**Algorithms for the treatment of potentially huge number of contingencies**

The simplest approach to solve a SCOPF is to add the full set of contingencies to the problem. However, this approach can lead to dramatically large optimization problems for large networks (such as ETN) and/or a potentially huge number of contingencies. Such a problem can not be solved on today’s computers. The enormous challenge given to the PEGASE project was to be able to solve problems with networks consisting of more than 10000 nodes, more than 10000 contingencies in less than 15 minutes.

In the new approach proposed by the project, called ISCOPF1, a potentially huge amount of post-contingency constraints is treated by two complementary methods:

- In order to reduce the number of contingencies that need to be analyzed simultaneously in a constrained optimization problem, a small superset of the binding contingencies is identified in a sequential manner, by using concepts of “constraint domination” or “umbrella contingencies” recently developed in the literature;
- In order to reduce the number of variables introduced by each contingency and thus to increase the number of contingencies that may be analyzed simultaneously in a constrained optimization problem an original “network compression” method has been implemented, which exploits the property that the impact of a contingency is limited to a localized region of the network and allows the replacement of the rest of the system by an equivalent network.

**Algorithms for the treatment of discrete variables in very large power system**

New ideas have been developed for the modelling of preventive/ corrective actions, and for security management under uncertainty. Those ideas were not considered at the start of the project but are fully aligned with the project global objective:

**1.** We propose a formulation which allows minimizing the amount of preventive actions while taking into account corrective actions. The preventive actions take care only of the limits that corrective actions cannot respect. Being able to solve such a problem becomes more and more important for TSOs due to the actual operating practices they adopt (SPS, security rules, voltage control policy, etc.).

**2.** We propose also a “worst case” approach to offer well defined screening methods. To cope with uncertainties without relying on probabilistic methods, a possible approach consists in checking whether, given some assumptions regarding uncertainties (e.g. defined as intervals on bus active/reactive power injections), the worst case with respect to each contingency is still controllable by appropriate combinations of preventive and corrective actions. In order to reduce the complexity of the global approach, possible implementations based on approximation have been considered. These proposals are still too complex to be efficient for a very large system like the ETN. Hence, these functionalities have not been implemented in a prototype. Nonetheless, in order to show the potential of the worst case method, a demonstrator was made available.

**Prototype for the treatment of potentially huge number of contingencies**

The proposed algorithms have been implemented in a full scale prototype which takes into account special devices such as PST and HVDC (CSC and VSC) and primary active and reactive control of the generating units. Its computational efficiency has been seriously improved through the parallel computation of inherently independent processes (Security Assessment, Network Compression and PCOPF2). For evaluation of performance and quality of results, the prototype has been put in the hands of actual users of that kind of tool. Number of TSOs participated in and reviewed the performed tests: SO-UPS (Russia), TEIAS (Turkey), HEP (Croatia), Transelectrica (Romania), RTE (France).

In order to demonstrate the possible use of the prototype for large, real systems operation, 2 test models have been used. The first one is an actual snapshot of the IPS-UPS system, provided by the Russian TSO (SO-UPS). The second one is built upon a merging of the load flow data of 2 systems: an actual snapshot of the Turkish system and an anonymous, noised but realistic model of the ENTSO-E grid. This results in a huge system: 9200 nodes, 14000 lines, 2500 transformers, and 1500 generation nodes.

The tests demonstrate the ability of the method to reduce dramatically and with a satisfactory accuracy the size of the SCOPF problems and to provide the solution in an acceptable computation time. They proved that the SCOPF algorithm is able to solve optimization problems of an unprecedented size, involving large systems and numerous contingencies. Indeed, a SCOPF on the ETN with more than 6000 contingencies has been solved in less than 45 minutes, which is still too slow for day-ahead operational planning. The present performances are nevertheless well-suitable for operational planning of systems of around 3000 buses, which covers virtually the needs of all European TSOs at the national level.