Automatic Tap Changing Algorithm Details

This page provides detailed algorithmic descriptions of the automatic tap changing optimization procedure implemented in power-grid-model. Automatic tap changing is an outer-loop optimization procedure that iteratively adjusts transformer tap positions and runs power flow calculations to achieve desired voltage control objectives.

For an overview of regulated power flow and strategy selection, see Regulated power flow with automatic tap changing.

Control logic for power flow with automatic tap changing

The automatic tap changer iterates over all regulators with automatic tap changing control. The control logic is described as follows:

• For each regulator, calculate the controlled voltage \(U_{\text{control}}\) based on control_side.

• If the transformer has a tap_pos which is not regulated and within tap_min and tap_max bounds, skip it and consider the next regulator. In all other cases, go to the next step.

• If \(U_{\text{control}}\) is outside the bounds, the tap position changes:

  • If \(U_{\text{control}} < u_{\text{set}} - u_{\text{band}} / 2\), the tap position is incremented by 1 (or according to the TapChangingStrategy chosen).

  • If \(U_{\text{control}} > u_{\text{set}} + u_{\text{band}} / 2\), the tap position is decremented by 1 (or according to the TapChangingStrategy chosen).

  • If the updated tap_pos reaches tap_min or tap_max, it is clamped to those values.

• Another power flow calculation is run with new tap positions for the regulated transformers.

• If the maximum number of tap changing iterations is reached, the calculation stops and raises an error of type MaxIterationReached.

Initialization and exploitation of regulated transformers

The initialization and exploitation of different regulated transformer types are unique and depend on whether the regulator is automatic. The following table specifies the behaviour of regulated transformers based on the TapChangingStrategy chosen and whether tap_pos is regulated.

TapChangingStrategy	tap_pos is regulated?	Initialization phase	Exploitation phase
any_valid_tap	Yes	Set the tap position to tap_nom (default middle tap position)	Binary search (default)
any_valid_tap	No	Clamp the tap position to stay within tap_min and tap_max	Do not regulate
min_voltage_tap / max_voltage_tap	Yes	Set the tap position to tap_min or tap_max respectively	Do not regulate
min_voltage_tap / max_voltage_tap	No	Clamp the tap position to stay within tap_min and tap_max	Do not regulate

Some transformer configurations require clamping due to regulated_object and tap_side pointing to different sides of the transformer. For a three-winding transformer the requirements are similar to a regular transformer with the additional consideration that the primary side tap changer regulates only the secondary or tertiary side voltages:

Tapping on side	Regulated object	Voltage control side	tap_side	regulated_object	control_side
HV (0)	LV (1)	LV (1)	BranchSide.from_side / Branch3Side.side_1	TransformerTapSide.side_1 / Branch3Side.side_2	BranchSide.to_side / Branch3Side.side_2
HV (0)	LV (1)	HV (0)	BranchSide.from_side / Branch3Side.side_1	TransformerTapSide.side_1 / Branch3Side.side_2	BranchSide.from_side / Branch3Side.side_1
LV (1)	HV (0)	LV (1)	BranchSide.to_side / Branch3Side.side_2	TransformerTapSide.side_2 / Branch3Side.side_1	BranchSide.to_side / Branch3Side.side_2
LV (1)	HV (0)	HV (0)	BranchSide.to_side / Branch3Side.side_2	TransformerTapSide.side_2 / Branch3Side.side_1	BranchSide.from_side / Branch3Side.side_1

Search methods used for tap changing optimization

By default, the algorithm uses binary search to find the optimal tap position to control voltage within the set band. Users can also choose other search methods via TapChangingStrategy:

TapChangingStrategy	Description
fast_any_tap	Very fast search (single step per iteration)
any_valid_tap	Binary search (default)
min_voltage_tap / max_voltage_tap	Set to extreme tap and do not regulate

Regulatable voltage range outside u_band

Since the regulated transformer has only a limited number of tap positions, it cannot always attain the target voltage (i.e., the controlled voltage \(U_{\text{control}}\) may remain outside the set band). The possible scenarios are:

• For tap_min: When increasing the tap position from tap_min in successive power flow calculations, the voltage might still be below the lower bound of the set band.

• For tap_max: When decreasing the tap position from tap_max in successive power flow calculations, the voltage might still be above the upper bound of the set band.

Error type MaxIterationReached

If the algorithm uses binary search, since the number of tap positions is often limited to tens of taps, binary search will find the optimal tap positions within a small number of iterations, typically under 10. When linear search is used, however, we avoid convergence if the search continues to iterate in an oscillatory fashion. However, the following could be a cause for MaxIterationReached:

• If all tap_pos are within tap_min and tap_max and converged to the targeted band:

  • The tap changing control has found a control point inside the band.

  • The calculation may be at a saddle point, and further iteration may not result in achieving values which are closer to the target voltage.

  • This is often expected behaviour.

• If no voltage control could find tap positions inside u_band:

  • A transformer is constantly oscillating between two tap positions depending on directions of measurement errors. In this case, it’s difficult for our algorithm to choose the more optimal tap position for controlled voltage.

• If a few voltages are out of band: The algorithm keeps oscillating due to constraint saturation at tap_max or tap_min. The regulated transformers at saturation cannot regulate further, although the voltage is outside the band. This is often expected behaviour.

• If voltages are inside the band but tap_pos are outside tap_min and tap_max bounds: This is a logical violation. It means the clamping inside the algorithm is not functioning. This is a bug and should be reported.