6- 3.1 Reactor Excitation

To determine the dynamic characteristics of a system, one must measure variables that are changing with time

(from the standpoint of reactor hardware). Also, although this table shows more periodic devices than random devices used as externally induced excitation, a trend in recent years to increased use of random excitation must be noted.

For externally excited experiments, a variety of methods is used (see Table 6.10) Except for the occasional use of on-line electronic analyzer methods, most experi­ments do not give transfer functions until the recorded data are processed off-line. Both electronic analyzers and digital computers are used for this processing.

As noted m Table 6.8, the excitation may be sinusoidal or pseudorandom and either a control rod or some other plant control device may be used to excite the system In

Table 6.9—Relative Use in Reactor Dynamics of Excitation Devices for Measurement of Transfer Functions and Allied Functions Type of fluctuations Percentage of zero-power-reactor (ZPR) or power-reactor (PR) experiments using a particular excitation device Neutron source Control rod Other Self-excited ZPR PR ZPR PR ZPR PR ZPR PR Periodic— sinusoidal 0 0 22 23 0 0 0 0 Nonperiodic —random 6 0 8 6 0 6 64 65 Total, % ~6 o’ 30 29 o’ 6 64 6?

Furthermore, the variations must have the following properties

1. Amplitudes sufficient to override unwanted effects that could reduce accuracy.

2. A sufficiently long duration or a sufficient number of repetitions to provide the desired accuracy

3. Frequencies in the ranges to be investigated

If the intrinsic variations, or random noise, of a system are used, the system is said to be self-excited. On the other hand, a system is said to be externally excited if a perturbation is introduced by a signal-generating device. In both instances transducers responsive to the variations of interest provide the experimental data.

Table 6.9 lists the kinds of excitation that have been used to date. The relative popularity of the various forms of excitation (Tables 6.6 and 6.8) is indicated somewhat arbitrarily by the number of dynamics experiments that have used each form. Transfer functions and related functions have been emphasized in Tables 6.6 and 6.8 Many other* dynamics tests (such as valve-position changes in power plants, rod drops, positive-period tests, and Rossi-alpha coincidence counting) are not represented even though they may be somewhat related to the tests discussed here. With this understanding the predominance of self­excitation experiments indicated in Table 6.9 can be attributed, at least in part, to their experimental simplicity

‘These tests may be used to measure specific effects rather than to extract transfer functions sinusoidal excitation the transfer function between the excitation variable (such as the reactivity of a control rod) and the system output variable (such as the reactor power) may be obtained at the excitation frequency by any one of the following approaches

1. Using the separately measured fundamental fre­quency amplitudes and phases of input and output, applying Eq 6.1 or Table 6.1.

2. Applying the appropriate electronic gain and phase to the output and using it to “null out” the input signal (see Sec. 6-5.2).

3. Cross-correlating the input and output signals, using Eq 6.9 in digital processing or Table 6.1 in continuous processing (see Sec. 6-5.4)

The last approach is commonly used at present.

Table 6.10—Data-Acquisition and Data-Processing Techniques Used in Externally Excited Reactor Dynamics Experiments On-line acquisition device Off-line processing device References to typical applications Chart or film recorder Digitizer, digital 18, 76 computer Electronic analyzer None 11, 14 F-m tape recorder Electronic analyzer 44, 85 F-m tape recorder Digitizer, digital 44, 107 computer Digitizer, tape recorder Digital computer 53, 78

Power MW Pressure psi

Center rod, in 8-rod bank, in

Peak reactivity % for
1-in peak stroke

Figure 6.5 shows typical rod-oscillator test results for a boiling-water reactor. In such tests one is interested in the difference between the at-power transfer function and the zero-power transfer function for this can determine the feedback, H, in Eq 6 17. In addition, the height and width of the resonance (in this example at со = 7 radians/sec) are of interest because they indicate the extent to which an instability of self-sustained oscillations is being approached In pseudorandom excitation you attempt to introduce all frequencies in the band of interest into the system at once rather than sequentially as in sinusoidal testing. In the commonly used binary excitation, an input control signal has two values, such as +1 and —1, however, ternary signals (having values +1, 0, and —1) have been suggested112 Rather than letting the duration of +1 and —1 values be determined by an ideal random process, it is more

advantageous to use a repetitive almost-random signal,41 such as that shown in Fig 6 6

In analyzing data in pseudorandom excitation experiments, you obtain the cross-correlation function by either on-line or off-line integration

: fT/2 x(t) y(t + r) dt

T •’-T/2 2 using the time^hifted product of the input variable, x(t), and the output variable, y(t). Figure 6.7 shows a typical experimental result. Using the relations in Table 6.1, you obtain the transfer function from Pxy(f), the Fourier transform of CXy(r)

(6.20)

With x(t) perfectly random, it can be shown that Cxy(r) in Eq 6.19 is the system impulse-response function41 and Px(f) in Eq. 6.20 is a constant. The transfer function in Fig. 6.7 was obtained in this manner.

2 5 CENTS

Fig. 6.6—A simple pseudorandom signal (above) that has been tailored to give the almost ideal autocorrelation function (below) 1 1 3

TIME, sec

It is not usual to measure transfer functions by pulse or step excitation, although this is possible.59 In the method the quotient of Fourier amplitudes is taken from an analysis of the input and the output signals to obtain the transfer function However, it is preferable to have a series of pulses or steps, such as pseudorandom excitation, because the added signal energy helps overcome unwanted noise.