1 © A. Kwasinski, 2015 Cyber Physical Power Systems Fall 2015 Power in Communications.

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© A. Kwasinski, 2015

Cyber Physical Power Systems

Fall 2015

Power in Communications

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Information and Communications Tech. Power Supply

• ICT systems represent a noticeable (about 5 % of total demand in U.S.) fast increasing load.• Increasing power-related costs, likely to equal and exceed information and communications technology equipment cost in the near to mid-term future.

Example of a server in a data center normalized to 100 W:• 860 W of equivalent coal power is needed to power a 100 W load

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Information and Communications Tech. Power Supply

• In addition to been efficient, ICT power plants need to be highly reliable/available.

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Land-line Telecommunications Network

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Land-line Telecommunications Network • Power infrastructure is for telecommunication networks as cardiovascular

system is for humans.

• Power needs to be provided to the switch (nowadays it is a “big computer” routing packets of information) and sometimes to remote terminals.

• CATV systems are similar

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Wireless Telecommunications Network

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Wireless Telecommunications Network

• Power needs to be provided to the switch (called Mobile Telecommunications Switching Office or MTSO) and to the remote terminals (the based stations).

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Power plants architectures

• DC: For telephony and wireless communication networks

• AC: For data centers RECTIFIER + DC-DC CONVERTER

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• Typical configuration in data centers:

• Total power consumption: > 5 MW (distribution at 208V ac)


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• Typical power plant for telephony networks:

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• Typical centralized architecture for telephony networks:

Centralized architecture

Only (centralized) bus bars


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Distributed architecture

Each cabinet with its own bus bars connected to its own battery string and loads. Then all cabinets’ bus bars are connected

• Typical distributed architecture for telephony networks:


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• 13 x 200 Amps. Rectifiers• 11 x 1400 Ah Batteries

TelecomPower Plant

Telecom central office power plant

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Telecom central office power plant

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Batteries

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Distribution frames

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Distribution frames

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Inverters

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Base station power plant

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Telephony outside plant

• Digital Loop Carrier and other outside plant broadband remote terminals may provide service up to 500 subscribers in average.

• Local backup is usually provided by batteries with 8 hrs of autonomy• Significant variations in power consumptions:

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RECTIFIERS


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Outside plant power supply

• Traditional emergency power solutions during long grid outages

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• Reliability applies to components. Once they fail, they cannot be repaired.

• Reliability, R, is defined as the probability that an entity will operate without a failure for a stated period of time under specified conditions.

• Unreliability is the complement to 1 of reliability (F = 1 – R)

F(t) = Pr{a given item fails in [0,t]}

• F(t) is a cumulative distribution function of a random variable t with a probability density function f(t).

• Both F(t) and f(t) can be calculated based on a hazards function h(t) defined considering that h(t)dt indicates the probability that an item fails between t and t + dt (“event A”) given that it has not failed until t (“event B”). From Bayes theorem

Reliability and Availability

• Reliability

Pr{ | }Pr{ } Pr{ }( ) Pr{ | }

Pr{ } Pr{ }

B A A Ah t dt A B

B B

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• Since • Pr{B|A} = 1• Pr{A} = f(t), • Pr{B} = 1 - F(t).

• Then

• and


• ReliabilityPr{ | }Pr{ } Pr{ }

( ) Pr{ | }Pr{ } Pr{ }

B A A Ah t dt A B

B B

( )( )

1 ( )

f th t dt

F t

0( )

( ) 1th d

F t e

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• The hazards function may take various forms and is a combination of various factors. Typical forms for electronic components (solid lines) and mechanical components (doted lines) with the three most characteristics components (early mortality, random and wear out) are


• Reliability

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• Considering electronic components during the useful life period, the hazards function is constant and equals the so called constant failure rate λ. So,

F(t) = 1 – e- λt

f(t) = λe- λt

R(t) = e- λt

• And,

• The inverse of λ is called the Mean Time to Failure. I.e.,it is the expected operating time to (first) failure


• Reliability

R(t)

t

0

1[ ( )] ( )E f t tf t dt

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• The failure rate of a circuit is in most cases the sum of the failure rate of its components.

• General form for calculating failure rate (from MIL-Handbook 217):

• Aluminum electrolytic capacitors tend to be a source of reliability concern for PV inverters. Although their base failure rate is low (about 0.50 FIT), the adjusted failure rate is among the highest (about 50 FIT). Compare it with a MOSFET adjusted failure rate of about 20 FIT.

• NOTE: FIT is failures per 109 hours.

adj base Q T E O

Production quality

Thermal stress

Electrical stress

Other factors (power and operational

environment factors)


• Reliability

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• Availability applies to systems (which can operate with failed components) or repairable entities.

• Definitions depending application:• Availability, A, is the probability that an entity works on demand. This

definition is adequate for standby systems.

• Availability, A(t) is the probability that an entity is working at a specific time t. This definition is adequate for continuously operating systems.

• Availability, A, is the expected portion of the time that an entity performs its required function. This definition is adequate for repairable systems.

• Consider the following Markov process representing a repairable entity:


• Availability

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λ is the failure rate and μ is the repair rate. The probability for a repairable item to transition from the working state to the failed state is given by λdt and the probability of staying at the working state is (1-λ)dt. An analogous description applies to the failed state with respect to the repair rate.

• The probability of finding the entity at the failed state at t = t +dt is identified by Prf(t + dt) then this probability equals the probability that the item was working at time t and experiences a failure during the interval dt or that the item was already in the failed state at time t and it is not repaired during the immediately following interval dt. In mathematical terms,

Prf(t + dt) = Prw(t)λdt + Prf(t)(1-µ)dt


• Availability

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• Hence,

• Which leads to the differential equation

• With solution (considering that at t = 0 it was at the working state)


• Availability

Pr ( ) Pr ( )Pr ( ) Pr ( )

f fw f

t dt tt t

dt

Pr ( )( ) Pr ( )f

f

d tt

dt

( )Pr ( ) 1 tf t e

( )1Pr ( ) t

w t e

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• When plotted:

• If we denote the inverse of λ as the Mean Up Time (MUT), TU, when the system is operating “normally” and the inverse of μ as the Mean Down Time (MDT or off-line time), TD, then as t tends to infinity

• That is,


• Availability

Pr ( ) U Uw

U D

T TA t

MTBF T T

Availability = Expected time operating “normally”

Total time (“normal” operation + off-line time)

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• Notes:

• Unavailability is defined as

• Mean time between failures (MTBF) is the sum of TD and TU

• Ways of improving availability• Modularity• Redundancy (parallel operation of same components)• Diversity (use of different components for the same function• Distributed functions


• Availability

aMDT

UMTBF

UP

DOWN

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• About the common claim of data center operators of having “diverse power feeds.” Two power paths imply redundancy, not diversity because the grid is one.


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• Now consider a two-components system (A and B). The Markov process is now

• So,

• Where,


• Availability

TTd

dt P

P A

( ) 0

( ) 0

0 ( )

0 ( )

A B A B

A A B B

B B A A

B A A B

A

1 2 3 4

Pr ( ) Pr ( ) Pr ( ) Pr ( )TS S S St t t tP

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• The expected time that the system remains in each of the states is given by

• The probability density function of being at state Si is

• the frequency of finding the system in state Si is


• Availability

1

1 1S

i Nii

ijjj i

Ta

a

( ) ii

i

aT i iif T a e

Pr ( )ii ii Sa t

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• Hence, for the two-components system (A and B).


• Availability

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• If in a system all components need to be operating in order to have the system operating normally, then they are said to be connected in series. This “series” connection is from a reliability perspective. Electrically they could be connected in parallel or series or any other way. The availability of a system with series connected components is the product of the components availability.

• If in a system with several components, only one of them need to be operating for the system to operate, then they are said to be connected in parallel from a reliability perspective. The system unavailability equals the product of components unavailability, where the unavailability, U, is the complement to 1 of the availability (U = 1 – A).

S iA a


• Availability

P iU u

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• For a series two-components system

(both A and B need to operate

for the system to operate).


• Availability

Working stateFailed states

System availability

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• For a parallel two-components system

(either A or B need to operate

for the system to operate).


• Availability

Working states

Failed state

System unavailability

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• n +1 redundant configuration. But more modules is not always better:

• Availability decreases when n increases to a point where A < a

1( 1) n nA n a u a

a = 0.97

• The most common redundant configuration is called n + 1 redundancy in which n elements of a system are needed for the system to operate, so one additional component is provided in case one of those n necessary elements fails.

A


• Availability

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• For more complex systems, availability can be calculated using minimal cut sets• A minimal cut set is a group of components such that if all fail the system

also fails but if any one of them is repaired then the system is no longer in a failed state. The states associated with the minimal cut sets are called minimal cut states.• Much simpler than Markov approaches.


• Availability

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• Unavailability with minimal cut sets:

• Calculation:

• Approximation with highly available components:

1

PCM

S jj

U K

1

1 2 1 1

P( ) P( ) 1 [1 P( )]c c cM M Mi

i i j S ii i j i

K K K U K

1

P( )cM

ii

K

,1 1 1

P( )jC C

cM M

S j l jj j l

U K u

u


• Availability

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Ac mains: 99.9 %

Genset: 99.4 % (includes TS) (failure to start = 2.41 %)

- 48 V

Power plant: 99.99 % (without batteries)

Each rectifier: 99.96 %n+1 redundant configuration is used for improved availability

Standby Power Plants

• Typical availabilities

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• Binary representation of Markov states: • 1st digit: rectifiers (RS) with n+1

redundancy• 2nd digit: ac mains (MP)• 3rd digit: genset (GS) (failure to start

probability given by ρGS

• Availability of power plant without batteries:

where


• Availability Calculation

1

( )GS GS MP MP

PP TS RSMP MP GS

A A A

2 ( 1)

( 1)R

RSR R

n n

n

2 11

11

10

2 n nr r n

RS ni i n i

n r ri

C

C

!

C( )! !

kn

n k

k n k n

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• System availability equation:

• Failure probability (in time):

• The probability density function fPPf(t) associated with the probability of leaving the set of failed states after being in this set from t = 0 and entering the set of working states at time t + dt is

where

( ) ( ) 1 ( )i i

i i

PPf S SS F S W

P t P t P t

( ) 0 (1 ) 0 0 0( ) 0 0 0 0

0 ( ) 0 0 00 ( ) 0 0 0

0 0 0 ( ) 0 (1 )0 0 0 ( ) 00 0 0 0 ( )

MP RS GS MP GS MP RS

GS GS MP RS MP RS

MP GS MP RS GS RS

MP GS GS MP RS RS

RS MP RS GS MP GS MP

RS GS GS MP RS MP

RS MP GS MP RS

A

0 0 0 0 ( )GS

RS MP GS GS MP RS

( ) ( )Tt tP A P



aF = 3μRS + μMP + μGS

( ) a tPPff t a e F

F

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• Notice that is the sum of the transition rates from failed states (called minimal cut states) to immediately adjacent working states.


• Availability CalculationaF = 3μRS + μMP + μGS

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• The probability of discharging the batteries is, then

• System unavailability or outage probability:

• Two cases are exemplified:• Case A: With a permanent

genset.• Case B: Without genset

lim ( )F BAT F BATa T a TO PPf at

P e P t e U



0( ) 1 ( )

BATBAT

T a TBD BAT PPfP t T f d e

F

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,

/ / /1MCS i BAT

i mcs

T

w B w oB w BU U e A

Total unavailabilityBase unavailability (without batteries) Batteries (local

energy storage) autonomy

Repair rate from a minimal cut state to an

operational state(Depends on logistics,

maintenance processes, etc.)

• In general, when batteries are considered the unavailability is

Total availability

Heavily depends on unavailability of the electric grid tie

Optimal sizing of energy storage depends on expected grid tie performance and local power

plant availability

Local energy storage contributes to reduce unavailability



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,

/ / /1MCS i BAT

i mcs

T

w B w oB w BU U e A

Total unavailabilityBase unavailability (without batteries) Batteries (local

energy storage) autonomy

Repair rate from a minimal cut state to an

operational state(Depends on logistics,

maintenance processes, etc.)


Total availability

Heavily depends on unavailability of the electric grid tie

Optimal sizing of energy storage depends on expected grid tie performance and local power

plant availability

Local energy storage contributes to reduce unavailability



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,

/ / /1MCS i BAT

i mcs

T

w B w oB w BU U e A

Related with minimal cut states




1 © A. Kwasinski, 2015 Cyber Physical Power Systems Fall 2015 Power in Communications.

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