Abstract: When a single-phase ground fault occurs in a neutral-point ungrounded system, analysis of the formation and distribution characteristics of the transient current components of each phase on the feeder reveals that the transient current component (TCC) of the fault phase is composed of the self-supplied TCC provided by the non-faulty phases of the faulty feeder and the similar TCC provided by other non-faulty feeders. This important characteristic makes the extraction of characteristic frequency bands based on orthogonal wavelet decomposition feasible, effective, and stable. The judgment criterion for constructing a single-phase ground fault protection relay proposed in this paper is a theoretical definition and is therefore fixed, meaning no setting calculation is required, making it suitable for any distribution network with a neutral-point ungrounded mode. This protection method is easily integrated into distributed feeder protection bay units without the need for a monitoring system line selection module or dedicated line selection device. Extensive ATP and MATLAB simulations demonstrate that this principle can accurately identify different types of single-phase ground faults with high reliability and sensitivity. Keywords: power distribution system; neutral point ungrounded mode; transient current component; single-phase grounding protection; orthogonal wavelet analysis; characteristic frequency band 1 Introduction Currently, in systems with non-effective neutral grounding (including grounding via arc suppression coil, neutral point grounding via high resistance, or neutral point ungrounded mode), the detection of single-phase grounding faults is mostly based on the steady-state zero-sequence current of all feeders of the substation bus, constructed according to the principle of centralized line selection. This requires embedding a dedicated line selection module or device in the monitoring system. This principle is greatly affected by factors such as system operation mode and fault state, resulting in low reliability and poor accuracy in field operation. Currently, the following problems exist in distribution network grounding detection [1-4]: fault signals are superimposed on the load current, the steady-state amplitude is relatively small, and electromagnetic interference from the environment affects the correctness of fault identification; the system operation mode is variable, the fault state is variable, and there are many uncertain factors, thus requiring the detection method to have stronger adaptability; the dedicated line selection device has complex wiring and is not integrated with feeder protection, which is not conducive to feeder automation. Although these problems have been studied extensively [1-6], they have not yet been well resolved. Based on the analysis of the formation mechanism and distribution characteristics of transient components of current in each phase of the feeder, this paper proposes a new principle and judgment criterion for transient feeder protection against single-phase grounding faults, using the transient current component (TCC) and orthogonal wavelet decomposition algorithm. It forms the relay judgment criterion by extracting the ratio of characteristic measures between the feature bands of the three-phase transient current (FBTC). This criterion is based on the ratio coefficient of the characteristic band measures in the FBTC of the faulty and non-faulty phases. This criterion is independent of the operating mode, load or TA symmetry, fault state characteristics, etc., and is a fixed criterion based on theoretical analysis, exhibiting higher reliability, stability, sensitivity, and adaptability in its operating characteristics. This has been verified through extensive ATP simulations and MATLAB wavelet analysis. Due to space limitations, this paper focuses only on the neutral-point ungrounded mode system. 2 Basic Principles of Single-Phase Ground Fault Relay in Distribution Network 2.1 Formation Mechanism of Single-Phase Ground Fault TCC In a neutral-point ungrounded system, when a single-phase ground fault occurs in the feeder, in addition to the original load current, there is also a high-frequency transient capacitive current in the fault phase caused by the sudden drop in voltage of the fault phase and the rise in voltage of the non-fault phase. The steady-state power frequency current in this TCC is relatively small, while the high-frequency transient component is relatively large [3-6]. When there is a metallic ground fault, the amplitude of the transient ground current can reach 7-8 times that of the steady-state component, and the duration is very short, about 0.5-1.0 power frequency cycles [8]. Obviously, the amplitude and attenuation performance of the TCC are related to factors such as the capacitance to ground of the non-fault line in the relevant system, the angle of the phase voltage at the time of the fault, the fault transition resistance, and the fault distance. It is also affected by factors such as the asymmetry of the fault feeder, the performance of the TA, and the operating mode. These will be addressed in the new ground protection principle proposed in this paper. To facilitate the analysis of the capacitive current distribution characteristics during single-phase grounding faults in low-current grounding systems, the system is divided into two categories: ① single-phase grounding protection for the faulty feeder (FF), which is considered an in-zone fault; and ② single-phase grounding protection for all non-faulty feeders (HF), which is considered an out-of-zone fault. The current flow path of the faulty phase TCC indicates that its magnitude is related to the parameters of the faulty phase on FF, the parameters of the non-faulty phases, and the parameters on HF. These are the main loops for the single-phase grounding TCC. On the faulty phase of FF, the strength of the TCC is related to the enhancement effect of the non-faulty phases of FF and HF. The residual voltage of the faulty phase in the system is related to the fault state characteristics. Theoretically, based on the current flow path, in a system with only one faulty feeder, the faulty phase TCC is approximately twice the TCC of any non-faulty phase. When there are multiple feeders, due to the enhancement effect of the non-faulty phases of HF, the faulty phase TCC can be more than twice the TCC of any non-faulty phase. The judgment criteria for the single-phase grounding fault transient current protection relay in this paper are derived from this. The distribution of TCC indicates that the TCC of the faulty FF phase is composed of the self-supplied TCC provided by the non-faulty FF phases and the similar TCC provided by other HF phases. Theoretically, in a system with only one faulty feeder, based on the current loop direction, the faulty phase TCC is approximately twice that of any non-faulty phase TCC. When there are multiple feeders, the TCC of the faulty phase can be more than twice that of the non-faulty phases due to the amplifying effect of the non-faulty HF phases. Based on the correlation characteristics determined between the TCCs of each phase of FF and HF under the above ungrounded mode, the measurement of the fault characteristic frequency band or combined frequency band can be extracted using corresponding analysis algorithms (such as designing matched filters) to form the measurement ratio between the ground faulty phases, which serves as the criterion for constructing a single-phase ground fault transient current protection relay. According to the formation mechanism of TCC, this criterion is related to the neutral point grounding mode. As long as the distribution system is in a neutral point ungrounded or resonant grounding mode, this criterion must hold, and it is an inherent relationship established from basic theory, a constant correlation. 2.2 Orthogonal wavelet decomposition algorithm and characteristic frequency band metric characterization Wavelet analysis is a tool for processing non-stationary transient signals and has been widely used in power systems, such as power quality, relay protection, transient analysis, high voltage discharge detection and analysis fields [7]. In this study, many factors affect the frequency, amplitude and attenuation of TCC, and they are random and uncertain. According to the correlation between the fault phase TCC and the TCC of other components, the most closely related component of TCC is the transient characteristic of the capacitor charging current. Therefore, it is feasible to extract its characteristics by applying wavelet analysis. In the multi-scale analysis method, the time-frequency resolution varies with the scale. Orthogonal wavelet analysis is a multi-scale analysis. It further decomposes the low-frequency information after decomposition, thereby enabling the extraction of the frequency band reflecting the grounding characteristics in the TCC information. Let cj(n) be the signal to be decomposed. Performing one orthogonal wavelet decomposition yields smooth information cj+1(n) and detail information dj+1(n). [IMG=Smooth information cj+1(n) and detail information dj+1(n)]/uploadpic/THESIS/2008/1/2008010311103026467L.jpg[/IMG] where {hn} and {gn} are conjugate filters defined in multi-scale analysis (MRA). The steps of the grounding transient current protection based on the orthogonal wavelet decomposition algorithm are as follows: (1) Extraction of fault transient components. In order to extract the characteristic frequency band information of each phase TCC, the influence of the load current should be eliminated first. The fault transient components are obtained according to Di=iafter-ibefore, where iafter is the instantaneous value of the fault current after a single-phase grounding fault and ibefore is the instantaneous value of the load current before a single-phase grounding fault. Then, the fault transient components are decomposed by orthogonal wavelets to extract the characteristic frequency band information reflecting the grounding. (2) Extraction of fault characteristic frequency band. After a large number of simulations of different levels of orthogonal wavelet and orthogonal wavelet packet decomposition using different sampling frequencies, it is determined that a frequency of 10kHz is selected to extract the fault characteristics. For the ungrounded mode, the TCC is decomposed by two layers of wavelets. The information on the low frequency band of the second layer, i.e. (2,0) frequency band, is used to extract the fault characteristic measure, which can reflect the different grounding fault characteristics of the neutral point ungrounded system more comprehensively. The lp (p=1) norm of the decomposition sequence of a certain frequency band is obtained as the characteristic value of the grounding fault. The formula for calculating the lp norm is [IMG=lp norm calculation formula]/uploadpic/THESIS/2008/1/2008010311103584662K.jpg[/IMG] where {WTjk} is the decomposed sequence in the j-th frequency band after wavelet decomposition; PI(j) is the lp norm in the j-th time-frequency band, p=1 is the integral of the time-frequency signal sequence in this frequency band, representing the measure of the signal in this frequency band. To eliminate boundary effects during the calculation, a sufficiently large data window length is required. In reality, transient processes generally do not exceed one power frequency cycle. Considering the error in the calculation boundary, this paper uses a data length of 50ms, encompassing the first half-week of the fault and the two weeks after the fault, as the data analysis window. (3) Calculation of the characteristic frequency band measurement ratio: For each outgoing line (i) of the distribution network, the characteristic frequency band after the three-phase TCC decomposition in each feeder is calculated according to formula (3). The larger of the frequency band measurement ratio coefficients can be used as the criterion for grounding relay. [IMG=Characteristic frequency band after three-phase TCC decomposition in each feeder]/uploadpic/THESIS/2008/1/2008010311104040964R.jpg[/IMG] Where PI(j)ˊnfp1 and PI(j)ˊnfp2 are the measurements of the (j)th frequency band after the TCC decomposition of the two non-faulty phases on feeder (i); PI(j)ˊfp is the measurement of the (j)th frequency band after the TCC decomposition of the faulty phase on feeder (i). (4) For the determination of the relay, the measurement ratio calculated in formula (3) is compared with the fixed judgment criterion value (taken as 1.9, the basis for taking this value is explained in the simulation of this paper). If the comparison result is greater than the judgment criterion value, it is an internal fault; otherwise, it is an external fault. 3 ATP Simulation Analysis 3.1 Basic Basis of Simulation Model This paper takes the neutral point ungrounded system model as the research basis. Assume that FF is A phase grounded. The simulation and analysis are divided into two cases: ① According to an independent FF, only its own TCC exists as the minimum mode of internal fault, to verify the proposed theoretical criterion; ② Multiple feeders are equivalent to one FF and one HF (i.e., the auxiliary feeder), as the basis for analyzing the internal and external fault characteristics. Various grounding faults are simulated in 10kV and 35kV distribution systems respectively. The parameters of the line are based on the parameters of the overhead line (because the auxiliary TCC of the cable feeder is larger), and the capacitance current of the whole system is guaranteed to be: no more than 20A for 10kV distribution network and no more than 10A for 35kV distribution network. The types of grounding fault state characteristics include: ① Three different cases where the instantaneous phase voltage angle at the time of the fault is 0°, 45°, and 90°; ② The transition resistance varies from 0W to 300W in 10W increments; ③ The length of the faulty line or the non-faulty line varies in 1km increments. Different fault state characteristics were combined to form 1272 samples for ATP simulation and MATLAB wavelet analysis. 3.2 Simulation and Analysis of a Single Fault Feeder: The minimum operating mode of the relay was tested using a distribution system with only one outgoing line (which is generally not present in actual systems). Based on this, the characteristic ratio KFF of each phase's TCC characteristic frequency band can be analyzed. The simulated fault types consist of 546 sample sets, as shown in Table 1. In the table, Rf is the transition resistance; LFD is the distance to the fault point; LFF is the length of FF; and q is the instantaneous angle of the faulty phase voltage. Figure 1 shows the KFF variation law of the FF characteristic frequency band. [IMG=Simulation Fault Type]/uploadpic/THESIS/2008/1/2008010311104753307S.jpg[/IMG] From the data in Figure 1 and Table 1, we can conclude that the ratio of the measure to any high-frequency band on the faulty phase to that on the non-faulty phase is 2.0, and the ratio of the measure to the corresponding frequency bands of two non-faulty phases is 1, as shown in Figure 1. Since the self-sustaining property of the faulty phase TCC comes from the TCC of the non-faulty phase itself, this fundamental property determines that KFF is unaffected by factors such as transition resistance, fault instantaneous angle, line length, and fault location. [IMG=Measurement ratio between corresponding frequency bands of two non-faulty phases]/uploadpic/THESIS/2008/1/2008010311111746506I.jpg[/IMG] 3.3 Simulation Analysis of One Faulty Feeder and One Non-Faulty Feeder This paper uses a two-feeder system as the research model to simulate the performance of the measurement ratio of the characteristic frequency bands of the faulty feeder and the non-faulty feeder when multiple feeders are running, in order to analyze the reliability of the KFF judgment criterion and determine the identification boundary of FF (i.e., fault within the zone). A total of 726 loaded sample sets were collected during the simulation. The combination of each fault type is shown in Table 2. In the table, LHF is the length of HF. Since the TCC on each non-faulty phase of HF needs to flow from the fault grounding point through the faulty phase of FF to form a loop, it obviously plays a role in enhancing the TCC of the faulty phase. Therefore, the characteristic ratio KFF of the characteristic frequency band value of the faulty phase TCC to the characteristic frequency band value of the non-faulty phase is greater than 2, that is, greater than the case of a single feeder. Based on this mechanism, the operating criteria for a single-phase grounding relay can be determined. This paper proposes that the criterion for grounding faults within the feeder area should be a measurement ratio KFF > 1.9 (not 2.0, mainly to consider the possible 10% feeder length error in engineering). According to the TCC distribution and flow loop, the TCC flowing through each phase of HF is the feeder's own TCC, but the faulty phase is different from the non-faulty phase. The difference is that the TCC of the faulty phase does not pass through the low-voltage coil impedance of the transformer. Therefore, through extensive simulations, the identification criterion for grounding faults outside the feeder area proposed in this paper is a measurement ratio KHF < 1.33 (see Table 2). Considering the possible errors in actual engineering, this paper proposes a criterion of KHF > 1.9 for HF identification. Obviously, this criterion leaves a sufficiently large safety margin between the identification area and outside the area. Therefore, the criterion principle proposed in this paper is reliable and feasible. The measurement ratios inside and outside the area for all simulations are shown in Table 2. Figure 2 shows the variation of the measurement ratios KFF and KHF in the characteristic frequency band. As shown in the figure, the proposed principle can be applied to any feeder simply by measuring the data within its own internal parameters. [IMG=Identification criterion for ground fault outside feeder area is measurement ratio]/uploadpic/THESIS/2008/1/2008010311113670468S.jpg[/IMG] [IMG=Identification criterion for ground fault outside feeder area is measurement ratio]/uploadpic/THESIS/2008/1/2008010311114862107M.jpg[/IMG] [IMG=Measurement ratio on characteristic frequency band]/uploadpic/THESIS/2008/1/20080103111158117136.jpg[/IMG] 3.4 Simulation results analysis and conclusions Through a large number of simulations and calculations, the following conclusions are drawn: (1) The characteristic ratio KFF of the fault phase on FF increases with the increase of the HF-to-ground capacitance current. Therefore, HF plays an auxiliary role in grounding protection. According to a large number of simulations, when there is an auxiliary feeder, the ratio of the measure for identifying and judging the fault phase of a single-phase ground fault (FF) (i.e., fault within the zone) can be ensured to be KFF>1.9, and the ratio of the measure for reliable identification of HF (i.e., fault outside the zone) can be KHF>1.9; (2) Since the TCC of the FF fault phase is the self-supplied TCC provided by the non-faulty phase itself and the similar TCC provided by other HF, it provides feasibility, effectiveness and stability for the extraction of characteristic frequency bands during wavelet decomposition; (3) Since the TCCs formed by FF and HF have basic self-suppliedness and similarity when a single-phase ground fault occurs, and the criterion proposed in this paper is the relative ratio of the characteristic frequency band measure between the faulty phase and the non-faulty phase, it is completely different from the earlier line selection principle. Moreover, since it is not based on zero sequence but on the principle of transient characteristic components of three phases and the relative ratio of characteristic frequency band measure, the steady-state performance before the fault, such as the asymmetry of load current and the characteristics of TA, is irrelevant to the criterion; since the relative ratio of the measure is adopted, the influencing factors of the ground fault state parameters are effectively suppressed. Numerous simulations have confirmed that factors such as transition resistance, fault distance, operating mode, and fault instantaneous angle can be effectively suppressed; (4) The calculation time of wavelet analysis is a particularly important issue. This paper uses a sampling frequency of 10kHz and a data window of 50ms, i.e., 500 points. For DB5 wavelets (support is 10, which means 10 points), calculating only the (2,0) frequency band sequence requires 3750 multiplications and 3475 additions. For a single-chip microcomputer with a main frequency of 12M, it takes about 12ms, and calculating three phases takes 36ms. The auxiliary time for memory operation is about 1.5 times, which is 54ms, for a total of 90ms. This calculation time is feasible. 4 Construction and implementation of single-phase grounding protection relay 4.1 Starting mode of single-phase grounding protection According to the transient characteristics of a neutral ungrounded system when a single-phase grounding occurs, different starting modes can be selected according to the specific situation on site. The available starting modes are: zero-sequence voltage mutation start, phase current mutation start and zero-sequence current mutation start. 4.2 Implementation of Single-Phase Ground Fault Protection for Feeders Considering the characteristics of ground fault protection, this paper proposes to use a measuring current transformer (TA) to obtain sampling data of three-phase TCC to improve detection accuracy. Therefore, a three-phase measuring TA is required. The sampling frequency is 10kHz. For conventional measurements, one point can be sampled every 10 points (i.e., 20 points/week) for calculation. After the protection is started, the waveform records 50ms of sampling data for the first half-week and the last two weeks of the fault time. Orthogonal wavelet decomposition is performed on the three-phase TCC signals to obtain the (2,0) characteristic frequency band measure values. The maximum measure is selected as the basis for judging the phase-to-phase measure ratio KFF>1.9... The protection principle requires the configuration of a three-phase measuring TA. If a two-phase TA and a zero-sequence TA are already in use, they can be converted to calculate the ground fault. If it is determined that a single-phase ground fault has occurred on the line, an alarm signal can be issued or the circuit can be tripped and then reclosed according to the actual operating conditions (except for cable feeders). 5 Conclusions This paper proposes a transient current protection for single-phase grounded feeders based on the principle of transient characteristic components of phase current. Its features are as follows: (1) In a neutral-point ungrounded system, the TCC in the FF fault phase is composed of the self-supply TCC provided by the non-faulty phase of this FF and the similar TCC provided by other HFs. This provides feasibility, effectiveness and stability for the characteristic frequency band extraction of wavelet decomposition, and provides a theoretical basis for the protection relay studied in this paper. (2) The proposed fixed judgment criterion is applicable to any ungrounded distribution network without the need for setting calculation. Among them, the ratio of identification and measurement of single-phase grounded FF (within the zone) fault phase is greater than the judgment criterion, i.e., KFF>1.9; the ratio of reliable identification and measurement of HF (outside the zone) is less than or equal to the judgment criterion, i.e., KHF>1.9. HF plays an auxiliary role in grounding protection. (3) The proposed criterion is the relative ratio of characteristic frequency band measurement, which is completely different from the conventional line selection principle and also different from the current protection principle setting. It has strong suppression and adaptive capabilities for the variable factors and uncertain factors of the system. (4) The proposed protection method can form an integrated bay unit with the distributed feeder protection unit and be installed locally on the switchgear, which is conducive to the convenient realization of feeder automation. Although the research in this paper has carried out a lot of simulation tests, it still needs to be verified in field operation.