation. A large quantity of optimal scheduling processes were obtained by calculating the daily runoff process within three typical years, and a large number of simulated daily runoff processes were obtained using the progressive optimality algorithm （POA） in combination with the genetic algorithm （GA）. After analyzing the optimal scheduling processes, the corresponding scheduling rules were determined, and the practical formulas were obtained. These rules can make full use of the rolling runoff forecast and carry out the rolling scheduling. Compared with the optimized results, the maximum relative difference of the annual power generation obtained by the scheduling rules is no more than 1%. The effectiveness and practical applicability of the scheduling rules are demonstrated by a case study. This study provides a new perspective for formulating the rules of power generation dispatching.

Learning to branch in the generation maintenance scheduling problem

To maximize the reliability index of a power system,this study modeled a generation maintenance scheduling problem that considers the network security constraints and rationality constraints of the generation maintenance practice in a power system.In view of the computational complexity of the generation maintenance scheduling model,a variable selection method based on a support vector machine(SVM)is proposed to solve the 0-1 mixed integer programming problem(MIP).The algorithm observes and collects data from the decisions made by strong branching(SB)and then learns a surrogate function that mimics the SB strategy using a support vector machine.The learned ranking function is then used for variable branching during the solution process of the model.The test case showed that the proposed variable selection algorithm-based on the features of the proposed generation maintenance scheduling problem during branch-and-bound-can increase the solution efficiency of the generation-scheduling model on the premise of guaranteed accuracy.

Non-dominated sorting culture differential evolution algorithm for multi-objective optimal operation of Wind-Solar-Hydro complementary power generation system

Due to the intermittency and instability of Wind-Solar energy and easy compensation of hydropower, this study proposes a Wind-Solar-Hydro power optimal scheduling model. This model is aimed at maximizing the total system power generation and the minimum ten-day joint output. To effectively optimize the multi-objective model, a new algorithm named non-dominated sorting culture differential evolution algorithm(NSCDE) is proposed. The feasibility of NSCDE was verified through several well-known benchmark problems. It was then applied to the Jinping Wind-Solar-Hydro complementary power generation system. The results demonstrate that NSCDE can provide decision makers a series of optimized scheduling schemes.

Day-ahead scheduling based on reinforcement learning with hybrid action space

Driven by the improvement of the smart grid,the active distribution network(ADN)has attracted much attention due to its characteristic of active management.By making full use of electricity price signals for optimal scheduling,the total cost of the ADN can be reduced.However,the optimal dayahead scheduling problem is challenging since the future electricity price is unknown.Moreover,in ADN,some schedulable variables are continuous while some schedulable variables are discrete,which increases the difficulty of determining the optimal scheduling scheme.In this paper,the day-ahead scheduling problem of the ADN is formulated as a Markov decision process(MDP)with continuous-discrete hybrid action space.Then,an algorithm based on multi-agent hybrid reinforcement learning(HRL)is proposed to obtain the optimal scheduling scheme.The proposed algorithm adopts the structure of centralized training and decentralized execution,and different methods are applied to determine the selection policy of continuous scheduling variables and discrete scheduling variables.The simulation experiment results demonstrate the effectiveness of the algorithm.

Research on the Model of Long Term Generation Planning in Power Market Reform

With the deepening of China’s power market, bilateral transactions will continue to grow in large scale. The release of bilateral transactions locked more regulatory resources of the power grid, will directly affect the operation mode of the unit and the implementation of planned electricity. In the paper, considering the large-scale bilateral trade effect on the peak regulation of power grid, energy saving and emission reduction, power system security and other factors, and then putting forward the method of long term generation planning and annual planning model to adapt to the safe operation of power grid in China. In the model, the target is minimizing the monthly load rate deviation and the annual electric quantity deviation rate, the latter includes the capacity factor. In addition, the constraints include the monthly quantity of electricity, adjustable utilization rate deviation, load rate, reserve and key sections, etc. Through an example to verify the correctness of the model, the planning and power transaction results can satisfy the peak regulation of load, energy saving and emission reduction and safety operation of the power grid requirements.

Economic Scheduling of Gaseous-liquid Hydrogen Generation and Storage Plants Considering Complementarity of Multiple Products

The accessible and convenient hydrogen supply is the foundation of successful materialization for hydrogen-powered vehicles(HVs).This paper proposes a novel optimal scheduling model for gaseous-liquid hydrogen generation and storage plants powered by renewable energy to enhance the economic feasibility of investment.The gaseous-liquid hydrogen generation and storage plant can be regarded as an energy hub to supply concurrent service to both the transportation sector and ancillary market.In the proposed model,the power to multi-state hydrogen(P2MH)process is analyzed in detail to model the branched hydrogen flow constraints and the corresponding energy conversion relationship during hydrogen generation,processing,and storage.To model the coupling and interaction of diverse modules in the system,the multi-energy coupling matrix is developed,which can exhibit the mapping of power from the input to the output.Based on this,a multi-product optimal scheduling(MPOS)algorithm considering complementarity of different hydrogen products is further formulated to optimize dispatch factors of the energy hub system to maximize the profit within limited resources.The demand response signals are incorporated in the algorithm to further enhance the operation revenue and the scenario-based method is deployed to consider the uncertainty.The proposed methodology has been fully tested and the results demonstrate that the proposed MPOS can lead to a higher rate of return for the gaseous-liquid hydrogen generation and storage plant.

Robust coordination of interdependent electricity and natural gas systems in day-ahead scheduling for facilitating volatile renewable generations via power-to-gas technology

The increasing interdependency of electricity and natural gas systems promotes coordination of the two systems for ensuring operational security and economics.This paper proposes a robust day-ahead scheduling model for the optimal coordinated operation of integrated energy systems while considering key uncertainties of the power system and natural gas system operation cost. Energy hub,with collocated gas-fired units, power-to-gas(Pt G) facilities, and natural gas storages, is considered to store or convert one type of energy(i.e., electricity or natural gas)into the other form, which could analogously function as large-scale electrical energy storages. The column-andconstraint generation(C&CG) is adopted to solve the proposed integrated robust model, in which nonlinear natural gas network constraints are reformulated via a set of linear constraints. Numerical experiments signify the effectiveness of the proposed model for handling volatile electrical loads and renewable generations via the coordinated scheduling of electricity and natural gas systems.

Performance Evaluation of Scheduling Algorithms for 4G (LTE)

Long Term Evolution (LTE) is designed to revolutionize mobile broadband technology with key considerations of higher data rate, improved power efficiency, low latency and better quality of service. This work analyzes the impact of resource scheduling algorithms on the performance of LTE (4G) and WCDMA (3G) networks. In this paper, a full illustration of LTE system is given together with different scheduling algorithms. Thereafter, 3G WCDMA and 4G LTE networks were simulated using Simulink simulator embedded in MATLAB and performance evaluations were carried out. The performance metrics used for the evaluations are average system throughput, packet delay, latency and allocation of fairness using Round Robin, Best CQI and Proportional fair Packet Scheduling Algorithms. The results of the evaluations on both networks were analysed. The results showed that 4G LTE network performs better than 3G WCDMA network in all the three scheduling algorithms used.

A Chance Constrained Optimal Reserve Scheduling Approach for Economic Dispatch Considering Wind Penetration

The volatile wind power generation brings a full spectrum of problems to power system operation and management, ranging from transient system frequency fluctuation to steady state supply and demand balancing issue. In this paper, a novel wind integrated power system day-ahead economic dispatch model, with the consideration of generation and reserve cost is modelled and investigated. The proposed problem is first formulated as a chance constrained stochastic nonlinear programming U+0028 CCSNLP U+0029, and then transformed into a deterministic nonlinear programming U+0028 NLP U+0029. To tackle this NLP problem, a three-stage framework consists of particle swarm optimization U+0028 PSO U+0029, sequential quadratic programming U+0028 SQP U+0029 and Monte Carlo simulation U+0028 MCS U+0029 is proposed. The PSO is employed to heuristically search the line power flow limits, which are used by the SQP as constraints to solve the NLP problem. Then the solution from SQP is verified on benchmark system by using MCS. Finally, the verified results are feedback to the PSO as fitness value to update the particles. Simulation study on IEEE 30-bus system with wind power penetration is carried out, and the results demonstrate that the proposed dispatch model could be effectively solved by the proposed three-stage approach. © 2017 Chinese Association of Automation.

Deep Cutting Plane Inequalities for Stochastic Non-Preemptive Single Machine Scheduling Problem

We study the classical single machine scheduling problem but with uncertainty. A robust optimization model is presented, and an effective deep cut is derived. Numerical experiments show effectiveness of the derived cut.

A branch and price algorithm for the robust WSOS scheduling problem

To analyze and optimize the weapon system of systems(WSOS)scheduling process,a new method based on robust capabilities for WSOS scheduling optimization is proposed.First,we present an activity network to represent the military mission.The member systems need to be reasonably assigned to perform different activities in the mission.Then we express the problem as a set partitioning formulation with novel columns(activity flows).A heuristic branch-and-price algorithm is designed based on the model of the WSOS scheduling problem(WSOSSP).The algorithm uses the shortest resource-constrained path planning to generate robust activity flows that meet the capability requirements.Finally,we discuss this method in several test cases.The results show that the solution can reduce the makespan of the mission remarkably.

A Novel Particle Swarm Optimization for Optimal Scheduling of Hydrothermal System

A fuzzy adaptive particle swarm optimization (FAPSO) is presented to determine the optimal operation of hydrothermal power system. In order to solve the shortcoming premature and easily local optimum of the standard particle swarm optimization (PSO), the fuzzy adaptive criterion is applied for inertia weight based on the evolution speed factor and square deviation of fitness for the swarm, in each iteration process, the inertia weight is dynamically changed using the fuzzy rules to adapt to nonlinear optimization process. The performance of FAPSO is demonstrated on hydrothermal system comprising 1 thermal unit and 4 hydro plants, the comparison is drawn in PSO, FAPSO and genetic algorithms (GA) in terms of the solution quality and computational efficiency. The experiment showed that the proposed approach has higher quality solutions and strong ability in global search.

Day-ahead Optimization Schedule for Gas-electric Integrated Energy System Based on Second-order Cone Programming

This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.

Generation maintenance scheduling based on multiple objectives and their relationship analysis

In a market environment of power systems, each producer pursues its maximal profit while the independent system operator is in charge of the system reliability and the minimization of the total generation cost when generating the generation maintenance scheduling(GMS). Thus, the GMS is inherently a multi-objective optimization problem as its objectives usually conflict with each other. This paper proposes a multi-objective GMS model in a market environment which includes three types of objectives, i.e., each producer's profit, the system reliability, and the total generation cost. The GMS model has been solved by the group search optimizer with multiple producers(GSOMP) on two test systems. The simulation results show that the model is well solved by the GSOMP with a set of evenly distributed Pareto-optimal solutions obtained. The simulation results also illustrate that one producer's profit conflicts with another one's, that the total generation cost does not conflict with the profit of the producer possessing the cheapest units while the total generation cost conflicts with the other producers' profits, and that the reliability objective conflicts with the other objectives.

Optimal generation scheduling in power system using frequency prediction through ANN under ABT environment

In a competitive and deregulated power scenario, the utilities try to maintain their real electric power generation in balance with the load demand, which creates a need for the precise real time generation scheduling （GS）. In this paper, the GS problem is solved to perform the unit commitment （UC） based on frequency prediction by using artificial neural network （ANN） with the objective to minimize the overall system cost of the state utility. The introduction of availability-based tariff （ABT） signifies the importance of frequency in GS. Under- prediction or over-prediction will result in an unnecessary commitment of generating units or buying power from central generating units at a higher cost. Therefore, an accurate frequency prediction is the first step toward optimal GS. The dependency of frequency on various parameters such as actual generation, load demand, wind power and power deficit has been considered in this paper. The proposed technique provides a reliable solution for the input parameter different from the one presented in the training data. The performance of the frequency predictor model has been evaluated based on the absolute percentage error （APE） and the mean absolute percentage error （MAPE）. The proposed predicted frequency sensitive GS model is applied to the system of Indian state of Tamilnadu, which reduces the overall system cost of the state utility by keeping off the dearer units selected based on the predicted frequency.

Integrated Frequency-constrained Scheduling Considering Coordination of Frequency Regulation Capabilities from Multi-source Converters

As the proportion of renewable energy(RE)increases,the inertia and the primary frequency regulation(FR)capability of the power system decrease.Thus,ensuring frequency security in the scheduling model has become a new technical requirement in power systems with a high share of RE.Due to a shortage of conventional synchronous generators,the frequency support of multi-source converters has become an indispensable part of the system frequency resources,especially variable-speed wind turbine generation(WTG)and battery energy storage(BES).Quantitative expression of the FR capability of multi-source converters is necessary to construct frequency-constrained scheduling model.However,the frequency support performance of these converter-interfaced devices is related to their working states,operation modes,and parameters,and the complex coupling of these factors has not been fully exploited in existing models.In this study,we propose an integrated frequency-constrained scheduling model considering the coordination of FR capabilities from multi-source converters.Switchable FR control strategies and variable FR parameters for WTG with or without reserved power are modeled,and multi-target allocation of BES capacity between tracking dispatch instruction and emergency FR is analyzed.Then,the variable FR capabilities of WTG and BES are embedded into the integrated frequency-constrained scheduling model.The nonlinear constraints for frequency security are precisely linearized through an improved iteration-based strategy.The effectiveness of the proposed model is verified in a modified IEEE 24-bus standard system.The results suggest that the coordinated participation of BES and WTG in FR can effectively reduce the cost of the scheduling model while meeting frequency security constraints.

Day-ahead Scheduling of Multi-carrier Energy Systems with Multi-type Energy Storages and Wind Power

The integration of large-scale wind power brings challenges to the operation of integrated energy systems(IES).In this paper,a day-ahead scheduling model for IES with wind power and multi-type energy storage is proposed in a scenario-based stochastic programming framework.The structure of the IES consists of electricity,natural gas,and heating networks which are all included in the model.Operational constraints for IES incorporating multi-type energy storage devices are also considered.The constraints of the electricity network,natural gas network and heating network are formulated,and non-linear constraints are linearized.The calculation method for the correlation of wind speed between wind farms based on historical data is proposed.Uncertainties of correlated wind power were represented by creating multiple representative scenarios with different probabilities,and this was done using the Latin hyper-cube sampling(LHS)method.The stochastic scheduling model is formulated as a mixed integer linear programming(MILP)problem with the objective function of minimizing the total expected operation cost.Numerical results on a modified PJM 5-bus electricity system with a seven-node natural gas system and a six-node heating system validate the proposed model.The results demonstrate that multi-type energy storage devices can help reduce wind power curtailments and improve the operational flexibility of IES.

An economic and low-carbon day-ahead Pareto-optimal scheduling for wind farm integrated power systems with demand response

Demand response(DR)and wind power are beneficial to low-carbon electricity to deal with energy and environmental problems.However,the uncertain wind power generation(WG)which has anti-peaking characteristic would be hard to exert its ability in carbon reduction.This paper introduces DR into traditional unit commitment(UC)strategy and proposes a multi-objective day-ahead optimal scheduling model for wind farm integrated power systems,since incentive-based DR can accommodate excess wind power and can be used as a source of system spinning reserve to alleviate generation side reserve pressure during both peak and valley load periods.Firstly,net load curve is obtained by forecasting load and wind power output.Then,considering the behavior of DR,a day-ahead optimal dispatching scheme is proposed with objectives of minimum generating cost and carbon emission.Non-dominated sorting genetic algorithm-II(NSGA-II)and satisfaction-maximizing method are adopted to solve the multi-objective model with Pareto fronts and eclectic decision obtained.Finally,a case study is carried out to demonstrate that the approach can achieve economic and environmental aims and DR can help to accommodate the wind power.