Optimization of power flow with transient stability constraints using semi-infinite programming

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Optimization of power flow with transient stability constraints using semi-infinite programming


Author: Xia, Yan
Title: Optimization of power flow with transient stability constraints using semi-infinite programming
Degree: Ph.D.
Year: 2007
Subject: Hong Kong Polytechnic University -- Dissertations.
Electric power system stability.
Transients (Electricity)
Department: Dept. of Electrical Engineering
Pages: xiii, 143 leaves : ill. ; 30 cm.
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2116761
URI: http://theses.lib.polyu.edu.hk/handle/200/1435
Abstract: Increased economical pressure and intensified transactions, especially in competitive environment, have forced modern electric power systems to operate much closer to their security limits than ever before. Nowadays, dynamic instability has become a major threat for system operation. Dynamic stability requires that when any of a specified set of disturbances (e.g. outages of generators or transmission lines) occurs, a feasible operation point should be able to withstand the fault and ensure that the power system moves to a new stable equilibrium after the clearance of the fault without violating equality and inequality constraints even during transient period of the dynamics. Due to the huge loss and expensive control cost associated with transient instability, dynamic security assessment must be considered in planning and operation analysis together with economic objectives. Mathematically, dynamic security assessment can be considered as an extended optimal power flow (OPF) problem, in which transient stability, for example, is regarded as one of the security constraints for the system operation, with the optimal objective to be obtained under a given set of system parameters by adjusting available controlling schemes. This research aims to develop a practical framework based on existing OPF techniques for integrated economy and dynamic security optimization such that the final system could be operated in an optimal state with lowest generation cost, for instance, and guaranteed dynamic security. By introducing transient stability indices to conventional OPF, OPF with transient stability constraints is generalized as a semi-infinite programming (SIP) problem with a finite number of state and control variables for the operation state and an infinite number of constraints for transient stability in the functional space of time domain. In this thesis, "infinite" constraints for transient stability mean that the stability has to be satisfied in the infinitely many continuous time points in the transients. Two transient stability indices based on rotor angle limit and potential energy boundary surface (PEBS) concept are employed. The features and performance of the two indices are compared theoretically and numerically. General scheme of the solution of SIP is extended to solve transient stability constrained OPF problem. Numerical methods for SIP are developed to locally reduce transient stability constraints to be finite-dimensional constraints based on L1 and L8 norm. L1 and L8 norm are defined as the norm integration and maximal norm of the violation of the semi-infinite constraints in their functional spaces, respectively. This transformation transcribes transient stability constrained OPF to conventional OPF with a finite number of constraints, which is solvable by using nonlinear programming theories and algorithms. The locally reduced SIP problem of transient stability constrained OFF is solved by direct nonlinear primal-dual interior point method. The theoretical difficulties in forming the Jacobian and Hessian Matrices of the transient stability constraints are overcome by using implicit relationship between the transient stability constraints and the differential-algebra-equations (DAEs) for the dynamic performance. The solution of the multi-local optimization in the buildup of L8 penalty functions is proposed based on intermediate value theorem. In addition, an improved BFGS (Broyden-Fletcher-Goldfarb-Shanno) method, which is a quasi-Newton method with superlinear convergence, is exploited to avoid the complicated derivation of Hessian matrix. By splitting the Hessian matrix into two parts - an 'easy' part for conventional OPF and a 'difficult' part for transient stability constraints, only the 'difficult part' is approximated according to BFGS updating while the 'easy' part is calculated accurately. Moreover, a new concept referred as "the most effective section" of transient stability constraints is proposed to alleviate the huge computational efforts and improve the convergence of the optimization calculation. The calculation of dynamic available transfer capability (ATC) and dynamic security dispatch are formulated as transient stability constrained OPF problems and are solved by the proposed methodology. The proposed methodology is fully validated in both the WSCC 9-bus system and New England 39-bus system. The necessity of transient stability involvement in OPF is illustrated in the case studies. The good performance of the introduction of the most effective section of transient stability constraints is illustrated in the case study of ATC computation. The effectiveness of transient stability constraints based on rotor angle limits and PEBS are compared and discussed. The advantage of the use of improved BFGS method to avoid complex Hessian matrix derivation is demonstrated. In the study of dynamic security dispatch, multi-contingency cases are handled by the proposed methodology in solving cases with difficult multiple contingencies for the improvement of the overall security level.

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