Distribution System State Estimation Algorithm Research Articles

Evaluation of Computational Complexity for Distribution Systems State Estimation

Distribution system state estimation (DSSE) is a key monitoring function for system operators to automate, control and operate the active distribution grids. The computational complexity of the DSSE algorithm is a design factor for implementing a real-time monitoring system. As a common criterion, the elapsed time has been used in many works to determine if a developed DSSE solver, regardless of data acquisition and bad data detection steps, can satisfy the requirement of real-time operation. This measure, however, is machine-dependent and thus may not be a good indicator to show the computational burden of a state estimation method in run-time. This article proposes instead to use floating point operation (FLOP) which is a machine-independent computational complexity measure. The number of FLOPs is a suitable relative performance indicator in determining how fast a method could be executed. In this paper, the computational cost of different DSSE algorithms is mathematically derived in terms of FLOPs. On this basis, this article shows that FLOP is a better measure than the more commonly used elapsed time for making design decisions about the choice of the DSSE method based on computational complexity.

Distribution System State Estimation Algorithm with Improved Angular Reference Treatment

The efforts to build smarter grids with automatic control and intelligent functionalities for Distribution Systems (DSs) rely upon correctly determining the operational condition of these circuits, which is the purpose of a State Estimator (SE). DSs are complex and unbalanced networks, and in the last years several studies have evaluated the use of SEs in DSs. Despite some good theoretical results, one incorrect assumption is usually made: considering the Reference Bus (RB) to have balanced voltage phase angles. This paper proposes a three-phase state estimation algorithm that enables a correct treatment of the RB, which allows the determination of the unbalance at this bus as part of its iterative process, without relying on Phasor Measurement Units or external information that can be imprecise. Simulation results on IEEE 34 and 123 bus test feeders show the feasibility of the algorithm and the effects of the RB’s mistreatment on the SE accuracy.

Fast multi-phase gain matrix computation for real time distribution system state estimation

Efficient distribution system state estimation (DSSE) is becoming increasingly important in modern grids. Building the gain matrix is carried out at every iteration of the weighted least squares (WLS) DSSE algorithm that employs the normal equations approach, and the computation of this matrix occupies a substantial portion of the total execution time. This paper presents a two-phase algorithm for the efficient gain matrix calculation suitable for modern CPU architectures. The preparation phase creates the necessary structures for effective data streaming and code execution. The gain matrix is calculated in the second phase using the prepared data and single instruction multiple data (SIMD) intrinsics. The Jacobian measurement matrix is organized as a sparse matrix of small dense blocks with double-precision complex values. The implementation exploits memory-aligned data blocks that require fewer CPU instructions and provide higher memory access speeds, in addition to modern C++ features for utilizing the instruction pipelining technique fully. Numerical results are reported on sizeable distribution networks having up to 3124 multi-phase nodes and 9537 three-phase nodes. They show that the proposed approach for computing the gain matrix is up to three times faster than the sparse matrix–matrix multiplication function in the SuiteSparse package, which makes the procedure useful for the development of real-time DSSE software.

Graph-Based Faulted Line Identification Using Micro-PMU Data in Distribution Systems

Motivated by increasing penetration of distributed generators (DGs) and fast development of micro-phasor measurement units ( ${\mu }$ PMUs), this paper proposes a novel graph-based faulted line identification algorithm using a limited number of ${\mu }$ PMUs in distribution networks. The core of the proposed method is to apply advanced distribution system state estimation (DSSE) techniques integrating ${\mu }$ PMU data to the fault location. We propose a distributed DSSE algorithm to efficiently restrict the searching region for the fault source in the feeder between two adjacent ${\mu }$ PMUs. Based on the graph model of the feeder in the reduced searching region, we further perform the DSSE in a hierarchical structure and identify the location of the fault source. Also, the proposed approach captures the impact of DGs on distribution system operation and remains robust against high-level noises in measurements. Numerical simulations verify the accuracy and efficiency of the proposed method under various fault scenarios covering multiple fault types and fault impedances.

Matrix Completion for Low-Observability Voltage Estimation

With the rising penetration of distributed energy resources, distribution system control and enabling techniques such as state estimation have become essential to distribution system operation. However, traditional state estimation techniques have difficulty coping with the low-observability conditions often present on the distribution system due to the paucity of sensors and heterogeneity of measurements. To address these limitations, we propose a distribution system state estimation algorithm that employs matrix completion (a tool for estimating missing values in low-rank matrices) augmented with noise-resilient power flow constraints. This method operates under low-observability conditions where standard least-squares-based methods cannot operate, and flexibly incorporates any network quantities measured in the field. We empirically evaluate our method on the IEEE 33- and 123-bus test systems, and find that it provides near-perfect state estimation performance (within 1% mean absolute percent error) across many low-observability data availability regimes.

Bayesian Approach for Distribution System State Estimation With Non-Gaussian Uncertainty Models

To deal with the increasing complexity of distribution networks that are experiencing important changes, due to the widespread installation of distributed generation and the expected penetration of new energy resources, modern control applications must rely on an accurate picture of the grid status, given by the distribution system state estimation (DSSE). The DSSE is required to integrate all the available information on loads and generators power exchanges (pseudomeasurements) with the real-time measurements available from the field. In most cases, the statistical behavior of the measured and pseudomeasured quantities cannot be approximated by a Gaussian distribution. For this reason, it is necessary to design estimators that are able to use measurements and forecast data on power flows that can show a non-Gaussian behavior. In this paper, a DSSE algorithm based on Bayes's rule, conceived to perfectly match the uncertainty description of the available input information, is presented. The method is able to correctly handle the measurement uncertainty of conventional and synchronized measurements and to include possible correlation existing between the pseudomeasurements. Its applicability to medium voltage distribution networks and its advantages, in terms of accuracy of both estimated quantities and uncertainty intervals, are demonstrated.

Distribution system state estimation using compressive sensing

This paper leverages the big data provided by micro-phasor measurement units (μPMUs) placed along the smart distribution networks for distribution system state estimation (DSSE). We propose a novel and straightforward DSSE algorithm by solving a set of linear equations without any iterative process. The μPMUs are placed at few buses to measure the voltage phasors. The measured voltage vector is expressed as the product of current injections vector and impedance matrix of the system. Since number of μPMUs is less than number of buses, the constructed set of linear equations are underdetermined. Furthermore, the injection currents vector is sparse because any single load/generator current is negligible when compared with the total current injected from the external grid to the distribution network. Subsequently, we use Compressive Sensing and ℓ1-norm minimization to recover the sparse current vector from the limited number of μPMUs. The voltages at all buses are obtained by multiplying the reconstructed current vector by the impedance matrix. Performance of our method is demonstrated on the IEEE 123-bus test system and a 13.8-kV, 134-bus real network with different distributed generations (DGs) penetration level and under a weakly meshed operation mode. Also, the performance of the proposed technique is compared with that of the conventional weighted least-square (WLS) method.

Branch-Current Algorithm Based Three-Phase State Estimation in Distribution System

This paper presents a branch-current distribution system state estimation algorithm considering zero-injection constraints. The algorithm takes the branch-current amplitude and phase angle as state variables, considering current-amplitude measurement easily without measurements conversion and makes full use of voltage amplitude measurements, power measurements and current measurements. In order to improve the robust performance of algorithm, exponential function is adopted as the objective function in this paper. The paper takes simulation test to verify the algorithm correctly and effectively on improved IEEE 34 nodes system.

A Unified Distribution System State Estimator Using the Concept of Augmented Matrices

Distribution system state estimation (DSSE) is becoming an essential element of many distribution management systems (DMS), serving as the basis of numerous smart grid applications. In this paper, a new DSSE approach is proposed based on the modified augmented nodal analysis formulation, which is known to have advantageous numerical characteristics. Special consideration is given to the estimation of transformer and regulator tap positions, as they are seldom telemetered on the distribution level. The proposed approach can be easily derived from existing power flow and short-circuit calculation algorithms, thus unifying the major steady-state analysis tools for distribution systems. The proposed DSSE algorithm is tested on the IEEE 8500-Node Test Feeder, and is shown to have good accuracy and efficiency. The proposed DSSE approach is also compared to existing algorithms and shown to have better convergence while yielding a more accurate solution.

A Nonlinearity-Retaining State Estimation for Three-Phase Distribution System

A three-phase distribution system state estimation algorithm is proposed in this paper based on the retaining of nonlinearity. It takes advantage of the characteristics of the radial feeder and is suitable for systems with high R/X ratios. Considering the imbalance of a three-phase distribution system, this method is suitable for the observed system which involves real-time measurements and some power and voltage metered information treated as pseudo measurements. Because the method retains the nonlinear second order terms, the Jacobian matrix is constant and the second order terms are easier to compute and computing time is faster. Theoretical analysis and digital simulations are carried out and the results show that the method is reliable, efficient and requires less memory, suits on-line application for radial distribution systems.

Distribution system state estimation

A three-phase distribution system state estimation algorithm is proposed in this paper. The normal equation method is used to compute the real-time states of distribution systems modeled by their actual a-b-c phases. A current based formulation is introduced and compared with other formulations. Observability analysis for the proposed distribution system state estimation is discussed. Test results indicate that the normal equation method is applicable to the distribution system state estimation and the current based rectangular form formulation is suitable for this application. >