An adaptive single-pole automatic reclosing method for uncompensated high-voltage transmission lines

Electric Power Systems Research 166 (2019) 210–222

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An adaptive single-pole automatic reclosing method for uncompensated high-voltage transmission lines

T

⁎

Ivars Zalitis, Aleksandrs Dolgicers , Jevgenijs Kozadajevs Faculty of Power and Electrical Engineering, Riga Technical University, Riga, Latvia

A R T I C LE I N FO

A B S T R A C T

Keywords: Adaptive single pole autoreclosing Line model Arc modeling

This paper proposes an adaptive single-pole reclosing method for uncompensated high-voltage transmission lines. This method is based on the dependence of the fundamental-frequency line-side voltage of the faulted phase on the equivalent fault path resistance representing the arc state and the healthy phase power flow. The moment of stabilisation of the post-arc regime is determined by the absolute value of the real part and the rate of change of the real and imaginary parts of this voltage, ensuring restoration of sufficient insulation strength. The setting is adapted on the basis of interconnected models used for online estimation of the pre-fault regime, fault distance estimation, calculation of the double line interruption regime of the whole network with symmetrical components to estimate infeed for the detailed line model and threshold voltage determination by line model output. The dynamic MATLAB SimPowerSystems simulations under different load flow and arc conditions demonstrate the feasibility and performance of the proposed method.

1. Introduction It has been well established that phase-to-ground faults represent the most common type of transmission line faults [1]. Fault statistics for the Baltic region have shown that, on average, (2012–2016) 87% of the 330 kV line faults and 75% of the 110 kV line faults were phase-toground faults [2]. Most of these faults are transient in nature: flashovers of insulators due to overvoltages caused by lightning strikes or stains of nesting bird excrements and temporary contacts with a trees [3]. It should be noted that in the Baltic region during the period from 2012 to 2016, an average of 85% of the 330 kV line faults and 64% of the 110 kV line faults were transient ones [2]. This means that in most cases a transmission line can be successfully reenergised for operation after the deionisation of an electric arc channel at the fault location. In highvoltage (HV) and extra-high-voltage (EHV) networks, single-pole automatic reclosing (SPAR) is often used because a disconnection of only the faulted phase decreases the impact of power imbalance and improves the system stability [4,5]. It is desirable to minimise the dead time of SPAR in order to decrease the time of power imbalance and circulation of significant zero-sequence currents caused by an openphase regime. However, an excessive decrease in the interruption time may lead to a reignition of an incompletely deionised electric arc channel, which would result in a serious blow to the dynamic stability of the power system and further damage to the switchgear and other

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system elements. The automatic reclose (AR) in the case of a permanent fault is undesirable for the same reasons. Conventional AR shots with a fixed dead time setting are still widely used [1,3], which considers the maximum necessary deionisation time with additional delays and performs AR without testing if the fault is of a transient nature. This allows the conclusion that an AR device that can adapt to the nature of the fault would prove to be beneficial both for the dynamic stability of the power system and for the longevity of its elements. Interest in the development of adaptive single-pole automatic reclosing (ASPAR) has surged since the 1990s when applications of digital relaying provided more opportunities to apply more complex algorithms. Several ASPAR methods were provided in Ref. [6], starting from the use of the absolute value of faulted phase voltage. The authors show that depending on the compensation of positive-sequence capacitance with shunt reactors, the faulted phase voltage would reach about 0.5–1 p.u. if the compensation coefficient was above 0.7 p.u. after the complete deionisation of the arc channel. This value is significantly higher than during the arcing process and provides a sufficient difference to ensure sensitivity but such an approach would be unsuitable when the line is uncompensated or the compensation coefficient is below 0.7 p.u. For uncompensated lines, a different approach is needed; one possible proposed solution is to use the angle between the faulted phase voltage and the zero-sequence current, which would decrease after the extinction of the fault arc [6]. However, the setting chosen is

Corresponding author. E-mail addresses: [email protected] (I. Zalitis), [email protected] (A. Dolgicers), [email protected] (J. Kozadajevs).

https://doi.org/10.1016/j.epsr.2018.10.012 Received 26 June 2018; Received in revised form 23 September 2018; Accepted 12 October 2018 0378-7796/ © 2018 Elsevier B.V. All rights reserved.

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criterion of the logic of the proposed ASPAR method is that the real part of the line-side faulted phase voltage should exceed a predefined setting, but in order to be certain that the arc extinction has concluded, additional criteria regarding the maximum value of the derivatives of the real and imaginary parts of the line-side voltage were included into the algorithm. An additional delay is then added, which is necessary to ensure the time required for the arc path to restore insulation strength up to the phase voltage after the arc extinction, according to statistics. The filtering of the fundamental harmonic allows avoiding the impact of transients caused by disconnection of the primary arc and arc nonlinearities. An online estimation of the pre-fault regime is used with the aim to determine the approximate power flow and electromotive forces angles before the fault, and calculations for a double-disconnected single-phase fault using the symmetrical components technique are performed, yielding the regime of the healthy phases, which makes it possible to calculate an adaptive setting of the real part of the line-side voltage of the faulted phase. In order to test the proposed method, multiple simulations were performed considering different secondary arc elongation speeds, fault locations and pre-fault power flow directions as well as permanent fault conditions with a significant equivalent fault path resistance. The key contribution of this paper is the development of the modelbased ASPAR method, which incorporates several interconnected models, an “outer” symmetrical-component-based model produces input values for a detailed “inner” line model, thus reducing the number of unknown variables and making the whole task feasible within an affordable time. The “outer” model, in its turn, receives feedin electromotive forces (EMF) values obtained as a result of an estimation of the pre-fault regime model parameters. Using interconnected models, on the one hand, makes it possible to reflect the impact of the wider network topology and the complexity of a disconnected fault in a particular transmission line, when determining an adaptive setting of ASPAR. On the other hand, each model operates with a minimal set of equations, making the task more feasible, especially for an embedded system with limited hardware.

driven by a hard compromise and would in most cases be between the angle value when the arc is present and that when the arc has been quenched. Therefore, an additional delay would be required not only after arc extinction to ensure full deionisation of the arc channel, but also between operation and actual arc extinction. The third method discussed in Ref. [6] is to control the period of the faulted phase voltage signal and it is proposed for cases with a partial compensation of line capacitance (up to 0.6 p.u.). The idea behind this approach is that when the arc is extinguished, a free voltage component with a lower frequency (defined by the number of the capacitance-shunt reactor circuits) will be present and by applying superposition it was calculated that the faulted phase voltage frequency could be 0.5–0.94 p.u. of the fundamental one depending on the compensation level. However, the decrease process of the measured faulted phase voltage frequency often has fluctuations, which may lead to a premature or delayed determination of arc extinction. Another approach was proposed in Ref. [7], where the time of arc extinction was determined by comparing a measured voltage signal with a modelled voltage sine signal with a DC offset. However, in order to evaluate the difference of the voltage signal introduced by higher-harmonic distortions, the ASPAR device would require a high sampling frequency and some additional voltage waveform distortions can be expected that are caused by the transient process triggered by the arc extinction. An approach using artificial neural networks (ANNs) for ASPAR is known, where the DC component and 1–4 harmonic components of recordings were used to train the ANN to recognise the moment when a full deionisation has occurred [8]. As has been mentioned before, ANNs require recordings for training and they are not guaranteed to be universal and different sets of training data might be necessary for different power systems. Another method recognises the moment when the arc is extinguished by an abrupt change in faulted phase voltage root mean square (RMS) value calculated over a running window [9]. This method considers disconnection of the healthy phases to quench the secondary arc, which may adversely affect the system stability and the presence of a sufficiently abrupt change of this RMS value should be tested for different fault and line loading conditions. The next method identifies two events of a voltage drop (the outset of the fault and the disconnection of the circuit breakers (CBs)) followed by a voltage increase at the moment when the secondary arc has been quenched [10]. This approach may fail if the fault is located close to the substation and with a small fault path resistance, because after the disconnection of the CBs the voltage drop would be insignificant or the algorithm would determine an increase in voltage because of the overvoltage wave after the fault disconnection. A method that detects the presence of a voltage DC component to determine the moment when the fault arc has been extinguished is also known [11]. A significant DC component surge is also present during the transient after the disconnection of the CBs and that requires an additional delay in order to prevent undesirable, premature operation of SPAR. A method implementing the Karrenbauer transformation in matrix form is also known, which is used to determine the change in the oscillation frequencies of the line-side voltage when the fault arc is extinguished [12]. This method is suitable only for lines with a high degree of compensation. Another method considers a sudden rise of second- and fourth-harmonic content in the current of the shunt reactor [13], which also requires the presence of shunt reactors. In this paper, a detailed steady-state model of an uncompensated line with a disconnected phase-to-ground fault has been analysed. It can be easily predicted that the steady-state fundamental frequency RMS value of the line-side voltage has a high degree of dependence on the equivalent fault path resistance and the power flow of the healthy phases. Further analysis of the real and imaginary parts of the fundamental frequency of the line-side voltage showed that the dependence of the real part of this voltage has a more uniform nature and contributes more to the RMS value after the deionisation, but sensitivity analysis shows a weakness at a high transient resistance corresponding to the pre-extinction state of the secondary arc. Therefore, the main

2. Theoretical background 2.1. The model of a disconnected faulted phase At first, a simplified model of a healthy phase and a disconnected faulted phase can be discussed (see Fig. 1). The fault has occurred at a distance of α p.u. from the beginning of the line, where the resistance RF has been connected to the ground representing the equivalent resistance of the electric arc channel. The healthy phase remains connected to its electromotive force (EMF) EH and current IH still flows to the load represented by the impedance ZL. The model shown in Fig. 1 can be represented with an equivalent circuit

Fig. 1. A simplified model of a disconnected faulted phase. 211

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Fig. 2. The equivalent circuit of the simplified model of a disconnected faulted phase.

(see Fig. 2). Here ZW denotes the wire’s own impedance, CH-E and CF-E are the capacitances to ground for the healthy phase and the faulted one, MF-H and CF-H are mutual inductances and capacitances. In order to obtain the parameters for this type of line equivalent circuit, it is necessary to consider the healthy phase and the faulted one as two circuits of phase wire and ground return path as proposed by Carson [14,15]. According to this method, the impedance of a phase wire can be calculated as follows:

Deq ⎞ ⎞ ⎛ ZW = RW + 9.88 × 10−4 ·f + i ⎜28.938 × 10−4 ·f ·lg ⎛⎜ ⎟ , ⎟ ⎝ req ⎠ ⎠ ⎝

CF − H =

ZF − H

⎜

2.413 × 10−8 ⎛ SHH ·dF − H ⎞ ·lg , Δ ⎝ SF − H ·rH ⎠

CH − E =

2.413 × 10−8 ⎛ SFF ·dF − H ⎞ ·lg , Δ ⎝ SF − H ·rF ⎠

⎜

⎜

⎟

(5) 2

⎜

⎟

⎜

⎟

⎜

⎟

(6)

where SFF, SHH are the distances between the phase wire and its own mirror image in the ground, SF-H is the distance between the faulted phase wire and the mirror image in the ground of the healthy phase, rF, rH are the radiuses of the faulted and healthy phase wires. The remaining voltage of the disconnected faulted phase UF consists of the capacitive component UFC and the mutual coupling component UFM . If the healthy phase current is IH = 0 A, the faulted phase voltage will be UF ≈ UFC , and since the impedance of capacitances is far greater than wire impedance, in this situation the line wire can be considered superconductive. This assumption allows expressing the capacitive component:

(1)

UFC = EH

ZF − E , (1/ jωCF − H ) + ZF − E

(7)

where ZF−E is

⎟

(2)

ZF − E =

where dF-H is the distance between the faulted phase wire and the healthy phase wire. The capacitance of both phase wires to ground and between them can be determined by equations [15]:

CF − E =

⎜

S S S Δ = lg ⎛ FF ⎞·lg ⎛ HH ⎞ − ⎛⎜lg ⎛ F − H ⎞ ⎞⎟ , ⎝ rF ⎠ ⎝ rH ⎠ ⎝ ⎝ dF − H ⎠ ⎠

where RW is the resistance of the phase wire, f is the voltage frequency, Deq is the equivalent depth of the current flowing in the ground (an average of 930 m) and req is the equivalent geometric radius of the phase wire. The mutual coupling impedance between the healthy phase and the faulted one is

Deq ⎞ ⎞ = 9.88 × 10−4 ·f + i ⎜⎛28.938 × 10−4 ·f ·lg ⎛ ⎟, ⎝ dF − H ⎠ ⎠ ⎝

2.413 × 10−8 ⎛ SF − H ⎞ ·lg , Δ ⎝ dF − H ⎠

RF (1/ jωCF − E ) . RF + (1/ jωCF − E )

(8)

Eqs. (7) and (8) show that if the fault path resistance RF = 0 Ω (metallic fault), UFC = 0 V and the faulted phase voltage will be UF ≈ UFM , which can be expressed as follows:

(3)

UFM = αIH ZF − H .

(4)

The approximate voltage distribution across the disconnected phase induced by mutual coupling can be seen from Fig. 3. It can be concluded that the capacitive component UFC is highly

⎟

⎟

Fig. 3. The distribution of voltage induced by mutual coupling across the disconnected phase in the case of a metallic fault. 212

(9)

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dependent on the fault path resistance, while the mutual coupling component UFM is dependent on the fault location and the current of the healthy phase. These parameters together constitute the actual faulted phase voltage UF. Assuming that the healthy phase loading can be measured or predetermined, the fault location is known and the voltage UF can also be measured at the substation, it should be possible to estimate the equivalent fault path resistance and determine the state of the arc channel.

2.2. The first approach towards the autoreclosing algorithm and the parameters necessary for its implementation Next, a more detailed three-phase line model with a ground wire connected between two systems will be analysed (see Fig. 4). The presented model considers all of the mutual couplings and capacitances between the phase wires and the ground wire but the ground-wire capacitance to ground has been omitted due to their minimal influence on the faulted phase voltage. The EMF sources shown are busbar phase-toground voltages obtained by solving the problem of two simultaneous open-phase faults at both ends of the line for the whole network model. The calculation process for this complex fault simultaneously performs regime calculation of two equivalent networks [16]. Approximate EMF values used for the detailed line model (see Fig. 4), are obtained by calculation of two separate single-open-phase fault regime at line ends. However, such calculations require knowledge of the EMFs, and their angles, of the actual network generators and the equivalent power system. Considering the relatively high inertia of electromechanical transients, the relative angles of the network generator EMFs inherited from the pre-fault state can be used with an acceptable tolerance. Therefore, an estimation of the pre-fault regime and corresponding EMFs is involved. Such estimation of EMFs significantly improves the accuracy of the calculation of the detailed line model regime. Separate calculation of the whole network regime with the symmetrical component method and a detailed line model regime as a phasor model allows reflecting the influence of the whole network as well as the effect of the disconnected fault on the line. It also yields a solution faster compared to a calculation of the whole network including the detailed line model. It should be mentioned that the model in Fig. 4 considers a non-transposed line, but transposition can be easily taken into account by extending the model with the same element sections, only reflecting changes due of phase positioning. The phase wire impedance ZW (not to be confused with the positive-sequence impedance), the ground wire impedance ZGW and the mutual coupling impedances ZMAB, ZMBC, ZMCA, ZMAGW, ZMBGW, ZMCGW representing MAB, MBC, MCA, MAGW, MBGW, MCGW can be calculated by Eqs. (1) and (2), respectively, based on the line tower configuration. The values of capacitances between phases CAB, CBC, CCA; between phases and ground CAG, CBG, CCG; as well as between phases and ground wire CAGW, CBGW, CCGW can be calculated by extending the scope of parameters of Eqs. (3)–(6) as shown in Ref. [15] according to the line tower configuration. The solution of the line model regime problem is performed by means of a topological nodal potential method, where equations are presented in matrix form [17]: YU = I − MZ−1E + YBUB. −1

T

(10)

where Y = MZ M is the matrix of nodal admittances, U is the vector of node voltages, I is the vector of current sources, M is the first incidence matrix of the network topology graph, Z is the matrix of network impedances, E is the vector of branch EMFs obtained by symmetrical components solution, YB is the base node admittance vector, which shows conductivities between the base node and other nodes, UB is the base node voltage. Additionally, ground is assumed as the base node (UB = 0 V) and the impedances of mutual coupling (see Fig. 4) are introduced into the impedance matrix Z as non-diagonal elements while the branch

Fig. 4. A detailed three-phase line model with a disconnected phase-to-ground fault.

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fault path resistances up to 1 MΩ for positive and negative pre-fault power flows. The obtained results are presented in graphs (see Figs. 5 and 6). The values of the impedances and capacitances used are the same as those of the 330 kV line used in the case study (see Table 1). It can be noted that the graphs presented in Figs. 5 and 6 show a significantly larger dependence on the fault distance α when the equivalent fault path resistance is between 0 and 1–5 kΩ. This indicates a larger impact of the mutual coupling component UFM for smaller fault path resistances. When the resistance RF exceeds this value, the impact of the fault distance decreases and a further increase of the faulted phase voltage is more linked to the increase of the capacitive component UFC . One can see that the absolute value of the faulted phase voltage stabilises when RF reaches 10–15 kΩ. According to a study about deionisation of HV fault arcs [18] it was considered that a 69 kV phaseto-ground voltage could not sustain ionisation of an arc with a resistance of above 50 kΩ, but in that paper a more conservative margin of 250 kΩ was used to determine deionisation time (for 330 kV it would be even higher). Thus, the absolute value of the phase voltage as a criterion for determining the extinction of fault arc is unreliable and a further analysis is necessary. Assuming that the currents of the healthy phases are zero and changing the equivalent arc resistance RF, one can see from voltage divider (7) that when RF is small, the voltage UFC ≈ UF is mainly determined by RF. A further increase of RF leads to an increase in the impact of CF−E on the faulted phase voltage and, consequently, the ratio Re (UF )/ Im (UF ) changes. In most cases there will be a power flow through the healthy phases and an additional rebalancing of the capacitive component and the mutual coupling component, which mostly influences the imaginary part of the faulted phase voltage, can be expected. To illustrate these effects, the dependences of the faulted phase voltage real and imaginary parts on the arc path resistance and the fault distance are presented in graphs (see Figs. 7 and 8). Graphs of the real and imaginary part for negative pre-fault power flow have practically the same form, but the imaginary part curves are shifted to positive values. Graphs of the real and imaginary part for a negative pre-fault power flow have practically the same form but the imaginary part curves are shifted to positive values. One can see that the characteristics of the real part of the faulted phase voltage closely resemble those of the absolute value from Fig. 5 with a more uniform dependence and, due to a higher absolute value, it has a larger impact on the RMS value of the faulted phase voltage when RF approaches a healthy insulation resistance. The real part of the faulted phase voltage also seems more sensitive to RF compared to just the RMS value of the voltage; therefore, a minimum value of this voltage could potentially be used as one of the arc extinction indicators, but more importantly, as a blocking mechanism to prevent AR to a permanent fault. The graph of

Fig. 5. The absolute value of complex voltage of the disconnected phase depending on the fault location and the fault path resistance for a positive prefault power flow.

Fig. 6. The absolute value of complex voltage of the disconnected phase depending on the fault location and the fault path resistance for a negative prefault power flow. Table 1 The specific parameters of the line. Parameter

Value

ZW, Ω/km ZGW, Ω/km ZMAB, Ω/km ZMBC, Ω/km ZMCA, Ω/km ZMAGW, Ω/km ZMBGW, Ω/km ZMCGW, Ω/km Z1L, Ω/km Z0L, Ω/km CAG, F/km CBG, F/km CCG, F/km CAB, F/km CBC, F/km CCA, F/km CAGW, F/km CBGW, F/km CCGW, F/km C1L, F/km C0L, F/km

0.108 + 0.609i 0.167 + 0.521i 0.049 + 0.297i 0.049 + 0.297i 0.049 + 0.254i 0.049 + 0.282i 0.049 + 0.298i 0.049 + 0.282i 0.059 + 0.326i 0.193 + 0.709i 5.255 × 10−9 4.291 × 10−9 5.255 × 10−9 1.665 × 10−9 1.665 × 10−9 0.544 × 10−9 1.942 × 10−9 2.276 × 10−9 1.942 × 10−9 10.774 × 10−9 7.673 × 10−9

impedances are the diagonal elements. In order to evaluate the dependence of the faulted phase voltage on the fault distance and the fault path resistance, numerous steady-state regime calculations of this line model (equation set in form of (10) for the equivalent circuit shown in Fig. 4) were performed with different fault locations and equivalent

Fig. 7. The real part of the complex voltage of the faulted phase as a function of the fault location and the fault path resistance for a positive pre-fault power flow. 214

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Up = 7500I p−0.4 V / m.

(12)

One of the main reasons why the secondary arc becomes extinguished is the elongation of the arc path and both the arc path voltage and the reignition voltage are initially calculated as gradients of the arc length, therefore it is important to describe the elongation process. The simplest approach is to use the linearized version shown in Ref. [19]:

larc

(13)

where larc is the arc length, larc0 is the initial arc length, tsec is the time counted from the beginning of the secondary arc, tenl is the time from the beginning of the secondary arc until the beginning of the arc elongation process, ksl is the slope coefficient defining the rate of increase of the arc length. The described approach to the depiction of the arc elongation is also used in the case study of this paper, with an assumption of the initial arc length larc0 being slightly larger than the insulator length, larc0 ≈ 1.1lins. The primary arc model is analogical to the secondary arc but the arc channel is assumed to be constant, retaining the initial arc length larc0. The primary arc cyclogram used in this paper is a piecewise linearization of the volt-ampere cyclogram shown in Ref. [20] (see Fig. 10). In the case of a primary arc, the peak voltage gradient Up is assumed to be 1500 V/m, which can used for arcs with a primary arc peak current Ip between 1.4 and 24 kA [20]. Since the primary arc is stable, the extinction and reignition of this arc are not considered. Both of the described arc models were implemented in MATLAB SimPowerSystems model, where two Thevenin equivalents of power systems S1 and S2 are connected by two line Π sections representing the parts of the line before and after the fault, two circuit-breaker groups (CB1A, CB1B, CB1C and CB2A, CB2B, CB2C). Measurements of voltages and currents from both sides of the line were taken (US1A, US1B, US1C, US2A, US2B, US2C, IS1A, IS1B, IS1C, IS12A, IS2B, IS2C). The SPAR block can also be seen controlling circuit-breaker CB1A (see Fig. 11). This model was also used for dynamic testing of the method proposed. The restrike occurring if the AR command is given while the secondary arc is present or the insulation strength of the arc path is below phase voltage is performed by switching from the secondary arc model to the primary arc model. As an example, a forced SPAR immediately after the secondary arc becomes extinguished and the arc restrike can be presented (see Fig. 12). It should be noted that for all of dynamic simulations of transient faults shown in this paper the primary arc model is connected 50–100 ms, and the secondary arc model — 100 ms, after the start of the simulations. When SPAR operates correctly, the restrike of the secondary arc does not occur and, after arc extinction, an increase and a DC offset of the arc voltage can be seen until the CB is switched on (see Fig. 13). However, what is more important for the proposed ASPAR algorithm is the line-side voltage at system S1 substation (see Fig. 14).

Fig. 8. The imaginary part of the complex voltage of the faulted phase as a function of the fault location and the fault path resistance for a positive prefault power flow.

the imaginary part of UF (see Fig. 8) shows the expected rebalancing of capacitive voltage component UFC and mutual coupling component UFM in the 2–10 kΩ section; one can see that the value of Im(UF) is not a reliable indicator itself. However, the change of the imaginary part in the section 10 kΩ–1 MΩ is more distinct compared to the real part; therefore, the stabilisation of at least the value of the imaginary part can be one of the indicators used to determine arc extinction. These considerations already provide some indication of possible criteria for an ASPAR algorithm; however, the real process involving a non-linear arc is much more complicated and a dynamic model of a secondary arc and, if possible, also a primary arc, should be considered. 2.3. The detailed model of the arc The secondary arc model used in this paper is an implementation of the piecewise linear volt-ampere cyclogram or the dependence of the voltage gradient on the secondary arc current (see Fig. 9) combined with a time-dependent arc reignition voltage described in Ref. [19]. The secondary arc reignition voltage Ure is calculated and applied during the arc extinctions:

Ure = (5 + 50Te )(t − Te ) h (t − Te ) kV /cm ,

⎧1, tsec < tenl larc 0 = ⎨1 + k (t − t ), t ≥ t , sl sec enl sec enl ⎩

(11)

where Te is the time from the beginning of the secondary arc till the fault arc extintion (intermediate of final), t is the simulation time and h (t − Te) is a delayed step function (0, t < Te; 1, t > Te). The Ip in the cyclogram denotes the secondary arc peak current, which can be determined by the steady-state regime calculation of a disconnected metallic fault, but the peak value of the arc path voltage gradient Up is determined from this current:

Fig. 9. The linearized cyclogram used for a secondary arc model.

Fig. 10. The linearized cyclogram used for a primary arc model. 215

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Fig. 11. The SimPowerSystems model used for the analysis and testing of the proposed method.

which the real and imaginary parts of the faulted phase voltage stabilise, graphs of the absolute values of the discrete derivatives of these signals were obtained (see Fig. 16). The graphs in Fig. 16 show that indeed after arc extinction the real and imaginary parts stabilise at their new values at about 0.4 s and, after further consideration, using the minimum value of the derivatives of the real and imaginary part can be regarded as a good precaution against possible intermediate arc extinctions, which would for a short time provide a sufficient value of the real part of the voltage. Based on the above considerations, it can be concluded that using the following criteria: the absolute value of the real part of the faulted phase line-side voltage exceeds the setting Re (UF ) ≥ SRe2 and the absolute values of the discrete derivatives of the real and imaginary part of the line-side faulted phase voltage fall below the settings ΔRe (UF )/Δt ≤ SRe , ΔIm (UF )/Δt ≤ SIm , should provide a safe way to detect a stable regime

2.4. Selection of ASPAR operation criteria As one can see from Fig. 14, during the dynamic simulations the arc extinction (0.369 s) is characterised by the line-side faulted phase voltage increase and a DC offset seen also at the fault location, but a large overvoltage with high-frequency components is also present after the disconnection of the primary arc current (in reality, this overvoltage would be more limited due to MOVs but these are more unfavourable conditions, which are useful to test the robustness of the proposed ASPAR algorithm). However, this overvoltage has little effect after the filtration of the fundamental harmonic, as can be seen by the graph of the real part of the line-side faulted phase voltage (see Fig. 15). The imaginary part graph is more unstable, but both parts indicate that after the arc extinction their values stabilise (the change after 0.42 s is due to the reclosure of the CB). In order to evaluate the time within 216

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Fig. 12. The arc voltage and current at the fault location during a premature autoreclose. Fig. 15. The real and imaginary part of the line-side faulted phase voltage at the system S1 substation during a successful autoreclose.

Fig. 13. The arc voltage and current at the fault location during a successful autoreclose. Fig. 16. The absolute values of the discrete derivatives of the real and imaginary part of the line-side faulted phase voltage at the system S1 substation during a successful autoreclose.

safety coefficient to secure operation in case of measurement errors (in this paper, 90% of the calculated value was used). The settings SRe and SIm also can adapt, for example, defined as percentages (above the noise level of the normal regime) of the current maximum value of these derivatives registered since the beginning of the secondary arc (in this paper, a 5% setting was used). The noise level can be decreased by additional filtering of the real and imaginary part signals (in this paper, the sliding average filter was applied). After closer examination of Figs. 15 and 16, one can also notice that the voltage drop does not occur immediately after the disconnection of the faulted phase (0.1 s) because of the sliding average filter and the line Π section capacitances sustaining the voltage according to the second law of commutation. In such situations, the derivative values are minimal and below the setting for a small time while the condition Re (UF ) ≥ SRe2 is also true. Therefore, a simple upper-boundary condition for the RMS value of the faulted phase voltage being below a setting UF ≤ SABS can be used, where SABS is the setting obtained by a primary fault regime calculation when the fault is on the other side of the line with a maximum possible fault

Fig. 14. The line-side faulted phase voltage at the system S1 substation during a successful autoreclose.

after arc extinction. The setting SRe2 would be calculated as an absolute value of the real part of the faulted phase line-side voltage, using the detailed line model (see Fig. 4) with online-updated steady-state EMFs and fault path resistance equal to insulation resistance, decreased by a

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resistance (about 100 Ω [21]) decreased by a safety margin (if this voltage significantly exceeds the setting SRe2, then using values of (1.5–3) SRe2 would be more beneficial). Additionally, a start signal, which indicates the open state of CBs, should be used. It should be noted that the proposed autoreclosing method is aiming at reducing the reclosing time to a minimum; the reclosing command from this method should be used for the leading switch reclose; this is why the synchronisation is not addressed. In addition to the main criteria of operation, additional delay block Δt1 is added, which first includes 5–10 ms on delay to further prevent undesirable SPAR operation during an immediate arc extinction or other unexpected short-duration compliance with the operation criteria. Then the signal for SPAR to operate is fixed but the final command given to the CB is delayed by 20 ms to ensure full arc channel deionisation after the extinction of the secondary arc. Based on the analysis of SPAR operation field data shown in Ref. [6], the maximal delay after the arc extinction required for secure reclosure for the 330 kV line is approximately 60 ms, but, since the algorithm operates when the regime stabilises after the arc extinction, it was observed that the chosen 20 ms delay is fully adequate. The start signal can also be used with a significant time delay exceeding possible reclose time Δt2 to indicate that the ASPAR has failed to operate, which means that the fault is permanent. This indication (RECLOSE FAIL) can be used as an alarm signal if the operation of the healthy phases is critical, or as a disconnection signal for circuit breakers of the healthy phases if it is necessary to avoid damage to transformer neutrals due to significant zero-sequence currents. The described criteria and functions can be implemented into the inner logic diagram of the proposed ASPAR method (see Fig. 17). Testing of the criterion Re (UF ) ≥ SRe2 is performed by a greater-than-or-equal block (GT2), and criteria UF ≤ SABS , ΔRe (UF )/Δt ≤ SRe , ΔIm (UF )/Δt ≤ SIm are tested by blocks of the same type (GT1, GT4 and GT5). Since all of the discussed criteria need to be met in order to safely perform AR, the outputs of these criteria blocks are connected by logical AND gates (AND1, AND2,

AND3, AND4). When all of the criteria are met, time delays of the block Δt1 are applied before the activation of output CB ON as described above. 2.5. The general structure of the proposed method The proposed inner logic block (see Fig. 17) of ASPAR is supported by other functions for adaptive setting purposes, as mentioned before. Most important of these are the online pre-fault regime estimation, the calculation of the network regime with a disconnected faulted phase and the detailed line model calculation. The required pre-fault regime estimation is described in Ref. [22] and the main idea of this procedure is to use random search within the possible limitations of free parameters with the aim to minimise the total model output difference compared to measurements: n

ξ=

∑ i

2 2 ⎛ (Re (ymi ) − Re (yi )) + (Im (ymi ) − Im (yi )) ⎞⎟ , Re (yi ) Im (yi ) ⎝ ⎠

⎜

(14)

where n is the number of available substation measurements, ymi is the value of measurement i, yi is the model output value for measurement i. Each time a set of unknown parameters X with a smaller total difference ξ is generated, this set is saved as the current best one, XB, and the current difference as its new minimum, ξMIN. The generation of new unknown parameter sets is repeated until a given number of such improvements, NIMPR, is reached. Then the limits of the random value generator are reduced:

K% ⎞ XN , XMAX , MIN = XB ± ⎛ ⎝ 100·2·s ⎠

(15)

where XMAX,MIN stands for the maximum and minimum parameter margins for the random generator, K% is the maximum difference from the nominal or average values of X elements in percent, s is the step

Fig. 17. Inner logic diagram of the proposed autoreclosing method. 218

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which interconnects two 330 kV systems, S1 and S2, with short-circuit powers of 2 GVA and 1 GVA and X/R ratios of 8 and 6 (see Fig. 11). The parameters of the detailed line model were calculated based on the phase and ground wire configuration shown in mm (see Fig. 20) and 2xAS-240 mm2 phase conductors with a separation of 40 cm and AS120 mm2 ground wire conductors. The line length is assumed at 120 km. The specific line parameters are presented in Table 1. These parameters are the same as defined in the description of Fig. 4 and were calculated by the same methodology, except Z1L, Z0L, C1L, C0L, which are the positive- and zero-sequence impedances and capacitances of the line used for line Π sections in the Simulink model. These were calculated according to Ref. [23]. During the calculation of both parameter types (phase and sequence), ground wires were considered as one equivalent ground wire. The testing will focus on the performance of the inner logic of the proposed ASPAR method because the fault location and estimation of the pre-fault regime were tested during the previous research [22]. Therefore, the fault locations and the EMFs for the systems are assumed to be known. As seen from the previous analysis, the fault distance has an insignificant impact on the steady-state value of the real part of the faulted phase line-side voltage and the setting SRe2. Because of this, only faults at the beginning, middle and end of the line (α = 0.001; 0.5; 0.999 p.u.) were considered. The operation of ASPAR was tested for faults at these locations in five different scenarios of arc elongation speed for both a positive pre-fault power flow (ES1A = 1.025ei0°; ES2A = 1e−i20° p.u.) and a negative pre-fault power flow (ES1A = 1ei0°; ES2A = 1.025ei20° p.u.). Scenarios of the secondary arc elongation speed are defined by the time from the start of the secondary arc until the beginning of the elongation process tenl and the slope coefficient ksl (see (13)). The insulator length used for the calculation of the initial arc length is assumed lins = 2.7 m. The list of the tested scenarios used for both power flow directions is presented in Table 2. The absolute steady-state values of the real part of the faulted phase line-side voltage was calculated to be 24371 V and 21819 V for positive

number of the parameter estimation process, XN stands for the nominal or average values of X elements. This process of unknown parameter generation and search limit restriction is repeated until the difference between a new best model output error and the previous best one, dξ = ξMIN − ξ, falls below an estimation process accuracy setting. The estimation of the pre-fault regime is to be performed online with regular updates until the occurrence of the fault. The measurements used for the estimation process are taken from power system branches connected to the substation where the device is installed. The unknown parameters estimated are the network load and generation active and reactive powers, which can then be used to calculate approximate pre-fault EMFs, which are later used for the calculation of a steady-state network regime with a disconnected faulted phase. The obtained EMFs are also necessary if the fault distance is estimated in the same way as in the pre-fault regime [22], but based on Figs. 7 and 8, it can be seen that steady-state values of the real and imaginary part of the faulted phase line-side voltage have a weak dependence on the fault distance when the equivalent resistance of the fault path reaches the insulation level. Therefore, obtaining an approximate fault distance for the detailed line model (see Fig. 4) with a simplified fault location method is also acceptable. Then the fault distance and the calculated busbar phase voltages can be used to obtain the setting SRe2 by calculating the detailed line model regime. The upper boundary setting SABS has to be calculated offline and the settings SRe and SIm adapt dynamically. Finally, the inner logic of the ASPAR method determines if and when to give a command to reclose the CB. This interacting sequence of operations can be illustrated with a general block diagram (see Fig. 18). The narrow arrows represent the input and output signals whereas the wide arrows represent the data flow within the proposed ASPAR method. 3. Case study The proposed ASPAR method has been tested on a 330 kV line,

Fig. 18. The general block diagram of the proposed method. 219

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Table 2 List of tested scenarios. The test number

tenl, s

ksl

α, p.u.

1 2 3

0.2

10

0.001 0.5 0.999

4 5 6

0.1

10

0.001 0.5 0.999

7 8 9

0

10

0.001 0.5 0.999

10 11 12

0

25

0.001 0.5 0.999

13 14 15

0

50

0.001 0.5 0.999

Fig. 21. The results of the proposed ASPAR method testing for a negative prefault power flow (transient faults).

on the interval mentioned in Section 2.4). The results including the time of arc extinction tEXT, the full deionisation time (when the reignition voltage exceeds the peak value of nominal phase voltage) – tDEION1 according to Eq. (11) –, the full deionisation time, tDEION2, considering the maximum statistical necessary time from the moment of the arc extinction (60 ms), the moment when the inner logic block AND4 with the 5 ms on delay is triggered, tAND4, the moment when the final output command to reclose the CB is given, tRECLOSE (for all results, zero time corresponds to the moment of secondary arc ignition), for positive and negative power flows are presented in Figs. 19, 20 and 21 . The constant setting recommendation is given for a comparison with the conventional AR shot method based on the empirical equation for deionisation time presented in Ref. [24]:

tdeoin =

Fig. 19. The line configuration considered during the testing of the proposed method.

1 U ⎡10.5 + N ⎤, 60 ⎣ 34.5 ⎦

(16)

where tdeoin is the time of full deionisation and UN is the nominal line-toline voltage in kV. According to Eq. (16), tdeoin ≈ 0.3344 s for 330 kV, this is close to the average value of local practice, the table in Ref. [1] and other empirical equations varying from 0.3 s up to 0.4 s. First, one can see that the constant setting covers most deionisation scenarios, with the exception of few scenarios, according to which the arc elongation process began with delays of 100 ms and 200 ms; however, usually this is of little importance since additional delays are often already added for safety reasons or introduced by the CB operation time [25]. However, as can be seen, for rapid arc elongation process scenarios there will be a significant unnecessary time gap between the moment of the actual deionisation and the reclosing command of a conventional AR device. On the other hand, the proposed ASPAR method has changed the time of the output signal, which exceeds the safe deionisation time according to the first approach, tDEION1, and is in most cases is the same, or exceeds, the statistical safe deionisation time tDEION2, which means that not only were the simulated AR procedures successful, but also the time reserve should be sufficient for deionisation in any case involving a real network. For further evaluation of the proposed algorithm, the operation diagrams of the inner logic of the proposed method for test 5 of positive power flow scenarios are presented in Figs. 22 and 23 (the graphs in Figs. 13–16 are also from this test). One can see that during the voltage drop after the disconnection of the fault, the logical AND2 becomes active for a short time but the possible operation is blocked by discrete derivative criteria tests GT4 and GT5. After that, the next time AND2 is active is shortly after the arc extinction at 0.37 s but AND4 is activated at 0.409 s because there is a

Fig. 20. The results of the proposed ASPAR method testing for a positive prefault power flow (transient faults).

and negative power flow directions resulting in settings SRe2 having the values of 21934 V and 19637 V. The study network used yields a SABS close to nominal phase voltage due to the proximity of both power systems, therefore this setting was simply assumed to be 30 kV (based

220

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Fig. 24. The line-side faulted phase voltage at system S1 substation during a permanent fault with a significant fault path resistance.

Fig. 22. The operation diagram of the inner logic of the proposed ASPAR method for the positive power flow test 5 scenario.

Fig. 23. The output of the proposed ASPAR method for the positive power flow test 5 scenario. Fig. 25. The operation diagram of the inner logic of the proposed ASPAR method during a permanent fault with a significant fault path resistance.

transient after the extinction of the arc as shown in Fig. 15; the GT4 and GT5 are activated later. As a result, the command to reclose the CB was issued 20 ms after the activation of AND4, about 330 ms since the ignition of the secondary arc. Besides the testing of the operation of the proposed ASPAR method during transient faults, it is also necessary to test its performance in the case of a permanent fault. In order to test the performance of the proposed method in possible unfavourable conditions, it was assumed that this permanent fault would occur at the other side of the line (α = 0.999 p.u.) and it would have a high equivalent fault resistance (RF) in the amount of 5 kΩ, which could represent a partially carbonised fallen tree. The test was performed for both power flow directions and for 1.5 s, while the delay Δt2 was chosen to be 1 s in order to test the blocking of the reclosing algorithm or indication of reclosure failure due to a permanent fault. During both tests, the algorithm of the proposed method successfully blocked the operation of SPAR. To illustrate the results of these tests, the faulted phase line-side voltage at the system S1 substation and operation diagrams of the test with a positive power flow are presented (see Figs. 24–26). On can see from Fig. 24 that after the disconnection of the primary fault, the measured voltage stabilises (about 0.3 s), but an insufficient value of the real part of this voltage is achieved, which is indicated by AND2 remaining deactivated after the initial voltage fall of the secondary arc (see Fig. 25), as it was expected according to the analysis in Section 2.2 of this paper. This is why the inner logic was not triggered and, as can be seen from Fig. 26, an indication about AR failure to activate was given at 1.1 s (1 s after the ignition of the secondary arc). This means that for permanent faults with an equivalent fault path resistance of up to at least 5 kΩ, the proposed ASPAR method would block operation (according to Fig. 7, it could be possible for this method

Fig. 26. The output of the proposed ASPAR method during a permanent fault with a significant fault path resistance.

to operate if RF reached the 10 kΩ limit; however, during permanent faults, which in the Baltic region are often caused by fallen trees, the tree tends to burn through in a short time, sometimes even before the operation of the relay protection, and thus cases with the equivalent fault path resistance remaining above this magnitude for a considerable time are rare [26]). 4. Conclusions The analysis of a detailed model of an uncompensated transmission line with a disconnected phase-to-ground fault has shown that the lineside voltage of the faulted phase is mostly dependent on the equivalent fault path resistance and the power flow of the healthy phases. It was found that the real part of this steady-state voltage can be effectively 221

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used as the main criterion for an adaptive single-pole autoreclosing algorithm, which can be further improved by adding the criteria of a minimum value of the discrete derivative of the real and imaginary parts of the voltage and a minimum time delay to avoid undesirable operation due to an intermittent arcing or other reasons. It was also concluded that modelling of nonlinearities and transients of the arcing faults is important for the development and testing of autoreclosing algorithms. In order to avoid an undesirable impact of these transients and nonlinearities on the autoreclosing algorithm, filters were applied and only the fundamental harmonic component of the faulted phase voltage was used. A potential disadvantage consisting in the dependence of the proposed method on a high accuracy class of the voltage transformers at the line side should be mentioned. The testing of the proposed method has shown that this method can successfully adapt to different fault locations, different loadings of the healthy phases and, more importantly, different arc elongation speeds, providing a sufficient time reserve to re-establish insulation strength and save reclosing time in cases of fast deionisation, which is beneficial for power system stability. The testing also showed that the proposed method can inhibit the autoreclosing command in case of permanent faults with high equivalent fault path resistances, which is also an important feature for adaptive autoreclosing algorithms compared to the conventional method of autoreclosing shots. The proposed method has a robust inner autoreclosing logic and this method is feasible and scalable due to separate calculations of the whole network regime and a detailed line model regime. These factors should facilitate the future development and implementation of the proposed method.

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