This paper addresses the main challenges to the security constrained optimal power flow (SCOPF) computations. We first discuss the issues related to the SCOPF problem formulation such as the use of a limited number of corrective actions in the post-contingency states and the modeling of voltage and transient stability constraints. Then we deal with the challenges to the techniques for solving the SCOPF, focusing mainly on: approaches to reduce the size of the problem by either efficiently identifying the binding contingencies and including only these contingencies in the SCOPF or by using approximate models for the post-contingency states, and the handling of discrete variables. We finally address the current trend of extending the SCOPF formulation to take into account the increasing levels of uncertainty in the operation planning. For each such topic we provide a review of the state of the art, we identify the advances that are needed, and we indicate ways to bridge the gap between the current state of the art and these needs. * Corresponding author Email addresses: capitane@montefiore.ulg.ac.be (F. Capitanescu), camel@us.es (J.L. Martinez Ramos), patrick.panciatici@rte-france.com (P. Panciatici), kirschen@uw.edu (D. Kirschen), alejandromm@us.es (A. Marano Marcolini), ludovic.platbrood@gdfsuez.com (L. Platbrood), l.wehenkel@ulg.ac.be (L. Wehenkel) Preprint submitted to Electric Power Systems ResearchMay 2, 2011Keywords: mixed integer linear programming, mixed integer nonlinear programming, nonlinear programming, optimal power flow, security constrained optimal power flow MotivationThe SCOPF [1,2] is an extension of the OPF problem [3,4] which takes into account constraints arising from the operation of the system under a set of postulated contingencies. The SCOPF problem is a nonlinear, nonconvex, large-scale optimization problem, with both continuous and discrete variables [1,2]. The SCOPF belongs therefore to the class of optimization problems called Mixed Integer Non-Linear Programming (MINLP).The SCOPF has become an essential tool for many Transmission System Operators (TSOs) for the planning, operational planning, and real time operation of their system [5,6, 7,8]. Furthermore, in several electricity markets (e.g. PJM, New-England, California, etc.) the locational marginal prices calculated using a DC SCOPF are used to price electricity. This approach is also under consideration in other systems [9,10,11].Several papers discussing the challenges to the OPF problem were published during the 90's [5,6, 7,8]. Since then several important changes have taken place not only in power systems operation and control but also in mathematical programming:• Power systems operate today in conditions that are more "stressed" and were not foreseen at the planning stage. In particular the increase in load has not been supported by an adequate upgrade of the generation and transmission systems. Furthermore the creation of electricity markets has led to the trading of significant amounts of electrical energy over lo...

Abstract-This paper deals with day-ahead security management with respect to a postulated set of contingencies, while taking into account uncertainties about the next day generation/load scenario. In order to help the system operator in decision making under uncertainty, we aim at ranking these contingencies into four clusters according to the type of control actions needed to cover the worst uncertainty pattern of each contingency with respect to branch overload. To this end we use a fixed point algorithm that loops over two main modules: a discrete bi-level program (BLV) that computes the worst-case scenario, and a special kind of security constrained optimal power flow (SCOPF) which computes optimal preventive/corrective actions to cover the worst-case. We rely on a DC grid model, as the large number of binary variables, the large size of the problem, and the stringent computational requirements preclude the use of existing mixed integer nonlinear programming (MINLP) solvers. Consequently we solve the SCOPF using a mixed integer linear programming (MILP) solver while the BLV is decomposed into a series of MILPs. We provide numerical results with our approach on a very large European system model with 9241 buses and 5126 contingencies. Index Terms-Bi-level programming, mixed integer linear programming, operation under uncertainty, optimal power flow, security-constrained optimal power flow, worst-case analysis.

Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in several practical cases. However, it does not in all cases, and such cases have been documented in recent publications. This paper presents another SDP method known as the momentsos (sum of squares) approach, which generates a sequence that converges towards a global solution to the OPF problem at the cost of higher runtime. Our finding is that in the small examples where the previously studied SDP method fails, this approach finds the global solution. The higher cost in runtime is due to an increase in the matrix size of the SDP problem, which can vary from one instance to another. Numerical experiment shows that the size is very often a quadratic function of the number of buses in the network, whereas it is a linear function of the number of buses in the case of the previously studied SDP method.

International audienceIn this paper, the stochastic characteristics of the electric consumption in France are analyzed. It is shown that the load time series exhibit lasting abrupt changes in the stochastic pattern, termed breaks. The goal is to propose an efficient and robust load forecasting method for prediction up to a day-ahead. To this end, two new robust procedures for outlier identification and suppression are developed. They are termed the multivariate ratio-of-medians-based estimator (RME) and the multivariate minimum-Hellinger-distance-based estimator (MHDE). The performance of the proposed methods has been evaluated on the French electric load time series in terms of execution times, ability to detect and suppress outliers, and forecasting accuracy. Their performances are compared with those of the robust methods proposed in the literature to estimate the parameters of SARIMA models and of the multiplicative double seasonal exponential smoothing. A new robust version of the latter is proposed as well. It is found that the RME approach outperforms all the other methods for "normal days" and presents several interesting properties such as good robustness, fast execution, simplicity, and easy online implementation. Finally, to deal with heteroscedasticity, we propose a simple novel multivariate modeling that improves the quality of the forecast

O OVER THE LAST TEN YEARS, WE HAVE HEARD SO OFTEN IN CONFERENCES,seminars, and workshops that the power system will soon be operated very near to its limits that this statement has become a cliché. Unfortunately, it is no longer possible to comply with the classical preventive N-1 security standards during all of the hours in a year. The system is indeed no longer able to survive all single faults without postfault actions. More and more corrective (i.e., postfault) actions are defi ned and prepared by operators, and the "cliché" is now a reality, as a matter of fact. To be more precise, it is no longer possible to maintain the N-1 security of the system at all moments by using only preventive actions, and the number of hours during which the system requires corrective actions to be secure is increasing. More and more, new special protection schemes (SPSs) are deployed to implement some of these corrective actions automatically. Devices such as phase-shifting transformers (PSTs) and static var compensators (SVCs) are added in the system to increase its controllability. As a result, the system becomes more and more complex. This state of affairs has various causes that will not disappear in the near future. One is that it is more diffi cult than ever to build new overhead lines because of the "not in my backyard" (NIMBY) attitude. People are more and more afraid of hypothetical electromagnetic effects, or they just don't like to see big towers in the landscape. This is particularly the case in protected areas, which are becoming more and more numerous around Europe. It is very diffi cult to explain the need for new interconnection lines to people who already have access to electricity at a reasonable price and with high availability. An increase in European social welfare with a positive feedback for the European economy and hopefully for all European citizens is a concept that is too theoretical compared with the negative local impact. Alternative solutions are technically complex, costly, and need even more time to be deployed.The second main reason is the massive integration of renewable but generally intermittent generation in the system. Power fl ows in the grid are created by difference in location between power sinks and sources. With a signifi cant amount of intermittent power generation, the predictability of the sources (location and levels of power injections) decreases and strongly affects the predictability of power fl ows. Furthermore, these new power plants are generally