In distribution systems, the coordination and selectivity of protection devices are essential for improving reliability and security indicators. In these systems, the overcurrent relays are widely used. During a fault...
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In distribution systems, the coordination and selectivity of protection devices are essential for improving reliability and security indicators. In these systems, the overcurrent relays are widely used. During a fault, the heat dissipation is high. Therefore, it is important that the relays act quickly. The problem of coordination is linear when the pickup currents are previously known. In this paper, a methodology for an optimal coordination of non-directional overcurrent relays in radial systems using mixed-integer linear programming (MILP) is proposed. The main objective is to compute the Time Dial Settings (TDSs) that minimize the relay operational times, without any loss of sensitivity, selectivity and reliability. The TDSs are considered as discrete variables, so the problem becomes discrete and is solved through MILP. The selectivity is guaranteed for a range of possible fault currents levels. The proposed methodology is successfully applied in a radial test system containing five overcurrent relays.
This study presents a mixed-integer linear programming (MILP) model to solve the short-term expansion planning problem of radial electrical distribution systems. The proposed model defines the construction of new circ...
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This study presents a mixed-integer linear programming (MILP) model to solve the short-term expansion planning problem of radial electrical distribution systems. The proposed model defines the construction of new circuits, the reconductoring of existing circuits, the allocation of capacitor banks (as well as the type and the number of units in operation) and the allocation of voltage regulators to minimise the total annualised investment and operation costs. In the proposed formulation, the steady-state operation of the radial distribution system is mathematically modelled through linear expressions. The use of an MILP model guarantees convergence to optimality by using existing classical optimisation tools. The model was implemented in the mathematical modelling language AMPL and solved using the commercial solver CPLEX. A 54-node test system and 201-node real distribution system were used to demonstrate the accuracy of the mathematical model, as well as the efficiency of the proposed solution technique.
A single product maritime inventory routing problem is addressed in this paper by exploring the use of continuous and discrete time models. We first present a continuous time model based on time slots for single docks...
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A single product maritime inventory routing problem is addressed in this paper by exploring the use of continuous and discrete time models. We first present a continuous time model based on time slots for single docks, which is enhanced by reformulating the time assignment constraints. Next, we present a model based on event points to handle parallel docks. A discrete time is also presented based on a single commodity fixed-charge network flow problem (FCNF). All the models are solved for multiple randomly generated instances of different problems to compare their computational efficiency, and to illustrate the solutions obtained. (C) 2015 Elsevier Ltd. All rights reserved.
This note concerns the problem of k-hop connectivity in a network of mobile agents, which is achieved if any pair of agents can communicate with each other through a link of k-1 or fewer intermediate nodes. We propose...
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This note concerns the problem of k-hop connectivity in a network of mobile agents, which is achieved if any pair of agents can communicate with each other through a link of k-1 or fewer intermediate nodes. We propose linear constraints involving binary optimization variables to ensure k-hop connectivity. Such constraints are then integrated into a mixed-integer linear programming (MILP) trajectory planning model. Simulation results illustrate the application of the proposed method and the effect of varying k in the context of a mission involving the visitation of multiple targets.
In this paper, we address the bin packing problem while minimizing the total loading cost of used bins. We focus on two different quantity discount schemes: the all-unit discount and the incremental discount. For both...
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In this paper, we propose a flexible mixed-integer linear programming formulation of the AC OPF problem for distribution systems, using convexification and linearization techniques. The proposed formulation allows the...
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In this paper, we propose a flexible mixed-integer linear programming formulation of the AC OPF problem for distribution systems, using convexification and linearization techniques. The proposed formulation allows the representation of discrete decisions via integer decision variables, captures the nonlinear behavior of the electrical network via approximations of controllable accuracy, and can be solved to global optimality with commercial optimization solvers. The formulation is based on conventional variables that describe network behavior, which ensures its flexibility and the possibility of application to various distribution system problems, as we indicate with case studies.
This paper presents a method in expansion planning of transmission systems using the AC optimal power flow (AC-OPF). The AC-OPF provides a more accurate picture of power flow in the network compared to the DC optimal ...
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This paper presents a method in expansion planning of transmission systems using the AC optimal power flow (AC-OPF). The AC-OPF provides a more accurate picture of power flow in the network compared to the DC optimal power flow (DC-OPF) that is usually considered in the literature for transmission expansion planning (TEP). While the AC-OPF-based TEP is a mixed-integer nonlinearprogramming problem, this paper transforms it into a mixed-integer linear programming environment. This transformation guarantees achievement of a global optimal solution by the existing algorithms and software. The proposed model has been successfully applied to a simple 3-bus power system, Carver's 6-bus test system, 24-bus IEEE reliability test system (RTS) as well as a realistic power system. Detailed case studies are presented and thoroughly analyzed. Simulations show the effectiveness of the proposed method on the TEP. (C) 2014 Elsevier B.V. All rights reserved.
This paper deals with "The Enchanted Journey," which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations...
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This paper deals with "The Enchanted Journey," which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland;moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time;in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integerlinear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.
This paper presents a multi-period auction for a day-ahead pool-based electricity market in which consumer payment for energy is minimized under uniform pricing. This optimization problem has been recently characteriz...
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This paper presents a multi-period auction for a day-ahead pool-based electricity market in which consumer payment for energy is minimized under uniform pricing. This optimization problem has been recently characterized as a non-separable, non-linear, mixed-integer, and combinatorial problem for which exact solution techniques are unavailable. We present a novel approach suitable for existing mixed-integerlinear solvers. A major contribution of this paper is the explicit characterization of uniform market-clearing prices as primal decision variables. The proposed methodology allows considering both quadratic and piecewise linear supply offers. In addition, the market-clearing procedure also takes into account inter-temporal operational constraints such as start-ups, ramp rates, and minimum up and down times, which may be part of generation offers. This approach provides the system operator and market agents with a valuable tool to assess consumer payment minimization versus currently used declared social welfare maximization. This conclusion is backed by simulation results obtained with off-the-shelf software. (C) 2013 Elsevier Ltd. All rights reserved.
The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear e...
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The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear expected surplus criterion for American contingent claims in finite state markets gives rise to a non-convex bilinearprogramming formulation which admits an exact linearization. The resulting mixed-integerlinear program can be readily processed by available software. (c) 2011 Elsevier B.V. All rights reserved.
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