Optimum Operasi dan KeandalanSistem Tenaga Listrik

Oleh :Prof. Ontoseno Penangsang, Ph.D

Dr. Eng. Rony Seto Wibowo

Laboratorium Simulasi Sistem Tenaga ListrikTeknik Elektro – ITS Surabaya

Contents

• Basic Probability Theory• Application of Binomial Distribution• Generation System Reliability Analysis• Transmission System Reliability Analysis• Distribution System Reliability Analysis

DAFTAR PUSTAKA

• Roy Billinton, Ronald N Allan, “Reliability Evaluation of Engineering Systems” Plenum Press : New York, 1992

• Roy Billinton, Ronald N Allan, “Reliability Evaluation of Power Systems” Plenum Press : New York, 1996

• Robert L. Sullivan, “Power System Planning”, McGraw-Hill, 1977

Basic Probability Theory

Oleh :Dr. Eng. Rony Seto Wibowo

Laboratorium Simulasi Sistem Tenaga ListrikTeknik Elektro – ITS Surabaya

Probability Concept

• Mathematically, it is a numerical index that can vary between zero to unity

• Probability of success and failure can formulated as follows:

Example

• Anggap kita melempar dua buah dadusekaligus, berapa peluang kita mendapatkanangka total dadu 9?

Permutations and Combinations

• The number of permutations of n different items is the number of ways these items can be arranged

• The number of combinations of n different items is the number of different selections of r items, each without regard to the order or arrangement of the items in the groups

Example

• Anggap kita mempunyai 3 buah buku dengannama A, B dan C. Berapa kemungkinan kitamenyusun ketiga buku tersebut?

• Berapa kemungkinan komposisi panitia yang terdiri dari 3 orang, dimana jumlah orang yang akan kita pilih adalah 4 orang?

Rules for Combining Probabilities

• Rule 1 – Independent events• Rule 2 – Mutually exclusive events• Rule 3 – Complementary events• Rule 4 – Conditional events• Rule 5 – Simultaneous occurrence of events• Rule 6 – Occurrence of at least one if two

events• Rule 7 – Application of conditional probability

Example

• Suatu pabrik mempunyai 2 plant. Plant 1 membuat 70% barang yang dibutuhkan danplant lainnya menghasilkan 30%. Jika 90 % produk plant 1 memenuhi standard dan 80% produk plant 2 memenuhi standard. Berapapeluang pabrik tersebut menghasilkan produkyang memenuhi standard?

Probability Density Function• The summation of

probabilities should equal unity

• Probability density Function (a) Separate data (b) Grouped data

Probability Distributions Function

• PDF is obtained by summating the density function (numerically, integrating)

• Discrete random variable : (a) Separate data (b) Grouped data

Probability Distributions

• Continuous random variable : (a) Probability distribution function f(x) (b) Probability density function F(x)

Mathematical Expectation

• Moments of distribution, also known as expected value, is referred to as the average value or population mean

Example

• The data of copper length measurement are as follows :

5,97 5,97 5,98 5,98 5,98 5,99 5,99 5,99 5,99 5,99 6 6 6 6 6 6,01 6,01 6,02 6,02 6,02

• Determine the average length of the copper?

Variance and Standard Deviation

• A measure of dispersion of a distribution is defined as Variance V(x)

• Standard deviation

Example

• The data of copper length measurement are as follows :

5,97 5,97 5,98 5,98 5,98 5,99 5,99 5,99 5,99 5,99 6 6 6 6 6 6,01 6,01 6,02 6,02 6,02

• Determine the variance and standard deviation?

Application of the Binomial Distribution

Oleh :Dr. Eng. Rony Seto Wibowo

Laboratorium Simulasi Sistem Tenaga ListrikTeknik Elektro – ITS Surabaya

General Characteristic

• Binomial distribution can be represented by general expression :

(p+q)2

• Required conditions are :– Fixed number of trial– Two possible outcomes : success ad failure– Probabilities of success and failure are remain

constant– All trial must be independent

Example

Binomial Coefficients

• One essential aspect of the binomial distribution is to evaluate nCr

11 1

1 2 11 3 3 1

1 4 6 4 1

Expected value

• Expected value of binomial distribution can be expressed as follows:

• Finally,E(x) = np

Example

• A small generating plant is to be designed to satisfy a constant 10 MW load. Four alternatives are being considered:1. 1 x 10 MW unit2. 2 x 10 MW unit3. 3 x 5 MW unit4. 4 x 3 1/3 MW unitUnavailable probability of each unit is equal to0.02 and therefore, the probability of available is0.98. Please develop capacity outage probabilitytables.

Capacity Outage Probability

Expected Load Losses

Investment Costs of Plant

Expected Load Curtailment

Effect of Unavailability

System Risk with One Unit in Reserve

Generation System Reliability Analysis

Oleh :Dr. Eng. Rony Seto Wibowo

Laboratorium Simulasi Sistem Tenaga ListrikTeknik Elektro – ITS Surabaya

Introduction

• Generation system planning is one of the crucial steps in modern electric utility.

• Generation expansion plan must satisfy customer needs for reasonably price, reliable and quality.

• The electricity industry is a very capital intensive industry

• Expansion plan should attract new investors

Expansion Plan Consideration

• Uncertainty of load in the future• Unit reliability and maintenance schedules• Fuel Costs• Environment Issues• Construction Costs• Construction Times• Financial Support

Reliability Indices

Reliability indices mostly used in generation system expansion are :

• Loss of Load Probability (LOLP)• Expected Value of Demand not served (DNS)• Frequency and Duration (FD)

Practical Generation Planning

In Practical, the considerations are :• Load Growth• Construction Time• Availability of Sites• Availability of Fuelthen, detailed reliability analysis is required to ensure that all satisfying the desired reliability level

Probabilistic Generating Unit Models

Mainly, generation systems consist of many type of generators. They can be categorized as the following :• Based Load units. Capacity factor : 90 – 95 %.

Nuclear, Coal Steam Turbine units• Midrange units. Capacity factor : 30 – 75 %.

Combine Cycle units, Steam Turbine Units• Peakers. Capacity factor : 5 – 10 %. Gas

turbines and Hydro units

Transmission System Reliability Analysis

Oleh :Dr. Eng. Rony Seto Wibowo

Laboratorium Simulasi Sistem Tenaga ListrikTeknik Elektro – ITS Surabaya

Distribution System Reliability Analysis

Oleh :Dr. Eng. Rony Seto Wibowo

Laboratorium Simulasi Sistem Tenaga ListrikTeknik Elektro – ITS Surabaya