A Simplified Treatment of Uncertainties in Complex Quantities

Yhland, K.; Stenarson, J.

doi:10.1109/cpem.2004.305464

Cited by 10 publications

(10 citation statements)

References 2 publications

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“…There are also some publications that cover this problem for complex multi valued quantities which in general have correlated uncertainties both between parameters and their real and imaginary parts this becomes a complicated task [6,7]. The process for complex quantities can be simplified if we assume uncorrelated uncertainties in all network parameters and that the real and imaginary parts of the uncertainties are equal and uncorrelated [8]. The basis of all these procedures is a linearization of the expression that transforms one set of network parameters into another set.…”

Section: Uncertainty Backgroundmentioning

confidence: 99%

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Uncertainty propagation through network parameter conversions

Stenarson¹,

Yhland²

2008

2008 Conference on Precision Electromagnetic Measurements Digest

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Section: Uncertainty Backgroundmentioning

confidence: 99%

“…To obtain the uncertainty expressions we linearize the conversion equations with respect to uncertainties in the network parameters following the assumptions of [8]. This is done by substituting Q+δQ into Q and Q'+δQ' into Q' in (4)(5), where the δ terms are small variations of Q.…”

Section: Linearize Conversionsmentioning

confidence: 99%

Uncertainty propagation through network parameter conversions

Stenarson¹,

Yhland²

2008

2008 Conference on Precision Electromagnetic Measurements Digest

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“…The real part of the standard measurement uncertainty of a complex quantity of interest

z

that is determined by a function of several variables

z = f (x_{1}, \dots, x_{n})

is given by [38]:

\begin{matrix} true \\ left u false(prefixRe false(z false) false) \\ left = {[{(u (Re false(x_{1} false)) (||, \frac{\partial z}{\partial x_{1}}))}^{2} + \dots + {(u (Re false(x_{n} false)) (||, \frac{\partial z}{\partial x_{n}}))}^{2}]}^{\frac{1}{2}}, \end{matrix}

where

u (\cdot)

is the uncertainty associated with the respective variable. An analogous expression can be obtained for the uncertainty in the imaginary part of the variable, by replacing the real part of the expressions with the imaginary part in (2) [30]. The uncertainty in the magnitude of the quantity of interest can be determined by [30]:

u false(false| z false| false) = \sqrt{u {(Re false(z false))}^{2} + u {(Im false(z false))}^{2}},

where

z

in this paper represents the ZSC determined by direct, indirect or PMU measurements.…”

Section: Analytical Approach To Error Analysismentioning

confidence: 99%

“…An analogous expression can be obtained for the uncertainty in the imaginary part of the variable, by replacing the real part of the expressions with the imaginary part in (2) [30]. The uncertainty in the magnitude of the quantity of interest can be determined by [30]:

u false(false| z false| false) = \sqrt{u {(Re false(z false))}^{2} + u {(Im false(z false))}^{2}},

where

z

in this paper represents the ZSC determined by direct, indirect or PMU measurements. By constructing expressions for the measurement chains as described in section 2, we can determine analytical expressions for the total measurement errors of the measured positive‐ and ZSCs.…”

Section: Analytical Approach To Error Analysismentioning

confidence: 99%

Zero‐Sequence current measurement uncertainty in three‐phase power systems during normal operation

Nauta

Serra

2021

IET Generation Trans & Dist

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Zero‐sequence currents in high‐voltage power systems during normal operation can have a significant influence on nearby infrastructure. It is therefore necessary to gain insight into typical levels of zero‐sequence currents in a variety of operational situations. Measurements can provide this insight. When performing measurements, one needs to know the uncertainty associated with the measurement to draw accurate conclusions. The measurement uncertainty associated with three different practical strategies to measure zero‐sequence currents during normal operation are studied: a direct and indirect measurement strategy using current clamps and oscilloscopes and a measurement strategy using phasor measurement units (PMU). Measurement uncertainty is studied using two methods: by analytical expressions and by Monte Carlo simulations. Both methods give consistent outcomes for the measurement uncertainty and show the same tendencies of the zero‐sequence current measurement uncertainty as a function of the positive‐sequence current. This paper studies measurement strategies with error sources based on realistic measurement devices that could be used in practice. The following outcomes were found: in the direct strategy, the primary current transformers are the largest uncertainty sources; in the indirect strategy, the current clamps are the largest uncertainty sources; in the PMU strategy, the PMU total vector error is the largest uncertainty source.

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“…In (6), (7) and (8), x m and y m are the real and imaginary parts of the CRV. x i and y i are the real and imaginary parts of the individual reported values.…”

Section: Comparison Reference Valuementioning

confidence: 99%

Key comparison SIM.EM.RF-K5b.CL: scattering coefficients by broad-band methods, 2 GHz–18 GHz — type N connector

Silva¹,

Monasterios²

2016

Metrologia

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The first key comparison in microwave frequencies within the SIM (Sistema Interamericano de Metrología) region has been carried out. The measurands were the S-parameters of 50 ohm coaxial devices with Type-N connectors and were measured at 2 GHz, 9 GHz and 18 GHz. SIM.EM.RF-K5b.CL was the identification assigned and it was based on a parent CCEM key comparison named CCEM.RF-K5b.CL. For this reason, the measurements standards and their nominal values were selected accordingly, i.e. two one-port devices (a matched and a mismatched load) to cover low and high reflection coefficients and two attenuators (3dB and 20 dB) to cover low and high transmission coefficients. This key comparison has met the need for ensuring traceability in high-frequency measurements across America by linking SIM's results to CCEM. Six NMIs have participated in this comparison which was piloted by the Instituto Nacional de Tecnología Industrial (Argentina). A linking method of multivariate values was proposed and implemented in order to allow the linking of 2-dimensional results. KEY WORDS FOR SEARCH Main text To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCEM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

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A Simplified Treatment of Uncertainties in Complex Quantities

Cited by 10 publications

References 2 publications

Uncertainty propagation through network parameter conversions

Uncertainty propagation through network parameter conversions

Zero‐Sequence current measurement uncertainty in three‐phase power systems during normal operation

Key comparison SIM.EM.RF-K5b.CL: scattering coefficients by broad-band methods, 2 GHz–18 GHz — type N connector

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