1. Electric Power System Reliability
GRIDSCHOOL 2010
MARCH 8-12, 2010  RICHMOND, VIRGINIA
INSTITUTE OF PUBLIC UTILITIES
ARGONNE NATIONAL LABORATORY
Prof. Joydeep Mitra
Electrical and Computer Engineering
Michigan State University 
Do not cite or distribute without permission
MICHIGAN STATE UNIVERSITY

2. Topics Covered Definition of reliability
Probability and stochastic processes
Component and system modeling
Reliability analysis of power systems
Concluding remarks

3. Definition of Reliability
Reliability is defined as the probability that a component or system will perform its designated functions for a given period of time under the conditions in which it was designed to operate.
Availability is defined as the probability that a component or system is performing its designated functions at a given point in time under the conditions in which it was designed to operate. 3

4. Why Reliability? Ascertain if system design is acceptable
System planning/design
System expansion
Operations planning
Reserve planning
Maintenance scheduling
Load management
Regulatory compliance 4

5. NERC Definition
The North American Electric Reliability Corporation (NERC) defines two components of system reliability:
Adequacy – Having sufficient resources to provide customers with a continuous supply of electricity at the proper voltage and frequency, virtually all of the time. “Resources” refers to a combination of electricity generating and transmission facilities, which produce and deliver electricity; and “demand-response” programs, which reduce customer demand for electricity.
Security – The ability of the bulk power system to withstand sudden, unexpected disturbances such as short circuits, or unanticipated loss of system elements due to natural or man-made causes. 5

6. Reliability-Cost Relationship6

7. Probability
Intuitively speaking, probability refers to the likelihood that an event (such as a component or system failure) will occur.
Rules:
The probability P of any event lies between 0 and 1:
The probability of a null (impossible) event is 0.
The total probability of all possible outcomes is 1.
The probability of a certain event is 1. 7

8. Random or Stochastic Processes
In a process, a component or system goes through a sequence of transitions in the course of its operation.
In a random (or stochastic) process, transitions do not occur deterministically—they can only be predicted with a probability, not with certainty.
In a Markov process, the probability of a transition depends only on the present state, and has no memory of prior transitions.
In this presentation, we consider only Markov processes. 8

9. Markov Process—A Simplified Presentation
Consider a component or system that can exist in two states, i and k (example: functional or ‘up’ state, and failed or ‘down’ state), and is Markovian. 9

10. The “Bathtub Curve” and Markov Processes10

11. Reliability Analysis Procedure
Model the system behavior as a stochastic process.
Quantify the system reliability in terms of probability and frequency of encountering the failure states, and the period of time the system spends in these states. 11

12. Power System Reliability
Definition
Reliability of a power system pertains to its ability to satisfy its load demand under the specified operating conditions and policies.
Indices
Loss of Load Probability (LOLP)
dimensionless
Loss of Load Expectation (LOLE)
unit: hours/year
Loss of Load Frequency (LOLF)
unit: failures/year
Expected Unserved Energy (EUE)
unit: MWh/year 12

13. Interpretation of Indices13

14. Reliability Analysis of a Small System
Consider a 2-generator system:
Each generator is 2-state Markovian: p q
States of 2-generator system:
Reliability Indices: 14

15. Reliability Analysis of a Larger System
Each generator modeled as 2-state Markovian: 15

16. State Space Representation
Hard to enumerate failed states! 16

17. State Space—Alternative Representation17

18. Method for Computation of Indices18

19. Computation of Indices for 2-bus System19

20. Modeling Considerations in Power Ssytems
Component modeling
Generator models
Transmission line models
Load models
Component dependencies
System operation representation
Power flow models
Operating constraints
Policies and contracts 20

21. Methods Used for Large Power Systems
Contingency ranking
Stochastic/probabilistic load flow
State space decomposition
Monte Carlo simulation
Hybrid methods 21

22. Monte Carlo Simulation
Concept
Imitate system behavior using random numbers and estimate indices from data collected from simulation.
Types used in power systems
Sequential
Synchronous timing (a.k.a. chronological)
Asynchronous timing (a.k.a. next event method)
Hybrid (mixed timing)
Non-sequential 22

23. Partitioning of Functional Zones
Predictive methods are used in bulk power systems, and less frequently in distribution systems.
Integrated analysis of complete system is rarely attempted because of complexity.
Load point indices are used in distribution system reliability computation. 23

24. Concluding Remarks
Reliability is a statistical index. Power system reliability evaluation is a complex procedure.
Two classes of methods:
Predictive methods are used predominantly in bulk system reliability analysis.
Analytical methods are faster and accurate;
Simulation methods take time but allow more flexibility.
Load point methods are used in distribution system reliability evaluation.
There have been few attempts to compare results from predictive methods with a posteriori or observed indices.
Integrated (bulk and distribution) system reliability analysis is very complex and rarely attempted. 24