a: En cos (col * o)

i. : I* cos (orl * 0)

The quantity or is the angular frequency and is expressed in electrical radians persecond. It follows that

2r,: T: ,of (5-4)

and Eq. (5-3) can be expressed in the alternative forms

'i.: r*cosr.rl: I^coshtrfr: t*rorTt (5-5)

In Fig. 5-2, the time origin or time reference axis is chosen at the point wherethe current is a maximum positive value. fn general, the origin can be chosenarbitrarily at any point on the wave and is selected for greatest convenience in thespecific problem at hand. fn many circuits, the current and voltage waves do not gothrough zero or their maxima at the same time but are displaced from one anotherby a phase angl.e. Figttre 5-3 shows current and voltage waves which neither are inphase with each other nor have their maxima at zero time; the equations of thesewaves are

The phase angle between the two wavcs is 0' The voltoge wave' wnlcn rcu

peak after the current *'"ulit toia to lag the current by the angle 0; or conv

the current, which reaJt' it' ptott ai an.earlier time than does tho v

l,eol.s thevoltage bv th;^;;gi;aiit should be noted that the quontitv o'

argument of the cosine it ii*t"tio"ally in radians; to be strictly corrcct'

fore, the values or t ""aij"^Bq-'-ii-oi and (5-7) should also be in ruclint

example, the voltage e might be

/ .,r\e : 155 cos f77t +;/Common usage, however, specifles the phase angles in degrees' tnd thc vo

then becomes

e : 155 cos (3771 + 30')

In calculating instantaneous values of the-wave' this dimensional incons

should be noted' Th";;;; upiitutio" of the voltage equation is such tl

il;+;;;;;'**:;;:i*{;_:;-,'::J#t1,\'$;'ff :l':lxllxtl;,-'"I1"J::1,ir'Jli[,,, regardless of when i" ii"" the ,rarxinrunr v*lttc

excitation occurs' Th": d" voltage and current functions clcscilrcd b

(5-6) and (5-7) are J*"i 'l'nu'oiial' function"s' Circuits excitcd wit'h lin

currents and voltages"l'"-oft"" callei alternati'rtg-currenl (ac) cirauilsi

excited with constant tttt"'t' and voltages are similarly cullccl rJrlrool'

**' ;{t#Jt;trent and voltage lunctions or Eqs' (5-6) and (5-7) rcpren

current in and l,ottug" oc'o's ipottion ol'l^ut circuit' the instantaneou$ l)

that portion of the ci'c"lJi;,;;- Eq' (1-19) ' the product ei' The'produc

b: eiis also shownit tf*]i-J' it:* which it should be noted thtrt ultl

ffi #;;;;;;;;;'dfiir oieach cvcle' thepower l ispredominantlv 1;

(The case of A : S0'l;-it "*ttptio"') Thus' alternating currents and voltr

effective means for the translei of power and energy' During a part of th

cycle equal to the phase angle 0 between current aiid voltage' the powcr I

negative and hence ;;;;:tt* of energy flow is reversed' Compared wit

case, this reversal i', oJ to"'"' a disadvantage' as is the fact that the instur

power transf"' i' "ot"to"'t"tt i' *ug'itttde' Practically speaking' htlwtlvt

disadvantage, *'" o'i*"igl'ed by the Jact that alternating currents tlnd

permit the use of t'u"fo'Lers' Transformers make possible electric genot

the most ..o'o*'"ui-g"nerator voltage' power transfer at the most ect

transmission voltage, and power utilization at the most economical and cl

;;;;;;il,h" d;;; ritilization device' The resulting advantages ore

that electricity is almost universally generated and transmitted in oc

direct curren, i' at'iJior a particular application'-it is'obtained by ct

from alternatiog tt""'t-u' o' "t'y near the point of utilization'

(5-6)

(5-7 )

1 i,*,P

P

\,'\

III E^

o

0 2700 360't0 <x

l*u--N 0 F-

FIGURE 5-3 lnstantaneous voltage, current, and power in sinusoidally excited circuit

Daniel Gerber, Vagelis Vossos, Wei Feng, Richard Brown,Aditya Khandekar, Bruce Nordman & Chris Marnay

Lawrence Berkeley National LaboratoryWe thank U.S. DOE and CEC for supporting this work!

Direct-DC Loads

380 V

≈ 380 V 380 V

380 V

High Voltage

DC Loads

380 V

380 V

Low Voltage

DC Loads 48 V

1

2

4

3

120/208 V

120 V 48 V

≈ 380 V 120 V 120/208 V

120/208 V

Low Voltage

DC Loads

120/208 V 380 V

High Voltage

DC Loads

Native-DC Loads

1

2

3

3

VoltageDomains:120VAC,48VDC, 380VDC

1.MPPTInverter2.BatteryInverter3.LoadPackagedRectifier

1.MPPT2.ChargeController3.GridTieInverter4.DCDistributionConverter

AC vs. DC Motivation• new California residential buildings to be ZNE by 2020• all commercial buildings by 2030• solar PV generation, batteries, and most loads natively DC• many efficient DC devices should be encouraged• less power quality problems & improved reliability-resilience with DC • islanding microgrid buildings facilitated by DC

Research Goal• use Modelica simulations to determine efficiency improvements• estimate economic benefits of DC distribution• model medium size Los Angeles office and other buildings• include realistic profiles for solar output and load• use converter efficiency curves, and detailed battery and wiring models

Modelica• object oriented modeling language with GUI provided by Dymola• popular for building, automotive, and other engineering simulation• useful for complex systems that include mixed electrical, thermal, etc.

▷ the building power we’re all accustomed to▷ has huge advantage of easy voltage changes▷ enables long distance transmission with local safety▷ voltage and current cycles at fixed frequency▷ when working well, energy is always being delivered▷ approach is closely related to rotating generators▷ has many power quality problems, e.g., power factor▷ has few advantages at end-use, but induction motors▷ end-use rectification to DC common and increasingly efficient

▷ the vehicle power we’re all accustomed to▷ many efficient DC loads (LEDs, variable speed motors, etc.) ▷ many power sources (PV, batteries) also DC▷ less losses and power quality issues with all DC distribution▷ simpler systems should be cheaper, more reliable & resilient▷ creates a favorable environment for PV integration & EVs▷ EVs and heat pump heating/cooling are significant DC loads ▷ safety and other standards needed and a formidable barrier▷ easy connection to electronics permits smart distribution

Alternating Current Direct Current

'luorJno 3u11eule1;e 1o qderg Z-I fUnelJ

eu!L

-luerrnr e 1o ,(1ruor,r. aq:I ur Suraq olur saruol arlo1 Jo plag Jo ed,ir puocas y Z'4-I 'les uI PsraPrsuof sr

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pue pcrlcerd lear8 ;o ar" r{f,rq.&\ s}Jega o.tr; 'sread erll relo uorleluarurradxaJo sseru e8nq eql ur perpnls pu" pere^of,srp ueeq e^Erl r{3rq.^a s}leJJe 'sesnec 1rrlf,rq.^r qrege eq1 Jo llnser erll sr luerrnc rrrlf,ale us Jo sseulnJesn lecilcerd eqa

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etu!I

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3qJ uI u-Iil . ..-' ._ :

JO] 'luar jr-. _ --lrJ'IiP : - - '.lo 11.,I-lr - .". - .

sr lr :-. :'i:'L'I,i.:--- ' : -

-i,I - :: , - -

-r;-:-- --.- . -- -

ur., .I- !l:. . .:- - :

salqLli.iil,\, '--::--- - -

IOLI (,)11' ii-'.- :

rrl iii ,

( 9-r

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( s-r)

erll :-xq iir -l - --:- -

ssr:d 1t aas r,.- :! - -

eJ? J.l\ llil- :-,. .l -

i"JlJlf,ala sLr .!--: ._ _'ere sqlr:cI rril .-,' .

-uoc rqirads r-.- ,

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IO S,toplt[tttt,.] - I:s3 rllns sFurt. --.

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a'a-

Experimental and Field Testing• experimentally estimate efficiency savings of identical AC vs. DC networks• verify the savings of removing the rectification stage in various loads• design and construct a DC microgrid, meter and measure the savings• collaborate with DC demonstrations in Europe and Asia

Analysis and Modeling• develop a generic DC efficiency modeling tool for commercial use• improve the techno-economic analysis and create future projection models• develop advanced control algorithms for load shedding in DC buildings• study the non-energy benefits of DC for power quality, resiliency, etc.

IBEW ZNE Building,San Leandro CA

baseline baseline

Efficiencydatafromproductcurves

MediumLosAngelesOfficeBuildingDOEReferenceBuilding

DOE Reference Building Model of Medium Office in Los Angeles, CAParametric Experiments• solar Experiment – baseline is amount of solar capacity needed

to power a ZNE building• battery experiment – baseline is half the amount of battery

capacity needed for a ZNE building to store all daily excess solar (= generation – load)

Efficiency Results• 12% baseline efficiency savings with DC• DC is more efficient with high solar and battery capacity

Loss Analysis• AC building loss is dominated by the poor efficiency of load

packaged rectifiers (wall adapters)• AC buildings with lots of storage see loss in the battery inverter• DC building loss dominated by the grid tie inverter• particularly heinous with high solar capacity and no storage

(fourth pair of bars at left)• both buildings suffer significant battery chemical loss

Techno-Economic Analysis• results determined from market cost data, grid tariffs, and

Monte-Carlo analysis• first cost is higher for DC• given the enormous efficiency savings, the payback period is

less than a year• end use costs, installation costs, and other soft costs not

considered in techno-economic analysis

The DC analysis model is used to scope the feasibility of DC distribution in a ZNE office building. The simulations are run with actual solar and load profile data, along with precise building wiring.

ABBREVIATIONS & ACRONYMS:

CEC – California Energy CommittionEV – electric vehicleGUI – graphical user interfaceLCC – life cycle costU.S. DOE – U.S. Department of EnergyZNE – zero net energy

AC ProductWeighted Efficiency

String Inverter 96.0%

Battery Inverter 92.1%

Low Power Rectifier 89.9%

High Power Rectifier 90.8%

AC LED Driver 90.2%

DC Product Weighted Efficiency

Power Optimizer 99.4%

MPPT Chg. Controller 98.5%

DC-DC Transformer 97.6%

Grid Tie Inverter 96.6%

DC LED Driver 95.6%

All DC floor inthe XingYe HQ building in Zhuhai, China

Research Objective

▷ research & demonstrate technicalviability of DC building distribution

▷ focus on low (< 600) voltage DC in commercial buildings

▷ direct integration of renewable sources and batteries

▷ simulate and measure potential energy efficiency & economic benefits

▷ evaluate communication opportunities