The knowledge of the state of the ETN in real time is needed at each TSO’s control centre. A perfectly synchronized snapshot of the whole ETN must be prepared by single calculation procedure, each control centre receiving the information it needs to ensure the security of its own system and contribute effectively to the security of the overall system.


The following developments have been undertaken:

  • New mathematical decomposition framework

Prior to the development of suitable Two-Step State Estimation (TSSE) algorithms, a major theoretical development was undertaken in an attempt to improve existing multi-area state estimation schemes. As a result, an elegant and simple factorization scheme was obtained, providing the theoretical kernel and implementation steps for the new multi-level hierarchical state estimation paradigm developed in Pegase, spanning in a seamless fashion from individual substations to the ETN. Such factorization scheme assures the optimality of the proposed algorithms, which become particular cases of the general framework.

  • Two-Step State Estimation suitable for a Pan-European solution

A new TSSE algorithm has been developed, dividing the ETN into TSO areas, for which decoupled SEs are locally run. Then, boundary coupling among areas is taken care of by means of a coordination process. Compared to the state of the art, the proposed TSSE makes use of the minimum area overlapping that allows all raw measurements to be processed during the first stage, which means that the coordination stage becomes linear. Furthermore, sparse weighting matrices are handled throughout the process, reducing the computational effort without sacrificing accuracy.
Tests have demonstrated that the proposed scheme involves a very modest amount of data exchange, while retaining essentially the same accuracy and capability for bad data identification as the conventional estimation of the entire ETN.

  • Phasor Data Concentrator (PDC)

The use of Phasor Measurement Units (PMUs) appears to be very promising for improving the robustness and the accuracy of the state estimation of large power systems.

An overall phasor measurements network architecture has been defined. Taking into account that it has to comply with the TSSE developed, a hierarchical structure has been adopted with PDCs both at the TSO and ETN levels. A set of minimum requirements specific to the SE application has been defined and a PDC/TSO has been developed according to these requirements.

  • SE algorithm using a mix of conventional and phasor measurements

Two alternative methods were investigated:

  • To adapt existing conventional estimator by directly introducing the new information provided by PMUs into the measurement vector, like any other measurement, using polar coordinates for voltage phasors and rectangular ones for current phasors to avoid numerical ill-conditioning problems;
  • To run SE using only the conventional measurements and handle PMU measurements through a post-processing linear estimation. It was shown that thanks to an appropriate representation of state variables and phasor measurements, a slight modification of a conventional Weight Least Square (WLS) algorithm can easily incorporate PMUs in addition to conventional measurements. Using those PMUs from the beginning of the process provides the added value of increasing observability, improving bad data identification and facilitating the synchronization of each TSO solution, reducing the number of iterations required by the coordination phase. All these elements confirm the first method as the most convenient.
  • Algorithms for a local state estimation at the substation level

Making use of all potential real time data available at substations, like conventional SCADA, PMUs and digital protection devices (IEDs), the developed algorithm performs state and topology estimation at the substation level. Better quality (i.e., filtered rather than raw) values are thus sent to upstream estimators (TSO level) and, even more important, topology errors and some bad data are removed from the beginning in the process of finding the most likely state of the network. Therefore, by exploiting local redundancy, without having to send any extra data to the TSO estimator, global accuracy is improved.

  • Algorithms for optimal placement of additional PMUs

Two types of problems have been studied, namely;

  • The optimal PMU location for full observability;
  • The incremental enhancement of an existing measurement configuration. The First one is mainly oriented to state estimators using only PMUs, while the second one is oriented to systems like the European one where the use of the existing conventional SCADA measurements will be kept in use as new PMUs are added to the set of preexisting measurements. This later approach is clearly more valuable for the ETN. Methodologies for both problems were developed and proved satisfactory.


To evaluate their performance and quality of results, the prototypes were put in the hands of actual users of that kind of tools. Several TSOs participated and reviewed the performed tests: REE (Spain), REN (Portugal) and TEIAS (Turkey).

  • Two-Step State Estimation (TSSE) prototype

The TSSE prototype is capable of solving any number of TSOs, arbitrarily interconnected, for any type of available measurements, including those provided by PMUs and Ampere measurements. In addition to conventional network models, it considers advanced components, such as phase shifters and HVDCs.

The TSSE prototype has been extensively tested to ensure the quality of results provided by this kind of algorithms, while minimizing the exchange of data between TSOs. The following scenarios have been tested:

  • France-Spain-Portugal TSO subsystem:

The advantage of this medium size scenario (over 2500 buses) is that it can be solved as well by a conventional estimator, providing the reference solution to compare with, in terms of accuracy, computation time and bad data identification capability. The speed-up of the TSSE prototype was about 3, for both low and high redundancy test cases, in spite of the small size of the Portuguese system. The computation time, about 2 sec. for the low redundancy case, is dominated by stage 1 in all cases.

  • Russian, Turkish and UCTE systems, including HVDC tie-lines:

In order to demonstrate the possible use of the prototypes for large, real power 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 ENTSO-E grid. The result is a huge system: 9200 nodes (640 of them being border buses), 14000 lines and 2500 transformers, over 50000 measurements, covering 26 countries (28 TSOs). Measurements were generated randomly from the load flow results, adding some noise and introducing erroneous measurements. The total solution time on a laptop (Intel Core i5) for the whole UCTE network was just about 4 sec., of which 3.5 sec. corresponds to stage 1. In view of the 2 sec. required to run the 3-TSO system described above, it can be concluded that the prototype scales very well, particularly stage 2 (the solution time of stage 1 is logically determined by the largest TSO). In addition, several scenarios with increasing proportion of PMU measurements, located in randomly chosen substations of the UCTE-TEIAS system, have been tested. The accuracy of the estimate improves for increasing numbers of PMU units, but tends to saturate when 500 units are considered.

  • Synchrophasor and Phasor Data Concentrator (PDC) protoype

Tests on real data illustrate the improvements brought to state estimation performance by the introduction of phasor measurements. The reported tests have been performed on the 400/220 kV Spanish system including PMU at ten 400 kV substations. The influence of the weights associated to the phasor measurements has also been analysed. The following main conclusions can be drawn:

  • The TSO state estimation prototype including phasor measurements was proved to perform properly on real data coming on one hand from SCADA snapshots for conventional measurements and on the other hand from PDC output streams for phasor;
  • As expected, the introduction of phasor measurements leads to higher estimates accuracy, more particularly in the direct neighbourhood of the substations provided with a PMU;

  • Increasing the weights associated to phasor measurements corresponds to a slight global enhancement of accuracy but at the price of more suspected measurements. The choice of too high weights is thus not recommended. A compromise has to be reached between accuracy and number of false alarms in bad data detection;
  • The reported tests considered a rather limited number of phasor measurements. It is expected that increasing the proportion of phasor measurements would confirm the above conclusions and provide even higher benefits.
  • Substation State Estimation mock-up

The local SE mock-up has been tested on a real 400/220/33 kV substation provided by the Spanish TSO. When the circuit breakers and the connectivity are modelled in detail, 147 state variables are obtained, which are estimated with the help of suitable equality constraints, conventional SCADA measurements and protection system (IEDs) extra measurements (the redundancy in this context is nearly 2). Accordingly, the accuracy of the estimated magnitudes is enhanced by over 50% compared to raw ones, which has a similar impact on the accuracy of the TSO estimator when it is fed with these estimates instead of the original (unfiltered) measurements. The relatively modest redundancy level in this context allows anyway all topology errors and a majority of bad data to be detected locally, without contaminating the TSO estimator.


The Two-Step State Estimator has demonstrated its technical feasibility. This opens the way to the TSOs for a superior level of visibility, through a frequently updated picture of the Extra High Voltage (EHV) European network. The development of commercial tools incorporating such methodology could start leaning on the already demonstrated basis.
PDC has been envisaged for usefulness at three different levels: apart from the classical PDC at TSO level, the substation and the ETN levels appear now as really interesting for the next future. New commercial PDCs should be able to receive from and send to other PDCs PMU data.
The use of PMUs and IEDs has been identified as a need from the beginning of the state estimation process: locally at the substation level. Making use of that information, along with the conventional analog and digital measurements currently being sent to the TSO’s SCADA, the quality of the data sent upstream can be improved and, even more important, detection and removal of harmful topology errors can be done before running SE at the TSO level. An innovative approach to the Local State Estimation has been developed and verified within the project and its implementation in the substation control computers would be quite straightforward.
The assessment on the use of PMUs at the other stages of the state estimation problem (TSO & ETN) has been also accomplished, and clear conclusions on the best ways of integrating them were achieved. New commercial SE packages should incorporate the treatment of PMUs in their code. Major remaining challenges for future research, that should be removed for industrialization of the prototypes, are:

  • TSO estimators should be suitably modified to be able to cope with filtered information coming from substation-level estimators, which is more accurate but statistically correlated. Diagonal weighting matrices are no longer valid;
  • TSO estimators should be modified to allow regional coordination during Stage 2. The border information provided by the coordination level should be handled by the TSO estimator much in the same way as any other pseudomeasurement, in order to refine or compensate the existing estimate of internal variables. The goal is to reuse the existing commercial code as much as possible;
  • Computation of residual covariances associated with border magnitudes is currently suboptimal, sometimes providing not very accurate normalized residuals when the redundancy is very low;
  • More refined models of some sophisticated components, such as phase shifters, should be considered.

    • Ways of implementing the coordination phase (stage 2) in a distributed manner, without physically resorting to a coordinator entity. This way, border data would only be interchanged between neighbours, instead of being submitted to a central point;
    • An in-depth evaluation of accuracy of phasor measurements, which is clearly of prime importance for state estimation. Consequently, an in-depth analysis of the influence of the weights associated to phasor measurements on the SE performances;
    • Evaluation of the needed communication infrastructure and corresponding delays.


      A list of the most relevant publications on these topics is included below:

    • A Gómez-Expósito, A de la Villa Jaén, “Two-Level State Estimation With Local Measurement Pre-Processing”, IEEE Transactions on Power Systems, Vol. 24, No. 2, May 2009, pp. 676-684.

    • Gómez-Expósito, A. Abur, A. de la Villa, C. Gómez, “A Multi-Level State Estimation Paradigm for Smart Grids”, Proceedings of the IEEE, pp. 952 - 976, June 2011.

    • Gómez-Expósito, A. de la Villa, C. Gómez, T. van Cutsem, P. Rousseaux, “A Taxonomy of Multi-Area State Estimation Methods”, Electric Power Systems Research, Volume 81, Issue 4, pages 1060-1069, April 2011.

    • Gomez-Exposito, Ali Abur, P. Rousseaux, A. de la Villa Jaen, C. Gomez-Quiles, “On the Use of PMUs in Power System State Estimation”, Accepted for PSCC 2011.