Zero Injection Constraints Research Articles

An Augmented Lagrangian Approach for Distributed Robust Estimation in Large-Scale Systems

Nonlinear estimation using maximum-likelihood estimation and maximum a posterior probability approaches is frequently employed for large-scale cyber-physical and complex systems in the big data era. Efficient distributed processing and robust estimation algorithms resilient to outliers are of great importance. This paper proposes a novel method for distributed solution of these robust estimation problems with equality constraints based on the augmented Lagrangian method (ALM). Specifically, a novel covariance normalization method and an automatic method for selecting regularization parameter with improved performance are proposed. Under the ALM framework, nonlinear equality constraints and nonsmooth L 1 regularization can be incorporated. The proposed method is illustrated with two emerging applications respectively in robust distributed power system state estimation (DSSE) with nonlinear zero injection constraints and gene regulatory network (GRN) identification. Experimental results in DSSE show that the covariance normalization method improves considerably the convergence speed over the alternating direction method of multipliers algorithm and the robust statistics employed effectively mitigates the adverse effects of extreme outliers. Zero-injection constraints can be effectively incorporated. For GRN identification, putative genes and connectivity for a yeast dataset with 1.57 million variables can be identified via sparsity and piecewise temporal continuity penalties and they generally align well with literature.

A Reliability-Oriented Fuzzy Stochastic Framework in Automated Distribution Grids to Allocate $\mu$ -PMUs

This paper proposes a reliability-oriented stochastic aggregated integer linear framework for full observability of the automated distributed systems based on the $\mu $ -synchrophasor units. The $\mu $ -synchrophasor unit as a newly introduced high-tech device makes it possible for an accurate and high-speed measurement of the voltage and current waveforms in the distribution systems. This paper proposes a multi-stage strategy for the $\mu $ -synchrophasor unit placement together with the communication system requirements in the reconfigurable distribution systems, considering the zero-injection constraints in the model. To determine the optimal topology at the end of each phase, a reliability-based cost function is developed to optimize the customer interruption costs and power losses simultaneously. In order to model the uncertainties of forecast error in the active and reactive load demands as well as the failure rate and repair rate parameters, a stochastic framework based on the fuzzy cloud theory is employed. The proposed bi-level mixed integer linear programing approach is used to co-optimize the network switching scheme as well as the optimal $\mu $ -synchrophasor positions and communication infrastructure costs in the same framework. The simulation results on a practical test system verify the observability of the automated reconfigurable distribution system during the reconfiguration process.

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.

An Efficient State Estimation Algorithm Considering Zero Injection Constraints

Traditional state estimation methods employ large weights for zero injection pseudo-measurements, which may result in numerical instability. The normal equations with constraints will increase the order of the coefficient matrix, thus reducing the speed of the calculations. To improve computational performance, this paper presents a modified Newton method to deal with zero injection constraints. The decoupled form of the proposed technique-a modified fast decoupled state estimation method-is also given. The computational speed of the proposed modified Newton method is similar to that of conventional state estimations based on normal equations, since they use the same type of coefficient matrices. Furthermore, it offers the advantage that zero injection constraints can be strictly satisfied, and the numerical stability problem caused by large weights will no longer exist. Extensive numerical results from test systems and a real provincial system are included to verify the performance of the proposed procedure.

Optimal Multistage Scheduling of PMU Placement: An ILP Approach

This paper addresses various aspects of optimal phasor measurement unit (PMU) placement problem. We propose a procedure for multistaging of PMU placement in a given time horizon using an integer linear programming (ILP) framework. Hitherto, modeling of zero injection constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints in an ILP framework. Minimum PMU placement problem has multiple solutions. We propose two indices, viz, BOI and SORI, to further rank these multiple solutions, where BOI is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bus</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">observability</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">index</i> giving a measure of number of PMUs observing a given bus and SORI is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">system</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">observability</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">redundancy</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">index</i> giving sum of all BOI for a system. Results on IEEE 118 bus system have been presented. Results indicate that: (1) optimal phasing of PMUs can be computed efficiently; (2) proposed method of modeling zero injection constraints improve computational performance; and (3) BOI and SORI help in improving the quality of PMU placement.

Reduced Substation Models for Generalized State Estimation

This paper deals with the problem of including detailed substation models in state estimators so that topological errors and/or bad internal data can be detected and identified. Instead of analyzing constraints and state variables related to individual circuit breakers, the whole substation is reconsidered in the light of topological properties, leading to a model where zero-injection constraints are not explicitly handled. In addition, it is shown how, if the new state variables are selected keeping certain rules in mind, the resulting constraints can be easily transformed into equivalent constraints, many of which appear as critical. This allows a reduced model to be used without losing any capability to perform error analysis.

Reduced substation models for generalized state estimation

This paper deals with the problem of including detailed substation models in state estimators so that topological errors and/or bad internal data can be detected and identified. Instead of analyzing constraints and state variables related to individual circuit breakers, the whole substation is reconsidered in the light of topological properties, leading to a model where zero-injection constraints are not explicitly handled. In addition, it is shown how, if the new state variables are selected keeping certain rules in mind, the resulting constraints can be easily transformed into equivalent constraints, many of which appear as critical. This allows a reduced model to be used without losing any capability to perform error analysis.

A tracking state estimator for nonsinusoidal periodic steady-state operation

This paper presents a tracking state estimator for systems operating under nonsinusoidal but periodic steady state conditions. Such operating states are being frequently observed in today's power systems due to the emerging nonlinear loads and power conditioning devices. Measurement equations are derived in discrete time and the sampling frequency is chosen according to the highest harmonic of interest. The proposed estimator is designed to be computationally efficient by transforming the measurement equations in a special manner so that the sparsity of the corresponding discrete time matrix equations is significantly enhanced. Zero injection constraints are also included to take advantage of the increased redundancy. The paper presents results of simulations under both normal measurement noise as well as with gross errors existing in the measurements. Performance of the developed algorithm is evaluated both in terms of cpu time and accuracy based on the simulations.

State estimation for distribution systems with zero-injection constraints

In this paper, a new fast decoupled state estimator with equality constraints is proposed for the three-phase distribution systems. The Lagrange multipliers were utilized to deal with the zero injections. The proposed method is based on the equivalent-current-measurement and rectangular coordinates. The method uses a compact constant-symmetric gain matrix which can be decoupled into two "identical" sub-gain matrices. The update and factorization of the gain matrix needs to be done only once. Tests have shown that the proposed low-storage method is efficient, accurate and robust in solving the unbalanced three-phase distribution systems.