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Single phase fault diagnosis and location in active distribution network using synchronized voltage measurement
Electrical Power and Energy Systems 117 (2020) 105572
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Single phase fault diagnosis and location in active distribution network using synchronized voltage measurement Tong Zhanga, Haibin Yub,c, Peng Zengb,c, Langxiang Sunb,c, Chunhe Songb,c, Jianchang Liua,
T ⁎
a
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110812, China c University of Chinese Academy of Sciences, Beijing 100049, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Active distribution network Single-phase-to-earth fault Phasor measurement unit Phasor distribution characteristic Fault diagnosis and location
To ensure the safe operation of the active distribution network (ADN), accurate fault diagnosis and location are crucial to improve the reliability indices and reduce the outage time. This paper proposes a characteristic modelbased method for the single phase to earth fault in the ADN system. Firstly, the characteristic model of the fault factor extracts the phasor distribution characteristics of the voltage and current along the distribution feeder line and estimates the current contribution of DG units to the fault point. Based on the minimum entropy theory, the solution of nonlinear characteristic model is transformed to a single-objective optimization of the characteristic entropy and the diagnosis criteria is formulated. Then, the two-stage fault location scheme for single phase fault is proposed. The fault diagnosis stage estimates the suspicious fault section to reduce the search area and the fault location stage locates the exact fault distance. The Fibonacci search algorithm is utilized for fault location to the optimize iterative and minimize the respond time. The proposed scheme is general for all DG types and overcomes the requirement of its individual model parameters. The proposed method is validated in the IEEE 34bus distribution test system using the phasor measurement unit (PMU). Test results of the model-based diagnosis and location method can reveal accurate fault location and rapid response at different fault impedance and small time delay comparing with the radial basis function neural network (RBF), and wavelet neural network (WNN) method.
1. Introduction With the growing sustainable power demand, the ADN system proposes higher demand on distribution fault management to maintain the power supply reliability and minimize the outage time [1]. As the consumer part of power systems, the active distribution network (ADN) system are geographically dispersed over vast urban areas and hence exposed to harsh and uncertain environments [2]. Due to the branched topological dispersity and the continuous operation after fault, the ADN system fault may cause large scale cascading faults and stress the rest of the grid [3]. Therefore, the fault location is an important task for fast maintenance and restoration of the electricity supply. The fault diagnosis and location methods for distribution networks are categorized as: intelligent methods, travelling wave methods and impedance-based methods [4–7]. The intelligent location schemes generally contain the feature extraction process and the training regression process. Fei [8] located the common faults using the support vector regression (SVR) with short feature extraction time. Then the
⁎
performance of the artificial intelligent method was correspondingly dependent on the sample size and the fault cases of the training process. A single-terminal traveling wave location method was presented in [9] and determined the fault distance by taking the time difference between the first two aerial modes of the current traveling wave. Furthermore Ngu demonstrated that the detail line model could improve the location accuracy of the traveling wave method. Although traveling wave methods yielded high accuracy and robustness to arcs, the complex refraction of traveling waves and the high sample rate (MHz) demand restrain its application in distribution networks [10]. The impedance-based methods analyze the voltage and current at both terminals of the fault branch using lower sample rate measurement. The fault location is determined by searching the fault characteristic index along the line such as the maximum zero-sequence current, minimum fault reactance and fault current flow [11,12]. Florez [13] summarized that the characteristic indexes are mainly differentiated by the system topological structure, line and load models. Furthermore, Saber [14] concluded the effect of the characteristic
Corresponding author at: College of Information Science and Engineering, Northeastern University, Shenyang 110819, China. E-mail address: [email protected] (J. Liu).
https://doi.org/10.1016/j.ijepes.2019.105572 Received 1 May 2019; Received in revised form 1 August 2019; Accepted 23 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
Electrical Power and Energy Systems 117 (2020) 105572
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Iḟ if Iḟ
Nomenclature f x lij Zc γ i, j Pm m n Vḟ Iḟ
the fault current component from upstream bus i
the fault current component from downstream bus j jf Z the expanding impedance matrix of the AND Zkf the k-f element of the expanding impedance matrix Vṅ post-fault voltage at the bus n measured by PMU pre Vṅ pre-fault voltage at the bus n measured by PMU difference of pre- and post-fault voltage phasors ΔVṅ ′ arg (Vḟ (x )) phase angle of post-fault voltage phasor at the fault point f Θ the n × m characteristic matrix H the entropy matrix
index of fault point fault location variate in per unit from bus i length of the fault branch the characteristic impedance propagation constant indices of fault line terminals index of bus whose voltage is measured number of buses installed PMU total number of network buses post-fault voltage at the fault point f post-fault current at the fault point f
model fitting degree on the location performance. Therefore, the fault characteristic model plays an important role in the impedance-based method. Teke [15] used the simple short-line approximation model to estimate the fault current difference and calculated the fault location through deriving of the equivalent voltage model. To enhance the location accuracy, based on the minimum fault reactance concept, Orozco [16] proposed an accurate estimation model of the fault reactance considering the lump parameter line model and achieved accurate fault location. Liang [17] analyzed the distribution characteristic of the zerosequence voltage to construct the fault measure matrix and distinguish the fault section. Recently the promoted trend for the phasor measurement units (PMU) application to the distribution system has attracted researcher attention [18,19]. The recent reports focused on the phasor estimation and feature extraction for distribution networks [20]. Alanzi [21] extracted the voltage phase angle shift as distinctive features to differentiate the faulty phases. The common fault events are classified accurately by comparing the phasor shift in the fault process. Marco [22] compared the weighted measurement residuals of the parallel state estimator to identify the fault branch. Dobakhshari [23] expressed the phase angle and magnitude of each voltage measurement as the fault location function using complex calculus. In the proposed nonlinear location function, the fault distance is solved iteratively by NewtonRaphson method and the initial values of positive-sequence fault
current is estimated. Within the context of PMU-based protection, this work proposes a characteristic-model based fault diagnosis and location method for single-terminal radial distribution system with mixed feeder lines. The characteristic model is formulated to extract the distribution phasor characteristics of the voltage drop and current flow along the distribution feeder line. Then, based on the entropy theory, the solution of the nonlinear characteristic model is converted to the linear optimization for the characteristic entropy index. Based on the entropy criterion, the fault location is estimated by searching the minimum characteristic entropy. To optimum iterative and reduce respond time, the Fibonacci search algorithm is utilized. The rest of the paper is organized as follows. In Section 2, the characteristic-model based on phasor analysis is demonstrated and solved by the Shannon entropy method. Section 3 generalizes the characteristic index to the ADN system. The detailed implementation of the two-stage fault location method is presented. Section 4 is devoted to the test results and the performance evaluations. The location results of the model-based method are compared with other fault location methods. Section 5 draws the conclusion.
Fig. 1. The circuit model of the single-phase-to-earth fault in the ADN system. (a) Fault distribution line model. (b) Distributed parameter equivalent circuit model of infinitesimal segment. 2
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2. Principle of the model-based location method
the distribution branch
2.1. Circuit analysis of fault characteristics
Iḟ =
Considering a fault occurring at point f along random distribution line i-j at distance dif = xlij from bus i, which divides the line section into two segments. The distribution line is considered as the fully transposed line and the distributed parameter line model for the medium-length distribution line is shown in Fig. 1. In Fig. 1, the fault point f is defined as the expanding virtual bus. Applying the boundary conditions [24] from the monitoring bus i and j, the voltage Vḟ and current Iḟ at the fault point f are calculated as follows,
From the line section se which is connected to the substation bus, the estimation of the fault voltage is obtained using the measured phasors of the upstream line section. In formula (1), the voltage of bus i is obtained from the upstream line section as
− Zc sinh(γxlij ) ⎤ ⎡Vi̇ ⎤ ⎡Vḟ ⎤ ⎡ cosh(γxlij ) ⎢ I ̇ ⎥ = ⎢− (sinh(γxl ))/ Z ⎢ ̇⎥ cosh(γxlij ) ⎥ ij c ⎦ ⎣ Ii ⎦ ⎣ if ⎦ ⎣
ΔVi̇ Zi, (n + 1) (x )
(8)
Vi̇ = cosh(γlui ) Vu̇ − sinh(γlui ) Zc Iu̇
(9)
The upstream current Ii̇ of the branch i-j is calculated by subtracting the load and laterals currents connected to bus i from the receiving current of the upstream line section u-i as
Ii̇ = Iui̇ − Ii,̇ Lt (1)
(10)
From formula (1), the current I j̇ at the downstream bus j is estimated from the random bus k.
where Ii,̇ Lt represents the load and lateral currents of bus i. By separating the load and lateral subsystem, the current Ii,̇ Lt of bus i can be estimated as
I j̇ = (Ik̇ Zjk cosh(γ (1 − x ) lij ) − Ii̇ Zc sinh(γxlij ) − Ik̇ Zik cosh(γxlij ))
Ii,̇ Lt = Z−di1Vi̇ − Z−di1
/(Zc sinh(γ (1 − x ) lij ))
N
̇ Zik IGk
̇ is the PMU-measured current at the DG unit export connected where IGk to bus k. Zdi represents the driving point impedance at bus i, which is the diagonal element of the expanding impedance matrix Z. Then, the sending-end current Ii̇ is calculated as
Iḟ = Iiḟ + Iiḟ Zc cosh(γxlij ) Zc ·I ḟ − ·Ii̇ sinh(γxlij ) sinh(γxlij )
N
Rf
(3)
Ii̇ = cosh(γxlui ) Iu̇ − sinh(γxlui ) Vu̇ / Zc − Z−di1Vi̇ + Z−di1
Iḟ = (Ik̇ Zjk − Ik̇ Zik cosh(γlij ) − Ii̇ Zc sinh(γlij ))/(Zc sinh(γ (x − 1) lij ))
N
+ Z−di1
∑
(13)
The model-based location method is derived considering the following assumption: the fault impedance of the metal fault is pure resistance [25]. The above assumption is common in the literature dealing with the location issue [26]. Therefore, from the observable bus i and j, the voltage and current phase angle signals at the fault branch satisfies the following principle
− Zik Rf cosh (γlij ) sinh (γxlij )
(5)
Therefore, considering the distributed parameter line model, the transfer impedance matrix Zkf between the fault point f and bus k is obtained. When the multi-concurrent fault occurs in the n-bus system, multiple coupling fault points appear. All the fault points are defined as the expanding virtual buses. Based on the topological structure and system component parameters, the expanding impedance matrix Z of the whole ADN system is derived as follows
arg (Vḟ (x )) arg (Vḟ (x )) = ̇ arg (ΔVi /(Zi, n + 1 (x ))) arg (ΔVj̇ /(Zj, n + 1 (x )))
(14)
where arg() represents the calculation for phase angle signal, Zi,n+1(x) implies the equivalent impedance at point f with the assumed fault location x as calculated in formula (6). Therefore, the fault feature is extracted as the phase angle characteristic. As the m PMUs installed in ADN system, the synchronized phasor signals of the wide area are obtained. In the whole network range, from the random measurable bus l, the phase angle relationship of the fault voltage and current satisfies the following principle
(6)
θ P1 = θl = θ Pm 2.2. Phasor characteristic model
(l = P1, P2, P3⋯Pm)
(15)
Then, the fault characteristic model θl (x) is defined as
θl (x ) = arg (Vḟ (x ))/ arg (ΔVl̇ /(Zlf (x )) 0 < x < 1
Assuming that m PMUs are installed in the n-bus ADN system; a fault has occurred at i-j bus branch. Based on the expanding resistance matrix Z, the voltage sag ΔVi̇ of the expanding ADN system as pre ⎡ V1̇ − V1̇ ⎤ 0⎤ ⎡⋯ ⋯ ⎢ ⎥ ⎥ ⎢ Vṅ − V̇ pre ⎥ = Z ⎢ ⎢0⎥ n ⎢ ⎥ İ ⎢ ̇ ̇ pre ⎣ f⎥ ⎦ ⎢ ⎣Vn + 1 − Vn + 1⎥ ⎦
̇ ) Zik IGk
k = 1, k ≠ i
− Zik Zc2 cosh (γxlij ) sinh (γxlij ) cosh (γlij )))
Z1n Z1, n + 1 (x ) ⎤ ⋯ ⋯ ⋯ ⋯ ⎥ Znn Zn, n + 1 (x ) ⎥ ⋯ ⎥ ⋯ Zn + 1, n (x ) Zn + 1, n + 1 (x ) ⎦
(12)
Vḟ = cosh(γxl) Vsk̇ − Zc sinh(γxl)(cosh(γxl) Isu̇ − sinh(γxl) Vḟ su/Zc − Z−di1Vi̇
Zik Zc2 cosh (γxlij )2sinh (γlij )
/(Zik Zc cosh (γlij ) − Zjk Zc + Zik Zc2 cosh (γxlij ) sinh (γlij ))
Zik IGk
Substituting (11) and (12) in (1), the fault voltage Vḟ is estimated as
(4)
On the basis of the mutual impedance definition, from (1) and (4), the transfer impedance vector Zkf between the bus k and fault point f is shown below
Zkf = (Zki (Rf Zjk sinh (γxlij ) +
∑ k = 1, k ≠ i
Substituting (1)–(3), the fault current Iḟ can be expressed as
Z12 ⎡ Z11 ⋯ ⎢ ⋯ Z=⎢ Z Zn2 n1 ⎢ ⎣ Zn + 1,1 (x ) Zn + 1,2 (x )
(11)
k = 1, k ≠ i
(2)
The fault current Iḟ is derived as
⎧ ⎪ ⎨ ̇ ⎪ If = ⎩
∑
(16)
When the Rf is higher than 187.7 Ω, the partial derivative d(θl(x,Rf))/d (Rf) is less than 0.011 and the proposed model is affected weakly by the fault resistance Rf. The proposed fault characteristic model θ(x) can extract accurate fault features based on the phasor analysis. Furthermore the fault characteristic model is applicable to other fault types, such as the three phase to earth fault. In the extension for other fault types, the phase-phase and phase-ground fault resistance effect should be considered and a two-terminal fault location method can
(7)
Therefore, the fault current Iḟ is obtained from other terminal i of 3
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3. The two-stage fault location scheme
reduce the fault resistance effect [27,28].
The precise fault location method contains 2 stages. First, based on the fault characteristic model, with PMU measurements, the potential fault section is estimated using the diagnosis criteria. Then, the voltage and current phasors of the estimated fault branch are extracted and h(x) is calculated for fault location. In the location stage, the Fibonacci algorithm is used to search the precise location result.
2.3. Entropy theory The entropy method measures the pattern similarity degree of the feature signals and shows well robustness for transient interference [29]. As entropy depends on the similarity degree more than the absolute value and is related to higher order moments. It can offer a better nonlinear characterization to measure the system consistency. From (11), the proposed characteristic model is nonlinear and fault features measured by PMU is non-stationary. Therefore combining the entropy theory and referring to (10), solving the nonlinear fault characteristic model is transferred to the following linear entropy problem. The fault characteristic vector θl(x) is normalized as
pl (x ) =
θl (x ) max{θθ P1 (x ), θθ P2 (x )⋯θ Pm (x )} m
3.1. Fault section diagnosis criteria Referring to (6) and (11), the fault characteristic matrix Θ of the whole ADN system is calculated as
⎧ ⎪ ⎪
(17)
⎨ ⎪ ⎪ θlk = ⎩
The characteristic entropy function h(x) is
1 h (x ) = − ln n
m
∑ pl (x ) ln pl (x ) l=1
⎡ θ11 θ12 ⎢θ θ Θ = ⎢ 21 22 ⋮ ⋮ ⎢ ⎣ θm1 θm2 arg (Vk̇ ) , arg (ΔVl̇ / Zlk )
⋯ θ1n ⎤ ⋯ θ2n ⎥ ⋱ ⋮ ⎥ ⎥ ⋯ θmn ⎦
1⩽ k ⩽ n,
1 ⩽ l ⩽ m.
(19)
To measure the consistency of fault characteristic index at bus k, the fault characteristic entropy (FCE) vector H is calculated as
(18)
The characteristic entropy function h(x) measures the consistency of fault characteristic index. The orderly system has lower information entropy. For example, the entropy of a Dirac delta distribution will be the minimum, where the probability mass is concentrated at a single point. Then, the corresponding distance of the minimum entropy h(x) is estimated as the fault location. Based on the above analysis, the modelbased method can estimate the quantitative fault location directly, which simplifies the training process of the artificial intelligence algorithms.
m
⎧ hk = − 1 ∑ p ln p , k = 1, 2, ⋯, n, lk lk ln n l=1 ⎨ H = [h1⋯ hk⋯hn]. ⎩
(20)
Then the FCE vector H is calculated as the diagnosis index to estimate fault branch. As the analysis in Section 2, after the fault occurs, the FCE value hk of the fault buses decreases. The fault section k* is selected as,
Fig. 2. The flowchart for fault diagnosis and location stage. 4
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k ∗ ∈ {hk ⩽ h 0}, k = 1, 2⋯39,
and θ862c remain at 4.419 and 4.371. After the single-phase to earth fault occurs, the fault characteristic θ836c and θ862c decrease to 78.208% to 0.963 at 1.06 s. The response time is within 0.1 s. In the fault progress, the fault characteristic value of C-phase decreases while those of A-phase and B-phase maintain the normal state, which indicates that the fault feature of the C-phase is extracted accurately.
(21)
where h0 is the entropy threshold for fault diagnosis, which is a threshold range to identify the fault state and the normal work state. In this paper h0 is set as 0.6. 3.2. Fault location criteria Based on the fault diagnosis result in Section 3.1, the voltage phasors of the potential fault branch i-j are extracted by PMU. By employing (1)–(11), the fault characteristic model θ(x) is extracted as
4.2. Fault diagnosis result analysis Based on the diagnosis criteria in formula (16), the entropy vector hi for C-phase to earth fault in the whole ADN system is calculated in Fig. 5. In Fig. 5, h836 is 0.090 and h862 is 0.091. The FCE values of bus 836 and 862 are significantly less than other buses, which matches the analysis in Section 2 that the characteristic vector of the fault branch is well ordered. Then, the branch 836–862 bus is diagnosed as the fault section, which conforms to the actual situation. Fig. 6 shows the synchronized fault diagnosis result of bus 862 in the fault process. In the normal state, the FCE value h862 maintains to 1.628 and fluctuates slightly. At the fault inception instant at 3 s, the FCE curves of bus 862 decline 94.103% in 0.08 s. In Fig. 6, when Rf is 0.01, 0.5, 2, 20 and 100 Ω, the h862 decreases to 0.096, 0.119, 0.122, 0.138 and 0.244 respectively. Due to the significant decrease of h862, bus 862 is diagnosed as the fault bus. In the 600 test cases, as the fault resistance increases, the characteristic entropy of the fault state rises slightly, which is far below the threshold 0.6. The diagnosis accuracy is 98.667% and the respond time is within 0.1 s. Therefore, the proposed diagnosis method can monitor the whole ADN system synchronously at low resistance and high resistance fault.
θli (x ) = arg (Vḟ )/ arg (ΔVl̇ /(Zlf (x ))) ̇ / Zc = arg (cosh(γxl) Vsk̇ − Zc sinh(γxl)(cosh(γxl) Isu̇ − sinh(γxl) Vsu − Z−di1Vi̇ + Z−di1
N
∑
̇ ))/ Zik IGk
k = 1, k ≠ i
(arg ((ΔVl̇ (z li z c cosh(γl) − z c z li z c2 z li cosh(γxl) sinh(γl))) /(z il (Rf zji sinh(γxl) + z c2 z li cosh(γx )2· sinh(γl) − Rf z li sinh(γxl) cosh(γl) − z c2 z li cosh(γxl) sinh(γxl) cosh(γl)))) (22) Therefore the fault characteristic matrix for fault location is θi(x) = [θ1i(x), θ2i(x)…θmi(x)]. Then referring (13), the corresponding model-based fault location function h(x) of the fault bus i is calculated as
h (x ) = −
1 ln n
m
∑ pli (x ) ln pli (x ). l=1
(23)
The characteristic entropy function h(x) fulfills the mirrored minimum energy (MME) property demonstrated in [30]. Then, solving formula (18) is transferred to the following optimization formula,
⎧ min{h (x )}, ⎨ ⎩ x ∈ [0, 1].
4.3. Effect of different noise levels In order to study the noise effect on the location accuracy, the location performance was tested with signal to noise ratio (SNR) values between 10 and 20 dB. The A-phase to earth fault occurs at 34% from bus 862. The fault location results are are analyzed with no-noise, 10 dB and 20 dB noise levels respectively in Fig. 7. Fig. 7(a) shows the detail location result at no-noise state. The global minimum FCE is located at xh_min = 33.98% and the location error is e = 0.02%. In the noise condition, Fig. 7(b) shows the location result at 20 dB noise level. The global minimum FCE is located at xh_min = 33.94% and the location error is e = 0.06%, while the location error in [32] is 2.832%. Fig. 7(c) shows the location result at 10 dB noise level. The fault location error of the proposed method is 0.13%, while the location error in literature [32] is 5.211%. The noise signals can affect the characteristic calculation in Formula (14). However, the entropy method measures the consistency of the character vector instead of comparing the magnitude directly and the noise effect is reduced. In Fig. 7, under different noise conditions, an overall location accuracy of 99.93% and diagnosis accuracy of 98.109% can be still obtained. Therefore, the proposed characteristic-model based method is robust for different noise levels.
(24)
where xh_min is the location result located at the minimum entropy point. Therefore, the systematic variation x can be solved based on the minimum FCE concept. Instead of analyzing the operating state at each bus, the fault diagnosis stage first estimates the fault branch to reduce the size of the searching space. Then, the Fibonacci search algorithm is applied in the iterative process, which reduces the number of iteration points greatly. Thus, in the large scale transmission and distribution network, the two-stage location method can achieve second level response. Then, the complete flowchart for fault diagnosis and location is shown in Fig. 2. 4. Simulation results and analysis 4.1. Fault characteristic extraction The characteristic model-based method is tested in the IEEE 34-bus distribution system. Transient simulations for fault events under different fault resistances and fault types were carried out in MATLAB. The online diagram of the 34-bus distribution system is provided in Fig. 3 and the system parameters are presented in [31]. The 24.9-kV IEEE 34bus system includes 34 buses, 33 branches, and 2 distributed generation (DG) integrated. The PMUs were installed in the ADN system based on the installation criteria: (a) at least one-terminal voltage of the distribution branch is directly measured or indirectly estimated by PMU, (b) the substation bus and the terminal of each DG units are measurable. The PMU installation in the IEEE 34-bus system is at 800, 808, 814, 816, 824, 828, 832, 836, 834, 844, 848, 854, 858, 890 bus. Supposing that a C-phase to earth fault occurs at 55.53% from bus 836 (as shown in Fig. 1, i = 862, j = 836, x = 0.5553). The fault occurs at 1 s and is cleared at 2 s. The fault characteristic values θ836 and θ862 are shown in Fig. 4. In the normal operation progress (0–1 s), the θ836c
Fig. 3. The IEEE 34-bus test distribution system. 5
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Fig. 4. The fault characteristic component signal.
Fig. 5. Fault diagnosis result for the C-phase to earth fault in ADN system.
Fig. 7. The detail location result at different noise levels. (a) no noise, (b) 20 dB noise level, (c) 10 dB noise level.
Fig. 6. Synchronized diagnosis result under different fault resistance.
4.4. Effect of DG penetration level In order to test the effect of DG penetration level, five groups of simulation tests are conducted in branch 848–846. The relative location errors of the proposed method are calculated as the ratio of the real fault distance with the increasing DG penetration level in Fig. 8. For this case, the proposed location method exhibits a trend to underestimate the fault distance as the DG penetration level increases, reaching an average error of 0.084% for a penetration level of 25%. This behavior is due to the increasing penetration, which increases the error in the estimation component of ZikIGk contributed to the fault location from the DG units. From Fig. 8, the fault location error decreases when the fault point close to the bus 848 (PMU installed), due to more accurate estimation of the fault voltage using the phasor signals measured by PMU. Thus, the proposed method is applicable to the medium and short distribution line.
Fig. 8. Location performance of the proposed method at increasing DG penetration level.
impedance-based method [32], the radial basis function neural network (RBF) and wavelet neural network (WNN) are compared. The location error efce, e[32], eRBFNN and eWNN are 0.325%, 2.104%, 5.741% and 3.688%; the respond time tfce, t[32], tRBFNN and tWNN is 0.847 s, 115.969 s, 57.088 s and 36.193 s, respectively. Table 1 clearly shows that the proposed method decreases 1.779% location error comparing with the location method in [32]. Furthermore, the model-based method has advantage of the operating speed and reduces respond time 63.583 s comparing with the iterative algorithm and the neural network
4.5. Comparative assessment for location accuracy and respond time The online fault location requires the performance index of the location error e and the respond time t. To evaluate the location performance, a C-phase to earth fault occurs at 80% from bus 846 in the 846–848 branch is considered. In Table 1, the location errors of the 6
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Table 1 Comparative assessment for location accuracy.
Location error (%) Rf = 0.01 Ω Location error (%) Rf = 2 Ω Location error (%) Rf = 100 Ω
The proposed method
Jiang [32]
RBF [33]
WNN [34]
0.023 0.186 0.767
1.365 1.692 3.254
3.255 5.769 8.198
2.515 3.032 5.517
Table 2 Location result with measurement error. Influence factors
Location result (%)
Error (%)
The parameters are totally accurate Both pre-fault and post-fault PMU magnitude measurement error ( ± ) 2% Both pre-fault and post-fault PMU phase angle measurement error ( ± ) 2% Pre-fault PMU phase angle measurement error ( ± ) 2% Post-fault PMU phase angle measurement error ( ± ) 2% Line parameter error in fault branch 846–848 is 20%
54.943 54.937 53.658 53.259 53.338 54.928
0.057 0.063 1.342 1.741 1.662 0.072
Table 3 Fault location result of different PMU installation scheme. Fault location
Fault type
Branch
Fault distance
836–862 836–862 846–848
45% from bus 836 75% from bus 836 65% from bus 848
AG BG BG
Bus 848 without PMU
Bus 848 with PMU
Error (%)
Error (%)
0.648 0.967 12.785
0.022 0.037 0.026
impedance fault, the proposed method can locate the fault distances accurately with an estimation error 1.647% at a time delay 59.58 μs. In the actual operating condition, the PMU delay time standard is typically tens of microseconds and the location error of the proposed method is less than 1.575%. These results demonstrated that the performance of the proposed method is reliable using PMUs with imperfect synchronization, within the time delay 59.58 μs. To test the effect of the PMU installation scheme on the location accuracy, different types of faults occurring in the distribution branch are analyzed. It is assumed that the fault occurs in 846–848 branch. Due to the complicated symmetry of the system, without PMU installed in the inner bus, the data loss of bus 848 increases the estimation error of fault voltage Vf (x). The phasor estimation error can increase the location error of the proposed method. With a PMU installed at bus 848, ̇ and the current I848 ̇ of the receiving terminal (bus 848) the voltage V848 can be measured directly. In Table 3, the fault location error does not exceed 0.04% with the optimal PMU install scheme. The location error significantly decreases 12.759% with bus 848 installing PMU. Therefore, an appropriate PMU placement scheme can ensure the accurate calculation of the FCE and maintain the location accuracy. The proposed characteristic-model based method can provide optimization index for the PMU installation scheme.
Fig. 9. Location result at different time delay cases.
with training process [32–34]. The main reason is that in the location stage, the Fibonacci search algorithm optimizes the iteration and reduces uncertainty range by xm and xm′. Then, the proposed location method can achieve second-level response. 4.6. Effect of measurement parameter To evaluate the sensitivity of the model-based method, the performance of the proposed method at different PMU factors are analyzed in Tables 2 and 3. The A-phase to earth fault occurs at 55% from bus 848 in the 846–848 branch. As network parameters vary in weather and loading practice conditions [35], test cases operate considering an additional situation of 2% error in network parameters. The mean error of the model-based location method is 0.823%, which is acceptable in the practice condition. To analyze the time delay of PMU effect on the proposed method, the performance of the proposed method at different time delay cases are evaluated in Fig. 9. The time delay tk causes the phase mismatch φp (φp = 2πftk) and the estimation of the voltage is modified as U’i,k(kT + tk) = Ui,k(kT + tk)sin(2πf(kT + tk) + φi(kT + tk)). The measurement time delay 60 μs can cause estimation error of 2.380%. In the time delay range 13.37–53.58 μs, the proposed method estimated the fault distances accurately with an average error 0.612%. In low-
5. Conclusion This paper presented an analytical method for the single phase to earth fault in ADN system based on the phasor characteristic model. It targets location identification of medium-length distribution line with the penetration of multiple DGs. The fault characteristic index is calculated to extract the phasor shift distribution feature based on characteristic model which is applicable for all fault types. Then, the consistency of the fault characteristics is measured adopting the Shannon entropy and the fault location problem is presented as a single-objective optimization. The potential fault location is identified using the Fibonacci search algorithm to improve the estimation process. The proposed method shows well performance and robustness against small delay time and high impedance fault using the locally available voltage 7
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phasors and synchronized current phasors at each DG. For common fault conditions, the diagnosis rate is 98.732%, the location error is below 0.767% and the respond time is less than 0.847 s. Furthermore, the location analysis of different PMU installation schemes implies that the characteristic model-based method has important significance in PMU optimized installation.
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Acknowledgement This work was supported in part by the National Natural Science Foundation of China (NSFC) No. 61773106, National Key R&D Program (2017YFB0902900 & 2017YFB0902901) and the Fundamental Research Funds for the Central Universities (N160403003). References [1] Dashti Rahman, Ghasemi Mohsen, Daisy Mohammad. Fault location in power distribution network with presence of distributed generation resources using impedance based method and applying pi line model. Energy 2018;159(15):344–60. [2] Rabiee Abbas, Mohseni-Bonab Seyed Masoud. Maximizing hosting capacity of renewable energy sources in distribution networks: a multi-objective and scenariobased approach. Energy 2017;120(1):417–30. [3] Ji Haoran, Wang Chengshan, Li Peng, Song Guanyu, Wu Jianzhong. SOP-based islanding partition method of active distribution networks considering the characteristics of DG, energy storage system and load. Energy 2018;155(15):312–25. [4] Girgis Adly A, Hart David G, Peterson William L. A new fault location technique for two- and three-terminal lines. IEEE Trans Power Deliv 1992;7(1):98–107. [5] Lopes Felipe V, Dantas Karcius M, Silva Kleber M, Costa Flavio B. Accurate twoterminal transmission line fault location using traveling waves. IEEE Trans Power Deliv 2018;33(2):873–80. [6] Novosel D, Hart DG, Udren E, Garitty J. Unsynchronized two-terminal fault location estimation. IEEE Trans Power Deliv 1996;11(1):130–8. [7] Daisy Mohammad, Dashti Rahman. Single phase fault location in electrical distribution feeder using hybrid method. Energy 2016;103(15):356–68. [8] Fei Chunguo, Qi Guoyuan, Li Chunxin. Fault location on high voltage transmission line by applying support vector regression with fault signal amplitudes. Electr Power Syst Res 2018;160(July):173–9. [9] Ngu EE, Ramar K. A combined impedance and traveling wave based fault location method for multi-terminal transmission lines. Int J Electr Power Energy Syst 2011;33(10):1767–75. [10] Kopyt Pawel, Salski Bartlomiej, Zagrajek Przemyslaw, Janczak Daniel, Sloma Marcin, Jakubowska Malgorzata, et al. Electric properties of graphene-based conductive layers from DC up to terahertz range. IEEE Trans Terahertz Sci Technol 2016;6(3):480–90. [11] Salim Rodrigo Hartstein, Resener Mariana, Filomena Andre Daros, Caino de Oliveira Karen Rezende, Bretas Arturo Suman. Extended fault-location formulation for power distribution systems. IEEE Trans Power Deliv 2009;24(2):508–16. [12] Xiu Wanjing, Liao Yuan. Accurate transmission line fault location considering shunt capacitances without utilizing line parameters. Elect Power Compo Syst 2011;39(16):1783–94. [13] Mora-Florez J, Melendez J, Carrillo-Caicedo G. Comparison of impedance based fault location methods for power distribution systems. Electr Power Syst Res 2008;78(4):657–66. [14] Saber Ahmed. Fault location algorithm for multi-terminal mixed lines with shared tower and different voltage levels. IET Gener Transm Distrib 2018;12(9):2029–37. [15] Gush Teke, Bukhari Syed Basit Ali, Haider Raza, Admasie Samuel, Oh Yun-Sik, Cho Gyu-Jung, et al. Fault detection and location in a microgrid using mathematical morphology and recursive least square methods. Int J Elec Power 2018;102(November):324–31.
8
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Single phase fault diagnosis and location in active distribution network using synchronized voltage measurement Tong Zhanga, Haibin Yub,c, Peng Zengb,c, Langxiang Sunb,c, Chunhe Songb,c, Jianchang Liua,
T ⁎
a
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110812, China c University of Chinese Academy of Sciences, Beijing 100049, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Active distribution network Single-phase-to-earth fault Phasor measurement unit Phasor distribution characteristic Fault diagnosis and location
To ensure the safe operation of the active distribution network (ADN), accurate fault diagnosis and location are crucial to improve the reliability indices and reduce the outage time. This paper proposes a characteristic modelbased method for the single phase to earth fault in the ADN system. Firstly, the characteristic model of the fault factor extracts the phasor distribution characteristics of the voltage and current along the distribution feeder line and estimates the current contribution of DG units to the fault point. Based on the minimum entropy theory, the solution of nonlinear characteristic model is transformed to a single-objective optimization of the characteristic entropy and the diagnosis criteria is formulated. Then, the two-stage fault location scheme for single phase fault is proposed. The fault diagnosis stage estimates the suspicious fault section to reduce the search area and the fault location stage locates the exact fault distance. The Fibonacci search algorithm is utilized for fault location to the optimize iterative and minimize the respond time. The proposed scheme is general for all DG types and overcomes the requirement of its individual model parameters. The proposed method is validated in the IEEE 34bus distribution test system using the phasor measurement unit (PMU). Test results of the model-based diagnosis and location method can reveal accurate fault location and rapid response at different fault impedance and small time delay comparing with the radial basis function neural network (RBF), and wavelet neural network (WNN) method.
1. Introduction With the growing sustainable power demand, the ADN system proposes higher demand on distribution fault management to maintain the power supply reliability and minimize the outage time [1]. As the consumer part of power systems, the active distribution network (ADN) system are geographically dispersed over vast urban areas and hence exposed to harsh and uncertain environments [2]. Due to the branched topological dispersity and the continuous operation after fault, the ADN system fault may cause large scale cascading faults and stress the rest of the grid [3]. Therefore, the fault location is an important task for fast maintenance and restoration of the electricity supply. The fault diagnosis and location methods for distribution networks are categorized as: intelligent methods, travelling wave methods and impedance-based methods [4–7]. The intelligent location schemes generally contain the feature extraction process and the training regression process. Fei [8] located the common faults using the support vector regression (SVR) with short feature extraction time. Then the
⁎
performance of the artificial intelligent method was correspondingly dependent on the sample size and the fault cases of the training process. A single-terminal traveling wave location method was presented in [9] and determined the fault distance by taking the time difference between the first two aerial modes of the current traveling wave. Furthermore Ngu demonstrated that the detail line model could improve the location accuracy of the traveling wave method. Although traveling wave methods yielded high accuracy and robustness to arcs, the complex refraction of traveling waves and the high sample rate (MHz) demand restrain its application in distribution networks [10]. The impedance-based methods analyze the voltage and current at both terminals of the fault branch using lower sample rate measurement. The fault location is determined by searching the fault characteristic index along the line such as the maximum zero-sequence current, minimum fault reactance and fault current flow [11,12]. Florez [13] summarized that the characteristic indexes are mainly differentiated by the system topological structure, line and load models. Furthermore, Saber [14] concluded the effect of the characteristic
Corresponding author at: College of Information Science and Engineering, Northeastern University, Shenyang 110819, China. E-mail address: [email protected] (J. Liu).
https://doi.org/10.1016/j.ijepes.2019.105572 Received 1 May 2019; Received in revised form 1 August 2019; Accepted 23 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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Iḟ if Iḟ
Nomenclature f x lij Zc γ i, j Pm m n Vḟ Iḟ
the fault current component from upstream bus i
the fault current component from downstream bus j jf Z the expanding impedance matrix of the AND Zkf the k-f element of the expanding impedance matrix Vṅ post-fault voltage at the bus n measured by PMU pre Vṅ pre-fault voltage at the bus n measured by PMU difference of pre- and post-fault voltage phasors ΔVṅ ′ arg (Vḟ (x )) phase angle of post-fault voltage phasor at the fault point f Θ the n × m characteristic matrix H the entropy matrix
index of fault point fault location variate in per unit from bus i length of the fault branch the characteristic impedance propagation constant indices of fault line terminals index of bus whose voltage is measured number of buses installed PMU total number of network buses post-fault voltage at the fault point f post-fault current at the fault point f
model fitting degree on the location performance. Therefore, the fault characteristic model plays an important role in the impedance-based method. Teke [15] used the simple short-line approximation model to estimate the fault current difference and calculated the fault location through deriving of the equivalent voltage model. To enhance the location accuracy, based on the minimum fault reactance concept, Orozco [16] proposed an accurate estimation model of the fault reactance considering the lump parameter line model and achieved accurate fault location. Liang [17] analyzed the distribution characteristic of the zerosequence voltage to construct the fault measure matrix and distinguish the fault section. Recently the promoted trend for the phasor measurement units (PMU) application to the distribution system has attracted researcher attention [18,19]. The recent reports focused on the phasor estimation and feature extraction for distribution networks [20]. Alanzi [21] extracted the voltage phase angle shift as distinctive features to differentiate the faulty phases. The common fault events are classified accurately by comparing the phasor shift in the fault process. Marco [22] compared the weighted measurement residuals of the parallel state estimator to identify the fault branch. Dobakhshari [23] expressed the phase angle and magnitude of each voltage measurement as the fault location function using complex calculus. In the proposed nonlinear location function, the fault distance is solved iteratively by NewtonRaphson method and the initial values of positive-sequence fault
current is estimated. Within the context of PMU-based protection, this work proposes a characteristic-model based fault diagnosis and location method for single-terminal radial distribution system with mixed feeder lines. The characteristic model is formulated to extract the distribution phasor characteristics of the voltage drop and current flow along the distribution feeder line. Then, based on the entropy theory, the solution of the nonlinear characteristic model is converted to the linear optimization for the characteristic entropy index. Based on the entropy criterion, the fault location is estimated by searching the minimum characteristic entropy. To optimum iterative and reduce respond time, the Fibonacci search algorithm is utilized. The rest of the paper is organized as follows. In Section 2, the characteristic-model based on phasor analysis is demonstrated and solved by the Shannon entropy method. Section 3 generalizes the characteristic index to the ADN system. The detailed implementation of the two-stage fault location method is presented. Section 4 is devoted to the test results and the performance evaluations. The location results of the model-based method are compared with other fault location methods. Section 5 draws the conclusion.
Fig. 1. The circuit model of the single-phase-to-earth fault in the ADN system. (a) Fault distribution line model. (b) Distributed parameter equivalent circuit model of infinitesimal segment. 2
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2. Principle of the model-based location method
the distribution branch
2.1. Circuit analysis of fault characteristics
Iḟ =
Considering a fault occurring at point f along random distribution line i-j at distance dif = xlij from bus i, which divides the line section into two segments. The distribution line is considered as the fully transposed line and the distributed parameter line model for the medium-length distribution line is shown in Fig. 1. In Fig. 1, the fault point f is defined as the expanding virtual bus. Applying the boundary conditions [24] from the monitoring bus i and j, the voltage Vḟ and current Iḟ at the fault point f are calculated as follows,
From the line section se which is connected to the substation bus, the estimation of the fault voltage is obtained using the measured phasors of the upstream line section. In formula (1), the voltage of bus i is obtained from the upstream line section as
− Zc sinh(γxlij ) ⎤ ⎡Vi̇ ⎤ ⎡Vḟ ⎤ ⎡ cosh(γxlij ) ⎢ I ̇ ⎥ = ⎢− (sinh(γxl ))/ Z ⎢ ̇⎥ cosh(γxlij ) ⎥ ij c ⎦ ⎣ Ii ⎦ ⎣ if ⎦ ⎣
ΔVi̇ Zi, (n + 1) (x )
(8)
Vi̇ = cosh(γlui ) Vu̇ − sinh(γlui ) Zc Iu̇
(9)
The upstream current Ii̇ of the branch i-j is calculated by subtracting the load and laterals currents connected to bus i from the receiving current of the upstream line section u-i as
Ii̇ = Iui̇ − Ii,̇ Lt (1)
(10)
From formula (1), the current I j̇ at the downstream bus j is estimated from the random bus k.
where Ii,̇ Lt represents the load and lateral currents of bus i. By separating the load and lateral subsystem, the current Ii,̇ Lt of bus i can be estimated as
I j̇ = (Ik̇ Zjk cosh(γ (1 − x ) lij ) − Ii̇ Zc sinh(γxlij ) − Ik̇ Zik cosh(γxlij ))
Ii,̇ Lt = Z−di1Vi̇ − Z−di1
/(Zc sinh(γ (1 − x ) lij ))
N
̇ Zik IGk
̇ is the PMU-measured current at the DG unit export connected where IGk to bus k. Zdi represents the driving point impedance at bus i, which is the diagonal element of the expanding impedance matrix Z. Then, the sending-end current Ii̇ is calculated as
Iḟ = Iiḟ + Iiḟ Zc cosh(γxlij ) Zc ·I ḟ − ·Ii̇ sinh(γxlij ) sinh(γxlij )
N
Rf
(3)
Ii̇ = cosh(γxlui ) Iu̇ − sinh(γxlui ) Vu̇ / Zc − Z−di1Vi̇ + Z−di1
Iḟ = (Ik̇ Zjk − Ik̇ Zik cosh(γlij ) − Ii̇ Zc sinh(γlij ))/(Zc sinh(γ (x − 1) lij ))
N
+ Z−di1
∑
(13)
The model-based location method is derived considering the following assumption: the fault impedance of the metal fault is pure resistance [25]. The above assumption is common in the literature dealing with the location issue [26]. Therefore, from the observable bus i and j, the voltage and current phase angle signals at the fault branch satisfies the following principle
− Zik Rf cosh (γlij ) sinh (γxlij )
(5)
Therefore, considering the distributed parameter line model, the transfer impedance matrix Zkf between the fault point f and bus k is obtained. When the multi-concurrent fault occurs in the n-bus system, multiple coupling fault points appear. All the fault points are defined as the expanding virtual buses. Based on the topological structure and system component parameters, the expanding impedance matrix Z of the whole ADN system is derived as follows
arg (Vḟ (x )) arg (Vḟ (x )) = ̇ arg (ΔVi /(Zi, n + 1 (x ))) arg (ΔVj̇ /(Zj, n + 1 (x )))
(14)
where arg() represents the calculation for phase angle signal, Zi,n+1(x) implies the equivalent impedance at point f with the assumed fault location x as calculated in formula (6). Therefore, the fault feature is extracted as the phase angle characteristic. As the m PMUs installed in ADN system, the synchronized phasor signals of the wide area are obtained. In the whole network range, from the random measurable bus l, the phase angle relationship of the fault voltage and current satisfies the following principle
(6)
θ P1 = θl = θ Pm 2.2. Phasor characteristic model
(l = P1, P2, P3⋯Pm)
(15)
Then, the fault characteristic model θl (x) is defined as
θl (x ) = arg (Vḟ (x ))/ arg (ΔVl̇ /(Zlf (x )) 0 < x < 1
Assuming that m PMUs are installed in the n-bus ADN system; a fault has occurred at i-j bus branch. Based on the expanding resistance matrix Z, the voltage sag ΔVi̇ of the expanding ADN system as pre ⎡ V1̇ − V1̇ ⎤ 0⎤ ⎡⋯ ⋯ ⎢ ⎥ ⎥ ⎢ Vṅ − V̇ pre ⎥ = Z ⎢ ⎢0⎥ n ⎢ ⎥ İ ⎢ ̇ ̇ pre ⎣ f⎥ ⎦ ⎢ ⎣Vn + 1 − Vn + 1⎥ ⎦
̇ ) Zik IGk
k = 1, k ≠ i
− Zik Zc2 cosh (γxlij ) sinh (γxlij ) cosh (γlij )))
Z1n Z1, n + 1 (x ) ⎤ ⋯ ⋯ ⋯ ⋯ ⎥ Znn Zn, n + 1 (x ) ⎥ ⋯ ⎥ ⋯ Zn + 1, n (x ) Zn + 1, n + 1 (x ) ⎦
(12)
Vḟ = cosh(γxl) Vsk̇ − Zc sinh(γxl)(cosh(γxl) Isu̇ − sinh(γxl) Vḟ su/Zc − Z−di1Vi̇
Zik Zc2 cosh (γxlij )2sinh (γlij )
/(Zik Zc cosh (γlij ) − Zjk Zc + Zik Zc2 cosh (γxlij ) sinh (γlij ))
Zik IGk
Substituting (11) and (12) in (1), the fault voltage Vḟ is estimated as
(4)
On the basis of the mutual impedance definition, from (1) and (4), the transfer impedance vector Zkf between the bus k and fault point f is shown below
Zkf = (Zki (Rf Zjk sinh (γxlij ) +
∑ k = 1, k ≠ i
Substituting (1)–(3), the fault current Iḟ can be expressed as
Z12 ⎡ Z11 ⋯ ⎢ ⋯ Z=⎢ Z Zn2 n1 ⎢ ⎣ Zn + 1,1 (x ) Zn + 1,2 (x )
(11)
k = 1, k ≠ i
(2)
The fault current Iḟ is derived as
⎧ ⎪ ⎨ ̇ ⎪ If = ⎩
∑
(16)
When the Rf is higher than 187.7 Ω, the partial derivative d(θl(x,Rf))/d (Rf) is less than 0.011 and the proposed model is affected weakly by the fault resistance Rf. The proposed fault characteristic model θ(x) can extract accurate fault features based on the phasor analysis. Furthermore the fault characteristic model is applicable to other fault types, such as the three phase to earth fault. In the extension for other fault types, the phase-phase and phase-ground fault resistance effect should be considered and a two-terminal fault location method can
(7)
Therefore, the fault current Iḟ is obtained from other terminal i of 3
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3. The two-stage fault location scheme
reduce the fault resistance effect [27,28].
The precise fault location method contains 2 stages. First, based on the fault characteristic model, with PMU measurements, the potential fault section is estimated using the diagnosis criteria. Then, the voltage and current phasors of the estimated fault branch are extracted and h(x) is calculated for fault location. In the location stage, the Fibonacci algorithm is used to search the precise location result.
2.3. Entropy theory The entropy method measures the pattern similarity degree of the feature signals and shows well robustness for transient interference [29]. As entropy depends on the similarity degree more than the absolute value and is related to higher order moments. It can offer a better nonlinear characterization to measure the system consistency. From (11), the proposed characteristic model is nonlinear and fault features measured by PMU is non-stationary. Therefore combining the entropy theory and referring to (10), solving the nonlinear fault characteristic model is transferred to the following linear entropy problem. The fault characteristic vector θl(x) is normalized as
pl (x ) =
θl (x ) max{θθ P1 (x ), θθ P2 (x )⋯θ Pm (x )} m
3.1. Fault section diagnosis criteria Referring to (6) and (11), the fault characteristic matrix Θ of the whole ADN system is calculated as
⎧ ⎪ ⎪
(17)
⎨ ⎪ ⎪ θlk = ⎩
The characteristic entropy function h(x) is
1 h (x ) = − ln n
m
∑ pl (x ) ln pl (x ) l=1
⎡ θ11 θ12 ⎢θ θ Θ = ⎢ 21 22 ⋮ ⋮ ⎢ ⎣ θm1 θm2 arg (Vk̇ ) , arg (ΔVl̇ / Zlk )
⋯ θ1n ⎤ ⋯ θ2n ⎥ ⋱ ⋮ ⎥ ⎥ ⋯ θmn ⎦
1⩽ k ⩽ n,
1 ⩽ l ⩽ m.
(19)
To measure the consistency of fault characteristic index at bus k, the fault characteristic entropy (FCE) vector H is calculated as
(18)
The characteristic entropy function h(x) measures the consistency of fault characteristic index. The orderly system has lower information entropy. For example, the entropy of a Dirac delta distribution will be the minimum, where the probability mass is concentrated at a single point. Then, the corresponding distance of the minimum entropy h(x) is estimated as the fault location. Based on the above analysis, the modelbased method can estimate the quantitative fault location directly, which simplifies the training process of the artificial intelligence algorithms.
m
⎧ hk = − 1 ∑ p ln p , k = 1, 2, ⋯, n, lk lk ln n l=1 ⎨ H = [h1⋯ hk⋯hn]. ⎩
(20)
Then the FCE vector H is calculated as the diagnosis index to estimate fault branch. As the analysis in Section 2, after the fault occurs, the FCE value hk of the fault buses decreases. The fault section k* is selected as,
Fig. 2. The flowchart for fault diagnosis and location stage. 4
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k ∗ ∈ {hk ⩽ h 0}, k = 1, 2⋯39,
and θ862c remain at 4.419 and 4.371. After the single-phase to earth fault occurs, the fault characteristic θ836c and θ862c decrease to 78.208% to 0.963 at 1.06 s. The response time is within 0.1 s. In the fault progress, the fault characteristic value of C-phase decreases while those of A-phase and B-phase maintain the normal state, which indicates that the fault feature of the C-phase is extracted accurately.
(21)
where h0 is the entropy threshold for fault diagnosis, which is a threshold range to identify the fault state and the normal work state. In this paper h0 is set as 0.6. 3.2. Fault location criteria Based on the fault diagnosis result in Section 3.1, the voltage phasors of the potential fault branch i-j are extracted by PMU. By employing (1)–(11), the fault characteristic model θ(x) is extracted as
4.2. Fault diagnosis result analysis Based on the diagnosis criteria in formula (16), the entropy vector hi for C-phase to earth fault in the whole ADN system is calculated in Fig. 5. In Fig. 5, h836 is 0.090 and h862 is 0.091. The FCE values of bus 836 and 862 are significantly less than other buses, which matches the analysis in Section 2 that the characteristic vector of the fault branch is well ordered. Then, the branch 836–862 bus is diagnosed as the fault section, which conforms to the actual situation. Fig. 6 shows the synchronized fault diagnosis result of bus 862 in the fault process. In the normal state, the FCE value h862 maintains to 1.628 and fluctuates slightly. At the fault inception instant at 3 s, the FCE curves of bus 862 decline 94.103% in 0.08 s. In Fig. 6, when Rf is 0.01, 0.5, 2, 20 and 100 Ω, the h862 decreases to 0.096, 0.119, 0.122, 0.138 and 0.244 respectively. Due to the significant decrease of h862, bus 862 is diagnosed as the fault bus. In the 600 test cases, as the fault resistance increases, the characteristic entropy of the fault state rises slightly, which is far below the threshold 0.6. The diagnosis accuracy is 98.667% and the respond time is within 0.1 s. Therefore, the proposed diagnosis method can monitor the whole ADN system synchronously at low resistance and high resistance fault.
θli (x ) = arg (Vḟ )/ arg (ΔVl̇ /(Zlf (x ))) ̇ / Zc = arg (cosh(γxl) Vsk̇ − Zc sinh(γxl)(cosh(γxl) Isu̇ − sinh(γxl) Vsu − Z−di1Vi̇ + Z−di1
N
∑
̇ ))/ Zik IGk
k = 1, k ≠ i
(arg ((ΔVl̇ (z li z c cosh(γl) − z c z li z c2 z li cosh(γxl) sinh(γl))) /(z il (Rf zji sinh(γxl) + z c2 z li cosh(γx )2· sinh(γl) − Rf z li sinh(γxl) cosh(γl) − z c2 z li cosh(γxl) sinh(γxl) cosh(γl)))) (22) Therefore the fault characteristic matrix for fault location is θi(x) = [θ1i(x), θ2i(x)…θmi(x)]. Then referring (13), the corresponding model-based fault location function h(x) of the fault bus i is calculated as
h (x ) = −
1 ln n
m
∑ pli (x ) ln pli (x ). l=1
(23)
The characteristic entropy function h(x) fulfills the mirrored minimum energy (MME) property demonstrated in [30]. Then, solving formula (18) is transferred to the following optimization formula,
⎧ min{h (x )}, ⎨ ⎩ x ∈ [0, 1].
4.3. Effect of different noise levels In order to study the noise effect on the location accuracy, the location performance was tested with signal to noise ratio (SNR) values between 10 and 20 dB. The A-phase to earth fault occurs at 34% from bus 862. The fault location results are are analyzed with no-noise, 10 dB and 20 dB noise levels respectively in Fig. 7. Fig. 7(a) shows the detail location result at no-noise state. The global minimum FCE is located at xh_min = 33.98% and the location error is e = 0.02%. In the noise condition, Fig. 7(b) shows the location result at 20 dB noise level. The global minimum FCE is located at xh_min = 33.94% and the location error is e = 0.06%, while the location error in [32] is 2.832%. Fig. 7(c) shows the location result at 10 dB noise level. The fault location error of the proposed method is 0.13%, while the location error in literature [32] is 5.211%. The noise signals can affect the characteristic calculation in Formula (14). However, the entropy method measures the consistency of the character vector instead of comparing the magnitude directly and the noise effect is reduced. In Fig. 7, under different noise conditions, an overall location accuracy of 99.93% and diagnosis accuracy of 98.109% can be still obtained. Therefore, the proposed characteristic-model based method is robust for different noise levels.
(24)
where xh_min is the location result located at the minimum entropy point. Therefore, the systematic variation x can be solved based on the minimum FCE concept. Instead of analyzing the operating state at each bus, the fault diagnosis stage first estimates the fault branch to reduce the size of the searching space. Then, the Fibonacci search algorithm is applied in the iterative process, which reduces the number of iteration points greatly. Thus, in the large scale transmission and distribution network, the two-stage location method can achieve second level response. Then, the complete flowchart for fault diagnosis and location is shown in Fig. 2. 4. Simulation results and analysis 4.1. Fault characteristic extraction The characteristic model-based method is tested in the IEEE 34-bus distribution system. Transient simulations for fault events under different fault resistances and fault types were carried out in MATLAB. The online diagram of the 34-bus distribution system is provided in Fig. 3 and the system parameters are presented in [31]. The 24.9-kV IEEE 34bus system includes 34 buses, 33 branches, and 2 distributed generation (DG) integrated. The PMUs were installed in the ADN system based on the installation criteria: (a) at least one-terminal voltage of the distribution branch is directly measured or indirectly estimated by PMU, (b) the substation bus and the terminal of each DG units are measurable. The PMU installation in the IEEE 34-bus system is at 800, 808, 814, 816, 824, 828, 832, 836, 834, 844, 848, 854, 858, 890 bus. Supposing that a C-phase to earth fault occurs at 55.53% from bus 836 (as shown in Fig. 1, i = 862, j = 836, x = 0.5553). The fault occurs at 1 s and is cleared at 2 s. The fault characteristic values θ836 and θ862 are shown in Fig. 4. In the normal operation progress (0–1 s), the θ836c
Fig. 3. The IEEE 34-bus test distribution system. 5
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Fig. 4. The fault characteristic component signal.
Fig. 5. Fault diagnosis result for the C-phase to earth fault in ADN system.
Fig. 7. The detail location result at different noise levels. (a) no noise, (b) 20 dB noise level, (c) 10 dB noise level.
Fig. 6. Synchronized diagnosis result under different fault resistance.
4.4. Effect of DG penetration level In order to test the effect of DG penetration level, five groups of simulation tests are conducted in branch 848–846. The relative location errors of the proposed method are calculated as the ratio of the real fault distance with the increasing DG penetration level in Fig. 8. For this case, the proposed location method exhibits a trend to underestimate the fault distance as the DG penetration level increases, reaching an average error of 0.084% for a penetration level of 25%. This behavior is due to the increasing penetration, which increases the error in the estimation component of ZikIGk contributed to the fault location from the DG units. From Fig. 8, the fault location error decreases when the fault point close to the bus 848 (PMU installed), due to more accurate estimation of the fault voltage using the phasor signals measured by PMU. Thus, the proposed method is applicable to the medium and short distribution line.
Fig. 8. Location performance of the proposed method at increasing DG penetration level.
impedance-based method [32], the radial basis function neural network (RBF) and wavelet neural network (WNN) are compared. The location error efce, e[32], eRBFNN and eWNN are 0.325%, 2.104%, 5.741% and 3.688%; the respond time tfce, t[32], tRBFNN and tWNN is 0.847 s, 115.969 s, 57.088 s and 36.193 s, respectively. Table 1 clearly shows that the proposed method decreases 1.779% location error comparing with the location method in [32]. Furthermore, the model-based method has advantage of the operating speed and reduces respond time 63.583 s comparing with the iterative algorithm and the neural network
4.5. Comparative assessment for location accuracy and respond time The online fault location requires the performance index of the location error e and the respond time t. To evaluate the location performance, a C-phase to earth fault occurs at 80% from bus 846 in the 846–848 branch is considered. In Table 1, the location errors of the 6
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Table 1 Comparative assessment for location accuracy.
Location error (%) Rf = 0.01 Ω Location error (%) Rf = 2 Ω Location error (%) Rf = 100 Ω
The proposed method
Jiang [32]
RBF [33]
WNN [34]
0.023 0.186 0.767
1.365 1.692 3.254
3.255 5.769 8.198
2.515 3.032 5.517
Table 2 Location result with measurement error. Influence factors
Location result (%)
Error (%)
The parameters are totally accurate Both pre-fault and post-fault PMU magnitude measurement error ( ± ) 2% Both pre-fault and post-fault PMU phase angle measurement error ( ± ) 2% Pre-fault PMU phase angle measurement error ( ± ) 2% Post-fault PMU phase angle measurement error ( ± ) 2% Line parameter error in fault branch 846–848 is 20%
54.943 54.937 53.658 53.259 53.338 54.928
0.057 0.063 1.342 1.741 1.662 0.072
Table 3 Fault location result of different PMU installation scheme. Fault location
Fault type
Branch
Fault distance
836–862 836–862 846–848
45% from bus 836 75% from bus 836 65% from bus 848
AG BG BG
Bus 848 without PMU
Bus 848 with PMU
Error (%)
Error (%)
0.648 0.967 12.785
0.022 0.037 0.026
impedance fault, the proposed method can locate the fault distances accurately with an estimation error 1.647% at a time delay 59.58 μs. In the actual operating condition, the PMU delay time standard is typically tens of microseconds and the location error of the proposed method is less than 1.575%. These results demonstrated that the performance of the proposed method is reliable using PMUs with imperfect synchronization, within the time delay 59.58 μs. To test the effect of the PMU installation scheme on the location accuracy, different types of faults occurring in the distribution branch are analyzed. It is assumed that the fault occurs in 846–848 branch. Due to the complicated symmetry of the system, without PMU installed in the inner bus, the data loss of bus 848 increases the estimation error of fault voltage Vf (x). The phasor estimation error can increase the location error of the proposed method. With a PMU installed at bus 848, ̇ and the current I848 ̇ of the receiving terminal (bus 848) the voltage V848 can be measured directly. In Table 3, the fault location error does not exceed 0.04% with the optimal PMU install scheme. The location error significantly decreases 12.759% with bus 848 installing PMU. Therefore, an appropriate PMU placement scheme can ensure the accurate calculation of the FCE and maintain the location accuracy. The proposed characteristic-model based method can provide optimization index for the PMU installation scheme.
Fig. 9. Location result at different time delay cases.
with training process [32–34]. The main reason is that in the location stage, the Fibonacci search algorithm optimizes the iteration and reduces uncertainty range by xm and xm′. Then, the proposed location method can achieve second-level response. 4.6. Effect of measurement parameter To evaluate the sensitivity of the model-based method, the performance of the proposed method at different PMU factors are analyzed in Tables 2 and 3. The A-phase to earth fault occurs at 55% from bus 848 in the 846–848 branch. As network parameters vary in weather and loading practice conditions [35], test cases operate considering an additional situation of 2% error in network parameters. The mean error of the model-based location method is 0.823%, which is acceptable in the practice condition. To analyze the time delay of PMU effect on the proposed method, the performance of the proposed method at different time delay cases are evaluated in Fig. 9. The time delay tk causes the phase mismatch φp (φp = 2πftk) and the estimation of the voltage is modified as U’i,k(kT + tk) = Ui,k(kT + tk)sin(2πf(kT + tk) + φi(kT + tk)). The measurement time delay 60 μs can cause estimation error of 2.380%. In the time delay range 13.37–53.58 μs, the proposed method estimated the fault distances accurately with an average error 0.612%. In low-
5. Conclusion This paper presented an analytical method for the single phase to earth fault in ADN system based on the phasor characteristic model. It targets location identification of medium-length distribution line with the penetration of multiple DGs. The fault characteristic index is calculated to extract the phasor shift distribution feature based on characteristic model which is applicable for all fault types. Then, the consistency of the fault characteristics is measured adopting the Shannon entropy and the fault location problem is presented as a single-objective optimization. The potential fault location is identified using the Fibonacci search algorithm to improve the estimation process. The proposed method shows well performance and robustness against small delay time and high impedance fault using the locally available voltage 7
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phasors and synchronized current phasors at each DG. For common fault conditions, the diagnosis rate is 98.732%, the location error is below 0.767% and the respond time is less than 0.847 s. Furthermore, the location analysis of different PMU installation schemes implies that the characteristic model-based method has important significance in PMU optimized installation.
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