atf2 power supply availability comparison february 5, 20061 atf2 power supply availability...

February 5, 2006 1ATF2 Power Supply Availability Comparison

ATF2 Power Supply Availability C0mparison

Paul Bellomo and Briant lam


ObjectiveTo compare the availability of non-redundant power systems

with modular, redundant power systems.

Conclusions

The SLAC-proposed redundant, modular power systems show

significantly greater availability than nonredundant power

supplies.

Hot-swap of the power modules alone does not yield a large

availability improvement. Other components must also be

redundant.

ATF2 potentially will use redundant power systems. The ILC

definitely will need redundant systems

Objective and Conclusions


Term Definition

MTBF Mean time between failures in hours

MTBFOThe increased MTBF in hours that considers equipment operation at lower than rated power levels

MTBFR The rated MTBF in hours

MTTR The mean time to repair and recover beam in hours

R(t) Reliability or probability of success with time

, O, R Failure rates in hr -1. These are the reciprocals of the MTBFs

1/1 One full rated power supply. Rated power = delivered power

1/2 One out of two redundant power supply configuration

2/3 Two out of three redundant power supply configuration

3/4 Three out of four redundant power supply configuration

4/5 Four out of five redundant power supply configuration

Glossary of Terms


References

1. Diamond Light Source

Under construction so no empirical Availability data, no reliability studies or analysis

450 Power supplies are redundant 4/5 configuration.

2. EMI-Lambda, IE Power, Power Ten power supplies MTBF > 100,000 hours

3. SPEAR 3 power supply operation MTBF >100,000 hours, MTTR 2 hours

4. Argonne Laboratory, APS, 2000 power supplies, MTBF >> 100,000 hours, MTTR 1 hour

1. MTBF of switchmode power supply or bulk power supply is 110,000 hours based on

Cherrill Spencer SLAC studies spanning several years

2. MTBF of a single power module is 220,000 hours based on parts count method

3. MTBF PS controllers is 288,889 hours per PAC 2001 reliability paper

4. MTBF cables is 2,600,000 hours per PAC 2001 reliability paper

5. MTTR is 4 hours, 2 hours for repair and 2 hours for beam recovery

6. When redundancy is considered it is Active redundancy

7. No replacement and hot swap replacement during a run are also compared

Analysis References and Basis


Availability Improvement By Oversizing and Redundancy



k n kt t

The general, exponential form of the Binomial Distribution is

n!R( t )

n k !k !

= constant=failure rate

m= minimum number of system power supplies needed for operation

n = total numb

n

k me 1 e

- n t t

er of power supplies in the system

A special case occurs when m = n or when m=n=1

R( t ) e R( t ) e


n 3t k t n kn!

2/3 ( n k )! k !k m 2

2 t t 2 t t

3 t t

Binomial Expansion 2 out of 3 example

R ( t ) ( )( e ) (1 e )

k 2

3!e (1 e ) 3 e (1 e )

1!2!

3 cases, probability of success, probability of failure

k=3

3!e (1 e )

0!3!

0 3 t

-2 t 3 t2/3

1 e

1 case, probability of success, no failure

R (t)=3e 2e

S S

SSS

SS

S S

F

F

F

3 Cases

1 Case



-2 t 3 t2/3

( t )t

( t )t ( t )t

( t )t ( t )t

R (t)=3e 2e

Derivation

When (t) is a function of time

General form R( t ) e

dR( t ) d ( t )e ( t )e

dt dt

d ( t ) is << ( t )

dt

dR( t )( t )e but e R( t )

dt

dR( t )

dt( t ) If R( t )

is a constant then the above reduces to (t)=

R( t )MTBF( t )

dR( t )

dt




O

O R

O R

RO R

O

O

OO1FR

O

t

1 power supply where operating power=the rated power

P P

MTBF MTBF

P

P

R ( t ) e

MTBFA

MTBF MTTR


O O O

O R

RO O

R

R R RO

m1/ 2

k n kt t

mEach power module operates at

For the m out of n case, where m n

mn quantity of rated power modules.

n

mP P

n

P n mMTBF MTBF MTBF

P m n

n!R ( t ) ne

n k !k

ra d Pn

!

te

n

k me 1 e

O

m / n

O O

t n t

m / n

Om / n

Om / n

O O

O O

m t n t

m t n t

me

ne meMTBF ( t )

mn e mn e

MTBF ( t )A ( t )

MTBF ( t ) MTTR



O O O O

RO R R O R

O

R

2 t 3 t2 / 3

2 / 3

k n kt t

For the m=2 out of n=3 case

3-1/2 rated power supplies.

P 3 2MTBF MTBF MTBF

P 2 3

n!R ( t ) 3e 2e

n k !k

Each power sup

!

3eMTBF ( t )

ply operates at 2/3 rated P

n

k me 1 e

2 / 3

O O

O2 / 3

O2 / 3

O O

O O

2 t 3 t

2 t 3 t2e

6 e 6 e

MTBF ( t )A ( t )

MTBF ( t ) MTTR

Availability Improvement By Oversizing and Redundancy - An Example


1sys PS controller transductor cables

1sys

1syssys

1sys4000sys

1sys1sys

1sys

1 1 1 1

110,000 288,889 1,300,000 2,600,000

1MTBF 72,960 hours

MTBFMTBF 18.2 hours

4000

MTTR 4 hours

MTBFAvailability

MTBF ( t ) MTTR

A

40004000sys 1sysvailability Availability 0.803

Availability is essentially constant

4000 Non-Redundant Power Supplies


Rack and Power System Layouts


Transductors

Cables

Magnet

PS Controller

AC Power

Remote Computer

Magnet

Transductors

Cables

PS Controller

Remote Computer

Bulk PS

Power Modules

Power Modules

1/2 200 systems & 2000 subsystems




System

Subsystem Subsystem

10 or 5 subsystems per system

Systems and Subsystems


1 1 / 2sys BPS 1 / 2PM controller transductor cabcon

1 1 / 2subsys1 1 / 2 subsys

1 1 / 2 subsys1 1 / 2 subsys

1 1 / 2 subsys

2000 1

( t ) 10 ( t ) 10 10 10

1MTBF ( t ) MTTR 4 hours

( t )

MTBF ( t )Availability ( t )

MTBF ( t ) MTTR

Availability

200/ 2 subsys 1 1 / 2 subsys

1 2 / 3 subsys BPS 2 / 3PM controller transductor cabcon


( t ) Availability ( t )

Note that avaialbility is a function of time and must be plotted

( t ) 10 ( t ) 10 10 10

1MTBF ( t )

( t )


1 2 / 3 subsys

1001000 2 / 3 subsys 1 2 / 3 subsys

MTTR 4 hours


MTBF ( t ) MTTR

Availability ( t ) Availability ( t )

Analysis for 1 / 2 and 2 / 3 Subsystems


1 3 / 4subsys BPS 3 / 4PM controller transductor cabcon



1 3 / 4 subsys

500 3 / 4

( t ) 5 ( t ) 5 5 5


( t )


MTBF ( t ) MTTR

Availability

100subsys 1 3 / 4 subsys

1 4 / 5 subsys BPS 4 / 5PM controller transductor cabcon



( t ) Availability ( t )

( t ) 5 ( t ) 5 5 5


( t )


MTB

1 4 / 5 subsys

100500 4 / 5 subsys 1 4 / 5 subsys

F ( t ) MTTR

Availability ( t ) Availability ( t )

Analysis for 3 / 4 and 4 / 5 Subsystems


4000 m / n subsys 2000 1 / 2 subsys 1000 2 / 3 subsys

500 3 / 4 subsys 500 4 / 5 subsys

A ( t ) A ( t )* A ( t )

* A ( t )* A ( t )

Availability Calculation for 4000 m / n Subsytsems


Availability of 4000 Non-Redundant Vs Redundant Modular PS

0 1000 2000 3000 4000 5000 6000 7000 80000.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1


Time in hours

A400011sys

A4000mn t( )

6600

t

No replacement of failed power modules

Nonredundant power supplies



0 1000 2000 3000 4000 5000 6000 7000 80000.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1


Time in hours

A400011sys

A4000mn t( )

6600

t

Hot replacement of failed power modules




0 1000 2000 3000 4000 5000 6000 7000 80000.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Availability of 4000 Non-redundant Vs Redundant Modular PS

Time in hours

A400011sys

A4000mn t( )

6600

t

Hot replacement of power modules and redundant bulk PS



• The SLAC-proposed redundant, modular power systems show significantly greater availability than the non-redundant systems

• Hot replacement of the power modules alone does not yield a large availability improvement. Other components must also be redundant.

• ATF2 potentially will use redundant power systems. The ILC will definitely need redundant systems

Conclusions

atf2 power supply availability comparison february 5, 20061 atf2 power supply availability...

Documents

rated power supply

bulk power supply

power modules

delivered power

power supply operation

power supplies mtbf

modular power systems

nonredundant power supplies