Aalborg Unverstet Power flow analyss for DC voltage droop controlled DC mcrogrds L, Chendan; Chaudhary, Sanjay Kumar; Dragcevc, Tomslav; Quntero, Juan Carlos Vasquez; Guerrero, Josep M. Publshed n: Proceedngs of the th Internatonal Multconference on Systems, Sgnals & Devces, SSD 204 DOI (lnk to publcaton from Publsher): 0.09/SSD.204.6808896 Publcaton date: 204 Document Verson Early verson, also known as pre-prnt Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): L, C., Chaudhary, S., Dragcevc, T., Vasquez, J. C., & Guerrero, J. M. (204). Power flow analyss for DC voltage droop controlled DC mcrogrds. In Proceedngs of the th Internatonal Multconference on Systems, Sgnals & Devces, SSD 204. (pp. -5). IEEE Press. 0.09/SSD.204.6808896 General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Downloaded from vbn.aau.dk on: May, 206
Power flow analyss for DC voltage droop controlled DC mcrogrds Chendan L, Sanjay K. Chaudhary, Tomslav Dragcevc, Juan C. Vasquez, and Josep M. Guerrero Department of Energy Technology, Aalborg Unversty, Aalborg, Denmark che@et.aau.dk Abstract Ths paper proposes a new algorthm for power flow analyss n droop controlled DC mcrogrds. By consderng the droop control n the power flow analyss for the DC mcrogrd, when compared wth tradtonal methods, more accurate analyss results can be obtaned. The algorthm verfcaton s carred out by comparng the calculaton results wth detaled tme doman smulaton results. Wth the droop parameters as varables n the power flow analyss, ther effects on power sharng and secondary voltage regulaton can now be analytcally studed, and specalzed optmzaton n the upper level control can also be made accordngly. Case studes on power sharng and secondary voltage regulaton are carred out usng proposed power flow analyss. Index Terms DC mcrogrd, droop control, power flow, power sharng, secondary control. I. INTRODUCTION Wth the promsng potental to provde means for the ntegraton of dstrbuted renewable energy, to facltate the modernzaton of present power system, as well as to mprove power qualty for costumer and to partcpant n demand respond, mcrogrd, wth ts defnton as a local grd that comprses dstrbuted generaton, energy storage systems and local loads, has been ncreasngly vewed as the one of most desrable solutons for the realzaton of smart grd. Accordng to the source type, mcrogrds can be dvded nto AC mcrogrds and DC mcrogrds. To cope wth nherent problems related to AC mcrogrds, such as the need for synchronzaton of the dstrbuted generators, the nrush currents due to transformers, reactve-power flow, harmonc currents, and three-phase unbalances, as well as to ncorporate ncreasng modern DC components wth less converson loss, such as photovoltac panels, batteres, fuel cells, LEDs, and electronc loads, DC mcrogrds have been chosen over AC mcrogrds []-[3]. Nowadays DC mcrogrds are found n data centers, telecom systems, and some buldngs and offces, and there s a trend toward adoptng more DC dstrbuton network. To manage the power flow of the DC mcrogrd, varous control strateges, e.g. Master-slave control [4], average current control method [5], and droop control usng vrtual mpedance [6], have been proposed. Among these strateges, due to ts autonomous feature, communcaton-less, and smplcty, droop control s most frequently adopted n the control of paralleled DC converters, whch s just the general form of DC mcrogrds. In ths method, the man dea behnd the droop control s that, smlar to the frequency n the AC bulk grd, the DC voltage n the DC mcrogrd can be treated as the control sgnal for the real power. Although transmsson lne losses mght not be the largest proporton for the system losses n the mcrogrd (e.g. PV system [7]), the power flow analyss s essental for DC mcrogrds due to the followng reasons. For one thng, due to the nherent defects of droop control n DC mcrogrds based on local voltage whch render the voltage regulaton and power sharng not accurate, a precse control strategy mght be proposed for DC power system based on power flow analyss results [8]. For another, the power sharng and voltage profle of the network are ndspensable for the plannng and operatonal stages of the DC mcrogrd, n term of systematc analyss, protecton coordnaton desgn, network optmzaton and optmal operaton, etc. Therefore, power flow analyss whch s sutable for the DC mcrogrd based on droop control s hghly needed, whle unfortunately not enough research work exsts n lterature besdes some work on HVDC [8]-[0]. Even some researches have been done for the hgh voltage DC power network, smlar to the tradtonal AC power flow, they use slack DC bus n the model wth the capablty of balancng the actve power n the network wth constant DC voltage [9],[0]. It s not, however, the case n realty. In order to fully analyze the steady state feature of the DC mcrogrd, droop control of the DC mcrogrd should be taken nto consderaton nto the power flow analyss algorthm. In ths paper, a power flow analyss algorthm s proposed for DC mcrogrds. The structure of ths paper s as follows. In the second secton, the mathematcal model of proposed power analyss s formulated by modfyng the tradtonal method. The verfcaton of the proposed algorthm s presented n the thrd secton based on a four-bus rng topology DC mcrogrd, and t shows effectveness of the algorthm. In order to show the addtonal features compared wth tradtonal methods, two case studes concernng power sharng and secondary regulaton of the system s demonstrated wth smulaton results. Fnally, conclusons are drawn n the last secton. II. MATHEMATICAL MODEL OF POWER FLOW CALCULATION FOR DROOP CONTROLLED DC MICROGRIDS In ths secton the tradtonal method s revewed and ts lmtaton for DC mcrogrds s dscussed frstly. Then, steady characterstc of droop controlled DC sources n DC mcrogrds
s presented as the foundaton for the proposed algorthm. The mathematcal model of the proposed algorthm s presented n the end of ths secton. A. Tradtonal power flow method Smlar to the power flow analyss n AC power system, the standard way has been set up for power flow analyss of DC system. In the standard way of modelng, all the generators and loads are connected wth the nodes defned as buses and, between the buses are the transmsson lnes whch are modeled as mpedance or mpedance network. In the steady state analyss, the overall power dspatch of the network s determned by the lne resstance and the dfference of bus voltage magntude between DC buses. Therefore, n the DC power system, at every bus, two varables need to be determned. They are the bus voltage and real njecton power. The objectve of the power flow s to calculate the power and voltage profle of each bus. In tradtonal method, t assumes that there s a bus workng as voltage regulator and keepng the voltage constant whle others control ther actve power njecton. So the slack bus has bus voltage magntude as known varable whle others have bus njecton real power as known varable. Accordng to the nodal power balance of matchng bus power njecton, load power njecton and generaton power njecton, the left unknown values wll be solved by the power flow algorthm through a certan teraton method. For DC mcrogrds, however, due to the lmted volume of the dsturbed DC sources, t s mpractcal to take any of them as slack bus whch can compensate whatever amount of real power. Moreover, the tradtonal way of modelng of the power flow analyss does not take the droop control parameters nto consderaton whch has decsve effects on the steady state characterstc of the system. The prncple of the droop control n the context of herarchcal control archtecture for DC mcrogrds wll be dscussed n the followng part. B. Steady characterstc of droop controlled DC sources n DC mcrogrds In DC mcrogrds, t s equvalent that many DC sources are connected n parallel. To avod the crculatng current and to acheve the proper power sharng for the load autonomously, the DC source should not work as stff voltage source. Takng the dea from speed droop regulated governors n the bulk grd, DC sources n DC mcrogrds are adoptng a droop by subtractng part of the converter output current, whch can also be done by multplcaton a value recprocal to devaton of measured voltage to reference voltage []. The frst method s llustrated by the followng equaton []. V = V R () * G 0 D G * Where V s the voltage reference to DC source whch G should be equal to the measured voltage value n a stable system n the steady state, V s the output reference at no load 0 condton whch s usually modfed from secondary control to acheve voltage regulaton, s the vrtual mpedance of the droop controller, and R D s the output current of the DC source. Accordng to (), the steady state characterstc of the DC mcrogrd s nfluenced by the droop control parameters,.e., V and R. 0 D C. Modfed power flow analyss for DC mcrogrds Wth takng the droop control of the DC source nto consderaton, all the DC sources are modeled as Droop-buses and they are obeyng the droop control prncple llustrated as () n the last secton. For smplcty, we assume loads n the system are only constant power loads, whose power s ndependent of the bus voltage, and consderng more load types wll be n the future work. There are two knds of buses n the system, one s droop bus, and the other s constant power bus. In the steady state model of the DC mcrogrd, t s possble to assume that the network s purely resstve wth pure resstance as lne mpedance []. Assumng there are totally n buses n the network, accordng to the Krchhoff's current law, that current njected at the bus equals to the sum of current flowng to other n- buses, the network equaton can be wrtten as follows Where I dc, s the DC njecton current n bus, Y dc, j s the admttance between the bus and bus j, and Vdc, s the voltage magntude n bus ; In a unpolar DC mcrogrd, for any bus, the njecton power has the followng relatonshp wth njecton current P = V I (3) Thus, network equaton (2) can also be wrtten as Addtonally, for the Droop-buses, there s one more constrant they have to follow (5) Where n I = Y ( V V ) dc, dc, j dc, dc, j j= j dc, dc, dc, P n dc, V dc, j= j = Y (V V ) V = V R 0 D dc, j dc, dc, j can be wrtten as, P = V Accordng to the real power balance of the system, the power balance equaton s as follows: (7) P P P D dc, = 0 The overall mathematcal model of power flow analyss s as follows: (2) (4) (6)
n Pdc, = Ydc, j (V dc, Vdc, j) (8) Vdc, j= j P V = V0 RD (9) V P PD Pdc, = 0 (0) III. VERIFICATION OF THE PROPOSED POWER FLOW ALGORITHM In order to verfy the effectveness of the algorthm, the calculated results by usng t are compared wth the results obtaned from a detaled tme doman smulaton based on Matlab Smulnk. To make the power supply more relable, rng topology s often adopted, thus here four-bus system usng the rng topology s taken as test system. The system topology s shown n Fg.. In ths system, two DC sources are controlled by P-V droop controller through vrtual mpedance n bus and bus 2. Two load buses are modeled as constant power load, wth defnte power demand. All the lne resstances are 0.05 Ω, and the rest of the parameters of the system s lsted n Table I. To compare wth the calculated results, the same system s set up n Smulnk of Matlab wth the same parameters. The comparson between results obtaned from tme doman smulaton wth results from calculaton usng proposed algorthm s shown n Table 2. It can be seen that the maxmum voltage ampltude devaton to the smulaton s less than 0.36%, and the maxmum bus njecton power devaton to the smulaton s less than 0.6%. The good agreement between these results ndcates the accuracy of the proposed algorthm for DC mcrogrds. DC source Lne 4 4 Lne 34 Lne 2 Fg. Topology of test four-bus system Many lmtatons are related to the tradtonal power flow algorthm for the DC mcrogrd. In order to show them, 4 more experments have been carred out based on tradtonal algorthm wth bus as the slack bus whle bus 3 set as the constant P bus. Snce n the tradtonal method, power sharng cannot be known beforehand, two dfferent load condtons n bus 3 are assumed as 0% of total demand and 70% of total demand respectvely. To show that calculaton results are also affected by the choce of ntal voltage of the slack bus usng tradtonal method, two dfferent flat voltage values are compared as well. From the Fg. 2, t can be seen that, n all 2 Lne 23 3 DC source 2 these voltage profles, the results calculated from the proposed algorthm are the closest to the results from the tme doman smulaton,.e., wth the consderaton of droop control n the proposed algorthm, more accurate results can be obtaned compared wth tradtonal algorthm usng slack bus. TABLE I. PARAMETERS OF THE FOUR BUS TEST SYSTEM DC source droop parameters parameters symbol value unts Reference voltage n bus V ref 48 V Reference voltage n bus 2 V ref2 48 V Vrtual resstance for DC source R d 0.2 Ω Vrtual resstance for DC source 2 R d2 0.5 Ω Load paramaters bus number power(w) 2 466.25 4 697.5 TABLE II. PARAMETERS OF THE FOUR BUS TEST SYSTEM SmPowerSystem results Power Flow Results No Mag.(p.u.) Power(W) Mag.(p.u.) Power(W) 0.97967 822.5 0.975766 87.23 2 0.97354 466.25 * 0.97367 466.25 * 3 0.973958 350.625 0.974035 349.62 4 0.968750 697.5 * 0.972306 697.5 * V m (pu).005 0.995 0.99 0.985 0.98 0.975 0.97 Smulaton results consderng droop control =0% load wth flat voltage p.u. n slack bus =0% load wth flat voltage 0.97 p.u. n slack bus =70% load wth flat voltage p.u. n slack bus =70% load wth flat voltage 0.97 p.u. n slack bus 0.965 2 3 4 Bus No. Fg. 2 Comparson of Voltage profles of the four-bus test system usng dfferent algorthms IV. CASE STUDIES In ths part, to show the addtonal features whch are desrable for the Energy Management System of the DC mcrogrd but unfortunately cannot be provded by the tradtonal algorthms, two case studes have been carred out based the four-bus rng topology DC mcrogrd. A. Power sharng control by modfyng the vrtual resstance As s known, the man purpose of the droop control s to acheve autonomous power sharng between dfferent DC sources, and the droop gan,.e., the vrtual resstance s often chosen accordng to the rated power of each DC source. That s to say, to change the value of the vrtual resstance, the power flow of the system wll be change, whch can be modfed accordng to the need or the optmzaton of the system. Wthout any representaton of ths mportant control varable n the power flow analyss, tradtonal methods cannot show
the power sharng changes accordng to the dfferent control parameters adopted n the DC mcrogrd system, thus cannot be used to analyss droop controlled DC mcrogrd n the plannng or operaton stages. To represent the feature that the proposed method can be used to analyze power sharng based on changng the droop gan, a comparson of the power sharng results based on two dfferent droop gan values s shown n Fg. 2. The R s chosen as 0.5Ω and R2 s 0.2 Ω n Case ; the R s 0.2 Ω and R2 s 0.5 Ω n case 2. Although power can be roughly reversely lnear wth the vrtual resstance, due to the voltage beng the local value and the exstence of the lne mpedance, there wll be some devaton from ths rough approxmaton. The proposed algorthm can get the accurate power sharng results n advance. Voltage Magntude (p.u.) Before secondary control After secondary control 0.9968 0.996 0.9963 0.9958 0.9757 0.9732 0.974 0.9723 2 3 4 Bus No. Power n Bus Power n bus3 Fg. 4 Voltage profle comparson before and after secondary control power (W) 337.87 826.82 87.23 case case 2 349.62 Fg. 3 Power sharng dfference comparson wth dfferent vrtual mpedance B. Secondary regulaton analyss To tackle the problem of voltage devaton, the secondary control n a herarchcal control archtecture are proposed n [] to restore the nomnal value of the voltage nsde the DC mcrogrd. In ths secondary layer, after the error between the nomnal bus voltage and measured bus voltage passng a PI controller, ths value obtaned s added to the V ref of the prmary control to restore the voltage. That s to say, the choce of the V ref relates to the voltage regulaton of the system, and thus to modfy ths value, the voltage profle of the DC mcrogrd can be regulated. To show that the proposed algorthm can analyze ths mportant characterstc n advance, voltage profles n per unt before and after secondary control are shown n Fg.4, whch shows that the secondary control levels voltage n all the buses n the system to close to the nomnal value. Ths addtonal feature of the proposed algorthm makes t possble for the upper level control layer of the Energy Management System to set the optmal reference value of V ref accordng to the need of the operaton based on the analyss results of t. V. CONCLUSION In ths paper, a new algorthm of power flow analyss for droop controlled DC mcrogrd s proposed. Voltage droop control n the prmary layer of the system has been taken nto consderaton n the power flow analyss for the DC mcrogrd. The algorthm verfcaton s carred out by comparng the calculaton results wth detaled tme doman smulaton results. Compared wth tradtonal methods, more accurate analyss results can be obtaned, usng the proposed algorthm. The proposed algorthm also makes t possble to analyze power sharng and secondary voltage regulaton. Case studes on power sharng and secondary voltage regulaton show that wth the droop gan (vrtual resstance) as a varable n the power flow analyss, effects of t on power sharng and secondary voltage regulaton can now be analyzed, and the new analyss algorthm provdes means for the upper level control layer to optmze the droop parameters beforehand. REFERENCES [] Guerrero, J.M.; Vasquez, J.C.; Matas, J.; de Vcuña, L.G.; Castlla, M., "Herarchcal Control of Droop-Controlled AC and DC Mcrogrds A General Approach Toward Standardzaton," Industral Electroncs, IEEE Transactons on, vol.58, no., pp.58,72, Jan. 20 [2] Dragcevc, T.; Guerrero, J.M.; Vasquez, J.C.; Skrlec, D., "Supervsory Control of an Adaptve-Droop Regulated DC Mcrogrd Wth Battery Management Capablty," Power Electroncs, IEEE Transactons on, vol.29, no.2, pp.695,706, Feb. 204; do: 0.09/TPEL.203.2257857 [3] Xaonan Lu; Ka Sun; Guerrero, J.M.; Vasquez, J.C.; Lpe Huang; Teodorescu, R., "SoC-based droop method for dstrbuted energy storage n DC mcrogrd applcatons," Industral Electroncs (ISIE), 202 IEEE Internatonal Symposum on, vol., no., pp.640,645, 28-3 May 202; do: 0.09/ISIE.202.6237336 [4] J. Rajagopalan, K. Xng, Y.Guo and F.C. Lee, Modelng and dynamc analyss of paralleled dc/dc converters wth masterslave current sharng control, n Proc. of APEC, pp.678-684, 996 [5] Wehong Qu and Zhxang Lang, \Practcal desgn consderatons of current sharng control for parallel VRM applcatons," 20th Annual Appled Power Electroncs
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