MONITORING | INSTRUMENTATION & CONTROL
Measured mass flow rate = 100 Measurement uncertainty = 10%
100 ≠ 42 +65
Measured mass flow rate = 42 Measurement uncertainty = 6%
Reconciled mass flow rate = 106.36 Reconciled uncertainty = 2.85% Penalty = 1.71
106.36 = 41.60 + 64.76
Reconciled mass flow rate = 41.60 Reconciled uncertainty = 5.88% Penalty = 0.99
Measured mass flow rate = 65 Measurement uncertainty = 3
Reconciled mass flow rate = 64.76 Reconciled uncertainty = 2.96% Penalty = 0.59
For a nuclear station, a DVR model will examine 200 to
300 measured variables and their associated uncertainties. This includes temperature, pressure, flow and power. DVR establishes the functional relationship between these measurements to produce a system of redundant measurements and uses the mathematical calculations and methodologies that are described in the German technical standard, VDI-2048. These methodologies include the use of empirical covariance matrices and the Gaussian correction principle.
The empirical covariance matrices relate the errors of
measurement uncertainties to fundamental equations, such as mass and energy balance and thermodynamic properties. With the matrices and the Gaussian correction principle, DVR eliminates systematic errors, minimises random errors and fits the measurements within the measurement accuracies with the smallest amount of correction. The corrections to the measurements are a function of the uncertainty placed on the measurement and the redundancies associated with that measurement. The final outcome is a set of statistically analysed most- probable values (closest to the true value) for all of the station measurements (reconciled measurements). This process also calculates the most probable values for locations throughout the cycle where no instrumentation is present.
In addition to providing the most probable values,
DVR calculates the uncertainty associated with each reconciled measurement, the penalty associated with each reconciled measurement and an overall quality rating for the data set. The calculated uncertainty is determined for each
of the reconciled measurements, providing a reduced uncertainty value and a more accurate reflection of the reconciled values. The calculated penalty is based on the difference between the reconciled and measured values (error) compared to the original measurement uncertainty. As the error increases, the penalty for the measurement increases. Once the penalty exceeds the 95% confidence interval associated with that measurement, the tag is flagged by the software and considered suspect. The quality rating validates the entire set of reconciled results and is calculated based on the ratio between the weighted sum of all the penalties and the Chi-square test value. The Chi-square test value is calculated based on the number of redundancies in the model and the statistical certainty of the test (95% confidence). The quality must remain below 1 to be considered valid and acceptable. If the quality goes above 1, it is likely that there are significant errors associated with the model or the measured values.
Implementing DVR has many benefits:
● Online validation of all the station-measured values that are included in the DVR model.
● Pseudo-measurements for locations in the cycle where no instruments are installed. By utilising the current station measurements and mass and energy balance equations, pressures, temperatures, flows, etc can be viewed for any part of the cycle, not just where instruments are installed. This provides additional visibility for other parts of the cycle and saves money by providing measurements in locations without additional instrumentation.
● Operation closer to specifications, by removing unnecessary margin.
● Less preventative maintenance performed on instrumentation, because it can be deferred. The measurement penalty can be used to help identify the instruments that are faulty, drifting, or that need to be calibrated. The result is reduced maintenance, and better aging management of plant instrumentation and control systems.
● Early detection of instrumentation degradation. This helps stations make repairs or corrections before issues develop and avoids the consequences of inaccurate measurements.
● Decreases the dependency on single-instrument measurements where no physical redundancy exists.
● Increased gross power output because the station can implement the correction factors from the DVR results for feedwater flow errors due to nozzle fouling.
● Margin uncertainty recapture, which would allow DVR to become a replacement for expensive flow meters. This is being evaluated in the US.
● Identify plant issues that result in lost generation, such as cycle isolation leaks.
● Provide a more accurate understanding of the station operating conditions and parameters by reducing the uncertainty related to station measurements.
These benefits have led many stations to implement DVR in recent years. GSE TrueNorth has successfully helped implement Belsim’s DVR software at more than 30 nuclear units in the USA. These stations are all using DVR to provide better online monitoring of their station performance, improve issue identification, and help troubleshoot lost generation. Three of the stations have implemented power recovery using DVR to determine the feedwater flow correction. The power recovery effort has been successful with a combined gain of 20MWe. ■
www.neimagazine.com | November 2021 | 29
Above left: Mass flow rate measurements before DVR
Above right: Mass flow rate reconciled results after DVR
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