Impact of advanced inverter functions on low-voltage power grids

Recei ed: 12 Janua y 2021 - Re ised: 15 Ma ch 2021 - Accep ed: 28 Ma ch 2021 - IET Ene gy Sys ems In eg a ion DOI: 10.1049/esi2.12018 ORIGINAL RESEARCH PAPER Impac o ad anced in e e unc ions on low‐ ol age powe g ids A jen Men ens 1,2 |Ha old R. Chamo o 2 |Valé y Ann Jacobs 3 |Da id Topolánek 4 | Jiří D ápela 4 |Wilma Ma inez 2 1 Depa men o Enginee ing Technology (INDI), V ije Uni e si ei B ussel, B ussels, Belgium 2 Depa men o Elec ical Enginee ing (ESAT), Ka holieke Uni e si ei Leu en, Diepenbeek, Belgium 3 Depa men o Elec onics and In o ma ics (ETEC), Depa men o Applied Physics and Pho onics (TONA), Rec o a e, V ije Uni e si ei B ussel, B ussels, Belgium 4 Depa men o Elec ical Powe Enginee ing (UEEN), B no Uni e si y o Technology, B no, Czech Republic Co espondence A jen Men ens, Depa men o Enginee ing Technology (INDI), V ije Uni e si ei B ussel, B ussels, Belgium. Email: [email p o ec ed] Abs ac In oday's powe g id, a g ea numbe o in e e ‐based dis ibu ed ene gy esou ces (DERs) a e connec ed and a e mainly designed o supply powe wi hou conside ing he ol age and equency de ia ions o he g id. The e o e, dis ibu ion sys em ope a o s (DSOs) a e challenged wi h an inc ease in g id e en s because o he andom implemen a ion o DERs. Vol age le els can a y beyond p ede ined limi s a he poin o connec ion and a e cu en ly no e alua ed by DSOs. Summa ized he e is he de elopmen o a simula ion model o e alua ing he impac o suppo unc ions in eg a ed in in e e ‐based DERs. The model aims o help g id ope a o s simula e ol age and equency e en s and s udy he impac o DERs o he g id wi h espec o di e en se ings o in eg a ed suppo unc ions. A model is de eloped in MATLAB/Simulink con o ming o Eu opean s anda ds and egula ions. G id dynamics can be e alua ed by imi a ing ol age and equency de ia ions. Suppo unc ions can be ei he adjus ed acco ding o he si ua ion o u ned o . Toge he wi h adjus able se ings acco ding o DSO eques , his model o e s lexibili y and insigh in he capabili ies o DERs o sol e ol age and equency issues. Case s udies show ha he model co esponds o expec ed beha iou and can be used o u he de elopmen . 1 | INTRODUCTION The wo ld is looking o oppo uni ies o p oduce clean ene gy. While households accoun o o e 27% o o al ene gy de- mand, hey (indi ec ly) accoun o an agg a a ion o global wa ming [1]. The Eu ope 2020 s a egy includes a ge s o clima e change and ene gy, and go e nmen s a e p omo ing DERs wi h incen i es [2, 3]. Wo ldwide, all (powe ‐consuming) sec o s con ibu e o a ound 38% o ene gy‐ ela ed CO 2 emissions. Inc easing and s imula ing pho o ol aic (PV) p o- duc ion can signi ican ly educe hese emissions, as 1 kWh p oduced by PVemi s as li le as 15 g/kWh CO 2 compa ed wi h he global a e age o 475 g/kWh CO 2 [3]. While me ely 3% o elec ici y is gene a ed by PV, i a oids a ound 4.5% o powe sec o emissions. This is because o coun ies wi h high ca bon elec ici y gene a ion, such as China and India, ins alling a g ea amoun o PV powe [3–5]. In he pas , powe was only consumed bu ne e supplied by households. And hus, o a long ime, an on‐load ap change (OLTC) was he only mechanism necessa y o change local ol age le els. They ely on he ac ha he e is a uni o m ol age d op ac oss he powe lines. Un o una ely, hey no longe su ice. Due o he implemen a ion o in e e ‐based DERs, mos ly PV panels, he uni o m ol age d op has become less common, and ol age le els can a y in bo h di ec ions [6]. Si ua ions e en exis whe e PV panels a e p ohibi ed in pa s o he g id [7]. Ins ead o p ohibi ing hem, hey can become pa o he solu ion. Households a e supplying an amoun o powe ha can no longe be igno ed. I was ound ha ol age de ia ions will no occu when he a e age pene a ion pe household lies below 2.5 kW [8]. The s udy in [8] assumed a DER pene a ion le el o 0%–11.25%, bu pene a ion le els ha e isen o 22% [9, p. 13]. As a esul , ol age de ia ions a e occu ing mo e equen ly and wi h a highe ampli ude bu only impac he local g id [10]. Ins ead o ein o cing he g id, PV in e e s can become an impo an pa o g id suppo . Fo his eason, This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion‐NonComme cial‐NoDe i s License, which pe mi s use and dis ibu ion in any medium, p o ided he o iginal wo k is p ope ly ci ed, he use is non‐comme cial and no modi ica ions o adap a ions a e made. © 2021 The Au ho s. IET Ene gy Sys ems In eg a ion published by John Wiley & Sons L d on behal o The Ins i u ion o Enginee ing and Technology and Tianjin Uni e si y. 426 - IET Ene gy Sys . In eg . 2021;3:426–436. wileyonlinelib a y.com/jou nal/esi2 egula ions ha e been implemen ed [11]. While PV is a clean al e na i e, i con ibu es only 2.9% o global elec- ici y demand. This indica es ha PV is no a comp e- hensi e solu ion o abandoning pollu ing powe ‐gene a ing acili ies. Ul ima ely, de elopmen o ene gy s o age (elec- ical, he mal, hyd ogen e c.) can play an impo an ole in s imula ing in es men s in enewable ene gy esou ces in gene al. The exponen ial g ow h o ins alled PV capaci y is a i s a gumen o how hese ins alla ions could impac he dis ibu ion g id and also why hey can and should be used as g id suppo . The wo ldwide cumula i e ins alled capaci y in 2008 was only 14.5 GW, while i exceeded 100 GW in 2012. Howe e , in 2018, a i e old le el was al eady ins alled. Following his end, i can be expec ed o each 1 TW by 2022 [3]. Dynamic models wi h ad anced unc ionali ies o con e e ‐based gene a ion a e c ucial o unde s anding he beha iou o he g id unde s essed ci cums ances [12, 13]. Howe e , such unc ionali ies b ing a ious challenges associ- a ed wi h inc eased pene a ion o DERs and hei g id in e - ac ion [14]. Sma in e e s wi h ol age and equency con ol abili ies a e aluable o DERs so hey can con ibu e o he g id wi h suppo unc ions and ancilla y se ices, such as eac i e powe con ol, aul ide‐ h ough, and ha monic compensa ion [15]. Many esea ch pape s ha e been published in ecen yea s ha discuss he ol age iola ion issues ha eme ge om he high pene a ion o in e e gene a ion in o he powe sys ems [16]. Fo ins ance, a es sys em adap ed om he medium‐ ol age dis ibu ion sys em in On a io, Canada, is s udied in [17], p o iding g id ol age suppo unc ionali ies. An op imized con ol s a egy o manage he eac i e powe esou ce gene a ed by in e e ‐based gene a ion is p esen ed in [18] o imp o e he quali y o he ol age dis- ibu ion ne wo k and ul il he la es echnical equi emen s lis ed by dis ibu ion sys em ope a o s (DSOs) in hei g id codes. A case s udy dealing wi h long‐ e m ol age ins abili y in sys ems hos ing ac i e dis ibu ion ne wo ks is epo ed in [19]. The documen ed simula ions show he e ec o he es o a ion o dis ibu ion ne wo k ol age. A hyb id con ol s a egy o suppo ing he ol age unde aul condi ions is p esen ed in [20], demons a ing he simul aneous mi iga ion o ol age sags by injec ing ac i e and eac i e powe o ide h ough he pe u ba ion and main ain g id ol age. Simila ly, a ol age egula ion scheme using a deadbea con olle ha helps o mi iga e as ol age dis u bances is p esen ed in [21] ha supp esses he ansien s in he sys em. The au ho s in [22] p opose a con ol scheme wi ha dynamic injec ion egion o he in e e sys em ha adap s o he se ‐ poin s assigned by a cen alized con olle . Simila ly, a con ol scheme ha op imizes he eal‐ ime ope a ion o ac i e dis i- bu ion ne wo ks while also conside ing he p o ision o ol age suppo as an ancilla y se ice o he ne wo k equi emen s in Swi ze land and in es iga e he ope a ional modes o he DER in e e s is p esen ed in [23]. The s a ic ol age con ol consid- e ing ol age‐ eac i e powe mode and dynamic and ex ensi e ol age con ol wi h maximum u iliza ion o DER capaci y and sys em s abili y a e s udied in [24]. As he p e ious con ibu ions discussed, a ious con ol s a egies exis and a e able o unc ion well unde di e en g id condi ions. Also, i shows ha applying a con ol s a egy depends hea ily on he chosen con ol me hod and pa ame e s. This pape discusses he de elopmen o a simula ion model o p o ide g id ope a o s wi h mo e insigh ega ding he e ec o in e e ‐based DERs. Since he con ol pa am- e e s can ha e a g ea impac on he g id esponse, he p o- posed simula ion model o e s lexibili y ega ding pa ame e choice. The es o his pape is o ganized as ollows. Sec ion 2 desc ibes he possible me hods o p o iding g id suppo . Sec ion 3p esen s he model design and implemen a ion in MATLAB and explains he impo ance o se ing he co ec ime cons an s. The simula ion esul s and discussions a e p esen ed in Sec ion 4. Finally, he conclusions a e gi en in Sec ion 5. 2 | METHODS FOR PROVIDING GRID SUPPORT 2.1 | Ac i e and eac i e powe compensa ion using in e e s As b ie ly men ioned abo e, he in eg a ion o DERs will esul in an inc eased ol age a he poin o connec ion (POC). Due o luc ua ing injec ion o powe (sola and wind powe a e no cons an ), he need o au oma ed solu ions is g owing, which implies ha (e en au oma ed) OLTCs a e no longe su icien . Using hese DERs o compensa e o low o high ol age is one o he mos commonly discussed me hods [6, 7, 25–30]. Figu e 1depic s an equi alen schema ic o a powe line. The esis ance and induc ance o he line co espond o he eplacemen R and L alue. The ol age in a ce ain poin is gi en by U¼ ðP;QÞ ð1Þ whe e dU¼∂U ∂P dPþ∂U ∂QdQð2Þ FIGURE 1 Powe line wi h R and L componen s o indica e esis ance and induc ance alues MENTENS ET AL. - 427 and ΔU¼U1−U2¼R⋅I2⋅cosφ2þX⋅I2⋅cosφ2ð3Þ wi h φ 2 he phase shi be ween ol age Uand cu en I 2 . To ew i e Equa ion (4) as a unc ion o P and Q, ΔU¼R⋅PþX⋅Q U2ð4Þ Equa ion (4) indica es ha he ol age d op ΔUis ela ed o he ac i e and eac i e powe . I can also be seen ha powe lines wi h a high R/X a io will expe ience mo e impac om a change in ac i e powe (P) han a change in eac i e powe (Q). Th ee main ypes o in e e —a s ing in e e , a mic o‐ in e e , and a cen al in e e —exis [31, 32]. A s ing in e e is based on sola panels connec ed in se ies. When one PV panel is shaded o mal unc ions, he en i e powe ou pu is limi ed by his one panel. A mal unc ioning PV panel can be eplaced, bu shade caused by ees can o en no be con olled by he owne . To o e come his, a mic o‐in e e can be ins alled ins ead. The PV panels a e connec ed in pa allel, and he e o e only he shaded o mal unc ioning panels a e limi ed in ou pu powe . The di e ence wi h a cen al in e e is i s size. Cen al in e e s a e mainly used in indus ial ins alla ions wi h ypical powe anges om 100 kW o 1 MW [32]. Due o i s size, hey a e no conside ed he e. The s udy in [31] also shows ha mic oin e e sys ems p esen be e pe o mances a bo h shaded and no ‐shaded condi ions. The main d awback o a mic oin e e is he highe cos . Howe e , acco ding o [33, p. 2885], he s ing in e e appea s o ha e a lowe pe ‐ wa capi al cos when jus he in e e is conside ed. Howe e , he in e e ep esen s only abou 15% o he en i e PV sys em cos whe eas he ins alla ion labou (…) cos accoun s o 40%, depending on he sys em con igu a ion and in e e echnology. These ac o s ha e made i di icul o pe o m a compa a i e cos s udy. The ollowing unc ions a e also known as ad anced in e e unc ions and a e discussed in [6, 34]. The se poin s a which hese unc ions a e deployed can di e acco ding o he local equi emen s. 2.1.1 | Ac i e powe compensa ion The possibili y o he in e e o abso b P when he e is o e ol age in he low‐ ol age (LV) g id is desc ibed as ac i e powe compensa ion. The in e e is se o s a abso bing ac i e powe when a h eshold ol age limi is me (e.g. a 3% o e ol age, he in e e shall s a his compensa ion). Fi s , i should be no ed ha his is only possible i a s o age sys em is p esen o abso b ac i e powe . I no , he in e e can educe i s P ou pu , and i necessa y, be disconnec ed om he g id. This will only happen in ex eme si ua ions. Also, being disconnec ed om he g id will cause a loss o income o he ene gy p oduce , so his should be a oided as much as possible. Second, his compensa ion is only a ailable un il he s o age sys em is ully cha ged o un il a h eshold cha ge is eached. 2.1.2 | Reac i e powe compensa ion In medium‐ ol age (MV) o LV g ids whe e he eac ance Xis impo an , Q(U) compensa ion is used. In o de o alle ia e a ol age d op caused by a g id e en , he in e e needs o p o ide a ce ain amoun o Q o he g id [26, 35]. A deadband a ound he nominal ol age le el is in oduced o p e en he in e e om swi ching be ween abso bing o deli e ing Q in a sho ime span [36]. 2.2 | Demand‐side managemen esul s in a educ ion o use com o Ins ead o limi ing he ou pu o an in e e , demand‐side managemen (DSM) ocuses on limi ing powe usage in case o high load and does he opposi e in case o high injec ion. Washing machines, ho wa e bu e s, and (in he u u e) elec ic ehicles may pose issues du ing peak hou s [37]. The pu pose is o pos pone he usage o hese appliances. In his manne , he load will be sp ead ac oss a g ea e amoun o ime. The amoun o pos poned powe is ep esen ed as lexibili y [38, 39]. DSM is seen as an impo an me hod o help mi iga e he e ec s o he inc easing sha e o unp edic able enewable en- e gy p oduc ion, he inc eased elec ical load due o ossil uel powe ed equipmen being eplaced by elec ical equipmen , and he dec easing in es men s in di ec ly con ollable ( ossil uel) plan s. To cla i y he p os and cons o DSM, he neces- si ies o a success ul implemen a ion and i s con ibu ion o blackou s a e discussed. 2.2.1 | Necessi ies Compa ed wi h using in e e s, he equi emen s a e mo e challenging. Fi s , sma appliances a e needed o con ol he powe usage acco ding o he ol age le el a he POC, which was measu ed by a sma me e . These appliances consis o pos ponable appliances, such as dishwashe s, washing ma- chines and umble d ye s, and bu e ed appliances such as ho wa e bu e s and elec ical ehicles. Ho wa e bu e s a e conside ed o ha e he mos in luence on lexibili y. Second, es amilies a e equipped wi h a home ene gy managemen sys em. In a case s udy, one g oup was asked o al e hei usage based on di e en ene gy a i s du ing he day and he 428 - MENTENS ET AL. o he g oup was equipped wi h an Au oma ed Home Ene gy Managemen Sys em [38]. Appliances wi hou sma capabil- i ies we e e o i ed wi h communica ion de ices o ensu e sma con ol. Sma appliances we e u ned on o o au o- ma ically, while basic com o , such as always being able o ake a ho showe , was s ill p o ided. Final, ene gy s o age can be in e es ing o PV owne s o p omo e sel ‐consump ion. I is no eally seen as a necessi y, as he p ice pe kWh as well as he kWh pe olume is s ill imp o ing. 2.2.2 | Demand‐side managemen as a solu ion o blackou s? Conside ing ha 18% o Flemish households hea hei wa e using elec ici y (ho wa e bu e s ha e he mos impac as men ioned abo e), ex apola ing his o he whole popula ion o Belgium, delayed powe usage would p o ide 207 MW o powe . Taking in o accoun he o he appliances (washing machines, elec ic ehicles e c.) adds up o 267.9 MW. Compa ing hese alues wi h he 725 MW s a egic ese e ha Belgian T ansmission Sys em Ope a o (TSO) Elia has o c ea e, i can be assumed ha , e en wi h a pa icipa ion g ade o 100% o households wi h ho wa e bu e s, he equi emen will no be me [38, 40]. Ne e heless, DSM can become an impo an pa o he solu ion. In Belgium, mos o he ol age suppo is p o ided by OLTCs. Once pe yea (o mo e, depending on he necessi y) he ap s and o he ans o me is changed o mee ol age limi s. This is done manually, bu mo e au oma ed solu ions a e being implemen ed. To complemen OLTC suppo , o e en ully eplace hem, in e e ‐based DERs can be used. Bo h P and Q suppo unc ions can be implemen ed o alle ia e ol age and equency de ia ions. Gi en he abo e, i is clea ha addi ional g id suppo unc ions should be implemen ed in in e e s o con ol ol age le els a he POC [11]. This should be ex ended om household DERs (e.g. PV panels) o in e e ‐based powe plan s. Be o e deploymen o suppo unc ions, ex ensi e es ing needs o be pe o med in o de o p e en e o s and op imize e ec i eness o implemen a ion. The lack o comp ehensible simula ion models makes i mo e di icul o pe o m plausible es s [25]. 3 | DESIGN AND IMPLEMENTATION USING MATLAB/SIMULINK 3.1 | In oduc ion Tes ing and modelling will be pe o med in MATLAB/Simu- link. Be o e i s implemen a ion, a basic LV g id model has o be de eloped. This model, as illus a ed in Figu e 2, consis s o a ol age sou ce, se e al loads ha simula e household o in- dus ial loads, and one o mo e DERs. The ope a o will be able o imi a e g id e en s by swi ching loads on and o o cause ol age de ia ions o by se ing he equency le el so ha he g id dynamics can be e alua ed. The ol age as a unc ion o he line leng h p o ides us insigh on he impac o DERs. An ac i e DER will cause a aised ol age nea he POC. In Figu e 2 his is shown as a posi i e e ec while he ol age le el s ays wi hin i s bounda ies o a longe line leng h. Issues will occu when mul iple DERs a e connec ed in an a ea whe e hey can ein o ce each o he 's beha iou . This may cause he maximum ol age le el o be exceeded. To esol e his, DERs should implemen unc ions o suppo he g id and change hei ou pu acco ding o ol age and equency le els [11, 25, 41]. Figu e 3depic s he simula ion model in one block dia- g am. Again, colou codes a e used o indica e he o igin o he se ings. The p ese cha ac e is ics consis o he P(U), P( ), Q (P), and Q(U) blocks. The measu emen s a e he ou pu o he equi alen g id model (see Figu e 4). The ime cons an s a e used as an inpu o he p ese cha ac e is ics and can be changed acco ding o DSO eques . The use se ings a e simula ion speci ic. On he one hand, a ol age and equency e o can be simula ed o compensa e o measu ing issues. On he o he hand, he minimum powe ac o can also be se . Needless o say, his will in eal li e be de i ed om he connec ion con ac be ween DSO and he owne o he in e e . 3.2 | Equi alen g id model The equi alen single‐phase g id model, as illus a ed in Figu e 4, is used as a ealis ic ep esen a ion o a g id. Since he ol age sou ce block is ideal ( his is he s anda d se ing in Simulink) a sou ce induc ance is added o compensa e o he sho ‐ci cui impedance o he second ans o me winding. The line impedance is calcula ed based on he line leng h, wi h a esis ance o 0.38 Ω pe km and an induc ance o 0.72 mH pe km. While his model ocuses on simula ing ol age de- ia ions by se ing he sou ce main ol age, only wo main loads o 9.2 kW a e used. A u he segmen a ion o loads should be made when he mu ual dis ance be ween households is o impo ance, and hus a line impedance be ween FIGURE 2 Basic in e p e a ion o dis ibu ed ene gy esou ce (DER) impac (Z =line impedance), (a) is wi h DER and has a posi i e impac , (b) is wi hou DER and ol age d ops below he limi a he end o he line MENTENS ET AL. - 429 households should also be added. The a o emen ioned alues o impedance and loads a e always unique o a speci ic si - ua ion and should be changed acco dingly when using his simula ion model o o he se ups. The alues o loads and PV sizes can be ob ained by alues gi en by he digi al sma me e . Simulink p o ides many use ul s anda d blocks. Simple cha ac e is ics, such as P(U), Q(P), and Q(U) cu es a e implemen ed using 1‐D lookup ables. The P( ) cha ac e is ic, implemen ed in laye 2, equi es ex a unc ionali ies. Mo e complex unc ions a e he e o e implemen ed using a combi- na ion o 1‐D lookup ables and MATLAB unc ions. 3.3 | Cha ac e is ics o con ol scheme 3.3.1 | P(U) cha ac e is ic I is necessa y o calcula e P(U) and Q(U) o calcula e I ampli ude and i phase . P is calcula ed by using a P(U) cha ac e is ic shown in Figu e 5. The ac ual implemen a ion is shown in Figu e 6. The ol age [p.u.] alues used o limi ing P can di e ac- co ding o DSO equi emen s. While mos egula ions a e based on p.u. alues, his model also uses he ol age p.u. as an inpu o he P(U) cha ac e is ic. The implemen a ion also equi es a limi in ou pu o p e en alues lowe han 0 and highe han 1. A e his, he P(U) cha ac e is ic ou pu is mul iplied by he a ailable P (P nominal mul iplied by an a ailabili y ac o , depending on uncon ollable a iables, e.g. sunligh ). The a ailabili y ac o can be used by he ope a o o limi he nominal powe ou pu caused by shadow, lack o sunligh , and so o h 3.3.2 | P( ) cha ac e is ic DERs can also ha e an impac on equency le els. A single DER will no ha e a isual impac , bu adding hem all FIGURE 3 This lowcha ep esen s he en i e simula ion model. All inpu s, measu emen s and calcula ions a e summa ized in one block diag am FIGURE 4 Equi alen single‐phase g id model. A isual ep esen a ion makes i s aigh o wa d o add o edi pa ame e s 430 - MENTENS ET AL. oge he will. To compensa e o his change in equency le el, he powe ou pu can be adap ed i o e ‐o unde - equency is p esen . The P( ) cha ac e is ic shown in Figu e 7is desc ibed in [41]. A alue h eshold is applied o main ain 0.6 p.u. P ou pu when equency eaches 51.1 Hz. To p e en equency le els om ising oo as again when equency d ops (P ou pu will also ise again), he P ou pu is limi ed o 0.6 p.u. un il he equency d ops below 50.1 Hz. 3.3.3 | Q(P) modes The ou pu o he P(U) o P( ) cha ac e is ic is used as an inpu o calcula ing Q(P). This can be calcula ed using di e en use ‐speci ic Q modes. The ollowing pa ag aphs explain all he con igu ed modes. In he simula ion model, a swi ch selec o de e mines which mode is cu en ly p e e ed. The applicabili y o Q(P) modes is no u he discussed, as his is beyond he scope o his pape . A speci ic case s udy wi h only changing he Q(P) mode could de e mine he mos sui able mode. Q(P) mode 1 The i s Q‐mode ou pu s he minimum alue be ween Q nominal and Q PFmin . The minimum powe ac o (PF) in he model is 0.85 bu can be changed by he ope a o . No e ha he P inpu o bo h subsys ems is di e en . Fo calcula ing Q nominal , a limi a ion in Q is no aken in o ac- coun ( he limi a ion being he a ailabili y ac o , depending on sunligh e c.). Q(P) mode 2 The second mode uses a a ying PF as a unc ion o P ou pu . Figu e 8illus a es ha he PF a ies om 0.9 o 1. The slope om 0.5 o 1.0 p.u. P can be changed acco ding o DSO o local equi emen s. Q(P) mode 3 The hi d mode uses PF nominal o calcula e he Q(P) ou pu . In his mode, he Q ou pu is always p opo ional o he P ou pu . Q(P) modes 4, 5, and 6 The emaining h ee modes a e he ollowing: �Q nominal calcula ed wi h PF nominal and P nominal , �cons an Q, �ze o Q when no Q suppo is expec ed. All six modes will ha e a di e en impac on ol age le els. The bes mode will di e acco ding o he si ua ion and he gene al ol age p o ile o he eede . Cu en ly, he p e e ed mode is chosen manually o be e e alua e he impac in speci ic si ua ions. Selec ing he Q‐mode wi h he lowes eac i e powe ou pu will be bene icial o he PV owne , bu less bene icial o suppo ing ol age le els a he POC. 3.4 | Q(U) cha ac e is ic The ou pu o he Q‐mode selec o is used o calcula e he ac ual Q ou pu . This calcula ion is done using a Q(U) cha - ac e is ic, shown in Figu e 9. FIGURE 5 P(U) cha ac e is ic wi h a linea ol age limi om 1.09 p.u. o 1.11 p.u. FIGURE 6 The me hod o implemen ing he P(U) cha ac e is ic in he model FIGURE 7 P( ) cha ac e is ic, p oposed in [41, p. 29] and implemen ed in simula ion model FIGURE 8 PF(P) cha ac e is ic indica ing a dec ease in PF when mo e han 0.5 P p.u. is deli e ed MENTENS ET AL. - 431 3.5 | Use o a iable ime cons an s in P(U), P( ), and Q(U) cha ac e is ics In o de o slow down he esponse o gene a ing uni s, addi ional delay in he o m o a i s o de low‐pass il e is in oduced. The P(U), P( ) and Q(U) cha ac e is ics use a di e en ime cons an . This ime cons an is changed manu- ally, bu in eal li e ope a ion i is eques ed by he ele an DSO. To o e mo e lexibili y ega ding ime cons an s, he Model Disc e ize (Simulink app) is used. A con inuous ime ans e unc ion can be con igu ed and is used o compu e he disc e e ans e unc ion. The ze o‐o de hold me hod is chosen, since his me hod uses he exac con inuous alue and holds i o (in his case) 0.02 s. The possibili y o changing he ime cons an , e en du ing simula ion, is in e es ing o compa ing he impac o di e en ime cons an s. Also, his can simula e he eques o DSOs. As men ioned abo e, a speci ic ime cons an can be eques ed by he DSO o in luence he impac o he DER. A smalle ime cons an will also b ing mo e isk, as his can cause oscilla ions due o sudden changes o a ail- able P and Q. 4 | SIMULATION RESULTS To alida e he simula ion model, andom alues o he ol age and equency se poin s (see Table 1) a e se o explain he ou pu and indica e he accu acy o imple- men a ion. Table 1summa izes he es condi ions. A ela- i ely la ge s ep size o 0.2 s is chosen o imp o e simula ion ime. Howe e , la ge sys em s udies can be pe o med wi h espec ing slow dynamics (in o de o seconds). These a e alid o bo h case s udies. An R/X a io o a ound 1 o 3 is usual in LV g ids [5]. In his case, a a io o a ound 2 is used. The eac ance X depends on he induc ance L and he equency . I is gi en by X¼ωLð5Þ whe e ω¼2π ð6Þ 4.1 | Case 1: unde ol age wi h o e equency Figu e 10 depic s he P( ) cha ac e is ic and he o e w i ing o he P(U) cha ac e is ic when he ol age le el is 0.94 p.u. o lowe (see Figu e 3). The o e w i e is implemen ed o p e en a bigge ol age d op when bo h unde ol age and o e - equency a e p esen a he same ime. A =4.58 s, he cu en limi is eached (see di e ence be ween calcula ed and measu ed P and Q ou pu ). This indica es one o he e- s ic ions o he in e e . No e ha his is also he bes ‐case scena io wi h an a ailable powe o 100%, hus ou pu po- we can e en be mo e es ic ed. A 2.00 s, o e equency occu s and P ou pu d ops acco ding o P( ) cha ac e is ic (see Figu e 7). A 4.04 s, ol age d ops below he le el, acco ding o Figu e 9, ha ac i a es he Q(U) cha ac e is ic. Vol age keeps d opping, and a 4.14 s, i eaches 0.94 p.u. and indica es an o e w i ing o he P( ) cha ac e is ic by he P(U) cha ac e is ic (see ∗bo om le in Figu e 3). Finally, a 4.58 s, a sa u a ion in FIGURE 9 Q(U) cha ac e is ic wi h he deadband as discussed in 2.1.2 TABLE 1Model se ings used in he case s udies Desc ip ion Value o se ing S ep size 0.02 s PF nominal 0.90 PF minimum 0.85 Q‐mode Q‐mode 1 (see 3.3.3) P nominal 10.00 kW P a ailable 1.00 p.u. P(U) τ0.40 s P( ) τ0.40 s Q(U) τ0.40 s Main sou ce ol age 414.00 V Line leng h 1.00 km Line esis ance 0.38 Ω/km Line induc ance 0.72 mH/km Two ex a loads Bo h o O e ol age se poin s [1.00 1.05 1.09 1.10 1.11] Unde ol age se poin s [1.00 0.98 0.96 0.94 0.92] Vol age e o 0.00% O e equency se poin s [50.00 50.50 51.10 50.50 50.00 50.00] Unde equency se poin s [50.00 49.80 49.50 49.00 50.00 50.00] F equency e o 0.00 Hz 432 - MENTENS ET AL. he in e e occu s and cu en is limi ed. The second pane indica es his as a di e ence be ween he calcula ed and ac ual powe ou pu . 4.2 | Case 2: o e ol age wi h o e equency Figu e 11 depic s he use o he minimum be ween P(U) and P ( ) cha ac e is ics o ol age le els o 0.94 p.u. o highe . S a ing om 4.04 s, he P(U) cha ac e is ic ou pu s less P and is he e o e de e mining he calcula ed P ou pu . A 2.00 s, o e equency occu s and P ou pu d ops acco ding o P( ) cha ac e is ic (see Figu e 7). A 4.04 s, he ol age exceeds 1.05 and ac i a es he Q(U) cha ac e is ic (see Figu e 9). No e ha case 2 ac i a es he opposi e side o he cha ac e is ic han case 1. A 6.04 s and 8.04 s, ol age eaches 1.11 p.u., and P and Q d op acco dingly o mi iga e he ol age iola ion (see Figu e 5). I also depic s he o e w i ing o he P( ) cha ac- e is ic by he P(U) cha ac e is ic (see ∗bo om le in Figu e 3). Finally, a 10.06 s, ol age is be ween he limi s—P FIGURE 10 Case 1: when bo h unde ol age and o e equency occu , he in e ac ion o he P(U) and P( ) cha ac e is ic can be deno ed. The simula ion pa ame e s a e se as de ined in Table 1 MENTENS ET AL. - 433 and Q ou pu s a e un es ic ed. This case is simila o o e - ol age wi h o e equency, as he P( ) cha ac e is ic is only ac i e be ween 2.00 s and 4.04 s. 5 | CONCLUSIONS This pape gi es a b ie o e iew o he ol age con ol me hods on LV powe g ids. The mos common suppo , ac i e and eac i e powe compensa ion using in e e s, is u he discussed. DSM is p omising bu equi es sma ap- pliances and household pa icipa ion. The e o e, i cu en ly is no a su icien solu ion. A li e a u e s udy iden i ies he p esen issues ha ol age con ol echniques a e acing. Con ol pa ame e s (such as he abili y o choose a Q(P) mode) a e o en ixed, which does no allow adequa e a ia ion when he simula ion model is used o de e mine he mos app op ia e solu ion o g id issues. The de elopmen in a isual simula ion model such as Simulink is he e o e ecommended. FIGURE 11 Case 2: when bo h o e ol age and o e equency occu , he minimum ou pu be ween P(U) and P( ) is chosen. Q ou pu is s ill con olled by he Q(U) cha ac e is ic. The simula ion pa ame e s a e se as de ined in Table 1 434 - MENTENS ET AL.