# 5.4 Physical Constraints on Tap Settings

The preceding sections treat a transformer’s tap setting as a continuous quantity. However, tap settings are discrete. There are three ways to handle discrete taps:

• Modify equations Equation 42 and Equation 45 so that the tap setting is computed discretely.

• Compute tap settings from Equation 42 or Equation 45. Round the tap setting to the nearest discrete value each time the tap changes.

• Compute tap settings from Equation 42 or Equation 45. Round the tap settings after the load flow has converged. Fix the transformer taps. Continue until the solution converges with the discrete fixed tap transformers.

As was discussed in Section 2.3, the tap changing mechanism is limited in its regulating abilities. Each TCUL device is subject to tap limits, i.e. maximum and minimum physically realizable tap settings. The implementation of Equation 42, Equation 43, or Equation 45 should reflect this fact. For example, Equation 43 should be implemented as

 $t^{new}=\begin{cases}t_{min}&\text{if }t^{new}t_{max}\end{cases}$ (48)