06980137

IEEE TRANSACTIONS ON SMART GRID, VOL. 6, NO. 3, MAY 2015 1137

Distributed Optimal Energy Management inMicrogrids

Wenbo Shi, Student Member, IEEE, Xiaorong Xie, Member, IEEE, Chi-Cheng Chu, and Rajit Gadh

AbstractEnergy management in microgrids is typically for-mulated as a nonlinear optimization problem. Solving it in acentralized manner does not only require high computationalcapabilities at the microgrid central controller (MGCC), but mayalso infringe customer privacy. Existing distributed approaches,on the other hand, assume that all generations and loads areconnected to one bus, and ignore the underlying power dis-tribution network and the associated power flow and systemoperational constraints. Consequently, the schedules producedby those algorithms may violate those constraints and thus arenot feasible in practice. Therefore, the focus of this paper is onthe design of a distributed energy management strategy (EMS)for the optimal operation of microgrids with consideration of thedistribution network and the associated constraints. Specifically,we formulate microgrid energy management as an optimal powerflow problem, and propose a distributed EMS where the MGCCand the local controllers jointly compute an optimal schedule.We also provide an implementation of the proposed distributedEMS based on IEC 61850. As one demonstration, we apply theproposed distributed EMS to a real microgrid in GuangdongProvince, China, consisting of photovoltaics, wind turbines, dieselgenerators, and a battery energy storage system. The simulationresults demonstrate the effectiveness and fast convergence of theproposed distributed EMS.

Index TermsDistributed algorithms, distribution networks,energy management, microgrids, optimal power flow (OPF),optimization.

I. INTRODUCTION

M ICROGRIDS are low-voltage distribution systems con-sisting of distributed energy resources (DERs) andcontrollable loads, which can be operated in either islandedor grid-connected mode [2]. DERs include a variety of dis-tributed generation (DG) units such as wind turbines (WTs),photovoltaics (PVs), and distributed storage (DS) units such asbatteries. Sound operation of a microgrid requires an energymanagement strategy (EMS) which controls the power flowsin the microgrid by adjusting the power imported/exported

Manuscript received July 18, 2014; revised October 2, 2014; acceptedNovember 16, 2014. Date of publication December 9, 2014; date of cur-rent version April 17, 2015. This work was supported by the Researchand Development Program of the Korea Institute of Energy Research underGrant B4-2411-01. This paper has been presented in part at the IEEEInternational Conference on Smart Grid Communications, Venice, Italy,Nov. 2014 [1]. Paper no. TSG-00738-2014.

W. Shi, C.-C. Chu, and R. Gadh are with the Smart Grid Energy ResearchCenter, University of California, Los Angeles, CA 90095 USA (e-mail:[email protected]).

X. Xie is with the State Key Laboratory of Power Systems, Department ofElectrical Engineering, Tsinghua University, Beijing 100084, China.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSG.2014.2373150

from/to the main grid, the dispatchable DERs, and the con-trollable loads based on the present and forecasted informationof the market, the generations, and the loads in order to meetcertain operational objectives (e.g., minimizing costs) [2].

Energy management in microgrids is typically formulatedas a nonlinear optimization problem. Various centralized meth-ods have been proposed to solve it in the literature, includingmixed integer programming [3], sequential quadratic program-ming [4], particle swarm optimization [5], neural networks [6],etc. The centralized approaches [3][6] require high computa-tional capabilities at the microgrid central controller (MGCC),which is neither efficient nor scalable. Moreover, a central-ized EMS requires the MGCC to gather information of theDERs (e.g., production costs, constraints, etc.) and the loads(e.g., customer preferences, constraints, etc.) as the inputs foroptimization. However, different DERs may belong to differ-ent entities and they may keep their information private [7].Customers may also be unwilling to expose their informationdue to privacy [8]. Therefore, in this paper, we are interestedin developing a distributed EMS which is efficient, scalable,and privacy preserving.

Several distributed algorithms have been proposed for theoperation of microgrids in the literature. In [7], a distributedalgorithm based on the classical symmetrical assignmentproblem is proposed. Energy management is formulated asa resource allocation problem in [9] and distributed algo-rithms are proposed for distributed allocation. A convexproblem formulation can be found in [10] and dual decom-position is used to develop a distributed EMS to maintain thesupplydemand balance in microgrids. A privacy-preservingenergy scheduling algorithm in microgrids is proposed in [8],where the privacy constraints are integrated with the linearprogramming model and distributed algorithms are developed.In [11], the additive-increase/multiplicative-decrease algorithmis adopted to optimize DER operations in a distributedfashion.

The problem with the existing distributed approaches formicrogrid energy management [7][11] is that they considerthe supplydemand matching in an abstract way where theaggregate demand is simply equal to the supply. They assumethat all generations and loads are connected to one bus andignore the underlying power distribution network and theassociated power flow (e.g., Kirchhoffs law) and system oper-ational constraints (e.g., voltage tolerances). Consequently, theschedules produced by those algorithms may violate thoseconstraints and thus are not feasible in practice. It is worthnoting that distribution networks have been taken into account

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1138 IEEE TRANSACTIONS ON SMART GRID, VOL. 6, NO. 3, MAY 2015

in a few recent demand response studies [12]. However,the idea of integrating distribution networks with distributedenergy management in microgrids, where both supply-side anddemand-side management (DSM) are considered has not beenexplored.

The focus of this paper is on the design of a distributed EMSfor the optimal operation of microgrids with consideration ofthe underlying power distribution network and the associatedconstraints. More specifically, we consider a microgrid con-sisting of multiple DERs and controllable loads. The objectiveof the EMS is to control the power flows in the microgrid inorder to: 1) minimize the cost of generation, the cost of energystorage, and the cost of energy purchase from the main grid;2) minimize the dissatisfactions of the customers in the DSM;and 3) minimize the power losses subject to the DER con-straints, the load constraints, the power-flow constraints, andthe system operational constraints.

Specifically, we formulate energy management in micro-grids as an optimal power flow (OPF) problem. The OPFproblem is difficult to solve due to the nonconvex power-flowconstraints. We convexify the OPF problem by relaxing thepower-flow constraints (see [13], [14] for a tutorial on con-vex relaxation of OPF). Sufficient conditions for the exactnessof the relaxation have been derived in [15][18], whichhold for a variety of IEEE test systems and real-worldsystems. Therefore, we focus on solving the relaxed OPFproblem (OPF-r) in this paper. Note that most of the convexrelaxations of OPF [15][18] assume a single-phase or bal-anced three-phase distribution network. See [19] for convexrelaxation of OPF in multiphase networks. The OPF-r prob-lem is a centralized convex optimization problem. To solve itin a distributed manner, we propose a distributed EMS wherethe MGCC and the local controllers (LCs) jointly compute anoptimal schedule.

In order to illustrate the feasibility of the proposed EMSin real systems, we provide an implementation based on theIEC 61850 standard which provides standardized communi-cation and control interfaces for all DER devices. As onedemonstration, we apply the proposed EMS to a real micro-grid in Guangdong Province, China, consisting of PVs, WTs,diesel generators, and a battery energy storage system (BESS).The simulation results demonstrate the effectiveness and fastconvergence of the proposed EMS. We show that the pro-posed EMS is able to manage the operations in the microgridto achieve the objective while maintaining the bus voltageswithin the allowed range. Furthermore, we discuss the loca-tion effect, the load shedding/shifting, the ramping constraint,and the trade-offs in the objective.

Compared with a preliminary version of this paper [1],this paper provides a more realistic and detailed systemmodel by incorporating the generation ramping constraint, theinverter capacity, the battery efficiency, and the load shift-ing. We also provide an IEC 61850 implementation of theproposed distributed EMS to demonstrate its feasibility inreal systems. A case study using the real pricing data isprovided to give better insights into microgrid energy manage-ment. A more comprehensive analysis of the proposed EMS isgiven, including the discussions on the location effect, the load

Fig. 1. System architecture.

shedding/shifting, the ramping constraint, and the trade-offs inthe objective.

The rest of this paper is organized as follows. We intro-duce the system model in Section II and propose the EMS inSection III. Simulation results are provided in Section V andthe conclusion is given in Section VI.

II. SYSTEM MODELIn this section, we describe the system model for devel-

oping the proposed distributed EMS. We first give anoverview of the system followed by the DG model, theDS model, and the load model. We then model thepower distribution network using a branch flow modeland formulate microgrid energy management as an OPFproblem.

A. System OverviewA low-voltage power distribution network generally has a

radial structure [12]. Thus, we consider a radial microgrid con-sisting of a set of DG units denoted by G {g1, g2, . . . , gG},DS units denoted by B {b1, b2, . . . , bB}, and controllableloads denoted by L {l1, l2, . . . , lL}. In the microgrid, thereis a MGCC which coordinates the operations of the DERs andthe controllable loads. At each of the DERs and the loads,there is a LC which is able to coordinate with the MGCC tocompute its schedule locally via a two-way communicationinfrastructure. Fig. 1 shows the system architecture.

In this paper, we use a discrete-time model with a finitehorizon. We consider a time period or namely a schedulinghorizon, which is divided into T equal intervals t, denotedby T {0, 1, . . . , T 1}.

B. DG ModelWe consider both renewable and conventional DGs in

the microgrid. Renewable DGs such as PVs and WTs arenondispatchable and conventional DGs such as diesel are dis-patchable. For each DG g G, we denote its complex outputpower by sg(t) pg(t) + iqg(t), where pg(t) is the activepower and qg(t) is the reactive power.

1) Renewable DG: A renewable DG unit such as PV orWT is not dispatchable and its output power is dependenton the availability of the primary sources (i.e., sun irradianceor wind). Therefore, forecast is required in order to considerthem in the energy management optimization. Methods for PVforecasting [20] and WT forecasting [21] can be utilized. In

SHI et al.: DISTRIBUTED OPTIMAL ENERGY MANAGEMENT IN MICROGRIDS 1139

our model, we assume that the complex power of a renewableDG unit over the scheduling horizon is given and there is nogeneration cost for renewable DGs.

2) Conventional DG: A conventional DG unit such asdiesel is a dispatchable source, its output power is a variablewith the following constraints:

0 pg(t) pg, t T , (1)|pg(t) pg(t 1)| rgpg, t T , (2)

where pg is the maximum output power and rg (0, 1] is theramping parameter.

For a given conventional DG unit, its reactive powergenerated at the inverter is bounded by

pg(t)2 + qg(t)2 s2g, t T , (3)where sg is the capacity of the inverter.

We model the conventional DG generation cost at each timet T using a quadratic model [10]

Cg( pg(t)) g(

pg(t)t)2 + gpg(t)t + cg, (4)

where g, g, and cg are constants.

C. DS ModelWe consider batteries as the DS units in the microgrid.

For a given battery b B, we denote its complex power bysb(t) pb(t) + iqb(t), where pb(t) is the active power (posi-tive when charging and negative when discharging) and qb(t)is the reactive power. Let Eb(t) denote the energy stored inthe battery at time t. A given battery can be modeled by thefollowing constraints:

pb pb(t) pb, t T , (5)

pb(t)2 + qb(t)2 s2b, t T , (6)Eb(t + 1) = bEb(t) + pb(t)t, t T , (7)

Eb Eb(t) Eb, t T , (8)Eb(T) Eeb, (9)

where pb is the maximum charging rate, pb is the maximum

discharging rate, sb is the capacity of the inverter, b (0, 1]captures the battery efficiency, Eb and Eb are the minimum andmaximum allowed energy stored in the battery, respectively,and Eeb is the minimum energy that the battery should maintainat the end of the scheduling horizon.

We use a cost function to capture the damages to the batteryby the charging and discharging operations. Three types ofdamages are considered: 1) fast charging; 2) frequent switchesbetween charging and discharging; and 3) deep discharging.We model the battery cost as [22]

Cb(pb) b

tTpb(t)2 b

T2

t=0pb(t + 1)pb(t)

+ b

tT

(min(Eb(t) bEb, 0)

)2, (10)

where pb (pb(t), t T ) is the charging/discharging vec-tor, b, b, b, and b are positive constants. b, b, and b

trade off among fast charging, switches between charging anddischarging, and deep discharging. The above function is con-vex when b > b. We choose b = 0.2, meaning thatthe cost function penalizes deep charging when the energystored in the battery Eb(t) is less than 20% of the batterycapacity Eb.

D. Load ModelWe consider two types of controllable loads in the micro-

grid: interruptible and deferrable loads. An interruptible loadcan be shedded and a deferrable load can be shifted in timebut need to consume a certain amount of energy before adeadline.

For each load l L, we denote its complex power bysl(t) pl(t) + iql(t) and it is bounded by

pl(t) pl(t) pl(t), t T , (11)

ql(t) ql(t) ql(t), t T , (12)

wherepl(t) and pl(t) are the minimum and maximum active

power, respectively, andql(t) and ql(t) are the minimum and

maximum reactive power, respectively.For a deferrable load, we assume that its consumed energy

is bounded by

El

tTpl(t)t El, (13)

where El and El are the energy lower and upper bound,respectively.For each load, we define a demand vector denoted by

pl ( pl(t), t T ) and a cost function Cl(pl) which mea-sures the dissatisfaction of the customer using the demandschedule pl.

The cost function of an interruptible load is dependent onthe shedded load and can be defined as

Cl(pl)

tTl

(min

(pl(t) p fl (t), 0

))2, (14)

where p fl (t) is the forecasted load and l is a positive constant.The above cost function is nonzero only when there is loadshedding, i.e., pl(t) < p fl (t).

The cost function of a deferrable load is dependent on theunfulfilled energy and can be defined as

Cl(pl) l

(

El

tTpl(t)t

)

, (15)

where l is a positive constant.

E. Distribution Network ModelA distribution network can be modeled as a connected graph

G = (N , E), where each node i N represents a bus and eachlink in E represents a branch (line or transformer). We denotea link by (i, j) E . Power distribution networks are typicallyradial and the graph G becomes a tree for radial distributionsystems. We index the buses in N by i = 0, 1, . . . , n, andbus 0 denotes the feeder which has a fixed voltage and flexiblepower injection.

1140 IEEE TRANSACTIONS ON SMART GRID, VOL. 6, NO. 3, MAY 2015

For each link (i, j) E , let zij rij + ixi,j be the compleximpedance of the branch, Iij(t) be complex current from busesi to j, and Sij(t) Pij(t) + iQij(t) be the complex powerflowing from buses i to j.

For each bus i N , let Vi(t) be the complex voltage at busi and si(t) pi(t) + iqi(t) be the net load which is the loadminus the generation at bus i. Each bus i N \{0} is connectedto a subset of DG units Gi, DS units Bi, and loads Li. The netload at each bus i satisfies

si(t) = sli(t) + sbi(t) sgi(t), i N \ {0},t T , (16)where sli(t)

lLi sl(t), sbi(t)

bBi sb(t), and

sgi

gGi sg(t).Given the radial distribution network G, the feeder volt-

age V0, and the impedances {zij}(i,j)E , then the other variablesincluding the power flows, the voltages, the currents, and thebus loads satisfy the following physical laws for all branches(i, j) E and all t T .

1) Ohms law:Vi(t) Vj(t) = zijIij(t). (17)

2) Power-flow definition:Sij(t) = Vi(t)Iij(t). (18)

3) Power balance:Sij(t) zij|Iij(t)|2

k:( j,k)ESjk(t) = sj(t). (19)

Using (17)(19) and in terms of real variables, we can modelthe steady-state power flows in a given distribution network Gas [13]: (i, j) E,t T

pj(t) = Pij(t) rijij(t)

k:( j,k)EPjk(t), (20)

qj(t) = Qij(t) xijij(t)

k:( j,k)EQjk(t), (21)

vj(t) = vi(t) 2(rijPij(t) + xijQij(t)

) +(

r2ij + x2ij)

ij(t),(22)

ij(t) = Pij(t)2 + Qij(t)2vi(t)

, (23)

where ij(t) |Iij(t)|2 and vi(t) |Vi(t)|2.Equations (20)(23) define a system of equations

in the variables (P(t), Q(t), v(t), l(t), s(t)), whereP(t) ( Pij(t), (i, j) E), Q(t) (Qij(t), (i, j) E),v(t) (vi(t), i N \ {0}), l(t) (ij(t), (i, j) E), ands(t) (si(t), i N \ {0}). The phase angles of the voltagesand the currents are not included. But they can be uniquelydetermined for radial systems [14].

F. Energy ManagementThe objective of the microgrid operator is to minimize its

operational cost, while delivering reliable and high-qualitypower to the loads. However, the introduction of DERs makesit challenging to balance the supply and demand in a micro-grid, especially in islanded mode where only DERs are usedas the supply. The integration of DERs may also increase the

voltage significantly, which reduces the quality of the volt-age received by other users in the distribution network. Thus,in this paper, we study microgrid energy management aimingat achieving the operational objective of the microgrid opera-tor, while meeting the supplydemand balance and the voltagetolerance constraints.

We consider the following voltage tolerance constraints inthe microgrid:

Vi |Vi(t)| Vi, i N \ {0},t T , (24)where Vi and Vi correspond to the minimum and maximumallowed voltage according to the specification, respectively.

The net power injected to the microgrid from the main gridis given by

s0(t) =

j:(0,j)Es0j(t), t T . (25)

If the microgrid is operated in islanded mode, thens0(t) = 0. If the microgrid is operated in grid-connected mode,then s0(t) is the net complex power traded between themicrogrid and the main grid.

We model the cost of energy purchase from the main gridat each time t T as

C0(t, p0(t)) (t)p0(t)t, (26)where (t) is the market energy price. Note that p0(t) can benegative, meaning that the microgrid can sell its surplus powerto the main grid.

The objective of the energy management in the microgridis to: 1) minimize the cost of generation, the cost of energystorage, and the cost of energy purchase from the main grid;2) minimize the dissatisfactions of the customers in the DSM;and 3) minimize the power losses subject to the DER con-straints, the load constraints, the power-flow constraints, andthe system operational constraints (voltage tolerances).

We define P (P(t), t T ), Q (Q(t), t T ), v (v(t), t T ), l (l(t), t T ), sg (sg(t), t T ), sb (sb(t), t T ), sl (sl(t), t T ), s (sg, sb, sl, g G, b B, l L), and Cg(pg) tT Cg( pg(t)). Microgrid energymanagement can be formulated as an OPF problem

OPFmin

P,Q,v,l,sg

gGCg(pg) + b

bBCb(pb) + l

lLCl(pl)

+ 0

tTC0(t, p0(t)) + p

tT

(i,j)Erijij(t)

s.t. (1)(3), (5)(9), (11)(13), (16),(20)(25),

where g, b, l, 0, and p are the parameters to tradeoff among the cost minimizations and the power lossminimization.

III. DISTRIBUTED EMSThe previous OPF problem is nonconvex due to the

quadratic equality constraint in (23) and is NP-hard to solve

SHI et al.: DISTRIBUTED OPTIMAL ENERGY MANAGEMENT IN MICROGRIDS 1141

in general [13]. We, therefore, relax them to inequalities

ij(t) Pij(t)2 + Qij(t)2vi(t)

, (i, j) E,t T . (27)We then consider the following convex relaxation of OPF:

OPF rmin

P,Q,v,l,sg

gGCg(pg) + b

bBCb(pb) + l

lLCl(pl)

+ 0

tTC0(t, p0(t)) + p

tT

(i,j)Erijij(t)

s.t. (1)(3), (5)(9), (11)(13), (16),(20)(22), (24), (25), (27).

If the equality in (27) is attained in the solution to OPF-r,then it is also an optimal solution to OPF. The sufficient con-ditions under which the relaxation is exact have been exploitedin [15][18]. Roughly speaking, if the bus voltage is keptaround the nominal value and the power injection at each busis not too large, then the relaxation is exact. Detailed condi-tions when the voltage upper bound is not important can befound in [15] and [16]. See [17], [18] on how to deal withthe voltage upper bound. In this paper, we assume that thesufficient conditions specified in [18] hold for the microgridand thus we focus on solving the OPF-r problem.

The above OPF-r problem is a centralized optimizationproblem. In order to design an efficient, scalable, and privacy-preserving EMS, we propose a distributed algorithm to solvethe OPF-r problem using the predictor corrector proximal mul-tiplier (PCPM) algorithm (refer to [23] or the Appendix fordetails). Note that we use PCPM to develop the proposeddistributed algorithm here. Other distributed algorithms suchas the alternating direction method of multipliers (ADMM)algorithm [24] may also apply to solve the OPF-r problem ina distributed manner.

Initially set k 0. The LCs of the DERs and the loadsset their initial schedules randomly and communicate them tothe MGCC. In the meantime, the MGCC randomly choosesthe initial ski (t) pki (t)+ iqki (t) and two virtual control signals{ki (t)}tT , {ki (t)}tT for each bus i N \{0}. i(t) and i(t)are the Lagrangian multipliers associated with the active andreactive power at bus i, respectively.

At the beginning of the kth step, the MGCC sends twocontrol signals ki (t) ki (t)+ (pkli(t)+pkbi(t)pkgi(t)pki (t))and ki (t) ki (t) + (qkli(t) + qkbi(t) qkgi(t) qki (t)) to theLCs of the DERs and the loads connected to bus i, where is a positive constant. Then the following occurs.

1) The LC of each conventional DG unit solves the follow-ing problem:

EMS LC(DG)min

sggCg(pg) +

(ki

)Tpg +

(ki

)Tqg

+ 12

pg pkg

2 + 1

2

qg qkg

2

s.t. (1) (3),where ki (ki (t), t T ) and ki (ki (t), t T ). Theoptimal sg is set as sk+1g .

Algorithm 1 Proposed Distributed EMS1: initialization k 0. The LCs set the initial schedules randomly

and return them to the MGCC. The MGCC sets the initial ki (t),ki (t) and the initial s

ki (t) randomly.

2: repeat3: The MGCC updates ki (t) and

ki (t) and sends two control

signals ki and ki to the LCs connected to bus i.

4: The LC at each DER and each load calculates a new scheduleby solving the corresponding EMS-LC problem.

5: The MGCC computes a new sk+1(t) for each time t T bysolving the EMS-MGCC problem.

6: The LC communicates the new schedule to the MGCC.7: The MGCC updates k+1i (t) and

k+1i (t).

8: k k + 1.9: until convergence

2) The LC of each DS unit solves the following problem:EMS LC(DS)

minsb

bCb(pb) +(ki

)Tpb +

(ki

)Tqb

+ 12

pb pkb

2 + 1

2

qb qkb

2

s.t. (5) (9).The optimal sb is set as s

k+1b .

3) The LC of each load solves the following problem:EMS LC(Load)

minsl

lCl(pl) +(ki

)Tpl +

(ki

)Tql

+ 12

pl pkl

2 + 1

2

ql qkl

2

s.t. (11)(13).

The optimal sl is set as sk+1l .

4) The MGCC solves the following problem for eachtime t T :EMS MGCC

minP(t),Q(t),

v(t),l(t),s(t)

0C0(t, p0(t)) + p

(i,j)Erijij(t)

(k(t)

)Tp(t)

(k(t)

)Tq(t)

+ 12

p(t) pk(t)

2 + 1

2

q(t) qk(t)

2

s.t. (20)(22), (24), (25), (27),

where k(t) (ki (t), i N \ {0}) and k(t) (ki (t), i N \ {0}). The optimal s(t) is set as sk+1(t).

At the end of the kth step, the LCs communicate their newschedules sk+1l , sk+1g , and s

k+1b to the MGCC and the MGCC

updates k+1i (t) ki (t) + ( pk+1li (t) + pk+1bi (t) pk+1gi (t) pk+1i (t)) and

k+1i (t) ki (t)+ (qk+1li (t)+qk+1bi (t)qk+1gi (t)

qk+1i (t)) for all i N \ {0} and all t T . Set k k + 1, andrepeat the process until convergence.

A complete description of the proposed distributed EMS canbe found in Algorithm 1. When is small enough, the abovealgorithm will converge to the optimal solution to OPF-r which

1142 IEEE TRANSACTIONS ON SMART GRID, VOL. 6, NO. 3, MAY 2015

Fig. 2. IEC 61850 implementation.

is also the optimal solution to OPF if the relaxation is exact and( pkli(t)+pkbi(t)pkgi(t)pki (t)) and (qkli(t)+qkbi(t)qkgi(t)qki (t))will converge to zero [23]. As we can see, the MGCC and theLCs jointly compute the optimal schedule.

In the proposed distributed EMS, the private information ofthe DERs and the loads is stored at the LC where the EMS-LCproblem is solved locally. The MGCC solves the EMS-MGCCproblem using the system information, including the topology,the power losses, the market energy price, etc. The informationexchanged between the MGCC and the LCs include only thecontrol signals and the schedules. Therefore, the privacy ofthe DERs (i.e., production costs and constraints) and the loads(i.e., customer preferences and constraints) are both preservedby the proposed EMS.

IV. IEC 61850 IMPLEMENTATIONIEC 61850 is a set of international standards designed

originally for communications within substation automationsystems [25]. More recently, IEC 61850 draws attention toresearchers in the area of microgrids as it provides standard-ized communication and control interfaces for all DER devicesto achieve interoperability in microgrids. Due to its essentialrole in microgrid systems, it is important that the microgridEMS is compatible with IEC 61850. To this end, we providean implementation of the proposed distributed EMS based onthe IEC 61850 standard.

In IEC 61850, each DER unit is modeled as a logicaldevice (LD). The LD is composed of the relevant logicalnodes (LNs) which are predefined groupings of data objectsthat serve specific functions. Refer to [26] for detailed defini-tions of LNs for DER devices. The LN named DER energy andancillary services schedule (DSCH) can be used to implementthe proposed EMS. In a DSCH LN, an array of the times-tamps and values can be read or written using the IEC 61850ACSI services (e.g., GetDataValues and SetDataValues) andmultiple schedules can be defined in parallel.

In order to implement the proposed EMS, we use fourDSCH LNs: active power, reactive power, price for activepower, and price for reactive power. The active power andreactive schedules are the results from solving the EMS-LCproblem. The control signals sent by the MGCC ki and kican be viewed as the price for active power and reactivepower, respectively. Fig. 2 illustrates the proposed IEC 61850implementation.

Fig. 3. Topology of the microgrid.

Algorithm 1 needs a few updates to support the proposedIEC 61850 implementation. In step 3, the MGCC sends thecontrol signals by writing to the DSCH LNs of the pricefor active and reactive power. In step 4, after the LC solvesthe EMS-LC problem using the control signals read from theDSCH LNs of the prices, the new schedules are written tothe corresponding DSCH LNs. In step 6, the LC sends the newschedules to the MGCC using the IEC 61850 report controlblock (RCB) mechanism. At convergence, the optimal sched-ules will be stored in the DSCH LNs and used to control theDER device.

V. PERFORMANCE EVALUATIONIn this section, we demonstrate the proposed distributed

EMS by applying it to a real microgrid. We first describethe microgrid system and the setup used in the simulation.We then present the simulation results in islanded and grid-connected mode followed by the discussions on the locationeffect, the load shedding/shifting, the ramping constraint, andthe trade-offs in the objective.

A. Simulation SetupFig. 3 shows the configuration of a real microgrid in

Guangdong Province, China. The numbers under the DERsand the loads in the figure correspond to the maximum power.We use this microgrid to demonstrate the proposed distributedEMS. In the simulation, a day starts from 12 A.M. The timeinterval t in the model is 1 h and we denote a day byT {0, 1, . . . , 23}, where each t T denotes the hour of[t, t + 1].

We set the cost function of the diesel generation asCg( pg(t)) 10( pg(t)t)2 + 70( pg(t)t). The generationramping parameter rg is chosen to be 0.3. The capacity ofthe BESS Eb is 3 MWh and Eb is chosen to be 0.1 MWh.We set Eb(0) = 1.5 MWh, Eeb = 1.0 MWh, and b = 0.95.The parameters in the cost function of the battery are chosenas b = 1, b = 0.75, and b = 0.5. We choose l = 103 and

SHI et al.: DISTRIBUTED OPTIMAL ENERGY MANAGEMENT IN MICROGRIDS 1143

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2430

40

50

60

70

80

90

100

110

120

130

140

150

Time

Pric

e ($/

MWh)

Fig. 4. Day-ahead price from CAISO.

Fig. 5. Output schedules in islanded mode.

l = 102 in the cost function of the interruptible and deferrableloads, respectively. We assume that bus 5 is a deferrable loadand the rest of the loads are all interruptible. For the interrupt-ible loads, the maximum load shedding percentage is chosenrandomly from the range [20%, 50%]. For the deferable load,the start time is chosen randomly from [10, 13] and the dead-line is chosen randomly from [20, 23]. The minimum energyrequirement El is chosen randomly from [3pl, 5pl] and theenergy upper bound is set to be El = El + 2pl, where plis the maximum power of load l. Perfect forecasting of thePV, the WT, and the loads is assumed. For the forecastingof the deferrable load, we assume that the load consumespower at the maximum rate from the start time until the con-sumed energy reaches the energy upper bound. We use thereal day-ahead energy price from California ISO (CAISO) inthe simulation as shown in Fig. 4.

B. Case StudyWe apply the proposed EMS to the microgrid using the

setup described above. The voltage tolerances are set to be[0.95 p.u., 1.05 p.u.]. The parameters in the algorithm arechosen as g = 1, b = 1, l = 1, 0 = 1, p = 1, and = 0.75.

The day-ahead schedules produced by the proposed EMSin islanded mode is shown in Fig. 5. In islanded mode, themicrogrid can utilize only the DERs to serve the loads. Sincethe nondispatchable renewable generations (i.e., PV and WT)in the microgrid only serve for a small proportion of the loads,diesel is the main power source. From the figure, we can seethat the total diesel generation changes in the same trend as

Fig. 6. Output schedules in grid-connected mode.

Fig. 7. Net power injected to the microgrid.

the total load. We can also observe the charging/dischargingcycles of the battery from the figure. The battery is chargedwhen the renewable generation is high and discharged whenit is low, serving as the storage for the renewables in themicrogrid.

Fig. 6 shows the results in grid-connected mode. Comparedwith Fig. 5, the total diesel generation is decreased sig-nificantly in grid-connected mode. Diesel generation is nolonger the main power source in grid-connected mode as themicrogrid is able to import power from the main grid. Thebattery in grid-connected mode is the storage for not onlythe renewables, but also the cheap power from the main grid.It is also charged when the energy price is low and dis-charged when the energy price is high, making profits for themicrogrid.

The net power injected to the microgrid in grid-connectedmode is shown in Fig. 7. It can be seen from the figure thatthe microgrid imports power when the energy price is lowand exports power when the price is high (t [16, 18]). Ifwe compare the total operational cost of the microgrid (i.e.,the value of the objective function) in the two modes, we canfind that grid-connected mode decreases the operational costby ($6491 $5484)/$6491 = 15.5%.

Fig. 8 shows the dynamics of EMS-MGCC and EMS-LC ingrid-connected mode. We can see that our proposed distributedalgorithm converges fast. For the simulations, we also verifythat the solution to the centralized OPF-r problem is the sameas the solution to the distributed algorithm. We further verify

1144 IEEE TRANSACTIONS ON SMART GRID, VOL. 6, NO. 3, MAY 2015

Fig. 8. Dynamics of EMS-MGCC and EMS-LC.

Fig. 9. Maximum and minimum bus voltage in the microgrid.

that the equality in (27) is attained in the optimal solution toOPF-r, i.e., OPF-r is an exact relaxation of OPF.

C. Discussion1) Location Effect: In order to exemplify the effect on volt-

age tolerances, we increase the line lengths by five times.Fig. 9 shows the maximum and the minimum bus voltagein the microgrid over time. It can be seen from the figurethat the bus voltages in the microgrid are well maintainedwithin the allowed range. The maximum voltage reaches theupper bound when the nondispatchable renewable generationis high and the minimum voltage reaches the lower boundwhen the load is high. This is because the generation injectspower to the distribution network and hence increases the volt-age, while the load consumes power and thus decreases thevoltage.

In order to understand how the voltage tolerances aremaintained by the proposed EMS, we look into the demandreduction of each load as shown in Fig. 10. From the figure, itcan be easily seen that the demand reduction of bus 2 and 3is significantly more than the other buses. This is becauseboth bus 2 and 3 are far from the generation or the feeder andthus the voltage drop along the line is significant. Therefore,more demand reduction is required at bus 2 and 3 in order tomaintain the bus voltage above the minimum allowed voltage.Similarly, those loads close to the nondispatchable renewablegeneration (bus 11 and 12) need to consume more in orderto reduce the high voltage due to the generation, leading toless demand reduction. The result shows the location effectthat a DSM scheme may discriminate the loads based on theirlocations [12].

Fig. 10. Demand reduction of the loads.

Fig. 11. Load shifting.

2) Load Shedding/Shifting: Fig. 10 also illustrates how theloads are shedded in grid-connected mode. As can be expected,the loads are shedded in response to the price: more loadsare shedded when the price is high in order to save cost.In islanded mode, load shedding is mainly used to balancethe local supply. If we compare the total amount of shed-ded loads in the two modes, we can find that islanded mode(8.91 WM) makes more load shedding than grid-connectedmode (6.21 MW).

Fig. 11 shows the load shifting in grid-connected mode. Ascan be seen from the figure, the load is shifted from the timewhen the energy price is high (t [14, 17]) to when the priceis low (t [19, 21]). The total consumed energy with loadshifting is the same as without load shifting.

3) Ramping Constraint: Fig. 12 illustrates the effect of theramping constraint on the objective. As can be seen fromthe figure, the total cost is nonincreasing with the ramp-ing parameter rg in both islanded and grid-connected mode.This is because the stricter the ramping constraint is, the lessavailable power the diesel generation can provide. It can bealso seen from the figure that the marginal cost decreasesin both modes as rg increases. In particular, the cost doesnot decrease much when rg 0.3, showing that the dieselgeneration supply is relatively sufficient in that region of rg.Furthermore, the marginal cost in islanded mode decreasesmuch faster than in grid-connected mode when rg is small.This is easy to understand as diesel is the main power sup-ply in islanded mode and a strict ramping constraint onit would cause more load shedding/shifting that leads to ahigher cost.

SHI et al.: DISTRIBUTED OPTIMAL ENERGY MANAGEMENT IN MICROGRIDS 1145

Fig. 12. Effect of rg on the objective.

TABLE ICOST COMPARISON UNDER DIFFERENT

4) Trad-Offs in the Objective: In the objective func-tion of the optimization, there are several parameters(g, b, l, 0, p). Each is associated with one cost mini-mization in the optimization. To evaluate their effects on theproposed EMS, we conduct simulations using different . Wechoose the baseline as the set of parameters used in our previ-ous simulation. We then change the parameter one at a timeand compare the individual costs as shown in Table I.

As can be seen from the table, the parameter affectsthe trade-offs among different cost minimizations. A large would decrease the corresponding cost in the optimization. Thechoice of depends on the importance of the correspondingcost minimization in energy management. For example, if themicrogrid operator is more interested in minimizing the gen-eration cost, g can be increased and the resulting generationcost would be decreased.

VI. CONCLUSIONIn this paper, we propose a distributed EMS for the optimal

operation of microgrids. Compared with the existing dis-tributed approaches, our proposed EMS considers the underly-ing power distribution network and the associated constraints.Specifically, we formulate microgrid energy management asan OPF problem and propose a distributed EMS where theMGCC and the LCs jointly compute an optimal schedule. Wealso provide an implementation of the proposed EMS basedon the IEC 61850 standard. As one demonstration, we applythe proposed EMS to a real microgrid in Guangdong Province,China. The simulation results demonstrate that the proposedEMS is effective in both islanded and grid-connected mode.It is shown that the proposed distributed algorithm convergesfast. A comprehensive analysis of its performance is given.Future work includes implementing the proposed EMS in areal system and analyzing its performance.

APPENDIXIntroduction to PCPM

In this paper, we develop a distributed EMS using the PCPMalgorithm [23]. PCPM is a decomposition method for solvingconvex optimization problem. At each iteration, it computestwo proximal steps in the dual variables and one proximal stepin the primal variables. We give a very brief description of thePCPM algorithm below.

Consider a convex optimization problem with separablestructure of the form

minxX ,yY

f (x) + g(y) (28)s.t. Ax + By = c. (29)

Let z be the Lagrangian variable for the constraint (29).The steps of the PCPM algorithm to solve the problem are

given as follows.1) Initially set k 0 and choose the initial (x0, y0, z0)

randomly.2) For each k 0, update a virtual variable zk := zk +

(Axk + Byk c) where > 0 is a constant step size.3) Solve

xk+1 = arg minxX

{f (x) +

(zk

)TAx + 1

2

x xk

2},

yk+1 = arg minyY

{g(y) +

(zk

)TBy + 1

2

y yk

2}.

4) Update zk+1 := zk + (Axk+1 + Byk+1 c).5) k k + 1, and go to step 2 until convergence.Steps 2 and 4 can be seen as a predictor step and a corrector

step to the Lagrange multiplier, respectively. It has been shownin [23] that the above algorithm will converge to a primal-dual optimal solution (x, y, z) for a sufficient small positivestep size as long as strong duality holds for the convexproblem (28).

ACKNOWLEDGMENTThe authors would like to thank Y. Dong from the

Department of Electrical Engineering, Tsinghua University, forproviding the microgrid data, and N. Li from the Departmentof Electrical Engineering, Harvard University, for insightfuldiscussions and comments.

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[5] S. Pourmousavi, M. Nehrir, C. Colson, and C. Wang, Real-time energymanagement of a stand-alone hybrid wind-microturbine energy systemusing particle swarm optimization, IEEE Trans. Sustain. Energy, vol. 1,no. 3, pp. 193201, Oct. 2010.

[6] P. Siano, C. Cecati, H. Yu, and J. Kolbusz, Real time operation ofsmart grids via FCN networks and optimal power flow, IEEE Trans.Ind. Informat., vol. 8, no. 4, pp. 944952, Nov. 2012.

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[18] L. Gan, N. Li, U. Topcu, and S. H. Low, Exact con-vex relaxation of optimal power flow in radial networks, IEEETrans. Autom. Control. [Online]. Available: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6843918

[19] L. Gan and S. H. Low, Convex relaxations and linear approximationfor optimal power flow in multiphase radial networks, arxiv:1406.3054,2014. [Online]. Available: http://arxiv.org/abs/1406.3054

[20] R. Huang, T. Huang, R. Gadh, and N. Li, Solar generation predictionusing the ARMA model in a laboratory-level micro-grid, in Proc. IEEEInt. Conf. Smart Grid Commun. (SmartGridComm), Tainan, Taiwan,Nov. 2012, pp. 528533.

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[26] Communication Networks and Systems for Power UtilityAutomationPart 7-420: Basic Communication StructureDistributedEnergy Resources Logical Nodes, IEC Standard 61850-7-420, 2009.

Wenbo Shi (S08) received the B.S. degree fromXian Jiaotong University, Xian, China, and theM.A.Sc. degree from the University of BritishColumbia, Vancouver, BC, Canada, in 2009 and2011, respectively, both in electrical engineering.He is currently pursuing the Ph.D. degree from theSmart Grid Energy Research Center, University ofCalifornia, Los Angeles, CA, USA.

His current research interests include demandresponse, microgrids, and energy management sys-tems.

Xiaorong Xie (M02) received the B.Sc. degreefrom Shanghai Jiao Tong University, Shanghai,China, and the Ph.D. degree from TsinghuaUniversity, Beijing, China, in 1996 and 2001, respec-tively.

He is an Associate Professor with the Departmentof Electrical Engineering, Tsinghua University. Hiscurrent research interests include analysis and con-trol of microgrids, and flexible ac transmissionsystems.

Chi-Cheng Chu received the B.S. degree fromNational Taiwan University, Taipei, Taiwan,and the Ph.D. degree from the University ofWisconsinMadison, Madison, WI, USA, in 1990and 2001, respectively.

He is currently a Project Lead with the SmartGrid Energy Research Center, University ofCalifornia, Los Angeles, CA, USA. He is aseasoned Research Manager who supervised andsteered multiple industry and academia researchprojects in the field of smart grid, radio frequency

identification technologies, mobile communication, media entertainment,3-D/2-D visualization of scientific data, and computer aided design.

Rajit Gadh received the Bachelors degree from theIndian Institute of Technology, Kanpur, India; theMasters degree from Cornell University, Ithaca, NY,USA; and the Ph.D. degree from Carnegie MellonUniversity, Pittsburgh, PA, USA, in 1984, 1986 and1991, respectively.

He is a Professor with the Henry Samueli Schoolof Engineering and Applied Science, University ofCalifornia, Los Angeles (UCLA), CA, USA, andthe Founding Director of the UCLA Smart GridEnergy Research Center, Los Angeles. His current

research interests include smart grid architectures, smart wireless communica-tions, sense and control for demand response, microgrids and electric vehicleintegration into the grid, and mobile multimedia.

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