Real-Time Data and Energy Management inMicrogrids

Zhichuan Huang and Ting ZhuUniversity of Maryland, Baltimore County

zhihu1@umbc.edu, zt@umbc.edu

Abstract—Microgrids are desired in remote areas, such asislands and under developed countries. However, given the limitedcapacities of local energy generation and storage in such acommunity, it is extremely challenging for an isolated microgridto balance the power demand and generation in real-time withdynamically changing energy demand. Meanwhile, more andmore sensing devices (such as smart meters) are deployed inindividual homes to monitor real-time energy data, which can behelpful for homes and microgrid to better schedule the workloadand generation. However, it is still difficult to conduct real-time distributed control due to the unreliable sensing devicesand communications between sensing devices and controllers.To address these issues in microgrids, we designed a novelapproach for the system to i) process the collected sensing data, ii)reconstruct the missing data caused by sensing error or unreliablecommunication, and iii) predict the future demand for real-timedistributed control with missing data in extreme situations. Thecontrol center then decides the operations of the local generatorand each home decides the scheduling of the flexible workloadof appliances based on the collected and predicted data. Weconducted extensive experiments and simulations with real worldenergy consumption data from 100 homes for one year. Theevaluation results show that our design can recover the missingdata with more than 99% accuracy and our distributed controlcan balance power demand and generation in real-time andreduce the operational cost by 23%.

I. INTRODUCTION

Microgrids play a important role in energy cyber-physicalsystems [1]. In a typical microgrid, it consists of local genera-tors and energy storage (e.g., batteries) to provide power for asmall community with commercial and residential buildings.Microgrids can provide power to places i) where the traditionalpower grid does not exist due to the poor economy orlimited number of residences (e.g., islands); and ii) when thetraditional power grid is temporarily not functioning due tosevere weather conditions (e.g., storms). Therefore, microgridshave gained increasing attention recently [2]. Due to thevery limited capacities of local energy storage and energygeneration, microgrids are more difficult to maintain thantraditional power grids. To ensure the stability and reliabilityof a microgrid, we need to conduct real-time schedulingand control the operations of local generators, batteries, andcontrollable workloads of appliances to offset the dynamicallychanging power demands of uncontrollable appliances.

Therefore, it is extremely important to collect the powerconsumption and generation data for distributed control inreal-time, which becomes possible with the recent rapid de-velopment of smart meters. However, the sensors in smart

meters and wireless communications between smart metersand controllers are not 100% reliable. The microgrid controllermay encounter missing data and delayed data when conductingthe scheduling for generators and distributed control operationsin each home. Furthermore, to cope with the dynamicallychanging demand, the microgrid controller needs informationto predict the future power demand to decide the operationsof local generators. Meanwhile, each home also needs topredict its own future demand to schedule workloads. Theexisting techniques on energy consumption forecasting aremainly for long term offline forecast for large generators[3], [4]. However, to realize real-time distributed control in amicrogrid, real-time data processing and short term predictionis needed. In this paper, we propose a novel data managementtechnique for distributed control in a microgrid to process thereceived data, reconstruct the missing data, and predict thefuture power demand with existing data. The key idea is toutilize the correlation between power, voltage and frequencydata of different homes in the microgrid. Then, the misses ordelayed data can be reconstructed with a portion of receiveddata or data from other homes. Because energy consumptionpatterns in one home are limited due to the limited numberof appliances, it provides us opportunity to reconstruct themissing data and predict future data in a short term based onexisting data and detected energy consumption patterns. Withthe reconstructed and predicted data, the controller decides thescheduling of workloads in each home and the operations ofgenerators to maintain the stability of the microgrid.

While the workload is scheduled in each home to avoidpower failures in the microgrid, the behaviors and comfort ofusers should not be affected. Therefore, we choose the flexibleand controllable workloads of appliances for scheduling. Forexample, water heaters are flexible and controllable loads be-cause we only need to make sure that there is enough hot waterin water heaters when people use hot water. Our approach canbe easily extended to support any other types of flexible andcontrollable workload (e.g., HVAC). For the local generator’sscheduling, we adopt a widely used generator model andpropose an optimal algorithm to minimize the operational cost.Specifically, we summarize our major contributions as follows:•We conducted a systematic investigation on the correlation

between power, voltage, and frequency in a microgrid anddeveloped a holistic sets of correlations models (i.e., power-voltage, frequency-voltage, temporal, and spatial correlation).Through extensive experiments and simulations, we show that

Power Generator

Energy Storage

Control Center

Microgrid

Energy flow

…

Fig. 1: Architecture of a microgrid

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60

60.1

Time (Hour)

Fre

quen

cy (

Hz)

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1

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Mis

sing e

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t

Fig. 2: Examples of data faults in energy monitoring

our design can recover the missing data with more than 99%accuracy for the short term prediction.• To reduce the operational cost of isolated microgrids, we

present holistic real-time scheduling algorithms for both localgenerators and controllable loads in individual homes evenwhen there exists communication failures between controlcenter and individual homes.• Utilizing the empirical energy consumption data from

100 residential homes, we conducted extensive simulations.The results indicate that our proposed distributed control canreliably balance power demand and generation in real-time andreduce operational cost by 23%.

II. BACKGROUND AND MOTIVATION

A microgrid is a distributed electric power system that canautonomously coordinate local generations and demands in adynamic manner [5]. Microgrids can operate in either grid-connected mode or isolated mode, some of which are nowdeployed in the US, Japan and European countries [6].

Background. In this paper, we consider a modern micro-grid, illustrated in Figure 1, consists of generation technology(e.g., local electricity generators) and batteries. To ensurecompatibility with the traditional power grid, we adopt themicrogrid architecture, which is similar to the one used in atraditional power grid. If the microgrid is built from nothing(e.g., island, where there is no electricity grid before), themicrogrid can be built the same architecture as traditionalgrid with a distribution network across the community ofhomes. If the microgrid is built from a traditional grid, weonly need to add local generators, batteries and a controlcenter into the microgrid. Within the microgrid, sensors are

deployed in each home to collect and send energy related data(e.g., power, voltage and frequency) to the control center. Thecontrol center decides the workload scheduling in each homeand the generations to balance the power demand and supply.

Motivation. To realize the real-time control, it is veryimportant to collect the energy related data from homes andsend back the control instructions in real-time. However, basedon our more than 6 years’ experiences of energy monitoring inresidential homes, the data collection from homes may sufferfrom different types of faults: i) data point missing; ii) sensingerror; iii) communication delay; and iv) communication loss.The first two faults are caused by the low reliability of sensorsdue to the long-term monitoring. The latter two faults arecaused by unreliable wireless communication. We show someexamples of faults in Figure 2. The first one is caused bysensing errors, which generate peaks but do not happen veryfrequently (we observe average 1.5 seconds sensing error in 12hours). The second one is whether we receive readings in thecloud server. The Y-axis value is set to be 1 if there is a datamissing event. We can see the missing events are very bursty,which means once we have a missing event, there will be highprobability there would be missing events in near future.

With the demand of real-time data collection and reality ofmultiple different faults in monitoring, it is crucial to managethe real-time collected data and reconstruct the missing datafor real-time control in a self-sustainable microgrid.

III. SYSTEM OVERVIEWTo ensure the reliability of the microgrid, we propose the

system design as shown in Figure 3, which includes threemain components: data management, central scheduler, andlocal scheduler. In summary, our system works as follows:i) power meters deployed in homes monitor the power con-sumption, voltage and frequency in the power line, then sendcollected data to control center; ii) control center receives thecollected data from homes and processes the data for missingdata reconstruction and future data prediction; iii) the centralscheduler decides the control instructions for each home andgenerators based on the processed data; iv) individual homesand the power generator execute the instructions from centralscheduler if control instructions are received; v) if controlinstructions are not received by the individual homes and thepower generator, local scheduler will conduct local control inthese homes and the power generator will maintain the sameamount of power generation.Data Management. Due to the sensing errors and unreliablecommunication, it is highly possible we will miss importantenergy data from sensors. To reconstruct and predict the sens-ing data, we investigate the correlation models among energydata for recovery. The received data will be used both for datareconstruction and update for correlation model. Specifically,we investigate i) correlation between power and voltage forhomes under the same transformer; ii) correlation betweenfrequency and voltage at individual homes; iii) temporal andspatial correlation for power consumption of all homes. Basedon these correlations, the missing data can be reconstructedand future data can be predicted for real-time control.

Communication

Sensing Circuit

Sensing Hardware

Generator

Data Reconstruction

Correlation Model

Real-time Sensing

Generator Control

Uncontrollable Load

Controllable Load

Data Management

Control Center

Central Scheduler

Home ControlLocal Control

Local Scheduler

Control

Instructions

Control

Instructions

Control Instructions

Recovered Data

Sensing Data

Sensing Data

Fig. 3: System overview

Central and Local Scheduler. Based on recovered and pre-dicted data, the central scheduler decides control instructionsfor both controllable workload in homes and the generationfrom the power generator. The key idea of workload controlin each home is to turn on some appliances when powerconsumption is low and turn off some appliances when powerconsumption is high. In our paper, we use the workload of thewater heater as an example because its workload is flexible andit is commonly installed in residential homes. Our design caneasily be extended to support the scheduling of HVAC systems.The generation control is to decide the power supply fromgenerators. Because the power supply of generators cannotbe changed as fast as workload at homes, we schedule thegenerators based on prediction of future power demand in themicrogrid. Batteries are used as buffer to offset the predictionerrors of the future power demand. Due to the unreliablecommunication, control instructions may not be received atthe local home or generator, then the local scheduler conductslocal control based on the local sensing data.

IV. DATA MANAGEMENT

To reconstruct and predict the sensing data, in this section,we introduce four correlation models for reconstructing themissing data and predicting the future data. While most ofexisting works focus on missing data reconstruction of a singletime series data [7], [8], we investigate the correlations amongmultiple time series data (power consumption from multiplehomes, voltage and frequency) in microgrids and utilize thecorrelation models to reconstruct the missing data.

A. Correlation Models

The most important part of data management is to buildand utilize the correlation models among the collected data.Specifically, we identified and built four correlation models: i)correlation between power and voltage; ii) correlation betweenfrequency and voltage; iii) temporal correlation of powerconsumption data in a single home; and iv) spatial correlationbetween power consumption data from multiple homes.

1) Power Voltage Correlation: Without loss of generality,we assume that N homes are connected under the same trans-former (shown in Figure 4). According to the Electric PowerDistribution Handbook [9], a transformer can be consideredas a constant kVA device for a voltage from 100% to 105%.If the power consumption of one home increases, the total

H1

V1

V HN

IN

…

VN

I1I

R21 RN

Fig. 4: The topology of homes and the transformer

0 2 4 6 8 10 12 14Time (Minute)

114

116

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120

122

Vo

ltag

e m

agn

itu

de

(V)

Home 1

Home 2

Turn on appliance 2

Turn on appliance 1 Turn off appliance 2

Turn off appliance 1

Fig. 5: Relationship between power and voltage

current I increases and voltage V drops. We find that homeHi−1’s voltage value depends on i) the transformer’s outputvoltage (V ); ii) the current from the transformer to Hi−1;and iii) resistances of the power line from the transformerto Hi−1. For example, H1’s voltage value only depends onthe transformer’s output voltage (V ), the current (I1) throughH1, and the resistance (i.e., R1). Based on the above analysis,the voltage values at homes Hi−1 and Hi can be calculatedby using Equation (1).

Vi−1 = V −i∑

j=1

N∑k=j

Ik−1Rj−1 i = 1, 2, ..., N (1)

To verify it, we conduct experiments with 2 homes underthe same transformer and keep power consumption at home2 stable to study the power voltage relationship. The mea-sured voltage in both homes are both related to the powerconsumption in home 1 (shown in Figure 5). Thus, basedon Equation (1) and evaluation results, the voltage drop fromtransformer to each home is in linear relationship of currentsgoing through the power line.

2) Frequency Voltage Relationship: A typical microgridmay contain multiple transformers. Therefore, it is also impor-tant to investigate the other features in a microgrid. Accordingto the Electric Power Distribution Handbook [9], frequency isa good indicator of the relationship between power supply anddemand. If the power demand surpasses the power supply, thenthe frequency decreases because the generator can not generateenough power. Thus, the frequency should be related to thetotal power consumption of the microgrid. Because voltageis related to power supply and demand, thus, the frequencyvalue has a linear relationship with the voltage value. Thisrelationship can be modeled as follows:

4F = 4V ∗ λ1 (2)

To verify it, we conduct experiments with 3 homes with onemonth data. Two of them are under the same transformer whilethe other home is under a different transformer. To make therelationship clear to see, a typical example of the measured

Time (Second)

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Fig. 6: Relationship between frequency and voltage

frequency and voltage relationship is shown in Figure 6. Thefrequency value is well synchronized with the voltage value.

Based on Equation (2) and experimental results, the fre-quency change in each home is in linear relationship of volt-age change. Therefore, we can utilize the frequency voltagerelationship to recover the missing data.

3) Temporal Correlation: In a microgrid, we need to re-construct the missing data and predict the power consumptionin the very near future (e.g., next 1 second) for real-timecontrol. Thus the power consumption data of yesterday orlast month is much less useful. To address this problem, weleverage the power consumption signatures of appliances toreconstruct the missing data and predict the short term powerconsumption. This is because there are limited number ofpower consumption signatures for different loads. To evaluatethis approach, we use the empirical data collected for 2 yearsfrom a home to investigate the temporal correlation betweenpower consumption data. We run a power consumption signa-ture detection algorithm on the data set to find the signatures.Specifically, the similarity between two vectors is calculatedby using a Euclidean distance-based function as shown below:

ρi,j =1

|Si|

|Si|∑t=1

(Si(t)− Sj(t))2 (3)

|Si| is the length of signature Si. If the distance of thesetwo vectors is small, then the similarity of two vectors ishigh. Then we go through the data set to find the possiblesignatures. To simplify the algorithm, we use a fixed lengthof energy consumption patterns which achieves very effectiveresults (detailed in Section VI). As shown in Algorithm 1, thesignature set S is empty initially. When t < T , we calculatethe similarity between power consumption data and signaturesof each appliances based on Equation (3). If we find thesimilarity between current power consumption and existingsignatures is higher than the current maximum similarity, wereassign the maximum similarity and mark index = i. Thenwe compare the maximum similarity we find to the thresholdof the minimum similarity ρmin. If ρmax > ρmin, we thendetect a new signature Snew, add it to the signature set S andupdate t = t + |Snew|. Otherwise, we update t = t + 1 andcontinue the detection process.

Based on the detection signatures, we can reconstruct themissing data and predict the near future data as:

Pi(t+k) = Sj(|Sj |/2+k)+|Sj |/2∑x=1

2 · (Pi(t+ x− |Sj |)− Sj(x))

|Sj |(4)

Algorithm 1 Signatures Detection Algorithm1: S = ∅;2: while t < T do3: ρmax = 0, index = −1;4: for detected signature Si do5: Calculate ρi(t) based on Equation (3);6: if ρi(t) < ρmax then7: ρmax = ρi(t), index = i,8: end if9: end for

10: if ρmax > ρmin then11: Detect a new signature Snew and add to S;12: t = t+ |Si|;13: else14: t = t+ 1;15: end if16: end while

0 4 8 12 16 20 240

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4

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2

4

Time (Hour)C

orr

ela

tion

Home 1

Home 2

Fig. 7: Spatial correlation of different homes over timewhere Sj is the detected signature that has shortest distanceto {Pi(t− l(Sj) + 1), · · · , Pi(t)}.

4) Spatial Correlation: Because homes in the same areamay have the similar power consumption pattern, we can usethe spatial correlation among power consumption of homesfor power consumption prediction. However, different homeswill have different correlations at different time. Thus, weneed to keep on updating the correlations among these homesfor prediction. To evaluate our idea, we use empirical powerconsumption data collected from 100 homes for one monthto investigate the spatial correlation of power consumptionamong different homes. The spatial correlation between homes1 and 3, and homes 2 and 3 is shown in Figure 7. X-axis isthe time, Y-axis is the correlation between either homes 1and 3 or homes 2 and 3. For most of the time, home 1 andhome 2 are quite similar to home 3. However, from hour 2 tohour 4, home 1 is closer to home 3 while from hour 4 to 6,home 2 is closer to home 3. Thus, we build a model to predictthe power consumption based on historical correlations amonghomes. The correlation between two homes can be calculatedas:

cij(t) =1

l

t∑x=t−l

(Pi(x)− Pj(x)−1

l

t∑x=t−l

(Pi(x)− Pj(x)))2

(5)

From the above equation, we can predict pi(t) based onreadings from other homes:

Pi(t) =

N∑j=1

Pj(t) ∗ cij(t)∑Nj=1 cij(t)

(6)

If cij(t) does not exist because of missing data, then wereplace cij(t) with cij(tk). Where tk is the latest time forupdating the correlation between homes i and j.

B. Data Reconstruction and Prediction

With the above four correlation models, we can reconstructthe missing data and predict the future data for real-timecontrol. In order to schedule the controllable workload ineach home and maintain the stability of the microgrid, thecontrol center needs to collect the data of real-time powerconsumption, voltage, and frequency. Then the reconstructionprocess is executed as follows: i) if only part of the data ismissing in one home, the power voltage relationship can beused to reconstruct the power consumption or voltage; ii) ifonly frequency data is collected from one home, frequencyvoltage correlation can be used to reconstruct the voltage andthen apply power voltage relationship to recover power; iii) ifno data is collected from one home, we can utilize the temporaland spatial correlation to reconstruct the data; iv) if no datais collected from any homes, only temporal correlation can beused to reconstruct the data; and v) if all the data is collectedfrom one home, the collected data is applied to update thecorrelation weight for temporal and spatial correlation models.

The prediction process is the same as the scenario thatno data is collected from any homes. Note the predictionwith temporal correlation is only accurate for short-termdata missing. Because generators can not be turned on/offvery frequently and the generation control needs long-termpower consumption prediction, other traditional consumptionprediction algorithms can be applied in this scenario.

V. CENTRAL AND LOCAL SCHEDULERS

With the reconstructed data and predicted future data, cen-tral and local schedulers need to schedule the future generationof generators and the controllable workload in each home. Thedesign goal is to balance the power demand and generationwith minimum operation cost in the microgrid.

A. Design GoalAssume there are N homes in the microgrid and the power

consumption of home i at time t is g(t). The microgrid has Munits of homogeneous local generators, each has a maximumpower output capacity L. Based on a common generator model[10], we denote β as the startup cost of turning on a generator.Startup cost β typically involves the heating up cost (in orderto produce high pressure gas or steam to drive the engine)and the time-amortized additional maintenance costs resultedfrom each startup (e.g., fatigue and possible permanent damageresulted by stresses during startups). We denote ym as thesunk cost of maintaining a generator in its active state perunit time, and yo as the operational cost per unit time for anactive generator to output an additional unit of energy. Notethat our design is not limited to any generator model. Table Isummarizes the definition of parameters. Our design goal is tobalance the power demand and generation while minimizingthe operational cost of power generators. The problem canformulated as follows:

Notation Definitionbi(t) Amount of energy in battery of home i at time tBi Battery’s capacity of home idi(t) Consumed power of home i at time tβ Cost of changing output power of generatorL Maximum power output of generatorym Sunk cost of maintaining generator per timeyo Operational cost of generator for output powerpu Maximum ramping-up ratepd Maximum ramping-down rateg(t) Output power of generator at time tgo(t) On/off status of generator at time tno(t) Equals 1 if output of generator changes at time tto Minimum time for generator to change output powerei(t) Power from generator to home i at time tbui (t) Power discharged from battery to home i at time tbgi (t) Power from generator to battery at time t

TABLE I: Definition of notations

MinM∑

(yog(t) + ymgo(t) + βno(t)[g(t)− g(t− 1)])

s.t. 0 ≤ bi(1) ≤ Bi; ∀i (a)

0 ≤ bi(t) + bgi (t)− bui (t) ≤ Bi; ∀i, t (b)

di(t) ≤ bui (t) + ei(t); ∀i, t (c)N∑i=1

(ei(t) + bgi (t)) ≤ g(t) ≤ L; ∀t (d)

go(t)− go(t− to) ≤ pu; ∀t (e)

go(t− to)− go(t) ≤ pd; ∀t (f)i=t+to∑i=t+1

go(i) = to,

i=t−1∑i=t−to

go(i) = 0;∀t, no(t) = 1 (g)

Constraints (a) and (b) ensures the battery energy level isalways not less than zero and not greater than the batterycapacity. Constraint (c) means a home consumes less energythan the amount of energy it obtains from generator andbattery. Constraint (d) limits the output power of generator.Constraints (e) and (f ) mean that the speed of increasing anddecreasing generator power. Constraint (g) ensures that theminimum time for generator to change output power is to. Theobject function and constraints are all linear functions, thusthe problem is a mixed integer programming problem, whichis NP-complete. In reality, it is not possible to obtain optimalsolutions in real-time for generation and workload scheduling.Therefore, the central scheduler uses a heuristic approach tosolve this problem (detailed in §V-B). Furthermore, becauseof the unreliable communication, the home controller may notreceive the control message from the control center. Therefore,a distributed algorithm is proposed for the local scheduler toschedule workload in each home (detailed in §V-C).

B. Central Scheduler

The central scheduler has the power consumption predictionin next few seconds and next minimum on/off time of genera-tor. Thus, central scheduler can schedule controllable workloadin homes to fulfill constraint (c) and schedule generation fornext minimum on/off time. Therefore, the optimization prob-lem can be decomposed into two subproblems: i) generation

Algorithm 2 Generation Scheduling Algorithm1: Calculate the power demand in next minimum on/off time 4E(t+1, t+to) based on Equation (7);

2: if 4E(t+ 1, t+ to) > b(t+ 1) + g(t) · to then3: Increase generation gu(t) based on Equation (8);4: else if 4E(t+ 1, t+ to) < b(t+ 1) + g(t) · to −B then5: Decrease generation gd(t) based on Equation (9);6: else7: Maintain the same generation g(t).8: end if

scheduling to fulfill the demand and minimize the operationalcost; and ii) workload scheduling in each home to stabilizethe aggregated demand.

1) Generation Scheduling: The key idea of the generationscheduling is to turn on the generator when power demandis low and turn off the generator when the power demand ishigh. Note that it is not able to change the output power ofgenerator due to the minimum on/off time. Thus, we shoulddecide whether to change the output power of generator basedon power demand in the next minimum on/off time. At time t,the power demand from time t+1 to t+ to can be calculatedas

4E(t+ 1, t+ to) =

k=t+to∑k=t+1

N∑i=1

di(k) (7)

With the given demand, we need first to ensure the powergeneration and energy storage in battery is higher than thepower demand. Assume the power generation at time t is g(t),we have three options: i) increasing generation with gu(t); ii)decreasing generation with gd(t); and iii) maintaining the samegeneration g(t) in next minimum on/off time. The algorithmof decision making for generation is shown in Algorithm 2.If power demand is higher than energy storage in batteryand energy generation g(t) in next to, we have to increasethe power generation to avoid power outage (Lines 1-3).To minimize the operation cost. The amount of generationincrease can be calculated as

gu(t) =4E(t+ 1, t+ to)− b(t+ 1)− g(t) · t0

to(8)

Otherwise, we can either decrease power generation ormaintain the same generation. Note that there is extra cost forchanging output power of generator, thus, we only decreasethe power generation when the power demand is too low thatthe battery can not store the extra power generation (Lines4-5). The amount of generation decrease can be calculated as

gd(t) =b(t+ 1) + g(t) · to −B −4E(t+ 1, t+ to)

to(9)

Otherwise, we maintain the same power generation g(t)(Lines 6-8).

2) Workload Scheduling: The goal of workload schedulingis to avoid power outage and minimize the extra cost forchanging power generation. The key idea is to turn off thecontrollable workload when aggregated power demand is highto avoid power outage and turn on the controllable workloadwhen power demand is low to maintain stable power demand.

Note that the demand in each home can be divided by con-trollable workload dci (t) and uncontrollable workload dui (t):

di(t) = dui (t) + dci (t) (10)

Based on the prediction of short time power consumptionin next time slot, our central scheduler decides the schedulingthe controllable workload demand in each home. At time t,we can calculate power demand at time t+ 1 as

4E(t+ 1) =

N∑i=1

di(t+ 1) (11)

If power demand is higher than power generation and energystorage in battery 4E(t + 1) > b(t + 1) + g(t + 1), we need toturn off some controllable workload. Otherwise, if 4E(t+1) <

b(t+1)+g(t+1), we need to turn on some controllable workload.In our simulation, we utilize water heater as controllableworkload. Thus, If 4E(t + 1) > b(t + 1) + g(t + 1), we turnoff some water heaters in homes with less hot water demanduntil 4E(t+1) = b(t+1)+g(t+1). If 4E(t+1) < b(t+1)+g(t+1),we turn on some water heaters in homes with most hot waterdemand until 4E(t+ 1) = b(t+ 1) + g(t+ 1).

C. Local Scheduler

However, if the communications between the control centerand homes are unreliable, the instructions for each home maybe lost or arrive late. Thus, we also provide a distributedcontrol when the control instructions from central controllerare not available. The key idea is to schedule controllableworkload based on power-voltage model proposed in §IV-A1because the local voltage in each home can be used to inferthe aggregated power demand in the microgrid. However,the problem is that every home may decide to turn on/offcontrollable workload simultaneously to balance power supplyand demand because they can not communicate with eachother. Then it may cause an endless loop for each home toturn on/off controllable workload at the same time, which isnot helpful to balance power generation and demand.

In our design, we take an adaptive feedback control toenable homes to stabilize the power demand cooperatively.When each home detects the power demand change (powergeneration is relative stable since there exist minimum on/offtime for generators), it does not turn on/off controllable work-load immediately but with some backoff time. The detailedalgorithm is shown in Algorithm 3. At time t, each homecalculates the consumption of its controllable workload andestimate the change of power demand 4d in the microgrid byutilizing power voltage correlation shown in § IV-A1 (Line1). When the power demand is stable, each home keepscontrollable workload with previous state. When it detectseither high or low demand and there is no backoff timer,each home calculates backoff time tbi (Lines 2-3). tbi can becalculated as

tbi =4d

N · dci (t)(12)

If tbi 6= 0, home updates the timer (Lines 4-5). Then each homecheck the timer again, if the timer expires, local controller

Algorithm 3 Local Scheduler Algorithm1: Calculate 4Vi, dci (t);2: if 4Vi 6= 0 & tbi = 0 then3: Calculate tbi based on Equation 12;4: else if tbi 6= 0 then5: tbi = tbi − 1;6: if 4Vi > 0 then7: Increase controllable workload;8: else if 4Vi < 0 then9: Decrease controllable workload.

10: end if11: end if

(a) Water flow & temperaturemonitor (b) Energy monitoring

Fig. 8: Experiment setup in residential homes

immediately turns on the controllable workload when demandis low and turn off the controllable workload when demand ishigh (Lines 6-10).

VI. EXPERIMENTAL EVALUATIONS

In this section, we evaluate the performance of our design.We collect empirical data of i) total power consumption andwater heater power consumption from 100 homes; ii) hotwater usage from three homes; and iii) voltage and frequencydata from three homes. Note that we only have controlaccess of three homes (in Binghamton, New York), in whichwe collected hot water usage, power consumption of waterheaters, voltage and frequency data and all the experimentsare conducted in these three homes. For the rest 97 homes (inAustin, Texas), we collected the power consumption data forsimulations. Because we do not have the hot water usage,voltage and frequency data from these 97 homes, we usewater heater power consumption to generate the hot waterusage data and apply correlations among power, voltage andfrequency obtained from the experiments to generate voltageand frequency data for simulations. The hot water usageand power consumption are measured by water flow sensorsand eGauge sensors every second. The experiment setup ofone home is shown in Figures 8(a) and 8(b). The powerconsumption in one year and water flow data in two monthsare shown in 9 and Figure 10, respectively.

A. Basic Evaluation ResultsIn this section, we evaluate the effectiveness of our system,

which includes three metrics: i) data reconstruction accuracy;ii) total operation cost in the microgrid; and iii) the impact onhomeowners’ hot water usage. All results are simulated withthe seven days’ empirical data of hot water usage and powerconsumption. Because our design goal is to minimize theoperation cost of generator, we refer our design as MOC in thelatter description. The baseline we compared with is original

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wer

(k

W)

Fig. 9: Power consumption in one year

April 25 May 5 May 15 May 25 June 5 June 15 June 250

5

10

15

Wat

er f

low

(L

iter

/Min

)

Fig. 10: Water flow in two month

power consumption in individual homes without workloadscheduling. In simulations of MOC, we also use baseline in thefirst day since the correlation model needs to be trained basedon historical data. Thus we mainly compare the performanceof MOC and baseline for the rest of six days.

1) Reconstruction Accuracy: We run the detection algo-rithm with one month data and predict the missing data for thenext month. The results are shown in Figure 11. The predictionmatches well with the ground truth. The maximum error ofprediction we observe is 0.498kW and the average error ofprediction is 0.0289kW .

We run spatial reconstruction algorithm to recover onehome’s energy data from other 99 homes. The results areshown in Figure 13. The prediction overall is very close toground truth. The maximum error of prediction and averageerror of prediction are 3.836kW and 0.131kW , respectively.

2) Generation and Consumption: To clearly illustrate thedifference between baseline and our design, we only show thepower consumption of baseline and our design for one day inFigure 12. For power consumption without water heater, thepeak demand is mainly from 8am to 12am and from 6pm to8pm. In the mean time, hot water usage is also during the

0

5

10

Po

wer

(kW

)

Ground Truth

0 4 8 12 16 20 24

Time (Hour)

-1

0

1

Pre

dic

tio

n E

rro

r (k

W)

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

Fig. 11: Prediction accuracy with temporal correlation model,the right figure shows the average, 25 percentile and 75percentile of the prediction error

20

40

60

80

(a) Fixed Load

Pow

er

(kW

)

20

40

60

80

(b) Baseline

0 4 8 12 16 20 24

20

40

60

80

Time (Hour)

Fixed Load

Total Load Generation

Total Load Generation

(c) MOC

Fig. 12: Power consumption and generation for one day

0

4

8

Pow

er

(kW

)

0 4 8 12 16 20 24−4

−2

0

2

4

Time (Hour)

Err

or

(kW

)

Ground Truth

Prediction

Fig. 13: Prediction accuracy with spatial correlation model

similar time. For baseline, when it detects hot water usage,it turns on water heater immediately. Furthermore, becausedifferent homes are highly possible to use hot water in similartime of evening, the peak demand rises from 50.31kW to75.45kW (at around 7pm and 11pm). The power of the waterheater in our simulation is 5.29kW , thus at least 5 homes turnon water heaters at the same time. For the generation, becauseit does not predict the future power consumption to smooth thegeneration, the hourly generation changes very quickly, whichintroduces more operation cost. For MOC, because it predictsshort-term and long-term power consumption in future, thehourly generation is stable.

3) Total Cost: The total operation cost for generators fora typical day are shown in Figure 14. In the beginning,because the power consumption is low, the cost for differentapproaches is similar. However, from 8am, power demandincreases quickly because most of the people wake up. Thus,the operation cost increases quickly in baseline and the opera-tion cost for MOC and offline optimal still increases linearly.For six days’ simulations, the average daily operation costin baseline is $292.5 while daily operation cost for MOC is$224.6, which is 23% lower.

4) Water Heater Scheduling: To better understand howhomes schedule water heater event, we show detailed waterheater energy consumption events of 15 homes in Figure 15.To show the detailed difference between baseline and MOC,we show the water heater events for 3 days. The upper figureis the water heater events of the baseline in one home. Forthe baseline, most of the water heater energy consumption

0 4 8 12 16 20 240

50

100

150

200

250

300

Time (Hour)O

per

atio

n c

ost

($

)

BaselineMOCOffline Optimal

Fig. 14: Total operation cost for generators

0

1

Ev

ent

Baseline

0

1

Ev

ent

MOC

0 1 2 3Time (Day)

0

10

20

Ev

ents

Events of all homes

Fig. 15: Water heater events over three days

events last for longer periods. This is because the water heatersare turned on right after hot water usage. After people take ashower or bath for ten minutes, the water heater will be turnedon for around 1 hour to reach the high temperature threshold.The middle figure shows the water heater events of MOC inone home. Compared to baseline, the water heater events aremore sparsely distributed to reduce the overlap of events fromdifferent homes. The bottom figure shows the total events ofMOC in all 15 homes.

5) Hot Water Temperature: Though MOC allows homesto turn on water heater earlier or later, MOC can also fulfillusers’ hot water usage efficiently. In Figure 17, we show thedistribution of difference between the targeted temperatureand the hot water temperature when there exists hot waterusage events. The targeted temperature of hot water in ourexperiment is set as 50◦C. For the baseline, it turns on waterheater immediately after hot water usage, then the temperatureof hot water is always a little lower than the targeted hot water

0

50

100

(a) B = 0kWh

0

50

100

(c) B = 60kWh

Pow

er

(kW

)

0 4 8 12 16 20 240

50

100

Time (Hour)

Total Load Generation

Total Load Generation

Total Load Generation

(b) B = 30kWh

Fig. 16: Power consumption and generation for different battery capacities

0 50 100 150 200 250 300 350 400

Hot water events

-3

-2

-1

0

1

2

3

Tem

per

atu

re d

iffe

ren

ce (

0C

) Baseline

MOC

Fig. 17: Temperature distribution of hot water events

0 10 20 30 40 50 600

100

200

300

400

500

Battery capacity (kWh)

Cost

($)

Operation Cost

Battery Cost

Total Cost

Fig. 18: Operation, battery and total cost for different batterycapacities

usage (mainly 1◦C lower than the targeted temperature inFigure 17). For MOC, when a home predicts future hot waterusage, it can turn on water heater earlier to better fulfill thehot water usage, thus the hot water temperature can be higherthan the targeted temperature for some time. In Figure 17, thehot water temperature in the water tank is at most 2◦C lowerthan the targeted temperature. Thus the impact of our designon people’s hot water usage is very low.

B. Advanced EvaluationsBecause our system is designed for severe environments,

such as islands, it is crucial to investigate the system’s sensi-tivity under diverse settings.

1) Impact of Battery Capacity: Because battery is expen-sive and has limited life-time, it is important to investigate thesystem benefit with different capacities of batteries. We showthe power consumption and generation with three differentbattery capacities in Figure 16. The top figure shows thescenario with no battery in the system. Because there is nobattery, the generators needs to generate the maximum power

0% 4% 8% 12% 16% 20%

0.7

0.8

0.9

1

Rec

onst

ruct

ion A

ccura

cy

Data missing rate rd

Fig. 19: Reconstruction accuracy with different rdin its working period to avoid power outage, which introduceshigh energy waste. The middle figure shows the results with30kWh battery capacity. With the battery, the differencebetween generation and consumption can be offset, thus theoverall generation is reduced. For the bottom figure, with veryhigh battery capacity, the generator can only generate theaverage power consumption in the next hour, thus the overallgeneration is minimized. The operation, battery and total costfor different battery capacities are shown in Figure 18. Withhigher battery capacity, the operation cost decreases especiallyfrom no battery to 10kWh battery. However, the decreaseslows down with higher battery capacity. For the total cost, wefind that microgrid with 20kWh battery performs best sinceit balances cost between generation and batteries.

2) Impact of Data Missing Rate: With different environ-ments, the data missing rate can be quite different. Thus, itis important to study the reconstruction accuracy of our datamanagement design under different scenarios. In these setsof simulations, we simulated the accurate data to generatemissing data with different missing rate from 4% to 20%. Theresults of reconstruction accuracy are shown in Figure 19. Withthe increase of data missing rate, reconstruction accuracy de-creases slowly. Even with 20% data missing rate, the averageof reconstruction accuracy is above 80%. Thus, our design isrobust in situations with high data missing rate.

3) Impact of Instruction Missing Rate: In the mean time,the instruction missing rate can also be quite different underdifferent environments. Thus, we study the performance ofcentralized control (instruction missing rate ri is 0%) anddistributed design (instruction missing rate ri is 100%). Wesimulated the different instruction missing rate for two extreme

0

1

(b) ri = 100%

0

1

(c) ri= 0%

Event

0 6 12 18 240

1

Time (Hour)

(a) Baseline

Fig. 20: Water heater events with different ricases (shown in Figure 19). The water heater is turned onand off more frequently when ri is 100%. That is becauseeach home lacks the knowledge of behaviors of other homes,thus they may collide to turn on/off water heater and thenimmediately turn off/on water heater. The frequent on/offoperations will decrease the lifetime of water heater. However,total cost for different instruction missing rate is similar, whichis not included due to the limited space.

VII. RELATED WORK

Our work is related to the following areas of previous work:Energy Management. Different techniques are proposed forenergy management in either demand side or generation [11],[12]. In [13], a decentralized optimal load control mechanismis proposed to provide contingency reserve in the presence ofsudden demand-supply mismatch. In [14], a model predictivecontrol algorithm is proposed to co-schedule HVAC control,EV scheduling and battery usage to reduce the building energyconsumption. In [15], stochastic and robust optimization areapplied for real-time price based demand response manage-ment. In [16], an optimal solution is provided to trade offbetween quantity and quality of variable renewable energysource in smart grid. Different from existing work, our paperpresents a holistic approach of real-time scheduling for bothdemand in individual homes and generation of the localgenerators in microgrids.Missing Data Management. There have been various worksin the research community to investigate how to managemissing data in cyber-physical systems [17]. Traditionally theapproach to obtaining missing values for linear time series hasinvolved the use of curve fitting [18]. Autoregressive integratedmoving average (ARIMA) model is fitted to time series datato predict future points in the time series data [7]. Maximumlikelihood based approach is applied to estimate the missingdata [8]. Different from existing work, we investigate thecorrelation between different energy data in microgrids andutilize the correlation models to cope with unreliable sensorsand wireless communication.

VIII. SUMMARY

The biggest challenge of maintaining a self-sustainable mi-crogrid is to balance the power demand and generation in real-time with dynamically changing power demand. Furthermore,

the unreliable data collection and communication betweenhomes and the control center in a microgrid makes the real-time control even harder. To address these issues, we proposea novel data management technique to process the collecteddata, reconstruct the missing data caused by sensing error orunreliable communication, and predict the future demand forreal-time control with missing data in extreme situations. Thecontrol center then decides the scheduling of the workloadof appliances in each home and the operations of the localgenerator based on the collected and predicted data. Throughextensive experiments and simulations, we show that ourdesign can recover the missing data with 99% accuracy and ourdistributed control can balance power demand and generationand reduce operation cost by 23%.

IX. ACKNOWLEDGMENT

This project is supported by NSF grant CNS-1503590 andUMBC COEIT Strategic Plan Implementation Grant.

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