Synchronous CTG Protection on the R–X Plane

A combustion-turbine generator (CTG) is a spinning electromagnet. The rotor field winding, fed with DC from the exciter, creates a flux that rotates in step with the grid. Two properties follow, and every function in this module comes back to them:

• The machine stays in step only while the field is strong enough. The magnetic coupling across the air gap is what holds the rotor in synchronism. If excitation is lost, that coupling weakens and the rotor slips.
• Its fault behaviour follows from flux decay. Immediately after a fault the machine looks like a voltage behind the small subtransient reactance $X''_d$. Over tens of milliseconds that rises to the transient reactance $X'_d$, and over seconds to the large synchronous reactance $X_d$. The same reactances set the protection characteristics.

Operators think in the P–Q plane. The OEM capability curve bounds safe operation with three thermal limits:

• Armature heating: a circle of radius $S = V\cdot I_{a,\max}$ centred at the origin.
• Field heating (over-excited, lagging): a circle centred at $(0,\,-V^2/X_d)$ with radius $V E_{fd,\max}/X_d$.
• End-region heating (under-excited, leading): stray flux heats the stator core ends. The shape is OEM-specific.

The steady-state stability limit (SSSL) adds a fourth boundary in the leading region. For a machine on manual excitation behind a system reactance $X_s$, the SSSL is a circle in the P–Q plane:

Relays measure impedance, not power. With generator-convention metering, the apparent impedance at the terminals is:

Under-excited operation ($Q<0$) lands in the fourth quadrant. Under this mapping the SSSL becomes a circle on the R–X plane with diameter running from $+jX_s$ down to $-jX_d$.

When the field fails (exciter trip, field breaker opening, a shorted or open field winding):

1. Internal EMF decays with the field time constant. The machine can no longer supply VArs and starts absorbing them.
2. The rotor accelerates slightly above synchronous speed and the machine runs as an induction generator. Slip-frequency currents heat the rotor body, wedges and the stator end iron.
3. The machine can draw reactive power of the order of its MVA rating from the grid. On a weak system, voltage sags across the area.
4. The apparent impedance swings from the first quadrant into the fourth and settles between $-X'_d$ (heavy load, high slip) and $-X_d$ (light load, low slip).

PRC-019: limiters must act before protection. NERC PRC-019 (coordination of voltage regulating controls with unit capability and protection; verify the current version) requires the Generator Owner to show that the excitation limiters operate before the protection does. The under-excitation limiter (UEL) must hold the machine inside the capability curve and the SSSL, and act before any 40 zone times out. The over-excitation limiter (OEL) and the V/Hz limiter must act before field-overload protection and the 24 trip. The usual evidence is one plot, on a common P–Q or R–X plane and at the relevant voltages, showing the capability curve, the SSSL, the limiter settings and the relay characteristics in the right order. The positive offset of Approach 2 makes this coordination tighter, which is one reason it needs a long delay. PRC-019 also applies to the voltage controls of IBR plants (inverter and plant-controller limiters against plant protection; verify the current applicability).

Things to try in the lab:

• Run the LOF simulation at P = 0.8, then at P = 0.2. The end point moves from near $-X'_d$ to near $-X_d$. Only Zone 2 catches the light-load case.
• Switch to Approach 2, set P = 0.2 and raise $X_{sys}$ to 0.4 or more. The weaker system sags V₁ below 0.9 pu and the accelerated Zone 2 timer trips first (about 4.8 s against 7.8 s for the normal delay). The threshold is sharp: at 0.3, V₁ only just dips below 0.9 pu and the accelerated element trips after the normal one. At P = 0.8, Zone 1 still operates first whatever the system strength.
• Drag the operating point into the leading region until you cross the SSSL. Compare where the SSSL sits relative to the Approach 2 Zone 2 circle.

The generator 21 element is a mho looking out through the GSU. It backs up line relays for faults that the system protection fails to clear. Because it is a backup, it trades speed for coverage, and its reach is limited on two sides:

• Zone 1 typically reaches the smaller of about 120% of the GSU impedance or the GSU plus ~80% of the shortest line's impedance (the rule the lab uses). It is delayed (≈0.5 s) so it never races the line's high-speed protection.
• Zone 2 reaches further into the system but has to stay clear of the load impedance at maximum output and depressed voltage. The lab draws it at the GSU plus 120% of the line impedance as an example; guides often start from the longest line and then cut the reach back for loadability. A quick screening rule keeps the reach along the load angle under ~80–90% of the load impedance, but that is a rule of thumb, not the regulatory test (see below). Delay is long (≳1 s) and power-swing blocking is usually applied.

What PRC-025 actually tests. PRC-025 does not use a percentage-of-load-impedance rule. Its attachment tabulates, for each relay type and location, the loading at which the element must not operate, and the options differ. For a distance relay at a synchronous generator, one commonly used option evaluates the apparent impedance at the unit's maximum gross MW as reported (for a CTG this can exceed nameplate at low ambient temperature), a reactive output of about 150% of that MW value, and 0.85 pu terminal voltage. The lab's second check uses that example loading with P fixed at the nameplate 0.85 pu and no extra margin factor. Treat it as an illustration and take the governing option, loading and margin from the current version of the standard. PRC-025 also applies to load-responsive relays at dispersed and inverter-based plants (for example GSU and collector overcurrent elements), through separate rows of the attachment with criteria of their own.

Any unbalance (an open conductor, a stuck breaker pole, an uncleared unbalanced fault) produces negative-sequence current $I_2$. Its field rotates backwards relative to the rotor, so the rotor sees it at twice system frequency. The 120 Hz eddy currents flow in the rotor surface, wedges and retaining rings, and heat builds up quickly.

The machine's short-time capability is expressed as a constant:

It is paired with a continuous I₂ capability, typically 5–10% depending on rotor construction (see IEEE C50.12/C50.13). The relay is set with K at or below the machine value and a pickup at or below the continuous limit.

The labs in this module cover 40, 21 and 46 because those are the functions that live on the R–X plane. A real CTG protection package does much more. IEEE C37.102 is the reference guide for all of the functions below; check which edition you are working to, and take the settings basis from the OEM and your utility's practice.

87G generator differential, and the overall (unit) differential. 87G compares the neutral-side and terminal-side CT currents of each phase. It is the primary, high-speed protection for stator phase faults, applied as a percentage-restrained or high-impedance element. On a high-impedance-grounded machine it does not see stator ground faults, because the fault current is limited to a few amps; that is the job of 64G. Most units also have an overall differential (87O; some drawings write 87GT, 87UD or 87U) around the generator, the GSU and usually the unit auxiliary transformer. Elsewhere in this course 87U means the unrestrained high-set differential element (Module 2.4), so check the drawing legend. It needs the same ratio and phase-shift compensation and harmonic restraint as the 87T in Module 2.4, and it gives a second, independent zone over the generator and GSU.

51V / 51C or 21 for system backup. A plain 51 is not enough for a generator. Its sustained fault current decays toward the level set by the synchronous reactance, which can fall below full-load current (especially with bus-fed static excitation), so a load-coordinated 51 may never pick up. A voltage-restrained 51V lowers its pickup in proportion to terminal voltage. A voltage-controlled 51C switches to a low pickup only below a voltage threshold. The 21 is usually chosen where the system lines are protected by distance relays, because its zones coordinate more naturally with theirs. Either element must be blocked on loss of potential and must meet PRC-025 loadability.

78 out-of-step. If the machine slips poles against the system, each slip cycle produces large current pulses and shaft torques. The 78 tracks the impedance locus through the generator and GSU region, typically with a mho supervised by blinders, and trips when the swing is unstable. It is most important when the electrical centre of the swing falls inside the generator or GSU, which is likely for large units on weak systems. The trip is usually timed so the breaker opens when the angle across it is small, because interrupting near 180° can exceed its out-of-phase rating.

81 abnormal frequency. Steam-turbine blades have resonant frequencies, so running away from nominal frequency accumulates fatigue. For combustion turbines the OEM limits also reflect compressor surge margin, combustion stability and output loss. IEEE C37.106 covers abnormal-frequency protection; the OEM supplies the time-at-frequency limits. Underfrequency settings must coordinate with the system under-frequency load-shedding program and stay outside the no-trip envelope in NERC PRC-024-4, which since 1 October 2026 covers frequency and voltage protection of synchronous generators (IBRs now fall under PRC-029-1; see Module 3.2).

50/27 inadvertent energization. If the generator breaker is closed in error, or flashes over, while the unit is at standstill or on turning gear, a three-phase energization makes the machine accelerate as an induction motor drawing several per-unit current, and rotor damage can occur within seconds. If only one or two poles close or flash over, the machine mostly heats from negative-sequence current with little acceleration, which 46 and the breaker-flashover logic cover. Many functions are blocked or insensitive at standstill. The scheme arms a fast overcurrent element whenever the terminal voltage has been low for a few seconds, and keeps it armed briefly after voltage returns so it is ready when the breaker closes. This matters most on CTGs started by a load-commutated inverter (LCI) static starter. An LCI start puts current into the machine at low voltage, which, depending on which CTs the 50/27 uses, can look exactly like inadvertent energization, so start-sequence logic normally blocks or desensitises the 50/27 during the start. Make sure that block cannot stay in place when the unit is not starting, and confirm the logic with the OEM.

60 loss of potential (LOP). A blown VT fuse makes the measured voltage collapse. To an impedance relay that looks like a close-in fault: a 21 mho through the origin operates, a voltage-restrained 51V drops its pickup below load, and an Approach 2 zone that encloses the origin can operate. A partial LOP (one fuse) distorts the apparent impedance instead of zeroing it, and can drive it into the Approach 1 offset zones too, which is why C37.102 practice blocks 40 on LOP whichever approach is used. The 60 detects LOP, either by comparing two VT sets or from sequence logic (voltage unbalance with no matching current unbalance), and blocks 21, 51V and 40.

64F field ground. The field winding is ungrounded, so a first ground fault does no harm on its own. A second ground shorts part of the field, unbalancing the air-gap flux; the result is vibration and possible rotor damage. The 64F detects the first ground, typically by injecting a DC or low-frequency signal, and alarms or trips according to the OEM's philosophy. Brushless exciters need a different measuring arrangement, such as a rotating detector with telemetry or pilot brushes.

Generator breaker failure and breaker flashover. Generator breaker failure works as in Module 1.3, but many generator trips involve little current: 32 reverse power and sequential tripping, and 24 or 81 trips at light load or during start-up and shutdown. (A 40 trip is not one of them, because a machine that has lost its field draws roughly rated reactive current.) So the current detector alone cannot confirm the breaker opened. The 52a path is essential. While the breaker is open and the unit is being synchronized, or after it has opened, up to about 2 pu voltage can appear across its contacts as the machine slips against the system, and one pole can flash over. A breaker-open-supervised neutral overcurrent element on the GSU neutral detects the flashover and initiates breaker failure.

Protection during start-up at low frequency. During an LCI start, and during coast-down, the machine runs from near zero up to rated frequency. Phasor relays that sample on a fixed 60 Hz basis can mis-measure well away from nominal frequency. Use frequency-tracking relays, or functions the vendor specifies for off-nominal operation, for at least 87G, 64G and 24. Overexcitation is a real risk during run-up because V/Hz rises if excitation is applied too early. 81 elements are normally blocked below a minimum frequency so they don't trip during the start.