06230623-1

IEEE TRANSACTIONS ON SMART GRID, VOL. 3, NO. 3, SEPTEMBER 2012 1333

Control of Flexible Smart Devices in the Smart GridGeorge Koutitas, Member, IEEE

Abstract—This paper investigates load control and demand re-sponse in a smart grid environment where a bidirectional commu-nication link between the operator and the smart flexible devicessupports command and data flow. Two control schemes are inves-tigated that can provide energy management, taking into accountuser’s comfort, via binary on-off policies of the smart flexible de-vices. A dynamic control algorithm is introduced that considersreal time network characteristics and initiates command flowwhencritical parameters exceed predefined thresholds. To sustain fair-ness in the system, priority based and round robin scheduling al-gorithms are proposed. A continuous control algorithm is also ex-plored to define the higher bounds of energy savings. To quan-tify the discomfort of users that participate in this type of ser-vices, a heuristic consumer utility metric is proposed and mea-surements with a flexible device (air conditioning unit) are per-formed to model empirically possible time intervals of the controlscheme. Reciprocal fair energy management schemes are investi-gated being both operator and user centric. It is shown that greatenergy and cost savings can be achieved providing the required de-grees of freedom to the smart grid to self-adapt during peak hours.Index Terms—Demand response, home energy management,

load control, scheduling, smart grids, smart sensors.

I. INTRODUCTION

T HE Information and Communication Technology (ICT)sector is called to hold a vital role in the 20-20-20 goal by

providing the energy sector the required technology and infra-structure for energy management [1]. The building and the elec-tricity grid sector are the most important sectors of interest sincethey are responsible for the greatest energy waste. Great energysavings can be achieved through sophisticated algorithms thatcontrol and schedule power tasks from smart devices in a dy-namic manner. These processes provide the necessary founda-tions for demand response (DR) and self-adaptable smart grids[2]. Smart devices are responsible in real time monitoring andactuation under command flow arriving from the smart grid. Ingeneral, the greatest the number of deployed smart devices is,more flexibility is given to the grid and thus more vibrant thegrid operation is expected to be.The smart-building is the fundamental element of the smart

power grid where real time energy and environmental data mon-itoring will be used at higher layers, for energy management andelectricity price forecasting. Furthermore, due to limited power

Manuscript received September 04, 2011; revised December 09, 2011, April19, 2012; accepted June 05, 2012. Date of publication July 03, 2012; date of cur-rent version August 20, 2012. This work was supported by the European UnionFP7/2007-2013 under Grant 257740 (Network of Excellence TREND) and bythe European Social Fund—ESF and Greek national funds through the Oper-ational Program “Education and Lifelong Learning” of the National StrategicReference Framework (NSRF). Paper no. TSG-00508-2011.The author is with the School of Science and Technology, International

Hellenic University, 14 km Thessaloniki-Moudania, 57001, Greece (e-mail:[email protected]), and also with the Department Computer Engineeringand Telecommunications, University of Thessaly, 38221, Volos (TRENDproject).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSG.2012.2204410

supply from renewable energy systems (RES) and microgrid in-stallations, it is important to develop scheduling and control al-gorithms to balance the operation of the smart grid andminimizecosts from imported energy or even minimize blackout events.In order to guarantee a reciprocal fair management scheme, thecontrol and scheduling algorithms need to take into accountusers’ comfort and profits as well as operator’s gains.Most of the papers found in the literature deal with optimiza-

tion or scheduling algorithms that meet certain criteria of energymanagement but are targeted only to the user or the operatorside, neglecting fairness and comfort issues. In [3] schedulingalgorithms for the offline and online problem of non-preemp-tive and preemptive scenarios are investigated. The goal is toguarantee cost minimization from power tasks with user ori-ented time thresholds. A satisfiability investigation of elasticdemand in the smart grid is presented in [4]. The authors studysystem behavior under uncertainties. In [5] the demand responseproblem is addressed to provide a fault tolerant operation of amicrogrid using multi-agent algorithms. User disruption underload control is addressed in [6]. Scheduling algorithms that facethe demand response problem and are based on forecasted elec-tricity price are presented in [7]–[9]. Dynamic decision for en-ergymanagement based onmulti-power supply systems is givenin [10]. The aim is to optimize the use of the available resourcesin a given local generation system. Network architecture for en-ergy management of smart households is presented in [11].To support the operation of such algorithms, advanced net-

work solutions are necessary to provide reliable communicationlinks between smart devices and controllers and enable com-mand flow. These are met in a home area network (HAN) ora machine to machine (M2M) formation over heterogeneouswireless sensor/actuator networks (HWSNs). In [12] M2M net-work architecture is presented for smart buildings and smart gridscenarios. A HAN architecture is given in [13]. A case study forambient environments in a University building is presented in[14], [15]. The authors present semantic web services for theintegration of HWSNs applied to home energy management.Smart grid technologies and protocols for networking of smartdevices are presented in [16], [17].The above mentioned algorithms and techniques focus on

the ICT infrastructure used for smart grid applications or theyfocus on algorithms for energy management either at the oper-ator or the user level, neglecting fairness or comfort criteria.This paper considers a bidirectional communication link be-tween smart buildings and the operator and proposes novel al-gorithms for energy management of flexible smart devices thatare both operator and user centric and take into account fairnessand user comfort criteria.Two control algorithms are proposed, the Continuous Con-

trol Algorithm (CCA) and the Threshold Algorithm (TA) andcompared to the No Control case (NC). These algorithms areable to change the state of operation of the flexible smart de-vice which can be described as a Markov chain. The CCA can

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1334 IEEE TRANSACTIONS ON SMART GRID, VOL. 3, NO. 3, SEPTEMBER 2012

Fig. 1. Smartgrid architecture for a neighborhood of smart buildings controlledby a single supervisor.

be regarded as a device level control algorithm where contin-uous on/off activations are performed by the flexible device.This scheme presents the minimum intelligence and it consti-tutes the higher bound of energy savings. Despite the fact thathigh energy savings are observed, the discomfort to the useris at the maximum level. The TA algorithm is a dynamic pre-emptive algorithm where external commands arrive at the userpremises to enable load control and demand response accordingto variable user demands and limited load capacities. In order toprovide a reciprocal fair management procedure, the algorithmsare both operator and user centric, they take into account users’comfort criteria and scheduling priorities.Two fair scheduling algorithms are proposed and compared.

The Highest Power Next (HPN) is a priority scheduling schemethat can be seen as a load balancing procedure. TheRound Robinscheduling scheme provides uniformly distributed number ofswitch off commands among the users of the network. For theefficient penetration of smart grid services in the user premises,one should study the subjective parameter of user satisfaction.For the purpose of our investigation, a heuristic satisfactionmetric is modeled, which is derived from the consumer utilityof the economic theory. The expected results by implementingthe proposed algorithms is cost reduction, load balancing, andcontrol and energy savings.

II. THE SMARTGRID MODEL

A. Network Architecture

Themain elements of the smart grid architecture are the smartbuildings, the bi-directional communication infrastructure, thesupervisors (controllers), the service provider, and the operator[18], as shown in Fig. 1. These form an Advanced MeteringInfrastructure (AMI) whose standards and guidelines have beenrecently developed [19].The smart building is the basic element of the smartgrid that

consumes energy, it may produce energy from RES, it moni-tors critical data with HANs of smart meters/actuators and trans-mits information in real time to the other parties. Characteristicexamples are energy plug sensors, usually over IEEE 802.15.4Zigbee platforms [20] and energy RF434 MHz clamp sensors.

The most critical data that is monitored in the smart buildingare the total energy consumption/production, the individual con-sumption from home appliances, the indoor environmental pa-rameters, which describe user comfort, and other user orienteddata like thresholds and policies for efficient equipment opera-tion [3]. The agent of the smart building is a central CPU unitand is responsible for the data aggregation within the houseand the transmission to other parties. Furthermore, the agent re-ceives and executes control and scheduling commands that ar-rive from the smart grid to meet certain goals. The execution ofthe commands is performed within the sensor network of smartactuators under binary on/off activation schemes of the homeappliances.A wide area network (WAN) is responsible for the data trans-

mission from the agents to other parties. The supervisor is re-sponsible for monitoring a group of smart buildings and receivesdata packets from the agents, usually using TCP/IP. The su-pervisor can also be the intelligent unit of a microgrid in orderto control and optimize the local generation. The operator andthe service provider communicate with all the supervisors ofthe network for further data manipulation and decision/policymaking.

B. Definition of Parameters

A set of users (smart buildings) is assumed to live in anarea which are served by a local energy generation system (mi-crogrid) or by a smart grid controller. The identifiers of eachuser are where is the maximumnumber of users . We use a discrete time modelwith a finite time horizon that models a day. Each day is di-vided into periods of equal duration, indexed by

. For the purpose or our investiga-tion, was assumed as 06:00 A.M. Each user arrives in thenetwork (start consumes power) at time and isactive for a time period described by uniformrandomly distributed values between the finite intervaland with ( is a generator of uniform dis-tributed random number).Flexible Smart Devices: Within the smart building there

are flexible devices that can be controlled by the agent, underthe supervisor commands performing an on/off policy, withoutaffecting users’ comfort. Comfort is related to parameters(a physical value) and (a threshold value) and by two

time thresholds, namely and (Fig. 2).Parameter describes the minimum time needed to reducea hypothetical discomfort metric, to the wanted value. Pa-rameter describes the time needed the discomfort metricto reach a maximum threshold, . These devices are named assmart flexible devices. Characteristic examples are air-condi-tioning units, washing machines, heat/cold water machines, etc.[8]. The nonflexible devices can not be controlled by externalparties since they are directly related to users’ activity withinthe smart building.The flexible smart device operates under the following

assumption: , a random uniformly dis-tributed number between 1 and and similarly

with . The discomfort metric, isassumed proportional to and can be different for each useraccording to other criteria (effectiveness of appliances, homeinsulation, etc.). A straight forward example is the increase of

KOUTITAS: CONTROL OF FLEXIBLE SMART DEVICES IN THE SMART GRID 1335

Fig. 2. User power profile and discomfort metric.

Fig. 3. The average user activity curve over a summer period [21].

a room’s temperature when the air-conditioning unit is turnedoff until it reaches a threshold value, above which the userfeels discomfort. In that case represents the time neededto decrease a room’s temperature to the desired value,represents the time needed that the temperature increases abovea comfortable threshold and models the room’s temperature.In most occasions it can be stated that .This assumption is used for the analytical computations ofSection III-D and is not a restriction in the algorithm.Demand Arrivals: Users are activated under Poisson arrivals

during the time period of the simulation. The distribution of theuser density during was modeled according to measuredaverage activity profiles of typical households and offices oversummer periods [21]. The normalized activity profile is pre-sented in Fig. 3. The summer period was considered since a di-rect application of the proposed algorithm concerns load controlfrom air-conditioning units. Of course, the algorithm is devel-oped in a generic approach and any activity profile can be in-corporated in the code.User States of Operation: Each user, , is described by the

state of operation which is given by a row vector, the indicator(Table I). This indicator is “captured” by the agent

of the smart building and is transmitted to the supervisor (up-link), as shown in Fig. 4. When the user has entered the system,meaning that or , the agent canreceive four operational/command states from the supervisor(downlink) which are described by the logical matrix,. The operational states are described by binary row vectors

which are the following: describes the charging statewhere the user first enters the system and the flexible devicecannot be switched off due to the time limitation . Thestate describes the recharging state where the flexibledevice of the user is turned on after a switch off deactivation

Fig. 4. Measurements of a typical flexible load. An air-condition unit was mea-sured using a plug wireless sensor.

and therefore cannot be switched off again due to the time lim-itation . The state models the case where theflexible device of the user receives a switched off command andfinally describes the maintenance state where the flex-ible device of the user is on and can be switched off at anytime.Following the time constraints of user as shown in Table I thefollowing equations are satisfied:

Since the number of switch off commands each user receivesis unknown, ( , with representing the identi-fier of the off command) and the time of the reception of switchoff command, , are unknown, the time inequalities in Table Idescribe the main idea and are not representative for all cases.Power Profile: The power profile of each user, , is divided

into two main components, as shown in Fig. 2. An averageconstant power load is used to model the power needs ofnon-flexible devices. Of course, in reality the non-flexible loadsare not constant with time but instead they are opportunistic innature or even follow their own probability curves. Due to thestochastic arrivals of the users in our system and the compar-ative simulations related to the no control case, a constant av-erage value can be used to simplify the computations, withoutsignificantly affecting final predictions. The second componentof the power profile is the power load of the flexible devices,

. Two cases are investigated. In the first case is as-sumed as a decreasing piecewise linear function of time, , [22]and for the second case is assumed constant with time. Ina mathematical form it is given in (1).Case 1: Piecewise linear function (see (1a) at the bottom


TABLE ISTATES OF OPERATION OF SMART DEVICES

of the page).Case 2: Binary valued function

(1b)

For the piecewise power profile is the power of the devicewhen it starts to operate and models the case ofstabilized operation after time . To capture the operationof multistate devices, one can assume that and describeaverage stabilized levels. The power needs of active user, isthus given by

(2)

The consumed energy of user over the activated period isthus given by

(3)

In the above formulation, represents the area enclosed bythe power consumption of nonflexible devices for the time pe-riod whereas and represents the area enclosed by thepower consumption of the flexible device over the reception ofswitch on/off commands (Fig. 2). For a binary valued flexible

device (case 2) it is .The total power load at any time instance, of

simultaneously active users and the total energy consumption atthe end of the simulations can be computed according to

(4a)

(4b)

The cost and the load assumed to present a convex relation [3]described by (5).

(5)

C. Measurements of a Typical Load

In order to model the profile of a typical flexible load, mea-surements of a commodity air condition unit connected to asmart metering device were performed. The measurement setupis presented in Fig. 4. A smart plug low power sensor transmit-ting 3 dBm at 2.4 GHz was connected to the agent PC througha Zigbee network and M2M communication was establishedthrough web services. The load measurements were sampled atevery time step s and saved in .txt file for further manip-ulation. The device under investigation was an air conditioningunit placed within a house of size 65 m . The temperature ofthe air conditioning unit was set at 23 C and the outside tem-perature during the measurements was 32 C. The mode of op-eration of the air-conditioning unit was set to auto mode. Thismeans that the air condition unit switches on or off automati-cally to maintain the air temperature near a constant value (24C). The measurement results are presented in Fig. 4. The figurepresents the stabilized air condition operation, meaning that theinitial time required to reach the preferred indoor temperatureis ignored (the required time was approximately 15 min). Twoscenarios were considered. In the first scenario, referring to theno control case, the air condition unit was operating without anyexternal management scheme. The other scenario refers to thecontrol case where the user controlled the air condition undercomfort constraints. The scope of this measurement set up is toinvestigate empirically, the degrees of freedom (feasible timeintervals) a smart grid controller could have upon an air condi-tion unit.No Control: It was found that when the air condition device

operates in auto mode was on (active) for min andoff for min approximately, maintaining aC. The power profile in this case is

W when the device was in full operation and Wwhen the device automatically switched off. A mean value canbe used to simplify computations and this is of(1b) as shown in Fig. 4.Control: For this case the user was able to switch on/off the

air condition according to the temperature comfort in the en-vironment. The purpose of this measurement is to obtain themaximum or minimum switch on/off time intervals that the con-troller should consider when external management is imposed.It was found that min and minapproximately, maintaining a C in the apartment. The

(1a)


power profile in this case is W when thedevice was on and W when the device was off.A mean value can be used to simplify computations and this is

of Fig. 4.For a working period of 70 min and taking into account the

mean load values, and , the total consumed energyin the no control and control cases was found to beWhr and Whr. A saving approximately 25%–30%was observed. This means that the smart grid can externally con-trol flexible devices (air condition in this case) without signifi-cantly affecting the comfort in the environment and at the sametime reduce peak loads in the grid and provide energy savingwithin user’s premise. It should be stated that the house wherethe measurements took place is an old apartment without properinsulation. The ratio in modern households isexpected to be smaller. It should be noted that in a real smartgrid environment, it is essential to provide the grid the ability tostore for each user and for each flexible device the required pa-rameters , and the power profiles. These parametersare stored in the agent of the smart building who transmits themto the local controller (supervisor). Parameters and thatare related to the power profile can easily be approximated bytabulated values according to the specifications of the devices.The user is required to inform the grid about the type of de-vices that can be externally controlled. For the comfort valuesthat are directly related to there are two options tofollow. One is a user oriented approach where the user uploadsthe time thresholds of his/her preference to the smart grid. Theother approach can be based on a self-learning systemwith feed-back where the user can inform the grid when he/she feels dis-comfort. In such a scheme the smart grid (agent and supervisor)will “understand” the preferred time thresholds after a workingtime period of the system. A similar approach is used in modern“smart” thermostatic controllers. Privacy issues related to thereadings of these values is an important issue but does not ex-ceed the already existing privacy concerns related to real timeenergy metering.

III. CONTROL AND SCHEDULING ALGORITHM

A. Objectives

A fundamental characteristic of the smart grid is the flexi-bility it offers to self-adapt, self-heal, and self-optimize its op-eration. It can be considered as a self-optimized network (SON)where the main targets are the “peak shave,” the demand re-sponse, and the cost minimization. A great amount of energy isexpected to be saved and this has a direct consequence on thereduction of carbon emissions that are related to energy underproportionality factors (x grCO /kWh) depending on the typeof generation.Fig. 5 presents in a block diagram of the required architecture

to meet these targets. A stochastic model is used to generate theusers’ energy requests in time. The smart grid is allowed to con-trol and schedule the operation of the flexible devices that canbe either formed in a cluster format or individually. The con-trol algorithm needs to take into account constraints related tousers’ comfort in order to effectively penetrate the services inthe market. The supervisor is responsible for monitoring a largenumber of premises and deciding under certain criteria on theperformed control and scheduling policy. The objective of the

Fig. 5. The general architecture of the system.

supervisor is to keep the load under (or minimize the load ex-ceeding) a given capacity or reduce costs during high elec-tricity price periods. The threshold capacity represents a limitedpower supply system where excess energy need to be importedor may cause a blackout. A characteristic example is a micro-grid that serves an isolated, off grid, area in an island mode. Thethreshold can be static or variable with time describing en-ergy production from RES during a day. The supervisor can takeactions to meet the objectives under a binary on/off activationscheme. This model can also be used for the case of an agent in asmart building that controls a large number of flexible devices.

B. Dynamic Scheduling and Control Actions

The control and scheduling problem is a dynamic preemp-tive one meaning that the flexible device can be switched on/offmany times during the activation period, according to realtime conditions. The state of operation of the flexible device isa Markov chain. Three categories of actions are investigated,namely the No Control algorithm (NC), the Continuous ControlAlgorithm (CCA), and the Threshold Algorithm (TA).NoControl (NC): This is the case where there is no command

flow between the supervisor and the flexible devices. All devicesin our network are considered to be nonflexible devices and thesmart grid has no permission rights to act externally. Based onthe indicators presented in Table I the flexible device can onlysend . For the NC case the states of operationof the flexible devices can only be:

and the following relationis thus satisfied:

Continuous Control Algorithm (CCA): The CCA algorithmcan be considered as a demand load control algorithm thatpushes the users’ comfort to the limits. It can be performedeither externally by the smart grid or within the device level,


Fig. 6. Control/scheduling process.

thus minimizing data exchange between the agent and thesupervisor. On many occasions the CCA algorithm needs tobe performed at different time periods during the day, thus theexternal control scheme is more preferable. A characteristicexample is the reduction of power load during high electricityprice time periods. During CCA the supervisor continuouslysends commands to switch on/off the flexible loads at everytime interval and . Taking into account queuingtheory and by modeling as the “wanted” task the switch offrequest , the CCA algorithm can be considered similarto a service system. The first parameter models thearrival time distribution (for our case is memoryless and iswritten as ), the second parameter models the service timedistribution (which is again memoryless- ) and the third pa-rameter models the number of servers in the system that servethe requests (they are infinite to model the case of continuouslyserved requests ). In other words, the server of the system ismodeled to be always free to satisfy the tasks . The termserver is used to describe a physical CPU unit or applicationsoftware in the controller (supervisor or the agent) and decideswhich requests to be served. The infinite number of servers ishypothetical and one could also consider the case of one serverwith zero service time of the tasks. For the CCA case, the statesof operation of the flexible devices are modeled as

The block diagram of the control/scheduling algorithmis shown in Fig. 6. There are active users which arepushed in the controller. The controller, according to thetime counter of each user and the decision variablesand , decides which users will be switched on or off.users are switched off if

and - users are on if whereand is the

identifier of the switch off command. Therefore, for the CCAalgorithm it is .The objective of the CCA algorithm is to minimize energy

consumption according to the following set of equations:

(6a)

(6b)

(6c)

The decision variables of the problem are the binary commands(states of operation) transmitted from the smart grid to the agent(6b). The constraints incorporate comfort issues, which are de-noted in the first and the last line of (6c) and the active durationof the user in the system which is described by the second lineof (6c).Threshold Algorithm (TA): The TA algorithm is a dynamic

demand load control algorithm that takes into account real timeload, and capacity, as shown in the decision vari-ables of Fig. 6. The aim is to try and keep the system’s load, atany time instance , under a given capacity threshold , takinginto account comfort and fairness issues. It must be stated thatthe TA algorithm can also be used for the time-of-use price sce-nario. For that case a price threshold can be defined by the su-pervisor or the agent of the system and the algorithm will try tokeep costs under the predefined threshold. On/off actions areperformed only when the thresholds are exceeded. In a sim-ilar to the CCA approach, the system can be considered as a

or servicesystem. The forth parameter models the service discipline, thefifth parameter the waiting space of the queue and the sixth pa-rameter the population size. In this case we have one server withzero service time, infinite waiting space, and population and ser-vice discipline that can be either general independent or basedon priority criteria similar to shortest job next (SJN). The pri-ority criteria reflect the fairness issues that are discussed in thenext paragraph of the paper. The server is assumed to becomefree only when the condition of (7a) is not met. The smartgridsends to the controller jobs that are satisfied according tothe priority criteria. When request is served, it means thatflexible device of user is switched off and thus .For the TA case, the flexible devices can perform transitions be-tween all possible states and these are defined as

The objective of the TA algorithm is described according tothe following set of equations:

(7a)

(7b)


(7c)

The decision variables for this case are the same with (6b).The constraints have changed and now take into account switchoff or maintenance states of the flexible devices, which are de-scribed by the first line of (7c). The TA algorithmmight becomesimilar to the CCA control policy if and only if .

Algrothim 1: ROUND ROBIN AND HPN FAIRNESS

commands for Round Robin algorithm onlycreate , (ST-Switch off Time)

commands for HPN algorithm onlycreate , (MP-Mean Power)

common for both Round Robin and HPN algorithmswhileLoopcreate

if truecontinue next

elsenext Loop

endend while

C. Fairness Issues

By letting external parties control and schedule flexible de-vices in a user premise, creates fairness and comfort issues thatneed to be taken into account by operators to sustain the effec-tive penetration of services. The CCA and TA policies reducethe total energy consumption of the system, compared to the NCpolicy but there are many occasions where specific users mightbe forced to consume extra energy compared to the NC case.This can be easily understood from the power profile presentedin (1a). According to the parameters and thenumber of received on/off commands the control policymight cause excess energy consumption. Furthermore, fairnessissues arise from the fact that users with high are more

responsible for the high power loads of the system and needto participate more in the on/off strategy, compared to others.In this paper, fairness is introduced in three different approx-imations: in a Round Robin scheduling scheme, in a HighestPower Next (HPN) priority scheme, and in a Reciprocal FairManagement (RFM) approximation. Both the Round Robin andthe HPN scheme incorporate sorting algorithms and thus theypresent a computational complexity of , wherethe number of active users.Round Robin: This is the case where the multi level queue of

is given priority according to a Round Robin fashion. Thescheduler switches off the first available user and then placesthe user back to the queue until all users that have not beenswitched off are “served.” In this way, all flexible devices areexpected to be switched on/off approximately equal number oftimes meaning that (Algorithm 1).Highest Power Next (HPN): This is the case where the multi

level queue of is given priority similar to the SJN. Forthe HPN the flexible devices that operate within users’ premisesthat present high background power loads, are pushedfirst in the queue. This algorithm can be considered similar toa load balancing technique where the goal is to try to equalizethe power loads of all users during the time period where thetotal load of the system exceeds the threshold. With the HPNalgorithm the number of received on/off commands follow alinear relationship with the average load of the user

(see Algorithm 1). A reward priority algorithmfor load shifting applications can be found in [23].Reciprocal Fair Management (RFM): The RFM algorithm is

not a scheduling algorithm but mainly a constraint that guaran-tees that the user that participates in the management procedurewill benefit compared to the NC case. In this way, both the op-erator and the user sides present energy savings and thus costsavings. This means or .Consumer Utility: Consumer utility, in economic theory, rep-

resents the satisfaction of the user, relative to a given value, byusing a given service. For the purpose of our investigation, aheuristic metric, the consumer disutility (DU)was used tomodelthe dissatisfaction of user that receives on/off commands fromthe smart grid. It was modeled by taking into account the totalamount of time the users were in off mode over the time thatthese users would be on for the NC case compared to the CCAscheme. In a mathematical form it follows :

(8)

where denotes the set of users that have received at least oneoff command .

D. Analytical Approximation

It is not always feasible to keep the total load of the systembelow the maximum capacity, similar to condition in (7a). Ac-cording to the simulation parameters and thecharacteristics of the users’ devices there


are cases where it is not feasible to reduce costs or energy underthe CCA or even satisfy the constraints of TA. In some occa-sions, energy saving at the perspective of the operator (super-visor or microgrid) can be achieved by sacrificing energy sav-ings for some users. Of course this holds only for the case ofpiecewise linear function .Energy Saving From a Single Flexible Device: Let us as-

sume that there is a single user in the system and we want tocompare the NC and CCA/TA algorithms. We are interested indefining the minimum ratio such that energy sav-ings are achieved from the on/off management scheme. Forthe binary valued function , the solution is obvious and is

. For the piece-wise linear function of (1a) the management scheme willprovide energy savings if

(9a)

This formulation provides the relationship of the operationalcharacteristics of the flexible devices in order to gain energyfrom the control scheme. One can also compute the maximumnumber of the received on/off commands above which energyis wasted. Assuming that and

(to simplify computations) the maximum numberis given by

(9b)

In the above formulation, operator defines the lower roundedinteger value. To achieve a reciprocal fair energy managementscheme (RFM) the rules presented in (9) should be satisfied.Peak Power Under a Given Threshold: In many occasions

the peak power is required to be kept under a given threshold.To simplify computations, we can assume that the user distri-bution density is described by a linearly increasing/decreasingfunction whose maximum is met at 14.00 P.M. In that instancethe maximum number of active users is approximately equal to

, where is the average duration of users inthe network and the maximum number of users. For a givenpower threshold defined as , the mean required number ofswitch on/off (assuming CCA policy) is computed by

(10a)

The minimum number of the switch off time interval can besimilarly computed as

(10b)

Fig. 7. Switch off time interval and number of switch on/off activationsas a function of number of users in the network. Solid line with asterisks

represents the user centric feasible solution.

To investigate the meaning of the simplified analytical ap-proximations lets assume that there is a microgrid with a max-imum capacity of kW that serves users each onehaving an average power load equal to kW. Each userhas an air-conditioning unit (flexible device) that requires poweras given in (1a) with kW and kW. The re-quired average time to reach the wanted room temperature is

hrs. Each user has a maximum switch off timehrs to sustain comfort and an average du-

ration in the network, h. The microgrid has a supervisorthat can send on/off requests in a CCA scheme in order the peakpower never to exceed the threshold. According to (10) it can beobserved that depending on the used simulation parameters, theequations of (9) are not always satisfied. This means that the mi-crogrid will achieve a peak power under a given threshold butmight cause excess energy consumption to certain users, non-reciprocal fair management (non-RFM). Fig. 7 presents the re-gions of possible solutions and the curves representing the fea-sible and fair solution that satisfies all the constraints.Three regions are distinguished. The non RFM region con-

tains the solution ( or ) where peak power is below thethreshold but some users suffer excess power consumption com-pared to the NC policy. The all conditions satisfied region isthe region of possible solutions where all conditions are met.This means that the peak power is under the threshold, the usergains from the on/off policy without affecting his/her comfort.After 1100 users arrive in the network, there are two options tofollow. By placing high priority on the user satisfaction index,the system selects the user centric solution (asterisks curve) sac-rificing costs. The other option is operator centric and selectsswitch off time internals (or number of off commands )higher than the imposed by the user discomfort values. The peakpower is under the threshold but there is dissatisfaction by theusers. The region no conditions satisfied is the region where bothparties are not satisfied. The region with no shading that fallsunder the feasible solution is the region where theload is higher than the capacity. The region above the feasiblesolution , with no shading, is the region where thesystem achieves a load smaller than the capacity but the switch


Fig. 8. User state of operation during the day. TA algorithm.

off interval is higher than the allowed margins. Thus, dis-comfort becomes critical.

IV. SIMULATION RESULTS

The scenario under investigation comprises userswith average load (nonflexible devices) described by uniformrandomly distributed values between and

W and kW to model houses and of-fice buildings in a typical urban environment). For the opera-tion of the flexible devices each user is characterized by uni-form randomly distributed values hrs,

hrs with tosatisfy (9a), hrs, kW, and kW.These values can model typical operation of air-conditioners,ovens, or water heaters.The users are served by a local generation system that has a

capacity 35% higher (safety margin) than the needs of nonflex-ible power demands at peak hours meaning that

with indicating the maximum number of simultaneously ac-tive users at peak hour. All simulation results are averaged over500 independent runs of the algorithms to capture a great diver-sity of possible scenarios that can be met in real life.Change of Operational States During a Day: The process of

the algorithm for the TA algorithm is presented in Fig. 8. Usersenter the system and become active (reduce number of userswith and increase number of users with ).When the total power exceeds the threshold, the flexible devicesfrom certain users need to be switched off . This oc-curs during the peak hour traffic where the highest power loadis met. When the time of operation of the flexible device ex-ceeds the threshold then the device exits the system and thus,

.Cost and Power Savings: The cost and load savings com-

pared to the NC algorithm are presented in Fig. 9. The costwas assumed as a convex function of the instantaneous load de-scribed by (5). The CCA and the TA algorithm for the HPNand the Round Robin fairness are compared to the NC case.

Fig. 9. Load and cost savings of the CCA and the TA algorithms relative to theNC algorithm for the HPN and the Round Robin fairness case.

The following conclusions can be derived. First of all, the loadand cost savings are independent on the type of fairness usedat the scheduling scheme. This is expected since the smart gridswitches off the required number of flexible devices to achievethe goals (demand response) under the given constraints. TheTA algorithm starts to present savings after the time where thetotal power approaches the threshold. Load savings of approxi-mately 18% are observed, resulting to cost savings of approxi-mately 33%. On the other hand, the CCA algorithm initiates theon/off control schemewhen the user is active for a period greaterthan independently to the threshold margin . This has asa consequence of more load and cost savings to be achieved thatare almost constant with time (21% and 36% respectively). De-spite the fact that the CCA algorithm presents high savings forthe operator, users might become dissatisfied with the systemsince they are continuously pushed to their discomfort limits.Fairness Issues: The HPN and Round Robin fairness algo-

rithms are presented in Fig. 10. The number of received on/offcommands is presented as a function of the users’ averagepower . For the simulation results, it was assumed thatall users connect to the system simultaneously and it was set

and kW. These values model the case thatall users are activated simultaneously, resulting to peak hourcharacteristics and so they are all forced to participate in thecontrol scheme during their activation period. These settings areused to gain a clearer picture for the comparison of the two fair-ness algorithms.The following observations are derived. The HPN fairness al-

gorithm yield users with high power needs to be forced to switchoff their flexible devices more times than the users with lowerpower needs. Since the RFM case is always satisfied, anytime auser switches off the flexible loads it means that he/she reduceshis/her overall power consumption. In that way, users with highpower loads are switched off more times, providing load bal-ance in the system. The fairness of this condition can be ex-plained by taking into account the fact that the users with highpower needs are more responsible for the excess of the system’sload thresholds. On the other hand, the Round Robin fairnessscheme is independent to the average power of the users, as ex-pected. For that case, all users are forced to switch on/off equalnumber of times providing another type of fairness policy in the


Fig. 10. Number of switch on/off commands as a function of users’ average-power load for the HPN and the Round Robin fairness (TA algorithm).

system. The final policy to be followed depends on the oper-ator’s strategy with respect to the consumers.Variable Capacity: Fig. 11 presents the simulation results

for the case of variable capacity. The operator centric and theuser centric graphs present the gains from the operator and theuser perspectives. The relation between the extra safety marginneeded at the installed capacity and the probability to exceedthe threshold is presented together with the percentage of time(relative to NC case) where the threshold is exceeded. The usercentric graph presents the user energy savings relative to the NCcase and the consumer disutility as described in (8). It can beobserved that by increasing the installed capacity, the operatorreduces the probabilities and the time required to import energy(cost reduction-OPEX) but requires a higher CAPEX for the in-stallation. In addition, the users save less energy (since they arenot forced to switch off) but are more satisfied (lower disutilityfactor). As expected, the CCA algorithm yields higher gains forboth the operator and the users but on the other hand, it createsa higher consumer disutility factor. It can be observed that bothTA and CCA have approximately the same time per day wherepeak power exceeds the threshold. Despite the fact that the CCAalgorithm reduces the total energy consumption of the system,it does not significantly reduces the peak power compared to theTA algorithm.Variable User’s Comfort: Fig. 12 shows the performance

of the TA and the CCA algorithms under a given (with%) and variable . It was assumed that the

RFM criterion stands for . When the ratioit was assumed that the discomfort metric

exceeds the allowable margin . It can be observed that thehigher the is, the higher are the savings at both theoperator and the user side. From the operator perspective, itis highly desirable for the served users to provide a high ratiosince it minimizes the costs and provides a more effective loadcontrol scheme. From the user perspective, the high value ofthe ratio indicates great energy savings and reduced consumerdisutility. In order to achieve a high ratio oneshould target to proper house insulation or use of efficientdevices (air conditions, etc.).

Fig. 11. Operator Centric graph) Probability to exceed given threshold andpercentage of time exceeding relative to NC, for variable capacity limits.User Centric graph) User energy saving and consumer disutility. It was assumedthat satisfying RFM.

Fig. 12. Operator Centric graph) Probability to exceed given threshold andpercentage of time exceeding relative to NC, for variable .UserCentric graph) User energy saving and consumer disutility.

V. CONCLUSION

Dynamic control and scheduling schemes for flexible devicesin the smart grid were presented taking into account real timesystem’s conditions and user centric fairness issues. The pro-posed algorithms can provide the required foundations to theoperators to minimize costs and carbon emissions and enablepeak “shave” operations in an effective way. For the smart grid,the proposed algorithm reflects to the demand response problemand provides the degrees of freedom for a self-adaptable-self-optimized network. Two control algorithms were proposed, thethreshold algorithm (TA) and the continuous control (CCA) al-gorithm. The TA algorithm initiates control commands betweenthe smart grid and the smart devices when the total load ex-ceeds a given threshold, which can be static or variable withtime. At the CCA algorithm control commands are continuouslyexchanged in an on/off scheme that pushes the user comfortto the limits. The CCA algorithm provided greater savings buthigher user discomfort. To maintain fairness in a reciprocal fairscheme, a highest power next (HPN) and a Round Robin sched-uling scheme were proposed and compared. In terms of savingsfrom the operator’s perspective, the two scheduling policies didnot cause any dramatic change. From the user’s perspective, theHPN policy sustains fairness since it obliges users that cause


extra load in the system to increase the number of switch on/offtransitions. It can be seen as a load balancing algorithm that istrying to keep “almost” equal power consumption between theusers in the network. The choice of the used fairness depends onthe operator’s policy opposite the users. Finally, the consumerdisutility showed a decreasing trend with the operator’s capacityand the ratio . To achieve an effective penetration ofsmart grid services in the future, it is important to maintain theratio to high values and thus provide the requiredallowable discomfort margins to the control algorithms to adaptto any load change, minimizing costs at both sides.

ACKNOWLEDGMENT

The author would like to thank Mellon Energy and Kimaticafor providing important feedback and Prof. Leandros Tassiulasand Prof. Ioannis Vlahavas for the fruitful discussions on smartgrids and algorithms. Finally, the author would like to thank Dr.T. Dergiades for the discussions concerning economic aspectsand Mr. Th. Stavropoulos for the measurements on the air con-ditioning unit.

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George Koutitas was born in Thessaloniki, Greece.He received the B.Sc. degree in physics fromAristotle University of Thessaloniki, Greece, 2002and the M.Sc. degree (with distinction) in mobileand satellite communications from the University ofSurrey, U.K., 2003.He defended his Ph.D. in radio channel modeling

from the Centre for Communications Systems Re-search (CCSR) of the University of Surrey in 2007under a full scholarship. Currently, he is a member ofthe academic and research staff at the School of Sci-

ence and Technology of the International Hellenic University, Greece, where healso works at the Smart IHU project (rad.ihu.edu.gr). Finally, he is a Postdoc atthe University of Thessaly (Dept. Computer Engineering and Telecommunica-tions). His main research interests are in the area of wireless communications(modeling and optimization), energy efficient networking, and smart grids. He isinvolved in research activities concerning energy efficient network deploymentsand design, green IT, and sensor networks/actuators for smart grid applications.Dr. Koutitas, during his studies, received the Nokia Prize and Advisory Board

Prize 2003 for the best overall performance and best M.Sc. Thesis.

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