Energy Sorage Deces
Objece of Lecure Descrbe he consrucon of a capacor and how charge s sored. Inroduce seeral ypes of capacors Dscuss he elecrcal properes of a capacor The relaonshp beween charge, olage, and capacance hargng and dschargng of a capacor Relaonshp beween olage, curren, and capacance; power; and energy Equalen capacance when a se of capacors are n seres and n parallel haper 6. n Basc Engneerng rcu Analyss by Irwn and Nelms
apacors omposed of wo conduce plaes separaed by an nsulaor (or delecrc). ommonly llusraed as wo parallel meal plaes separaed by a dsance, d. = e A/d where e = e r e o e r s he relae delecrc consan e o s he acuum permy
Effec of Dmensons apacance ncreases wh ncreasng surface area of he plaes, decreasng spacng beween plaes, and ncreasng he relae delecrc consan of he nsulaor beween he wo plaes.
Types of apacors Fxed apacors Nonpolarzed May be conneced no crcu wh eher ermnal of capacor conneced o he hgh olage sde of he crcu. Insulaor: Paper, Mca, eramc, Polymer Elecrolyc The negae ermnal mus always be a a lower olage han he pose ermnal Plaes or Elecrodes: Alumnum, Tanalum
Nonpolarzed Dffcul o make nonpolarzed capacors ha sore a large amoun of charge or operae a hgh olages. Tolerance on capacance alues s ery large +50%/-5% s no unusual PSpce Symbol hp://www.marac.com/fun/ceramc_capacor_codes.a spx
Elecrolyc Pspce Symbols Fabrcaon hp://www.dgy.com/arcles/008//choosng-he-rghcapacor.hml
Varable apacors ross-seconal area s changed as one se of plaes are roaed wh respec o he oher. PSpce Symbol hp://www.pub.com/nees/book/3f.hm
MEMS apacor MEMS (Mcroelecromechancal sysem) an be a arable capacor by changng he dsance beween elecrodes. Use n sensng applcaons as well as n RF elecroncs. hp://www.slaco.com/ech_lb_tad/smulaonsandard/005/aug/a3/a3.hml
Elecrc Double Layer apacor Also known as a supercapacor or ulracapacor Used n hgh olage/hgh curren applcaons. Energy sorage for alernae energy sysems. hp://en.wkpeda.org/wk/fle:supercapacor_dagram.sg
Elecrcal Properes of a apacor Acs lke an open crcu a seady sae when conneced o a d.c. olage or curren source. Volage on a capacor mus be connuous There are no abrup changes o he olage, bu here may be dsconnues n he curren. An deal capacor does no dsspae energy, akes power when sorng energy and reurns when dschargng.
Properes of a Real apacor A real capacor does dsspae energy due leakage of charge hrough s nsulaor. Ths s modeled by pung a ressor n parallel wh an deal capacor.
Energy Sorage harge s sored on he plaes of he capacor. Equaon: Q = V Uns: Farad = oulomb/volage Farad s abbreaed as F
Sgn onenons The sgn conenon used wh a capacor s he same as for a power dsspang dece. When curren flows no he pose sde of he olage across he capacor, s pose and he capacor s dsspang power. When he capacor releases energy back no he crcu, he sgn of he curren wll be negae.
hargng a apacor A frs, s easy o sore charge n he capacor. As more charge s sored on he plaes of he capacor, becomes ncreasngly dffcul o place addonal charge on he plaes. oulombc repulson from he charge already on he plaes creaes an opposng force o lm he addon of more charge on he plaes. Volage across a capacor ncreases rapdly as charge s moed ono he plaes when he nal amoun of charge on he capacor s small. Volage across he capacor ncreases more slowly as becomes dffcul o add exra charge o he plaes.
Addng harge o apacor The ably o add charge o a capacor depends on: he amoun of charge already on he plaes of he capacor and he force (olage) drng he charge owards he plaes (.e., curren)
Dschargng a apacor A frs, s easy o remoe charge n he capacor. oulombc repulson from charge already on he plaes creaes a force ha pushes some of he charge ou of he capacor once he force (olage) ha placed he charge n he capacor s remoed (or decreased). As more charge s remoed from he plaes of he capacor, becomes ncreasngly dffcul o ge rd of he small amoun of charge remanng on he plaes. oulombc repulson decreases as charge spreads ou on he plaes. As he amoun of charge decreases, he force needed o dre he charge off of he plaes decreases. Volage across a capacor decreases rapdly as charge s remoed from he plaes when he nal amoun of charge on he capacor s small. Volage across he capacor decreases more slowly as becomes dffcul o force he remanng charge ou of he capacor.
urren-volage Relaonshps q dq d d d o d
Power and Energy p w p d d w q
apacors n Parallel
eq for apacors n Parallel 4 3 eq 4 3 4 4 3 3 4 3 d d d d d d d d d d d d d d d d d d eq n n n
apacors n Seres
eq for apacors n Seres 4 3 eq 4 3 4 4 3 3 4 3 d d d d d d d d d o o o o o o o o o eq n n n
General Equaons for eq Parallel ombnaon If P capacors are n parallel, hen Seres ombnaon If S capacors are n seres, hen: P eq P p eq S s s
Summary apacors are energy sorage deces. An deal capacor ac lke an open crcu a seady sae when a D olage or curren has been appled. The olage across a capacor mus be a connuous funcon; he curren flowng hrough a capacor can be dsconnuous. The equaons for equalen capacance for capacors n parallel P eq P p d d capacors n seres eq o d S s s