A power system is a complex dynamic process displaying a series of possibly unstable phenomena. Those phenomena are:

  • The loss on synchronism of generators;
  • Unstable growing oscillations (of power, voltage, etc.);
  • Voltage instability;
  • Frequency stability;
  • Cascade trippings.

All those phenomena can be intermingled and can propagate to the entire interconnected system, leading to complex scenarios ending possibly to a blackout

To simulate the dynamic behaviour of the power system, an extended electromechanical model (EEM) must be used. The EEM includes a detailed representation of the generating units and their controllers.

The EEM has very tough mathematical properties. It is large typically 5 times the static model, non-linear, stifixing fast and slow variable, oscillating, poorly damped and full of discontinuities.

The EEM requires a very robust integration algorithm: implicit, simultaneous, A-stable and using a variable step size.

The Dynamic Security Assessment (DSA) of a power system consists in simulation the system facing a series of incidents like short-circuit, line switching or generating unit tripping.

DSA is today most of the time run off-line. It is used to understand the dynamic behaviour of the system, to tune the parameters of the controllers, to check the protection settings or to assess the stability of an operating point, for the day ahead.

In case of well-known typical behaviour of the studied network, some simplifications of the EEM can apply, for instance to measure the distance to instability resulting from a known phenomenon (such as voltage collapse). The resulting speed-up of the computation has allowed implementing on-line phenomenon-oriented DSA.

In all other case, the accuracy of the EEM model must be as high as possible and the entire ETN should be represented to track all kind of possible unstable phenomenon.

Due to the change of paradigm of the European Transmission Network (ETN) operation, the classical approach of the on-line security assessment must be reconsidered. Today, the so-called (N-1) rule consists in checking the existence of an acceptable steady state point after the tripping of each line, one by one, without consideration for dynamics. This could be no more sufficient as, when operating the system close to its stability limits, the trajectory to the new steady state equilibrium point could be unstable. For this kind of application, the computation speed is paramount.


The PEGASE target for time domain simulation is very ambitious.

  • Simulating the whole ETN (the size of the EEM is around 125.000 state variables);
  • Less than 15 minutes for an off-line simulation where no compromise is done on the accuracy and much faster for an on-line simulation where a tradeoff between accuracy and efficiency applies.

    Simplified simulation is usually performed by replacing a detailed model by a simplified one. The drawback of this approach is that two sets of models must be maintained. The innovative approach taken in PEGASE was to use only one model for both simulations and to introduce the simplification in the numerical scheme.

    To achieve the required performances, new algorithms were needed. Different approaches
    were considered:

  • Fine grain parallelization approach for the function and Jacobean evaluation. It allows
    exploiting the new computer architecture presenting a constant increase of shared memory

  • Advanced direct and iterative linear algebra algorithms dedicated to power system.
  • Domain decomposition methods allowing exploiting the new parallel computers characterized by a reduction of their clock frequency counter-balanced by a significant increase of the number of cores:
  • Schwarz method coupled with advanced preconditioning techniques to exploit shared memory architectures;
  • Waveform Relaxation algorithm to exploit distributed computation architectures.
  • Multirate algorithm dedicated to power system to exploit the strong localization of some events.
  • Localization techniques, which allows to automatically replace components with negligible impact by linear equivalents.
  • A new step size control strategy dedicated to very large system, which prevents missing some local instability. All these algorithms have been developed and evaluated. For the two targets considered (Full Dynamic simulation and Simplified Dynamic simulation), the best mixes have been identified. These mixes have allowed achieving very important speed-up:
  • The time needed for a detailed dynamic simulation has been reduced by a factor 10 with respect to industrial simulators available before the start of the PEGASE project.
  • It is now possible to replace N-1 static security analysis by simplified dynamic simulations while respecting the on-line time constraint.


Based on the research results of the PEGASE project two time-domain simulation prototypes have been developed;

  • The first one is the Full accuracy prototype, which includes a new fine grain parallelization, the best up-to-date direct linear algebra and the new stepsize control;
  • The second one is the Simplified simulation prototype which includes the best up-to-date direct linear algebra and the new localization technique. This prototype being dedicated to security assessment, the parallelization is introduced at the contingency level and not in the core of the computation engine.

    These two prototypes use the same model, which can be described by the user through block diagrams. It allows to include easily all the new models developed in the framework of PEGASE like wind turbines, wind farms and HVDC.

    Generic models for wind turbines, wind farms, and VSC HVDC have been developed. The models can be adapted to some FACTS devices as well. The models are simplified to the extent that they are capable of reproducing only the phenomena affecting the power system stability. They do not necessarily represent specific control architectures or rely on parameters of a particular wind turbine. As a result the same model is capable of simulating wind turbines of different manufacturers or even different turbine concepts or whole wind farms consisting of any realistic number of wind turbines.
  • Most relevant testers: Transmission System Operators (TSO)

To evaluate these 2 prototypes in terms of performance and quality of results, they were put in the hands of actual users of that kind of tools. Number of Transmission System Operators participated in an intensive testing framework: SO-UPS (Russia), TEIAS (Turkey), HEP (Croatia), Transelectrica (Romania), RTE (France), LITGRID (Lithuania). Also participated ENERGOSETPROJECT (Consultancy company in Russia) and Riga Technical University.

  • Realistic test models of the European, Russian and Turkish systems

In order to demonstrate the capability of the prototypes to run large, real systems, 2 test models have been built.

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 grid of continental Europe. The energy mix of each country is respected and typical dynamic models are used for each kind of generator (nuclear, hydro...), including standard speed governors, AVR and PSS.

The network structure includes step-up and load transformers to represent accurately a broader range of phenomena (voltage collapse...). Complex controls have also been introduced: secondary voltage regulations, 4-loop PSS and complex devices models have been included: HVDC LCCs and VSCs, SVCs, wind farms.

This results in a huge system: 16000 nodes, 13000 lines, 9000 transformers, 3000 synchronous generators, 700 wind farms,... The size of the mathematical problem is 140000 variables.

It reproduces some characteristics similar to the real European system, like weak damping, slow inter-area oscillation modes between West and East, around 0.3 Hz.

European grid-like model has been made public for benchmarking purposes: it is fully described in a paper submitted at ISGT 2012 Berlin, and downloadable from the PEGASE website.

  • Unprecedented accuracy/performance ratio for system-wide phenomena on Pan European scale

Tests proved that the algorithm is able to achieve an unprecedented ratio accuracy/performance for large systems, on local events simulation, but more importantly on full-scale scenarios involving large parts of the system:

  • Network splitting with cascade tripping of overloaded lines;
  • Inter area oscillations;
  • Whole areas losing synchronism Each of these tests was performed in less than 10 minutes. For example;
  • A voltage collapse scenario activating more than 10 LTC and 2 generator field current limiter: 4.4 minutes;
  • A simple generator set point change: 0.3 minute Changing the AC grid impedance in parallel with an embedded VSC HVDC: 1.4 minute
  • Extreme case of voltage collapse with system splitting: 9.8 minutes.
  • Making on-line DSA possible at the Pan European scale

Tests proved the algorithm (simplified numerical scheme) is able to achieve unprecedented performances for dynamic simulation on such a large system and in the range of targeted phenomena (slow dynamics), making online dynamic security analysis at the Pan European level possible.

The following figures were extracted from tests performed on the “UCTE+TEIAS” system:

  • Trip a line below 400 kV: 26 seconds;
  • Tripping of two parallel 400 kV lines: 44 seconds. Both contingencies lead to significant voltage deviation over a large zone with the triggering of many automata.
A whole online dynamic security assessment at the Pan European scale would require the consideration of 2000 N-1 contingencies in less than 5 minutes. With an average of 26 seconds by N-1 contingency, this target can be reached through the simultaneous use of 192 cores. This could be performed using less than the computation power available in a single modern blade enclosure.


The computation engines developed can now be considered as perfectly suitable for Security Assessment at the ETN level. Even if the Waveform Relaxation has shown promising results for a decentralized computation, the best results are obtained with a centralized approach were all the data are, during the computation, centralized on the same computer.

Before proceeding to the industrialization, additional elements still need to be considered:

  • Filtering: depending on the number of simulations, which have to be performed and the time constraint on the DSA, additional contingency filtering could be needed;
  • HPC aspects: All the IT aspects surrounding the computation engines needs to be taken into account: How are the data stored and handled? How to minimize the power consumption of many parallel simulations? How to set-up automatic backup system?
  • Framework for TSOs collaboration in the field of Security Analysis: TSOs need a framework to collaborate. A single model of the whole ETN is needed to perform Security Analysis. This model must be automatically updated on the basis of the available national models;
  • Definition of a Common Information Model (CIM) for system dynamics: CIM is mature for definition of static characteristics of transmission systems. Similar approach for system dynamics, already initiated by two members of the PEGASE consortium, would help for model aggregation and consistency.


    The following non-exhaustive list of publications illustrates the numerous scientific advances performed during the PEGASE project:

  • D. Fabozzi, T. Van Cutsem, “On Angle References in Long-Term Time-Domain Simulations”, Power Systems, IEEE Transactions on, vol.26, no.1, pp.483-484, Feb. 2011

  • D. Fabozzi, T. van Cutsem, “Assessing the Proximity of Time Evolutions through Dynamic Time Warping” Proc. IET Generation, Transmission & Distribution (2011), 5(12), pp. 1268-1276.

  • D. Fabozzi, T. Van Cutsem , “Localization and latency concepts applied to time simulation of large power systems”, Proc. IREP Symposium on Bulk Power System Dynamics and Control - VIII, Buzios (Brazil), 1-6 Aug. 2010.

  • V. Savcenco, B. Haut, E. Jan W. ter Maten, R. M.M. Mattheij, “Time domain simulation of power systems with different time scales”, Proceedings of Scientific Computing in Electrical Engineering (SCEE) Conference, Toulouse, France, September 19-24, 2010.

  • V. Savcenco, B. Haut, “Multirate Integration of a European Power System Network Model”, Proceedings of 8th International Conference of Numerical Analysis and Applied Mathematics, Volume 1281, pp. 2037-2040, 2010

  • B. Haut, V. Savcenco, P. Panciatici, “A multirate approach for time domain simulation of very large power systems”, HICSS 45 Proceedings, pp 2125-2132, 2012.

  • F. Pruvost, P. Laurent-Gengoux, F. Magoulès, F.X-Bouchez, “Speed-up the Computing efficiency of waveform relaxation for Power system Transient Stability”, SC’11, Seattle, WA, USA, November 13, 2011.

  • F. Pruvost, T. Cadeau, P. Laurent, F. Magoulès, F.-X. Bouchez, B. Haut, “Numerical Accelerations for Power Systems Transient Stability Simulations”, Proceedings of the 17th PSCC conference, Stockholm, Sweden, 22-26 August 2011.

  • D. Fabozzi, A.S. Chieh, P. Panciatici, T. Van Cutsem, “On simplified handling of state events in time-domain simulation”, Proceedings of the 17th Power System Computation Conference (PSCC), Stockholm, Sweden, Aug. 2011.

  • F.-X. Bouchez, B. Haut, L. Platbrood, K. Karoui, “HPC for power systems in the framework of the PEGASE project”, Proceedings of IEEE PES General Meeting 2012, San Diego, CA, USA, 22-26 July 2012.