Line Parameter Estimation Research Articles

A Joint Estimation Method of Distribution Network Topology and Line Parameters Based on Power Flow Graph Convolutional Networks

Accurate identification of network topology and line parameters is essential for effective management of distribution systems. An innovative joint estimation method for distribution network topology and line parameters is presented, utilizing a power flow graph convolutional network (PFGCN). This approach addresses the limitations of traditional methods that rely on costly voltage phase angle measurements. The node correlation principle is applied to construct a node correlation matrix, and a minimum distance iteration algorithm is proposed to generate candidate topologies, which serve as graph inputs for the parameter estimation model. Based on the topological dependencies and convolutional properties of AC power flow equations, a PFGCN model is designed for line parameter estimation. Parameter refinement is achieved through an alternating iterative process of pseudo-trend calculation and neural network training. Training convergence and loss function values are used as feedback to filter and validate candidate topologies, enabling precise joint estimation of both topologies and parameters. The proposed method’s accuracy, transferability, and robustness are demonstrated through experiments on the IEEE-33 and modified IEEE-69 distribution systems. Multiple metrics, including MAPE, IAE, MAE, and R2, highlight the proposed method’s advantages over Adaptive Ridge Regression (ARR). In the C33 scenario, the proposed method achieves MAPEs of 4.6% for g and 5.7% for b, outperforming the ARR method with MAPEs of 7.1% and 7.9%, respectively. Similarly, in the IC69 scenario, the proposed method records MAPEs of 3.0% for g and 5.9% for b, surpassing the ARR method’s 5.1% and 8.3%.

Identification of Distribution Network Topology and Line Parameter Based on Smart Meter Measurements

Accurate line parameters are the basis for the optimal control and safety analysis of distribution networks. The lack of real-time monitoring equipment in grids has meant that data-driven identification methods have become the main tool to estimate line parameters. However, frequent network reconfigurations increase the uncertainty of distribution network topologies, creating challenges in the data-driven identification of line parameters. In this paper, a line parameter identification method compatible with an uncertain topology is proposed, which simplifies the model complexity of the joint identification of topology and line parameters by removing the unconnected branches through noise reduction. In order to improve the solving accuracy and efficiency of the identification model, a two-stage identification method is proposed. First, the initial values of the topology and line parameters are quickly obtained using a linear power flow model. Then, the identification results are modified iteratively based on the classical power flow model to achieve a more accurate estimation of the grid topology and line parameters. Finally, a simulation analysis based on IEEE 33- and 118-bus distribution systems demonstrated that the proposed method can effectively realize the estimation of topology and line parameters, and is robust with regard to both measurement errors and grid structures.

Accurate Kalman filter based estimation of transmission line parameters utilizing synchronized phasor measurements

Transmission line parameters are needed to be precisely known to ensure accurate power system analyses. In spite of various noise reduction methods, measurement noise can still affect the phasor measurement unit (PMU) data, leading to errors in the estimated parameters. A Kalman filter can be used to estimate these parameters from PMUs data which may suffer from noise. The existing methods often ignore the presence of noise in voltage measurements and therefore are vulnerable to errors when noise is presented in voltage measurements. In this paper, a new method that considers the noise in both voltage and current synchrophasors is introduced. A novel formulation for considering the voltage measurement noise is introduced when estimating transmission line parameters from PMU data. Consequently, an analytic derivation of the measurement noise covariance matrix for the Kalman filter is presented. Extensive simulation results demonstrate that compared to the existing methods, the developed formulation and the associated measurement covariance matrix significantly improve the accuracy of estimates.

Distribution line parameters estimation framework with correlated injections using smart meter measurements

Accurate estimation of power system line parameters (resistance and reactance) is vital for operational and planning studies in power distribution systems. However, obtaining these estimates is challenging due to temperature and aging dependencies, limited measurements, correlated injections from renewable sources, and change/addition in network elements in due course of time. Most of the existing research for line parameter estimation (LPE) uses regression-based approaches, which are highly susceptible to noise in measurement data. In addition, these methods are unable to converge in the case of an ill-conditioned matrix, which often occurs in the active distribution system due to correlated injections. Furthermore, existing work requires μPMUs at each node of the distribution network, which may increase the overall cost. To address these challenges, this paper presents a data-driven error-in-variable model in the optimization-based framework for LPE in low and medium-voltage networks using smart-meter data. The proposed LPE method is specifically designed to handle correlated power injections and noise in measurement data. An equidistant loss sampling approach is also introduced for injection sample selection, reducing sample complexity. Simulation results on a real 6-Bus and IEEE 33-Bus system depict the ability of the proposed method to obtain line parameters with correlated and erroneous injections.

Line parameter, topology and phase estimation in three-phase distribution networks with non-[formula omitted]PMUs

The increasing penetration of distributed energy sources demands higher observability of the distribution networks for better scheduling, operation, dispatching and control. However, the huge amounts of nodes in the distribution networks implies that any additional measuring instrument would be of huge costs burden for DSO. In this paper, we proposes a full-scale framework for line parameters, topology, phase label estimation and angle recovery utilizing smart meter measurements only for the non-μPMU distribution networks. Firstly, we linearize the three-phase power flow model and induce the relationship of nodal voltage magnitudes and power injections. Then, a joint estimation method based on linear regression and topology characteristics is proposed to find line parameters, topology, and phase label. Finally, the nodal angle information is recovered by non-linear regression based on the estimation result. Simulations on both single-phase and three-phase networks are implemented. The results suggest that the proposed framework can provide an accurate estimation result with limited measurements.

A robust method for transmission line sequence parameter estimation using synchronized phasor measurements

We present a positive and zero sequence line parameter estimation method, that is robust to systematic errors in the instrument transformers, especially when they are within the specified tolerance as per standards. Using Monte Carlo simulations, it is shown that the proposed approach is robust and accurate for all operating conditions, specifically for short length and lightly loaded transmission lines. We also validate the proposed approach on 400 kV and 765 kV transmission lines using actual field phasor measurement unit (PMU) data. Further, estimation of zero sequence line parameter values is somewhat tricky because not enough unbalance exists during the normal operation of the power grid. Therefore, we quantify the minimum percentage unbalance needed in currents to determine zero sequence line parameter values within 1% tolerance. We also present the line length and line loading effects in estimating zero sequence line parameter values using simulations. Simulation and field PMU data results on 765 kV and 400 kV lines of different lengths and loading levels show that the proposed method estimates accurate positive and zero sequence line parameter values.

Comprehensive fault reporting for three-terminal transmission line using adaptive estimation of line parameters

In this study, the post-fault synchronized phasors acquired from the local phasor measurement units (PMUs) are used to provide comprehensive fault reporting in Three terminal transmission line system (TTTL). The reporting data incorporates the classification, section identification, and localization of the fault based on the post-fault measurements of positive, negative, and zero sequence quantities. For accurate reporting, a proposed algorithm computes transmission line parameters, on hourly basis, to account for fluctuations in characteristics caused by temperature influences arising from either the loading factor or the climatic vagaries. Upon fault occurrence, the algorithm firstly determines fault classification and faulty section. Thereafter, localization of symmetrical faults is achieved via the positive sequence quantities to solve the positive sequence fault loop equation while that of asymmetrical faults is obtained through the negative sequence quantities to solve the negative sequence fault loop equation. The fault localization speed of the reporting proposed algorithm is attributed to the fact that synchronized data are obtained after one and half cycles from the fault onset. PSCAD/EMTDC platform is dedicated for time-domain investigations, while the proposed algorithm is carried out in MATLAB. The proposed algorithm was tested against 1537 fault characteristics at different locations along the TTTL, including varying fault resistances, loading conditions, and network configurations, in addition to assessing its sensitivity to changes in the TTTL parameters. These tests confirmed the algorithm’s reliability to be used with confidence in a variety of scenarios as the only 13 tests were observed with an error of estimation greater than 1%.

Transmission line parameters estimation in the presence of realistic PMU measurement error models

Proposals have been presented in literature to estimate line parameters and monitor their changes. Synchrophasor measurements from phasor measurement units (PMUs) have appeared as a possible breakthrough for accurate estimation. However, few methods consider a realistic measurement chain including PMUs and instrument transformers and their systematic and random error contributions. This paper proposes an improved method to simultaneously estimate line parameters and systematic measurement errors on multiple network lines. The algorithm is designed to deal with realistic PMU measurement errors and, in particular, with phase-angle errors caused by common time-base errors on multiple PMU channels. The impact of PMU measurement errors is investigated to achieve a comprehensive view of the performance under realistic conditions. The results obtained on an IEEE test network prove the advantages of the proposed method with respect to other recent methods and its robustness in the presence of mismatches in the error model.

System Identification in Distribution Grid Without Phase Angle using Expectation Maximization

There has been a large increase in distributed energy resources (DERs) on the distribution grid (DG) and it is expected to continue. To support this increase active grid management and optimisation is required, for which accurate information of system state variables is required. This study presents a method for simultaneously estimating the line parameters and system state variables; active and reactive power at nodes. In addition, the study estimates the voltage magnitude accurately and requires no information about phase angle. The proposed approach uses a novel combination of Linearized Distflow and expectation maximisation (EM). The proposed approach is demonstrated on the IEEE 37 node test feeder and achieves accurate estimates of line parameters and state variables. Furthermore, the results show that the estimated line parameters give better voltage estimates using Linearised Distflow than the true parameters from the AC model which we argue is due to the estimated parameters making up for the approximation error.

Refined Modeling and Compensation of Current Transformers Behavior for Line Parameters Estimation Based on Synchronized Measurements

Nowadays, in modern management and control applications, line parameters need to be known more accurately than in the past to achieve a reliable operation of the distribution grids. Phasor Measurement Units (PMUs) may improve line parameters estimation processes, but the accuracy of the result is affected by all the elements of the PMU-based measurement chain, in particular by the instrument transformers. Current transformers (CTs) are nonlinear and therefore their behavior is not easily described: their models cannot be straightforwardly included in estimation problem. In this regard, the paper refines modeling and compensation of CT systematic errors in line parameters estimation processes, based on different methods to describe the transformer behavior under various operating conditions. As main result, the systematic errors of CTs are remarkably identified and mitigated. Moreover, estimation of shunt susceptance values is significantly improved.

Line Parameter, Topology and Phase Estimation in Three-Phase Distribution Networks with Non-Μpmus

Line Parameter, Topology and Phase Estimation in Three-Phase Distribution Networks with Non-Μpmus

A New Transmission Line Parameter Estimation Technique and Its Impact on Fault Localization

A New Transmission Line Parameter Estimation Technique and Its Impact on Fault Localization

Parameters estimation of AC transmission line by an improved moth flame optimization method

The parameters calculation for a transmission line is described in the proposed work, and the estimation of transmission line parameters is essential for properly managing transmission and distribution networks. The research work deals with the concept of optimization of the transmission line parameters. To this purpose, an improved moth flame optimization technique is applied to different test cases of the transmission lines. Moth movement with respect to the light source is the basis for improved moth flame optimization. In this research work, simulations are performed on various test cases to determine the effectiveness of the suggested method. Results from the suggested method are compared with those from other methods mentioned in the literature. The comparison shows that the proposed method rapidly and smoothly converges to the best-obtained value. The improved moth flame optimization performs better than other algorithms in terms of solution quality and feasibility, proving its effectiveness and competence. The optimal values obtained for capacitance in (mathrm{mu F}) are 0.22406, 0.022935, and 0.0049734, and for inductance in (mH) are 0.65055, 0.41258, and −0.76593, respectively.

ISO Linear Calibration and Measurement Uncertainty of the Result Obtained With the Calibrated Instrument

Abstract We address the problem of linear comparative calibration, a special case of linear calibration where both variables are measured with errors, and the analysis of the uncertainty of the measurement results obtained with the calibrated instrument. The concept is explained in detail using the calibration experiment of the pressure transducer and the subsequent analysis of the measurement uncertainties. In this context, the calibration and the measurements with the calibrated instrument are performed according to ISO Technical Specification 28037:2010 (here referred to as ISO linear calibration), based on the approximate linear calibration model and the application of the law of propagation of uncertainty (LPU) in this approximate model. Alternatively, estimates of the calibration line parameters, their standard uncertainties, the coverage intervals and the associated probability distributions are obtained using the Monte Carlo method (MCM) based on the law of propagation of distributions (LPD). Here we also obtain the probability distributions and the coverage interval for the quantities measured with the calibrated instrument. Furthermore, motivated by the model structure of this particular example, we conducted a simulation study that presents the empirical coverage probabilities of the ISO and MCM coverage intervals and investigates the influence of the sample size, i.e. the number of calibration points in the measurement range, and the different combinations of measurement uncertainties. The study generally confirms the good properties and validity of the ISO technical specification within the considered (limited) framework of experimental designs motivated by real-world application, with small uncertainties in relation to the measurement range. We also point out the potential weaknesses of this method that require increased user attention and emphasise the need for further research in this area.

Total Msplit estimation

Msplit estimation is a method that enables the estimation of mutually competing versions of parameters in functional observation models. In the presented study, the classical functional models found in it are replaced by errors-in-variables (EIV) models. Similar to the weighted total least-squares (WTLS) method, the random components of these models were assigned covariance matrix models. Thus, the proposed method, named Total Msplit (TMsplit) estimation, corresponds to the basic rules of WTLS. TMsplit estimation objective function is constructed using the components of squared Msplit and WTLS estimation objective functions. The TMsplit estimation algorithm is based on the Gauss–Newton method that is applied using a linear approximation of EIV models. The basic properties of the method are presented using examples of the estimation of regression line parameters and the estimation of parameters in a two-dimensional affine transformation.

Augmented State Estimation of Line Parameters in Active Power Distribution Systems With Phasor Measurement Units

The line parameters of power distribution systems stored in the dispatching center may have large errors due to the line aging and system operational dynamics. Such line parameter errors may directly affect the state estimation accuracy, and the advanced management functionalities rely on these parameters. This paper proposes an augmented state estimation method of erroneous distribution line parameters considering the presence of phasor measurement units (PMUs). The augmented state-space models under single and multiple measurement snapshots are established separately by combining the parameter state equation with the state-space model of the distribution network. The augmented state estimation based on the improved adaptive unscented Kalman filter (IAUKF) is developed. The proposed method can effectively perceive the process noise statistical parameter of the erroneous parameters during the estimation to accurately estimate line parameters. The proposed solution is validated through simulation experiments using the IEEE 33-bus system and the numerical results demonstrated its accurate parameter estimation performance.Also, the scalability of the proposed algorithm is demonstrated based on the simulation of the 118-bus system with distributed generators.

Synchrophasor Data Analytics: Transmission Line Parameters Online Estimation for Energy Management

Transmission line parameters are fundamental parameters of power system models that influence the safety, stability, and economy of power utility grids. Transmission line parameter estimation is a basic and necessary function and module of a power grid energy management system. However, traditional offline parameter estimation methods cannot cope well with parameter uncertainties caused by transmission line aging, environmental factors, and modern power grid developments. The widespread deployment of phasor measurement units (PMUs) in power networks has paved the way for accurate real-time-measurement-based transmission line parameter tracking. This article proposes PMU-based parameter estimation models considering series and shunt compensators. An online parameter estimation method is developed based on recursive least squares with a variable forgetting factor, which can adapt to various parameter mutations and has strong robustness to outlier measurements. This article also analyzes the sensitivity of parameters with respect to synchrophasor data. The simulation results under different scenarios verify the effectiveness, robustness, and adaptivity of the proposed method, which exhibits significant advantages over other existing parameter estimation methods.

Estimation of Line Parameters, Tap Changer Ratios, and Systematic Measurement Errors Based on Synchronized Measurements and a General Model of Tap-Changing Transformers

A primary requirement for the transmission system operator is an accurate knowledge of grid parameters. Moreover, the availability of effective and accurate monitoring tools allows the proper operation of power transmission grids. However, in spite of the now widespread possibility of having monitoring systems based on synchronized measurements, the monitoring applications can be affected not only by the inevitable uncertainty sources but also by the simplified or incomplete modelling of the network components. For this reason, the impact on power system monitoring and control applications of tap-changing transformer models is a key point. In this scenario, this paper presents a method to estimate simultaneously line parameters, tap changer ratios and systematic measurement errors associated with the instrument transformers. The method exploits a flexible model of the tap-changing transformer based on a parameter representing the ratio between the two winding impedances of the transformer. The proposal is based also on the suitable modelling of the measurement chain and on the constraints introduced by the equations of involved transmissions lines and transformers. The validation has been carried out by means of tests performed on the IEEE 14 Bus Test Case.

Enhanced PMU-Based Line Parameters Estimation and Compensation of Systematic Measurement Errors in Power Grids Considering Multiple Operating Conditions

Several monitoring, protection, and control applications designed for modern power grids are based on detailed grid models and thus require accurate knowledge of line parameters. A synchronized monitoring infrastructure based on phasor measurement units (PMUs) may be of great support to the task of line parameters estimation, but the accuracy of the estimated parameters may be largely affected by the uncertainty of all the elements of the PMU-based measurement chain. Thus, an accurate parameters estimation must appropriately consider the metrological behavior of all these elements, in particular that of instrument transformers (ITs). To address this challenge, this article proposes an enhanced multibranch method for accurate estimation of the line parameters and the systematic measurement errors introduced by the ITs when measurements for multiple operating conditions are considered. Indeed, multiple operating conditions are dealt with properly due to an in-depth analysis of the problem modeling within the framework of Tikhonov regularization. The validity of the proposed approach is confirmed by the results obtained on the IEEE 14-bus test system.

PMU-Based Estimation of Systematic Measurement Errors, Line Parameters, and Tap Changer Ratios in Three-Phase Power Systems

The availability of accurate data is fundamental for several monitoring and control applications of modern power grids. Nevertheless, the knowledge of critical data, such as transmission line and transformer parameters, is often affected by uncertainty. This can lead to important problems in the correct management of the power systems. In spite of a monitoring infrastructure that is being renewed due to new generation devices providing synchronized measurements, the actual values of line parameters and tap changer ratios are still affected by uncertainty sources that need to be properly considered. The behavior of all the elements involved in the measurement chain must be duly modeled. This article proposes an improved method to carry out the simultaneous estimation of line parameters, tap changer ratios, and systematic measurement errors for a three-phase power system. The proposed method is based on the suitable modeling of the measurement chain and three-phase constraint equations (voltage drop and current balance) of all the components involved. Its effectiveness is confirmed by tests performed on an IEEE 14-bus test system reproduced as a three-phase system under different operative conditions.