Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part II. Performance evaluation

The parameterized fast decoupled power flow (PFDPF), versions XB and BX, using either theta or V as a parameter have been proposed by the authors in Part I of this paper. The use of reactive power injection of a selected PVbus (Q(PV)) as the continuation parameter for the computation of the maximum loading point (MLP) was also investigated. In this paper, the proposed versions obtained only with small modifications of the conventional one are used for the computation of the MLP of IEEE test systems (14, 30, 57 and 118 buses). These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approaches are presented and discussed. The results show that the characteristics of the conventional FDPF method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that these versions can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. A trivial secant predictor, the modified zero-order polynomial, which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used for the predictor step. (C) 2003 Elsevier B.V. All rights reserved.

Alternative continuation method for loading margin improvement and transmission losses reduction

This paper presents an alternative methodology for loading margin improvement and total real power losses reduction by using a continuation method. In order to attain this goal, a parameterizing equation based on the total real power losses and the equations of the reactive power at the slack and generation buses are added to the conventional power flow equations. The voltages at these buses are considered as control variables and a new parameter is chosen to reduce the real power losses in the transmission lines. The results show that this procedure leads to maximum loading point increase and consequently, in static voltage stability margin improvement. Besides, this procedure also takes to a reduction in the operational costs and, simultaneously, to voltage profile improvement. Another important result of this methodology is that the resulting operating points are close to that provided by an optimal power flow program. © 2004 IEEE.

Are transitions in human gait determined by mechanical, kinetic or energetic factors?

It is currently unclear whether it is the need to maintain metabolic efficiency, the need to keep skeletal loading below critical force levels, or simple mechanical factors that drive the walk-to-run (W R) and run-to-walk (R-W) transitions in human gait. Eighteen adults (9 males and 9 females) locomoted on an instrumented treadmill using their preferred gait. Each completed 2 ascending (W-R) and 2 descending (R-W) series of trials under three levels of loading (0%, 15% and 30% body weight). For each trial, participants locomoted for 60 s at each of 9 different speeds -4 speeds both above and below their preferred transition speed (PTS) plus their PTS. Evidence was sought for critical levels of key kinetic (maximum vertical force, impulse, first peak force, time to first peak force and maximum loading rate), energetic (oxygen consumption, transport cost) and mechanical variables (limb lengths, strength) predictive of the gait transition. Analyses suggested the kinetic variables of time to first peak force and loading rate as the most likely determinants of the W-R and R-W transitions. (C) 2003 Elsevier Science B.V. All rights reserved.

Kullan talteenotto takaisinuuttoliuoksista

Työssä tutkittiin kirjallisuuden ja laboratoriomittausten avulla vaihtoehtoja kullan pelkistämiseen ja talteenottoon kultauuton takaisinuuttoliuoksista. Tavoitteena oli löytää menetelmä, jolla saadaan puhdasta kiinteää lopputuotetta ilman kullan häviöitä. Käytettyjä pelkistimiä olivat D-(+)-glukoosi, natriumboorihydridi, L-askorbiinihappo, D-(-)-isoaskorbiinihappo ja aktiivihiili. Laboratoriokokeiden perusteella D-(-)-isoaskorbiinihappo sekä aktiivihiili olivat sopivimmat pelkistimet kokeissa käytetylle kultaliuokselle. Isoaskorbiinihapolla suoritettiin panoskokeita lasireaktorissa eri alku-pH:ssa sekä erilaisilla pelkistimen ja kullan moolisuhteilla. Tulosten perusteella havaittiin pH:n ja pelkistimen ylimäärän vaikuttavan merkittävästi lopputuotteen puhtauteen. Myös redox-potentiaalia säätämällä ja happopesulla pelkistyksen jälkeen voidaan vaikuttaa lopputuotteen puhtauteen. Aktiivihiilellä suoritettiin panoskokeita adsorptiotasapainojen (latausisotermi) ja kinetiikan tutkimiseksi. Hiileen on mahdollista saada kultaa 383 mg/g kuivaa hiiltä. Suurempi lataus voitaisiin saavuttaa käyttämällä hiiltä, jolla on pienempi partikkelikoko. Kolonnikokeita tehtiin eri virtausnopeuksilla. Kolonnikokeissa kullan dynaaminen adsorptiokapasiteetti hiileen odotetusti kasvoi virtausnopeuden laskiessa. Pienin käytetty virtausnopeus oli 2,40 BV/h, jolloin kapasiteetti oli 75,4 mg/g kuivaa hiiltä (c (Au feed) = 129 mg/L). Kullasta voidaan poistaa myös kolonnipelkistyksen jälkeen epäpuhtauksia happopesulla. Isoaskorbiinihapolla pelkistyksen kinetiikka on nopea ja sillä saatiin pelkistettyä puhdasta lopputuotetta. Sekä isoaskorbiinihappo, että aktiivihiili ovat potentiaalisia menetelmiä kullan talteenottoon.

Magnetic and processability studies on rubber ferrite composites based on natural rubber and mixed ferrite

Polycrystalline single phasic mixed ferrites belonging to the series Ni1−xZnxFe2O4 for various values of x have been prepared by conventional ceramic techniques. Pre-characterized nickel zinc ferrites were then incorporated into a natural rubber matrix according to a specific recipe for various loadings. The processability and cure parameters were then determined. The magnetic properties of the ceramic filler as well as the ferrite loaded rubber ferrite composites (RFC) were evaluated and compared. A general equation for predicting the magnetic properties was also formulated. The validity of these equations were then checked and correlated with the experimental data. The coercivity of the RFCs almost resemble that of the ceramic component in the RFC. Percolation threshold is not reached for a maximum loading of 120 phr (parts per hundred rubber by weight) of the filler. These studies indicate that flexible magnets can be made with appropriate magnetic properties namely saturation magnetisation (Ms) and magnetic field strength (Hc) by a judicious choice of x and a corresponding loading. These studies also suggest that there is no possible interaction between the filler and the matrix at least at the macroscopic level. The formulated equation will aid in synthesizing RFCs with predetermined magnetic

Processability, hardness, andmagnetic properties of rubber ferrite composites containingmanganese zinc ferrites

Rubber ferrite composites have the unique advantage of mouldability, which is not easily obtainable using ceramic magnetic materials. The incorporation of mixed ferrites in appropriate weight ratios into the rubber matrix not only modi es the dielectric properties of the composite but also imparts magnetic properties to it. Mixed ferrites belonging to the series of Mn(1 – x )Znx Fe2O4 have been synthesised with diVerent values of x in steps of 0·2, using conventional ceramic processing techniques. Rubber ferrite composites were prepared by the incorporation of these pre-characterised polycrystallineMn(1 – x )Znx Fe2O4 ceramics into a natural rubber matrix at diVerent loadings according to a speci c recipe. The processability of these elastomers was determined by investigating their cure characteristics. The magnetic properties of the ceramic llers as well as of the rubber ferrite composites were evaluated and the results were correlated. Studies of the magnetic properties of these rubber ferrite composites indicate that the magnetisation increases with loading of the ller without changing the coercive eld. The hardness of these composites shows a steady increase with the loading of the magnetic llers. The evaluation of hardness andmagnetic characteristics indicates that composites with optimummagnetisation and almost minimum stiVness can be achieved with a maximum loading of 120 phr of the ller at x=0·4. From the data on the magnetisation of the composites, a simple relationship connecting the magnetisation of the rubber ferrite composite and the ller was formulated. This can be used to synthesise rubber ferrite composites with predetermined magnetic properties

Magnetic and processability studies of nitrile rubber vulcanisates containing barium ferrite and carbon black

Fine particles of barium ferrite (BaFe12O19) belonging to the M-type hexagonal ferrites were prepared by the conventional ceramic techniques. They were incorporated into a nitrile rubber matrix according to a specific recipe for various loadings to produce rubber ferrite composites (RFC). The percolation threshold is not reached for a maximum loading of 130 phr (parts per hundred rubber). Here in this paper, the magnetic properties and processability of the nitrile rubber based RFCs containing barium ferrite (BaF) and HAF carbon black is reported. The magnetic properties of the ceramic ferrite and these rubber ferrite composites were evaluated and it was found that the coercivity values of RFCs were less than that of the ceramic BaF, but remained constant with the loading of both the ferrite filler and carbon black. However, other properties like saturation magnetization and magnetic remanence increased with the loading of ferrite filler.

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Continuation fast decoupled power flow with secant predictor

The conventional Newton and fast decoupled power flow methods are considered inadequate for obtaining the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. At this point, the Jacobian matrix of the Newton method becomes singular. In addition, it is widely accepted that the P-V and Q-theta decoupling assumptions made for the fast decoupled power flow formulation no longer hold. However, in this paper, it is presented a new fast decoupled power flow that becomes adequate for the computation of the maximum loading point by simply using the reactive power injection of a selected PV bus as a continuation parameter. Besides, fast decoupled methods using V and 0 as parameters and a secant predictor are also presented. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained for the IEEE systems (14 and 118 buses) show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged.

Alternative parameters for the continuation power flow method

The conventional Newton's method has been considered inadequate to obtain the maximum loading point (MLP) of power systems. It is due to the Jacobian matrix singularity at this point. However, the MLP can be efficiently computed through parameterization techniques of continuation methods. This paper presents and tests new parameterization schemes, namely the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, the reactive power at shunts (capacitor or reactor), the transmission lines power losses (real and reactive), and transmission lines power (real and reactive). Besides their clear physical meaning, which makes easier the development and application of continuation methods for power systems analysis, the main advantage of some of the proposed parameters is that its not necessary to change the parameter in the vicinity of the MLP. Studies on the new parameterization schemes performed on the IEEE 118 buses system show that the ill-conditioning problems at and near the MLP are eliminated. So, the characteristics of the conventional Newton's method are not only preserved but also improved. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Método da continuação aplicado na análise de contingência de linhas de transmissão

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

Esquemas alternativos para o passo de parametrização do método da continuação baseados em parâmetros físicos

O método de fluxo de carga convencional é considerado inadequado para se obter o ponto de máximo carregamento (PMC) de sistemas de potência, devido à singularidade da matriz Jacobiana neste ponto. Os métodos da continuação são ferramentas eficientes para a solução deste tipo de problema, visto que técnicas de parametrização podem ser utilizadas para evitar a singularidade da matriz Jacobiana. Neste trabalho, novas opções para a etapa de parametrização do método da continuação são apresentadas. Mostra-se que variáveis com claro significado físico podem ser utilizadas na etapa de parametrização. As seguintes variáveis foram testadas: perda total de potência ativa e reativa, potência ativa e reativa na barra de referência, potência reativa das barras de geração, e as perdas de potência ativa e reativa nas linhas de transmissão (LT). Além de facilitar a implementação computacional do método de continuação, as técnicas de parametrização apresentadas simplificam a definição matemática e o entendimento do método por parte de engenheiros de potência, visto que os métodos de continuação existentes na literatura sempre utilizam técnicas de parametrização complexas, e de interpretação puramente geométrica. Resultados obtidos com a nova metodologia para os sistemas testes do IEEE (14, 30, 57 e 118 barras) mostram que as características de convergência do método de fluxo de carga convencional são melhoradas na região do PMC. Além disso, durante o traçado das curvas PV, as diversas técnicas de parametrização podem ser comutadas entre si possibilitando o cálculo de todos os pontos da curva com um número reduzido de iterações. Diversos testes são realizados para proporcionar a comparação do desempenho dos esquemas de parametrização propostos.

Técnicas de parametrização global para o fluxo de carga continuado

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

Técnica de parametrização geométrica para o fluxo de carga continuado baseado nas variáveis tensão nodal e fator de carregamento

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