Transmission-expansion planning using the DC model and nonlinear-programming technique

The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.

Solution approaches for the soft drink integrated production lot sizing and scheduling problem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Transmission system expansion planning by a branch-and-bound algorithm

A branch and bound (B& B) algorithm using the DC model, to solve the power system transmission expansion planning by incorporating the electrical losses in network modelling problem is presented. This is a mixed integer nonlinear programming (MINLP) problem, and in this approach, the so-called fathoming tests in the B&B algorithm were redefined and a nonlinear programming (NLP) problem is solved in each node of the B& B tree, using an interior-point method. Pseudocosts were used to manage the development of the B&B tree and to decrease its size and the processing time. There is no guarantee of convergence towards global optimisation for the MINLP problem. However, preliminary tests show that the algorithm easily converges towards the best-known solutions or to the optimal solutions for all the tested systems neglecting the electrical losses. When the electrical losses are taken into account, the solution obtained using the Garver system is better than the best one known in the literature.

A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimized Allocation of Control and Protective Devices in Electric Distribution Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An implementation of modified scatter search algorithm to transmission expansion planning

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Planning of secondary distribution circuits through evolutionary algorithms

In this work, the planning of secondary distribution circuits is approached as a mixed integer nonlinear programming problem (MINLP). In order to solve this problem, a dedicated evolutionary algorithm (EA) is proposed. This algorithm uses a codification scheme, genetic operators, and control parameters, projected and managed to consider the specific characteristics of the secondary network planning. The codification scheme maps the possible solutions that satisfy the requirements in order to obtain an effective and low-cost projected system-the conductors' adequate dimensioning, load balancing among phases, and the transformer placed at the center of the secondary system loads. An effective algorithm for three-phase power flow is used as an auxiliary methodology of the EA for the calculation of the fitness function proposed for solutions of each topology. Results for two secondary distribution circuits are presented, whereas one presents radial topology and the other a weakly meshed topology. © 2005 IEEE.

GPS ambiguity resolution and validation under multipath effects: Improvements using wavelets

Integer carrier phase ambiguity resolution is the key to rapid and high-precision global navigation satellite system (GNSS) positioning and navigation. As important as the integer ambiguity estimation, it is the validation of the solution, because, even when one uses an optimal, or close to optimal, integer ambiguity estimator, unacceptable integer solution can still be obtained. This can happen, for example, when the data are degraded by multipath effects, which affect the real-valued float ambiguity solution, conducting to an incorrect integer (fixed) ambiguity solution. Thus, it is important to use a statistic test that has a correct theoretical and probabilistic base, which has became possible by using the Ratio Test Integer Aperture (RTIA) estimator. The properties and underlying concept of this statistic test are shortly described. An experiment was performed using data with and without multipath. Reflector objects were placed surrounding the receiver antenna aiming to cause multipath. A method based on multiresolution analysis by wavelet transform is used to reduce the multipath of the GPS double difference (DDs) observations. So, the objective of this paper is to compare the ambiguity resolution and validation using data from these two situations: data with multipath and with multipath reduced by wavelets. Additionally, the accuracy of the estimated coordinates is also assessed by comparing with the ground truth coordinates, which were estimated using data without multipath effects. The success and fail probabilities of the RTIA were, in general, coherent and showed the efficiency and the reliability of this statistic test. After multipath mitigation, ambiguity resolution becomes more reliable and the coordinates more precise. © Springer-Verlag Berlin Heidelberg 2007.

Heuristic algorithm to solve the short term transmission network expansion planning

In this paper, a method for solving the short term transmission network expansion planning problem is presented. This is a very complex mixed integer nonlinear programming problem that presents a combinatorial explosion in the search space. In order to And a solution of excellent quality for this problem, a constructive heuristic algorithm is presented in this paper. In each step of the algorithm, a sensitivity index is used to add a circuit (transmission line or transformer) or a capacitor bank (fixed or variable) to the system. This sensitivity index is obtained solving the problem considering the numbers of circuits and capacitors banks to be added (relaxed problem), as continuous variables. The relaxed problem is a large and complex nonlinear programming and was solved through a higher order interior point method. The paper shows results of several tests that were performed using three well-known electric energy systems in order to show the possibility and the advantages of using the AC model. ©2007 IEEE.

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (1) the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice. © 2006 Elsevier Ltd. All rights reserved.

Planeamiento de la expansión de sistemas de transmisión considerando contingencias y demanda incierta

This paper presents a methodology and a mathematical model to solve the expansion planning problem that takes into account the effect of contingencies in the planning stage, and considers the demand as a stochastic variable within a specified range. In this way, it is possible to find a solution that minimizes the investment costs guarantying reliability and minimizing future load shedding. The mathematical model of the expansion planning can be represented by a mixed integer nonlinear programming problem. To solve this problem a specialized Genetic Algorithm combined with Linear Programming was implemented.

Reformulação para um problema integrado de dimensionamento e sequenciamento de lotes

In this paper, some new constraints and an extended formulation are presented for a Lot Sizing and Scheduling Model proposed in the literature. In the production process considered a key material is prepared and is transformed into different final items. The sequencing decisions are related to the order in which the materials are processed and the lot sizing decisions are related to the final items production. The mathematical formulation considers sequence-dependent setup costs and times. Results of the computational tests executed using the software Cplex 10.0 showed that the performance of the branch-and-cut method can be improved by the proposed a priori reformulation.

Distribution system restoration in a DG environment using a heuristic constructive multi-start algorithm

This paper proposes a heuristic constructive multi-start algorithm (HCMA) to distribution system restoration in real time considering distributed generators installed in the system. The problem is modeled as nonlinear mixed integer and considers the two main goals of the restoration of distribution networks: minimizing the number of consumers without power and the number of switching. The proposed algorithm is implemented in C++ programming language and tested using a large real-life distribution system. The results show that the proposed algorithm is able to provide a set of feasible and good quality solutions in a suitable time for the problem. © 2011 IEEE.

Optimal switch allocation for automatic load transfer in distribution substations

This work proposes a methodology for optimized allocation of switches for automatic load transfer in distribution systems in order to improve the reliability indexes by restoring such systems which present voltage classes of 23 to 35 kV and radial topology. The automatic switches must be allocated on the system in order to transfer load remotely among the sources at the substations. The problem of switch allocation is formulated as nonlinear constrained mixed integer programming model subject to a set of economical and physical constraints. A dedicated Tabu Search (TS) algorithm is proposed to solve this model. The proposed methodology is tested for a large real-life distribution system. © 2011 IEEE.

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.