This document discusses the application of data science techniques to problems in electric power systems. It begins by defining data science as comprising statistics, system identification, and control theory. It then describes the electric power grid and typical challenges, such as dealing with the increasing complexity of power networks. As an example, it presents research using particle filtering to estimate power plant parameters and quantify uncertainty in the estimates. The document concludes by noting the need for new modeling and simulation tools to help power grid planning and operation cope with ongoing changes.

1. Data Science for Electric
Power Systems
Tetiana Bogodorova, Ph.D., Assoc. Prof., Faculty of Applied Sciences,
Ukrainian Catholic University

2. • Data Science as emerging field that comprises Statistics, System
Identification, and Control Theory
• Electric Power Grid and it’s specifics
• Typical problems of Electric Power Grid
• Example of research problem and its solution
• What’s next?

3. Data Science as emerging field
• Data science is an interdisciplinary field that uses scientific methods,
processes, algorithms and systems to extract knowledge and insights
from data in various forms, both structured and unstructured, similar
to data mining. (Wiki)
Before….
• System Identification deals with the problem of building
mathematical models of dynamical systems based on observed data
from the system.(Lennart Ljung)
• Statistics - a branch of mathematics dealing with the collection,
analysis, interpretation, and presentation of masses of numerical
data. Merriam-Webster dictionary)

4. Before….
• Control theory is a subfield of mathematics that deals with the
control of continuously operating dynamical systems in engineered
processes and machines.
The objective is to develop a control model for controlling such systems
using a control action in an optimum manner without delay or
overshoot and ensuring control stability. (Wiki)

5. • Data Science as emerging field that comprises Statistics, System
Identification, and Control Theory
• Electric Power Grid and it’s specifics
• Typical problems of Electric Power Grid
• Example of research problem and its solution
• What’s next?

6. Electric Power Grid
* From Slides: https://www.researchgate.net/figure/Flow-of-
electricity-in-a-traditional-power-system-3_fig1_257810325

7. Large Scale Power Systems
To operate large power networks, planners and operators need to
analyze variety of operating conditions – both off-line and in near
real-time (power system security assessment).
Different SW systems have been designed for this purpose.
But, the dimension and complexity of the problems are increasing
due to growth in electricity demand, lack of investments in
transmission, and penetration of intermittent resources.
New tools are needed!
Current and new tools will need to perform simulations:
•Of complex hybrid model components and networks with very
large number of continuous and discrete states.
•Models need to be shared, and simulation results need to be
consistent across different tools and simulation platforms…
•If models could be “systematically shared at the equation level”,
and simulations are “consistent across different SW platforms” –
we would still need to validate each new model (new
components) and calibrate the model to match reality.

8. Motivation and Terminology
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∆P(pu)
Time (sec)
Measured Response
Model Response
WECC Break-up 1996Bad ModelNormal Gird Operation
Eric Allen, Dmitry Kosterev, and Pouyan Pourbeik. "Validation of power system models." Power and
Energy Society General Meeting, 2010 IEEE. IEEE, 2010.
Observed California-Oregon Intertie
Power (Dittmer Control Center)
8
• Modeling is a process of defining a set of rules and dependencies, in the form
of equations, to reproduce the required system behavior by computer-based
simulation.
• Model Validation is a process when an engineer checks if the model is good
enough to serve its purpose.
• Uncertainty identification is a process of defining a level of confidence in
results given existing knowledge about a system.

9. Different Validation
Levels
• Component level
• e.g. generator such as wind
turbine or PV panel
• Cluster level
• e.g. gen. cluster such as wind or
PV farm
• System level
• e.g. power system small-signal
dynamics (oscillations)

10. The Power System “Data”
Set
•Needs and Roles of Models and
Measurements for Off-line
Dynamic Model Validation

11. • Data Science as emerging field that comprises Statistics, System
Identification, and Control Theory
• Electric Power Grid and it’s specifics
• Typical problems of Electric Power Grid
• Example of research problem and its solution
• What’s next?

12. 12
Parameter Estimation & Uncertainty Quantification
Identifying Uncertainty Distributions and Confidence Regions of
Power Plant Parameters

13. Motivation
• To derive new knowledge for power system operators about the power
system parameters that are estimated given measurements and a model
• To derive an estimated parameter uncertainty using an arbitrary
distribution shape
• To facilitate design model validation experiments that consider
implications of the derivations
• Solution: The proposed methodology is based on particle filtering, it is
applicable for non-linear systems, and robust to arbitrary noise
characteristics. The proposed method calculates the uncertainty of
parameter estimates in the form of multimodal Gaussian mixture
distributions
13

14. Problem formulation and the
methodology
• To identify the model parameters and their confidence regions
• assuming: the model structure of a power plant that includes a generator with
controls and, having measurements from the tests and on the terminal bus.
14
Generator with
controllers
connected to an
infinite bus

15. Choosing the bandwidth for the Gaussian kernel
15
Covariance in the Gaussian kernel plays the role of a smoothing parameter that defines
the shape of the reconstructed estimate distribution.
Three methods for
bandwidth selection are
used:
-Rule of Thumb (ROT)
-Least-Squares Cross
Validation (LCV)
-Plug-in method (HSJM)*.
*Hall, Sheather, Jones, and Marron

16. Reconstruct the uncertainty
distribution and Estimate the confidence
intervals
16
The posterior distribution that is an output of PF is described by a number of samples
(particles) with weights assigned according to a fitness function. The continuous pdf can
be constructed from PF by assigning kernel over each particle.
To estimate confidence intervals:
Find the cutting surface C: p(x)=b that intersects with the Gaussian mixtures pdf
p(x) given by (8) and gives a projection contour area on (x1, .. , xM) coordinates
plane equal to S, where S – union of ellipses.
b

17. Case Study: Illustrative Example
• Confidence limits of the 95% probability for each
parameter vs the number of particles (N)
17
Reconstructed estimate uncertainty probability density function (N=10) of identified turbine-
governor parameters (R – droop. Ts – time constant)
95% confidence region of [R, Ts] parameters
uncertainty of estimate

18. Case Study: Discussion
18
Estimation error (a) and confidence area (region) (b) dependency on number of particles
- The choice of the number of particles for PF was based on the minimal estimation error value.
- Variance was chosen of such method giving the minimal uncertainty (confidence interval).
- The confidence area steeply growing with increase N from 5 to 10. This could mean that when N=5
there is a lack of knowledge about the uncertainty.

19. • Data Science as emerging field that comprises Statistics, System
Identification, and Control Theory
• Electric Power Grid and it’s specifics
• Typical problems of Electric Power Grid
• Example of research problem and its solution
• What’s next?

20. What’s next?
• https://ses.jrc.ec.europa.eu/electricity-supply-security-and-resilience

21. What’s next?
• http://ec.europa.eu/research
/participants/data/ref/h2020
/wp/2018-2020/main/h2020-
wp1820-energy_en.pdf

22. Thank you!