Abst r act . Most of t he wor k on behavi or pr edi ct i on on t he f i el d of Qual i t at i ve Physi cs has f ocused on t r ansi ent be- havi or and r esponses to per t ur bat i ons ( de Kl eer & Br own 1984 ; For bus 1984 ; Kui per s 1985 ; W illiams 1984) ; ver y little has been done about behavi or of sys- tems in st eady st at e ( Sus s man & St eel e 1980) . An under st andi ng of t he si nusoi dal st eady st at e of el ect r i - cal ci r cui t s is i mport ant f or sever al r easons . A l ar ge cl ass of devi ces and net wor ks, especi al l y t hose in t he ar ea of power gener at i on, t r ansm i ssi on, and di st r i bu- t i on, ar e desi gned f or si nusoi dal st eady- st at e oper - at i on ( Fi t zger al d 1945 ; Grai nger & St evenson 1994 ; Gonen 1988) . Thi s paper pr esent s a f ramework to r eason about l i n- ear el ect r i cal ci r cui t s in si nusoi dal st eady st at e . Thi s appr oach const i t ut es a qual i t at i ve ver si on of Phasor Anal ysi s, so it is cal l ed Qual i t at i ve Phasor Anal ysi s ( QPA) . I nt r oduct i on One of t he mai n obj ect i ves of qual i t at i ve physi cs is to der i ve t he behavi or of a syst em f r om a descr i pt i on of its component s and t hei r i nt er r el at i onshi ps ( de Kl eer & Br own 1984 ; For bus 1984 ; Kui per s 1985 ; W illiams 1984) . Pr edi ct i on of behavi or has been achi eved by t r a- di t i onal physi cs t hr ough numeri cal appr oaches . In par - t i cul ar , in t he ar ea of ci r cui t anal ysi s ( Ker r 1977) t her e exi st a number of numeri cal met hods to anal yze cir- cui t s of di f f er ent ki nds and under di f f er ent condi t i ons . These met hods t ake as i nput a ci r cui t t opol ogy and exact val ues f or t he par amet er s, per f or m s ome c om- put at i on (mai nl y based on l i near al gebr a or i t er at i ve met hods to sol ve non- l i near or di f f er ent i al equat i ons) , and r et ur n exact val ues f or t he var i abl es r epr esent i ng t he unknown quant i t i es . In al l t hi s pr ocess, causal i t y and expl anat i on is di scar ded f or t he sake of pr eci si on . Thi s paper pr esent s a f ramework f or qual i t at i ve anal - ysi s of l i near el ect r i cal ci r cui t s in si nusoi dal st eady st at e . We cal l t hi s appr oach Qual i t at i ve Phasor Anal - ysi s ( QPA) . QPA t akes as i nput a descr i pt i on of cir- Qual i t at i ve Phasor Anal ysi s Juan Fl or es and Ar t Far l ey Comput er and I nf ormat i on Sci ence Depar t ment Uni ver si t y of Or egon Eugene, Or egon, 97403 phone ( 541) 346- 4416 f ax ( 541) 683- 5373 emai l juan@cs . uor egon . ed u cui t component s and t hei r connect i ons, with qual i t a- t i ve val ues and const r ai nt s on t he ci r cui t par amet er s . Val ues of t he par amet er s can be i nt er val s, def aul t i ng to ( 0, oo) (i .e . al l par amet er s ar e posi t i ve) . Const r ai nt s on par amet er s can be pr ovi ded by t he user ; f or i n- st ance, in a ci r cui t i nvol vi ng t wo r esi st or s, t he user can asser t (< Rl R2) , or Rl = [ 5, 10] , et c . QPA will comput e as muc h i nf ormat i on as possi bl e and r et ur n it to t he user in t he f or m of new val ues f or ci r cui t var i abl es and new const r ai nt s . The r esul t s pr o- vi de t he user with i nf ormat i on about t he consequences of a gi ven const r ai nt in t he ci r cui t , A set of const r ai nt s r epr esent s a set of pr edi ct ed behavi or s . A pri mary di f - f er ence f r om ci r cui t si mul at ors is t hat t hey r equi r e pr e- ci se val ues f or al l par amet er s and r et ur n pr eci se val ues f or al l of t he ci r cui t var i abl es . QPA can pr oduce r e- sul t s even if we do not pr ovi de any i nf ormat i on about t he ci r cui t par amet er s ; of cour se, t he mor e speci f i c t he i nput i s, t he mor e speci f i c t he out put will be . If al l t he par amet er s ar e pr eci sel y speci f i ed, t he r esul t s of QPA will be l i ke t hose of convent i onal ci r cui t si mul at ors (i .e. onl y one behavi or is pr edi ct ed) . QPA is based on a const r ai nt anal ysi s appr oach to qual i t at i ve physi cs . Fi r st , it devel ops a const r ai nt - based model of a ci r cui t , wher e t he const r ai nt s ar e der i ved f r om gener al knowl edge of ci r cui t t heor y and t he ci r cui t ' s t opol ogy . Second, it is abl e to pr opagat e const r ai nt s of di f f er ent ki nds ; we have di f f er ent set s of const r ai nt s, r angi ng f r om conf l uences, or der i ng con- st r ai nt s, or der of magni t ude r el at i ons, and phase angl e const r ai nt s . We ext end t he pr evi ous qual i t at i ve ap- pr oaches t o ci r cui t anal ysi s t o deal not onl y with scal ar magni t udes, but al so to i ncl ude phase angl e i nf orma- t i on . Thi s ar t i cl e expl ai ns t he basi c probl ems t hi s r esear ch pr oj ect addr esses, i dent i f i es s ome of t he i mport ant r e- sear ch i ssues, and di scusses i mpl ement at i on and eval - uat i on pl ans . The sect i on QPA, pr esent s an over vi ew of our mai n ci r cui t anal ysi s engi ne, cal l ed Qual i t at i ve Phasor Anal ysi s ( QPA) . The sect i on An Appl i cat i on Fl or es 43