D6.3 Part 1.1 Demonstration report for Two-Step State Estimation Prototype

Transcription

1 D6.3 Part 1.1 Demonstration report for Two-Step State Estimation Prototype Proprietary Rights Statement This document contains information, which is proprietary to the "PEGASE" Consortium. Neither this document nor the information contained herein shall be used, duplicated or communicated by any means to any third party, in whole or in parts, except with prior written consent of the "PEGASE" Consortium. Grant Agreement Number: implemented as Large-scale Integrating Project Coordinator: Tractebel Engineering S.A. Project Website:

2 Document Information Document Name: ID: D6.3 Part 1.1 : Demonstration report for Two-Step State Estimation Prototype DEL_WP64_D63_Part11_two_step_state_estimation WP: 6 Task: 4 Revision: 4 Revision Date: 4/7/212 Author: M.Escribano, M. Kara, U. Buyukdagli, N. Machado Diffusion list STB, SSB, EC Approvals Authors Name Company Date Visa Miguel Escribano Mehmet Kara Umit Buyukdagli Nelio Machado REE TEIAS TEIAS REN Task Leader Miguel Escribano REE WP Leader Sylvain Leclerc RTE Partner Mehmet Kara TEIAS Partner Nelio Machado REN Partner Patricia Rousseau ULg Partner Fortunato Villella TE Partner Catalina Gómez AICIA Partner Antonio Gómez AICIA Partner Antonio de la Villa AICIA Documents history Revision Date Modification Author 21/6/212 First version 1 21/6/212 Addition of executive summary, formatting S. Leclerc 2 26/6/212 Inclusion of some comments from STB S. Leclerc M.Escribano, M. Kara, U. Buyukdagli, N. Machado Date: 4/7/212 Page: 2 DEL_WP64_D63_Part11_two_step_state_estimation

3 Document Information /6/212 Inclusion results of UCTE_TEIAS network tests N. Machado 3 2/7/212 Comments from STB, formatting S. Leclerc 4 4/7/212 Comments from SSB S. Leclerc Date: 4/7/212 Page: 3 DEL_WP64_D63_Part11_two_step_state_estimation

4 Table of content Executive Summary General overview of this document Test procedure description Redundancy level Quality of measurements Bad data Scenarios Results presentation and analysis Test Results TSO_RTEREEREN 14 LOW REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator LOW REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator LOW REDUNDANCY, HIGH NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection HIGH REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Date: 4/7/212 Page: 4 DEL_WP64_D63_Part11_two_step_state_estimation

5 HIGH REDUNDANCY, LOW NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection HIGH REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator UCTE_TEIAS 77 LOW REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator LOW REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator LOW REDUNDANCY, HIGH NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection IPS_UPS 12 LOW REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator State vs. estimations Date: 4/7/212 Page: 5 DEL_WP64_D63_Part11_two_step_state_estimation

6 Pseudomeasurments, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator LOW REDUNDANCY, HIGH NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection HIGH REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator HIGH REDUNDANCY, LOW NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurments, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator UCTE_TEIAS_HVDC 188 LOW REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator LOW REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Date: 4/7/212 Page: 6 DEL_WP64_D63_Part11_two_step_state_estimation

7 Performance of the estimator LOW REDUNDANCY, HIGH NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection HIGH REDUNDANCY, LOW NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator HIGH REDUNDANCY, LOW NOISE, BAD DATA SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator Bad data detection HIGH REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations Pseudomeasurements, estimations and exact values Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) Performance of the estimator General conclusions General conclusions for 3TSO_RTEREEREN network General conclusions for all the networks Summary References Date: 4/7/212 Page: 7 DEL_WP64_D63_Part11_two_step_state_estimation

8 Executive Summary This document describes the tests that have been performed on the two step state estimation prototype developed in the frame of Work Package 2. The tests have been carried out by the following testing team: Miguel Escribano from REE Mehmet Kara and Umit Buyukdagli from TEIAS Nelio Machado from REN. Four different system models, developed in the frame of task 6.3, have been used. The first one is a merging of three real-life synchronous snapshots from the French, Spanish and Portuguese systems (RTE, REE and REN). The second one is a model of the IPS-UPS system (Russia and neighbouring countries). The third one is a realistic model of European and Turkish systems with 27 TSOs. The last one is the European and Turkish systems, including 3 HVDC as tie lines (France-Spain, Greece-Italy, Denmark-Netherlands). The 4 models ensure that the prototype is tested under very different conditions: while the first one only consists in the interconnection of 3 TSOs with no loop, the last two networks are composed of 27 TSOs highly interconnected. The size of the test systems goes from 23 nodes for IPS-UPS to 92 nodes for UCTE+TEIAS. For each one of those 4 models, several runs have been performed, using different sets of parameters, in order to assess the behaviour of the prototype for various types of measurements sets: different levels of noise have been used to generate measurements from the load flow state, and different levels of redundancy have been used to determine the measurements density and localizations (a specific treatment has been applied to tie lines, which play a critical role in the algorithm). Additionally, some scenarios involve the introduction of large errors in measurements to assess the capability of the prototype to detect those errors as outliers and remove them from the input data. Finally, to check the robustness of the prototype to similar distributions of measurements, for each given level of noise and redundancy, 1 sets of measurements have been generated and run. As performance is not a challenge for this prototype, not more than it has been an objective in its implementation, all tests have been run standard computers: for instance an Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. Results are analysed through statistical indexes and histograms studying, in particular, the distribution of differences between the load flow state and the estimated state. Tests have shown the prototype generally behaves as expected, which also includes a degradation of results when facing bad data and highly noised or ill-placed measurements: Average deviation from the exact underlying state has been consistently low, including with cases with HVDCs as tie-lines, showing that they are correctly handled Its behaviour has been robust to the use of different measurement sets As expected, results showing largest deviation from the exact state are the ones from high noise, low redundancy. Inversely, low noise, high redundancy scenarios show very good results. Bad data have been effectively detected for some cases with low noise and high redundancy (24 errors out of 25 for REE-REN-RTE), but only partially for other, in particular for cases with high noise and low redundancy (13 errors out of 25 for REE- REN-RTE). Bad data detection degrades performances since additional iterations need to be performed Although this was not a specific challenge, computation times remain low (around 1s) for largest cases. However, in one case the introduction of bad data in UCTE+TEIAS network caused a numerical failure of the algorithm (singular matrix). Therefore further work could be devoted to make the method more robust to the presence of bad data. The feasibility of the approach is demonstrated, but further work would be needed to cope with a broader variety of real-life situations, for instance: Cases of divergence at the TSO level Date: 4/7/212 Page: 8 DEL_WP64_D63_Part11_two_step_state_estimation

9 Handling of unobservable islands Handling of separate islands at TSO level connected through another TSO Handling of topological errors Robustness to large measurement errors... Date: 4/7/212 Page: 9 DEL_WP64_D63_Part11_two_step_state_estimation

10 1. General overview of this document The goal of this document is to describe the tests that have been performed on the two step state estimation prototype developed in the frame of Work Package 2. Only scheme 1, corresponding to TSO level state estimations in the first step, is tested, and PMU measurements are not considered. The tests have been carried out on four different network models: French, spanish and portuguese electrical system (3TSO_RTEREEREN) Russian system (IPS_UPS) European system and turkish system (UCTE_TEIAS) European system and turkish system including inter-tsos HVDC links (UCTE_TEIAS_HVDC) The main characteristics of those systems in terms of size are collected in next table: 3TSO_RTE_REE_REN IPS_UPS UCTE_TEIAS UCTE_TEIAS_HVDC # Buses # Branches # Transformers # PST # HVDC 3 2. Test procedure description The procedure that has been followed to perform the tests is described in the document WP4. Running the tests. Guide to carry out the tests for state estimation prototype. As requested in tests specifications (deliverable D6.2 Specification of the methodology for prototypes validation [1]), for each network model described above, different scenarios have been generated, with different levels of redundancy and quality of measures (addition of a simple Gaussian noise, or introduction of bad data). In the next subsections, these variants are described in more details Redundancy level Next figure illustrates the localization of generated measurements for each one of the 2 different levels of redundancy that have been used: low redundancy and high redundancy. Date: 4/7/212 Page: 1 DEL_WP64_D63_Part11_two_step_state_estimation

11 2.2. Quality of measurements In all tests, measurements are generated from the load flow state of the system. Different levels of quality of the measurements set are simulated by adding a Gaussian noise to the exact value (generated from a chosen seed in order to be able to regenerate identical measurements sets). For each network model, two levels of noise (low and high) have been defined through values of standard deviation (Voltage, PQ injection, PQ flow) for each voltage level, as illustrated in next table. The three values of each cell correspond to the 3 voltage levels. In this study, standard deviations have been chosen equal for all 3 voltage levels, and for the measurements related to tie-lines and the rest of TSO network. 3TSOs UCTE+TEIAS UCTE+TEIAS+HV DC IPS/UPS Voltage.1;.1;.1.15;.15;.15.4;.4;.4.5;.5;.5 TIE LINES PQ injection.2;.2;.2.3;.3;.3.5;.5;.5.6;.6;.6 Low Noise PQ flow.15;.15;.15.25;.25;.25.45;.45;.45.55;.55;.55 Voltage.1;.1;.1.15;.15;.15.4;.4;.4.5;.5;.5 TSO PQ injection.2;.2;.2.3;.3;.3.5;.5;.5.6;.6;.6 PQ flow.15;.15;.15.25;.25;.25.45;.45;.45.55;.55;.55 Voltage.2;.2;.2.3;.3;.3.5;.5;.5.6;.6;.6 TIE LINES PQ injection.5;.5;.5.4;.4;.4.6;.6;.6.7;.7;.7 High Noise PQ flow.25;.25;.25.45;.45;.45.55;.55;.55.65;.65;.65 Voltage.2;.2;.2.3;.3;.3.5;.5;.5.6;.6;.6 TSO PQ injection.5;.5;.5.4;.4;.4.6;.6;.6.7;.7;.7 PQ flow.25;.25;.25.45;.45;.45.55;.55;.55.65;.65;.65 Table 1.1: standard deviations (p.u) Date: 4/7/212 Page: 11 DEL_WP64_D63_Part11_two_step_state_estimation

12 2.3. Bad data 2.4. Scenarios In dedicated scenarios, bad data (wrong measurements) have been included manually. Five measurements for voltage magnitude, five measurements for active power flow through several lines, five measurements for reactive power flow through the same lines, five measurements for active power injection and five measurements for reactive power injection. In following tests, the relative increment of the bad measurement compared to the original one is kept as constant when the measurements set is changed for a new state estimation. For each network model described in section 1, the following scenarios have been tested: Low redundancy, low noise scenario Low redundancy, high noise scenario Low redundancy, high noise, bad data scenario High redundancy, low noise scenario High redundancy, low noise, bad data scenario High redundancy, high noise scenario For each one of those 6 scenarios, 1 different seeds have been used to generate 1 different sets of noised measurements, in order to assess the robustness of the prototype to the use of different but similar sets of measurements Results presentation and analysis The results will be presented according to the next scheme: State vs. estimations The results of the Two Step State Estimator (voltage magnitude and angle) will be compared with original values of the load flow. A statistical analysis comparing phasors will be presented. The difference between two phasors needs to be used: the voltage phasor corresponding to each node and the voltage phasor corresponding to the slack node. In this case the magnitude of the complex difference is used. This is shown in the next figure. U 21 2 U 1 U U11 ( U 2 cos( 2) U1 cos( 1)) ( U 2 sin( 2) U1 sin( 1)) 1 Pseudomeasurements, estimations and exact values For all the measured values, differences between measurements, estimations and exact values will be analysed from a statistical point of view. Uncertainty of estimated values compared to measurements The difference between the standard deviation of the measurements and the standard deviation of estimations will be analyzed. Performance of the estimator The time spent in step one and step two will be analyzed Bad data detection will be assessed (only for scenarios that include them, the third one and the fifth one) Date: 4/7/212 Page: 12 DEL_WP64_D63_Part11_two_step_state_estimation

13 In order to perform a statistical analysis of the state estimation results, next indexes have been used to analyze differences between 2 sets of values (either measurements, estimated values, or exact values): Mean absolute error 1 MAE S S k 1 1 N N i 1 e ik Root mean square error RMSE 1 S S k 1 1 N N i1 e 2 ik Mean absolute percentage error 1 MAPE S S k 1 1 N N e 1 y ik i1 actual, ik Where S is the number of set of measurements (number of seeds), N is the number of measurements, e ik is the difference between the exact state y actual,ik and estimated state (voltage magnitude and angle). Next indexes will also be used for each seed and each scenario: Where is the realistic k th measurement, used as input for the estimation process, and calculated by adding Gaussian noise to the exact value of the measurements; is the exact measurement calculated from the initial state of the system; is the estimated measurement; k is the standard deviation associated to the k th measurement; m is the number of measurements being used for the specific scenario. While simply illustrates the quality of the inputs of the prototype, is the objective function we try to minimize, and represents the distance of the estimated state to the actual state, and is therefore a better measure of the quality of the solution. Different histograms will be used for the statistical analysis of different results that have been obtained. It is important to emphasize the huge amount of data that have been used. It is possible to show the information for each seed, for each voltage level, for each TSO, so the number of statistical charts that can be shown is huge. In this work only the most relevant and interesting results will be shown. Date: 4/7/212 Page: 13 DEL_WP64_D63_Part11_two_step_state_estimation

14 3. Test Results TSO_RTEREEREN LOW REDUNDANCY, LOW NOISE SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and slack bus are shown. The information is classified using histograms: Seed 1 16 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 greater than... s Seed 2 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 greater than... B ins Seed 1-Highest voltage level State-Estimations-Absolute difference-4kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 greater than... s Date: 4/7/212 Page: 14 DEL_WP64_D63_Part11_two_step_state_estimation

15 Seed 1-Second highest voltage level 5 State-Estimations-Absolute difference-38kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 greater than... s Seed 1-TSO 1 5 State-Estimations-Absolute difference-france-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 greater than... s Seed 1-TSO2 State-Estimations-Absolute difference-spain-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 greater than... s In the next table and figures, MAE, RMSE and MAPE indexes for each seed are reported. SEED MAE RMSE MAPE Date: 4/7/212 Page: 15 DEL_WP64_D63_Part11_two_step_state_estimation

16 State-Estimations-MAE (absolute differences) State-Estimations-RMSE (absolute differences) State-Estimations-MAPE (absolute differences) Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 8 Pseudomeasurements-Exact value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- histogram Pseudomeasurements-Estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 16 DEL_WP64_D63_Part11_two_step_state_estimation

17 SEED1 - Exact value.- Estimated values- histogram Exact value-estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Second highest voltage-histogram 7 Measurements-Exact value-38kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- TSO1-histogram 7 Measurements-Estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- TSO2-histogram Date: 4/7/212 Page: 17 DEL_WP64_D63_Part11_two_step_state_estimation

18 7 Measurements-Estimated value-spain E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram 8 Exact value-estimated value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1- Exact value.- Estimated values- TSO1- Histogram 8 Exact value-estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 18 DEL_WP64_D63_Part11_two_step_state_estimation

19 Most differences between measurements and exact values are in the range [1-3, 1-2 ] p.u, which is expected since this is the order of magnitude of the chosen standard deviation. On the other side, the estimated state is much closer to the exact values since more than half of the differences get lower than 1-3 p.u. As a consequence, the pattern of differences between measurements and estimated values is very close to the pattern of differences between measurements and exact values. One can notice that this behaviour is consistent in different TSOs and voltage levels. In the next charts and table MAE, RMSE and MAPE are shown for several differences (measurements, exact values, estimations). Again, they illustrate that as expected, estimated values get much closer to exact values than raw measurements. This behaviour is consistent for the 1 different measurements patterns that have been tested. Measurements-Exact value Measurements-Exact value MAE RMSE MAPE Measurements-Estimations Measurements-Estimations MAE RMSE 2 15 MAPE Exact value-estimations Exact value-estimations MAE RMSE MAPE Date: 4/7/212 Page: 19 DEL_WP64_D63_Part11_two_step_state_estimation

20 SEED Meas-Exact MAE RMSE MAPE SEED Meas-Estim MAE RMSE MAPE SEED Exact-Estim MAE RMSE MAPE In the next tables and charts indexes for measuring the quality of state estimation for each seed are shown. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Js Je Jm Indexes for state estimation Indexes for state estimation Js Jm Je Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram 1 Uncertainty-State Estimation-Measurement Estimations E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s SEED 1- type of measurement 1-histogram Date: 4/7/212 Page: 2 DEL_WP64_D63_Part11_two_step_state_estimation

21 35 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s SEED 1- type of measurement 3-histogram Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s SEED 1- TSO1-histogram 5 Uncertainty-State Estimation-Measurement Estimations-FRANCE E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s SEED 1- TSO2-histogram Date: 4/7/212 Page: 21 DEL_WP64_D63_Part11_two_step_state_estimation

22 8 Uncertainty-State Estimation-Measurement Estimations-SPAIN E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s SEED 1- Highest voltage level- histogram Uncertainty-State Estimation-Measurement Estimations-4kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s SEED 1- Second highest voltage level- histogram 8 Uncertainty-State Estimation-Measurement Estimations-38kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 greater than... s Date: 4/7/212 Page: 22 DEL_WP64_D63_Part11_two_step_state_estimation

23 Execution Time Execution Time Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. Time Execution/SEED Maximum execution time (step1) (s) Execution time (step2) (s) Total time (s) Seeds Execution time Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time 1.4 Execution time (step2) Execution Time (step2) (s) Seeds One can conclude that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: below 5s in the worst case. Date: 4/7/212 Page: 23 DEL_WP64_D63_Part11_two_step_state_estimation

24 LOW REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified using histograms. Seed 1 14 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 greater than s Seed 2 25 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 greater than... s Seed 1-Highest voltage level 25 State-Estimations-Absolute difference-4kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 greater than s Date: 4/7/212 Page: 24 DEL_WP64_D63_Part11_two_step_state_estimation

25 Seed 1-Second highest voltage level 8 State-Estimations-Absolute difference-38kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 greater than... s Seed 1- TSO1 9 State-Estimations-Absolute difference-france-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 greater than... s Seed 1- TSO2 State-Estimations-Absolute difference-spain-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 greater than... s In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE RMSE MAPE Date: 4/7/212 Page: 25 DEL_WP64_D63_Part11_two_step_state_estimation

26 State-Estimations-MAE (absolute differences) State-Estimations-RMSE (absolute differences) MAE RMSE State-Estimations-MAPE (absolute differences) MAPE Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 6 Pseudomeasurements-Exact value-complete System E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- histogram Pseudomeasurements-Estimated value-complete System E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 26 DEL_WP64_D63_Part11_two_step_state_estimation

27 Frecuencia SEED1 - Exact value.- Estimated values- histogram 8 Exact value-estimated value-complete System E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Highest voltage-histogram 6 Measurements-Exact value-4kv E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Second highest voltage-histogram 5 Measurements-Exact value-38kv E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... Clase SEED1 - Measurements- Estimated value- TSO1-histogram 5 Measurements-Estimated value-france E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 27 DEL_WP64_D63_Part11_two_step_state_estimation

28 SEED1 - Measurements- Estimated value- TSO2-histogram 7 Measurements-Estimated value-spain E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram 8 Exact value-estimated value-4kv E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s SEED1- Exact value.- Estimated values- TSO1- Histogram 7 Exact value-estimated value-france E-6 1.E-5 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 28 DEL_WP64_D63_Part11_two_step_state_estimation

29 In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). Again, they illustrate that as expected, estimated values get much closer to exact values than raw measurements. This behaviour is consistent for the 1 different measurements patterns that have been tested. Measurements-Exact value Measurements-Exact value MAE RMSE MAPE Exact value-estimations Exact value-estimations MAE RMSE MAPE Measurements-Estimations Measurements-Estimations MAE RMSE MAPE SEED Meas-Exact MAE RMSE MAPE SEED Meas-Estim MAE RMSE MAPE SEED Exact-Estim MAE RMSE MAPE In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. In the next tables and charts indexes for measuring the quality of state estimation for each seed are shown. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Js Je Jm Date: 4/7/212 Page: 29 DEL_WP64_D63_Part11_two_step_state_estimation

30 Indexes for state estimation Indexes for state estimation Js Jm Je Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram 1 Uncertainty-State Estimation-Measurement Estimations E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 1-histogram 35 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 3-histogram Date: 4/7/212 Page: 3 DEL_WP64_D63_Part11_two_step_state_estimation

31 35 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO1-histogram Uncertainty-State Estimation-Measurement Estimations-FRANCE E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO2-histogram Uncertainty-State Estimation-Measurement Estimations-SPAIN E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Highest voltage level- histogram Date: 4/7/212 Page: 31 DEL_WP64_D63_Part11_two_step_state_estimation

32 8 Uncertainty-State Estimation-Measurement Estimations-4kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Second highest voltage level- histogram Uncertainty-State Estimation-Measurement Estimations-38kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. SEED Maximum Execution Time (step1)(s) Execution Time (step 2) (s) Total Time (s) Date: 4/7/212 Page: 32 DEL_WP64_D63_Part11_two_step_state_estimation

33 Execution Time Execution Time 6 Execution time-step 1- Step 2-Total Maximum Execution Time (step1)(s) Execution Time (step 2) (s) Total Time (s) Seeds 1.6 Execution time Execution Time (step 2) (s) Seeds One can conclude that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: below 5s in the worst case. Date: 4/7/212 Page: 33 DEL_WP64_D63_Part11_two_step_state_estimation

34 LOW REDUNDANCY, HIGH NOISE, BAD DATA SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified using histograms. Seed 1 16 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 2 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-Highest voltage level State-Estimations-Absolute difference-4kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Date: 4/7/212 Page: 34 DEL_WP64_D63_Part11_two_step_state_estimation

35 Seed 1-Second highest voltage level State-Estimations-Absolute difference-38kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO 1 State-Estimations-Absolute difference-france-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO2 State-Estimations-Absolute difference-spain-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE RMSE MAPE Date: 4/7/212 Page: 35 DEL_WP64_D63_Part11_two_step_state_estimation

36 State-Estimations-MAE (absolute differences) State-Estimations-RMSE (absolute differences) MAE RMSE State-Estimations-MAPE (absolute differences) MAPE Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 7 Pseudomeasurements-Exact value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- histogram Pseudomeasurements-Estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 36 DEL_WP64_D63_Part11_two_step_state_estimation

37 SEED1 - Exact value- Estimated values- histogram 9 Exact value-estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Highest voltage-histogram 7 Measurements-Exact value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Second highest voltage-histogram Measurements-Exact value-38kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- TSO1-histogram 8 Measurements-Estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 37 DEL_WP64_D63_Part11_two_step_state_estimation

38 SEED1 - Measurements- Estimated value- TSO2-histogram Measurements-Estimated value-spain E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value- Estimated values- Highest voltage- Histogram Exact value-estimated value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1- Exact value- Estimated values- TSO1- Histogram Exact value-estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 38 DEL_WP64_D63_Part11_two_step_state_estimation

39 Most differences between measurements and exact values are in the range [1-3, 1-2 ] p.u, and a large amount is in the range [1-2, 1-1 ] p.u, which is expected since this is the order of magnitude of the chosen standard deviation. On the other side, the estimated state is much closer to the exact values, with a shift of the differences to the lower classes, with almost no difference higher than 1-2. As a consequence, the pattern of differences between measurements and estimated values is very close to the pattern of differences between measurements and exact values. One can notice that this behaviour is consistent in different TSOs and voltage levels. In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). Again, they illustrate that as expected, estimated values get much closer to exact values than raw measurements. This behaviour is consistent for the 1 different measurements patterns that have been tested. Measurements-Exact value Measurements-Exact value MAE RMSE MAPE Measurements-Estimations Measurements-Estimations MAE RMSE MAPE Exact value-estimations Exact value-estimations MAE RMSE MAPE SEED Meas-Exact MAE RMSE MAPE SEED Meas-Estim MAE RMSE MAPE SEED Exact-Estim MAE RMSE MAPE Date: 4/7/212 Page: 39 DEL_WP64_D63_Part11_two_step_state_estimation

40 In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Js Je Jm Indexes for state estimation Indexes for state estimation Js Jm Je Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram Uncertainty-State Estimation-Measurement Estimations E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 1-histogram Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 3-histogram Date: 4/7/212 Page: 4 DEL_WP64_D63_Part11_two_step_state_estimation

41 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO1-histogram Uncertainty-State Estimation-Measurement Estimations-FRANCE E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO2-histogram 8 Uncertainty-State Estimation-Measurement Estimations-SPAIN E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Highest voltage level- histogram Date: 4/7/212 Page: 41 DEL_WP64_D63_Part11_two_step_state_estimation

42 8 Uncertainty-State Estimation-Measurement Estimations-4kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Second highest voltage level- histogram Uncertainty-State Estimation-Measurement Estimations-38kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. SEED Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Date: 4/7/212 Page: 42 DEL_WP64_D63_Part11_two_step_state_estimation

43 Execution time Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Execution time (step2) Execution Time (step2) (s) One can see that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: around 11s in the worst case Bad data detection Several measurements have been modified to analyze bad data detection. Five changes for each type measurement (25 changes as a whole): Voltage measurements (type 1): 18% Active power flow through a branch (type 3): 19% Reactive power flow through a branch (type 4): 19% Active power injection (type 7): 2% Reactive power injection (type 8): 2% In the next table, it can be seen how the bad data have been detected, using maximum normalized residual approach. Initial and corrected value for the measurements of bad data, the type of measurement and the TSO are shown too. Only 13 out of the 25 bad data have been detected. This is explained by the combination of factors that make the detection difficult: redundancy is low, hence there are fewer data to question the validity of these bad measurements, and noise is high, making the distinction between bad measurement and simple noised measurement more difficult. Date: 4/7/212 Page: 43 DEL_WP64_D63_Part11_two_step_state_estimation

44 Iteration Max. Normalized residual Initial value Corrected value Type of measurement TSO Date: 4/7/212 Page: 44 DEL_WP64_D63_Part11_two_step_state_estimation

45 HIGH REDUNDANCY, LOW NOISE SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified using histograms. Seed 1 16 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 2 2 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-Highest voltage level State-Estimations-Absolute difference-4kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Date: 4/7/212 Page: 45 DEL_WP64_D63_Part11_two_step_state_estimation

46 Seed 1-Second highest voltage level State-Estimations-Absolute difference-38kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO 1 State-Estimations-Absolute difference-france-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO2 State-Estimations-Absolute difference-spain-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE E E E-5 RMSE MAPE Date: 4/7/212 Page: 46 DEL_WP64_D63_Part11_two_step_state_estimation

47 State-Estimations-MAE (absolute differences) State-Estimations-RMSE (absolute differences) MAE RMSE State-Estimations-MAPE (absolute differences) MAPE Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 16 Pseudomeasurements-Exact value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- histogram Pseudomeasurements-Estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 47 DEL_WP64_D63_Part11_two_step_state_estimation

48 SEED1 - Exact value.- Estimated values- histogram 2 Exact value-estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Highest voltage-histogram 14 Measurements-Exact value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Second highest voltage-histogram 14 Measurements-Exact value-38kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- TSO1-histogram Measurements-Estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 48 DEL_WP64_D63_Part11_two_step_state_estimation

49 SEED1 - Measurements- Estimated value- TSO2-histogram Measurements-Estimated value-spain E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram 18 Exact value-estimated value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1- Exact value.- Estimated values- TSO1- Histogram 18 Exact value-estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 49 DEL_WP64_D63_Part11_two_step_state_estimation

50 Most differences between measurements and exact values are in the range [1-3, 1-2 ] p.u, which is expected since this is the order of magnitude of the chosen standard deviation. On the other side, the estimated state is much closer to the exact values, with a shift towards the [1-4, 1-3 ] p.u class and no more differences higher than 1-2 p.u. As a consequence, the pattern of differences between measurements and estimated values is very close to the pattern of differences between measurements and exact values. One can notice that this behaviour is consistent in different TSOs and voltage levels. In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). Again, they illustrate that as expected, estimated values get much closer to exact values than raw measurements. This behaviour is consistent for the 1 different measurements patterns that have been tested. Measurements-Exact value Measurements-Exact value MAE RMSE MAPE Measurements-Estimations Measurements-Estimations MAE RMSE MAPE Exact value-estimations Exact value-estimations MAE RMSE MAPE SEED Meas-Exact MAE RMSE MAPE SEED Meas-Estim MAE RMSE 2.459E E E E E E-5 MAPE SEED Exact-Estim MAE RMSE MAPE Date: 4/7/212 Page: 5 DEL_WP64_D63_Part11_two_step_state_estimation

51 In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Js Je Jm Indexes for state estimation Indexes for state estimation Js Jm Je Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram 25 Uncertainty-State Estimation-Measurement Estimations E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 1-histogram Date: 4/7/212 Page: 51 DEL_WP64_D63_Part11_two_step_state_estimation

52 7 Uncertainty-State Estimation-Measurement Estimations- Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 3-histogram 8 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO1-histogram 25 Uncertainty-State Estimation-Measurement Estimations-FRANCE E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO2-histogram Date: 4/7/212 Page: 52 DEL_WP64_D63_Part11_two_step_state_estimation

53 25 Uncertainty-State Estimation-Measurement Estimations-SPAIN E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Highest voltage level- histogram 25 Uncertainty-State Estimation-Measurement Estimations-4kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Second highest voltage level- histogram 25 Uncertainty-State Estimation-Measurement Estimations-38kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s Date: 4/7/212 Page: 53 DEL_WP64_D63_Part11_two_step_state_estimation

54 Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. SEED Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Execution time Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Execution time (step2) Execution Time (step2) (s) One can observe that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: below 1s in the worst case. Date: 4/7/212 Page: 54 DEL_WP64_D63_Part11_two_step_state_estimation

55 HIGH REDUNDANCY, LOW NOISE, BAD DATA SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified using histograms. Seed 1 18 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 2 2 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 y mayor... s Seed 1-Highest voltage level State-Estimations-Absolute difference-4kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Date: 4/7/212 Page: 55 DEL_WP64_D63_Part11_two_step_state_estimation

56 Seed 1-Second highest voltage level State-Estimations-Absolute difference-38kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO 1 State-Estimations-Absolute difference-france-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO2 State-Estimations-Absolute difference-spain-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE E E E-5 RMSE MAPE Date: 4/7/212 Page: 56 DEL_WP64_D63_Part11_two_step_state_estimation

57 State-Estimations-MAE (absolute differences) State-Estimations-RMSE(absolute differences) MAE RMSE State-Estimations-MAPE (absolute differences) MAPE Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 16 Pseudomeasurements-Exact value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- histogram Pseudomeasurements-Estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 57 DEL_WP64_D63_Part11_two_step_state_estimation

58 SEED1 - Exact value.- Estimated values- histogram 2 Exact value-estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Highest voltage-histogram 14 Measurements-Exact value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Second highest voltage-histogram 14 Measurements-Exact value-38kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- TSO1-histogram 16 Measurements-Estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 58 DEL_WP64_D63_Part11_two_step_state_estimation

59 SEED1 - Measurements- Estimated value- TSO2-histogram 16 Measurements-Estimated value-spain E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram 18 Exact value-estimated value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1- Exact value.- Estimated values- TSO1- Histogram 18 Exact value-estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 59 DEL_WP64_D63_Part11_two_step_state_estimation

60 Most differences between measurements and exact values are in the range [1-3, 1-2 ] p.u, which is expected since this is the order of magnitude of the chosen standard deviation. On the other side, the estimated state is much closer to the exact values, with a shift towards the [1-4, 1-3 ] p.u class and no more differences higher than 1-2 p.u. As a consequence, the pattern of differences between measurements and estimated values is very close to the pattern of differences between measurements and exact values. One can notice that this behaviour is consistent in different TSOs and voltage levels. In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). Again, they illustrate that as expected, estimated values get much closer to exact values than raw measurements. This behaviour is consistent for the 1 different measurements patterns that have been tested. Measurements-Exact value Measurements-Exact value MAE RMSE MAPE Measurements-Estimations Measurements-Estimations MAE RMSE MAPE Exact value-estimations Exact value-estimations MAE RMSE MAPE SEED Meas-Exact MAE RMSE MAPE SEED Meas-Estim MAE RMSE MAPE SEED Exact-Estim MAE RMSE MAPE Date: 4/7/212 Page: 6 DEL_WP64_D63_Part11_two_step_state_estimation

61 In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Js Je Jm Indexes for state estimation Js Jm Indexes for state estimation Je Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram 25 Uncertainty-State Estimation-Measurement Estimations E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 1-histogram Date: 4/7/212 Page: 61 DEL_WP64_D63_Part11_two_step_state_estimation

62 7 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 3-histogram 8 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO1-histogram 25 Uncertainty-State Estimation-Measurement Estimations-FRANCE E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO2-histogram Date: 4/7/212 Page: 62 DEL_WP64_D63_Part11_two_step_state_estimation

63 25 Uncertainty-State Estimation-Measurement Estimations-SPAIN E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Highest voltage level- histogram 25 Uncertainty-State Estimation-Measurement Estimations-4kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Second highest voltage level- histogram 25 Uncertainty-State Estimation-Measurement Estimations-38kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s Date: 4/7/212 Page: 63 DEL_WP64_D63_Part11_two_step_state_estimation

64 Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. SEED Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Execution time Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Execution Time (step2) (s) Execution Time (step2) (s) One can conclude that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time is however significantly higher than for other scenarios, due to the additional iterations performed to delete bad measurements in step 1. Total execution times almost reaches 1 minute Bad data detection Several measurements have been modified to analyze bad data detection. Five changes for each type measurement (25 changes as a whole): Voltage measurements (type 1): 18% Active power flow through a branch (type 3): 19% Reactive power flow through a branch (type 4): 19% Active power injection (type 7): 2% Reactive power injection (type 8): 2% Date: 4/7/212 Page: 64 DEL_WP64_D63_Part11_two_step_state_estimation

65 In the next table, it can be seen how the bad data have been detected, using maximum normalized residual approach. Initial and corrected value for the measurements of bad data, the type of measurement and the TSO are shown too. Iteration Max. Normalized residual Initial value Corrected value Type of measurement TSO out of 25 errors have been correctly detected, showing very good performance of this mechanism. This behaviour was expected due to factors making the detection easier: low noise emphasizes bad data as outliers, and high redundancy makes easier the detection of local inconsistency. Date: 4/7/212 Page: 65 DEL_WP64_D63_Part11_two_step_state_estimation

66 HIGH REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified using histograms. Seed 1 16 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 2 16 State-Estimations-Absolute difference for voltage-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-Highest voltage level State-Estimations-Absolute difference-4kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-Second highest voltage level Date: 4/7/212 Page: 66 DEL_WP64_D63_Part11_two_step_state_estimation

67 State-Estimations-Absolute difference-38kv-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO 1 7 State-Estimations-Absolute difference-france-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s Seed 1-TSO2 State-Estimations-Absolute difference-spain-seed E-7 5.E-7 1.E-6 5.E-6 1.E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 greater than... s In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE RMSE MAPE Date: 4/7/212 Page: 67 DEL_WP64_D63_Part11_two_step_state_estimation

68 State-Estimations-MAE (absolute differences) MAE State-Estimations-RMSE (absolute differences) State-Estimations-MAPE (absolute differences) RMSE MAPE Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 14 Pseudomeasurements-Exact value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Estimated value- histogram Date: 4/7/212 Page: 68 DEL_WP64_D63_Part11_two_step_state_estimation

69 18 Pseudomeasurements-Estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value.- Estimated values- histogram 16 Exact value-estimated value-complete System E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 y mayor... s SEED1 - Measurements- Exact value- Highest voltage-histogram 14 Measurements-Exact value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Measurements- Exact value- Second highest voltage-histogram 14 Measurements-Exact value-38kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Date: 4/7/212 Page: 69 DEL_WP64_D63_Part11_two_step_state_estimation

70 SEED1 - Measurements- Estimated value- TSO1-histogram 16 Measurements-Estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 y mayor... s SEED1 - Measurements- Estimated value- TSO2-histogram 18 Measurements-Estimated value-spain E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram 14 Exact value-estimated value-4kv E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s SEED1- Exact value.- Estimated values- TSO1- Histogram Date: 4/7/212 Page: 7 DEL_WP64_D63_Part11_two_step_state_estimation

71 14 Exact value-estimated value-france E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 greater than... s Most differences between measurements and exact values are in the range [1-3, 1-2 ] p.u, which is expected since this is the order of magnitude of the chosen standard deviation. On the other side, the estimated state is much closer to the exact values, with a shift towards the [1-4, 1-3 ] p.u class and no more differences higher than 1-2 p.u. As a consequence, the pattern of differences between measurements and estimated values is very close to the pattern of differences between measurements and exact values. One can notice that this behaviour is consistent in different TSOs and voltage levels. In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). Again, they illustrate that as expected, estimated values get much closer to exact values than raw measurements. This behaviour is consistent for the 1 different measurements patterns that have been tested. Measurements-Exact value Measurements-Exact value MAE RMSE.19 MAPE Measurements-Estimations Measurements-Exact value MAE RMSE.19 MAPE Date: 4/7/212 Page: 71 DEL_WP64_D63_Part11_two_step_state_estimation

72 Exact value-estimations Exact value-estimations MAE RMSE.19 MAPE In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Meas-Exact MAE RMSE MAPE SEED Meas-Estim MAE RMSE MAPE SEED Exact-Estim MAE RMSE MAPE Indexes for state estimation Indexes for state estimation Js Jm Je Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram Date: 4/7/212 Page: 72 DEL_WP64_D63_Part11_two_step_state_estimation

73 3 Uncertainty-State Estimation-Measurement Estimations E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 1-histogram 7 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- type of measurement 3-histogram 7 Uncertainty-State Estimation-Measurement Estimations-Type E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO1-histogram Date: 4/7/212 Page: 73 DEL_WP64_D63_Part11_two_step_state_estimation

74 25 Uncertainty-State Estimation-Measurement Estimations-FRANCE E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- TSO2-histogram 25 Uncertainty-State Estimation-Measurement Estimations-SPAIN E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Highest voltage level- histogram 25 Uncertainty-State Estimation-Measurement Estimations-4kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s SEED 1- Second highest voltage level- histogram Date: 4/7/212 Page: 74 DEL_WP64_D63_Part11_two_step_state_estimation

75 25 Uncertainty-State Estimation-Measurement Estimations-38kV E-5 5.E-5 1.E-4 5.E-4 1.E-3 5.E-3 1.E-2 5.E-2 greater than... s Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E655, 2.33GHz, 2Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. SEED Maximum Execution Tim Execution Time (step2) ( Total Time Execution time Maximum Execution Time (step1) (s) Execution Time (step2) (s) Total Time Execution Time (step2) (s) Execution Time (step2) (s) Date: 4/7/212 Page: 75 DEL_WP64_D63_Part11_two_step_state_estimation

76 One can conclude that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: below 1s in the worst case. Date: 4/7/212 Page: 76 DEL_WP64_D63_Part11_two_step_state_estimation

77 3.2. UCTE_TEIAS LOW REDUNDANCY, LOW NOISE SCENARIO State vs. estimations It is shown the difference between the original values of voltages and angles (load flow) and the state estimation values. The information is classified using histograms: Seed 1 35 State-Estimations-Absolute difference for voltage - Seed s 35 State-Estimations-Absolute difference for Angle - Seed s Date: 4/7/212 Page: 77 DEL_WP64_D63_Part11_two_step_state_estimation

78 Seed 2 3 State-Estimations-Absolute difference for voltage - Seed s 3 State-Estimations-Absolute difference for Angle - Seed s Seed 1-Highest voltage level State-Estimations-Absolute difference for voltage 38kV - Seed s Date: 4/7/212 Page: 78 DEL_WP64_D63_Part11_two_step_state_estimation

79 35 State-Estimations-Absolute difference for Angle 38kV - Seed s Seed 1-Second highest voltage level 12 State-Estimations-Absolute difference for voltage 22kV - Seed s State-Estimations-Absolute difference for Angle 22kV - Seed s Date: 4/7/212 Page: 79 DEL_WP64_D63_Part11_two_step_state_estimation

80 Seed 1- France TSO 6 State-Estimations-Absolute difference for voltage FRANCE - Seed s State-Estimations-Absolute difference for Angle FRANCE - Seed s Seed 1- Spain TSO 3 State-Estimations-Absolute difference for voltage SPAIN- Seed s Date: 4/7/212 Page: 8 DEL_WP64_D63_Part11_two_step_state_estimation

81 State-Estimations-Absolute difference for Angle SPAIN - Seed s The statistical evaluation of estimations for all seeds was computed as follow: Total MAE, RMSE, MAPE 1, In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE,167672, ,178967, , ,163627,176351,1658, , RMSE,452659, ,618745, , , , , ,47113, MAPE, , , , , , , , , , State-Estimations-MAE Seed Date: 4/7/212 Page: 81 DEL_WP64_D63_Part11_two_step_state_estimation

82 .7 State-Estimations-RMSE Seed 5. State-Estimations-MAPE Seed Some particular cases were deeply analysed to understand the reason why so many indexes have values outside the mean. For example, using seed 5 the high MAPE values were calculated for the following measurements: Date: 4/7/212 Page: 82 DEL_WP64_D63_Part11_two_step_state_estimation

83 type exact meas estimate abs(error) MAPE 4 -,7449 -, ,26292, ,8 8 -,7449 -,7435 -,26292, ,8 4 -,7286 -, ,258337, ,6 8 -,7286 -, ,258337, ,6 4 -,78 -,7733 -,42383, ,4 3,117,118 -,1654, ,7 4,12573, ,18763, ,2 4,31,31 -,198, ,1 4,1,1 -,8,9 9, 4 -,164 -,162,28, ,8 4 -,45 -,45,136, ,2 4 -,41 -,42,1327, ,6 4,381,387 -,5526, ,8 4,2742,272,17418, ,2 4 -,874 -,8162 -,99962, ,1 4 -,362 -,362,1596, ,1 4,6,6,1581, , Most of the high MAPE values are type 4 measurements (reactive power flow through a branch) and some type 8 measurements (reactive power injection into an electrical node). Looking to these branches the active powerflow is less than 1MW and it appears to be a problem to compute small flows of reactive power. Date: 4/7/212 Page: 83 DEL_WP64_D63_Part11_two_step_state_estimation

84 Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 25 Pseudomeasurements - Exact Value - Complete System - Seed s SEED1 - Measurements- Estimated value- histogram 3 25 Pseudomeasurements - Estimated value - Complete System - Seed s SEED1 - Exact value.- Estimated values- histogram 3 Exact value - Estimated value - Complete System - Seed s Date: 4/7/212 Page: 84 DEL_WP64_D63_Part11_two_step_state_estimation

85 SEED1 - Measurements- Exact value- Highest voltage-histogram Pseudomeasurements - Exact Value - 38kV- Seed s SEED1 - Measurements- Exact value- Second highest voltage-histogram 12 Pseudomeasurements - Exact Value - 22kV- Seed s SEED1 - Measurements- Estimated value- TSO1-histogram 6 Pseudomeasurements - Estimated value - FRANCE - Seed s SEED1 - Measurements- Estimated value- TSO2-histogram Date: 4/7/212 Page: 85 DEL_WP64_D63_Part11_two_step_state_estimation

86 3 Pseudomeasurements - Estimated value - SPAIN - Seed s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram Exact value - Estimated value - 38kV - Seed s SEED1- Exact value.- Estimated values- TSO1- Histogram Exact value - Estimated value - FRANCE - Seed s Date: 4/7/212 Page: 86 DEL_WP64_D63_Part11_two_step_state_estimation

87 In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). They illustrate that as expected, estimated values get much closer to exact values (see last chart) than raw measurements (see second chart). This behaviour is consistent for the 1 different measurements patterns that have been tested. Meas-Exact MAE,34745,35117,35165,35127,34857,34745,34976,35225,34987,34777 RMSE,68277,68897,69347,69174,68662,68277,68813,6919,68693,68122 MAPE, , ,171654, , , , ,179324, , Meas-Estim MAE,35215,3682,3738,35215,353,35691,3732,36171,3653,35532 RMSE,69843,74778,85797,69843,7135,7513,83721,75125,76374,7114 MAPE 1, , , , , , , , , , Exact-Estim MAE,16767,16511,1781,15694,15626,16362,17635,1658,16973,16273 RMSE,45266,43773,6187,34289,38165,44615,57627,44218,471,3789 MAPE, , , , , , ,41739, , , In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. Date: 4/7/212 Page: 87 DEL_WP64_D63_Part11_two_step_state_estimation

88 SEED Js 932, , , , , , , , , ,13 Je 56, , ,311 89,23 185, , , , , ,77 Jm 9339, , ,2 9331, , , , ,94 115, , Indexes for state estimation 3 Indexes for state estimation Js Jm 15 1 Je Seed Seed Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- histogram Uncertainty-State-Estimations--Measurements-Complete System s SEED 1- type of measurement 1-histogram Date: 4/7/212 Page: 88 DEL_WP64_D63_Part11_two_step_state_estimation

89 Uncertainty-State-Estimations--Measurements-Type s SEED 1- type of measurement 3-histogram Uncertainty-State-Estimations--Measurements-Type s SEED 1- TSO1-histogram 7 Uncertainty-State-Measurements-Estimations-FRANCE s SEED 1- TSO2-histogram Date: 4/7/212 Page: 89 DEL_WP64_D63_Part11_two_step_state_estimation

90 3 Uncertainty-State-Measurements-Estimations-SPAIN s SEED 1- Highest voltage level- histogram 16 Uncertainty-State-Measurements-Estimations-38kV s SEED 1- Second highest voltage level- histogram Date: 4/7/212 Page: 9 DEL_WP64_D63_Part11_two_step_state_estimation

91 25 Uncertainty-State-Measurements-Estimations-22kV s Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E84, 3.GHz, 4Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. Time Execution/SEED Maximum execution time (step1) [s] Execution time (step2) [s] Total time [s] ,8271 3,8762 3,7935 3,7765 3,793 3,7672 3,7662 3,7948 3,7819 3,7792,763,3197,4659,7397,4645,4619,7585,3311,3231,7572 4,591 4,1959 4,2594 4,5162 4,2576 4,2291 4,5248 4,1259 4,15 4,5364 Date: 4/7/212 Page: 91 DEL_WP64_D63_Part11_two_step_state_estimation

92 [s] [s] 5, 4,5 4, 3,5 3, 2,5 2, 1,5 1,,5, Execution time Seeds Maximum execution time (step1) [s] Execution time (step2) [s] Total time [s],9,8,7,6,5,4,3,2,1, Execution time (step2) Seeds One can conclude that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: below 5s in the worst case. Date: 4/7/212 Page: 92 DEL_WP64_D63_Part11_two_step_state_estimation

93 LOW REDUNDANCY, HIGH NOISE SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified using histograms. Seed 1 Voltage complete system 4 State-Estimations-Absolute difference for voltage - Seed s Seed 1 Angle complete system 3 State-Estimations-Absolute difference for Angle - Seed s Date: 4/7/212 Page: 93 DEL_WP64_D63_Part11_two_step_state_estimation

94 Seed 1-Highest voltage level State-Estimations-Absolute difference for voltage 38kV - Seed s State-Estimations-Absolute difference for Angle - 38kV- Seed s Seed 1-Second highest voltage level State-Estimations-Absolute difference for voltage 22kV - Seed s Date: 4/7/212 Page: 94 DEL_WP64_D63_Part11_two_step_state_estimation

95 12 State-Estimations-Absolute difference for Angle - 22kV- Seed s Seed 1- TSO State-Estimations-Absolute difference for voltage FRANCE - Seed s 7 State-Estimations-Absolute difference for Angle - FRANCE- Seed s Date: 4/7/212 Page: 95 DEL_WP64_D63_Part11_two_step_state_estimation

96 Seed 1- TSO2 3 State-Estimations-Absolute difference for voltage SPAIN - Seed s 45 State-Estimations-Absolute difference for Angle - SPAIN- Seed s The total statistical indexes are the follows. Total MAE, RMSE, MAPE 1, In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE,2673,27769,298477,26727,2697,27683,3297,274923,28879,27339 RMSE,61,79257,149782,67,686361,82731,18937,7729,8336,67387 MAPE 1, , , , , , , , ,2392-1, Date: 4/7/212 Page: 96 DEL_WP64_D63_Part11_two_step_state_estimation

97 ,31,3,29 State-Estimations-MAE,12,1 State-Estimations-RMSE,28,8,27,26,25,6,4,24,2, Seed, Seed State-Estimations-MAPE Seed Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram 25 2 Pseudomeasurements - Exact Value - Complete system- Seed s SEED1 - Measurements- Estimated value- histogram Pseudomeasurements - Estimated value - Complete system - Seed s Date: 4/7/212 Page: 97 DEL_WP64_D63_Part11_two_step_state_estimation

98 SEED1 - Exact value.- Estimated values- histogram Exact value - Estimated value - Complete system - Seed s SEED1 - Measurements- Exact value- Highest voltage-histogram 7 Pseudomeasurements - Exact Value - 38kV - Seed s SEED1 - Measurements- Exact value- Second highest voltage-histogram 12 Pseudomeasurements - Exact Value - 22kV - Seed s Date: 4/7/212 Page: 98 DEL_WP64_D63_Part11_two_step_state_estimation

99 SEED1 - Measurements- Estimated value- TSO1-histogram 6 Pseudomeasurements - Exact Value - FRANCE - Seed s SEED1 - Measurements- Estimated value- TSO2-histogram 3 Pseudomeasurements - Estimated value - SPAIN - Seed s SEED1 - Exact value.- Estimated values- Highest voltage- Histogram Exact value - Estimated value - 38kV - Seed s Date: 4/7/212 Page: 99 DEL_WP64_D63_Part11_two_step_state_estimation

100 SEED1- Exact value.- Estimated values- TSO1- Histogram 8 Exact value - Estimated value - FRANCE - Seed s In the next charts and table it is shown MAE, RMSE and MAPE for several differences (measurements, exact values, estimations). They illustrate that as expected, estimated values get much closer to exact values (last chart) than raw measurements (second chart). This behaviour is consistent for the 1 different measurements patterns that have been tested.,14 Measurements-Exact value,375 Measurements-Exact value,12,1,37,8,6,4 MAE RMSE,365,36 MAPE,2,355, Seed, Seed,18,16,14,12,1,8,6,4,2, Measurements-Estimations value Seed MAE RMSE Measurements-Estimations value Seed MAPE,12,1,8,6,4,2, Measurements-Estimations value Seed MAE RMSE Measurements-Estimations value Seed MAPE Date: 4/7/212 Page: 1 DEL_WP64_D63_Part11_two_step_state_estimation

101 Meas-Exact MAE,64451,6478,64828,64699,64282,6411,64567,64988,6454,6472 RMSE,132632,13229,133252,132733,131977,13137,132451,132659,1324,13769 MAPE,364431, , ,369931, , ,3782,372465,364124,36123 Meas-Estim MAE,66832,6716,69163,65262,65184,66623,69366,66992,6656,65977 RMSE,145281,145114,161474,13588,139168,146395,16341,144318,145187, MAPE 1, , , , , , , , , , Exact-Estim MAE,27899,27761,29848,2673,2691,2768,3291,27492,2888,27339 RMSE,79326,7926,14978,61,68636,8273,18937,773,8331,6739 MAPE, , , , , , , , ,2392-1, In the next tables and charts it is shown indexes for measuring the quality of state estimation for each seed. Again, is consistently much lower than by 1 order of magnitude, which shows that as expected, estimated values get much closer to exact values than raw measurements. SEED Js 932, , , , , ,6 9282, , ,59 911,1 Je 1681, , ,1 979,1 1283, , , , ,3 1223, Jm 1136, ,78 199,1 9428, , ,53 116,1 159,79 175, ,53 14 Indexes for state estimation 35 Indexes for state estimation Js Jm 2 15 Je Seed Seed Uncertainty among state estimations and measurement estimations (standard deviation for estimated values and measurements) In the next figure it is shown the histograms for the difference between standard deviation for measurements and standard deviation for estimations. SEED 1- complete system histogram 14 Uncertainty-State-Measurements-Estimations s Date: 4/7/212 Page: 11 DEL_WP64_D63_Part11_two_step_state_estimation

102 SEED 1- type of measurement 1-histogram Uncertainty-State-Measurements-Estimations-type s SEED 1- type of measurement 3-histogram Uncertainty-State-Measurements-Estimations-type s SEED 1- TSO1-histogram Uncertainty-State-Measurements-Estimations-FRANCE s Date: 4/7/212 Page: 12 DEL_WP64_D63_Part11_two_step_state_estimation

103 SEED 1- TSO2-histogram Uncertainty-State-Measurements-Estimations-SPAIN s SEED 1- Highest voltage level- histogram 12 Uncertainty-State-Measurements-Estimations-38kV s SEED 1- Second highest voltage level- histogram 25 Uncertainty-State-Measurements-Estimations-22kV s Date: 4/7/212 Page: 13 DEL_WP64_D63_Part11_two_step_state_estimation

104 [s] [s] Performance of the estimator The machine that has been used to carry out the test is the next one: Intel Core 2 DUO E84, 3.GHz, 4Gb memory. To measure the performance of the estimation process, it is shown in the next table and charts the execution time for each step and each seed. Time Execution/SEED Maximum Execution Time (step1) [s] 3, , ,7875 3, ,7721 5, ,942 6, ,8832 6,44332 Execution Time (step2) [s],6329,47352,9643 1,1841,6613, ,925,5965, ,4581 Total time [s] 4, , , , , , ,1327 6, , , , Execution time 7, 6, 5, 4, 3, Maximum execution time (step1) [s] Execution time (step2) [s] Total time [s] 2, 1,, Seeds 1,4 Execution time (step2) 1,2 1,,8,6,4,2, Seeds One can conclude that the time spent in the coordination step (2 nd step), is much smaller than the time spent in the TSO-level state estimation. It is expected since the coordination step is not an iterative process. Total time remains reasonably low: below 1s in the worst case. Date: 4/7/212 Page: 14 DEL_WP64_D63_Part11_two_step_state_estimation

105 LOW REDUNDANCY, HIGH NOISE, BAD DATA SCENARIO State vs. estimations It is shown the difference between the original values (load flow) and the state estimation. Phasor differences (magnitude) between each bus and swing bus are shown. The information is classified Seed 1 Total System Seed 2 Total System Date: 4/7/212 Page: 15 DEL_WP64_D63_Part11_two_step_state_estimation

106 Seed 1-Highest voltage level Seed 1-Second highest voltage level Date: 4/7/212 Page: 16 DEL_WP64_D63_Part11_two_step_state_estimation

107 Seed 1-TSO 1 Date: 4/7/212 Page: 17 DEL_WP64_D63_Part11_two_step_state_estimation

108 Seed 1-TSO 2 Date: 4/7/212 Page: 18 DEL_WP64_D63_Part11_two_step_state_estimation

109 In the next table and figures, it is show MAE, RMSE and MAPE indexes for each seed. SEED MAE,27352,28148,354,263131,262682,27849,35626,278347,28879,27339 RMSE,66993,8614,149481,6277,695689,826715,111752,785727,8336,67387 MAPE -1, , , , , , , , ,2392-1, ,31,3,29,28 State-Estimations-MAE,12,1,8 State-Estimations-RMSE,27,6,26,4,25,2, Seed, Seed State-Estimations-MAPE Seed Pseudomeasurements, estimations and exact values The measurements that have been generated have been compared with the same estimated values and exact values from the original load flow. SEED1 - Measurements- Exact value- histogram SEED1 - Measurements- Estimated value- histogram Date: 4/7/212 Page: 19 DEL_WP64_D63_Part11_two_step_state_estimation

110 SEED1 - Exact value- Estimated values- histogram SEED1 - Measurements- Exact value- Highest voltage-histogram SEED1 - Measurements- Exact value- Second highest voltage-histogram Date: 4/7/212 Page: 11 DEL_WP64_D63_Part11_two_step_state_estimation