Steady State Optimization is a key tool to create anticipated states of the system by automating the process of generating network conditions that reflect actual operating practices of the TSOs (security rules, voltage control policy etc.).

Building anticipated states of the system using a Security Constrained Optimal Power Flow (SCOPF) is nowadays a very hard process due to the mathematical complexity of the problem (nonlinear functions, discrete variables, etc.). Running this process at the European level (for obvious coordination reasons), integrating an increasing level of uncertainty (wind power, photovoltaic, market, demand response) and taking into account that the system is operated with very little security margins and with more and more possible preventive and corrective actions (Special Protection Schemes (SPS), operating rules) is an enormous challenge. Even by using heuristics as the linearization of the equations for start/stop of controllable generating units and treating separately corrective and preventive actions, it is a real challenge to propose a methodology able to provide an acceptable operating point in a reasonable computation time.


  • 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.

  • Prototype for the treatment of discrete behaviour of equipment for very large system

A prototype has been developed, which implements optimization for different objective functions (minimal deviation of generated active powers, active losses) taking into account the discrete behaviour of equipment: taps of OLTC and PST, switching of capacitors/reactors banks, shutdown/startup of generators for very large system like the ETN but without contingency constraints.

The state of the art shows that existing true MINLP3 solvers are not capable of finding a solution in most cases in reasonable computation time. Tests on the most well-known MINLP solvers have been run to confirm this point. Therefore, in order to reduce the complexity of the problem, a solution based on a sequence of optimization problems, relaxing at each step integrality constraint for some discrete variables has been proposed and combined with the use of a solution based on MPEC4 constraints, which consists in substituting the discrete variables by continuous variables with complementary constraints. This approach doesn’t strictly guarantee optimum values for discrete variables but at least provides a feasible solution, “improved” values of discrete variables, and a local optimum for continuous variables.


The prototype for the treatment of potentially huge number of contingencies could be implemented in an industrial way.

While it supports discrete variables for device modelling (transformer taps and capacitors/reactors bank steps) through a heuristic method, it could be combined with the methodology proposed to manage the startup/shutdown of generators.
The resulting tool could support HVDC modelling (CSC and VSC) for Load Flow, Security Analysis and SCOPF.

It could also integrate the Contingency Filtering and Network Compression. All those calculations modules are able to process very large networks. Moreover, a parallel version of the Security Analysis and Network Compression could be delivered to exploit efficiently HPC resources. Some improvements could still be expected:

  • On an algorithmic point of view, especially to ensure the quality of the reduction of each contingency by improving the criterion used to automatically determine the part of the network to be reduced;
  • On a performances point of view, to reduce the time needed to solve the SCOPF which remains the most important task (65%) of the whole process. The prototype for the treatment of discrete variables for very large system demonstrates the possibility to use MPEC. Existing OPF could be enhanced reusing this idea. Although further work is needed to ensure a better robustness on very large test cases and to better assess the optimality of the solution.
    The modelling of preventive/corrective actions developed in the project and the experience gained using this approach allows the proposal of a new optimization formulation which will be very useful to manage the new HVDC link between France and Spain.
    The new formulation of the SCOPF taking into account the priority of corrective action on preventive action and a realistic modelling of corrective actions associated to constraint violations are two very important aspects on the methodological point of view. They introduce discrete decision variables which are very difficult to take into account. Work has still to be done to efficiently solve such kind of problems. Concerning the new formulation for security management under uncertainty, an important work remains to be done in order to propose an approximation trying to reduce the complexity of the problem.
    Using a DC approximation (Linear model), these two new ideas could be implemented more efficiently. In the FP7 iTesla project, screening methods based on these ideas will be developed.


    Several scientific papers describing these new formulations have been published:

  • F. Capitanescu, J.L. Martinez Ramos, P. Panciatici, D. Kirschen, A. Marano Marcolini, L. Platbrood, L. Wehenkel, “State-of-the-art, challenges, and future trends in security constrained optimal power flow,” Electric Power Systems Research, Volume 81, Issue 8, August 2011, Pages 1731-1741, ISSN 0378-7796, DOI: 10.1016/j.epsr.2011.04.003.

  • P. Panciatici, Y. Hassaine, S. Fliscounakis, L. Platbrood, M. A. Ortega-Vazquez, J.L. Martinez-Ramos, L. Wehenkel, “Security Management Under Uncertainity: from Day-Ahead Planning to Intraday Operation”, Proceedings of the IREP Symposium 2010, Buzios, Rio de Janeiro, Brazil, 1-6 August 2010.

  • F. Capitanescu, S. Fliscounakis, P. Panciatici, L. Wehenkel, “Day-ahead Security Assessment under Uncertainty Relying on the Combination of Preventive and Corrective Controls to Face Worst-Case Scenarios”, Proceedings of 17th PSCC conference, Stockholm, Sweden, 22-26 August 2011.

  • L. Platbrood, H. Crisciu, F. Capitanescu, L. Wehenkel, “Solving very large-scale Security-Constrained Optimal Power Flow problems by combining iterative contingency selection and network compression”, Proceedings of 17th PSCC conference, Stockholm, Sweden, 22-26 August 2011.

  • L.Platbrood, F.Capitanescu, H. Crisciu and L.Wehenkel, “A generic approach for leveraging security-constrained optimal power flow computations to very large-scalesystems”, IEEE TPWRS Special Issue On Very Large Power Systems, submitted.

  • F. Capitanescu, S. Fliscounakis, P. Panciatici and L. Wehenkel, “Cautious operation planning underun certainties”, IEEE, submitted.

  • S. Fliscounakis, P. Panciatici, F.Capitanescu and L.Wehenkel, “Ranking of contingenci esseverity in very large power system taking into account uncertainty, preventive and corrective actions”, IEEE TPWRS Special Issue On Very Large Power Systems, submitted.