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PRISM PROGRAMME CALCULATION METHOD OF INACCURACIES IN THE FIELD OF THE LENGTHWISE POWER DISTRIBUTION APPROXIMATION IN RBMK-1000 REACTOR.

Bogens A.A Smolensk NPP, Russia

1. INTRODUCTION

1.1 PDMS - Power Distribution (physical) Monitoring System (on RBMK-1000 height). This system is intended for the neutrons stream density monitoring on the reactor height. PDMS fulfills the APDS signal processing and transmits them to the “SKALA” Centralized Monitoring System (CMS) on their deviation from permissible limits. Light and nuisance alarms produced from “SKALA” Centralized Monitoring System are used for the power operating regulation. APDS sections signals are set in the “SKALA” CMS computing part and used for the reactor core parameters calculation (neutrons stream lengthwise distribution, operating reactivity margin, graphite temperature, etc.) in accordance with PRISM programme.

1.2 The PDMS of one SNPP unit includes: - 12 APDS located in the Control and Protection System (CPS) lattice free

channels; - Lengthwise power monitoring equipment (УИ-22-00 rack) and chambers

feed equipment for APDS located at MCR-I; - Multichannel recorder (УВЦ-30) that registers on the digital recorder the

time, coordinates and signal of the sensor that has increased alarm emergency level and that is located on MCR-I;

- PDMS instrumentation and APDS - БВН-11 number indication units located on the panel 4 of “O” panel;

- Detectors calibration equipment; - Ring ionization γ-chamber; - Calibration detectors. 1.3 As APDS on Unit 3 the eight-sections APDS are used. Each APDS

contains in fours two-sections ionization chambers КТ-21 evenly located in the core (Figure 1).

1.4 Constructively the chamber consists of 3 main parts: 1) A detector presenting 2 gas-filled ionization chambers lengthwise spaced

on 875 mm; 2) A special connector produced at the basis of the 2РМ-type connector

assembly and intended for communication cable line connection; 3) A cable line (“routing”) made of КНМС 2С brand cable. 1.5 The detector is made of КНМС2С brand triaxial cable segment with the

external diameter of 4 mm with 2 central steel cores and 2 coaxial coverings (Fig. 2).

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The cable is included into the hermetic case with the external diameter of 7 mm made of corrosion-resistant steel and ranged by isolated bushings. The case internal volume is filled with pressure containing 2% of helium and 98% of argon. The external covering of the cable lower part divided by ring turnings into separate isolated areas acting as collecting electrodes of 2 ionization chambers. Each collecting electrode electrically connected with one of the central cores by a bond through special “windows” in the inner cable covering. The case upper part and the cable external covering are mechanically connected and ended with a special four-pin connector. Feeding voltage =100 В is supplying to every collecting electrode on it’s own central core and to the common case – chamber housing (on “earth”).

1.6 The chamber operation principle is based on gas ionization property in the gas cavity under the influence of gamma-quantum stream. This stream is proportional to the average density of the thermal neutron flux at the chamber sensitive section location. In the gas cavity between the collecting electrode and the chamber housing under the influence of feeding voltage the ionizing current is appearing that is proportional to the average density of the neutron flux at the chamber section location. The triaxial cable inner covering that is supplied by feeding voltage acting as a guard electrode eliminating leakage current in the collecting electrode circle. The chamber operating currents range is (1÷80) mcA. Plateau slope of voltage-current characteristic of each chamber section mustn’t exceed 0,3%/B in the range from 40 to 100 D.

1.7 Triaxial chambers of different length are set in the specified order (Figure1,2) into the 4 rough tubes of special “measuring” channel mounted in the CMS circuit channel.

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Fig. 1 The scheme of the chambers location in the “measuring” channel

Fig. 2 Triaxial chamber Kт. 21

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1.8 Chamber КТ-21 operating principle for Unit 3 is the following: -Two-sections chambers КТ-21 are located in the measuring channel

103.12.000 acting as (n-γ) convector. One central electrode that has electrically independent outlet is mounted in each section. While supplying the operating voltage on the electrode from chambers feeding equipment between the electrode and the chamber case as a result of gamma-quantum interaction the current ionization that is proportional to the average density of the thermal neutron flux at the chamber sensitive section location is occurred. The section signal entries the chambers feeding equipment inlet and then the PDMS equipment inlet.

1.9 The APDS section signal entries the БУсТ-16 amplifier inlet where it is transferred to the Uij voltage signal with БУсТ-16 Кдij unit transfer coefficient.

Uij = Kдij * Iij, (В) 1.10 The APDS sections voltage signal entries the Centralized Monitoring

System “SKALA” where they are used for the lengthwise power distribution and also they entries the БСА-31Comparison Unit entry where they are multiplied on Кfi coefficients. The multiplication is necessary for the comparison of APDS sections signals with the similar reference voltage that influence on signaling according to the PDMS.

Ufij = Uij * Kfi, (В) 1.11 The APDS sections current signal entries БПФ-06 unit on the common

adding bus bar. The amplifier adder transforms the total current signal so that the average signal on APDS at the output would be equal:

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∑=

=nc

incUijUсрj

1/ ,(B)

where: nc – the quantity of the j-APDS operable sections. 1.12 Depending on the APDS average signal the reference voltage U оп ав, U

оп пр and U оп зан are formed. 1.13 The APDS sections signal multiplied on Кfi is compared with the

reference levels and the performance of the conditions: Ufij ≥ U оп ав Ufij ≥ U оп пр Ufij ≤ U оп зан Results in the alarm actuation, thereafter: emergency (red flashing light and

nuisance alarm), warning (red light) and understated (green light).

2. REGULATION OF THE КFI COEFFICIENTS AND PDMS REFERENCE LEVELS

2.1 БСА-31 Comparison Unit coefficients are calculated by a formula: Кfi = 1 / Fi, Fi – the assigned profile of the lengthwise field on the reactor in the relative

unit. 2.2 The assigned profile is selected from the necessary field form taking into

consideration the running average lengthwise distribution (on sensors currents), average neutron flux distribution obtained during calibration (on chamber currents) and maximum ampere density non-exceeding on the fuel bundle that is 350 Wt/sm.

2.3 The assigned profile forms are shown in Figure 3.

0.8481.030.7771.081.1061.081.1451.081.1441.081.1431.021.0520.790.661

Fiсекция

Блок 3

jijij iUKU ϕϕ =i

i FK 1

=ϕ

Figure 3

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2.4 Reference levels for j-APDS are defined by correlations: U оп ав = 1.15 * U ср, (В) U оп пр = 1.10 * U ср, (В) U оп зан = 0.85 * U ср, (В) Where: U ср – an average signal on j-APDS sections,

∑=

=nc

incUijUср

1/ ,(B)

Uij – a j-APDS section signal сигнал секции, (В) nс – j-APDS sections quantity.

3. PDMS ALARM ACTUATION CONDITIONS

3.1 APDS section emergency signal determines the lengthwise neutron flux distribution field excess with respect to the assigned profile on 15%.

3.2 During PDMS equipment operation adjusted in accordance with p.p. 4.2 the alarm actuation is happening on the following conditions.

- For the emergency alarm; Uij * Кfi ≥ U оп ав Uij / U ср j ≥ 1.15 Fi - For the warning alarm; Uij * Кfi ≥ U огр пр Uij / U ср j ≥ 1.10 Fi - For the understated alarm: Uij * Кfi ≤ U огр зан Uij / U ср j ≤ 0.85 Fi

4. THE LENGTHWISE POWER DISTRIBUTION CALCULATION METHOD BY PRISM PROGRAMME

For each section the neutron flux density: (2)

вKSJ - A S-APDS every section signal, В вапК - PDMS implementation constant, mcA/V (general for all APDS) вksК - An absolute calibrated coefficient for the S- APDS every section

neutr/sm2*s*mcA (general for all APDS) в вD KS(I )ζ - A coefficient considering the S- APDS every section emitter burning-out of

it’s integrated current (general for one APDS) вKSI - The S- APDS every section integrated current

Further for APDS every section the distribution on the reactor height is approximated by the following form:

3'

ks ms km 1

Ф b sin( * z *m)=

= ∗ α∑ (3)

в в в в вKS KS ап ks D KSФ J *К *К * (I )= ζ

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where, msb - Coefficients subject to determination kz - A distance from APDS every section up to the core upper part 'k k эфz z H= + Δ

эфHΔ - An effective reflector addend

эфH 2* Hπ

α =+ Δ

H –Core height Coefficients msb are determined from the linear equation (4) systems solutions

8 8 8 82 ' ' ' ' ' '

1 k 2 k k 3 k k k k

k 1 k 1 k 1 k 1

8 8 8' ' 2 ' ' '

1 k k 2 k 3 k k k

k 1 k 1 k 1

b * sin ( * z ) b * sin( * z ) * sin(2 * * z ) b * sin( * z ) * sin(3 * * z ) Ф * sin( * z )

b * sin(2 * * z ) * sin( * z ) b * sin (2 * * z ) b * sin(2 * * z ) * sin(3 * * z ) Ф * sin(2 *

= = = =

= = =

α + α α + α α = α

α α + α + α α = α

∑ ∑ ∑ ∑

∑ ∑ ∑8

'

k

k 1

8 8 8 8' ' ' ' 2 ' '

1 k k 2 k k 3 k k k

k 1 k 1 k 1 k 1

* z )

b * sin(3 * * z ) * sin( * z ) b * sin(2 * * z ) * sin(3 * * z ) b * sin (3 * * z ) Ф * sin(3 * * z )

=

= = = =

α α + α α + α = α

∑

∑ ∑ ∑ ∑

where, 1 1s 2 2s 3 3s k ksb b ;b b ;b b ;Ф Ф≡ ≡ ≡ ≡

the relative neutron flux density distribution on every APDS S- assembly ks

КS 8

ksk 1

Ф *7F

Ф=

=

∑

Then the irregularity coefficient of neutron flux density on the reactor height for every APDS S-assembly is calculated ZS KSK max(F )=

The checking calculation of the lengthwise power distribution calculating method for sensor 40-27 on 2.03.07 6:46 performed in MATHCAD software is shown in Attachment 2. The received results are fully coincided with the PRISM printing given in Attachment 1.

5. PRISM METHOD INACCURACIES

At definite currents values of APDS (Axial Power Density Sensor) separate sections some inadmissible inaccuracies can occur. So, at obvious “pulled up” power field up to emergency dropout (see Attachment 1 – sections’ currents and Kz APDS 40-27) PRISM programme calculates the irregularity ratio of lengthwise power on 6th section, i.e. in accordance with PRISM the power field is displaced downward.

Approximated currents were calculated in MATHCAD in accordance with the above-mentioned method – Attachment 2.

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0 1 2 3 4 5 6 71.5

2

2.5

3

3.5

4

4.5

Fk

FF k

Z k

Table 1. Sensors currents on PDMS and approximated on PRISM Current on PDMS-N (Fk) Approximated current on

PRISM (FFk) The irregularity ratio of lengthwise power on PRISM programme

1775 1911 3070 3324 3895 3616 3640 3473 3615 3649 3670 4058 3785 3813 2810 2205

Кz=1.25 on 6th section

Figure 4. Sensors currents on PDMS and approximated on PRISM

Roughly speaking, in the reactor the power field is “upward” but PRISM programme considers it as “downward”. This inaccuracy occurs due to imperfection of the approximation method of sections’ currents values on three sins.

In accordance with Weiershtrasse theorem any continuous function can be separated into the sins sum:

ny(x) a1*sin(x) a2*sin(3*x) a3*sin(5x)*a4*sin(7x) a5*sin(9x)..... a *sin(k*x)= + + + +

Theoretically the three sins decomposition method must work as it’s shown on Figure 5

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Figure 5. Decomposition of the power field on three sins.

However owing to the little amount of sins (three) the mentioned inaccuracy appears. Three sins were chosen because of the centralized monitoring system SKALA calculating limitations but at the present moment PRISM programme carries out calculations at the modern computer and the approximation method complication would make longer the calculation process on a splits of milliseconds and would not affect on the calculating efficiency.

Now I would like to explain why this mentioned inaccuracy is dangerous during RBMK – 1000 operation. Approximation inaccuracy of lengthwise power sensors distorts Кz – the lengthwise power irregularity ratio but Кz has an influence on the graphite design temperature and on the operating reactivity margin. These two parameters are the limitation of safety operation, i.e. technological process parameters values deviation from which may result in breakdown.

The inaccuracy effect on the graphite design temperature.

Graphite design temperature is calculated by formula:

гр t k 4kT t *W *= + α ϕ In the frame of this report there is no use to explain the meaning of all formula

members for graphite design temperature calculation except 4kϕ . 4kϕ - the relative density of neutron flux on height on the central converters

level, where for the columns joints locating within the limits of 5 steps of reactor

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core lattice from the functioning APDS 4k 4SFϕ = (irregularity ratio for 4th section), and for the rest joints 4k 4Fϕ = (average irregularity ratio on all 4th sections of the functioning APDS).

Now imaging the situation. Graphite design temperature near the APDS is about 40-27 – 715 0С. Power actual field is upward (field on PDMS), the field on PRISM owing to approximation inaccuracy is downward with Kz =1.27(such reactor state of SNPP Unit 3 was in the first decade of March of 2007). The lengthwise field goes more upward up to the emergency alarm on 3rd section actuation. In accordance with SNPP RBMK-1000 reactor of Unit 3 САЭС – ИРУС-003-ОТУ operation procedure:

1.3 The principle engineer for reactor control monitors the reactor power level and volumetric power distribution in the reactor core not allowing the warning signals from the reactor physical protection scheme and emergency signals from PDMS from MCR – O control panel “A” with the help of Control and Protection System (CPS), PDMS and Centralized Monitoring System SKALA.

8.3.5 During the reactor facility power operation over 160 MWt(t) the principle engineer for reactor control must eliminate emergency (red flashing signals) with the aim of lengthwise power distribution leveling.

The principle engineer for reactor control must eliminate the emergency signal, i.e. to load in the core a low-drowned rod near the 40-27 sensor. At this moment the lengthwise power according to the PRISM is downward. The low-drowned rod dipping pushes the height and further down increasing Kz along the lower sections up to the 4th section but Kz increasing along the 4th section linearly influences on the graphite temperature in 5*5 cell around APDS-40-27. It possibly can result in the graphite calculating temperature increase up to 730 0С. If that happened, so principle engineer for reactor control must in accordance with ИРУС-003-ОТУ undertake definite actions right up to power descent. As a result at definite parameters combination the inaccuracy of PRISM programme calculating method might lead to power descent and generation loss.

Inaccuracy influence on the operating reactivity margin

The calculation reactivity margin is figured out by the formula

ρ суз1

211

k

cхх0

hххzFl z( )2⌠

⎮⌡

d

0

H

zFl z( )2⌠⎮⌡

d

⋅∑=

where, Схх – weights of the appropriate rods types(automatic regulator ,

manual regulator, shortened bottom entry absorber rod) hхх – depth of rod dipping Н- height of the core

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Fl(z)- relative macrodistribution of neutrons flux density in each CPS (Control and Protection System) channel.

Fl z( ) FF z( )1

N

j

Wj∑=

ξсузj R1( ) N⋅⋅

We wouldn’t discuss every component of the relative macrodistribution of

neutrons flux density in each CPS channel. We will consider FF(z) – approximated term for the average relative

lengthwise distribution of neutrons flux density : 3

ms эфm 1

FF(z) d sin( *(z Н )*m)=

= ∗ α + Δ∑

bn

msms 8

к 1bks

k 1

b * 81d

n Ф=

=

= ∑∑

As we can see from the calculating method of the operating reactivity margin the relative macrodistribution of neutrons flux density in each CPS channel is influenced by ksФ , msb - approximated currents values on three sins (3) and coefficients from four sins (4) method. As it has been mention already “three sins” method at definite composition of APDS currents (the field according to the PDMS is heavily above) calculates the lengthwise distribution by bottom. Accordingly the inaccuracies of lengthwise distribution approximation influence on the operating reactivity margin value. Especially it might influence on the passing modes of “iodine pit”. “Iodine pit” is the operating reactivity margin decrease (reactor poisoning) at the power descent falls at operating reactivity margin = 32-35 rods. The safety operation limit for operating reactivity margin is the value of 30 rods. If the inaccuracy makes a 29.9 margin at least for 1 second, so the principle engineer for reactor control in accordance with ИРУС-003-ОТУ would shut down the reactor manually:

2.3.1 Cases of immediate reactor shut down: …………… 7) Reactivity margin decrease up to the value of less than 30 effective rods

of manual regulator; ………………

Inaccuracy influence on the principle engineer for reactor control daily work.

At definite currents values of APDS (Axial Power Density Sensor) separate sections some inadmissible inaccuracies can occur. So, at obvious “pulled up” power field up to emergency dropout (see Attachment 1 – sections’ currents and Kz APDS

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40-27) PRISM programme calculates the irregularity ratio of lengthwise power on 6th section, i.e. in accordance with PRISM the power field is displaced downward.

There were situations when the 3rd section has given an PDMS emergency signal at the same time as the irregularity ratio of the lengthwise power on PDMS 40-27 was 1.28 according to the 6th section (i.e. according to the PRISM the field was downward). Кz=1.28 is very “bad” irregularity ratio value of the lengthwise power because usually Кzmaх=1.22-1.24.

In accordance with SNPP RBMK-1000 reactor of Unit 3 САЭС – ИРУС-003-ОТУ operation procedure:

8.3.5 During the reactor facility power operation more than 160 MWt(t) the principle engineer for reactor control must eliminate emergency (red flashing signals) and take appropriate measures to eliminate warning (red constant signals) and power density sensor understated signals (green constant signals) with the aim of lengthwise power distribution leveling.

These means that at PDMS emergency signal on 3rd section it’s necessary to dip any rod not more than 2.1-2.2 m (3rd section is located at 2.18 m from the core upper part). Such action made lower the lengthwise distribution on PRISM, i.e. by eliminating one signal we intensify another.

8.3.8 In the presence of only lengthwise warps the distribution leveling is carried out by the weight equivalent exchange in the field of shortened bottom entry absorber rod and manual regulator rods areas located in it’s upper and lower parts.

What does equivalent exchange mean? This is the extraction of one rod and dipping of another. If the power field is displaced downward so it’s necessary to dip in the core either “deep” rod (the dipping depth more than 4.5 m) or short-cut absorber rod and to extract the low-drowned rod. But taking in account the PRISM inaccuracy such action made this situation worse. Deep rod dipping and low-drowned rod extracting only made higher the lengthwise distribution on PDMS up to emergency signal on 3rd section. Again if we were trying to eliminate one signal we intensify another.

Ways of problem solving

In that situation the author suggests to modify the approximation method of neutrons stream density distribution on the reactor height. The “three sins” method as it was mentioned above has essential shortcomings and at the definite conditions and the reactor facility parameters may result in the safety operation limits breakdown. One of the ways of solving this problem can be the transfer from the “three sins” method to the “four sins” method.

In this case the system 4 will look like: 8 8 8 8 8

2 ' ' ' ' ' ' ' '

1 k 2 k k 3 k k 4 k k k k

k 1 k 1 k 1 k 1 k 1

8 8' ' 2 '

1 k k 2 k 3

k 1 k 1

b * sin ( *z ) b * sin( *z )*sin(2* *z ) b * sin( *z )*sin(3* *z ) b * sin( *z )*sin(4* *z ) Ф *sin( *z )

b * sin(2* *z )*sin( *z ) b * sin (2* *z ) b * sin(2* *z

= = = = =

= =

α + α α + α α + α α = α

α α + α + α

∑ ∑ ∑ ∑ ∑

∑ ∑8 8 8

' ' ' ' '

k k 4 k k k k

k 1 k 1 k 1

8 8 8 8' ' ' ' 2 ' ' '

1 k k 2 k k 3 k 4 k k k

k 1 k 1 k 1 k 1

)*sin(3* *z ) b * sin(2* *z )*sin(4* *z ) Ф *sin(2* *z )

b * sin(3* *z )*sin( *z ) b * sin(2* *z )*sin(3* *z ) b * sin (3* *z ) b * sin(3* *z )*sin(4* *z ) Ф

= = =

= = = =

α + α α = α

α α + α α + α + α α =

∑ ∑ ∑

∑ ∑ ∑ ∑8

'

k

k 1

8 8 8 8 8' ' ' ' ' ' 2 ' '

1 k k 2 k k 3 k k 4 k k k

k 1 k 1 k 1 k 1 k 1

*sin(3* *z )

b * sin(4* *z )*sin( *z ) b * sin(2* *z )*sin(4* *z ) b * sin(3* *z )*sin(4* *z ) b * sin (4* *z ) Ф *sin(4* *z )

=

= = = = =

α

α α + α α + α α + α = α

∑

∑ ∑ ∑ ∑ ∑

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The approximated currents values on PRISM will be calculated by a formula: 4

'ks ms k

m 1

Ф b sin( * z *m)=

= ∗ α∑

The approximation calculation of lengthwise power distribution on the “4th

sins” method is given in Attachment 2. However “four sins” would give the distortion to the approximation anyway

because any function decomposition into periodic functions series implicates the tie points mismatching. Undoubtedly the “four sins” would increase the approximation accuracy but currents values in the sensors location points will always differ from approximated currents values on PRISM. The method of functions decomposition into the sinusoidal series curves near the tie points. The more sins would be in the series the closer an approximation curve would be to the tie point.

Spline interpolation.

At large amount of interpolation nodes the degree of interpolating polynomials is heavily increased that makes them inconvenient for calculations. If we split the interpolation segment into several parts and build an independent interpolating polynomial on each part we might possible avoid the high degree of the polynomial. But such interpolation has a significant drawback: in the different interpolating polynomials tie points the breaking point would be their first derivative.

In this case it’s comfortable to use a special kind of the piecewise-polynomial interpolation – spline interpolation.

Spline - the function that is the algebraic polynomial at every partial interpolation segment but at the given segment it is continuous together with some of it’s own derivatives. Consider the construction method of the splines of 3rd degree (so called cubic splines) that is in common practice.

Let the interpolating function f is set by it’s values of yi in nodes xi. The partial segment length [ ]ii xx ,1− we would designate as 1−−= iii xxh ( )ni ,...,2,1= . We would search the cubical spline on each of the partial segments [ ]ii xx ,1− in the form of:

31

211 )()()()( −−− −+−+−+= iiiiiii xxdxxcxxbaxS ,

where, ia , ib , ic , id - a quadruple of unknown coefficients (therefore, their total sum is n4 ).

It can be proved that the sum of cubical spline finding has only one solution. Demand a values coincidence )(xS in the nodes with tabulated values of

f function:

iii ayxS == −− 11 )( , 32)( iiiiiiiii hdhchbayxS +++== .

The number of these equations ( n2 ) is a half of the unknown coefficients number; to get the additional conditions demand the )(xS ′ and )(xS ′′ continuity in

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all points including nodes. For this we should equate left and right derivatives )0( −′ xS , )0( +′ xS , )0( −′′ xS , )0( +′′ xS in the inner node ix . At first we would

get )(xS ′ and )(xS ′′ , consecutively differencing (1): 2

11 )(3)(2)( −− −+−+=′ iiiii xxdxxcbxS , )(62)( 1−−+=′′ iii xxdcxS .

We have: 232)0( iiiiii hdhcbxS ++=−′ , 1)0( +=+′′ ibxS , 1,...2,1 −= ni

(in the second case it was necessary to replace i by 1+i in the expression

)(xS ′ ) Similarly for the second derivative: )(62)( 1−−+=′′ iii xxdcxS , iii hdcxS 62)0( +=−′′ , 12)0( +=+′′ ii cxS

Making the left and right derivatives equal we would get: 2

1 32 iiiiii hdhcbb ++=+ ,

iiii hdcc 31 +=+ , 1,...2,1 −= ni Equations 4 and 5 in the aggregate give some more )1(2 −n conditions. Two

more conditions are still missing. Usually as a case of these conditions the requirements to the splines behavior in the frontier points 0x and nx are taken. If we require the spline zero curvature at ends (i.e. the equation of the second derivative zeros) we would get:

01 =c , 03 =+ nnn hdc . Rewrite all equations 2-6, excluding n of unknown ia :

132

−−=−− iiiiiiii yyhdhchb ni ,...2,1=

032 21 =−−−+ iiiiii hdhcbb 1,...2,1 −= ni

031 =−−+ iiii hdcc 1,...2,1 −= ni 01 =c ,

03 =+ nnn hdc System 7 consists of [ ] nnn 32)1(2 =+−+ equations. If we solve it we

would get the values of ib , ic , id unknowns determing the integrity of all formulas for the required interpolating spline.

31

2111 )()()()( −−−− −+−+−+= iiiiiii xxdxxcxxbyxS

ni ,...2,1=

CONCLUSIONS

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0 1 2 3 4 5 6 71

1.5

2

2.5

3

3.5

4

4.5

FFF x( )

Fk

FFk

FF4k

x Zk, Zk, Zk,

The checking calculation “three sines” method and the ”four sines” method as well as calculation on the cubic splines method are given in Attachment 2.

Figure 6 shows the curve for currents distribution on PDMS (Power Distribution Monitoring System), the approximation curve on “three sines” method, the approximation curve on “four sines” method, the approximation curve on the cubic splines method.

Undoubtedly the cubic splines method gives maximal accuracy in spite of the fact that this method is the simplest one. The curve that was schemed on the cubic splines method practically repeats currents distribution of 40-27 sensor sections and passes through the tie points. Transition to the cubic splines method at currents approximation of lengthwise power distribution sensors allows avoiding above stated problems and finally will increase the NPP with RBMK type reactors safety level.

Figure 6

Attachment 1

Partial listing of PRISM programme printing –a doubler on 2.03.07 6:46

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Attachment 2 Checking calculation of the lengthwise power irregularity ratio on APDS - 40-27 on 2.03.07 6:46 am

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0 1 2 3 4 5 6 71

1.5

2

2.5

3

3.5

4

4.5

FFF x( )

Fk

FF k

FF4 k

x Z k, Z k, Z k,