A new distance relaying algorithm based on complex differential equation for symmetrical components

This paper presents a new digital impedance measuring technique for transmission lines that combines symmetrical components and the complex differential equation of an equivalent fault loop circuit. The phase voltages and currents at the relaying point are transformed into symmetrical components using Fourier filters of short window length. Depending on fault type, an appropriate fault loop circuit is formed, signals of which are the appropriate symmetrical components, while a parameter of which is the positive sequence impedance being a geometrical measure of the distance from the relaying point to a fault. The impedance, however, is measured very fast by on-line solving the complex differential equation originated for this fault loop circuit. Consequently, this approach combines frequency domain estimation of symmetrical components (accurate filtration) and time domain measurement of positive sequence impedance (high speed response).

The presented method suits well the protection of parallel lines against high-resistance faults occurring very close to the far end of a line. A new method is proposed for detecting high-resistance faults and deciding which line out of two parallel lines actually suffers a fault.

The included EMTP test results demonstrate the efficiency of the proposed relaying algorithm.     

An algorithm using a shape-based approach in Park's plane for transformer differential relaying on the basis of time-dependent symmetrical components

Discrimination between inrush transients and internal faults is an issue of most concern in differential relaying when protecting power and distribution transformers. Based on an analysis of the symmetrical components obtained during inrush and during internal fault conditions, a linkage between their instantaneous evolution and the shapes of plots in Park's plane is presented in this paper. The use of Park transformation allows to avoid conventional spectrum analysis, what results in a quite simplified protective technique. By introducing a vector, which is defined as the sum of the vectors corresponding to measurements in both sides of the transformer, a categorization of shapes of plots is done here. Thus, a shape-based rule is presented for discriminating between inrush and fault in this paper. In addition, an algorithm is presented for fast classification of shapes. The proposed algorithm is based on the periodicity generated by the modulus of the defined Park's vector. The approach presented in this paper has been tested in a laboratory transformer, showing a robust, accurate and fast performance.     

A CT saturation detection algorithm using symmetrical components for current differential protection

A method of symmetrical component analysis for the detection of current-transformer (CT) saturation in a numerical current differential feeder protection relay is presented in this paper. The performance of the differential relay is investigated for various faults on a typical Electro-Magnetic Transients Program/Alternative Transients Program (EMTP/ATP) simulated transmission feeder. The simulator includes the effects of CT saturation. A comparison between simulation and tests conducted on an analog model testbench are also evaluated. The results show a high degree of similarity and illustrate the effect that CT saturation imposes on the sensitivity and stability of the protection scheme. An algorithm is presented that shows significant improvement in sensitivity on internal faults while still maintaining a high level of stability on external faults and nonfault events.     

A digital relaying algorithm for detecting transformer windingfaults

A digital algorithm for detecting faults in single-phase and three-phase power transformers is proposed. The algorithm is suitable regardless of whether it is possible to measure winding currents. The algorithm does not require B-H curve data. A variety of operating conditions simulated on a computer were used to test the algorithm. The results show that it performs well     

A recursive Newton type algorithm for digital frequency relaying

This paper presents a new recursive Newton type algorithm devoted to frequency relaying. The algorithm is designed from the nonrecursive Newton type algorithm and recursive least error squares algorithm. The frequency is estimated from the uniformly sampled voltage signal. The algorithm testing based on computer simulated and experimentally obtained data record processing confirmed the good features of the algorithm developed. Due to its computational efficiency, the algorithm is suitable for various real-time power system measurement applications.     

A recursive least-squares digital distance relaying algorithm

A new digital distance relaying algorithm based on the well-known theory of least-squares is developed, and the results of testing it using numerical simulation are presented. The new technique estimates the distance to the fault and the fault resistance. To minimize the computational requirements of the digital relay, a recursive least-squares approach is used. Computer simulation results of the new least-squares algorithm seem promising, indicating that it should be considered for further testing and evaluation     

Fault impedance estimation algorithm for digital distance relaying

Fault impedance is one of the major parameters that must be estimated accurately in digital distance relaying application. In this paper, a new algorithm is proposed based on symmetrical components theory. The proposed algorithm has computational advantage over previously suggested symmetrical components based algorithms. A procedure for applying shunt fault conditions to the sequence equations to estimate fault impedance of the protected transmission line is discussed. The Alternative Transient Program (ATP) that is available on personal computers was used in evaluating the proposed algorithm. ATP models a power system and simulates many fault conditions on a selected transmission line. Fault data obtained were used in calculating fault impedance using the proposed algorithm. Fault impedance estimates were inserted in relay characteristics to determine suitability of the proposed algorithm for first zone distance protection. Sample results of these studies which show stable fault distance estimates are presented and discussed in the paper     

A fast method for identification of symmetrical components for power system protection

This paper presents a novel dynamic technique for identifying and measuring the symmetrical components of three-phase voltage or current waveforms in electrical power systems. The proposed technique is based on stochastic estimation theory. The problem is formulated as an estimation problem and presented in state space form. The algorithm is then used to estimate the active and reactive components of the positive, negative and zero components of unsymmetrical waveforms. The method is tested using practical study cases. Different factors affecting the identification process such as data window size, sampling frequency and number of samples are studied. Effects of bad data on the solution accuracy are also studied. The speed of convergence is examined by changing the estimator initial conditions. The results obtained show that the proposed technique can estimate and track the symmetrical components of non-stationary three-phase unbalance voltage or current waveforms in noisy environments. Fast accurate solutions are guaranteed regardless of the initial conditions. It is also shown that bad measurements have no effect on the final accuracy of the estimation.     

Fast and accurate parameter estimation algorithm for digital distance relaying

Response of digital distance relaying depends on the fast and accurate calculation of parameters such as voltage and current phasors and fault impedance. This paper describes a new apparent impedance estimation algorithm that is based on modal components theory. It is shown in the paper that the proposed algorithm has several advantageous features in terms of speed and accuracy over previously suggested symmetrical and modal components based algorithms. The paper discusses a procedure for deriving a fault impedance estimation algorithm that can be used for protecting power transmission lines. The proposed algorithm was evaluated using an alternative transient program (ATP). The program models a power system, simulates many fault conditions on a selected transmission line and generates fault data. The relay software then obtains filtered, scaled and sampled data and calculates fault impedance using the proposed algorithm. The relay characteristic makes trip decisions based on the fault impedance estimates. The paper shows the feasibility of the proposed algorithm for first zone distance protection. Some results of these studies are presented and discussed in the paper.     

A new algorithm for relaying and fault location based on autocorrelation of travelling waves

The technique employs correlation of the incident and reflected wave signals at one end of the line. Since the reflected wave is very similar in shape to the incident wave causing it, except for a constant time delay and attenuation, autocorrelation results. The property of ‘evenness’ of the autocorrelation is used to determine the delay time, which is a function of fault position, employing numerical integration which is suitable for a digital computer. It is shown that fast relaying as well as accurate fault location is accomplished on a real-time basis, even in the presence of a considerable amount of high frequency line transients. The technique has been tested by numerical simulations using the standard Electromagnetic Transient Program (EMTP).     

Charles LeGeyt Fortescue and the method of symmetrical components

The author gives a brief review of the life and work of Charles LeGeyt Fortescue with particular reference to his 1918 paper on the "Method of Symmetrical Co-Ordinates Applied to the Solution of Polyphase Networks" which grew out of his investigations of problems related to railway electrification, which began in 1913. As a postlude to the author's article, the paper presents Fortescue's own writing on the topic of symmetrical components, which he included in a document he produced on 8 October 1934, titled "High Points in My Career"     

A simple iterative algorithm for the towers of Hanoi problem

The towers of Hanoi game is well known. The basic version, a favorite example for many authors, is often used in introductory textbooks on computer programming to demonstrate the elegance of writing recursive code. Here, a simple iterative optimal algorithm for the towers of Hanoi problem is presented     

一种精确滤除衰减非周期分量的新算法

提出了精确滤除衰减非周期分量的新算法.新算法对衰减的非周期分量时间常数τ未作假定和要求,是从信号的离散采样值出发,严格推导得到精确结果.文中同时给出了基于该精确算法的简化算法,在τ较小时,精度仍很高.因此,该简化算法具有较高的理论和实用价值,本算法已运用在课题组研制的110 kV微机保护通用平台上.     

一种精确滤除衰减非周期分量的新算法

提出了精确滤除衰减非周期分量的新算法。新算法对衰减的非周期分量时间常数τ未作假定和要求,是从信号的离散采样值出发,严格推导得到精确结果。文中同时给出了基于该精确算法的简化算法,在τ较小时,精度仍很高。因此,该简化算法具有较高的理论和实用价值,本算法已运用在课题组研制的110kV微机保护通用平台上。     

基于负序功率方向比较原理的广域继电保护算法

提出一种基于负序功率方向比较原理的广域继电保护算法。根据智能电子设备（Intelligent Electric Device,IED）的安装位置,形成包含有母线及线路在内的IED关联域。系统发生故障后,通过IED在关联域内对故障信息的采集和共享,结合定义的故障判别原则,确定故障的位置;并根据IED预定的动作策略,快速地切除故障。该算法既能做系统发生故障后快速动作的主保护,同时又兼顾后备保护的功能。通过仿真验证了该算法的有效性,表明该算法可以很好地实现主保护和后备保护的功能。     

A simple two stage optimization algorithm for constrained powereconomic dispatch

A simple two stage optimization algorithm is proposed and investigated for fast computation of constrained power economic dispatch control problems. The method is a simple demonstration of the hierarchical aggregation-disaggregation (HAD) concept. The algorithm first solves an aggregated problem to obtain an initial solution. This aggregated problem turns out to be classical economic dispatch formulation, and it can be solved in 1% of overall computation time. In the second stage, a linear programming method finds optimal solution which satisfies power balance constraints, generation and transmission inequality constraints and security constraints. Implementation of the algorithm for IEEE systems and EPRI Scenario systems shows that the two stage method obtains an average speedup ratio of 10.64 as compared to the classical LP-based method     

A virtual environment for protective relaying evaluation and testing

Protective relaying is a fundamental discipline of power system engineering. At Georgia Tech, we offer three courses that cover protective relaying: an undergraduate course that devotes one-third of the semester on relaying, a graduate course entitled "Power System Protection," and a three-and-a-half-day short course for practicing engineers. To maximize student understanding and training on the concepts, theory, and technology associated with protective relaying, we have developed a number of educational tools, all wrapped in a virtual environment. The virtual environment includes a) a power system simulator, b) a simulator of instrumentation for protective relaying with visualization and animation modules, c) specific protective relay models with visualization and animation modules, and d) interfaces to hardware so that testing of actual relaying equipment can be performed. We refer to this set of software as the "virtual power system." The virtual power system permits the in-depth coverage of the protective relaying concepts in minimum time and maximizes student understanding. The tool is not used in a passive way. Indeed, the students actively participate with well-designed projects such as a) design and implementation of multifunctional relays, b) relay testing for specific disturbances, etc. The paper describes the virtual power system organization and "engines," such as solver, visualization, and animation of protective relays, etc. It also discusses the utilization of this tool in the courses via specific application examples and student assignments.     

A high-resolution spectral analysis algorithm for power-system disturbance monitoring

In a previous paper, the author presented a Fourier-based algorithm for monitoring the characteristics of the damped oscillating "modes" which are set up after a disturbance in an electric power-distribution system. This earlier paper permitted the analysis of multiple modes but only if the modes were sufficiently well separated to be resolved with conventional Fourier techniques. This current paper extends the previous work to enable the processing of multiple modes which are very closely spaced in frequency. Importantly, the proposed algorithm has good noise performance. A theoretical justification for the new method is presented, and simulations are provided to confirm the theory. The scheme is also tested on a real power-system example.     

A substitution algorithm for solving nonlinear circuits with multi-frequency components

In this paper, we present an efficient algorithm for calculating the steady-state response of nonlinear circuits such as forced circuits driven by multi-frequency-component signals, forced oscillators, and coupled oscillators. We call the technique a substitution method because the variation at each step is calculated by solving an associated time-invariant sensitivity circuit at each frequency component of the residual error, whose circuit is derived from a relaxation method. the algorithm is very simple and efficient, and it can be applied to a wide variety of nonlinear circuits.