4.1. MSET Model Validation
Energy consumption characteristic data are then selected from steady state database from May 1 to May 30 in 2017, under a 550 MW working condition (with the load in the range (548, 552) MW), and the environment temperature in the range (27, 30) °C. According to Equation (1), unit characteristic parameters of energy consumption containing 13 attributes are seen in
Table 3.
After independence and importance analysis, No. 2–7 and No. 13 energy consumption characteristic parameters are respectively selected as condition attributes and decision attribute for clustering under a 550 MW working condition.
The modeling process is shown in
Figure 4 for data mining guidance. The 325 data are then clustered by Kmeans method into four clusters, and clustering results based on heat rate can be seen in
Table 4. The table shows that #1 cluster contains data samples with the best heat rate, indicating the best working condition. Furthermore, #4 cluster contains those with the highest heat rate, meaning the highest energy consumption, while #2 and #3 clusters are those in the middle level. A total of 50 data from the #1 cluster are then taken as training samples for MSET model, while the remaining 16 data are used to test the established model, seen in
Figure 5,
Figure 6,
Figure 7 and
Figure 8.
Figure 5a–f shows the MSET multi parameter estimation model training results of main steam temperature, main steam pressure, reheated steam temperature, reheated steam pressure, feedwater temperature and condenser vacuum. The error percentage values of these energy consumption characteristic parameters are almost equal to zero. Heat rate samples are also trained by the model, with the estimated values, actual values and the error percentage values listed in
Figure 6, illustrating a good coincidence degree in the training data. The heat rate values in the figure, calculated with the average value 7839.1 kJ/kWh and the standard deviation value 8.3890 kJ/kWh, indicate the #1 cluster is in a high energy efficiency operation station.
In
Figure 7a–f, the MSET multi parameter estimation model is then tested by the remaining 16 samples. The largest error value exists in
Figure 7b, displaying the model estimating for main steam pressure with the highest error percentage value of just 0.5%, still small enough for model evaluation. Thus, the error percentage values of these energy consumption characteristic parameters show the accuracy of the MSET model. Heat rate samples are also tested by the model, with the estimated values, actual values and the error percentage values shown in
Figure 8. The estimated heat rate values are averaged as 7836.3 kJ/kWh, and with the standard deviation value 2.519 kJ/kWh, while the actual running ones with the average value 7830.1 kJ/kWh and the standard deviation value 4.151 kJ/kWh. The largest error percentage absolute value is 0.24%. The data distribution and error percentage absolute values testify that the MSET model obtains a high accuracy in the #1 cluster.
Moreover, the MSET model established by partial data in cluster #1 is utilized to test the rule between the change in unit operation level and the estimation accuracy. The data from cluster #1, cluster #2, cluster #3 and cluster #4 are taken as test data. Error percentage values are then calculated by parameters as main steam temperature, main steam pressure, reheated steam temperature, reheated steam pressure, feedwater temperature, condenser vacuum and heat rate, seen in
Figure 9. Cluster #1 obtains the lowest error percentage values as 0.09%, 0.33%, 0.03%, 0.02%, 0.01%, 0.08% and 0.07%. Further, with the increase in heat rate in cluster #2 to cluster #4, the accuracy of the MSET multi parameter estimation model based on cluster #1 decreases gradually.
Thus, the MSET multi parameter estimation model can be established through the samples in the lowest heat rate group (cluster #1 in the paper), and the residual changes between actual values of the parameters and the estimated ones in the model can be used to monitor unit working condition variation.
4.2. Case Analysis of Unit Energy Efficiency Monitoring
Unit energy efficiency status can be reflected by differences between actual observed and model estimated values, seen in
Section 4.1. Therefore, the deviation degree index calculated by errors of energy consumption characteristic parameters as Equation (17) can measure the energy efficiency.
where
and
are the actual observed and model estimated values of the
ith characteristic parameters, respectively.
d is the energy consumption characteristic parameter number. Since parameters have different influences on heat rate, weight values should be added in the deviation degree calculation, as Equation (18).
where
represents the weight value of
kth characteristic parameter, calculated by the modified information entropy weight method in
Section 3.2.2.
In
Section 4.1, four classes have been clustered by heat rate value with Kmeans method. The deviation degree average value of MSET model with the data from cluster #4 (group with the highest heat rate) as the observation vector can then be taken to determine the energy efficiency warning threshold
.
Random factors such as measurement errors and noises in the actual operation may lead to a large fluctuation of deviation degree, and even error warnings. Thus, a sliding window method should be used to deal with the deviation calculation.
Assume deviation degree sets
in time sequence, and time window width is
, seen in
Figure 10. The ith deviation degree
can be calculated as Equation (19).
Therefore, the deviation degree index and energy efficiency warning threshold, combined with MSET model under different conditions can be used to handle energy efficiency monitoring in the steam turbine system, and the method’s flow chart can be seen as
Figure 11. The steps can be described as follows:
Step 1: based on the heat consumption characteristic parameter condition library, the samples with the highest heat rate under each condition are selected.
Step 2: the energy efficiency deviation warning threshold under each condition is determined by the multi parameter estimation model.
Step 3: according to the estimated vector of characteristic parameters under MSET multi parameter estimation model, the deviation degrees of energy efficiency are calculated, and are then processed by the sliding window method for the final deviation degree as Equation (19).
Step 4: operation data indicate a normal working condition, unless exceeds . If exceeds , there is the necessity for energy efficiency diagnosis and abnormal characteristic parameter location.
Historical data from 2020/05/17 09:34 to 2020/05/17 13:49 with 1 min as the time interval are then taken for the 600 MW steam turbine monitoring, partly listed in
Table 5. The environment temperature and power output are (27, 30) °C and (548, 552) MW, respectively.
Characteristic parameters of heat rate in cluster #1 (from
Section 4.1) are taken to establish the MSET multi parameter estimation model, and energy efficiency warning threshold
is 1.916, calculated by data in cluster #4.
The deviation degree values during the period are then shown in
Figure 12a, with window width
. The red line in the figure represents the energy efficiency warning threshold value. The warning happens when the deviation degree value is larger than
. A partial view is enlarged to clearly tag the 37th deviation degree value, which is the first one larger than
in the time series. Then, the time stamp of the 37th deviation degree value, 2020/05/17 10:10, is tagged in the figure as the warning time.
Characteristic parameters are then monitored to locate the reason for the abnormal deviation degree values during operation.
Figure 12b–d shows the variation of main steam pressure, condenser vacuum and heat rate in time series. In
Figure 12b, main steam pressure values cannot be detected, as they contain obvious differences during the period compared with the normal operation data. Other parameters, such as main steam temperature, reheated steam temperature, feedwater temperature and reheated steam pressure have the similar performance.
Figure 12c shows that the condenser vacuum suffered a significant decrease at 10:20, 10 min later than the warning time at 10:10. A lower condenser vacuum value indicates a worse working level in the steam turbine system, resulting in a higher heat rate value, seen in
Figure 12d. In
Figure 12d, the obvious heat rate jump can be caught at 10:31, which is 21 min later than the warning time and 11 min later than the time when the condenser vacuum suffered the significant decrease.
Thus, the heat rate’s abnormal variety in this case can be detected to be caused by the condenser vacuum anomaly. The sudden drop of the condenser vacuum will lead to the decrease in steam energy capacity. In other words, the main steam flow will increase in order to remain at the unit load, which will result in the sudden increase in heat rate value. In this case, the misoperation of valves in the circulating water system causes a sudden decrease in circulating water flow. Thus, a lower condenser vacuum happens when the wet steam into the condenser cannot be sufficiently condensed. When the circulating water system returns to the normal working condition, the heat rate and the deviation degree will gradually fall back.
Actually, many operation parameters influence the heat rate calculation, thus, the time stamp of abnormal heat rate values can be explained later than that of the condenser vacuum in most cases. On the other hand, the heat storage in the boiler can also extend the steam turbine’s heat rate response time when characteristic parameters’ abnormal values exist in operation. Furthermore, while warning time by deviation calculation tagged in
Figure 12a is even earlier than the time stamp of the condenser vacuum anomaly, the energy efficiency deviation index can better reflect the change of unit operation state and provide warning information in advance, when combined with the warning threshold
.