Complexity in Electrical Power Systems

1
Complexity in Electrical Power Systems

• Ronan Fitzmaurice

2
Characteristics of Complex Systems

• Many interacting parts
• High degrees of Freedom
• Non-linearity
• Asymmetry
• Nonholonomic constraint
• Hierarchy
• Open system

3
Self-Organized Criticality (SOC)

• Self-Organized Criticality an explanation of
  1/f noise
• Bak, Tang and Weisenfeld

4
Criticality (Critical Point)

• Point at which system properties change abruptly.
• Small changes can push the system into fixed or
  chaotic behavior (Edge of Chaos).

5
Self-Organization

• Structure appears due to internal interactions.
• Movement to an attractor in the State Space.

6
What is a SOC system?

• A dynamic system that has a critical point as an
  attractor.
• Macroscopically the system shows the spatial
  and/or temporal scale invariance of the critical
  point without the need to tune control parameters.

7
What kind of systems exhibit SOC behaviour?

• Separation of time scales of the external driving
  force and the internal relaxation process.
• The system exists in a non-equilibrium but
  temporarily stable state.
• Moves towards a marginally stable state (the
  critical point).

8
Properties of the SOC Systems

• Relaxation event size PDF follow Power Laws
• Long range time correlations

9
SOC in Electrical Power Systems
10

• Evidence for Self-Organized Criticality in
  Electric Power System Blackouts
• Benjamin A. Carreras, David E. Newman, Ian
  Dobson, and A. Bruce Poole

11
Power Law
12
Long term time correlation
13
Explanation of Complex Dynamics

• The slow increase in Load acting as the external
  driving force.
• Repairs and upgrades act as the short term
  relaxation process.

14

• Dynamics, criticality and self-organization in a
  model of blackouts in power system transmission
  systems
• Benjamin A. Carreras, V.E. Lynch,
• Ian Dobson, David E. Newman

15
OPA Model

• Fixed transmission systems are used with separate
  generator and load nodes.
• The model is based on the DC flow equations
• The slow dynamics are modeled by random load
  fluctuations with an overall increase over long
  periods of time.

16
OPA Model

• The dispatch is solved using LP methods.
• Using the Cost Function

17
OPA Model

• Under the constraints

18
OPA Model

• The systems State Space Variables where defined
  for each line as
• The probability of a line outage is given as a
  function of M.

19
OPA Model

• A line outage may cause cascading events that
  triggers a blackout.
• The system responds by raising the limit on lines
  that were overloaded during the blackout.
• The generation is increased at a generator node
  after the difference between the total load
  demand and generation capacity reach a certain
  limit.

20
OPA Model
21
Considerations for Operational Policies

• Blackouts are unavoidable.
• The risk of large blackouts is larger than
  previously considered.
• The financial risk of large blackouts is
  comparable to that of small ones.
• Operational policies that attempt to mitigate
  small blackouts cause an increase in larger ones
  and could possibly cause the financial risk of
  larger ones to be higher than small events.

22
Questions?

• Thank you for your time.