JP2918266B2 - Monitoring method for core stability of boiling water reactor - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Field of Industrial Application) The present invention relates to a method for monitoring core stability of a boiling water reactor.

(Prior art) The operation of a boiling water reactor is usually controlled by controlling both the control rod and the core flow to increase or decrease the reactor power, but under certain conditions, The core may become unstable due to the coupling of the nuclear and thermo-hydraulic dynamics in the reactor. Therefore, at present, the reactor power and the core flow rate are changed within a range set by design calculation in advance.

On the other hand, if the stability can be measured and monitored at all times, not only will it be useful for safe operation of the nuclear power plant, but also the conventional operating range can be expanded, leading to more efficient operation of the nuclear power plant. Conventionally, as a method for measuring such core stability, for example, there is a "method and apparatus for monitoring the core stability of a boiling water reactor" proposed by the present inventors (JP-A-58-211694). .

(Problems to be Solved by the Invention) In the above core stability monitoring method, it is required to shorten the response time as much as possible and to monitor the stability with high accuracy. However, the response time and the high accuracy conflict with each other. Because of the demands, a compromise was needed to speed up response time at the expense of some accuracy. However, since this compromise differs depending on the core stability that changes depending on the operating conditions of the plant, if monitoring is performed with a response time determined under certain operating conditions, monitoring accuracy is poor in another operating state. There was a problem of becoming.

The present invention has been made based on the above circumstances, and an object of the present invention is to provide a method for monitoring the core stability of a boiling water reactor that can sequentially monitor the core stability online with certain accuracy. To provide.

[Configuration of the invention]

(Means and Actions for Solving the Problems) In order to achieve the above object, a method for monitoring the core stability of a boiling water reactor according to the present invention uses a real-time method based on a fluctuation component of a neutron flux signal of a boiling water reactor. The autoregression coefficient is obtained sequentially in the following manner, and a reduction ratio, which is a representative measure of core stability, is obtained in real time from the autoregression coefficient, and the time constant of the sequential calculation of the autoregression coefficient is calculated according to the estimated reduction ratio. Is made variable, and the width reduction ratio is estimated with a constant accuracy.

Therefore, according to the present invention, it is possible to quantitatively monitor the stability with a certain degree of accuracy, and it is possible to more quickly estimate the state as the plant approaches an unstable state.

 Hereinafter, the principle of the present invention will be described.

First, the variable component of the neutron flux obtained from the plant is x
Assuming (t), the autoregressive (AR) model is expressed as the following equation (1).

Here, y (t) is a predicted value at time t, and x (tm)
The observed value at time (t-m) is, AR at a _m (t) is the time t
The coefficient, M, is the AR model order.

The AR coefficient a _m (t) is the observed time series data of N points retroactively from the time t x (i), (i = t-N + 1,
.. T) and y (i) in equation (1) so as to minimize equation (2) below.

Equations (1) and (2) can be solved using the least squares method. Specific algorithms include a sequential processing type and a batch processing type as described below.

(Sequential processing type) A (t) = A (t-1) + P (t) Z (t) (x (t)
−Z ^T (t) A (t)) P (t) = (P (t−1) −P (t−1) Z (t) Z
^{T (t) P (t-} 1) / (d-Z T (t) P (t-1) Z
(T)) / d (t = 0,1,2, ...) where _{A (t) = {a 1} (t), a 2 (t), ..., a M (t)} (AR
Coefficient vector) Z (t) = {x (t), x (t−1),..., X (t−M)}
(Observation vector) d; forgetting factor * initial value A (0) = {0,0, ..., 0} P (0) = bI (b is a sufficiently large positive number, I is a unit matrix of (M, M)) (Batch processing type) From the AR coefficient thus obtained, the impulse response obtained by the following equation (3) is a measure of the neutron flux response characteristics, that is, the core stability. At specific times, However, Q (0) = 1.0 Q (t) = 0.0 (t <0) LAGH; This impulse response R
(T) usually has a shape as shown in FIG. At this time, the reduction ratio (D
R) and the resonance frequency (FR) can be obtained by the following equations (4) and (5).

In addition, the method of obtaining the reduction ratio using the frequency domain as disclosed in Japanese Patent Application Laid-Open No. 58-211694, which was invented by the present inventors, is also effective. In this method, the frequency spectral density is obtained from the AR coefficient by Fourier transform, and the reduction ratio is quantitatively obtained from the shape (sharpness of the spectral waveform at a specific frequency).

In the above-described various methods, if the method is performed each time the time is updated, the reduction ratio, which is a measure of stability, can be obtained in real time. In the case of the sequential processing type, this AR coefficient is updated each time data is input, so the AR coefficient is constantly updated, but in the case of the batch processing type, calculation is performed using the data of the past N points each time one point data is input. Therefore, there is a disadvantage that the amount of calculation increases. However, the data sampling cycle for core stability monitoring is usually about 0.2 seconds, and the monitoring of the reduction ratio of 5 to 10 seconds is sufficient. Therefore, it is not necessary to estimate the AR coefficient of batch processing every time. Performing once every 10 seconds is sufficient and does not pose a practical problem.

On the other hand, the most important problem in such monitoring is the number N of data used in the above calculation. In the case of the sequential processing type, the forgetting factor corresponds to this, and the relationship is expressed by equation (6).

If this N is reduced, the number of data used for estimating the AR coefficient decreases, and the estimation error of the coefficient increases.
The estimation error of the width reduction ratio also increases. Therefore, it is necessary to determine the number of data for monitoring after quantitatively grasping the relationship between the number N of data (that is, the response time constant) and the estimation error of the reduction ratio.

Here, the estimation error of the AR coefficient and the reduction ratio will be considered. The estimation of the AR coefficient by the above equations (1) and (2)
Because of the multiplication method, the error can be theoretically evaluated as follows. For example, in the case of a quadratic AR model, Var (a ₁ ) = Var (a ₂ ) = ｛1−a ₁ ² −a ₂ ² −2 ₁ ² a ₂ / (1−a
₂ )｝ / {1- (a ₁ / (1-a ₂ )) ^{2 2} / N (7) Here, a ₁ and a ₂ are true AR coefficients, abbreviated to a _m (t) (m = 1, 2) in equation (1), and N is the number of data used for estimation. It should be noted that the estimation error of the AR coefficient is inversely proportional to the number N of data, and also depends on the coefficient value itself. That is, the smaller the data number N is, the larger the error is. Further, since the AR coefficient differs depending on the operation state of the plant, even if the same data number N is used, the error of the coefficient differs.

On the other hand, the reduction ratio can be obtained from the AR coefficient by eigenvalue calculation as follows.

Here, dt is a data collection cycle (second). Since equation (8) is a non-linear function, it is expressed as DR = f
If (a ₁ , a ₂ ), Var (DR) = (∂f / ∂a ₁ ) ² Var (a ₁ ) + (∂f / ∂a ₂ ) ² Va
The estimation error of the reduction ratio can be obtained in the form of r (a ₂ ) (9).

From the form of the above equation (9), it is easily understood that the estimation error of the width reduction ratio is also inversely proportional to the number N of data. On the other hand, if the true width reduction ratio of the plant is determined, the AR coefficient is also uniquely determined depending on it, so that the estimation error of the equation (9) depends on the true width reduction itself. FIG. 3 shows the estimation error Var (DR) obtained by the expression (9) as a function of the reduction ratio DR under a constant data number N.
It can be seen that there is a tendency for the reduction ratio to be smaller at large (close to unstable) and small (stable regions). In particular, the tendency that the error is small near the unstable state is important in practical use. That is, in such an area, the stability can be estimated with high accuracy with a smaller number of data than in other areas. This indicates that quicker estimation is possible as the stability becomes worse.

From the above relationship, the number of data used for monitoring the stability is expressed as N (t) = N ₀ / Var (DR (t)) (10) By changing the estimated error Var (DR (t)) in inverse proportion to the estimated error Var (DR (t)) calculated from the expressions (9) to (9), it is possible to monitor the stability with a constant accuracy, where N ₀ is a proportionality coefficient. is there.

Since the number of data N (t) directly corresponds to the response time constant for monitoring the stability, according to the present invention, it is possible to quantitatively monitor the stability with constant accuracy. Further, the present invention can provide a state estimation that can be performed more quickly as the plant approaches an unstable state, and can provide a very effective method in practical use.

(Example) An example of the present invention will be described with reference to the drawings.

 FIG. 1 is a block diagram of one embodiment of the present invention.

As shown in the figure, a plant signal measured in a plant is converted into a digital signal by an A / D converter 1.
This digital signal is input to the preprocessing device 2. The pre-processing device 2 includes a high-pass filter and removes unnecessary low-frequency components. The AR coefficient calculation devices 3 and 4 select a sequential processing type or a batch processing type as an option, and calculate AR coefficients at regular intervals (normally 5 to 10 seconds) from time series data output from the preprocessing device 2. At this time, a time constant (N (t) in equation (10) for the batch processing type and d in equation (11) for the sequential processing type) given as an output of the time constant setting device 6 is used as a parameter. The AR coefficient obtained from the AR coefficient calculator 3 or 4 is input to the reduction ratio calculator,
Here, the reduction ratio is calculated. The calculated width reduction ratio is input to the time constant setting device 6, and the time constant is obtained according to the above-described equations (10) to (11).

The display device 7 displays the width reduction ratio obtained by the width reduction ratio calculating device 5, and when the width reduction ratio exceeds a certain value, the alarm device 8
Generates an alarm.

〔The invention's effect〕

As described above, according to the present invention, it is possible to quantitatively monitor the stability under a certain accuracy, and furthermore, it becomes possible to quickly estimate a state as the plant is closer to an unstable state. It is possible to provide a practically very effective monitoring method that can contribute to improvement in plant operability.

[Brief description of the drawings]

FIG. 1 is a block diagram of one embodiment of the present invention, FIG. 2 is an impulse response diagram, and FIG. 3 is a diagram showing the reduction ratio dependence of the estimation error. DESCRIPTION OF SYMBOLS 1 ... A / D conversion device 2 ... Pre-processing device 3 ... Sequential processing type AR coefficient calculation device 4 ... Batch processing type AR coefficient calculation device 5 ... Width reduction ratio calculation device 6 ... Time constant setting device 7 ... Display device 8 ... Alarm apparatus

Continuation of the front page (56) References JP-A-61-181995 (JP, A) JP-A-59-135396 (JP, A) JP-A-58-211694 (JP, A) JP-A-58-124994 (JP) , A) Shigeru Kanemoto, "Introduction of Structural Matrix to AR Model", Systems and Control, Vol. 27, No. 5, pp. 344-348 (1983) Kanemoto S, et al "Development of an on-line reactor facility monitoring system. in a boyi restor ", Prog. Nucl. Energy, Vol. 21, p 745-752 (1988) Mitsutaka T, et al, "Core Stability test analysis using the autoregressive model", Nucl Technol. Vol. 65, no. 3 p 365-373 (1984) (58) Fields investigated (Int. Cl. ⁶ , DB name) G21C 17/00 JOIS

Claims (1)

(57) [Claims] An autoregressive coefficient is sequentially obtained in real time from a fluctuation component of a neutron flux signal of a boiling water reactor, and a reduction ratio, which is a representative measure of core stability, is obtained from the autoregressive coefficient in real time. The boiling water reactor core characterized in that the time constant of the successive calculation of the autoregression coefficient is made variable according to the estimated attenuation ratio and the attenuation ratio is estimated with a constant accuracy. Stability monitoring method.