Specialised branch-and-bound algorithm for transmission network expansion planning

An algorithm is presented that finds the optimal plan long-term transmission for till cases studied, including relatively large and complex networks. The knowledge of optimal plans is becoming more important in the emerging competitive environment, to which the correct economic signals have to be sent to all participants. The paper presents a new specialised branch-and-bound algorithm for transmission network expansion planning. Optimality is obtained at a cost, however: that is the use of a transportation model for representing the transmission network, in this model only the Kirchhoff current law is taken into account (the second law being relaxed). The expansion problem then becomes an integer linear program (ILP) which is solved by the proposed branch-and-bound method without any further approximations. To control combinatorial explosion the branch- and bound algorithm is specialised using specific knowledge about the problem for both the selection of candidate problems and the selection of the next variable to be used for branching. Special constraints are also used to reduce the gap between the optimal integer solution (ILP program) and the solution obtained by relaxing the integrality constraints (LP program). Tests have been performed with small, medium and large networks available in the literature.

Produção de leite, leite residual e concentração hormonal de vacas Gir × Holandesa e Holandesa em ordenha mecanizada exclusiva

In a machine milking system in which calves were not present, oxytocin concentration (OT), cortisol release (CORT), milk yield and residual milk were evaluated for cows of three genetic groups: 1/2Gir x 1/2Holstein (n=6, genetic group F2), 1/4Gir x 3/4Holstein (n=6, genetic group F3) and Holstein (n=6, genetic group H). Group H had higher milk yield than groups F2 and F3, whereas OT was similar among groups. The increase in OT during milk-ing was greater for H and F3 than for F2. Residual milk for F2 was' higher than for F3 and H. The CORT for F2 was higher than for cows of the other two genetic groups. Cows from F2 and F3 were more stressed than H cows during machine milking, but the Gir x Holstein groups did release suffficient OT to induce an effective milk letdown response.

Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

Power system transmission network expansion planning using AC model

An optimisation technique to solve transmission network expansion planning problem, using the AC model, is presented. This is a very complex mixed integer nonlinear programming problem. A constructive heuristic algorithm aimed at obtaining an excellent quality solution for this problem is presented. An interior point method is employed to solve nonlinear programming problems during the solution steps of the algorithm. Results of the tests, carried out with three electrical energy systems, show the capabilities of the method and also the viability of using the AC model to solve the problem.

The high-eccentricity asymmetric expansion of the disturbing function for non-planar resonant problems

In this paper we present an extension to the nonplanar case of the asymmetric expansion of the averaged resonant disturbing function of Ferraz-Mello & Sato (1989, A&A 225, 541-547). Comparions with the exact averaged disturbing function are also presented. The expansion gives a good approximation of the exact function in a wide region around the center of expansion.

Residual and annual potassic fertilization for soybeans

There is a lack of long-term research on potassium fertilization for soybean in the tropical and subtropical soils of Brazil and the residual effect of the fertilizer has generally not been considered. An experiment was conducted in plots that had been fertilized with 0, 40, 80, 160 and 240 kg ha(-1) of K2O for 3 years on a Dark Red Latosol, loamy sand (Acrortox). The effects of annual or residual fertilization with those rates of K were studied for three additional years. Potassium was supplied as potassium chloride or potassium sulphate. Soil and leaf samples were taken annually. There was a residual effect of the nutrient, which provided for high yields up to the 3rd year with the highest rate of K. In order to maintain the K contents of the soil in the medium range and obtain at least 90% of the maximum grain yield, an annual application of 80 kg ha(-1) of K2O was necessary, irrespectively of the source. The highest soybean yields were always associated with K levels above 15 mg kg(-1) in the leaves and 1.2 mmol(c) dm(-3) in the soil.

Transmission network expansion planning considering uncertainty in demand

This paper presents two mathematical models and one methodology to solve a transmission network expansion planning problem considering uncertainty in demand. The first model analyzed the uncertainty in the system as a whole; then, this model considers the uncertainty in the total demand of the power system. The second one analyzed the uncertainty in each load bus individually. The methodology used to solve the problem, finds the optimal transmission network expansion plan that allows the power system to operate adequately in an environment with uncertainty. The models presented are solved using a specialized genetic algorithm. The results obtained for several known systems from literature show that cheaper plans can be found satisfying the uncertainty in demand.

Thermodynamic analysis of the cogeneration system expansion in a sugar-alcohol factory

In this work it was performed energetic and exergetic analyses of three thermal plants to assessment a cogeneration system in expansion of a sugar-alcohol factory. The initial configuration considered is constituted by a low pressure steam generator, single stage steam turbines for electricity generation and crusher, shredder and mills with mechanical driving. In the intermediary configuration, the low pressure steam generator was substituted by another which generates steam at higher pressure and higher temperature, the steam turbines for electricity generation were substituted by a multiple stages extraction-condensation turbine and the other steam turbines were maintained. The final configuration consists in the substitution of these last turbines by electrical motors. Thermodynamic analyses were performed to evaluate the equipment and the overall plants efficiencies to permit a comparison among the plants. Besides of this, some important parameters of the sugar-alcohol factories were calculated.

Evaluation of the thermal shrinkage of titanium and the setting and thermal expansion of phosphate-boded investments

Statement of problem. There are few studies on titanium casting shrinkage, and phosphate-bonded investments for titanium casting have not produced appropriate marginal fit.Purpose. The purpose of this study was to determine the thermal shrinkage of titanium and the setting and thermal expansion of 3 phosphate-bonded investments.Material and methods. The thermal shrinkage between the melting temperature and room temperature was calculated using a titanium thermal expansion coefficient. The thermal and setting expansion were measured for 3 phosphate bonded investments: Rematitan Plus (RP) specific for titanium, Rema Exakt (RE), and Castorit Super C (CA), using different special liquid concentrations (100%, 75%, and 50%). Setting expansion was measured for cylindrical specimens 50 mm long x 8 mm in diameter with a transducer. The heating and cooling curves were obtained with a dilatometer (DIL 402 PC). The total expansion curve was drawn using software, and temperatures to obtain expansion equivalent to titanium casting shrinkage were determined (n=5). In addition, the total expansion of the control group (RP at 430 degrees C) was measured, as well as the temperatures at which the other groups achieved equivalent total expansion (n=5). Data were analyzed by 1-way ANOVA and the Tukey HSD test (alpha=.05).Results. Titanium casting shrinkage was estimated as 1.55%. RP did not achieve this expansion. RE achieved expansion of 1.55% only with a special liquid concentration of 100% at 594 degrees C. CA with all special liquid concentrations attained this expansion (351 degrees C to 572 degrees C). Total expansion of the control group was 0.86%, and the other groups reached that expansion within the range of 70 degrees C to 360 degrees C.Conclusions. Only RE and CA demonstrated sufficient expansion to compensate for titanium casting shrinkage. All groups reached total expansion equivalent to that of the control group at significantly lower temperatures.

STOCHASTIC QUANTIZATION AND 1/N EXPANSION

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

Comparative studies on non-convex optimization methods for transmission network expansion planning

We have investigated and extensively tested three families of non-convex optimization approaches for solving the transmission network expansion planning problem: simulated annealing (SA), genetic algorithms (GA), and tabu search algorithms (TS). The paper compares the main features of the three approaches and presents an integrated view of these methodologies. A hybrid approach is then proposed which presents performances which are far better than the ones obtained with any of these approaches individually. Results obtained in tests performed with large scale real-life networks are summarized.

Parallel simulated annealing applied to long term transmission network expansion planning

The simulated annealing optimization technique has been successfully applied to a number of electrical engineering problems, including transmission system expansion planning. The method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Moreover, it has the ability to provide solutions arbitrarily close to an optimum (i.e. it is asymptotically convergent) as the cooling process slows down. The drawback of the approach is the computational burden: finding optimal solutions may be extremely expensive in some cases. This paper presents a Parallel Simulated Annealing, PSA, algorithm for solving the long term transmission network expansion planning problem. A strategy that does not affect the basic convergence properties of the Sequential Simulated Annealing algorithm have been implementeded and tested. The paper investigates the conditions under which the parallel algorithm is most efficient. The parallel implementations have been tested on three example networks: a small 6-bus network, and two complex real-life networks. Excellent results are reported in the test section of the paper: in addition to reductions in computing times, the Parallel Simulated Annealing algorithm proposed in the paper has shown significant improvements in solution quality for the largest of the test networks.

The influence of residual stress and crystallite size on the magnetic properties of electrodepo sited nanocrystalline Pd-Co alloys

Nanocrystalline Pd-Co alloys were obtained by electrodeposition from an ammoniacal chloride bath. The influence of the crystallite size and the residual stress on the magnetic properties of the alloys was investigated. The residual stress increased as the applied current density was increased. It was associated to the high nucleation rate during electrodeposition and correlated to the lattice strain, estimated from the XRD patterns. Also from the XRD patterns the average crystallite size and the lattice constant were determined by Scherrer's and Rietveld's methods, respectively. Both parameters were directly influenced by the applied current density. Magnetic properties such as coercivity, remanence, saturation magnetization and squareness showed strong dependence on the residual stress and crystallite size. Coercivity higher than 1 kOe was achieved when a high current density was applied. High coercivity was attributed to the presence of residual stress and to the small crystallite size of deposits. (C) 2007 Elsevier B.V. All rights reserved.