Two generators on a common bus can exchange reactive power even when their combined export hardly changes. One unit supplies vars, the other absorbs them, and the bus meter reports the net result. The individual winding currents still carry the exchange. Keep the selected winding arrangement within the general power-transformer specification framework [1].
A useful first model has two internal voltage sources E1 and E2, connected through reactances X1 and X2 to the shared node. All quantities must be referred to one voltage base. Transformer leakage, generator equivalent reactance and connecting conductors belong in the relevant paths.
What a small voltage mismatch predicts
For sources with approximately equal phase angle, a mainly reactive connecting impedance and a small magnitude difference, circulating current is approximately Ic = (E1 − E2)/(jXΣ), where XΣ = X1 + X2. Use phase RMS volts, ohms and amperes. The current is approximately in quadrature with the sources.
This expression shows why a small voltage mismatch can matter when coupling reactance is small. It is a sensitivity estimate, not a complete power-sharing calculation. Different phase angles add active-power exchange; resistance, controls and network branches change the result.
Separate the two causes of voltage mismatch
| Possible cause | Observation to retain | Interpretation trap |
|---|---|---|
| Excitation setting or droop mismatch | Each regulator mode, terminal voltage and Q | Assuming identical voltage indications mean identical internal EMF |
| Transformer ratio mismatch | Actual tap, ratio and common voltage base | Comparing machine-side volts without referring them to one side |
| Unequal coupling impedance | Branch reactances and conductor configuration | Expecting equal currents from equal MW dispatch |
| Common meter masking | Individual branch P, Q and RMS current | Treating small net Q as small branch duty |
Compare measurements taken at the same time. A regulator responding to a changing grid can create an apparent mismatch if one unit’s reading is logged several seconds later. Preserve meter location and sign convention, especially for absorbed reactive power.
Calculate the branch exchange hidden by net vars
Assume same-angle internal phase-RMS voltages 10.10 kV and 10.00 kV, referred to one side, with total coupling reactance 2.0 Ω at 50 Hz. Circulating current magnitude is 100/2 = 50 A. For a screening phase voltage of 10 kV, reactive exchange is approximately 3 × 10,000 × 50 = 1.50 Mvar. The net bus exchange can be near zero while both branches carry that current. Review individual current margins and coordinated regulator/ratio settings rather than accepting the common-bus var indication.
Check the transformer duty locally
Plot each branch current against its winding and connection limits, then examine the shared winding or bus current. The shared path carries the vector sum; individual paths carry their own current. A thermal assessment based only on the shared export point can miss a heavily loaded branch.
Corrections belong in a coordinated excitation and ratio review. Changing one voltage setpoint to improve a meter reading can move the other unit toward its excitation boundary. Use the small-signal model to choose measurements and study cases, then verify the revised settings in the complete plant model.
Verify the selected terminal ratio with a test method matched to the winding connection [2].
References
- IEC, IEC 60076-1:2011, Power transformers – Part 1: General.
- Ohlen, M., and Werelius, P., A Guide to Transformer Ratio Measurements, Megger Sweden, 2010-01-18, Definitions and TTR measurements.