Decentralised Allocation of Generation in Autonomous Power Networks

Transcription

1 1 Decetralsed Allocato of Geerato Autoomous Power Networks J. Frut, Member, IEEE, ad W. L. Klg, Member, IEEE, ad J. M. A. Myrzk Abstract Due to much larger umbers of small geerators t wll be more complex to cotrol the balace betwee supply ad demad future systems. To deal wth ths complexty, autoomous etworks could be effectve. Autoomous etworks are aggregatos of producers ad cosumers o both physcal ad ecoomcal level ad have the capablty to cotrol complex systems wth smple rules. To demostrate ecoomc dspatch wth a autoomous etwork, ths paper descrbes the setup of a model for matchg supply ad demad wth cotrol zoes. Next, a method for dstrbuted ecoomc dspatch s corporated the model to show how allocato of geerators ca be executed a decetralsed way. Idex Terms Frequecy cotrol, Dstrbuted cotrol, Power geerato dspatch, Power system ecoomcs, Autoomous etworks. I I. INTRODUCTION the Europea system, most coutres are sychroously tercoected the Uo for the Coordato of Trasmsso of Electrcty (UCTE). Ths meas that the frequecy these coutres s always detcal ( steady state). The reasos for ths tercoecto are the creased relablty ad the possblty to trade electrcty. Curretly about 5 mllo people are suppled va ths grd whch together have a maxmum load of over 4 GW ad a yearly cosumpto of over 25 TWh [1]. Most of the electrcty the grd s geerated wth sychroous geerators. The frequecy of the grd s created by these rotatg maches. As log as supply ad demad of electrcty are balace, the frequecy of the grd wll rema omal. owever, ay mbalace betwee supply ad demad wll be compesated by a chage the stored ketc eergy of the rotatg maches thus leadg to a frequecy devato. Frequecy devatos should rema wth certa lmts to avod blackouts or damaged equpmet. To esure ths, several cotrol strateges have bee corporated to the system. Due to the tegrato of dstrbuted geerators, whch are less predctable ad poorly cotrollable, future systems t wll be more complex to cotrol the balace betwee supply ad demad [2], [3]. Oe of the solutos s to set up so-called autoomously operated etworks tercoected wth the future grd [4]. Autoomous etworks are aggregatos of producers ad cosumers of electrcty o both physcal ad ecoomcal level. To the outsde world a autoomous etwork behaves as a sgle etty whch s capable of tradg eergy. More detals o the cocept of autoomous etworks s gve [5] where t s stated that autoomous etworks are etworks whch rema part of the total grd but for the rest prcple are fully self cotrolled. Each autoomous etwork esures ts ow balace betwee supply, demad ad mport or export terally. Based o the margal costs for dfferet servces, geerators ad loads wth the autoomous etwork are cotrolled ether autoomously, whle esurg the requremets for trade ad takg costrats to accout. To evaluate the effect of dstrbuted geerators ad autoomous etworks o the balace the system, a smulato model was created. Ths paper descrbes the setup of ths model by explag all ts compoets detal. Frst a overvew of the complete model s gve secto II. Secto III descrbes the dvdual compoets. The model s verfed wth measuremet data. Some results are show secto IV. Autoomous etworks should be cotrolled terally such that they provde ad acllary servces at the lowest costs. Secto V gves two methods to cotrol uts autoomous etworks both a cetralsed ad a decetralsed way. It s show that cost mmsato by allocato of geerators s possble wthout cetralsed aggregato. Coclusos of the study are gve secto VI. II. MODEL DESCRIPTION The model cosders the dyamc behavour of a sgle cotrol zoe wth a larger sychroous grd. Wth oe cotrol zoe, dfferet producto facltes are preset. The other cotrol zoes are modelled as oe sgle block wth erta. The full model s dsplayed fgure 1. Fg. 1. Block scheme of the frequecy stablty model Ths work was supported by the Dutch Mstry of Ecoomc Affars as a EOS-project /9/$ IEEE

2 2 Electrcty s produced by the producto block. The load the cotrol zoe s subtracted from ths producto. For smplcty t s assumed that the scheduled cross-border exchage s equal to zero. Thus, the dfferece betwee load ad supply s the mbalace of the modelled cotrol zoe. Imbalace wth the modelled cotrol zoe causes a frequecy devato the whole etwork, for whch the total erta s mportat. Ths frequecy devato actvates prmary cotrol. The combato of cross-border exchage ad the frequecy devato actvates secodary cotrol. Both cotrollers am to stop the frequecy devato ad to brg back the frequecy to ts omal value. I the ext subsectos the dvdual blocks are explaed detal. III. BLOCK DESCRIPTION The model, as explaed secto II cossts of several parts. A. Producto The producto block for the cotrol cosdered here cossts of ether coal or gas fred producto plats. The basc model for producto s derved from Roffel ad de Boer [6] who suggest usg a fast ad a slow part to model plats. Accordg to [6] the trasfer fucto of a plat ca be approxmated by (1), (2) ad (3). fast s s K s 1 s 1 e s slow s s 1 fast L slow (1) (2) s s s (3) effect. Accordg to UCTE [7] ths self-regulatg effect s betwee 1% ad 2% per ertz. P out / P setpot P out / P setpot Gas fred plat step respose Coal fred plat step respose fast slow total fast slow total Fg. 2. Step resposes of gas (upper fgure) ad coal (lower fgure) fred plats C. Grd erta Imbalace causes a frequecy devato [8]. The speed at whch a certa mbalace creates ths frequecy devato depeds o the total erta of the tercoected grd [7]. Furthermore, the frequecy devato s flueced by the selfregulatg effect of all other loads (outsde of the cotrol zoe uder study), as dcated before. The erta block s therefore modelled as follows (Fg. 3). 1 s The costats these equatos should have the followg values (Table I) accordg to [6]. TABLE I TIME CONSTANTS D P GRID Fg. 3. Ierta block for a tercoected grd f L K Gas 25 s 12.5 s s 17 s Coal 85 s 1. s s 6 s Usg the data from table I, step resposes for coal ad gas fred plats ca be derved (Fg. 2). The step respose cossts of a fast ad slow reactg part. The fast secto s the result of opeg the steam valves whle the slow secto s due to the creased fuel put. For the step respose t s assumed that the plat s already beg operated close to ts omal operato pot ad the chage set pot for the step respose s small compared to the total capacty of the ut. B. Load The load the model s desged as a costat whch wll be flueced by the frequecy. Because the load partly cossts of rotatg maches, that release ketc eergy as ther rotatg speed decreases, the load has a self-regulatg The mbalace dampg effect depeds o the curret load the etwork (P GRID ) ad the self-regulatg effect (D). I the model the varables P GRID ad D have values of 3GW ad 2% respectvely. The erta of the UCTE grd was determed based o frequecy measuremets from TeeT TSO B.V. for whch t was kow what the mbalace the etwork was. The erta of the grd s defed by (4). P (4) f ere P s the mbalace ad f s the frequecy devato whch s measured some secods after the occurrece of the mbalace. s called the etwork frequecy characterstc. Accordg to a statstcal aalyss the value of s betwee 19 MW/z ad 47 MW/z wth a mea value of 26 MW/z. Accordg to UCTE [7] ths value

3 3 should have a mmum of 18 MW/z. I fgure 4, several stuatos have bee aalysed leadg to values of 27 MW/z, 38 MW/z ad 29 MW/z. A replacemet of large sychroous geerators by dstrbuted geerato, whch s ofte based o verters wth electrocs, could result a decrease of erta [9]. As a cosequece, sudde mbalaces wll result larger frequecy devatos. f [z] Frequecy resposes the UCTE for 15MW faults 27 MW/z 38 MW/z 29 MW/z Fg. 4. Three 15MW loss evets the UCTE grd wth dfferet values for. D. Prmary cotrol Prmary cotrol has the am to cotuously mata the balace betwee supply ad demad. The prmary cotroller creases the set pot of a plat proportoally wth the frequecy devato. Prmary cotrollers work wth a droop fucto whch s defed wth (5). f / fom s (5) P/ P om ere f, f om, P ad P om are the frequecy devato, the omal frequecy, the chage set pot ad the omal set pot respectvely. The droop defes the relatve chage frequecy devato that results a specfc relatve chage producto. A smaller value for the droop meas that a prmary cotroller reacts more to frequecy devatos. Accordg to UCTE [7], the droop for each plat should be set to 1%. owever, practce partes do sometmes choose to set the droop o a lower value thus creasg ther share frequecy cotrol. The goal of prmary cotrol s to stop the frequecy devato ad to hold the frequecy at a so-called quas-steady-state value. E. Secodary cotrol After prmary cotrol has stablsed the frequecy devato, secodary cotrol s actvated to restore the frequecy from the quas-steady-state value to ts omal value. The secodary cotroller s slower tha the prmary cotroller ad t s oly actve the cotrol zoe where the mbalace s caused. Therefore secodary cotrol s ot oly based o frequecy measuremet but t also takes the uscheduled (beg the dfferece betwee the actual ad the scheduled) cross-border flows to accout. A secodary cotroller uses a tegral cotroller to regulate the area cotrol error (ACE) to zero. The ACE s defed (6). ACE P P K f (6) meas sched ere P meas s the actual cross-border flow, P sched s the scheduled cross-border flow. K s a costat ( MW/z) whch s defed for each cotrol zoe based o ts characterstcs ad f s the frequecy devato. Curretly the trasmsso system operators calculate the ACE. Ths ACE s the processed (smootheed) to a processed area cotrol error. A proportoal tegral cotroller coverts the processed area cotrol error to a total delta sgal, whch s the splt to several delta sgals, usg selecto crtera whch may be based o market mechasms. The delta sgals represet the chage set pot that each utlty should apply to cotrbute to secodary cotrol. Based o dscussos wth experts of the trasmsso system operator the Netherlads t was decded to clude a delay betwee the calculato of the delta sgal ad chagg the set pot to have a more realstc respose from the model. Ths tme correspods to the tme whch partes take to respod to a delta sgal. IV. VERIFICATION OF TE MODEL The results of the model ca be verfed usg frequecy measuremets. For each seres of measuremets, whch a frequecy devato occurs, t was kow what caused ths frequecy devato. The model ca be used to smulate ths evet ad the system varables ca be adjusted such that the output of the model fts wth the measuremets. For a umber of evets the results of the model are gve. I fgures 5a, 5b ad 5c for three dfferet evets the measuremets are show ad the smulatos wth the model are gve. Frequecy [z] Frequecy [z] Measuremet Data Smulato Data (a) (b) Measuremet Data Smulato Data

4 4 Frequecy [z] Measuremet Data Smulato Data (c) Fg. 5. Frequecy resposes for three dfferet evets (a, b ad c). The grey le shows measuremet data whle the black le shows the respose of the model. The faults smulated are two 15MW ad oe 13MW falures respectvely that took place the UCTE etwork 25. It ca be cocluded that evets ca be smulated wth ths model accurately. I fgure 5b t s clear that the secodary cotrol acto s delayed by market players as metoed before secto III.E. The delay was oly cluded example b sce from measuremets t was cocluded that market players ths case took more tme (approx. 35 sec.) to respod to the delta sgal. V. ECONOMIC DISPATC As descrbed the troducto of ths paper, future systems wll corporate larger shares of less predctable ad poorly cotrollable dstrbuted geerato. Autoomous etworks mght eable the troducto of dstrbuted geerato. I ths secto, the cocept of autoomous etworks wll be explaed, after whch a method for ecoomc dspatch wth a sgle autoomous etwork s dscussed usg the dyamc model explaed before. A. Autoomous etworks Accordg to Jokc [4] autoomous etworks are aggregatos of producers ad cosumers o both physcal ad ecoomcal level a relatvely small area compared to the total grd. Towards the outsde world autoomous etworks behave as sgle ettes wth a certa et producto or cosumpto. Each autoomous etwork mght be operated by a market aget whch s capable of tradg both eergy o markets ad acllary servces (for balace maagemet, cogesto maagemet, etc.) o specfc markets. To be able to do ths, each market aget must be aware of the avalable capactes for both geerato ad acllary servces wth the autoomous etwork. Jokc [4] descrbes a mechasm based o odal prces to cotrol a system wth multple autoomous etworks. Power flow betwee autoomous etworks s based o ther odal prces. These odal prces deped o the costs to produce electrcal eergy sde the autoomous etwork ad cogesto of coectos betwee the autoomous etworks. Isde the autoomous etwork, dfferet geerators ad loads are operatoal. Depedg o the scheduled mport, export ad load the autoomous etwork, a allocato of geerators wll be made. Ths allocato s usually based o margal costs. Autoomous etworks etal a market aget whch decdes upo trade of eergy ad acllary servces wth other autoomous etworks. It s capable of dog ths sce t has formato o the costs of the dfferet servces (eergy ad acllary servces). The teral fuctog of a autoomous etwork s modelled usg the model explaed before. It s assumed that a autoomous etwork has multple producers ad the plat block fgure 1 s replaced by multple plats parallel. Furthermore, for smplcty, t s assumed that the autoomous etwork s ot tradg ay eergy wth other autoomous etworks, thus o beforehad supply ad demad wth the etwork must be balace ad ts area cotrol error must be cotrolled to zero. I order to keep ths balace, the autoomous etwork has cotrol avalable for prmary ad secodary cotrol. B. Dspatch by aggregato Isde a sgle autoomous etwork a optmal selecto of resources must be made to supply the requred amout of ad the acllary servces a optmal way. Ths optmsato ca ether be doe by the market aget va dspatch or locally all uts of the autoomous etwork. If the selecto of teral resources s to be made by the autoomous market aget, the aget must have access to dvdual formato of ts producers ad cosumers. The covetoal way to optmse the allocato of producers s by aggregatg ther dvdual supply curves per ut of tme to a aggregated curve. The dvdual shares to producto for the ext perod of tme ca the be derved from each dvdual curve ad the aggregated curve. Ths s explaed fgure 6. Margal Costs P* Qa a Qb b Qt total Quatty Fg. 6. Ecoomc dspatch by aggregato. Curves a ad b are aggregated to total. The dvdual productos of A ad B are Qa ad Qb. Suppose two supply curves a ad b for two producers A ad B respectvely. The aggregated curve s gve by the total. For smplcty the demad s supposed to be elastc ad equal to Qt. The correspodg margal costs are P*. At the tersecto pots of P* ad the curves a ad b, the quattes Qa ad Qb for producers A ad B ca be foud. The ma advatage of ths dspatch techque s that t ca hadle all dfferet types of supply curves. The ma dsadvatage of ths techque s that the dspatch cetre (or market aget) eeds to have all supply curves to be able to defe the aggregated supply curve. Oe cocluso from fgure 6 s that the dvdual margal costs (MC) for a ad b are detcal the optmum. Ths s prove by Dey [1] ad Brabadere [11] ad ca be

5 5 explaed by the fact that f the producers would ot have equal margal costs, t would have bee more effcet to have the cheaper producer produce more ad the expesve producer produce less. Equato (7) gves ths mmsato problem wth the costrats (8) ad (9). m Q Q 1 Subject to: Q MC q dq (7) (8) Q Demad (9) 1 Accordg to what s stated above t results (1) ad (11). If: Q * The: arg m Q Q 1 MC qdq * * * (1) MC Q MC Q MC Q (11) I (7) to (11) MC (q) are the cremetal cost fuctos for the dfferet producers as a fucto of quatty q, Q * are the optmal set pots for the producers ad Demad s the total amout to be produced. The optmsato has to mmse total costs the system ad the costrats state that the producto of all supplers should be oegatve ad that the total producto should always be equal to the demad. For most cases ths optmsato problem ca be solved aalytcally showg that the optmum s that pot where the margal costs are equal for all producers. C. Dstrbuted dspatch The assumpto that total costs are mmal at that pot where all cremetal costs are equal ca be used to cotrol dfferet uts wth a autoomous etwork. By calculatg the average margal costs for all uts wth the etwork ad comparg ths wth ther dvdual margal costs t ca be determed whether a producer should ether crease or decrease ts producto. Whe all producers produce at the same margal costs ther dvdual margal costs wll be equal to the average margal costs ad optmal dspatch has bee acheved. Locally, oly formato o the ow margal costs ad the estmated average margal costs are requred. Therefore dfferet producers the model of ths research are supposed to be equpped wth a margal cost fucto whch gves the margal costs as a cotuous ad mootocally creasg fucto of ther output up to ts maxmum capacty. Ths value s set to a cotroller whch cotuously compares t wth the estmated average margal costs the etwork ad determes whether to crease or decrease producto. Ths acto s modelled as a tegral fucto. The cotroller receves the value for estmated average margal costs from ay other cotroller the etwork. The cotroller also derves the ew estmated average margal costs by takg the mea of the prevous estmated average ad ts curret local margal costs ad seds t to the ext cotroller for aother producer. The order of commucato betwee cotrollers ca ether be based o geographcal locato or ay radom selecto. The tal set pot of the estmated average margal costs, whch the frst cotroller uses, ca have ay value betwee the possble mmum ad maxmum margal costs. Ths value wll quckly coverge to the actual estmated average costs value. The structure s show fgure 7. The multple plats ad cotrollers ths fgure provde puts for the plat block fgure 1. setpot cotrol A average costs cotrol B average costs cotrol C average costs sum setpot margal costs setpot margal costs setpot plat A plat B plat C margal costs Fg. 7. Cotrol structure for dstrbuted dspatch usg margal costs, the average margal costs ad the sum of the set pots. Each producer has ts ow cotroller whch receves the total set pot (.e. total demad). The cotrollers cotuously determe the dvdual set pot for all dvdual plats. To esure that the ecoomc dspatch cotroller does ot fluece the balace betwee supply ad demad, also the sum of set pots eed to be cotrolled a decetralsed way. I the cotrol structure dsplayed fgure 7, the values for the estmated average margal costs ad the total set pot are set to the ext cotroller thus creatg a loop. owever a cotrol structure whch ths data s set to a radomly selected other cotroller also proves to fucto. Ths chage would actually crease relablty sce a fault commucato betwee two cotrollers would ot terrupt the system s operato. After all, commucato wth other cotrollers would cotue to exst. owever, ths also creases the complexty of the system sce more commucato lks eed to be created. More about ths has bee wrtte by Brabadere [11] ad Vathourout [12]. The complete ecoomc dspatch cotrol loop s outsde the prmary ad secodary cotrol loops ad s therefore ot

6 6 fluecg balace maagemet. owever a detcal cotrol structure ca be used to splt up the total delta sgal for secodary cotrol to dfferet set pot for dfferet producers. D. Results of the dspatch cotroller A smulato was performed cludg the ecoomc dspatch cotrollers. Durg ths smulato part of the producto capacty s lost at t= sec. Sce the margal costs are a fucto of the output of the rug uts, a loss of producto wll lead to a crease of the costs. The fgures 8a, 8b, 8c ad 8d show the producto of three producers A, B ad C, the frequecy of the grd, the real-tme margal costs for all three producers ad the delta-sgal to A, B ad C. Power [MW] Frequecy [z] Power [MW] 15 1 Producto 5 Producer A Producer B Producer C (a) Frequecy respose Margal Costs [] (b) Margal Costs.5 Producer A Producer B Producer C (c) -sgal 5 Producer A Producer B Producer C (d) Fg. 8. Results of the model wth the decetralsed ecoomcal dspatch Before the loss of producto all three producers produce at the same margal costs. At t= sec. there s loss of producto for producer B ad all margal costs wll devate before covergg aga a ew ecoomc optmum. Due to the loss of producto all costs are hgher at the secod optmum. It ca be see that the frequecy s restored a ormal way also. I ths model trasport capacty lmtatos ad trasmsso losses are ot take to accout. owever, these ca be cluded by alterg the margal cost fuctos, thus fluecg the ed results. VI. CONCLUSIONS I ths paper sght formato was gve o a model to smulate the frequecy respose of a sychroously tercoected electrcty grd. The dfferet (.e. prmary ad secodary) cotrol mechasms ca be evaluated usg ths model. The model was used to dscuss ecoomc dspatch autoomous etworks. Although dspatch s usually performed o a cetral level per ut of tme by utltes or market agets that eed full sght the supply curves for each ut to perform ths acto, t s also possble to perform a dstrbuted dspatch of uts sde autoomous etworks whch are cosdered to be the buldg blocks of future systems wth hgher peetrato of dstrbuted geerato. It s show that, by comparg the dvdual margal costs wth the estmated average margal costs the etwork, a cotrol structure wth dstrbuted dspatch does ot requre full sght o all supply curves of all plats to cotuously acheve ecoomcally optmal dspatch. Oly the mometaeous margal costs of a sgle plat ad a estmato of the average margal costs are of terest for the optmsato. Further research wll clude the tegrato of block bddgs ad start-up costs of plats. VII. ACKNOWLEDGMENT Ths artcle s part of the project Regelduurzaam, whch s a EOS-project (Eergy Research Subsdy Project) fuded by the Dutch Mstry of Ecoomc Affars. The authors ackowledge TeeT TSO B.V. for the provso of frequecy measuremet data. VIII. REFERENCES [1] Uo for the co-ordato of trasmsso of electrcty, Memo 27, UCTE, Belgum, [Ole]. Avalable: [2] J. J. Meeuwse, ad J. M. A. Myrzk, ad G. P. J. Verbog, ad W. L. Klg, ad J.. Blom, Electrcty etworks of the future: varous roads to a sustaable eergy system, Cgré sesso 28, Pars, Frace, 28. [3] Mstry of Ecoomc Affars, Eergerapport 28, The Netherlads, [Ole]. Avalable: [4] A. Jokc, Prce-based optmal cotrol of electrcal systems, Ph.D. dssertato, Dept. Elec. Eg., Edhove Uv. of Techology, 27. [5] F. Provoost, ad A. Ishcheko, ad A. Jokc, ad J. M. A. Myrzk, ad W. L. Klg, Self cotrollg autoomous operatg etworks, CIRED 18 th Iteratoal Coferece o Electrcty Dstrbuto, Tur, Italy, 25. [6] B. Roffel, ad W. W. de Boer, Aalyss of ad frequecy cotrol requremets vew of creased decetralsed producto ad market lberalzato, Cotrol Egeerg Practce, vol. 11, o. 4, pp , Apr. 23.

7 7 [7] Uo for the co-ordato of trasmsso of electrcty, Operatoal hadbook, UCTE, Belgum, [Ole]. Avalable: [8] P. Kudur, Power system stablty ad cotrol, McGraw-ll Ic., 1994, pp [9] B.C. Ummels, M. Gbescu, W.L. Klg, ad G.C. Paap, Developmet of a smulato model for secodary cotrol performace assessmet wth sgfcat wd a market evromet, 16 th Power Systems Computatos Coferece, Glasgow, Scotlad, 28. [1] F.I. Dey, ad D.E. Dsmukes, Power System Operatos ad Electrcty Markets, vol. I. Boca Rato: CRC Press, 22, chapter 9. [11] K. De Brabadere, Voltage ad frequecy droop cotrol low voltage grds by dstrbuted geerators wth verter frot-ed, Ph.D. dssertato, Dept. Elec. Eg., Leuve Uv. of Techology, 26. [12] K. Vathourout, A sematc overlay etwork based robust datafrastructure, appled to the electrc grd, Ph.D. dssertato, Dept. Elec. Eg., Leuve Uv. of Techology, 26. IX. BIOGRAPIES Jasper Frut was bor 's-ertogebosch e receved hs B. degree electrcal egeerg 23 from the Uversty of Professoal Educato 's-ertogebosch. I 26 he receved hs M.Sc. degree sustaable eergy techology from Edhove Uversty of Techology. For hs graduato projects he worked wth Kema N.V. ad Teet TSO bv (Dutch Trasmsso System Operator) respectvely. Curretly he s a PhD the EOS (Eergy Research Subsdy) project 'Regelduurzaam' for Edhove Uversty of Techology. s research focuses o curret ad future deploymet, legslato ad orgasato of cotrol for balace maagemet. Wl L. Klg receved hs M.Sc. degree electrcal egeerg from the Techcal Uversty of Edhove Sce 1993 he has bee a (parttme) professor the Departmet of Electrcal Egeerg at Delft Uversty of Techology, the feld of Power Systems Egeerg. I addto, he s wth the Trasmsso Operatos departmet of TeeT (the Dutch Trasmsso System Operator). Sce 2, he has also bee a part-tme professor at the Techcal Uversty of Edhove. s area of terest s related to plag ad operatos of systems. Prof. Klg s volved scetfc orgasatos such as CIGRE ad the IEEE. As Netherlads' represetatve, he s a member of CIGRE Study Commttee C6 Dstrbuto Systems ad Dspersed Geerato, ad the Admstratve Coucl of CIGRE. Johaa M. A. Myrzk was bor Darmstadt, Germay She receved her MSc. Electrcal Egeerg from the Darmstadt Uversty of Techology, Germay From 1993 to 1995 she worked as a researcher at the Isttute for Solar Eergy Supply Techology (ISET e.v.) Kassel, Germay. I 1995 Mrs. Myrzk joed to the Kassel Uversty, where she fshed her PhD thess the feld of solar verter topologes 2. Sce 2, she s wth the Edhove Uversty of Techology, the Netherlads. I 22, Mrs. Myrzk became a assstat professor the feld of dstrbuted geerato. er felds of terests are: electrocs, reewable eergy, dstrbuted geerato, electrcal supply.