A novel microgrid support management system based on stochastic mixed-integer linear programming

Using different dominance criteria in stochastic fuzzy linear multiobjective programming: A case of fuzzy weighted objective function

Many planning problems involve choosing a set of optimal decisions for a system in the face of uncertainty of elements that may play a central role in the way the system is analyzed and operated. During the past decade, there has been a renewed interest in the modelling, analysis, and solution of such problems due to a remarkable development of both new theoretical results and novel computational techniques in stochastic optimization. A prominent approach is to develop upper and lower bounding approximations to the problem along with procedures to sharpen bounds until an acceptable tolerance is satisfied. The contributions of this dissertation are concerned with the latter approach. The thesis first studies the stochastic linear programming problem with randomness in both the objective coefficients and the constraints. A convex concave saddle property of the value function is utilized to derive new bounding techniques which generalize previously known results. These approximations require discretizing bounded domains of the random variables in such a way that tight upper and lower bounds result. Such techniques will prove attractive with the recent advances in large scale linear programming. The above results are also extended to obtain new upper and lower bounds when the domains of random variables are unbounded. While these bounds are tight, the approximating models are large-scale deterministic linear programs. In particular, with a proposed order-cone decomposition for the domains, these linear programs are well-structured, thus enabling one to use efficient techniques for solution, such as parallel computation. The thesis next considers convex stochastic programs. Using aggregation concepts from the deterministic literature, new bounds are developed for the problem which are computable using standard convex programming algorithms. Finally, the discussion is focused on a stochastic convex program arising in a certain resource allocation problem. Exploiting the problem structure, bounds are developed via the Karush-Kuhn-Tucker conditions. Rather than discretizing domains, these approximations advocate replacing difficult multidimensional integrals by a series of simple univariate integrals. Such practice allows one to preserve differentiability properties so that smooth convex programming methods can be applied for solution.

A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain; indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.

Multi-objective optimization approach to design and planning hydrogen supply chain under uncertainty: A Portugal study case

The integration of fluctuating renewable energies leads to higher price fluctuations in day-ahead markets, consequently the incentives for the activation of flexible loads increase. Even if relative forecasting errors decrease, the absolute forecasting error of renewable power production is expected to increase, therefore the demand for reserve power will rise. To fully exploit the economic potential of evolving energy markets through the utilization of production process flexibility, multiple markets need to be considered at the same time. Production planning and the participation in the reserve markets can be formulated as a multistage Stochastic Mixed-Integer Linear Programming (SMILP) problem that minimizes the expected total costs, which consists of cost for purchasing power subtracted by the revenues from offering reserve energy. The presented approach incorporates a production process model which considers uncertainties of spot and reserve market prices in terms of a stochastic process.

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.

This paper models the offers and bids of a generic storage system in an electricity market through stochastic mixed integer linear programming. The objective function aims at maximizing the profit from buying or selling energy for a general storage system. Some parameters such as storage system efficiency, losses of the energy stored and marginal costs are parameterized to evaluate the offers and bids. Market prices are forecasted for 24 hours using AR, MA and ARIMA time series models. The problem is tested for a case study, analyzing the behaviour of the offers and bids. Also, the results obtained are studied and relevant conclusions are presented.

The self Help Group (SHG) is group of rural poor who have organized themselves into a group for eradicationof poverty. The members of the group belong to families below the poverty line. This will help the families of occupational groups like agricultural labourers, marginal farmers, designers and artisans marginally above the poverty line, or who may have been excluded from the Below Poverty Line (BPL) list to become members of the Self Help Group. A self help group consists of two categories. One named as magalier thittam and another is non- magalier thittam. The factors of Self help group categories are random in nature. These factors can be handled using stochastic linear programming problem (SLPP). Here the data is collected from Tuticorin district. The optimization technique such as two stage programming and chance constrained programming can be adopted for SLPP. In this paper chance constrained programming (CPP) is used to obtain optimal solution.

The aim of this paper is to derive a method for solving a stochastic linear programming problem with Cauchy distribution. Assuming that the coefficients are distributed as Cauchy random variables, the stochastic linear programming is converted to a deterministic non-linear programming problem by a suitable transformation. Then an algorithm can be used to solve the resulting deterministic problem .A numerical example can be considered to illustrate the above methodology.

We formulate and discuss a model of two-period stochastic optimization which allows for the possibility of the probability distribution over a non-empty finite set of states of nature-exactly one member of which will be realized in the future period- to depend on the control variable chosen in the initial period. In the second and terminal period, the decision maker chooses the value of a control variable vector which along with the control variable vector chosen in the initial period, solve a linear programming problem. The parameters of the linear programming are determined by an uncertain state of nature that is realized at the beginning of the terminal period. In order to obtain specific results, we assume that in the initial period, the decision maker can choose any one alternative from a finite set of alternatives, each such alternative being “a system of linear inequality constraints.” It is further assumed that solution sets of any two different systems are mutually disjoint and the probability distribution of the uncertain components of the state variables that is realized in the second period is determined by the system of linear inequalities chosen in the initial period. We refer to the overall problem as a “two-period stochastic linear programming game”. Our first result for a two-period stochastic linear programming game is that the optimal value for such a game as well as the optimal solutions for each of the finite number of stochastic linear programs can be found by solving a linear programming problem and our second result in this context says that the (optimal) solution for the dual of this linear programming contains a component that determines “at least one” stochastic linear programming problem any solution of which when substituted in its objective function, yields the optimal value of the two-period stochastic linear programming game. There is no need to solve any other subproblem or the primal problem to derive the optimal value of the game. AMS Classifications: 90C05, 90C15, 90C39, 90C46, 91A65 JEL Classifications: C61, C79, D81

For a class of stochastic linear bilevel programming problem, we firstly transform it into a deterministic linear bilevel covariance programming problem. Then, the deterministic bilevel covariance programming problem is solved by backpropagation artificial neural network based on elite particle swam optimization algorithm (BPANN-PSO). Finally, we perform the simulation experiments and the results show that the computational efficiency of the proposed algorithm has a potential upside compared with the classical algorithm.

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.

The study of the network design problems related to reverse supply chain and reverse logistics is of great interest for both academicians and practitioners due to its important role for a sustainable society. However, reverse logistics network design is a complex decision-making problem that involves several interactive factors and faces many uncertainties. Thus, in order to improve the reverse logistics network design, this paper proposes a new optimization model under stochastic environment and an improved solution method for network design of a multi-stage multi-product reveres supply chain. The study is presented in a series of two parts. Part I presents the relevant literature and formulates a stochastic mixed integer linear programming (MILP) for improving the decision-making of the reverse logistics network design. Part II improves the solution method for the proposed stochastic programming and illustrates the application through a numerical experimentation.

To mitigate outpatient care delivery inefficiencies induced by resource shortages and demand heterogeneity, this paper focuses on the problem of allocating and sequencing multiple medical resources so that patients scheduled for clinical care can experience efficient and coordinated care with minimum total waiting time. We leverage highly granular location data on people and medical resources collected via Real-Time Location System technologies to identify dominant patient care pathways. A novel two-stage Stochastic Mixed Integer Linear Programming model is proposed to determine the optimal patient sequence based on the available resources according to the care pathways that minimize patients’ expected total waiting time. The model incorporates the uncertainty in care activity duration via sample average approximation.We employ a Monte Carlo Optimization procedure to determine the appropriate sample size to obtain solutions that provide a good trade-off between approximation accuracy and computational time. Compared to the conventional deterministic model, our proposed model would significantly reduce waiting time for patients in the clinic by 60%, on average, with acceptable computational resource requirements and time complexity. In summary, this paper proposes a computationally efficient formulation for the multi-resource allocation and care sequence assignment optimization problem under uncertainty. It uses continuous assignment decision variables without timestamp and position indices, enabling the data-driven solution of problems with real-time allocation adjustment in a dynamic outpatient environment with complex clinical coordination constraints.

Wind energy is rapidly growing. While wind brings us clean and inexpensive energy, its inherent variability and uncertainty present challenges for the power grid. In particular, employing wind energy for power system restoration is very challenging. A fast and reliable restoration plays a vital role to achieve the self-healing power grid. This paper develops a novel offline restoration planning tool for harnessing wind energy to enhance grid resilience. The wind-for-restoration problem is formulated as a stochastic mixed-integer linear programming problem with generated wind energy scenarios. The problem is then decomposed into two stages and solved with the integer L-shaped algorithm. Numerical experiments have been conducted through different case studies using the modified IEEE 57-bus system. The developed tool can provide the scheduled wind power at each restoration time. The impact of wind energy is investigated from the aspects of location and inertia capability, as well as wind penetration, fluctuation, and uncertainty. Moreover, a dynamic response validation tool is developed to validate the results of optimization problem in a dynamic simulation software. Simulation results demonstrate that the optimal wind harnessing strategy can help improve system restoration process and enhance system resilience.