Distribution Of Factors Research Articles

Robust Data-Driven Sparse Estimation of Distribution Factors Considering PMU Data Quality and Renewable Energy Uncertainty - Part I: Theory

Data-driven sparse estimation of distribution factors (DFs) facilitates online power flow sensitivity analysis for secure system operation. However, existing methods are vulnerable to time-varying non-Gaussian PMU measurement noise, bad data, and uncertain renewable energy sources (RESs). Moreover, they lack scalability to large-scale systems. This two-part paper proposes a robust and scalable sparse DF estimation framework considering PMU data quality and RES uncertainty. In this Part I, a novel Adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -Lasso estimator with theoretically guaranteed robustness is proposed. It mitigates the impacts of measurement and RES uncertainties to yield accurate dominant DF estimates while promoting sparsity. The key idea is to integrate the robust statistics theory with sparse representation techniques, in particular the Huber loss function, adaptively-weighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization, concomitant scale estimate, and pseudo-residuals. Two important robustness properties of this estimator are theoretically proven, i.e., the bounded influence function and the asymptotic consistency of dominant DF estimates given limited samples. The breakdown points of this estimator to measurement and RES uncertainties are derived. Test results validate that the proposed estimator allows accurate estimation without relying on power flow models or massive operating data. It achieves significantly superior robustness over existing methods in multiple scenarios.

Robust Data-Driven Sparse Estimation of Distribution Factors Considering PMU Data Quality and Renewable Energy Uncertainty - Part II: Scalability and Applications

This two-part paper proposes a data-driven, robust, and scalable sparse estimation framework of distribution factors (DFs). Part I proposes a novel Adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -Lasso estimator with theoretically guaranteed robustness. For solving this estimator, common algorithms are not scalable to large-scale systems since they often fail to converge under parallelism. This is addressed in Part II, where a novel Online Parallel Stochastic Coordinate Descent algorithm with theoretically guaranteed scalability is proposed. It can simultaneously update massive DF estimates by stochastic parallelism with fast convergence. It also works recursively under a multi-core setting and does not need step-size tuning, which is applicable for cloud-computing-based online parallel estimation. Convergence bounds of this algorithm are theoretically proven, and its speedup and maximum parallel core number are derived. These guide practical computational resource allocation for high efficiency. The benefits of the framework are showcased in real-time market operations under locational marginal pricing (LMP) and financial transmission right (FTR) mechanisms for congestion management. Thanks to its sparsity-promoting effect, robustness, and scalability, it allows for correctly and fast solving LMPs, congestion patterns, and FTR revenues against uncertainties. Test results on IEEE 300- and European 9241-bus systems via Alibaba Cloud validate the high scalability of this algorithm and benefits of the proposed framework to system applications.

Distribution Characteristics of Heavy Metals in Different Particle Size Fractions of Chinese Paddy Soil Aggregates

In recent years, the migration and transformation of heavy metals (HMs) in soil has become a hot issue. Soil particle size has an important effect on the environmental behavior of HMs in soil. The distribution of HMs in soil is strongly affected by the size of a soil aggregate. In this study, paddy samples in both cultivated and uncultivated soils were collected from Anhui Province, China. The soils were sieved into six particle size fractions (diameters of &gt;4000, 4000–2000, 2000–1000, 1000–250, 250–53, and &lt;53 μm) and the wet digestion method was used to determine the concentrations of Cd, Cr, Pb, and As in the soil aggregates. The results showed that the surface soils were characterized by the largest proportion of coarsest aggregates of &gt;4000 μm particles. Moreover, the concentrations of Cd, Cr, Pb, and As were elevated in cultivated paddy soils compared to uncultivated soils. The accumulation of HMs in all paddy soils increased with decreasing particle size. Although the smallest particle size fractions accounted for only 5.65–17.28%, they provided the highest distribution factor (DF) of Cr (1.35), As (1.25), Cd (1.28), and Pb (1.38). The highest contributions of HMs came from the coarser fractions (&gt;2000 μm); however, for Cr, Pb, Cd, and As, the mass loading of &lt;53 μm particles was up to 15.90%, 14.41%, 15.21%, and 15.70%, respectively. The highest content of HMs was found in the finest aggregate, with a pattern of decreasing with increasing aggregate size. In addition, the leachability behaviors of different HMs in different particle size aggregates were different. The leachability behaviors of Cr and Pb in the coarse particle size fractions were the highest, while the leachability behaviors of As and Cd in the less than 250 μm particle size fractions were 10–100 times higher than those of Cr and Pb. A correlation analysis showed that the particle distributions of Fe, TOC, and Mn had significant influences on the distributions of Pb, Cd, As, and Cr. This study provides a theoretical basis for the prevention, treatment, and remediation of HMs pollution in soil.

Real-time and consistent sparse estimation of power system distribution factors using online adaptive elastic-net

Distribution factors (DFs) are vital for power system monitoring and secure operation. However, it is challenging to accurately estimate dominant DFs while promoting the sparsity of DFs in real time, especially in large-scale power systems with high-dimensional data. This paper proposes a novel Online Adaptive Elastic-net (AdaEnet) method to address this challenge, which allows the real-time and consistent sparse estimation of DFs in large-scale power systems. The problem is formulated as a sparse regression problem using data measured by phasor measurement units. The AdaEnet estimator is advocated to promote the sparsity of DFs, and a LARS-AdaEnet algorithm is developed for the real-time estimation of DFs. Thanks to the oracle properties and the grouping effect of the AdaEnet, the method yields unbiased dominant estimates with stability to collinear predictor variables, even for underdetermined systems. Moreover, due to the online updated adaptive weights and the early-stopping property of the LARS-AdaEnet, the method efficiently solves the estimator using only a few latest samples. Test results on the IEEE 300- and the Polish 3375-bus systems demonstrate that the proposed method achieves high estimation consistency and real-time adaptability in the presence of high-dimensional data (i.e., massive collinear predictor variables of small sample size). Hence this method promotes the data-driven, sparsity-aware, and computationally efficient sensitivity analysis of active power line flows in large-scale power systems. It can broadly facilitate real-time situational awareness and decision-making for improving power system security.

An algorithm for contingency analysis of the AC-DC networks using modified Z-bus technique

The steady state Contingency Analysis (CA) utilizes non-iterative distribution-factors (DFs) based linear estimation method of current-redistribution, to deliver approximate solutions in a shorter timeframe, which is favored over recurrent usage of iterative power flow-based non-linear techniques. However, the established principles of conventional DF-based CA cannot be directly implemented on burgeoning AC-DC networks. The DFs obtained from single unified Z-bus constructed for the entire AC-DC network leads to erroneous estimation of current redistribution post any contingency event. The reason being unified Z-bus built overlooked the characteristics of AC and DC lines. As a paradigm change toward a co-existing AC-DC network emerges, an adequate framework for understanding contingencies within such a network becomes critical. We present a quick non-iterative DF-based approach for the CA of any AC-DC network in this research by merging the use of separate AC and DC impedance matrices while accounting for the intertwined implications of the AC and DC networks. The interlinking converters (ILCs) are simulated using a reactive current bypassing approach. The proposed CA method is capable of handling contingencies occurring within ILCs, AC and the DC networks. The ETAP simulations and the Newton-Raphson (NR) technique for the AC-DC network have been utilized to corroborate the results.

Coordinated, sensitivity-based DSM for enhanced cross-border power transfers

This paper discusses the use of coordinated wide area demand side management (DSM) for facilitating cross-border power transfers between the interconnected transmission networks. It proposes a methodology for ranking transmission network loads eligible for DSM programs based on the network topology and the size of DSM assets. The influence of network topology is accounted for by considering distribution factors (DFs), and the size of DSM assets by considering the available demand flexibility (upward or downward variation) of load buses. The industrial end-users connected directly to transmission network and the bulk supply points of distribution networks are considered the two main types of DSM providers at the transmission level. The proposed approach facilitates analytical evaluation of the effects of DSM on power transfers and such makes a valuable decision-support tool for any transmission system operator, whether it is used for network operation or planning. The methodology is illustrated on a simplified model of four interconnected European transmission networks and thus provides a realistic assessment of the extent to which cross-border DSM can be used to regulate power transfers between countries.

Improving screening model of pesticide risk assessment in surface soils: Addressing regional specific human exposure risks and regulatory management

In this study, a simple screening approach was proposed to evaluate region-specific population health risks of soil pesticides, which was achieved by introducing region-specific factors of pesticides, including fate factors (FFs), environmental distribution factors (DFs), and intake factors (IFs). These region-specific factors were characterized using simple weather variables and calculated the characterization factors (CFs) to link pesticide emissions to population exposure risks. The CF at the reference state indicates the potential of a pesticide entering the human body. Simulations for over 700 pesticides showed that pesticides that are thermodynamically stable in soil organics have large CFs. In addition, we conducted a case study on the region-specific risk assessment of malathion in the United States. The results indicated that colder regions have larger CFs of malathion than those of the warmer regions due to the large FF values for the same emission rates. However, from a regulatory perspective, colder regions should have less strict malathion soil standards than those of warmer regions as children in colder regions spend limited time outdoors. Although other region-specific factors such as soil type and population density need to be considered to improve the model, the approach proposed in this study can be used as a simple screening tool to evaluate region-specific population health risks and manage soil residues for different regions.

Intelligent Assessment of Active and Reactive Power Flow with Satisfying Accuracy for N - k1 - k2 Cascading Outages

Addressed to the $N-k_{1}-k_{2}$ cascading outages, it is computationally burdensome for the reliable calculation of active and reactive power flows. This paper builds a comprehensive framework with three algorithms, including the distribution factor (DF), the Newton-Raphson (NR), and the first iteration of NR algorithm (termed as 1J). Classifiers are designed to determine whether the NR algorithm should be employed for accuracy. Classifier features are extracted upon the analytical error of 1J. As reactive power is partially considered in the 1J but neglected in the DF algorithm, the deviation between the solutions is taken as one crucial feature. The support vector machine (SVM) is then utilized for classifier training. As the deep integration of the causal inference and the statistical paradigm, this framework calculates active and reactive power flows rapidly, reliably, and robustly. The effectiveness and robustness are fully validated in three typical IEEE systems.

Partitioning, leachability, and speciation of chromium in the size-fractions of soil contaminated by chromate production

Soil particle size significantly affects the distribution and migration of chromium (Cr) in soil. Limited studies have investigated the impact of soil particle size on Cr partitioning at chromate contaminated sites. In this study, the physicochemical properties of coarse sand, medium sand, fine sand, and silt-clay were analyzed. And the particle size effects on partitioning, leachability, and bioaccessibility of total Cr and Cr(VI) were determined. The results showed the distribution factor (DF) of Cr(VI) in the coarse sand, medium sand, fine sand, and silt-clay fractions were 0.70, 0.79, 1.35, and 1.60, respectively. The total Cr DF values also had the similar result. The leached concentrations of total Cr and Cr(VI) in silt-clay (562.89 mg/L and 551.71 mg/L) was higher than in coarse sand (238.55 mg/L and 228.68 mg/L) fraction. The bioaccessibility of total Cr and Cr(VI) in silt-clay (77.72% and 88.58%) was higher than in fine sand (60.72% and 79.55%) fraction. The total Cr proportion of the exchangeable fraction (45.92%–73.67%) was relatively high in the four soil particle size fractions and gradually increased as soil particle size decreased. These implied that finer soil particles are more capable of enriching, mobilizing, and bioaccessibility of Cr and Cr(VI) than the coarse particles, which was related to the higher organic matter, cation exchange capacity, specific surface area, and clay components in smaller particles. The results suggested that higher environmental risk occurred in the finer fraction than in the coarser fraction for the chromate production contaminated soil.

Bridge Load Testing for Identifying Live Load Distribution, Load Rating, Serviceability and Dynamic Response

In this article, dynamic and static load tests of a concrete highway bridge, which is a deteriorated and repaired, are presented depending on displacement and strain data for engineering decision making about the operation of a critical bridge. Static load test was carried out to determine the live load distribution factor (DF) and load-rating (RF) as well as serviceability by means of deflection limits. Modal characteristics in terms of structural frequencies and mode shapes and impact factor (IM) were identified from the dynamic load test for different truck-load and speed cases, and FE model. The distribution factor (DF) and load rating factor (RF) were also compared with those calculated according to AASHTO standard and FE model. The results showed that the distribution factor (DF) calculated by AASHTO standard gave more conservative results when compared with the experimental and FEM approaches. Similarly, the load-rating factor (RF) calculated by AASHTO standard yielded to more conservative results comparing with the experimental FEM approaches using practical distribution factors. Maximum deflections in static cases and dynamic cases were found to be within the limit calculated by (L/800) given in the AASHTO code. Impact factors among all the cases were obtained much smaller than the one recommended by AASHTO standard (33%). The modal properties were obtained to track changes in dynamic behavior due to stiffness and boundary effects as well as for finite element model calibration. The calibrated FE model of the bridge also indicated that the load carrying capacity of the bridge is adequate after repair. Finally, the results from the current study reveal that use of experimental data can be utilized to obtain load rating with minimum interruption to bridge operations through computer vision technology and methods.

Lateral Load Distribution for Hollow Slab Bridge: Field Test Investigation

Distribution factors (DFs) for one typical cross-section as specified in the AASHTO LRFD specification can be varied when the bridge parameters such as span length, loading lanes and skew are changed. The diversity between design and actual DFs may be varied as the bridge parameters changed. To study this diversity, this paper presents an evaluation of lateral load DFs for prefabricated hollow slab bridges. The response of the bridge was recorded during the field test. This field test was divided into two stages: a concentrated force loading test on the prefabricated girder that settled on the bridge supports before the girders were connected transversely and a vehicle loading test after the girders were connected transversely. The instruments used to record the response of the bridge were strain gauges and dial indicators. The measured data in the multi-stages of the field test could be used to calibrate the support condition of the bridge and transverse connection between adjacent girders in the finite element model (FEM) using beam and plate elements. From the FEM, DFs for this hollow slab bridge were determined and compared with the DFs in the AASHTO LRFD specification. A parametric study using the calibrated FEM was then used to investigate the effect of various parameters including span length, skew and bridge deck thickness on the DFs. It was found that AASHTO LRFD specification is conservative compared with the analysis in the FEM, while this conservatism decreased as the span length and skew of the hollow slab bridge increased.

Effects of wheat straw derived biochar on cadmium availability in a paddy soil and its accumulation in rice

This study was carried out to investigate the effect of biochar amendment on cadmium (Cd) availability in a paddy soil with biochar amendment and its effect on the accumulation in rice. Biochar was applied once at rates of 0 (A0), 10 (A10), 20 (A20), 30 (A30), and 40 (A40) t ha−1 on the soil surface layer (0–17 cm). Results showed that the soil organic matter (SOM) content and pH in 0–17 cm soil layer increased as biochar application rate increased, whereas the content of dissolved organic carbon (DOC), and available iron (Fe), manganese (Mn), aluminum (Al) in diethylenetriamine pentaacetic acid (DTPA) extracts declined with biochar added. Available Cd in DTPA extracts in the 0–17 and 17–29 cm soil layer of A40 treatments was significantly lower (p < 0.05) by 49.4 and 51.7% than that in A0. Compared with A0, the distribution factor (DF) of DTPA extracted Cd in the 0.053–0.25 mm and <0.053 mm aggregates of A40 treatments increased by 136 and 269%, respectively, and the DF values in these micro-aggregates of A40 treatments were greater than 1.0. Based on European Community Bureau of Reference (BCR) sequential extraction results, 40 t ha−1 rate of applied biochar reduced the proportion of acid extractable Cd fractions in both 0–17 and 17–29 cm soil layers, but increased the Cd in the oxidizable and residual fractions. The Cd concentration in the rice plants of different biochar treatments was in the order of A0>A10 > A20 > A30 > A40. DTPA extractable Cd concentration in soil was the key factor affecting the Cd uptake by rice roots. In conclusion, biochar application at 40 t ha−1 can effectively reduce the availability of Cd in soil profile, enhance the available Cd enrichment in micro-aggregates, and thus limit the Cd uptake by rice.

Transient stability monitoring and preventive control based on CCT distribution factor

AbstractThis paper proposes a monitoring and control method for transient stability (TS). First, it is clarified that there may exist various critical patterns of uncertain power flows causing instability due to photovoltaic generations. Then, the use of critical clearing time (CCT) is suggested as a TS index, which can be computed by conventional TS analysis tools. A distribution factor (DF) for controlling CCT is investigated, referred to as CCT‐DF in this paper. Then, three optimization problems using CCT‐DF are formulated based on bilevel optimization to obtain reliable operation planning. The combined use of the optimizations guarantees the power system robust security under uncertainties.

Effect of sensor system noise and load positioning on the precision of load testing and rating of highway bridges: a case study

This paper discusses the load testing of a three-span simply supported multi-girder/stringer bridge superstructure in northern New York. The first part of the testing deployed a custom developed wireless sensor system (WSS) measuring high-rate real-time strain measurements on all three spans of the steel superstructure. Controlled progressive damage was introduced to one of the three spans for the second part of testing where the span was monitored using wired strain transducers mounted at the top and bottom flanges of each girder at midspan. A single test vehicle was used to apply prescribed loads to the structure to acquire estimates of neutral axis (NA) and transverse load distribution factors (DF), two common parameters typically measured for a load rating. A sensitivity analysis was conducted using the peak-to-peak noise in the measurement signals. As expected, the farther the axle loads were positioned from the measured girder, the lower the measurement signal. In certain cases, this produced significant uncertainty in the NA measurement. On the other hand, the peak-to-peak noise did not appear to affect the DF estimates. This data was combined to illustrate the variation in the overall inventory and allowable stress design (ASD) load rating of the steel superstructure.

Analysis of load test on composite I-girder bridge

This paper showcases the importance of field testing in efforts to deal with the deteriorating infrastructure. It shows that when tested, bridges do not necessarily behave as expected under load, particularly with respect to boundary conditions. This is demonstrated via a load test performed on a healthy but ageing composite reinforced concrete bridge in Exeter, UK. The bridge girders were instrumented with strain transducers and static strains were recorded while a four-axle, 32 tonne lorry remained stationary in a single lane. Subsequently, a 3-D finite element model of the bridge was developed and calibrated based on the field test data. The bridge deck was originally designed as simply supported, however, it is shown (from the field test and calibrated model) that the support conditions were no longer behaving as pin-roller which affects the load distribution characteristics of the superstructure. Transverse load distribution factors (DFs) of the bridge deck structure were studied for different boundary conditions. The DFs obtained from analysis were compared with DFs provided in Design Manual for Roads and Bridges (DMRB) Standard Specification. Having observed in the load test that the ends of the deck appeared to be experiencing some rotational restraint, a parametric study was carried out to calculate mid-span bending moment (under DMRB assessment loading) for varying levels of restraint at the end of the deck.

Black carbon (BC) of urban topsoil of steel industrial city (Anshan), Northeastern China: Concentration, source identification and environmental implication

Black carbon (BC) and total carbon (TC) concentrations in urban topsoils and vertical profiles from steel industrial city, Anshan, Northeastern China, were determined. A total of 115 topsoil samples and 4 soil profiles were collected, in which the BC concentrations were determined using chemical oxidation technique. The BC concentrations in urban topsoils are in the range of 1.86 to 246.46gkg−1 with an average of 33.86gkg−1. Both BC and TC concentrations decrease sharply with soil depth, whereas BC/TC ratio shows a little variation with depth. The spatial distribution of BC in urban topsoils reveals that the BC concentration is much higher in the northern part of the city, which is consistent with the steel production. The distribution factors (DF) of BC are the highest in 1000–500 and 500–250μm size fractions, while the lowest in 50–2μm fraction. The mass loading of BC in 250–50 and 50–2μm size fractions accounts for 76.2% of bulk soil, indicating these two size fractions responsible for BC accumulation in soils. Enrichment factor (EF) of BC in urban topsoils ranges from 0.92 to 122.01 with an average of 16.76, indicating that the urban topsoils studied are moderately or severely accumulated by the BC. Strong correlation is found between BC and pollution load index (PLI) of heavy metals, indicating the possibility of similar sources of BC and heavy metals in soils. The BC/TC ratio in soils ranges from 0.45 to 0.97, with an average of 0.75. The BC/TC ratio shows the mixed sources of BC derived from fossil fuel combustion and vehicle emissions. The BC concentration and BC/TC ratio may reflect the degree of industrial activities and pollution sources in urban soils. The study demonstrated that BC is an effective indicator of degree and “hotspots” of heavy metals pollution in urban soils.

Distribution, bioavailability, and leachability of heavy metals in soil particle size fractions of urban soils (northeastern China).

This study examines the distribution, mobility, and potential environmental risks of heavy metals in various particle size fractions of urban soils. Representative urban topsoils (ten) collected from Anshan, Liaoning (northeastern China), were separated into six particle size fractions and their heavy metal contents (Cr, Cu, Cd, Pb, and Zn) were determined. The bioaccessibility and leachability of heavy metals in particle size fractions were evaluated using the toxicity characteristic leaching procedure (TCLP) and ethylenediaminetetraacetic acid (EDTA) extraction, respectively. The results indicated that the contents of five heavy metals (Cd, Cr, Cu, Pb and Zn) in the size fractions increased with the decrease of particle size. The clay fraction of <2μm had the highest content of heavy metals, indicating that the clay fraction was polluted by heavy metals more seriously than the other size fractions in urban topsoils. Cr also concentrated in the coarse fraction of 2000-1000μm, indicating a lithogenic contribution. However, the dominant size fraction responsible for heavy metal accumulation appeared to belong to particle fraction of 50-2 μm. The lowest distribution factors (DFs) of heavy metals were recorded in the 2000- to 1000-μm size fraction, while the highest in the clay fraction. The DFs of heavy metals in the clay fraction followed Zn (3.22) > Cu (2.84) > Pb (2.61) > Cr (2.19) > Cd (2.05). The enrichment factor suggested that the enrichment degree of heavy metal increased with the decrease of the particle size, especially for Cd and Zn. The TCLP- and EDTA-extractable concentrations of heavy metals in the clay fraction were relatively higher than those in coarse particles. Cd bioavailability was higher in the clay fraction than in other fractions or whole soils. In contrast, Cr exhibits similar bioaccessibilities in the six size fractions of soils. The results suggested that fine particles were the main sources of potentially toxic metals in urban soils. The variation of heavy metals in various size fractions should be taken into account in environment assessments.

A Sparse Representation Approach to Online Estimation of Power System Distribution Factors

In this paper, we propose a method to compute linear sensitivity distribution factors (DFs) in near real time without relying on a power flow model of the system. Specifically, we compute the injection shift factors (ISFs) of a particular line of interest with respect to active power injections at all buses (all other DFs can be determined from ISFs). The proposed ISF estimation method relies on the solution of an underdetermined system of linear equations that arise from high-frequency synchronized measurements obtained from phasor measurement units. We exploit a sparse representation (i.e., one in which many elements are zero) of the vector of desired ISFs via rearrangement by electrical distance and an appropriately chosen linear transformation, and cast the estimation problem into a sparse vector recovery problem. As we illustrate through case studies, the proposed approach provides accurate DF estimates with fewer sets of synchronized measurements than earlier approaches that rely on the solution of an overdetermined system of equations via the least-squares errors estimation method.

A novel and fast voltage estimation scheme for assessment of power system component outages

Purpose – The purpose of this paper is to pursue two following main goals: first, theorizing a new concept named as equivalent bus load in order to make a promising simplification over power system analysis. Second, proposing an outstanding fast and simple approach based on introduced concept for voltage estimation after multiple component outages while satisfying required accuracy. Design/methodology/approach – Equivalent load bus theory introduces three transfer matrices that describe power system topology. Mentioned matrices could be calculated simply after system reconfiguration without matrix inversion. Using transfer matrices a large-scale power system can be modeled by a simple two-bus power system from the viewpoint of any desired bus so that load flow calculation leads to same value. The analysis of simplified power system yields to extract a new incremental model based on equivalent bus load theory that will be distinguished as an outstanding fast method for voltage estimation aim. Findings – A deep study for fast voltage estimation aim is dedicated to evaluate proposed method from the accuracy and quickness point of view and the outcomes are compared to a well-known method as Distribution Factors (DF). Results and computational times unveil that presented approach is more accurate and much faster. Originality/value – A novel and new fast voltage estimation method for assessment of power system component outages is introduced.

Measurement-Based Estimation of Linear Sensitivity Distribution Factors and Applications

In this paper, we propose a method to compute linear sensitivity distribution factors (DFs) in near real-time. The method does not rely on the system power flow model. Instead, it uses only high-frequency synchronized data collected from phasor measurement units to estimate the injection shift factors through linear least-squares estimation, after which other DFs can be easily computed. Such a measurement-based approach is desirable since it is adaptive to changes in system operating point and topology. We further improve the adaptability of the proposed approach to such changes by using weighted and recursive least-squares estimation. Through numerical examples, we illustrate the advantages of our proposed DF estimation approach over the conventional model-based one in the context of contingency analysis and generation re-dispatch.