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 Joydeep Mitra Electrical and Computer Engineering Michigan State University  Do not cite or distribute without permission MICHIGAN STATE UNIVERSITY

Camp Mitra, 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

Camp Mitra, 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.

Camp Mitra, 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

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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.

Camp Mitra, IPU-MSU Electricity Networks and Reliability Reliability-Cost Relationship

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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

Camp Mitra, 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.

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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.

Camp Mitra, IPU-MSU Electricity Networks and Reliability The “Bathtub Curve” and Markov Processes

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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.

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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

Camp Mitra, IPU-MSU Electricity Networks and Reliability Interpretation of Indices

Camp Mitra, IPU-MSU Electricity Networks and Reliability Reliability Analysis of a Small System Consider a 2-generator system:Each generator is 2-state Markovian: States of 2-generator system: Reliability Indices: pq

Camp Mitra, IPU-MSU Electricity Networks and Reliability Reliability Analysis of a Larger System Each generator modeled as 2-state Markovian:

Camp Mitra, IPU-MSU Electricity Networks and Reliability State Space Representation Hard to enumerate failed states!

Camp Mitra, IPU-MSU Electricity Networks and Reliability State Space—Alternative Representation

Camp Mitra, IPU-MSU Electricity Networks and Reliability Method for Computation of Indices

Camp Mitra, IPU-MSU Electricity Networks and Reliability Computation of Indices for 2-bus System

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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

Camp Mitra, IPU-MSU Electricity Networks and Reliability Methods Used for Large Power Systems Contingency ranking Stochastic/probabilistic load flow State space decomposition Monte Carlo simulation Hybrid methods

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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.

Camp Mitra, IPU-MSU Electricity Networks and Reliability 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.