3D diagrams of Eurostag generator models for improved dynamic simulations

Transcription

1 3D diagrams of Eurostag generator models for improved dynamic simulations

2 Achieve online dynamic security analysis To make good network situations short-term forecast, initializing dynamic simulations with steady states is necessary. 2 solutions are used nowadays (1) Manually correcting the data (P,Q injections and generators voltage setpoints) (2) Letting the simulation stabilize for some time Why it is a Problem? For TSO bulk massive dynamic simulations (like in itesla) (1) and (2) are not possible Input files are large The purpose: Set up a Database of 3D steady states Generators Domains described with linear constraints Use those domains to stabilize network situations at the initialization step 2

3 A new method to compute the steady state simulation domains of power generators 3

4 a) Context et hypothesis 4

5 The capability domain of a power generator unit is a 3D polyhedron 5

6 For a triplet [P,Q,V], the generator unit has to follow the set point without oscillation The derivatives of machine variables have to be null In practice: (Dynamic simulator feedback OR stability criteria) AND X consigne X end ε Stability depends on the generators modelling in the dynamic simulator. 6

7 Convex domain Non Convex domain Convexity hypothesis the capability domain can be described with a.p + b.q + c.v d 7

8 1.5 S, 1.5 S 1.5 S, 1.5 S [0.5 Unom, 1.5 Unom S: apparent power Unom: nominal voltage 8

9 b) 3D (P,Q,V) domain computation 9

10 Dichotomy is made between a steady state point and an unstable point belonging to the study boundary The last steady state is a support point A numerical threshold is chosen given the precision of the simulator and the size of the generator to stop the dichotomy. 10

11 1. Determination de 8 neighboring points 2. Tangent plane = plane minimizing the distance between the 9 points and the plane (P) P i αx i + βy i + γz i + δ 2 α 2 + β 2 + γ 2 = min a,b,c) R 3 i ax i + by i + cz i + d 2 a 2 + b 2 + c 2, 1 i n 11

12 The one defined by the tangent planes (completely includes the steady state domain) : Intersections of the domains tangent planes AND Verifying all the constraints: Ax b The convex hull of all the central support points (completely included inside the steady state domain) 12

13 c) Implementation 13

14 Python 2.7 Program + numpy/scipy, matplotlib Call the simulator through the API Can fit to another dynamic simulator 14

15 Network modelling: SMIB (Single-Machine infinite bus system) Entrées : set point (ech file) Sorties : machine equations data (out file), working point (through the API) Dynamic simulation parameters: Simulation time: 1000s Eurostag s default accuracy 15

16 One time in the 3 main directions As many times as necessary In practice: - Two complete steps of refinement - Corner assessment to get more support points 16

17 d) Results 17

18 Viewing of the different steps (Initialization, 1st refining, 2 nd refining) INITIALIZATION Convex hull of setting points Domain created from tangent planes 18

19 1st REFINING Convex hull of setting points Domain created from tangent planes 19

20 2 nd REFINING Convex hull of setting points Domain created from tangent planes 20

21 VERTICES EXPLORATIONS Convex hull of setting points Domain created from tangent planes 21

22 COMPARISON WITH THE DOMAIN COMING FROM RANDOM TESTS Convex hull of setting points Domain created from tangent planes 22

23 COMPARISON WITH THE CONTRACTUAL DIAGRAM Overlay of UQ cross-section: The majority of the reference diagram is inside the domain Two small areas are outside: unstable areas according to the simulator A way to validate the dynamic model of a generator 23

24 Convex hull of setting points Domain created from tangent planes 24

25 Problem 1 : not enough support point makes the initialization impossible For another unit, Ustator > the authorized limit in the dynamic simulator: The simulation is not in steady state Problem 2 : non-convexity of domains Solution : Modify machine regulators Solution : Impose some operational limits that corresponds to the usage of the generator Isolate the stable points to compute the convex hull of those points 25

26 Implementation: - Python machine library: sklearn - Algorithm added at the end of the process of computation of support points Support Vector Machine (SVM) algorithm Definition - Machine learning algorithm of binary classification: - Construct a hyperplane in 3D which separates the stable and unstable points. 26

27 Automatization of the process and use for network situations analysis 27

28 28

29 Network situations: 95 snapshots from the French network The set point of each machine connected in the snapshot is compared to the convex hull of support points: Mean Standard Deviation Median Min Max Out of domain generators In the domain generators Generators not connected Generators with no data Distance from PQ domain at the set-point voltage in % of apparent power Minimum distance in % of apparent power Maximum distance in % of apparent power

30 The OPF objective: to stabilize snapshots of the French power network Optimization under constraints The OPF minimizes the sum of squared variations of active and reactive power injection and voltages, subject to linear constraints (including the steady state simulation domains) Analysis of 380 snapshots: 119 initialized in steady state (emachine < 0,01) The rest is stabilized after 2000s dynamic simulation They are still some generators units, especially hydraulic, that have to be studied deeper: one unstable unit in the whole grid is enough to destabilize the whole simulation. 30

31 CONCLUSION 31

32 All steady state domains have been computed (with linear constraints). This method can easily be adapted to another dynamic power network simulator as it is using its initialization report. The steady state domains can be used to initialize better power network dynamic simulation by ensuring that the initial state is a steady state. Most of the code is already online (opensource): 32

33 Continue to work on remaining inconsistencies between static and dynamic data and generators models Adjust the industrialization process with itesla files IIDM Use the whole methodology with HV network to launch dynamic security analysis with Eurostag dynamic simulator. Add SVC and HVDC modelling in the process 33

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35 P i αx i + βy i + γz i + δ 2 α 2 + β 2 + γ 2 = min a,b,c) R 3 i ax i + by i + cz i + d 2 a 2 + b 2 + c 2, 1 i n Theorem : Let X the matrix of points that are centered on their centroid, the left singular vector that is assigned to the smallest singular value of X is solution of (P) Preuve : n i=1 d i 2 = n XXT n n 2 X = UΣV T XX T = UΣ 2 U T n i=1 d 2 i = n XXT n = a2 σ 2 1 +b 2 σ 2 2 +c 2 σ 2 3 n 2 a 2 + b 2 +c 2 Where a, b, c is the decomposition of n in the orthonormal basis U and σ 1, σ 2, σ 3 are singular values of X 35

36 Refinement steps: For every corner of the domain 1. Find the support points containing the corner and choose the three closer ones 2. Compute the plane from the 3 support points and the projection of the coin on this plane 3. Verify that the projection is located in the triangle of the support points 4. Find the new origin (the projection point) + direction 36

37 x symbolizes the training examples closest to the hyperplane called support vectors. This is a problem of Lagrangian optimization that can be solved using Lagrange multipliers to obtain the weight vector w and the bias b of the optimal hyperplane.

38 Method to isolate the steady state point: Use LinearSVM to get the «first» hyperplane Fit the model with training sample (points far from the first hyperplane) Cross-validation: - validate the model with test sample: 93% - Adjust the models parameters Stable points Unstable points Apply the new model with all the points to classify the points and isolate the «stable» points to construct the convex hull of those points

39 Domain obtained by MonteCarlo approach Final Convexhull obtained after SVM algorithm