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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.

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.

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. >

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.

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.

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