Optimal Distributed Energy Resources Sizing for Commercial Building Hybrid Microgrids

Transcription

1 Optimal Ditributed Energy Reource Sizing for Commercial Building Hybrid Microgrid Yihen Wang, Zhehan Yi, Di Shi, Zhe Yu, Bibin Huang, Zhiwei Wang GEIRI North America, San Joe, CA, USA State Grid Energy Reearch Intitute, Beijing, China. arxiv: v1 [math.oc] 1 Mar 2018 Abtract A microgrid have advanced from early prototype to relatively mature technologie, converting data center integrated commercial building to microgrid provide economic, reliability and reiliency enhancement for the building owner. Thu, microgrid deign and economically izing ditributed energy reource (DER) are becoming more demanding to gain widepread microgrid commercial viability. In thi paper, an optimal DER izing formulation for a hybrid AC/DC microgrid configuration ha been propoed to leverage all benefit that AC or DC microgrid could olely contribute. Energy torage (ES), photovoltaic () and power electronic device are coordinately ized for economic grid-connected and reliable ilanded operation. Time-of-ue (TOU) energy uage charge and peak demand charge are explicitly modeled to achieve maximum level of cot aving. Numerical reult obtained from a real commercial building load demontrate the benefit of the propoed approach and the importance of jointly izing DER for the grid-connected and ilanded mode. Keyword Ditributed Energy Reource (DER), hybrid microgrid, AC/DC, izing, building A. Set and Indice NOMENCLATURE S Set of repreentative day, indexed by. T Set of time interval, indexed by t. B. Deciion variable Total invetment. Energy/demand charge at day. Lot of critical/non-critical load cot at day. Energy torage degradation cot at day. Intalled capacitie. Intalled batterie power rating. Intalled interfacing converter capacitie. Intalled inverter capacitie. Intalled converter capacitie. Energy purchaed from utility at day time t. Net load peak demand at day. AC/DC load hedding at day time t. Non-critical AC/DC load hedding at day time t. v DC DC output at day time t. /DC ES AC/DC dicharge at day time t. c inv c e/d c lcl/lnl c deg x P V x ES x IC x INV x CON p grid p peak lcl AC/DC lnl AC/DC ch AC/DC ES AC/DC charge at day time t. oc ES tate-of-charge at day time t. Thi work i funded by SGCC Science and Technology Program. f DCin f DCout z DC AC bu flow at day time t. DC bu injection at day time t. DC bu extraction at day time t. Binary indicator for DC bu flow direction at day time t, 1 for injection, 0 otherwie. y ES Binary indicator for ES dicharging tatu at day time t, 1 for dicharging, 0 otherwie. Ilanded DC output at day time t. Ilanded ES AC/DC dicharge at day time t. Ilanded AC bu flow at day time t. Ilanded DC bu injection at day time t. Ilanded DC bu extraction at day time t. Ilanded DC bu flow direction indicator at day time t, 1 for injection, 0 otherwie. u ES /κ ES Auxiliary variable for ES dicharging tate. vi DC /DC fi AC fi DCin fi DCout zi DC C. Parameter π Probability of repreentative day. C P V Annualized invetment for. C ES Annualized invetment for ES. C IC Annualized invetment for interfacing converter. C INV Annualized invetment for AC/DC inverter. C CON Annualized invetment for DC/DC converter. C deg Degradation cot for ES. λ e t Price for energy uage charge at time t. λ d Price for demand charge. V OLL CL Value-of-lot-load for critical load. V OLL NL Value-of-lot-load for non-critical load. P T ariff Tariff allowed maximum peak demand. η IC Efficiency for interfacing converter. η INV Efficiency for DC/AC inverter. η CON Efficiency for DC/DC converter. η ch/dch Efficiency for ES charging/dicharging. CL AC/DC AC/DC load at day time t. NL AC/DC Non-critical AC/DC load at day time t. ES max Maximum ES power capacitie. P V max Maximum available capacitie. V availability profile in p.u. at day time t. ρ EP Batterie energy-power ratio. α min/max Minimum/maximum battery energy level. M Large enough contant. I. INTRODUCTION A microgrid can be defined a a ingle controllable entity which include a group of interconnected load and ditributed energy reource (DER) to act with repect to the grid [1].

2 DC/DC Bi-DC/DC Interfacing Converter DC/AC DC/D Additionally, it can connect and diconnect from the main grid to operate in either grid-connected or ilanded mode upporting cutomer critical reource a needed. A it ha advanced from early prototype to relatively mature technologie, the microgrid concept ha attracted growing attention from both indutry and academia for implementation and deployment [2]. Interfacing between the utility grid and cutomer, microgrid are effective olution to provide multiple ervice to both partie with reduced operating cot [3], [4], [5], improved reliability [6], [7], [8] and enhanced reiliency [9], [10], [11]. Optimal DER izing to determine energy torage [12], [13], [14], [15] and demand repone [16], [17], [18] capacitie are eential to gain all the benefit microgrid can offer. Chen et al. [3] ized energy torage from a cot-benefit analyi with microgrid unit commitment cheduling. A cooperative planning approach wa propoed for networked microgrid conidering wind and olar [5]. Bahramirad et al. [6] formulated a mixed-integer linear program (MILP) to invet energy torage to minimize the operating cot a well a the reliability impact from generator outage and renewable intermittency. Similarly, community microgrid reliability wa taken into account a in [7], [8]. Reiliency againt natural diater i a preing iue, and Khodaei [9] propoed a decompoition framework to iteratively olve for optimal chedule. A robut approach to conider the renewable, load and market price uncertainty wa introduced by the ame author in [19]. Compared to the conventional AC microgrid mentioned before, DC microgrid [20], [21] recently are gaining popularity for their direct link with DC generation and load, uch a, ES, LED lightning and DC data center. However, it i till cotly to build or upgrade to pure DC microgrid. Hence, hybrid AC/DC microgrid [22] are good alternative to leverage all the benefit from both AC and DC microgrid without huge contruction upgrade. Thi i particularly appealing to achieve widepread commercial viability. Lotfi et al. ha compared AC or DC configuration [24] and propoed a hybrid microgrid formulation [23]. Currently, commercial building owner pay expenive electricity bill for both energy uage charge and peak demand charge and follow tringent reliability requirement for the critical load inide. Converting thee building into hybrid microgrid with properly ized DER augment the overall economic and reliability. However, exiting microgrid izing approache either neglect two-part charge with underized DER or are conervative leading to overized one. Full formulation for the hybrid microgrid i miing a well. Thi paper propoe a two-tage optimal DER izing trategy for commercial building hybrid microgrid. It jointly minimize the invetment of energy torage, and power electronic device a well a the expected operating cot which include grid-connected mode energy charge, demand charge, torage degradation cot and ilanded mode load hedding penaltie. Thi formulation i then linearized into a computational efficient MILP. With optimized DER capacitie, thi model achieve economic grid-connected mode and reliable ilanded mode performance. Numerical reult baed on real commercial building load profile alo demontrate the importance and neceity of imultaneouly conidering gridconnected mode energy charge and demand charge together Fig. 1. AC Bu DC Bu ES PCC Hybrid Microgrid Configuration Utility AC Load DC Load with ilanded load hedding reliability cot. AC Non- Load DC Non- Load The ret of the paper i organized a follow. Section II preent the commercial building hybrid AC/DC microgrid configuration and the mathematical formulation of the propoed izing approach. Section III preent a detailed cae tudy baed on the real data collected from a Californian commercial building. The influence of the energy charge, demand charge and critical load are dicued. Section IV conclude the paper. II. MATHEMATICAL FORMULATION Thi ection provide the mathematical formulation of a DER izing trategy for a commercial building hybrid AC/DC microgrid. It optimize the ES, and power electronic device capacitie to minimize the combination of invetment, grid-connected electricity bill, ilanded load hedding penaltie and torage degradation. A. Commercial Building Hybrid Microgrid Configuration Fig. 1 illutrate the adopted hybrid microgrid configuration in thi paper. The microgrid i deigned for a commercial building with critical load reource a data center. Thi microgrid include an AC bu and a DC bu where critical load are attached. ES i hared by both bue via a DC/AC inverter and a DC/DC converter. The other DER component,, i linked to the DC bu by a DC/DC converter for maximum power point tracking (MPPT) and direct power control. Utility grid i connected at the point of common coupling (PCC) for AC bu voltage and frequency control and collecting energy and demand charge from the microgrid (building) owner. Revere flow i not permitted for utility regulation purpoe. B. Optimal Sizing Strategy min obj = c inv + π (c e + c d + c lcl + c lnl + c deg ) (1)

3 c deg (vi DC c inv = C P V x P V + C ES x ES + C IC x IC + C INV x INV + C CON x CON (2) CL DC c lcl c lnl c e c deg ( λ e t p grid (3) c d = λ d p peak (4) V OLL CL (lcl AC V OLL NL (lnl AC + ch AC η INV ch AC /η INV + p grid (dch DC f DCout + CL AC + NL AC ) (5) + lcl DC ) (6) + lnl DC ) (7) = + v DC )η CON ch DC /η CON = f DCin + CL DC + NL DC (8) (9) = f DCin /η IC f DCout η IC (10) 0 f DCin 0 f DCout ch AC z DC M (11) (1 z DC ) M (12) x ES y ES (13) x ES (1 y ES ) (14) α min ρ EP x ES oc α max ρ EP x ES (15) oc = oc 1 + (ch AC ( )η ch )/η dch (16) v DC V x P V (17) 0 p grid p peak (18) p peak P T ariff (19) η INV = fi AC + CL AC lcl AC + NL AC lnl AC ) η CON + fi DCin fi DCout lcl DC fi AC + NL DC 0 lcl AC 0 lnl AC 0 lcl DC 0 lnl DC lnl DC = (20) (21) CL AC (22) NL AC (23) CL DC (24) NL DC (25) = fi DCin /η IC fi DCout η IC (26) 0 fi DCin 0 fi DCout zi DC M (27) (1 zi DC ) M (28) vi DC V x P V (29) x ES (30) oc 1 (31) The objective function (1) minimize the annualized microgrid invetment and expected operating and reliability cot. Equation (2) decribe the purchae cot for, ES, bidirectional interfacing converter (IC), AC/DC inverter and DC/DC converter. Utility bill for energy and demand charge are calculated in (3) and (4). Grid-connected mode torage degradation i alo accounted in (5) to avoid frequent deep cycle charging and dicharging. and non-critical load hedding during the ilanded mode are penalized in (6) (7). Grid-connected mode operation are modeled in (8) (19). Equation (8) and (9) enforce the power balance for the AC and DC bue where load hedding i not allowed. The power flow through the interfacing converter i formulated in contraint (10) (12). Due to the bidirectional converion lo, binary variable z DC are ued to indicate the flow direction with big- M contraint a in [12], [25]. ES charging, dicharging, tateof-charge (SoC) limit and SoC tranition are decribed in (13) (16). To avoid imultaneou charging/dicharging, ES dicharging tate are alo optimized with binary variable y ES. With MPPT and direct power control, generation hould not exceed the maximum available output a in (17). Following tariff plan, peak demand for the net load i calculated and limited in (18) and (19). Ilanded mode i one of the mot alient feature of microgrid, which enable a diconnected ervice from the main feeder. During the ilanded mode, the propoed hybrid microgrid need to minimize the involuntary load hedding epecially for the critical load. One-hour-long backup i required here for every elected operating period. Contraint (20) (31) repreent thi reliable and reilient operation where energy are reerved in ES to provide neceary upport along with. With ite phyical pace limit, contraint (32) and (33) indicate the maximum allowable and ES ize. Power electronic capacitie are then determined baed on the gridconnected and ilanded operation a in (34) (41). x P V P V max (32) x INV x ES ES max (33) + ch AC /η INV (34) x INV (35) x CON x P V /η CON (36) x CON x P V (37) x IC f DCin /η IC (38) x IC f DCout (39) x IC fi DCin /η IC (40) x IC fi DCout (41) To deal with the nonlinear product x ES y ES, auxiliary variable are introduced in (42) to replace nonlinear contraint in (13) and (14) with the exact linear reformulation (43) (47). x ES y ES = u ES (42)

4 u ES = x ES κ ES (43) 0 u ES 0 κ ES ch AC A. Simulation Setup My ES (44) M(1 y ES ) (45) III. u ES (46) x ES u ES (47) CASE STUDY The propoed hybrid microgrid izing approach ha been teted with the load data from a commercial building located at California, USA. load include the AC/DC load in data center, AC cooling and heating a well a neceary AC/DC lighting and appliance. The peak load at thi building i at 846 kw. The profile are baed on NREL WATTTS Dataet [26]. For planning purpoe, the complete annual load could be ued to capture the temporal evolution. However, ince the load data are imilar with a limited number of pattern, cenario reduction technique [27] i applied here to elect typical day to preerve accurate load variation a well a to improve computational efficiency. In thi imulation, 6 day are choen to repreent different load hape in different month, and profile are elected accordingly. The planning horizon for thi microgrid i conidered to be 10 year with 10% annual dicount rate. Annualized invetment cot and the technical parameter are lited in the Table I. A two-hour Lithium-ion battery i adopted here. Thi microgrid participate the PG&E E19 tariff plan where the peak load hould be below 1000 kw. The load hedding penaltie for critical and non-critical load are elected a $ 3,000 /kwh and $ 500 /kwh, repectively. TABLE I. INVESTMENT PARAMETERS Annualized Allowable Invetment Capacitie Technical Parameter $ 108 /kw 400 kw N/A ES $ 424 /kw 350 kw η dch = η ch = 0.93 DC/AC Inverter $ 6.5 /kw N/A η INV = 0.96 DC/DC Converter $ 4.3 /kw N/A η CON = 0.98 Interfacing Converter $ 8.1 /kw N/A η IC = 0.96 All imulation were carried out in Julia uing the JuMP package [28] and CPLEX olver on an Intel Core 4.00 GHz proceor with 12GB of RAM. The MIP optimality gap wa et to 0.01%. The approximate running time for each imulation i le than 1. B. Numerical Reult Four cae are tudied in thi paper. 1) Cae 0: Bae cae with no DER; 2) Cae 1: only deployment; 3) Cae 2: ES only deployment; 4) Cae 3: full DER deployment. The planning reult are ummarized in the Table II. From the table, and ES intallation alway hit the phyical izing limit to gain economic and reliability benefit for invetment recovery. However, the benefit from thee two DER are not quite the ame. mainly lead to electricity bill reduction and ES contribute to the reliability enhancement. hape are highly correlated with the building load, o the output can directly have the peak to reduce the energy charge and demand charge at the ame time. Compared with the bae cae when no DER i intalled, Cae 1 only cae achieve 27.1% energy charge aving, 17.5% demand charge aving and 25.6% total bill payment aving. On the contrary, Cae 2 only obtain 1.2% energy charge aving, 11.6% demand charge aving and 2.7% total bill payment aving, which i urpriingly low. The reaon i that unlike, ES cannot generate power from it own, and it ha to charge firt from either or the grid. The price difference between the peak hour and off-peak hour plu demand charge reduction have to compenate for the torage degradation cot, the charging/dicharging lo and the energy converion lo through inverter, convert or IC. Thi requirement ubtantially hinge ES peak having behavior epecially when the i abent. Combining the advantage from both and ES, Cae 3 DER cae demontrate 28.5% energy charge aving, 35.3% demand charge aving and 29.5 % total aving. Interetingly, thee cot aving number are all larger than the um of the cot aving from each ingle deployment (e.g. 28.5% > 27.1% + 1.2%) even though the exceeding amount i not large. Thi confirm the benefit to the microgrid from the DER joint operation. TABLE II. INVESTMENT RESULTS Cae 0: Bae Cae Cae 1: only Cae 2: ES only Cae 3: DER (kw) ES (kw) DC/AC inverter (kw) DC/DC converter (kw) Interfacing converter (kw) Energy charge ($ 10 4 ) Demand charge ($ 10 4 ) Total payment ($ 10 4 ) Fig. 2 preent the load curtailment for thee four cae. When there i no DER in the ytem, inconvenient load hedding occur for both critical load and non-critical load during the ilanded mode. Cae 1 only cae reduce the curtailment to a extent during the daytime, but it cannot contribute at evening or night when there i no unlight. Even though Cae 2 ES only cae doe not help much on the bill reduction, the reliability improvement i ignificant. The critical load are fully covered and non-critical load are well preerved a well. Again, Cae 3 DER cae lead to the mot reliable cae which improve ytem emergency upport. Bae ES DER Fig. 2. Non-critical load hedding load hedding Expected Load Curtail (kwh) Curtailment for critical load and non-critical load Fig. 3 how the net load profile before/after DER deployment and the correponding DER output. The upper plot preent a peak day cenario. Before intalling and ES,

5 the peak demand i 846 kw, wherea it i only 454 kw after DER integration. Thi reduced peak i mainly contributed from generation. ES alo dicharge to help reducing the peak at noon time. A only generate during the daytime, the energy reduction at ret of the day i not ignificant. The lower plot diplay a normal day cenario. At thi particular day, output can fully cover the commercial building load and lead to a Duck Curve haped load. In addition, due to the ilanded mode contraint, ES ha cheduled to tore adequate energy to hedge againt potential reliability and reiliency event. Power (kw) Power (kw) Fig Load Before DER Load After DER ES Dicharge Peak Day Load Profile Hour Normal Day Load Profile Hour Load profile before and after DER integration IV. CONCLUSION In thi paper, a new MILP-baed commercial building hybrid AC/DC microgrid izing model i propoed to leverage the benefit from both AC and DC microgrid. Energy torage, photovoltaic and power electronic device are optimally ized to coordinate between grid-connected mode economic and ilanded mode reliability. The model integrate the electricity bill reduction into the optimization cheme and enable a minimized involuntary load hedding to ecure critical load. Numerical reult from a commercial building load demontrate the effectivene of the propoed model on economic and reliability enhancement with DER in the hybrid microgrid. REFERENCES [1] D. Ton and J. Reilly, Microgrid Controller Initiative: An Overview of R&D by the U.S. Department of Energy, IEEE Power Energy Mag., vol. 15, no. 4, pp , July-Aug [2] R. Uluki et al., Microgrid Controller Deign, Implementation, and Deployment: A Journey from Conception to Implementation at the Philadelphia Navy Yard, IEEE Power Energy Mag., vol. 15, no. 4, pp , July-Aug [3] S. X. Chen, H. B. Gooi and M. Q. Wang, Sizing of Energy Storage for Microgrid, IEEE Tran. 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