A publication of

CHEMICAL ENGINEERING TRANSACTIONS

The Italian Association
VOL. 35, 2013 of Chemical Engineering
www.aidic.it/cet
Guest Editors: Petar Varbanov, Jiří Klemeš, Panos Seferlis, Athanasios I. Papadopoulos, Spyros Voutetakis
Copyright © 2013, AIDIC Servizi S.r.l.,
ISBN 978-88-95608-26-6; ISSN 1974-9791 DOI: 10.3303/CET1335202

A Data Reconciliation Based Approach to Accuracy

Enhancement of Operational Data in Power Plants
Xiaolong Jiang, Pei Liu*, Zheng Li
State Key Laboratory of Power Systems, Department of Thermal Engineering, Tsinghua University, Beijing 100084,
China
liu_pei@tsinghua.edu.cn

Accuracy of operational data of a power plant is essential for power plant performance monitoring and fault
diagnosis. However, due to inevitable occurrence of systematic and measurement errors in the course of
obtaining operational data, these errors can only be reduced to a certain level but never be eliminated. In
this work, we propose a data reconciliation based approach to reduce the errors of operational data thus
enhance the accuracy of the data. The reconciled data can then be used in performance monitoring and
fault diagnosis systems to improve their performances. The proposed method is based on more efficient
use of redundant data and a first-principle mathematical model of a power plant. Then an optimization
process is performed where the weighted least square form of aggregated differences between measured
data and their estimated values are minimized. To illustrate the capability of the proposed method, we
provide a case study of data reconciliation for feedwater heater heat balance analysis in a 660 MW coal-
fired power plant in China. Results show that uncertainty of four key parameters, namely feed water mass
flow rate, condensate mass flow rate, deaerator pressure and outlet temperature, can be reduced by 24 %,
30 %, 5 % and 65 %, whilst the uncertainty of other parameters are also reduced to various extent.
Moreover, the results also indicate that the proposed approach is effective over a wide range of measured
data quality, where quality of some data could be much worse than others and the estimated
measurement uncertainties of operational data may not be accurate.

1. Introduction
To pursue higher process reliability and efficiency, performance monitoring methods for fault diagnosis and
operation optimization were widely used. Da Silva et al., (2009) proposed a quantitative model-based fault
detection and diagnosis algorithm which can classify the discrepancies between the actual system
behavior, represented by a phenomenological model and that of the input-output Laguerre function based
system model to help the operator to take confident decisions in case of operation disturbances. Curilem
et al., (2011) designed a data-driven Neural Networks and Support Vector Machine model for on-line
estimation of the filling level of a semiautogenous mill to help operators for optimizing its energy
consumption. When applying these methods for real operating processes, the accuracy of measured
operational data is of great importance. Data reconciliation is a technique to improve the accuracy of
measured data by reducing effect of random errors occurred during data measurement. The major
difference between data reconciliation and other data filtering techniques is that data reconciliation
explicitly uses process redundancy model and obtains estimates which satisfy the process constraints
(Narasimhan and Jordache, 2000).
Data reconciliation was firstly introduced in 1961 by Kuehn and Davidson (1961) and is an already
important technique used in chemical and petrochemical industries. For power industry, data reconciliation
has been used in boiler heat balance analysis to improve the accuracy of feed water flow rate, heat value
and flow rate of coal to a boiler (Liu et al. 2003). Fuchs (2003) used data reconciliation in steam turbine
heat balance analysis, with performance test data where the accuracy of data is much higher than
measured operational data. Harter et al., (2005) embedded data reconciliation algorithm into an existing
heat balance program of a coal-fired power plant, which greatly reduced effort of process modeling.

Please cite this article as: Jiang X., Liu P., Li Z., 2013, A data reconciliation based approach to accuracy enhancement of operational data
in power plants, Chemical Engineering Transactions, 35, 1213-1218 DOI:10.3303/CET1335202

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Valdetaro and Schirru (2011) developed a method to perform simultaneously: the tuning of the Hampel’s
three part redescending estimator constants, the robust data reconciliation and gross error detection for a
nuclear power plant. Martini et al. (2013) applied the data reconciliation and gross error detection
technique to a micro-turbine-based test rig.
In this work, we present a simulation study to illustrate the capability of data reconciliation for operational
data accuracy improvement in feedwater heater system heat balance analysis in a 660 MW coal-fired
power plant in China. We also illustrate application of data reconciliation in cases where redundant
measured data have different accuracies or estimated uncertainties of measured data deviate greatly from
their true values.

2. Principle of data reconciliation

Redundancy exists in a process measurement when the number of measured values is larger than the
number of unknown parameters. Due to inevitable errors, the redundant measured data will not fulfil the
constraint equations, but result in conflicts. By means of correction calculation, it is possible for data
reconciliation to proceed from contradictory measured values y to non-contradictory estimates x for the
true values of the measured variables. The most likely estimates x are obtained by maximizing the
likelihood function of the multivariate normal distribution (Narasimhan and Jordache, 2000):

Max
x
2S
1
n /2
Σ
n /2 ^
exp 0.5 y  x
T
Σ yx ` (1)

2
The covariance matrix of the measured data is represented by Σ. The diagonal element of Σ, σ i, is the
2
variance in measured variable i, and the off-diagonal element σ ij is the covariance of the errors in
variables i and j. |Σ| is the determinant of Σ.
It is assumed that the matrix Σ is diagonal, if the measured data are independent from each other. As a
result, Eq(1) can be simplified as:
n
Min
x
[0 ¦
i 1
yi  xi / V i2 (2)

The estimates are required to satisfy the constraints, which would have to be fulfilled by the true values of
the measured variables, as shown in Eq(3):

f x, v 0 (3)

The unmeasured variables are represented by v. The constraints equations may include simple laws of
physics, like the principles of the conservation of mass or energy or simple relationships from chemistry,
e.g. the laws of stoichiometry.
In general, data reconciliation problem can be formed as:
n
[0 ¦
2
Min yi  xi / V i2
x (4)
i 1

s.t. f x, v 0

3. Case study problem

3.1 System description

In this work, we use the high pressure feed-water heater and deaerator system in a 660 MW coal-fired
power plant to illustrate the effect of data reconciliation, as shown in Figure 1.
The system includes three high pressure feedwater heaters, a feedwater pump and a deaerator. In the
deaerator, gases dissolved in the condensate are removed by a mixing process with the drain water from
high pressure feedwater heater and extracted steam from turbine stage. Feedwater pump is located
downstream of the deaerator and pressurize the feedwater to specified pressure. Feedwater is then
preheated by extracted steam in the high pressure feedwater heater. After heating the feedwater,
extracted steam becomes subcooled drain water and is sent to the next feedwater heater and finally enters
the deaerator.

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Table 1: Relative measurement uncertainty
Measurement point Base case Case A Case B
Mass flow rate 1% 2% 3%
Pressure 0.8 % 1.6 % 2.4 %
Temperature 0.5 % 1% 1.5 %

4. Results discussion
In the simulation study, calculations were repeated many times for each case. In each calculation, a group
of simulated measurement data was first generated and then reconciled. After repeating the calculations
for many times, the relative uncertainty for data was calculated as Eq(7).

n 2
RU i 1.96 ¦j 1
yi , j  yi / n  1 / yi (7)

where yi,j represent the value of measured or reconciled data for the ith variable at the jth calculation and
yi represents the average of the ith variable in all the numerical experiments.

4.1 Accuracy improvement of data reconciliation for the Base Case

For the Base Case operational data, the simulation calculation was repeated for 100 times. Relative
uncertainty of the measured and reconciled data for the proposed system is shown in Figure 2.

Figure 2: Relative uncertainties of measured and reconciled data for base case operational data

Results show that the relative uncertainty of four key parameters, namely feed water mass flow rate,
condensate mass flow rate, deaerator pressure and outlet temperature, can be reduced by 24 %, 30 %,
5 % and 65 % for the Base Case. It is whilst the relative uncertainty of other parameters are also reduced
to various extent. For Case A and Case B, similar results were obtained and were not discussed here.
4.2 Data reconciliation effect for redundant data with different accuracies
In the Base Case, measured data of the same kind was assumed to have the same accuracy, which may
not be true for the actual situation in a power plant. For example, the measurement for the condensate
mass flow rate usually has better accuracy compared with those for the feedwater mass flow rate. For
traditional heat balance calculation using operational data in China, it is recommended to use the
condensate mass flow rate as input for heat balance analysis.

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For the data reconciliation approach, redundant data with different accuracies are all used. To investigate
the effect of data reconciliation at this situation a case study was carried. From Case C-1 to Case C-5, the
relative uncertainty of measured feedwater mass flow rate was set to be 1 %, 2.5 %, 5 %, 7.5 % and 10 %,
while the relative uncertainty of other measured data was the same as in the Base Case.
As the results in Figure 3 shows, in this case study reconciled data always have smaller relative
uncertainties than measured data for both the condensate and feedwater mass flow rate. Even in Case C-
5, when the feedwater mass flow rate measured relative uncertainty was 10.09 %, the reconciled relative
uncertainty was 1.06 %. At the same time, the relative uncertainty of condensate mass flow rate, whose
accuracy was improved efficiently in the Base Case, was changed from 1.10 % to 1.06 % after data
reconciliation. The results show that data reconciliation can always reduce the data uncertainty, even
when redundant data are of different accuracies.

Figure 3: Relative uncertainties of measured and reconciled data from Case C-1 to Case C-5

Figure 4: Relative uncertainties of measured and reconciled data from Case D-1 to Case D-5

4.3 Data reconciliation effect with poorly estimated measurement uncertainty

To carry out data reconciliation for real on-line operational data, another potential obstacle is how to
estimating the measured data uncertainty accurately. The estimated measurement uncertainties are used
in the data reconciliation process as an evaluation of the measured data accuracy and have direct impacts
on the reconciliation results. As the process data cannot be measured repeatedly, the measured data
uncertainties can only be estimated by their instrument grades. These estimations may not be accurate
since the situations in power plants are rather complicated. We carried out a case study to investigate the
impact of poorly estimated measurement uncertainty on data reconciliation. From Case D-1 to Case D-5,
the relative uncertainties of measured feedwater mass flow rate was set to be 1 % as in Base Case, while
the estimated relative uncertainties of the feedwater mass flow rate were set to be 0.5 %, 0.75 %, 1 %,

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1.25 % and 1.5 % . Case D-1 and D-2 means the measurement uncertainty of the feedwater mass flow
rate was underestimated, while Case D-4 and D-5 means an overestimation of the measurement
uncertainty.
Results in Figure 4 shows that poorly estimated measured data uncertainties will have impact on the data
reconciliation effects. As in Case D-5 the relative uncertainty of the reconciled feedwater mass flow rate
was 0.89 % although in Case D-3 it can be reduced to be 0.74 %. However, in Case D-5, the relative
uncertainty of the reconciled feedwater mass flow rate is still smaller than the measured one of 1.06 %,
which still shows an obvious accuracy improvement effect. In this Case study, the reconciled data always
have a smaller relative uncertainty compared with the measured data.

5. Conclusions
In this work, we propose a data reconciliation approach to improve the operational data accuracy for coal-
fired power plants. To illustrate the capability of the proposed method, we provide a simulation study of
data reconciliation for the heat balance analysis of the feedwater heater system in a 660 MW coal-fired
power plant in China. A MATLAB program is used to solve the proposed data reconciliation problem. It is
found that in the Base Case the relative uncertainties of four key parameters, namely feed water mass flow
rate, condensate mass flow rate, deaerator pressure and outlet temperature, can be reduced by 24 %, 30
%, 5 % and 65 %, whilst the relative uncertainties of other parameters are also reduced to various extent.
The simulation results also indicate that the proposed approach is effective over a wide range of measured
data quality, where quality of some data could be much worse than others and the estimated
measurement uncertainties of operational data may not be accurate.

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