Stochastic Scheduling Research Articles

Two-stage stochastic scheduling model of wind-photovoltaic-storage providing flexible ramp capacity

The increasing penetration of renewable energy resources in power system has contributed to the increasing demand for operation flexibility. To address the deficiency of flexibility in wind-photovoltaic-storage hybrid system with deepening penetration of intermittent and uncertain renewable energy resources, this paper proposes emerging flexible resources including wind, photovoltaic and energy storage providing flexible ramp capacity to improve flexibility. Considering the uncertainty of load and intermittent generation, the wind-photovoltaic-storage providing flexible ramp capacity are integrated into a two-stage stochastic dispatch model including 1h day-ahead unit commitment and 15min real-time economic dispatch. To test the efficiency of the proposed model, simulation are carried out on a modified IEEE 118-bus with 54 thermal units, the results indicate that wind-photovoltaic-storage providing flexible ramp capacity can effectively alleviate the deficiency of operation flexibility, and improve the overall economic benefit.

Security Sliding Mode Control of Interval Type-2 Fuzzy Systems Subject to Cyber Attacks: The Stochastic Communication Protocol Case

This article addresses the security control problem of a class of interval type-2 fuzzy systems via the sliding mode control strategy. A stochastic communication scheduling protocol is utilized to govern the transmission from the sensors to the controller, by which only one sensor node has the chance to transmit its value at every instant. Meanwhile, cyber attacks from malicious adversaries might be launched in vulnerable communication channels. To quantitatively analyze the effect of the stochastic communication protocol and cyber attacks, their mathematical model is first constructed based on a compensation scheme. Since the scheduling signal may be unavailable once cyber attacks are activated, a desirable sliding mode control law is synthesized with token-independent control gains, whose membership functions are mismatched with those of the fuzzy system. To deal with these mismatched membership functions, the relations between the membership functions of the system and the control law are reconstructed. Consequently, the favorable property of perfectly matched memberships could be employed. Sufficient conditions are derived so that the resultant closed-loop interval type-2 fuzzy system is stochastically stable and, at the same time, the state trajectories can be forced into a small domain around the prescribed sliding surface. The proposed control design approach is verified by two examples.

Optimal scheduling of multiple multi-energy supply microgrids considering future prediction impacts based on model predictive control

Renewable energy based multi-energy supply microgrids not only can cover different types of demands (such as, electricity/heat/gas), but also can interconnect with different utility grid networks (electricity/heat/gas). When there are large numbers of grid-connected microgrids, how to operate these multiple microgrids in real-time is a problem. In this paper, day-ahead stochastic optimization scheduling and real-time sliding window model predictive control are used to control the operation of microgrids. In order to consider the influence of future prediction on the current optimal decision results, different prediction methods are adopted to predict the load demands and renewable energy output. For example, online learning Markov chain prediction, and support vector machine are used to predict the future values. As for comparison, robust prediction and bilevel optimization are adopted to describe the future prediction uncertainty. The real-time operation of microgrids aims to follow the day-ahead exchanged energy with utility grids, which can minimize the impact of the microgrid on the utility grids. The supply network is an IEEE30 + gas20+heat14 network. The results show that: 1) when the sliding window number is smaller, the total operation cost is larger, but the calculation time is smaller, the trade-off between sliding window numbers and calculation time should be considered; 2) the accuracy of the prediction impacts the 2-norm error of the operation cost, when we decrease by “1” unit of 2-norm prediction error of the whole system, the 2-norm operation cost will decrease by “0.15” unit; 3) from the view of the post-event analysis (total operation cost), for the Markov chain prediction method, the relative error is about 0.32%, is better than the support vector machine method; 4) in the robust cases, the larger the conservative value, the higher the stored hydrogen energy. At last, the results of real-time sliding window model predictive control problem are influenced by the future prediction methods and the window numbers.

Day-ahead profit-based reconfigurable microgrid scheduling considering uncertain renewable generation and load demand in the presence of energy storage

Due to the penetration of renewable energy sources (RESs) with probabilistic natures into microgrids (MGs), optimal scheduling and reconfiguration (RG) processes are associated with uncertainty. This paper presents the stochastic profit-based optimal day-ahead scheduling of a reconfigurable microgrid (RMG) as a new generation of the conventional microgrid. The proposed algorithm finds the optimal RMG's topology from the profit maximization point of view, the optimal hourly MG's unit set-points like micro-turbines (MTs) and energy storage, and power exchange with the main grid, simultaneously. The generated power of wind turbine (WT) and PV panel, as well as load demand are considered as uncertain parameters. To solve the profit maximization problem of RMG, time-varying acceleration coefficients particle swarm optimization (TVAC-PSO) algorithm is employed. Also, to ensure simulation accuracy in the presence of high-level uncertainties, the autocorrelation model is used based on actual data for the uncertainty of renewable power output. The feasibility and applicability of the proposed framework are demonstrated on a 69-bus radial RMG with various distributed generators in different cases. The results show the effectiveness of the proposed model.

Multi-Time Scale Coordinated Control and Scheduling of Inverter-Based TCLs With Variable Wind Generation

To address microgrid tie flow errors caused by wind generation variability, this paper proposes and develops a multi-time scale coordinated control and scheduling strategy for inverter-based thermostatically controlled loads (TCLs). First, in hour-time scale, inverter-based TCLs with adjusting temperature set-point are modeled as virtual generators to compensate tie flow deviations in the day-ahead plan. Next, in minute-time scale, virtual batteries representing operating behaviors of inverter -based TCLs with frequency control are scheduled determined by the control of virtual generators in hour-time scale. The virtual batteries are scheduled to smooth out tie flow errors corresponding to day-ahead plan and hour-time scale schedules. The multi-time scale control methods are coordinated to employ the response potential of inverter-based TCLs and response curve-based methods are proposed to control inverter-based TCLs considering the customer privacy. The multi-time scale stochastic schedules which are based on response curves of inverter-based TCLs are coordinated to accommodate wind generation variability. Simulation results demonstrate that the microgrid tie flow errors are effectively mitigated by the proposed multi-time scale coordinated control and scheduling of inverter-based TCLs.

Stochastic master surgery scheduling

The aim of the Master Surgery Scheduling Problem (MSSP) is to schedule the medical specialties to the different operating rooms available, such that surgeries may be performed efficiently. We consider a MSSP where elective and emergency patients can be treated in the same operating rooms. In addition to elective-dedicated operating room slots, flexible operating room slots are introduced to handle the fluctuating demand of emergency patients.To solve the MSSP, we propose a simulation-optimization approach consisting of a two-stage stochastic optimization model and a discrete-event simulation model. For the two-stage stochastic optimization model, uncertain arrivals of emergency patients are represented by discrete scenarios. The discrete-event simulation model is developed to address uncertainty related to the surgery duration and the length of stay at the hospital, and to test the Master Surgery Schedule (MSS) developed by the optimization model in a stochastic operational-level environment. In addition, the simulation model is used to generate scenarios for the optimization model.We present some general advice for surgery scheduling based on testing the optimization model in a numerical study. The simulation-optimization approach is applied to a case study from a hospital department that treats both elective and emergency patients. The optimized MSS outperforms the manually generated MSS, both in terms of emergency waiting time for surgery, and emergency interruptions to the flow of electives.

Day-ahead stochastic scheduling of integrated multi-energy system for flexibility synergy and uncertainty balancing

Secure operation of the power system is challenged by the high level of uncertainty and fluctuation introduced by renewable energy sources. More flexibility is needed to cope with the uncertainty and improve the utilization of renewable energy. A prominent solution to provide flexibility, and simultaneously increase the efficiency of the system, is the integration of different energy sectors. This paper proposes a two-stage stochastic scheduling scheme of an integrated multi-energy system, which considers the wind power uncertainty and the synergy of different energy sectors to achieve the optimal economic operation of the whole system with minimum curtailment of wind power. In the first stage, energy and reserve scheduling of generating units is performed, while accommodation of wind power production is realized through reserves in the second stage. In the proposed scheme, the electric power system, natural gas system, and district heating system are coordinated to achieve more flexibility, both in the day-ahead and real-time stage. The stochasticity of the wind power uncertainty is represented by realistic scenarios with corresponding probabilities, which are obtained from a scenario generation algorithm based on historical observations taking into account the temporal correlation of wind power. The simulation results on a small-scale test system show that both, the economic efficiency and wind power utilization, have been improved with more flexibility and more reliable scenario set. It is shown, that the total system cost is reduced and reserves are optimized.

PFR ancillary service in low‐inertia power system

A high level of renewable resource penetration could lead to displacement of conventional synchronous generators from dispatch, and consequently, reduce the system inertia. The decline in the system inertia will increase the primary frequency response (PFR) need requiring to maintain grid frequency stability. This study proposes a new market design to co-optimise energy, inertia and PFR while considering uncertainties in renewable energy productions. A full dynamic model of Electric Reliability Council of Texas (ERCOT) interconnection is used to quantify the PFR requirement for the system inertia. The proposed method explicitly incorporates frequency dynamics and uncertainties in energy production from renewable resources in the scheduling process, which is formulated as a stochastic unit commitment problem. A case study of ERCOT grid demonstrated that the proposed stochastic scheduling of energy, inertia and PFR could yield a more cost-effective solution than the traditional deterministic formulation for the grids with a high penetration of renewable resources.

Robust operation of microgrid energy system under uncertainties and demand response program

<span>Microgrid energy systems are one of suitable solutions to the available problems in power systems such as energy losses, and resiliency issues. Local generation by these energy systems can reduce the role of the upstream network, which is a challenge in risky conditions. Also, uncertain behavior of electricity consumers and generating units can make the optimization problems sophisticated. So, uncertainty modeling seems to be necessary. In this paper, in order to model the uncertainty of generation of photovoltaic systems, a scenario-based model is used, while the robust optimization method is used to study the uncertainty of load. Moreover, the stochastic scheduling is performed to model the uncertain nature of renewable generation units. Time-of–use rates of demand response program (DRP) is also utilized to improve the system economic performance in different operating conditions. Studied problem is modeled using a mixed-integer linear programming (MILP). The general algebraic modeling system (GAMS) package is used to solve the proposed problem. A sample microgrid is studied and the results with DRP and without DRP are compared. It is shown that same robustness is achieved with a lower increase in the operation cost using DRP.</span>

Probabilistic optimal coordinated planning of molten carbonate fuel cell-CHP and renewable energy sources in microgrids considering hydrogen storage with point estimate method

The ever-growing augmentation of Renewable Energy Sources (RES) and Combined Heat and Power (CHP) units in microgrids (MG) exacerbates schedule management requirements in such systems. In this paper, a modified hybrid Bird Mating Optimization Differential Evolution (BMO-DE) algorithm is developed to address the mixed integer nonlinear programming problem of MG units’ probabilistic optimal planning. The proposed MG structure is consisted of MCFC-CHP, Wind Turbines (WT) and Photovoltaics (PV). The presented stochastic model schedules MG units coordinately, while the strategy of MCFC-CHP hydrogen storage is taken into account. The proposed solution models the uncertain parameters of electricity price, wind speed and sun irradiation using the 2m + 1 Point Estimate Method (PEM). The modeling of uncertain parameters results in more accurate planning and operation of the entire system. The proposed solution is applied on a 33-bus distribution network. In this manner, the total power loss decreased to 358.5 kW and the total operation cost is 3.1349 × 104$, which shows 18% decrease compared to MINLP method and 25% decrease compared to GA-PSCAD method of the total operation cost using the BMO-DE method. The results also justified the usage of CHPs while supplying thermal loads due to increased efficiency and profit.

RETRACTED: Risk-involved stochastic scheduling of plug-in electric vehicles aggregator in day-ahead and reserve markets using downside risk constraints method

Abstract A single plug-in electric vehicle (PEV) cannot participate in reserve and day-ahead markets as they cannot meet the energy requirements of independent system operators (ISO). However, they can be gathered by a PEV aggregator and play a role in so called markets. On the other hand the PEV aggregators are to deal with the uncertainties that go along with these markets and can highly affect their profit. In order to cover these uncertainties scenario-based stochastic approach can be taken into to account to optimally schedule the PEV aggregators so that the maximum profit is obtained. The main contribution of this paper is to involve risk related uncertainties through the downside risk constraints (DRC) which results in risk-constrained stochastic optimization model. The main advantage of this method is that it can provide the owner of PEV aggregator with decisions that are made by considering various quantities for risk. CPLEX solver of GAMS software is employed to solve the problem which is formulated as mixed-integer linear programming (MILP) model. To investigate the accomplishment of DRC, risk-averse state of model is compared to risk-neutral which in former one the profit is reduced meanwhile that risk-in-profit (RIP) is declined.

Sharing delay costs in stochastic scheduling problems with delays

An important problem in project management is determining ways to distribute amongst activities the costs that are incurred when a project is delayed because some activities end later than expected. In this study, we address this problem in stochastic projects, where the durations of activities are unknown but their corresponding probability distributions are known. We propose and characterise an allocation rule based on the Shapley value, illustrate its behaviour by using examples, and analyse features of its calculation for large problems.

On Stochastic Link and Energy Scheduling for Energy Harvesting Bidirectional Communications

In this paper, a solar-powered bidirectional communication system is studied for a pair of energy harvesting (EH) nodes that intend to communicate with each other over wireless fading channels. The conventional time-division duplex (TDD) transmission is revisited by proposing a stochastic resource scheduling scheme to minimize an average rate outage probability based on a Markov decision process (MDP) design framework. Different from the conventional TDD transmission, the proposed scheme can adjust the link direction and energy expenditure for data transmissions between the two EH nodes, in response to the dynamics of the solar EH, channel fading and battery storage conditions. A downstairs threshold structure is theoretically proved under a special optimal on-off policy, in which two-dimensional thresholds pinpoint the interplay between the transmission actions and the available energy in the batteries of the two nodes. Also the optimal on-off policy at asymptotically high signal-to-noise power ratios (SNRs) is revealed. The outage performance of the proposed stochastic resource scheduling scheme is validated by extensive computer simulations, and it shows that the proposed optimal MDP policy can achieve significant performance gains over the combinations of other compared schemes, including round-robin and battery state-oriented link scheduling schemes, and greedy and conservative energy scheduling schemes.

Flexibility Services Management Under Uncertainties for Power Distribution Systems: Stochastic Scheduling and Predictive Real-Time Dispatch

Over the last years, the role of the distribution system operator (DSO) has largely expanded. This is necessitated by the increased penetration of intermittent energy resources at the distribution level, as well as the new, more complex interactions with the transmission system operator (TSO). As such, to properly manage its system and to have an effective joint cooperation with the TSO, the DSO is required to procure and carefully manage flexibility services from distributed energy resources (DER). This paper introduces a thorough framework on optimal operational planning (day-ahead scheduling) and operational management (real-time dispatch) of active distribution systems under uncertainties, to avoid line congestions and voltage limit violations, and efficiently balance the distribution system. A two-stage stochastic programming model based on weighted scenarios is proposed to optimize the multi-period optimal power flow day-ahead scheduling, i.e., scheduled power flows at the TSO-DSO interface and reserved DER flexibility services. Subsequently, the operational management, realized with a predictive real-time dispatch model based on a constantly updated rolling horizon, aims to efficiently activate the available flexibility services to minimize deviations from the committed schedule. Different sources of flexibility are considered, with their respective response times also taken into account at real-time dispatch. The proposed framework is applied on two distribution systems and investigates the DSO’s level of risk exposure while minimizing its total cost (reservation and activation expenses). The results indicate that a less conservative approach at planning stage, despite the potential risk exposure, can lead to significant reduction in total expenses.

A Stochastic Two-Stage Model for the Integrated Scheduling of the Electric and Natural Gas Systems

The inherent coupling of the electric and natural gas systems due to the operation of gas generating units and power-to-gas facilities, along with the uncertainties faced in both systems due to the variability in electricity and gas demand and the vastly increasing volatile renewable injections, create an imperative need to schedule and operate the two systems in a coordinated manner. In this paper a new model for the fully integrated stochastic day-ahead scheduling of electric and gas systems is presented, coping with the uncertainties of both systems. The stochastic parameters comprise the electricity demand and the renewable injections, which collectively create several net electricity load scenarios, and the gas residential/industrial demand. The integrated scheduling problem concerns a unit commitment for the electricity problem, amended with additional constraints imposed by the underlying natural gas transmission system considering steady-state flow. A two-stage stochastic programming model is devised, having as second stage the possible realizations of net electricity load and gas demand in real-time. The model is tested in medium-size real-world test systems – the Greek electricity and gas systems – deriving useful insights on the advantages of the integrated stochastic scheduling versus the deterministic scheduling of the electricity and gas systems.

On Applications of the Earliest Due Date Rule in Stochastic Scheduling and in Queueing

We consider an environment with m servers in parallel and n jobs. The n jobs have i.i.d. exponentially distributed processing requirements. The servers operate at different speeds and preemptions are allowed. The jobs have random release dates that are not known in advance, but whenever a job is released, its due date is fixed and becomes known to the scheduler. We first consider three stochastic scheduling problems with three due date related objective functions and consider variations of the Earliest Due Date (EDD) rule, including the preemptive policy that at any point in time assigns the job with the Earliest Due Date to the Fastest Server (EDD-FS). Our optimality results turn out to be examples of stochastic scheduling problems that have relatively simple priority rules that are optimal while their deterministic counterparts do not allow such priority rules to be optimal. We furthermore extend our results to include a priority queueing model with m exponential servers that operate at different speeds and preemptions being allowed. The jobs arrive according to an arbitrary renewal process, and we assume that the utilization factor of the system is less than 1. Upon a job’s arrival the time difference between its due date and arrival date is set by the draw of a random variable from a given distribution. At a job’s arrival date, its due date is immediately fixed and known while its actual processing time only becomes known upon its service completion. We show that for this priority queueing model the preemptive EDD-FS rule also minimizes the limit of several due date related objective functions as the number of jobs converges to infinity.

A bi-level optimal scheduling model for virtual power plants and conventional power plants considering environmental constraints and uncertainty

To effectively realise the distributed energy resources participating in the system scheduling and reduce pollutant emissions from conventional plants, a bi-level stochastic optimal model for conventional plants and VPPs was built considering the uncertainty and environmental constraints. Firstly, a method of scenario generation and reduction is proposed to simulate the output of WPP and PV based on interval method and Kantorovich distance. Secondly, a bi-level stochastic optimal scheduling model for VPPs and conventional plants in a day-ahead plan is constructed. Finally, different simulation scenarios are designed to verify the effectiveness of the proposed model. The results illustrate that the model can overcome the influence of uncertainty and realise optimal economic jointly dispatch for VPPs and conventional plants under environmental constraints, through VPP technology, distributed power generation resources can be integrated effectively and have good environmental effect. Plants with high environmental performance will gain a larger share and generate more power.

Application of modified progressive hedging to stochastic unit commitment in electricity-gas coupled systems

The increasing number of gas-fired units has significantly intensified the coupling between electric and gas power networks. Traditionally, nonlinearity and nonconvexity in gas flow equations, together with renewable-induced stochasticity, resulted in a computationally expensive model for unit commitment in electricity-gas coupled integrated energy systems (IES). To accelerate stochastic day-ahead scheduling, we applied and modified Progressive Hedging (PH), a heuristic approach that can be computed in parallel to yield scenario-independent unit commitment. Through early termination and enumeration techniques, the modified PH algorithm saves considerable computational time for certain generation cost settings or when the scale of the IES is large. Moreover, an adapted second-order cone relaxation (SOCR) is utilized to tackle the nonconvex gas flow equation. Case studies were performed on the IEEE 24-bus system/Belgium 20-node gas system and the IEEE 118-bus system/Belgium 20-node gas system. The computational efficiency when employing PH is 188 times that of commercial software, and the algorithm even outperforms Benders Decomposition. At the same time, the gap between the PH algorithm and the benchmark is less than 0.01% in both IES systems, which proves that the solutions produced by PH reach acceptable optimality in this stochastic UC problem.

Stochastic Optimization Approaches for Elective Surgery Scheduling and Downstream Capacity Planning: Models, Challenges, and Opportunities

Elective surgery patients receive surgery in the operating room (OR) and then recover in one or more subsequent downstream recovery units for several consecutive hours or days after surgery. Indeed, upstream scheduling that focuses on OR alone or a resource-constrained scheduling approach that fails to account for the inherent uncertainty in surgery durations and postoperative downstream recovery times yield sub-optimal or infeasible schedules and, consequently, higher cost and reduced quality of care. However, modeling such uncertainties at multiple levels is challenging, especially with limited reliable data on the random parameters in the models. Moreover, sequencing of surgical and recovery activities, and the multiple conflicting objectives of all parties involved (including management, clinicians, patients), lead to a class of complex combinatorial and multi- criteria stochastic optimization problems. In this review, we focus on stochastic optimization (SO) approaches for elective surgery scheduling and downstream capacity planning. We describe the art of formulating and solving such a class of stochastic resource-constrained scheduling problems, provide an analysis of existing SO approaches and their challenges, and highlight areas of opportunity for developing tractable, implementable, and data-driven approaches that might be applicable within and outside healthcare operations, particularly where multiple entities/jobs share the same downstream limited resources.

Flexibility Provisions in Active Distribution Networks With Uncertainties

This paper proposes a risk-averse time-series joint scheduling method to release inherent benefits for improvements on operational cost, voltage profile and risk control, through flexibility extraction from grid-storage-demand resources in active distribution networks (ADNs). In particular, a flexibility analytical framework is developed to fully harness the controllability of various resources in both spatial and temporal scales, and is available for future analysis. The expected operational cost and the risks imposed by uncertainties are simultaneously addressed via conditional value at risk while satisfying physical and operating constraints, in which a sample weighted average approximation (SWAA) technique is employed for approximating the faced uncertainties. The SWAA-based stochastic scheduling problem is further transformed into a second-order cone programming problem via linearization and conic relaxation. Numerical simulations on 33-bus and 123-bus test systems verify the effectiveness of the proposed method.