energes Artcle Island DC Mcrogrd Herarchcal Coordnated Mult-Mode Control Strategy Zhongbn Zhao 1, Jng Zhang 1, *, Yu He 1, * and Yng Zhang 2 1 School of Electrcal Engneerng, Guzhou Unversty, Guyang 550025, Chna 2 Guzhou Power Grd Company, Guyang 550001, Chna * Correspondence: zhangjng@gzu.edu.cn (J.Z.); yhe7@gzu.edu.cn (Y.H.) Receved: 2 July 2019; Accepted: 1 August 2019; Publshed: 5 August 2019 Abstract: As renewable energy sources connectng to power systems contnue to mprove and new-type loads, such as electrc vehcles, grow rapdly, drect current (DC) mcrogrds are attractng great attenton n dstrbuton networks. In order to satsfy the voltage stablty requrements of sland DC mcrogrds, the problem of naccurate load power dspatch caused by lne resstance must be solved and the defects of centralzed communcaton and control must be overcome. A herarchcal, coordnated, multple-mode control strategy based on the swtch of dfferent operaton modes s proposed n ths paper and a three-layer control structure s desgned for the control strategy. Based on conventonal droop control, a current-sharng layer and a mult-mode swtchng layer are used to ensure the stable operaton of the DC mcrogrd. Accurate load power dspatch s satsfed usng a dfference dscrete consensus algorthm. Furthermore, vrtual bus voltage nformaton s appled to guarantee smooth swtchng between varous modes, whch safeguards voltage stablty. Smulaton verfcaton s carred out for the proposed control strategy by power systems computer aded desgn/electromagnetc transents ncludng DC (PSCAD/EMTDC). The results ndcate that the proposed control strategy guarantees the voltage stablty of sland DC mcrogrds and accurate load power dspatch under dfferent operaton modes. Keywords: drect current (DC) mcrogrd; mult-mode smooth swtch; droop control; dfference dscrete consensus algorthm; herarchcal coordnated control 1. Introducton The mcrogrd has played an mportant role n provdng relable access to dstrbuted generaton n recent years [1 3]. There are three types of mcrogrd, namely the DC mcrogrd, the alternatng current (AC) mcrogrd, and the alternatng current/drect current (AC/DC) hybrd mcrogrd, defned n terms of the dfference n bus voltage forms [4]. In comparson wth AC mcrogrds, the advantages of DC mcrogrds, such as effcent energy converson, low loss and wthout converson of mult-level converters and wthout consderng reactve power loss and frequency, attract constant attenton [5,6]. Meanwhle, a large number of flexble technologes and peces of equpment based on power electroncs are appled to the dstrbuton network. It s crucal to understand the coordnated control of each unt of a DC mcrogrd n order to recognze reasonable load power dspatch and stable voltage [7,8]. The coordnated control strateges of DC mcrogrds manly nclude centralzed control, dstrbuted control, and decentralzed control. Under the centralzed control strategy [9,10], the power balance of varous unts n the DC mcrogrd s realzed wth the help of central controller. A bdrectonal and hgh-bandwdth communcaton lne s requred to establsh a connecton between the central controller and each unt. The mcrogrd s hghly dependent on the central controller and ths may lead to communcaton block. Decentralzed control [11,12] has no communcaton requrement and each agent completes ts control objectve ndependently. However, owng to the lack of exchange of Energes 2019, 12, 3012; do:10.3390/en12153012 www.mdp.com/journal/energes
Energes 2019, 12, 3012 2 of 20 necessary nformaton, the overall control objectve cannot be completed. The maxmum advantage of dstrbuted control [13 15] s that t has no need to rely on the central controller to acheve pont-to-pont nformaton exchange. Wth a sparse communcaton network, each unt can complete control n terms of ts own nformaton and that of the adjacent unt. Ths may overcome the dsadvantage of centralzed control, whle also achevng the objectve of overall control. Even when some unts break down or the communcaton structure changes, stable operaton can stll be guaranteed. In a parallel-operated mcrogrd, current-sharng s acheved by means of dstrbuted droop control, so as to meet the plug-and-play requrement of system. However, consderng that system load dspatch precson s affected by lne parameters, power dspatch errors may occur under the tradtonal droop control strategy and, consequently, system stablty may be affected [16,17]. To understand power coordnaton control of each unt n a system and guarantee bus voltage stablty, a DC mcrogrd real-tme power coordnated strategy was proposed [18]. The system was desgned n mult-mode operaton n terms of common bus voltage fluctuaton. In ths way, the DC mcrogrd can be operated stably. However, the power flow may cause an nequalty of bus voltage at dfferent nodes due to the nfluence of lne resstance. In addton, the nfluence of lne resstance on load power dspatch was not consdered, whch may have caused an overload of some energy storage unts and even system breakdown. As a major control mode of DC mcrogrd operaton, droop control s usually adopted n parallel connecton wth the mult-converter n a DC mcrogrd. Researchers [19] put forward a coordnated control strategy for an autonomous DC mcrogrd wth a dynamc load power dspatch. The mcrogrd coordnately operated under dfferent workng modes n terms of adaptve droop control. Nevertheless, t faled to consder the nfluence of factors, such as the nconformty of outlet parameters and the nternal resstance of the converter on load power dspatch. Furthermore, the precson of the mode swtch may have been reduced due to lne resstance. Researchers [20] put forward a decentralzed control method for DC mcrogrds wth mproved current-sharng accuracy. However, the charge dscharge capacty of the energy storage unt was not consdered, whch can lead to a power mbalance n the system and consequent system breakdown. Researchers [21] proposed an accurate power dspatch and zero steady-state error voltage-control strategy based on adaptve droop characterstcs. Ths overcame the defects of centralzed communcaton and the system dsorders caused by communcaton breakdown, achevng bus voltage stablty and accurate load power sharng. However, the dstrbuted generaton capacty may not have been fully utlzed and the nfluence of bus pecewse resstance on load power dspatch was not consdered. In order to solve the problems mentoned above, a herarchcal, coordnated control strategy for an sland DC mcrogrd based on mult-mode smooth swtch s proposed n ths paper. It ams at fully utlzng dstrbuted generaton and guaranteeng stable operaton of the system. A three-layered control structure s desgned. Based on conventonal droop control, a current-sharng layer control for the purpose of accurate load power dspatch and a mult-mode smooth swtch layer control amng at guaranteeng voltage stablty are proposed. By means of real-tme montorng of vrtual bus voltage nformaton, the smooth swtch among varous modes of each unt s completed. At the same tme, each unt conducts nformaton among adjacent unts under dfferent operaton modes. Utlzng a dfference dscrete consensus algorthm (DDCA), accurate load power dspatch and stable operaton of the DC mcrogrd are guaranteed. Ths paper ntroduces the DC mcrogrd mode n Secton 2 and puts forward sland DC mcrogrd mult-mode. Furthermore, t presents the herarchcal, coordnated control strategy based on mult-mode smooth swtch. Fnally, t utlzes PSCAD/EMTDC to verfy the effectveness of the proposed control strategy. 2. DC Mcrogrd Structure The structure of the sland DC mcrogrd s shown n Fgure 1. The sland DC mcrogrd contans photovoltac arrays, energy storage unts, common DC loads, and converters.
Energes 2018, 2019, 11, 12, x 3012 FOR PEER REVIEW 3 of 3 of 2120 Energes 2018, 11, x FOR PEER REVIEW 3 of 21 ESS ESS DC bus DC bus B-DC/DC B-DC/DC PESS PESS B-DC/DC B-DC/DC DC-DC DC-DC Pload Pload PDG PDG DC/DC DC/DC Common DC Common load DC load Fgure 1. Structure of DC mcrogrd. Fgure 1. 1. Structure of ofthe thesland DC mcrogrd. (1) (): nto the DC bus va a (1) (1) Photovoltac Photovoltac array array (): (): Integrated Integrated nto nto the the DC DC mcrogrd mcrogrd bus bus va va a a one-way one-way DC/DC DC/DC converter. converter. the to fully usually usually adopts adopts the the maxmum maxmum power power pont pont trackng trackng (MPPT) (MPPT) mode mode to to fully fully utlze utlze energy. energy. (2) (ESS): The (2) (2) Energy Energystorage storagesystem system (ESS): (ESS): The Theenergy energystorage storagesystem systemutlzes utlzesmultple multplegroup groupbattery batteryenergy energy () to and and ths the storage storage () () to tomeet meetgeneraton generatonand andload loadfluctuaton fluctuatonand andntegrates ntegratesths thswth wththe thedc DCmcrogrd bus a to the of bus busva vaa two-way two-waydc/dc DC/DCconverter converterto toadjust adjustthe thepower powerbalance balanceof ofthe thesystem. (3) Common DC DC load can be ntegrated nto DC mcrogrd bus. In (3) Common DC load: The The common common DC DC load load can can be ntegrated be ntegrated nto the nto DCthe mcrogrd DC mcrogrd bus. In addton, bus. In addton, s possble t s possble to carry out to carry constant out constant voltage control voltage for control mportant for mportant loads through loads a through double closed-loop a double addton, t s possble to carry out constant voltage control for mportant loads through a double closed-loop DC/DC control DC/DC system. control In ths system. way, In theths voltage way, fluctuaton the voltage sfluctuaton reduced and s power-supply reduced and powersupply s mproved. stablty s mproved. closed-loop DC/DC control system. In ths way, the voltage fluctuaton s reduced and stablty powersupply stablty s mproved. (4) Drect current/drect current converter (DC/DC): Ths s utlzed to acheve connectons between (4) Drect current/drect current converter (DC/DC): Ths s utlzed to acheve connectons between varous generaton unts n n the grd and mportant loads, whch facltates power exchange of varous generaton unts n the grd and mportant loads, whch facltates power exchange of varous unts. varous unts. 3. 3. Mult-Modeof of IslandDC DC 3. Mult-Mode of Island DC Mcrogrd Mcrogrd The The slanddc DC mcrogrd operatons s dvdednto ntothree three modesn nths ths paper, as as ndcatedn The sland DC mcrogrd operaton s dvded nto three modes n ths paper, as ndcated n n Fgure2. 2. It ams It ams at fully at fully utlzng utlzng photovoltac photovoltac energy energy and and safeguardng safeguardng the power the power balance balance of the of - Fgure 2. It ams at fully utlzng photovoltac energy and safeguardng the power balance of the the - load load n the nsland the sland DC mcrogrd. load n the sland DC DC mcrogrd. mcrogrd. Mode 1 Mode 1 Droop control Droop control Mode 2 Droop Mode control 2 Droop control Mode 3 Load sheddng Mode 3 Load sheddng Fgure 2. Mult-mode of DC mcrogrd. Fgure 2. Mult-mode of DC mcrogrd. (1) Mode 1: utlzes MPPT control to fully use the photovoltac energy and mantan a power (1) Mode 1: utlzes MPPT control to fully use the photovoltac energy and mantan a power balance n the system wth the help of. The power relatonshp between photovoltac energy balance n the system wth the help of. The power relatonshp between photovoltac energy and storage load n the system at ths pont s ndcated by the followng formula: and storage load n the system at ths pont s ndcated by the followng formula:
Energes 2019, 12, 3012 4 of 20 (1) Mode 1: utlzes MPPT control to fully use the photovoltac energy and mantan a power balance n the system wth the help of. The power relatonshp between photovoltac energy and storage load n the system at ths pont s ndcated by the followng formula: N M P + =1 j=1 P MPPT.j = P sum load + P L, (1) where P ers to the developed power of, P MPPT ndcates the maxmum power pont.j trackng power of j, P sum load represents the common DC overall load of the system, and P L ndcates the power consumed by lne resstance. (2) Mode 2: In case of the power requred by the system exceedng safe output capacty wth excess power, the system power balance s guaranteed by reducng output power. At ths pont, the system power satsfes the followng formula: N =1 P max + M j=1 P.j = P sum load + P L, (2) where P max ndcates the maxmum safe output power of storage. (3) Mode 3: When the bus voltage plummets due to the power vacancy of the system, t s necessary to carry out load-sheddng control to guarantee the power supply qualty of mportant loads. At ths tme, the system power satsfes the followng formula: N =1 P max + M where P load ndcates the resdual load after load sheddng. j=1 P MPPT.j = P load + P L, (3) 4. Herarchcal, Coordnated Control Strategy Based on Mult-Mode Smooth Swtch of an Island DC Mcrogrd When the mcrogrd s affected by the lne resstance, tradtonal droop control cannot acheve precse load power dspatch. In addton, consderng that lne resstance s hard to measure precsely and the lne current s constantly changng, t s dffcult to fnd the precse value of P L. Theore, t s hard to acheve accurate mode swtchng n terms of system power fluctuaton, as mentoned n Secton 3. In order to solve the problem, a herarchal, coordnated mult-mode control strategy for sland DC mcrogrds s put forward n ths paper, as ndcated n Fgure 3. Ths strategy fully consders the maxmum charge dscharge capacty of, as well as the fluctuaton of and load. In Secton 4.1, the nfluence of lne resstance on precse load power dspatch s analyzed on the bass of tradtonal droop control. To address the nfluence of lne resstance, current-sharng layer control s ntroduced n Secton 4.2, where the dfference dscrete consstency algorthm s llustrated n detal. The DDCA mplements real-tme trackng DC/DC converter output voltage and teratvely converges to rapdly average the values. The average value s utlzed as the vrtual bus voltage, so as to provde a unfed erence nput for each DC/DC converter, thus achevng current-sharng control. In Secton 4.3, vrtual bus voltage nformaton s used as a crteron for mult-mode smooth swtchng of the system. A smooth swtch between dfferent modes can be acheved wth voltage nformaton only usng real-tme montorng of voltage fluctuaton. Wth the help of the strategy mentoned above, voltage stablty of the system and precse load power dspatch can be guaranteed. Flow dagrams of sland DC mcrogrd current-sharng based on Fgure 3 and voltage stablty control strategy are shown n Secton 4.2.
Energes 2019, 12, 3012 5 of 20 Energes Energes 2018, 2018, 11, 11, x FOR FOR PEER PEER REVIEW REVIEW 5 of of 21 21 Mode swtch layer Mode swtch layer U < avg avg U Voltage judgment Voltage judgment U < U < U 1H avg 1H avg U < U < U avg avg Current sharng layer Current sharng layer Adjacent communcaton Adjacent communcaton Voltage nformaton Voltage nformaton collecton collecton U. U. DDCA DDCA U U --Load --Load normal normal operaton operaton Load sheddng Load sheddng I Load sheddng Load sheddng U 1H U U 1H U U mn max I mn 0 max I 0 MPPT I MPPT P Ppv I Ppv - droop control - droop control - - droop droop control control K K Equpment layer Equpment layer I.1 I.1 - I - 1/K + 1/K + - - U I I I I I.N I.N Current PI Current PI controller controller D R1 2 R1 2 PWM PWM R 2 R 2 RN 2 RN 2 Load Fgure 3. 3. The The The herarchcal, herarchcal, coordnated coordnated control control strategy strategy of of an an ofsland sland DC DC mcrogrd DC mcrogrd based based on on a mult- on a mode mult-mode smooth smooth swtch. swtch. 4.1. The Frst Layer: The Equpment Layer In In the sland DC DC mcrogrd system, system, the voltage the voltage regulaton regulaton unts are unts connected are connected to the DCto to mcrogrd the DC mcrogrd bus through bus a DC/DC through converter, a DC/DC.e., converter, a DC mcrogrd.e., a DC voltage mcrogrd stablty voltage controller stablty (). controller To accelerate (). the To To accelerate speed of the the dynamc speed of of response the dynamc of droop response control of of [22], droop thecontrol current-voltage [22], the (I-U) current-voltage droop control (I-U) structure, droop control as ndcated structure, n Fgure as as ndcated 4, s adopted n n Fgure n the 4, 4, system. s s adopted n n the system. U I I + + Current Current PI 1/K PI D 1/K - - controller controller PWM PWM U.. I. I. Fgure Fgure 4. 4. I-U I-U I-U droop droop control control dagram. dagram. In Fgure 4, the transfer functon of the PI controller s k In In Fgure 4, 4, the transfer functon of of the PI PI controller s s p + k kp p + /s. Let k / s. s. Let p and k kp and represent the k kp represent k the proporton and ntegral terms of current PI controller, respectvely. U s the no-load voltage of, proporton.e., the erence and ntegral voltageterms of droop of of current control. PI PI Ucontroller,. and respectvely. I. represent U thes s output the no-load voltage voltage and the of of, current.e., of the the erence DC/DC converter, voltage of respectvely. of droop control. K ers U to the and droop I. coeffcent represent of I. the. output D represents voltage and the.. pulse wdth modulaton (PWM) duty rato. the current of of the DC/DC converter, respectvely. K ers K to to the droop coeffcent of of. D The - load DC mcrogrd model utlzed n ths secton, whch takes lne resstance nto represents the pulse wdth modulaton (PWM) duty rato. consderaton, s ndcated n Fgure 5. U The - load DC mcrogrd model PCC s the voltage of the common connecton pont and R utlzed n n ths secton, whch takes lne resstance nto ers to the total resstance of the ntegrated lne,, the value of whch s equal to the sum of the consderaton, s s ndcated n n Fgure 5. 5. U s PCC s the voltage of of the common connecton pont and R equvalent vrtual resstance, R 1 PCC ers to to the total resstance of of the, of the ntegrated droop coeffcent lne,,, the and value the of ntegrated of whch s lne s equal resstance, to to the sum R2. of of the Wthout takng the nfluence of the bus pecewse resstance nto consderaton, the smplfed 1 2 equvalent structure of vrtual the sland resstance, DC mcrogrd R, of of the droop coeffcent and the ntegrated lne resstance, R. wth a double parallel operaton s shown n Fgure 6. In terms Wthout of conventonal takng the nfluence droop control, of of the the bus output pecewse current resstance I. ofnto, consderaton,, s calculatedthe as smplfed follows: structure of of the sland DC mcrogrd wth a double parallel operaton s s shown n n Fgure 6. 6. In In terms of of conventonal droop control, the output current I. of I. of,,, s s calculated as as follows: I. = U U pcc R U 1 + R U 2 [1, 2]. (4) pcc I pcc. = 1 2 [ 1, 2]. (4) (4) [ ]. 1, 2 R1 2 + R
Energes 2019, 12, 3012 6 of 20 Energes 2018, 11, x FOR PEER REVIEW 6 of 21 Energes 2018, 11, x FOR PEER REVIEW 6 of 21 1 U 1............ U N U N 2 1 2 R 1 2 R 2 R 2 N 2 R N Ivsc.1 Ivsc.1 Ivsc. Ivsc. Ivsc.N Ivsc.N Load Load Load Load DC 1 2 source DC 1 2 R source R segment common resstance segment common load resstance load Fgure 5. Parallel structure of the DC mcrogrd mult-converter. Fgure 5. Parallel structure of the DC mcrogrd mult-converter. 1 U 1 + + 2 U 2 + + 1 1 R 1 1 2 1 R 2 I.1.1 I.2.2 2 1 2 R 1 2 2 R 2 U pcc pcc Fgure 6. Smplfed structure of the double parallel converters. Fgure 6. Smplfed structure of the double parallel converters. Accordng to Equaton (4), load power dspatch s affected by lne resstance and vrtual Accordng to to Equaton (4), (4), load load power power dspatch dspatch affected s affected by lne by resstance lne resstance and vrtual and resstance. vrtual resstance. In the case of the lne resstance beng equal to and the droop curve erence voltages In resstance. the case of In the lne case resstance of the lne beng resstance equal to beng 0 and equal the droop to 0 and curve the erence droop curve voltages erence of voltages beng of beng dentcal, the output current and droop coeffcent of satsfy the followng dentcal, of beng the output dentcal, current the and output droopcurrent coeffcent and ofdroop satsfy coeffcent the followng of proportons satsfy the to followng acheve proportons to acheve accurate power sharng: accurate proportons power to acheve sharng: accurate power sharng: 1 1 1 1 1. 1N N 1, (5) R [ ] 1 R1 I.1 I. RNI. N= K, 1, N. (5) 1 I.1 = R 1 I. = R 1 N I.N = K, [1, N]. (5) Due to the nfluence of lne resstance, the converter R 1 R 2 s not equal n Equaton (4). Due to the nfluence of lne resstance, the converter R Consderng that both the vrtual and lne resstance under R 2 s not equal n Equaton (4). Due to the nfluence of lne resstance, the converter R 1 + R 2 closed-loop s not equal state n are Equaton relatvely (4). Consderng that both the vrtual resstance and lne resstance under closed-loop state are relatvely Consderng low, the obvous that both devaton the vrtual of the resstance two resstances and lnemay resstance lead to under consderable a closed-loop power state mbalance are relatvely and low, the obvous devaton of the two resstances may lead to consderable power mbalance and low, an naccurate the obvous load devaton power dspatch. of the two Consderng resstances that may the lead unts ton a consderable the system are power connected mbalance to the and DC an naccurate load power dspatch. Consderng that the unts n the system are connected to the DC an mcrogrd naccurate bus load n the power dstrbuted dspatch. way, Consderng the bus pecewse that the unts resstance n the system may aggravate are connected the unbalanced to the DC mcrogrd bus n the dstrbuted way, the bus pecewse resstance may aggravate the unbalanced mcrogrd dspatch of bus power n the n the dstrbuted system. way, the bus pecewse resstance may aggravate the unbalanced dspatch of power n the system. dspatch of power n the system. 4.2. The Second Layer: The Current-Sharng Layer 4.2. The The Second Second Layer: Layer: The The Current-Sharng Layer Layer Accordng to the analyss n Secton 4.1, the output voltages, of are dfferent from. Accordng to to the the analyss analyss n n Secton Secton 4.1, 4.1, the the output output voltages, voltages, U U, of are dfferent from. each other because of the exstence of lne resstance, thus, there s., of are dfferent from each no unfed voltage nput for other each other because because of theof exstence the exstence of lneof resstance, lne resstance, thus, there thus, s there no unfed s no unfed voltage voltage nput for nput for droop droop control, whch results n falure to acheve precse power dspatch. To address the nfluence control, droop control, whch whch results results n a falure n a falure to acheve to acheve precse precse power power dspatch. dspatch. To address To address the nfluence the nfluence of lne of lne resstance on the current-sharng system, researchers usng tradtonal practces tred to resstance of lne resstance on the current-sharng on the current-sharng system, researchers system, researchers usng tradtonal usng practces tradtonal tredpractces to ncrease tred droop to ncrease droop coeffcent to mprove current-sharng [23]. Ths method leads to relatvely larger coeffcent ncrease droop to mprove coeffcent current-sharng to mprove [23]. current-sharng Ths method[23]. leads Ths to amethod relatvely leads larger to a voltage relatvely devaton larger voltage devaton and t may stll be mpossble to acheve precse power dspatch. Theore, and voltage t may devaton stll be mpossble and t may tostll acheve be mpossble precse power to acheve dspatch. precse Theore, power adspatch. current-sharng Theore, layer a current-sharng layer control based on the dfference dscrete consstency algorthm s adopted n ths control current-sharng based onlayer the dfference control based dscrete on the consstency dfference algorthm dscrete consstency adopted n algorthm ths paper, s adopted as ndcated ths n paper, as ndcated n Fgure 3.. ers to the droop control coeffcent of -th, Fgure paper, 3. as Kndcated ersn to the Fgure droop 3. control K. ers coeffcent to the of -th droop, control U ndcates coeffcent theof no-load -th, voltage U of droop ndcates control the no-load of, voltage I of droop control of, represents the output current of, ndcates the no-load voltage represents the output current of, I of droop control of, I represents max ers to the maxmum safety the output current of, output max max ers current to of the, maxmum and U avg safety ndcates output the current averageof value, of and the termnal ndcates voltagethe U. average of each value, of avg whch I are ers teratvely to the maxmum convergedsafety through output DCCA. current of, and U ndcates the average value of avg the termnal voltage of each, whch are teratvely converged through DCCA.. the termnal voltage U of each, whch are teratvely converged through DCCA..
Energes 2018, 11, x FOR PEER REVIEW 7 of 21 Energes 2019, 12, 3012 7 of 20 To reduce the requrement for the communcaton system, the n the system only allows adjacent communcaton unts to nteract. The output voltage, U, of each s tracked n real To reduce the requrement for the communcaton system, the. n the system only allows tme adjacent through communcaton DDCA and unts the nformaton to nteract. The s rapdly output converged voltage, U. nto, of an each average value, s tracked U n. The avg real average tme through voltage, DDCA U and, lects the nformaton real-tme sfluctuaton rapdly converged of the DC ntobus an average voltage value, and provdes U avg. The a average unfed avg voltage, U avg, lects real-tme fluctuaton of the DC bus voltage and provdes a unfed erence erence nput for the droop control of each. Thus, t s regarded as a vrtual bus voltage n ths nput for the droop control of each. Thus, t s regarded as a vrtual bus voltage n ths secton and secton and provdes a unfed erence nput for droop control of each to acheve a balanced provdes a unfed erence nput for droop control of each to acheve a balanced dspatch of dspatch of load power n the system. The current-sharng layer control strategy based on DDCA s load power n the system. The current-sharng layer control strategy based on DDCA s ndcated n ndcated n Fgure 7. Fgure 7. Fgure 7. The current-sharng layer strategy based on the dfference dscrete consensus algorthm. Fgure 7. The current-sharng layer strategy based on the dfference dscrete consensus algorthm. By utlzng the output voltage, U., of each n the sland DC mcrogrd system as an nformaton node and only allowng communcaton wth adjacent nodes, we fnd the average By utlzng the output voltage, U, of each n the sland DC mcrogrd system as an. value, U avg, of U. through DDCA teraton. The dscrete consstency algorthm s expressed as [24]: nformaton node and only allowng communcaton wth adjacent nodes, we fnd the average value, U, of U through DDCA teraton. ( The dscrete consstency algorthm s expressed as avg. x (k + 1) = x (k) + a j xj (k) x (k) ) = 1, 2,, N, (6) [24]: j N ( ) where N s the total number of agent nodes, k ers to the Kth teraton, x ( k+ 1) = x( k) + aj xj( k) x( k) = 1,2, (k) ers to the output of unt, N, after the kth teraton, x (6) j (k) ndcates the output of unt j after the kth teraton, a j s the edge weght j N between node and node j, a j = 0 when the nodes and j are not neghborng nodes, and N ers to where the setn ofs ndexes the total of the number agents of that agent arenodes, connected k ers wth to agent the Kth. teraton, x(k) ers to the output of unt Ifafter we consder the kth teraton, each xj(k) as an ndcates agent node, the output then x of (k) unt n Equaton j after the (6) kth s represented teraton, aj as s Uthe. edge (k) weght and x j (k) between s represented node and as Unode vsc.j (k). j, aj = 0 when the nodes and j are not neghborng nodes, and N ers After to the consoldaton, set of ndexes Equaton of the agents (6) can that beare expressed connected as: wth agent. If we consder each as an agent node, then x(k) n Equaton (6) s represented as U. ( k ) and xj(k) s represented as Uvsc.j x ( k ). (k + 1) = x (k) 1 a j + a j x j (k). (7) After consoldaton, Equaton (6) can be expressed j N as: j N It can be further ndcated as: x k x k aj ajxj k j N j N. (7) ( + 1= ) ( ) 1- + ( ) x (k + 1) = W (k)x (k) + W j (k)x j (k), (8) where It Wcan (k) be and further W j (k) ndcated er to as: the weght factor of the kth teraton, respectvely. The teratve algorthm of Equaton (8) s adapted as: x k+1 =W k x k +W k x k, (8) ( ) ( ) ( ) ( ) ( ) j j where W(k) and Wj(k) er to the weght X(k factor + 1) of = the W kth X(k). teraton, respectvely. (9) The teratve algorthm of Equaton (8) s adapted as: After the kth teraton: X(k + 1) = W k+1 X(0), (10)
Energes 2019, 12, 3012 8 of 20 where X(k) = [x 1 (k), x 2 (k), x N (k)] T and X(0) = [x 1 (0), x 2 (0), x N (0)] T. W ers to weght matrx of the communcaton network: W = 1 a 1j j N 1 a 1N..... a 1N... 1 a N j j N. (11) If the constant edge weght, a, s always adopted [25], then Equaton (11) can be further ndcated as: W= E al, (12) where E ndcates the N-order unt matrx, L ndcates the Laplacan matrx, a ers to the constant edge weght, and L ers to the undrected connected graph composed of the output voltage N nformaton nodes of s. L j = N = j 1 j N 0 other, (13) where N ndcates the number of nodes nvolved n communcaton couplng wth node. To guarantee that all nformaton nodes n Equaton (10) acheve teratve convergence, the followng requrements must be met: lm k Wk = 1 N 1 1T, (14) where 1 ers to all column vectors wth element of 1. To guarantee the convergence after teraton, Equaton (14) holds only f [26]: 1 T W = 1 T, (15) W1 = 1, (16) ρ (W 1 ) N 1 1T < 1, (17) where ρ ers to the spectral radus of matrx. The fast convergence s acheved by adjustng the value of a, whch s valued as [25]: a = 2 λ 1 (L) + λ n 1 (L), (18) where λ 1 (L) ers to the maxmum egenvalue of the Laplacan matrx, L, and λ n 1 (L) ndcates the second mnmum egenvalue of L. The system stablty of low-bandwdth communcaton (LBC) under dfferent delays s analyzed and the results ndcate that the dstrbuted control based on LBC mantans stablty, even when a relatvely larger communcaton delay s adopted [27]. Consderng that the sland mcrogrd s relatvely small, the nfluence of communcaton delay s not taken nto consderaton. In order to accelerate convergence and reduce fluctuaton, whch s caused by changes n communcaton topologcal structure and node state values, smooth convergence of the consensus algorthm s utlzed. Based on the dscrete consensus algorthm (DCA), the dfference values of two contguous teratons are ntroduced to predct future state changes. In ths way, the update value for each tme ndcates a mxture of the predcted value and the node adjacent sde calculated value. Ths process accelerates to skp the ntermedate state of the teraton and speed up the convergence rate further. Regardng the β
teratons are ntroduced to predct future state changes. In ths way, the update value for each tme ndcates a mxture of the predcted value and the node adjacent sde calculated value. Ths process accelerates to skp the ntermedate state of the teraton and speed up the convergence rate further. Regardng the β tmes of the dfference value, namely β(x(k) X(k 1)), whch s the predcted value n Equaton (19), the DCA s updated as: Energes 2019, 12, 3012 9 of 20 ( k+ 1 ) ( k) + β ( ( k) - ( k 1) ) X =WX X X -. (19) tmesaccordng of the dfference to Equaton value, (19), namely the output β(x(k) X(k 1)), voltage of each whch s the satsfes: predcted value n Equaton (19), the DCA s updated as: U k X(k + 1 + =WU 1) = WX(k) k + β(x(k) β U kx(k -U 1)). k- 1, (20) (19) ( ) ( ) ( ) ( ) ( ) where [ ] Accordng to Equaton (19), the output voltage of each T satsfes: U ( k) = U.1 ( k), U.2 ( k), U. ( N k). Accordng to Equaton U (20), (k + the 1) = output WU voltage (k) + β(u of each (k) Uafter (k convergence 1)), satsfes: (20) = 1 N N where U (k) = [U.1 (k), U.2 (k), U.N (k)] T. U Accordng to Equaton avg = U.1= U (20), the.2 U output voltage. of = U each. = after N U convergence. satsfes:. (21) By DDCA, the droop control curve ndcated n Equaton U avg = U.1 = U.2 = U. = U.N = 1 (22) N s developed from the U N.. (21) conventonal droop control. U = U K I, (22) By DDCA, the droop control curve avgndcated n Equaton. avg (22). s developed from the conventonal droop control. where, takng nto account the maxmum U capacty avg = U of the K, I I avg., avg. s the, output current under (22) current-sharng control, namely the erence current, I. where, takng nto account the maxmum capacty of the, I avg. s the, output current under current-sharng Under the dentcal control, namely erence the voltage, erenceu current,, and I the. nput voltage, U avg, n the case of the output Under current, the dentcal I erence voltage, U, and the nput voltage, U, of beng nversely proportonal to the droop avg, coeffcent, n the case K of the output., currentsharng current, control I, of s acheved. beng nversely proportonal to the droop coeffcent, K, current-sharng control s acheved. K K.1 I I avg.1 = = K. I avg.. = = K.N. IN avg.n I avg. N (23) After DDCA, the the sland DC mcrogrd model, whch consders the thelne resstance n nfgure 5, 5, s s mproved, as shown n Fgure 8. U Iavg.1... U Iavg. Load... U Iavg.N Fgure 8. Equvalent model of the DC mcrogrd current-sharng control. When DDCA current-sharng control s acheved, the average current, I avg.., of, I, and the maxmum output current, I max max, shall satsfes the followng equaton: maxmum output current,, shall satsfes the followng equaton: I avg. = I avg., (24) I un I max where I un s the average unt current under current sharng control, whch s used to ndcate the load avg. rate of. I un avg.1 = Iun avg.2 = Iun avg. = Iun avg.n = Iun avg (25) To verfy the effectveness of the current-sharng strategy, a topologcal structure wth fve nformaton nodes, as ndcated n Fgure 9a, s establshed n the paper. Fgure 9b shows the correspondng Laplacan matrx, L, of ths structure.
I = I = I = I = I (25) un un un un un To verfy the effectveness of the current-sharng strategy, a topologcal structure wth fve avg.1 avg.2 avg. avg. N avg nformaton nodes, as ndcated n Fgure 9a, s establshed n the paper. Fgure 9b shows the correspondng To verfy Laplacan the effectveness matrx, of L, of the ths current-sharng structure. strategy, a topologcal structure wth fve nformaton nodes, as ndcated n Fgure 9a, s establshed n the paper. Fgure 9b shows the correspondng Energes 2019, 12, 3012 Laplacan matrx, L, of ths structure. 10 of 20 (a) 2 1 0 0 1 1 2 1 0 0 2 0 0 1 L = 0 1 2 1 0 1 2 0 0 L = 0 0 1 2 1 0 1 2 0 1 0 0 1 2 0 0 1 2 1 1 0 0 1 2 (b) Fgure 9. Communcaton topology and ts Laplacan matrx. (a) A topologcal structure wth fve (a) (b) nformaton nodes; (b) Laplacan matrx. Fgure Fgure9. 9. Communcatontopology topologyand andts tslaplacan Laplacanmatrx. (a) (a) Atopologcal topologcalstructure structurewth wthfve T nformatonnodes; nodes; (b) (b) Laplacanmatrx. X (0) = 1, 2,3,4, 5. The egenvalues of L are The system starts wth 0, 1.382,1.382, 3.618, 3.618 The system starts wth (0) = [ 1, 2,3,4, 5] verfed n ths paper by Matlab smulaton. [ 0, 1.382,1.382,3.618, 3.618] T. The convergence when T 2/5 The system starts wth X(0) = [1, 2, X 3, 4, 5] T. The egenvalues a=. of The L are, a= egenvalues [0, 1.382, 1/5, 1.382, and of 3.618, a= 1/10 L 3.618] s are T. The convergence when a = 2/5, a = 1/5, and a = 1/10 s verfed n ths paper by Matlab smulaton. T Fgure 10 shows that a = 2/5 has. The the convergence fastest teraton when speed a= and 2/5 the, lowest a= 1/5 fluctuaton., and a= 1/10 s verfed n ths paper by Matlab smulaton. 5.0 5.0 5.0 Fgure 10 shows that a = 2/5 has the fastest teraton speed and the lowest fluctuaton. 4.5 4.5 4.0 5.0 4.0 5.0 4.0 5.0 4.5 3.5 4.5 3.5 4.5 3.5 4.0 3.0 4.0 3.0 4.0 3.0 3.5 2.5 3.5 2.5 3.5 2.5 3.0 2.0 3.0 2.0 3.0 2.0 2.5 1.5 2.5 1.5 2.5 1.5 2.0 0 5 10 15 20 25 30 35 2.0 1.0 0 5 10 15 20 25 30 1.0 352.0 0 5 10 15 20 25 30 35 1.5 Tmes(s) 1.5 Tmes(s) 1.5 Tmes(s) (a) (b) (c) 1.0 1.0 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 3 Tmes(s) Tmes(s) Tmes(s) Fgure 10. Convergng speed comparson under dfferent constant weghts, a. (a) Consensus dynamc (a) (b) (c) at a = 2/5; (b) Consensus dynamcat ata a = 1/2; (c) (c) Consensus dynamcat ata a = = 1/10. Fgure 10. Convergng speed comparson under dfferent constant weghts, a. (a) Consensus dynamc 4.3. 4.3. The The at a Thrd Thrd = 2/5; (b) Layer: Layer: Consensus The The Mult-Mode Mult-Mode dynamc at Smooth Smooth a = 1/2; Swtch Swtch (c) Consensus Layer Layer dynamc at a = 1/10. Consderng Consderngthat thatthe thepower powerconsumpton consumptonof oflne lneresstance, PL, P L, s shard hardto toacqure acqureaccurately, accurately, t ts s 4.3. The Thrd Layer: The Mult-Mode Smooth Swtch Layer not notapproprate approprateto toutlze utlzethe thereal-tme real-tmepower powerof ofthe thesystem systemunts untsn nsecton 3as asthe thecrteron crteronfor forthe mult-mode mult-mode Consderng smooth smooth that swtch the power layer, layer, consumpton whch whch may may lead lead of lne to to serous resstance, serous devaton. devaton. PL, s hard When When to usng acqure usng DC DC accurately, bus bus voltage voltage t s as not as the the approprate key key ndex ndex for to for the utlze the system system the real-tme operaton, operaton, power the the power of power the status system status of unts of the the DC n DC Secton mcrogrd mcrogrd 3 as system the system crteron s s lected lected for the n mult-mode real tme. The smooth DC bus swtch voltage layer, s of whch great may sgnfcance lead to serous for the mult-mode devaton. When smooth usng swtch. DC bus Meanwhle, voltage as the the average key ndex voltage, for the U avg system, ntroduced operaton, n Secton the power 4.2, lects status the of true the DC level mcrogrd of bus voltage. system Thus, s lected average voltage, U avg, s regarded as a vrtual bus voltage n ths secton to provde a unfed voltage crteron for mode swtchng of the system unts. At the same tme, t provdes a unfed erence nput for all s. A mult-mode smooth swtch control strategy, based on vrtual bus voltage nformaton, s proposed n ths paper, as ndcated n Fgure 3. Among them, U ers to the no-load voltage of -, U and U1H ndcate the scope of the droop voltage regulaton of -, U represents the no-load voltage of droop control of -, U ndcates the mnmum voltage of droop control of -, and P ers to the output power of. The mult-mode smooth swtch strategy based on the vrtual bus voltage nformaton s shown n Fgure 11. 4.5
voltage nformaton, s proposed n ths paper, as ndcated n Fgure 3. Among them, U ers to 1H the no-load voltage of -, U and U ndcate the scope of the droop voltage regulaton of -, U represents the no-load voltage of droop control of -, U ndcates the mnmum voltage of droop control of -, and P ers to the output power of. Energes 2019, The 12, mult-mode 3012 smooth swtch strategy based on the vrtual bus voltage nformaton s shown 11 of 20 n Fgure 11. Equaton 20 Voltage judgment NO U.<<U. YES - droop control U.<<U1H. NO Load sheddng YES - droop control Equaton 31 Equaton 28 K. Kbes. Fgure Fgure 11. 11. Mult-mode swtch strategy based on vrtual bus bus voltage nformaton. (1) Mode (1) Mode 1: - 1: droop control Accordng Accordng to Fgure to Fgure 11, 11, to to fully fully utlze photovoltac energy, MPPT MPPT control control s adopted s adopted under under ths ths mode and the bus voltage s regulated through control of -. As ndcated the fgure, mode and the bus voltage s regulated through droop control of -. As ndcated n the fgure, 1H the admssble the admssble fluctuaton scope of of bus voltages s between between U U and andu U1H. The. The vrtual vrtual bus voltage, bus voltage, U avg, U s, s as the for and the nput for each avg ntroduced as the crteron for the mult-mode smooth swtch and the erence nput for each.. Thus, Thus, the I-U the I-U droop droop control adopted under ths modes s expressedas: as: U I avg. I = U U avg. = U avg I k = I k. (26). (26) To fully To fully utlze utlze the the voltage regulaton capacty of, n ncase case of of the the vrtual vrtual bus bus voltage voltage U avg U avg exceedng exceedng the fluctuaton the scope, all all s mplement mult-mode smooth swtchng smultaneously. Ths Ths means means that, that, when when U avg U avg reaches the the bounds of the droop voltage regulaton area area of -, of -, the output current of each, I un the output current of each, un I, meets the followng equatons: avg., meets the followng equatons: avg. I un avg.1 = Iun avg. = Iun avg.n = Iun avg = 1 I un avg.1 = Iun avg. = Iun avg.n = Iun avg= 1 U avg = U. U avg = U 1H.. (27) To acheve mult-mode smooth swtchng, the - droop coeffcent, K, s set as: (2) Mode 2: - droop control K = U U I max = U U1H I mn. (28) Accordng to Fgure 11, when there s a surplus of power n the system, the vrtual bus voltage exceeds the maxmum value of energy storage n the droop voltage regulaton area and the system voltage enters nto the - droop voltage regulaton area. Under ths mode, adopts a constant output current, I mn, and the bus voltage s under the droop control regulaton of -. The fluctuaton scope for the vrtual bus voltage under the droop control voltage regulaton of - s between U and U. As Fgure 3 shows, to acheve a smooth swtch between mode 1 and mode 2, when P. reaches P MPPT, namely:. P. /P MPPT. = 1, (29)
When the DC mcrogrd operates normally under Stuaton 1, the photovoltac array uses MPPT control and the four groups of energy storage unts adopt droop control to regulate the voltage. Before 1.8 s, both the photovoltac array output and common load are 0, theore the system s under a no-load state. At 1.8 s, the common DC load ncreases to 8 kw, wth the four groups of energy Energes 2019, 12, 3012 12 of 20 the vrtual bus voltage, U avg, satsfes the followng equaton: U avg = U 1H = U. (30) Smlarly, to acheve mult-mode smooth swtchng between mode 1 and mode 2, the droop control coeffcent, K., satsfes the followng equaton: (3) Mode 3: Load sheddng K. = U U P MPPT. = U U1H P MPPT.. (31) Accordng to Fgure 11, n the case of the system havng power vacancy and ths leadng to a reducton n bus voltage, the mult-mode swtch strategy s ntated when the vrtual bus voltage s lower than U. A load wth a lower prorty level s shed to complete load-sheddng control and guarantee stable operaton of the system. When load-sheddng control s mplemented, the total load power of the system s reduced and the system operaton returns to the droop control voltage regulaton area of -, as ndcated n Fgure 3. 5. Example Smulaton Analyss To verfy the effectveness of the herarchcal, coordnated control strategy of the sland DC mcrogrd under multple modes proposed n ths paper, the sland DC mcrogrd ndcated n Fgure 5 s establshed n PSCAD/EMTDC. Ths DC mcrogrd contans four groups of battery energy storage unts, from 1 to 4, ncludng one group of common DC load and one group of photovoltac power generaton array, and acheves ntegrated operaton through a DC/DC converter. The communcaton topologcal structure among the four groups of the energy storage system s ndcated n Fgure 12. Its communcaton matrx egenvalue λ s [0,2,2,4]. The value of a s obtaned from Equaton (18) as 1/3. The energy storage maxmum current output rato s 1:2:3:4. In addton, the bus pecewse resstances Energes 2018, 11, x FOR PEER REVIEW are 0.5, 0.2, and 0.4 Ω, respectvely, and the energy storage no-load voltage, U 13 of 21, s 380 V. Furthermore, the voltage 1H range of the mult-mode swtch from U and U1H s between 370 and 385 V and for U U s between 370 and 385 V and for U and U. the range s between 385 and 390 V. The and U. the range s between 385 and 390 V. The operatonal stuaton of ths DC mcrogrd s operatonal stuaton of ths DC mcrogrd s ndcated n Table 1. Smulaton analyss s carred out ndcated n Table 1. Smulaton analyss s carred out for ths DC mcrogrd n terms of the source load for ths DC mcrogrd n terms of the source load fluctuaton. To verfy the effectveness of the control fluctuaton. To verfy the effectveness of the control strategy proposed n ths paper under dfferent strategy proposed n ths paper under dfferent stuatons, the smulatons of all sx stuatons lsted stuatons, n Table the 1 are smulatons acheved wthn of all sx 0 8 stuatons s sequentally. lsted n Table 1 are acheved wthn 0 8 s sequentally. 1 2 Current nformaton 3 Current nformaton 4 Fgure Fgure 12. 12. Topologcal Topologcal structure structure of of four four groups of of energy energy storage storage communcaton. communcaton. Table Table 1. 1. Operatonal stuatons of DC mcrogrd. Stuaton Stuaton Operaton Operaton Mode Mode Operaton Operaton Tme/s Tme/s 1 1 0 2.5 s 1 1 0 2.5 s 2 1-3-1 2.5 4.4 2 1-3-1 2.5 4.4 s 1-2 4.4 6.2 3 1-2 4.4 6.2 s 4 2-1 2-1 6.2 6.8 6.2 6.8 s 5 1 6.8 8 s 6 1 0 2.5 s 5.1. Stuaton 1
Energes 2019, 12, 3012 13 of 20 5.1. Stuaton 1 When the DC mcrogrd operates normally under Stuaton 1, the photovoltac array uses MPPT control and the four groups of energy storage unts adopt droop control to regulate the voltage. Before 1.8 s, both the photovoltac array output and common load are 0, theore the system s under a no-load state. At 1.8 s, the common DC load ncreases to 8 kw, wth the four groups of energy storage unts adoptng droop control voltage regulaton, consequently reducng system voltage. After 2 s, the DDCA s ntated to complete current-sharng control. Accordng to Fgure 13, current-sharng control does not occur n the frst 2 s. The unt currents of I un and Iun are over 1.0, whch means these two energy storage unts are overloaded at ths pont..1.2 Meanwhle, devaton exsts between the bus voltages at dfferent nodes, whch makes t mpossble to mplement accurate mult-mode swtchng. After 2 s, the system ntates the current-sharng control strategy and the Iavg un of the four groups of energy storage unts mantan the current at 0.7. In addton, the output current of the energy storage unts s nversely proportonal to the droop coeffcent, allowng the system to acheve current-sharng. The vrtual bus voltage gradually converges and s mantaned at Energes 373 V, 2018, whch 11, x FOR s wthn PEER REVIEW the range of the energy storage droop voltage regulaton of mode 1. 14 of 21 5.2. Stuaton 2 Fgure Fgure 13. 13. Verfcaton Verfcaton for for the the effectveness effectveness of of DDCA DDCA convergence. convergence. At 2.5 s, the photovoltac array output ncreases to 6 kw and the voltage also rses. At 3 s, the DC load ncreases by 8 kw whle the voltage reduces to U. At 3.6 s, the DC load ncreases by 2 kw; at ths pont, the system has a power vacancy, wth the voltage level lower than U. At 3.65 s, the mult-mode smooth swtch strategy s ntated and the system enters nto mode 3, where loadsheddng voltage regulatons exst, removng 8 kw load sequentally, accordng to prorty level.
Energes 2019, 12, 3012 14 of 20 5.2. Stuaton 2 At 2.5 s, the photovoltac array output ncreases to 6 kw and the voltage also rses. At 3 s, the DC load ncreases by 8 kw whle the voltage reduces to U. At 3.6 s, the DC load ncreases by 2 kw; at ths pont, the system has a power vacancy, wth the voltage level lower than U. At 3.65 s, the mult-mode smooth swtch strategy s ntated and the system enters nto mode 3, where load-sheddng voltage regulatons exst, removng 8 kw load sequentally, accordng to prorty level. After ths, the bus voltage rses agan to the range of mode 1 energy storage droop control. As shown n Fgure 14, at 2.5 s, the Iavg un of the four groups of energy storage unts drops to 0.17, whle the vrtual bus voltage rses to 378.3 V and the system completes current-sharng and voltage stablty control. At 3 s, the DC load ncreases and the Iavg un of energy storage unt ncreases to 1; the voltage at ths pont stablzes at U. At 3.6 s, the load ncrease leads to a system power vacancy and the bus voltage drops contnuously to a level lower than U. At 3.65 s, the mult-mode swtch strategy s ntated and the system starts the load-sheddng voltage regulaton process to complete load-sheddng control; at ths pont the Iavg un of the energy storage unt s mantaned at 0.32 and the vrtual bus voltage rses to 376.8 V. The system enters nto the energy storage unt droop control range under mode 1. Energes 2018, 11, x FOR PEER REVIEW 15 of 21 5.3. Stuaton 3 Fgure 14. 14. Smulaton waveformof of Stuaton 2. 2. At 4.6 s, the DC load falls by 10 kw and the vrtual bus voltage rses contnuously, exceedng the energy storage unt no-load voltage of U ; n addton, the energy storage system converts from dscharge mode to charge mode. At 5.0 s, the photovoltac output ncreases by 2.5 kw and the vrtual 1H bus voltage rses to U. At 5.5 s, the photovoltac output enhances by 2.5 kw wth excess system
Energes 2019, 12, 3012 15 of 20 5.3. Stuaton 3 At 4.6 s, the DC load falls by 10 kw and the vrtual bus voltage rses contnuously, exceedng the energy storage unt no-load voltage of U ; n addton, the energy storage system converts from dscharge mode to charge mode. At 5.0 s, the photovoltac output ncreases by 2.5 kw and the vrtual bus voltage rses to U 1H. At 5.5 s, the photovoltac output enhances by 2.5 kw wth excess system power and the vrtual bus voltage exceeds U 1H. At 5.51 s, the mult-mode swtch strategy s ntated and the photovoltac array swtches from MPPT control to droop control; the vrtual bus voltage s restored to the range of photovoltac droop voltage regulaton. As shown n Fgure 15, at the tme of 4.6 s, the DC load drops and the four groups of energy storage unts adopt droop control; the vrtual bus voltage rses to 383.5 V and the Iavg un of the energy storage unt drops to 0.7. At 5.0 s, the photovoltac output rses, wth the Iavg un of the energy storage unt droppng to 1.0 and the bus voltage reachng 385 V. At 5.5 s, wth the ncrease n photovoltac output, the system contans excess power and the vrtual bus voltage rses contnuously to exceed U 1H Energes 2018, 11, x FOR PEER REVIEW 16 of 21. At 5.51 s, the mult-mode swtch strategy s ntated and the photovoltac unt enters nto a lmted power mode, wth1h U the. At vrtual 5.51 s, bus the voltage mult-mode rsng swtch aganstrategy to 386 Vs and ntated the system and the voltage photovoltac enterng unt enters nto a nto the photovoltac droop lmted voltage power regulaton mode, wth range. the vrtual bus voltage rsng agan to 386 V and the system voltage Fgure 15. Smulaton waveform of Stuaton 3. Fgure 15. Smulaton waveform of Stuaton 3. 5.4. Stuaton 4 At 6.3 s, wth the DC load ncreasng by 12 kw, the photovoltac output rses and the vrtual bus
Energes 2019, 12, 3012 16 of 20 5.4. Stuaton 4 At 6.3 s, wth the DC load ncreasng by 12 kw, the photovoltac output rses and the vrtual bus voltage s lower than U. As the mult-mode swtch strategy s ntated, the system s under the energy storage droop control range of mode 1. In addton, as the photovoltac unt ntates MPPT control, the energy storage unt adopts the droop control voltage regulaton and the output current s postve. Accordng to Fgure 16, at 6.3 s, the DC load ncreases and the vrtual bus voltage s lower than U. As the mult-mode strategy s ntated, the voltage locates wthn the droop control range of the energy storage system and s mantaned at 379 V; the Iavg un of the energy storage unt s 0.1. The photovoltac array converts from droop control to the MPPT mode and the system operates n a stable manner under mode 1. Energes 2018, 11, x FOR PEER REVIEW 17 of 21 5.5. Stuaton 5 Fgure Fgure 16. 16. Smulaton waveform of of Stuaton4. 4. At 7.0 s, the output of publc DC loads and photovoltac unts remans unchanged and the four energy storage unts complete dscharge and ext the operaton. The system voltage s controlled by the remanng energy storage unt by droop control. Accordng to Fgure 17, at 7.0 s, I s reduced to 0 and the system voltage s adjusted by the un avg
Energes 2019, 12, 3012 17 of 20 5.5. Stuaton 5 At 7.0 s, the output of publc DC loads and photovoltac unts remans unchanged and the four energy storage unts complete dscharge and ext the operaton. The system voltage s controlled by the remanng energy storage unt by droop control. Accordng to Fgure 17, at 7.0 s, Iavg un s reduced to 0 and the system voltage s adjusted by the droop control of the remanng three unts. The vrtual bus voltage s reduced to 378.4 V and Iavg un Energes s rased 2018, to11, 0.16. x FOR The PEER system REVIEW voltage remans n the energy storage saggng pressure area. 18 of 21 Fgure 17. Smulaton waveform of Stuaton 5. Fgure 17. Smulaton waveform of Stuaton 5. 5.6. Stuaton 6 5.6. Stuaton 6 Takng photovoltac and load fluctuaton nto consderaton n Stuaton 1 5, to verfy the robustness Takng ofphotovoltac current-sharng and control load fluctuaton when the dsturbance nto consderaton of lne resstance n Stuaton s ntroduced, 1 5, to verfy Stuaton the 6 robustness nvestgates of the current-sharng control condtons when the under dsturbance a +20% and of lne 30% resstance lne resstance ntroduced, dsturbance. Stuaton 6 nvestgates the current-sharng condtons under a +20% and 30% lne resstance dsturbance. Fgure 18a,b ndcates the response curves wth dsturbances of +20% and 30%, respectvely. Accordng to Fgure 18, n the case of the lne resstance beng dsturbed, the system stll acheves rapd current-sharng. Ths verfes the robustness of the strategy when dsturbances are ntroduced.
Energes 2019, 12, 3012 18 of 20 Energes 2018, 11, x FOR PEER REVIEW 19 of 21 Fgure 18a,b ndcates the response curves wth dsturbances of +20% and 30%, respectvely. (a) (b) Fgure Fgure 18. 18. Smulaton Smulaton waveform waveform of Stuaton of Stuaton 6. (a) 6. (a) +20% +20% dsturbance; dsturbance; (b) (b) 30% 30% dsturbance. dsturbance. 6. Conclusons Accordng to Fgure 18, n the case of the lne resstance beng dsturbed, the system stll acheves rapd current-sharng. Ths verfes the robustness of the strategy when dsturbances are ntroduced. A herarchcal, coordnated control strategy of an sland DC mcrogrd based on a mult-mode 6. swtch Conclusons s proposed n ths paper. To solve the naccurate load dspatch caused by lne resstance and guarantee system voltage stablty, ths work proposes the establshment of a three-layer control structure, A herarchcal, ncludng coordnated an equpment control layer, strategy a current-sharng of an sland layer, DC mcrogrd and a mode based swtchng on a mult-mode layer, on the swtch bass s of proposed conventonal n ths droop paper. control. To solve The the naccurate smulaton load verfcaton dspatch caused s carred by lne out resstance based on and PSCAD/EMTDC guarantee system and voltage the results stablty, ndcate ths that: work proposes the establshment of a three-layer control structure, ncludng an equpment layer, a current-sharng layer, and a mode swtchng layer, on the bass (1) ofin conventonal the mode swtchng droop control. layer, Thethe smulaton control strategy verfcaton solves s carred the bus out based voltage ondevaton PSCAD/EMTDC problem and thecaused resultsby ndcate lne resstance that: and the nfluence of power loss on a mult-mode swtch. Based on vrtual bus voltage nformaton, the smooth swtch between dfferent operaton modes of an (1) In the mode swtchng layer, the control strategy solves the bus voltage devaton problem caused sland DC mcrogrd s acheved. by lne resstance and the nfluence of power loss on a mult-mode swtch. Based on vrtual (2) In the current-sharng layer, whch avods centralzed control and upper energy management, bus voltage nformaton, the smooth swtch between dfferent operaton modes of an sland DC the control strategy utlzes DDCA to track the output of each unt n real tme, elmnatng mcrogrd s acheved. the nfluence of lne resstance and provdng relable vrtual bus voltage nformaton for the (2) In the current-sharng layer, whch avods centralzed control and upper energy management, equpment layer and the mode swtchng layer. the control strategy utlzes DDCA to track the output of each unt n real tme, elmnatng (3) In the equpment layer, the output current of each unt wth current-sharng control acheves the nfluence of lne resstance and provdng relable vrtual bus voltage nformaton for the accurate load power dspatch. In addton, the control strateges of each unt are regulated n equpment layer and the mode swtchng layer. terms of the fluctuaton of vrtual bus voltage nformaton to acheve system voltage stablty. (3) In the equpment layer, the output current of each unt wth current-sharng control acheves Author Contrbutons: Conceptualzaton, Z.Z., J.Z. and Y.H.; Formal analyss, Z.Z. and J.Z.; Methodology, accurate load power dspatch. In addton, the control strateges of each unt are regulated n Z.Z. and J.Z.; Software, Z.Z.; Wrtng orgnal draft, Z.Z., J.Z. and Y.H.; Supervson, J.Z. and Y.H.; Revson, terms of the fluctuaton of vrtual bus voltage nformaton to acheve system voltage stablty. Z.Z., J.Z. Y.Z. and M.L. All authors have contrbuted to the edtng and proofreadng of ths paper. Author Fundng: Contrbutons: Ths research Conceptualzaton, was funded by Natonal Z.Z., J.Z. Natural and Y.H.; Scence Formal Foundaton analyss, Z.Z. of Chna, and J.Z.; grant Methodology, number 51867005. Z.Z. and The J.Z.; Scence Software, and Z.Z.; Technology Wrtng orgnal Foundaton draft, of Z.Z., Guzhou J.Z. and Provnce, Y.H.; Supervson, grant number J.Z. [2016]1036. and Y.H.; Revson, Guzhou Z.Z., Provnce J.Z. and Scence Y.Z. All and authors Technology have contrbuted Innovaton totalent the edtng Team and Project, proofreadng grant number of ths [2018]5615. paper. Guzhou Provnce Reform Fundng: Foundaton Ths for research Postgraduate was funded Educaton, by Natonal grant Natural number Scence [2016]02, Foundaton The Scence of Chna, and Technology grant number Foundaton 51867005. of The Guzhou ScenceProvnce, and Technology grant number Foundaton [2018]5781. of Guzhou Provnce, grant number [2016]1036. Guzhou Provnce Scence and Technology Innovaton Talent Team Project, grant number [2018]5615. Guzhou Provnce Reform Foundaton Conflcts of forinterest: Postgraduate The authors Educaton, declare grant no conflcts number of [2016]02, nterest The Scence and Technology Foundaton of Guzhou Provnce, grant number [2018]5781. Conflcts References of Interest: The authors declare no conflcts of nterest 1. Afar, S.A.; Mohamed, Y.A.R.I. DG Mx, Reactve sources and energy storage unts for optmzng mcrogrd relablty and supply securty. IEEE Trans. Smart Grd 2014, 5, 1835 1844.
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