Fault location method for petal-shaped distribution network with inverter-interfaced distributed generators

0 Introduction

The radial structure is widely adopted in traditional distribution network.However, the radial distribution network operates in the open-loop mode, resulting in some problems, such as large affected range and long power outage time when faults occur.On the contrary, the distribution network with closed-loop operation mode is potential to overcome above difficulties.The petal-shaped distribution network (PSDN) is one of the typical closed- loop distribution networks.It has the advantages of flexible operation control strategies and high economic benefits [1-3].Recently, the PSDN has been built in several urban grids in China, Singapore and France.On the other hand, a large number of photovoltaic powers, wind turbines and other new energy generators connected to the grid in the form of inverter-interfaced distributed generators (IIDGs) [4-6].The change of grid structure and the access of IIDGs make the fault characteristics of distribution network much more complicate.Accordingly, the protection configuration and fault location methods for the traditional distribution network are difficult to apply to PSDN with IIDGs.

Up to now, several fault location methods have been reported for low-voltage active distribution network.These methods include the algorithms based on artificial intelligence [7-10], travelling wave-based methods [11-13], impedance-based methods [14-18] and so on.The methods based on intelligence algorithm have good fault-tolerance performance and can adapt to the distribution network with complex structure [19].However, due to the limitation of the algorithm, only the fault line or fault section can be located.Travelling wave-based methods can accurately locate the fault point according to the time characteristics of refraction and reflection of the traveling wave.Methods of this type are widely applied to high voltage transmission lines with simple structure [20].However, these methods are vulnerable to the interference from branch lines in the distribution network.The refracted and reflected traveling waves generated in the traveling wave transmission process will interfere with each other, which makes it extremely difficult to identify the traveling wave head reflected from the fault point.In addition, these methods require high cost to install devices.

The impedance-based methods are derived from circuit theory, and have flexible applicability.These methods can be used not only to locate fault line, but also to calculate fault distance.A location method for single-phase-to- ground fault in the unbalanced power system is described in [21].The current phasors at the two ends of the fault line are demanded, which means high requirements for data synchronization.This problem is solved in [22] by developing a fault-locating algorithm using current magnitude only.However, the effectiveness of the method is affected by system operation mode, load current, and fault resistance.For the distribution network with IIDGs, a fault location algorithm based on synchronous transients energy is proposed in [23].The algorithm can locate the line with single-phase-to-ground fault accurately.A fault-line location method based on impedance matrix and voltage sag measurements is described in [24].The method is both insensitive to the fault resistance and validated for all fault types.However, it is not cost-effective to install potential transformers at multiple nodes.

In the PSDN, both ends of the loop line are connected to the same bus, resulting in a correlation between the currents at both sides of the fault line [25].This feature can facilitate the application of impedance-based method in the PSDN.With the development of closed-loop operation mode in the distribution network, some impedance-based fault-locating approaches have been proposed to shorten maintenance time of the closed-loop network.In [25], a grounding fault location approach based on the zerosequence current at both ends of the fault line for the PSDN is proposed.The approach is sensitive to load current, and the situation of IIDG access is not considered.A method based on negative-sequence current comparison for the PSDN with synchronous distributed generator is studied in [26].The effectiveness of this method is not affected by load current and fault resistance, but this method is invalid for three-phase faults.The bi-directional overcurrent relays and time-current characteristics are applied for the PSDN with distributed generators to locate and cut off the fault line in [27].As a protection scheme, the main goal of [27] is to identify the fault line.Therefore, the research results cannot be utilized to locate the accurate fault position, which is one of the necessary processes for fault maintenance.

The review of above methods shows that the existing fault location methods can hardly calculate the fault position in the PSDN with IIDGs.Therefore, it is necessary to propose a method that is suitable for the PSDN with IIDGs to pinpoint the fault position.Based on the Kirchhoff’s Voltage Laws (KVL), the fault location method proposed in this paper is developed in following two parts: fault location for the asymmetrical fault, and fault location for the symmetrical fault.In the former part, the phase differences between the negative-sequence current at both ends of lines are used to identify the fault line, and the negative-sequence current amplitudes are used to calculate the fault position.In the latter part, the positive-sequence current at both ends of lines and the current output from IIDGs are used in the process of identifying fault lines, and the positivesequence current on multiple lines are used to pinpoint the fault position.In addition, considering the limitation of communication level, the algorithm separates the amplitude and phase of the current to reduce the pressure on communication.

The rest of this paper is arranged as follows.A description of PSDN and the fault equivalent model of the PSDN with IIDGs are presented in Section 2.The derivation of the proposed approach is illustrated in Section 3.In Section 4, the proposed method is evaluated in the PSCAD/EMTDC simulation software.Section 5 draws the main conclusion.

1 Fault equivalent model of PSDN with IIDG

1.1 Introduction of the PSDN

A 10 kV PSDN with an IIDG is shown in Fig.1.The two terminals of the loop line are connected to the same bus in substation.Therefore, the PSDN can operate in both closed-loop mode and open-loop mode.In order to ensure high power supply reliability, the PSDN often operates in the closed-loop mode.

Fig.1 A 10 kV PSDN with an IIDG

In Fig.1, the loop line of the PSDN consists of five same-type lines, numbered L1～L5 according to clockwise direction.For a certain line, the line with smaller number is defined as the upstream line, and the line with larger number is defined as the downstream line.Protection devices are arranged at both ends of each line, and current differential protection is usually configured in the PSDN as main protection scheme.

Since the PSDN can meet the N-1 security criterion, it is not necessary to adopt small current grounding mode to ensure that the distribution network operates for 2 hours during fault conditions.On the other hand, the low resistance grounding mood can improve the current level when asymmetric faults occur, which is beneficial to improve the protection performance.Therefore, the PSDN usually adopts the low resistance grounding mode.In Fig.1,T2 is the system grounding transformer.RN is the neutral grounding resistance.Therefore, when an asymmetrical fault occurs, the sequence current in the circuit is relatively larger than that in a small current grounding system.

Moreover, since the fault component is about zero during normal operation, the fault location method based on fault component cannot prevent the protection from malfunction in this situation.Therefore, the full current is utilized in this paper to locate the fault position and help to avoid the protection misjudgment during normal operation.

1.2 Output characteristics of the IIDG

The output characteristics of the IIDG are mainly determined by the control strategy.Grid-connected IIDGs usually adopt the PQ control strategy.The strategy keeps the power output from the IIDG steady when the voltage or frequency at the point of common coupling (PCC) fluctuates.On the other hand, in order to avoid the influence on power quality of distribution network, the three-phase balance control strategy is adopted [28].The strategy ensures that the IIDG only output positive-sequence current when the asymmetrical fault occurs.The positive-sequence current is determined by the positive-sequence voltage at PCC.Therefore, the fault equivalent model of the IIDG can be represented by a voltage- controlled current source in the positive-sequence network and an open circuit in the negative-sequence network [29-30].

1.3 Fault equivalent model of the PSDN with the IIDG

According to the previous analysis, when the fault occurs at the point f in Fig.1, the positive-sequence network and negative-sequence network of the PSDN with the IIDG are shown in Fig.2 (a) and (b).

In Fig.2, the subscripts (1) and (2) represent positive- and negative-sequence components, respectively.Es and ZS are the equivalent electromotive force and impedance of the system, respectively.ZT1 is the equivalent impedance of the IIDG grid-connected transformer T1.Z1 and Z2 represent the impedance of loop lines on both sides of PCC, i.e., Z1 is the total impedance of line L1～L4, and Z2 is the impedance of line L5.Zf is the additional impedance of the fault branch and related to fault type and fault resistance.α indicates the position of the fault branch.I1 and I2 represent the current at both terminals of the fault line.If(1) represents the positivesequence current of the fault branch.-Uf(1) and -Uf(2) is respectively the virtual positive-sequence potential and virtual negative-sequence potential.When the symmetrical fault occurs, -Uf(1) is zero.UPCC(1) is the positive-sequence voltage at PCC and IDG is the output current of the IIDG.

Fig.2 Positive- and negative-sequence network of PSDN with an IIDG during asymmetrical faults

2 Fault location method

2.1 Location method for the asymmetrical fault

When the asymmetrical fault occurs in the PSDN, negative-sequence current always exists in the circuit whether the fault type is the phase-to-ground fault or the phase-to-phase fault.In addition, according to the output characteristics of the IIDG, the features of negative- sequence current are not affected by IIDG access, which is conducive to the calculation of fault location.Therefore, the characteristics of negative-sequence current are analyzed and utilized to locate the asymmetrical fault in this paper.

According to Fig.2 (b), the expression of I1(2) and I2(2) can be obtained as follows:

Since the unit impedance of each line is the same, it can be deduced that I1(2) and I2(2) have the same phase.In other words, the phase difference between the negative-sequence current at both ends of the fault line is zero.On the other hand, it is easy to know that the phase difference between the negative-sequence current on both sides of the nonfaulty line is 180°.

The above conclusion can be used to identify the fault line.In order to reduce the influence of current transformer (CT) measurement error, the following criteria are used to identify fault line:

where φlock is the locking angle, taking a reference value of 35° [31].

The above formula has low requirement for data synchronization and can be used as an auxiliary criterion for main protection of the PSDN to cut off the fault line.

After removing the fault line, it is necessary to further locate the fault point to minimize the maintenance time.The fault position α can be derived from (1) and (2), as following:

where I1(2) and I2(2) are the amplitudes of I1(2) and I2(2), respectively.

The distance from bus A to the fault point f can be obtained by the following formula:

where Z0(2) is the negative-sequence impedance per kilometer line.ltotal is the total length of the loop line.

If the types and diameters of some lines are different with other lines due to maintenance, the impedance phase angle and unit impedance of the lines will be different from other lines.The phase difference between the negative-sequence current at both sides of the fault line will be a relatively large value.In this case, the fault line identification formula shown in (3) can be still valid, because there is sufficient redundancy.However, due to the inconsistency of unit negative-sequence impedance, the fault location result calculated from (5) might be not accurate.The distance between fault point f and the upstream bus of fault line can be calculated by the following formula:

where ZLy(2) is the negative-sequence impedance of the line Ly, which is upstream of the fault line.ZLf0(2) is the unit negative-sequence impedance of the fault line.

Note that the fault location formula in (5) and (6) only requires the total length of the loop line, the line impedance, and the amplitudes of negative-sequence current at both ends of the fault line.These factors are independent of the grid-connected capacity and position of the IIDG.Therefore, the effectiveness of the proposed method is not affected by the IIDG access and its capacity.Moreover, the proposed method has low requirements for data synchronization and above location process is very easy to implement.

In addition, the above formulas are derived based that the voltage drop from the fault position through the upstream line to the substation bus is equal to that from the fault position through the downstream line to the substation bus.Therefore, as long as the protection can accurately obtain the current information, the accurate fault position can be calculated and is not affected by fault resistance and load current.However, in practical engineering, the accuracy of current measurement is actually correlated with the current amplitude.If the current amplitude is too small, the phase measurement error may be large, thereby reducing the accuracy of fault location.The current amplitude is mainly affected by fault position and fault resistance.On one hand, when the fault occurs near the substation bus, the fault current at one end of the fault line is very small, which may lead to a failure of (3).In this case, the fault position, which is near the busbar, can be found by artificial inspection.On other hand, if the fault resistance is too large and the negative-sequence current is too small, the measurement error of the negative-sequence current will be large, which may reduce the accuracy of asymmetric fault location.

It should be emphasized that the fault location is usually realized after the protection action.The criterion proposed in this paper cannot replace the protection to remove the fault line, but can only play an auxiliary role.The magnitude of the fault resistance also affects the protection action.If the fault resistance is too large to cause refusal-operation of protection, the proposed fault location will not start.If the protection can be started correctly, the current magnitude can meet the identification degree of CTs.At this time, the proposed method can accurately calculate the fault position.

2.2 Location method for the symmetrical fault

When the symmetrical fault occurs in the PSDN, the fault current does not contain negative-sequence component and zero-sequence component.Therefore, the features of positive-sequence current are analyzed for the location of the symmetrical fault.

From Fig.2 (a), the expression of I1(1) and I2(1) can be deduced as follows:

The magnitude of If(1) mainly depends on the fault resistance, and the magnitude of IDG is affected by the IIDG grid-connected capacity and the PCC voltage UPCC.When a symmetrical fault occurs in the PSDN without the IIDG, the positive-sequence current in (7) and (8) have the same feature as the negative-sequence current in (1) and (2).However, in the PSDN with the IIDG, the influence of the IIDG should be considered.

By solving simultaneous equations (7) and (8), the expression of α can be derived as follows:

The current I1(1), I2(1) and IDG in (9) are phasors, which means that strict data synchronization is necessary.To lower the requirements, α in (9) is rewritten as follows:

where I1(1), I2(1) and IDG are the amplitudes of I1(1), I2(1), and IDG, respectively. φ1-2 is the phase difference of I1(1) and I2(1).φDG-2 is the phase difference of IDG and I2(1), which can be obtained at the switching station corresponding to the PCC.

If the positive-sequence current at both ends of each line are taken as I1(1) and I2(1) respectively into (10), the calculation result at non-faulty line will be infinite, whereas the result at fault line will be within [0, 1].This property can also assist the fault line identification.

From (10), the fault location formula for symmetrical fault requires the information of the IIDG output current and the IIDG grid-connected position.Therefore, when the IIDG grid-connected quantity and position changes, the formula needs to be changed correspondingly.However, these two factors generally keep unchanged.

When multiple IIDGs are connected to the PSDN at different PCCs, the positive-sequence current at both sides of the fault line can be expressed as follows:

where ZL is the total positive-sequence impedance of the loop line.α′ is the ratio of the length of upstream line from fault point f to the substation bus and the length of loop line.IDGi is the output current of the IIDGi, which is connected at PCCi.Zmi is the total positive-sequence impedance of the upstream line of the PCCi, and Zni is the total positivesequence impedance of the downstream line of PCCi.j is the number of IIDGs connected to the upstream of the fault line and k is the number of IIDGs connected to the downstream of the fault line.

The expression of α′ can be derived as follows:

The corresponding formula with low synchronization requirement is as follows:

where φDGi-2 is the phase difference of IDGi and I2(1).

α′ in (14) has similar property with α in (10), i.e., α′ calculated by the non-faulty line is infinite, whereas that calculated by the fault line is within [0, 1].

The influence of the load current is ignored in above derivation process.As a result, the calculation results are complex numbers.In engineering applications, the modulus of α′ can be used for the fault line identification.When the fault resistance is low, the proportion of load current in the positive-sequence current recorded in the relays is very small.Therefore, the fault distance calculated by (10) and (14) is precise in locating a bolted fault (i.e., no fault resistance).However, when the fault resistance is high, the proportion of load current is large, and the error between the estimated and actual distances will be large.

If the communication level of distribution network automation system can meet the requirement of synchronous transmission of different current phasors (e.g., the 5G-based stations or the optical fibers are fully configured), a fault location result with higher accuracy can be obtained according to the KVL.The formula is shown as follows:

where ZLf(1) is the positive-sequence impedance of the fault line Lf. ZLx(1) is the positive-sequence impedance of the line Lx, which is downstream of the fault line. ZLy(1) is the positive-sequence impedance of the line Ly, which is upstream of the fault line.ZLf0(1) is the unit positivesequence impedance of the fault line.Ii(1) is the positivesequence current phasor at the protection i.

Formula (15) requires the current phasors at multiple positions on the loop line.In order to reduce requirements for data synchronization, the current phase difference, which can be directly obtained in each switching station, is used to rewrite the formula, as follows:

where φi-j is the phase difference between Ii(1) and Ij(1) (where i=2x, 2y-1,and 2f-1.j=2f ).Taking the PSDN in Fig.1 as an example, φ2-3, φ4-5, φ6-7, φ8-9, and φ1-10 can be obtained directly in the switching station.The other phase differences can be obtained by accumulating the above phase differences, e.g., φ10-6 =φ8-9-φ6-7.Since there is no synchronization error in the calculation process of two current phases in the same switch station, the phase error mainly comes from the measurement error of CTs.If P-level CTs are used in the PSDN, the phase difference between the current in a switching station is less than 7° [31-32].In the process of accumulating the phase difference obtained in several switching stations, the phase measurement errors in different switching stations may offset by each other, resulting in a smaller error of the new phase difference.In the most extreme conditions, the accumulated phase measurement errors may increase with the amount of switching stations.In a loop line with five lines, the maximum accumulated phase measurement error is less than 35°.For these extreme conditions, the accuracy of fault location formula might be reduced.

Formula (16) can be used not only for the estimation of symmetrical fault position, but also for the calculation of asymmetrical fault location.In addition, since the positive- sequence current on all the lines is utilized in (16), its accuracy is not affected by fault resistance and load current.

Moreover, if the fault occurs on the substation bus or in the switching station, the results calculated from (3) and (14)can conclude that the fault is not on the corresponding line, which is helpful for the line protection to avoid malfunction.In the meantime, busbar protection is usually configured at the bus in the substation and switching stations in the PSDN.When the fault occurs on the bus in the substation and switching stations, the busbar protection at the fault bus can operate correctly.Therefore, it is easy to identify the fault position according to the operating states of the line protection and the busbar protection.

3 Case study

To evaluate the effectiveness of the method proposed in Section 3, the 10 kV PSDN test system shown in Fig.1 is built in PSCAD/EMTDC.The system parameters are shown in Table 1.

Table 1 System parameters

Parameter Value System equivalent capacity 100 MVA System equiva lent impedance 0.294+j0.282 Ω Line impedance 0.047+j0.062 Ω/km Length of each line 1 km Load at bus B 2+j0.97 MVA Load at bus C 1+j0.48 MVA Load at bus D 1.5+0.72 MVA Load at bus E 1+ j0.48 MVA Capacity of IIDG 1 MW

In order to visualize the effect of fault analysis, the relative error shown as follows is cited [33]:

3.1 Influence of the fault type

In this section, different types of faults, including A-phase-to-ground (A-G) faults, phase-to-phase (BC) faults, two-phase-to-ground (BC-G) faults, and three-phase (ABC) faults, are set at the midpoint of line L2 (actual distance=1.5 km).The fault resistance is 0 Ω.The test results are shown in Table 2.

The location results of asymmetrical faults in Table 2 are calculated from (3) and (5).The data in the row “ABC(10)” is calculated from (10), and in the row “ABC(16)” is calculated from (10) and (16).The data in Table 2 show that when different types of asymmetrical faults occur in the PSDN, the φ1-2(2) of no-fault line is 180° whereas that of fault line is extremely small.When the symmetrical fault occurs, the α calculated from current at no-faulty line is extremely large whereas that of fault line is smaller than 1.Otherwise, the estimated distances calculated from (10) and (16) are so precise that the relative error is less than 0.1%.Therefore, the fault line identification method and fault location technology proposed in this paper have good performance for different types of faults.

Table 2 Fault location results for different types of faults

Fault type Fault line identification(φ1-2(2) or α) Estimate distance Non-faulty line(L1) Fault line(L2) d (km) ε (%)A-G 180° 1.16° 1.509 0.18 BC 180° 1.16° 1.509 0.18 BC-G 180° 1.16° 1.509 0.18 ABC(10) 5.77×108 0.374 1.499 0.02 ABC(16) 5.77×108 0.374 1.500 0.00

3.2 Influence of the fault position and fault resistance

In order to test the performance of the proposed method for different fault positions, a series of “A-G” faults and “ABC” faults are set on the line L1, L3, and L4 (actual distance= 0.5 km, 2.5 km, 3.5 km), respectively.The fault resistance is between 0 and 100 Ω.The test results are shown in Table 3.

It can be seen from Table 3 that the fault location method for the asymmetrical fault can locate the fault accurately under different fault resistances and fault positions.The error of the location results originates from the load current in the distribution network.The data show that the load current has little effect on the locating accuracy for asymmetrical fault.

The location results of the symmetrical fault calculated from (10) are accurate for bolted faults.However, when the fault resistance is large, the load current has a great influence on the positive-sequence current.As a result, the error of calculation results for the high-resistance fault is large.On the contrary, the results calculated from (16) are precise and the accuracy is not influence by the fault resistance and fault position.

3.3 Influence of the IIDG penetration

In this section, the performance of the proposed method for different IIDG penetrations is tested.The grid- connected capacity of IIDG is changed from 1MW to 5MW.Some “A-G” faults and “ABC” faults are set on the line L2 (actual distance=1.5 km) and the fault resistance is 0 Ω.The calculation results are shown in Table 4.

Table 3 Fault location results for different fault positions and different fault resistances

Fault type Actual distance (km)Fault resistance (Ω)Estimate distance d (km) ε (%)A-G 0.5 0 0.530 0.60 1 0.530 0.60 10 0.530 0.60 100 0.530 0.60 2.5 0 2.500 0.00 1 2.500 0.00 10 2.500 0.00 100 2.500 0.00 3.5 0 3.486 0.29 1 3.486 0.29 10 3.486 0.29 100 3.486 0.29 ABC(10)0.5 0 0.498 0.04 1 0.364 2.72 10 1.096 11.9 100 11.25 215.0 2.5 0 2.500 0.00 1 2.500 0.00 10 2.501 0.02 100 2.509 0.19 3.5 0 3.500 0.00 1 3.571 1.42 10 4.215 14.3 100 10.96 149.3 ABC(16)0.5 0 0.500 0.00 1 0.500 0.00 10 0.500 0.00 100 0.500 0.00 2.5 0 2.500 0.00 1 2.500 0.00 10 2.500 0.00 100 2.500 0.00 3.5 0 3.500 0.00 1 3.500 0.00 10 3.500 0.00 100 3.500 0.00

Table 4 Fault location results for different IIDG capacities

Fault type IIDG(MW)Fault line identification(φ1-2(2) or α)Estimate distance Non-faulty line(L1)Fault line(L2) d (km) ε (%)A-G 1 180° 1.16° 1.509 0.18 3 180° 1.16° 1.509 0.18 5 180° 1.16° 1.509 0.18 ABC(10)1 5.77×108 0.374 1.499 0.02 3 3.08×109 0.375 1.500 0.00 5 7.77×108 0.375 1.499 0.02 ABC(16)1 5.77×108 0.374 1.500 0.00 3 3.08×109 0.375 1.500 0.00 5 7.77×108 0.375 1.500 0.00

The data in Table 4 show that when only one bus in the PSDN is connected to the IIDG, the accuracy of the proposed method is not affected by the IIDG capacity.

In order to test the performance of the proposed method in the case that IIDGs connect at multiple buses, several 1 MW IIDGs are set at bus B, C, D, and E, respectively.The calculation results are shown in Table 5.In Table 5, the data in the row “ABC(14)” are calculated from (14).

Table 5 Fault location results in the PSDN with multiple IIDGs

Fault type Fault resistance (Ω)Fault line identification(φ1-2(2)or α)Estimate distance Non-faulty line(L1)fault line(L2) d (km) ε (%)A-G 0 180° 1.16° 1.509 0.18 100 180° 1.16° 1.509 0.18 ABC(14)0 8.26×108 0.375 1.499 0.02 10 9.85×108 0.265 1.060 8.80 ABC(16)0 8.26×108 0.375 1.500 0.00 100 9.85×108 0.265 1.500 0.00

Table 5 shows that the proposed method can locate the bolted fault precisely when IIDGs connect at multiple buses.When the fault resistance is high, the accuracy of the asymmetrical fault location method and the symmetrical fault location method based on (16) can be ensured.Overall, the test results in this section show that the proposed fault location method can adapt to different IIDG penetrations.

3.4 Influence of the line length

In this section, the line lengths in the PSDN test system are modified to test the performance of the proposed method in the PSDN with several lines of different lengths.The lengths of line L1～L5 are set to 1 km, 2 km, 1 km, 3 km, and 2 km, respectively.Several 1 MW IIDGs are set at bus B, C, D, and E, respectively.A series of “A-G” faults and “ABC” faults are set on L1, L3, and L4 (actual distance= 0.5 km, 3.5 km, 5.5 km), respectively.The test results are shown in Table 6.

Table 6 Fault location results in the PSDN with several lines of different lengths

Fault type Actual distance (km)Fault resistance (Ω)Estimate distance d (km) ε (%)A-G 0.5 0 0.571 0.79 100 0.571 0.79 3.5 0 3.510 0.11 100 3.510 0.11 5.5 0 5.482 0.20 100 5.482 0.20 ABC(14)0.5 0 0.498 0.02 100 11.92 126.9 3.5 0 3.500 0.00 100 2.025 16.4 5.5 0 5.502 0.02 100 14.44 99.3 ABC(16)0.5 0 0.500 0.00 100 0.500 0.00 3.5 0 3.500 0.00 100 3.500 0.00 5.5 0 5.500 0.00 100 5.500 0.00

It can be seen from the Table 6 that the proposed method has high accuracy for the low-resistance fault location in the PSDN with unequal-length lines.For the high-resistance fault, both the asymmetrical fault location method and the symmetrical fault location method based on (16) perform excellent and have strong ability against fault resistance.The above conclusion is consistent with the conclusion in Section 4.2.Therefore, the line length scarcely affects the performance of the proposed method.

3.5 Comparison Tests

Currently, there are few impedance-based method that can locate both asymmetrical and symmetrical fault positions in the closed-loop distribution network.Therefore, to verify the superiority of the proposed method, an excellent method proposed for the radial distribution network with IIDGs by Alwash is selected to compare with the proposed method [34].

The method in [34] is based on the principle that the dissipative reactive power is equal to zero at the resistive fault position.The dissipative reactive power is estimated by iteration from the voltage and current at the substation bus and PCC.The method is chosen since it has an excellent accuracy and has a great ability against fault resistance in the radial distribution network with IIDGs.

In the test system, the length of each line is 1 km, and several 1 MW IIDGs are set at bus B, C, D, and E, respectively.Table 7 shows the fault location result comparison of the mentioned method and the proposed method for different types of faults on the line L2 with fault resistances of 0 and 10 Ω.

Table 7 Fault location result comparison of proposed method and method in [34] for the PSDN with multiple IIDGs

Fault type Actual distance (km)Fault resistance (Ω)Fault location error (%)Proposed method Method in [34]A-G 1.25 0 0.18 3.26 10 0.18 51.2 1.5 0 0.18 6.50 10 0.19 42.4 1.75 0 0.19 9.75 10 0.19 34.2 ABC(16)1.25 0 0.00 0.06 10 0.00 56.2 1.5 0 0.00 0.00 10 0.00 45.8 1.75 0 0.00 0.00 10 0.00 46.0

It can be seen from Table 7 that the accuracy of the method in [34] is high for the metallic ABC fault, but dramatically decreased with increasing fault resistance.On the other hand, the proposed method has a high accuracy.The voltage iterative algorithm according to the method in [34] is difficult to converge in short-line networks such as the PSDN, and it ignores the fault current supplied by the system from the other end of the loop line.This problem also exists in many impedance-based methods for the radial distribution network [35].The preceding discussion demonstrates the superiority of the proposed scheme in terms of the accuracy and the ability against fault resistance in the PSDN with IIDGs.

4 Conclusion

A practical impedance-based fault-locating method for the PSDN with IIDGs is proposed in this paper based on the negative-sequence current and the positive-sequence current.The following conclusions can be drawn.

(1) Considering the closed-loop structure of the PSDN and the control strategies of IIDGs, the correlation between the negative-sequence current at both ends of the fault line is fully exploited and utilized to calculate the asymmetrical fault position.For the symmetrical fault, the phases and amplitudes of the positive-sequence current on multiple lines are fully utilized to pinpoint the fault position.

(2) The proposed method can give accurate estimates within 1% error from the actual fault position.The method has an excellent ability against transient resistance, and can be well adapted to the flexible connection of IIDGs.

(3) The proposed method has low requirements on the communication channel and data synchronization.In addition, the method only requires current information and avoid the cost for installing potential transformers and traveling wave devices.The proposed criterion for fault line location can also be used as a supplement to the traditional protection.

In order to avoid the fault location error due to the communication synchronization error, the superposition of phase differences is used to replace the current phase measured by the instantaneous value directly transmitted.However, the accumulated phase measurement errors between upstream and downstream switching stations may reduce the accuracy of fault location.In the future, further research can be carried out in two directions: reducing the data synchronization error and locating the fault position based on local or dual-end information.

Acknowledgements

This work was supported by State Grid Science and Technology Project: Research on Key Protection Technologies for New-type Urban Distribution Network with Controllable Sources and Loads (5100-201913019A-0-0-00).

Declaration of Competing Interest

We declare that we have no conflict of interest.