dr. mohammed t.lazim al-zuhairi - philadelphia university · 2017. 10. 23. · 5- transmission...

Power System Reliability Lecture No.1 Dr. Mohammed Tawfeeq Al-Zuhairi

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Power System Reliability Dr. Mohammed T.Lazim Al-Zuhairi


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PHILADELPHIA UNIVERSITY

FACULTY OF ENGINEERING

Department of Electrical Engineering

Course Title: Power Systems Reliability (610586)

Prerequisite: Power Systems (1). (610481)

Text Books: Reliability Evaluation of Power Systems By: R.Billinton and R.N.Allan

Publisher: Kluwer Academic Publishers 2nd

Edition – 2001-ISBN-13-9780306452598

Semester: First 2013/2014

Instructor: Dr. Mohammed Tawfeeq

Course Goals:

Introduce the student to the theory, techniques, and application of reliability engineering for electrical power

system.

Time Schedule:

Duration: 16 Weeks Lectures: 3hours / week

Objectives:

1. Understand the principles of reliability engineering. 2. Learn statistical distributions as applied to power system components, circuit topologies in reliability

consideration, redundancy techniques, and applications.

3. Learn analysis and aspects of distribution and transmission systems reliability evaluation. 4. Understand the reliability of generating systems and spinning reserve. 5. Learn the methods of reliability evaluation for composite systems.

Course Contents Weeks

1- Introduction to Reliability Theory. 1

2- Reliability Mathematics: Review of Theory of Probability, Theory of Sets, Binomial Distribution, Poisson

distribution, Exponential Distribution, Failure Rate, MTTF and MTBF. 3

3- System Configuration: Series Reliability, Parallel Reliability, Series-Parallel Reliability, Redundancy. 2

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4- Distribution System Reliability: Single- Bus Bar Schemes , Double- Bus BarSchemes ,Double- Bus Bar

Double- Breaker Schemes, Double- Bus Bar System with Bus Couplers ,Ring Systems. 2

5- Transmission System Reliability: Frequency and Duration Method, Probabilistic Approach, Markov

Technique Applied to Transmission System. 2


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6- Generating Capacity Reliability Evaluation: Non-Probabilistic Method, Probabilistic Method, Loss of Load

Probability Technique, State Probabilities, Loss of Energy probability 3

7- Composite System Reliability Evaluation, Reliability of Combinations of Generators Transformers &

Transmission Lines. 2

8- Spinning Generating Capacity Reliability. 1

Mode of Assessment

1. First exam: (20%) 2. Second exam (20%) 3. Quizzes, Reports, H. works, and/or Projects: (20%) 4. Final exam: (40%)

References

Reference Books:

1. M.L.Shooman " Probabilistic Reliability: An Engineering Approach". Publisher: McGraw-Hill.

2. P.D.T.O Conner "Practical Reliability Engineering". Publisher: John Wiley. New York -3rd

Edition.

3. R.Billinton and R.N.Allan". Reliability Evaluation of Engineering systems: Concepts and Techniques".

Pitman Books, 1983.

4. I. Bazovsky "Reliability Theory and Practice". Publisher: Prentice Hall.

5. W.Blischke and D.Murthy,"Reliability modeling, Prediction, and optimization ", John

Wilely ,New York ,2000.


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Power System Reliability

Course Coordinator and Lecturer: Prof.Dr. Mohammed Tawfeeq Al-zuhairi

Office: Room No. 814

Email: [email protected]

2014-2015


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Introduction to Power system Reliability

Reliability is a term relates to the ability of a system to deliver electricity to all points of utilization within the accepted standard and desired

amount

Historically, a power system has been divided into three almost independent areas of operation as follows:

1. Generation System: facilities for the generation of electricity from

economical energy sources.

2. Transmission System: transportation system to move large energy

blocks from generation facilities to specific geographical areas.

3. Distribution System: within a specific geographical area distribute the

energy to individual consumers (e.g., residential, commercial,

industrial, etc.).

Power system reliability studies are categorised into two:

1) System adequacy System adequacy: related to the existence of sufficient facilities within

the system to satisfy the consumer load demand. These include the

necessary generators, transmission and distribution facilities.

2) System security System security: Related to the ability of the system to respond to

disturbances. These include the minor and major disturbances resulting

in dynamic, transient or voltage instability of power system.

The reliability studies are mainly depending on the probability and

statistics theories which are also use set theories. Hence in order to

understand power system reliability the basic concepts of statistics,

probability and set theory must be reviewed .


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Introduction to Reliability

Reliability is a term meaning endurance, dependability, and good performance.

For engineering systems, however reliability of a component or system is defined as the probability that this component or system is performing its

function adequate under stated conditions for a specified period of time.

Faults on plain are not acceptable


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Faults due not good engineering design can cause disasters


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Power System Reliability Dr. Mohammed Tawfeeq Lazim Al-Zuhairi

INTRODUCTION

1.2. FUNDAMENTALS OF STATISTICS

Reliability science depends on statistics , theory of sets and probability theory.

In this lecture we shall give some fundamental concepts in engineering statistics

that are mainly concerned with reliability theory.

1.2.1 CONCEPT OF FREQUENCY

The duration of distribution feeder outages for a particular substation lasted 8 times between

0 and 1 h, 15 times between 1 and 2 h, 5 times between 2 and 3 h, and 3 times between 3 and

4h, as illustrated in Fig. 2.1.

Figure 2.1. Frequency histogram of duration of feeder outages.

Concept of Class

The classes in the duration of feeder outages example have a class width of 1 h. In general,

the classes have equal widths and are consecutive.

There are also classes that are discrete numbers instead of intervals, for example, age of

students (age rounded off to integers).


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Frequency Graphs

The relationship between relative frequency and class can be shown graphically as illustrated

in Fig. 2.2. If shown as a bar graph, it is a histogram. Histograms can also be used for

qualitatively defined classes.

Figure 2.2. Relative frequency histogram of duration of feeder outages.

Cumulative Frequency Distribution Model

Instead of the frequency of a class, the sum of frequencies of all proceedings or subsequent

classes can be shown as illustrated in Fig. 2.3. Cumulative frequency distributions have a lot

of applications, one of which is the load duration curve used in generation capacity adequacy

studies.

Figure 2.3. Cumulative frequency histogram of duration of feeder outages.


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1.2.2 The Mean

Also called the arithmetic mean is the most commonly used measure of central tendency. It is

calculated by adding up all the observations in a data set and then dividing the result by the

number of observations.

Example 1 : Calculate the mean of the following data

11 17 18 10 22 23 15 17

14 13 10 12 18 18 11 14

Solution: The mean is

The mean can also represents the average value of each item in the frequency distribution,

such as the average height of a group of students in a class, the average income of employees

in a company, and so on.It can also be written as :


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1.2.3 Median

Median is the value of the middle item when all the items are arranged in either ascending or

descending order. It is the 50% point of the spectrum; so there are an equal number of items

on both sides of the median.

The computation of the median depends on whether an odd or even number of the

observations in the data set.

If n = odd , then the median will be = n+1/2

If n = even , then the median will be = n /2

Example 2 : Compute the median for the following set of data:

11 17 18 10 22 23 15 17

14 13 10 12 18 18 11 14 21

Slution : Here n= odd = 17 , Hence the median = 17 +1 /2 =9 th order observation :

Ordered array 10 10 11 11 12 13 14 14 15 17 17 18 18 18 21 22 23

1.2.4 Mode

Mode is the value in a frequency distribution that occurs most often, that is, the value of

the class with the highest frequency. When represented in a graph form, it is the class value

corresponding to the highest point of the curve.

Example 3: Compute the mode for the following set of data:

11 17 18 10 22 23 15 17

14 13 10 12 18 18 11 14 21

Solution:

Ordered array 10 10 11 11 12 13 14 14 15 17 17 18 18 18 21 22 23

We see that the observation 18 is the most frequent value and thus the mode = 18.


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1.2.5 Standard Deviation

Standard deviation is a measure of the extent of variation in a frequency distribution. It is

defined as the square root of the average of squared deviations of the frequency

distribution. Deviation is the difference between the value of an item and the mean value,

and it could be negative. The squared deviation is the square of that and is always positive.

Example 4:

The following chart shows the seniority of 40 workers at a plant:

Seniority 1 2 3 4 5 6 8 9 11 15 18 20

Number 2 2 4 6 6 10 3 2 1 2 1 1

What is the average seniority?

What is the standard deviation?

Solution:

1.2.6 Variance

Variance is the square of the standard deviation and has more direct applications in some

statistical analyses than the standard deviation.

dr. mohammed t.lazim al-zuhairi - philadelphia university · 2017. 10. 23. · 5- transmission...

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