Data processing: generic control systems or specific application – Specific application – apparatus or process – Electrical power generation or distribution system
Reexamination Certificate
1999-03-19
2004-08-10
Picard, Leo (Department: 2125)
Data processing: generic control systems or specific application
Specific application, apparatus or process
Electrical power generation or distribution system
C700S297000, C703S002000, C703S018000
Reexamination Certificate
active
06775597
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to the field of electrical power generation and distribution systems.
BACKGROUND INFORMATION
Optimal power flow (OPF) algorithms based on successive linearization techniques are widely used to solve different problems in power system planning, operation and control.
Security Constrained OPF (SCOPF) problems are a special class of OPF problems which consider constraints derived from a normal system state (the “base case”) and a set of predefined contingency states. SCOPF is an extension of the classical constrained economic dispatch problem in an effort to satisfy the system security requirements.
The definition of system security in actual power system operation varies throughout the power industry. Different operation policies and rules are applied to define security requirements. A widely accepted system security concept is so-called “n−1 security.” Based on this concept, one of the main objectives in system operation and control is to keep the system in a normal state during normal system operation (the base case) and in the case of any one major contingency in the predefined list of contingencies. In order to satisfy the n−1 security criteria the power system should be secure (no violations) after the occurrence of any single contingency in the system. This leads to the implementation of preventive control actions in the system, or the preventive mode of SCOPF.
SCOPF in preventive mode is conservative, because it does not consider the system's post-contingency (corrective) control capabilities. By introducing corrective rescheduling to the n−1 security concept, three different modes of control adjustments that affect the SCOPF solution can be identified: 1) Preventive mode; 2) Corrective mode; and 3) Preventive/corrective mode.
In the preventive mode, all control variables are optimized such that no post-contingency adjustments are necessary in order to avoid violation of base case and post-contingency constraints. This is the most secure solution mode, since no operator intervention is required following an anticipated contingency. The consequences of such a solution are a higher pre-contingency objective function, and a generally more difficult problem to solve. In some cases the preventive mode solution may not even exist, especially for more severe contingencies.
In the corrective mode, the control variables are permitted to adjust after the contingency occurs. This is a less secure mode of operation since operator action is required soon after the occurrence of a contingency to reach an acceptable operating state. Such a problem is generally easier to solve, since there are more degrees of freedom in the control adjustments. The corrective mode is solved as a sequence of independent optimization problems, one per contingency.
In the preventive/corrective mode, some of the violations for the violated constraints are relieved in the preventive mode, and the rest in the corrective mode. The preventive/corrective mode SCOPF produces a significantly larger optimization problem to be solved than the preventive mode SCOPF. However, it is more likely to have a feasible solution than the preventive mode SCOPF. It should be the preferred solution mode, especially in those cases where the preventive mode SCOPF requires expensive rescheduling of the base case generations. Normally operating a power system at a much higher cost in order to avoid limit violations in some contingency cases, may not be justifiable considering that the problem can be avoided by combining preventive and corrective control actions.
Execution of the SCOPF function in any of the previously mentioned modes is time consuming. Historically, the performance problems are dealt with by introducing in the model a relatively small number of critical contingencies. This approximation presents an unresolved modeling problem for all known SCOPF formulations. That is, by fixing just a small subset of most critical contingencies, there is no guaranty that other contingencies labeled as non-critical will not become critical after a new SCOPF solution. The only practical solution to this problem is to directly involve a large number of critical contingencies in the SCOPF formulation, resulting in a very large optimization problem to be solved.
Many different solution approaches have been proposed to solve the OPF problem. These methods can be generally classified into the following two categories: 1) successive linear programming (SLP) based methods; or 2) non-linear programming (NLP) based methods.
In the past, the SLP-based methods have been used almost exclusively for the solution of Security Constrained Economic Dispatch (SCED) problems. This is due to an inability of NLP-based methods to efficiently solve large numbers of cases simultaneously. An approach for the solution of the CED problem with piecewise linear cost curves and regulating margin constraints has been developed by Lugtu and Elacqua et al. (See R. Lugtu, “Security Constrained Dispatch”,
IEEE Transactions on Power Apparatus and Systems,
Vol. PAS-98, pp. 270-274, January/February 1979; and A. J. Elacqua, et al., “Security Constrained Dispatch at the New York Power Pool”,
IEEE Transactions on Power Apparatus and Systems,
Vol. PAS-101, pp. 2876-2883, August 1982.) That approach is based on the differential algorithm and the simplex method.
One approach has been to formulate the CED problem as a quadratic programming optimization problem and solved using Wolfe's algorithm. (See G. F. Reid et al., “Economic Dispatch Using Quadratic Programming”,
IEEE Transactions on Power Apparatus and Systems,
Vol. PAS-92, pp. 2015-2023, November/December 1973.) Furthermore, the Dantzig-Wolfe decomposition can be used efficiently for the solution of CED problems with reserve and contingency constraints. (See, e.g., M. Aganagic et al., “Security Constrained Economic Dispatch Using Nonlinear Dantzig-Wolfe Decomposition”,
IEEE Transactions on Power Systems,
Vol. PWRS-12, pp. 105-112, February 1997.)
An efficient NLP-based implementation is described in A. Monticelli et al., “Security-Constrained Optimal Power Flow with Post-Contingency Corrective Rescheduling”,
IEEE Transactions on Power Systems,
Vol. PWRS-2, pp. 175-182, February 1987. That approach is based on an AC power flow model and a generalized Benders decomposition. It is capable of solving SCOPF problems in both preventive and preventive/corrective modes.
Linear programming has been recognized as a reliable and robust technique for solving a large subset of specialized OPF problems characterized by linear separable objective functions and linear constraints. Many practical implementations of different OPF functions in modern energy management system (EMS) environments use an LP optimizer. Among various LP implementations probably the most efficient one is dual simplex successive linear programming with a special logic for traversing the segments of piecewise linearized cost curves called segment refinement. (See B. Stott et al., “Review of Linear Programming Applied to Power System Rescheduling”,
IEEE PICA Conf. Proc.,
pp. 142-154, Cleveland, May 1979; Alsac et al., “Further Developments in LP-Based Optimal Power Flow”,
IEEE Transactions on Power Systems,
Vol. PWRS-5, pp. 697-711, August 1990.) This method has been successfully implemented in solving general OPF problems including active loss minimization. It is very efficient in solving OPF problems with relatively small numbers of constraints and controls, which is not usually the case for SCOPF problems. The dual simplex LP algorithm and segment refinement are described in P. Ristanovic, “Successive Linear Programming Based OPF Solution”,
IEEE Tutorial Course, Optimal Power Flow: Solution Techniques, Requirements, and Challenges,
96 TP 111-0, 1996.
Interior point methods (IPMs) for mathematical programming problems were introduced by Frisch more than 30 years ago. Fiacco and McCormick further developed IPMs as a tool for the solution of nonlinear programming problems
Aganagic Muhamed
Obadina Oladiran
Ristanovic Petar
de la Rosa José R.
Frank Elliot
Picard Leo
Siemens Power Transmission & Distribution
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