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Two-stage stochastic mixed-integer linear programming: The conditional scenario approach

OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2017年 70卷 31-42页

作者： Beltran-Royo, C. Rey Juan Carlos Univ Comp Sci & Stat Madrid Spain

In this paper we consider the two-stage stochastic mixed-integer linear programming problem with recourse, which we call the RP problem. A common way to approximate the RP problem, which is usually formulated in terms of scenarios, is to formulate the so-called Expected Value (EV) problem, which only considers the expectation of the random parameters of the RP problem. In this paper we introduce the Conditional Scenario (CS) problem which represents a midpoint between the RP and the EV problems regarding computational tractability and ability to deal with uncertainty. In the theoretical section we have analyzed some useful bounds related to the RP, EV and CS problems. In the numerical example here presented, the CS problem has outperformed both the EV problem in terms of solution quality, and the RP problem with the same number of scenarios as in the CS problem, in terms of solution time. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： stochastic mixed-integer linear programming Conditional expectation Scenario Conditional Scenario

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stochastic mixed-integer programming for Integrated Portfolio Planning in the LNG Supply Chain

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ENERGY JOURNAL 2013年第1期35卷 79-97页

作者： Werner, Adrian Uggen, Kristin Tolstad Fodstad, Marte Lium, Arnt-Gunnar Egging, Ruud SINTEF Technol & Soc Dept Appl Econ & Operat Res Trondheim Norway Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management N-7034 Trondheim Norway

We present a new model to support strategic planning by actors in the liquefied natural gas market. The model takes an integrated portfolio perspective and addresses uncertainty in future prices. Decision variables include investments and disinvestments in infrastructure and vessels, chartering of vessels, the timing of contracts, and spot market trades. The model accounts for various contract types and vessels, and it addresses losses. The underlying mathematical model is a multistage stochastic mixed-integer linear problem. Industry-motivated numerical cases are discussed as benchmarks for the potential increases in profits that can be obtained by using the model for decision support. These examples illustrate how a portfolio perspective leads to decisions different than those obtained using the traditional net present value approach. We show how explicitly considering uncertainty affects investment and contracting decisions, leading to higher profits and better utilization of capacity. In addition, model run times are competitive with current business practices of manual planning.

关键词： Liquefied natural gas supply chain Decision support system Strategic planning stochastic mixed-integer linear programming

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Price-Maker Economic Bidding in Two-Settlement Pool-Based Markets: The Case of Time-Shiftable Loads

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IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第1期31卷 695-705页

作者： Kohansal, Mahdi Mohsenian-Rad, Hamed Univ Calif Riverside Dept Elect Engn Riverside CA 92521 USA

In this paper, a new scenario-based stochastic optimization framework is proposed for price-maker economic bidding in day-ahead and real-time markets. The presented methodology is general and can be applied to both demand and supply bids. That is, no restrictive assumptions are made on the characteristics of the pool and its agents. However, our focus is on the operation of time-shiftable loads with deadlines, because they play a central role in creating load flexibility and enhancing demand response and peak-load shaving programs. Both basic and complex time-shiftable load types are addressed, where the latter includes time-shiftable loads that are uninterruptible, have per-time-slot consumption limits or ramp constraints, or comprise several smaller time-shiftable subloads. Four innovative analytical steps are presented in order to transform the originally nonlinear and hard-to-solve price-maker economic bidding optimization problem into a tractable mixed-integer linear program. Accordingly, the global optimal solutions are found for the price and energy bids within a relatively short amount of computational time. A detailed illustrative case study along with multiple case studies based on the California energy market data are presented. It is observed that the proposed optimal price-maker economic bidding approach outperforms optimal price-maker self-scheduling as well as even-load-distribution.

关键词： Day-ahead market demand response energy bids price-maker economic bidding price bids real-time market stochastic mixed-integer linear programming time-shiftable loads

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A Fast Technique for Smart Home Management: ADP With Temporal Difference Learning

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IEEE TRANSACTIONS ON SMART GRID 2018年第4期9卷 3291-3303页

作者： Keerthisinghe, Chanaka Verbic, Gregor Chapman, Archie C. Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

This paper presents a computationally efficient smart home energy management system (SHEMS) using an approximate dynamic programming (ADP) approach with temporal difference learning for scheduling distributed energy resources. This approach improves the performance of an SHEMS by incorporating stochastic energy consumption and PV generation models over a horizon of several days, using only the computational power of existing smart meters. In this paper, we consider a PV-storage (thermal and battery) system, however, our method can extend to multiple controllable devices without the exponential growth in computation that other methods such as dynamic programming (DP) and stochastic mixed-integer linear programming (MILP) suffer from. Specifically, probability distributions associated with the PV output and demand are kernel estimated from empirical data collected during the Smart Grid Smart City project in NSW, Australia. Our results show that ADP computes a solution much faster than both DP and stochastic MILP, and provides only a slight reduction in quality compared to the optimal DP solution. In addition, incorporating a thermal energy storage unit using the proposed ADP-based SHEMS reduces the daily electricity cost by up to 263% without a noticeable increase in the computational burden. Moreover, ADP with a two-day decision horizon reduces the average yearly electricity cost by a 4.6% over a daily DP method, yet requires less than half of the computational effort.

关键词： Demand response smart home energy management distributed energy resources approximate dynamic programming dynamic programming stochastic mixed-integer linear programming value function approximation temporal difference learning

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Parallelized stochastic Short-term Hydrothermal Generation Scheduling

Parallelized Stochastic Short-term Hydrothermal Generation S...

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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Araya, Juan Gil, Esteban Univ Tecn Federico Santa Maria Dept Elect Engn Valparaiso Chile

ISBN: (纸本)9781509041688

This paper proposes a stochastic mixed-integer linear programming (SMILP) formulation for Short-Term Hydrothermal Generation Scheduling (STHTGS) under uncertainty. STHTGS seeks to minimize present and future operation costs by deciding the commitments of thermal generators and the allocation of hydro resources during the planning horizon. The stochastic STHTGS is decomposed using the Progressive Hedging Algorithm (PHA) and each sub-problem is solved in parallel. Numerical tests are conducted for the Chilean Central Interconnected System with 12 stochastic scenarios and a weekly decision horizon. The stochastic and deterministic formulations are compared by solving standard variations of the stochastic problem. Numerical results show that the proposed decomposition and parallelization strategy can help reduce simulation times and hedge against uncertainty, but the level of benefits and the convergence properties are highly dependent on the amount of water available in the scheduling horizon and the diversity of the scenarios.

关键词： Power Systems Optimization Short-term Hydrothermal Scheduling stochastic mixed-integer linear programming Parallel Computing Unit Commitment

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A Two-stage stochastic programming Method for Optimal Power Scheduling with Solar Power Integration

A Two-stage Stochastic Programming Method for Optimal Power ...

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Chinese Automation Congress (CAC)

作者： Han Hanhuawei Wang Chunli Jiang Weiwei Shi Ning Li Chuankun Gao Xinjiang Wang Haozhi Key State Lab Safety & Control Chem Qingdao 266000 Peoples R China SINOPEC Res Inst Safety Engn Qingdao 266071 Peoples R China Univ Elect Sci & Technol China Chengdu 611731 Sichuan Peoples R China

ISBN: (纸本)9781538635247

The traditional power grid is confronted with great challenges brought by the integration of renewable power sources (such as solar and wind) for their uncertain, volatile, and intermittent characteristics. This paper investigates the unit commitment problem with stochastic solar power integration and makes the following major contributions. First, the scheduling problem is formulated as a two-stage stochastic programming. In the first stage the unit commitment, economic dispatch, and solar power scheduling decisions are made based on the day ahead solar power prediction and in the second stage the solar power is rescheduled with real-time solar power generation as each decision instant approaching. Second, in the rescheduling, cost for buying reserve and penalty for curtailing solar power are considered for higher penetration and better utilization of solar power. Third, the problem is reformulated as a stochastic mix-integer linear programming to facilitate computation and the influences of spinning reserve price, penalty for curtailing solar power, and solar power uncertainty are analyzed and discussed. The performance of the proposed method is compared with a deterministic programming, a robust programming, and a stochastic programming through a modified six-bus system and the results demonstrate that the proposed method can better accommodate the fluctuation of solar power.

关键词： unit commitment solar power integration stochastic programming stochastic mixed-integer linear programming

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Addressing the stochastic nature of energy management in smart homes

Addressing the stochastic nature of energy management in sma...

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2014 Power Systems Computation Conference (PSCC)

作者： Keerthisinghe, Chanaka Verbic, Gregor Chapman, Archie C. Univ Sydney Sch Elect & Informat Engn Sydney NSW Australia

ISBN: (纸本)9788393580132

In the future, automated smart home energy management systems (SHEMSs) will assist residential energy users to schedule and coordinate their energy use. In order to undertake efficient and robust scheduling of distributed energy resources, such a SHEMS needs to consider the stochastic nature of the household's energy use and the intermittent nature of its distributed generation. Currently, stochastic mixed-integer linear programming (MILP), particle swarm optimization and dynamic programming approaches have been proposed for incorporating these stochastic variables. However, these approaches result in a SHEMS with very costly computational requirements or lower quality solutions. Given this context, this paper discusses the drawbacks associated with these existing methods by comparing a SHEMS using stochastic MILP with heuristic scenario reduction techniques to one using a dynamic programming approach. Then, drawing on analysis of the two methods above, this paper discusses ways of reducing the computational burden of the stochastic optimization framework by using approximate dynamic programming to implement a SHEMS.

关键词： future grid demand response smart home stochastic mixed-integer linear programming dynamic programming scenario reduction techniques approximate dynamic programming

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Evaluation of a multi-stage stochastic optimisation framework for energy management of residential PV-storage systems 24

Evaluation of a multi-stage stochastic optimisation framewor...

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Australasian Universities Power Engineering Conference (AUPEC)

作者： Keerthisinghe, Chanaka Verbic, Gregor Chapman, Archie C. Univ Sydney Sch Elect & Informat Engn Sydney NSW Australia

ISBN: (纸本)9780646923758

In Australia, the penetration of rooftop photovoltaic (PV) systems with storage is expected to increase in the future because of rising electricity costs, decreasing capital costs and growing concerns about climate change. Residential energy users can seize the full financial benefits of these systems by using an automated energy management system (EMS) to schedule and coordinate their energy use. An important aspect of an effective EMS is to control the battery state of charge, taking into consideration of the intermittent nature of PV generation and variability of electrical demand over a decision horizon of several days. However, this is difficult because of the computational burden associated with the currently proposed solution techniques. Given these existing shortcomings, this paper evaluates a two-stage stochastic optimisation framework for energy management of residential PV-storage systems to identify the benefits of having a longer decision horizon. That is: a simplified longer-horizon solver that uses stochastic mixed-integer linear programming (MILP) and a more detail shorter horizon solver using dynamic programming. In doing so, this paper discusses the general benefits of residential PV-storage systems coupled with an EMS.

关键词： future grid renewable energy sources demand response PV-storage systems home energy management stochastic mixed-integer linear programming dynamic programming

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Energy management of PV-storage systems: ADP approach with temporal difference learning 19

Energy management of PV-storage systems: ADP approach with t...

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19th Power Systems Computation Conference (PSCC)

作者： Keerthisinghe, Chanaka Verbic, Gregor Chapman, Archie C. Univ Sydney Sch Elect & Informat Engn Sydney NSW Australia

ISBN: (纸本)9788894105124

In the future, residential energy users can seize the full potential of demand response schemes by using an automated home energy management system (HEMS) to schedule their distributed energy resources. In order to generate high quality schedules, a HEMS needs to consider the stochastic nature of the PV generation and energy consumption as well as its inter-daily variations over several days. However, extending the decision horizon of proposed optimisation techniques is computationally difficult and moreover, these approaches are only computationally feasible with a limited number of storage devices and a low-resolution decision horizon. Given these existing shortcomings, this paper presents an approximate dynamic programming (ADP) approach with temporal difference learning for implementing a computationally efficient HEMS. In ADP, we obtain policies from value function approximations by stepping forward in time, compared to the value functions obtained by backward induction in DP. We use empirical data collected during the Smart Grid Smart City project in NSW, Australia, to estimate the parameters of a Markov chain model of PV output and electrical demand, which are then used in all simulations. To evaluate the quality of the solutions generated by ADP, we compare the ADP method to stochastic mixed-integer linear programming (MILP) and dynamic programming (DP). Our results show that ADP computes a solution much quicker than both DP and stochastic MILP, while providing better quality solutions than stochastic MILP and only a slight reduction in quality compared to the DP solution. Moreover, unlike the computationally-intensive DP, the ADP approach is able to consider a decision horizon beyond one day while also considering multiple storage devices, which results in a HEMS that can capture additional financial benefits.

关键词： demand response home energy management distributed energy resources approximate dynamic programming dynamic programming stochastic mixed-integer linear programming value function approximation temporal difference learning

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Risk-Constrained Offering Strategies for a Price-Maker Demand Response Aggregator 20

Risk-Constrained Offering Strategies for a Price-Maker Deman...

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20th IEEE International Conference on Electrical Machines and Systems (ICEMS)

作者： Abbasi, Mohammad Hossein Rajabi, Amin Taki, Mehrdad Li, Li Zhang, Jiangfeng Ghavidel, Sahand Ghadi, Mojtaba Jabbari Univ Qom Qom Iran Univ Technol Sydney Fac Engn & Informat Technol Sydney NSW Australia

ISBN: (纸本)9781538632468

Offering strategy of a price-maker demand response aggregator (DRA) in a two-settlement market is presented in this paper. The aggregator minimizes its cost by offering energy and price bids in the day-ahead market and energy bids in the balancing market. On the other hand, DRA optimally manages the aggregated demands of a large number of electric vehicles and properly distributes them through the time. The problem is formulated as a stochastic mixed-integer nonlinear optimization problem. The risk of the problem is managed by conditional value-at-risk measure and finally, the proposed approach is numerically evaluated through a detailed case study.

关键词： Risk management Price maker economic bidding stochastic mixed-integer linear programming Demand response aggregator

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