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 Universitymitraj@msu.edu 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Do not cite or distribute without permission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

Camp09 - 3Mitra, IPU-MSU Electricity Networks and Reliability

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.

Camp09 - 4Mitra, IPU-MSU Electricity Networks and Reliability

Why Reliability?

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

– Reserve planning– Maintenance scheduling– Load management

• Regulatory compliance

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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.

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Reliability-Cost Relationship

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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

Camp09 - 8Mitra, IPU-MSU Electricity Networks and Reliability

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.

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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.

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The “Bathtub Curve” and Markov Processes

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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.

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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

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Interpretation of Indices

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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

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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

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State Space Representation

Hard to enumerate failed states!

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State Space—Alternative Representation

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Method for Computation of Indices

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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

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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

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Methods Used for Large Power Systems

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

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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

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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.

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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.