Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table

A best-fit model of power losses in cold rolled-motor lamination steel operating in a wide range of frequency and magnetization

A procedure is described for identifying a mathematical model of core losses in ferromagnetic steel based on a minimal amount of experimental data. The new model has a hysteresis loss multiplicative coefficient variable only with frequency, a hysteresis loss power coefficient variable both with frequency and induction and a combined coefficient for eddy-current and excess losses that is, within a set frequency range, variable only with induction. Validation was successfully performed on a large number of different samples of nongrain oriented fully and semiprocessed steel alloys. Over a wide range of frequencies between 20 Hz and 2.1 kHz and inductions from 0.05 up to 2 T, the errors of the proposed model are substantially lower than those of a conventional model with fixed value coefficients

Load Balancing with Energy Storage Systems Based on Co-Simulation of Multiple Smart Buildings and Distribution Networks

In this paper, we present a co-simulation framework that combines two main simulation tools, one that provides detailed multiple building energy simulation ability with Energy-Plus being the core engine, and the other one that is a distribution level simulator, Matpower. Such a framework can be used to develop and study district level optimization techniques that exploit the interaction between a smart electric grid and buildings as well as the interaction between buildings themselves to achieve energy and cost savings and better energy management beyond what one can achieve through techniques applied at the building level only. We propose a heuristic algorithm to do load balancing in distribution networks affected by service restoration activities. Balancing is achieved through the use of utility directed usage of battery energy storage systems (BESS). This is achieved through demand response (DR) type signals that the utility communicates to individual buildings. We report simulation results on two test cases constructed with a 9-bus distribution network and a 57-bus distribution network, respectively. We apply the proposed balancing heuristic and show how energy storage systems can be used for temporary relief of impacted networks

Measuring, Registering and Recording the vectors' characteristics of Induction Machines

Evolution of power semiconductor devices and power static frequency converters is a key factor in development of advanced applications. Availability of energy sources derived adjustable frequency AC motor allowed to reach a new horizon in research studies and technical applications, completely untapped today.However, the advantages inherent in the operation of adjusting the frequency cannot be fully exploited without adopting a proper control strategy, which is essential in characterizing the parameters and the overall performance of a command system. Control techniques are to ensure a fair and effective command of the operation. During normal operation, the nominal engine and inverter must be secured and the engine order should be placed in area of maximum torque. In case of overloads or faults of another nature, redesigning of installation parts is preferable in order to adopt advanced operating strategies and to determine the parameters

Saliency Ratio and Power Factor of IPM Motors Optimally Designed for High Efficiency and Low Cost Objectives

This paper uses formal mathematical optimization techniques based on parametric finite-element-based computationally efficient models and differential evolution algorithms. For constant-power applications, in the novel approach described, three concurrent objective functions are minimized: material cost, losses, in order to ensure high efficiency, and the difference between the rated and the characteristic current, aiming to achieve very high constant-power flux-weakening range. Only the first two objectives are considered for constant-torque applications. Two types of interior permanent magnet rotors in a single- and double-layer V-shaped configuration are considered, respectively. The stator has the typical two slots per pole and phase distributed winding configuration. The results for the constant-torque design show that, in line with expectations, high efficiency and high power factor machines are more costly, and that the low-cost machines have poorer efficiency and power factor and most importantly, and despite a common misconception, the saliency ratio may also be lower in this case. For constant-power designs, the saliency ratio can be beneficial. Nevertheless, despite a common misconception, when cost is considered alongside performance as an objective, a higher saliency ratio does not necessarily improve the power factors of motors suitable for ideal infinite flux weakening

Assessment of torque components in brushless permanent-magnet machines through numerical analysis of the electromagnetic field

For the calculation of torque in brushless (BL) alternating current motors a local method is proposed, based on the Maxwell stress theory and the filtered contributions due to the harmonics of the magnetic vector potential in the motor air gap. By considering the space fundamental field only, the method can efficiently estimate the average synchronous torque for a variety or motor topologies, including concentrated winding designs. For BL direct current motor analysis a global method is introduced, based on the virtual work principle expressed in terms of energy components in various motor regions. The method leads to simplifications in the average torque calculation and enables the direct identification of the cogging and ripple components. The mathematical procedures have been validated against experiments and other numerical techniques

Analysis and design of a two-speed single-phase induction motor with 2 and 18 pole special windings

The motor presented employs multiple independent windings for operation with two very different pole numbers. The 18-pole field is produced with a symmetrical three-phase winding connected in a Steinmetz arrangement to a single-phase supply. A unified analysis method has been developed and used to demonstrate the equivalence of a Steinmetz delta or star connection with a main and auxiliary winding of a single-phase motor. The method has been experimentally validated and also included are some specific motor design considerations

Optimal Design of IPM Motors With Different Cooling Systems and Winding Configurations

Performance improvement of permanent magnet (PM) motors through optimization techniques has been widely investigated in the literature. Oftentimes the practice of design optimization leads to derivation/interpretation of optimal scaling rules of PM motors for a particular loading condition. This paper demonstrates how these derivations vary with respect to the machine ampere loading and ferrous core saturation level. A parallel sensitivity analysis using a second-order response surface methodology followed by a large-scale design optimization based on evolutionary algorithms are pursued in order to establish the variation of the relationships between the main design parameters and the performance characteristics with respect to the ampere loading and magnetic core saturation levels prevalent in the naturally cooled, fan-cooled, and liquid-cooled machines. For this purpose, a finite-element-based platform with a full account of complex geometry, magnetic core nonlinearities, and stator and rotor losses is used. Four main performance metrics including active material cost, power losses, torque ripple, and rotor PM demagnetization are investigated for two generic industrial PM motors with distributed and concentrated windings with subsequent conclusions drawn based on the results

Computationally Efficient Strand Eddy Current Loss Calculation in Electric Machines

A fast finite element (FE) based method for the calculation of eddy current losses in the stator windings of randomly wound electric machines is presented in this paper. The method is particularly suitable for implementation in large-scale design optimization algorithms where a qualitative characterization of such losses at higher speeds is most beneficial for identification of the design solutions that exhibit the lowest overall losses including the ac losses in the stator windings. Unlike the common practice of assuming a constant slot fill factor s f for all the design variations, the maximum s f in the developed method is determined based on the individual slot structure/dimensions and strand wire specifications. Furthermore, in lieu of detailed modeling of the conductor strands in the initial FE model, which significantly adds to the complexity of the problem, an alternative rectangular coil modeling subject to a subsequent flux mapping technique for determination of the impinging flux on each individual strand is pursued. Rather than pursuing the precise estimation of ac conductor losses, the research focus of this paper is placed on the development of a computationally efficient technique for the derivation of strand eddy current losses applicable in design optimization, especially where both the electromagnetic and thermal machine behavior are accounted for. A fractional-slot concentrated winding permanent magnet synchronous machine is used for the purpose of this study due to the higher slot leakage flux and slot opening fringing flux of such machines, which are the major contributors to strand eddy current losses in the windings. The analysis is supplemented with an investigation on the influence of the electrical loading on ac winding loss effects for this machine design, a subject that has received less attention in the literature. Experimental ac loss measurements on a 12-slot 10-pole stator assembly will be discussed to verify the existing trends in the simulation result