IEEE Transactions on Power Systems, Vol. 14, No. 1, February 1999 327 zy Determination of secure operating limits with respect to voltage collapse T. Van Cutsem C. Moisse R. Mailhot University of Likge, Institut Montefiore, Sart-Tilman, B28, B-4000 Likge, Belgium Hydro-Qukbec, Control center Complexe Desjardins, Montreal, Canada H5B 1H7 vct,Omontefiore.ulg.ac. be Abstract. A secnre operating limit, is t,he most stressed among a given set of operating points, such that the sfs- tem can withstand specified contingencies. It zyxwvutsr is a general measure of security with respect to incidents, iricorporat- ing pre-contingency operator or controller actions and post- contingency corrective controls. The proposed approach deals with long-term voltage stability limits. It combines a dicliotomic search with quasi steady-state simulation to compute these limits with the efficiency required by real- time applications. The limit search acceleration and contin- gency filtering issues are also discussed. Illnstrative exam- ples are given on the Hydro-Qiifhec system. 1. INTRODTJCTION The need to perform dehiled voltsage stabilit,y studies for various system conditions a,nd cont,ingeiicies is likely to increase with the line loadings, the operating constraints and the use of shunt compensation. Security nmrgins must be determined in operational planning a.nd real-time oper- ation in order to best utilize the a.va.ilablesystem coinpo- nents. This paper deals with zyxwvutsrqp long-term voltage stability [l], in which load restoration by L0a.d Ta,p Changers (LTCs) a.nd thermostatic effects, genemtor currelit, limiters, shunt com- pensation switching a.nd secondary volt,age play a. major role. The vast majority of voltgage securit,y margins proposed in the literature deal with t,he syst,em response to slow vari- ations in parameters associa.ted with a. system st,ress likely to endanger voltage st>ability. The corresponding liniit,s will be referred to in this paper as loadabilify limifs. Sucli lim- its can be comput,ed by considering the system evolution zyxwvu PE-942-PLVKS-0-07-1997 A paper recommended and approved by the IEEE Power System Operations Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power Systems. Manuscript submitted December 31, 1996; made available for printing August 19, 1997. richardOrti. hydro.qc.ca as a succession of equilibria and determining the (saddle- node) bifurcation point where equilibrium is lost or the relevant Jacobian matrix has a zero eigenvalue. This can be done using e.g. non-divergent load flows, continuation power flows, special optimal power flows, or fast time do- main simulation together with sensitivity techniques [2]. However almost all voltage collapse incidents experi- enced so far resulted from large disturbances, typically the loss of transmission and/or generation facilities. There is thus a need to define better security margins with respect to contangeiicies and devise the appropriate computational methods. Moreover, this paper reports on the development of a methodology that meets the requirements of real-time applzcatzons. Of course, its efficiency makes it attractive for planning and operational planning studies as well. A well-known practice in security analysis consists in checking against limits the post-contingency voltages, usu- ally given by a load flow, This approach however is unsat- isfactory in two respects. First, it is a pointwise analysis, focusing on a particular operating point; second, the post- contingency volt,ages do not provide an explicit measure of systein security. A first securit#y margin is provided by the zyx post- confingency loadabilify lzmat, i.e. the loadability limit eval- uated on the post-contingency configuration, using one of the above mentioned method. Such a limit corresponds to an experience where the post-contingency situation is stressed to evaluate its robustness. An alternative to the above security measure is the secure operating limit that will be considered more thor- oughly in this paper. This limit corresponds to the most stressed, pre-contingency situation such that the system can withstand the specified contingencies. Unlike to the previous limit, this one is expressed in terms of pre- contingency quantities that the operator can observe or control, at the time of taking his decision. A similar ap- proach has been discussed for transient angle stability zy as- sessment in [4, 51. Secure operating limits, although used by some utili- ties, have been comparatively less documented in the lit- erature [3]. However the development of efficient and ac- curate comput,ing tools deserves further attention. This paper reports on an extension of the ASTRE soft- ware developed at the University of Litge [6, 71. This ex- tension takes advantages of the several-year-long experi-