Application of fuzzy logic control system for reactor feed-water control

FU||Y

sets and systems Fuzzy Sets and Systems 74 (1995) 61 72

ELSEVIER

Application of fuzzy logic control system for reactor feed-water control Takashi Iijima *'a, Yoshiaki Nakajima a, Yasushi Nishiwaki b'¢ aFugen Nuclear Power Station, Power Reactor and Nuclear Fuel Development Corporation, 3 Myojin-cho, Tsuruga-shi, Fukui-ken, 914 Japan b University of Vienna, Austria ¢Jagdschlossgasse 91, A-1130 Vienna, .4ustria

Abstract

On the occasion of the 2nd World Congress of IFSA held in Tokyo in July, 1987, a small meeting was convened by Prof. Nishiwaki, Ex-deputy director of the Division of Nuclear Safety and Environmental Protection of IAEA, to discuss possible application of fuzzy set theory and fuzzy logic control in nuclear plants. This paper describes successful actual application of fuzzy logic control system (FLCS) to the feed-water control system of the 165 MWe Fugen Advanced Thermal Reactor (ATR). Fugen is a heavy-water moderated, light-water cooled reactor. The introduction of fuzzy logic control system (FLCS) has enabled operators to more effectively control the steam drum water level as compared with a conventional proportional-integral (PI) control system. Keywords: Fuzzy logic control; Nuclear reactor; Feed-water control

1. Introduction

A nuclear power plant consists of many components and systems, and most of them are controlled by a proportional-integral (PI) controller. Some of the systems, however, cannot be controlled skillfully by such a usual PI controller when the process systems have an extreme non-linear peculiarity, a long delay time and an inverse response, a n d / o r when process values such as flow rate, temperature, pressure, etc. which are necessary to enhance controllability cannot be measured precisely. These process systems are often controlled manually by skilled operators. A feed-water control system of the 165 MWe Fugen Advanced Thermal Reactor (ATR) is involved in this group of the systems. Because fuzzy set theory can easily formulate the qualitative features of a target system and subtle human reaction into control rules, Power Reactor and Nuclear Fuel Development Corporation (PNC) decided to apply fuzzy logic control to the feed-water control system. A simulation study (1987-1988) and development of prototype system which had an on-line support function (1989-1991) were completed.

*Corresponding author. 0165-0114/95/$09.50 © 1995 - ElsevierScienceB.V. All rights reserved SSDI 0165-01 14(95)00036-4

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T. lijima et al. / Fuzzy Sets and Systems 74 (1995) 61 72

2. Outline of the feed-water control system The feed-water control system governs a feed-water valve to sustain the water level in a steam drum to set value. The water level must be maintained all the time within a certain range during the reactor operation to secure reliable fuel cooling and to prevent water from being carried over together with steam to a turbine system. Fig. 1 shows outline of the feed-water control system. The feed-water control in the reactor of Fugen is assigned to the main-valve with a three-element PI controller in the higher output range covering between 18% and 100% of the rated reactor output. The feed-water control is taken over by a lower-flow-rate-value with a single-element PI controller in the lower output range, upon the reactor start-up or shutdown. The lower-flow-rate-valve is, however, slow in regulating the water level to set value, and cannot cope with rapid changes in the reactor output. So far, in such an operation, the water level is sometimes needed to be controlled manually by a skilled operator for a faster settlement of the water level than the PI controller can do. Fig. 2 shows outline of the conventional automatic controllers for these valves. In this manual regulation case, the operators cannot recognize a feed-water flow rate and a steam flow rate because these process values are too small to measure. The operators therefore conducted a corrective action for the opening of the lower-flow-rate-valve based on a control strategy which the operators had created on their operating experiences.

FromSteamDrum of B-loop

(Steam from B4oop)

IX~

MainSteam Steam ~' Stop Valve Controlvalve I~.A k~A

(Steam) Main Steam Isolation Valve

Turbine-BypassValves Condensate Pump +

From Steam Drumof B-loop Reactor

I

I Oemineralizer Feedwater Lower-Flow-Rate-Valve

CoolantClean-up System To RCP of

B-loop

(Blow-DownFlow)

-4-

To Steam Drum ~ of B-loop 4

Feed-water Pump

(ReturnFlowfor B-loop) Feed-waterfor B-loop Fig. 1. Outline of the steam and feed-water system of F U G E N .

T. lijima et al. / Fuzzy Sets and Systems 74 (1995) 61-72

63

~- ToTurbineSystem

(Steam)

"1

SetF ~int

(

r

,] t

(Feed-water) [

4~

Pate Valve I FromTurbineSystem

MainControlValve Fig. 2. Outline of controllers for the feed-watercontrol valves.

3. Design of FLCS Plant process parameters which the operators observe mainly on regulating the water level in the steam drum at the lower output range are as follows: (1) The water level in the steam drum and the level set point. (2) The opening of the main-valve, the lower-flow-rate-valve and turbine bypass valves, and a blowing down flow rate from a coolant clean-up system to a main condenser. (3) The reactor output. The operators estimate a flow balance between the feed-water and the steam flow rate based on the above parameters and decide whether the feed-water flow rate should be increased or decreased and regulate the opening of the lower-flow-rate-valve according to the decision. After the regulation, the operators evaluate control performance which appears as a result of regulation they have done, and they add further regulation if it was insufficient or excessive. FLCS was designed in accordance with the above mentioned process. A proper regulation value for the lower-flow-rate-valve is obtained from inference results of three independent inference sections of FLCS which are, respectively, concerned with the water level in the steam drum, the flow balance and the reactor output. Fig. 3 shows the inference flow diagram of FLCS.

3.1. Inference section (,4)

The first inference section (A) infers the proper value 'CA 1' to be regulated for the lower-flow-rate-valve from how far the actual water level in the steam drum deviates from the desired level 'LE' and the changing

64

T. lijima et al. /Fuzzy Sets and Systems 74 (1995) 61-72

Water Level in Steam Durrn

--q

Level Error

r

v I

Water Level Set Point

::hangein Level

Fuzzy Inference vl ~tion(A)

De-Fuzzy Calculation

Opening degree of Turbine Bypass Valve )pening dgree of Lower Flow Rate Valve v

Plant

Opening degree of Main Control Valve

Data Processing

Feed/Breed Flow Rate Deviation

I Inference Section(B)

De-Fuzzy Calculation

Iv

Reactor Output

Power/Feed Flow Rate Deviation

Fuzzy Inference

~d~

Secaon(C) J J Convert to the Target Opening Degree of the Lower Flow Rate Valve

De-Fuzzy Calculation

Integrate with Weighting ml CA1 +m2CAZ+m3CA3

'1 I~ J

I

I

Fig. 3. Inference flow diagram of FLCS.

ratio of the water level 'CL'. LE(t) = L V ( t ) - LS(t), CL(t) --

dLV(t)/dt,

(1) (2)

where LV(t) is the water level in the steam drum, LS(t) is the level set point and t is the time. The inference in this section is performed in accordance with such fuzzy linguistic rules as If LE is ZO and CL is ZO then CA is ZO. If LE is PB and CL is NS then CA is NB. If LE is NS and CL is NS then CA is PM. (Total 35 rules) Where, the former propositions following 'If' are called antecedent parts and the latter proposition following 'then' is called a consequent part. There are 35 rules in the section (A) including above rules, and the characters such as NB, NM, NS, ZO, PS, PM and PB are fuzzy linguistic variables as shown below. NB: Negative Big, NM: Negative Medium, NS: Negative Small, ZO: Zero,

T. lijima et al. / Fuzzy Sets and Systems 74 (1995) 61-72

65

PS: Positive Small, PM: Positive Medium, PB: Positive Big. These linguistic variables are, respectively, defined by membership functions whose features are formed to be reflected experiences of the skilled operators. 3.2. Inference section (B)

The second inference section (B) infers the proper values to be regulated for the lower-flow-rate-valve 'CA2' from how much the inflow of the drum differs from the outflow 'FE2'. The inference in this section is performed in accordance with such fuzzy linguistic rules as If FE2 is PB then CA is NB. If FE2 is ZO then CA is ZO. If FE2 is NB then CA is PB. (Total 7 rules) Because Fugen has two loops of coolant recirculation system called A-loop and B-loop, and a different steam drum is installed in each loops, the 'FE2' must be considered by loop (ref. Fig. 1). FE2A(t) = FDA(t) + CURA(t) + RCPA(t) -- TBA(t) - CUA(t),

(3)

where FE2A(t) is the deviation between inflow and outflow for A-loop, FDA(t) is the feed-water flow rate for A-loop, CURA(t) is the return flow rate from a coolant clean-up system for A-loop, RCPA(t) is the ground-seal water injection rate of recirculation pump for A-loop, TBA(t) is the steam flow rate through the turbine bypass valves for A-loop, and CUA(t ) is the water breeding rate to the coolant clean-up system for A-loop. In these parameters, CURA(t), TBA(t) and CUA(t) cannot be measured, but Eq. (3) can be replaced as below because the unbalance in these parameters between A-loop and B-loop can be ignored for their symmetrical arrangement. FE2A(t) = F D A ( t ) - {(TB(t) +

BLOW(t))/2},

(4)

where TB(t) is the steam flow rate through the turbine bypass valves, and BLOW(t) is the blowing flow rate from the coolant purification system to the main condenser. In Eq. (4), since BLOW(t) can be measured precisely but FDA(t) and TB(t) are too small to measure precisely in the lower output range, FDA(t) and TB(t) should be replaced by fuzzy variables: FDA(t) and TB(t). These fuzzy variables could be obtained from membership function assemblies depending on the opening of the concerning valves as shown in Eqs. (5) and (6). FDA(t) = F2L(FVLA(t) + F2M(FVMA(t)),

(5)

TB(t) = FT(TVI(t) + TV2(t)),

(6)

where F2L(FVLA(t)) is the membership function assembly which gives the feed-water flow rate as a fuzzy variable depending on the opening of the lower-flow-rate-valve of A-loop: FVLA(t). F2u(FVMA(t)) is the membership function assembly which gives the feed-water flow rate as a fuzzy variable depending on the opening of the main-valve of A-loop: FVMA(t). F T ( T V I ( t ) + TV2(t)) is the membership function assembly which gives the steam flow rate as a fuzzy variable depending on the opening of the turbine bypass valves: TVl(t) and TV2(t). Figs. 4 and 5 show the membership function assemblies F2L(FVLA(t)) and F2M(FVMA(t)).

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T lijima et al. / Fuzzy Sets and Systems 74 (1995) 61 72

Fig. 4. Membership function assembly for the main-valve.

Fig. 5. Membership function assembly for the lower-flow-ratevalve.

These membership function assemblies are formulated based on statistical assessment of plant operating experiences. 3.3. Inference section (C)

The third inference section (C) infers the proper value to be regulated for the lower-flow-rate-valve 'CA3' from how much the actual feed-water differs from ideal feed-water flow rate calculated from the reactor output: 'FE3'. The inference in this section is performed in accordance with such fuzzy linguistic rules as If FE3 is PB then CA is NB. If FE3 is ZO then CA is ZO. If FE3 is NB then CA is PB. (Total 7 rules) Since the 'FE3' must be considered by loop also in this case, the flow rate deviation for A-loop FE3A(t) can be described as below. FE3A(t) = FDA(t) - DFDA(t),

(7)

where DFDA(t) is the ideal feed-water flow rate. Fig. 6 shows a relationship between the feed-water flow rate and the reactor output when the water level in the steam drum was controlled very well. A membership function assembly which gives a fuzzy variable DFDA(t) could be formulated on this relationship. FE3A(t) = FDA(t) -- DFDA(t) = FDA(t) - FRA (PO (t)),

(8)

where FRA(PO(t)) is the membership function assembly which gives the ideal feed-water flow rate as a fuzzy variable depending on the reactor output: PO(t).

T. lo'ima et al. / Fuzzy Sets and Systems 74 (1995) 61-72

67

o

o

" D a t a on 18 Aug. 1986 • Data on 30 Mar. 1987

t" 8

v .e-.,

,¢¢~"¢

¢0 rr

,g

o

0 LL t,,..

0

.~°~,~' ° °

e,a~ L (3.) 0 LL

0

f

S"

o

0

q

I

4

o

8

Reactor Output

I

12

~

16

i

20

(%)

Fig. 6. Relationship between feed-water flow rate and reactor output.

3.4. Fuzzy inference method The fuzzy inference is executed based on the fuzzy linguistic rules above mentioned in each inference sections. Fig. 7. shows these rules. The inference in each section depends on the " M i n - M a x " method:

CA I(x) = Max{ {W~(LE). W ) ( C L ) . X,~(x)},:,_ 7,~:, -5},

(9)

CA2(x) = Max { { W~ (FEZ) • X~ (x)}, =, -v },

(10)

CA3(x) = Max { { W~ (FE3) • X? (x) }i =a -7 },

(11)

where W~,(c) is the compatibility grade for a rule numbered "b" depending on input condition "c" in the inference section "a", X~(x) is the membership function for a consequent part of a rule numbered "b" in the inference section "a', * is the minimum calculation operator. The fuzzy variables CA1 (x), CA2(x), and CA3(x) are converted to non-fuzzy values: CA1, CA2 and CA3.

CAn=fCAn(x)xdx/fCAn(x)dx

.=,-3

(12)

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T. lijima et ai. / Fuzzy Sets and Systems 74 (1995) 61-72

Level Error (LE)'I NB

NM

NS

ZO

PS

P~

PB

NB] PB

PB

PB

PB

PS

7.0

NS

\N8 PB

PB

PB

PM

P5

ZO

NM

NB

SO

PB

PB

PS

ZO

NS

NB

NB

PB

PM

ZO

NS

NM

NB

NB

NS

ZO

PS

PM

PB

PM

PS

ZO

NS

NM

NB

PS

ZO

N5

NB

bib

NB

NB

00) Linguistic Rules oi the inference Section (B) Deviation o! Flow Rate (FE3)'4

r

o

NM

• 3:( Feed-water flow rate ) - (Steam flow rate )

o__.NS Q

Deviation o! Row Rate (FE2)'3

PB

"1: (Water level in the steam drum ) -( Level set point } "2:Change in the water level.

NB

NM

NS

ZO

PS

PM

PB

PB

PM

PS

ZO

NS

NM

NB

"4:( Actual Feed-water f low rate ] water flow rate )

(Ideal feed-

(c} Linguistic Rules of the Inference Section (C)

(a) Linguistic Rules of the Inference Section (A)

Fig. 7. Fuzzy inference rules of the inference section (Aj-(B).

Table 1 Weight gains ml, rn2 and m3 Pressure of the steam drum

ml

m2

m3

Below rated pressure ( < 68 kg/cm 2) Over rated pressure ( > = 68 kg/cm 2)

1.0

0.5

0.1

1.0

0.75

0.5

These three inference results are integrated with weighting to provide a conclusion. CA = ml-CA1 + m2.CA2 + m3.CA3,

(13)

where, ml, m2 and m3 are weight gains and they were adjusted in the validation tests so that the system could show excellent responses. Table 1 shows the values of the weights ml, m2 and m3.

4. Components of prototype FLCS The prototype FLCS was developed in 1989, and it consisted of data processing device, fuzzy inference machines and engineering workstation. Input signals such as the water level in the steam drum, the opening of each valves, reactor output, etc. are converted in the data processing device to forms acceptable to the fuzzy inference machines. The fuzzy inference calculations are executed in the three inference machines, respectively, and their results are integrated and the opening of the lower-flow-rate-valve proposed by the FLCS is displayed together with the actual opening values.

T lijima et al. /Fuzzy Sets and Systems 74 (1995) 61-72

69

5. Validation tests 5.1. Validation method

Since the recirculating water system has two loops which are almost independent of each other, the water level in each steam drum should be regulated individually. Accordingly, the prototype FLCS was applied to controlling for only one loop and the water level in the steam drum of the other loop was regulated by the usual PI controller and manual adjusting as usual during the validation tests. An operator in charge of the recirculating water system of FLCS-applied loop adjusted of the lower-flow-rate-valve manually so that the opening of the valve was equivalent to the proposed opening degree displayed on CRT of the FLCS. The features of change in the water level of both steam drums were compared with each other to review a performance of the FLCS. 5. 2. Results o f the tests

Ten times of validation tests for the prototype FLCS have been performed upon the start-up and shutdown of the Fugen. Table 2 shows the results of the tests: maximum change value in the water level of the

Table 2 Results of validation tests Date

Condition

Reactor output (%)

Maximum change value (cm) A-loop B-loop

Factor a

29 Oct. 1989

Power up Valve switching Power up Valve switching Power up Valve switching Power up Valve switching Power up Valve switching Power up Valve switching Power up Valve switching

2-19 19 5-20 20 3-22 22 4-19 19 6-21 21 7-16 16 3-17 17

2.1(FU) 1.6(FU) 1.1(FU) 5.6(FU) 5.1(FU) 3.2(FU) 2.0(FU) 3.5(FU) 2.3(FU) 2.5(FU) 2.6(FU) 3.0(FU) 15.0 5.6

12.5 6.4 3.0 5.7 19.7 7.5 8.0 2.0 12.4 2.6 9.6 7.6 2.0(FU) 2.8(FU)

0.17 0.25 0.37 0.98 0.26 0.43 0.25 1.75 0.19 0.96 0.27 0.39 0.13 0.50

11.5 5.3

0.22 0.60

13.8 10.9 7.5 8.4 4.7(FU) 4.3(FU)

0.29 0.42 0.47 0.70 0.39 0.78

11.2 8.3

0.37 0.59

10 Nov. 1989 4 Jun. 1990 2 Nov. 1990 29 Apr. 1991 7 Sep. 1991 17 Dec. 1991 Average

Power up Valve switching

14 May 1990

Power down Valve switching Power down Valve switching Power down Valve switching

14 Dec. 1990 31 Oct. 1991 Average

Power down Valve switching

2.5(FU) 3.2(FU) 18-4 18 18-2 18 18-2 18

4.0(FU) 4.6(FU) 3.5(FU) 5.9(FU) 12.2 5.5 4.1 (FU) 4.9(FU)

a Reduction factor of change on the water level = (maximum change value in FLCS applied Ioop)/(that in the other loop).

7~ lijima et al. / Fuzzy Sets and Systems 74 (1995) 61 72

70

steam drums during the reactor output changing operation and valve switching operation from the lower-flow-rate-valve to the main-valve in start-up, or its reverse in shutdown. The results proved that the prototype F LCS reduced the change value in the water level to about 1/2-1/5 of those with the conventional system in average for the lower output range. Figs. 8-10 show one of the results of the tests performed in October 1989 when the reactor is started up. It is clearly proved by these figures that the water level in the steam drum of A-loop, where the prototype FLCS was applied, was maintained more accurately than those of B-loop.

6. Application of practical FLCS A practical model of the new system was designed and built after previously mentioned study because the prototype model only displays signals on the screen, and an operator performs the actual manipulations of the valve after checking the displayed signal. The practical FLCS consists of dual type of digital control system to enhance the reliability of the feed-water control system and its software which executes the

A

E E '

O. O

CL

O O d

Water Level in the Steam Drum o| A-loop (Controlled by an Operator with support ol FLCS)

<

0[3 "a

"6 E

E 2 £3

£3

EQ d o

-

oJ

i

=-

!

Water Level in the Steam Drum of R-loop (Controlled by an Usual PI Controller)

.c O ..J o

o

l

Reaclor Oulput

! q

c::~! m !

¢::::) O ut')

I0

i

75

i

150 Time (rain)

Fig. 8. Results of the validation tests during reactor start-up.

=

225

300

T. lijima et al. / Fuzzy Sets and Systems 74 (1995) 61 72 0 0

71

Q

Switching Period of lhe Feed-water Control Valves

!A

-I

A

O0eo,o0o, •

-

~j ~.3 Lower.Flow.Rale.Valve ./3

tlO

;> d,

Water Level in the Steam Drum ol A-loop (Controlled by an Operalor with Support of FLCS)

rr

_o~ LL d. 0

o

Reactor Output

1.

o 171

°12: ~ C

(31..

0

8 Opening of Main-Control-Valve

C

C

L

' 0

10

20 Time (min)

30

40

Fig. 9. Results of the validation tests during valve-switching (A-loop: FLCS applied loop),

fuzzy inference and the associated calculation is succeeded to the prototype's program just as it is. The practical FLCS was introduced to the actual feed-water control system of Fugen in July 1992, and it has successfully fulfilled its function.

7. Conclusion

The fuzzy logic control system was developed to enhance an ability of reactor feed-water control of Fugen Nuclear Power Station. After a simulation study and development of prototype system, the on-line practical FLCS was developed and it was installed to the real feed-water control system in July 1992. The introduction of this new system has enabled operators at Fugen to more effectively control the steam drum water level when compared to a conventional proportional-integral (PI) control system. This precise control is expected to lighten an operator's burden when monitoring the steam drum water level upon start-up and shutdown of a plant, and it is a further improvement of reliability during plant operations. To increase reliability and to improve risk assessment and safety it would be important to try to apply fuzzy theory and other intelligent technologies in relevant fields of science and engineering where non-probabilistic uncertainties would be involved [5-7].

72

7~ lijima et al. / Fuzzy Sets and Systems 74 (1995) 61-72

o

ta~

!

I I ~

I,

Switching Period of the Feed-water Control Valves

'I

E

~

E

i

~ • o0 -r ~o

•~•

Opening of Lower-Flow-Rate-Valve "4_ Level Set Point

Water Level in the Steam Drum o! B-loop

m

~."~" t~ ~"

(Controlledby an Usual PI Conlroller)

~'o~-=¢~" ~

o

ReactorOutput

IlJ

o

Opening of Main-Control-Valve

8

C

-

cL

c-

Q

I

v o

1'o

/

i

3'o "time

(min)

40

Fig. 10. Results of the validation tests during valve-switching (B-loop: controlled as usual).

References [1] A. Arakawa et al., Fuzzy logic control application for BWR recirculation flow control system, J. Nuclear Sci. Technol. 25 (1988) 263 273. [2] S. Terunuma et al., Application of fuzzy algorithm for feedwater control system in Fugen HWR, IAEA Conf. on Man-Machine Interface in the Nuclear Industry, Tokyo (1988). [3] K. Kishiwada et al., A simulation study on the application of a fuzzy algorithm to a feedwater control system in a nuclear power plant, Reliability Eng. System Safety 28 (1990). [4] T. Iijima, Applying fuzzy theory to nuclear reactor control, Sci. Technol. Japan 8 (1989). [5] Y. Nishiwaki et al., Risk asessment of atmospheric contamination due to cumbustion of fossil-fuels in Japan and possible application of fuzzy set, lOth Regional Congr. IRPA and SFRP Annual Congress 1982, Avignon, France, October 18-22, 1982. [6] M. Sugeno, T. Onisawa and Y. Nishiwaki, A new approach based on fuzzy sets concept to fault tree analysis and diagnosis of failure at nuclear power plants, Proc. IAEA Seminar on the Diagnosis of and Response to Abnormal Occurrences at Nuclear Power Plants, Dresden, Germany, June 12 15, 1984. [7] Y. Nishiwaki et al., Human factors and fuzzy set theory for nuclear safety analysis., 1st Worm Congress oflFSA, Palma de Mallorca, Spain, July 1-6, 1985.