i

CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

RELIABILITY OF DISTRIBUTION SYSTEMS

USING MARKOV PROCESS AND ETAP

A graduate project submitted in partial fulfillment of the requirements

For the degree of Master of Science in Electrical Engineering

By Kunal Raut

December 2018

ii

The graduate project of Kunal Raut is approved:

_______________________________ _____________

Xiyi Hang, Ph.D. Date

_______________________________ _____________

John Valdovinos, Ph.D. Date

_______________________________ _____________

Ignacio B. Osorno, Chair Date

California State University, Northridge

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ACKNOWLEDGEMENT

I would love to grab this opportunity to impart appreciation to my mentor for this

project, my project chair, Prof. Bruno Osorno. I got to learn a lot about power system

reliability through my project “Reliability of distribution systems using Markov process

and ETAP” which would have not been possible without the guidance of my advisor.

I also convey my acknowledgement to Dr. Valdovinos, John and Dr. Hang, Xiyi.

Their expertise related to the subject has been helpful in resolving many issues during the

project.

Also, I’m much obliged to my kinfolks for having my back through the entire

process of my education.

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TABLE OF CONTENTS

Signature Page ii

Acknowledgement iii

List of Figures v

List of Tables vii

Abstract viii

Section 1 – Introduction 1

1.1 Reliability concepts 1

1.2 Reliability assessment techniques 2

1.3 Continuous Markov process 2

Section 2 – Reliability assessment module in ETAP 3

2.1 Single Contingency 10

2.2 Double Contingency 11

Section 3 – Roy Billinton Test System (RBTS) 13

Section 4 – Evaluation of reliability indices 16

Section 5 – Reliability Analysis using RBTS model 19

Section 6 – Results and discussion 20

6.1 Reliability assessment without any DG connected 20

6.2 Reliability assessment with penetration of one DG 25

6.3 Reliability assessment with penetration of multiple DGs 28

6.4 Reliability assessment vs Distance 31

Section 7 – Conclusion 33

References 34

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LIST OF FIGURES

Figure 1.1 – System subdivision………………………………………………………...…2

Figure 1.2 – Two state model………………………………………………………….…..3

Figure 1.3 – Stages of a component…………………………………………………….….3

Figure 2.1 – Radial distribution system……………………………………………………4

Figure 2.2 – Reliability parameters for buses………………………………………………5

Figure 2.3 – Data for cable…………………………………………………………………5

Figure 2.4 – Reliability parameter for Cable………………………………………………5

Figure 2.5 – System Annual Outage Duration in (hour/year) and (hour)…………………6

Figure 2.6 – Parallel system……………………………………………………………….7

Figure 2.7 – Parallel system annual outage duration (hr)…………………………………8

Figure 2.8 – Parallel system annual outage duration (hr/yr)………………………………8

Figure 2.9 – Single and double contingency………………………………………………9

Figure 2.10 – Single contingency, System annual outage duration (hr)………….………11

Figure 2.11 – Double contingency, System annual outage duration (hr/yr)………..……11

Figure 2.12 – System annual outage duration (hr)……………………………….….……11

Figure 2.13 – System annual outage duration (hr/yr)…………………………….………11

Figure 3.1 – Complete SLD of RBTS……………………………………………………13

Figure 3.2 – System data…………………………………………………………………15

Figure 3.3 – System for RBTS Bus 2………………………………………………..……15

Figure 4.1 – Analytical technique for reliability calculation………………………..……18

Figure 5.1 – Modified bus 2 of RBTS……………………………………………………19

Figure 6.1 – Reliability assessment results for modified bus 2 of RBTS without DG

connected……………………………………………………………..……20

Figure 6.2 – Summary (left) and output load point report (right)………………..………21

Figure 6.3 – Example elements contribution towards ECOST and EENS……..…………22

Figure 6.4 – Sensitivity analysis for ECOST at load point ‘Commercial 1’……..………23

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Figure 6.5 – Sensitivity analysis for EENS at load point ‘Commercial 1’………….……24

Figure 6.6 – DG insertion at load point ‘G&I 4’…………………………………….……25

Figure 6.7 – RA after DG insertion at load point ‘G&I 4’…………………………..……26

Figure 6.8 – Sensitivity analysis for EENS after DG insertion at load point

‘Commercial 1’……………………………………………………..………26

Figure 6.9 – Sensitivity analysis for ECOST after DG insertion at load point

‘Commercial 1’………………………………………………………..……27

Figure 6.10 – Summary after insertion of DG at load point ‘G&I 4’……………………27

Figure 6.11 – Multiple DG penetration at load point ‘G&I 4’………………………..….28

Figure 6.12 – RA for multiple DG penetration at load point ‘G&I 4’……………………29

Figure 6.13 – Summary for multiple DG penetration at load point ‘G&I 4’……….……30

Figure 6.14 – Location of DG insertion at various load points……………………..……31

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LIST OF TABLES

Table 3.1 – Peak load contribution……………………………………………………….14

Table 3.2 – Feeder lengths…………………………………………………………..……14

Table 6.1 – Comparison of DG insertion in case of single DG and multiple DG

Insertion………………………………………………………………….….29

Table 6.2 – Comparison of reliability indices for DG insertion at various locations……32

viii

ABSTRACT

RELIABILITY OF DISTRIBUTION SYSTEMS

USING MARKOV PROCESS AND ETAP

By

Kunal Raut

Master of Science in Electrical Engineering

Studies carried out by the US Department of Energy [10] states that out of the total

generating capacity 20% is derived from distributed generation. Power systems utilities

predict that in near future, the number of “Distributed Energy Generators” installed will

increase due to its reliability, flexibility, efficiency, upgradability and diversity. Electricity

could not be stored readily and thus is generated and consumed instantaneously, thereby

making it mandatory to maintain a tradeoff between the generated and consumed power.

On the other hand, the ever increasing demand for electricity makes system planning and

operations an important task. This can be achieved and done precisely with the aid of

system reliability.

This project pinpoints assessment of a system designed by Roy Billinton [3]. The

intention is to examine the consequences of DEG on the network. The analysis being

carried out on HLIII and the improvement in system reliability is studied using various

indices. Additionally, system response in terms of overall reliability is observed and

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analyzed after penetration of single DG and multiple DG near the load point. Later, the

relation between system reliability and the distance of the installed DEG is analyzed.

Recollecting the importance of system reliability for distribution companies from

an investment point of view is also one of the objective. Studies and analysis are supported

and are verified using ETAP software [9].

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SECTION 1: INTRODUCTION

Electrical power system being the most vital system is also the most complex

system designed by mankind. Since its invention, electrical power system has been

constantly developing and expanding to meet the increasing demands. The prime function

of such a system is to provide uninterrupted electricity to its consumers, and this has always

been the priority of the utility companies.

A grid comprises of generating stations, transmission line and distribution network.

Initially, reliability study was carried out on the generating and transmission level rather

than on distribution system since generating and transmission system outages are costly

and the latter being comparatively cheap and localized. However, recent studies have

shown that distribution system accounts for up to 80% - 85% of all the reliability problems.

Thus, reliability improvement at the distribution level is of utmost importance as it goes

hand in hand with the cost of electricity and consumer satisfaction. Failure in doing so can

lead to a series of problems which include system overloading, power outages and transient

behavior of the system.

This research work is aimed at assessment of reliability of the RBTS – 2 bus test

system [3] using the Reliability assessment tool of the Electrical Transient Analyzer

Program (ETAP) [9] and analytical techniques. This research will have 9 sections in total.

Section 1 gives a quick introduction, followed by network reliability in section 2. Section

3 explains the basics of reliability using Markov process and 2 state models, the reliability

assessment module of ETAP is being explained in the succeeding section, whereas the

reliability parameters and its calculation is presented in the subsequent section. Simulation

of a RBTS test model and its analysis for different scenario are explained in section 6 and

section 7 respectively. Finally, the results and conclusion are explained in section 8 and

section 9 respectively.

1.1 Reliability concepts

Reliability has a very broad definition, but a universally accepted definition would

be: “Reliability is the probability of a device performing its purpose adequately for the

period of time intended under the operating conditions encountered.” [10]

Based on this on can say that reliability can be broken down into:

a) Probability

b) Performance

c) Time

d) Operating conditions

Probability is the input for reliability assessment and is a numerical value. The rest

being engineering parameters, does not follow probabilistic methods.

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System reliability is governed by two parameters as shown in below figure :

Figure 1.1 – System sub-division

Adequacy is ability of the system to meet customer load demands continuously with

the help of facilities available within the system. Whereas, security is system’s potential to

tolerate certain disruptions.

1.2 Reliability assessment techniques

No specific formula for reliability calculation exist, the approach used by engineers

to deduce reliability is either by understanding the problem or by making assumptions. The

guidelines followed by engineers to deduce reliability in a power system are as follows

a. Know how the system operates

b. Point out ways it could fail

c. Identify how the failure will affect the system

d. Perform reliability survey

Reliability can be estimated by analytical or simulation methods. Mathematical

models serve as a base for reliability calculations using analytical methods, where system

indices are calculated and compared. Simulation methods like Monte Carlo have a

relatively high computing time and simulate random nature of the system. A standard

procedure would be to divide and simplify the entire system into small components and

estimate the reliability of those components. Once the individual component reliability is

known the reliability of the entire network can be calculated after combining the

component reliability with the aid of available analytical techniques.

1.3 Continuous Markov process

In a continuous Markov process the probability of a component to be either in a failed

state or healthy state is constant for a fixed time interval. Components in power system

thereby can be represented by these two states. As seen in Figure 1.2, “State 0” indicates

healthy state and is operational, whereas “State 1” indicates a failed state and its inability

to perform the task. The change in state occurs with a rate of "𝜆" (failure rate) and from

‘State 1’ to ‘State 0’ with a rate of "𝑟" (repair rate). Here the failure rate depends upon the

active and passive failure rate of the component.

Reliability

Adequacy Security

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Figure 1.2 – Two state model

The stages of a component are described in Figure 1.3.

Figure 1.3 – Stages of a component

(Source:https://www.researchgate.net)

The addition of MTTD, MTTR and MTTF is MTBF. The equations below depict

the relations between the transition rates.

𝑀𝑇𝑇𝐹 = 1/𝜆

𝑀𝑇𝑇𝑅 = 1/𝑟

𝑀𝑇𝐵𝐹 = 𝑀𝑇𝑇𝐷 + 𝑀𝑇𝑇𝑅 + 𝑀𝑇𝐵𝐹 = 1/𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

State 0

UP

State 1

DOWN

𝜆 = 𝜆𝐴 + 𝜆𝑃

𝑟

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SECTION 2 : RELIABILITY ASSESSMENT MODULE IN ETAP

The reliability assessment module in ETAP serves as a tool for engineers for

estimating the reliability of a system. Reliability can be calculated for radial as well as

looped systems. Calculating network reliability, its indices and ability to use single

contingency or double contingency method are some of the key features of this tool. This

tool also allows user to plot the energy (cost) indices for the entire system or specific

components graphically.

Consider a simple radial distribution system as mentioned below. The utility has a

short circuit rating of 100 MVAsc and both the buses are rated at 10kV. A 3C x 50 mm2

Copper cable with XLPE insulation, measuring 1 km in length connects Bus 1 and Bus 2.

Failure and repair rates for various components are shown below.

Figure 2.1 – Radial distribution system

Here the average failure rate is,

𝜆 = (𝑛𝑜. 𝑜𝑓 𝑏𝑢𝑠𝑒𝑠 × 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒𝑠) + (𝑛𝑜. 𝑜𝑓 𝑐𝑎𝑏𝑙𝑒𝑠 × 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 )

𝜆 = [3 (𝑈1, 𝐵𝑢𝑠 1 𝑎𝑛𝑑 𝐵𝑢𝑠 2) × 0.001 (𝐹 𝑦𝑟⁄ )] + 0.05 (𝐹 𝑦𝑟⁄ )

𝜆 = 0.053 𝐹𝑎𝑖𝑙𝑢𝑟𝑒/𝑦𝑒𝑎𝑟 …...(1)

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Figure 2.2 – Reliability parameters for buses Figure 2.3 – Data for cable

Also, the unavailability of the

system can be calculated from the

formula mentioned below,

𝑈 = (𝑛𝑜. 𝑜𝑓 𝑏𝑢𝑠𝑒𝑠 × 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒

× 𝑀𝑇𝑇𝑅)

+ (𝑛𝑜. 𝑜𝑓 𝑐𝑎𝑏𝑙𝑒𝑠

× 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒

× 𝑀𝑇𝑇𝑅)

𝑈 = [3 × 0.001 (𝐹 𝑦𝑟⁄ ) × 2 (ℎ𝑟)]

+ [1 × 0.05 (𝐹/𝑦𝑟)× 30 (ℎ𝑟)]

𝑈 = 1.506 𝐻𝑜𝑢𝑟 𝑦𝑒𝑎𝑟⁄ ...…(2)

Figure 2.4 – Reliability parameter for Cable

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From eq. 1 and eq. 2, load side reliability is formulated and the same can be compared with

the result obtained in ETAP as depicted in figure 2.5

𝐿𝑜𝑎𝑑 𝑝𝑜𝑖𝑛𝑡 𝑟𝑒𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑖𝑛𝑑𝑒𝑥 =𝑈𝑛𝑎𝑣𝑎𝑖𝑙𝑖𝑏𝑖𝑙𝑖𝑡𝑦

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒=

1.506 ℎ𝑟/𝑦𝑟

0.053 𝑓/𝑦𝑟

𝐿𝑜𝑎𝑑 𝑝𝑜𝑖𝑛𝑡 𝑟𝑒𝑖𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑖𝑛𝑑𝑒𝑥 = 28.42 ℎ𝑟/𝑓𝑎𝑖𝑙𝑢𝑟𝑒

Figure 2.5 – System Annual Outage Duration in (hour/year) and (hour)

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Now, consider a parallel structure as depicted in figure 2.6. Here the reliability of

the system is regulated by the two 10MVA transformers (T1 and T2) and the two lines

supplying power to the motors (Mtr1 and Mtr2). Data for various components in the system

is as follows:

Utility and buses:

Active failure rate (λa) = 0.001 failure/year

MTTR = 2 hours

MTTF = 1000 years

Switching time = 2 hours

Breakers:

Active failure rate (λa) = 0.003 failure/year

Passive failure rate (λp) = 0.002failure/year

MTTR = 30 hour

MTTF = 200 years

Switching time = 50 hours Figure 2.6 – Parallel structure

Transformers:

Active failure rate (λa) = 0.025 failure/year

MTTR = 200 hours

MTTF = 40 years

Switching time = 200 hours

Here, reliability indices at the main bus are to be calculated. As seen from figure

2.6, main bus would de-energize in one of the below mentioned cases

1. Breaker 1 fails actively or passively

2. Breaker 2 or breaker 3 fails actively

3. Utility grid fails

4. Main bus fails itself

Based on these cases the failure rate for the main bus can be calculated.

𝜆𝑚𝑎𝑖𝑛 = (𝜆𝑎 + 𝜆𝑝)𝐶𝐵1 + (𝜆𝑎)𝐶𝐵2 + (𝜆𝑎)𝐶𝐵3 + 𝜆𝑈1 + 𝜆𝑚𝑎𝑖𝑛

= (0.003 + 0.002) + 0.003 + 0.003 + 0.001 + 0.001

𝜆𝑚𝑎𝑖𝑛 = 0.013 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑦𝑒𝑎𝑟⁄ …...(3)

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Similarly, the unavailability of the main bus can be formulated as,

𝑈𝑚𝑎𝑖𝑛 = [𝑀𝑇𝑇𝑅𝐶𝐵1 × (𝜆𝑎 + 𝜆𝑝)𝐶𝐵1

] + [𝑀𝑇𝑇𝑅𝐶𝐵2 × (𝜆𝑎)𝐶𝐵2]

+ [𝑀𝑇𝑇𝑅𝐶𝐵3 × (𝜆𝑎)𝐶𝐵3] + [𝑀𝑇𝑇𝑅𝑈1 × 𝜆𝑈1] + [𝑀𝑇𝑇𝑅𝑚𝑎𝑖𝑛 × 𝜆𝑚𝑎𝑖𝑛]

= [30 × (0.003 + 0.002)] + [30 × 0.003] + [30 × 0.003] + [2 × 0.001]

+ [2 × 0.001]

𝑈𝑚𝑎𝑖𝑛 = 0.334 ℎ𝑜𝑢𝑟 𝑦𝑒𝑎𝑟⁄ …...(4)

The time to replace the main bus can be calculated using equation 3 and equation 4,

𝑅𝑚𝑎𝑖𝑛 =𝑈𝑚𝑎𝑖𝑛

𝜆𝑚𝑎𝑖𝑛=

0.334 ℎ𝑜𝑢𝑟 𝑦𝑒𝑎𝑟⁄

0.013 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑦𝑒𝑎𝑟⁄

𝑅𝑚𝑎𝑖𝑛 = 25.692 ℎ𝑜𝑢𝑟𝑠

Figure 2.7 : System annual outage duration Figure 2.8 : System annual outage duration (hr/yr) (hr)

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ETAP provides an added advantage of selecting the method of analysis, one can

choose either single contingency or double contingency. To understand this concept let us

consider a system with two parallel branches as shown in Figure 2.9. In case of single

contingency analysis, ETAP considers that only one of the two branches have failed

whereas in double contingency simultaneous failure of both the branches is considered

along with failure of either one of the branch.

Figure 2.9 – Single and double contingency

In the case of single contingency, failure of either transformer 1 or transformer 2 is

considered at a time. Whereas in case of double contingency simultaneous failure of

transformer 1 and transformer 2 is considered in addition.

The data for various components in the system are as follows:

Breakers (CB1 and CB9):

Active failure rate (λa) = 0.003 failure/year

Passive failure rate (λp) = 0.002failure/year

MTTR = 30 hour

MTTF = 200 years

Switching time = 50 hours

Buses (Bus 1 and Bus 2) and Utlity (U-1):

Active failure rate (λa) = 0.001 failure/year

MTTR = 2 hours

MTTF = 1000 years

10

Switching time = 2 hours

Transformers:

Active failure rate (λa) = 1 failure/year

MTTR = 200 hours

MTTF = 1 year

Switching time = 200 hours

For simplicity of analytical calculations, the failure rates of the breakers connecting the

transformers to the buses are considered to be zero.

2.1 Single contingency

𝜆𝑠𝑖𝑛𝑔𝑙𝑒 = 𝜆𝑈1 + (𝜆𝑎 + 𝜆𝑝)𝐶𝐵1 + 𝜆𝑚𝑎𝑖𝑛 + (𝜆𝑎)𝐶𝐵2 + (𝜆𝑎)𝐶𝐵6

= 0.001 + (0.003 + 0.002) + 0.001 + 0.001 + 0.003

𝜆𝑠𝑖𝑛𝑔𝑙𝑒 = 0.011 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑦𝑒𝑎𝑟⁄ …...(5)

The unavailability of the main bus can be formulated as,

𝑈𝑠𝑖𝑛𝑔𝑙𝑒 = [𝑀𝑇𝑇𝑅𝑈1 × 𝜆𝑈1] + [𝑀𝑇𝑇𝑅𝐶𝐵1 × (𝜆𝑎 + 𝜆𝑝)𝐶𝐵1

] + [𝑀𝑇𝑇𝑅𝑚𝑎𝑖𝑛 × 𝜆𝑚𝑎𝑖𝑛]

+ [𝑀𝑇𝑇𝑅𝐶𝐵2 × (𝜆𝑎)𝐶𝐵2] + [𝑀𝑇𝑇𝑅𝐶𝐵6 × (𝜆𝑎)𝐶𝐵6]

= [2 × 0.001] + [30 × (0.003 + 0.002)] + [2 × 0.001] + [2 × 0.001]

+ [30 × 0.003]

𝑈𝑠𝑖𝑛𝑔𝑙𝑒 = 0.246 ℎ𝑜𝑢𝑟 𝑦𝑒𝑎𝑟⁄ …...(6)

The time to replace the main bus can be calculated using equation 3 and equation 4,

𝑅𝑠𝑖𝑛𝑔𝑙𝑒 =𝑈𝑠𝑖𝑛𝑔𝑙𝑒

𝜆𝑠𝑖𝑛𝑔𝑙𝑒=

0.246 ℎ𝑜𝑢𝑟 𝑦𝑒𝑎𝑟⁄

0.011 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑦𝑒𝑎𝑟⁄

𝑅𝑠𝑖𝑛𝑔𝑙𝑒 = 22.36 ℎ𝑜𝑢𝑟𝑠

11

Figure 2.10 – System annual outage duration Figure 2.11 – System annual outage duration

(hr) (hr/yr)

2.2 Double contingency

Figure 2.12 – System annual outage duration Figure 2.13 – System annual outage duration

(hr) (hr/yr)

12

In case of double contingency analysis, the indices at Bus 1 are the same whereas

the same are a lot higher at Bus 2. This is due to the consideration that both the transformers

(Tr 1 and Tr 2) fail at the same time. As mentioned earlier, for simplicity the failure rates

of both the transformers is considered 1 and λ for the breakers connecting both the

transformers to the buses are assumed to be 0.

Failure rate at Bus 2:

𝜆𝑑𝑜𝑢𝑏𝑙𝑒 =

𝜆1𝜆2(𝑟1 + 𝑟2)8760

1 +𝜆1𝑟1 + 𝜆2𝑟2

8760

=

1 × 1 × (200 + 200)8760

1 +(1 × 200) + (1 × 200)

8760

𝜆𝑑𝑜𝑢𝑏𝑙𝑒 = 0.0437 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑦𝑒𝑎𝑟⁄

The total failure rate (λtotal) would be,

𝜆𝑡𝑜𝑡𝑎𝑙 = 𝜆𝑠𝑖𝑛𝑔𝑙𝑒 + 𝜆𝑑𝑜𝑢𝑏𝑙𝑒

= 0.011 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑦𝑒𝑎𝑟⁄ + 0.0437 𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑦𝑒𝑎𝑟

𝜆𝑡𝑜𝑡𝑎𝑙 = 0.0547 𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑦𝑒𝑎𝑟

13

SECTION 3 : ROY BILLINTON TEST SYSTEM (RBTS)

A test system was presented to estimate the overall indices and predict system

reliability from a customer point of view. This test system, also called as RBTS, consists

of three level of hierarchy:

1. Level one, HLI – Reliability evaluation of generation system

2. Level two, HLII – Reliability evaluation of generation and transmission system

3. Level three, HLIII – Overall system reliability

Figure 3.1 – Complete SLD of RBTS [3]

14

This research work focuses on the HLIII and helps in assessing customer side

reliability. The primary system reliability indices at HLIII are ‘λ’, ‘r’ and annual

unavailability (U). HLIII reliability indices at the load are called as customer oriented

indices and are:

a) Average Service Availability Index (ASAI)

b) System Avg. Interruption Duration Index (SAIDI)

c) Average Service Unavailability Index (ASUI)

d) System Avg. Interruption Freq. Index (SAIFI)

e) Customer Avg. Interruption Duration Index (CAIDI)

As seen in Figure 3.1, the 6-bus test system has voltage levels of 230kV, 138kV,

33kV, 11kV and 220V. It consists of 11 generators, 9 transmission lines and five load

buses. This research is dedicated to the distribution system located at bus 2 which

represents a typical urban system with household loads, institutional loads, commercial

load and industrial load which adds up to a total of 1256 customers and has a peak load of

20MW. The contribution of various customers towards the peak load is as follows:

Sr. No. Customer Type Peak load (MW)

1 Residential 7.25

2 Industrial 3.50

3 Government/Institution 5.55

4 Commercial 3.70

Total 20 Table 3.1 – Peak load contribution

The 11kV feeders and laterals are considered to be cables and their lengths are

mentioned in Table 3.2, whereas the diagram for RBTS bus-2 and its network data is shown

in Fig. 3.3 and Fig. 3.2 respectively.

Sr. No. Length (km) Feeder numbers (as per Figure 3.3)

1 0.60 2, 6, 10, 14, 17, 21, 25, 28, 30, 34

2 0.75 1, 4, 7, 9, 12, 16, 19, 22, 24, 27, 29, 32, 35

3 0.80 3, 5, 8, 11, 13, 15, 18, 20, 23, 26, 31, 33, 36 Table 3.2 – Feeder lengths

The RBTS bus 2 system consists of 17 transformers in total which includes 2 x

16MVA 33kV/11kV HT transformers and 15 x 2MVA 11kV/220V LT transformers. The

system data in Figure 3.2 provides the user important data like the permanent and active

failure rates (λa and λp), repair time (r), switching time (s), outage rate during maintenance

(λ’’) and outage time during maintenance (r’’) for various components.

15

Figure 3.2 – System data [4]

Figure 3.3 – System for RBTS Bus 2 [4]

16

SECTION 4 : EVALUATION OF RELIABILITY INDICES

In a distribution system consisting of components, loads and customers the

reliability can be calculated using the parameters mentioned below. These reliability

indices help us determine the reliability of the entire system. As per IEEE standards any

interruption which is longer than 5 mins is termed as “sustained interruption”. The primary

system reliability indices are:

1. Failure rate @ ‘j’ (λj)

𝜆𝑗(𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑦𝑒𝑎𝑟) = ∑ 𝜆𝑒,𝑖(𝑎𝑣𝑔. 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑖)

𝑛𝑜.𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠(𝑖)

2. Annual Outage Duration @ ‘j’ (Ui)

𝑈𝑗(ℎ𝑟 𝑦𝑒𝑎𝑟⁄ ) = ∑ 𝜆𝑒,𝑖(𝑎𝑣𝑔. 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑖)

𝑛𝑜.𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠(𝑖)

× 𝑟𝑖𝑗(𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 @ 𝑗 )

3. Avg. Outage duration @ ‘j’

𝑟𝑗(ℎ𝑟𝑠. ) =𝑈𝑗(𝐴𝑛𝑛𝑢𝑎𝑙 𝑜𝑢𝑡𝑎𝑔𝑒 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 @ 𝑗)

𝜆𝑗(𝐴𝑣𝑔. 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 @ 𝑗)

Similarly, the sustained interruption indices:

1. SAIFI

𝑆𝐴𝐼𝐹𝐼 =𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛𝑠

𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. 𝑠𝑒𝑟𝑣𝑒𝑑

𝑆𝐴𝐼𝐹𝐼 (𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟) =∑ 𝜆𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. @ ′𝑗′)

∑ 𝑁𝑗

2. SAIDI

𝑆𝐴𝐼𝐷𝐼 =𝑆𝑢𝑚 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛𝑠 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛

𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 𝑠𝑒𝑟𝑣𝑒𝑑

𝑆𝐴𝐼𝐷𝐼 (ℎ𝑜𝑢𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟) =∑ 𝑈𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. @ ′𝑗′)

∑ 𝑁𝑗

17

3. CAIDI

𝐶𝐴𝐼𝐷𝐼 =𝑆𝑢𝑚 𝑜𝑓 𝑐𝑢𝑠𝑡. 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛𝑠 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛

𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛𝑠

𝐶𝐴𝐼𝐷𝐼 (ℎ𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛) =∑ 𝑈𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 @ ′𝑗′)

∑ 𝜆𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 @ ′𝑗′)

4. ASAI

𝐴𝑆𝐴𝐼 =𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑓𝑜𝑟 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 (𝑖𝑛 ℎ𝑟𝑠. )

𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝑑𝑒𝑚𝑎𝑛𝑑𝑒𝑑 𝑏𝑦 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 (𝑖𝑛 ℎ𝑟𝑠. )

𝐴𝑆𝐴𝐼 (𝑝𝑢) =∑ 𝑁𝑗 × 8760 (𝑛𝑜. 𝑜𝑓 ℎ𝑟𝑠. 𝑖𝑛 𝑎 𝑐𝑎𝑙𝑒𝑛𝑑𝑎𝑟 𝑦𝑒𝑎𝑟) − ∑ 𝑁𝑗𝑈𝑗

∑ 𝑁𝑗 × 8760 (𝑛𝑜. 𝑜𝑓 ℎ𝑟𝑠. 𝑖𝑛 𝑎 𝑐𝑎𝑙𝑒𝑛𝑑𝑎𝑟 𝑦𝑒𝑎𝑟)

5. ASUI

𝐴𝑆𝑈𝐼 (𝑝𝑢) = 1 − 𝐴𝑆𝐴𝐼

6. EENS

𝐸𝐸𝑁𝑆 = ∑ 𝐸𝐸𝑁𝑆𝑗

𝐸𝐸𝑁𝑆𝑗(𝑀𝑊. ℎ𝑜𝑢𝑟/𝑦𝑒𝑎𝑟) = 𝑃𝑗(𝐷𝑒𝑚𝑎𝑛𝑑 𝑎𝑡 𝑙𝑜𝑎𝑑 𝑝𝑜𝑖𝑛𝑡 ′𝑗′) × 𝑈𝑗

18

Analytical technique for reliability calculation of power system uses the flowchart

depicted in Figure 4.1.

Figure 4.1 – Analytical technique for reliability calculation

Start

Get system and customer data

X=1

Consider failure for a component ‘x’

Identify the affected load points

Calculate λlp, rlp and Ulp for that affected load point

More

components.?

Accumulate load point indices to evaluate λ, r and U

Report

End

X=X+1

19

SECTION 5 : RELIABILITY ANALYSIS USING RBTS MODEL

In this research, modified RBTS bus 2 system is taken into consideration and

reliability assessment is carried out by using the ETAP software. The system data for the

bus 2 is as per RBTS and the failure rates for various components, feeder length and loads

are as per data mentioned in section 3.

.

Figure 5.1 – Modified bus 2 of RBTS

Analysis of this model is done using four different scenarios and the results for each

of the case is tabulated and compared to show the diverse effect of DG and its distance on

the overall reliability of the system. The different scenarios considered in this research are

as follows:

1. Reliability assessment without any DG connected

2. Reliability assessment with penetration of one DG

3. Reliability assessment with penetration of multiple DGs

4. Reliability assessment vs Distance

20

SECTION 6 : RESULTS AND DISCUSSION

6.1 Case 1: Reliability assessment without any DG connected

Reliability analysis for the RBTS system without any DG connected in the system

was carried out utilizing the RA tool in ETAP and the output attained are:

Figure 6.1 – Reliability assessment results for modified bus 2 of RBTS without DG connected

The customer oriented indicia are analytically evaluated using network, load point

and bus. ETAP provides a summary of all the various customer oriented indices along with

the results for sensitivity analysis which includes EENS and ECOST. ETAP also provides

graphical display of the reliability results and helps the user to understand the contribution

of various components towards the overall system reliability. The report generated by

ETAP contains all of the aforementioned data along with load point output report and

sensitivity analysis.

21

Figure 6.2 – Summary (left) and output load point report (right)

𝑆𝐴𝐼𝐷𝐼 (ℎ𝑜𝑢𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟) =∑ 𝑈𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 𝑎𝑡 𝑙𝑜𝑎𝑑 𝑝𝑜𝑖𝑛𝑡 ′𝑗′)

∑ 𝑁𝑗

=

(7.64) + (9.67) + (6.99 × 210) + (10.15 × 210) + (10.33 × 200) + (12.17) +(12.33) + (14.15 × 10) + (7.66 × 10) + (7.17 × 200) + (9.68 × 200)

+(10.33 × 200) + (12.82) + (14.66) + (14.82 × 10)

1 + 1 + 210 + 210 + 200 + 1 + 1 + 10 + 10 + 200 + 200 + 200 + 1 + 1 + 10

=11536.99

1256

𝑆𝐴𝐼𝐷𝐼 (ℎ𝑜𝑢𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟) = 9.1855 ℎ𝑜𝑢𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟

Similarly,

𝑆𝐴𝐼𝐹𝐼 (𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟) =∑ 𝜆𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 𝑎𝑡 𝑙𝑜𝑎𝑑 𝑝𝑜𝑖𝑛𝑡 ′𝑗′)

∑ 𝑁𝑗

=

(1.7285) + (2.1375) + (1.5985 × 210) + (2.2350 × 210) + (2.2720 × 200) +(2.6440) + (2.6765) + (3.0410 × 10) + (1.7345 × 10) + (1.6370 × 200) +(2.1435 × 200) + (2.2735 × 200) + (2.7740) + (3.1445) + (3.1770 × 10)

1 + 1 + 210 + 210 + 200 + 1 + 1 + 10 + 10 + 200 + 200 + 200 + 1 + 1 + 10

22

=2564.865

1256

𝑆𝐴𝐼𝐹𝐼 (𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟) = 2.042 𝑓𝑎𝑖𝑙𝑢𝑟𝑒/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟. 𝑦𝑒𝑎𝑟

Also,

𝐶𝐴𝐼𝐷𝐼 (ℎ𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛) =∑ 𝑈𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 ′𝑗′)

∑ 𝜆𝑗 × 𝑁𝑗(𝑛𝑜. 𝑜𝑓 𝑐𝑢𝑠𝑡. 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 ′𝑗′)

=2564.865

2.042

𝐶𝐴𝐼𝐷𝐼 (ℎ𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛) = 4.498 ℎ𝑟/𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑟𝑢𝑝𝑡𝑖𝑜𝑛

Figure 6.3 – Example of elements contribution towards ECOST and EENS

For Average Service Availability Index (ASAI),

𝐴𝑆𝐴𝐼 (𝑝𝑢) =∑ 𝑁𝑗 × 8760 (𝑛𝑜. 𝑜𝑓 ℎ𝑟𝑠. 𝑖𝑛 𝑎 𝑐𝑎𝑙𝑒𝑛𝑑𝑎𝑟 𝑦𝑒𝑎𝑟) − ∑ 𝑁𝑗𝑈𝑗

∑ 𝑁𝑗 × 8760 (𝑛𝑜. 𝑜𝑓 ℎ𝑟𝑠. 𝑖𝑛 𝑎 𝑐𝑎𝑙𝑒𝑛𝑑𝑎𝑟 𝑦𝑒𝑎𝑟)

=(1256 × 8760) − (11536.99)

(1256 × 8760)

23

𝐴𝑆𝐴𝐼 (𝑝𝑢) = 0.9989 𝑝𝑢

Thus,

Average Service Unavailability Index, 𝐴𝑆𝑈𝐼 (𝑝𝑢) = 1 − 𝐴𝑆𝐴𝐼

𝐴𝑆𝑈𝐼 (𝑝𝑢) = 0.001048 𝑝𝑢

And for EENS,

𝐸𝐸𝑁𝑆 = ∑ 𝐸𝐸𝑁𝑆𝑗

= ∑

(7.64 × 0.961) + (9.67 × 1.105) + (6.99 × 0.455) + (10.15 × 0.455) +(10.33 × 0.382) + (12.17 × 0.481) + (12.33 × 0.481) + (14.15 × 0.386)

+(7.66 × 0.386) + (7.17 × 0.382) + (9.68 × 0.382) + (10.33 × 0.382)

+(12.82 × 0.481) + (14.66 × 0.481) + (14.82 × 0.386)

𝐸𝐸𝑁𝑆 = 79.237 𝑀𝑊. ℎ𝑜𝑢𝑟/𝑦𝑒𝑎𝑟

Sensitivity analysis for ECOST and EENS was carried out near load point

‘Commercial 1’ which has a total of 10 customers and load of 0.454 MVA. As seen from

the graph the element that is closest to the load point contributes the maximum whereas

the elements which are farther away from the load point contribute minimum and the

same could be observed.

Figure 6.4 – Sensitivity analysis for ECOST at load point ‘Commercial 1’

24

Figure 6.5 – Sensitivity analysis for EENS at load point ‘Commercial 1’

25

6.2 Case 2: Reliability assessment with penetration of one DG

Consider a case where a Wind turbine is placed near load point ‘Government and

Institution 4’. The wind turbine is considered as a source of DG and its reliability data is

as follows:

Wind Turbine rating : 1 MW

λ (F/yr) : 0.020

r (hours) : 50 hrs.

Switching time (hr) : 1 hr.

The reliability analysis results for this case is shown in figure 6.7 whereas the

sensitivity analysis for ECOST and EENS and the summary of customer oriented indices

and are shown in figure 6.8, 6.9 and 6.10 respectively.

Figure 6.6 – DG insertion at load point ‘G&I 4’

26

Figure 6.7 – RA after DG insertion at load point ‘G&I 4’

Figure 6.8 – Sensitivity analysis for EENS after DG insertion at load point ‘Commercial 1’

27

Figure 6.9 – Sensitivity analysis for ECOST after DG insertion at load point ‘Commercial 1’

Figure 6.10 – Summary after insertion of DG at load point ‘G&I 4’

When compared with the customer oriented indices obtained in case 1, the overall

reliability is improved drastically.

28

6.3 Case 3: Reliability assessment with penetration of multiple DGs

Figure 6.11 – Multiple DG penetration at load point ‘G&I 4’

As seen from figure 6.11, two DG sets are connected at load point ‘G&I 4’. The

rating and failure rates of both the DGs are the same and are similar to the one used in

case 2. Results from case 2 and case 3 are tabulated and compared in table 6.1 whereas

the reliability assessment results and the summary for the customer oriented indices are

shown in figure 6.12 and 6.13 respectively.

From table 6.1 injection of more than one DG units at one location had an adverse

effect on the system and its reliability by a measurable amount.

29

Table 6.1 – Comparison of DG insertion in case of single DG and multiple DG insertion

Figure 6.12 – RA for multiple DG penetration at load point ‘G&I 4’

Point of

injection

G&I 4

SAIFI

(f /

cust.

yr)

SAIDI

(hr/

cust.

yr)

CAIDI

(hr/

cust.

Intr.)

ASAI

(pu)

ASUI

(pu)

EENS

(MWH

/yr

ECOST

($/year)

Single DG 1.2008 6.9361 5.776 0.9992 0.00079 58.907 261792.9

Multiple

DG

1.2010 6.9449 5.783 0.9992 0.00079 59.774 268841.3

30

Figure 6.13 – Summary for multiple DG penetration at load point ‘G&I 4’

31

6.4 Case 4: Reliability vs Distance

After analyzing DG penetration on the system reliability, the effect of DG location

is evaluated. Six different load points marked as ‘A-F’ are selected which include load

classes that include residential, industrial, government and institutional and commercial

loads. Customer oriented reliability indices are evaluated for these six points. The figure

shown below depicts the various location where the DG would be inserted.

Figure 6.14 – Location of DG insertion at various load points

The customer oriented reliability indices and the sensitivity indices are compared

with case 1 and are tabulated in table 6.2.

32

Table 6.2 – Comparison of reliability indices for DG insertion at various locations

As seen from the above table it can be concluded that the optimum location for DG

insertion would be near load point A. Also, one can conclude that the overall system

reliability is increased upon addition of a DG near the load points.

Case SAIFI

(f / cust.

yr)

SAIDI

(hr / cust.

yr)

CAIDI

(hr / cust.

Intr.)

ASAI

(pu)

ASUI

(pu)

EENS

(MWH/

yr)

ECOST

($/year)

W/O DG 2.0421 9.1853 4.498 0.9990 0.00105 79.306 335176.40

A 1.2008 6.9361 5.776 0.9992 0.00079 58.907 261792.90

B 1.2158 7.300 6.004 0.9992 0.00083 65.690 289815.70

C 1.3957 8.3441 5.978 0.9990 0.00095 72.106 312587.70

D 1.2101 6.9803 5.768 0.9992 0.00080 59.815 263797.40

E 1.2244 7.3488 6.002 0.9992 0.00084 65.992 291103.00

F 1.3944 7.8833 5.653 0.9991 0.00090 71.344 310861.90

33

SECTION 7 : CONCLUSION

Reliability analysis on modified bus 2 of the test system portrayed the effect of DG

insertion on overall system reliability. A total of four cases were considered and the system

behavior in each of these cases was observed and tabulated. The customer oriented indices

and the system reliability indices clearly indicate that system reliability is increased after

DG placement near to the load or far away from the feeder. We could also observe that

when multiple DG are placed near to the load, the system reliability decreases. This

concludes that system reliability is highly sensitive to the location of the DG.

Based on the results obtained, system designers and planners can identify the weak

points and take necessary actions to improve overall system reliability. Additionally, one

could also benchmark the system performance and compare it after system expansion. One

major advantage of this analysis is that supply interruption cost can be reduced drastically

by investing more on one of the load points during system planning.

34

REFERENCES

[1] Billinton Roy,, and R. Norman,. “Reliability Evaluation of Engineering Systems:

Concepts and Techniques”, Second ed., Plenum Press, 1983.

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