ECE3795 CPPS power in communicationsakwasins/ECE3795 CPPS power in... · 2018-01-15 · • I dditi t b ffi i t ICT l t d t b hi hlIn addition to been efficient, ... For telephony

1

Cyber Physical Power Systems

Power in Communications

© A. Kwasinski, 2015

2Information and Communications Tech. Power SupplyInformation and Communications Tech. Power Supply

ICT t t ti bl ( b t 5 % f t t l d d i• 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 theinformation and communications technology equipment cost in the near to mid-term future.

Example of a server in a data center normalized to 100 W: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


3Information and Communications Tech. Power SupplyInformation and Communications Tech. Power Supply

I dditi t b ffi i t ICT l t d t b hi hl• In addition to been efficient, ICT power plants need to be highly reliable/available.


4Land-line Telecommunications Network


5Land-line Telecommunications Network • Power infrastructure is for telecommunication networks as cardiovascular• 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

6Wireless Telecommunications Network


7Wireless Telecommunications Network

• Power needs to be provided to the switch (called Mobile Telecomm nications S itching Office or MTSO) and to the remote


Telecommunications Switching Office or MTSO) and to the remote terminals (the based stations).

8Power plants architectures

• DC: For telephony and wireless communication networks

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


9

T i l fi ti i d t t

Power plants architectures

• Typical configuration in data centers:


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


• Typical power plant for telephony networks:


11

• Typical centralized architecture for telephony networks:

Power plants architectures• Typical centralized architecture for telephony networks:

Only (centralized) bus bars

Centralized architecture



• Typical distributed architecture for telephony networks:

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

Distributed architecture


Distributed architecture

13Telecom central office power plant

TelecomPower Plant


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

14Telecom central office power plant


15Batteries


16Distribution frames


17Distribution frames


18Inverters


19Base station power plant






22Telephony outside plant

Di it l L C i d th t id l t b db d t t i l• 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:


23

RECTIFIERS

Telephony outside plantRECTIFIERS


24Telephony outside plant


25Outside plant power supply

• Traditional emergency power solutions during long grid outages


26Reliability and Availability

R li bilit• Reliability applies to components. Once they fail, they cannot be

repaired.

• Reliability

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

U li bilit i th l t t 1 f li bilit ( )• 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• 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

Pr{ | }Pr{ } Pr{ }B A A A


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

B A A Ah t dt A BB B


R li bilit• ReliabilityPr{ | }Pr{ } Pr{ }( ) Pr{ | }

Pr{ } Pr{ }B A A Ah t dt A B

B B

• Since • Pr{B|A} = 1

• Pr{A} = f(t),

• Pr{B} = 1 - F(t).

Then• Then

( )( )1 ( )

f th t dtF t

• and

( )th d


0( )

( ) 1F t e


R li bilit• The hazards function may take various forms and is a combination of

various factors. Typical forms for electronic components (solid lines)

• Reliability

and mechanical components (doted lines) with the three most characteristics components (early mortality, random and wear out) are



R li bilit• Considering electronic components during the useful life period, the

hazards function is constant and equals the so called constant failure

• Reliability

rate λ. So,

F(t) = 1 – e- λt

f( ) λ λ

R(t)

f(t) = λe- λt

R(t) = e- λt

• And

t

1

And,

• The inverse of λ is called the Mean Time to Failure. I.e.,it is the

0

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


,expected operating time to (first) failure


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

• Reliability

its components.

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

adj base Q T E O

Production Thermal Electrical

Other factors (power and operational

environment factors)

• Aluminum electrolytic capacitors tend to be a source of reliability

quality stress stresse o e t acto s)

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.


A il bilit• Availability applies to systems (which can operate with failed

components) or repairable entities.

• Availability

• Definitions depending application:• Availability, A, is the probability that an entity works on demand. This definition is adequate for standby systems.q y y

• 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• 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:



A il bilit• Availability

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 g p ginterval 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


A il bilit

• Hence,

• Availability

• Which leads to the differential equation

Pr ( ) Pr ( )Pr ( ) Pr ( )f f

w ft dt t

t tdt

• Which leads to the differential equation

Pr ( )( ) Pr ( )f

fd t

tdt

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

( )Pr ( ) 1 tt e Pr ( ) 1f t e

( )1Pr ( ) tt e


( )Pr ( )w t e


A il bilit

• When plotted:

• Availability

• 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

( ff ) fTime (MDT or off-line time), TD, then as t tends to infinity

Pr ( ) U Uw

U D

T TA tMTBF T T

• That is,

U D

Availability =Expected time operating “normally”


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


A il bilit• Notes:

• Unavailability is defined as

• Availability

Unavailability is defined as

Mean time between failures (MTBF) is the sum of T and T

aMDTUMTBF

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

UP

DOWN

• Ways of improving availability• Modularity

DOWN

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


• Distributed functions


• 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.



A il bilit

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

• Availability

process is now

Td P• So,

Tddt

P P A

( ) 0A B A B • Where,

( )( ) 0

0 ( )0 ( )

A B A B

A A B B

B B A A

B A A B

A


( )B A A B

1 2 3 4Pr ( ) Pr ( ) Pr ( ) Pr ( )T

S S S St t t tP


A il bilit

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

• Availability

given by

1

1 1S

i Nii

ijj

Ta

a

• The probability density function of being at state Si is

1jj i

( ) iii

aT i iif T a e

• the frequency of finding the system in state Si is

Pr ( )i ii Sa t


Pr ( )ii ii Sa t


A il bilit

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

• Availability



• 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

• Availability

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 theof a system with series connected components is the product of the components availability.

S iA a• 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).

U © A. Kwasinski, 2015

P iU u


A il bilit

• For a series two-components system

(b th A d B d t t

• Availability

(both A and B need to operate

for the system to operate).

Working stateFailed states

System availability



A il bilit

• For a parallel two-components system

( ith A B d t t

• AvailabilityFailed state

(either A or B need to operate

for the system to operate).

Working statesSystem unavailability



• The most common redundant configuration is called n + 1 redundancy in which n elements of a system are needed for the system to operate

• Availability

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 nnecessary elements fails.

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

a = 0.97A

better:

1( 1) n nA n a u a

• Availability decreases when nincreases to a point where A < a



• For more complex systems, availability can be calculated using minimal cut sets

• Availability

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.



•Unavailability with minimal cut sets:

• Availability

•Unavailability with minimal cut sets:

PCM

S jU K

• Calculation:1j

1M M Mi M

A i ti ith hi hl il bl t

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

• Approximation with highly available components:

P( )jC C cM M

S j l jU K u u


,1 1 1

( )S j l jj j l

46Standby Power Plants

Ac mains: 99.9 %

Power plant: 99.99 %(without batteries)

• Typical availabilities

- 48 V

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

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


p y


A il bilit C l l ti

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

• Availability Calculation

• 1st digit: rectifiers (RS) with n+1redundancy

• 2nd digit: ac mains (MP)3 d di it t (GS) (f il t t t• 3rd digit: genset (GS) (failure to start

probability given by ρGS

• Availability of power plant without batteries:y p p

1

( )GS GS MP MP

PP TS RSMP MP GS

A A A

where2 ( 1)

( 1)R

RSR R

n nn

2 11

11

1

2 n nr r n

RS ni i n i

n r r

C

C

!C

( )! !k

n

n kk n k n


10

n r ri


• System availability equation: ( ) ( )Tt tP A P• Availability Calculation

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

0 ( ) 0 0 00 ( ) 0 0 0

0 0 0 ( ) 0 (1 )

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

A

• Failure probability (in time):

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

RS MP RS GS MP GS MP

RS GS GS MP RS MP

RS MP GS MP RS

0 0 0 0 ( )

GS

RS MP GS GS MP RS

• Failure probability (in time):

• The probability density function fPPf(t) associated with the probability of

( ) ( ) 1 ( )i i

i i

PPf S SS F S W

P t P t P t

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

( ) a tPPff t a e


where aF = 3μRS + μMP + μGS

( )PPff


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

• Availability CalculationaF = 3μRS + μMP + μGS

failed states (called minimal cut states) to immediately adjacent working states.



• The probability of discharging the batteries is, then


S t il bilit t b bilit

0( ) 1 ( )BAT

BATT a T

BD BAT PPfP t T f d e

• System unavailability or outage probability:

lim ( )F BAT F BATa T a TO PPf aP e P t e U

• Two cases are exemplified:

( )O PPf at

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

genset.• Case B: Without genset


• Case B: Without genset


• In general, when batteries are considered the unavailability is


,

/ / /1MCS i BAT

i mcs

T

w B w oB w BU U e A

Total availability

/ / /w B w oB w B

Total unavailabilityBase unavailability (without batteries) Batteries (local

Repair rate from a minimal cut state to an

operational state( t out batte es)energy storage)

autonomyoperational state

(Depends on logistics, maintenance

processes, etc.)Heavily depends on unavailability of the electric grid tieof the electric grid tie

Optimal sizing of energy storage depends on

Local energy storage contributes to reduce unavailability


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

power plant availability


• In general, when batteries are considered the unavailability is


,

/ / /1MCS i BAT

i mcs

T

w B w oB w BU U e A

Related with minimal cut states


Documents

ECE3795 CPPS power in communicationsakwasins/ECE3795 CPPS power in... · 2018-01-15 · • I dditi t b ffi i t ICT l t d t b hi hlIn addition to been efficient, ... For telephony