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interval quadratic programming for day-ahead dispatch of uncertain predicted demand

AUTOMATICA 2016年 64卷 163-173页

作者： Ishizaki, Takayuki Koike, Masakazu Ramdani, Nacim Ueda, Yuzuru Masuta, Taisuke Oozeki, Takashi Sadamoto, Tomonori Imura, Jun-ichi Tokyo Inst Technol Meguro Ku 2-12-1 Ookayama Tokyo 1528552 Japan Tokyo Univ Marine Sci & Technol Minato Ku 4-5-7 Kounan Tokyo 1080075 Japan Tokyo Univ Sci 6-3-1 Niijuku Tokyo 1620825 Japan Univ Orleans INSA CVL PRISMEEA 4229 F-45072 Orleans France Inst Appl Energy Minato Ku 14-2-1 Nishi Shimbashi Tokyo 1050003 Japan Natl Inst Adv Ind Sci & Technol 1-2-1 Namiki Tsukuba Ibaraki 3058564 Japan Japan Sci & Technol Agcy CREST 4-1-8 Honcho Kawaguchi Saitama 3320012 Japan

In this paper, we propose an interval quadratic programming method for the day-ahead scheduling of power generation and battery charge cycles, where the prediction uncertainty of power consumption and photovoltaic power generation is described as a parameter vector lying in an interval box. The interval quadratic programming is formulated as the problem of finding the tightest box, i.e., interval hull, that encloses the image of a function of the minimizer in parametric quadratic programming. To solve this problem in a computationally efficient manner, we take a novel approach based on a monotonicity analysis of the minimizer in the parametric quadratic programming. In particular, giving a tractable parameterization of the minimizer on the basis of the Karush-Kuhn-Tucker condition, we show that the monotonicity analysis with respect to the parameter vector can be relaxed to the sign pattern analysis of an oblique projection matrix. The monotonicity of the minimizer is found to be essential in the day-ahead dispatch problem, where uncertain predicted demand, described by a parameter vector, is dispatched to power generation and battery charge cycles while the economic cost is minimized. Finally, we verify the efficiency of the proposed method numerically, using experimental and predicted data for power consumption and photovoltaic power generation. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： interval quadratic programming Monotonicity analysis Prediction uncertainty Demand dispatch

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Development of an interval quadratic programming water quality management model and its solution algorithms

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JOURNAL OF CLEANER PRODUCTION 2020年 249卷 119319-000页

作者： Zhang, Qianqian Li, Zhong Chengdu Univ Informat Technol Sch Management Chengdu 610225 Peoples R China McMaster Univ Dept Civil Engn 1280 Main St West Hamilton ON L8S 4L7 Canada

interval quadratic programming (IQP) is one of the most popular programming techniques for addressing the uncertainties associated with nonlinear environmental management problems. However, efficient algorithms for solving IQP problems in water quality management (WQM) have not been well studied. In this study, an IQP model is developed for WQM under uncertainty. Three solution algorithms, including a piecewise linear approximation (PLA) method, a derivative algorithm (DEA) and a duality-based algorithm (DUA) are proposed for solving the IQP-WQM problem. The developed model and the corresponding solution algorithms are applied to a hypothetic WQM problem to demonstrate their applicability. The results show the lower bounds of the total cost obtained by three algorithms have a relationship of f(DUA)(-) = f(DEA)(-) <= f(PLA)(-), while that of the upper bounds is f(DEA)(+) <= f(PLA)(+) <= f(DUA)(+). Moreover, the sensitivity analysis shows that no matter how the IQP-WQM model is solved, the model response from the three solution algorithms is consistent. The results indicate that all of the three algorithms can efficiently deal with quadratic programming problems under uncertainties in the format of intervals. Comparison among the three algorithms shows that DUA provides interval solutions with wider ranges than the other two methods, and it requires less computational efforts than DEA. It is also found that PLA is more flexible and might require lower computational efforts for large scale problems. This study can provide useful technical support for effective WQM. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： interval quadratic programming Piecewise linear approximation Derivative algorithm Duality-based algorithm Water quality management Solution algorithm

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Some results on the upper bound of optimal values in interval convex quadratic programming

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2016年 302卷 38-49页

作者： Li, Wei Xia, Mengxue Li, Haohao Hangzhou Dianzi Univ Inst Operat Res & Cybernet Hangzhou 310018 Zhejiang Peoples R China Zhejiang Univ Finance & Econ Sch Math & Stat Hangzhou 310018 Zhejiang Peoples R China

One of the fundamental problems in interval quadratic programming is to compute the range of optimal values. For minimized problem with equality constraint, computing the upper bound of the optimal values is known to be NP-hard. One kind of the effective methods for computing the upper bound of interval quadratic programming is so called dual method, based on the dual property of the problem. To obtain the exact upper bound, the dual methods require that the duality gap is zero. However, it is not an easy task to check whether this condition is true when the data may vary inside intervals. In this paper, we first present an easy and efficient method for checking the zero duality gap. Then some relations between the exact upper bound and the optimal value of the dual model considered in dual methods are discussed in detail. We also report some numerical results and remarks to give an insight into the dual method's behavior. (C) 2016 Elsevier B.V. All rights reserved.

关键词： interval quadratic programming Optimal values range Duality gap

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Some properties of the lower bound of optimal values in interval convex quadratic programming

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OPTIMIZATION LETTERS 2017年第7期11卷 1443-1458页

作者： Li, Wei Jin, Jianghong Xia, Mengxue Li, Haohao Luo, Qi Hangzhou Dianzi Univ Inst Operat Res & Cybernet Hangzhou 310018 Zhejiang Peoples R China Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou 310018 Zhejiang Peoples R China Nanjing Univ Informat Sci & Technol Sch Informat & Control Nanjing 210044 Jiangsu Peoples R China

One of the fundamental problems in interval quadratic programming is to compute the range of optimal values. In this paper, we derive some results on the lower bound of interval convex quadratic programming. We first develop complementary slackness conditions of a quadratic program and its Dorn dual. Then, some interesting and useful characteristics of the lower bound of interval quadratic programming are established based on these conditions. Finally, illustrative examples and remarks are given to get an insight into the problem discussed.

关键词： interval quadratic programming Optimal value range Lower bound

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Simulation-based interval chance-constrained quadratic programming model for water quality management: A case study of the central Grand River in Ontario, Canada

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ENVIRONMENTAL RESEARCH 2021年 192卷 110206-110206页

作者： Zhang, Qianqian Li, Zhong Huang, Wendy Chengdu Univ Informat Technol Sch Management Chengdu 610225 Peoples R China McMaster Univ Dept Civil Engn Hamilton ON L8S 4L8 Canada

Effective river water quality management and planning is a complex issue challenged by various complexities and uncertainties. A simulation-based interval chance-constrained quadratic programming (ICCQP) model is developed for the seasonal planning of water quality management (WQM) under various uncertainties. The proposed model incorporates interval quadratic programming, chance-constrained programming, and a seasonal water quality simulation model within a general framework for WQM. Uncertainties associated with the objective and the coefficients in the left-hand sides of the constraints are tackled as intervals. Meanwhile, parameter uncertainties on the right-hand sides are characterized using probability distributions. Nonlinearities in the cost function are reflected by quadratic programming. A multi-segment water quality model is used to simulate the dynamic interactions between wastewater discharges and river water quality. The proposed ICCQPWQM model is applied in a real case study for the control of total phosphorus (TP) in the central Grand River in Ontario, Canada. The results demonstrate that the proposed model is able to incorporate uncertainties expressed as intervals and probability information into an optimization framework and provide interval solutions. Thus, different cost-effective schemes for seasonal WQM could be generated. The results show the Kitchener wastewater treatment plant (WWTP) affects the value of the objective function more than the other WWTPs in the study area. It is also found that the Kitchener WWTP's cost accounts for the highest proportion (approximately 35.1-37.9%) of the total annual cost, which implies the control of TP at the Kitchener plant is the most important to the system. Moreover, river water TP standards in spring and autumn are usually difficult to meet, indicating different TP control strategies are needed in these two seasons. The generated results are valuable for local decision makers to generate TP control st

关键词： interval quadratic programming Chance-constrained programming Water quality management Uncertainty The grand river

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An interval quadratic Fuzzy Dependent-Chance programming Model for Optimal Irrigation Water Allocation under Uncertainty

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WATER 2018年第6期10卷 684页

作者： Wang, Hang Zhang, Chenglong Guo, Ping China Agr Univ Ctr Agr Water Res China Tsinghuadong St 17 Beijing 100083 Peoples R China

In this study, an interval quadratic fuzzy dependent-chance programming (IQFDCP) model is proposed for irrigation water management under uncertainty. This model can deal with the interval and fuzzy uncertainties encountered in optimal irrigation water resources allocation problems. It takes optimal credibility level of system revenue as the objective function for addressing the conflict between maximum system revenue and the credibility level of the system revenue. By providing three scenarios of precipitation, the optimal solutions are obtained. The developed model is applied to a case study for irrigation water allocation in Minqin Oasis, Wuwei city, northwest China. This study can help determine how much irrigation water should be allocated to different crops under the maximum credibility level of the system revenue. The optimal solutions can provide a certain credibility level of system revenue corresponding to different scenarios and mitigate the system-failure risk level of water shortages in arid areas. Moreover, because the IQFDCP can objectively reflect the interrelationship among crop irrigation water amount, system revenue, and system-failure risk level, the results are able to provide advices to decision makers for efficiently managing water resources in different scenarios.

关键词： uncertainty irrigation water resources allocation interval quadratic programming fuzzy dependent-chance programming credibility level

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Optimal scheduling of battery storage systems and thermal power plants for supply-demand balance

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CONTROL ENGINEERING PRACTICE 2018年 77卷 213-224页

作者： Koik, Masakazu Ishizaki, Takayuki Ramdani, Nacim Imura, Jun-ichi Tokyo Univ Marine Sci & Technol Koutou Ku 2-1-6 Echujima Tokyo 1358533 Japan Tokyo Inst Technol Meguro Ku 2-12-1 Ookayama Tokyo 1528552 Japan Univ Orleans INSA CVL PRISME EA 4229 F-45072 Orleans France

This paper focuses on the day-ahead scheduling problem of generating power for thermal power plants and charging/discharging battery energy storage systems based on interval predictions of photovoltaic power. Our previous approach to this problem used the Jacobian of a solution with respect to the variation in demand. However, this study was limited in the sense that the output capacity constraints of thermal power plants were not taken into account. To overcome this problem, we introduce a virtual thermal plant and apply several properties of an M-matrix. To provide guidelines for the amount of power that should be generated, we determine the exact regulating capacity for each thermal power plant and a storage battery so as to maintain the supply-demand balance. The efficiency of the proposed method is verified numerically. We show that a brute-force Monte Carlo method cannot estimate the exact regulating capacity of the thermal power plants when the batteries effectively balance the supply and demand. Moreover, it is found that, unless their deterioration cost decreases significantly, storage batteries cannot be effectively utilized.

关键词： Photovoltaic power generation Prediction uncertainty Regulating capacity Battery storage system Optimal scheduling interval quadratic programming M-matrix

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An Inexact Chance-constrained quadratic programming Model for Stream Water Quality Management

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WATER RESOURCES MANAGEMENT 2009年第4期23卷 661-695页

作者： Qin, X. S. Huang, G. H. Univ Regina Ctr Energy & Environm Studies Regina SK S4S 0A2 Canada N China Elect Power Univ Chinese Res Acad Environm Sci Beijing 100012 Peoples R China Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada

Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for stream water quality management. A multi-segment stream water quality (MSWQ) simulation model was provided for establishing the relationship between environmental responses and pollution-control actions. The relationship was described by transformation matrices and vectors that could be used directly in a multi-point-source waste reduction (MWR) optimization model as water-quality constraints. The interval quadratic polynomials were employed to reflect the nonlinearities and uncertainties associated with wastewater treatment costs. Uncertainties associated with the water-quality parameters were projected into the transformation matrices and vectors through Monte Carlo simulation. Uncertainties derived from water quality standards were characterized as random variables with normal probability distributions. The proposed ICCQP model was applied to a water quality management problem in the Changsha section of the Xiangjiang River in China. The results demonstrated that the proposed optimization model could effectively communicate uncertainties into the optimization process, and generate inexact solutions containing a spectrum of wastewater treatment options. Decision alternatives could then be obtained by adjusting different combinations of the decision variables within their solution intervals. Solutions from the ICCQP model could be used to analyze tradeoffs between the wastewater treatment cost and system-failure risk due to inherent uncertainties. The results are valuable for supporting decision makers in seeking cost-effective water management strategies.

关键词： interval quadratic programming Chance-constrained programming Water quality management Uncertainty

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Optimal Scheduling of Storage Batteries and Power Generators Based on interval Prediction of Photovoltaics-Monotonicity Analysis for State of Charge

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IEEE CONTROL SYSTEMS LETTERS 2020年第1期4卷 49-54页

作者： Koike, Masakazu Ishizaki, Takayuki Ramdani, Nacim Imura, Jun-Ichi Tokyo Univ Marine Sci & Technol Dept Marine Elect & Mech Engn Tokyo 1528552 Japan Tokyo Inst Technol Dept Syst & Control Engn Tokyo 1528552 Japan Univ Orleans PRISME F-45072 Orleans France

This letter focuses on a day-ahead scheduling problem on thermal power plants and storage batteries based on the information of the interval prediction of photovoltaic (PV) power and demand. To realize an optimal operation, there are three kinds of decision variables to plan, which correspond to a generating power schedule, a charge/discharge (C/D) power schedule, and a state of charge (SOC) schedule. Our purpose is to obtain the exact range of each optimal schedule for any possible PV/demand profiles of the interval prediction. In the previous work, we proposed a method to find the exact ranges of the optimal generation power schedule and the optimal C/D power schedule by showing the sign patterns of the Jacobians with respect to an uncertain renewable parameter. However, the range of the optimal SOC schedule is not derived so far. If the exact range is found, we can offer a guideline for a necessary and sufficient capacity of storage batteries at each time step. To get the range, we show that the sign pattern of the Jacobian for SOC is invariant, more specifically, its sign pattern has negative elements in the lower triangle and positive elements in others. The key to analyzing the sign pattern is to utilize particular properties of an M-matrix and a diagonally dominant matrix. As a result, we clarify the sign pattern mathematically, which enables to effectively calculate the exact range of the optimal SOC schedule. This letter completes the monotonicity analysis of all the decision variables in the optimal scheduling problem.

关键词： Photovoltaic power generation prediction uncertainty interval quadratic programming M-matrix

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Integrated optimization of water and fertilizer coupling system under uncertainty

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DESALINATION AND WATER TREATMENT 2018年 126卷 268-277页

作者： Liu, Xiao Li, Mo Guo, Ping Zhang, Zhongxue China Agr Univ Ctr Agr Water Res China Tsinghuadong St 17 Beijing 100083 Peoples R China Heilongjiang Prov Hydraul Res Inst Harbin 150080 Heilongjiang Peoples R China Northeast Agr Univ Sch Water Conservancy & Civil Engn Harbin 150030 Heilongjiang Peoples R China Minist Agr Key Lab Agr Water Resources Use Harbin 150030 Heilongjiang Peoples R China

Water and fertilizer jointly affect the growth of crops. A nonlinear programming model for the optimal utilization of water and fertilizer under uncertainty was developed to maximize net benefits. The complexities in estimating crop yields, water requirements as well as economic profits were considered. The developed model improved upon existing management models through incorporating water-fertilizer production functions of crops, in which uncertainties in parameters and functions expressed as intervals were reflected. Moreover, it could improve irrigation efficiency, protect ecological environment, and thus promote the sustainable development of the agricultural system. The model was solved by interval quadratic programming method. Based on the experimental data from Qing'an experimental station as well as a representative experimental station in Heping irrigation district, Heilongjiang province, China, the developed model was applied to simultaneously optimize the utilization of water and fertilizer. The developed model and the corresponding solution method are beneficial to the optimization of fertigation schedule, and have broad prospects for addressing other issues that are related to agricultural water management.

关键词： interval quadratic regression interval quadratic programming Water and fertilizer production function Rice Uncertainty

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