Abstract
In this paper, a new method for uncertainty analysis in fuzzy state estimation is proposed. The uncertainty is expressed in measurements. Uncertainties in measurements are modelled with different fuzzy membership functions (triangular and trapezoidal). To find the fuzzy distribution of any state variable, the problem is formulated as a constrained linear programming (LP) optimization. The viability of the proposed method would be verified with the ones obtained from the weighted least squares (WLS) and the fuzzy state estimation (FSE) in the 6-bus system and in the IEEE-14 and 30 bus system.
Highlights
An important aspect of power system operation is the availability of an accurate picture of the system-state
The idea of an uncertainty range is recognizable in engineering practice, where the accuracy of a particular measurement is often described in percent e.g. plus or minus 2 %, rather than by quantifying the standard deviation or variance
(which in this case can be provided by the WLS) and a series of linear programming are solved to obtain updates dYi to the uncertainty bounds on the state variables
Summary
An important aspect of power system operation is the availability of an accurate picture of the system-state. A state estimator can be used to filter the available information creating an accurate and complete picture of the system conditions, while a supervisory control and data acquisition (SCADA) system is capable of providing operators with measured information with less accuracy. The objectives of state estimation methods are to reduce the variance of the estimates and improve their overall accuracy, detection of gross errors, invalid topological information and model parameter errors. It is difficult to characterize statistics of observation errors in practice In such circumstances, it is desirable to provide not just a single ‘optimal’ estimate of each state variable and an uncertainty range within which we can be assured that the ‘true’ state variable must lie. The uncertainty is modeled via deterministic upper and lower bounds on measurement errors, which take into account known meter accuracies [6]. By utilizing appropriate mathematical programming techniques, the confidence interval (or bounds) of the state variables can be computed
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