The Cumulative Method for Multiplication and Division

This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.

Seismic hazard analysis for central-western Argentina

In this study, we present a PSHA（Probabilistic Seismic Hazard Analysis） for the city of San Juan, which is located in the central-western region of Argentina（30°S-35.5°S; 66.5°W-71°W）. In addition to crustal earthquakes provided by catalogues, recent paleoseismological and neotectonic investigations have permitted to consider events which occurred during the last 400 years.Four seismogenic sources that could cause damages to the studied site corresponding to Precordillera,Western Sierras Pampeanas, Basement of the Cuyana Basin and Cordillera Principal were identified.Based on the evaluation of the contribution of these sources,maximum moment magnitudes above 7.5（Mw） are expected.High values of SA（spectral acceleration）（0.2 and 1 s periods） and PGA（peak ground acceleration） were found in the city of San Juan, which suggests that it is located in a zone of high seismic hazard.Finally, the obtained SA spectra were compared with the seismic-resistant construction standards of Argentina INPRES-CIRSOC 103 [1]. Results suggest that for the city of San Juan and for a return period of475 years, it covers the seismic requirements of the structures.

Probabilistic Load Flow Algorithm with the Power Performance of Double-Fed Induction Generators

Probabilistic load flow(PLF)algorithm has been regained attention,because the large-scale wind power integration into the grid has increased the uncertainty of the stable and safe operation of the power system.The PLF algorithm is improved with introducing the power performance of double-fed induction generators(DFIGs)for wind turbines(WTs)under the constant power factor control and the constant voltage control in this paper.Firstly,the conventional Jacobian matrix of the alternating current(AC)load flow model is modified,and the probability distributions of the active and reactive powers of the DFIGs are derived by combining the power performance of the DFIGs and the Weibull distribution of wind speed.Then,the cumulants of the state variables in power grid are obtained by improved PLF model and more accurate power probability distributions.In order to generate the probability density function(PDF)of the nodal voltage,Gram-Charlier,Edgeworth and Cornish-Fisher expansions based on the cumulants are applied.Finally,the effectiveness and accuracy of the improved PLF algorithm is demonstrated in the IEEE 14-RTS system with wind power integration,compared with the results of Monte Carlo(MC)simulation using deterministic load flow calculation.

Unified probabilistic gas and power flow

The natural gas system and electricity system are coupled tightly by gas turbines in an integrated energy system. The uncertainties of one system will not only threaten its own safe operation but also be likely to have a significant impact on the other. Therefore, it is necessary to study the variation of state variables when random fluctuations emerge in the coupled system. In this paper, a multislack-bus model is proposed to calculate the power and gas flow in the coupled system. A unified probabilistic power and gas flow calculation, in which the cumulant method and Gram–Charlier expansion are applied, is first presented to obtain the distribution of state variables after considering the effects of uncertain factors. When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution. Compared to the Monte Carlo method, the proposed method can reduce computation time greatly while reaching a satisfactory accuracy.The validity of the proposed methods is verified in a coupled system that consists of a 15-node natural gas system and the IEEE case24 power system.

Cumulant-based correlated probabilistic load flowconsidering photovoltaic generation and electric vehiclecharging demand

This paper applies a cumulant-based analytical method for probabilistic load flow (PLF) assessment in transmission and distribution systems. The uncertainties pertaining to photovoltaic generations and aggregate bus load powers are probabilistically modeled in the case of transmission systems. In the case of distribution systems, the uncertainties pertaining to plug-in hybrid electric vehicle and battery electric vehicle charging demands in residential community as well as charging stations are probabilistically modeled. The probability distributions of the result variables (bus voltages and branch power flows) pertaining to these inputs are accurately established. The multiple input correlation cases are incorporated. Simultaneously, the performance of the proposed method is demonstrated on a modified Ward-Hale 6-bus system and an IEEE 14-bus transmission system as well as on a modified IEEE 69-bus radial and an IEEE 33-bus mesh distribution system. The results of the proposed method are compared with that of Monte-Carlo simulation.

EVALUATION OF THE CUMULATIVE FORMATION OF HIGH-SPEED LIQUID JETS

This paper describes the generation of pulsed, high-speed liquid jets usingthe cumulation method. This work mainly includes (1) the design of the nozzle assembly, (2) themeasurement of the jet velocity and (3) flow visualization of the injection sequences. Thecumulation method can be briefly described as the liquid being accelerated first by the impact of amoving projectile and then further after it enters a converging section. The experimental resultsshow that the cumulation method is useful in obtaining a liquid jet with high velocity. The flowvisulization shows the roles of the Rayleigh-Tay-lor and Kelvin-Helmholtz instabilities in thebreakup of the liquid depend on the jet diameter and the downstream distance. When the liquid jetfront is far downstream from the nozzle exit, the jet is decelerated by air drag. Meanwhile, largecoherent vortex structures are formed surrounding the jet. The liquid will break up totally by theaction of these vortices. Experimental results showing the effect of the liquid volume on the jetvelocity are also included in this paper. Finally, a method for measuring the jet velocity bycutting two carbon rods is examined.