Static load modelling and voltage stability indices

This paper analyzes the performance of some of the widely used voltage stability indices, namely, singular value, eigenvalue, and loading margin with different static load models. Well-known ZIP model is used to represent loads having components with different power to voltage sensitivities. Studies are carried out on a 10-bus power system and the New England 39-bus power system models. The effects of variation of load model on the performance of the voltage stability indices are discussed. The choice of voltage stability index in the context of load modelling is also suggested in this paper.

Assessment of Convective Activity Using Stability Indices as Inferred from Radiosonde and MODIS Data

The combined use of both radiosonde data and three-dimensional satellite derived data over ocean and land is useful for a better understanding of atmospheric thermodynamics. Here, an attempt is made to study the ther-modynamic structure of convective atmosphere during pre-monsoon season over southwest peninsular India utilizing satellite derived data and radiosonde data. The stability indices were computed for the selected stations over southwest peninsular India viz: Thiruvananthapuram and Cochin, using the radiosonde data for five pre- monsoon seasons. The stability indices studied for the region are Showalter Index (SI), K Index (KI), Lifted In-dex (LI), Total Totals Index (TTI), Humidity Index (HI), Deep Convective Index (DCI) and thermodynamic pa-rameters such as Convective Available Potential Energy (CAPE) and Convective Inhibition Energy (CINE). The traditional Showalter Index has been modified to incorporate the thermodynamics over tropical region. MODIS data over South Peninsular India is also used for the study. When there is a convective system over south penin-sular India, the value of LI over the region is less than −4. On the other hand, the region where LI is more than 2 is comparatively stable without any convection. Similarly, when KI values are in the range 35 to 40, there is a possibility for convection. The threshold value for TTI is found to be between 50 and 55. Further, we found that prior to convection, dry bulb temperature at 1000, 850, 700 and 500 hPa is minimum and the dew point tem-perature is a maximum, which leads to increase in relative humidity. The total column water vapor is maximum in the convective region and minimum in the stable region. The threshold values for the different stability indices are found to be agreeing with that reported in literature.

Transient stability indices from a hybrid approach

This paper deals with hybrid method for transient stability analysis combining time domain simulation and a direct method. Nowadays, the step-by-step simulation is the best available tool for allowing the uses of detailed models and for providing reliable results. The main limitation of this approach involves the large time of computational simulations and the absence of stability margin. On the other hand, direct methods, that demand less CPU time, did not show ample reliability and applicability yet. The best way seems to be using hybrid solutions, in which a direct method is incorporated in a time domain simulation tool. This work has studied a direct method using the transient potential and kinetic energy of the critical machine only. In this paper the critical machine is identified by a fast and efficient method, and the proposal is new for using to get stability margins from hybrid approaches. Results from systems, like 16-machine, show stability indices to dynamic security assessment. © 2001 IEEE.

Novel algorithm for online voltage stability assessment based on feed forward neural network

This paper presents an artificial feed forward neural network (FFNN) approach for the assessment of power system voltage stability. A novel approach based on the input-output relation between real and reactive power, as well as voltage vectors for generators and load buses is used to train the neural net (NN). The input properties of the feed forward network are generated from offline training data with various simulated loading conditions using a conventional voltage stability algorithm based on the L-index. The neural network is trained for the L-index output as the target vector for each of the system loads. Two separate trained NN, corresponding to normal loading and contingency, are investigated on the 367 node practical power system network. The performance of the trained artificial neural network (ANN) is also investigated on the system under various voltage stability assessment conditions. As compared to the computationally intensive benchmark conventional software, near accurate results in the value of L-index and thus the voltage profile were obtained. Proposed algorithm is fast, robust and accurate and can be used online for predicting the L-indices of all the power system buses. The proposed ANN approach is also shown to be effective and computationally feasible in voltage stability assessment as well as potential enhancements within an overall energy management system in order to determining local and global stability indices

Derivation of lake mixing and stratification indices from high-resolution lake buoy data

Lake Analyzer is a numerical code coupled with supporting visualization tools for determining indices of mixing and stratification that are critical to the biogeochemical cycles of lakes and reservoirs. Stability indices, including Lake Number, Wedderburn Number, Schmidt Stability, and thermocline depth are calculated according to established literature definitions and returned to the user in a time series format. The program was created for the analysis of high-frequency data collected from instrumented lake buoys, in support of the emerging field of aquatic sensor network science. Available outputs for the Lake Analyzer program are: water temperature (error-checked and/or down-sampled), wind speed (error-checked and/or down-sampled), metalimnion extent (top and bottom), thermocline depth, friction velocity, Lake Number, Wedderburn Number, Schmidt Stability, mode-1 vertical seiche period, and Brunt-Väisälä buoyancy frequency. Secondary outputs for several of these indices delineate the parent thermocline depth (seasonal thermocline) from the shallower secondary or diurnal thermocline. Lake Analyzer provides a program suite and best practices for the comparison of mixing and stratification indices in lakes across gradients of climate, hydro-physiography, and time, and enables a more detailed understanding of the resulting biogeochemical transformations at different spatial and temporal scales.

Characterisation of Large Disturbance Rotor Angle and Voltage Stability in Interconnected Power Networks with Distributed Wind Generation

Wind generation in highly interconnected power networks creates local and centralised stability issues based on their proximity to conventional synchronous generators and load centres. This paper examines the large disturbance stability issues (i.e. rotor angle and voltage stability) in power networks with geographically distributed wind resources in the context of a number of dispatch scenarios based on profiles of historical wind generation for a real power network. Stability issues have been analysed using novel stability indices developed from dynamic characteristics of wind generation. The results of this study show that localised stability issues worsen when significant penetration of both conventional and wind generation is present due to their non-complementary characteristics. In contrast, network stability improves when either high penetration of wind and synchronous generation is present in the network. Therefore, network regions can be clustered into two distinct stability groups (i.e. superior stability and inferior stability regions). Network stability improves when a voltage control strategy is implemented at wind farms, however both stability clusters remain unchanged irrespective of change in the control strategy. Moreover, this study has shown that the enhanced fault ride-through (FRT) strategy for wind farms can improve both voltage and rotor angle stability locally, but only a marginal improvement is evident in neighbouring regions.

Application of UPFC for system security improvement under normal and network contingencies

Electric power systems are exposed to various contingencies. Network contingencies often contribute to over-loading of network branches, unsatisfactory voltages and also leading to problems of stability/voltage collapse. To maintain security of the systems, it is desirable to estimate the effect of contingencies and plan suitable measures to improve system security/stability. This paper presents an approach for selection of unified power flow controller (UPFC) suitable locations considering normal and network contingencies after evaluating the degree of severity of the contingencies. The ranking is evaluated using composite criteria based fuzzy logic for eliminating masking effect. The fuzzy approach, in addition to real power loadings and bus voltage violations, voltage stability indices at the load buses also used as the post-contingent quantities to evaluate the network contingency ranking. The selection of UPFC suitable locations uses the criteria on the basis of improved system security/stability. The proposed approach for selection of UPFC suitable locations has been tested under simulated conditions on a few power systems and the results for a 24-node real-life equivalent EHV power network and 39-node New England (modified) test system are presented for illustration purposes.

Development and assessment of an incremental fatigue protocol for contemporary dance

Nine trained contemporary dancers performed a modality-specific, heart-rate-monitored, choreographed fatiguing dance protocol with an assumption of fatigue at volitional exhaustion (RPE 16). Postural stability was assessed as the variability of ground reaction forces and the centre of pressure during the performance of a flat-foot arabesque. Psychological response was assessed using self-reported fatigue, psychological distress (PD), and psychological well-being (PWB) (Subjective Exercise Experience Scale). After reaching RPE 16 in 15.7 ± 2.6 mins, heart rate decreased to the post-warm-up level within 64 ± 9 sec. Variability of ground reaction forces or the centre of pressure was not changed. There were no significant changes in fatigue, psychological distress, or psychological well-being. Within fatigue, there was a significant increase in the item tired (p = 0.04). As supported by the heart rate data and RPE, the protocol achieved an appropriate level of physical demand. No changes in the stability indices were observed, possibly attributed to the rapid recovery in heart rate. The expression of only tiredness suggests the use of a disassociative attentional style by the dancers. The project represents pilot work toward the validation of a monitoring process that supports dancer health and awareness training.

Continuation load flow using automatically determined branch megawatt losses as parameters

The conventional Newton's method is considered to be inadequate for the computation of the maximum loading point (MLP) of power systems since: (i) it encounters difficulties in the vicinity of the MLP: and (ii) the load flow Jacobian matrix becomes singular at the MLP. It is well known that continuation methods are powerful and useful tools that are able to trace the solution PV curve without experiencing such diffculties. However, continuation methods require a parameterisation so that a modified, well conditioned set of load flow equations is obtained. In particular, the Jacobian matrix associated with this modified set of equations should not be singular at the MLP. The authors propose that the actual power losses in transmission branches (lines and transformers) are used to parameterise the approach. Specific procedures for the automatic determination of the most appropriate parameter (branch) are proposed. Such procedures include the utilisation of fast voltage-stability indices. Simulation results are presented to show that the proposed method is able to trace the whole solution PV curve very efficiently.

Utilização de índices de estabilidade transitória para a avaliação de segurança dinâmica

Indices that report how much a contingency is stable or unstable in an electrical power system have been the object of several studies in the last decades. In some approaches, indices are obtained from time-domain simulation; others explore the calculation of the stability margin from the so-called direct methods, or even by neural networks.The goal is always to obtain a fast and reliable way of analysing large disturbance that might occur on the power systems. A fast classification in stable and unstable, as a function of transient stability is crucial for a dynamic security analysis. All good propositions as how to analyse contingencies must present some important features: classification of contingencies; precision and reliability; and efficiency computation. Indices obtained from time-domain simulations have been used to classify the contingencies as stable or unstable. These indices are based on the concepts of coherence, transient energy conversion between kinetic energy and potential energy, and three dot products of state variable. The classification of the contingencies using the indices individually is not reliable, since the performance of these indices varies with each simulated condition. However, collapsing these indices into a single one can improve the analysis significantly. In this paper, it is presented the results of an approach to filter the contingencies, by a simple classification of them into stable, unstable or marginal. This classification is performed from the composite indices obtained from step by step simulation with a time period of the clearing time plus 0.5 second. The contingencies originally classified as stable or unstable do not require this extra simulation. The methodology requires an initial effort to obtain the values of the intervals for classification, and the weights. This is performed once for each power system and can be used in different operating conditions and for different contingencies. No misplaced classification o- - ccurred in any of the tests, i.e., we detected no stable case classified as unstable or otherwise. The methodology is thus well fitted for it allows for a rapid conclusion about the stability of th system, for the majority of the contingencies (Stable or Unstable Cases). The tests, results and discussions are presented using two power systems: (1) the IEEE17 system, composed of 17 generators, 162 buses and 284 transmission lines; and (2) a South Brazilian system configuration, with 10 generators, 45 buses and 71 lines.

Utilização de índices de estabilidade transitória para redespacho de geração

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise de desempenho de índices de instabilidade atmosférica na previsão de fenômenos convectivos de mesoescala na região metropolitana de São Paulo entre 28 de janeiro e 04 de fevereiro de 2004

Discute-se o potencial prognóstico de índices de instabilidade para eventos convectivos de verão na Região Metropolitana de São Paulo. Cinco dos oito dias do período analisado foram considerados chuvosos, com observação de tempestades a partir do meio da tarde. O Índice K (IK) obteve valores abaixo de 31 nos 5 eventos, afetado pela presença de uma camada fria e seca em níveis médios da atmosfera em relação aos baixos níveis. O Índice Total Totals (ITT) falhou na detecção de severidade em 3 dos 5 eventos, apresentando valores inferiores ao mínimo limiar tabelado para fenômenos convectivos (ITT < 44) nesses dias. O Índice Levantado (IL) variou entre -4.9 e -4.3 em todos os 5 casos, valores associados a instabilidade moderada. O Índice de Showalter (IS) indicou possibilidade de tempestades severas em 4 dos 5 casos. Tanto o IS como o CAPE Tv tiveram seus valores fortemente reduzidos em uma sondagem com camada isotérmica entre 910 e 840 hPa. As séries temporais de CAPE Tv e IL mostraram significativa concordância de fase, com alta correlação linear entre ambas. CINE Tv ≈ 0 J kg-1 em associação com baixo cisalhamento vertical e com IS, IL e CAPE Tv, pelo menos moderados, parecem ser fatores comuns em dias de verão com chuvas abundantes e pequena influência da dinâmica de grande escala na área de estudo.

Alteração climática dos índices de estabilidade na Peninsula Iberica

Este trabalho tem como objetivo a comparação da intensidade, frequência e distribuição de um conjunto de índices de estabilidade atmosférica simulados entre o clima histórico (1986-2005) e um cenário climático (2081-2100) na Península Ibérica. Considerou-se o cenário de emissão de gases RCP8.5. Estes índices avaliam a instabilidade atmosférica que é um elemento fundamental e percursor no desenvolvimento de tempestades. Através dos seus valores limite, é possível estimar alterações na probabilidade de ocorrência de eventos extremos que se poderão desenvolver no clima futuro, relativamente ao histórico. Primeiro, utilizou-se um conjunto de simulações do WRF com dois forçamentos: reanálises do ERA-Interim e um modelo do Max Planck Institute. De seguida, foram calculados diferentes índices de estabilidade. A validação do modelo consistiu no cálculo das médias sazonais, da sua diferença e das respetivas PDFs dos índices simulados pelo WRF-MPI e WRF-ERA. Verifica-se uma sobrestimação do CAPE, SHR6km (vento de corte) e SWEAT simulados pelo WRF-MPI. No entanto, nos campos dos índices simulados pelos dois forçamentos para o período histórico, verifica-se que os padrões espaciais são semelhantes apesar das diferenças na intensidade. Como as alterações climáticas dos índices são avaliadas através de diferenças, estas discrepâncias não invalidam a utilização do modelo no futuro. Posteriormente foram estudadas as alterações climáticas dos índices através da comparação entre o clima histórico e futuro. Estima-se um aumento da intensidade do CAPE e uma diminuição (aumento) da frequência de eventos com intensidade reduzida (elevada). Estas alterações são robustas no verão e outono. Também é esperado um aumento da intensidade do SHR6km na primavera e inverno tal como da frequência de SHR6km elevado nestas estações e uma redução da intensidade e da frequência de eventos com SHR6km elevado nas restantes. Haverá um possível aumento robusto da intensidade do SWEAT no verão e outono, bem como da frequência destes valores. Concluindo, será provável um aumento da frequência dos ambientes favoráveis ao desenvolvimento de tempestades, devido a uma maior intensidade e probabilidade de ocorrência de valores extremos do CAPE e do SWEAT. No entanto, a redução do SHR6km, poderá diminuir a organização das tempestades e o seu tempo de vida.

Power system stability analysis based on descriptive study of electrical indices

In a power network, when a propagation energy wave caused by a disturbance hits a weak link, a reflection is appeared and some of energy is transferred across the link. In this work, an analytical descriptive methodology is proposed to study the dynamical stability of a large scale power system. For this purpose, the measured electrical indices (angle, or voltage/frequency) following a fault in different points among the network are used, and the behaviors of the propagated waves through the lines, nodes and buses are studied. This work addresses a new tool for power system stability analysis based on a descriptive study of electrical measurements. The proposed methodology is also useful to detect the contingency condition and synthesis of an effective emergency control scheme.