MPT Differential (87T), REF (87N) & V/Hz (24)

A differential relay applies Kirchhoff's current law to a protected zone. Measure every current entering and leaving the zone; if they don't sum to zero, current is going somewhere it shouldn't, and that is a fault inside the zone. For a bus or a line, that is nearly the whole story.

A transformer is harder because, even with nothing wrong, the currents on its two sides do not simply cancel:

• Different magnitudes. The 34.5 kV side carries several times the current of the HV side, measured through CTs of different ratios.
• Phase shift. A YNd1 MPT shifts the LV currents by 30°.
• Zero sequence. A grounded-wye winding can carry I₀ that the delta side never sees.
• Magnetising current flows only on the energised side: small in steady state, enormous during inrush or overexcitation.
• On-load tap changers change the ratio in service, so the "balance" you set on day one does not hold at every tap.
• CT errors, small in steady state and large if a CT saturates (Module 2.3).

Every 87T setting exists to manage one of those effects. This module walks through them in order, with the operate–restraint plane as the central picture.

A numerical relay first scales each winding's secondary current by a TAP so that rated power on a chosen MVA base reads 1.0 pu on every winding:

It also applies internal phase-angle compensation for the vector group and removes zero-sequence current from any grounded-wye winding, so an external ground fault on the HV system does not look like differential current. That is why modern practice connects every CT in wye and lets the relay compensate, rather than delta-connecting CTs as electromechanical schemes did.

Worked example

A representative collector MPT is rated 100/133/167 MVA (ONAN/ONAF/ONAF), 230/34.5 kV YNd1. It has 1200:5 multi-ratio HV bushing CTs used at full ratio and 3000:5 LV CTs. Compute the TAPs on a 100 MVA base and a 167 MVA base. What does O87P = 0.30 pu mean in primary MVA on each?

The relay computes an operate quantity and a restraint quantity for each phase. This lab uses the average-magnitude definition (others use maximum or sum; check your relay):

Here $\vec I_{W1}$ and $\vec I_{W2}$ are the TAP-scaled, compensated winding currents, not the positive- and negative-sequence currents $I_1, I_2$ used elsewhere in the course.

A through-current with perfect CTs gives $I_{OP}=0$. An internal fault fed from one side gives $I_{OP} = 2I_{RT}$. The characteristic sits between the two:

Sizing SLP1 from the tap changer

Suppose the same 230 kV MPT has an HV on-load tap changer spanning 195.5–253 kV (a representative range; many MPTs have a de-energised tap changer instead, with a much smaller in-service error). Relative to the nominal ratio used for TAP:

Inrush. Energising a transformer at an unfavourable point on the voltage wave, especially with remanent core flux, drives the core into saturation for part of each cycle. IEEE C37.91 and manufacturer literature put the instantaneous peak at roughly 8–30× rated current depending on size and design (12–15× is commonly cited for large units; treat these as representative), decaying over hundreds of milliseconds to seconds. It flows on one side only, so it is all differential current. The waveform is asymmetric and rich in 2nd harmonic, which is the basis for 2nd-harmonic blocking or restraint.

Overexcitation. High voltage or low frequency (V/Hz above about 1.05–1.10 pu) saturates the core symmetrically. The exciting current carries odd harmonics; the 3rd is trapped in delta windings and removed by zero-sequence filtering, so the 5th harmonic is the usable signature.

For a ground fault at a fraction $x$ of the way from the neutral of a grounded-wye winding, the driving voltage is only $x$ of phase voltage, and only $x$ of the turns couple the fault current to the line side. The phase current change scales roughly as $x^2$, and 87T's zero-sequence removal subtracts a further third. Faults in the bottom 20–30% of the winding can be invisible to 87T.

REF compares the neutral CT current with the residual sum of the phase CTs ($3I_0$) for that winding only. It is supervised directionally and checked for CT saturation, and it sees a current proportional to $x$. REF matters most on impedance-grounded windings where fault current is limited.

The 5th-harmonic block keeps 87T secure during overexcitation, but something still has to protect the core. That is the Volts-per-Hertz element (24), usually a definite-time alarm stage plus an inverse-time trip stage, coordinated below the manufacturer's overexcitation capability curve.

The complete MPT package in a collector substation typically includes: dual-slope 87T with 87U, REF on grounded-wye windings, 24, sudden pressure (63) and other mechanical devices (gas accumulation, oil and winding temperature), backup phase and ground overcurrent (50/51, 51G on the neutral), and HV breaker-failure logic that keys direct transfer trip to the remote utility terminal.