1
Optimal Phasor Measurement Units Placement for Fault Location on Overhead Electric Power Distribution Feeders A. A. P. Bíscaro, Student Member, IEEE, R. A. F. Pereira and J. R. S. Mantovani, Member, IEEE
Abstract--This paper proposes a new approach for optimal phasor measurement units placement for fault location on electric power distribution systems using Greedy Randomized Adaptive Search Procedure metaheuristic and Monte Carlo simulation. The optimized placement model herein proposed is a general methodology that can be used to place devices aiming to record the voltage sag magnitudes for any fault location algorithm that uses voltage information measured at a limited set of nodes along the feeder. An overhead, three-phase, three-wire, 13.8 kV, 134node, real-life feeder model is used to evaluate the algorithm. Tests show that the results of the fault location methodology were improved thanks to the new optimized allocation of the meters pinpointed using this methodology. Index Terms— Optimal allocation, phasor measurement units (PMUs), fault location, Monte Carlo methods and optimization methods.
I. NOMENCLATURE NM NB nf np distMAX dpf_plk,i bi Z μ σ f(Z,μ,σ) ε |CL| |RCL| Rpg Rpp Bs As iter ITERmax VPj[i] Snom cosφ
: : : : : : : : : : : : : : : : : : : : : : : :
number of meters; number of nodes of the system; number of faults applied; number of positions considered for sum of distances; max distance between faulted point and located one; distance between faulted point k and located point i; node i with voltage sag greater than a preset value; random number generated by normal distribution; mean; std. deviation; function of normal probability density; random variable with normal distribution;; size of candidate list; size of restricted candidate list control parameter of RCL size; single-line-to-ground resistance; resistance between phases; best solution; actual solution; number of iterations; max number of iterations; voltage at phase j, node i; nominal apparent power power factor
This work was supported in part by the National Council for Scientific and Technological Development (CNPq) and in part by Foundation of Teaching, Research and Extension of Ilha Solteira (FEPISA). A. A. P. Bíscaro, R. A. F. Pereira and J. R. S. Mantovani are with UNESP – Univ Estadual Paulista, FEIS, Electrical Engineering Department, Ilha Solteira, São Paulo, 15385-000, Brazil (e-mails:
[email protected];
[email protected];
[email protected])
II. INTRODUCTION
P
ower systems are subject to several problems of either deterministic or stochastic nature, which can compromise the supply quality, resulting in losses for both electric utilities and customers. Among these problems, those related to voltage sags and fault location in electric power distribution systems can be emphasized. The focus of this paper is the optimal phasor measurement units (PMUs) placement for fault location. These devices are related to the analysis and control of voltage magnitude in the network and computer algorithms that use these voltage measurements to perform the fault location. The optimized allocation of such devices on the feeder and digital processing of the measures contribute directly to the efficiency, accuracy and reliability of fault location algorithms. In the literature, there are a few works related to the optimized allocation of phasor measurement units for fault location in electric power distribution systems. The proposals differ basically in methodology or optimization technique used. Reference [1] proposes a method based on fuzzy inference systems to make the allocation of fault indicator devices. The allocation is done considering only the main feeder. Reference [2] proposes a tabu search algorithm aiming to place the measurement devices. This algorithm explore the structure of historical data of the searches performed, using this information as a condition for the new movement in the search space. Reference [3] presents a comparison of various methods for optimal allocation of PMUs in order to make the estimation of network state. A graph method, based on rules, is initially used to solve the problem. Then, three metaheuristics are presented, namely: simulated annealing, genetic algorithm and tabu search. The mathematical model herein proposed in this paper for optimal allocation of such equipment in distribution feeders considers the fault location algorithm presented in [4] as an auxiliary tool to evaluate the objective function of the problem. The mathematical model seeks to define the position where the meters must be installed on the feeder, to establish the best cost/benefit relation of investments as well as to provide results with suitable quality and accuracy for any fault location algorithm that uses voltage sags information to locate faults.
2
Following, a fault location system used to perform the optimal phasor measurement placement is briefly described.
Pre-fault and during-fault current and voltage phasors measured in substation. Data Acquisition and Digital Signal Processing Magnitude of voltages during-fault measures in dispersed points along the feeder.
III.
FAULT LOCATION SYSTEM BASED ON VOLTAGE SAGS
Feeder’s data base
Fault location in distribution systems involves the instrumentation used for acquisition and processing of current and voltage signals and computational algorithms that use these specific measurements to determine with an acceptable accuracy and security the faulty node or the faulty area of the feeder. The fault location system, depicted in Fig. 1, used in this work is based on the method presented in [4]. Below, the main concepts adopted for this fault location system will be described. Substation data acquisition and sparse measurements along the feeder
Digital Signal Processing (FFT)
Loading data from feeder
Set the load model and estimate the transformers loading i = 1, total nodes
Assign to every node, the voltage measured during-fault at root node
Calculate the fault current
Power flow for fault condition
The process converged ?
N
Y
Calculation of deviations of the magnitude of voltage sags for all nodes
Fault Location Algorithm
Calculation of the index of local failure
Fault Type Identifier (Fuzzy System)
Machine-Man Interface (M.M.I) Definition of faulted area (Indication of the likely faulty nodes)
Fig. 1. Fault location system.
Fig. 2. Flow-chart of fault location algorithm used in fault location system.
A. Voltage and Current Digital Signal Processing The voltage and current signals simulated are performed using the Alternative Transients Program (ATP) [5] software. By applying the Fast Fourier Transform (FFT) [6] in the samples of available voltage and current signals the frequency spectrum of these signals along with the magnitude and phase of each frequency compounding the signals are given. Thus, the analysis and digital signal processing was performed using FFT to provide the phasors of voltages and fault currents required to implement the fault location system. B. Fault Type Identifier In order to indentify the fault type and the faulted phases, a fuzzy inference system employing the signal currents measured from the three phase at the feeder root node is applied. C. Basic Algorithm for Fault Location The method presented in [4] is applied for fault location, where the main concept is the usage of phasors of voltages and currents pre- and during-fault at the root node in combination with the analysis of the magnitude of voltage sags measured at a limited set of nodes along the feeder. The network equations are developed based on the backward/forward sweep load flow method [9]. This algorithm presents some advantages compared to the conventional algorithms for fault location using measurements of currents and voltages only at the feeder root node, because the nodes geographically located far from the real faulted node are eliminated of the likely fault location. Fig. 2 presents the flow-chart of fault location algorithm used in the fault location system.
IV.
OPTIMIZED ALLOCATION ALGORITHM
Optimal allocation of phasor measurement units on overhead electric power distribution feeders is a complex combinatorial optimization problem for large distribution feeders. In order to solve this problem, a new approach using a Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic [7] in combination with the concepts of the methodology for fault location [4], previously described, and Monte Carlo simulation [8] is proposed. Monte Carlo simulation is used to calculate the objective function inside an algorithm for fault simulations and for generating the stochastic variables of the problem, such as resistances for single-line-toground and double-line faults, faulted node, faulted phase and the failure rate of the meters. A. Stochastic Model The Objective Function (OF) aims to reduce the distance error between the true location of the fault and the indication given by the fault location algorithm and obtaining the largest possible number of nodes with a voltage sag above preset values, as can be seeing in (1). It ensures the maximum sensitivity to the configuration of meters under analysis, and allows monitoring the distribution system voltage level. OF NM
nf np nf nf nf dpf _ plk ,i dist MAX j 1 i 1 NB j 1
NB
b i 1
i
(1)
Following the main variables and parameters involved in the studies and simulations of faults in electrical systems considered in the mathematical model for optimal allocation of phasor measurement units, either deterministic or stochastic, will be presented.
3
1) Measurement equipments As any other equipment in distribution systems measurement equipments are subject to failures and errors of accuracy introduced by current and potential transformers. Due to equipment failure or sensitivity settings the voltage sags and fault currents cannot be identified as a system failure or other operating problem. Thus, a probability of failure of the measuring equipment should be properly considered. This is done by a normal probability density function, given a failure probability of 5% for each meter. The function of normal probability density is represented by (2) and describes the probability of failures in operation or measurement, for example, when the information required for the fault location algorithm processing is not sent. Then, the fault location system will work with a few meters and information, affecting their performance. f ( Z , , )
100 e 2
( Z )2 2 2
( 2)
The number of meters is an important factor for good performance of the fault location programs. The greater the number of meter, the better is the results [2] and, depending on the resources made available by electric utilities, this number may be quite limited. For a good performance of the fault location system, at least, 2 measurement equipments are required. 2) Faults in Electric Power Distribution systems Faults in electric power distribution systems are typically caused by the action of lightning, tree or animal contact to live parts of the system, equipment failures and human error. These shortages have a stochastic variation with respect to their nature, magnitude of short circuit currents and local of incidence. Table I shows the statistics of fault types and their composition. TABLE I PROBABILISTIC COMPOSITION OF FAULTS. Fault
Total (%)
Permanent (%)
The value of fault resistances can be particularly meaningful for single-line-to-ground faults, which represent the majority of faults, which can directly affect the identification of the fault. The technical solution proposed in [4] considers the fault resistance values as intrinsic data to the problem, i.e., the fault location is not directly dependent of the resistance values. However, for simulations of the signals of voltage and current made through the ATP software, such values are important because the short circuit currents are strongly influenced. Both the values of the single-line-to-ground and the double-line resistances can be obtained from (3).
( R pg , R pp ) Z *
(3)
Table II presents the ranges of values for single-line-toground and double-line resistances can take in the simulations, with their respective means and standard deviations. TABLE II VARIATION OF FAULT RESISTANCE VALUES Resistance
Mean
Std. Deviation
Variation
Single-line-to-groung
25
4,8544
10 ≤ Rpg < 40 Ω
Double-line
0,5
0,1294
0,1 < Rpp < 0,9 Ω
3) Distribution Transformer Power Rating The algorithm for fault location [4] estimates the loading of each transformer based on the complex power of the substation and the power rating of each transformer. However, the actual loads of distribution transformers exhibit stochastic behavior due to the needs of each customer. Thus, the feeder has many transformers presenting different loadings when a fault occurs. In order to make the simulations closer to reality during the faults simulation using the software ATP, transformers loading were generated assuming a random loading. For this purpose, a random variable with normal distribution was selected. Thus, the complex power of each transformer used in the faults simulations is given by (4).
S ATP i i Snomi (cos jsen )
( 4)
Transitory (%)
Single-line-to-ground
79
20
80
Double-line
11
70
30
Three-phase
2
95
5
Others
8
-
-
All nodes of the feeder are subject to some kind of fault, whether single-line-to-ground, double-line or three-phase fault. It is considered that there is no order of priority for the faulted phase for single-line-to-ground faults, having thus the same probability of occurrence for the three phases, being represented by a uniform distribution. The double-line faults are also represented by a uniform distribution.
Another important factor that strongly influences the degree of transformer loading is the level of operation of the network because, depending on the moment that the fault occurs in the system, it can be operating at a low, medium or high level of loading. Table III presents possible variations for the distribution transformer loads. TABLE III DISTRIBUTION TRANSFORMER LOADS. Level of Loading
Mean
Std Deviation
Variation
Low
0,6
0,06473
0,4 ≤ < 0,8
Medium
0,8
0, 06473
0,6 < < 1,0
High
1,0
0, 06473
0,8 <
4 Begin
B. GRASP Metaheuristic N
GRASP consists on an iterative probabilistic procedure where, in each iteration, is obtained a good quality solution for the optimization problem under study. Each iteration consists of two phases: the first one is the construction phase, where, element by element, a solution set to the problem is created. In this phase, which each element is randomly selected from a Restricted Candidate List (RCL) and added to the solution set. These steps are repeated until an initial feasible solution is found to be submitted to the second phase, which consists of a local search phase in the neighborhood of the solution. Similar solutions are investigated aiming to seek an improvement in current solution. The basic structure of GRASP algorithm is illustrated in Fig. 3. The stopping criterion is based on the maximum number of iterations. The best solution among those found in all iterations is maintained as a result of the procedure.
Optimal Allocation (Bs, OF)
iter < ITERmax ?
Y
End
Construction Phase
Define Faulted Phase
Generate Candidate List (CL)
Allocate new meter
Define Restricted Candidate List(RCL)
Calculate Actual OF
allocate 1st meter (if nm = 0)
Actual OF < OF ?
N
Y Y
Bs = As OF = Actual OF
NM < Nmax ? N
Local Search Phase N local < localMAX ? Y Reallocate meters
1) Construction Phase N
The construction phase is initially composed by the simulation of a random fault in the distribution network. Then a program for calculating three-phase power flow for the network is processed, classifying the nodes in descending order of voltage sags. For a double-line fault the classification is carried out taking into account the two phases involved, according to (5). The classification for a three-phase fault must take into account the three phases.
Min V i , V i P1 P2
(5)
After sorting the nodes in descending order of voltage sags a candidate list (CL) is generated. CL contains all nodes candidate to be part of actual solution (AS) of the problem, excluding the nodes already allocated in AS. Then, a restricted candidate list (RCL) containing the first n nodes of candidate list (CL), earlier created, will be generated. The size of RCL is controlled by parameter which can range between [0-1], as in (6). RCL 1 ( CL 1)
(6)
At the beginning of construction phase the AS is empty. An element from the RCL is chosen at random to be part of the actual solution (AS) and calculate the objective function value for the AS. This process is repeated until the AS is completed, containing the maximum number of meters (Nmax).
Reallocate meters
Meters are correctly positioned ? Y Calculate Actual OF
N Actual OF < OF ?
Y Bs = As OF = Actual OF
Fig. 3. GRASP algorithm implemented in C++.
2) Local Search Phase The local search takes the initial construction phase and explores the neighborhood around this solution. The solution found in the construction phase is not necessarily the optimal solution. Therefore, a local search procedure in order to try to improve the solutions generated by the construction phase is necessary to be applied. This search performs several changes in the current solution, trying to find a better solution in the neighborhood. When an improvement is found, the current solution is updated and the neighborhood around the new solution is searched again. This process is repeated until a maximum number of iterations (localMAX) are reached, as can be seen in Fig. 3. 3) Objective Function Calculation Algorithm The objective function is calculated using (1). The parameters for fault simulations are chosen randomly, such as, the faulted node, the faulted phase, the phase-to-ground and the double-line resistances. Then it holds the fault simulation and its location considering the presence of meters allocated in the positions indicated by AS. The expected distance between the faulted node and the node found by the fault location algorithm is calculated using the results provided by the fault location system.
5
The expected number of nodes with voltage sag above a predetermined value is also calculated. This process is repeated until the maximum number of iterations (iterobjMAX) is reached. This number of iterations corresponds to the amount of faults applied to the system. The objective function algorithm is presented in Fig 4. Begin
N Return Actual OF
iterobj < iterobjMAX
Y
V. SIMULATION RESULTS In the fault simulations using the ATP software, loads were modeled as constant impedance and transformer loadings were defined using (4). In the fault location algorithm, loads were modeled as constant impedance, mean load condition and the average load of transformers estimated according to the power ratings of each transformer. An overhead, three-phase, threewire, 13.8 kV, 134-node, real-life feeder model, shown in Fig. 5, is used to evaluate the algorithm. Test results show that the algorithm found an optimal allocation, increasing the accuracy of the fault location algorithm.
Define faulted node aleatorily
A. Digital Signal Processing Define faulted phase aleatorily
Define resistance between phases aleatorily (Rpp)
Define phase-to-ground resistance aleatorily (Rpg)
Execute fault location
The waveforms used in the fault location system were generated in the ATP software [5] with an appropriate sampling rate, considering some stochastic variables, presented in Table IV. Transformer loading is generated assuming a random loading for each simulation, given by (4), and operating condition at low, medium or high level of loading, according to Table III. A sample of the loading levels of transformers generated for fault simulations in the software ATP is shown in Fig. 6.
Calculate Σdpf_dplk,i and Σbi
Fig. 4. Objective Function calculation algorithm.
Fig. 5. Real-life feeder used to evaluate the fault location system.
6 120
In order to demonstrate the real improvement in the system for fault location, some tests comparing the results of the fault locations obtained through the two sets of meters listed in Table V are presented below.
110
Loading (%)
100 90 80 70
C. Tests of Accuracy and Robustness
60 50 40
Low Medium High
4
16
30
43
55 67 78 90 Node with loads allocated
105
119
135
Fig. 6. Distribution transformers loading.
Fig.7. shows an example of three-phase voltage signal processed for a single-line-to-ground fault at phase A. 8500
Phase A
Several simulations were performed under different test conditions and operating scenarios in order to evaluate the performance improvements in the fault location system with the optimized allocation defined by the proposed technique. For each configuration, 5,000 single-line-to-ground faults was applied and the distance error between the real fault location and the indication given by the fault location algorithm is shown in Fig. 8, by means of its cumulative frequency.
Phase B
Voltage (v)
300
Phase C
7500
Stochastic Model Deterministic Model [2]
Mean StDev N 100,8 140,3 5000 154,2 209,5 5000
250
6500 200
Frequency
5500
4500 1
2
3
4
5
6
Measure
Fig. 7. Voltage magnitude for a single-line-to-ground fault at phase A.
150
100
50
0
B. Optimal Allocation The optimized allocation was carried out considering a maximum of 4 devices to be allocated in the system, voltage sag limit of 10%, equal to 0.5, maximum number of iterations (ITERmax) equal to 500, number of faults applied to the feeder (iterobjMAX) for the objective function calculation equal to 50 and number of nodes for sum of distances (np) equal to 20.
Mean
Std. Deviation
Uniform
-
-
2 ≤ Node < 134
Rpp
Normal
0,5
0,1294
0,1 < Rpp < 0,9
Rpg
Normal
25
4,8544
Faulted Phase
Normal
0
1
Failure rate (meters)
Normal
0
1
10 < Rpg < 40 0 < f(Z,μ,σ) ≤ 10 → three-phase 10 < f(Z,μ,σ) ≤ 40 → double-line f(Z,μ,σ) > 40 → single-line-to-ground f(Z,μ,σ) ≤ 5
Table V presents the optimal allocations encountered by the optimized allocation algorithm using the stochastic model proposed in this paper as well as a deterministic model, presented in [2], for further comparison. TABLE V COMPARISON OF THE OPTIMIZED ALLOCATIONS. Proposal Stochastic Model Deterministic Model [2]
Position 26, 75, 87, 115 21, 31, 43, 107
0 200 Distance (m)
400
600
2034
800
Stochastic Model Deterministic Model [2]
2000 1843
Variation
Faulted Node
-200
Fig. 9 shows that 81.8% of the faulted nodes were located among the top 5 positions for the allocation proposed by the stochastic model and the configuration proposed by the deterministic model concentrates 77.1% of the faulted nodes within top 5.
Number of nodes located
Distribution
-400
Fig. 8. Histogram of distance error for single-line-to-ground faults.
TABLE IV STOCHASTIC VARIABLES CONSIDERED. Variable
-600
1500
1000 698 727 503 510
500
463 477
391 297
0
1
2
3
4
5
Position located
Fig. 9. Position of nodes located for a single-line-to-ground fault.
Fig. 10 shows the classification made by the fault location system for a double-line fault at phases A and B applied to each nodes of the feeder.
7 60
60
Stochastic Model Deterministic Model [2]
Number of nodes located
50
40
30 24 21
20 12
12
10 5
0
1
7
2
6
3
Further, the optimized placement model herein proposed is a general methodology that can be used to place devices aiming to record the voltage sag magnitudes for any fault location algorithm that uses these data. Additionally, the allocation of phasor measurement units in the network can be used to monitor the quality of the voltage supplied to the customers by means of state estimation of the network.
12 6
5
4
6
5
5
5
3
6
3
7
4
8
6
8
32
9
5 2
2
4 1
3
5 1
6
4 0
0
11
VII. REFERENCES
5 0
2
3 0
32
[1]
10 11 12 13 14 15 16 17 18 19 20 20+
Position
Fig. 10. Position of nodes located for a double-line fault. [2]
The fault location system presented greater efficiency using the placement proposed by the stochastic model, with 84.2% of the faults located before the twentieth position. The allocation proposed by the deterministic model gave an efficiency of 54.9% in the fault location considering the same range of positions. This improvement of 29.3% in the fault location results arises, mainly, because the deterministic allocation proposed in [2] considers only single-line-to-ground faults. Double-line and three-phase faults were not considered. For random faults, considered by Monte Carlo simulation, 20,000 faults were generated for each configuration. Figure 10 shows the probability plot found for the actual position of the nodes classified by the location system.
[3]
[4]
[5] [6] [7] [8]
[9]
D. M. B. S. Souza, A. F. Assis, I. N. Silva, W. F. Usida, "Efficient fuzzy approach for allocating fault indicators in power distribution lines," in Proc. 2008 IEEE Power Engineering Society Transmission and Distribution Conf., pp. 1-6. R. A. F. Pereira, L. G. W. da Silva and J. R. S. Mantovani, "PMUs optimized allocation using a tabu search algorithm for fault location in electric power distribution system," in Proc. 2004 IEEE Power Engineering Society Transmission and Distribution Conf., pp. 143-148. X. Donguie, H. Renmu, W. Peng, X. Tao, "Comparison of several PMU placement algorithms for state estimation," in Proc. 2004 IEEE Developments in Power System Protection conf., pp. 32-35. R. A. F. Pereira, L. G. W. Silva, M. Kezunovic and J. R. S. Mantovani, "Improved fault location on distribution feeders based on matching during-fault voltage sags," IEEE Trans. Power Delivery, vol. 24, pp. 852-862, Apr. 2009. ATP Rulebook, Latin American EMTP Users Group, 1983. Available: http://www.engenharia.furnas.gov.br/dptt/atp-rulebook/rule_book.zip P. M. Embree, D. Daniel, C++ Algorithm for Digital Signal Processing, 2nd ed., Upper Saddle River: Prentice Hall, 1998, p. 608. T. A. Feo, M. G. C. Resende, "Greedy randomized adaptive search procedures," Journal of global Optimization, vol. 6, pp.109-133, 1995. R. F. W. Coates, G. J. Janacek and K. V. Lever, "Monte Carlo simulation and random number generation", IEEE Journal on Selected Areas in Communications, v. 6, n. 1, pp.58-66, 1988. C. S. Cheng, D. A. Shirmohammadi, "Three-phase power flow method for real time distributions system analysis," IEEE Trans. on Power Systems, vol. 10, n. 2, pp. 671-679, 1995.
VIII. BIOGRAPHIES
Fig. 10. Probability plot for position of nodes.
André do Amaral Penteado Bíscaro received the B. Sc and M. S. degrees in electrical engineering from UNESP/Ilha Solteira, São Paulo, Brazil in 2005 and 2009, respectively. Currently, he is a Ph. D. Student at UNESP/Ilha Solteira. His research areas are optimization methods, reliability, fault location and protection of electric power systems.
The new optimized allocation presented a significant improvement in average ranking of the nodes and the average error of distance between the true location of the fault and the indication given by the algorithm of fault location. There was an improvement of approximately 20% compared to the configuration found by the deterministic model [2] for the classification of nodes until the twentieth position
Rodrigo Aparecido Fernandes Pereira received the B.Sc., M.S., and Ph.D. degrees in electrical engineering from UNESP/Ilha Solteira, São Paulo, Brazil, in 2001, 2003, and 2007, respectively. Currently, he is an associate researcher in Electric Power Systems Planning Laboratory at UNESP/Ilha Solteira. His research areas are fault location on distribution feeders as well protection and reliability of electric distribution systems.
VI. CONCLUSION
José Roberto Sanches Mantovani received the B.Sc. degree from UNESP/Ilha Solteira, São Paulo, Brazil, in 1981, and the M.S. and Ph.D. degrees in electrical engineering from UNICAMP-Campinas-SP-Brazil, in 1987 and 1995, respectively. Currently he is an Associate Professor in the Electrical Engineering Department at UNESP/Ilha Solteira. His research areas are planning and control of electric power systems.
The results obtained with the optimized allocation have improved the performance of the fault location system. The optimal allocation has reduced the error in the distance between the true location of the fault and the indication given by the fault location algorithm, thus providing more accurate results.
