Price-based unit commitment for bidding under price uncertainty

Bidding plays an important role for Gencos participating in competitive electricity markets with the objective of maximising profit. While making bidding strategies, factors like characteristics of generators and price uncertainty need to be considered as they have direct impact on the expected profit. In this work, a method of building an optimal bid curve under price uncertainty using price-based unit commitment (PBUC) is presented. The results indicate a simple yet an effective bidding method.     

Market oriented bidding strategy considering market price dynamics and generation cost characteristics

This study presents a new approach to bidding for Gencos participating in a competitive market, which takes account of both the uncertainty as well as the cost characteristics of the generating units in an effort to make a reasonable profit from the operation. The price uncertainty is accounted for by representing the price appropriate statistical distributions. Such statistical representation of market price is utilised to enable a Genco to be successful in a bidding process with a specified degree of confidence. The screening curve commonly used in planning and operation of generators in traditional operation of power systems to characterise the economic merits of the generating units are utilised in this study to account for the costs incurred by the Genco in its operation and establish the desired level of bidding success in the market place. The logical development of the strategy is illustrated by implementing it for a Genco with three generating units, which are chosen to have competitive cost characteristics with respect to the market price. The results of the Genco operation are presented to illustrate that the methodology succeeds in securing reasonable profit. The simulation is extended to illustrate how the accuracy of the price modelling is important to ensure better profits.     

Automatic design of guyed masts subject to deflection constraints

In the design of a guyed mast the design specification often imposes limits on the allowable deflection of the mast under wind and other lateral loads. While the deflected form of a mast depends on many different design parameters, the guy erection tensions form one of the simplest means of controlling the lateral displacements. The paper describes a procedure for calculating these tensions in the case of a mast required to have a specified set of displacements under a given set of lateral loads. It also discusses the case where specified deflections are not to be exceeded under a number of different loading conditions.     

Optimal production runs of processes subject to systematic trends

This article describes how to fit a non-linear model to the process mean of processes subject to systematic trends. Determination of the optimal length of the production run is discussed for single and double specification limits. The results are also applicable for linear trends. Illustrative examples show how the optimal production run is calculated.     

Stable numerical integration of dynamical systems subject to equality state-space constraints

Numerical simulation of constrained dynamical systems is known to exhibit stability problems even when the unconstrained system can be simulated in a stable manner. We show that not the constraints themselves, but the transformation of the continuous set of equations to a discrete set of equations is the true source of the stability problem. A new theory is presented that allows for stable numerical integration of constrained dynamical systems. The derived numerical methods are robust with respect to errors in the initial conditions and stable with respect to errors made during the integration process. As a consequence, perturbations in the initial conditions are allowed. The new theory is extended to the case of constrained mechanical systems. Some numerical results obtained when implementing the numerical method here developed are shown.     

Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints

This article presents a case study of developing a space-filling design (SFD) for a constrained mixture experiment when the experimental region is specified by single-component constraints (SCCs), linear multiple-component constraints (LMCCs), and nonlinear multiple-component constraints (NMCCs). Traditional methods and software for designing constrained mixture experiments with SCCs and LMCCs (using either optimal design or SFD approaches) are not directly applicable because of the NMCCs. A SFD algorithm in the JMP^® software was modified to accommodate the NMCCs; the modification is described in this article. The case study involves high-level waste (HLW) glass that is subject to the formation of nepheline crystals as the glass cools. This can significantly reduce the durability of HLW glass (which is undesirable). The goal of the study was to develop a SFD for the HLW glass compositional region where nepheline may form, and generate data for modeling nepheline formation as a function of HLW glass composition. The HLW glass composition region was specified in terms of eight components with SCCs, two LMCCs, and two NMCCs. The NMCCs were based on a nonlinear logistic regression model for a binary nepheline response that was developed from previous data. This article discusses the HLW glass example, the constraints specifying the experimental composition region, and how an existing algorithm for generating SFDs was modified to accommodate the NMCCs. The methodology discussed in this article can be applied to any example in which the experimental region is specified by one or more nonlinear constraints in addition to linear constraints on mixture components and/or non-mixture variables.     

Continuous-wave power transmission and thermal lensing of a saturable absorber subject to excited-state absorption

Rate-equation analysis has been used in an investigation of the role of saturation and excited-state absorption in the power transmission characteristics and thermal lensing of an absorber. Use of an iterative approach gives explicit analytical results for power transmission and thermal focal length in the presence of excited-state absorption. Sample calculations indicate that pump absorption can increase or decrease with increasing incident pump power, depending on the relative strength of the excited-state absorption cross section with respect to the ground-state absorption cross section. In the case of thermal lensing, results further indicate that saturation and excited-state absorption act as two competing effects, the former reducing the strength of the thermal lens and the latter causing the opposite effect. The analytical formulas derived in this analysis should prove useful to experimentalists in determination of ground-state and excited-state absorption cross sections from experimental power transmission and lensing data.     

Optimization of clamped columns under distributed axial load and subject to stress constraints

The optimum designs are given for clamped-clamped columns under concentrated and distributed axial loads. The design objective is the maximization of the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. In the case of a stress constraint, the minimum thickness of an optimal column is not known a priori, since it depends on the maximum buckling load, which in turn depends on the minimum thickness necessitating an iterative solution. An iterative solution method is developed based on finite elements, and the results are obtained for n=1, 2, 3 defined as I=α _n A ⁿ , with I being the moment of inertia, and A the cross-sectional area. The iterations start using the unimodal optimality condition and continue with the bimodal optimality condition if the second buckling load becomes less than or equal to the first one. Numerical results show that the optimal columns become larger in the direction of the distributed load due to the increase in the stress in this direction. Even though the optimal columns are symmetrical with respect to their mid-points when the compressive load is concentrated at the end-points, in the case of the columns subject to distributed axial loads the optimal shapes are unsymmetrical.     

Integration of vendor selection into production and remanufacturing planning subject to emission constraints

This paper presents a new model formulation that incorporates vendor selection into production and remanufacturing planning subject to emission constraints. The objective is to determine a feasible production and remanufacturing plan at minimal cost. In each period, the given external demand must be satisfied for both new and remanufactured products. Remanufactured products can be substituted by new products, but not vice versa. When a product is (re)manufactured, the appropriate machine must be set up, which entails set-up costs and/or set-up time. The procurement of raw material that is offered by several vendors at different prices is integrated into this planning problem. To solve this integrated production and remanufacturing planning problem, we apply two solution approaches based on mathematical programming: first, a combination of column generation and a period-oriented fix-and-relax heuristic and second, an adapted fix-and-optimise heuristic. The results of our numerical investigation demonstrate the high solution quality of both solution approaches.     

Progressive thermal desorption of vapor mixtures from a preconcentrator with a porous metal foam internal architecture and variable thermal ramp rates

A vapor preconcentrator has been designed with the porous polymer (Tenax) packed into a highly porous metal foam to facilitate thermal conductivity and temperature uniformity throughout the bed of the preconcentrator during heating. Vapors were desorbed using linear temperature programming from room temperature to a maximum temperature of 170 or 200 degrees C; the programmed duration of the thermal ramp was varied from 10 to 180 s. The partial separation of vapor mixtures that are thermally desorbed from the preconcentrator has been examined in terms of a metric for resolution, using methyl ethyl ketone, toluene, and dimethyl methylphosphonate as a test mixture. Vapors desorbed as a sequence of partially separated overlapping peaks, as observed with a polymer-coated flexural plate wave sensor. It was shown that vapor mixture resolution improved as the total time of the thermal ramp was extended from 30 to 120 s. In this way, the preconcentrator serves to act as a preseparator in addition to its usual functions for sampling, signal modulation, and improving sensitivity. Overlapping peaks were modeled, and peak areas were extracted using an exponentially modified Gaussian model. Peak areas were independent of the thermal ramp rate. Uses of such preconcentrators with multivariate detectors, such as sensor arrays, are discussed.     

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.     

Bi-stable pore size during electrochemical etching of n-type silicon during a thermal ramp

We have investigated the change in size and density of pores during electrochemical etching of n-type (5 Ωcm) silicon under backside illumination and subjected to a thermal ramp. The pore structure was allowed to self organize, and for the parameters reported here this results in macropores with diameters in the ∼ μm order of magnitude range. As the etching progressed under constant current conditions, the electrolyte and the sample heated slowly up in the temperature range 20-60 °C. The resulting pore structure was obtained by scanning electron microscope examination of cross sections of cleaved samples. The temperature ramp caused the pore diameters and pore densities to change abruptly rather than continuously. The change can thus phenomenologically be described as a transition between two stable pore size configurations; bi-stable switching or phase transition. This phenomenon is observed for a range of parameters yielding macropores: current densities between 2-20 mA/cm² and varying light intensity. The transition is between known configurations.     

Cost minimization of repairable systems subject to availability constraints using efficient cuckoo optimization algorithm

System availability is a key element for any industry. System designers and operators try to do their best to maintain the required availability of the systems to avoid production stoppages. They set up and undertake different maintenances, and these interventions imply cost. Therefore, the goal is to minimize the cost, but considering the constraint of the availability requirement. The problem involves three main aspects: redundancy allocation, component failure rates, and repair rates. In this paper, a novel solution approach is proposed based on an efficient cuckoo optimization algorithm (EF-COA). Two numerical case studies are solved, and the results confirm the effectiveness of the approach proposed.     

Sequencing of imperfect inspection operations subject to constraints on the quality of accepted and rejected units

Several imperfect inspection operations are available in a discrete production environment. A decision regarding acceptance or rejection of the produced items needs to be made without exceeding specified limits for the probabilities of accepted units being non-conforming and rejected units conforming to quality specifications. A branch and bound approach is used to find the inspection sequence resulting in least expected total inspection cost. Following the heuristic construction of a trial solution, a dominance relationship is applied to search the tree of possible sequences for the optimal sequence. A numerical example is included.     

Service task partition and distribution in star topology computer grid subject to data security constraints

The paper considers grid computing systems in which the resource management systems (RMS) can divide service tasks into execution blocks (EBs) and send these blocks to different resources. In order to provide a desired level of service reliability the RMS can assign the same blocks to several independent resources for parallel execution.The data security is a crucial issue in distributed computing that affects the execution policy. By the optimal service task partition into the EBs and their distribution among resources, one can achieve the greatest possible service reliability and/or expected performance subject to data security constraints. The paper suggests an algorithm for solving this optimization problem. The algorithm is based on the universal generating function technique and on the evolutionary optimization approach. Illustrative examples are presented.     

Phase-plane analysis of multiplicity and thermal runaway in a hollow sphere subject to a constant internal radiative power source

In this paperwe present an analysis of the steady-state solutions of a classical equation describing thermal runaway in spherical symmetrymodified to study the hazard presented by a fractured optical fibre in a flammable atmosphere. Exothermic reaction is coupled with a radiation source that imposes a temperature gradient at the edge of an inert spherical core within the reaction zone. Reactant consumption is neglected. The governing equation is integrated directly and the steady-state profiles are examined with the Frank-Kamenetskii parameterbas the bifurcation parameter. Gross multiplicity of steady states is seen to be a feature for certain parameter values. Subsequentlya phase-plane approach is used which renders some features of the solutions more accessible. In particularthe point at which the system ceases to exhibit criticalitywhich is important from the hazard assessment point of viewis easily identified     

Phase-plane analysis of multiplicity and thermal runaway in a hollow sphere subject to a constant internal radiative power source

In this paperwe present an analysis of the steady-state solutions of a classical equation describing thermal runaway in spherical symmetrymodified to study the hazard presented by a fractured optical fibre in a flammable atmosphere. Exothermic reaction is coupled with a radiation source that imposes a temperature gradient at the edge of an inert spherical core within the reaction zone. Reactant consumption is neglected. The governing equation is integrated directly and the steady-state profiles are examined with the Frank-Kamenetskii parameterbas the bifurcation parameter. Gross multiplicity of steady states is seen to be a feature for certain parameter values. Subsequentlya phase-plane approach is used which renders some features of the solutions more accessible. In particularthe point at which the system ceases to exhibit criticalitywhich is important from the hazard assessment point of viewis easily identified     

Elasticity and viscoelasticity in layered shells and plates subject to thermal and force loading

A revised model has been devised for the thermoelastic equilibrium in a multilayer shell of rotation that incorporates the thermal sensitivity of the material and the variable layer thicknesses, as well as the temperature dependence of the transverse tangential stress distribution. The linear theory of inherited elasticity is employed to derive differential equations for the quasistatic equilibrium of a multilayer viscoelastic shell or plate made from thermorheologically complicated materials. The solution is obtained as double trigonometric series for a hinge-supporied viscoelastic cylindrical shell or plate subject to sinusoidal temperature and force loadings.Translated from Problemy Prochnosti, Nos. 5–6, pp. 95–103, May–June, 1995.