Rod Worth Calibration

Motivation

The control rod worth curve is assumed to follow a sine or cosine curve, while utilizing estimated delayed neutron related kinetic parameters. This page provides a tool to optimize not only the curve-related parameters that constitute the control rod worth curve but also other kinetics parameters. Furthermore, after control rod worth calibration, users can directly use the data to determine curve parameters suitable for the specific core configuration.

• Adjust the control rods to make the reactor critical.
• Insert a small positive reactivity by moving a specific control rod further upward.
• Measure the reactor period \(t\) after insertion.
• Record the start and end positions of the control rod and define the midpoint position \(X_j\).
• Measure the total rod movement \(l\), and compute the reactivity inserted per unit length.
• Fit the obtained differential rod worth values \(r(t)\) to a sinusoidal model to determine the rod’s characteristics.

Differential Method

For each control rod \(j \in \{\mathrm{TR}, \mathrm{S1}, \mathrm{S2}, \mathrm{RR}\}\,\),

where \(X_j = (X_{j_2}+X_{j_1})/2\) which is the middle location between critical \((X_{j_1})\) and supercritical \((X_{j_2})\)

The measured reactor period \(t\) is related to the reactivity \(\rho(t)\) by the Inhour equation:

Here, \(\Lambda\) is the prompt neutron lifetime, \(\beta\) is the effective delayed neutron fraction, \(f_i = \beta_i / \beta\) is the fractional contribution of delayed group \(i\), and \(\lambda_i\) is the decay constant for group \(i\). (The factor 100 is included to express reactivity in percent units.)

Dividing \(\rho(t)\) by the rod movement length \(l\) gives the differential rod worth: \( r(t) = \rho(t)/l \), where \(l=X_{j_2}-X_{j_1}\).

For each rod \(j\), given \(n_j\) calibration trials (\(k = 1, 2, \dots, n_j\)), the parameters \(\{a_j, b_j, L_j\}\) are obtained by minimizing:

Integral Method

Integral rod worth defined as:

Define

where \(\kappa\) is the constant which makes the equation equal. When the reactor is critical \(\rho(\mathrm{CR})=0\), while if the reactor is supercritical at some rod positions, \(\rho(\mathrm{CR})=\rho(t)\). So, the minimization problem can be written as:

where \(N\) is the total number of rod calibration trials.

Optimization results table

The table below presents the results from three different optimization methods:

• NETL (Differential): This method utilizes the Differential approach currently implemented at NETL. The reactor period for this method is assumed to be measured using a 'stop watch'. The parameters displayed in this column are fixed to their initial default values and are not influenced by any changes made to the input variables on the left side of the page.
• Differential Method: This optimization is performed using the Differential method, taking into account the variable values (a, b, L, \(\beta\), \(\lambda\), \(\Lambda\), \(\kappa\)) set in the left panel, as well as the selected 'Period' measurement method ('real-time' or 'stop watch'). If all input variables on the left are set to their default values and the 'Period' method is selected as 'stop watch', the results from this column will be identical to those of the 'NETL (Differential)' column.
• Integral Method: This optimization is conducted using the Integral method. It also considers the variable values (a, b, L, beta, lambda, Lambda, kappa) provided in the left panel and proceeds as described in the theoretical explanation above.