Sensitivity Analysis of Impedance Measurement Alogrithms Used in Distance Protection

Nanang Rohadi (1,2) The University of Adelaide, Australia (1)

The State Polytechnique of Jakarta, Indonesia (2)

Rastko Zivanovic The University of Adelaide, Australia

Abstract— This paper presents the methodology for Global Sensitivity Analysis (GSA) of impedance measurement algorithms that are used in distance protection of transmission lines. The analysis is using Quasi-Monte Carlo technique in calculating variance of the measurement error as well as parts of this variance that are contributed by uncertainty of some parameters. Specifically, fault resistance is the parameter that cannot be measured and it is treated as uncertain. Such parameters are called factors and they are represented with specific distribution function within specified domain of variation. The proposed methodology is implemented using automation of DIgSILENT and SIMLAB programs. The program in DPL scripting language of DIgSILENT is developed to automate simulation of transmission line faults when uncertain factors are varied. Each variation represents a sample in factor space. They are generated using Sobol quasi-random sequence in SIMLAB. This program also calculates variance-based sensitivity indices based on the factor space samples and corresponding simulation results obtained in DIgSILENT. To illustrate this methodology, the paper presents results of the GSA of SEL-412 impedance measurement algorithm implemented as a model in DIgSILENT.

Keywords- Distance protection, transmission line faults, impedance measurement algorithms, Global Sensitivity Analysis

I. INTRODUCTION Distance protection function is the main element in an

overhead transmission line protection scheme. This function requires accurate measurement of the fault-loop impedance using a selection of voltage and current signals measured at a single line-terminal. In the case of a single-phase to ground fault, the measurement of the fault-loop impedance is influenced by values of fault resistance and impedance of ground return path of the fault current. It is not possible to measure fault resistance and zero-sequence impedance value is not known with high precision. Hence the fault impedance measurement algorithms provide only estimated values, i.e. the true value is never known exactly. If the fault is resistive, infeed of the fault current from the remote-side of the line, which is not measured, represents another factor that impact the fault impedance measurement.

In this paper, we present the methodology for systematic study of how sensitive are the fault-loop impedance measurement algorithms to fault resistance value and remote-side fault current infeed. Two factors are used in this study: fault resistance (RF) and power flow angle (PF). The PF is a phase angle difference of sending-end and remote-end voltage sources. This factor determines current flow on the line and the amount of remote-end fault current infeed. The study requires mathematical models of transmission line and the fault-loop measurement element as implemented in

Intelligent Electronic Devices (IEDs). We selected DIgSILENT PowerFactory simulation environment [1] for power system modelling purposes. This tool provides the scripting language (called DPL) which is required for automation of short-circuit fault simulations when factor values are varied. In addition, tools for modelling of IED functions are also provided, and we modelled and tested the measurement algorithm implemented in SEL-421 multifunctional IED [2]. To study impact of the factors on uncertainty of the measurement algorithm we have used Global Sensitivity Analysis (GSA) technique based on estimation of variances through Quasi-Monte Carlo sampling in the two-dimensional factor space. This method was originally proposed by Sobol [3] and implemented in the SIMLAB software environment [4, 5]. The paper demonstrates application of the GSA technique for the case of a single-phase to ground fault. The method can be used for other fault types. In practice, this technique can help to quantify impact of various factors to distance protection function, and it can be implemented as a part of the application testing procedure to help in selecting an optimal IED for required task.

II. THE PROPOSED METHODOLOGY Faulted transmission line and distance relay, as shown in

Fig. 1, are modelled in the DIgSILENT simulation environment. The circuit in Fig. 1 represents a positive-sequence model. The simulated fault is: phase A to ground via resistance RF. The current used in measurement of the impedance between S-terminal and fault is compensated by the relay algorithm for the zero-sequence current using the factor k0 [6]. The factor k0 depends on the zero-sequence impedance which is not known exactly. In this paper we assume that the influence of this uncertain factor to the measurement algorithm is negligible. In practice this factor should be taken into account and the GSA that includes k0 will be presented in the future paper.

In Fig. 1, the external system is represented using Thevenin’s equivalents comprising of voltages sources and and their corresponding impedances and . Transmission line positive sequence impedance is in Fig. 1. Since the fault current IF, in Fig. 1, is fed from both sources, the measured impedance between S-terminal and fault, seen by distance relay, is sensitive to fault resistance (RF) and power flow angle (PF). For the purpose of illustrating the effect of RF and PF on the impedance measurement, we simulated the phase A to ground faults in the middle of the line for four characteristic values of the factors and used the simulated voltages and currents as inputs to the impedance measurement algorithm implemented in SEL-421 model of DIgSILENT software.

978-1-4577-0255-6/11/$26.00 ©2011 IEEE 995 TENCON 2011

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Figure 1. Impedance seen by Distance Relay

Figure 2. Impedance measurements for varying factors: RF and PF (i.e. rf and pf in the legend)

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Figure 3. Implementation diagram explaining GSA procedure and interaction of SIMLAB and DIgSILENT

The traces in time of measured impedance for variation of the factors are shown in Fig. 2. The results of the simulation provide the following characteristic points:

a) the point in XR diagram in Fig. 1 for RF = PF = 0; the trace of the impedance measurement algorithm is shown using green line in Fig. 2;

b) the point <1> in XR diagram in Fig. 1 for RF ≠ 0 (equal to 10Ω) and PF = 0; the trace of the impedance measurement algorithm is shown using red line in Fig. 2;

c) the point <2> in XR diagram in Fig. 1 for RF ≠ 0 (equal to 10Ω) and PF ≠ 0 (equal to 10°); the trace of the impedance measurement algorithm is shown using black line in Fig. 2;

d) the point <3> in XR diagram in Fig. 1 for RF ≠ 0 (equal to 10Ω) and PF ≠ 0 (equal to -10°); the trace of the impedance measurement algorithm is shown using blue line in Fig. 2;

The simulation shows how the fault resistance impacts the measurement error, i.e. deviation from the actual impedance . In the case when a fault is close to the border of Zone 1 and still in Zone 1, this error will make the relay see the fault in Zone 2. To quantify this error we calculate the performance index for each simulated case which is defined as the absolute difference between true value of distance to fault and estimated value using the measurement algorithm: | | 100/ .

Uncertainty of the performance index is represented by its variance , which is calculated by running a large number of simulation cases for different factor values. To asses importance of a factor (i.g. , ), we need to

determine part of the performance index variance that is contributed by uncertainty of this factor. This variance is calculated by taking the average over all factors except , i.e. | , and then calculating the variance over factor : | . The expectations and variances are computed according to their definitions by solving the multidimensional integrals using Quasi-Monte Carlo technique [7]. The sensitivity measure that describes the main effect of a factor on the performance index is defined as / . If the sum (i.e. sum of sensitivities to and ) does not add up to one, the performance index variance is not described only by individual effects of the factors. The remaining part of the variance is described by interaction effect of two factors and . The following variance describes this interaction effect: , , | , . The corresponding sensitivity index is defines as , , / . Finally we have Analysis of Variance (ANOVA) decomposition: , ; and the sensitivities add up to one, i.e. 1 , .

The implementation of the proposed GSA technique using SIMLAB and DIgSILENT simulation environments is outlined in Fig. 3. The Sobol’s quasi-random sequence [7] is used to draw samples from the two dimensional factor space. The generator for this sequence of numbers is available in SIMLAB [5]. Each sample constituting of values for and represents one simulation case in DIgSILENT program where the transmission line as well as SEL-421 and instrument transformers are modelled. All the parameters for the model in DIgSILENT are fixed except

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and . We have used DPL language to automatically vary and , run simulation, collect results and communicate with SIMLAB. For each sample of and , the result of the DIgSILENT simulation is the measured impedance between S-terminal and fault point which is obtained through SEL-421 measurement algorithm. Using DPL we also calculate performance index by comparing true impedance with the measured one. For each sample of and we obtain one sample of performance index which is read by SIMLAB. All input and output samples are used to calculate variances and sensitivity measures using the formulas described in this section and implemented in SIMLAB.

III. TEST RESULTS AND DISCUSSION To illustrate application of the GSA technique in

assessing performance of the impedance measurement algorithms we have used the circuit in Fig. 1 modelled in DIgSILENT simulation environment. The algorithm we assessed is the one implemented in SEL-412 relay model available in DIgSILENT. The electrical network parameters are: positive sequence line impedance 0.06250.488 Ω⁄ and zero-sequence line impedance 0.2309 1.531 Ω⁄ . The Thevenin’s voltages are 230 and 230 . The factor space boundaries are defined by the domains of variation of the factors: fault resistance RF varies in range 0-10Ω, and the angle PF in the range -10o to +10o . Quasi-random sequence having 8192 numbers is generated in SIMLAB and it is used to create samples from the factor space. The fault location is varied from 0.1pu till 0.8 pu (border of Zone 1) with the step 0.1pu. For each fault location 8192 cases with different and are simulated, and sensitivity indices are calculated.

The GSA results in the form of sensitivity indices (individual and interaction) are shown in Fig.4. After analysing the results we can conclude that the error of impedance measurement using the SEL-421 algorithm is the most sensitive to RF. Close to the border of the Zone 1 (0.8pu) this sensitivity is slightly reduced and the algorithm becomes sensitive to PF and interaction between and .

Figure 4. Sensitivity Indices (SI)

IV. CONCLUSIONS This paper presents application of the Global Sensitivity

Analysis in testing of impedance measurement algorithms used in distance protection of transmission lines. The analysis is based on estimation of certain measurement error variances using Quasi-Monte Carlo approach. This technique requires that uncertain parameters (i.e. factors) are specified using distribution functions within specified boundaries. These factors are forming the bounded factor space. For each sample from the factor space we have simulated a fault on transmission line and use obtained currents and voltages to measure impedance. Fault simulation and the measurement algorithm of SEL-412 are implemented in DIgSILENT software. The whole simulation process with varying parameters is automated using DPL language. Calculation of variance-based sensitivity measures are performed using SIMLAB software. The paper provides demonstration of the methodology in the sensitivity analysis of the SEL-421 impedance measurement algorithm available as a model in DIgSILENT.

ACKNOWLEDGMENT The first author would like to thank The Directorate General of Higher Education, Department of National Education, Indonesia, for providing the PhD Scholarship.

REFERENCES [1] DIgSILENT PowerFactory, “PowerFactory User’s Manual”,

DIgSILENT PowerFactory Version 14.0, Germany, 2008. Available: http://www.digsilent.de

[2] Schweitzer Engineering Laboratories, “SEL 421 Relay Protection and Automation System user’s Guide”, USA, 2007. Available: http://www.selinc.com

[3] I. M. Sobol’, “Sensitivity estimates for nonlinear mathematical models”, Matematicheskoe Modelirovanie 2 (1) (1990) 112–118 (in Russian), translated in I.M. Sobol’, “Sensitivity estimates for nonlinear mathematical models”, Mathematicai Modeling and Computational Experiment. 1 ( 1993) 407–414.

[4] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, John Wiley & Sons, 2004

[5] A.Saltelli, Sensitivity analysis in practice : a guide to assessing scientific models: John Willey & Sons Inc, 2004. Available : http://simlab.jrc.ec.europa.eu/

[6] L. Hulka, U. Klapper, M. Pütter and W. Wurzer, “Measurement of line impedance and mutal coupling of parallel lines to improve the protection system”, 20th International Conference on Electricity Distribution (CIRED), Prague, Czech Republic, June 2009

[7] I. M. Sobol’, Numerical method Monte Carlo. Moscow, 1973 ( in Russian )

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