Fast Decoupled State Estimation Research Articles

Fast decoupled state estimation including thyristor controlled series compensator devices

This paper extends the weighted-least-square state estimation (WLS-SE) formulation to enable the solution of networks with embedded thyristor-controlled series compensation (TCSC). In the proposed methodology, the TCSCs reactances are treated as new state variables along with the complex voltage at the network nodes. Information regarding the specified active power flow through transmission lines connected to TCSCs and net power injection at their connecting nodes are strategically modeled as new active and reactive pseudo-measurements to be included into both: the linear and the fast-decoupled WLS-SE problem. Applications of the proposed extension in connection with the exact solution of a TCSC embedded power flow algorithm are presented and discussed. The IEEE 14- and 118-bus test systems are employed to illustrate and evaluate the proposed approach. The results point out that the new tool is effective to accurately estimate the system states and the control parameters of the TCSCs under distinct operating conditions.

A Fully Distributed Coordination Method for Fast Decoupled Multi-Region State Estimation

Distributed state estimation (DSE) is effective for the analysis of multi-region state estimation problems, avoiding integrating complicated data sets and models. In this work, the peer-to-peer decomposition of the Karush-Kuhn-Tucker (KKT) condition is applied to formulate the fully distributed fast decoupled state estimation (FD2SE) algorithm. Then, a fixed-matrix form data-exchanging interface incorporating the fast decoupled algorithm is designed, reducing the communication costs and allowing it to be used for various system operating conditions. Further, a convergence detecting method for dispatch centers is proposed in order to infer, locally and asynchronously, about the global convergence. Case studies carried out on IEEE systems and a real power grid of China verify the accuracy and efficiency of the FD2SE algorithm.

Generalised‐fast decoupled state estimator

Nowadays the fast-decoupled state estimation (FDSE) is widely used in almost every power system control centre. FDSE is effective and efficient for most transmission systems but it may not converge for systems with a large ratio of branch resistance to reactance (R/X); meanwhile the branch current magnitude measurements (BCMMs) cannot be reliably used in FDSE, thereby limiting its applications especially for the distribution systems where BCMMs abound. In this study, the above two problems have been addressed by transforming all measurements so that they can be classified as quasi-real power measurements and quasi-reactive power measurements, leading to a generalised FDSE (GFDSE) with a solid theoretical foundation. The formulation of GFDSE is based on only the assumption, rather than three assumptions used in FDSE. As a result, GFDSE has good adaptability to transmission systems as well as distribution systems; additionally, BCMMs can be reliably used in GFDSE. Case studies based on IEEE benchmark systems and a real grid of China demonstrate that the proposed GFDSE has very good convergence properties for transmission systems and distribution systems; and at the same time, the proposed GFDSE is also superior to FDSE in terms of computational efficiency under almost all cases.

Fast Decoupled State Estimation for Distribution Networks Considering Branch Ampere Measurements

Fast decoupled state estimation (FDSE) is proposed for distribution networks, with fast convergence and high efficiency. Conventionally, branch current magnitude measurements cannot be incorporated into FDSE models; however, in this paper, branch ampere measurements are reformulated as active and reactive branch loss measurements and directly formulated in the proposed FDSE model. Using the complex per unit normalization technique and special chosen state variables, the performance of this FDSE can be guaranteed when it is applied to distribution networks. Numerical tests on seven different distribution networks show that this method outperforms Newton type solutions and is a promising method for practical application.

A Fast Decoupled State Estimator for Systems Measured by PMUs

Given the rapid increase in the number of phasor measurement units (PMU) installed in substations in recent years, it is not unrealistic to assume that most transmission systems will be fully observable by only PMU measurements in the not so distant future. Such a scenario will enable faster and numerically easier state estimation solution which will be non-iterative due to the linearity of the PMU measurement equations. However, as will be shown in this paper, the benefits do not end there and a closer look at these equations reveals further possibilities of simplification and therefore improved performance of state estimators that use only PMU measurements. Specifically, the paper formulates an alternative decoupled solution, which reduces the size of the state estimation problem, increases computational performance yet maintains high solution accuracy. Both state estimation as well as bad data processing can be efficiently carried out within the developed decoupled formulation.

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.

Mathematical model of transmission network static state estimation

In this paper the characteristics and capabilities of the power transmission network static state estimator are presented. The solving process of the mathematical model containing the measurement errors and their processing is developed. To evaluate difference between the general model of state estimation and the fast decoupled state estimation model, the both models are applied to an example, and so derived results are compared.

Convergence Improvement and Bad Data Detection for Fast Rectangular Coordinates State Estimator

From power system on-line operation and security control view point, state estimation, a methodology used to obtain reliable estimate of power system state, has become one of the important issues. Among some state estimation methods, the fast-decoupled state estimator is commonly used as a prevailed method and has been implemented by many utilities. However, it has been recognized that its convergence characteristics may become deteriorated when it encounters bad system conditions. Therefore, in this paper, first of all, we present the fast-decoupled state estimator which is used in present power systems. Next, we propose a method to improve the convergence characteristics of fast-decoupled state estimator (in rectangular coordinates) using the optimal multiplier μ, followed by a reliable technique to detect bad data. The proposed method has been tested on several types of load flow test systems and successful results have been obtained.

A new transmission fast-decoupled state estimation with equality constraints

In this paper, a new fast decoupled state estimator with equality constraints is proposed. The Langrange multipliers were utilized to deal with the zero injections. The proposed method is based on the equivalent-current-measurement and rectangular coordinates. The conventional assumptions on voltage magnitudes, angles and r/ x ratios are no longer necessary by the new method in decoupling the network. 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 sub-gain matrix needs to be carried out only once. Tests have shown that the proposed low-storage method is efficient, accurate and robust in solving the equality-constrained state estimation.

Fast super decoupled state estimator for power systems

A new method is developed and presented in this paper to solve the state estimation problem of power systems. The method involves application of a rotational operator to the state and measurement functions resulting in an automatic decoupling of the Jacobian and gain matrices. The elements of these matrices are different from those in the existing decoupled state estimators. A solution is obtained through alternately iterating the active and reactive equations using the constant gain matrix and avoiding the approximation due to the decoupling of the Jacobian matrix. Digital simulation studies on a variety of systems indicate that the new estimator is comparable to the best available version of the fast decoupled state estimator in terms of core size, solution time, mathematical structure, convergence behavior, accuracy, robustness, reliability and versatility. Systems with low and high R/X ratio lines, heavy loading, ill-conditioning, and low/high reference bus voltage are tested. Typical results are provided for illustration.

Distribution fast decoupled state estimation by measurement pairing

A three-phase fast decoupled state estimation method is presented for distribution systems. The weighted least square (WLS) approach is used. A current-based formulation is discussed first and then the decoupled version. The proposed method produces a constant symmetric gain matrix which can be decoupled into two identical sub-gain matrices. The method offers good performance in handling the distribution system and is many times faster than other formulations, especially for large systems. An observability test is discussed.

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.

Topology processing and static state estimation using artificial neural networks

The paper presents a new approach based on artificial neural networks (ANN) for power system network topology determination and static state estimation. The state estimator model considers dynamic change in network topology and bad data processing. ANN models based on the counterpropagation network (CPN) and functional link network (FLN) have been tried out for solving topology processing and static state estimation on the IEEE 14-bus, IEEE 57-bus and a 19-bus practical Indian system. In addition the results of state estimation using the Hopfield neural network and the conventional fast decoupled state estimator (FDSE) have also been obtained and compared. It has been established that the ANN based models provide results much faster, and work well even for non-Gaussian noise and in the presence of bad data.

Efficient storage scheme and algorithms for W-matrix vector multiplication on vector computers

The W-matrix method has been proposed in many literatures to exploit parallelism in the solution of many power system problems. This paper presents a storage scheme for storing the sparse W-matrix in solving linear equations on vector computers. Based on the proposed storage scheme, several efficient algorithms have been developed to perform the W-matrix vector multiplication for finding linear system solutions. In this paper, attention is given to the issues of vector length, data movement between vector registers and memory, and the vector stride. The proposed storage scheme and algorithms are tested on Convex 3840 and Alliant FX/80 vector machines. It is shown that a speedup of two to four times is obtainable as compared to traditional scalar operation. The proposed storage scheme and algorithms can be applied to power system problems that require repeat solutions of linear system, such as load flow, contingency analysis, fast decoupled state estimation and short circuit calculations. >

A decoupled second order state estimator for AC-DC power systems

This paper presents a new framework for decoupled state estimation of AC-DC power systems. Decoupling is not done by zeroing the off-diagonal submatrices of the Jacobian and gain matrices but as a two-step procedure. The mathematical model involves both the first and second order derivatives of the performance equations. Only diagonal blocks of the gain matrix are required to be factorized, and they remain constant in the iterative solution scheme. Their size and structure are similar to those in the fast decoupled state estimator which is based on the linearised version of the Taylor series equations. Test results are presented,compared and discussed. The proposed method performs satisfactorily and its computational requirements are comparable with those of the fast decoupled state estimator. >

Fast and accurate technique for power system state estimation

The paper presents a fast and accurate technique for power system state estimation. The proposed technique is based on the exact linearisation of the Cartesian co-ordinate formulation of nodal load flow equations. The complete Taylor series expansion is used to solve these equations while retaining the nonlinearity. In this technique, the Jacobian and Hessian matrices are kept constant, and hence need to be computed once only, at the beginning of the solution, and then stored in the computer memory using the sparsity storage procedure. Because, in this technique the active and reactive power problems are attempted simultaneously, not sequentially, there is no need to use decomposition into two subproblems, namely P–Θ and Q–V. The linear programming (LP) technique is used to solve the state estimation problem without any approximation for the load flow equations. For small changes in active and reactive power, the right-hand side of the LP is compensated only when the state estimation solution of the real component of the bus voltages is obtained with a minimum number of iterations compared with the fast decoupled state estimation (FDSE). For large band-data points, however, the imaginary components of the bus voltages must be computed, in addition to the real components. The proposed technique is more suitable than FDSE for solving ill-conditioned networks which have large bad-data points. An extensive study was carried out on a standard 23-bus test system to demonstrate the capability of the proposed technique for solving the state estimation problems.

Fast-decoupled rectangular co-ordinate state estimation with efficient data structure management

The paper presents two different state estimation decoupling techniques using node voltages in rectangular co-ordinates: the exact-decoupled technique and the modified fast-decoupled technique. The proposed techniques decouple the Jacobian matrix into real- and reactive-power submatrices, which are evaluated only once at the beginning of the process. The paper also presents efficient data structure management algorithms to improve the computational process required in calculating the nonzero elements of the Jacobian matrix, and the elements of the mismatching vector, which are essential to any state estimation problem. The performance of these techniques and algorithms are evaluated using several power system networks.

Fast decoupled state estimators

A framework for fast decoupled state estimators is presented. Decoupling is not seen as neglecting coupling submatrices in the Jacobian, but as a two-step procedure to solve full-Newton equations, without major approximations. In addition to a sound derivation of the standard version of the fast decoupled state estimator, another version is proposed which presents better performance when applied to power systems with critical r/x ratios. Test results and illustrative examples are presented and discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Evaluation of Techniques Which Avoid Information Matrix Recalculation in Fast Decoupled State Estimation

Simple, easy to implement techniques are investigated which avoid updating the fast decoupled state estimator Information Matrix when bad data is being detected, measurements are lost or restored or the network configuration changes and/or splits occur creating new nodes. The modified state estimator converges to the correct solution if switching does not involve circuits whose impedance is less than that of neighbouring circuits. The Information Matrix now is only updated when the modified state estimator does not converge to the correct solution and now occurs less than 5% as often as with conventional fast decoupled state estimation.

Integral state estimation for well-conditioned and ill-conditioned power systems

This paper describes a generalized integral solution method to solve the power system state estimation problems for well-conditioned and ill-conditioned power systems. By simple graph analysis, the condition number, which is derived from the simple graph analysis, can be used for justification and determination of various power system operating situations. The modified fast decoupled state estimation method for well-conditioned power systems and the Crout decomposition method for ill-conditioned power systems are formulated and discussed in this paper. Simulations and results are discussed to support the feasibility and effectiveness of the proposed methods for well- and ill-conditioned power system state estimation.