Desired Power Distribution Research Articles

Multiobjective optimization of nuclear microreactor reactivity control system operation with swarm and evolutionary algorithms

To improve the marketability of novel microreactor designs, there is a need for automated and optimal control of these reactors. This paper presents a methodology for performing multiobjective optimization of control drum operation for a microreactor under normal and off-nominal conditions. Two different case studies are used where the control drum configuration is optimized for the reactor to be critical with some desired power distribution that would satisfy peaking limits. A surrogate model for power distribution is developed based on a feedforward neural network. The process for determining weights for scalarization of the multiobjective optimization problem is also detailed. Six optimization algorithms: evolutionary strategies, differential evolution, grey wolf optimization, Harris hawks optimization, moth flame optimization and particle swarm optimization, are all applied to these cases and the results analyzed. Although all these algorithms will demonstrate optima-seeking behavior, for real-time control it is necessary to identify the best algorithm to efficiently provide reasonable optima without operator interference. The moth flame optimization algorithm was found to perform particularly well on both cases. Overall, it was found that the algorithms capable of supplying the best optima were also the most consistent. Finally, the found optima were verified with the original model used to train surrogates.

Hierarchical Model Predictive Control for Hydraulic Hybrid Powertrain of a Construction Vehicle

Hybrid hydraulic technology has the advantages of high-power density and low price and shows good adaptability in construction machinery. A complex hybrid powertrain architecture requires optimization and management of power demand distribution and an accurate response to desired power distribution of the power source subsystems in order to achieve target performances in terms of fuel consumption, drivability, component lifetime, and exhaust emissions. For hybrid hydraulic vehicles (HHVs) that are used in construction machinery, the challenge is to design an appropriate control scheme to actually achieve fuel economy improvement taking into consideration the relatively low energy density of the hydraulic accumulator and frequent load changes, the randomness of the driving conditions, and the uncertainty of the engine dynamics. To improve fuel economy and adaptability of various driving conditions to online energy management and to enhance the response performance of an engine to a desired torque, a hierarchical model predictive control (MPC) scheme is presented in this paper using the example of a spray-painting construction vehicle. The upper layer is a stochastic MPC (SMPC) based energy management control strategy (EMS) and the lower layer is an MPC-based tracking controller with disturbance estimator of the diesel engine. In the SMPC-EMS of the upper-layer management, a Markov model is built using driving condition data of the actual construction vehicle to predict future torque demands over a finite receding horizon to deal with the randomness of the driving conditions. A multistage stochastic optimization problem is formulated, and a scenario-based enumeration approach is used to solve the stochastic optimization problem for online implementation. In the lower-layer tracking controller, a disturbance estimator is designed to handle the uncertainty of the engine, and the MPC is introduced to ensure the tracking performance of the output torque of the engine for the distributed torque from the upper-layer SMPC-EMS, and therefore really achieve high efficiency of the diesel engine. The proposed strategy is evaluated using both simulation MATLAB/Simulink and the experimental test platform through a comparison with several existing strategies in two real driving conditions. The results demonstrate that the proposed strategy (SMPC+MPC) improves miles per gallon an average by 7.3% and 5.9% as compared with the control strategy (RB+PID) consisting of a rule-based (RB) management strategy and proportional-integral-derivative (PID) controller of the engine in simulation and experiment, respectively.

Integrated Optical Coupler With an Arbitrary Splitting Ratio Based on a Mode Converter

Optical couplers with different power splitting ratios are essential building blocks in photonic integrated circuits. We theoretically and experimentally demonstrate a broadband and fabrication-tolerant $1\times 2$ integrated optical coupler with an arbitrary splitting ratio, based on a mode converter (MC). The MC converts the input mode into a targeted output mode with a desired power distribution, which determines the power splitting ratio at outputs. The geometry of the MC is engineered and optimized by using the particle swarm optimization algorithm combined with the finite-difference time-domain method. Couplers with 10/90, 20/80, 30/70, 40/60, and 50/50 splitting ratios are designed and fabricated on the silicon-on-insulator platform as representatives, with footprints smaller than $2.75~\mu $ m $\times 18.41~\mu $ m. The experimental results show that the ±1 dB bandwidths of these devices are greater than 42 nm around 1550 nm, and the average insertion losses are less than 0.65 dB.

The inverse problem for power distributions in committees

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.

The Inverse Problem for Power Distributions in Committees

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.

Variable Power Combiner for RF Mode Shimming in 7-T MR Imaging

This contribution discusses the utilization of RF power in an MRI system with RF mode shimming which enables the superposition of circularly polarized modes of a transmit RF coil array driven by a Butler matrix. Since the required power for the individual modes can vary widely, mode-shimming can result in a significant underutilization of the total available RF power. A variable power combiner (VPC) is proposed to improve the power utilization: it can be realized as a reconfiguration of the MRI transmit system by the inclusion of one additional matrix network which receives the power from all transmit amplifiers at its input ports and provides any desired (combined) power distribution at its output ports by controlling the phase and amplitude of the amplifiers' input signals. The power distribution at the output ports of the VPC is then fed into the "mode" ports of the coil array Butler matrix in order to superimpose the spatial modes at the highest achievable power utilization. The VPC configuration is compared to the standard configuration of the transmit chain of our MRI system with 8 transmit channels and 16 coils. In realistic scenarios, improved power utilization was achieved from 17% to 60% and from 14% to 55% for an elliptical phantom and a region of interest in the abdomen, respectively, and an increase of the power utilization of 1 dB for a region of interest in the upper leg. In general, it is found that the VPC allows significant improvement in power utilization when the shimming solution demands only a few modes to be energized, while the technique can yield loss in power utilization in cases with many modes required at high power level.

An Improved Inverse Analysis Model for Fuel Loading Pattern Optimization

An improved inverse analysis model for fuel loading pattern (LP) optimization is proposed to reproduce a desired in-core power distribution from available fuel assemblies based on the inverse analysis of diffusion equations. In the present approach, the inverse analysis is simplified as a fixed-source problem rather than an eigenvalue problem in a previous work. By using the one-to-one correspondence between the power distribution and reactivity distribution, a target reactivity distribution is solved from a desired power distribution through the inverse analysis. The reactivity of available assemblies is evaluated using a modified effective fast-group model with a higher order correction of leakage effect. A candidate LP is determined by individually matching the reactivity of available assemblies to the target in-core reactivity distribution using a stable matching algorithm. The process of predicting the reactivity of available assemblies and matching them to the target reactivity distribution is repeated until the convergence condition is satisfied. Validation of the model has been confirmed with a reference PWR core. The model is expected to be applicable to a problem of multicycle loading pattern optimization.

A Waveform Diversity Method for Optimizing 3-D Power Depositions Generated by Ultrasound Phased Arrays

A waveform-diversity-based approach for 3-D tumor heating is compared to spot scanning for hyperthermia applications. The waveform diversity method determines the excitation signals applied to the phased array elements and produces a beam pattern that closely matches the desired power distribution. The optimization algorithm solves the covariance matrix of the excitation signals through semidefinite programming subject to a series of quadratic cost functions and constraints on the control points. A numerical example simulates a 1444-element spherical-section phased array that delivers heat to a 3-cm-diameter spherical tumor located 12 cm from the array aperture, and the results show that waveform diversity combined with mode scanning increases the heated volume within the tumor while simultaneously decreasing normal tissue heating. Whereas standard single focus and multiple focus methods are often associated with unwanted intervening tissue heating, the waveform diversity method combined with mode scanning shifts energy away from intervening tissues where hotspots otherwise accumulate to improve temperature localization in deep-seated tumors.

An Improved Inverse Analysis Model for Fuel Loading Pattern Optimization

An improved inverse analysis model for fuel loading pattern (LP) optimization is proposed to reproduce a desired in-core power distribution from available fuel assemblies based on the inverse analysis of diffusion equations. In the present approach, the inverse analysis is simplified as a fixed-source problem rather than an eigenvalue problem in a previous work. By using the one-to-one correspondence between the power distribution and reactivity distribution, a target reactivity distribution is solved from a desired power distribution through the inverse analysis. The reactivity of available assemblies is evaluated using a modified effective fast-group model with a higher order correction of leakage effect. A candidate LP is determined by individually matching the reactivity of available assemblies to the target in-core reactivity distribution using a stable matching algorithm. The process of predicting the reactivity of available assemblies and matching them to the target reactivity distribution is repeated until the convergence condition is satisfied. Validation of the model has been confirmed with a reference PWR core. The model is expected to be applicable to a problem of multicycle loading pattern optimization.

Optimisation of radio coverage in urban microcells using a UTD based ray-tracing model

In cellular communications, requirements for increased system capacity, improved coverage, better quality and reduced transmitter power, along with the need to rationalise cellular system planning, have prompted a considerable interest in the development of valid and efficient radiowave propagation models. This work utilises recent advances that improve the accuracy and efficiency of ray-tracing models, using a three-dimensional representation of the terrain and urban topographies, in conjunction with adaptive and selective ray-tracing. These improvements allow utilisation of the field computation algorithms in the network design and radio coverage planning processes. They include optimum automated selection of base station locations and phased array excitation. A reliable ray-tracing scheme can be utilised directly in the optimum and, potentially, adaptive beamforming of base station antenna systems by interfacing field computations with design aims. The paper addresses a cellular planning process, which involves determination of the antenna array position and beam shape or, equivalently, the array excitation coefficients, for a desired power distribution over the defined cell area.

Optimization of thermal conditions during crystal growth in a multi‐zone resistance furnace

AbstractThe thermal condition is one the of most important control parameters for crystal growth. In this paper we present an effective numerical method in detail for optimizing thermal conditions in multi‐zone crystal growth facilities, especially for crystal growth by the float zone (FZ) technique. A furnace function Ω is introduced to integrate the character of a growth furnace into a linear equation system. The desired power distribution can be therefore approached by solving the linear equation system iteratively. An expert systemlike algorithm has been developed in order to obtain a more suitable solution for practical applications. This method was used to investigate thermal parameters for experiments of SiGe/GeSi single crystal growth by the FZ technique. It is an individual program which can be combined with any commercial finite element/finite volume (FE/FV) program such as FIDAPTM.

Tailored edge-ray reflectors for illumination

The edge-ray principle can be used to tailor a reflector. However, one set of edge rays already fully determines the reflector profile. We present a design method for tailoring compact compound elliptical concentrator (CEC)-type reflectors to a given source and a desired angular power distribution. Two reflected images of the source, one on each side of the source, contribute together with the direct radiation from the source to produce the desired power distribution. We determine the reflector profile by numerically solving a differential equation. No optimization is required. Beyond the angular region in which the power distribution can be strictly controlled, the power drops to zero in a finite decay range. This decay range becomes narrower as the reflector increases in size. We show a reflector for producing a strictly constant irradiance from −43 to 43 deg from a cylindrical source of constant brightness. The reflector extends to a maximum distance of 8 source diameters. No power is radiated beyond ± 50 deg.

Light beam redistribution using computer-generated phase plates

The use of two phase plates for light-beam power redistribution is proposed. The first plate is designed so that the desired power distribution is obtained by near-field diffraction; the purpose of the second plate is the correction of the phase front. The deviation is based on ray optics, which is a good approximation in practical situations. As an example, design and fabrication of the phase plate for 1:2 branching of single-mode fibers are described. The phase plates have a computer-generated pattern and are fabricated by electron-beam lithography. Experimental verification of beam branching is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Theory of Fuel Management via Backward Diffusion Calculation

Diffusion equations are generally solved forwardly, namely, for a given core loading condition one solves for the flux and power distribution. For fuel management applications, a theory of backward diffusion calculation is developed which for a given power distribution solves the diffusion equation backwardly for the core reactivity distribution. Loading pattern searches can be facilitated by matching the available fuel assemblies to the reactivity distribution predicted backwardly from the desired power distribution. Optimization of fuel utilization can also be performed by determining the optimum power shape, under imposed constraints, that gives a reactivity distribution requiring the least fuel loading.

Optimization of Boiling Water Reactor Control Rod Patterns Using Linear Search

A computer program for searching the optimal control rod pattern has been developed. The program is able to find a control rod pattern where the resulting power distribution is optimal in the sense that it is the closest to the desired power distribution, and it satisfies all operational constraints. The search procedure consists of iterative uses of two steps: sensitivity analyses of local power and thermal margins using a three-dimensional reactor simulator for a simplified prediction model; linear search for the optimal control rod pattern with the simplified model. The optimal control rod pattern is found along the direction where the performance index gradient is the steepest. This program has been verified to find the optimal control rod pattern through simulations using operational data from the Oyster Creek Reactor.

Automatic control system by power distribution in a power-generating reactor

The development of the theoretical principles of construction of these systems and of sufficiently detailed nonlinear dynamic numerical models of a power-generation unit with an RBMK reactor have allowed a consistent procedure to be produced for the engineering synthesis of an (local automated control) LAC-LEP (local emergency protection) system. The LAC system facilitates the shaping and maintenance of the desired power distribution in the whole volume of the reactor. In emergency situations, the LAC-LEP system qualitatively reduces the power to a safe level and effectively suppresses the power warpings in one-half of the reactor, which are characteristic for these reactors.

Enrichment Zoning and Control Rod Programming for Reactivity and Power Shape Control

An efficient optimization method has been developed that determines simultaneously beginning-of-cycle (BOC) enrichment distribution and the control rod programming in reactors that lose reactivity during burnup such that (a) reactor criticality and a desired power distribution are satisfied throughout the cycle and (b) all the control rods are withdrawn at end-of-cycle (EOC). The method uses (a) an iterative scheme of uncontrolled burnup calculations (and linear programming (LP) for more than two enrichment zones) to determine a good approximation of the EOC reactor composition that satisfies reactor criticality and the desired power distribution and (b) LP in a reversed burnup process starting from the EOC conditions to determine the control rod programming and the BOC enrichment distribution.

Reactivity and Power Shape Control

An optimization method, based on linear programming, has been developed that determines the enrichment distribution in a multizone reactor such that the desired power distribution is achieved at beginning-of-life conditions, as well as the poison distribution during reactor operation such that the reactor is kept critical and the desired power distribution is retained. Results of the numerical application of the method are presented.

A Multilevel Approach to Nuclear Fuel Burnup Optimization

The aim of the paper is to show how the complex, overall burnup optimization problem, subject to the constraint of the desired power distribution, can be solved by decomposition into less complex c...

Wave Coupling by Warped Normal Modes

It has been shown by J.S. Cook that wave power may be transferred from one to another of two coupled waveguides through a variation of their phase constants. It is now clear that this is but one example of a new principle of coupling which is here called "nomal mode warping." Wave power inserted at one end of a coupled waveguide system may be made to appear at the other end with any desired power distribution by gradual warping of the normal mode field patterns along the coupler. In general, both variation of the coupling coefficient and phase constants are required. Much wider bands are theoretically possible than with any other distributed type of coupler. This principle may be applied to dielectric waveguides, birefringent media, and waveguides containing ferrite, to obtain both reciprocal and nonreciprocal couplers.