Interval arithmetic in power flow analysis

Wang, Z.; Alvarado, F.L.

doi:10.1109/59.207353

Cited by 236 publications

(56 citation statements)

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“…In [13], interval techniques were also used to try to solve the power flow problem, comparing the results with those obtained by Monte Carlo simulations and by stochastic power flow. Although their methodology presented some problems, one important conclusion of that work was that interval analysis can substitute the repeated simulations required by Monte Carlo method.…”

Section: Discussionmentioning

confidence: 99%

Power Flow with Load Uncertainty

Barboza¹,

Dimuro²,

Reiser³

2004

TEMA - Tendências Em Matemática Aplicada E Computacional

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Abstract. This paper presents a methodology to solve load flow problems in which the load data are uncertain due to measurement errors. In order to deal with those uncertainties we apply techniques of Interval Mathematics. The algorithm uses the Interval Newton's method to solve the nonlinear system of equations generated by the problem. The implementation was performed in the Matlab environment using the Intlab toolbox. In order to assess the performance of the proposed algorithm, the method was applied to hypothetical electric systems. In this paper, we present results for a three-bus network.

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Section: Discussionmentioning

confidence: 99%

Power Flow with Load Uncertainty

Barboza¹,

Dimuro²,

Reiser³

2004

TEMA - Tendências Em Matemática Aplicada E Computacional

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“…The uncertainty is an acute problem in power systems because of the complexity of power systems, so several interval arithmetic-based methods have been proposed for solving power system problems [12][13][14][15]. However, the naive use of IA is prone to pessimistic conclusions, which at times limits the industrial practicality of such methods.…”

Section: Introductionmentioning

confidence: 99%

“…Widespread applications of interval arithmetic (IA) have appeared in recent years [9][10][11][12][13][14][15]. The uncertainty is an acute problem in power systems because of the complexity of power systems, so several interval arithmetic-based methods have been proposed for solving power system problems [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Power system transient stability simulation under uncertainty based on Taylor model arithmetic

Wang

Zheng

Wang

2009

Front. Electr. Electron. Eng. China

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The Taylor model arithmetic is introduced to deal with uncertainty. The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model (TM). Thus, time domain simulation under uncertainty is transformed to the integration of TM-based differential equations. In this paper, the Taylor series method is employed to compute differential equations; moreover, power system time domain simulation under uncertainty based on Taylor model method is presented. This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation. It is computationally fast compared with the Monte Carlo method, which is another technique for uncertainty analysis. The proposed method has been tested on the 39-bus New England system. The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.

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“…What's worse, convolution is computationally cumbersome for online analysis of the distribution network. On the contrary, the model of interval power flow is rather simple and the solution is much more intuitionistic, which exports the upper bound and lower bound of the bus voltage if power injection interval of each bus is given [15]. When implementing interval power flow analysis, the uncertain output power of each DG or load power is expressed as an interval number [16], then non-linear power flow equations including interval numbers are solved according to interval analysis theory [17].…”

Section: Introductionmentioning

confidence: 99%