Hierarchical Control Framework for Integrated Coordination between DERs and Demand Response

0.6 MB·

by  Di Wu

1
Hierarchical Control Framework for Integrated
Coordination between DERs and Demand Response
Di Wu, Jianming Lian, Yannan Sun, Tao Yang, and Jacob Hansen
Abstract—Demandresponserepresentsasignificantbutlargely states of potentially thousands of devices and broadcasts
untapped resource that can greatly enhance the flexibility and control signals to them. Such a centralized control strategy
reliability of power systems. This paper proposes a hierarchical
isoftensubjecttoseveraldisadvantages,suchashighrequire-
7 control framework to facilitate the integrated coordination be-
ment and cost in communication, substantial computational
1 tween distributed energy resources and demand response. The
0 proposed framework consists of coordination and device layers. burden, limited flexibility and scalability, and disrespect of
2 In the coordination layer, various resource aggregations are privacy [7]. As an alternative, a distributed control strategy
n optimally coordinated in a distributed manner to achieve the has been proposed, where each control agent maintains a set
system-level objectives. In the device layer, individual resources
a of variables and updates them through information exchange
J are controlled in real time to follow the optimal power dispatch with a few neighboring agents. During the past few years,
signalsreceivedfromthecoordinationlayer.Forpracticalappli-
8 cations,amethodispresentedtodeterminetheutilityfunctionsof many studies have been dedicated to distributed approaches

controllableloadsbyaccountingforthereal-timeloaddynamics for DER coordination. In [8], the authors developed a dis-
]
C and the preferences of individual customers. The effectiveness tributed algorithm that is resilient against potential packet
of the proposed framework is validated by detailed simulation
O drops and applied the algorithm to DER coordination. In [9],
studies.
a strategy based on the local replicator equation was pre-
.
h IndexTerms—Distributedcontrol,distributedenergyresource, sented for economic dispatch of DGs. Other algorithms that
t demand response, hierarchical control, resource allocation.
a can be applied to the DER coordination include the leader-
m follower consensus algorithm [10], two-level incremental cost
[ I. INTRODUCTION consensus algorithm [11], distributed algorithm based on the

1 Withgrowingemphasisonsystemefficiencyandreliability, consensus and bisection method [12], and minimum-time
consensus algorithm [13], just to name a few. There are also
v a great effort has been made in developing distributed energy
3 resources (DERs) such as distributed generator (DG) and studies that incorporated power losses into the distributed
1 algorithm design [14], [15]. Recently, coordination between
energy storage. These resources are small and highly flexible
9 DERs and DR has been reported in [16] and [17]. Although
compared with conventional generators, and are playing an
1 usefulinsightsregardingDERandDRcoordinationhavebeen
0 increasingly important role in the future smart grid [1], [2].
reportedinthesestudies,theexistingresultscannotbedirectly
. On the other hand, demand-side control has presented a
1 extendedandappliedtopracticalapplications.Thisisbecause
novel and viable way to supplement conventional supply-side
0
the controllable loads were simply modeled as a “generator”
7 control [3]–[5]. In fact, demand response (DR) represents a
with negative generation, where the load characteristics and
1 significant but largely untapped resource in the power grid.
: According to National Energy Technology Laboratory, with dynamics were totally ignored. Furthermore, the studies did
v
not address the issue of designing real-time load control
i only 10% customer participation, the potential nationwide
X strategies to achieve optimal power consumption. This paper
value of demand dispatch could be several billion dollars per
r year in reduced energy costs [6]. The deployment of DERs proposes a hierarchical control framework with two layers to
a
achieve integrated coordination of DERs and DR. The under-
and DR will not only defer infrastructure investments in the
lying control strategy accounts for the detailed characteristics
power grid, but also meet additional reserve requirements
anddynamicsofcontrollableloads,andaddressestheissueof
from renewable generation. Although the deployment of DR
designing real-time control strategies.
and DERs can lead to more economic and reliable system
Therestofthispaperisorganizedasfollows.InSectionII,
operation, it requires proper coordination between DERs and
themajorchallengesofintegratedcoordinationbetweenDERs
DR to harvest their potential benefits.
and DR are first discussed in detail, and then the proposed
The coordination problem can be solved in a completely
hierarchicalcontrolframeworkisbrieflyintroducedwithmain
centralized manner, where a single control center accesses
contributionshighlighted.Thetoplayeroftheproposedframe-
ThisworkwassupportedbytheLaboratoryDirectedResearchandDevel- work is described in Section III, where a general coordi-
opmentprogramatPacificNorthwestNationalLaboratory.PacificNorthwest nation problem between DERs and DR is formulated and
NationalLaboratoryisoperatedfortheU.S.DepartmentofEnergybyBattelle
solved using a distributed approach. The bottom layer of the
MemorialInstituteunderContractDE-AC05-76RL01830.
D.Wu,J.Lian,Y.Sun,andJ.HansenarewiththePacificNorthwestNa- proposed framework is described in Section IV, where the
tionalLaboratory,Richland,WA99354USA(e-mail:{di.wu,jianming.lian, device aggregation and real-time control are presented and
yannan.sun,jacob.hansen}@pnnl.gov).
illustrated using air conditioners (ACs). In Section V, various
T. Yang is the Department of Electrical Engineering, University of North
Texas,Denton,TX76203USA(e-mail:[email protected]). casestudiesalongwithdetailedsimulationresultsareprovided
2
Fig.1. IllustrationoftheproposedhierarchicalcontrolframeworkforintegratedcoordinationbetweenDERsandDR.
to demonstrate the effectiveness of the proposed framework. often not the case for controllable loads. Some controllable
Finally, concluding remarks are given in Section VI. loadssuchasthermostaticallycontrollableloadshavenotbeen
designedwiththecapabilitytocontinuouslyadjusttheirpower
II. PROBLEMSTATEMENTANDPROPOSEDFRAMEWORK consumption. Furthermore, their power consumption cannot
be directly controlled and is usually indirectly affected by
Power system operation requires instantaneous power bal-
other control variables. For example, the thermostat of an AC
ance between generation and demand that is constantly vary-
receivesthetemperaturesetpointasthecontrolinputandthen
ing. Most balancing is achieved through energy scheduling.
automatically switches the compressor on and off to maintain
In this paper, the short-term scheduling and operation prob-
the indoor air temperature around the setpoint. Therefore, a
lems are considered for DGs and controllable loads. At the
real-time load controller has to be designed for individual
scheduling stage, the optimal resource allocation problem is
controllable loads using the locally acceptable control input
formulated and solved between DGs and DR, where the real-
while capturing the underlying economics.
time dynamics of controllable loads must be captured. At the
Effectively coordinating and controlling DERs and DR for
operation stage, real-time control is carried out so that DGs
short-termschedulingandreal-timecontrolcannotberealized
and controllable loads follow optimal power generation and
by simply adding one coordination algorithm to another load
consumption, respectively.
control approach. A systematic method is needed to capture
the underlying economics and dynamics of controllable load
A. Technical Challenges synthetically in both scheduling and real-time control. The
AlthoughmanyresultsregardingDERandDRcoordination proposed framework herein exactly meets such a need. The
have been presented in the literature, there are still several main contributions of this paper are summarized as follows:
technical gaps that are significant enough to prohibit practical • Wediscussthegapbetweenshort-termschedulingandreal-
application of these existing results. timecontrolfromexistingcoordinationalgorithmsandload
First, the cost functions of DGs and the utility functions control approaches, and identify challenges to bridging the
of controllable loads are required to formulate and solve the gap.
optimal coordination problem. Existing studies such as [16] • We design a holistic hierarchical control framework, which
and [17] assume that those functions are available and can be is capable of directly adopting existing coordination algo-
directlyusedintheproposeddistributedapproaches.However, rithms and load modeling/control approaches.
it is not straightforward to construct the utility functions of • We define the functionality and formulate mathematic
powerforcontrollableloadsasthecostfunctionsofpowerfor problems in each layer, and specify the information to
DGs.Forinstance,theutilityofusinganACisdirectlyrelated be exchanged between layers/sublayers in both short-term
to the comfort an individual customer perceives at different scheduling and real-time control.
indoor air temperatures rather than the power consumption. • We identify candidate coordination algorithms and load
Therefore, it is required in practice to extract the utility control approaches that can fit in the proposed framework,
functions and capture the underlying economics based on the and use example algorithm and approach to illustrate the
preferences of individual customers. proposed framework.
Second, it is required for practical applications to consider
the operation stage as well. After the coordination problem
B. Proposed Framework
is solved at the scheduling stage, individual resources are
expectedtofollowoptimalgenerationorconsumptionthrough To overcome the technical challenges described above, this
real-time control. It is straightforward for DGs to meet this paper proposes a hierarchical control framework as shown in
expectationbecausetheirgenerationlevelcanbecontinuously Fig. 1 to facilitate integrated coordination between DERs and
adjusted with existing generator controllers. However, this is DR.Theproposedframeworkconsistsoftwolayersincluding
3
coordination (top) and device layers (bottom). In Fig. 1, dash economic schedule of power generation and consumption for
lines represent information flow between layers/sublayers, DERs and DR, respectively. The objective is to maximize the
where the information exchange frequency is the same as socialwelfare,i.e.,thedifferencebetweentheutilityofpower
short-term scheduling. Solid lines represent information flow consumption and the cost of power generation, while meeting
within a layer/sublayer, where the information exchange fre- the desired total power output without violating operating
quency is typically much higher than short-term scheduling. constraints of individual resources.
Anoverviewofeachlayerisprovidedhereinandmoredetails The mathematical formulation of the scheduling problem
are provided in the following sections. for each coordination period is presented as follows, where
• The coordination layer is only involved in short-term powergenerationorconsumptionshouldbeunderstoodasthe
scheduling stage. Prior to each scheduling period, each average value during each coordination period,
coordinator receives aggregated utility or cost functions
(cid:88)NG (cid:88)NL
from aggregators or device controllers, as indicated by the min C (p )− U (p ) (1a)
green dash lines with up arrows. Then, the aggregation pGi,pLj i=1 Gi Gi j=1 Lj Lj
of various resources including DGs and controllable loads
(cid:88)NG (cid:88)NL
are optimally coordinated to achieve power balance. To subject to p − p =D (1b)
Gi Lj
overcome the disadvantages associated with centralized
i=1 j=1
coordination algorithms, a distributed coordination method 0≤Pmin ≤p ≤Pmax (1c)
can be employed, where local variables are exchanged Gi Gi Gi
0≤Pmin ≤p ≤Pmax (1d)
iteratively following algorithms as explained in Section III. Lj Lj Lj
Once the coordination problem is solved, the regulation where different notations are defined as follows:
signals are sent back to aggregators or device controllers
– N (orN )isthenumberofgenerator(orload)aggregation
G L
for real-time control, as indicated by the green dash lines
in the network;
with down arrows.
– C (p ) is the cost of the i-th generator aggregation as a
• Thedevicelayerincludestwosublayers:deviceaggregation fuGncitioGniof the power generation p ;
and device control. Gi
– U (p ) is the utility of the j-th load aggregation as a
– Intheaggregationsublayer,DERsaredividedintogroups fuLnjctioLnjof the power consumption p ;
as appropriate. Prior to each scheduling period, each ag- – D is the desired total power output; Lj
gregatorreceivedutilityorcostfunctionsfromitsunder- – [Pmin,Pmax] is the range of power generation for the i-th
lyingdevicecontrollers(asindicatedbythereddashlines geGneiratorGaiggregation;
with up arrows), determines the aggregated functions, – [Pmin,Pmax] is the range of power consumption for the
and then sends these information to the corresponding j-tLhjloadLajggregation.
coordinator in the top layer (as indicated by the green
Note that [Pmin,Pmax] for each load aggregation can be
dash lines with up arrows). After coordination problem Lj Lj
obtained by aggregating the power range of individual con-
is solved, each aggregator receives the regulation signals
trollable loads. For example, the average power consumption
from top layer (as indicated by the green dash lines with
of an AC for the next 5 minutes depends on the temperature
down arrows) and then broadcasts these signals to its
setpoint selected by the homeowner, the current indoor air
underlying devices (as indicated by the red dash lines
temperature and the outside air temperature, etc.
with down arrows) to collectively provide the desired
power generation or consumption.
– The device control sublayer is involved in both schedul- B. Proposed Approach
ing and real-time operation stages. At the scheduling Withoutlossofgenerality,alltheDGscanbeenumeratedas
stage,thecontrollerateachdevicereportstoitscomman- thefirstN agents.Theoptimizationproblemdefinedin(1a)–
G
der (either an aggregator or a coordinator) the required (1d) can then be generalized as
information(asindicatedbythegreen/reddashlineswith
N
up arrows), which is then used for coordination. After (cid:88)
min C (p ) (2a)
coordination problem is solved, it receives the regulation pi i i
i=1
signalsfromitscommander(asindicatedbythegreen/red
N
dashlineswithdownarrows).Duringreal-timeoperation, (cid:88)
subject to p =D (2b)
i
it regulates devices to fulfill their functionality (e.g.,
i=1
control the indoor air temperature within the comfort Pmin ≤p ≤Pmax, i=1, ..., N (2c)
zone) while following the scheduled energy generation i i i
or consumption. where N =N +N ,
G L
(cid:26)
p , i=1,...,N
III. OPTIMALRESOURCECOORDINATION pi = −Gpi , i=N +1,G...,N +N (3)
A. General Description Li−NG G G L
(cid:40)
C (·), i=1,...,N
In the coordination layer, the optimal coordination problem C (·)= Gi G (4)
i
is solved for each coordination period to determine the most −ULi−NG(·), i=NG+1,...,NG+NL.
4
The optimal solution can be obtained through various dis- determine the supply and demand curves of various resources
tributed coordination algorithms reviewed in Section I. Most and send them to the coordination layer at the beginning
of these algorithms are consensus-based with marginal cost of each coordination period. To maintain the scalability of
modeled as consensus variables. They solve the problem the proposed framework in dealing with a large number
essentially through price-directive decomposition, which is of resources, the device layer is further divided into two
actually the gradient method applied to the dual problem. sublayers:deviceaggregationanddevicecontrol.Inthedevice
Different methods have been proposed to update the dual aggregation sublayer, resources of similar type are grouped
variable using partial or total mismatch between demand and together when their individual sizes are small. In practice,
supply (the gradient of the dual problem) [8], [10]–[12], [16]. the resource aggregation is usually employed to either fa-
In this paper, we use the distributed coordination algorithm cilitate coordination processes or represent business models.
proposed in [18]. Each aggregator serves as the message channel between the
Prior to each scheduling period, each coordinator receives coordination layer and the device control sublayer. It collects
the aggregated utility or cost functions as well as the power theindividualsupply ordemandcurves fromresourceswithin
operating ranges from aggregators or device controllers, as its aggregation (as indicated by the red dash lines with up
indicated by the green dash lines with up arrows in Fig. 1. arrows in Fig. 1), and then sends the aggregated curve to the
Next, each coordinator converts the received cost/utility func- coordination layer (as indicated by the green dash lines with
tionsandpoweroutputtoC (·)andp ,respectively,according uparrowsinFig.1).Thenitsendstheoptimaldispatchsignals
i i
to (2). Then, the coordinator starts to run the coordination received from the coordination layer to the device control
algorithm as shown in (5). sublayer (as indicated by the red dash lines with down arrows
(cid:88) in Fig. 1). In the device control sublayer, real-time control
λ (k+1)=λ (k)−β (λ (k)−λ (k))
i i k i j translatestheoptimaldispatchsignalsintolocalcontrolinputs
j∈Ni so that individual resources can follow the optimal generation
−α (p (k)−D ), (5a)
k i i or consumption.
pi(k+1)=∇Ci−1(λi(k+1)), (5b) The supply curves of DGs can be easily determined based
on generator operational cost, fuel efficiency, and fuel cost.
where N = {j ∈ V|(j,i) ∈ E} is the neighboring set of the
i
It is also straightforward for them to follow the optimal
i-thagent,∇C (·)isthederivativeofcostfunctionand∇C−1
i
generation in real time because their generation level can
denotesitsinversefunction,α andβ arethegainparameters
k k
be continuously adjusted with well established controllers.
atstepkforinnovationtermandconsensusterm,respectively,
and D is chosen such that (cid:80)N D =D. The determination However, for controllable load, technical challenges exist in
i i=1 i i) determining the demand curves of controllable loads based
of D can be arbitrary. In practice, one option to determine
i
on individual customer preference, and ii) designing real-time
D is that the system operator forecasts the total demand D,
i
control that can translate optimal power demand into locally
and then arbitrarily distributes this demand to a small set of
acceptable control input. As pointed out in Section II, one
agents or even a single agent (D is zero for the remaining
i
essential step is to obtain the relationship between marginal
agents). Alternatively, each agent can also determine its own
utility and local control input.
D . This strategy is used in this paper. Please refer to Section
i
V.A for more details.
With this algorithm, each coordinator i only maintains a B. Proposed Approach
localvariableλ thatistheestimateoftheoptimalincremental
i The demand curve dynamically represents how individual
cost, and updates it through information exchange with its
customersvalueconvenienceorcomfortandthecorresponding
neighboring coordinators (as indicated by the black lines in
energy usage. It is essential to capture the opportunity cost of
the coordinator layer in Fig. 1.) By executing (5), λ (k) and
i DR. To extract the demand curve, it is necessary to quanti-
p (k) at each coordinating agent will converge to the optimal
i tatively relate the marginal utility of individual customers for
dual variable (clearing prices) and power output, which are
power demand to the local control input based on customer
sent back to aggregators or device controllers for real-time
preference. Herein, a practical method is presented for ACs
control,asindicatedbythegreendashlineswithdownarrows
to extract such a relationship. This method was originally
in Fig. 1.
proposed in the GridWise(cid:13)R demonstration project [19], and
thenrigorouslyanalyzedin[20].Althoughithasbeenspecifi-
IV. DEVICEAGGREGATIONANDCONTROL
callypresentedforACs,theunderlyingcontrolphilosophycan
A. General Description
be easily extended and applied to other types of controllable
AlthoughitisnecessarytohaveC (p )andU (p )to loads.
Gi Gi Lj Lj
formulatetheoptimalcoordinationproblemasshownin(1a)– This method represents the relationship between marginal
(1d), the distributed algorithms only require their derivatives, utility and local control input by a response curve as illus-
C(cid:48) (p ) and U(cid:48) (p ), to solve this coordination problem. trated in Fig. 2, which is determined by several parameters.
Gi Gi Lj Lj
The derivative of C (p ) (or U (p )) is often referred The parameters λ and σ are the average and variance,
Gi Gi Lj Lj avg
to as the supply (or demand) curve, which characterizes the respectively, of the electricity prices over a period of time
relationship between marginal cost (or utility) and power in the past, which can be calculated by a local controller or
generation (or consumption). Hence, the device layer has to load aggregator. The parameters T , T , and T are
desired min max
5
Fig.4. Illustrationofthedemandresponsecurvesofairconditioners.
Fig.2. Illustrationoftheresponsecurvesforairconditioners.
Equivalent Thermal Parameter model. The detailed model can
be found in [21], [22], and can be represented in a simplified
form as
(cid:26) A x (t)+Bi if q (t)=1
x˙ (t)= ¯i¯i ¯on i (6)
Fig.3. UserinterfaceintheGridWise(cid:13)R demonstrationproject ¯i A¯ix¯i(t)+B¯ioff if qi(t)=0,
wherex (t)isthecontinuousstatevectorconsistingofindoor
¯i
air temperature Ti(t) and mass temperature Ti (t), and q (t)
a m i
directly specified by users, where Tdesired is the desired indoor denotes the operating mode of the AC with qi(t) = 1 when
air temperature setpoint, and Tmin and Tmax are the lower and it is ON and qi(t) = 0 when it is OFF. The operating mode
upperboundsoftheacceptableindoorairtemperaturesetpoint. of the AC for cooling is usually controlled by a hysteretic
The parameter k is a positive number completely abstracted controller,
fromtheowner’spreferenceofindoorairtemperaturesetpoint  1 if Ti(t)≥T +δ/2
 a set
over the electricity price. For example, when k is very large, q (t+)= 0 if Ti(t)≤T −δ/2 (7)
i a set
the response curve becomes an almost vertical line at Tdesired.  q (t) otherwise,
i
Thisimpliesthatthehomeownerisverysensitivetotheindoor
where δ is the hysteresis band centered around the indoor
air temperature, and would like to maintain the indoor air
air temperature setpoint T . When the model parameters
temperature setpoint at T regardless of the electricity set
desired (A ,Bi ,Bi ) are known to local controllers, the relationship
price. When k is close to zero, the response curve becomes ¯i ¯on ¯off
between indoor air temperature setpoint and power consump-
an almost horizontal line at λ . This implies that the house
avg
tion can be derived, which finally leads to the demand curve
owner is very sensitive to the electricity price, and would
like to sacrifice comfort for cost saving. In the GridWise(cid:13)R as shown in Fig. 4 by taking into account the corresponding
response curve. The determination of Ei , Ei , λi , and
demonstration project, the abstraction of k is done by letting max min min
λi is provided in the Appendix. If the model parameters
individual homeowners specify their preferences of comfort max
are unknown, they can be estimated based on the measured
over cost through a user interface as shown in Fig. 3.
indoor air temperature as proposed in [23]. The individual
In the proposed framework, prior to each coordination
demandcurveswillbesenttotheloadaggregator,wherethey
period, each load controller at the device layer determines
are aggregated together, and sent to the coordination layer to
its DR curve (which is equivalent to the utility/cost function)
solve the optimal coordination problem.
considering the load dynamics. These curves are sent to
With this method, the load utility/cost functions depend
aggregators (as indicated by the red dash lines with up arrows
on the market clearing price during previous periods, the
in Fig. 1), and then aggregated at aggregators and later used
outside air temperature, and customer preference for comfort.
by coordinators to run the distributed coordination algorithms
Therefore, these functions in (4) are time-varying from one
for determining the optimal power consumption and real-time
schedulingperiodtoanother.TheDRcurveillustratedinFig.4
price signal. The price signal is then broadcasted to each
isthederivativeofutilityfunction(1a).SincetheDRcurveis
deviceevery5minutes,asindicatedbythereddashlineswith
monotonically non-increasing, the utility function is concave.
downarrowsinFig.1.Withineach5-minuteoperatingperiod,
The negative utility function in (1a) becomes a cost function
this response curve will be used by a real-time controller to
in (2a), which is convex.
translate the optimal power demand represented by clearing
price λ into the indoor air temperature setpoint T for
clear set
this operating period. Recall that the demand curve is the V. CASESTUDIES
mapping from marginal utility to power demand. Since the This section demonstrates the proposed hierarchical control
response curve is the mapping from marginal utility to the framework by case studies on the IEEE 123-node system
indoorairtemperaturesetpoint,itisonlylefttodeterminethe that was prepared by IEEE PES Distribution System Analysis
relationshipbetweenindoorairtemperaturesetpointandpower Subcommittee’sDistributionTestFeederWorkingGroup[24].
demand. The dynamics of each AC i can be described by the The simulation studies are implemented in GridLAB-D [25],
6
coordinated with DGs so that they can meet
contr. load+uncontr. load−DG gen.=ref. (8)
In (8), ref. represents the desired power consumption of
the distribution system and can be commanded by system
operators. For example, in island microgrid operation, the
command will be set to zero, i.e., DGs and controllable loads
are scheduled to balance the uncontrollable load within the
microgrid for each 5-minute period. For a grid-connected
distributionsystem,DGsandDRcanbecontrolledtofollowa
given signal for either reducing energy cost or providing grid
services.Forexample,theycanactivelyparticipateintheload
following service by setting the reference signal as
ref.=feeder hourly schedule−load following signal.
In the coordination problem (2), the desired total output from
Fig.5. IEEE123-nodetestsystem.
DGs and DR is
TABLEI
D =ref.−uncontr. load. (9)
GENERATORPARAMETERS
DGNo. ai(kW2h) bi ($/kWh) ci ($/h) Range(kW) In order to apply the distrib(cid:80)uted algorithm in (5), we need
to determine D such that D = D. In this paper, we
1 0.00015 0.0267 0.38 [50,500] i i i
2 0.00052 0.0152 0.65 [20,100] choose to distribute D only among three load aggregators and
3 0.00042 0.0185 0.4 [40,200] set Di to zero for DGs. The distribution of D is realized by
4 0.00031 0.0297 0.3 [20,250] distribution of ref. signal and local uncontr. load. First, ref.
5 0.00025 0.0156 0.33 [30,300] signal can be arbitrarily distributed among load aggregators
offline, prior to scheduling period. In this paper, we evenly
distribute this signal among three aggregators. On the other
which is an advanced open-source power systems modeling hand, the uncontrollable load at each aggregator is unknown
and simulation environment developed at Pacific Northwest andneedstobeforecasted.Whiletherearedifferentloadfore-
National Laboratory. castingmethodologies,e.g.,artificialneuralnetworks[28],au-
toregressivemovingaveragemodels[29],andsemi-parametric
additive models [30], this work simply assumes that the
A. Test System Description forecast of local uncontrollable load in the next 5-minute
periodisequaltothemeasuredlocaluncontrollableloadinthe
The IEEE 123-node test system shown in Fig. 5 consists current period. Please note that renewable generation as one
of 123 nodes and 118 lines. It has been modified to include kindofimportantdistributedgenerationcouldalsobemodeled
houses with ACs and other residential loads. The number of as negative uncontrollable load as it is typically controlled for
houses has been adjusted to match the peak load provided maximum power tracking. It is forecasted and adjusted every
in the test system dataset, which results in 1,222 houses. 5 minutes, and becomes a component of ‘uncontr. load’. In
The following studies assume that 988 ACs participate in the such a way, controllable load and DGs can be optimally used
DR program, and the remaining 234 ACs are uncontrollable to help address the uncertainty and variability from renewable
as other residential loads. The controllable ACs are grouped generation.
into three load aggregations, where the number of houses When performing DGs and DR coordination for the time
under each aggregation are 98, 254, and 632, respectively. period t using (5a) and (5b), the initial values of power p
i
TherearefiveDGsconnectedtothesystem,whosegeneration and marginal costs λ are set to be converged values in the
i
cost parameters are adopted from [26] and [27] and listed in time period t−1. This can help to greatly reduce the required
Table I. Although it is typical to represent generation cost number of iterations.
by quadratic functions, the distributed algorithms reviewed in
the Introduction section are able to handle convex functions
B. Simulation Results
that are more general than quadratic functions. In fact, the
cost functions of DR in this paper are convex, as explained 1) Base case (Case 1): The test system is first simulated
in Section IV-B. The distributed algorithm for solving the without any DGs and controllable loads for a typical summer
optimal coordination problem is selected to be the leaderless day with a minimum time step of 30 seconds. The 5-minute
algorithm defined in (5a) and (5b), which requires undirect averagefeederpowerconsumptionisplottedinFig.6,together
communication networks. with the outside air temperature. Since AC load accounts for
Prior to each coordination period, which is selected to more than 80% of the total load in this system, the system
be 5 minutes, controllable loads are aggregated and then load increases as the outside air temperature rises.
7
6 100 0.4
0.35
F)
W)4 90 ure (° 0.3
Feeder load (M2 80 Outside air temperat Power [MW]00..0012..5512
Feeder load
Temperature 0.05
DG1 DG2 DG3 DG4 DG5
0 70
00 11 22 33 44 55 66 77 88 99 110011111122113311441155116611771188119922002211222222332244 0
Hour of day 0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Hour of day
Fig.6. Basecasefeederload(5-minuteaverage)andoutsideairtemperature.
Fig.8. GenerationoutputfromDGsinCase2.
4
Agg. 1
3.5 1
W] Scheduled Actual Max Min
3 M
er [0.5
W]2.5 ow
M P
wer [ 2 00 1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Po1.5 Hour of day
Agg. 2
1 1.5
W]
0.5 DAcetsuiraeld er [M 1
w0.5
0 o
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 P
Hour of day 0
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Hour of day
Fig.7. Desiredvs.resultedfeederload(bothare5-minuteaverage). Agg. 3
W]3
M
2) Active DER and DR Coordination (Case 2): The test ower [12
system is then simulated with DGs and controllable loads P
0
under the proposed hierarchical control framework for the 0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Hour of day
same summer day. In general, the reference signal can be
any time series within the capability of the active distribution Fig.9. LoadundereachaggregatorinCase2.
system.Toverifytheeffectivenessoftheproposedframework,
the desired feeder load consumption is set to be 0.7 of the
feeder load in base case, as shown by the blue dashed line approximation of optimal solution in coordination layers.
in Fig. 7. Such a reference signal is simple to construct yet
The output of DGs is shown in Fig. 8. DG2 is the cheapest
useful for testing the proposed method because
generator and is at its maximum output almost all the time.
• The 30% reduction of load at the feeder requires the Other DGs generate more during peak hours, because the
participation of DG and DR during scheduling, which is reference signal essentially requires more reduction from the
exactly what we need to study. base case during peak hours. It can be easily verified that
• The reduction is proportional to the load feeder in the the marginal cost of all DGs that are not at their generation
base case and therefore varies with time. Such varying load limits is the same, using the cost parameters in Table I. The
reduction requires DG and DR to vary their generation or scheduled and actual load from aggregators together with
consumption in a coordinative manner. their dynamic capability (max and min) are plotted in Fig. 9.
• Such a desired signal requires DG and DR to support the The feasible load range for each AC in each time period
local system more during peak hours than off-peak hours, depends on the current indoor air temperature, temperature
whichseemsplausible.Thetestcaseenablesustocompare setpoint and acceptable range, price information etc., and
DER participation in peak hours with off-peak hours, as therefore varies significantly from one time period to another.
well as the difference in energy price of the distribution Nevertheless, the feasible load range from aggregating a large
system. numberofACsdoesnotvarymuch.Theactualaveragepower
The obtained 5-minute average power consumption is plot- consumption closely follows the desired value, which verifies
tedbytheredcurveinFig.7.Ascanbeseen,theactualfeeder the effectiveness of the proposed coordination and control.
load follows the desired value with reasonable accuracy. The The acceptable temperature settings and the simulated in-
small mismatch is due to a few factors such as approximation door air temperature are plotted in Fig. 10 for a house under
of demand curve, errors in uncontrollable load forecast, and Aggregator 1. Based on how customers value their com-
8
80 meetthelocalconstraint.Comparedwiththecasewherethere
is not line capacity constraints, these load and price are just
some different solutions of the optimal coordination problem
75
F) (2) with some updated parameters.
°
e (
ur
erat70 VI. CONCLUSIONS
p
m Inside air temperature
Te T This paper presents a hierarchical control framework to
max
65
T integrateDRintoDERcoordination.Theproposedframework
min
takes the advantage of existing coordination algorithms and
60 device controllers, and bridges the gap between short-term
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324
scheduling and real-time control of controllable loads. This
Hour of day
is done by synthetically capturing the underlying economics
Fig.10. IndoorairtemperatureofHouse1underAggregator1inCase2. fromDRaswellasdetaileddynamicsfordevice-levelcontrol.
Simulationresultsshowedthattheproposedmethodiscapable
Agg. 3 load to optimally coordinate DR with DGs and control DR in real-

3 w/o constraints w/ constraints Thermal capacity time to realize the desired allocation of power consumption.
W) The future work is to expand this framework to include
er (M2 distributed energy storage into this coordination between DGs
Pow1 and controllable loads.
0
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 APPENDIXA
Hour of day
Agg. 3 price DEMANDCURVEDETERMINATION
25
h) w/o constraints w/ constraints ThedemandcurveofeachACasshowninFig.4ischarac-
W
k20 terized by the maximum and minimum energy consumptions
s/
cent (Emiax and Emiin), and the corresponding energy prices (λimin
e (15 and λi ), which can be calculated as follows:
Pric max
10 • Emiax andλimin:Forthei-thunit,thetheoreticalupperbound
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 ofaveragepowerconsumptioncorrespondstotheoperation
Hour of day
whenthedeviceisONfortheentireperiod.Inthiscase,the
Fig.11. PowerconsumptionandclearingpriceunderAggregator3inCase3. average power consumption is simply equal to pc, which
is the instantaneous power when the device is ON and
is constant through the 5-minute operating period. With
fort, temperature setpoint varies with the system energy cost q (t) = 1, the closed-form analytical expression of indoor
i
throughoutaday.Duringoff-peakhourswhentheenergyprice air temperature Ti(t) can be obtained by solving (6). The
a
islow,thetemperaturesetpointandindoorairtemperatureare setpointT mustbelowenoughtosatisfy(10)tomaintain
set
closer to the desired value, which is 72.3◦F in this case. the ON status for the entire period assuming the device is
3) Active DER and DR Coordination with Line Capacity operated in cooling mode,
Constraints (Case 3): It follows from Fig. 9 that the load
from Aggregator 3 exceeds 2 MW during peak hours. Now Tset ≤Tsoent, (10)
suppose that the thermal capacity is at 2 MW for the branch
whereTon =min {Ti(t)}−δ/2whenthedeviceisinitially
that connects Aggregator 3 to the distribution system. Since set t a
OFF, and Ton = min {Ti(t)} + δ/2 when the device is
the branch connects only Aggregator 3 to the distribution set t a
initially ON.
system, the power consumption by Aggregator 3 is equal to
the power flow in the branch (ignoring losses for simplicity). – If Tsoent ≥ Tmin, where Tmin is the lowest acceptable
Therefore, the capacity limit of such a branch can be taken temperaturesetpointspecifiedbytheuser,findtheenergy
care of by imposing the limit to Aggregator 3’s power range, priceλiminwhichcorrespondstoTsoent onthecurveinFig2.
i.e., modifying the maximum power consumption pmiax of For any price that is less than λimin, AC i will be ON for
Aggregator 3 in (2c). In this case, the maximum power limit the entire operating period and the maximum average
of Aggregator 3 in (2c) becomes active for some time. The power consumption Emiax is pc.
simulationresultsareshowninFig.11.Itcanbeseenthatthe – If Tsoent < Tmin, the device can only be ON for part of
proposed framework can account for local thermal constraints the period, because Tset (≥ Tmin > Tsoent) will trigger the
as well when coordinating DERs and DR. When congestion devicetobeOFFforatleastsometimeduringtheperiod.
occurs, the active local constraint significantly raises the en- In this case, the energy price λimin simply corresponds
ergy price for the load under Aggregator 3. It should be noted to Tmin on the curve in Fig 2. The corresponding upper
that the load and price are obtained using the same optimal bound of feasible average power consumption Emiax can
coordinationalgorithm,ratherthanbeingmanuallymodifiedto be found by solving (6) and (7) by letting Tset =Tmin.
9
• Emiin and λimax: The theoretical lower bound of average [8] A.D.Domínguez-García,C.N.Hadjicostis,andN.F.Vaidya,“Resilient
power consumption is zero and it corresponds to the op- networkedcontrolofdistributedenergyresources,”IEEEJ.Sel.Areas
Commun.,vol.30,no.6,pp.1137–1148,Jul.2012.
eration when the device is OFF for the entire period. The
[9] A. Pantoja, N. Quijano, and K. M. Passino, “Dispatch of distributed
setpoint Tset must satisfy (11) to maintain the OFF status generatorsunderlocal-informationconstraints,”inProc.IEEEAmerican
for the entire period when the device is operated in cooling ControlConf.,Jun.2014,pp.2682–2687.
[10] Z. Zhang, X. Ying, and M.-Y. Chow, “Decentralizing the economic
mode,
dispatchproblemusingatwo-levelincrementalcostconsensusalgorithm
T ≥Toff, (11) inasmartgridenvironment,”inProc.NorthAmer.PowerSymp.(NAPS),
set set
2011,pp.1–7.
whereToff =max {Ti(t)}−δ/2whenthedeviceisinitially [11] Z. Zhang and M.-Y. Chow, “Convergence analysis of the incremen-
set t a tal cost consensus algorithm under different communication network
OFF, and Tsoeftf = maxt{Tai(t)}+δ/2 when the device is topologiesinasmartgrid,”IEEETrans.PowerSyst.,vol.27,no.4,pp.
initially ON. 1761–1768,2012.
[12] H. Xing, Y. Mou, M. Fu, and Z. Lin, “Distributed bisection method
– If Toff ≤ T , where T is the highest acceptable
set max max for economic power dispatch in smart grid,” IEEE Trans. Power Syst.,
temperaturesetpointspecifiedbytheuser,findtheenergy vol.30,no.6,pp.3024–3035,Nov.2015.
price λi which corresponds to Toff on the curve in [13] T.Yang,D.Wu,Y.Sun,andJ.Lian,“Minimum-timeconsensusbased
max set approach for power system applications,” IEEE Trans. Ind. Electron.,
Fig 2. For any price that is higher than λi , AC i will
max vol.63,no.2,pp.1318–1328,Feb.2016.
be OFF for the entire operating period and there is no [14] G.Binetti,A.Davoudi,F.L.Lewis,D.Naso,andB.Turchiano,“Dis-
energy consumption. tributed consensus-based economic dispatch with transmission losses,”
IEEETrans.PowerSyst.,vol.29,no.4,pp.1711–1720,Jul.2014.
– If Toff > T , the device can only be OFF for part of
set max [15] W. T. Elsayed and E. F. El-Saadany, “A fully decentralized approach
the period, because T (≤T <Toff) will trigger the forsolvingtheeconomicdispatchproblem,”IEEETrans.PowerSyst.,
set max set
devicetobeONforatleastsometimeduringtheperiod. vol.30,no.4,pp.2179–2189,Jul.2015.
[16] G. Hug, S. Kar, and C. Wu, “Consensus + innovations approach for
In this case, the energy price λi simply corresponds to
max distributedmultiagentcoordinationinamicrogrid,”IEEETrans.Smart
T on the curve in Fig 2. The corresponding lower Grid,vol.6,no.4,pp.1893–1903,Jul.2015.
max
bound of feasible average power consumption Ei can [17] Y.Xu,Z.Yang,W.Gu,M.Li,andZ.Deng,“Robustreal-timedistributed
min optimalcontrolbasedenergymanagementinasmartgrid,”IEEETrans.
be found by solving (6) and (7) by letting T =T .
set max SmartGrid,pp.1–12,2015,toappear.
• For any point between λimin and λimax, the device will only [18] Ssy.sKteamrs:anAdcGo.nsHeungsu,s“D+isintrnibouvtaetdionrosbaupsptreocaocnho,”miincPdriospca.tIcEhEiEn Ppoowweerr
be ON for part of the period. The closed-form analytical
EnergySoc.Gene.Meet.,Jul.2012.
expression does not exist, but the numerical method can be [19] J. C. Fuller, K. P. Schneider, and D. Chassin, “Analysis of residential
used to find the corresponding average power consumption. demand response and double-auction markets,” in Proc. IEEE Power
andEnergySoc.Gene.Meet.,Jul.2011,pp.1–7.
This process needs to be repeated for a large number of
[20] S.Li,W.Zhang,J.Lian,andK.Kalsi,“Market-basedcoordinationof
points to accurately characterize the demand curve. On thermostatically controlled loads—Part I: A mechanism design formu-
the other hand, submitting the entire demand curve to lation,” IEEE Trans. Power Syst., vol. 31, no. 2, pp. 1170–1178, Mar.
2016.
aggregators requires sending all the points, which also
[21] “Residentialmoduleuser’sguide.”[Online].Available:http://gridlab-d.
burdensthecommunicationnetwork.Infact,manypractical sourceforge.net/wiki/index.php/Residential_module_user’s_guide
applications do not require the entire demand curve, and its [22] A. Thomas, P. Jahangiri, D. Wu, C. Cai, H. Zhao, D. C. Aliprantis,
and L. Tesfatsion, “Intelligent residential air-conditioning system with
approximationshouldgoodenoughforengineeringpurpose.
smart-grid functionality,” IEEE Trans. Smart Grid, vol. 3, no. 4, pp.
For example, the demand curve shown in Fig. 4 can be ap- 2240–2251,Dec.2012.
proximatedbyastepcurveaslongasthedifferencebetween [23] S. Li, W. Zhang, J. Lian, and K. Kalsi, “Market-based coordination
ofthermostaticallycontrolledloads—PartII:Unknownparametersand
λi and λi is small. In this case, only three quantities
min max casestudies,”IEEETrans.PowerSyst.,vol.31,no.2,pp.1179–1187,
including Ei , Ei and (λi +λi )/2 are required to Mar.2016.
min max min max
characterize the approximated step curve, thereby reducing [24] Distributiontestfeeders.DistributionTestFeederWorkingGroup,IEEE
PES Distribution System Analysis Subcommittee. [Online]. Available:
communication requirement and computational cost.
http://ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html
[25] GridLAB-D.[Online].Available:http://www.gridlabd.org/
[26] T. Logenthiran, D. Srinivasan, A. M. Khambadkone, and H. N. Aung,
REFERENCES “Multiagent system for real-time operation of a microgrid in real-time
digitalsimulator,”IEEETrans.SmartGrid,vol.3,no.2,pp.925–933,
[1] J. Driesen and F. Katiraei, “Design for distributed energy resources,” Jun.2012.
IEEEPowerEnergyMag.,vol.6,no.3,pp.30–40,May2008. [27] M.Modiri-Delshad,S.Koohi-Kamali,E.Taslimi,S.H.AghayKaboli,
[2] J.Huang,C.Jiang,andR.Xu,“Areviewondistributedenergyresources and N. A. Rahim, “Economic dispatch in a microgrid through an
andMicrogrid,”Renew.Sust.EnergyRev.,vol.12,no.9,pp.2472–2483, iterated-basedalgorithm,”inProc.IEEECleanEnergyTech.,Nov.2013,
2008. pp.82–87.
[3] A. Ipakchi and F. Albuyeh, “Grid of the future,” IEEE Power Energy [28] H. S. Hippert, C. E. Pedreira, and R. C. Souza, “Neural networks for
Mag.,vol.7,no.2,pp.52–62,Mar./Apr.2009. short-termloadforecasting:areviewandevaluation,”IEEETrans.Power
[4] P. Palensky and D. Dietrich, “Demand side management: Demand Syst.,vol.16,no.1,pp.44–55,Feb.2001.
response,intelligentenergysystems,andsmartloads,”IEEETrans.Ind. [29] S.-J. Huang and K.-R. Shih, “Short-term load forecasting via ARMA
Informat.,vol.7,no.3,pp.381–388,Aug.2011. model identification including non-Gaussian process considerations,”
[5] D.S.CallawayandI.A.Hiskens,“Achievingcontrollabilityofelectric IEEETrans.PowerSyst.,vol.18,no.2,pp.673–679,May2003.
loads,”Proc.IEEE,vol.99,no.1,pp.184–199,Jan.2011. [30] S.FanandR.Hyndman,“Short-termloadforecastingbasedonasemi-
[6] J. Goellner, M. Prica, J. Miller, S. Pullins, J. Westerman, J. Harmon, parametricadditivemodel,”IEEETrans.PowerSyst.,vol.27,no.1,pp.
T.Grabowski,H.Weller,B.Renz,S.Knudsen,andD.Coen,“Demand 134–141,Feb.2012.
dispatch—intelligentdemandforamoreefficientgrid,”NationalEnergy
TechnologyLaboratory,Tech.Rep.DOE/NETL-DE-FE0004001,2011.
[7] H. Farhangi, “The path of the smart grid,” IEEE Power Energy Mag.,
vol.8,no.1,pp.18–28,Jan.2010.