This paper presents the determination of capacity and operational schedule for a grid-tied microgrid system based on a stochastic optimization method. A photovoltaic power system is used as a renewable energy source, ...
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ISBN:
(纸本)9781509013357
This paper presents the determination of capacity and operational schedule for a grid-tied microgrid system based on a stochastic optimization method. A photovoltaic power system is used as a renewable energy source, while battery system is utilized as energy storage systems. The microgrid system can be operated using the usual priority scheme or the proposed scheduling scheme. The mathematical model for the microgrid system is developed. The objective function is formulated from a capital and operational costs. The constraints for the optimization are formulated based on system model, physical limitations, and performance requirements. Performances required for microgrid system are high renewable energy penetration with low curtailed renewable energy. Two-stage stochastic linear programming method is used to solve the optimization problem. Proposed scheduling scheme is able to increase renewable energy penetration ratio by 4% and reduce curtailed renewable energy production ratio by 7%. The combination of scheduling scheme and stochastic optimization to improve performances of microgrid system are the key outcomes of this research.
In this work a recently developed mathematical programming formulation called adaptation is compared with the widely used stochastic programming method in the context of electric infrastructure expansion planning. Alt...
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ISBN:
(纸本)9781509032709
In this work a recently developed mathematical programming formulation called adaptation is compared with the widely used stochastic programming method in the context of electric infrastructure expansion planning. Although the structure of the adaptation method closely resembles that of a generic stochastic program it diverges from the temporal conventions of traditional electric infrastructure formulations. While traditional stochastic programming formulations restrict first and later stage capacity investments to separate time periods, the first and later stage capacity investments in adaptation overlap in time. Additionally, recourse decisions for all scenarios are defined relative to the central core trajectory in the same time period rather than the node at the previous time period in the stochastic programming scenario tree. After an in-depth discussion of stochastic programming and adaptations' formulations, a six bus simulation is provided to facilitate a more concrete comparison of the two methods. Uncertainties considered in the simulation include, wind and solar build costs, carbon taxes, demand and peak demand growth, natural gas fuel prices, and transmission costs.
We introduce disciplined convex stochastic programming (DCSP), a modeling framework that can significantly lower the barrier for modelers to specify and solve convex stochastic optimization problems, by allowing model...
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ISBN:
(纸本)9780996643108
We introduce disciplined convex stochastic programming (DCSP), a modeling framework that can significantly lower the barrier for modelers to specify and solve convex stochastic optimization problems, by allowing modelers to naturally express a wide variety of convex stochastic programs in a manner that reflects their underlying mathematical representation. DCSP allows modelers to express expectations of arbitrary expressions, partial optimizations, and chance constraints across a wide variety of convex optimization problem families (e.g., linear, quadratic, second order cone, and semidefinite programs). We illustrate DCSP's expressivity through a number of sample implementations of problems drawn from the operations research, finance, and machine learning literatures.
This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables...
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This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables with fuzzy means and fuzzy variances in proposed multi-objective fuzzy stochastic transportation problem. The first step in fuzzy simulation based genetic algorithm is to deal with aspiration level of the constraints with the help of alpha-cut technique to obtain multi-objective stochastic transportation problem. In next step, fuzzy probabilistic constraints (fuzzy chance constraints) are handled within fuzzy stochastic simulation based genetic algorithm to obtain a feasible region. The feasibilities of the chance constraints are checked by the stochastic programming with the genetic process without deriving the deterministic equivalents. The feasibility condition for the transportation problem is maintained through out the problem. Finally, multiple objective functions are considered in order to generate a Pareto optimal solutions for the fuzzy stochastic transportation problem using the proposed algorithm. The proposed procedure is illustrated by two numerical examples.
In this work a scenario-based two-stage stochastic programming model is proposed to solve a microgrid's tertiary control optimization problem taking into account some renewable energy resource's uncertainty as...
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ISBN:
(纸本)9781467366922
In this work a scenario-based two-stage stochastic programming model is proposed to solve a microgrid's tertiary control optimization problem taking into account some renewable energy resource's uncertainty as well as uncertain energy deviation prices in the electricity market. Scenario generation methods for wind speed realizations are also studied. Results show that the introduction of stochastic programming represents a significant improvement over a deterministic model.
In this paper, a mathematical optimization approach for green energy portfolio is presented to strike a right balance between risk and profit associated with retailing in power market. This approach emphasizes on the ...
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ISBN:
(纸本)9781467373890
In this paper, a mathematical optimization approach for green energy portfolio is presented to strike a right balance between risk and profit associated with retailing in power market. This approach emphasizes on the increasing use of renewable resources to overcome conservation concerns to some degrees. Three different uncertainties are considered for electricity price and energy output of wind and solar distributed generation units. In order to model the uncertainties properly, scenario construction schemes, namely Monte Carlo and time series with ARIMA (Auto regressive integrated moving average) are implemented in this paper. Moreover, risk and elasticity analysis are considered simultaneously to enable consumers and retailers to manage their risk and incomes. Two-stage stochastic programming with fixed recourse is used to model the probabilistic space of decision making process in this paper. At the end, numerical results and simulations are presented which demonstrate the applicability of the proposed approach in a retail electricity market.
This paper addresses a multi-objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneous...
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This paper addresses a multi-objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi-objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance-constrained approach and a goal-programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright (C) 2016 John Wiley & Sons, Ltd.
This paper addresses the optimal design and strategic planning of the integrated biofuel and petroleum supply chain system in the presence of pricing and quantity uncertainties. The drop-in properties of advanced hydr...
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This paper addresses the optimal design and strategic planning of the integrated biofuel and petroleum supply chain system in the presence of pricing and quantity uncertainties. The drop-in properties of advanced hydrocarbon biofuels pose considerable potential for biofuel supply chains to leverage the existing production and distribution infrastructures of petroleum supply chains, which may lead to significant capital savings. To achieve a higher modeling resolution and improve the overall economic performance, we explicitly model equipment units and material streams in the retrofitted petroleum processes and, propose a multi-period planning model to coordinate the various activities in the petroleum refineries. Furthermore, in order to develop an integrated supply chain that is reliable in the dynamic marketplace, we employ a stochastic programming approach to optimize the expectation under a number of scenarios associated with biomass availability, fuel demand, crude oil prices, and technology evolution. The integrated model is formulated as a stochastic mixed-integer linear program, which is illustrated by a case study involving 21 harvesting sites, 7 potential preconversion facilities, 6 potential integrated biorefineries, 2 petroleum refineries, and 39 demand zones. Results show the market share of biofuels increases gradually due to the increasing crude oil price and biomass availability.
We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous w...
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We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333-346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation algorithm where we iterate between a mixed-integer linear programming (MILP) master problem and a nonconvex nonlinear programming (NLP) subproblem. We prove that the optimal solutions and optimal value obtained by the SAAOA algorithm converge to the optimal solutions and the optimal value of the true SP problem as the sample size goes to infinity. The convergence rate is also given to estimate the sample size. Since the theoretical sample size estimate is too conservative in practice, we propose an SAAOA algorithm with confidence intervals for the upper bound and the lower bound at each iteration of the SAAOA algorithm. Two policies are proposed to update the sample sizes dynamically within the SAAOA algorithm with confidence intervals. The proposed algorithm works well for the special case of pure binary first stage variables and continuous stage two variables since in this case the nonconvex NLPs can be solved for each scenario independently. The proposed algorithm is tested with a stochastic pooling problem and is shown to outperform the external sampling approach where large scale MINLPs need to be solved.
We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and how to solve these equations using the St...
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We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and how to solve these equations using the stochastic Dual Dynamic programming algorithm. Finally, we consider a portfolio selection problem over an optimization period of random duration. For several instances of this problem, we show the gain obtained using a policy that takes the randomness of the number of stages into account over a policy built taking a fixed number of stages (namely the maximal possible number of stages).
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