Nuclear power plant operational diagnostics and control

Progress in Nuclear Energy. Vol. 1, pp. 735 to 745. Pergamon P r e s s 1977. P r i n t e d i n Grea t B r i t a i n .

NUCLEAR POWER PLANT OPERATI(]~AL DIAGNOSTICS AND CONTROL

Leslie G. Kemeny School of Nuclear Engineering, university of New South Wales

Kensington 2033, New South Wales, Australia

~ S T ~ C T

Before the end o f the p resen t cen tu ry , a s i g n i f i c a n t p r o p o r t i o n o f the w o r l d ' s needs f o r e l e c t r i c a l energy w i l l be s u p p l i e d by nuc lea r power p l a n t . The c a p i t a l i nves ted i n these s t a t i o n s , as opposed t o t h e i r o p e r a t i n g cos ts , w i l l be cons ide rab le . For t h i s reason and to ensure their optimal and safe operation, both as individual unite and in a generating network, computer based on-line monitoring, identification and control techniques will be associated with each nuclear plant.

1. INTRODUCTION

The normal operation of nuclear power plant is characterized by a series of correlated vibrations or fluctuations ranging from flow induced structural vibrations to fluctuations in the neutron or gamma photon population density. The identification in the time or frequency associated with these fluctuations gives rise to elegant power plant monitoring and control techniques. The forecasting or prediction of the state vectors associated with such fluctuations can, in principle, be used as a basis for emergency procedures associated with po- tentially abnormal operating conditions. [i]

The constraints on experimental measuremente are set by the transducer employed; by the band- width of the data processing equipment, and by the sophistication of the mathematical algorithms used for analysis or control.

In this paper a theoretical and system-conceptual model is outlined for the diagnosis and real-function detection of an operating nuclear power plant. The HIFAR reactor of the Australian Atomic Energy Commission is being used to simulate power reactor conditions. A computer based data acquisition system is being interfaced with the reactor to undertake both monitoring and control functions based on fluctuating signals associated with the nuclear plant. In particular, mechanical and hydroelastic vibrations, temperature fluctuations and neutron population and ga,m~ density variations are being monitored and, where possible, adapted for control surfaces.

2. PLANT MONITORING PROCEDURES

The School of Nuclear Engineering Data Acquisition Computer - the SNEDAC system - is shown in Fig. I. All signal flow operations are controlled by system software. At the machine language level, each input/output device is assigned a device number. Input/output transfer instructions contain this device number and three levels of micro instructions. The hardware is designed to interpret the above and in turn to control and transfer the data to and from the devices. Some of the typical I/0 instructions are shown below.

Mmemonic Octal O~eration

ADSF 6301 Skip if A/D converter flag is a 1

ADVC 6302 Clear A/D converter flag, convert input voltage

ADRB 6311 Read A/D converter buffer into the acctiRulator

All input/output devices are connected to the computer standard data channel and thus operate under "programmed data transfers". Magnetic tape deck can operate on the high speed data channel (the "data break" channel) as well, enabling high speed block data transfers to and from the CPU memory, bypassing all program control logic.

The system also includes a hardware priority interrupt system. All input/output devices are acco~dated in a preset priority, enabling higher throughput of data on the standard data channel.

The following program example illustrates how one of the analog to digital converters would

735

736 L.G. Kemeny

be serviced (without the use of the hardware interrupt system).

Tag

FLG CK

Instruction

IOT 6301

JMP. - 1

IOT 6302

IOT 6301

Remarks

Skip if Dev 30 is ready

Jump back, wait till ready

Clear flag, convert voltage

Skip if Dev 30 is ready

Since the CPU is equipped with program interrupt, software overhead during the search of the device flags is minimized. This feature is extremely useful since in some cases a large amount of computing is required between I/0 instructions. Addition of the hardware priority

interrupt option reduces software overhead even further by providing the particular I/0 device number in the accumulator of the CPU (after the execution of the Test Device Instruc- tion).

All signal flow operations are controlled by software programming from the computer. For high speed "on-line" applications the correlation coefficients of one or two time series can be rapidly computed in a special purpose hard-wired correlator, prior to mathematical processing in the computer. Alternatively signals can be routed on to an FM/DR tape recorder or an incremental tape recorder prior to processing.

With the sampled data - neutron density, temperature, pressure, void fraction or vibration - stored either in the core of the computer, on the incremental tape deck or in the correlator in the form of coefficients, SNEDAC carries out its threefold task of data acquisition and monitoring, identification of normal and abnormal operating conditions and simulating potential digital control strategies. The system configuration at the present time consists of five cabinets of hardware as follows:

i. Ancillary storage and recording equipment consisting of FM/DR instrumentation tape recorder, ultraviolet galvanometer recorder and chart recorder.

2. Transducers and signal conditioning equipment and power supplies.

3. Slow speed data logger to scan twenty channels at speeds up to 15 Hz with both paper tape and decimal print output.

4. High speed digital data acquisition unit for dynamic and impulse response testing.

This unit contains scalers, a digital pseudo random noise generator with provision made for an on-line correlator.

5. Computing section equipped with mini-computer and incremental tape recorder. This unit also contains fast analog to digital converters and has been equipped with a hard wired correlator with its own Fourier transform unit to provide two channels for very fast data analysis.

Signal flow is possible between each of the above cabinets and the addressing and scheduling of the operation of each of the transducer channels is under the control of the computer. At the present time the computer provides a limited arithmetical capability and all time con- suming calculations have to be carried out off-line on a large computer installation.

3. POWER REACTOR SIMULATION

As HIFAR is a l0 MW research reactor, the characteristics of the observed noise sources differ from a commercial nuclear plant. To introduce realism into the monitoring of neutron density, temperature, pressure and mechanical and hydroelastic vibration, modifications were made to standard reactor facilities and instrumentation. Typically - Fig. 2 - Helium gas was introduced into a fuel element to simulate dynamic voidage. The identification task, in this instance, was to attempt to discern changes in the impulse response characteristics of the fuel element with and without the bubble stream. The figure shows a full scale model of the fuel element undergoing rig tests prior to placement in the reactor. These tests inclu- ded neutron and gamma transmission measurements to identify voidage characteristics and wall pressure fluctuation and ultrasonic pulse echo measurements to investigate the behaviour of individual bubbles.

The computer is interfaced in such a way that up to 20 stochastic variables may be scanned in any one experiment. Usually, for practical reasons the choice consists of the four below.

Nuclear power plant operational diagnostics and control 737

TABLE 1 Properties and Observability of Stochastic Variates

Variate Governing Distribution RMS Fluctuation to Transducer Mean Ratio Characteristic

Neutron and Poisson 50% to 0.001% Excellent sensi- gan~na photon Depending on mean tivity and density power level frequency response

Temperature Normal but can be 2% to 0.001% Limited frequency correlated with response and cooling process lifetime

Mechanical Frequency band Typically 0.5% Difficult in-core vibration limited instrumentation

problems

Pressure Normal but may be Typically 3% Difficult in-core fluctuation weighted by flow instrumentation

conditions problems

4. EXPERIMENTAL RESULTS

The investigation is, as yet, at an early stage, but it is possible to draw the following conclusions:

1. Systematic, on-line, global scanning of a nuclear power plant core to produce a coherence function (Fig. 3) creates a most effective continuous reactor core mal-fanction monitor. The bar chart at the bottom of Fig. 3 can be used as a "signature" of the plant. Abrupt changes in the shape of this function can indicate the onset of unusual conditions and possibly the need for plant shutdown

2. All transfer functions (Figs. 4 and 5) between the system dynamic variables can be readily computed with a minimum of time lap - say 20 minutes

3. Routine control action can be initiated from such statistical a~alyses. Emergency operations, with time constants of seconds will have to be initiated from the raw statistical data or from data which has been optimally filtered.

Some mathematical models and statistical algorithms used are given in the Appendix.

5. SUMMARY AND CONCLUSIONS

A powerful technique for monitoring nuclear power systems has been described. Its relevant areas of application are listed in Table 2 below.

TABLE 2 Typical Malfunction Identification Procedures

Identification Problem Stochastic Technique

Core identification. Burnup and fission Neutron and gamma photon time

product accumulation. Reactivity effects, series analysis.

Fuel channel operation. Safety monitor- Temperature cross-correlation ing and emergency control, and predictive filtering.

Structural vibration and component Vibration and pressure fluctua- integrity, tion time series analysis.

In due course these techniques should become acceptable to power station operators and be adapted for routine surveillance. At some later time their application to reactor power

plant control should follow.

ACKNOWLEDGEMENTS

The author gratefully acknowledges profitable discussion with Professor J.J. Thompson of the School of Nuclear Engineering, and members of the staff of the Australian Atomic Energy

738 L.G. Kemeny

Commission. Financial assistance for the project is being provided by the Australian Insti- tute for Nuclear Science and Engineering.

REFERENCES

[i] KEMENY L.G. The Impact of Twenty Years of Noise Research on Nuclear Power Plant Design, Instrum~n- tatiun and Control, Annals of Nuclear Energy, Vol. 2, pp. 241-249, Pergamon Press, 1975.

APPENDIX

Mathematical models and computational algorithms used in the interpretat/on of the experiments are given below.

Following

where

Zik

Yi

1. G~NERAL LANGEVIN MODEL FOR REACTOR AT POWER

Wang and Uhlenbeck (Wax, 1954) the complex dynamic system can be represented by:

Z l l Y 1 + Z12Y 2 + . . . Zl_nY n = f l ( t )

Z21Y I + Z22Y 2 + ... Z2nY n = f2(t)

ZnlY 1 + Zn2Y 2 + . . . ZnnY n = f n ( t )

Linear differential operators of arbitrary order with constant cq~fficients

"n" time dependent functions representing "n" macroscopic variables defining dynamic behaviour of system

"n" functions representing noise sources arising in each loop of reactor.

(1)

A simple model which serves to describe the power spectral densities and correlation functions described above can be formulated as follows:

+ ~ n = N r(t) + q(t) (5) dt o

where the texms are defined as follows :

N(t) = N + n(t) o

= Total nlm~ber of neutrons in reactor.

R(t) = R O + r(t)

= Prompt neutron production rate.

1,2 ... n

FLUCTUATION SPECTRAL ~ WI~ DENSITY F ELEPhaNTS Fkj (~) = J~Pkj (T)e2~I~TdT

MATRIX k,j

2. MOEEL FOR NEUTI~3~IC FLUCTUATIONS

fn(t)

NOW, according to Wang & Uhlenbeck,

w h e r e IZl is 'n' by 'n' matrix whose elements are 'n' x 'n' operators in (i) IYl column matrix with elements functions Yi(t) . .Ifl column matrix with elements functions fi(t).

Next we define a noise correlation matrix I Pl with el~ments T

lim 1 Pij (T) = T ~ ~ 2--T -~T at Yi(t)yj (t+~)

i,j = 1,2 ... n (3) and a function correlation matrix

T lira 1

~ij (T) = T + ~ 2-~ -~T dt fi(t) fj (t+T)

i,j = 1,2 ... n (4) as well as their transforms

NOISE SPECTRAL R WITH ~ENSITY ELEMENTS ~j (~) = -~kj (T) e--2~l~TdT

MATRIX k,j 1,2 ... n

Nuclear power plant operational diaEnostics and control 739

Q(t) = Qo + q(t)

= Delayed neutron production rate. Taking Fourier transforms

oo

_~ n(t) e j~t dt = N(j~) ao

_/=r(t) e jc0t d t = R( ja~)

a n d ~o _J 'ooq( t ) e j=t dt = Q(j(d)

whence N(j~) + ~ N(jt0) = N O R(j~) + Q(j~)

and thus R(j~O) + Q(j~O)

~+ j~o

N ~(j~) = o

where = ~-_n~.

1 Furthermore,

(6)

(7)

,-,~ ,I~'~)12= o A (ii)

and

1 A ~ A ~2 + ~2 2~ (12)

Hence the constant A may be evaluated and is found to be

A = 2 ~ n - ~ (13)

whence

~2 + ~2

Some simple algebra can be used to show that the time variation of the shape of the cross- spectral or cross-correlation functions can be used to characterize both the power level and the reactivity of a reactor system. In particular the zero crossing of the cross-correlation function, Fig. 3, can be used as a precise and sensitive monitor of system sub-criticality.

3. MODEL FOR TEMPERATURE FLUCTUATIONS

Similarly, when monitoring a fuel channel at power, we can consider the auto-correlation function of, say, temperature fluctuations from a nuclear fuel element. The analyzed data is suspected of having the form

~xx(T) = ~ + ~ exp(-T/T I) + y exp(-T/T 2) (15)

Logical questions which may arise immediately include:

i. Can a least squares fitting program reliably estimate ~, 8 and 7, or should the investi- gator preferably work in the frequency domain with the Fourier transform of the equation above

48T 1 4T~ 2 W(j~) = ~6 + (16)

I+(2~j~T I) l+(2gj~T 2)

2. What is the effect of system drift, transducer frequency response and input and output filtering on the parameters d, 8and 7 and the system break frequencies?

3. How realistic is the formulation of an auto-correlation function with two exponential coefficients in the light of the analytical model?

4. Is the sample set sufficiently large to give a reasonable confidence limit about the correlation coefficients and spectral estimates? Does the sampling frequency adequately include the high frequency end of the system spectrum? Is aliasing of frequencies exclu- ded and correct filtering procedures adopted either in the experiment or by use of mathematical digital filtering techniques?

4. TI~ SERIES ALGORITHMS

The basic algorithms for time-series analysis of the stochastic variates such as neutron density, gamma photon density, temperature and pressure, are given below. Consider two or more time series

XoYoXlYl --. Xn_lYn_ 1

(i0)

(8)

(9)

740 L.G. Kemeny

then the following statistical expressions may be computed in order to evaluate the dynamic parameters of a system - such as a nuclear reactor - and to gain an insight into the physical processes which are taking place therein.

Mean Values X = (l/n) ~x (17) Y = (l/n) Ey (18)

Variances If each value of x and y is replaced by

x= x- X Z= y - Y

then the variances are given by

1 x2 Varxx = n_-~Z _ (19)

1 Zz Var Z (20) yy = ~

1 Varxy = n--~ g ~ Z (21)

Normalised Auto and Cross-Covariances

For a lag number s these are given by

n-s-1

,xx(S) i (n_s_l) Varxxl-i ~ ~+s " Xr (22) r=0

n-s-i

l-1 ~ ~r+s'~r (23) ~yy(S) = I (n-s-l) Varyy r=0

n-s-i ~xy (s) = I (n-s-l) ~ar Varyy [ -I ~ ~+a . ~r (24)

xx r=0

n-s-i ~yx (s) = l(n-s-1) /Varxx Varyy I-I ~ ~+a "~ (25)

r=0

Auto Spectra

If S is the largest lag and [ means the sum with the first and last terms halved and s is the harmonic ntm%ber, then

and

where

Wxx(S) = (i/4)w (s-l) + (I/2)Wxx(S) + (i/4)Wxx(S+l) xx

Wxx(O) = (i/2)Wxx(0) + (i/2)Wxx(1)

s rs~

Wxx(S) = 4 Vxx xx().cos(--~)

Co and Quad Spectrum

The cross spectrum is defined as the complex quantity W + i W *. computed as follows : xy xy

Gxy(S) = (l/4)gxy(S-l) + (l/2)gxy(S) + (i/4)gxy(S+l) for s ~ 0

and Gxy(0) = (1/2)gxy(0) + (1/2)gxy(1)

whe re s

gxy(S) = 4 ~ar Var ~ (1/2)l~xy(r) + ~yx(r) I rs~ • cos (--~-) xx yy

and s

gxy*(S) = 4 ~arxx Varyy ~ (1/2)]~xy(r) - ~yx (r) l Srsg • s in (~)

from which Gxy*(S) can be defined similarly to Eqs. (24) and (25). the time delay are applied to give

Wxy(S) = Gxy(S) cos(½ ps) + Gxy (s) sin(½ ps)

and

W *(s) = G *(s) cos(½ ps) - G (s) sin(½ ps) xy xy xy

(26) for s ~ 0

(27)

(28)

These quantities are

(29)

(30)

(31)

(32)

Finally, corrections for

(33)

(34)


Where p = w/S.

Phase Lag This computed from

= arc tan (Wxy*/Wxy)

Coherence Function This is defined by

2 .2 W + W = xy xy

W W xx yy

5. PREDICTION ALGORITHMS FROM TIME SERIES DATA

(35)

(36)

We seek to synthesize a time variant linear filter [6] whose output y(t) at any time t is an estimate of the input at a later time t+T. Thus if x(t) is a typical member of a non-sta- tionary statistical process, we require the filter to minimize the mean square error [~2 (t)] between the output y(t) and the input x(t+T) at time t+T.

For an error (t) at time t, we have

~(t) = y(t) - x(t+T) (37)

from which we derive the mean square error

[62 (t) ] = [y2 (t) ] - [2y(t)x(t+T) ] + [x 2 (t+T) ] (38)

Assuming that h(t~) is the output of the filter at time t due to a delta function input at

time (t then the output y(t) due to the input x(t) is given by

t y(t) = / h (t,~) x(~) d~ (39)

o

Rearranging and combining (37) and (38) gives

t t t

~2(t) = / f h(t,~)h(t,~')~(~,~')d~ d~' -21 h(t,~)~(t+T,~)dct + ~(t+T,t+T) (40) o o o

where ~(~,~') represents the autocorrelation function of the process

~ (~,~') = [x(~)x(d') ] (41)

If we now vary the impulse response function h(t,e) by 6h(t,~) then the first order corres- ponding variation in [~2 (t) ] is given by

t t [6~2(t)] = 2/ ~h(t,~) {/ ~(~,~')h(t,~')d~' - ~(t+t,T~)d~ (42)

o o

If h(t,~) is the impulse response function of the optimum filter which minimizes [~2 (t)], 2

then the variation [6~ (t)] vanishes for all 6h(t,~). Thus we have

t

fo ~(~,~')h(t,e')d~' ~(t+T,e) for 0 < e < t (43)

The equation above can be recognized as a modified Wiener-Hopf integral equation. The solution h(t,~) is the impulse response of the optimum Wiener filter and the resulting mean square error is given by

t

[~2 (t) ]min - ~(t+T,t+T) - / h(t,~)~(t+T,h) dh (44) o

In the above equation ~(t+T,t+T) is the mean power at time t+T and the integral on the right hand side represents the maximum difference between the mean power and the mean square error that can be obtained by linear filtering. The autocorrelation function ~(e,~') uniquely specifies the impulse response function h(t,~) of the Wiener filter.

In order to be able to apply this predictor in time series analysis, we must be able to con- struct a representative autocorrelation function from a set of sample functions of the process Xn(t) thus

745 L.G. Kemeny

N 1

~ (e,~') = ~ ~ Xn Cd) Xn (~') n=l

(45)

Ideally, the set Xn(t) is determined by performing N sets of measurements under similar condi tions. Alternatively the sample functions may be represented by their characteristic modes which must be mathematically determined.

Fig. ]. Section of "SNEDAC" data acquis~ition computer with dummy puel pin to be used in simulation studies.


Fig. 2. Dynamic voidage simulation.

744 L.G. Kemeny

j 1.

P~:T c o ~ ~c~

DZSeLy r~ , ,N~ Ex Mis= e NAX~

2@

r P,~0~.. NCY 2e

REAL SIZEm 128 I 6 , H ~ N I N G . . . . . Q 1 1 o A T T N . C O O E . . . . . 5 5 I 1 3 , F I L T E R C O D E . . . . o 17, FP, AN~ S I Z E . . 2 5 6 I i i , BUFFER C O D E . . . J 114, ~ . F R ~ S . . . . . . i@~ 18. s ~ q P . FREO. ~. l e 112, T R I G . C ~ . . . . . e l l S , CH . cooE . . . . . . . . 3

Fig. 3. Dynamic display of reactor core coherence functions with potential for signature storage and recall.

- 2 R E A L A X 2 .

C O M P L E X

Fig. 4. Nyqvist presentation of system stability utilising noise signals.


L,~ REF=

0 0 1

:RET ~I CROSS ~% SPECT~JM I ;

--I~JB ' ' ' r ~ ~,JFH~ . . . . 11 ~ : ' ( : :El

COMPLEX 'SIZE= 16,1-W.~IHG . 0 110,ATTN COOE 55 1 7 , F R ~ SIZE. 1024 IIt,~JFFER CODE 0 IB,SII~.FI~Q ..6 II2,TRI~ CODE . . . . Ig,FF~EQ.F~ICTCI~.3

512 II3,FIL~ER CODE . . . . 2 I~4,NO.FRYMES . . . . 65 IIS,CH'COOE. 3

Fig. 5. Response of cross-spectral density function to 8H 3 neutron absorber vibration.

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Nuclear power plant operational diagnostics and control