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Condition Monitoring of the Electric Circuit Elements of the Nuclear Reactor Measuring Channels A.M. Pankin, S.A. Basharin, V.P. Danilenko Contact

The reliable operation of a nuclear reactor depends on state of its separate elements and systems and on a possibility to diagnose their state in the permanent monitoring mode. The power circuits of measuring channels are the defining link of any monitoring system of a nuclear reactor, providing its normal operation during all the life-time.Exactly they define the reliability of the entire system and the reactor safety operation depends on their state in the long run.
The continuous and qualitative monitoring of power circuit element states of measuring channels can be performed by connection of the extra testing sources to an input. These sources permit to create effects of the dynamic phenomena in all its elements. The responses in circuit elements in the form of surge characteristics on state variables can serve as prior information for element characteristic identification. The observable vector of state variables of a power circuit is registered and processed by the computer. The processing aim is to resume linear or nonlinear characteristics of the separate elements. For example, an ionization chamber (IC) or other detector performing the functions of a primary converter in a measuring channel can act as an element of the circuit.
The key diagram of connection of nuclear reactor ionization chamber with a source of padding (testing) voltage is represented in Fig. 1.

Fig 1

The circuit contains: U1 direct current source, ionization chamber in the form of nonlinear dipole, its properties depend on the parameter N (neutron stream or reactor power), spurious inductance of chamber L, stray capacitance C, load impedance R2, a source of complementary (testing) voltage U2 and adjusting resistance R1.
Such circuit allows making necessary measurements of circuit state vector without any changing of operation mode of a reactor measuring channel, where the ionization chamber (IC) enters. And the diagnostic tests of the circuit element parameters are carried out at the circuit state vector.
An operating and additional voltage is given on a positive electrode of an ionization chamber for the circuit diagnosing. The additional voltage changes the chamber operating voltage, so that it doesn't overstep the tolerance limits. At that the rate of change of the target current of an ionization chamber doesn't exceed the value, at which the automatic protection actuation occurs on rate of reactor power increasing [1].
The variable vector of power circuit state in the form of surge characteristics is the prior information for diagnosing algorithm construction of power circuit macrostructure properties or its separate elements characteristics. Macrostructure is understood as a part of the circuit containing system of elements, the dynamic properties of which can be described by the mathematical pattern in the form of Kosh^'s equation system in a normal form:


The mathematical pattern of the circuit represents by itself the basis for diagnosing of parameters and the macrostructure characteristics. The pattern is generated by using a topological pattern in the form of a normal planar graph. The graph is put in for unification of the mathematical pattern creation of a dynamic circuit. The topological graph defines transition from the graphics pattern of a circuit to the numerical one, and further to the mathematical pattern. Voltage sources and the capacitive elements define branches of the graph tree, and inductive elements define chords.
For the circuit of Fig. 1 a normal planar graph is represented in Fig. 2

Fig 2

The branches with voltage welding sources and capacitive elements are part of the graph tree. The missing branches are formed at the expense of R- branches to which the branch containing an ionization chamber (Cam) can be treated . Structure of chords includes branches with inductive elements and G-branches with resistors. The graph forms the basis for a matrix creation of the main sections Q, numbering a submatrix F as an incidence submatrix of chords:

For the topological graph of Fig. 2 these matrixes look like as:

The matrix F is the basic matrix necessary for the mathematical pattern creation of a dynamic circuit. Except for it the resistance and conductance matrixes of branches of graph tree are shaped [2]:

The matrixes of branches of connection (chords) are similarly shaped:

Except for given matrixes the auxiliary matrixes

and matrix of reaction-type components are shaped

The formed set of matrixes allows defining matrixes of state equations factors

which, being written in the symbolical form, look like as:

It will better to write down the gained matrix equation in an extended form
for diagnosing the circuit parameters on Fig. 1:

In the course of diagnosing the differential equations are replaced by difference equations, which are inverted and solved relative to unknown parameters within the limits of the restricted time interval. At inverting difference equations the effects should be considered as known, and variable states should be defined empirically.
For characteristics diagnosing the ionization chamber is represented as a dipole pattern with the implicitly expressed structure. The procedure of chamber diagnosing consists in a definition of parameters (factors) of state equations and characteristics recovery. Generally the characteristics are nonlinear.
In this case the diagnosing procedure is reduced to determination of the elements of matrix A. Matrix A can be constructed by different methods depending on algorithm of an elected numerical procedure. As the operational experience has shown, the best results for receiving stable and precise calculations can be received by using multistage algorithm of numerical integration of Kouall's type [3].
While using Kouall's algorithm the interval of identification is symmetrized relative to a concerned discretization interval. The quadrature formula, approximating definite integral, is recorded as:

Here the parameters of an algorithm are defined by solution of the algebraic equation system:

For q=0 the algorithm of the second order of accuracy is obtained. This algorithm uses one sampling interval for the identification. At that two parameters of algorithm are defined from the expressions:

For definition of factors of a matrix A the differential equations are also substituted by the equations in finite increments and are converted as:

or in a matrix form d .L.W - Dx = 0 In this expression: d - discretization interval of dot spectra, L -matrix of identifiable parameters, W - generalized vector of state and effects, Dx - vector of finite differences of variable state. The effects in the form of step-functions and dot spectra of variable state u_C and i_L. are accepted as the prior information
The finite result of diagnosing is the receiving of the last matrix expression of a variety of magnitudes of matrix L elements by inversion. These values define characteristics of the dynamic system. On these elements it is possible to restore all attributes and characteristics of the object described by state equations. Such object is the ionization chamber in this example.
The element states monitoring of power circuits of reactor measuring channels can be taken continuously and automatically without a working process shutdown at realization of such algorithm in a corresponding diagnostic system. In this case the operator continuously receives information about all diagnosing elements. At any moment the operator can display on the monitor screen the traced pattern of technical condition of these elements and blocks.

Literature

1. A.M.Pankin, S.A.Basharin, V.P.Danilenko, V.F.Borisov Method of Working Diagnosing of an Ionization Chamber. The patent of Russian Federation 2145427 date - 10.02.2000.
2. L.O.Chya, Lin Pen Min. Computerized Analysis of Electronic Circuits: Algorithms and Computing Methods. Translation from English -M.Energy, 1980. - p.640.
3. V.I.Krylov, V.V.Bobkov, P.I.Monastyrny Origins of the Computing Method Theory. The Differential Equations. - Minsk: Science, 1982. - p.286.

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