Full Translation

8/17/2019 Full Translation

1/14

A new power flow method for radial networks

Manuel A. Matos, Member, IEEE MỘT PHƯƠNG PHÁP !NG "#NG$%&T M'( "H) "Á" *Ư'( +(N

H-NH T(AManuel A. Matos, Member, IEEE

Abstract The need of fast alorithms for radial

distri/ution networks that take ad0antae of their parti1ular stru1ture has /eenin1reasin, namel2 due to the use of eneti1alorithms and meta3heuristi1s foroptimi4ation in plannin and operation.

(n this paper, a new method for powerflow 1al1ulation in radial networks is

presented. (t uses an iterati0e pro1ess alonthe /ran1hes, in a wa2 similar to othermethods, /ut the main idea is 0er2 differentfrom pre0ious approa1hes, sin1e it is /asedon the e5a1t power flow solution for a sinle/ran1h and also /e1ause it pro0ides a1omplete solution 6not onl2 0oltaemanitudes7. The method is fast and ro/ustfor different t2pes of networks and loads,in1ludin hea02 loads.

The paper in1ludes the theoreti31alderi0ation of the method, an illustratione5ample and tests with /en1hmarkinnetworks.

(nde5 Terms 8Power istri/u3tion,*oad flow anal2sis, (terati0e methods,Plannin, )peration.

(. (NT9)%"T()NThe special structure of radial

networks has lead, in the past, to anumber of specialized algorithms thattried to take advantage of the absence of meshes to simplify the calculations andsave memory [1]-[6] !n some cases, themethods are e"tended to weekly meshednetworks with some success

#alculation of the power flow inradial networks was not a priority in the

past, since appro"imate methods weresufficient to have a general picture of the power flow and, if necessary, a general-

Tóm tắt $: 1;n thi1 thu?t to>n nhanh 1ho

1>1 m@n lBi phCn phDi hEnh tia mF 0i1 t?ndn 1Iu trJ1 liKn Luan 1n O1 tn d;n,1 thQ lF 0i1 sR dn 1>1 thu?t to>n ph>tsinh 0F kinh nhim Q tDi u tron 0i1 l?pk< ho@1h 0F 0?n hFnh.

Tron /Fi />o nF2, trEnh /F2 mStphn ph>p mBi Q tUnh to>n dVn 1Wn

suIt tron lBi in hEnh tia. NX dYn mStLu> trEnh lZp d[1 theo 1>1 nh>nh, tn t: nh 1>1 phn ph>p kh>1 nhn \ t]n1hUnh thE rIt kh>1 /it t^ 1>1h ti

1h nF2 O1 d:a trKn dVn1Wn suIt 1hUnh 5>1 1`a mSt nh>nh 0F 1n1X thQ, /]i 0E nX 1un 1Ip mSt ii ph>p ;2` 6khWn phi 1hb 1X 1>1 S lBn in >p7.Phn ph>p nF2 ii Lu21 nhau 1`a 1>1m@n in 0F ti, /ao cm 1 ti nZn.

Fi />o nF2 /ao cm 1 s] l\ thu21 ph;n kiQm 1hn0Bi 1>1 m@n in 1hun

">1 thu?t ng PhCn /D 1Wn suIt, phCntU1h lu lOn ti, phn ph>p lZp, thi


2/14

purpose method Ilike Jewton-KaphsonLcould always be used Mse of geneticalgorithms and meta-heuristics in theoptimization of distribution networks,however, lead to the need of fast

calculation methods with some degree of accuracy [N] On the other hand, moreand more PQR IPistribution Qanage-ment RystemsL[N] are being developedand installed, and fast methods for radialnetworks are again welcomed Sinally,dispersed generation connected todistribution networks is growing, andadeuate algorithms are needed to deal

with it((. )%NAT()N ) THjMjTH)

The main idea of the method is touse the e"act power flow solution for one

branch, when we know the voltage in thesending end IUVL and the inWected power in the receiving end IR1L, z1 being theimpedance of branch V-1 Isee Sig 1L

Sig 1 - Jetwork with a single branchOf course, we haveX

Or

I1LThe analytical solution of thiscomple" uadratic euation may befound in a number of ways Sor instance,changing to rectangular coordinates andassuming that YVZV Iso UV Z eVL,U1Ze1Wf 1, z1Zr 1W"1 and R1Z\1W1, weget

and, after separating real and imaginary partsX

m0t ph*?ng ph3p c c;ng dng t^ng u3tInh* Jewton-KaphsonL lu;n &*7c d_ngUi(c s` dng c3c thu2t to3n di truy9n vBr%t kinh nghi(m &*7c ti *u ha c)am


3/14

IbL

Jow, from IbL we takeimmediately the value of f 1, since all the

other uantities are known, and then wefind e1 by substituting f 1 in IaL and solv-ing the IrealL uadratic euation, wheree1 will be the biggest solution Thisanalytical solution of the power flow

problem is well known, but generally notused, since it is only applicable to thetrivial case of two buses

Sig Rimple radial network model

!f we have now a radial network with successive branches 1, ,n, wherenode V is the root, with a specifiedvoltage UVZ eV Isee Sig L

!n the first branch, I1L transforms toX

V 1 11

n

k

k k

S V V z

V =

− = − ÷

∑

or, multiplying by U1 and conWugatingX

Rimilar e"pressions may be establi-

shed for the remaining nodes, in eachcase using the predecessor node voltageas a constant The general e"pressionIiZ1nL is thereforeX

IL

The idea is then to apply IL, beginning in the first node after the root -which corresponds to IL in order tosuccessively calculate the voltages, untilgetting the leaves of the tree This

IaL

IbL

/y giC, tF IbL, ch%ng ta l$y ngaygi3 tr c)a f 1, tF t$t c@ c3c gi3 tr kh3c &4

bi8t, vB sau & ch%ng ta tm &*7c e1 bngc3ch thay f 1 trong IaL vB dq dBng gi@i&*7c ph*?ng trnh b2c hai, v+i e1 s lBlCi gi@i duy nh$t i@i ph3p ph/n tAch nByv9 v$n &9 c3c d=ng c;ng su$t lB n^iti8ng, nh*ng th*Cng kh;ng s` dng&*7c, v n ch 3p dng &i v+i c3ctr*Cng h7p &?n gi@n c)a hai thanh c3i

nh Q; hnh l*+i &i(n hnh tia

J8u b/y giC, ta c m0t mu thGc t*?ng t: c th> &*7cthi8t l2p cho c3c n%t c=n lu thGc r^ng u3t Ii Z 1 nL lBX

IL

& lB &> 3p dng IL, b5t &.u tFn%t &.u tiEn sau & &8n n%t gc - mBt*?ng Gng v+i IL - &> tAnh to3n &i(n 3p

q

nq

qn

3$

n3

3$

3$n3

3$n

q

nq

qn

3$

n3

3$

3$n3

3$n


4/14

corresponds to an iteration that can berepeated with the updated values of thevoltages, until some convergencecriterion is met

(((. "A*"%*AT()N P9)"j$$jTA(*$A. jLuations

!n order to conduct the iterative process, IL is conveniently transformedtoX

IxL

where IpL denotes the iterationOnce its clear that the voltage of the predecessor node is always known whenwe calculate the updated value of Ui, wemay write, simply Ithe meaning of Ri isobviousLX

corresponding to the model of Sig s

mentioned before, a formulation inrectangular coordinates is the best way tosolve the euation in order to get Ui,avoiding the need for trigonometriccalculations with small angles

Sig eneral branch model Jote that other modified forms of

IL could be used, but our results shownthat they are less efficient than IxL

{ith the proposed formulation, it isnot necessary to estimate initial valuesfor the voltages, but only to consider thatX

INL

This corresponds to using, in the

liEn ti8p, cho &8n khi tAnh &*7c mu thGc

IL lB thu2n ti(n &> bi8n &^iX

IxL

U+i IpL bi>u th c3c b*+c l'p • mil.n, r rBng &i(n th8 c)a n%t ph.n t`tr*+c lu;n lu;n lB &*7c bi8t khi ch%ng tatAnh to3n nh2p gi3 tr c)a c3c U i, ta c th>vi8t &?n gi@n I ngh€a c)a Ri &*7c rrBngLX

t*?ng Gng v+i c3c m; hnh D hnh Jh* &4 &9 c2p tr*+c &, bi>u thGc trongh( ta &0 vu;ng gc lB c3ch tt nh$t &>gi@i ph*?ng trnh nhm tm Ui, kh;ngc.n thi8t gi@i bBi to3n l*7ng gi3c v+i gc&0 nh~

nh Q; hnh t^ng h7p nh3nh‚*u rng c3c d s` dng &*7c, nh*ng k8tu@ c)a ch%ng t;i cho th$y ch%ng At hi(uu@ h?n bi>u thGc IxL

U+i ph*?ng trnh &4 nEu trEn, nkh;ng ph@i lB c.n thi8t &> *+c tAnh gi3 tr&i(n 3p ban &.u, nh*ng ch &> "ƒt rngX

pred6i7

i

3$vi

qi

pred6i7

i

3$vi

qi


5/14

first iteration, instead of I6L

Of course, if good initial values are

known, they may always be used withthe normal version of the euation.

. (terati0e pro1esss mentioned before, the method

progresses, in each iteration, from theroot to the leaves, with successive use of I6L The updated values of Ui areimmediately used in their successorseuations

The seuence of calculations isvery straightforward and similar to other forward sweep methods, so well onlysketch it with the help of Sig

Sig j"ample distribution network Rince node V is the root IUV is

knownL, calculation of U1 is the first stepof an iteration !n the second step, U andUx may be calculated independentlyUand U6 will follow, and U will beupdated in the final step of the iterationThis shows the possibility of partial

parallel calculation in typical distributionnetworks, with important time savings

The updated values of the voltagesare then used in a new top-downiteration, and the process is repeateduntil a specified tolerance on thevoltages successive values is met final convergence test on the specified

inWected power is recommended.". ran1h model

v+i k ЄsuccIiL INL

|i9u t*?ng Gng nBy &*7c s` dng,trong l.n l'p &.u tiEn,thay v d_ng bi>uthGc I6L

P€ nhiEn, n8u c3c gi3 tr ban &.u tt&*7c bi8t, ch%ng c th> lu;n &*7c s`dng v+i phiEn b@n bnh th*Cng c)a

ph*?ng trnh. Ti ti8n hBnh ph*?ng ph3p, trong mi l.n l'p, tF trcchAnh &8n nh3nh, v+i s: liEn ti8p s` dngI6L R: c2p nh2t c3c gi3 tr c)a c3c Ui ths` dng ngay vBo c3c ph.n t` D c3c

ph*?ng trnh k8 ti8p

#3c d4y s c)a c3c phƒp tAnh r$t &?ngi@n vB t*?ng t: nh* c3c ph*?ng ph3pmu tr*+c &H do v2y, ch%ng ta s ch

ph3c ho< n v+i s: gi%p &„ c)a hnh

nh - UA d m tF n%t V lB gc IUV &4 bi8tL, vi(c

tAnh to3n U1 lB b*+c &.u tiEn c)a m0t b*+c l'p Trong b*+c thG hai, U vB Uxc th> &*7c tAnh to3n &0c l2p U vB U6 s

tAnh ti8p theo, vB U s &*7c c2p nh2ttrong b*+c cui c_ng c)a b*+c l'p |i9unBy cho th$y kh@ n†ng tAnh to3n songsong m0t ph.n trong c3c mn hnh, &i9u uan trng lB ti8tki(m &*7c thCi gian

#2p nh2t gi3 tr c)a c3c &i(n 3p thsau & &*7c s` dng trong m0t b*+c l'pm+i tF trEn "ung, vB u3 trnh nBy &*7c

l'p &i l'p l


6/14

Mp to this point, a simple model for the branches has been used, consideringonly the branch impedance, which iscommon in distribution networksowever, a more detailed model can be

used if necessary, with minor changes inthe euations This feature may beimportant in underground networks,where the capacitance of the cables is notnegligible

Sig x shows the typical ‡ modelfor a branch, where ysi is the semi-admittance of the branch

Sig x - Petailed branch modelThe other variables are the same of

Sig ecause there is more than one branch connected to each node, it is nowconvenient to define a branch admittancefor each node iX

IˆL

where sconIiL is the set of successors connected to node i !n thiscase, the total current through branch iincludes terms related to all theadmittances in i and in its succesorsX

and I6L transforms into

!n order to maintain the structure of the euation, and since is a constant, we

l.n l*7t &*7c tha m4n …i>m tra h0i tcui c_ng bng c3ch ch &nh b?m c;ngsu$t vBo th &*7c khuy8n khAch

". MW hEnh nh>nhTAnh &8n thCi &i>m nBy, m0t m;

hnh &?n gi@n cho c3c nh3nh &4 &*7c s`dng, ch "ƒt c3c nh3nh trD kh3ng r$t ph^ bi8n trong l*+i ph/n phiTuy nhiEn, m0tm; hnh chi ti8t h?n c th> &*7c s` dngn8u c.n thi8t, v+i c3c thay &^i nh~ trongc3c ph*?ng trnh TAnh n†ng nBy c th>uan trng trong mn hnh cho m0t nh3nh, lB n?i mB ysi b3n t^ng dn c)a nh3nh

nh x -Q; hnh chi ti8t c)a nh3nh#3c bi8n kh3c ging nh* hnh U

c nhi9u h?n m0t nh3nh k8t ni v+i min%t, b/y giC, thu2n l7i &> "3c &nh m0tnh3nh t^ng dn cho mi n%t iX

IˆL

• &/y, sconIiL lB t2p h7p c3c ph.n t`

k8 ti8p k8t ni v+i n%t i Trong tr*Cngh7p nBy, t^ng d=ng &i(n ch@y ua nh3nh i bao gm c3c &i9u ki(n liEn uan &8n t$tc@ c3c t^ng dn trong i vB trong c3c ph.nt` k8 ti8pX

vB bi8n &^i I6L ta &*7cX

U predIiL ‰i

Ui

ysi

ysi

-Ri

U predIiL ‰i

Ui

ysi

ysi

-Ri


7/14

may now writeX

IŠL

{ith this formulation, the resolu-tion process in rectangular coordinates isnot altered Obviously, if all the ‹s arenegligible,IŠL reduces to I6L

. Node admittan1es

!t is also easy to include constantnode admittances ‹i, ie, capacitors or reactors connected to node i, or loadsrepresented by a constant impedance !nfact, it is sufficient to change IˆL in order to include ‹i, and then use IŠL as thegeneral e"pression of the algorithmX

(. $)Mj jNHAN"jMjNT$A. P nodes

lthough the method is primaryintended to deal with \ Ior impedanceLnodes, it possible to consider \U nodesas well The e"istence of a \U nodeaffects the calculations of itself and of all

its predecessors Kegarding the firstissue, we start by rearranging IL in order to isolate the constant terms Inote that, todeal with the more general euation IŠL,a similar process is possibleLX

|> &@m b@o c$u tr%c c)a ph*?ngtrnh, vB lB m0t hng s, ngay b/y giC ch%ng ta c th> vi8tX

IŠL

• c;ng thGc trEn, u3 trnh gi@iuy8t trong h( ta &0 vu;ng gc kh;ng

ph@i thay &^i K rBng, n8u t$t c@ c3c ‹R

lB kh;ng &3ng k>, bi>u thGc IŠL gi@m v9 bi>u thGc I6L

D. Nút tổng dẫn J cng dq dBng, bao gm c3c n%t

t^ng dn b$t bi8n ‹i, ngh€a lB, dungkh3ng ho'c &i(n kh3ng k8t ni v+i n%t i,ho'c t@i &*7c &'c tr*ng bDi m0t t^ng trDTrong th:c t8, n lB &) &> bi8n &^i ph_h7p IˆL bao gm ‹i, vB sau & s` dngIŠL nh* lB bi>u thGc t^ng u3t c)a c3cthu2t to3nX

(. MỘT ( "( T(NA. ">1 nJt P

Q'c d_ ph*?ng ph3p nBy c mc

&Ach chAnh &> gi@i uy8t c3c n%t \ Iho'ct^ng trDL, n c th> &*7c "em "ƒt tt nh*c3c n%t \U R: tn t


8/14

where # is a comple" constant withobvious meaning Jow, we must solveI1VL to calculate Ui and i The best wayis to eliminate i from the two realeuations that result from I1VL and thenuse the fact that we know ŒUiŒ to obtainthe real and imaginary parts of Ui Then,using I1VL again, well obtain i

Sor control purposes, it is conveni-ent to calculate also the generat-edreactive power, usingX

!f i is outside its limits, theadeuate limit must be used instead,while the bus is temporarily classified as

a \ busThe values of i obtained in the

process will be used in the ne"t iteration,in the calculation of the predecessors of node i owever, this is not sufficient for the algorithm to work, since in the firstcalculation of a node, we need the valuesof k for all its successors {e may getahead of this problem by using k IVLZV or

k IVLZ\k γ Iwith some typical value for Las initial values for all \U nodes or, if non-trivial initial values are available for the Uk , by using I1VL from the leaves tothe root Ithat is, in the opposite directionof the normal algorithmL before

beginning the iteration process

{e summarize now the inclusion of \U nodes in the general algorithmXaL jstimate initial values for k of all

D &/y # lB m0t hng s phGc c ngh€a rrBng /y giC, ta ph@i lBm r I1VL &> tAnhto3n Ui vB i #3ch tt nh$t lB &> lom so3t, n lBthu2n ti(n &> tAnh to3n cng nh* s: ph3tra c;ng su$t ph@n kh3ng, bng c3ch s`dngX

J8u i v*7t u3 gi+i hn hnhv+i m0t s gi3 tr cho L nh* lB gi3 tr ban&.u cho t$t c@ c3c n%t \U, ho'c n8u gi3 tr

ban &.u kh;ng &3ng k> c sŽn cho c3c U… , bng c3ch s` dng I1VL tF nh3nh &8ntrc Ic ngh€a lB, ng*7c l


9/14

the \U busesH bL {hen reaching a \U node in the

iterative process, use I1VL to obtainUi and iLH

cL Rave the value of i to be used in

the ne"t iterationn important point is that this process may suffer from some instability,if the initial values for the voltages in the

buses are too far from the correct onesecause of this, it is advisable to waittwo or three iterations before using bLand cL

. ispersed enerationPispersed generation is now freuentin distribution networks, namely bymeans of asynchronous machinesQodeling these nodes as traditional \or \U nodes has been tried, but thatapproach doesnt capture correctly the

behavior of asynchronous generators [ˆ]

{ell implement here the idea of

\ node‘, developed in [ˆ] and [Š]riefly, the generated reactive power of one such unit can be appro"imated byiZ-Ui’i Inegative, since the machineactually gets reactive power from thenetworkL, with i Z fIUiL

!n order to integrate this kind of node in our method, we may usetabulated values for iZfIUiL, or a simplemodel like iZI-|Ui|L’iV, where is thevalue of the magnetizing reactance atnominal voltage [Š] !n any case, welluse ŒUiŒ to get i and then include it in thee"pression of ‹siX

!n this case, Iˆ‘L must be updatedfor all the \ nodes in each iteration Ifor the remaining nodes, it is a constantL On

th;ng th*CngL tr*+c khi b5t &.u c3c u3trnh l'p

/y giC ta tm t5t t^ng u3t n%t \Utrong c3c thu2t to3n t^ng h7pX

aL “+c gi3 tr ban &.u cho k c)a t$t c@c3c thanh c3i \U H bL …hi tm &*7c m0t n%t \U trong u3trnh l'p s` dng I1VL &> c &*7c Ui vBiLHcL ‚*u gi3 tr c)a i s &*7c s` dngtrong c3c b*+c l'p k8 ti8p

Q0t &i>m uan trng lB u3 trnhnBy c th> ch$p nh2n tF m0t vBi b$t ^n,n8u gi3 tr ban &.u c)a &i(n 3p trong c3cthanh c3i b l(ch nhi9u v+i gi3 tr &%ngc)a nhng thanh c3i kh3c U &i9u nBy,ti8n trnh &*7c chC hai ho'c ba b*+c l'ptr*+c khi s` dng bL vB cL

B. Nguồn phân tán Jgun ph/n t3n lB hi(n hu th*Cng

"uyEn trong c3c m lB do m3y &i(n kh;ng &ng b0 #3c

m; hnh truy9n thng nh* n%t \ hay n%t\U &4 &*7c th`, nh*ng c3ch ti8p c2nhi(n kh;ng n5m b5t m0t c3ch chAnh "3ctr &*7c

lBm "$p " i

Z-Ui

’i Id$u trF, khi cm3y &i(n th:c t8 nh2n c;ng su$t ph@nkh3ng tF m c th> tAch h7p c3c lo s` dng c3c b@ng gi3 tr cho i Z fIUiL, ho'c m0t m;hnh &?n gi@n nh* i Z I - |Ui|L’iVH khigi3 tr c)a &i(n kh3ng tF ha t tAnh ra i vB sau& n bao gm trong bi>u thGc c)a ‹siX


10/14

the other hand, if a battery is installed inthe node, as it usually happens, it may beincluded as ‹i in Iˆ‘L, as e"plained

before Jo other changes in thealgorithm are necessary

. (**%$T9AT()N jxAMP*jThe performance of the method

was tested with case studies found in theliterature

Sirst, a 1-bus network Idata andresults in [1]L was calculated as a basecase I1 \ busesL #omparison with [1]and other power flow calculation toolsshowed that the method gives the correctresults, as displayed in T‚j ! Jotethat [1] Ilike many similar methodsL onlygives the voltage magnitudes and totallosses, while the new method alsocalculates the voltage angles Idisplayedin degreesL and therefore all the usual

power flow results

TA*j (9j$%*T$ 63N)j NjTy)9z7

Trong tr*Cng h7p nBy, Iˆ”L ph@i &*7cc2p nh2t cho t$t c@ c3c n%t \ trong mi

b*+c l'p Icho c3c n%t c=n l


11/14

The new method was also testedagainst more demanding systems, like a6Š-bus network [1V] [] and an ˆx-busrural network [] !n both cases, detaileddata and results can be found in thereferences and will not be repeated here

T‚j !! shows the number of

iterations needed in these cases, and alsoin the tests with \U and \ nodes thatwill be mentioned later ll the resultscorrespond to a convergence error of 1V-6

pu in the real and imaginary parts of thevoltages j"ecution times are onlyindicative of the relative computationaleffort, since no optimized code wasdeveloped !nformal tests that need

further confirmation shown the newmethod is faster than other methods for radial networks and also faster than

Jewton-Kaphson based methods, for thesame tolerance

TA*j ((Tj$T$ y(TH (j9jNT

$•$TjM$

Jodes !terations Time IsL

1 1VVVVV V 1VVVVV VŠŠ V116 VŠŠ VŠˆŠV V VŠˆŠV VŠˆVxˆ VV VŠˆVxNx VŠ6Šˆ V6Š VŠ6Šˆ

6 VŠ66x V6Šˆ VŠ66xN VŠ6Nx VNxˆ VŠ6Nˆ VŠxx1 1V11 VŠxxVŠ VŠNˆ 1 VŠNN

1V VŠ6 11ˆ VŠ611 VŠx6 1 VŠx61 VŠx 1Š VŠx

\h*?ng ph3p m+i &4 &*7c ki>m tra

ph@n bi(n nhi9u h?n v+i yEu c.u kh5ckhe c)a h( thng, nh* m0t mu th kh@n†ng tAnh to3n t*?ng &iH v rng, m4 ti*u kh;ng &*7c khai th3c #3c th`nghi(m kh;ng chAnh thGc, "3c nh2n rngc.n ph@i ti8p tc trnh bBy ph*?ng ph3p

m+i nhanh h?n c3c ph*?ng ph3p kh3ccho c3c m nhanh h?n ph*?ng ph3p Jewton-Kaphson c? b@n v+i c_ng m0t dung sai

TA*j (("Á" TH€ NGH(M '( NH(% H

THNG zHÁ" NHA%

|> ki>m tra m; hnh \U, n%t cui

Jode voltageImethodL

rgument voltageI[1]L

1 1VVVVV V 1VVVVV VŠŠ V116 VŠŠ VŠˆŠV V VŠˆŠV

VŠˆVxˆ VV VŠˆVxNx VŠ6Šˆ V6Š VŠ6Šˆ6 VŠ66x V6Šˆ VŠ66xN VŠ6Nx VNxˆ VŠ6Nˆ VŠxx1 1V11 VŠxxVŠ VŠNˆ 1 VŠNN

1V VŠ6 11ˆ VŠ611 VŠx6 1 VŠx61 VŠx 1Š VŠx


12/14

1 \ x – VVVx6Š \ 6 VVVxˆx \ 6 VV16

11 1 \U – VVVx11 1 \ N – VVVx

!n order to test the \U model, thelast node of the 1-node network wasfirst reversed Istill as a \ nodeL to anegative load‘ Then, the voltagemagnitude was used as the specifiedvoltage for the \U test Ithats why UZVŠxxˆL is not a round‘ valueLKesults, shown in T‚j !!!, of the \U

test were validated against the prelimi-nary \ run and also with a Jewton-Kaphson based tool s e"pected,voltages increase in all the nodes, due tothe inWection of reactive power in node1

TA*j (((9j$%*T$ 6N)j A$ P7

Sinally, the \ model was alsotested in a similar way, showing againthe ability of the method to deal with thattype of nodes, although a greater number

of iterations was necessary Ualidation of these results is more difficult, since usualmethods do not include this feature, so

c_ng Ic)aL m cm0t ”t@i /m tAnh” Rau &, &0 l+n &i(n 3p&*7c s` dng nh* &i(n 3p danh &nh c)a

phƒp th` \U I& lB tm tra \U &*7c hi(u l:c

ha &i l2p v+i s: hom tra t*?ng t:, l.n na cho th$y kh@n†ng c)a ph*?ng ph3p &> gi@i uy8t c3cd


13/14

we checked all the power flow euationsand also the relation between , U and in the asynchronous generators

(. A"zN)y*jGMjNT

The author would like to thank students gostinho Rousa, and JunoKibeiro, both from the Saculty of jngineering of the Mniversity of \ortogostinho implemented the first versionof the code of the new method, and Junodeveloped it and helped in the teststudies

((. 9jj9jN"j$[1] P Pas, R Jagi and P \ …othari,”Jovel method for solving radialdistribution networks”, !jj \rocenTransm Pistrib, Uol 11, pp Š1-Šˆ, —uly 1ŠŠ

[] P Pas, P \ …othari and …alam,”Rimple and efficient method for loadflow solution of radial distributionnetworks”, jlectric \ower ˜ jnergyRystems, Uol 1N, pp x-6, 1ŠŠx

[] j"psito and j K Kamos,Keliable ‚oad Slow Techniue for Kadial Pistribution Jetworks‘, !jjjTrans \ower Rystems, Uol 1, Jo ,

pp 1V6-1V6Š, ugust 1ŠŠŠ[] R hosh, P Pas, ”Qethod for load

flow solution of radial distributionnetworks”, !jj \roc-ener Transm

Pistrib, Uol 16, Jo 6, Jovember 1ŠŠŠ

[x] R S Qekhamer, R Roliman, Q Qostafa, Q j jl-awary, ‚oadSlow Rolution of Kadial PistributionSeedersX new pproach‘, in \rocVV1 !jjj \orto \ower Tech, Uol ,\orto, Reptember VV1

[6] ugugliaro, ‚ Pusonchet, Q

!ppolito, j K Ranseverino, nefficient iterative method for load-flow solution in radial distribution

ki>m tra mi ph*?ng trnh d=ng c;ngsu$t vB uan h( na gia , U vB trongnhng m3y ph3t kh;ng &ng b0

(. *‚( "M ƠN

T3c gi@ g`i lCi c@m ?n &8n nhngsinh viEn Aostinho $ousa, vB Nuno9i/eiro thu0c …hoa …™ thu2t, Tr*Cng|n n vB tr7 gi%ptrong u3 trnh nghiEn cGu th` nghi(m

((. T( *(% THAM zH)[1] P Pas, R Jagi and P \ …othari,”Jovel method for solving radialdistribution networks”, !jj \rocenTransm Pistrib, Uol 11, pp Š1-Šˆ, —uly 1ŠŠ

[] P Pas, P \ …othari and …alam,”Rimple and efficient method for loadflow solution of radial distributionnetworks”, jlectric \ower ˜ jnergyRystems, Uol 1N, pp x-6, 1ŠŠx

[] j"psito and j K Kamos,Keliable ‚oad Slow Techniue for Kadial Pistribution Jetworks‘, !jjjTrans \ower Rystems, Uol 1, Jo ,

pp 1V6-1V6Š, ugust 1ŠŠŠ[] R hosh, P Pas, ”Qethod for load

flow solution of radial distributionnetworks”, !jj \roc-ener Transm

Pistrib, Uol 16, Jo 6, Jovember 1ŠŠŠ

[x] R S Qekhamer, R Roliman, Q Qostafa, Q j jl-awary, ‚oadSlow Rolution of Kadial PistributionSeedersX new pproach‘, in \rocVV1 !jjj \orto \ower Tech, Uol ,\orto, Reptember VV1

[6] ugugliaro, ‚ Pusonchet, Q

!ppolito, j K Ranseverino, nefficient iterative method for load-flow solution in radial distribution


14/14

networks‘, in \roc VV1 !jjj \orto\ower Tech, Uol , \orto, Reptember VV1

[N] U Qiranda, Q Qatos, — \ ‚opes —T Raraiva, — J Sidalgo, Q T \once

de ‚e4o, !ntelligent tools in a real-world PQR environment‘, \roc!jjj \ower jngineering RocietyRummer Qeeting, UolX 1, ppX 16-16ˆ, VVV

[ˆ] —\ ‚opes, S Q arbosa, — # \idrƒ,Operation simulation of QUdistribution networks withasynchronous local generation

sources‘, \roc Qj‚j#OJŠ1, Qay1ŠŠ1[Š] — # \idrƒ, — Q Uelasco, —\ ‚opes,

S Q arbosa, Qodeling of non-linear nodal admittances in load-flowanalysis‘, \roc !S# Rymposium on\ower \lants and Rystems, Qunich,Qarch 1ŠŠ

[1V] Q #hakravorty, P Pas, ”Uoltagestability analysis of radial distributionnetworks”, jlectrical \ower ˜jnergy Rystems IVV1L 1Š-1x

(((. ()G9APH•Manuel A. Matos (El. Eng.,Ph.D., Aggregation) was born in1955 in Porto (Portugal). He ispresently ull Pro!essor at theaculty o! Engineering o! the

"ni#ersity o! Porto, Portugal, an$the %anager o! the Power&yste's "nit o! E&* Porto. Healso colla+borates with the%anage'ent &chool o! the"ni#ersity o! Porto. His researchinterests inclu$e !uy 'o$elingo! power syste's, opti'iationan$ $ecision+ai$ 'etho$s. He is

a 'e'ber o! EEE.

networks‘, in \roc VV1 !jjj \orto\ower Tech, Uol , \orto, Reptember VV1

[N] U Qiranda, Q Qatos, — \ ‚opes —T Raraiva, — J Sidalgo, Q T \once

de ‚e4o, !ntelligent tools in a real-world PQR environment‘, \roc!jjj \ower jngineering RocietyRummer Qeeting, UolX 1, ppX 16-16ˆ,VVV

[ˆ] —\ ‚opes, S Q arbosa, — # \idrƒ,Operation simulation of QUdistribution networks withasynchronous local generation

sources‘, \roc Qj‚j#OJŠ1, Qay1ŠŠ1[Š] — # \idrƒ, — Q Uelasco, —\ ‚opes,

S Q arbosa, Qodeling of non-linear nodal admittances in load-flowanalysis‘, \roc !S# Rymposium on\ower \lants and Rystems, Qunich,Qarch 1ŠŠ

[1V] Q #hakravorty, P Pas, ”Uoltagestability analysis of radial distributionnetworks”, jlectrical \ower ˜ jnergyRystems IVV1L 1Š-1x

(((. ()G9APH•Manuel A. Matos Ijl jng, Ti8n s€, t^ngh7pL sinh vBo 1Šxx t

Full Translation

Documents

Transcript of Full Translation