electric power system reliability gridschool 2010 march 8-12, 2010 richmond, virginia institute of...

Electric Power System Reliability

GRIDSCHOOL 2010MARCH 8-12, 2010 RICHMOND, VIRGINIA

INSTITUTE OF PUBLIC UTILITIESARGONNE NATIONAL LABORATORY

Prof. Joydeep MitraElectrical and Computer Engineering

Michigan State [email protected] 517.353.8528

Do not cite or distribute without permission

MICHIGAN STATE UNIVERSITY

Camp09 - 2Mitra, IPU-MSU Electricity Networks and Reliability

Topics Covered

• Definition of reliability• Probability and stochastic processes• Component and system modeling • Reliability analysis of power systems• Concluding remarks


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.


Why Reliability?

• Ascertain if system design is acceptable• System planning/design• System expansion• Operations planning

– Reserve planning– Maintenance scheduling– Load management

• Regulatory compliance


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.


Reliability-Cost Relationship


Intuitively speaking, probability refers to the likelihood that an event (such as a component or system failure) will occur.

Rules:1. The probability P of any event lies between 0 and

1:2. The probability of a null (impossible) event is 0.3. The total probability of all possible outcomes is 1.4. The probability of a certain event is 1.

Probability

0 1.P


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.


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.


The “Bathtub Curve” and Markov Processes


Reliability Analysis Procedure

1. Model the system behavior as a stochastic process.

2. 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.


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


Interpretation of Indices


Reliability Analysis of a Small System

Consider a 2-generator system: Each generator is 2-state Markovian:

1 2

1 2

1 2

1 2

0.0022/h0.02/h

0.90.1

p p pq q q

States of 2-generator system:

Reliability Indices:

1 2

1 2 1 2

0.01( ) 0.0004/h

8760 87.6 h/y80 8760 7008 MWh/y

L

L

L

L

LOLP P q qLOLF F q qLOLE PEUE P

p q


Reliability Analysis of a Larger System

Each generator modeled as 2-state Markovian:

λ = 0.0022/h μ = 0.02/h p = 0.9 q = 0.1


State Space Representation

Hard to enumerate failed states!


State Space—Alternative Representation


Method for Computation of Indices


Computation of Indices for 2-bus System

0.02570.000138/h 1.207/y8760 225.1 h/y

L

L

L

LOLP PLOLF FLOLE P


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


Methods Used for Large Power Systems

• Contingency ranking• Stochastic/probabilistic load flow• State space decomposition• Monte Carlo simulation• Hybrid methods


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


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.


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.

electric power system reliability gridschool 2010 march 8-12, 2010 richmond, virginia institute of...

Documents