Elizete M. Lourenço

Bayesian-based hypothesis testing for topology error identification in generalized state estimation

This paper develops a Bayesian-based hypothesis testing procedure to be applied in conjunction with topology error processing via normalized Lagrange multipliers. As an advantage over previous methods, the proposed approach eliminates the need of repeated state estimator runs for alternative hypothesis evaluation. The identification process assumes that the set of switching devices is partitioned into suspect and true subsets. A geometric test is devised to ensure that all devices with wrong status are included in the suspect set. In addition, the results of criticality analysis performed at substation physical level prevents the occurrence of matrix singularities, which otherwise would degrade the performance of topology error identification. The IEEE 24-bus test system represented at physical level is employed to evaluate the proposed approach, considering diverse substation layouts and distinct types of topology errors.

A Topology Error Identification Method Directly Based on Collinearity Tests

A method for topology error identification based on collinearity tests involving Lagrange multipliers and the columns of the corresponding covariance matrix is presented. It relies on a geometric interpretation of multipliers associated with the equality constraints which model circuit breaker status in generalized state estimation. The method is conceptually simple and its implementation requires little computational effort, being therefore suitable for real-time applications. Results of several simulated cases conducted at the substation level on the IEEE 30-bus network are used to illustrate the performance of the proposed technique.

Power system topological observability analysis including switching branches

The conventional topological observability analysis based on the network representation at the bus-branch level is generalized to include the explicit modeling of circuit breakers and switches. This generalization is motivated by the present trend towards a more detailed representation (at the substation level) of the power network in state estimation studies. After developing the topological representation of switching branches according to their current status, it is shown that existing algorithms for observability and criticality analysis can be adapted to solve the extended problem. Results of the proposed approach for generalized observability and criticality analysis are validated by checking their consistency with numerical state estimation results.

Modeling Ferroresonance Phenomena With a Flux-Current Jiles-Atherton Hysteresis Approach

The ferroresonance phenomena in electrical power systems can cause very important quality and security problems. Although it has been extensively analyzed with different approaches since the birth of electrical systems, it still remains a challenge due the complexity of factors that can lead to the phenomenon. In this paper, a scalar Jiles-Atherton (JA) hysteresis model is applied to model a nonlinear ferromagnetic core allowing to analyze magnetic circuits, which can be in ferroresonant mode. It is used an inverse JA approach, which had originally the magnetic induction as its independent variable. The analysis here proposed applies a flux-current methodology to obtain a hysteresis behavior of a nonlinear inductor.

Reduced Anomaly Zone Determination for Topology Error Processing in Generalized State Estimation

The emergence of methods based on representing parts of the electrical network at the bus-section level has brought about new perspectives for topology error identification in real-time power system modeling. This work addresses the problem of determining the relevant portions of the network to be modeled in detail so as to ensure favorable topological conditions for topology error identification. Starting from the conventional bus-branch network model, the proposed approach performs error analysis and defines correlation indices from which an anomaly zone is identified. A graph theoretic algorithm is then used to expand the anomaly zone into a relevant subnetwork to be modeled at the bus section level. This subnetwork is greatly reduced in size, contains all suspect substations and exhibits the required properties for topology error identification conducted through generalized state estimation. The proposed methodology is evaluated through results obtained from test systems derived from the IEEE 14-bus and 30-bus networks.

Fast Decoupled Power Flow to Emerging Distribution Systems via Complex pu Normalization

This paper proposes a generalized approach of the per unit normalization, named complex per unit normalization (cpu), to improve the performance of fast decoupled power flow methods applied to emerging distribution networks. The proposed approach takes into account the changes envisaged and also already faced by distribution systems, such as high penetration of generation sources and more interconnection between feeders, while considering the typical characteristics of distribution systems, as the high R/X ratios. These characteristics impose difficulties on the performance of both backward-forward sweep and decoupled-based power flow methods. The cpu concept is centred on the use of a complex volt-ampere base, which overcomes the numerical problems raised by the high R/X ratios of distribution feeders. As a consequence, decoupled power flow methods can be efficiently applied to distribution system analysis. The performance of the proposed technique and the simplicity of adapting it to existing power flow programs are addressed in the paper. Different distribution network configurations and load conditions have been used to illustrate and evaluate the use of cpu.

Power system state and topology coestimation

A joint power system state and topology estimator based on a combined Weighted Least Squares (WLS) and Weighted Least Absolute Value (WLAV) strategy is proposed. The resulting coestimation algorithm is devised to simultaneously provide estimates to the analog power system variables and validate the current topology of the electric network. This is accomplished by formulating state & topology coestimation as an optimization problem whose objective function involves both the analog measurement residuals and the operational conditions dictated by circuit-breaker statuses. The former are treated as arguments of a conventional WLS function, whereas the latter compose the LAV term. The paper presents a theoretical framework for state & topology coestimation and proposes a specialized primal/dual Interior Point approach to solve the corresponding optimization problem. Results obtained by applying the joint estimator to the IEEE 30-bus test system and to a real metropolitan system in Southern Brazil are reported in the paper, and indicate that this is a very promising approach to provide simultaneous solutions to both real-time modeling problems.

Fast decoupled steady-state solution for power networks modeled at the bus section level

Conventional tools to provide steady-state power network solutions rely on bus-branch models, in which a “bus” is actually the result of merging internal electrical nodes pertaining to given substation. The corresponding network solutions are thus unable to readily provide information about variables internal to the substations, such as power flows through circuit breakers and bus-section nodal voltages. Since the knowledge of such variables is important to several applications, such as real-time topology estimation and corrective switching methods, the need then arises to re-examine the power flow formulation in order to obtain detailed solutions at the substation level. This paper addresses that problem by extending the decoupled power flow formulation in order to allow the representation of selected parts of the network at the substation level. For that purpose, the state vector is expanded so as to include power flows through switching branches as new state variables, in addition to the conventional nodal voltages. Moreover, information regarding the status of switching branches is taken into account as additional linear equations to be solved along with the traditional power flow equations. Simulating results considering several substation layouts and two IEEE test systems are used to illustrate and evaluate the proposed approach.

Unified load flow analysis for emerging distribution systems

This paper proposes a unified load flow analysis for transmission and distribution systems, based on the fast decoupled power flow method (FDPF). The method is centered on an extension of the conventional per unit normalization to circumvent the problems caused by low X/R ratio faced by distribution systems. The proposed extension establishes a complex voltampere basis. A properly definition of the base angle can adequate the X/R ratio of distribution systems as for instance the axis rotation previously presented in the technical literature. This paper also proposes a simple procedure that allows the utilization of different base angles for different parts of an interconnected system, so that conventional FDPF can be used to determine power flow solution of interconnected T&D systems in off line studies. Simulation results are conducted through IEEE standard test feeders, a south Brazilian distribution system and an interconnected T&D test system. Several operation conditions, including specific situations, such as closed ring operation of distribution systems, were simulated to evaluate the proposed approach.

Topology Error and Bad Data Processing in Generalized State Estimation

This paper presents a method for processing real-time data error in generalized state estimation (GSE). Attention is focused on the two main types of error: network topology errors and bad data on analog measurements. The proposed approach is able to handle both errors without making any previous assumption regarding the nature of those errors. The degrading effects of topology errors over bad data processing when both topology and measurement errors occur at the same time are evaluated and new strategy is proposed to overcome it. GSE is treated as a constrained optimization problem where measurements and circuit-breaker status are modeled as equality constraints. Geometric tests based on the geometric interpretation of the Lagrange multiplier vector are then utilized to determine the source of the error. The proposed strategy is tested on two model power networks represented at the bus-section level which is derived from the IEEE 30-bus and 118-bus systems.