• Title, Summary, Keyword: Chance constrained programming

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Dynamic Economic Dispatch for Microgrid Based on the Chance-Constrained Programming

  • Huang, Daizheng;Xie, Lingling;Wu, Zhihui
    • Journal of Electrical Engineering and Technology
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    • v.12 no.3
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    • pp.1064-1072
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    • 2017
  • The power of controlled generators in microgrids randomly fluctuate because of the stochastic volatility of the outputs of photovoltaic systems and wind turbines as well as the load demands. To address and dispatch these stochastic factors for daily operations, a dynamic economic dispatch model with the goal of minimizing the generation cost is established via chance-constrained programming. A Monte Carlo simulation combined with particle swarm optimization algorithm is employed to optimize the model. The simulation results show that both the objective function and constraint condition have been tightened and that the operation costs have increased. A higher stability of the system corresponds to the higher operation costs of controlled generators. These operation costs also increase along with the confidence levels for the objective function and constraints.

DUALITY FOR LINEAR CHANCE-CONSTRAINED OPTIMIZATION PROBLEMS

  • Bot, Radu Ioan;Lorenz, Nicole;Wanka, Gert
    • Journal of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.17-28
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    • 2010
  • In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

A Study of the Reformulation of 0-1 Goal Programming (0 - 1 목표계획모형의 재구조화에 관한 연구-기회제약계획법(CCP)과 계층화 분석과정(AHP)의 결합 가능성을 중심으로-)

  • 이영찬;민재형
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.525-529
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    • 1996
  • Decision environments involve a high degree of uncertainty as well as multiple, conflicting goals. Although traditional goal programming offers a means of considering multiple, conflicting goals and arrives at a satisficing solution in a deterministic manner, its major drawback is that decision makers often specify aspiration level of each goal as a single number. To overcome the problem of setting aspiration levels, chance constrained programming can be incorporated into goal programming formulation so that sampling information can be utilized to describe uncertainty distribution. Another drawback of goal programming is that it does not provide a systematic approach to set priorities and trade-offs among conflicting goals. To overcome this weekness, the analytic hierarchy process(AHP) is used in the model. Also, most goal programming models in the literature are of a linear form, although some nonlinear models have been presented. Consideration of risk in technological coefficients and right hand sides, however, leads to nonlinear goal programming models, which require a linear approximation to be solved. In this paper, chance constrained reformulation with linear approximation is presented for a 0-1 goal programming problem whose technological coefficients and right hand sides are stochastic. The model is presented with a numerical example for the purpose of demonstration.

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A New Chance-Constrained Programming Approach to Capital Budgeting (확률제약조건계획법(確率制約條件計劃法)을 이용(利用)한 자본예산모형(資本豫算模型))

  • Lee, Ju-Ho
    • Journal of Korean Institute of Industrial Engineers
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    • v.6 no.2
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    • pp.21-29
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    • 1980
  • This paper deals with the capital budgeting problem of a firm where investments are risky and interrelated. The established models might be classified into two categories; One is the chance-constrained programming model and the other is the expected utility maximization model. The former has a rather limited objective function and does not consider the risk in direct manner. The latter, on the other hand, might lead to a wrong decision because it uses an approximate value of expected utility. This paper attempts to extend the applicability of the chance-constrained programming model by modifying its objective function into a more general form. The capital budgeting problem is formulated as a nonlinear 0-1 integer programming problem first, and is formulated into a linear 0-1 integer programming problem for finding a lower-bound solution of the original problem. The optimal solution of the original problem is then obtained by branch & bound algorithm.

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Support Vector Machine Based on Type-2 Fuzzy Training Samples

  • Ha, Ming-Hu;Huang, Jia-Ying;Yang, Yang;Wang, Chao
    • Industrial Engineering and Management Systems
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    • v.11 no.1
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    • pp.26-29
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    • 2012
  • In order to deal with the classification problems of type-2 fuzzy training samples on generalized credibility space. Firstly the type-2 fuzzy training samples are reduced to ordinary fuzzy samples by the mean reduction method. Secondly the definition of strong fuzzy linear separable data for type-2 fuzzy samples on generalized credibility space is introduced. Further, by utilizing fuzzy chance-constrained programming and classic support vector machine, a support vector machine based on type-2 fuzzy training samples and established on generalized credibility space is given. An example shows the efficiency of the support vector machine.

A New Solution for Stochastic Optimal Power Flow: Combining Limit Relaxation with Iterative Learning Control

  • Gong, Jinxia;Xie, Da;Jiang, Chuanwen;Zhang, Yanchi
    • Journal of Electrical Engineering and Technology
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    • v.9 no.1
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    • pp.80-89
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    • 2014
  • A stochastic optimal power flow (S-OPF) model considering uncertainties of load and wind power is developed based on chance constrained programming (CCP). The difficulties in solving the model are the nonlinearity and probabilistic constraints. In this paper, a limit relaxation approach and an iterative learning control (ILC) method are implemented to solve the S-OPF model indirectly. The limit relaxation approach narrows the solution space by introducing regulatory factors, according to the relationship between the constraint equations and the optimization variables. The regulatory factors are designed by ILC method to ensure the optimality of final solution under a predefined confidence level. The optimization algorithm for S-OPF is completed based on the combination of limit relaxation and ILC and tested on the IEEE 14-bus system.

Valuation of Irrigation Water: A Chance-Constrained Programming Approach (확률제약 계획모형법을 이용한 농업용수의 경제적 가치 평가)

  • Kwon, Oh-Sang;Lee, Tae-Ho;Heo, Jeong-Hoi
    • Journal of Korea Water Resources Association
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    • v.42 no.4
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    • pp.281-295
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    • 2009
  • This study estimates the value of irrigation water in Korea using an economic programming model that is constructed with all the resource endowment constraints, technology restrictions and policy variables. The variability and uncertainty of water resource endowment are incorporated into the model through the chance-constrained technique. Solving the profit maximization problems with gradually reduced water endowments, we derive a series of shadow values of irrigation water. It has been found that uncertainty in water supply raises the damage from water loss, and the marginal damage increases in water loss.

Evaluation of the Effective Storage of Existing Agricultural Reservoir (기존 농업용 저수지에서의 유효저수량의 평가)

  • Ahn, Tae-Jin;Cho, Dong-Ho;Lee, Sang-Ho;Choi, Gye-Woon;Yoon, Yong-Nam
    • Journal of Korea Water Resources Association
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    • v.37 no.5
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    • pp.353-361
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    • 2004
  • Effective storage in agricultural reservoir has been determined through the reservoir simulation operation based on the water budget analysis. Since each watershed has the native property for runoff, considering the runoff yielding from the basin is feasible to the determination of reservoir effective storage. In this study the stochastic linear programming model considering mainly runoff from watershed has been also formulated to analyze the effective storage of the exiting reservoir. The linear decision rule coupled with chance-constrained model in the linear programming model contributes to reduce the size of linear program model without considering the period of analysis. The Geum-Gang reservoir located in Ansung have been adopted to evaluate the effective storage. It has been shown that the effective storage based on the linear programming model is greater than that based on the water budget analysis. It has been also desired that once the effective storage is obtained through the linear programming model, operation of the reservoir should be performed to check the designed capacity.

Optimal Var allocation in System planning by Stochastic Linear Programming(II) (확률선형 계획법에 의한 최적 Var 배분 계뵉에 관한 연구(II))

  • Song, Kil-Yeong;Lee, Hee-Yoeng
    • Proceedings of the KIEE Conference
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    • pp.191-193
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    • 1989
  • This paper presents a optimal Var allocation algorithm for minimizing power loss and improving voltage profile in a given system. In this paper, nodal input data is considered as Gaussian distribution with their mean value and their variance. A stochastic Linear Programming technique based on chance constrained method is applied to solve the probabilistic constraint. The test result in IEEE-14 Bus model system showes that the voltage distribution of load buses is improved and the power loss is more reduced than before Var allocation.

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Optimal Var Allocation in system planning by stochastic Linear Programming (확률 선형 계획법에 의한 최적 Var 배분 계획에 관한 연구)

  • Song, Kil-Yeong;Lee, Hee-Yeong
    • Proceedings of the KIEE Conference
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    • pp.863-865
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    • 1988
  • This paper presents a optimal Var allocation algorithm for minimizing transmission line losses and improving voltage profile in a given system. In this paper, nodal input data is considered as Gaussian distribution with their mean value and their variance. A Stocastic Linear programming technique based on chance constrained method is applied, to solve the var allocation problem with probabilistic constraint. The test result in 6-Bus Model system showes that the voltage distribution of load buses is improved and the power loss is more reduced than before var allocation.

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