Active-reactive scheduling of active distribution system considering interactive load and battery storage

Transcription

1 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 DOI /s Protecton and Control of Modern Power Systems ORIGINAL RESEARCH Actve-reactve schedulng of actve dstrbuton system consderng nteractve load and battery storage Qxn Chen, Xangyu Zhao and Dahua Gan * Open Access Abstract Dstrbuted generaton (DG) are crtcal components for actve dstrbuton system (ADS). However, ths may be a serous mpact on power system due to ther volatlty. To ths problem, nteractve load and battery storage may be a best soluton. Ths paper frstly nvestgates operaton characterstcs of nteractve load and battery storage, ncludng operaton flexblty, nter-temporal operaton relatons and actve-reactve power relatons. Then, a mult-perod coordnated actvereactve schedulng model consderng nteractve load and battery storage s proposed n order to mnmze overall operaton costs over a specfc duraton of tme. The model takes nto accounts operaton characterstcs of nteractve load and battery storage and focuses on coordnaton between DGs and them. Fnally, valdty and effectveness of the proposed model are demonstrated based on case study of a medum-voltage 135-bus dstrbuton system. Keywords: Actve dstrbuton system, Actve-reactve schedulng, Interactve load, Battery storage 1 Introducton Actve dstrbuton system (ADS) s defned as dstrbuton networks that have systems n place to control a combnaton of dstrbuted energy resources (DERs), ncludng dstrbuted generators (DGs), battery storage, demand response, etc. [1]. In recent, hgh levels of DERs that could be effcently scheduled are beng ntegrated n order to acheve specfc operatonal obectves, for example, costs mnmzaton. Therefore, t would be necessary for the Dstrbuton System Operators (DSOs) to transform from the tradtonal passve undrectonal flow operaton approach to novel actve b-drectonal flow operaton approach [2]. To ths end, a crtcal challenge s to formulate the operaton characterstcs of dfferent knds of DERs and ntegrate them nto the schedulng scheme of ADS. At present, many nterestng researches related to the operaton of ADS have been conducted [3 6]. Plo et al. [1] and Keane et al. [7] proposed models and methodology to mnmze system operaton cost by optmzng the producton of the local DGs, ncludng the wnd turbne, photovoltac, consderng power exchanges wth * Correspondence: gandahua0151@sna.com State Key Lab of Power Systems; Dept. of Electrcal Engneerng, Tsnghua Unversty, Beng 10004, Chna the man dstrbuton system. As power outputs of DGs are always restrcted by meteorologcal factors [7], the volatlty characterstcs become a heavy burden to the DSOs. In ths case, battery storage could serve as an opton for accommodatng volatle outputs of DGs []. An optmal model for ADS proposed n [9] contans DGs and battery storage, but only take the capacty lmtaton of battery storage nto consderaton. Further, the relaton between actve-reactve power outputs of battery storage s consdered n [10 12], and the actve-reactve coordnaton model for DGs and battery storage s proposed. Though battery storage could solve the volatlty of DGs, ther hgh nvestment cost may ncrease the total operaton cost of the dstrbuton system [13]. Therefore, demand response may be another soluton. In fact, demand response s a prce mechansm between DSOs and the local users, and nteractve load s an mportant type of demand response. Under the agreement, the DSOs could change the orgnal load shape, whle users could get some payback from the DSOs. Compared to battery storage, demand response could acheve smlar ams and, at the same tme, there would be hardly no nvestment cost. Dozens of demand response proects have been establshed and operated n many countres The Author(s) Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton 4.0 Internatonal Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made.

2 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 2 of 11 [14 1]. Whle an optmal model of ADS consderng demand response and battery storage s not yet proposed. Based on the above analyss, ths paper focuses on mult-perod coordnated actve-reactve schedulng of ADS consderng demand response and battery storage. Frstly, we desgn a new form of demand response, namely nteractve load and the structure of battery storage s also analyzed. Then, the problem descrpton and the mathematcal model of nteractve load and battery storage are presented. Based on these model, a novel mult-perod actve-reactve coordnated schedulng model s proposed for ntegrated operaton of ADS, n order to mnmze overall operaton costs over a specfc duraton of tme. The model takes nto accounts operaton characterstcs of varous DERs and formulates mult-perod operaton of ADS. Fnally, valdty and effectveness of the proposed model are demonstrated based on case study of a medum-voltage 135-bus dstrbuton system. 2 Flexble operaton of nteractve load and battery storage 2.1 Introducton to nteractve load Accordng to the report of Federal Energy Regulatory Commsson about demand response (DR) and advanced meterng, DRs could be dvded nto 15 types on the bass of ther response form, such as Drect Load Control, Interruptble Load, Crtcal Peak Prcng wth Control, etc. Interactve Load desgned n ths paper s a combnaton of Drect Load Control, Demand Bddng and Buyback. Its basc feature s that the DSOs would obtan the rght to nvoke the electrcal equpment accordng to the agreement, thus the shape of power load could be changed to the most economcal way. Whle at the same tme, consumers could get economc compensaton due to ther partcpatons n load shftng. Accordng to the effect on the load curve, nteractve load could be dvded nto Peak Cuttng Load and Peak Shftng Load. As shown Fg. 1, Peakng Cuttng Load would restrct power load durng Peakng perod and cause the loss of electrcty consumpton. Whle the load cut durng peak perod by Peak Shftng Load would be shfted to the valley perod and the electrcty consumpton could be remaned, as shown as Fg. 2. (Please delete the followng Fg. 2 Peak Shftng Load, t s added automatcally when buldng up the PDF and I cannot tell why). In fact, Peak Cuttng Load s another category of Peak Shftng Load whose load cut durng peak perod wouldn t be compensated. And consderng that Peak Cuttng Load may cause uncontrollable load rebound durng valley perod, ths paper focuses on the Shftng one. Furthermore, t could be dvded nto two types, namely Shapeable Load and Removable Load. Ther characterstc and modelng wll be presented n the followng chapters. 2.2 Characterstc and modelng of shapeable load Introducton to shapeable load As shown n Fg. 3, Shapeable Load could change the load shape durng load shftng accordng to the agreement, but electrcty consumpton and the duraton tme of Shapeable load should be remaned Load shftng potental analyss of shapeable load Thermal storage, such as large-scale central condtonng system, s an mportant resource of Demand Sde Response. Its applcaton could be descrbed as Shapeable Load and ts electrcal characterstcs s descrbed n. The thermal storage proects mplemented n Chna are nvestgated n ths paper and the load shftng potental s lsted n Table Characterstc and modelng of removable load Introducton to removable load Compared wth Shapeable Load, Removable Load has strct requrements when shftng. As shown n Fg. 4, t requres that load shape should stay the same. Fg. 1 Peak Cuttng Load Fg. 2 Peak Shftng Load

3 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 3 of 11 Fg. 3 Shapeable Load Fg. 4 Removable Load Load shftng potental analyss of removable load Removable Load can be used to descrbe the producton process transfer of ndustral user. Industral producton tend to have a relatvely fxed producton process. So when transferrng ther producton process, ther load shape should be the same. Ths paper nvestgates load shftng potental of ndustral users n Beng, Chna. The results of the survey are shown n Table 2. Total load shftng potental s 90 ~ 120 MW, about 2.5% of the peak load. If all the load shftng potental of ndustral users could be made full use of, power grd operaton wll be mproved sgnfcantly. 2.4 Characterstc and modelng of battery storage Accordng to the energy storage form, battery storage can be dvded nto superconductng energy storage, chemcal battery energy storage, flywheel energy storage, etc. Though ther energy storage form are qute dfferent, they share smlar structure. As shown n Fg. 5, generally speakng, battery storage ncludes two components. Storage unt s used for energy storage, ts capacty decdes how much power energy can be stored n Table 1 Load shftng potental analyss of thermal storage n Chna Locaton Proect Name Load Shftng Potental Beng 94 Thermal Storage 200 MW proects n 2002 Beng Industral consumer 100 MW(1996), 2.3% of the peak load Guangzhou Cold storage proect at Economc Trade Commsson buldng n kw Guangx Provnce Shangha Shangha Thermal Equpment n 11 consumers Cold storage proect n Jndu Buldng Central Ar condtons system n hotel and mall 162 MW, 2.3% of the peak load 220 kw 59 MW As a concluson, load shftng potental of Shapeable Load would be enormous as thermal storage proects are promoted wdely n Chna the battery. Power condtonng system (PCS) s an electrc power devce, whch s used to exchange power energy wth the power grd. Its control mode decdes actve and reactve power of the battery. 3 Methods 3.1 Modelng of nteractve load Ths secton s focus on formulatons on operaton characterstcs of shapeable load and the removable one. The analyzed characterstcs nclude load shftng cost curve, load shftng poston and constrants for load shape and electrcty consumpton Load shftng cost curve For descrbng the load shftng cost, load shftng cost curve s desgned as shown n Fg. 6. The farther load s shfted, the heaver t changes the habt of users, so the cost wll be more expensve. Thus, we can get a load shftng cost curve lke a tub. The load shftng cost could be expressed as: C IL ¼ XT X NSL ¼1 P RL;A λ shft P SL;A þ XT X NRL ¼1 λ shft ð1þ where C IL denotes total load shftng cost of nteractve load, ncludng two parts, the cost of shapeable load and t of removable load. T devotes the total perod number. NSL Table 2 Load shftng potental analyss of ndustral users n Beng Industral User Name Load Shftng Potental(MW) Shougang Corporaton 50 Tegang Corporaton 10 ~ 20 Yanhua Corporaton 5 ~ 10 Chemcal Industry 10 ~ 20 Buldng Materals Industry 10 Total 90 ~ 120

4 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 4 of 11 Fg. 5 The Structure of Battery Storage (should be Fg. 5, t s changed to Fg. 1 after buldng the PDF and I cannot fgure out why) and NRL respectvely denote the number of shapeable load and removable load. λ shft denotes the load shft cost of shapeable load or removable load at perod. P SL;A and P RL;A respectvely denote the load of shapeable load and removable load at perod after ther shftng Load shftng poston In order to descrbe load shftng poston of nteractve load, we ntroduce a set of state varables, η SL and η RL, respectvely denotng whether the head of shapeable load and removable load s shfted to perod. It should be ensured that every head of shapeable load or removable load can be shfted to only one poston. And n order to not affect operaton of next day, the state varables from η SL T T 0 ; to ηsl T; and from η RL T T 0 ; to ηrl T; are set to 0. It could be expressed as: η SL η SL ¼ 1 η RL ¼ 1 ¼ T T SL 0; þ 1; T þ 1; T ¼ 0 η RL ¼ 0 ¼ T T RL 0; ð2þ Where T SL 0; and η RL 0; respectvely denotes the length of shapeable load and removable load Constrants for load shape and electrcty consumpton Load shape of shapeable load could be changed before and after shftng, but electrcty consumpton should be the same. Whle load shape of removable load should be the same. Load at perod could be expresses as: P SL;A m; m¼1 P SL ¼ XT SL 0; X P RL;A P SL;B m; m¼1 m¼ T SL 0; þ1 RL ¼ XT 0; η SL mþ1; m¼1 η SL m; PSL;A P SL PRL;B m; X m¼ T SL 0; þ1 η SL m; ð3þ where P SL;A and P RL;A respectvely denote the load of shapeable load and removable load at perod before ther shftng. P SL and P SL denote the upper and lower bounds of shapeable load. The relaton between actve and reactve load of nteractve load s complcated. It s assumed that ther power factor stay the same before and after shftng. It could expressed as: P SL;A P SL;B P RL;A P RL;B ¼ C SL ¼ C SL ¼ C RL ¼ C RL Q SL;A Q SL;B Q RL;A Q RL;B ð4þ where C SL and C RL respectvely denote the fxed coeffcent between actve load and reactve load of shapeable load and removable load. 3.2 Modelng of battery storage Ths secton s focus on formulatons on operaton characterstcs of battery storage. The analyzed Fg. 6 Load Shftng Cost Curve (should be Fg. 6, t s changed to Fg. 2 after buldng the PDF and I cannot fgure out why)

5 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 5 of 11 characterstcs nclude operaton cost for battery, constrants for energy storage, power exchange and state transton number Constrants for energy storage It must be nsured that the stored energy s wthn the storage capacty lmtaton at any perod. Besdes power loss should also be taken nto consderaton, ncludng the loss wthn chargng process, dschargng process and storage process. Ths paper converts all these losses nto chargng process n order to smplfy the ssue. Then the stored energy at fnal perod should be equal to that at ntal perod after consderng lmtatons. All these constrants could be expressed as: E S ES;pre ¼ 1 T n¼1 þ X n¼1 μ S P S;C n; μ S P S;C n; PS;D n; ¼ 0 ΔT P S;D n; ΔT E S ð5þ where E S and E S denote the upper and lower bounds of storage capacty of battery storage. E S;pre denotes the ntal stored energy. P S;C and P S;D respectvely denote the actve power charged or dscharged between battery storage and the grd at perod. u S s the loss rate of the storage battery at charge process Constrants for power exchange Devce type and control mode of PCS decdes the actve and reactve power characterstcs of battery storage. Nowadays, full-controlled electrcal devces are wdely used n battery storage, thus makng the battery could operatng n four-quadrant zone as shown n Fg. 7. Constrants for actve and reactve power could be expressed as: 2 P S;C þ Q S 2 2 S S 2 P S;D þ Q S 2 2 S S P S;C 0 P S;D 0 ð6þ where Q S denote reactve power of the battery storage at perod and S S denote the power bound to the battery storage Constrants for state transton number Lfetme of battery storage s hghly affected by ther state transton number. To prolong the lfetme of battery storage, only one cycle charge/dscharge per day s Fg. 7 Actve and Reactve Power of Battery Storage typcally chosen for optmal operaton. Consderng the contnuty of battery storage operaton, as shown n Fg., every storage would go through one charge/dscharge state change and one dscharge-charge state change. These constrants could be expressed as: η S;S ; η S;CD ; η S;DC f0; 1g η S;S η S;S 1; ηs;cd þ η S;DC ¼ 0 η S;CD ¼ 1 η S;DC ¼ 1 ð7þ where η S;S denotes the state of battery storage at perod. It wll be set to one when the battery s n dscharge process, whle zeros corresponds to the charge process. η S;CD and η S;DC respectvely denote the operaton state change from charge process to dscharge process and from dscharge process to charge process. It s guaranteed by the second sub-formula n () that η S;CD wll be assgned as one f the operaton state of battery storage s changed from charge process to dscharge process at perod. Whle t wll be zero at other perod. Smlar stuaton can be mplemented to as t wll be assgned as one f the operaton state of battery storage s changed from dscharge process to charge process at perod. Besdes the thrd and fourth sub-formula guarantee that the state transton number would be ust one. η S;DC

6 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 6 of 11 Fg. The Contnuty of battery storage Operaton cost for battery storage Operaton cost for battery storage ncludes the deprecaton of nvestment cost and daly operaton cost. The deprecaton of nvestment cost could be expressed by a fxed constant and daly operaton cost could be calculated by the exchanged power. These relaton could be expressed as: C BS ¼ M BS;D þ XT λ S;P P S;C þ λ S;Q Q S ðþ where C BS and M BS;D denote the total operaton cost and the deprecaton of nvestment cost of battery storage. λ S;P and λ S;Q are the actve and reactve cost coeffcents of battery storage. 4 Mult-perod coordnated schedulng model consderng battery storage and nteractve load 4.1 Decson varables The decson varables nclude contnuous ones for actve and reactve power of source bus, dstrbuted generaton, battery storage as well as nteractve load, and 0 1 bnary nteger ones for operaton states of battery storage and nteractve load. Noted that there are two operaton processes for battery storage, dscharge and charge, three sets of decson varables would be assgned for each process Contnues decson varables Contnues decson varables nclude P Sou Q DG, P SL;A where P Sou, Q SL;A, P RL;A and Q Sou power of source bus at tme nterval and P DG, Q Sou, P DG,, Q RL;A, P S;C, P S;D, Q S, V,, θ,, denote the actve and reactve and Q DG are the actve and reactve power of dstrbuted generaton at tme nterval. V, and θ, denote the voltage ampltude and angle of bus at tme nterval bnary nteger decson varables 0 1 bnary nteger decson varables nclude η SL, ηs;s, η CD, η DC. 4.2 Obectve functon The obect s to mnmze the overall operaton costs of dstrbuton system over a specfc duraton of tme, ncludng power generaton/operaton costs from source bus, dstrbuton generaton, and battery storage, load shftng cost of nteractve load and nvestment costs of ) battery storage f t s bult by DSO. It can be expressed as: mn λ Sou;P þ XT X NG ¼1 þ XT X NS ¼1 þ XT X NSL λ shft ¼1 P Sou λ DG;P þ λ Sou;Q P DG þ λ DG;Q Q Sou Q DG λ S;P P S;C þ λ S;Q Q S þ XNS P SL;A ¼1 þ XT X NRL C shft ¼1 M BS;D P RL;A ð9þ Where λ denotes cost coeffcents. The superscrpts of the varables and parameters n (10) are used to dstngush dfferent knds of DERs (Sou, DG and S,P) and actve and reactve power output (P, Q). NG and NS respectvely denote sets of dstrbuton generaton and battery storage. In (9), generaton costs of the source bus are related to ts actve and reactve power. The costs of reactve power mght come from contracts or auxlary markets, these two mechansms could both be reflected by cost coeffcents. The same stuaton would be mplemented to dstrbuted generatons. 4.3 Constrants Constrants manly consst of two categores, respectvely related to system operaton and varous DERs System operaton constrants System operaton constrants are safety operaton constrants for the dstrbuton system, ncludng constrants

7 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 7 of 11 for power balance, bus voltage and transmsson power flow. Power balance constrant on source bus s expressed as: < : P Sou P load ;s Q Sou Q load ;s ¼ F 1 ðv ; θ Þ ¼ F 2 ðv ; θ Þ ð10þ Power balance constrants on other buses are expressed as: X NG m P DG ;m þ ¼ F 1 ðv ;;θ Þ X NG m Q DG ;m þ ¼ F 2 ðv ;;θ Þ XNS m XNS m P S;D ;m Q S;D ;m XNS m XNS m P S;C ;m þ Q S;C ;m þ XNSL m XNSL m P SL;A ;m Pload Q SL;A ;m Qload ð11þ where P load and Q load respectvely denote actve and reactve load of bus at tme nterval. V s vector of bus voltage magntude and θ s vector of bus voltage angle at tme nterval. F 1 and F 2 are actve and reactve power flow functons. Note that crcut parameters and operaton state of dstrbuton system are qute dfferent from those of transmsson system, transmsson power flow should be calculated based on AC power flow. Constrants on transmsson power flow are expressed as: S lne Where S lne 2 þ Q lne 2 P lne and S lne are upper and lower capacty lmtatons of lne. P lne 2 lne 2 S ð12þ and Q lne are the actve and reactve transmsson power flow of lne at tme nterval. Constrants on bus voltage are expressed as: V b V V b V ¼ V s;set θ ¼ 0 ð13þ where V,s and θ,s denote voltage magntude and angleofsourcebus.v b and V b respectvely denote upper and lower lmtaton of voltage magntude of bus DER operaton constrants Operaton constrant constrants on dstrbuted generaton, battery storage and nteractve load are establshed based on ther operaton characterstcs. The generaton range and the relatons on actvereactve power output are two mportant operaton characterstcs for dstrbuted generaton. The output range of wnd turbne and photovoltac s based on ther power predcton, whle power output of gas turbne should be adusted wthn ts generaton capacty lmtaton. Dstrbuted generaton are always connected to dstrbuted system through power electroncs equpment. Relatons on actve reactve power output are manly decded by types and control strateges of the equpment. And there are manly two knds of control strateges: constant voltage control (CVC) and constant power factor control (CPFC). These relatons could be formulated as: P G PG PG Q G QG QG CPFC : P G ¼ CG G Q CVC : V G ¼ V G;set ð14þ where P G and Q G respectvely denote the actve and reactve power output of dstrbuted generaton at perod and P G, P; G, Q G and Q; G are ther upper and lower bounds. C G s the controlled power factor between actve and reactve power of dstrbuted generaton. V G s the bus voltage whch dstrbuted generaton s connected to and V G;set ndcates the controlled voltage level. Formulatons on operaton of nteractve load and battery storage have been dscussed n chapter III ncludng formula (2 ). 4.4 Soluton method Obvously the formulated mult-perod coordnated schedulng model s essentally a typcal nonlnear mxed nteger programmng problem. GAMS could be used to solve ths problem. 5 Case study Ths proft mnmzaton problem s a standard SOCP problem. We used MATLAB on a computer wth a Pentum-M (2.0 GHz) processor and 1GB of DDR-RAM and selected CPLEX 12.0 as the solver.

8 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page of 11 Table 4 Characterstcs of the battery storage Num Bus Intal electrcty/kwh Maxmum capacty/kwh Maxmum exchangng power/kw Power exchange loss Fg. 9 The profle of system load 5.1 Basc data System data The proposed model s mplemented on the tested REDS (Repostory of Dstrbuton Systems) 135-bus dstrbuton system. The test system has been extended from sngle-perod to mult-perod, wth 1 day as the scheduled duraton and 1 h as basc tme nterval. The profle of system load s shown n Fg. 9. The curves wth crosses denote actve power load; whle the ones wth trangles denote reactve power load. 5.2 DER data Eght DGs are added, ncludng fve GTs, two WTs and one PV; one SD and one CL are added as well. Table 3 gves the characterstcs of the dstrbuted generators. The buses whch DGs s connected to are lsted n the second column. And the frst two DGs are used to smulate wnd turbne (W), the last one for photovoltac (P) and the rest for gas turbne. The power factor of the DGs s set to 0. f exsted and the voltage s set to 1.05, ramp rate s 100 kw/ 15 mn. Table 4 gves the characterstcs of the battery storage. There s one battery storage added to the case whch s connected to bus 39. Its ntal electrcty s 4000kWh and maxmum capacty s 000kWh. Its maxmum exchangng power s 500 kw and power loss rate durng chargng s We desgn one removable load and one shapeable load n the case. Removable load s connected to bus 30, and shapeable load to bus 6. Ther orgnal load shape are shown n Fgs. 10 and 11. We desgn the same load shftng cost curve for them shown n Fg Results and dscusson 6.1 Schedules of the source bus The curve wth crosses n Fg. 13 shows actve power schedules of the source bus; whle the one wth trangles denotes the total load demand. The trends of the two curves are roughly consstent, wth devatons reflectng power outputs from varous DERs. 6.2 Schedules of the DGs Fgure 14 shows actve and reactve power schedules of the DGs. The curves wth crosses denote actve power schedules; whle the ones wth trangles denote reactve power schedules. Table 3 Characterstcs of the dstrbuted generators Num Bus Type Power Factor Voltage Ramp Rate (kw/15 mn) 1 2 W W G G G G G P Fg. 10 The profle of orgnal Shapeable Load

9 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 9 of 11 Fg. 11 The Profle of orgnal removable load Fg. 13 Actve power schedules of the source bus No curtalments are observed for WTs and PV, as ther capactes are relatvely low n ths tested system; therefore, the fluctuatons could be easly offset by the source bus and the GTs. Reactve power schedules of DG 3, 5 and 7 are approprately adusted to keep the bus voltages at the set range, as they adopt CVC control strategy. Therefore, schedules of reactve power are ndependent of that of actve power. However, For DG 4 and 6, as they adopt CPFC strategy, reactve power schedules are proportonal to that of actve output. 6.3 Schedules of the storage battery Fgure 15 shows actve power schedule of the SD. Postve values ndcate charge state whle negatve ndcate dscharge. It could be observed that operaton state of the SD s well scheduled, whch s n charge state durng valley load perods and n dscharge state durng peak load perods. Ths schedule could smooth bus load curve and thus mght be helpful to reduce overall dstrbuton power losses to some extent. 6.4 Schedules of the nteractve load Fgure 16 shows actve power schedule of the removable load. The curves wth crosses denote Orgnal load curve; whle the ones wth trangles denote load curve after removng. They have the same shapes. Fgure 17 shows actve power schedule of the shapeable load. The curves wth crosses denote Orgnal load curve; whle the ones wth trangles denote load curve after removng. Though ther have the dfferent shapes, ther load stay the same. Fg. 12 The profle of load shftng cost Fg. 14 Actve-reactve power schedules of the DGs

10 Chen et al. Protecton and Control of Modern Power Systems (2017) 2:29 Page 10 of 11 Fg. 17 Actve power schedule of the Shapeable Load Fg. 15 Actve power schedule of the storage battery 7 Conclusons Implementaton of DGs mposes great challenges on tradtonal dstrbuton system operaton. And nteractve load and battery storage would reduce ther volatlty. So schedulng coordnated DG and them wll be an mportant research topc, whch mposes remarkable mpacts on system economcs and securty. Ths paper frstly nvestgates operaton characterstcs of nteractve load and battery storage. Load shftng cost, load shftng postve, load shftng shape and the relaton between actve and reactve load of nteractve load are respectvely dscussed and formulated. And to battery storage, constrants for energy storage, power exchange, state transton number and operaton cost are also formulated n detal. Then, a mult-perod coordnated schedulng model s proposed for ntegrated operaton of ADS, wth the obect of costs mnmzng. A tested case s studed, whch s based on a 135-bus dstrbuton system wth eght DGs, one SD and one CL connected. Soluton of the proposed model ncludes optmal schedules of the DERs, whch help to smooth bus load and cut dstrbuton losses n the premse of secure operaton constrants. Authors contrbutons QC: Intated the research and establshed models and schedules used for ths study, XZ: Cope wth establshng the formulaton on Operaton of Interactve Load and Battery Storage. DG: Manpulated the load data and summarzed results n the case study. All authors read and approved the fnal manuscrpt. Competng nterests The authors declare that they have no competng nterests. Receved: 1 Aprl 2017 Accepted: 3 July 2017 Fg. 16 Actve power schedule of the Removable Load References 1. Plo, F., Psano, G., & Soma, G. G. (2009). Dgtal model of a Dstrbuton Management System for the optmal operaton of actve dstrbuton systems. SmartGrds for Dstrbuton, 200. IET-CIRED. CIRED Semnar IEEE Xplore, Hdalgo, R., Abbey, C., & Joós, G. (2010). A revew of actve dstrbuton networks enablng technologes. Power and Energy Socety General Meetng IEEE, 1 9.

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