SANDIA REPORT

SAND2006-1277

NREL/TP-620-39561

Unlimited Release

Printed March 2006

Impact of Distributed Energy Resources

on the Reliability of a Critical

Telecommunications Facility

David Robinson

Christopher Atcitty

Jason Zuffranieri

Doug Arent

Prepared by

Sandia National Laboratories

Albuquerque, New Mexico 87185 and Livermore, California 94550

in support of the

National Renewable Energy Laboratory

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Office of Energy Efficiency and Renewable Energy

by Midwest Research Institute Battelle under Contract No. DE-AC36-99-GO103

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•
 •


NITED STATES OF AMERICA

2
SAND2006-1277NREL/TP-620-39561

Unlimited Release

Printed March 2006

Impact of Distributed Energy Resources on the

Reliability of a Critical Telecommunications

Facility

David Robinson, Christopher Atcitty, Jason Zuffranieri

Risk and Reliability Analysis Department

Sandia National Laboratories

Albuquerque, NM 87185-0748

drobin@sandia.gov

Douglas Arent

National Renewable Energy Laboratory

Director, Strategic Analysis

Golden, CO 80401

Abstract

This report documents a probabilistic risk assessment of an existing power supply system at a large telecommunications office. The focus is on characterizing the 

increase in the reliability of power supply through the use of two alternative power 

configurations. Telecommunications has been identified by the Department of Homeland Security as a critical infrastructure to the United States. Failures in the power 

systems supporting major telecommunications service nodes are a main contributor 

to major telecommunications outages. A logical approach to improve the robustness 

of telecommunication facilities would be to increase the depth and breadth of technologies available to restore power in the face of power outages. Distributed energy 

resources such as fuel cells and gas turbines could provide one more onsite electric 

power source to provide backup power, if batteries and diesel generators fail. The 

analysis is based on a hierarchical Bayesian approach and focuses on the failure probability associated with each of three possible facility configurations, along with assessment of the uncertainty or confidence level in the probability of failure. A risk-based 

characterization of final best configuration is presented. 

3 
Acknowledgment

This project was funded by the U.S. Department of Energy through the Office of Policy 

and Budget Analysis. The DOE Project Manager is Dr. Allan Hoffman. The authors 

acknowledge contributions from Sprint Corporation, and thank Larry Johnson and his team 

for assisting with configuration clarification and data. Additionally, the authors thank Whit 

Allan of Leibman and Associates for his technical assistance, and Abbas Ahkil and the 

SNL DER team for their assistance with reliability assessments of gas fired turbines and 

microturbines. 

4
1

2

3

4

5

6

7

8

Contents

1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1 Robust Telecommunications Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Operational Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Analysis Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Event Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.1 Basic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2 Stochastic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6 Base Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.1 Utility Availablility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.2 Probability Distribution for Utility Reliability . . . . . . . . . . . . . . . . . . . . . . . . 26

6.3 Distribution for Generator Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6.4 Battery Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.5 Base Case Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

7 Base Case Considering Utility Repair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

7.1 Utility Down-time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

7.2 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

8 Distributed Energy Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

8.1 Natural Gas Pipeline Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

8.2 Capstone Microturbine Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

8.3 Kawasaki Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Appendix

A Original Fault Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

B Base Case.v7 - WinBugs Code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

C Capstone.v2- WinBugs Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

D Kawasaki.v5- WinBugs Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Figures

MSB-1 Fault Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Base Case Fault Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Base Case Time Line of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

MSB-1 One-line Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

MSB-2 One-line Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Earth Station One-line Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Florida PSC Reliability Metrics (2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

National Hurricane Center 2004 Season . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5
9 Summary of Restoration Time (min) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

10 Summary of Failure Rate (events/yr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

11 PDF of the Number of Utility Outages per Year . . . . . . . . . . . . . . . . . . . . . . 28

12 Utility Reliability Summary (TU ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

13 Diesel Generator Failure Rate Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 32

14 Generator Failure to Start Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

15 Generator Reliability Summary (TG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

16 Battery Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

17 Battery Reliability Summary (TB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

18 Base Case Reliability Summary (Tbase) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

19 Time Line with Utility Repair (Tdelta) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

20 PDF of the Rate of Utility Repairs per Year . . . . . . . . . . . . . . . . . . . . . . . . . 41

21 Time to Restore Utility Power (TR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

22 Net Utility Down Time (Tdelta = TR −(TG +TB)) . . . . . . . . . . . . . . . . . . . . . 43

23 Time Line for DER Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

24 Natural Gas Time to Failure (TNG). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

25 Six Capstone C60 Turbines at Guisborough Hall, UK . . . . . . . . . . . . . . . . . 49

26 Capstone Single Turbine Hours to Failure (TC1 ) . . . . . . . . . . . . . . . . . . . . . . 51

27 Capstone Configuration w/7 Failures (Tcap7) . . . . . . . . . . . . . . . . . . . . . . . . . 52

28 Facility Time to Failure w/Capstone Configuration (TFC) . . . . . . . . . . . . . . . 53

29 Kawasaki Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

30 Kawasaki Footprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

31 Kawasaki Turbine Hours to Failure (TK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

32 Facility Time to Failure for Kawasaki Configuration (TFK ) . . . . . . . . . . . . . . 57

33 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6
Executive Summary

Telecommunications has been identified by the Department of Homeland Security as a 

critical infrastructure to the United States. Failures in the power systems supporting major 

telecommunications service nodes are a main contributor to major telecommunications outages, as documented by analyses of Federal Communications Commission (FCC) outage 

reports by the National Reliability Steering Committee (under auspices of the Alliance for 

Telecommunications Industry Solutions). There are two major issues that are having increasing impact on the sensitivity of the power distribution to telecommunication facilities: 

deregulation of the power industry, and changing weather patterns. 

A logical approach to improve the robustness of telecommunication facilities would be 

to increase the depth and breadth of technologies available to restore power in the face of 

power outages. Distributed energy resources such as fuel cells and gas turbines could provide one more onsite electric power source to provide backup power, if batteries and diesel 

generators fail. But does the diversity in power sources actually increase the reliability of 

offered power to the office equipment, or does the complexity of installing and managing 

the extended power system induce more potential faults and higher failure rates? 

The goal of this effort is to perform Probabilistic Risk Assessments (PRAs) on an existing power configuration for a large telecommunications office (a Sprint Mega-Site with 

battery backup, and diesel generator backup) and for two alternative power configurations 

involving gas turbines as a primary power source. The analysis focuses on the failure probability associated with each of the three facility configurations, along with some assessment 

of the uncertainty or confidence level in the failure probability estimate. Aging effects are 

not included in the analysis. Failure probability estimates will provide a necessary component to service availability estimates from the alternative configurations, but availability 

estimates per se will not be part of the study. 

Due to the importance of time and the operational dependencies between power system 

elements, the analysis approach taken involved modeling the supply of power to the facility 

as a stochastic process. The time to failure for each of the elements necessary to provide 

power were modeled as a random variable with an associated probability distribution function. Due to the limited availability of data, the parameters of the distributions were further 

assumed to be random variables. This approach provided a basis for conducting a riskbased comparison of the alternative power configurations. 

The system analyzed in the report involved a telecommunications facility consisting of 

two switch-bays and a satellite reception system. Power is supplied through a 12470 V 

public utility line. In the event of the loss of power from the utility, there are three diesel 

generators available and sufficient fuel to operate each of the generators for 72 hours. At 

least two of the three generators are needed to provide the minimum level of power. In the 

event that generator power is lost, a backup system of lead-acid batteries can be used to 

provide a minimum level of power for up to 4 hours. 

7 
For this analysis, a worse case scenario was assumed; typical of that encountered in the 

event of a severe weather event. If utility power was lost, it was assumed that restoration 

of power could not be achieved before all segments of the backup power were system were 

exhausted. Similarly, if a diesel generator or gas turbine failed, minor repair was possible, 

but replacement of the entire generator (or turbine) was not an option. The only available 

fuel for the generators was that currently stored on-site (assumed to be 72 hours worth 

for each generator); fuel lost through consumption or contamination could not be replaced 

within the 4 hours of power assumed to be available from the backup batteries. 

Three scenarios were investigated. The first scenario to be investigated was the current 

configuration, referred to as the Base Case. As discussed above, this consisted of utility 

power, with backup diesel generators and a bank of batteries. Two alternative power system 

were also investigated; both of these involved the use of turbines fueled by natural gas. 

The first configuration consisted of an array of 24 60kW Capstone microturbines. All 

24 turbines were under constant load and a minimum combination of 18 turbines were 

required to provide the minimum level of power for the facility. The second configuration 

involved the use of a single Kawasaki 1.5 mW turbine as the primary power source. For 

both turbine configurations, the reliability of the natural gas supply was included in the 

reliability characterization. 

Table 1 summarizes the results of the analyses. Comparing the median time to failure 

(TTF) for each configuration, it is easy to see that the use of the single Kawasaki turbine 

was by far the most promising alternative with a 76-fold increase in the expected operation 

time. The array of Capstone microturbines also showed promise with more than a 6-fold 

increase in power supply reliability. 

Table 1. Analysis Summary 

Time to Failure 10.00% median 90.00% 

Capstone TTF TFC 2698 4960 8706 

Kawasaki TTF TFK 7969 59010 249100 

Base Case Total Tbase 178.8 776.9 2531 

A risk-based perspective provided even more support for the conclusions and permitted 

accounting for the uncertainty in the available failure information. Consider a comparison 

between the reliability of the current power supply (i.e. Base Case) and the array configuration of Capstone microturbines suggested by Sprint. There is a 90% chance that the utility 

power will fail before 2531 hours, while there is a 90% chance that the Capstone array will 

provide power for at least 2698 hours. Finally, consider that there is a 90% probability that 

the Capstone array will fail to provide power for less than approximately 8706 hours, while 

there is a 90% probability that the single Kawasaki turbine will provide power for at least 

7969 hours. 

8 
It should be noted that a significant element in the lower reliability estimate for the Capstone was the configuration and operational plan suggested by Sprint. Other configurations 

could have quite different reliability characteristics and may warrant further investigation. 

However, there are installation issues associated with the Capstone, e.g. special enclosure, 

that could be a factor in the final decision also. 

In conclusion, given the operational scenario assumed and given the uncertainties in the 

three alternatives, the suggested choice is the use of the Kawasaki 1.5 mW turbine as the 

primary power source for the Sprint telecommunication facility. 

9
10
Impact of Distributed Energy

Resources on the Reliability of a

Critical Telecommunications Facility

1 Background

Telecommunications has been identified by the Department of Homeland Security as a 

critical infrastructure to the United States. Failures in the power systems supporting major 

telecommunications service nodes are a main contributor to major telecommunications outages, as documented by analyses of Federal Communications Commission (FCC) outage 

reports by the National Reliability Steering Committee (under auspices of the Alliance for 

Telecommunications Industry Solutions). There are two major issues that are having increasing impact on the sensitivity of the power distribution to telecommunication facilities: 

deregulation of the power industry and changing weather patterns. 

In 1995-96 Sandia National Laboratories initiated a study of the impact of deregulation 

on the reliability of the bulk power network [28, 27, 28]. The initial study was based on 

the ERCOT power grid and was extended to examine the impact of deregulation on the 

reliability of the Western States Coordinating Council (WSCC) bulk power network. The 

conclusions of both of these studies highlighted two issues: lack of reserve generation and 

insufficient/poorly located transmission capacity. The conclusion of the investigation was 

that, unless a national regulatory body interceded, the result of restructuring would be a 

national bulk power system that was more sensitive to external disturbance. 

A major factor on both the operation of the network and the consumer consumption 

will be the growing uncertainty in weather events [11, 12, 21, 31]. One of the most 

widely recognized experts in understanding the impact of weather is Sir John Houghton. In 

Houghton’s book [13], he notes that the recent changes are not part of a short term trend, 

but are part of a much longer, sustained change. Houghton summarizes weather changes 

over the 21st century and suggests that, among other significant climate phenomena, it is 

expected that there will be: 

• more intense precipitation events 

• increased summer temperatures (leading to higher cooling demands) 

• increase in tropical cyclone peak wind intensities, accompanied by increased mean 

and peak precipitation intensities, 

• increased intensity of mid-latitude storms leading to increased infrastructure losses 

11
All of these will have first or second order impacts on the telecommunications and power 

infrastructures. There is no incentive for the power utilities to make their systems more 

robust to these disturbances; rather, the industry has moved to change the reliability reporting requirements to avoid financial penalties [30]. As noted by Sandia researchers in 2000, 

telecommunication companies, emergency services, etc. dependent on a reliability source 

of power need to be prepared for increased uncertainty in the operation of the national 

electrical infrastructure [16]. 

1.1 Robust Telecommunications Infrastructure

One approach toward improving the robustness of the power systems supporting telecommunications offices is to improve the reliability of the necessary supply of power. Current 

best practices involve a combination of onsite battery backup (for short, intermittent power 

interruptions) and diesel generators (for longer term interruptions). Occasionally, universal 

power systems (UPS) technologies are also used for specific data communications equipment backup. 

A logical approach to improve reliability would be to increase the depth and breadth 

of technologies available to restore power in the face of power outages. Distributed energy resources such as fuel cells and gas turbines could provide one more onsite electric 

power source to provide backup power, if batteries and diesel generators fail. But does the 

diversity in power sources actually increase the reliability of offered power to the office 

equipment, or does the complexity of installing and managing the extended power system 

induce more potential faults and higher failure rates? 

The goal of this effort is to perform Probabilistic Risk Assessments (PRAs) on an existing power configuration for a large telecommunications office (a Sprint Mega-Site with 

battery backup, and diesel generator backup) and for two alternative power configurations 

adding gas microturbines as a primary power source. The product from the study will be 

a failure probability associated with each of the three facility configurations, along with 

some assessment of the uncertainty or confidence level in the failure probability estimate. 

Aging effects will not be included in the analysis. Failure probability estimates will provide 

a necessary component to service availability estimates from the alternative configurations, 

but availability estimates per se will not be part of the study. 

2 Introduction

Distributed energy resources technology is a growing focus of research across the energy 

industry and within the Department of Energy. For example, Sandia National Laboratories 

has established the Distributed Energy Technologies Laboratory (DETL) to assist in the development and implementation of distributed energy resources. DETL tests microturbine, 

engine-generator, photovoltaic, fuel cell, and energy-storage technologies both individually 

12
and in a collective microgrid. Collaborators include manufacturers, utilities, the National 

Renewable Energy Laboratory (NREL), DOE, DoD, the California Energy Commission, 

universities, standards organizations, and other national and private laboratories. Energy 

security is one of several important benefits that distributed energy resources will offer to 

the nations electric power infrastructure. 

Natural gas turbines, or microturbines, derivatives of aircraft auxiliary power systems, 

are one DER technology for cogeneration with particular appeal. Turbines are highly efficient with fuel conversion efficiency on the order of 40% and have a number of fuel options 

including biofuels, ethanol and natural gas. These turbines are designed for continuous operation, generally operating at 90% of their rated value. Emissions are necessarily low to 

meet the local environmental pollution requirements (e.g. California NOx limit of 2.5 ppm, 

6 ppm of CO corrected to 15% exhaust oxygen). 

Two gas turbine alternatives are investigated in the following sections. The first configuration is based on a generation package composed of 4 pallets of 6 Capstone microturbines. 

The second configuration is based on a single Kawasaki turbine. Both are co-located with a 

remote telecommunication facility and operate off an external supply of natural gas. In both 

cases, the primary source of power is co-generation production with the utility subsuming a 

role as a backup source of power in the event of turbine system failure. The existing diesel 

generators (in conjunction with the facility battery system) would then be employed if both 

the turbines and utility power become unavailable. 

However, the objective of this effort is to investigate the impact of distributed energy 

resources (DER) on the reliability of the power supplied to the telecommunications center. 

The following section outlines the operational scenario assumed with this study and the 

analysis approach. Following this is a discussion of the fundamental issue driving this 

analysis: the uncertainty associated with the ability of the local utility to supply power to 

the telecommunications center. The current facility configuration, referred to as the Base 

Case, is then characterized. 

3 Operational Scenario

Sandia was requested to analyze the impact of distributed energy resources on the reliability

of a telecommunication center, assuming that the time to repair was not a factor. This 

analysis constraint, effectively assumes that the facility is isolated from major logistics 

support, and operation is restricted to the physical equipment currently available for a given 

configuration. Such a situation might result, for example, from a severe weather incident. 

The location of interest is the Sprint Orlando wireline switch facility. This facility is 

remote - access is via approximately 7 miles of unpaved roads. The utility power at this 

particular location is particularly unreliable requiring an unusual reliance on standby power 

at the facility. In the most recent four year period there were 35 utility outages (compared 

13
with a national average of approximately 3 outages per year for 2001 and 2002) [23, 24, 

26, 25] 

For this analysis, an (almost) worse case scenario is assumed. If utility power is lost, 

restoration of power will not occur within a time period that will have a significant impact. 

(The impact of this assumption is investigated early in the report.) Similarly, if a diesel 

generator or gas turbine fails, minor repair is possible, but replacement of the entire generator (or turbine) is not an option. The only available fuel for the generators is that currently 

stored on-site (assumed to be 72 hours worth for each generator); fuel lost through consumption or contamination cannot be replaced within 4 hours. The time of 4 hours is used 

since the batteries are required to provide a minimum level of support for the plants for an 

additional 4 hours in the event that power is lost from the generators. 

4 Analysis Approach

The focus of this effort is to characterize the impact of distributed energy resources (DER) 

on the reliability of a major telecommunication center. Sandia was initially asked to focus 

on the application of fault trees for characterizing the reliability impact and a typical fault 

tree developed to support the analysis is depicted in Figure 1. The remaining fault trees are 

presented in Appendix A. 

The telecommunication center consists of a main facility supported by two switch bays 

(MSB-1 and MSB-2) and the Earth Station. Power is supplied to the facility primarily 

through a traditional utility drop. In the event that utility power is lost, at least two of the 

on-location 1.5MW diesel generators must function. In addition to the two generators, the 

battery system must be available to provide minimal support for an addditional 4 hours in 

the event that the generators fail. 

However, for the DER configurations to be explored in this effort, the majority of the 

elements in MSB-1, MSB-2 and the Earth Station would be consistent fixtures. In addition, the fuses, breakers, and other components which lend complexity to the analysis have 

demonstrated extremely high reliability over many years of field operation and would not 

have a significant impact on the reliability assessment. For this reason, it was decided to 

simplify the fault trees and a typical simplified fault tree is presented in Figure 2. However, 

the need to consider repair was raised as a possible area for investigation. For this reason it 

was decided not to explore the use of fault trees to support the analysis. 

Two alternative analysis approaches were then considered: Markov Chains and stochastic processes. The initial review of the data suggested a great deal of variability in possible 

parameter estimates. In addition, there was the increasing likelihood of wide variation in 

the scenarios and equipment configurations to be investigated. For these reasons, it was 

finally decided to employ a stochastic process approach based in Bayesian statistics (to 

account for uncertainty in parameter values). 

14 
No Power 

@ Dist-2

No Power 

thru DC

No Power 

thru DG

DC 

open

T1

fails

utility

fails

A1

open

DG

open

No Power

thru E1

E1

open

No power

thru E2

Kirk

failure

No Power

thru C1

E2

open

G1

fails

C1

open

No Power

thru C2

C2

open

G2

fails

No Power

thru TB1

TB1

open

MG1

fails

No Power @ Dist-1

No Power 

thru BC

No Power 

thru BG

BC 

open

T1

fails

utility

fails

A1

open

BG

open

No Power

thru C1

C1

open

Kirk

failiure

No Power

thru E1

E1

open

No Power

thru E2

E2

open

G1

fails

No Power

tthu TB1

TB1

open

MG1

fails

Plant 1

No Power

to BG

No power

thru C2

C2

open

G2

fails No Power

to C1

No Power

to DG

No Power

to E1

TBDORAND 

Figure 1. MSB-1 Fault Tree

15
No Power 

at Plants

Utility

Power Fails

GA

AND

OR

TBD

GB GC M1 M2

4/5 fail

Batteries DC Plant

Backup Power 

Capability Lost

Plant AC

Lost

Figure 2. Base Case Fault Tree 

The stochastic process approach allows the analysis to be broken down into a series 

of potentially dependent events. The parameters characterizing the length of each of the 

events will be assumed to be random variables with uncertainty about the parameters of the 

probability density functions. 

5 Event Characterization

5.1 Basic Approach

The standard methods and data used to estimate the reliability of power systems are documented in the IEEE Std 493-1997 IEEE Recommended Practice for the Design of Reliable 

Industrial and Commercial Power Systems [2]. A traditional approach is not applied because of the sequential, time-dependent nature of how the system is operated. Analysis 

methods associated with Markov Chains were investigated and showed promise as an alternative that allowed inclusion of repair. However, Markov Chains rely on a strong historical 

basis for estimating failure and repair rates. 

As noted previously, the lack of an extensive database suggests addressing uncertainty 

in parameter values, e.g. the failure rate of natural gas pipelines. The approach used in 

this analysis assumes that the rate at which failure occurs or the time required for repair 

will be random variables; that is, the time to failure distribution will actually be a family 

of distributions. As more information and/or experience is gained, then the family of distributions collapses to a single distribution and more traditional methods, such as Markov 

16
Chains, can be employed. Specifically, if there was conflict or confusion regarding the final 

decision, these advanced methods would provide insight into areas where funding spent on 

additional data would be of greatest return. 

For illustration of the approach, consider the supply of utility power. There are two elements to the analyses of power availability: rate at which failures occur and, for the utility 

power, the time required to restore service. Failure events will be assumed to occur after 

periods of time Ti has passed. The length of time will be considered a random variable and 

the choice of the underlying distribution will be a function of the system element being analyzed. For example, since there is not sufficient information to support a more complicated 

characterization of the utility failure rates, the times will be assumed to be exponentially 

distributed random variables: Ti ∼ exp[−λit], where λi represents the rate at which failures occur. Similarly, the length of time to recover from an outage, will be considered a 

random variable characterized with an exponential distribution: Tj ∼ exp[−μjt], where μj

represents the rate at which repairs occur. (Note that the assumption of the exponential 

distribution is also consistent with the reliability approach outlined in IEEE Std 493-197.) 

Since there is significant variability in the failure (and repair) rates from year-to-year, 

the failure rate for the outage time will also be considered a random variable. The probability distribution function describing the uncertainty in the utility failure rate, λ will be 

assumed to be a gamma distribution: 

g(λ|α,θ) = Γ

θ

(α

α

)

λα−1 exp[−θλ], λ,α,θ > 0.

5.2 Stochastic Process

Figure 3 depicts a typical sequence of events. Each event logically follows at the conclusion 

of the previous event. For example, for the Base Case, the time that the utility is available 

TU is randomly selected from f(T|λU ) = exp[−λUt]. Since the rate at which the utility fails, 

λU , is not known with certainty, a random parameter is chosen from the distribution Λ ∼

g(λ|α,θ). Because of the conditional structure of the the distributions for T and λ, Gibbs 

sampling must be used. The WinBugs computer software was used for all simulations 

conducted in this report [29] and the computer codes for each system configuration are 

provided in the Appendices. 

Similar to the utility reliability, values for diesel generator operation reliability, TG, 

and battery reliability, TB are simulated. The values are then combined to get the time 

until system failure, Tbase = TU +TG +TB. Figure 3 depicts the typical time line of events 

associated with what is referred to in the following discussion as the Base Case. 

The following sections address each of the elements of the various scenarios. The Base 

Case is a function of the availability of power from the utility, the backup diesel generators, 

and the batteries. The additional alternatives explored include the addition of natural gas 

microturbines from Capstone and Kawasaki. 

17 
6 Base Case

TU

0

TG

TB

Utility w/o Repair

Base Case

2/3

Fuel

Available

Gen

Start

Figure 3. Base Case Time Line of Events 

The primary reliability impact of DERs will be related to their use to augment or replace 

utility power as the primary power source. The utility (or DER) is then coupled with 

combinations of diesel generators and the battery backup systems within the facility. The 

current backup power for MSB-1 and MSB-2 is provided through three 1.5 mW stationary 

diesel generators and the option of two mobile 1.5 mW generators. The Earth Station has 

a separate backup power source consisting of two 300 kW generators. 

The Base Case (depicted in Figure 3) is defined as the configuration of the telecommunication center as it exists today - without support of additional distributed energy resources. The telecommunication center consists of a main facility supported by two switch 

bays (MSB-1 and MSB-2) and the Earth Station. Power is supplied to the facility primarily 

through a traditional utility drop. In the event that utility power is lost, at least two of the 

on-location diesel generators must function. In addition to the two generators, the battery 

system must be available to provide minimal support for an addditional 4 hours in the event 

that the generators fail. 

The current analysis is based on the peak power requirement for MSB-1 and MSB-2 

of approximately 1.1mW (total) and 65kW for the Earth Station. These requirements may 

expand as the demand on the system grows; additional fixed and mobile generators can be 

added to the Base Case to increase the backup power capacity. 

18 
The one-line diagrams for the Base Case are presented in Figures 4, 5 and 6. (For 

reference, the original fault trees for each of the three major elements are provided in 

Appendix A.) 

6.1 Utility Availablility

To be consistent with the literature, the terms utility availability and utility reliability will 

be used synonomously. The reliability of the utility power source will be defined as the 

probability that, at any point in time, the telecommunication center is supplied with sufficient power from the local utility. For this study this probability is effectively the fraction 

of time that utility power is available at the telecommunications center. 

Power utility reliability is typically characterized using a number of indices proscribed 

the IEEE Guide for Electric Power Distribution Reliability Indicies (IEEE Std 1366-2003 [1]); 

however, not all states have adopted standards as a means of characterizing utility power 

reliability. For example, the state of Florida has requirements for reporting reliability metrics, but no quality of service incentives or penalties and the state of New Mexico has no 

power reliability requirements [6]. In addition, weather is recognized by the utilities as a 

major influence in estimating these indices and, in most cases, power disruptions related to 

severe weather are discounted in the calculations. For example, major events are not necessarily included in reliability indices where a major event might be defined as an outage 

where more than 10% of the customers within a region are without electricity and power is 

not restored within a 24 hour period [30]. 

The following discussion summarizes the major reliability measures used by public 

power utilies. An interruption is considered countable if the time duration of the interruption exceeds 5 minutes. All indices defined below are for sustained interruptions. Let NT

be the total number of customers served, and Ni be the number of interrupted customers for 

each sustained interruption. 

System average interruption frequency index (SAIFI) The system average interruption 

frequency index indicates how often the average customer experiences a sustained 

interruption. 

Total Number of Customers Interrupted SAIF I = Number of Customers Served 

∑iNi CI = = NT NT

System average interruption duration index (SAIDI) This index indicates the total duration of interruption for the average customer. It is commonly measured in customer 

19 
Figure 4. MSB-1 One-line Diagram

20
Figure 5. MSB-2 One-line Diagram

21
Figure 6. Earth Station One-line Diagram

22
minutes or customer hours of interruption. Let ri be the restoration time for each interruption event: 

Total Number of Customer Interruptions SAIDI = Number of Customers Served 

∑iriNi CMI = = NT NT

Customer average interruption duration index (CAIDI) CAIDI represents the average 

time required to restore service. 

Total of Customer Interruption Duration CAIDI = Total Number of Customers Interrupted 

∑iriNi SAIDI = = ∑iNi SAIF I

Lbar The overall average length of the outages 

Minutes of Interruption Lbar =Total Number of Outages 

Note that the CAIDI index can be deceptively low since customers may be counted 

multiple times; once for each interruption. An alternative measure that is not generally 

reported by utilities is the Customer total average interruption duration index (CTAIDI), 

which counts customers with multiple interruptions only once (Ni

∗): 

Total of Customer Interruption Duration CTAIDI =Total Number of Customers Interrupted (*) 

∑iriNi = ∑iNi

∗

Service availability is given by:

Total Customer Hours of Service

ASAI = Total Customers Hours Demand 

(8760)NT −∑iriNi = (8760)NT

23 
6.1.1 Florida Public Service Commission Data

The state of Florida, while not having Quality of Service requirements, does require each 

utility to submit a formal report documenting the reliability metrics for the previous year [8]. 

Data is adjusted to account for severe storm events; it is believed, but not conclusively clear, 

that Florida requires the utilities to use the IEEE Std 1366 [1] definitions to adjust the metrics for major events. Table 2 summarizes the 2005 report for the data obtained in 2004 

and Figure 7 depicts the data graphically. Note that some of the utilities reported an approximate 20% improvement in 2004 numbers over those from 2003 after one of the most 

notable hurricane seasons on record (Figure 8). 

Table 2. Summary of Utility Recovery Time Related Metrics 

Utility Reliability Metrics

SAIDI CAIDI LBAR SAIFI 

PEF 77 64.7 111.9 1.19 

FPL 73.9 59.4 181 1.24 

FPUC 138.06 107.47 77.35 1.26 

GULF 93.33 105.93 129.55 0.88 

TECO 72.63 75.26 178.07 0.97 

Average

Std Dev

90.98 82.55 135.57 

27.60 22.78 44.32 

1.11 

0.17 

6.1.2 Sprint Data

In the four years, 2001-2004, Sprint noted 35 incidents where power to the switching station was disrupted [25] for a failure rate estimate of 8.75 events/year. In addition, Sprint 

collected data on the length of diesel generator operation during these same outages. This 

may be a consideration since the utility may not demonstrate stability immediately following an outage; the facilities continue to use the already functioning diesel generators during 

this additional period. 

• Data are not available for the specific incidents, but similar Sprint telecommunication 

facilities have experienced power outages with an average outage time of μoutage =

6.45 hours, and a standard deviation of σoutage = 6.54 hours [22]. To appreciate the 

uncertainty in outage length, the shortest duration was an instantaneous outage, while 

the longest outage lasted approximately 27 hours. 

• The generators during these incidents were in-use for lengths of time with the following mean and standard deviation: μGenrun = 9.41 hours, σGenrun = 8.14 hours. 

24 
Florida PSC Reliability 

0

20

40

60

80

100

120

140

160

180

200

PEF FPL FPUC GULF TECO

Utility

Reliability Measure (min)

SAIDI

CAIDI

LBAR

SAIFI

Figure 7. Florida PSC Reliability Metrics (2004)

25
Figure 8. National Hurricane Center 2004 Season

26
6.1.3 IEEE Std 493-1997

As noted previously, the standard methods and data used to estimate the reliability of power 

systems is documented in the IEEE Std 493-1997 [2]. While an industry standard, the 

source of much of the data relevant to this effort are from surveys taken prior to 1976. 

Reference [2], Table 3-33, suggests using an average outage duration of 125 minutes (2.08 

hours). 

For utility supplies to industrial plants where the voltage line is ≤ 15kV the suggested 

failures per year (again from Table 3-33 [2]) is 3.621. (Note that when verifiable operational/field information is not available, data from this standard will be used in the analysis.) 

6.1.4 Loss of Off-site Power (LOSP)

A second, very reliable source of utility data is available from each of the 103 nuclear power 

plants across the US. It is well recognized that the availability of power to commercial 

nuclear power plants is essential for safe operations and accident recovery. A loss of offsite 

power (LOSP) event is therefore considered an important contributor to total risk at nuclear 

power plants [3]. 

However, caution must be used when using data from nuclear plants related to utility 

availability since utilities will do everything possible to assure delivery of power to the 

nuclear plant; both for safety reasons and since nuclear power plants provide a significant 

base power load. For example, the two major electrical disturbances on July 2, 1996 and 

August 10, 1996 that blacked-out most of the western US, did not results in LOSP events. In 

addition, for similar reasons, restoration times for nuclear plants can be substantially shorter 

than for industrial loads. Finally, since reactors will often be shutdown in anticipation of a 

grid or weather related disturbance, the rate at which off-site power is lost is not applicable 

to the current analysis. Highlights of the published data [3]: 

• Recovery time for grid-related events ranged from 125 to 360 minutes with a mean 

of 190.2 minutes and a standard deviation of 97.4 minutes 

• The time to recover from weather related incidents ranged from 37 minutes to 5.5 

days, with a mean of 1258 minutes and a 90% probability interval of [23, 5009] 

using a log-normal probability density function. 

6.1.5 Utility Data Input Summary

Figures 9 and 10 summarize the data available for restoration time and failure rate. The data 

from the utilities reported to the Florida Public Service Commission likely discounts severe 

events of any type, e.g. weather, and is therefore optimistic. While not clear, the estimates 

27
from the IEEE Std 493 most likely have similar liabilities. The values developed for the 

Nuclear Regulatory Commission and reported to support LOSP estimates lean toward the 

optimistic side since reactors are shutdown in anticipation of severe events. 

For the remainder of the analyses, the mean restoration and failure rate data from Sprint 

will be used to support the utility availability analyses since this data appears to be the most 

realistic and applicable to the problem being investigated. 

0

200

400

600

800

1000

1200

1400

Sprint FPSC (Lbar) IEEE Std 493-

1997

LOSP (grid) LOSP

(weather)

Source

Restoration Time (min)

Figure 9. Summary of Restoration Time (min) 

6.2 Probability Distribution for Utility Reliability

It is assumed that the length of time that a utility is up and operating, TU , is an exponentially distributed random variable with parameter λ: f(t λ) = exp[−λt]. The parameter λ

represents the number of utility interruptions per year. 

|

However, the estimate λ

ˆ = 8.75 

represents a simple average rate at which events occurred over the four years; in reality, 

there will be a great deal of variation or uncertainty about the rate, λ at which events might 

occur each year. 

Therefore, let λ be a random variable with an average value of 8.75. Without additional information regarding how the rate varies each year, the assumption of a Gamma 

28
� �

0

1

2

3

4

5

6

7

8

9

10

Sprint FPSC (SAIFI) IEEE Std 493-1997

Source

Frequency (events/yr)

Figure 10. Summary of Failure Rate (events/yr) 

distribution for λ is the simplest assumption that can be made: 

f(λ|α,β) = βαΓ

1 

(α)

λα−1 exp −β

λ ,λ > 0 

A distribution for λ and the mean of that distribution are now available. To completely 

describe the Gamma distribution, one more assumption is necessary to characterize the 

second parameter of the distribution. Assume that we are confident that the rate at which 

events occur lies in the range [2, 14] events/year. This range will typically reflect [μ −

3σ,μ+3σ]. Solving, we find that a standard deviation of σ = 2.0 is a good place to start. 

The mean and variance for the Gamma distribution are given by E[λ] = αβ = 8.75, 

and V[λ] = αβ2 = 4, respectively. Simultaneously solving the two equations for the two 

unknowns yields values of: α = 19.1406 failures/year and β = 0.457143. 

The resulting probability density function (PDF) describing the uncertainty in the number of utility outages each year is presented in Figure 11. As noted previously, assume 

that the length of time that a utility is up and operating, TU , is an exponentially distributed 

random variable with parameter λ: f(t|λ) = exp[−λt]; since the failure rate, λ is a random 

variable, the PDF f(t|λ) will inherently have an associated probabilistic uncertainty. 

Figure 12 depicts this uncertainty as a probability band about the utility time to failure, 

TU : there is a 90% probability that the power will be continuously available for more than 

1126 hours, a 50% chance that it will be available for less than 106 hours, and a 90% 

probability that power will be available for less than 2484 hours. 

29 
0

10000

20000

30000

40000

50000

60000

01

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

1920

λU (Number of Failure Events per Year)

Frequency

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Cumulative Dist Function

Figure 11. PDF of the Number of Utility Outages per Year

30
0

5000

3000025000200001500010000

0

300600

900

1200 1500

1800

2100 2400

2700 3000

3300 3600 3900

4200 4500 4800

5100

5400

5700 6000

6300 6600

6900

7200

7500 7800 8100

8400

TU (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(107) (2457)

(706)

Figure 12. Utility Reliability Summary (TU ) 

31
� �

6.3 Distribution for Generator Reliability

Failure of a diesel generator is defined as a malfunction of the generator or associated 

support subsystems that prevents the generator from starting and running when a demand 

has occurred. Failures can occur in two modes: 

Failure to start (FTS) A failure of the generator to either manually or automatically start 

on a bus under-voltage condition, reach rated voltage and speed, close the output 

breaker, or sequence safety-related electrical loads onto the respective safety-related 

bus. 

Failure to run (FTR) A failure of the generator to continue to supply power to its respective safety-related electrical bus given the generator successfully started. 

Using IEEE Std 493 [2], engineers at Sprint estimated a mean time to failure (MTTF) for 

diesel generators of 9056 hours with a mean time to repair of 3.9 hours [25]. However, 

the expected failure rate (λ = 1/MTTF) for diesel generators used in nuclear power plants 

(NPPs) is approximately 0.0223 failures/hour. In addition, for diesel generators at nuclear 

power plants the Pr{failure to start} = 0.0241 per demand [9, 10]. 

As with the utility analysis, the reliability of the generators will be assumed to be a 

random variable described by the distribution: 

R(t|λ) = exp(−λt)

The required operating period for the generators is t = 72 hours at which time the fuel at 

the facility is expended; refueling is assumed to not be possible. 

Given the wide disparity in the reliability data for the diesel generators, assume that the 

time to failure for the generators is a random variable. The failure rate for the NPP diesel 

generators: λ = 0.00223 is based on considerable data for a variety of diesel generators 

from across the nuclear power plant industry. However, based on operational experience, 

Sprint has also published an estimate of λ = 0.00011 failures/hours for the generators. 

Given the strong historical basis, λ = 0.00223 will be used as the expected time to 

failure and it will be assumed that the λ = 0.00011 is a lower 5% credibility limit (i.e. 95% 

probability that the true MTTF is less than 9056 hours). A gamma distribution will be used 

to describe the variation in the generator failure rate: 

f(λ|α,β) = βαΓ

1 

(α)

λα−1 exp −β

λ ,λ > 0 

The mean and variance are given by E[λ] = αβ, V[λ] = αβ2, respectively. Simultaneously 

solving these two equations: 

E[λ] = αβ

Z 0.00011 � � F(λ < 0.00011|α,β) = βαΓ

1 

(α) 0 

λα−1 exp −λ

β

≈0.05 

32
�

for the two unknowns yields values of: α = 0.0001115 failures/hours or α = 0.976741 

failures per year and β = 20. (Units of years are used in the remainder of the analysis 

for consistency.) Given these parameters, the expected number of diesel generator failures 

per year is approximately 19.54. The resulting probability density function describing the 

uncertainty in the rate at which failures occur is presented in Figure 13. The results are 

presented for a single generator; recall that at least two of the three generators must function. Also, the point estimates initially provided by Sprint and the US Nuclear Regulatory 

Commission are noted. 

6.3.1 Failure to Start

Define p to be the probability that a generator will not start on demand. Let p be a beta 

distributed random variable conditioned on the variables r, s: 

f(p|r,s) = B(

1 

r,s)

pr−1(1− p)

s−1 ,r,s > 0 

where B(r,s) is the incomplete Beta function. The mean and variance of p are given, 

respectively, by: 

r

E[p] =r +s

rs

V[p] =(r +s)2(r +s+1)

Given the NRC experience, let the mean be E[p] = 0.0241 and the standard deviation be 

V[p] = 2 ∗ E[p]. This results in a prior distribution that is relatively uniform over the 

area of interest so that the prior does not overly influence the results. Figure 14 depicts the 

resulting prior distribution. 

Typically, the maximum allowed load on each generator is 60% of the rated value, 

therefore at least two of the generators are necessary for minimum support of the power 

required by the two plants. In the event that only two generators are operational, air conditioning (A/C) and other support functions would be cycled on/off to keep the plants fully 

operational. Figure 15 depicts the time to failure distribution of the diesel generators considering that 2 of 3 must be functioning and that each generator has a certain probability of 

not starting when called. The sharp rise at 72 hours is due to the limited source of on-site 

fuel. 

6.4 Battery Reliability

Battery backup consists of a bank of valve-regulated lead-acid (VRLA) batteries. VRLA 

batteries are a well established technology [4] used as a backup power source for short 

33
Single Generator

0

900080007000600050004000300020001000

10000

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

λG (Failure Events per Year)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(0.8) (49.6) (11)

(Sprint = 0.967)

(Sprint)

(NRC= 19.55)

(NRC)

Figure 13. Diesel Generator Failure Rate Distribution

34
0

5000

25000200001500010000

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

Probability Generators Fail to Start

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(2 E-6) (0.075)

(0.003)

Figure 14. Generator Failure to Start Distribution

35
Diesel Generators (2/3)

0

5000

500004500040000350003000025000200001500010000

0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

TG (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Figure 15. Generator Reliability Summary (TG) 

36
periods of time. Common batteries used in the telecommunications site include C&D [15] 

and East Penn [7]. The batteries are assumed to be in three groups of strings: Earth Station 

(16 strings), MSB-1 (28 strings), MSB-2 (16 strings). In particular, Plant 1 has an 8,000 

amp shunt and has 16 strings of C&D HD-1300, Plant 2 has a 10,000 amp shunt and has 

28 strings of C&D HD-1300, and Plant 3 has a 15,000 amp shunt and has 8 strings of C&D 

HD-1300 and 8 strings of East Penn AVR95-33. 

Cantor et al [5] describes the performance characteristics of VRLA batteries by examining the capacity for the cells in its survey of VRLA batteries. Their definition of failure

as used in their tables is that a cell did not meet a specific battery capacity level (e.g. 80%, 

60%, or 50% capacity). Typically, the 80% capacity-level is used by manufacturers to determine a failed battery for the purposes of warranty protection. In communications with 

Sprint to determine the sizing of the batteries used at their Orlando site, it is assumed that 

Sprint uses the 80% capacity-level in order to size their batteries to meet a 3-hour backup 

power protection. If the batteries have not degraded and have closer to 100% capacity, it 

would be expected that the backup power might last up to 4 hours. 

Per IEEE Std 1188 [14], the percent capacity of a VRLA battery at 25◦C (77◦F): 

ta Pc = ×100 (1) ts

where ta is the actual time of the test to specified voltage level as corrected for temperature 

and ts is the rated time to specified terminal voltage. 

Per IEEE Standard 1188, it is assumed that although the Cantor paper lists a cell as 

failed, the battery cell is still providing some residual capacity. In particular, in Cantor [5] 

for VRLA batteries still in their useful life only 2% of the cells (332 out of 13733) failed to 

maintain a 50% capacity-level, 4% failed to maintain a 60% capacity-level, and 13% failed 

to maintain an 80% capacity-level. Assuming that this is an appropriate mixture of ages 

that are seen in the real world and normalizing the results: 5% of the cells would have failed 

to maintain a 50% capacity-level, 8% would have failed to maintain a 60% capacity-level, 

and 22% would have failed to maintain an 80% capacity-level. 

Since the degradation of capacity is dependent on the use temperature, cycling, charging 

characteristics, etc., it is assumed that cells in a facility experience the same degradation of 

capacities over their lifetimes. In particular, consider the East Penn AVR95-33 (a complete 

48V string comprised of 2 stacks being 6 modules high where each module has 2 cells and 

all 24 cells housed in the same cabinet), it is expected that all of the cells in the strings 

would have the same performance characteristics over their lifetimes. 

From a reliability perspective, the multiple string arrangements at the Orlando site are 

assumed to take on a skewed probability density function curve as depicted in Figure 16. 

Given IEEE Standard 1188 and that Sprint uses 80% capacity for sizing a 3 hour backup 

time, the assumed capacities can be translated into the times to failure that would reasonably apply at the Orlando site. For 16-string: 2% chance of not working at all , 5% 

chance of discharging ≤ 2 hours , 25% chance of discharging ≤ 3 hours , 100% chance of 

discharging < 4 hours. 

37
Figure 16. Battery Reliability 

For 28-string: 3% chance of not working at all (increased chance over the 16-string), 

8% chance of discharging ≤ 2 hours, 40% chance of discharging ≤ 3 hours, 100% chance 

of discharging < 4 hours. Considering this distribution of discharge times, the final probability of failure of the supply of battery power to the facility is given in Figure 17. 

6.5 Base Case Summary

Table 3 summarizes the results for the Base Case configuration; recall that this represents a 

summary of the reliability characteristics of the current configuration at the Sprint telecommunications facility under the operational scenario assumed. Figure 18 depicts the results 

graphically. 

Table 3. Base Case Time to Failure Summary 

Time to Failure μ σ 10.00% median 90.00% 

Base Case Total Tbase = TU +TG +TB 1130 1119 178.8 776.9 2531 

Utility Time to Failure - TU 1058 1120 107 706.2 2457 

Generator Failure to Start 0.02414 0.04833 2.03E-06 0.00343 0.07514 

Diesel Generator - TG 69.57 10.04 72 72 72 

Battery (time) - TB 2.625 0.9331 1.294 2.869 3.53 

38
0

5000

3000025000200001500010000

0

0.150.3

0.450.6

0.750.9

1.051.2

1.351.5

1.651.8

1.95

2.1

2.252.4

2.552.7

2.85 3

3.153.3

3.453.6

3.753.9

More

Tb (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Figure 17. Battery Reliability Summary (TB) 

39
0

5000

500004500040000350003000025000200001500010000

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

3300

3600

3900

4200

4500

4800

5100

5400

5700

6000

Tbase (Hours to Faiiure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(179) (2531) (777)

Figure 18. Base Case Reliability Summary (Tbase) 

40
7 Base Case Considering Utility Repair

In this section, the possibility of repair of the utility power is explored. The analysis quantifies the power availability and provides a basis for comparison of the analysis results 

associated with the Base Case with the experience of Sprint engineers. 

Let TR be the time that it takes for the utility to restore power after an outage. If the time 

to restore utility power is more than the time that power is available through a combination 

of diesel generators and batteries, than the facility is without power for a period of time: 

P{facility down}=P{TR < TG + TB} (see Figure 19). If Tbase is the time that power is 

available for the Base Case (no utility repair), then Tdelta = TU +TR −Tbase. The P{facility

down}= P{Tdelta < 0}. 

TU

0

TG

TB

Tbase=TU+TG+TB

Utility w/ Repair

2/3

TR

Tdelta

Figure 19. Time Line with Utility Repair (Tdelta) 

7.1 Utility Down-time

As with the reliability characterization, it will again be assumed that the length of time that a 

utility power is not available is also an exponentially distributed random variable. Based on 

41
data from Sprint the average outage time of μoutage = 6.45 hours, and a standard deviation 

of σoutage = 6.54 hours [22]. By definition, λ = 1/μ so E[λ] = 0.155 and V[λ] = 0.0234. 

As before, assume that the rate λ is a random variable characterized by a Gamma distribution with E[λ] = αβ, V[λ] = αβ2, respectively. Simultaneously solving the two equations 

for the two unknowns yields values of: α = 1.0281 failures/year and β = 0.150801. Figure 20 depicts the resulting Gamma distribution. The above analysis implies that there is 

a 90% probability that the repair rate is in the interval [0.108634,0.459933] repairs/hour 

or equivalently, that there is a 90% probability that the time to repair is in the interval 

[2.17423,117.464], as depicted in Figure 21. 

7.2 Comparison

Figure 22 depicts the probability of the event Tdelta = TR − (TG + TB) and the results are 

summarized in Table 4. As noted previously, the Pr{Tdelta > 0}is the probability that, 

under the assumptions in this analysis, the telecommunications facility is without power; 

the generators and batteries will either fail or be exhausted before utility power is restored. 

From the analysis, there is approximately an 8% chance the facility will be without power 

and a 7% chance that it will be without power for 10 hours or less. Conversations with 

engineers at Sprint have confirmed that, given the scenario, these results are reasonable. 

(For convenience, the specific values from Figure 22 are presented in Table 5.) 

Table 4. Base Case Time to Failure Summary (w/Utility Repair) 

Time to Failure μ σ 10.00% median 90.00% 

Base Case Total Tbase = TU +TG +TB 1130 1119 178.8 776.9 2531 

Utility Time to Failure - TU 1058 1120 107 706.2 2457 

Generator Failure to Start 0.02414 0.04833 2.03E-06 0.00343 0.07514 

Diesel Generator - TG 69.57 10.04 72 72 72 

Battery (time) - TB 2.625 0.9331 1.294 2.869 3.53 

Utility Time to Restore TR 106.2 15300 0.7199 6.409 56.08 

Tdelta 35.49 12970 -73.99 -67.1 -9.985 

42
0

8000600040002000

16000140001200010000

0

0.0350.07

0.1050.14

0.1750.21

0.2450.28

0.3150.35

0.3850.42

0.4550.49

0.5250.56

0.5950.63

0.6650.7

0.7350.77

0.8050.84

0.8750.91

0.9450.98

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

λR (Number of Repair Events per Year)

Figure 20. PDF of the Rate of Utility Repairs per Year

43
0

8000070000600005000040000300002000010000

0

1530

4560

7590

105120135

150165

180

195210

225240

255270

285

300

315330

345

360375

390

405420435

450465

480495

TR (Hours to Restore Power)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(0.7) (56.1) (6.4)

Figure 21. Time to Restore Utility Power (TR) 

44
0

80000600004000020000

200000180000160000140000120000100000

-80

-60

-40-20 0

2040

60

80

100120

140160180

200220240

260

280300320340

360

380

400420

440460

480500

Tnet (Net Hours)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Figure 22. Net Utility Down Time (Tdelta = TR −(TG +TB)) 

45
Table 5. Frequency Table of Tdelta = TR −(TG +TB)

Tdelta Frequency Cumulative %

-80 

-75 

-70 

-65 

-60 

-55 

-50 

-45 

-40 

-35 

-30 

-25 

-20 

-15 

-10 

-5 

0 

0 

10137 

182653 

87289 

46811 

29781 

20760 

15691 

12500 

10333 

8900 

7611 

6491 

5831 

5075 

4468 

3856 

.00% 

2.03% 

38.56% 

56.02% 

65.38% 

71.33% 

75.49% 

78.62% 

81.12% 

83.19% 

84.97% 

86.49% 

87.79% 

88.96% 

89.97% 

90.87% 

91.64% 

5 

10 

3207 

2567 

92.28% 

92.79% 

15 

20 

25 

30 

35 

40 

45 

2245 

1917 

1681 

1522 

1333 

1258 

1112 

93.24% 

93.62% 

93.96% 

94.27% 

94.53% 

94.78% 

95.01% 

46
8 Distributed Energy Resources

The following sections discuss the analysis of two alternatives to traditional utility power. 

These alternatives are based on the use of natural gas turbines to provide generation of 

power immediately at the telecommunications facility. Two configurations of interest to 

Sprint were a single Kawasaki turbine and an arrangement of four pallets, each with six 

Capstone natural gas microturbines. Both of these configurations depend on a supply of 

natural gas; therefore, the reliable supply of the natural gas is critical. The immediate 

section addresses the supply of natural gas and the following sections document research 

into the two turbine configurations. 

Effectively analysis of the operational scenario proposed by Sprint involves relying on 

the turbine as the primary facility power source and the use of the Base Case configuration 

as the backup power supply. This is depicted in Figure 23. 

TU

0

TG

TB

Utility w/o Repair

DER Case

2/3

Fuel

Available

Gen

Start

TTurbine+NG

Figure 23. Time Line for DER Analyses 

8.1 Natural Gas Pipeline Reliability

The Office of Pipeline Safety (OPS), within the U. S. Department of Transportation, Pipeline 

and Hazardous Materials Safety Administration (PHMSA), has overall regulatory responsibility for hazardous liquid and gas pipelines under its jurisdiction in the United States. 

Federal safety standards are described in U.S. Code of Federal Regulations (CFR), Title 49 

Transportation, Parts 190 - 199 [19]. There are over 2 million miles of pipelines that support the movement of hazardous liquids, natural gas and propane. The two types of natural 

gas pipelines are transmission and distribution. Transmission lines typically involve the 

transportation of natural gas between a storage facility or between a distribution center and 

a large volume customer. There are approximately 305,000 miles of transmission pipeline 

in the US. In general, pipelines that are not transmission related are distribution pipelines. 

Distribution lines branch from transmission lines and supply natural gas to consumers. The 

47
focus of this effort involves the 1,860,000 miles of pipeline involved with distribution of 

natural gas. 

There are a number of failure modes for pipelines, most of which are unique to the area 

where the pipeline is located and include corrosion, external forces (such as excavation 

or natural forces), and material failure among many other factors. To characterize the 

probability of failure of a particular distribution line can be extremely complicated. For 

example, failure due to corrosion is dependent on such factors as the type and condition of 

the pipes coating, the effectiveness of corrosion control equipment, and the soil conditions 

surrounding the pipe. Alternatively, the probability of pipeline damage as the result of third 

party damage depends on, for example, the extent and type of excavation or agricultural 

activity along the pipeline right-of-way and the depth of cover over the pipeline. 

The natural gas provider in Orlando has indicated that they will furnish and install the 

pipeline some 4 miles (6.437 km) away. A typical feeder line for a natural gas turbine (e.g. 

a 1.5 mW Kawasaki turbine site in San Luis Obispo, CA) has a 4” (101.6 mm) feeder 

with cutoff connected into an on-site turbine compressor station. A 4” (101.6 mm) pipe is 

connected into the turbine from the pump station. 

Historically, the dominant failure mode for natural gas distribution pipe line is a result 

of external factors involving third-parties, e.g. excavation. The rate at which these failures 

occur are a function of the buried depth, how well the pipeline is marked, the density of the 

population and the land use of the area of interest. The factors can be used to augment the 

basic failure rate established for pipes of a particular diameter [17]. 

Contribution of external factors to the failure rate of the pipeline: 

λExt = λdKdcKwtKpdKpm

where λd is the basic failure rate for pipes of diameter d, and the correction factors Kdc, Kwt, 

Kpd, and Kpm account for failure due to third-party activities: buried depth, wall thickness, 

population density and prevention method. Assuming a distribution pipe diameter of 102 

mm, an estimate of the basic failure rate is λd = 0.218 failures/ 1000 km-year (Table 2, 

[17]) . 

It is assumed that for the facility in question that the area is rural Kpd = 0.81 and best 

protection method is employed and the length of pipe is 6.44 km. Estimates of the failure 

rates are from [20], and [17]. Specifically, the following assumptions are made in the 

analysis: 

Kdc - worst case is to assume depth of cover is less than 0.91 m: Kdc = 2.54, best case is 

to assume that depth of cover is greater than 1.22 m: Kdc = 0.54. 

Kwt - worst case is to presume that the wall thickness of pipe will be no more than the 

minimum of 4.8 mm: Kwt = 1.0 and best case assumes that the thickness is greater 

than 4.8 mm: Kwt = 0.2. 

48 
�

Kpd - the location of the telecommunication center appears to be rather remote (7 miles 

of dirt road). Assume that the area is rural (best case): Kpd = 0.81 and the worst 

case assumption is that the distribution pipe is laid through a densely populated area: 

Kpd = 18.77. 

Kpm - worst case situation implies that there are only marker posts to delineate the location 

of the distribution line: Kpm = 1.03 while for best case additional methods are used: 

Kpm = 0.91. 

Best Case (failures/year): 

λb =λdKdcKwtKpdKpm ∗ d

=(0.000218)(0.54)(0.2)(0.81)(0.91)(6.44)

=0.000112 

Worst Case (failures/year): 

λb =λdKdcKwtKpdKpm ∗ d

=(0.000218)(2.54)(1.0)(18.77)(1.03)(6.44)

=0.06894 

The probability of failure in one year is then assumed to be in the range: Fng = {1 −

exp[−0.000112] = 0.000012,1−exp[−0.06894] = 0.06662}. The failure rate of pipeline 

is assumed to be a random variable characterized by a lognormal distribution with a 5% 

lower limit of 0.000112 and an upper 95% limit of 0.06894. 

τ � τ �

f(λ|μ, τ) = 2πλ2 exp −2

(logλ−μ)

2 , λ > 0 (2) 

Solving for μ and τ given the upper and lower bounds yields values of μ = −5.88577 and 

τ = 0.262366. Figure 24 depicts the final distribution for the time to failure of the natural 

gas pipeline. As with other elements in the system, the time to failure for the pipeline is 

assumed to be an exponentially distributed random variable: TNG ∼ exp[−λNGt], where 

λNG represents the rate at which pipeline failures occur. 

8.2 Capstone Microturbine Analysis

The Capstone microturbines were suggested by Sprint as one possible alternative power 

generation source. Emissions are low: approximately 2.3 ppmvd NOx per generator for 

75% loading and about 2.0 ppmvd NOx for 100% loading (parts per million on dry volume 

basis). 

Figure 25 shows six C60 microturbines being used to provide prime power and heat at 

the Guisborough Hall luxury hotel in the UK (photo courtesy of Capstone). 

49 
0

600005000040000300002000010000

0.00E+00

3.40E+06

6.80E+06

1.02E+07

1.36E+07

1.70E+07

2.04E+07

2.38E+07

2.72E+07

3.06E+07

3.40E+07

3.74E+07

4.08E+07

4.42E+07

4.76E+07

TNG (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Figure 24. Natural Gas Time to Failure (TNG) 

50
Figure 25. Six Capstone C60 Turbines at Guisborough Hall, UK 

The current planned configuration of Capstone turbines consists of four pallets of six 

turbines for a total of 24 turbines. Each turbine is capable of 60 kW of output and for 

efficiency purposes the turbines are exercised at 90% of their capacity. The total available 

power is then 1.296 mW. The current maximum demand is approximately 1.1 mW, leaving 

an excess capacity of 196 kW. At the peak level of loading, only 21 of the 24 Capstone 

turbines are needed to supply power for MSB-1, MSB-2 and the Earth Station combined. 

Sprint suggested that the facility could be supported at a minimum level if even seven of 

the microturbines were unavailable. 

According to Capstone engineers, these turbines are currently in-place at a variety of 

locations and have attained 95% availability. The overall design life is 40,000 hours and 

Capstone engineers have estimated the mean time to failure to be 8000 hours and noted 

that they expect this to double over the next few years. There are scheduled maintenance 

activities at 8,000 and 20,000 hours. The 8,000 maintenance is to change air and some 

other filters and replacing the igniter. The downtime for this service is 3 hours. The 20,000 

hour service includes the 8,000 hour actions plus changing of fuel injectors. The downtime 

for this service is 12 hours. 

To characterize the uncertainty in the failure rate for a single Capstone microturbine, 

it was assumed that there was a 20% chance that the failure rate would be greater than 

λ = 1/8000. Further, it was assumed that there was an 90% probability that the failure rate 

51
would be less than λ = 1/16000. (The relatively large value of 20% was due to the lack of 

field data to support the 1/8000 estimate.) 

Finally, assuming an underlying lognormal distribution for the turbine failure rate and 

solving for μ and τ yields values of μ = −9.40558 and τ = 9.38253. The time to failure for 

a single Capstone turbine is assumed to be an exponentially distributed random variable: 

TC1 ∼ exp[−λC1t], where λC1 represents the rate at which turbine failures occur. Figure 26 

depicts the resulting distribution for the time to failure for a single Capstone turbine. 

Since there is excess capacity with the Capstone package of turbines, the system can be 

operated in two modes: cold standby or hot standby. In cold standby, the excess turbines are 

not operated and are started only in the event of a failure of one of the primary generators. 

In hot standby, all 24 turbines are operated continuously, but each at a lower load level. In 

either case, the minimum number of turbines operating at full capacity defines the point at 

which the DER system can successfully provide power to the facility. 

One configuration suggested by Sandia consisted of running the 21 turbines with the 

full available load and the cycling through the remaining three turbines during peak load. 

In this case the three turbines are available in ’cold standby’. In this configuration, the 

turbines are running at approximately 87% of their capacity for a net efficiency of about 

28%. While this configuration was not fully investigated, the overall reliability of the 

Capstone system would increase (relative to the following discussion). However, issues 

associated with failure at turbine start-up from cold-standby would need to be considered 

and may offset the gain in reliability. 

An alternative configuration suggested by Sprint involved running the full bank of 

twenty-four turbines to support the available load. The drawback of this approach is a small 

drop in turbine efficiency. In this configuration, the turbines are running at approximately 

76% of their capacity for a net efficiency of approximately 27.5%. The final configuration 

proposed by Sprint and addressed in the following discussion, involves running all 24 turbines until seven turbines fail. It was felt by Sprint engineers that this was a more likely 

scenario and that the seven failures would reflect a worst case operational configuration. 

Figure 27 depicts the results for the analysis assuming the failure of seven turbines or 

the loss of the supply of natural gas. The median time to failure for the seventh turbine is 

perhaps a bit surprising at 3800 hours, considerably less than the 8300 hour median time to 

failure for an individual Capstone turbine. This is an artifact of running all 24 Capstones 

simultaneously with no repair. As depicted in Figure 23, assume that the Capstone microturbines as the primary power source for the facility and the current system, (i.e. Base 

Case) is used as a backup power source. Figure 28 summarizes the probability distribution 

of the time to failure for the Capstone configuration. Finally, another reliability issue relates to the physical configuration of four pallets of six turbines. Depending on how the the 

power system was configured, it is possible that a single failure of the power distribution 

system might result in an entire pallet of six (operational) turbines being off-line. The outcome would be configuration that was a single point of failure for the entire facility. The 

likelihood of these events is very low, but requires attention during design. 

52 
0

5000

4500040000350003000025000200001500010000

0

3000

6000

9000

12000

15000

18000

21000

24000

27000

30000

33000

36000

39000

42000

45000

48000

51000

54000

57000

60000

63000

66000

69000

72000

75000

78000

More

Tfc1 (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(1219) (29930)

(8300)

Figure 26. Capstone Single Turbine Hours to Failure (TC1 ) 

53
0

5000

25000200001500010000

0

800

1600

2400

3200

4000

4800

5600

6400

7200

8000

8800

9600

10400

11200

12000

12800

13600

14400

15200

16000

Tcap[7] (Hours to Failure) 

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Figure 27. Capstone Configuration w/7 Failures (Tcap7) 

54
0

5000

25000200001500010000

0

600

1200

1800 2400

3000

3600 4200

4800

5400 6000

6600 7200

7800

8400 9000 9600

10200 10800 11400

12000

12600 13200

13800

14400 15000 15600

16200

16800

17400

18000 18600

19200 19800

TFcap (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(2698) (8706)

(4960)

Figure 28. Facility Time to Failure w/Capstone Configuration 

(TFC ) 

55
8.3 Kawasaki Turbine

A second power system configuration involves the use of a single Kawasaki natural gas 

turbine. A typical turbine for this application is the GPB 15X 1.5 mW turbine (Figure 29). 

With the addition of an combustion/catalyst system the emissions of the Kawasaki turbine 

are low: approximately 3 ppmvd (parts per million on dry volume basis) NOx (15% O2) 

over a broad range of power. Kawasaki has provided an MTTF = 200,974 hours and an 

Figure 29. Kawasaki Turbine 

MTTR = 3.1 hours, based on a sample of 150 installed units. The pictures in Figure 30 

are from the Kawasaki GPB brouchure [18]. To characterize the uncertainty in the failure 

rate for a Kawasaki turbine, it is assumed that there was a 10% chance that the failure 

rate would be greater than λK = 1/200974. Since this number is exceptionally high, to be 

conservative, it is assumed that the median failure rate was twice as bad as that reported by 

Kawasaki. This implies that there is a 50% chance that the failure rate might be as high as 

2×λK. 

As with the Capstone mircroturbine, the failure rate is assumed to be a random variable characterized with a lognormal distribution. Solving for μ and τ yields values of 

μ = −11.5.178 and τ = 3.41839. The time to failure for a single Kawasaki turbine is 

assumed to be an exponentially distributed random variable: TK ∼ exp[−λKt], where λK

represents the rate at which turbine failures occur. Given the estimated values for μ and τ, 

Figure 31 depicts the resulting distribution for the time to failure for a Kawasaki turbine. 

Note that, while the lower bound on the uncertainty interval is very high, there is substantial uncertainty in the time to failure. This is an artifact of the assumption that there may be 

56
Figure 30. Kawasaki Footprint 

considerable uncertainty assumed in the failure rate estimate provided by Kawasaki. The 

assumptions used in characterizing the failure rate ’pulled’ the time to failure distribution 

in Figure 32 to the left while allowing for the possibility that the estimates of the failure 

rate provided by Kawasaki may be reasonable. One perspective on this result is that there 

is a high probability that the Kawasaki turbine will result in a much higher reliability. 

As depicted in Figure 23, assume that the Kawasaki turbine acts as the primary power 

source for the facility and the current system, (i.e. Base Case) is used as a backup power 

source. The time to failure for a facility depending on a single Kawasaki natural gas turbine 

as the power source is summarized in Figure 32. 

57
0

70000600005000040000300002000010000

0 30000 60000 90000

120000

150000 180000

210000 240000

270000 300000 330000 360000

390000

420000

450000 480000 510000 540000

570000 600000 630000 660000

690000 720000

750000

780000 810000 840000

870000

900000

TK (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

MedianUncertainty Interval

(7909) (24200)

(58860)

Figure 31. Kawasaki Turbine Hours to Failure (TK) 

58
0

600005000040000300002000010000

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

550000

600000

650000

700000

750000

800000

850000

900000

950000

1000000

1050000

1100000

1150000

1200000

1250000

TFkaw (Hours to Failure)

Frequency

1.000.900.800.700.600.500.400.300.200.100.00

Cumulative Dist Function

Uncertainty Interval

Median

(7969) (249100)

(59010)

Figure 32. Facility Time to Failure for Kawasaki Configuration 

(TFK ) 

59
9 Conclusion

Figure 33 summarizes the results of the three analyses: Base Case, Capstone microturbine 

array, and the single Kawasaki turbine. The overlay provides the capability to make a 

risk-based decision of the relative reliability benefits of the the three alternatives through a 

comparison of the credibility limits for each alternative. Table 6 provides a summary of all 

previous related analysis. 

Table 6. Analysis Summary 

Time to Failure μ σ 10.00% median 90.00% 

Capstone TTF TFC 5419 2514 2698 4960 8706 

Kawasaki TTF TFK 1.04E+05 137200 7969 59010 249100 

Base Case Total Tbase 1130 1119 178.8 776.9 2531 

Utility Time to Failure - TU 1058 1120 107 706.2 2457 

Generator Failure to Start 0.02414 0.04833 2.03E-06 0.00343 0.07514 

Diesel Generator - TG 69.57 10.04 72 72 72 

Battery (time) - TB 2.625 0.9331 1.294 2.869 3.53 

Since there is no overlap between the credibility limits a comparison is relatively straightforward. Consider a comparison between the reliability of the current power supply (i.e. 

Base Case) and the array configuration of Capstone microturbines suggested by Sprint. 

There is a 90% chance that the utility power will fail before 2457 hours, while there is a 

90% chance that the Capstone array will provide power for at least 2698 hours. 

Finally, consider that there is a 90% probability that the Capstone array will fail to 

provide power for less than approximately 8706 hours, while there is a 90% probability 

that the single Kawasaki turbine will provide power for at least 7969 hours. 

A significant, but not decisive element in the lower reliability estimate for the Capstone 

was the configuration and operational plan suggested by Sprint. Other configurations could 

have quite different reliability characteristics and may warrant further investigation. However, there are installation issues associated with the Capstone, e.g. special enclosure, that 

could be a factor in the final decision. 

Not considered in the analysis for either the Kawasaki or Capstone configurations is the 

probability that the turbines will fail to start when called. Just as with the diesel generators, 

there is a likelihood that if the Capstone turbines are left in cold-standby, they will fail to 

start. Clearly, this is less of a consideration of the Kawasaki turbine since this turbine is on 

24/7. Also, not considered in the analyses is consideration for the differences in the control 

systems for the two turbines. 

In conclusion, even given the uncertainties in the three alternatives, the clear choice 

60
is the use of the Kawasaki 1.5 mW turbine as the primary power source for the Sprint 

telecommunication facility. 

61
Risk-based Comparison

1.000.900.800.700.600.500.400.300.200.100.00

0 5000 10000 15000 20000 25000 30000

Time to Failure

Cumulative Dist Function

KawasakiCapstoneBase Case

4960 8706

9048

59990 248400

179

777

2698

2529

Figure 33. Summary of Results

62
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[11] P. Hoeppe and G. Berz. Risks of climate change - the perspective of the (re-)insurance 

industry. In 2005 IEEE POWER ENGINEERING SOCIETY GENERAL MEETING,

VOLS, 1-3, pages 2023–2026, 2005. Article English. 

[12] C. Hor.Analyzing the impact of weather variables on monthly electricity demand. 

IEEE transactions on power systems, 20(4):2078–2085, 2005. 0885-8950. 

[13] J. Houghton.Global Warming. Cambridge University Press, Cambridge, 4 edition, 

2005. 

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[14] IEEE-STD-1188-1996. IEEE recommended practice for maintenance, testing, and replacement of valve-regulated lead-acid (VRLA) batteries for stationary applications. 

IEEE Std ; 1188-1996. IEEE, New York, 1996. 

[15] C& D Technologies Inc. Standby Power Division, 2005. 

http://www.cdstandbypower.com/. 

[16] M. Ivey, A. Ahkil, D. Robinson, K. Stamber, J. Stamp, and K. Chu.Accomadating uncertainty in the planning and operations of electric power systems. Technical 

Report SAND2000-1681, Sandia National Laboratories, July 2000. 

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2005. 

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accidents. Journal of Loss Prevention in the Process Industries, 12:91–107, 1999. 

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65
66
A Original Fault Trees

Figure A.1

No Power 

@ Dist-2

No Power 

thru DC

No Power 

thru DG

DC 

open

T1

fails

utility

fails

A1

open

DG

open

No Power

thru E1

E1

open

No power

thru E2

Kirk

failure

No Power

thru C1

E2

open

G1

fails

C1

open

No Power

thru C2

C2

open

G2

fails

No Power

thru TB1

TB1

open

MG1

fails

No Power 

@ Dist-1

No Power 

thru BC

No Power 

thru BG

BC 

open

T1

fails

utility

fails

A1

open

BG

open

No Power

thru C1

C1

open

Kirk

failiure

No Power

thru E1

E1

open

No Power

thru E2

E2

open

G1

fails

No Power

tthu TB1

TB1

open

MG1

fails

Plant 1

No Power

to BG

No power

thru C2

C2

open

G2

fails No Power

to C1

No Power

to DG

No Power

to E1

AND 

OR

TBD

Figure A.1. MSB-1 Fault Tree

67
No Power 

@ Dist-4

No Power 

thru JC

No Power 

thru JG

JC 

open

T2

fails

utility

fails

F1

open

JG

open

No Power

thru H2

No Power

thru I2

I2

open

G4

fails

No Power

thru I1

I1

open

TB2

fails

MG2

fails

No power

thru H1

H1

open

G3

fails

No Power 

thru GC

GC 

open

T2

fails

utility

fails

F1

open

No Power 

thru GG

No Power 

@ Dist-3

GG

open

No Power

thru H2

Kirk

failure

No Power

thru C1

C2

open

G2

fails

No Power

thru I2

I2

open

G4

fails

No Power

thru I1

I1

open

TB2

fails

MG2

fails

No power

thru H1

H1

open

G3

fails

No Power

thru E1

E1

open

No Power

thru E2

Plant 2

H2

open

No Power

to H2

E2

open

G1

fails

C1

open

No Power

to C1

No Power

thru TB1

TB1

open

MG1

fails

No Power

thru C2

Kirk

failure

No Power

thru C1

C2

open

G2

fails

No Power

thru E1

E1

open

No Power

thru E2

H2

open

No Power

to H2

E2

open

G1

fails

C1

open

No Power

to C1

No Power

thru TB1

TB1

open

MG1

fails

No Power

thru C2

AND 

OR

TBD

No Power 

to GG

No Power 

to JG

Figure A.2. MSB-2 Fault Tree

AND 

OR

TBD

No Power 

@ ESD

No Power 

thru SGA

No Power 

thru SGB

SGA

open

T1

fails

utility

fails

No Power 

thru MS1

MS1

open

TE

fails

utility

fails

SGB

open

EG2

fails

No Power 

thru SGC

SGC

open

EG1

fails

Figure A.3. Earth Station Fault Tree

68
B Base Case.v7 - WinBugs Code

Analysis based on using WinBugs 1.4, 100000 burn-in followed by an additional 500000 

samples. 

model{

fstart1 ̃dbeta(af,bf)

fstart2 ̃dbeta(af,bf)

fstart3 ̃dbeta(af,bf)

e1 ̃ dbern(fstart1)

e2 ̃ dbern(fstart2)

e3 ̃ dbern(fstart3)

# ei=1 (if generator fails to start) with probability fstarti

# we need to be careful to keep the time units the same

# LambdaG is in units of years

tfG1 ̃dexp(LambdaG)I(0,fueltime)

tfG2 ̃dexp(LambdaG)I(0,fueltime)

tfG3 ̃dexp(LambdaG)I(0,fueltime)

tg1<-(1-e1)*tfG1*hours

tg2<-(1-e2)*tfG2*hours

tg3<-(1-e3)*tfG3*hours

LambdaG ̃dgamma(aG,bG)

tfG<- min(min(tg1, tg2)+tg3, max(tg1,tg2) )

LambdaUu ̃dgamma(aUu, bUu)

tyUu ̃dexp(LambdaUu)

tfUu<- hours*tyUu

#LambdaUd is already in hours

LambdaUd ̃dgamma(aUd, bUd)

tfUd ̃dexp(LambdaUd)

fbat ̃dbeta(aB,bB)

eb ̃ dbern(fbat)

# we will assume that if the battery works, we will get timebat hours of use from t

# eb=1-> success eb=0 (failure)

tfB<- eb*timebat

TFdelta<- tfUu + tfUd

TF<- tfUu + tfG + tfB

Tdelta <- TFdelta - TF

69 
}

list(af=0.22, bf=8.9, fueltime=0.008219, hours=8760, timebat=3,

aG=0.6667, bG=0.03412,

aUu=19.14, bUu=2.19,

aUd=1.0281, bUd=6.63126,

aB=3.70868, bB=2.78512)

list(fstart1=1, fstart2=1, fstart3=1,LambdaG=1)

70
C Capstone.v2- WinBugs Code

Analysis based on using WinBugs 1.4, 100000 burn-in followed by an additional 500000 

samples. 

model{ # Capstone 7/24 v2.2 lognormal turbine failure rate PDF)

fstart1 ̃dbeta(af,bf)

fstart2 ̃dbeta(af,bf)

fstart3 ̃dbeta(af,bf)

e1 ̃ dbern(fstart1)

e2 ̃ dbern(fstart2)

e3 ̃ dbern(fstart3)

# ei=1 (if generator fails to start) with probability fstarti

# we need to be careful to keep the time units the same

# LambdaG is in units of years

LambdaG ̃dgamma(aG,bG)

ttfG1 ̃dexp(LambdaG)

ttfG2 ̃dexp(LambdaG)

ttfG3 ̃dexp(LambdaG)

tfG1<- min(ttfG1, fueltime)

tfG2<- min(ttfG2, fueltime)

tfG3<- min(ttfG3, fueltime)

tg1<-(1-e1)*tfG1*hours

tg2<-(1-e2)*tfG2*hours

tg3<-(1-e3)*tfG3*hours

tfG<- min(min(tg1, tg2)+tg3, max(tg1,tg2) )

# utility up-time

LambdaUu ̃dgamma(aUu, bUu)

tyUu ̃dexp(LambdaUu)

tfUu<- hours*tyUu

#LambdaUd is already in hours

LambdaUd ̃dgamma(aUd, bUd)

tfUd ̃dexp(LambdaUd)

#Battery Code

j  ̃ dunif(0, 1)

tfb16 <- alpha16[J] + beta16[J]*(j - x.change16[J])

71 
J <- 1 + step(j - x1.change16) + step(j - x2.change16) + step(j - x3.change16)

k  ̃ dunif(0, 1)

tfb28 <- alpha28[K] + beta28[K]*(k - x.change28[K])

K <- 1 + step(k - x1.change28) + step(k - x2.change28) + step(k - x3.change28)

tfB <- min(tfb16, tfb28)

# natural gas

# for the Turbine, two failure modes are possible

# either the natural gas line is cut or the turbine fails

ttfNG ̃dexp(LambdaNG)

LambdaNG ̃dlnorm(aNG,bNG)

tfNG<-ttfNG*hours

LambdaC ̃dlnorm(aC,bC)

#generate failure times for operational turbine

for (i in 1:24) {

tfc[i]  ̃dexp(LambdaC)

}

# Capstones are lost when 7th turbine fails

tfCh <- ranked(tfc[],7)

tfC1 <- ranked(tfc[],1)

# power can only last as long as either

# the NG is available or Capstones are operating

tfCap<-min(tfNG, tfCh)

#Tdelta = time without backup (including restoration)

TFdelta<- tfUu + tfUd

Tbase <- tfUu+tfG+tfB

TF<- tfCap + tfUu + tfG + tfB

Tdelta <- TFdelta - (tfUu+tfG+tfB)

}

list(af=0.22, bf=8.9, fueltime=0.008219, hours=8760,

aG=0.6667, bG=0.03412,

aUu=19.14, bUu=2.19,

aUd=1.0281, bUd=6.63126,

aNG=-5.89, bNG=0.26236,

aC= -9.40558, bC=9.38253,

beta16 = c(0, 66.67, 5, 1.333),

72 
alpha16 = c(0, 0, 2, 3),

x.change16 = c(0, 0.02, 0.05, 0.25),

x1.change16 = 0.02,

x2.change16 = 0.05,

x3.change16 = 0.25,

beta28 = c(0, 40, 3.125, 1.667),

alpha28 = c(0, 0, 2, 3),

x.change28 = c(0, 0.03, 0.08, 0.40),

x1.change28 = 0.03,

x2.change28 = 0.08,

x3.change28 = 0.40)

list(fstart1=1, fstart2=1, fstart3=1,LambdaG=19, LambdaC=1)

73
74
D Kawasaki.v5- WinBugs Code

Analysis based on using WinBugs 1.4, 100000 burn-in followed by an additional 500000 

samples. 

model{ #Kawasaki v8 (lognormal Kawasaki failure rate PDF)

fstart1 ̃dbeta(af,bf)

fstart2 ̃dbeta(af,bf)

fstart3 ̃dbeta(af,bf)

e1 ̃ dbern(fstart1)

e2 ̃ dbern(fstart2)

e3 ̃ dbern(fstart3)

# ei=1 (if generator fails to start) with probability fstarti

# we need to be careful to keep the time units the same

# LambdaG is in units of years

LambdaG ̃dgamma(aG,bG)

ttfG1 ̃dexp(LambdaG)

ttfG2 ̃dexp(LambdaG)

ttfG3 ̃dexp(LambdaG)

tfG1<- min(ttfG1, fueltime)

tfG2<- min(ttfG2, fueltime)

tfG3<- min(ttfG3, fueltime)

tg1<-(1-e1)*tfG1*hours

tg2<-(1-e2)*tfG2*hours

tg3<-(1-e3)*tfG3*hours

tfG<- min(min(tg1, tg2)+tg3, max(tg1,tg2) )

# utility up-time

LambdaUu ̃dgamma(aUu, bUu)

tyUu ̃dexp(LambdaUu)

tfUu<- hours*tyUu

#LambdaUd is already in hours

LambdaUd ̃dgamma(aUd, bUd)

tfUd ̃dexp(LambdaUd)

#Battery Code

j  ̃ dunif(0, 1)

tfb16 <- alpha16[J] + beta16[J]*(j - x.change16[J])

75 
J <- 1 + step(j - x1.change16) + step(j - x2.change16) + step(j - x3.change16)

k  ̃ dunif(0, 1)

tfb28 <- alpha28[K] + beta28[K]*(k - x.change28[K])

K <- 1 + step(k - x1.change28) + step(k - x2.change28) + step(k - x3.change28)

tfB <- min(tfb16, tfb28)

# natural gas

# for the Turbine, two failure modes are possible

# either the natural gas line is cut or the turbine fails

ttfNG ̃dexp(LambdaNG)

LambdaNG ̃dlnorm(aNG,bNG)

tfNG<-ttfNG*hours

LambdaK ̃dlnorm(aK,bK)

ttfK ̃dexp(LambdaK)

tfKh<-ttfK

tfK<-min(tfNG, tfKh)

#Tdelta = time without backup (including restoration)

TFdelta<- tfUu + tfUd

Tbase <- tfUu+tfG+tfB

TF<- tfK + tfUu + tfG + tfB

Tdelta <- TFdelta - Tbase

}

list(af=0.22, bf=8.9, fueltime=0.008219, hours=8760,

aG=0.6667, bG=0.03412,

aUu=19.14, bUu=2.19,

aUd=1.0281, bUd=6.63126,

aNG=-5.89, bNG=0.26236,

aK=-11.5178, bK=3.14839,

beta16 = c(0, 66.67, 5, 1.333),

alpha16 = c(0, 0, 2, 3),

x.change16 = c(0, 0.02, 0.05, 0.25),

x1.change16 = 0.02,

x2.change16 = 0.05,

x3.change16 = 0.25,

beta28 = c(0, 40, 3.125, 1.667),

alpha28 = c(0, 0, 2, 3),

x.change28 = c(0, 0.03, 0.08, 0.40),

x1.change28 = 0.03,

76 
x2.change28 = 0.08,

x3.change28 = 0.40)

list(fstart1=1, fstart2=1, fstart3=1,LambdaG=19, LambdaK=0.01)

77
DISTRIBUTION: 

1 Larry L. Johnson 

Sprint 

Power Standards - Research and 

Testing 

6100 Sprint Parkway 

Overland Park, KS 66251 

USA 

1 Hilary Whitaker

Liebman & Associates, Inc.

2401 Pennsylvania Ave NW,

Suite 410

Washington, DC, 20037

USA

1 Doug A. Arent, Director,

Strategic Analysis

National Renewable Energy

Laboratory

1617 Cole Blvd

Golden CO 80401

U.S.A. 

5 MS 0748 

David Robinson, 6861 

1 MS 0710 

Abbas Akhil, 6251 

2 MS 9018 

Central Technical Files, 8945-1 

2 MS 0899 

Technical Library, 4536 

1 MS 0161 

Intellectual Property , 11500 

78