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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 39, NO. 4,1992

Nuclear Power Plant Performance Study by Using Neural Networks

Zhichao Guo and Robert E. Uhrig Nuclear Engineering Department ,The University of Tennessee

Knoxville, TN 37996-2300, USA

Abstract - T h e thermal performance data obtained f rom Tennessee Valley Author i t y (TVA) Sequoyah Nuclear P o w e r P lan t show that the heat rate i s changing constantly and the plant is probably losing some Megawatts of elec- tr ic power due t o the variat ion of the heat rate. It i s ve ry dif icul t t o analyze the raw data recorded weekly during the ful l power operation of the plant because a nuclear power plant is a very complex s y s t e m with thousands of param- eters. The hybrid type of neural networks w a s se t up t o work as the internal thermodynamic model of the plant f o r the prediction of heat rate . Then , sensi t iv i ty s tudy w a s ap- plied to the neural network model t o extract information about the key parameters which might strongly affect the plant thermal performance.

I. INTRODUCTION

Heat rate is a very important measure to the perfor- mance of nuclear power plants. The thermal performance data have been taken weekly from the Tennessee Valley Authority (TVA) Sequoyah Nuclear Power Plant Unit 1 and Unit 2, which include about 40 measured or calcu- lated variables. Heat rate is one of the calculated variables. The recorded data show that the heat rate is changing con- stantly and the plant is probably losing some Megawatts of electric power due to the heat rate variation. It is difficult to find the causes of the heat rate deviation through tra- ditional analytical methods because a nuclear power plant is a very complex system with thousands of variables.

In the past few years, several systems for monitoring heat rate performance of power plants have been devel- oped. Generally, these systems are based on energy bal- ance equations applied to the many subsystems of the power plant and integrated into an overall system for heat rate determination. Recently, expert systems have been introduced to advise operators on steps to be taken to im- prove the heat rate. Some of these systems have knowledge bases that rely on the knowledge of experts while others rely on embedded models based on both fundamental and empirical thermodynamic relationships. Three such sys- tems are the “Heat Rate Degradation Expert System Ad- visor” by Sargent and Lundy and EPRI[l], the “Smart Operator Aid for Power Plant Optimizationm” by Impel1 Corporation and Southern California Edison[2], and the

“Thermal Performance Advisor Expert System” by Gen- eral Physica Corporation, EPRI and Public Service Elec- tric and Gas of New Jersey[3].

Potential drawbacks of theses approaches are that they are dependent upon models of the systems that may de- viate from ideal conditions, and usually involve empirical relationships, approximations of the actual processes, and often linerization of nonlinear phenomena. In this study, the model of the thermodynamic process is obtained using a neural network (which can handle nonlinearities) trained on actual measurements from the plant over a one-year peroid of time. Hence the model represents the thermo- dynamic process as it actually exists in the plant, and the dynamic range of the data covers the normal range of variables during a typical annual cycle. This method- ology could be implemented in any of the systems listed above.

11. HYBRID TYPE NETWORK

In order to use neural networks to study the heat rate, a proper network type has to be chosen, and the network structure has to be set up. The network used in this study is a hybrid type neural network which is the combination of self-organization[4] and backpropagation[5] neural net- works. The self-organization network functions as an orga- nizer which rearranges the original training patterns into different classes represented by clusters. Then, the cen- troids of these clusters are used as the training patterns for the backpropagation network. The training time for the backpropagation network can be greatly reduced through this combination, because the number of clusters is usually much less than the original training patterns. The appli- cation to the TVA Sequoyah nuclear power plant shows that both the training convergence rate and the prediction accuracy can be improved by using this special network combination.

111. SENSITIVITY STUDY

A successfully trained neural network works essentially 2 a mapping function, which maps a set of input veciors X in n-dimensional space to a set of output vectors Y in

0018-9499192$03.00 0 1992 IEEE

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Figure 1: A 3-Layer Backpropagation Neural Network

m-dimensional space. It can be expressed as:

F = f(2) (1) *

where X = ( x ~ , x z , . . . , xn) and ? = ( Y I , 312,. . . , y m ) . The partial derivative, d y k / a X i , is the rate of change

in Y k with respect to a change in x i . Therefore, a y k / a x i can be used to measure the importance among the input variables, x i , i = 1 , 2 , . . . , n, by ranking them according to the Values Of l&k/&il.

A three layer backpropagation neural network is shown schematically in Figure 1, where wij is the connection fiom the ith neuron in the input layer to the j t h neuron in the second or hidden layer, and V j k is the connection from the j t b neuron in the hidden layer to the kth neuron in the output layer.

The neiwork mapping process is that when an input pattern, X, is received by the neurons in, the input layer it is first mapped as an output pattern, B = ( b l , b 2 , . . . , bp) of the hidden layer, and then, B' is mappedSorward to the output layer 40 form-an output pattern, Y, to finish the mapping of X - Y . Mathematically, the mapping process is the following:

where f(z) = l / e x p ( - t / a ) is the sigmoid transfer func- tion, and 6 is the sigmoid slope. S j and P k are the thresh- old values of the j t h neuron in the hidden layer and the kth neuron in the output layers, respectively.

Taking the first derivative of an output variable yk with respect to an input variable z i by applying chain rule:

The equation shows that the partial derivative depends not only on the network connections, wij and v j k which are the memory of the training, but also on the activation of neurons in both hidden layer and output layer, which in turn depend on the input patterns. The importance of the input variables can then be measured by the values of a y k / a x i .

IV. NEURAL MODELING

In order to find the important variables which might strongly affect the heat rate, 24 variables were selected as the inputs, and 2 variables were chosen as the desired out- puts. Table 1 gives the list of the variables where variable 25 and 26 are desired outputs.

Table 1. Variables Selected For The Neural

- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 -

Networks Reactor Power during Test (%) Gen. Output AT Reactor Power during Test (MWe Conden. Perf. Change Based on River Temp.(Mwe: Other Condenser Losses (MWe) (Loss +) Throttle Pressure Greater Than Design Improved MSR Performance (MWe) Auxiliary Steam Loads (Mwe) (Loss +) Other Misc. Loads (MWe) (Loss +) Measured Generator Output during Test (MWe) Total Unaccounted Megawatts (MWe) (Loss +) Primary to Secondary Calorimetric Ratio Measured Condenser Backpressure (inches HG abs.' Expected Condenser Backpressure (inches HG abs.) Condenser Circulating Water Inlet Temp. (deg F) Final Feed Water Temperature (deg F) Impulse Pressure [PT-1-73] (psig) Impulse Pressure [PT-1-72] (psig) Feedwater Flow (lo6 lbm/hr) Avg Rx Delta Temp. (deg F) Turbine Power Corrected to Design (Mwe) Unexpected Power Deviations (Mwe) (Loss +) Thermal Power Normalized RX Delta T (%) Impulse Pressure Avg (pia) Impulse Pressure Normalized (Frac.)

Selected Desired Output Variables 25 I Thermal Performance'(INP0) (%)

I , r

26 I Gross Heat Rate (Btu/Kwh) .

'Thermal performance is not thermal efficiency. It is the ratio at a reference heat rate to the measured gross heat rate corrected for river temperature, multiplied by 100 to express it in percent.

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The training patterns were prepared from the data of the Sequoyah Unit 1 with 45 patterns in total. The train- ing patterns for the backpropagation were reduced to 22 by using the centroids of the clusters formed by the training of the self-organization neural network. The backpropagation network waa set up with 24 neurons in the input layer, 10 in hidden layer, and 2 in the output layer. The network was trained successfully with system error of 0.0001, which is the average of pattern errors of all patterns. The recall was performed with the original 45 patterns from Unit 1, which were not used directly for the training of the backpropaga- tion network but for the training of the self-organization network. The average error of the network prediction was about 0.06% and the largest error was 0.34%. The recall was also performed with 36 patterns from the Unit 2, sim- ilar, but not identical plant. The data from Unit 2 were used neither for the training of the self-organization nor for the training of the backpropagation network. The av- erage error of the network prediction was less than 0.32% and the largest error was 1.3%. The small prediction error for Unit 2 indicates that the thermodynamic behaviors of these two plants are similar. Figure 2 and 3 show the com- parisons of the plant data with the outputs of the network for Unit 1.

W..k

V. ANALYSIS FOR NEURAL MODELING

The small prediction error from the network indicates that the training was successful and the trained network could be studied further for the sensitivity analysis to find out the important variables which might strongly affect the heat rate and thermal performance of the plant. The trained backpropagation neural network was used together with plant data from Unit 1 and Unit 2 for the sensitivity study by using equation (4). Since the partial derivatives, d y k l d x i , may be different by using different input pat- terns, the results of the sensitivity study were represented by pattern average of the absolute values of d y k l d x i over all input patterns, which gave the measure of the sensi- tivity on a global sense. Table 2 gives the results of the sensitivity analysis, where TP is the acronym for Ther- mal Performance, and GHR is the acronym for Gross Heat Rate.

The results from the sensitivity study showed that there was a very good agreement for identifying the important variables between the data from Unit 1 and Unit 2. The most important variables selected for Gross Heat Rate (GHR) for both Unit 1 and Unit 2 are listed in Table 3 in the order of importance.

VI. MORE EXPLORATION

The sensitivity study can be applied further to explore more information about the system. Table 2 shows that variable number 21, Unexpected-Power-Deviations, is the

Figure 2: Comparison of plant data with neural network outputs for Unit 1

Figure 3: Comparison of plant data with neural network outputs for Unit 1

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Table 2. Results of the Sensitivity Study

Unit ToTP

18 14 2 11 5 6

21 17 7 3 10 9 8 13 19 23 22 20 15 12 1

16 24 4

- Va.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-

-

1 ToGHR

23 17 10 5 6 13 18 15 7 4 8 2 9 3 16 20 22 24 19 11 1

14 21 12

1portanc U

To TP 16 10 7 21 8 12 20 17 6 3 2 4 18 5 14 22 23 19 13 9 1

15 24 11

t 2 To GHR

20 14 10 8 9

12 14 15 6 4 5 2 7 3 13 21 24 23 19 11 1

16 22 18

Table 3. Important Variables Selected By Sensitivity Analysis

most important variable for both Gross Heat Rate and Thermal Performance. It is useful to carry the analysis one step further to evaluate the most important variables related to Unexpected-Power-Deviation. Another neural network was set up with Unexpected-Power-Deviations as its target variable and the 23 remaining variables in Table 1 (excepting Gross Heat Rate and Thermal Performance) as its input variables. The training process was the same as before, which used the self-organization network first to cluster the original data patterns to reduce the total training patterns for the following backpropagation net- work by using the centroids of the formed clusters. Again, the training was successful and the sensitivity study was applied to the trained network to explore more informa- tion. The results of the study are listed in Table 4.

Table 4. Important Variables for Power Deviation

These process can be carried out on and on to explore more and more detailed information about the system. The results from the sensitivity study indicate that the heat rate variation might be caused mainly by the param eters listed in Table 3, And the Unexpected Power Devi- ation might be caused by the parameters listed in Table 4. This information gives the clues to the plant personnel as to which variables are most important to the plant ef- ficiency and which efforts to improve the efficiency will be mo8 t effective.

VII. DISCUSSION AND REMARKS

The preliminary results show that neural networks may be used to analyze plant data and extract some useful in- formation which may be diflicult to obtain through the tra- ditional analytical methods. The application to heat rate and thermal performance study for the nuclear power plant may provide some useful information to the power plant personnel to find what may cause the deviation in the plant thermal performance and the heat rate, and then, try to control them in order to operate the plant more efficiently.

Acknowledgement The authors wish to acknowledge the support of this project by the Department of Energy under the contract #DE - FG07 - 88ER12824 and Tennessee Valley Authority (TVA) who provided the data on its Sequoyah Unit 1 and Unit 2 plants.

Reference

1. D. M. Sopocy, R. E. Henry, S. M. Gehl, and S. M. Divakaruni, “Development of an On-Line Expert System: Heat Rate Degradation Expert System Advisor,” Proceedings of Expert Systems Applications for the Electric Power Industry, vol. 2, pp. 911-924, Orlando Florida, June 5-8, 1989.

2. M. McClintock, R. Metzinger, and N. Hirota,“Thermal Performance Advisor System Development ,” Proceedings of Expert Systems Applications for the Electric Power Industry, vol. 2, pp. 1193-1203, Orlando Florida, June

3. P. R. Papilla and E. J . Sugay,“SMOP: Smart Operator’s Aid for Power Plant Optimization,” Proceedings of Expert Systems Applications for the Electric Power Industry, vol. 2, pp. 1009-1021, Orlando Florida, June 5-8, 1989.

4. Kohonen, T., “Self-Organization and Associative Memory,” New York: Springer-Verlag, 1984. 5. D. Rumelhart, J. L. McClelland, and PDP Research Gruoup, “Parallel Distributed Processing: Volume 1: Foundation; Volume 2: Psychological and Biological Models,” MIT Press, Cambridge, Massachusetts, 1988.

5-8, 1989.