1. Introduction
With the continuous improvement of cable utilization rate and the gradual increase of system capacitance current, the arc-suppression coil may no longer fully compensate for fault current. Therefore, some substations are gradually being transformed into neutral point grounding with small resistor [1]-[3]. The small resistance grounding mode cannot distinguish between instantaneous grounding faults and permanent grounding faults, and initiates circuit breaker tripping for all single-phase grounding (SPG) types, reducing power supply reliability [4]. The flexible grounding mode only trips for permanent grounding faults. For instantaneous grounding faults, due to the compensation effect of the arc-suppression coil, the residual grounding current is reduced to a very small amount, which can effectively ensure the power supply of users [5], [6].
At present, the flexible grounding method of arc-suppression coil parallel connecting the small resistor has been applied to important lines. The fault protection for flexible grounding system mainly adopts the protection method [7], [8] commonly used low-resistance grounded neutral system, including methods using transient characteristics (wavelet method [9]-[11], energy method [12], [13], etc.) and artificial intelligence (AI) methods [14], [15]. Reference [16] has proposed a grounding fault protection method that utilizes the projection coefficient of the ZSC of each line on the ZSC of the neutral point, but the ability of withstand transition resistor (R_{g}) is poorer. A ground fault detection method using ZSC waveform distortion concavity and convexity is proposed in [17], but it may fail in situations where the fault ZSC is smaller and the noise is higher. In response to the issue of low sensitivity for high resistance faults, reference [18] proposes that high resistance faults can be detected based on the current and voltage characteristics of the line passing through nonlinear conductor grounding faults. The detection sensitivity is higher, but it is only limited to situations with high nonlinearity. In addition, the PMU has been successfully applied in transmission systems [19], [20]. After further technological innovation, the PMU for distribution network have significant impact on fault diagnosis and location technology, mainly manifested in providing synchronous clocks and achieving online estimation [21], [22].
The grounding fault of flexible grounding system is analyzed in this paper. Comparing the projected amount of ZSC of each PMU on the ZSV, the correlation coefficient method is used to calculate the correlation of the projected amount of each adjacent PMU to achieve fault location. The method is simulated to prove the effectiveness of the method.
2. Fault analysis of flexible grounding system
2.1 Flexible grounding system fault zero-sequence network
The zero-sequence equivalent network for the flexible grounding system with 5 lines when a SPG fault occurs is shown in Fig. 1, assuming that R is a small parallel resistor with neutral points (the value is generally 10 \(\Omega\)) [23]-[25]. K is the small fling-cut switch; \(C_{0i}\) (\(i=1,2,3,4\)) denotes zero-sequence capacitance to ground of the healthy line \(L_1\)-\(L_4\); a, b, d and e denote the monitoring point at upstream and downstream of faulty line \(L_5\), respectively. f is set as the fault point; \(C_{\rm 0a}\), \(C_{\rm 0b}\), \(C_{\rm 0d}\), \(C_{\rm 0e}\) the zero-sequence capacitance to ground in sections ab, bf, fd, and de of the faulty line \(L_5\), respectively; \(U_{\rm 0f}\) denotes the virtual voltage source; \(\dot{U}_0\) denotes ZSV of the bus.
2.2 ZSV and ZSC before small resistor input
Before the small resistor is put into operation, the switch K is disconnected, the system grounding mode is resonance grounding mode, and the zero-sequence impedance of the system is obtained by paralleling the arc-suppression coil with the zero-sequence capacitance to the ground of other lines:
\[\begin{equation*} Z_{\rm s0}=\frac{1}{\dfrac{1}{\rm j3\omega L}+j\omega C_{0\Sigma}} \tag{1} \end{equation*}\] |
In Eq. (1), \(C_{0\Sigma}\) represent the sum of the zero-sequence capacitance of each line to ground. Before small resistor input, the ZSC upstream at the fault point is equal to the sum of the zero-sequence capacitance current to ground of all non-faulty lines
\[\begin{equation*} i_{\rm 0a}=-\dot{U}_0\left(\mathrm{j}\omega C_{0\Sigma}+\frac{1}{\rm j3\omega L}\right) \tag{2} \end{equation*}\] |
The ZSC downstream at the fault point is equal to the capacitance current to the ground of the downstream line.
2.3 ZSV and ZSC after small resistor input
After the small resistor is put into operation, the switch K is closed, then the zero-sequence impedance of the system is:
\[\begin{equation*} Z^*_{\rm s0}=\frac{1}{\dfrac{1}{\rm j3\omega L}+j\omega C_{0\Sigma}+\dfrac{1}{\rm 3R}} \tag{3} \end{equation*}\] |
The ZSC of upstream at the fault point increases the resistive component compared to before the small resistor is put into operation, namely
\[\begin{equation*} i^*_{\rm 0a}=-\dot{U}_0\left(\rm j\omega C_{0\Sigma}+\frac{1}{\rm j3\omega L} +\frac{1}{3\mathrm{R}}\right) \tag{4} \end{equation*}\] |
The ZSC of downstream at the fault point is not affected by the parallel connection low resistor.
Based on the above analysis, the fault point position can be determined by comparing the changes in ZSV and ZSC of upstream and downstream at the fault point before and after the small resistor is put into operation.
3. Principle of fault location based on steady state projection method
3.1 Steady-state feature orthogonalization processing
When the fault occurs, the ZSV and current of each detection point of the fault feeder are collected by the PMU. As shown in Fig. 2, \(\dot{I}_{\mathrm{up}}\) and \(\dot{I}_{\text{down}}\) are the ZSC of upstream and downstream at the fault point; \(\dot{I}_{\text{up.P}}\) and \(\dot{I}_{\text{down.P}}\) denote the projection vector ZSC of upstream and downstream at the fault point; \(I_{\text{up.P}}\) and \(I_{\text{down.P}}\) express the magnitude of the projection value on the voltage vector (\(\dot{U}\)) between \(\dot{I}_{\mathrm{up}}\) and \(\dot{I}_{\text{down}}\); \(\phi_1\), \(\phi_2\) represents the angle between \(\dot{U}\) and \(\dot{I}_{\mathrm{up}}\), \(\dot{I}_{\text{down}}\).
Fig. 2 Vector diagram of upstream and downstream ZSC projection components at fault point projection component calculation. |
Taking \(\dot{I}_{\mathrm{up}}\) as an example:
\[\begin{align} \begin{cases} P_{\mathrm{up}}=|I| \cos \varphi \\ \dot{I}_{\text{up.P}}=\dfrac{\dot{U}}{|U|}P_{\text{up}} \end{cases} \tag{5} \end{align}\] |
According to Eq. (5), the projection amount of \(\dot{I}_{\text{up}}\) on \(\dot{U}\) can be obtained
\[\begin{equation*} \dot{I}_{\text{up.P}}=\frac{\dot{U}}{|U|^2}\left(\dot{U}\cdot \dot{I}_{\text{up}}\right) \tag{6} \end{equation*}\] |
Among them, \(\left(\dot{U}\cdot \dot{I}_{\text{up}}\right)\) represent the inner product of vector, \(\dot{U}\) and vector, \(\dot{I}_{\text{up}}\).
According to the same derivation principle, the steady-state projection component of the ZSC of downstream at the fault point, \(\dot{I}_{\text{down}}\) can be obtained [26]-[28].
3.2 Pearson correlation coefficient
In order to reflect accurately and fully the correlation between various variables, Carl Pearson proposed the correlation coefficient [29], [30], which is a linear correlation coefficient. Its numerical value can reflect the similarity between two signals. The correlation coefficient of continuous functions \(x(t)\) and \(y(t)\) is
\[\begin{equation*} r_{xy}=\frac{\int_{-\infty}^{+\infty}x(t)y(t)dt}{\sqrt{\int_{-\infty}^{+\infty}x^2(t) dt{\int}_{-\infty}^{+\infty}y^2(t)dt}} \tag{7} \end{equation*}\] |
Among them, the calculation range of the correlation coefficient is \([-1,1]\), which means:
(1) When the value of \(\left|r_{\mathrm{xy}}\right|\) is equal to 1, it indicates that the two signals are completely correlated.
(2) When the correlation coefficient is equal to zero, it indicates that two signals are completely independent.
(3) When the value of the correlation coefficient is greater than zero, it indicates that the two signals are proportional; When the value of the correlation coefficient is less than zero, it indicates that the two signals are negatively correlated.
3.3 Fault location principle
The steady-state projection values, I\(_{i.\mathrm{P}}\) and I\(_{j.\mathrm{P}}\), of adjacent sections \(i\) and \(j\) of the faulty line can be calculated from Eq. (6), and the \(r_{ij}\) of adjacent sections can be obtained from Eq. (7):
\[\begin{equation*} r_{ij}=\frac{\int_0^TI_{i.\mathrm{P}}(t)I_{j.\mathrm{P}}(t)dt}{ \sqrt{\int_0^TI_{i.\mathrm{P}}(t)dt\int_0^TI_{j.\mathrm{P}}(t)dt}} \tag{8} \end{equation*}\] |
The positivity and negativity of \(r_{ij}\) represent the degree of correlation between \(I_{i.\mathrm{P}}\) and \(I_{j.\mathrm{P}}\). When SPG fault occurs in the distribution network, after the small resistor is put into operation, the ZSV of the bus and ZSC of upstream at the fault point have changed correspondingly. According to Eq. (6), the steady-state projection values of PMUs on opposite side of the fault point are calculated. When there is no branch section on the line, as shown in Fig. 3(a), the fault point is \(f_1\). The ZSC and ZSV are collected by PUM1 and PMU2, the steady-state projection correlation coefficient, \(r\) (PUM1, PMU2), values are close or even equal, and the polarity is consistent; On the opposite side of the monitoring point, based on the information collected by PMU2 and PMU3, \(r\) (PUM2, PMU3) is calculated, and the absolute values are roughly equal, but the polarity of the values is opposite. When the fault point is \(f_2\), the values between \(r\) (PUM1, PMU2) and \(r\) (PUM2, PMU3) are close in magnitude and same in polarity.
In summary, criterion ① can be obtained: if there is no branch on the line, the correlation coefficients of adjacent PMUs are compared. If the value is approximately equal to \(-1\), that is
\[\begin{equation*} r(\mathit{PUM}_i, \mathit{PMU}_{i+1})(i=1,2,\cdots)\approx -1 \tag{9} \end{equation*}\] |
Then, it is determined as the faulty section; If the values are approximately equal to \(+1\), it is determined that the downstream section of the terminal PMU is the faulty section.
When there is a branch section on the line, as shown in Fig. 3(b). If the fault occurs at \(f_3\) or \(f_4\), then the numerical polarity of \(r\) (PUM1, PMU2) and \(r\) (PUM1, PMU3) are both negative, and the absolute value is close to 1; If there is a fault at \(f_5\), then the polarity of \(r\) (PUM1, PMU2) is negative, and the polarity of \(r\) (PUM1, PMU3) is positive.
In summary, criterion ② can be obtained: if there is a branch on the line, the correlation coefficients of adjacent PMUs need to be calculated based on the ZSV and ZSC collected by PMU of the upstream and downstream, If the polarity of the calculation results is all negative and the absolute value is close to 1, it is determined that there is the fault in this section; If the polarity of the calculation results is different, it is determined that there is no fault in this section.
3.4 Fault location flow
In summary, the differentiation process of the flexible grounding system fault section location method proposed in this article is as follows:
(1) When the fault occurs, the fault location device starts based on the ZSV exceeding the limit, and collects the ZSV of the bus and the ZSC of each PMU.
(2) Based on the ZSV of bus and ZSC collected by each PMUs, the steady-state projection amounts of each PMU are calculated by Eq. (6).
(3) If there is no branch section on the line, the correlation coefficients of the steady-state projection amounts of each PMU are calculated by Eq. (8), and based on Eq. (9), the fault section is judged.
(4) If there is a branch section on the line, then based on the description of criterion 2, the fault point position can be determined.
4. Simulation analysis
The distribution network model is built by Matlab/Simulink as shown in Fig. 4, and the system consists of four overhead cable hybrid lines and one overhead line. The line parameters are shown in Table I. The system is in overcompensation operation mode, with overcompensation degree of 110%. The small resistor is connected 1 s after the fault occurs.
Based on the above model and parameter settings, three types of fault situations, namely different R_{g}, different fault inception angles (\(\delta\)), and different fault point positions, have been set. A large amount of simulation analysis have been conducted. Figs. 5 and 6 show the ZSV and ZSC waveforms at PMU2 and PMU3 before and after K closing when grounding via 10 \(\Omega\) and 2000 \(\Omega\) resistors, respectively.
It can be seen that after K is closed, the amplitude of ZSV and downstream ZSC at the fault point decrease when grounding via 10 \(\Omega\) resistor, but the amplitude of the upstream ZSC at the fault point increases significantly; When grounding via 2000 \(\Omega\) resistor, the ZSV and ZSC of upstream and downstream at the fault point decrease, but the ZSC of upstream at the fault point is much greater than that downstream, proving the effectiveness of the method proposed in this paper.
4.1 Simulation analysis under different R_{g}
Based on the above analysis, the size of the R_{g} does have a certain impact on the data collected by each PMU. Therefore, in the established simulation model, the fault point position is set to \(F_2\), and the impact of the resistance value on the judgment result is analyzed based on different R_{g} values (10 \(\Omega\)-5000 \(\Omega\)). Table II shows the correlation coefficients between adjacent PMUs under different resistance values calculated.
According to the data analysis in Table II, as the resistance value increases from 10 \(\Omega\) to 5000 \(\Omega\), there is almost no significant change in the correlation coefficient of steady-state projection between adjacent PMUs. If the resistance value is 3000 \(\Omega\), r_{12} is \(+1\), r_{23} is \(-1\), r_{34} is \(-1\), it can be determined that the fault point is located between PMU2 and PMU3. Therefore, the method for calculating the correlation coefficient of steady-state projection is not affected by the R_{g}.
4.2 Simulation analysis under different \(\delta\)
To verify the impact of the \(\delta\) on the location results, in the established distribution network model, a ground fault occurred at the PMU2 to PMU3 of the \(L_2\), with the transition resistance of 1000 \(\Omega\), and set different angles, \(\delta\) (0\(^\circ\)-90\(^\circ\)). Table III represents calculation results of correlation coefficient under different \(\delta\).
According to data analysis in Table III, as \(\delta\) varies from 0\(^\circ\) to 90\(^\circ\), although there is a certain variation in the correlation coefficient of steady-state projection between adjacent PMUs, it does not affect the judgment results. For example, when \(\delta\) is 45\(^\circ\), r_{12} is \(+0.921\), r_{23} is \(-0.964\), and r_{34} is \(+0.913\), which indicates the fault point is located between PMU2 and PMU3. Therefore, the method for calculating the correlation coefficient of steady-state projection is not affected by \(\delta\).
4.3 Simulation analysis under different fault point positions
Due to the complex topology of the current distribution network, it is necessary to consider the impact of branches on the positioning results. Therefore, different fault point positions have been set in the established distribution network model. Table IV shows the calculation results of correlation coefficients for different fault point positions.
According to the simulation data in Table IV, assuming the fault occurs between PMU1 and PMU2 in the system, r_{12} is \(-1\), and r_{23} and r_{34} are both \(+1\). Therefore, based on criterion 1, it is determined that the fault point occurs between PMU1 and PMU2; When a ground fault occurs between PMU5 and PMU6, then r_{56} and r_{57} are both \(-1\), and the fault point is determined to be between PMU5 and PMU6 based on criterion 2; When a fault occurs in the downstream section of PMU4, r_{12}, r_{23}, and r_{34} are both \(+1\). Therefore, based on criterion 1, it is determined that the fault point is in the downstream section of PMU4.
5. Verification of field data
The recorded field data of actual SPG fault are collected by fault location device. The field data of four monitoring points of the faulty feeder are recorded. The SPG fault occurs between the PMU1 and PMU2, namely section 1. The waveforms collected by the fault location device are shown in Fig. 7.
The proposed method is used to calculate the data recorded, and the results are shown in Table V. The r_{12} is \(-0.925\), r_{23} is 0.978, and r_{34} is 0.928. Therefore, according to fault criterion, and PMU1-2 is selected as faulty section, which comply with judgment of fault location device.
6. Conclusion
To address the difficulty in locating SPG faults in flexible grounding systems of distribution networks with complex topological structures, a fault location method based on steady-state projection is proposed. This method preprocesses steady-state fault information and combines them with the correlation coefficient method to determine the fault section. The simulation results show that the ability of withstand R_{g} is stronger, and it can accurately locate the fault location on lines with branches. This method is not affected by the \(\delta\) and fault point position, and the reliability is stronger.
Acknowledgments
Funding: This work was supported by State Grid Shanghai Electric Power Company Technology Project 52094022004N.
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Authors
Shu Liu
State Grid Shanghai Municipal Electric Power Company Electric Power Research Institute
Jinsong Liu
State Grid Shanghai Municipal Electric Power Company Electric Power Research Institute
Honglu Xu
Shandong University of Technology
Haoyue Sun
Shandong University of Technology
Fuqian Wang
Shandong University of Technology
Jiaxi Zhu
Shandong University of Technology