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Nowadays, the electric connection circuits of power plants (based on fossil fuels as well as renewable sources) entail generator circuit-breakers (GCBs) at the generator terminals, since the presence of that electric equipment offers many advantages related to the sustainability of a power plant. In an alternating current (a.c.) circuit the interruption of a short circuit is performed by the circuit-breaker at the natural passing through zero of the short-circuit current. During the current interruption, an electric arc is generated between the opened contacts of the circuit-breaker. This arc must be cooled and extinguished in a controlled way. Since the synchronous generator stator can flow via highly asymmetrical short-circuit currents, the phenomena which occur in the case of short-circuit currents interruption determine the main stresses of the generator circuit-breaker; the current interruption requirements of a GCB are significantly higher than for the distribution network circuit breakers. For shedding light on the proper moment when the generator circuit-breaker must operate, using the space phasor of the short-circuit currents, the time expression to the first zero passing of the short-circuit current is determined. Here, the manner is investigated in which various factors influence the delay of the zero passing of the short-circuit current. It is shown that the delay time is influenced by the synchronous machine parameters and by the load conditions which precede the short-circuit. Numerical simulations were conducted of the asymmetrical currents in the case of the sudden three-phase short circuit at the terminals of synchronous generators. Further in this study it is emphasized that although the phenomena produced in the electric arc at the terminals of the circuit-breaker are complicated and not completely explained, the concept of exergy is useful in understanding the physical phenomena. The article points out that just after the short-circuit current interruption by the generator the circuit-breaker (when the GCB has been subjected at the metal contact terminals to the high temperature of a plasma arc, up to 50,000 K) between its opened contacts, there arises the transient recovery voltage (TRV) which constitutes the most important dielectric stress after the electric arc extinction. Since the magnitude and shape of the TRV occurring across the generator circuit-breaker are critical parameters in the recovering gap after the current zero, in this paper, we model, for the case of the faults fed by the main step-up transformer, the equivalent configurations, with operational impedances, for the TRV calculation, taking into account the main transformer parameters, on the basis of the symmetrical components method.

The concepts of science, including concepts related to sustainability such as exergy and embodied energy, were developed to describe aspects of the universe. A convincing example of the usefulness of embodied energy and exergy for analyzing systems which transform energy is the generator circuit-breaker (GCB) disconnection process.

Nowadays, the electric connection circuits of power plants (based on fossil fuels as well as renewable sources) entail GCBs at the generator terminals, since the presence of that electric equipment offers many advantages related to the sustainability of a power plant [

Possible faults interrupted by a generator breaker GB.

The configuration of the key fault current encountered by the generator breaker (GB) is represented in

Faults at location K_{1} are called Generator (G)-source faults or Generator-fed faults (which can be insulated or grounded three-phase and two-phases short-circuits);

Faults at location K_{2} are called System-source faults or Transformer (MT)-fed faults (which can be insulated or grounded three-phase and two-phases short-circuits);

Faults at location K_{3} are called Generator-fed faults, on the high voltage side of the main step-up transformer (which can be insulated or grounded three-phase and two-phases short-circuits, as well as single-phase short-circuits).

To interrupt these kinds of faults, generator circuit-breakers must be capable of interrupting not only the high symmetrical fault current, but also the higher asymmetrical faults currents resulting from high d.c. components of the fault current [

The highest asymmetry of the short-circuit current appears at Generator-fed fault (location K_{1}), and this is the reason that the next section of this study encompasses an analysis of delayed short-circuit current zeros.

Research findings [

In this paper the time interval is assessed when the current, in the case of the sudden three phase short-circuit, has not a zero passing. To shed light on the proper moment when the generator breaker must operate, using the space phasor of the short-circuit currents, the time expression to the first zero passing of the short-circuit current will be determined. We aim to investigate the manner in which various factors influence the zero passing delay of the short-circuit current.

A representation of phase currents in the case of sudden short-circuit at the terminals of synchronous generator emphasizes that, regardless of the switching conditions, within each time cycle there are two zero passings of the short-circuit current [

The study of transient processes of a synchronous generator sudden short-circuit can be performed with the space phasor of short-circuit currents [_{ss}_{a}_{d}_{d}_{q}_{0}_{d}_{a}

The scalar expressions of the sudden three-phase short-circuit currents _{A}_{B}_{C}_{ss}_{A}_{A}_{ss}_{ss}_{B}_{B}_{ss}^{2}_{ss}_{C}_{C}_{ss}_{ss}^{j}^{2π/3}.

As an example, the sudden short-circuit current through the stator phase A is as follows:
_{d}_{d}_{d}_{q}_{q}_{d}_{d}_{a}_{din}_{0}_{d}

Note that an a.c. circuit-breaker operates the circuit disconnection at the zero passing of the current. Still, in the case of a generator circuit-breaker the first zero passing of a short-circuit current can be delayed, since the analysis of relation (5) highlights three components of the short-circuit current, respectively: an aperiodic current, and the fundamental and the second harmonic currents. The full short-circuit current will not have a zero passing as long as the periodic component with fundamental frequency will be smaller than the resultant of the other two component. Since the last two components of the short-circuit current are damping with the same time-constant _{a}_{A}_{A}

It must be noted that the initial value of the aperiodic pulsating current of the sudden short-circuit depends both on the rotor position at the short-circuit appearance (through the angle _{0}

The aperiodic pulsating current will miss only if at the moment of short-circuit appearance:

Further we account for the hard situation, when _{0}

Analytically, the zero passing delay time _{zθ}

Under the assumption _{q}_{d}_{d}_{q}_{max}_{zθ}

Taking into consideration that the delay time is influenced by the synchronous machine parameters and the load conditions which precede the short-circuit, several numerical simulations are presented of the asymmetrical currents performed for the case of the sudden three-phase short-circuit at the terminals of synchronous generators from Turceni-Romania electrical power plant.

The calculated relations and simulations of the short-circuit currents (

Current locus (upper representation) and short-circuit current on phase A (lower representation) for a generator of 370 MVA of Turceni power plant, after an operation at rated load, with: (

Equation (9), although an approximate solution, emphasizes the immediate conclusions on upper value of _{max}_{max}_{d}_{a}_{d}_{d}

Related to the load regime preceding the short circuit, Equation (9) highlights that _{max}_{din}_{q}

The previous remarks are confirmed by the short-circuit current simulations. The first zero passing of the short-circuit current could occur only after 0.2–0.4 s after the short-circuit appearance, if the generator previously has operated with an inductive load. The asymmetrical current duration can reach 0.6–0.8 s if previously to short-circuit the generator was operating in an under-excited regime.

The action of voltage regulator should be also taken into consideration. Recall that a short circuit means a drop of the voltage at the machine terminals, and could note that moment precisely when the generator regulator has the tendency to raise the voltage to the rated value. For that purpose, the regulator increases the excitation current to the maximum limit. Because the field winding operates only on the direct axis, the regulator determines an increase of the short-circuit alternating component on this axis. The alternating current on the quadrature axis is not influenced by the regulator action. This way, the regulator influences the short-circuit current zero-passing moment. A phase current has a zero passing at the moment when the instantaneous value of the alternating component with the pulsation ω is greater than the pulsating current. The increase, determined by the regulator, of the short-circuit alternating current on the direct axis, always has a favourable effect on the breaking conditions, because it is accompanied by the rise of the alternating component of the short-circuit total current. Consequently, the corresponding increase of electric energy represents a useful component, meaning that exergy is not destroyed during the action of the voltage regulator.

Electric arc interruption is of great importance because an uncontrolled electrical arc in the apparatus could become destructive since, once initiated, an arc will draw more and more current from a fixed voltage supply until the apparatus is destroyed [

Although the phenomena produced in the electric arc at the terminals of the circuit-breaker are complicated and not completely explained, the concept of exergy is useful for understanding the physical phenomena [

We approach the electric arc analysis within Faraday’s theory for shedding light from the exergetic point of view of the interruption process. The arc resistance _{A}_{A}_{A}_{A}_{A}_{A}

With this result, we can write the electric arc power as:

The energy embedded in the arc circuit during its burning is:
_{max}

The amount of the energy embedded in the arc circuit between separating contacts is the most important factor governing the design of circuit-opening equipment. On one hand, if the electric arc does not appear, the network embedded magnetic energy would be converted to energy embedded in the electric field of the interrupted circuit, leading further to high over-voltages in the network. On the other hand, the circuit-breaker must resist the thermal stress of the energy embedded in the burning arc column.

An energy balance of the arc circuit can be assessed by writing the embedded energy _{A}_{S}_{M}_{m}_{A}_{a}_{A}_{a}

Consequently, in the circuit which includes the fault, the time constant of the armature pulsating current decreases according to the relation:

From an exergetic point of view we can write the exergy balance of the interrupted circuit during the arc burning as:
_{in}_{max}_{out}_{max}_{stored}

At the instant when the current passes through zero, the energy embedded in the magnetic field of the interrupted alternating-current circuit is returned to the source of supply.

At this point, it is useful to note and discuss several important points:

Taking into consideration the previous findings one could conclude that the appearance of an electric arc at the terminals of the circuit-breaker should not be seen as a damaging phenomenon since, if the electric arc would not appear the network embedded magnetic energy would be converted to electric energy, leading further to high over-voltages.

Due to the exergy of the arc, the aperiodic pulsating current of the short-circuit currents will decrease very quickly, starting at the moment of contact separation. Since the alternating components with the pulsation ω are not influenced by this resistance increase, the output exergy of the electric arc determines the first zero-passing of the phase currents and reduces the circuit-breaker stress. For an analytical assessment of the described phenomena, it is useful to know the ratio _{A}_{a}_{A}_{max}

Also, since, in the high currents domain, the electric arc voltage actually remains constant, the arc resistance increases, even when the current is decreasing. For a simple calculation, it is preferred to choose, on the stationary characteristic of the arc, the minimum value of the resistance _{A}_{max}_{a}_{aA}

Just after the short-circuit current interruption by the generator circuit-breaker (when the GCB has been subjected at the metal contact terminals to high temperatures, reported to be 20,000 K, and for special types of arcs up to 50,000 K [

The dielectric strength within the extinction chamber of the circuit-breaker should increase at a rate higher than the TRV; otherwise the electric arc may re-strike. The circuit-breaker capability in interrupting the new arc is strongly affected since the gas-filled space between the two electrodes has already an important conductivity and this time the electric arc exergy would be entirely used in a destructive process.

Although the mechanical disconnection of the three phases is performed simultaneously, because of the currents angle phase, the arcs extinction on the phases cannot be simultaneous. It is switching, first, the arc on the phase so its current is passing first through zero. Therefore, the TRV on the three phases are different, even in the same three-phase fault interruption. Moreover, the TRV occurring across the generator circuit breaker depends both on the fault location and on the fault nature. In the framework of this paper, we determine the TRV when the short circuits fed by the main transformer (MT) are interrupted, using the operational symmetrical components method.

Basically, any non-symmetrical three-phase system of currents or voltages can be decomposed into two symmetrical three-phase systems (of different sequences) and a system of single-phase quantities [

The TRV occurring across the generator circuit breaker is considered only at

Applying the operational calculus to the relations determined by the instantaneous symmetrical components method, we obtain the _{t+}(p)_{t-}(p)_{t0}(p)

Applying the o.s.c. method, the operational image of the TRV occurring across the GB poles after the current interruption can be determined. If the phase current interruption is modelled by the current injection _{k}_{k}_{e}

The method is general, and is suitable for application at the poles of any breaker, for any eliminated fault type, if both the elements across it and the network configuration are known.

Further in the paper we determine the TRV when short-circuits fed by the main transformer are interrupted.

The currents of short-circuits in _{2} (and interrupted by GB) are fed by the main transformer (MT). The generator transformers taken into consideration have the windings connected by the configuration _{0}

The TRV calculation configuration for the moment of the GB first phase opening is represented in

The current interruption has been considered as result of injection on phase _{k}_{A}

First phase opening at insulated three-phase short circuit.

When _{t+}(p) = Z_{t-}(p)= Z_{t}(p)

Operational equivalent circuit: (_{t+}(p) ≠ Z_{t-}(p)_{t+}(p) = Z_{t-}(p) = Z_{t}(p)

The TRV calculation configuration for the moment when the short circuit has been eliminated is represented in

The current interruption has been considered as result of injection on phase _{k}_{B}

Interruption of insulated two-phases short circuit.

Applying the o.s.c. method, the TRV operational equation becomes:

Equation (29) allows the operational representation in

When _{t+}(p) = Z_{t-}(p) = Z_{t}(p)

Operational equivalent circuits: (_{t+}(p) ≠ Z_{t-}(p)_{t+}(p) = Z_{t-}(p) = Z_{t}(p)

Applying the method of operational symmetrical components to determine the TRV which appears after the interruption of a short circuit fed by the main transformer represents an original contribution of the authors of this study. The method is suitable for application at the poles of any circuit breaker, for any eliminated fault type (fed by the main transformer or by the synchronous generator, as well), if the elements and configuration of the power network are known. The TRV which appears after the interruption of a short circuit fed by the transformer may be considered as an oscillation with the oscillation factor and the rising rate (RR) of TRV established by the transformer parameters: resistance, inductance, capacitance, and conductance.

Since the synchronous generator stator can flow via high asymmetrical short-circuit currents, which will not pass through zero many cycles after the fault appearance, in this paper, for shedding light on the proper moment when the generator circuit-breaker must operate, using the space phasor of the short-circuit currents, the time expression to the first zero passing of the three-phase short-circuit current fed by the generator has been determined. The manner in which the various factors influence the delay lasting of the first zero passing of the short-circuit current has been investigated.

This study demonstrated that, even though the phenomena produced in the electric arc at the terminals of the circuit-breaker are complicated and not completely explained, the concept of exergy is useful in understanding the physical phenomena. The appearance of an electric arc at the terminals of the circuit-breaker should not be necessarily be seen as a damaging phenomenon since if the electric arc would not appear the network embedded magnetic energy would be converted to a circuit electric field energy, leading further to high over-voltages in the network. Due to the arc exergy, the aperiodic pulsating component of the short-circuit current decreases very quickly, starting with the moment of contact separation. Since the alternating components with the pulsation ω are not influenced by this resistance increase, the output exergy of electric arc determines the first zero-passing of the phase currents and reduces the circuit-breaker stress. One could conclude that the embodied energy in the electric arc that appears in the generator circuit-breaker at the contacts opening has a favourable influence on the short-circuit current zero-passing, determining the decrease of time constant value T_{a}. We may conclude that, from the view point of the short-circuit current zero-passing, it is necessary that the generator circuit-breaker either has an important voltage drop in the arc (meaning a high electric arc resistance) or is able to interrupt the currents with an aperiodic pulsating component greater than the values stipulated by IEC Publication 60056 for the distribution circuit-breakers or those recommended by IEEE Std. C37.013-1997.

Modelling transient recovery voltage (TRV) of circuits has emphasized aspects with direct implication on commutation equipment. Thus, the o.s.c. method is able to be applied at the poles of any breaker, for any eliminated fault type, if the network configuration and elements are known. The rising rate (RR) of the TRVs occurring across the generator circuit breaker when the short circuits fed by the main transformer are eliminated can exceed the demands on standard distribution circuit-breaker. Hence, not only the IEC 62271-100 norm must be taken into consideration, but the capability to withstand high values of TRV and RR of TRV should be in compliance with IEEE Std. C37.013-1997.

The authors declare no conflict of interest