RELIABILITY

OF

UNINTERRUPTIBLE POWER SUPPLY

&

BATTERY CHARGERS

OVERVIEW

An uninterruptible power supply, also uninterruptible power source, UPS or battery backup is

an electrical apparatus that provides emergency power to a load when the input power source,

typically mains power, fails. The Primary objective in the implementation of a UPS system is

to improve the reliability to the limits of technical capability, the ultimate aim being to totally

eliminate the possibility of any disturbance or downtime.

In the 50’s, when the first static UPS systems appeared, they were composed of a rectifier,

battery and inverter and were used to stabilize the output power and to continue to supply the

load for a short period of time (autonomy of battery) in the event of a rectifier failure. The

reliability of this simple UPS chain depends dominantly on the inverter reliability. An inverter

failure meant an immediate load crash. Furthermore, the downtime (no supply to the load)

would last as long as the inverters repair.

In the early 60’s the static bypass switch was introduced to enable an interruption-free load

transfer to the stand-by mains in the event of inverter failures or overloads. The stand-by mains

although far not as reliable as the UPS, serves as a reserve power supply in case of an inverter

failure to enable the continuation of the power supply to the load while the inverter is being

repaired. This new architecture had substantially improved the overall reliability which did not

depend dominantly on the inverter reliability anymore. The reliability of the new UPS with

static bypass depended on the quality of the mains (MTBFM), the time to repair of the UPS

(MTTRUPS) and on the reliability of the static switch.

For each observation, downtime is the instantaneous time it went down, which is after (i.e.

greater than) the moment it went up, uptime. The difference (downtime minus uptime) is the

amount of time it was operating between these two events.

RELIABILITY, MTBF AND FAILURE RATE

The reliability of a UPS system is often expressed in terms of Mean Time Between Failures or

MTBF, stated in years or hours. MTBF equals the average time that elapses between the moment

that the system is set in operation and the first occasion on which the system fails. Another

measure of reliability is the failure rate (λ) which expresses the number of failures per unit of

time. The failure rate is not constant, but a function of time as shown in the graph (the so-called

bath-tub curve).

During the first period (A) failures occur due to bad components and manufacturing faults. These

early failures are likely to occur during the testing and burn-in period. During the normal lifetime

(B) the failure rate is low and stable. At the end of the normal lifetime (C) ageing causes an

increasing number of failures and the system has to be replaced. During the normal lifetime

Mean Time Between Failure (MTBF) is inversely proportional to the failure rate (λ),

i.e. MTBF = 1/λ.

The most obvious way to determine the reliability of a UPS system is to observe the number of

failures of installed systems over a certain period of time. From the collected data the average

failure rate (λ) and the MTBF can be calculated. However, this method only reveals statistically

valid figures if a large number of identical systems have been sold and have been working for a

considerable time under similar working conditions. For UPS systems therefore the reliability is

often calculated from known MTBF figures of components and sub-assemblies. The failure rate

depends on the complexity of the system, the number of components and the failure rate of its

parts. With this method the reliability of different types of UPS system can be predicted and

compared.

SINGLE UPS WITH STATIC BYPASS SWITCH

Description of the variables that are used in the equations:

MTBFUPS+SBS: Mean Time Between Failures of Single Unit with static bypass switch (SBS)

MTBFM : Mean Time Between Failures of MAINS

λUPS : Failure Rate of Single Unit without static bypass switch

λRECT : Failure Rate Rectifier

λBATT : Failure Rate Battery

λ INV : Failure Rate Inverter

λUPS+SBS : Failure Rate of Single Unit with static bypass switch

λSBS : Failure Rate of Static Bypass Switch with control circuit

λPBUS : Failure Rate of Parallel Bus (only for parallel systems)

λM : Failure Rate of MAINS

μSU : Repair Rate of Static Bypass Switch (μSU = 1 / MTTRUPS)

μ M : Repair Rate of MAINS (μM = 1 / MTTRM)

MTTRSBS : Mean Time To Repair of Static Bypass Switch

MTTRM : Mean Time To Repair of MAINS

MTBFUPS = 1 / λUPS

λUPS = λRECT+ λBATT + λINV ..…………………........................……………........….. (E.1)

The figures from statistical failure-analysis λRECT =20x10-6

/h, λBATT =10x10-6

/h, λINV. = 20X10-6

[h-1

]

applying Values in equation (E.1), the Mean Time Between Failure (MTBFUPS) for a UPS system

without static bypass switch will be:

λUPS = 50x10-6

MTBFUPS = 20'000 h

Please note that all calculations are performed by using the following constants:

MTBFM =50 [h], this figure represents a “good quality” of mains. MTTRUPS = 5 [h]

MTTRM = 0.1 [h]

From statistical failure-analysis we have the following figures for the failure rates of the static

bypass switch for the power part and the control electronic part: λSBS =2x10-6

[h-1

]

CALCULATION OF MTBF FOR UPS WITH STATIC BYPASS SWITCH

MTBFUPS+SBS = 1 / λ UPS+SBS

λUPS+SBS = λUPS//λM+λSBS ----------------------------------------------------------------------------------------------- (E.2)

λUPS // λ M = λUPS λM (λUPS + λM +μUPS+μM) = λUPS λM (μUPS+μM) = 5x10 -6 [h-1]

λUPS λM +μUPS μM +(λUPS+λM) (μUPS+μM)+(λ2UPS)(λ2M) μUPS μM

λUPS+SBS = λUPS // λM + λSBS = 6 10-6 [h-1] + 2 10-6 [h-1] = 7x10-6 [h-1]

MTBFUPS+SBS = 142,857 h

Load

Electrical Block Diagram Reliability Block Diagram

λRECT

λSBS

λBATT

λINV

MA

INS

MA

INS

Load

&

RECTIFIER INVERTER STATIC BYEPASS SWITCH

BATTERY

NOTE:

In the above formula it can be seen that the reliability of the UPS with static bypass switch (MTBFUPS+SBS)

depends largely on three parameters: reliability of the mains, the MTTR of the UPS and the reliability of the static

bypass switch.

PARALLEL REDUNDANT UPS WITH STATIC BYPASS SWITCH

Electrical and Reliability Block Diagram of Parallel Redundant UPS Configuration.

The reliability of a single UPS can be increased significantly by introducing a redundant

configuration.

Load

λRECT

λSBS

λBATT

λINV

UP

S 2

UP

S 1

Load

RECTIFIER INVERTER STATIC BYEPASS SWITCH

Load

λRECT

λSBS

λBATT

λINV

UP

S 1

UP

S 2

Load

RECTIFIER INVERTER STATIC BYEPASS SWITCH

BATTERY

BATTERY

PA

RA

LL

EL

BU

S

PA

RA

LL

EL

BU

S

Calculation of MTBF for a REDUNDANT PARALLEL UPS System (MTBF(1+1)UPS+SBS): We will start by the equations used for the calculation of the failure rate: λ(1+1)UPS+SBS = (λUPS1//λUPS2….//λUPS(1+1)) + (1+1) λPBUS + (λSBS1//λSBS2……..//λSBS(1+1))-------------- (E.3)

Failure Rate: λ(1+1)UPS+SBS ~ (1+1) λPBUS …………………… (E.4)

Reliability: MTBF(1+1)UPS+SBS = 1 / λ(1+1)UPS+SBS …………… (E.5)

Availability: A (1+1)UPS+SBS = MTBF(1+1)UPS+SBS / MTBF(1+1)UPS+SBS + MTTR UPS …… (E.6)

The reliability of a (1+1) parallel redundant system depends largely on the reliability of the

failure rate of the PARALLEL BUS which is the only single point failure.

The UPS parallel redundant chain, the static bypass switches and their control electronics as

well as the mains power lines are all redundant and have therefore minor or even neglecting

impact on the overall reliability.

We will perform some calculations for parallel redundant systems, by using the following

constants:

MTBFM = 50 [h], this figure represents a “good quality” mains.

λPBUS = 0.4 10 -6 [h-1]

Redundant Parallel Configuration Reliability (MTBF) Failure Rate (λ) (1+1) redundant

configuration 1,428,570 [h] ~ 0.8 10-6 [h-1]

BATTERY CHARGERS

Load

λRECT

λBATT

MA

INS

MA

INS

Load

RECTIFIER

BATTERY

Electrical Block Diagram Reliability Block Diagram &

PARALLEL REDUNDANT BATTERY CHARGERS

CALCULATION OF MTBF FOR BATTERY CHARGER

MTBFBATTCHARG = 1 / λBATTCHARG

λBATTCHARG = λRECT + λBATT …………………........................……………........….. (E.7)

The figures from statistical failure-analysis λRECT =20x10-6

/h, λBATT =10x10-6

/h, applying Values in equation

(E.7), the Mean Time Between Failure (MTBFBATTCHARG) for a Battery Charger will be

MTBFBATTCHARG=1 / 30x10 -6

MTBFBATTCHARG = 33,333 h

Load

λRECT

λBATT

MA

INS

MA

INS

Load

RECTIFIER

BATTERY

Electrical Block Diagram Reliability Block Diagram &

Load

λRECT

λBATT

MA

INS

MA

INS

Load

RECTIFIER

BATTERY