Switchgear and Circuit Breakers

Everything from Chapter 21 to Chapter 25 was arithmetic in service of a single decision. The sequence networks, the \(Z\)-bus, the subtransient reactances and the DC offset all existed to answer one question: how much current flows when this point of the network is faulted, and how much of it is still flowing when the contacts part? Chapter 25 ended with that number written on a nameplate. This chapter opens the nameplate and asks how the device behind it actually does the job.

Switchgear is the collective name for the apparatus that connects, disconnects and protects a circuit: circuit breakers, isolators, load-break switches, fuses, earthing switches, the instrument transformers of Chapter 36, the busbars they sit on and the enclosure around them. Within that family the circuit breaker is the only device that can make and break a circuit carrying fault current, on command, and repeatedly. Everything else either carries current, or breaks it once, or breaks it only when there is nothing worth breaking.

A breaker has three separate duties, and they conflict.

It must carry rated current continuously without its contacts or joints exceeding their temperature-rise limit — an argument about contact resistance and heat transfer that favours large, firmly pressed contacts. It must withstand fault current for the time the protection takes to decide, absorbing an \(I^2 t\) that may be a thousand times the rated \(I^2\) for a second — an argument about thermal mass and about the electromagnetic forces that try to blow the contacts apart at the first peak. And it must interrupt that current within a few cycles of being told to — an argument that favours light, fast-moving contacts with a long travel. No design satisfies all three comfortably; every breaker is a compromise among them.

The third duty is the hard one, and the reason is a single equation from Chapter 6. The network between the source and the fault is dominantly inductive, so

If a breaker could force \(i\) to zero in zero time, \(di/dt\) would be infinite and so would the voltage across the opening gap. Equivalently, the magnetic energy \(\tfrac12 Li^2\) stored in the network — for \(20\) kA in \(20\) mH, some \(4\) megajoules — has to be disposed of, and it cannot vanish. Something must either dissipate it or convert it. The arc that appears between the parting contacts is not a failure of the breaker; it is the controlled channel through which the network is persuaded to give up its energy at a survivable rate. Designing a breaker is therefore not the art of preventing an arc but the art of making one and then destroying it on schedule.

Follow the contacts as they separate. Long before any visible gap exists, the contact area has shrunk to a few microscopic bridges. The whole current crowds through them, the current density becomes enormous, and the bridges melt and then boil. What now fills the opening gap is not air but metal vapour at several thousand kelvin, and that vapour is already partly ionised.

Two mechanisms then keep the channel conducting. Thermal ionisation dominates in the body of the arc: at \(5000\)–\(20\,000\) K the gas molecules collide hard enough to strip electrons, and the free electrons accelerated by the field ionise still more. Field emission dominates at the cathode: the gap is short and the voltage across it, though small, gives a field of the order of \(10^6\) V/m at the contact surface, which pulls electrons directly out of the metal. Between them these supply the charge carriers the current needs.

Working against them are recombination of ions and electrons — favoured by high pressure, which brings the carriers together — and diffusion of charged particles out of the arc column into cooler surroundings. Everything a breaker does to extinguish an arc is a way of tipping this balance: cool the column, raise the pressure, blow the ionised gas away, replace it with an unionised medium, or lengthen the path so that the same voltage produces a weaker field.

The arc's terminal behaviour is peculiar and worth stating precisely, because it explains several later results. The voltage across an established arc consists of a cathode drop of roughly \(10\)–\(20\) V, an anode drop of a few volts, and a column drop proportional to length. Empirically the total obeys the Ayrton equation:

Here \(\ell\) is the arc length and \(A,B,C,D\) are constants of the electrode material and the surrounding medium. The important feature is the sign: \(V_{arc}\) falls as \(I\) rises. An arc is a negative-resistance element. Push more current through it and it gets hotter, more fully ionised, and less resistive, so the voltage needed to sustain it drops. This is why an arc, once struck, is stable and will not extinguish itself, and why an arc in series with a purely resistive circuit cannot be controlled by voltage alone.

Reading the same equation the other way gives the recipe for killing it. Arc resistance rises when \(\ell\) rises (a longer arc), when the current is forced down, when the column is cooled so that thermal ionisation weakens, and when the cross-section is constricted so the same current must flow through less ionised gas. Those four levers are, in order, arc lengthening, series-resistance insertion, cooling, and splitting or constriction — and every breaker in Section 35-8 uses some combination of them.

Only two strategies exist, and the choice between them is settled by whether the current ever reaches zero on its own.

The high-resistance method attacks the arc directly. Lengthen it, cool it, constrict it and split it into a series string of short arcs, each with its own cathode and anode drop. The arc resistance climbs until the voltage the arc demands exceeds the voltage the source can supply, and the current falls smoothly to zero. Splitter plates in an air-break breaker do this: a stack of steel plates draws the arc in magnetically and cuts one long arc into a dozen short ones whose cathode drops add to perhaps \(200\) V, which at \(415\) V is enough to choke the arc. The method is simple and needs no timing, but all the energy of the arc is dissipated inside the breaker. That is tolerable at \(415\) V and impossible at \(400\) kV. It is also the only method available for direct current, which is precisely why DC circuit breaking is so much harder than AC and why the HVDC schemes of Chapter 38 avoid it wherever they can.

The low-resistance or current-zero method exploits a gift that alternating current makes twice per cycle. At \(50\) Hz the current is genuinely zero every \(10\) ms, and at that instant the arc is momentarily starved: no current, no ohmic input, no fresh ionisation. The energy input to the arc column has already been falling for the previous quarter cycle, and around the zero the column cools rapidly. If in the microseconds that follow the gap can regain insulating strength faster than the circuit rebuilds voltage across it, the arc never restarts and the interruption is complete. The breaker's job is reduced to keeping the arc voltage low and harmless for up to a cycle, and then winning a short race at the current zero.

That race has two rounds, and a breaker can lose either. In the first few microseconds the gap still contains hot residual plasma and a small post-arc current flows. If the power fed back into that plasma by the rising voltage exceeds the rate at which the gap can carry heat away, the column re-heats and the arc restarts: this is thermal reignition, and it is governed by the rate of rise of voltage. Survive that and the gap becomes a cold dielectric, but a dielectric whose strength is still building as the contacts continue to travel apart. If the voltage crest arriving tens or hundreds of microseconds later exceeds that strength, the gap breaks down again: this is dielectric restrike, and it is governed by the peak of the voltage rather than its slope.

If the breaker loses the race it does not usually explode. The arc simply restarts, carries current for another half cycle, and gets a second chance at the next zero — by which time the contacts are further apart and the gap is stronger. A well-designed medium-voltage breaker may take two or three current zeros to clear. What it must not do is fail repeatedly until the contacts are fully open with the arc still burning, because then there is no more travel left to buy and the fault energy has nowhere to go but into the breaker itself.

Three terms are used loosely in conversation and must be kept apart in analysis.

The restriking voltage is the transient voltage that appears across the breaker contacts in the instants immediately after the arc current reaches zero. It is a high-frequency oscillation, it lasts a few hundred microseconds at most, and it is what the gap must withstand. Modern standards call the same thing the transient recovery voltage or TRV. The recovery voltage is the power-frequency voltage that remains across the open contacts once that transient has died away — for a terminal fault it is essentially the system voltage. And the rate of rise of restriking voltage, universally written RRRV, is the slope \(dv/dt\) of the transient, quoted in kV/µs.

To see where the transient comes from, reduce the network to the simplest circuit that contains the essential physics. Between the source and the breaker there is series inductance \(L\) — the source, transformer and line reactance the fault current flows through. Across the breaker terminal to earth there is capacitance \(C\) — busbar capacitance, bushing capacitance, the winding capacitance of transformers, the stray capacitance of the switchgear itself. Before interruption the arc short-circuits that capacitance and holds its voltage near zero. At the current zero the arc vanishes, and the capacitance must now charge up to whatever the source is offering. It does so through \(L\), and the result is an oscillation.

Write Kirchhoff's voltage law around the loop after interruption. The current now flowing is the charging current of the capacitance, \(i = C\,dv/dt\), so

Two observations make the solution immediate. First, because the fault current is limited by \(L\) it lags the source voltage by very nearly \(90^\circ\); at the instant the current passes through zero the source voltage is therefore at its peak \(E_m\). Second, the transient we are about to compute lasts tens of microseconds while the power-frequency source takes \(10\) ms to move appreciably, so over the whole transient \(e(t)\) may be treated as the constant \(E_m\). The equation becomes a step-driven undamped oscillator:

Everything the switchgear engineer needs is contained in those two lines. The capacitance overshoots the source voltage by exactly as much as it started below it, so the peak restriking voltage is \(2E_m\) — twice the crest of the phase voltage, reached after half a period of the natural oscillation. The slope is greatest where the cosine crosses its own mean, at \(\omega_n t = \pi/2\), and there the transient is climbing at \(E_m\omega_n\). An "average RRRV" is often quoted as well: the peak divided by the time taken to reach it.

Three refinements convert this idealisation into something a standard would recognise.

Damping. Real circuits have resistance, so the overshoot never quite reaches \(2E_m\). The peak is written \(v_{peak} = k\,E_m\) with an amplitude factor \(k\) between about \(1.3\) and \(1.7\), the smaller values belonging to circuits with cable or several lines connected at the bus.

The first pole to clear. A three-phase breaker does not clear all three phases at the same instant; the poles reach a current zero at different times. The pole that clears first has to hold off more than the phase voltage, because the other two phases are still connected through the fault and drag the neutral. The multiplier is the first-pole-to-clear factor \(k_{pp}\), equal to \(1.5\) for a system with an isolated or high-impedance-earthed neutral and \(1.3\) for an effectively earthed system, the difference being exactly the neutral-shift argument of Chapter 23.

Short-line fault. If the fault is a kilometre or two down the line rather than at the breaker terminals, the line behaves as the distributed circuit of Chapter 12, not as a lumped capacitance. Travelling waves reflect from the fault and return, so the line-side voltage is a sawtooth whose initial slope is \(2 Z_0\,di/dt\) with \(Z_0\) the surge impedance. That slope is far steeper than the terminal-fault value even though the current is smaller, which is why the short-line fault is a separate and often decisive test duty.

The whole argument of Section 35-4 rested on the breaker waiting politely for a natural current zero. A breaker with a very powerful arc-quenching mechanism does not always wait. When the current to be interrupted is small — the magnetising current of an unloaded transformer, a few amperes; the current of a shunt reactor; a lightly loaded motor — the cooling applied to the arc is out of all proportion to the energy the arc is receiving. The arc becomes unstable, and the current is forced abruptly to zero some microseconds before its natural zero. This is current chopping, and the value \(i_{ch}\) at which it happens is a property of the interrupter, not of the circuit.

Chopping is a problem because it violates the premise that made interruption gentle. At the moment of the chop the inductance is carrying \(i_{ch}\) and holds magnetic energy \(\tfrac12 L i_{ch}^{2}\). The current is gone in an instant, so that energy has nowhere to go except into the capacitance across the interrupter. Equating the two stores gives the overvoltage directly.

The dangerous factor is \(\sqrt{L/C}\), the surge impedance of the trapped circuit. For a loaded feeder it is a few hundred ohms and the overvoltage is negligible. For an unloaded transformer or a reactor, where \(L\) is the magnetising inductance — tens of henries — and \(C\) is only the winding and bushing capacitance of a few nanofarads, \(\sqrt{L/C}\) can exceed \(50\) kΩ. A chop of four or five amperes then produces hundreds of kilovolts across equipment rated for a fraction of that, as Example 3 works out. The failure that follows is usually not in the breaker but in the transformer winding it was switching.

Three defences are used, and they are used together. Contact materials are chosen to chop as gently as possible: the chromium–copper alloys of a modern vacuum interrupter chop at \(3\)–\(5\) A where the pure-copper contacts of early designs chopped at \(10\)–\(15\) A. Surge arresters are installed at the terminals of the switched equipment, clipping the transient at a level the insulation can accept. And the resistance switching of the next section damps the oscillation before it can develop a crest.

Both problems so far — a restriking voltage that overshoots to \(2E_m\), and a chopping surge of \(i_{ch}\sqrt{L/C}\) — have the same root cause: an undamped \(L\!-\!C\) oscillation. The cure is therefore the same in both cases, and it is the oldest trick in switchgear. Connect a resistor \(R\) permanently across the breaker's main contacts, and let it stay in circuit for the few milliseconds between the main contacts parting and a small auxiliary interrupter opening in series with the resistor. This is resistance switching.

What the resistor does can be read straight out of the differential equation. After the main arc is extinguished the source current divides between the capacitance and the resistor, \(i = C\,dv/dt + v/R\), and the loop equation becomes

This is the standard second-order form of Chapter 27's swing equation and of every damped oscillator: the natural frequency is unchanged at \(\omega_n = 1/\sqrt{LC}\), and the damping term is \(1/RC\). The response is oscillatory only while the damping term is smaller than \(2\omega_n\). Setting the two equal locates the boundary.

A shunt resistance equal to half the surge impedance of the interrupting circuit makes the response critically damped. Below that value the response is overdamped and slower still; above it the oscillation reappears. Note the direction of the inequality carefully: smaller resistance gives more damping, because the resistor is in parallel with the capacitance, not in series with the loop.

At exactly \(R = R_c\) the two roots of the characteristic equation coincide at \(-\alpha\) with \(\alpha = 1/(2RC)\), and substituting \(R_c\) gives \(2R_cC = \sqrt{L/C}\cdot C = \sqrt{LC}\), so \(\alpha = \omega_n\) exactly. The response and its slope are then

Resistance switching is not free and is not universal. The resistor must absorb real energy for the few milliseconds it is in circuit, so on an EHV breaker it is a substantial stack of ceramic elements with its own thermal rating and its own auxiliary interrupter to maintain. Where the duty permits, designers prefer the cheaper relative: a grading capacitor connected across each interrupting chamber. Its first job is to share the recovery voltage equally among the two or four breaks in series, since without it the stray capacitance to earth would load them unequally and the outermost break would take most of the voltage. Its second job is to add to \(C\) in the formulae above, lowering \(\omega_n\) and therefore lowering the RRRV. Example 2 quantifies the second effect.

Chapter 25 produced the fault currents; the nameplate is where they are compared with what the breaker can do. Every entry answers a specific physical question, and a breaker is suitable only if every entry clears its corresponding duty.

Four of these deserve their arithmetic written out.

Breaking capacity in MVA. Historically a breaker was rated not in kiloamperes but in megavolt-amperes, the product of the rated line voltage and the rated breaking current in three-phase form. The number is fictitious as a power — no real \(3\phi\) apparatus delivers it — but it is the quantity a fault-level study naturally produces, and it survives in specifications and in examination questions.

Symmetrical and asymmetrical breaking current. Chapter 21 showed that the fault current in the first cycles is an AC component plus a decaying DC offset. The rms of that combination, evaluated at the instant of contact separation, is the asymmetrical breaking current. Writing the DC component as a fraction \(\delta\) of the AC peak, so \(I_{dc} = \delta\sqrt2 I_{ac}\),

Making current. Closing onto an existing fault is a purely mechanical and magnetic duty, decided by the crest of the very first loop of a fully offset wave. The theoretical crest is \(2\sqrt2 I_{ac} = 2.83 I_{ac}\), but the DC offset decays measurably during the first half cycle, so a doubling factor of \(1.8\) rather than \(2\) is used, giving \(1.8\sqrt2 = 2.55\). IEC 62271-100 rounds this to \(2.5\) at \(50\) Hz and \(2.6\) at \(60\) Hz, the shorter \(60\) Hz half cycle allowing less decay.

Short-time rating. While the fault persists the breaker is simply a conductor being heated. For durations under a second or so the heating is adiabatic, so the temperature rise depends on \(\int i^2 dt\) alone and a rating at one duration converts to another by holding \(I^2t\) constant.

Finally, the rated operating sequence states how quickly the duty may be repeated. The standard non-autoreclosing duty is \(\text{O}-3\,\text{min}-\text{CO}-3\,\text{min}-\text{CO}\): open, wait three minutes, close-and-immediately-open, wait, repeat. For a line with rapid autoreclosing the interval shrinks to \(\text{O}-0.3\,\text{s}-\text{CO}-3\,\text{min}-\text{CO}\), and the \(0.3\) second dead time is what allows the arc path of a transient flashover to deionise before the line is re-energised — the same deionisation physics as Section 35-2, applied to the air around an insulator string instead of to the inside of an interrupter.

Every breaker in service solves the same problem — remove charge carriers from the gap faster than the restriking voltage can exploit them — and the classification of breakers is simply a classification of the substance used to do it.

Air-break breakers interrupt in air at atmospheric pressure and rely on the high-resistance method. The arc is drawn into an arc chute by the magnetic field of its own current, sometimes helped by a blow-out coil, and there it is lengthened, cooled against insulating side walls and split by steel splitter plates into a series of short arcs. Adding up the cathode and anode drops of a dozen short arcs produces an arc voltage exceeding the supply, and the current is choked. This is the mechanism of every low-voltage moulded-case and air circuit breaker and of medium-voltage designs up to about \(15\) kV. Above that the arc voltage needed becomes impractical.

Air-blast breakers switch to the current-zero method and attack the arc with a jet of compressed air at \(20\)–\(30\) bar, blown either along the arc axis or across it. The blast removes the ionised gas bodily and replaces it with cold air, so the dielectric recovery is very fast and the arcing time very short. Air-blast breakers dominated the \(220\)–\(400\) kV range for a generation. They have no fire risk and no carbonising medium, but they require a compressed-air plant with its own reliability problems, they are extremely noisy, and their fast recovery is accompanied by a strong tendency to chop small currents. They have been almost entirely displaced by SF₆.

Oil breakers strike the arc under insulating mineral oil. The arc decomposes the oil into a gas that is roughly \(70\%\) hydrogen — which has an exceptionally high thermal conductivity and is therefore an excellent arc cooler — and the gas bubble raises the local pressure, which drives recombination. In a bulk-oil breaker the tank holds a large volume of oil that serves both as the interrupting medium and as the insulation to earth. In a minimum-oil breaker the arc is confined to a small insulating chamber and the oil volume falls by an order of magnitude, with cross-jet or axial explosion pots directing the gas flow across the arc at the current zero. Oil breakers are robust and cheap but they carbonise their own medium, so the oil must be tested and replaced, the contacts eroded by each operation must be inspected, and the fire risk of hot oil under pressure is real. New installations are rare.

Vacuum breakers remove the medium altogether. At \(10^{-7}\) torr there are too few molecules to ionise, so the only conducting material in the gap is metal vapour boiled off the contacts themselves. That vapour is generated only while current flows; at the current zero the supply stops and the vapour condenses on the shields in a few microseconds. Dielectric recovery is therefore extraordinarily fast, of the order of tens of kilovolts per microsecond, and a gap of \(8\)–\(20\) mm suffices at \(36\) kV. A vacuum interrupter is sealed for life, needs no maintenance, has no fire risk, produces no by-products, and tolerates tens of thousands of load-current operations, which makes it the natural choice for the medium-voltage distribution switchgear and motor-starting duty of Chapter 2's distribution level. Its weaknesses are the chopping of Section 35-5 and, historically, a voltage ceiling — although vacuum interrupters at \(72.5\) kV and above are now in service and the ceiling is rising.

SF₆ breakers use sulphur hexafluoride, a heavy, inert, non-toxic gas that is strongly electronegative: a free electron colliding with an SF₆ molecule is captured to form a heavy, slow negative ion. Removing free electrons is exactly what deionisation means, so SF₆ both quenches the arc quickly and, once quenched, insulates far better than air — about two and a half times the dielectric strength at the same pressure, and more at the \(5\)–\(7\) bar used in practice. In a puffer design the moving contact drives a piston that compresses gas and blows it through the arc; self-blast and rotating-arc designs let the arc's own energy generate the blast pressure, cutting the mechanical operating energy sharply. SF₆ now covers the whole range from \(12\) kV to \(800\) kV and makes gas-insulated substations possible. Its drawback is environmental: SF₆ has a global warming potential some \(23\,500\) times that of carbon dioxide and an atmospheric lifetime of millennia, so leakage is tightly regulated and the industry is actively developing fluoronitrile mixtures, CO₂-based gases and clean air as replacements.

A breaker is not the only way to open a circuit, and on most of the network it is not the cheapest.

A fuse is a deliberately weak conductor that melts, vaporises and then extinguishes the resulting arc. It is detector and interrupter in one component, it needs no relay, no CT, no trip supply and no moving parts, and its operating time falls extremely steeply with current — which is exactly the characteristic wanted, and hard to obtain from a relay. Its vocabulary is small and precise:

The HRC (high rupturing capacity) fuse is the engineered version: a silver or silver-plated copper element, punched with restricted sections so that melting starts simultaneously at several points, embedded in graded quartz sand inside a ceramic body. The sand absorbs the arc energy and quenches the several short arcs almost instantly, and a small blob of tin alloyed to the element — the M-effect — lowers the melting point locally so that a sustained mild overload also clears without needing the element to reach the melting point of silver.

The property that a breaker cannot match is current limiting. At high prospective currents the element melts within the first two or three milliseconds, long before the first peak of the fault wave is reached, so the current is cut off at a value far below the prospective peak. Both the electromagnetic force, which goes as \(i^2\), and the let-through \(I^2t\) are then reduced by an order of magnitude or more. That is why a fuse is used to back up a contactor or a moulded-case breaker whose own breaking capacity is modest, and why cable protection at a switchboard is so often a fuse rather than a relay. The trade is that a fuse is single-shot, cannot be tripped by anything but its own current, and can leave a three-phase load single-phased if only one phase clears.

An isolator, or disconnector, is at the opposite extreme of sophistication: a switch with no arc-quenching capability whatever. Its purpose is not to interrupt current but to provide a visible, verifiable, air-insulated break so that maintenance staff can work on a circuit knowing it is dead. Because it cannot quench an arc it must be operated only when the current through it is already essentially zero, which means only after the associated circuit breaker has opened. Opening an isolator on load is one of the classic switchgear accidents, and it is prevented by mechanical and electrical interlocking rather than by instruction.

The standard sequence for taking a feeder out of service runs: open the circuit breaker; confirm it is open; open the line-side isolator; open the bus-side isolator; close the earthing switch; apply the safety document. Restoration reverses it exactly. The interlock scheme enforces two rules — an isolator may move only when its breaker is open, and an earthing switch may close only when both isolators are open — and those two rules eliminate the entire class of accidents. Between the isolator and the breaker sits the load-break switch, which has enough arc control to interrupt load current but not fault current, and which combined with a fuse makes the cheap and very common switch-fuse unit of a distribution substation.

Take \(50\) Hz throughout and treat the source voltage as constant at its peak over the duration of any restriking transient.