Browsing by Author "Phadke, Arun G."
Now showing 1 - 20 of 85
Results Per Page
Sort Options
- Accurate frequency estimation with phasor anglesChen, Jian (Virginia Tech, 1994-04-04)A power system should always operate in a balanced and stable condition at its designed frequency. Any significant upset of this balance will produce a change in the power system frequency. It is the responsibility of the monitoring and protective devices to detect and restore the system to the equilibrium operating condition at the nominal frequency as soon as it is practical to do so. An accurate measurement of both frequency deviation and rate of change of frequency will greatly facilitate the restoration process. In this thesis, a recursive algorithm for precise frequency and rate of change of frequency measurement is presented. The algorithm consists of three major steps. First, a rough frequency estimation for a data window is computed using a second order least error square approximation on the phasor angles of the input waveform. Then, a resampling based on the rough frequency estimation is carried out, followed by another second order least error square approximation to obtain the final results. The results of simulations using this approach are provided.
- Adaptive optimal control of AC/DC systemsRostamkolai, Niusha (Virginia Polytechnic Institute and State University, 1986)The dissertation presents a new control strategy for two terminal HVDC systems embedded in an AC network. The control is based upon real-time measurements performed on the AC/DC system. Use is made of a technique for high speed accurate measurement of positive sequence voltages and currents, first developed in the field of computer relaying. The real-time measurements provides a term in the control law to compensate for inaccuracies following departure from the operating point. The control criterion is to damp out the electromechanical oscillations following a disturbance. The main contribution of the dissertation is to describe a new optimal controller formulation which contains a measurement based component. Optimal controllers are commonly constructed using linearized equations of the system around the operating point. In DC systems this approach is of a very limited value because of a highly nonlinear nature of the system. With the controller developed in this dissertation, it becomes possible to describe the system as a nonlinear dynamic system. The approximation resulting from the usual linearization of the system equations is thus avoided, and leads to a better controller design. The control technique is illustrated with a small AC/DC system. However, the equations formulated are sufficiently general, so that the technique can be applied to a larger system. Simulation results are included to represent the effectiveness of the developed controller.
- Adaptive out-of-step relaying with phasor measurementZaldivar, Virgilio Antonio Centeno (Virginia Tech, 1995)This work describes the development of an adaptive out-of-step relay, from the formulation of its concept to its field implementation and one year testing at the Florida- Georgia interface. This dissertation describes the theory of such a relay, its hardware configuration, the system as it was installed in the field, the major results and improvements obtained after the one year field test, and the adaptive features developed after the analysis of the collected data. Most of the adaptive concepts applied on this relay were used on field application for the first time and proved their value through the one year field test. Synchronized phasor measurements were used for the first time for relaying application, proving their ability to detect and analyze system disturbances through the measurement of angle differences between any two points in a system. It is shown that for a system that behaves primarily as a two-machine power system, the out-of-step relay could be enhanced and made more secure by applying the principle of equal area criterion. The main contribution of this dissertation is the use and application of old and new adaptive concepts as well as new technology to the solution of the out-of-step problem for a system that behaves like a two machine system. This work provides a solution for the basic stability problem with currently available technology and knowledge. In addition, the data collected during this research has been and will be of great help for those studying the power system stability problem and those developing new adaptive relaying techniques.
- Adaptive power system controlManansala, Edgardo Celestino (Virginia Polytechnic Institute and State University, 1989)This work presents a centralized control scheme applied to a power system. The scheme has adaptive characteristics which allow the controller to keep track of the changing power system operating point and to control nonlinear functions of state variables. Feedback to the controller is obtained from phasor measurements at chosen power system buses, generator field voltage measurements, and state estimators. Control effort is aimed at minimizing the oscillations and influencing the power system state trajectory through the control of linear and nonlinear functions of state variables during a power system disturbance. The main contributions of this dissertation are the simultaneous introduction and utilization of measurement based terms in the state and output equations in the derivation and implementation of the control law, the study of limits on controller performance as the state residual vector becomes very large, and the simulation of the performance of local state estimators to prove the need for faster phasor measurement systems. The test system is a hypothetical 39-Bus AC power system consisting of typical components which have been sufficiently modelled for the simulation of power system performance in a dynamic stability study.
- Advanced System Monitoring with Phasor MeasurementsZhou, Ming (Virginia Tech, 2008-05-19)Phasor Measurement Units (PMUs) are widely acknowledged as one of the most promising developments in the field of real-time monitoring of power systems. By aligning the time stamps of voltage and current phasor measurements that are consistent with Coordinated Universal Time (UTC), a coherent picture of the power system state can be achieved through either direct measurements or simple linear calculations. With the growing number of PMUs planned for installation in the near future, both utilities and research institutions are looking for the best solutions to the placement of units as well as to the applications that make the most of phasor measurements. This dissertation explores a method for optimal PMU placement as well as two applications of synchronized phasor measurements in state estimation. The pre-processing PMU placement method prepares the system data for placement optimization and reduces the size of the optimization problem. It is adaptive to most of the optimal placement methods and can save a large amount of computational effort. Depth of un-observability is one of the criteria to allow the most benefit out of a staged placement of the units. PMUs installed in the system provide synchronized phasor measurements that are highly beneficial to power system state estimations. Two related applications are proposed in the dissertation. First, a post-processing inclusion of phasor measurements in state estimators is introduced. This method avoids the revision of the existing estimators and is able to realize similar results as mixing phasor data with traditional SCADA with a linear afterwards step. The second application is a method to calibrate instrument transformers remotely using phasor measurements. Several scans of phasor measurements are used to accomplish estimating system states in conjunction with complex instrument transformer correction factors. Numerical simulation results are provided for evaluation of the calibration performance with respect to the number of scans and load conditions. Conducting theoretical and numerical analysis, the methods and algorithms developed in this dissertation are aimed to strategically place PMUs and to incorporate phasor measurements into state estimators effectively and extensively for better system state monitoring. Simulation results show that the proposed placement method facilitates approaching the exact optimal placement while keep the computational effort low. Simulation also shows that the use of phasor measurement with the proposed instrument transformer correction factors and proposed state estimation enhancement largely improves the quality of state estimations.
- Analysis of Electric Disturbances from the Static Frequency Converter of a Pumped Storage StationRosado, Sebastian Pedro (Virginia Tech, 2001-05-11)The present work studies the disturbances created in the electric system of a pumped storage power plant, which is an hydraulic generation facility where the machines can work as turbines or pumps, by the operation of a static frequency converter (SFC). The SFC is used for starting the synchronous machines at the station when in the pump mode. During the starting process several equipment is connected to the SFC being possible to get affected by the disturbances generated. These disturbances mainly include the creation of transient overvoltages during the commutation of the semiconductor devices of the SFC and the introduction of harmonics in the network currents and voltages. This work analyzes the possible effects of the SFC operation over the station equipment based on computer simulations. For this purpose, the complete system was modeled and the starting process simulated in a computer transient simulator program. The work begins with a general review of the effects of electric disturbances over high voltage equipment and in particular of the disturbances generated by power electronics conversion equipment. Then the models for the different kind of equipment present in the system are discussed and formulated. The control system that governs the operation of the SFC during the starting process is analyzed later as well as the operation conditions. Once the model of the system is set up, the harmonic analysis of the electric network is done by frequency domain and time domain methods. Time domain methods are also employed for the analysis of the commutation transient produced by the SFC operation. Finally, the simulation results are used to evaluate the impact of the SFC operation on the station equipment, especially on the generator step up transformer.
- Analysis of power system disturbances due to relay hidden failuresTamronglak, Surachet (Virginia Tech, 1994)This research analyzes the linkage between power system disturbances and failures in relaying systems. The annual disturbance reports prepared by the North American Electric Reliability Council were examined. It has been found that relaying system failures plays very important role in power system cascading outages. The type of relaying system failures that are the most troublesome are the ones that have a potential to remain hidden until being exposed by some abnormal power system states to trigger relay misoperations. Each commonly used relaying scheme in transmission system is examined for any hidden failures that can lead to relay misoperations and multiple power system contingencies. Each hidden failure mode has a region, called region of vulnerability. Inside this region, some abnormal power system states can expose the hidden failure. The reach of the region depends largely on the settings of the relay in question. A method of computing the relative importance of each region of vulnerability, called vulnerability index, was proposed. The calculation of the index can be based on some measurements of power system performances. In this research, the stability measurements of the system following some contingencies that may occur in the region are chosen. With this approach, vulnerable relays can be identified. A preventive method was proposed so that the number of relay misoperations due to hidden failures and, ultimately, the number of power system disturbances can be reduced.
- Analysis, monitoring and control of voltage stability in electric power systemsBegovic, Miroslav M. (Virginia Polytechnic Institute and State University, 1989)The work presented in this text concentrates on three aspects of voltage stability studies: analysis and determination of suitable proximity indicators, design of an effective real-time monitoring system, and determination of appropriate emergency control techniques. A simulation model of voltage collapse was built as analytical tool on 39-bus, 10-generator power system model. Voltage collapse was modeled as a saddle-node bifurcation of the system dynamic model reached by increasing the system loading. Suitable indicators for real-time monitoring were found to be the minimum singular value of power flow Jacobian matrix and generated reactive powers. A study of possibilities for reducing the number of measurements of voltage phasors needed for voltage stability monitoring was also made. The idea of load bus coherency with respect to voltage dynamics was introduced. An algorithm was presented which determines the coherent clusters of load buses in a power system based on an arbitrary criterion function, and the analysis completed with two proposed coherency criteria. Very good agreement was obtained by simulation between the results based on accurate and approximate measurements of the state vector. An algorithm was presented for identification of critical sets of loads in a voltage unstable power system, defined as a subset of loads whose changes have the most pronounced effect on the changes of minimum singular value of load flow Jacobian or generated reactive powers. Effects of load shedding of critical loads were investigated by simulation and favorable results obtained. An investigation was also done by sensitivity analysis of proximity indicators of the effects that locations and amounts of static var compensation have on the stability margin of the system. Static compensation was found to be of limited help when voltage instabilities due to heavy system loading occur in power systems. The feasibility of implementation of the analyses and algorithms presented in this text relies on development of a feasible integrated monitoring and control hardware. The phasor measurement system which was designed at Virginia Polytechnic institute and State University represents an excellent candidate for implementation of real-time monitoring and control procedures.
- Analytical methods for electromechanical forces and torque computation in brushless permanent magnet machinesGangla, Vineeta (Virginia Tech, 1991-02-05)The calculation of electromechanical forces that are present in a machine due to the magnetic field set up by current-carrying conductors and coils, especially when in the presence of permeable iron, is one of the most important and difficult problems in the vast field of the theory and design of electrical machines. It is a problem, moreover, which is usually dealt with by empirical methods based upon test results or by the use of numerical techniques such as Finite Element Analysis (FEA). In this thesis, analytical formulas are developed to evaluate the electromechanical forces and torques involved in brushless surface-mounted permanent magnet machines directly from, design parameters. In the first model, a slotless stator design is assumed while in the second model, the conductors are considered as being embedded in the stator iron. Both the models thus developed are then tested by means of a numerical method (FEA) and their utility in performing parametric studies is demonstrated in the case of the first model.
- Application of Bifurcation Theory to Subsynchronous Resonance in Power SystemsHarb, Ahmad M. (Virginia Tech, 1996-12-16)A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA# generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical compensation values, while in the CHOLLA#4 system, we show that there is only one Hopf bifurcation. The results show that as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability via a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions. When a damper winding is placed either along the q-axis, or d-axis, or both axes of the BOARDMAN system and the machine saturation is considered in the CHOLLA#4 system, the study shows that, there is only one Hopf bifurcation and it occurs at a much lower level of compensation, indicating that the damper windings and the machine saturation destabilize the system by inducing subsynchronous resonance. Finally, we investigate the effect of linear and nonlinear controllers on mitigating subsynchronous resonance in the CHOLLA#4 system . The study shows that the linear controller increases the compensation level at which subsynchronous resonance occurs and the nonlinear controller does not affect the location and type of the Hopf bifurcation, but it reduces the amplitude of the limit cycle born as a result of the Hopf bifurcation.
- The application of phasor measurements for adaptive protection and controlHuang, Chiung-Yi (Virginia Tech, 1991-06-05)This thesis describes an adaptive protection scheme that performs the collection of the voltage and current phasors during post-fault period, tracking the power swing phenomena, identifying the onset of instability, and then issuing a stabilizing command. In this work, the protection system is to maintain the reliability! ensure the secure operation, and prevent total collapse of the power system. The work is based upon methods of clustering for meter placement in a bulk power system, and selecting the pilot points for installing the phasor measurement units (PMU) to measure the bus voltage phasors and associated branch current phasors. According to the network law, fast calculation of state estimation can be made from these measurements. Because the on-line assessment of transient stability has to provide a quick and approximate result, the direct method which determines stability without explicit integration techniques is applicable in this study. The results of the system stability prediction in real-time by digital computer simulation under stable and unstable operating conditions are presented.
- Applications of phasor measurements to the real-time monitoring of a power systemBarber, David Edward (Virginia Tech, 1994-03-05)This thesis discusses applications of phasor measurement units to power system monitoring and synchronous generator modeling. Adjustments to a previously developed PMU placement algorithm are described which observe generator and tie line flows explicitly and reduces the number of PMUs required for a system, still observing the major dynamic components of a system. This adjusted methodology leaves some buses unobserved. A method for estimating the state of the unobserved region is developed based on using constant admittance or constant current load models. These models are accurate for a small neighborhood around the operating point when they were calculated. To determine the maximum error expected for any given system estimate, an equation relating the maximum error in the voltages to the maximum change in load power is derived. Once the issue of power system monitoring has been presented, the application of PMUs to the synchronous generator modeling is explored. This thesis deals with the on-line identification of the generator transient model using a recursive version of the generalized least squares algorithm. Simulations have been performed to demonstrate the validity and difficulties with these methods.
- Applications of superconducting magnetic energy storage systems in power systemsKumar, Prem (Virginia Tech, 1989-08-05)A Superconducting Magnetic Energy Storage (SMES) system is a very efficient storage device capable of storing large amounts of energy. The primary applications it has been considered till now are load-leveling and system stabilization.This thesis explores new applications/benefits of SMES in power systems. Three areas have been identified. • Using SMES in conjunction with PV systems.SMES because of their excellent dynamic response and PV being an intermittent source complement one another.A scheme for this hybrid system is developed and simulation done accordingly. • Using SMES in an Asynchronous link between Power Systems. SMES when used in a series configuration between two or more systems combines the benefits of asynchronous connection, interconnection and energy storage. A model of such a scheme has been developed and the control of such a scheme is demonstrated using the EMTP. The economic benefits of this scheme over pure power interchange, SMES operation alone and a battery/dc link is shown. Improvement of transmission through the use of SMES. SMES when used for diurnal load leveling provides additional benefits like reduced transmission losses, reduced peak loading and more effective utilization of transmission facility, the impact of size and location on these benefits were studied, and if used as an asynchronous link provides power flow control.
- Assessment of direct methods in power system transient stability analysis for on-line applicationsLlamas, Armando (Virginia Polytechnic Institute and State University, 1992)The advent of synchronized phasor measurements allows the problem of real time prediction of instability and control to be considered. The use of direct methods for these on-line applications is assessed. The classical representation of a power system allows the use of two reference frames: Center of angle and one machine as reference. Formulae allowing transition between the two reference frames are derived. It is shown that the transient energy in both formulations is the same, and that line resistances do not dampen system oscillations. Examples illustrating the mathematical characterization of the region of attraction, exit point, closest u.e.p. and controlling u.e.p. methods are presented. Half-dimensional systems (reduced-order systems) are discussed. The general expression for the gradient system which accounts for transfer conductances is derived without making use of the infinite bus assumption. Examples illustrating the following items are presented: a) Effect of the linear ray approximation on the potential energy (inability to accurately locate the u.e.p.’s); b) Comparison of Kakimoto’s and Athay’s approach for PEBS crossing detection; c) BCU method and; d) One·parameter transversality condition. It is illustrated that if the assumption of the one-parameter transversality condition is not satisfied, the PEBS and BCU methods may give incorrect results for multi-swing stability. A procedure to determine if the u.e.p. found by the BCU method lies on the stability boundary of the original system is given. This procedure improves the BCU method for off~line applications when there is time for a hybrid approach (direct and conventional), but it does not improve it for on-line applications due to the following: a) It is time consuming and b) If it finds that the u.e.p. does not belong to the stability boundary it provides no information concerning the stability/instability of the system.
- Computer relaying for EHV/UHV transmission linesYang, Lifeng (Virginia Tech, 1994)As the power systems grow, system connections become more complex. Due to cost and environmental concern, more and more parallel lines and series compensated lines may be installed in the system. In order to efficiently use the transmission network, more nonlinear flexible devices such as the phase shifter and the advanced compensation system will be put into use. Once a fault occurs on such a system, a delay in clearing the fault is usually not permissive. This requires a new generation of relays which have high security and dependability and high operating speed. With the advent of high speed microprocessor and fiber optic communication technologies, it is possible to develop high performance relays. In this dissertation, a new generation of pilot relays and non-pilot relays were developed for a transmission line. The pilot relays include the instantaneous percentage current differential (IPD), the phase comparison and the phasor based percentage current differential (PPD) principles. In the pilot protections the synchronized phasor measurement techniques are employed and digital CT saturation detectors are incorporated. All these schemes in primary protections feature charging current (or shunt current ) compensation. The phasor based principles are designed to work within one and a half cycles; while others based on sample by sample comparison are assumed to work in less than a cycle. The non-pilot relays to be investigated in this dissertation include the fault location based and phase angle based directional distance relays. One cycle data window is used in the phasor calculation. Both the distance relays are assumed to make a trip decision in about one and a half cycles. All algorithms were simulated against different fault conditions using EMTP outputs. The simulation results show all the pilot relay algorithms work well for EHV IUHV transmission lines including the series compensated lines. The fault location based distance relay works well in most cases, but it may give a wrong decision for the close-in fault with the fault resistance and may have a singularity problem. The phase angle based distance relay works very well for different fault conditions and is insensitive to fault resistance. The modified phase angle based distance relay was also developed for the series compensated line. It would not lose the direction for faults with or without fault resistance, either for a compensated system in forward direction, or in an adjacent line in reverse direction. The overreach is within 20% of the protected zone. This relay algorithm is also based on the one-cycle data window DFT, and it can give a reliable trip decision in about two cycles. All pilot relays with a fiber optic link and the phase angle based distance relay can constitute a new generation of protection systems for EHV IUHV transmission lines.
- Confidence Interval Estimation for Distribution Systems Power Consumption by Using the Bootstrap MethodCugnet, Pierre (Virginia Tech, 1997-07-15)The objective of this thesis is to estimate, for a distribution network, confidence intervals containing the values of nodal hourly power consumption and nodal maximum power consumption per customer where they are not measured. The values of nodal hourly power consumption are needed in operational as well as in planning stages to carry out load flow studies. As for the values of nodal maximum power consumption per customer, they are used to solve planning problems such as transformer sizing. Confidence interval estimation was preferred to point estimation because it takes into consideration the large variability of the consumption values. A computationally intensive statistical technique, namely the bootstrap method, is utilized to estimate these intervals. It allows us to replace idealized model assumptions for the load distributions by model free analyses. Two studies have been executed. The first one is based on the original nonparametric bootstrap method to calculate a 95% confidence interval for nodal hourly power consumption. This estimation is carried out for a given node and a given hour of the year. The second one makes use of the parametric bootstrap method in order to infer a 95% confidence interval for nodal maximum power consumption per customer. This estimation is realized for a given node and a given month. Simulation results carried out on a real data set are presented and discussed.
- A continuum Approach to Power system simulationDonolo, Marcos A. (Virginia Tech, 2006-09-04)The behavior of large and tightly interconnected power systems resembles, in certain circumstances, the behavior of a continuously distributed system. This resemblance motivated the derivation of continuum models, which were used to explain and predict disturbance propagation, un-damped power oscillations, and the stability of power systems. In this dissertation, we propose a one-dimensional continuum representation suitable for meshed power systems. Previous continuous representations of meshed power systems used two-dimensional spatial domains. Thus our approach has the potential to provide better resolution for comparable computational burden. It is important to note that, the computational burden required to obtain solutions for PDEs involved in the continuum representation varies notably with the solver implementation. The contributions of this dissertation are: a) Reviewing a previous continuum model and providing a detailed derivation for the one-dimensional version of it. b) Providing and describing in detail a parameter distribution technique adequate for the continuum approach. c) Identifying and documenting limitations on the continuum model voltage calculation. e) Providing a procedure to simulate the behavior of meshed power systems using the one dimensional continuum model. And f) Identifying and applying a numerical PDE solver for the continuum approach.
- Critical Substation Risk Assessment and MitigationDelport, Jacques (Virginia Tech, 2018-06-01)Substations are joints in the power system that represent nodes that are vital to stable and reliable operation of the power system. They contrast the rest of the power system in that they are a dense combination of critical components causing all of them to be simultaneously vulnerable to one isolated incident: weather, attack, or other common failure modes. Undoubtedly, the loss of these vital links will have a severe impact to the to the power grid to varying degrees. This work creates a cascading model based on protection system misoperations to estimate system risk from loss-of-substation events in order to assess each substation's criticality. A continuation power flow method is utilized for estimating voltage collapse during cascades. Transient stability is included through the use of a supervised machine learning algorithm called random forests. These forests allow for fast, robust and accurate prediction of transient stability during loss-of-substation initiated cascades. Substation risk indices are incorporated into a preventative optimal power flow (OPF) to reduce the risk of critical substations. This risk-based dispatch represents an easily scalable, robust algorithm for reducing risk associated with substation losses. This new dispatch allows operators to operate at a higher cost operating point for short periods in which substations may likely be lost, such as large weather events, likely attacks, etc. and significantly reduce system risk associated with those losses. System risk is then studied considering the interaction of a power grid utility trying to protect their critical substations under a constrained budget and a potential attacker with insider information on critical substations. This is studied under a zero-sum game theoretic framework in which the utility is trying to confuse the attacker. A model is then developed to analyze how a utility may create a robust strategy of protection that cannot be heavily exploited while taking advantage of any mistakes potential attackers may make.
- Decentralized pole placement using polynomial matrix fractionsAl-Hamadi, Helal M. (Virginia Polytechnic Institute and State University, 1988)As the dimension and the complexity of large interconnected systems grow, so does the necessity for decentralized control. One of the interesting challenges in the field of decentralized control is the arbitrary pole placement using output feedback. The feasibility of this problem depends solely on the identification of the decentralized fixed modes. As a matter of fact, if the system is free of fixed modes, then by increasing the controller’s order, any arbitrary closed loop poles can always be assigned. Due to this fact, reducing the controller’s order constitutes another interesting challenge when dealing with decentralization. This research describes the decentralized pole placement of linear systems. It is assumed that the internal structure of the system is unknown. The only access to the system is from a number of control stations. The decentralized controller consists of output feedback controllers each built at a control station. The research can be divided into two parts. In the first part, conditions for fixed modes existence as well as realization and stability of the overall system under decentralization are established using polynomial matrix algebra. The second part deals with the solution of decentralized pole placement problem, in particular, finding a decentralized controller which assigns some set of desired poles. The solution strategy is to reduce the controller’s order as much as possible using mathematical programming techniques. The idea behind this method is to start with a low order controller and then attempt to shift the poles of the closed loop system to the desired poles.
- Distance Protection Aspects of Transmission Lines Equipped with Series Compensation CapacitorsSummers, Clinton Thomas (Virginia Tech, 1999-09-29)In order to meet the high demand for power transmission capacity, some power companies have installed series capacitors on power transmission lines. This allows the impedance of the line to be lowered, thus yielding increased transmission capability. The series capacitor makes sense because it's simple and could be installed for 15 to 30% of the cost of installing a new line, and it can provide the benefits of increased system stability, reduced system losses, and better voltage regulation.1 Protective distance relays, which make use of impedance measurements in order to determine the presence and location of faults, are "fooled" by installed series capacitance on the line when the presence or absence of the capacitor in the fault circuit is not known a priori. This is because the capacitance cancels or compensates some of the inductance of the line and therefore the relay may perceive a fault to be in its first zone when the fault is actually in the second or third zone of protection. Similarly, first zone faults can be perceived to be reverse faults! Clearly this can cause some costly operating errors. The general approach of interest is a method leading to the determination of the values of series L and C of the line at the time of the fault. This is done by analyzing the synchronous and subsynchronous content of the V and I signals seperately which provides adequate information to compute the series L and C of the line.