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Methods for power network parameter estimation and correction are discussed in this paper. A sequential-type method for real-time processing of network parameters is proposed. The method exploits the information contained in the measurement residuals to estimate a better network parameter; it uses a linearized sensitivity model to relate the measurement residuals to the parameter error. The proposed method has been coded in FORTRAN using several short-cuts and has been thoroughly tested in the estimation of transformer ratios in the Belgian HV system.

Hydrothermal coordination (HTC) is a problem that has been solved using direct and decomposition solution methods. The latter has shown shorter solution times than the former. A direct solution method for the HTC problem that is based in semidefinite programming (SDP) is presented. SDP is a convex programming method with polynomial solution time. The variables of the problem are arranged in a vector, which is used to construct a positive-definite matrix; the optimal solution is then found in the cone defined by the set of positive-definite matrices. An HTC problem can be formulated as a convex optimization problem without explicitly stating the integer value requirements for the thermal-plants discrete variables. Thus, it is possible to replace the nonconvex integer-value constraints by convex quadratic constraints and then use SDP. Due to its polynomial complexity, it is not necessary to use decomposition or other tools for discrete optimization, such as enumeration schemes or other exponential-time procedures. No initial relaxation is necessary when applying a SDP algorithm; the solution shows only minor mismatches in the integer variables, which are easily corrected by a heuristic method. Different size test cases are presented. The solution quality is assessed by comparing with that produced by a Lagrangian relaxation method.

Large-scale nonlinear optimal power flow (OPF) problems have been efficiently solved lately by extensions from linear programming to nonlinear programming of the primal-dual logarithmic barrier interior-point method and its predictor-corrector variant. Motivated by the impressive performance of the nonlinear predictor-corrector extension, in this paper we extend from linear programming to nonlinear OPF the efficient multiple centrality corrections (MCC) technique that was developed by Gondzio. The numerical performance of the proposed MCC algorithm is evaluated on a set of power networks ranging in size from 118 buses to 2098 buses. Extensive computational results demonstrate that the MCC technique is fast and robust, and outperforms the successful predictor-corrector technique.

The reactive-power dispatch is formulated as the minimization of real-power losses in the system, utilizing a full set of control variables: generator voltages, switchable shunt susceptances, and transformer taps. The solution of the loss problem is obtained by successively solving quadratic programming problems. First- and second-order loss sensitivity coefficients are derived for the quadratic problem formulation. The derivations are based on the Jacobian method for sensitivity calculations. Sensitivity relations for the dependent constraints are based on the complete reactive-power model of the fast decoupled load flow method. The active-set projection method for quadratic programming is described and utilized as the solution algorithm for the quadratic reactive-power dispatch problems. Tests are conducted on the IEEE 30-bus and Mexican 253-bus systems. The computer results are discussed. >

This paper presents a fast, reliable and storage -saving algorithm for Power System State Estimation (PSSE). Instead of using a Single sub-Matrix of a Decoupled Gain matrix (SMDG), the new algorithm employs a Single sub-Matrix of a Decoupled Jacobian matrix (SMDJ); the Givens transformations is then used to solve a PSSE weighted least-squares problem. Thus, the algorithm has the advantages of both decoupling and orthogonal transformations. It will be shown in theory and practice that the new algorithm performs better than the algorithm using the SMDG. The new algorithm has been tested on two power systems, including an IEEE 30-bus test power system. From the numerical results we conclude that the proposed algorithm is considerably superior to the conventional normal equation algorithm and other decoupling algorithms.

Reviews the methods for network parameter estimation and correction in power system state estimation and proposes a sequential-type method for real-time processing of transformer tap positions. The method exploits the information contained in the measurement residuals to estimate a better tap position; it uses a linearized sensitivity model to relate the measurement residuals to the tap position error. Based on part of the Belgium HV system, several testing results are reported.

A hierarchical computing scheme for power system state estimation is developed by carefully considering mismatches arising from the system decomposition. The method makes use of an extension of a fast second-order load-flow method that allows a fixed Jacobian matrix to be used in the hierarchical algorithm. In the problem formulation, the power network is decomposed into two or more subsystems; the interaction among them is taken into account through the tie-line bus voltages. The hierarchical structure of the method consists of two levels: the upper level, where the optimal tie-line bus voltages are evaluated; and the lower level, where the optimal states of each subsystem are determined by minimizing a cost function that involves the entire system. Three test cases using the method are reported here and the test results are compared with those obtained by another hierarchical power system state estimation method. >

The economic dispatch problem with constraints on line flows and spinning reserve is formulated as a linear optimization program. Such a linear program is then solved using the Dantzig-Wolfe decomposition principle. The sub-programs of the decomposition may correspond to physical areas of the power network, and are individually solved employing the revised simplex method with upper bounds. A fast decoupled load flow algorithm is used to calculate penalty and sensitivity factors. Several illustrative examples are included.

In this paper a sequential algorithm for power system state estimation based on the use of Givens rotations is investigated. The fact that the rotations are orthogonal transformations assures the numerical stability of the algorithm. The Jacobian matrix is processed one row at a time, and sparsity can be easily exploited. Also, the method presents some features which are advantageous from the point of view of bad data detection, identification and elimination. Both the description and the implementation of a fast version of the Givens rotations are presented. The method is applied to three different power systems, including real size networks, and the results are used to assess its performance.

It is well known in numerical analysis that the least-squares solution via the conventional Gauss' normal equation used in power system state estimation is prone to ill-conditioning problems by its own nature. Under unfavorable circumstances, this may be detrimental to the method's performance. This paper utilizes a numerically more reliable algorithm, known as Golub's method, to solve the least-squares problem as formulated in power system state estimation. Its improved numerical properties stem from the use of orthogonal transformations, which are perfectly conditioned. Details of the algorithm and its implementation are given, as well as results of its application to three different networks, including an actual 121-bus power system.

The operation planning of a hydro-thermal power system involves the coordination of the production schedule of various types of generation, including hydro. A good model is needed to minimize the system energy production costs over a given period in the mid-range time frame. A method is proposed to optimize the discharge of the hydro reservoirs over the period of one year. Explicit Stochastic Dynamic Programming (ESDD) [1] is employed to deal with the M-stage stochastic return function, the random inflows to the reservoirs and the bounded nature of the system constraints. Aggregation of the reservoir and hydro plant sub-systems is used to reduce the dimensionality of the problem, permitting a; realistic modeling of the hydro portion of the power system. The cost of operation for various valve loadings, the scheduled downtime for various unit maintenance activities, the predicted partial and total forced outages, and the stochastic river inflows to the reservoirs are input requirements to the program which yields the monthly hydro energy scheduling for the most economic loading over a one year period

This paper presents procedures for the low-trajectory sensitivity design of reduced-order output feedback dynamic controllers for linear stochastic systems with uncertain parameters having zero-mean random variations around their expected values. Both the finite and infinite terminal time designs are discussed. Matrices are conveniently partitioned to reduce computational effort. Several special cases are considered, leading to simpler problem designs. Two numerical examples are included.

This paper presents a clipping-off technique which, when used in association with gradient methods in function space, can be used to solve non-linear optima control problems with magnitude constraint on the control inputs. The proposed clipping-off gradient algorithms are simple to implement on a digital computer and preserve the large range of convergence of first-variational methods. Several numerical examples are included, one of which contains two state-variable inequality constraints and a magnitude constraint on the control input

Presents a brief survey of the major advances on numerical techniques to solve the power system state estimation (PSSE) problem. A brief review of the conventional batch estimator based on the solution of the normal equation is presented, together with a discussion on its performance from a numerical point of view. Two numerically robust techniques are described for the solution of the PSSE problem: Golub's method for the solution of the weighted least squares (WLS) problem of a PSSE batch processor, using the Householder orthogonal transformations; and Givens method for the sequential WLS state estimators, using orthogonal transformations performed by rows. A discussion on the sparsity and ordering techniques is included. Finally, a comparison of the two orthogonal techniques with the conventional method, from a computer execution time and storage requirement point of view, is also presented. Several numerical examples are used for such a comparison.

The use of a non-conventional linear programming technique, involving a piecewise differentiable penalty function minimization, is presented in this paper in connection with power system Constrained Economic Dispatch (CED) problems.

The purpose of this paper is to extend a family of variable metric methods, of which the BFGS algorithm (Ref. 1) is a member, into function space, in particular, for the solution of unconstrained optimal control problems. An inexact one-dimensional minimization as suggested by Fletcher (ref. 2) is used. It is shown that, with this stepsize rule and under some mild assumptions, the sequence constructed by this family of methods converges superlinearly for a strictly convex functional defined on a suitable Banach space. This result is shown to remain valid on a Hilbert space and on a Euclidean space under more relaxed assumptions. The BFGS method without line searches is used to solve several standard numerical examples, and excellent performance is observed.

Presents a novel method based on node tearing analysis for the solution of power system load flow problems. The technique is applied to the linearized real and reactive power models obtained in the fast decoupled load flow method. By considering node tearing as the reduction of subnetworks to multiterminal equivalents, sparsity and sparse network reduction techniques are widely used. Heuristic structural decomposition techniques are presented. The results of applying this methodology to standard test systems are illustrated and compared with a one-piece solution.

In this paper two computational techniques are presented, to solve non-linear differential games which have a value. It is assumed that there may be interaction in the dynamics of the players and that the conflicting index of performance of the game is a scalar function of the final state of the players of the miss-distance type. The first of these techniques is based on the Newton-Raphson method in function space in association with one of the two following non-iterative procedures to solve linear differential games with quadratic pay-off function : the generalized Riccati transformation or the transition matrix method. The second computational technique presented is based on the gradient of the Hamiltonian function with respect to the strategies. Some numerical examples are given to illustrate the methods.

This paper presents a numerical technique which automatically computes the unspecified terminal-time of an optimal control problem as a systematic part of the whole procedure for finding the optimal control inputs. In the proposed technique, a given unspecified terminal-time problem is transformed into a fixed terminal-time problem by a time-sealing method. Then, by considering the time-scaling parameter as either an extra control input or as an additional variable, and by applying the necessary conditions of optimality, a fixed terminal-time two-point boundary-value problem is obtained. Three algorithms are proposed to solve such a class of two-point boundary-value problems : two of them are based on the gradient methods, and one on the Newton-Raphson method in function space. Several numerical examples are included. A comparison of the rate of convergence of different algorithms used in the solution of each example problem is given.

Hierarchical computing methods for large-scale Power System State Estimation (PSSE) has gained considerable interest over the last few years. So far, however, no method has been developed that is both practical and optimizes the total system's cost function. The Newton-Raphson method for PSSE has the drawback that the Jacobian matrix is evaluated at each iteration and, each time, must be sent to all the other computers in the hierarchical system. In this paper a new hierarchical computing scheme is developed by carefully considering mismatches arising from the system decomposition. The proposed method makes use of an extension of a fast second-order load-flow method which allows to employ a fixed Jacobian matrix in the hierarchical algorithm. In the problem formulation the power network is decomposed into two or more subsystems; the interaction among the systems is taken into account through the tie-line bus voltages. The hierarchical structure of the proposed method consists of two levels: the upper level, where the optimal tie-line bus voltages are evaluated; and the lower level, where the optimal states of each subsystem are determined by minimizing a cost function that involves the entire system. Three test cases of the proposed method are reported in the paper;more » the test results are compared with those obtained by another hierarchical PSSE method.« less

Various methods of providing VAR injection have been used to compensate the inductive current in power distribution feeders. Some were based on the optimization of the location and the rating of the compensators by minimizing the resistive losses. However, these methods were limited and their range and benefit reduced due to the approximation of the reactive load profile using a single or a limited multi-level model. This paper describes the design and the testing of a compensator that continuously. adapts to the inductive current in the feeder, ensuring a maximum reduction of the resistive power losses at all levels of inductive load for a singly located compensator. The system is based on a microprocessor controlled susceptance consisting of a fixed inductor in series with a thyristor biased by a fixed capacitor in parallel. By adjusting the firing angle of the thyristor in series with the inductor, a continuously controlled compensator is obtained. A detailed analysis of the harmonics and the means For their suppression are presented. The analysis have been verified experimentally by designing and fabricating a suitable system in which the modelled feeder is tested in a laboratory environment. Good agreement is obtained between the analysis and the experimental results. The results of the application of a simplified version of the compensator to a real feeder are also presented.

This paper deals with the estimation of parameters involved in the classical steady-state modelling of network elements within the context of power system state estimation. A general method is proposed for the identification and correction of the real-time data, based on the sensitivity relationship between the measurement residuals and the parameter error; this relationship is treated as an estimation problem, yielding a parameter error estimate. Special emphasis is put on the real-time correction of erroneous transformer tap positions, the most frequent parameter errors during the real-time operation of state estimators. The proposed method is very simple and efficient, since it merely requires a single substitution in the state estimation linear system. Relationships with other methods are also discussed. Simulation results on a real-life system are reported.