Cyber Physical Power Systems Power in Communications

Transcription

1 1 Cyber Physical Power Systems Power in Communications

2 Information and Communications Tech. Power Supply 2 ICT systems represent a noticeable (about 5 % of total t demand d 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

3 Information and Communications Tech. Power Supply 3 In addition to been efficient, i ICT power plants need to be highly hl reliable/available.

4 Land-line Telecommunications Network 4

5 Land-line Telecommunications Network Power infrastructure is for telecommunication networks as cardiovascular system is for humans. 5 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

6 Wireless Telecommunications Network 6

7 Wireless Telecommunications Network 7 Power needs to be provided to the switch (called Mobile Telecommunications Switching Office or MTSO) and to the remote terminals (the based stations).

8 Power plants architectures 8 DC: For telephony and wireless communication networks AC: For data centers RECTIFIER + DC-DC CONVERTER

9 Power plants architectures 9 Typical configuration in data centers: Total power consumption: > 5 MW (distribution at 208V ac)

10 Power plants architectures 10 Typical power plant for telephony networks:

11 Power plants architectures 11 Typical centralized architecture for telephony networks: Only (centralized) bus bars Centralized architecture

12 Power plants architectures 12 Typical distributed architecture for telephony networks: Each cabinet with its own bus bars connected to its own battery string and loads. Then all cabinets bus bars are connected Distributed architecture

13 Telecom central office power plant 13 Telecom Power Plant 11 x 1400 Ah Batteries 13 x 200 Amps. Rectifiers

14 Telecom central office power plant 14

15 Batteries 15

16 Distribution frames 16

17 Distribution frames 17

18 Inverters 18

19 Base station power plant 19

20 Base station power plant 20

21 Base station power plant 21

22 Telephony outside plant 22 Digital it Loop Carrier and other outside plant broadband d 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: 22

23 Telephony outside plant 23 RECTIFIERS

24 Telephony outside plant 24

25 Outside plant power supply 25 Traditional emergency power solutions during long grid outages

26 Reliability and Availability 26 Reliability 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 Pr{ B A }Pr{ A } Pr{ A } htdt () Pr{ A B} Pr{ B} Pr{ B}

27 Reliability and Availability 27 Reliability Pr{ B A}Pr{ A} Pr{ A} htdt () Pr{ A B} Pr{ B} Pr{ B} Since Then Pr{B A} = 1 Pr{A} = f(t), Pr{B} = 1 - F(t). htdt () f () t 1 F ( t ) and Ft () 1 e t h 0 ( ) d

28 Reliability and Availability 28 Reliability 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

29 Reliability and Availability 29 Reliability Considering electronic components during the useful life period, the hazards function is constant and equals the so called constant failure rate λ. So, R(t) F(t) = 1 e - λt f(t) = λe - λt R(t) = e - λt t And, E[ f( t)] tf( t) dt 0 1 The inverse of λ is called the Mean Time to Failure. I.e.,it is the expected operating time to (first) failure

30 Reliability and Availability 30 Reliability 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): adj base Q T E O Production Thermal Electrical quality stress stress Other factors (power and operational environment e factors) 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 10 9 hours.

31 Reliability and Availability 31 Availability 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:

32 Reliability and Availability 32 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 Pr f (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, Pr f (t + dt) = Pr w (t)λdt + Pr f (t)(1-µ)dt

33 Reliability and Availability 33 Availability Hence, Pr ( tdt) Pr ( t) f dt f Pr ( t) Pr ( t) w f Which leads to the differential equation d Pr ( t) f dt ( )Pr ( t) f With solution (considering that at t = 0 it was at the working state) ( ) t Pr ( ) 1 f t e 1 Pr ( ) w t e ( ) t

34 Reliability and Availability 34 Availability 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 TU TU A Pr w( t ) MTBF T T U D That is, Availability = Expected time operating normally Total time ( normal operation + off-line time)

35 Reliability and Availability 35 Availability Notes: Unavailability is defined as MDT Ua MTBF Mean time between failures (MTBF) is the sum of TD and TU UP DOWN Ways of improving availability Modularity Redundancy (parallel operation of same components) Diversity (use of different components for the same function Distributed functions

36 Reliability and Availability 36 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.

37 Reliability and Availability 37 Availability Now consider a two-components system (A and B). The Markov process is now So, d P dt T T P A Where, ( A B ) A B 0 A ( A B) 0 B A B 0 ( B A) A 0 B A ( A B ) P T Pr () t Pr () t Pr () t Pr () t S S S S

38 Reliability and Availability 38 Availability The expected time that the system remains in each of the states is given by 1 1 Ti N a S ii a The probability density function of being at state S i is j 1 ji ij aii f ( T ) a e T i ii i the frequency of finding the system in state S i is a i ii S i Pr ( t )

39 Reliability and Availability 39 Availability Hence, for the two-components system (A and B).

40 Reliability and Availability 40 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. 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. A S 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). i U P u i

41 Reliability and Availability 41 Availability For a series two-components system (both A and B need to operate for the system to operate). System availability Working state Failed states

42 Availability Reliability and Availability For a parallel two-components system (either A or B need to operate for the system to operate). Failed state 42 System unavailability Working states

43 Reliability and Availability 43 Availability 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. n +1 redundant configuration. But more modules is not always better: A( n1) a n ua n 1 A a = 0.97 Availability decreases when n increases to a point where A < a

44 Reliability and Availability 44 Availability 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.

45 Reliability and Availability 45 Availability Unavailability with minimal cut sets: Calculation: U S M C P K j j1 M M i 1 M c c c P( K ) P( K K ) U 1 [1 P( K )] i i j S i i1 i2 j1 i1 M c P( Ki ) i1 Approximation with highly hl available components: M C U P( K ) u S j l, j j1 j1 l1 M C c j u

46 Standby Power Plants 46 Typical availabilities Ac mains: 99.9 % Power plant: % (without batteries) - 48 V Genset: 99.4 % (includes TS) (failure to start = 2.41 %) Each rectifier: % n+1 redundant configuration is used for improved availability

47 Standby Power Plants 47 Availability Calculation l Binary representation of Markov states: 1st digit: rectifiers (RS) withn+1 redundancy 2nd digit: ac mains (MP) 3ddi 3rd digit: it genset (GS) (failure to start t probability given by ρgs Availability of power plant without batteries: A 1 GS GS MP MP PP TS RS MP ( MP GS ) A A where RS n 2 ( n1) R ( n 1) R R RS 2 C 2 nn1 r r n1 n1 i i n 1 i C n 1 r r i0 k C n n k! k ( n k)! n!

48 Standby Power Plants 48 Availability Calculation T System availability equation: P () t A P() t ( MP RS ) 0 (1 GS ) MP GSMP RS GS ( GS MP RS ) 0 MP 0 RS 0 0 MP 0 ( GS MP RS ) GS 0 0 RS 0 0 MP GS ( GS MP RS ) RS A ( ) 0 (1 ) RS MP RS GS MP GS MP 0 RS 0 0 GS ( GS MP RS ) 0 MP 0 0 RS 0 MP 0 ( GS MP RS ) GS RS 0 MP GS ( GS MP RS ) Failure probability (in time): P () t P () t 1 P () t PPf Si S S F S W The probability density function f PPf (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 t t a e fppf () where a F = 3μ RS + μ MP + μ GS i i i

49 Standby Power Plants 49 Availability Calculation Notice that a F = 3μ RS + μ MP + μ GS is the sum of the transition rates from failed states (called minimal cut states) to immediately adjacent working states.

50 Standby Power Plants 50 Availability Calculation The probability of discharging the batteries is, then T BAT P ( t T ) 1 f ( ) d e BD BAT 0 PPf a T BAT System unavailability or outage probability: bilit aftbat aftbat P e lim P () t e U O PPf a t Two cases are exemplified: Case A: With a permanent genset. Case B: Without genset

51 Standby Power Plants 51 Availability Calculation In general, when batteries are considered the unavailability is MCS, itbat i mcs w / B w / ob 1 w / B U U e A Total availability Total unavailability Heavily depends on unavailability of the electric grid tie Base unavailability (without batteries) es) Repair rate from a minimal cut state to an operational state (Depends on logistics, maintenance processes, etc.) Batteries (local energy storage) autonomy Local energy storage contributes to reduce unavailability Optimal sizing of energy storage depends on expected grid tie performance and local power plant availability

52 Standby Power Plants 52 Availability Calculation In general, when batteries are considered the unavailability is MCS, itbat i mcs w/ B w/ ob 1 w/ B U U e A Related with minimal cut states