32_Customer Engagement Plans for Peak Load Reduction in Residential Smart Grids.pdf

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IEEE TRANSACTIONS ON SMART GRID 1

Customer Engagement Plans for Peak LoadReduction in Residential Smart Grids

Naveed Ul Hassan, Member, IEEE, Yawar I. Khalid, Chau Yuen, Senior Member, IEEE, andWayes Tushar, Member, IEEE

Abstract—In this paper, we propose and study the effec-tiveness of customer engagement plans that clearly specify theamount of intervention in customer’s load settings by the gridoperator for peak load reduction. We suggest two differenttypes of plans, including constant deviation plans (CDPs) andproportional deviation plans (PDPs). We define an adjustablereference temperature for both CDPs and PDPs to limit theoutput temperature of each thermostat load and to control thenumber of devices eligible to participate in demand responseprogram. We model thermostat loads as power throttling devicesand design algorithms to evaluate the impact of power throt-tling states and plan parameters on peak load reduction. Basedon the simulation results, we recommend PDPs to the cus-tomers of a residential community with variable thermostatset point preferences, while CDPs are suitable for customerswith similar thermostat set point preferences. If thermostatloads have multiple power throttling states, customer engage-ment plans with less temperature deviations from thermostat setpoints are recommended. Contrary to classical ON/OFF control,higher temperature deviations are required to achieve similaramount of peak load reduction. Several other interesting tradeoffsand useful guidelines for designing mutually beneficial incen-tives for both the grid operator and customers can also beidentified.

Index Terms—Customer engagement plan, demand response,peak load, smart grid, user inconvenience.

NOMENCLATURE

K Number of operable states of thermostat loads.K j

i Number of operable states of thermostat load i ofcustomer j.

k Index of each operable state of thermostat load.J Number of customers in the residential community.I Set of flexible loads for which customer engage-

ment plans are defined.IT Set of thermostat loads for which customer engage-

ment plans are defined.

Manuscript received July 5, 2014; revised October 1, 2014 andDecember 31, 2014; accepted February 11, 2015. This work was supportedin part by the Lahore University of Management Sciences Research StartupGrant and in part by the Energy Innovation Research Program Singapore underGrant NRF2012EWT-EIRP002-045. Paper no. TSG-00687-2014.

N. U. Hassan and Y. I. Khalid are with the Electrical EngineeringDepartment, Lahore University of Management Sciences, Lahore 54792,Pakistan (e-mail: [email protected]; [email protected]).

C. Yuen and W. Tushar are with Engineering Product Development,Singapore University of Technology and Design, Singapore 487372 (e-mail:[email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TSG.2015.2404433

IS Set of shiftable loads for which customer engage-ment plans are defined.

ITc Set of thermostat loads used for cooling for whichcustomer engagement plans are defined.

ITh Set of thermostat loads used for heating for whichcustomer engagement plans are defined.

I j Set of flexible loads owned by customer j.I jT Set of thermostat loads owned by customer j.

I jS Set of shiftable loads owned by customer j.

I jTc Set of thermostat loads used for cooling owned by

customer j.I jTh Set of thermostat loads used for heating owned by

customer j.i Each flexible load index.j Each customer index.n Index of each local peak in Algorithm 2.θj,i Preference of customer j for the set point of

thermostat load i.θ ref

i Reference temperature for thermostat load i.�θmax

i Constant value representing the maximum temper-ature deviation for thermostat load i.

�θj,i Inconvenience severity experienced by customer jfor thermostat load i.

θj,i(t) Output temperature of thermostat load i ofcustomer j.

θkj,AC(t) Output temperature of air conditioner (AC) of

customer j, which is operated in state k, at time t.θk

j,WH(t) Output temperature of water heater (WH) of cus-tomer j, which is operated in state k, at time t.

θj,i(t) Output temperature of thermostat load i of cus-tomer j at time t during Algorithm 2 computations.

θaveAC Average temperature deviation of AC loads over

the demanded intervals in the simulations.θave

WH Average temperature deviation of WH loads overthe demanded intervals in the simulations.

θinlet Temperature of the inlet water of WH.θa(t) Room temperature at t.fr(t) Rate of water flow in WH.Vtank Volume of the water tank of WH.Atank Tank surface area of WH.Rtank Heat resistance of the water tank of WH.Gj(t) Heat gain rate of the house of customer j at

time t.T Number of intervals in the considered time

duration.

1949-3053 c© 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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2 IEEE TRANSACTIONS ON SMART GRID

t Index of each time interval.�t Time duration of each interval.�smax

i Maximum scheduling delay of each shiftableload i.

�dmaxi Maximum inconvenience duration of each thermo-

stat load i.tstartj,i Actual start time of shiftable load i of customer j.

tprefj,i Preferred start time of shiftable load i of

customer j.tduri Maximum number of time slots a thermostat load i

can deny operation at its full rated power.tmax-nj,i Time index corresponding to nth largest local peak

in the demanded operation interval of thermostatload i of customer j in Algorithm 2.

tpeakj,i Time index vector containing local peaks in

Algorithm 2.bj,i Set of time indexes during which customer j

demands thermostat load i.βi Scaling factor for thermostat load i.wj,i Demand status vector of flexible device i of cus-

tomer j.wj,i(t) Entry, which is a binary variable, of the demand

status vector at t.pr

j,i Rated power of flexible load i of customer j.l Index to denote scheduling delay in terms of

number of time slots in Algorithm 1.pj,i Vector of demanded power requirement by flexible

load i of customer j.pj,i(t) Demanded power consumption requirement of load

i of customer j at time t.pl

j,i Demanded power requirement vector of shiftableload i of customer j when delayed by l time slots.

Cj,i A matrix of binary variables of order T × K ji .

ckj,i(t) Binary variable indicating the operational state

of thermostat load i of customer j in state k attime t.

cj,i(t) tth row vector of matrix Cj,i.ck

j,i kth column vector of matrix Cj,i.α Energy required for a unit degree rise in room

temperature.1(·) (·) × 1 vector of all 1’s.eτ

K ji

Vector of all 1’s except a 0 at Kith position.

x A given aggregated load profile vector of residen-tial community.

x(t) Aggregated load demand at time t.x Aggregated load profile obtained by solving sub-

problem 1.xj Aggregated load profile obtained from the cus-

tomer j in Algorithm 1.x Final aggregated output load profile.F(·) A circular shift operator.m Particular order of shiftable devices.m∗ Optimal order of shiftable devices.yl Aggregated load profile in Algorithm 1 when

shiftable load i of customer j is delayed by l timeslots.

φl Peak value of yl in Algorithm 1.

l∗i Optimal scheduling delay for shiftable load i deter-mined by Algorithm 1.

y Output of Algorithm 1 (aggregated load profile).ym Output of Algorithm 1 for mth particular order

(aggregated load profile).φm Peak value of ym (for shiftable device order m).qk

j,i(t) Power consumption of thermostat load i of cus-tomer j while operating in state k at time t.

Qj,i A matrix of order T × K ji , which has the entry of

qkj,i(t), ∀j, k, i ∈ IT .

Zkj,AC Cooling capacity of customer j’s AC operating in

state k at time t.EER Energy efficiency ratio (EER) of the AC.h Output of Algorithm 2 (aggregated load profile).NAC Number of eligible AC loads in the simulations.NAC Number of eligible WH loads in the simulations.

I. INTRODUCTION

DEMAND response program (DRP) can be used toreduce cost and improve efficiency of power grids by

engaging customers and modifying their power consump-tion pattern [1]–[7]. Current smart metering and bi-directionalcommunication technologies, allow the inclusion of industrialas well as residential consumers in DRPs [8]–[13]. Customerengagement for peak load reduction can be achieved throughmotivating customers by either time-based DRP or incentive-based DRP [14], [15]. In time-based DRP, electricity pricesare dynamically varied at different times and the customers canmodify their electricity consumption in response to the changeof price. In incentive-based DRP, fixed or time-varying pay-ments are offered to the customers under specific constraints.In general, residential customers are not very responsive toDRPs due to the uncertainty in their electricity bills and thelack of clarity about the resulting inconvenience that theymight experience [16]. The participation of residential cus-tomers in DRP, however, is extremely important to address thepredictable and nonpredictable supply and demand variationsin order to reduce the electricity generation cost [17], [18].

The increased penetration and usage of AC and WH loadsin residential sector are the main reasons for increasing thepeak load demand on the grid [19]–[21]. Kondoh et al. [22]proposed a direct load control algorithm to investigate thepotential of WH loads in providing load-balancing service,while Lu [23] evaluated the potential of heating, ventilationand air-conditioning (HVAC) loads for providing regulationservices. These two papers suggest that the aggregated reg-ulation service provided by the WH and HVAC loads canbecome one of the major sources of revenue for the grid.Lu and Zhang [24] proposed a controller for thermostaticallycontrolled loads, which can be used for peak shaving andload shifting by managing the aggregated HVAC load shapes.Pipattanasomporn et al. [25] proposed HVAC control algo-rithm to regulate the indoor air temperature inside a defineddead band by using an ON/OFF power control. However, thealgorithm does not consider the retail price of electricity in theHVAC control, and therefore may fail to curtail load duringpeak price period.

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HASSAN et al.: CUSTOMER ENGAGEMENT PLANS FOR PEAK LOAD REDUCTION IN RESIDENTIAL SMART GRIDS 3

In [26], a price responsive control strategy is proposed forHVACs to reduce peak load. The controller changes the ther-mostat set point of HVAC loads depending on the electricityretail price published in every 15 min. The authors demonstratea significant peak load reduction with a modest variation inthermal comfort. Totu et al. [27] considered the problem ofmanaging large number thermostat appliances with ON/OFFpower control for peak load reduction. They discuss a cen-tralized, model predictive approach and a distributed structurewith a randomized dispatch strategy.

Several authors have also designed algorithms that may helpthe grid operator to reduce peak demand by controlling andscheduling common household appliances. For instance, [28]proposes an optimal and automatic residential load com-mitment framework, in which the households achieve theminimum payment by responding to the time-varying pricesoffered by the grid. Similarly, a Stackelberg game is studiedin [29] to maximize both the revenue of the grid operator andthe payoff to each user by determining the optimal electricityprice and the optimal price consumption. Shinwari et al. [30]used a water-filling based scheduling algorithm, which doesnot require any communication between scheduling loads,to obtain a flat demand curve. The authors also explorethe possible errors in demand forecast and potential incen-tives for customer participation. A genetic algorithm basedenergy resource scheduling technique, which includes day-ahead, hour-ahead, and 5 min ahead scheduling is proposed forsmart grid in [31]. Finally, a heuristic method called signaledparticle swarm optimization is proposed in [32] for distributedenergy resource scheduling in smart grids.

These DRP algorithms certainly present feasible solutionsto address the problem of increased peak load on the grid.However, designing schemes, which can attract the interest ofsignificantly large number of customers to participate in DRPremains a major challenge [16]–[18]. The reluctance to partic-ipate by the residential customers is due to the lack of clarityin specifying key information such as the number of timescustomers would be called upon to participate, the range oftemperature variation of AC and WH loads, and the financialbenefits associated with such participation. In recent years,companies like Idaho Power have introduced direct load con-trol methods, such as AC Cool Credit program, to switchOFF the AC loads of their residential customers [33], wherethe duration of OFF time is set according to a predeterminedagreement. Such agreement has been reported to be very effec-tive in considerably reducing the peak load. However, theresulting room temperature deviations during the OFF inter-vals are not specified in the agreement, which can result inexcessively high inconvenience for some customers.

In this paper, we propose customer engagement plans thatclearly specifies all the key inconvenience parameters forshiftable and thermostat loads, and thus may encourage thecustomers to pick plans according to their behavioral andfinancial requirements.1 For each shiftable load, maximumscheduling delay is specified in the plan. For each thermostat

1Designing actual financial rewards or incentives for customers is out ofscope of this paper.

load, maximum temperature deviation from the thermostat setpoint and the maximum time duration during which the actualtemperature deviates from the thermostat set point are clearlydefined.2 It is important to note that this paper is an extensionof [34]. In [34], we proposed demand response managementplans for AC loads. We modeled the AC load as a powerthrottling thermostat device and specified the thermostat setpoint, temperature deviation and inconvenience duration forthe customers. We showed that a power throttling thermostatdevice can operate in K ≥ 2 states, where K is the number ofpossible power states. Note that in a two-states model, ther-mostat loads can only be turned ON/OFF for DRP, wherebythey can operate in K different states for K > 2. For exam-ple, in a three-states model, the thermostat load can be turnedOFF, operated at 50% of the rated power or operated at fullrated power. In [34], we determined the effectiveness of suchplans and studied the impact of temperature deviation, timeduration of inconvenience, and the impact of increasing thepower throttling states on peak load reduction. However, theinclusion of thermostat set point as a plan parameter in [34],requires all the customers to adjust their thermostat set pointto the same specified value and thus experience additionaltemperature deviation for the time duration as laid out in theplan. Such customer engagement plans, therefore, may havepractical limitations and fairness concerns.

To this end, we extend [34] in this paper to include multi-ple shiftable and thermostat loads. In this context, we proposetwo new types of customer engagement plans: the constantdeviation plan (CDP) and proportional deviation plan (PDP),which allow customers to have different thermostat set points.We model thermostat loads as power throttling devices suchas in [34]. However, in contrast to [34], the model adopted inthis paper is quite generic and can allow different customers tohave different number of loads including thermostat loads withdifferent number of power throttling states. We propose algo-rithms that enable us to identify mutually beneficial plans forboth the grid operator and the customers with power throt-tling thermostats and shiftable loads through the introducedcustomer engagement plans, i.e., CDPs and PDPs. ThroughMATLAB simulations, we study the impact of the numberof power throttling states, magnitude of temperature devia-tions, and scheduling delays on the peak load reduction. Theimpact of scheduling delays in the presence of thermostat loadswith multiple power throttling states is investigated, and cer-tain observations and comparisons of CDP and PDP type plansare made. The impact of CDP and PDP parameters in control-ling and determining the number of eligible thermostat loadsand average temperature deviations are also investigated. Someuseful design guidelines for CDP and PDP plans are provided,which could be helpful in designing the financial incentives forparticipating customers. Further, several new and interestingresearch directions are identified.

2Customers generally cannot understand the amount of intervention byspecifying the energy consumption limits on their loads or by announcingthe dynamic price on energy consumption. It is much easier for them tocomprehend the inconvenience if specified in terms of scheduling delays andtemperature deviations of loads.

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4 IEEE TRANSACTIONS ON SMART GRID

The rest of this paper is organized as follows. The cus-tomer load model, residential community model, and customerengagement plans are explained in Section II, the optimizationproblem for peak load reduction and the algorithmic solutionsare presented in Section III, simulation results are given inSection IV, while this paper is concluded and future researchdirections are identified in Section V.

II. CUSTOMER LOAD, RESIDENTIAL COMMUNITY

MODELS, AND CUSTOMER ENGAGEMENT PLANS

A. Customer Load Model

In this paper, we group the appliances, also called loadsor devices, in a home into two categories: essential appli-ances, and flexible appliances. The power required for all theentire essential appliances serves as a base load, which alwayshas to be provided by the grid operator. We further clas-sify flexible loads into shiftable and thermostat loads.3 Weassume that the shiftable loads, such as dishwashers (DWs)or clothes dryer (CD), require a constant power draw for aspecified duration. We further assume that neither the powerdraw nor the operational duration of shiftable loads can bereduced. The customer has a preferred operation interval foreach shiftable load that best suits his/her behavioral require-ments. Scheduling delays in the operation of shiftable loads,can cause inconvenience to customers.

Thermostat loads such as AC and WH, on the other hand,have to maintain an output temperature that matches thecustomer-defined thermostat set point, and any deviation fromthese set points cause inconvenience. Temperature deviationcan be controlled in two different ways: 1) by readjustingthe thermostat set point; or 2) by readjusting the power con-sumption of the device. During the readjustment of set point,a smart thermostat automatically adjusts the thermostat set-tings to control temperature deviations. One such example isGoogle Nest, which can be used to readjust the thermostat setpoint of AC loads [35]. Conversely, power consumption canbe readjusted by providing a smart electrical interface witheach device which enables it to respond to the control sig-nals received from a controller. For example, Idaho Powercontrols the temperature deviations of AC loads by adjust-ing the number of ON/OFF switching frequency. Thermostatreadjustment method requires mathematical models (for eachthermostat load) to compute the resulting power consump-tion for some specified temperature deviation, while powerreadjustment method requires models to compute the resultingtemperature deviations for specified power consumption.

In this paper, we consider thermostat loads that are capableof operating in K ≥ 2 power consumption states. We have alsoadopted the power readjustment method to control the tempera-ture deviations of thermostat appliances [25]–[27], [33], [36].This method allows us to determine the exact amount of

3Other categories of flexible loads e.g., electrical vehicles, which require anunfixed amount of power and operation duration depending on the customerusage are also possible. Such load categories are not considered in this paper.However, our framework can be easily extended in future to accommodateelectrical vehicles or any other new category of flexible loads.

power consumption by the appliances and using the ther-mal models readily available in [36], we can determinethe output temperature (e.g., room temperature or hot watertemperature). Moreover, the thermal models can be easilyextended to include multiple power throttling states. TheAS/NZS 4755 Standard (jointly adopted by the Australian andNew Zealand Governments) [37] for thermostat loads beingmanufactured and sold in Australia and New Zealand alsomandates physical/electrical interface as well as mandatoryand optional modes, which permit these loads to operate indifferent power consumption states. Variable frequency drivesand variable speed drives are generally used to throttle powerof thermostat loads between different states.

B. Residential Community Model

We model a residential community comprising of J cus-tomers (also called homes, users or consumers). We considerthe aggregated power consumption profile of the communityfor a duration of 24 h, and divide the total duration into T equalintervals. Each interval �t comprises of �t = (24 × 60)/Tminutes. Each customer has a base load, a set of thermostatloads and a set of shiftable loads. We further differentiate ther-mostat loads into two types depending on whether the load isused for cooling application or heating application. For exam-ple, in summer AC is used to cool the room, while WH is usedto heat water. In this paper, we assume that the grid opera-tor identifies a set of flexible devices denoted by I, furthercategorized into IS shiftable and IT thermostat loads, which itwants to control. Let ITc and ITh, respectively, denote the setof thermostat loads used for cooling and heating applications(IT = ITc ∪ ITh). The grid operator will then propose customerengagement plans only for these flexible devices. Let I j ⊆ I,I jS ⊆ IS and I j

T ⊆ IT , respectively, denote the set of flexi-ble, shiftable and thermostat loads of customer j. Similarly,let I j

T = I jTc ∪ I j

Th, where, I jTc ⊆ ITc and I j

Th ⊆ ITh denotethe set of thermostat loads of customer j used respectively forcooling and heating applications. All the remaining devices ofcustomer j are treated as essential loads. For example, if thegrid operator is only interested in controlling the AC load ina residential community and defines a customer engagementplan only for this load, then all the remaining loads such asCD or WH of all the customers will be treated as essentialloads. This model, however, is flexible enough to allow dif-ferent customers to have different number of flexible devices.This model also allows I j to be a strict subset of I, i.e., it ispossible for some customers to own less flexible loads than thenumber of flexible devices I for which the grid operator hasdefined customer engagement plans. In such a case, it is up tothe grid operator to either allow such customers to participatein DRP with their available devices and offer them reducedfinancial incentives or does not allow them at all. In the restof this paper, in order to have a generic model, we assumethat a customer with I j ⊂ I is allowed by the grid operatorto participate in the DRP (the problem on how the financialincentives are computed is out of scope of this paper).

Each home is assumed to be equipped with a home con-troller as part of its advance metering infrastructure, whichacts as an interface between the customer and the grid operator.

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HASSAN et al.: CUSTOMER ENGAGEMENT PLANS FOR PEAK LOAD REDUCTION IN RESIDENTIAL SMART GRIDS 5

Fig. 1. System model elaborating the implementation and communicationrequirements of our proposed methodology.

There is a two-way communication link between the grid oper-ator and each home controller. In our proposed method, thegrid operator and the home controller only exchange the aggre-gated load profiles in order to minimize the communicationbandwidth required and also to protect the privacy of individ-ual customers. The home controller executes the algorithms(proposed in Sections III-A and III-B) in order to determine thescheduling time and power throttling states of its appliancesaccording to the customer engagement plan. These values arestored at the home controller and the new aggregated loadprofile is communicated back to the grid. The home con-troller then schedules and operates its appliances accordingly.There is a two-way communication link between the homecontroller and every flexible load (shiftable or thermostat).The power flow is unidirectional i.e., from the grid operatorto the home controller and appliances. The home controllergenerates appropriate control signals for each of its flexi-ble device. These devices report back their status (ON/OFFstatus, power throttling state, temperature, etc.) to the homecontroller. The implementation and communication require-ments of our proposed methodology are further elaboratedin Fig. 1.

C. Customer Engagement Plans

Customer engagement plans can be designed in one of thefollowing ways:

1) by defining the power consumption pattern for customerse.g., by announcing power consumption limits in peakload hours;

2) by defining the inconvenience parameters for flexibleloads of the customers.

Generally, it is difficult for customers to translate powerconsumption limits into scheduling delays and temperaturedeviations experienced by the loads, and easier for the gridoperator to understand the amount of peak reduction anddemand shaping. On the other hand, customer engagementplans that define the inconvenience parameters for the flexi-ble loads can be easily understood by the customers, whiletheir effectiveness for the grid operator is unclear. Thesecond approach, however, is more promising to convince

and encourage customer participation (because it providesclarity to the customers), which is therefore adopted inthis paper.

In our proposed customer engagement plans, the inconve-nience related to any shiftable load i ∈ IS is defined in termsof scheduling delay from the preferred start time of the load.The plan defines �smax

i as the maximum scheduling delay(in minutes) for each shiftable device i. The inconveniencerelated to any thermostat load i ∈ IT have two dimensions:1) inconvenience duration: which is defined as the total timeduration during the demanded interval the thermostat loadis denied operation at its full rated power and 2) inconve-nience severity: which is defined as the temperature deviationfrom the desired thermostat set point. Maximum inconve-nience duration �dmax

i (in minutes) for each thermostat loadi is specified in the plan. However, defining inconvenienceseverity is not straightforward since each customer has a dif-ferent preference for thermostat set point (denoted by θj,i),which also impacts the experienced inconvenience and thermalcomfort [38], [39]. For example, if the outdoor temperature ona hot summer day is 82 ◦F, then a temperature deviation of4 ◦F is more severe for a customer with AC thermostat setpoint at 76 ◦F compared to another customer with AC ther-mostat set point at 70 ◦F. We therefore propose two differenttypes of plans: CDPs and PDPs. For each thermostat load i,both CDP and PDP define a reference temperature denotedby θ ref

i .In CDPs, a constant value representing the maximum

temperature deviation for each thermostat load i, denotedby �θmax

i , is announced. Accordingly, the inconvenienceseverity experienced by customer j for thermostat load i iscomputed as

�θj,i =⎧⎨

⎩

(min

(θ ref

i − θj,i,�θmaxi

))+ ∀i ∈ I jTc

(min

(θj,i − θ ref

i ,�θmaxi

))+ ∀i ∈ I jTh

(1)

where, x+ is defined by, x+ = max{0, x}. In PDPs, a scalingfactor 0 < βi ≤ 1 is defined in the plan for each thermostatload i. The inconvenience severity experienced by customer jfor thermostat load i is then computed as

�θj,i =⎧⎨

⎩

βi ×(θ ref

i − θj,i

)+ ∀i ∈ I jTc

βi ×(θj,i − θ ref

i

)+ ∀i ∈ I jTh.

(2)

To summarize; for each thermostat load i, the followingparameters are defined by the grid operator:

1) CDP: (�dmaxi , �θmax

i , θ refi ) i.e., (maximum inconve-

nience duration, maximum temperature deviation, andreference temperature) and (1);

2) PDP: (�dmaxi , βi, θ ref

i ) i.e., (maximum inconvenienceduration, scaling factor, and reference temperature)and (2).

As mentioned before, the reference temperatures in CDPsand PDPs bound the output temperature of thermostat loads,and can also be used to control the total number of loads expe-riencing temperature deviations. For example, if the thermostatset point of AC is below the reference temperature, then the

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6 IEEE TRANSACTIONS ON SMART GRID

TABLE ISAMPLE CUSTOMER ENGAGEMENT PLANS AND AN EXAMPLE OF RESULTING TEMPERATURE

DEVIATIONS IN CDP AND PDP FOR TWO CUSTOMERS

output temperature for this customer cannot exceed the ref-erence temperature. On the other hand, if the thermostat setpoint of AC is above the reference temperature, then such acustomer will be allowed to operate at the preferred set pointwithout any intervention. Generally, a high value of referencetemperature for AC and a low value of reference temperaturefor WH will make a high number of AC and WH loads eli-gible for DRP. The values of reference temperatures can bedecided by the grid operator depending on the local weather,geographical location, user preferences and the desired peakload reduction.

A sample CDP and PDP for a residential community com-prising of AC, WH, CD, and DW as flexible loads is givenin Table I. In this table, we also give an example of resultingtemperature deviations of AC and WH loads of two customerswith different thermostat set points to explain the differencebetween CDP and PDP and the role of reference tempera-tures [temperature deviations are computed using (1) for CDPand (2) for PDP]. Note that the thermostat set points of ACand WH loads of the customers in this example, are assumedto lie in a typical range associated with the thermal comfortof humans [38], [39].

The customers may subscribe to a plan on a daily, weeklyor monthly basis. Similarly the grid operator can also changethe set of its customer engagement plans on monthly, bi-monthly or seasonal basis (depending on the geography,weather patterns, etc.). Such issues, however, are not dis-cussed in this paper and are left as an interesting futurework.

III. OPTIMIZATION PROBLEM FORMULATION AND

ALGORITHM DEVELOPMENT

The objective of this paper is to determine the effectivenessof a given customer engagement plan (CDP or PDP) for peakload reduction. In this section, we mathematically formulatethe optimization problem. Let wj,i = [wj,i(1), . . . , wj,i(T)]τ

denote the demand status vector of flexible device i of user j([ · ]τ denotes the transpose operation). Each entry wj,i(t) ofthis vector is a binary variable: a “1” indicates that the deviceoperation is demanded, while a “0” indicates that it is notdemanded. Let pr

j,i denotes the rated power of flexible loadi of customer j. Then pj,i = [pj,i(1), . . . , pj,i(T)]τ = pr

j,iwj,i

denotes the demanded power requirement vector of flexi-ble load i of customer j, while pj,i(t) is used to denote thedemanded power consumption requirement of load i of cus-tomer j at time t. The operation of shiftable loads can bedelayed from the preferred time interval. Let tstart

j,i denotesthe actual start time of shiftable load i of customer j, then

according to the plan, we have the following constraint:

tstartj,i − tpref

j,i ≤ �smaxi , ∀j, i ∈ I j

S (3)

where, tprefj,i denotes the preferred start time of shiftable load i

of user j. This constraint is sufficient to describe the termsof engagement as laid out in the plan for the shiftable loads.Also note that this constraint only allows shiftable loads tobe delayed from their preferred start time (our frameworkcan easily allow advance scheduling of shiftable loads, whichhowever, is not considered in this paper).

We assume that thermostat load i of customer j has thecapability to operate in K j

i possible states. This model allowsdifferent customers to own thermostat loads with differentnumber of operable states. For example, the AC of customer 1can operate in only two states, while that of customer 2 canhave five states. Let Cj,i denotes a T × K j

i matrix of binaryvariables. The entries of this matrix are given by variablesck

j,i(t), which represent the operational state of thermostat load

i ∈ I jT of customer j in state k at time t. If thermostat load

of customer j is operated in state k in time interval t, thenck

j,i(t) is set to 1; otherwise to 0. In the subsequent discussion,ck

j,i = [ckj,i(1), . . . , ck

j,i(T)]τ will be used to denote the kth col-

umn vector, while cj,i(t) = [c1j,i(t), . . . , c

K ji

j,i (t)]τ will be used

to denote the tth row vector of the matrix Cj,i. Since a ther-mostat load can operate in only one state in any given timeinterval t, we have the following constraint on its operation:

Cj,i1K ji

= 1T , ∀j, i ∈ I jT (4)

where, 1K j

iis a K j

i × 1 vector of all 1’s, while 1T denotes aT × 1 vector of all 1’s. Similarly, we can represent the con-straint on the maximum inconvenience duration, i.e., �dmax

iof thermostat load i mathematically as

eτ

K jiCτ

j,iwj,i ≤ �dmaxi , ∀j, i ∈ I j

T (5)

where, eτ

K ji

= [1 1 · · · 1 0] i.e., it is a vector of all 1’s except

a 0 in the K ji th position. This constraint bounds the number of

time slots in the demanded interval during which the operationof thermostat load is denied at its full rated power. The outputtemperature of a thermostat load at any time t depends on itsoperational state. Let θj,i(cj,i(t)) denotes the output tempera-ture of thermostat load i of customer j at time t (appropriatemathematical models are required to determine the output tem-perature as a function of power state of the load). Duringthe time slots when the thermostat load is demanded by thecustomer, the difference in output temperature between anytwo consecutive intervals should be less than or equal to �θj,i

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HASSAN et al.: CUSTOMER ENGAGEMENT PLANS FOR PEAK LOAD REDUCTION IN RESIDENTIAL SMART GRIDS 7

Fig. 2. Decomposition of the optimization problem according to loadcategories.

[computed using (1) for CDP and (2) for PDP], which can beexpressed in terms of the following constraint:

wj,i(t)∣∣∣θj,i

(cj,i(t)

) − θj,i

∣∣∣ ≤ �θj,i, ∀j, t, i ∈ I j

T . (6)

As stated before, our objective is to determine the effec-tiveness of customer engagement plan in terms of peak loadreduction. Let x = [x(1) . . . x(T)]τ denotes the given aggre-gated load profile vector of the residential community, where,x(t) = ∑

j∑

i pj,i(t). Then, we have the following optimizationproblem:

minCj,i,tstart

j,i

maxt

x

subject to constraints: (3)−(6). (7)

The objective function (7) seeks to minimize the maximumvalue of x. The optimal solution of this problem depends onthe order in which customers are considered for optimization.Due to the combinatorial nature of the problem, it is NP-hardand therefore finding the optimal solution has exponential timecomplexity [40]–[42]. We develop a sub-optimal heuristic bydecomposing the problem into two sub-problems based on theload categories, i.e., shiftable and thermostat loads as shownin Fig. 2. We first minimize the peak load by reschedulingthe shiftable loads subject to (3). The new aggregated loadprofile is denoted by x. The peak of this load profile is furtherreduced by controlling the thermostat loads subject to (4)–(6)to obtain the final aggregated output load profile x. It shouldbe noted that the order in which these steps are carried outcan be interchanged but could result in a different amount ofpeak load reduction.

Our sub-division of the problem and the subsequent algo-rithms based on the load categories provides flexibility andeasily allows us to include or exclude some load category fromoptimization. For example, the grid operator can implement theframework without the shiftable load category or without thethermostat load category if required controls (interfaces) arenot available. Moreover, if a third category of flexible loads(e.g., electrical vehicles) is available, then the framework canbe easily extended by adding a third algorithm for the new cat-egory of flexible loads. Such flexibility can also be helpful inthe actual implementation, where the proposed framework canbe implemented in stages, as the interfaces and controls canbe different for different load categories. Other alternatives, inwhich all the appliances of a customer are considered beforemoving on to the second customer are less flexible comparedto our approach.

In Sections III-A and III-B, we develop distributed offlinealgorithms for the two sub-problems. We assume prior knowl-edge on the aggregated load profile of the residential commu-nity. This information can be obtained either from past power

consumption patterns of the community during the same timeperiod or it can be deduced using some load prediction/forecastmodels [43], [44].

Remark 1: It should be noted that the proposed algorithmsare heuristics since there is no optimization on the customerorder. One way to determine the optimal customer order is byexhausting all the possible options, which unfortunately is notpossible in polynomial time for a residential community com-prising of several hundred customers (due to NP-hardness ofthe problem). Thus, for any given customer order (among thehuge number of possibilities), our algorithms and frameworkcould be used to study the effectiveness of customer engage-ment plans and to obtain useful guidelines for designing theseplans.

A. Sub-Problem 1: For Shiftable Loads

We develop a distributed algorithm in which the grid opera-tor provides coordination among the customers. To be mindfulof the security and privacy concerns of the customers, onlythe aggregated load profiles are exchanged between the gridoperator and customers. The given aggregated load profile ofthe community, i.e., x, is communicated to the home con-troller of customer 1, which runs an algorithm developed forshiftable loads (which will be explained below). This algo-rithm determines the scheduling time slots for the shiftableloads of customer 1 with the objective of peak load minimiza-tion and (3). The new aggregated load profile denoted by x1 issent back to the grid. The grid operator communicates x1 to thehome controller of customer 2. This process is repeated andthe aggregated profile obtained from the last customer J in thesequence is denoted by xJ , which is also the final aggregatedoutput profile x for sub-problem 2.

1) Algorithm for Shiftable Loads: We now explain thealgorithm for shiftable loads that is carried out at the homecontroller. The starting time of the shiftable load i of cus-tomer j can lie anywhere in the interval tstart

j,i ∈ {tprefj,i , tpref

j,i +1, . . . , tpref

j,i +�smaxi }. Thus, when a home controller j receives

an aggregated load profile xj−1 from the grid, the algorithmdetermines the best starting time for each of its shiftable loadin order to minimize the peak load. Let us define a circularshift operator denoted by F(.), which rearranges the entries ofa vector by shifting them one unit to the right and moving thelast entry to the first position.4 The scheduling algorithm for aspecified sequence of shiftable devices at the home controllerof customer j is given as Algorithm 1.

The optimal device order, which shiftable loads should beconsidered for scheduling, can be determined by exhaustingall the possibilities, and this requires Algorithm 1 to be exe-cuted (I j

S)! times. Let the index m denote a particular order ofshiftable devices. For this order we denote the final output ofAlgorithm 1 by ym. Let φm = max ym denote the peak load.Then the optimal device order denoted by m∗ is the one thatcorresponds to the minimum value in the set {φ1, . . . , φ(I j

S)!}4We assume that the demanded scheduling parameters of all the shiftable

loads are defined in such a way that despite being delayed they can alwaysbe completed until midnight i.e., we do not allow tasks to spill over tonext day.

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8 IEEE TRANSACTIONS ON SMART GRID

Algorithm 1 Algorithm For Shiftable Loads

1: Initialize: p1j,i = pj,i, ∀i ∈ I j

S, y = xj−1 − ∑

i∈I jS

pj,i

2: for i ∈ I jS do

3: for l = 1:�smaxi do

4: yl = y + plj,i

5: Find the peak: φl = max yl

6: pl+1j,i = F(pl

j,i)

7: end for8: Find the index: l∗i = minl :{φ1, . . . , φ�smax

i}

9: tstartj,i = tpref

j,i + l∗i − 110: y = yl∗i11: end for

and the aggregated output profile xj = ym∗ is communicatedback to the grid. Typically the number of shiftable devices ineach home is small (1–5 devices), which makes it possibleto determine the optimal device order and hence the optimaloutput profile.

B. Sub-Problem 2: For Thermostat Loads

For thermostat loads, we again develop a distributed sequen-tial algorithm coordinated by the grid. The grid operatorcommunicates the aggregated load profile x that is obtainedfrom the solution of sub-problem 1 to the home controller ofcustomer 1. At the home controller we have an algorithm forthermostat loads (which will be explained below) and the loadprofile obtained from this algorithm denoted by x1 is sent backto the grid operator for onward transmission to customer 2 andthe process is repeated until we obtain the final aggregatedoutput profile x.

The power consumption of thermostat load i of customer jat time t when it is operating in state k can be modeled interms of the rated power of the appliance by the followingequation:

qkj,i(t) = k − 1

K ji − 1

× prj,i, ∀j, k, i ∈ I j

T . (8)

For example, an AC that can operate in five-states has thecapability to throttle power at 0%, 25%, 50%, 75%, and 100%of the rated power. Let us define a T × K j

i matrix Qj,i, wherethe entries qk

j,i(t) of this matrix are given according to (8).We also require thermal load models that can relate the out-

put temperature obtained by an appliance when it is operatedin some power throttling state. Each thermostat load has itsown thermal characteristics and hence the modeling varies.Since AC and WH are the most significant thermostat loads,we discuss their thermal load models in details. We adapta simple model, where the output temperature depends onlyon the current state k in which the device is operated i.e.,θj,i(cj,i(t)) = θk

j,i(t).1) Thermal Model of AC: The output of an AC is

the room temperature that can be obtained by its oper-ation. The room temperature variation between any twoconsecutive time intervals is modeled by the following

equation (inspired from [36]):

θkj,AC(t + 1) − θk

j,AC(t) = �tGj(t)

α+ �t

Zkj,AC

αwj,AC(t). (9)

In this model, Gj(t) is the heat gain rate of the house ofcustomer j, which depends on heat gain coefficients of thewalls, windows, roof, solar radiation, people and air changerate of the AC, inside and outside temperature difference, etc.,(Gj(t) is independent of state k), α is the energy required for aunit degree rise in room temperature and Zk

j,AC is the coolingcapacity of the AC when it is operating in state k. Coolingcapacity of an AC is specified by the manufactures in kW,BTU/hr or Tons. The cooling capacity is a function of thepower state in which AC is operated and can be modeled as

Zkj,AC = EER × qk

j,i(t) (10)

where EER is typically defined as the ratio of cooling capacitygiven in BTU/hr to the power input in Watts. The higher theEER rating, the greater is the performance. The U.S. nationalappliance standards dictate all AC loads to have a minimumvalue of EER ≥ 8.0 [45]. For example, an AC with a coolingcapacity of 1 ton (equivalent to 12000 BTU/hr or 3.516 kW)with an EER of 8.0 will consume 1.5 kW power.

2) Thermal Model of WH: Hot water temperature obtainedfrom operating the WH for one time slot in any given powerstate k can be modeled by the following equation (inspiredfrom [36]):

θkj,WH(t + 1) = θk

j,WH(t)(Vtank − fr(t).�t)

Vtank+ θinlet.fr(t).�t

Vtank

+⎡

⎣qkj,i(t) −

Atank.(θk

j,WH(t) − θa(t))

Rtank

⎤

⎦.�t

Vtank.

(11)

In this model, water temperature in the next time slot t + 1,by operating WH in power state k (which consumes qk

j,i(t)amount of power) depends on water temperature at the start ofthe time interval, temperature of the inlet water (θinlet), currentroom temperature (θa(t)), water flow rate (fr(t)) during timeslot t, volume of the tank (Vtank), tank surface area (Atank) andthe heat resistance of the water tank (Rtank). In this model,there are three terms and some necessary conversions mightbe required to make the units of all these terms consistent.

3) Algorithm for Thermostat Loads: The home controllerof user j receives the aggregated load profile denoted byxj−1 from the grid. The objective of Algorithm 2 again isto reduce the peak load, while respecting (4)–(6) as laid outin the customer’s terms of engagement with the grid. Thereare two inconvenience dimensions (severity and duration) foreach thermostat load. Thermostat loads are considered in asequential order. Each thermostat load can be denied opera-tion at its full rated power for a maximum of tdur

i = �dmaxi /�t

number of time slots in its demanded operation interval.Let bj,i denotes the set of time indexes during which cus-tomer j has demanded thermostat load i. For each thermostatload, the algorithm determines tdur

i local peaks in the inter-val bj,i. Let, tmax

j,i = maxbj,i h and tmax−nj,i , n = 1, . . . , tdur

i + 1

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HASSAN et al.: CUSTOMER ENGAGEMENT PLANS FOR PEAK LOAD REDUCTION IN RESIDENTIAL SMART GRIDS 9

represent the time index corresponding to nth largest localpeak. The time index vector representing the local peaksarranged in descending order is then denoted by tpeak

j,i =[tmax

j,i , tmax−1j,i , . . . , t

max−tduri −1

j,i ]. The objective is to operate thethermostat load i of customer j in its lowest possible state at

time index tmaxj,i , followed by tmax−1

j,i until tmax−tdur

i −1j,i , without

violating the inconvenience severity constraint anywhere inthe demanded interval bj,i. The algorithm starts by switchingOFF the thermostat load i of customer j at all the time indexesin vector tpeak

j,i (i.e., c1j,i(t) = 1, ∀t ∈ tpeak

j,i ). Once the opera-tional states are fixed at the desired time indexes, the algorithmdetermines a sequence of output temperatures denoted byθj,i(t),∀t ∈ bj,i. If the inconvenience severity constraint is notviolated anywhere in the demanded time interval, the algo-rithm will terminate. Otherwise, the algorithm will increasethe operational state of the thermostat load i at the time index

tmax−tdur

i −1j,i (i.e., c1

j,i(tmax−tdur

i −1j,i ) = 0 and c2

j,i(tmax−tdur

i −1j,i ) = 1)

and recomputes the output temperature sequence. This pro-cess is repeated until the inconvenience severity constraint issatisfied everywhere in demanded operational interval of thecustomer. This algorithm ensures that at the highest local peakpoints, the thermostat load is either switched OFF or it is oper-ating in the lowest possible power state. Since least preferenceis given to the lowest local peak points, the thermostat loadmight operate at the full rated power at these points. Thus,for some customers, the algorithm will achieve the inconve-nience duration constraint with strict inequality, in order tosatisfy inconvenience severity constraint in all of its demandedtime slots.5

This algorithm again requires optimization over all devicesorders, since considering thermostat loads in a differentsequence can result in a different amount of peak load reduc-tion. This can be done by executing Algorithm 2 for (I j

T)! timesat home controller of customer j. The number of thermostatloads in every home is limited, therefore, this optimizationstep does not result in significant increase in the complex-ity. For instance, if we assume that every customer has onlytwo thermostat loads (AC and WH), then there are only twodevice orders: AC followed by WH or WH followed by AC,and Algorithm 2 will only be executed twice.

IV. SIMULATION RESULTS

We consider a residential community comprising of1000 homes. Each customer is assumed to have two ther-mostat loads i.e., AC and WH and two shiftable loads i.e.,CD and DW. All other devices contribute toward an essentialbase load. The average daily household energy consumptionis assumed to be about 41 kWh, which corresponds to typ-ical household energy consumption in many U.S. states likeLouisiana, Tennessee, Alabama, etc. The appliance usage and

5The worst case complexity in terms of number of iterations is∑

i∈I jT(K j

i )!

For example, if we consider two thermostat loads per customer each havingfive-states, the worst case complexity of Algorithm 2 is 240 iterations. Weshow in the simulations, that increasing the power states beyond three is notmuch beneficial for peak load reduction. The number of thermostat loads aswell as the power throttling states of devices are generally low, therefore, thiscomplexity is manageable.

Algorithm 2 Algorithm For Thermostat Loads

Initialize: h = xj−1 − ∑

i∈I jT

pj,i, Cj,i = 0,∀i ∈I jT

1: for i ∈ I jT do

2: Determine and arrange in descending order the timeindexes of tdur

i local peaks in the aggregated pro-file h in the time interval bj,i denoted by: tpeak

j,i =[tmax

j,i tmax−1j,i . . . t

max−tduri −1

j,i ]

3: Initialize: k = 0, t + a = tmax−tdur

i −aj,i , a = 1, c1

j,i(t) =1, ∀t ∈ tpeak

j,i , θj,i(t) = 0,∀t ∈ bj,i

4: while |θj,i(t) − θj,i| > �θj,i for any t ∈ bj,i do5: ck

j,i(t + a) = 06: Increment: k = k + 17: ck+1

j,i (t + a) = 18: Determine θj,i using the thermal load model9: if k = K j

i then10: k = 0, a = a + 111: end if12: end while13: pj,i = (Qj,i Cj,i)1K j

i(Note: denotes element-wise

matrix multiplication)14: Update the aggregated load profile: h = h + pj,i15: end for

TABLE IIAPPLIANCE POWER RATING AND USAGE PATTERNS

the power consumption pattern of each device is given inTable II, which are generated using realistic assumptions asgiven in [46] and [47] and also to match a load curve shapefrom the RELOAD database on a typical summer day. TheRELOAD database is an industry accepted database of loadcurve shapes and is used by the electricity module of theNational Energy Modeling System and several authors for theirstudies [36], [48], [49]. The thermostat set points of AC andWH are uniformly distributed random variables in the interval[68 ◦F, 76 ◦F] and [104 ◦F, 120 ◦F]. The resulting aggre-gated load profile of the community is shown in Fig. 3, witha peak load value of 3701 kW. In the simulations, we assumeK j

i = K,∀j, i ∈ I jT and evaluate the impact of two-state, three-

state, and five-state models for AC and WH. The EER valueof AC load is assumed to be 10. We run the simulations inMATLAB and divide the total time duration i.e., 24 h intoT = 288 equal interval time segments (�t = 5 min).

We evaluate the effectiveness of CDPs and PDPs and theimpact of increasing the power throttling states on peak loadreduction in Figs. 4 and 5, respectively. The common planparameters in both these figures are: �smax

CD = 0 min and

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10 IEEE TRANSACTIONS ON SMART GRID

Fig. 3. Aggregate load profile of the residential community.

Fig. 4. Percentage peak reduction achieved by CDPs. y-axis shows themaximum inconvenience durations of AC and WH loads in the format:�dmax

AC − −�dmaxWH . The maximum temperature deviations of AC and WH

loads are shown along the bars in the format: (�θmaxAC − −�θmax

WH ).

Fig. 5. Percentage peak reduction achieved by PDPs. y-axis shows themaximum inconvenience durations of AC and WH loads in the format:�dmax

AC −−�dmaxWH . The scaling factors of AC and WH loads are shown along

the bars in the format: (βAC − −βWH).

�smaxDW = 0 min, θ ref

AC = 80 ◦F, and θ refWH = 96 ◦F. In Fig. 4, we

vary the parameters, which define the temperature deviationsand inconvenience durations of AC and WH loads for CDPs.While in Fig. 5, we vary the scaling factors and inconveniencedurations of AC and WH loads for PDPs. Based on these twofigures, we have the following observations.

1) Increasing the inconvenience durations of AC and WHloads, the temperature deviations in CDPs, the scalingfactors in PDPs, and the number of states of AC andWH loads increase the peak load reduction.

2) When inconvenience durations of AC and WH loadsin CDPs and PDPs are fixed, we observe a marginalpeak load reduction with increasing temperature devia-tions in CDPs and scaling factors in PDPs (also termedas diminishing returns). This is due to the saturationof the inconvenience severity dimension of the plan.Similarly, when temperature deviations of AC and WHloads in CDPs and scaling factors in PDPs are fixed,we again observe diminishing returns when the incon-venience durations of loads are increased. This is due tothe saturation of the inconvenience duration dimensionof the plan.

Fig. 6. Top graph shows the temperature deviations experienced by the ACand WH loads of 100 customers in the community in CDP and PDP. Thebottom graphs show the percentage peak reduction for different schedulingdelays for CD and DW loads in CDPs and PDPs. x-axis of the bottom graphshows the maximum scheduling delays of CD and DW loads in minutes, inthe format: �smax

CD − −�smaxDW .

3) The inconvenience severity dimension saturates at afaster rate compared to the inconvenience durationdimension of the plan for both the CDPs and PDPs.

4) For both CDPs and PDPs, diminishing returns areobserved with an increase in the number of powerthrottling states.

5) There is a tradeoff between the returns on the num-ber of states and inconvenience severity dimension ofthe plan. Plans offering less inconvenience severity (lesstemperature deviations for CDPs and less scaling fac-tors for PDPs) exhibit more gains with the increasein the number of power states. On the other hand,plans with high inconvenience severity, do not offerany significant gains with the increase in the numberof states. In high inconvenience severity plans, interme-diate states are generally not required even if they areavailable, since operating the loads in OFF states savemore power without violating the inconvenience severityconstraints.

In Fig. 6, we plot the impact of scheduling delays of CD andDW loads on the peak load reduction. The CDP plan parame-ters are: AC load (60 min, 2 ◦F, 80 ◦F) and WH load (60 min,4 ◦F, 96 ◦F), while PDP parameters are: AC load (60 min, 0.25,80 ◦F) and WH load (60 min, 0.25, 96 ◦F). The temperaturedeviations experienced by the AC and WH loads of differentcustomers are different in PDP but constant in CDP, which canbe visualized from the top graph in this figure. In these simula-tions, the choice of βAC = βWH = 0.25 in PDPs, results in anaverage temperature deviation of 2.04 ◦F for AC load and 4 ◦Ffor WH load, which match the temperature deviations of 2 ◦Ffor AC and 4 ◦F for WH in CDPs. From the bottom graphs,we can observe that as we increase the scheduling delays,the amount of peak load reduction and the rate of peak loadreduction both increase. Furthermore, PDPs, while offeringmore fair temperature deviations (inversely proportional tothermostat set points), also achieve almost identical peak loadreduction that is obtained by the CDPs.

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HASSAN et al.: CUSTOMER ENGAGEMENT PLANS FOR PEAK LOAD REDUCTION IN RESIDENTIAL SMART GRIDS 11

TABLE IIIIMPACT OF REFERENCE TEMPERATURES ON THE NUMBER OF ELIGIBLE LOADS, AVERAGE TEMPERATURE DEVIATIONS

OVER THE DEMANDED INTERVAL AND % PEAK REDUCTION FOR CDPS AND PDPS

Finally, we study the impact of reference temperature onpeak reduction for CDPs and PDPs and the results are pre-sented in Table III. Common Parameters of CDPs and PDPsare �smax

CD = �smaxDW = �dmax

AC = �dmaxWH = 60 min. CDP

parameters: �θmaxAC = 2 ◦F, �θmax

WH = 4 ◦F. PDP parameters:βAC = βWH = 0.25. In this table, NAC and NWH, respectively,denote the number of AC and WH loads with nonzero incon-venience severity, while θave

AC and θaveWH, respectively, denote the

average temperature deviations experienced by NAC and NWHloads. Different values of reference temperatures result in dif-ferent values of NAC and NWH. As we increase the referencetemperature for AC and decrease that of WH, more peak loadreduction is observed for CDPs and PDPs, since more devicesare controlled. We can observe another tradeoff between thenumber of states and reference temperatures (which impactNAC and NWH) especially for PDPs. When the reference tem-peratures result in less number of ACs and WHs experiencinginconvenience, providing an additional power throttling statecan provide very high performance gains compared to the two-state (basic ON/OFF switching) models. We can also observe asimilar trend (but in lesser magnitude) for CDPs. Furthermore,when θ ref

AC ≥ θj,AC +�θmaxAC ,∀j and θ ref

WH ≤ θj,WH −�θmaxWH ,∀j,

then increasing θ refAC and decreasing θ ref

WH has no further impacton the peak load reduction in CDPs (since there is no furtherimpact on the number and temperature deviations, as evidentfrom the last two rows of Table III). On the other hand, inPDPs, increasing θ ref

AC and decreasing θ refWH always increase the

amount of peak load reduction (since temperature deviationsalso increase).

V. CONCLUSION

In this paper, we have designed two types of customerengagement plan, namely CDP and PDP, which describe thekey inconvenience parameters of flexible loads in terms ofscheduling delays and temperature deviations so as to makethe customers easily understand the inconvenience causedby these plans. To facilitate the grid operator in determin-ing the effectiveness of such plans on peak load reduction,we have developed appropriate DRP algorithms by model-ing the thermostat loads as power throttling devices. Despitethe suboptimality (due to NP nature of the optimization prob-lem), the proposed algorithms have been shown to be able toprovide very clear insights into the design of customer engage-ment plans. Through simulations, we have determined that

increasing temperature deviations result in diminishing returns.We have also observed diminishing returns as the number ofpower throttling states increase. In particular, more peak loadreduction occurs when the number of power throttling statesare increased from 2 to 3 for those DRP plans with less numberof thermostat loads. The temperature deviation from thermo-stat set point cannot exceed the given limit in all the time slots,therefore, with two states, the only option to avoid exceedingthe temperature deviation limit is to turn ON the appliance(consuming full power). On the other hand, the third stateprovides more flexibility and we can avoid exceeding the tem-perature deviation limit by operating the device at 50% power(hence resulting in 50% power reduction) compared to the twostate model.

We also have some recommendations for the design of cus-tomer engagement plans. The grid operator should generallydesign plans with low to moderate inconvenience severity. Ina community with thermostat loads having more fine control(three or more states), the plans that offer low inconvenienceseverities are more beneficial. On the other hand, for a res-idential community with only ON/OFF power control forthermostat loads, more peak reduction can be achieved bydesigning plans with high inconvenience duration of thermo-stat loads and scheduling delay of shiftable loads. PDPs can beoffered to the customers of a residential with highly variablethermostat set point preferences, while CDPs can be offeredto the customers with similar thermostat set point preferences.The grid operator can use the reference temperatures in theplans to control the number of eligible devices. The value ofreference temperatures can also be adjusted by the grid opera-tor depending on the weather patterns, geographical location,user preferences, surveys, etc.

These results can be seen as useful guidelines in proposingfinancial rewards and mutually beneficial incentives, which isan interesting future work. Extending the framework to includemore load categories e.g., electrical vehicles are another inter-esting research direction. Modeling the transient behavior andreducing the additional power consumption due to frequentswitching of thermostat appliances from one power throttlingstate to another might also be an interesting future work.Finally, grid operator may also introduce multiple plans, eachwith different parameters, to cater for the preference of dif-ferent customers. Managing and designing various plans alsoappears to be an interesting future work.

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12 IEEE TRANSACTIONS ON SMART GRID

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Naveed Ul Hassan (S’08–M’10) received the B.E.degree in avionics engineering from the Collegeof Aeronautical Engineering, Risalpur, Pakistan, in2002, and the M.S. and Ph.D. degrees in electri-cal engineering with specialization in digital andwireless communications from Ecole Superieured’Electricite, Gif-sur-Yvette, France, in 2006 and2010, respectively.

Since 2011, he has been an Assistant Professorin the Department of Electrical Engineering,Lahore University of Management Sciences, Lahore,

Pakistan. He was a Visiting Assistant Professor at the Singapore Universityof Technology and Design, Singapore, in 2012 and 2013. His current researchinterests include cross layer design and resource optimization in wireless net-works, demand response management in smart grids, indoor localization, andheterogeneous networks. He has several years of research experience, and hasauthored/co-authored several research papers in refereed international journalsand conferences.

Yawar I. Khalid received the B.S. degree in elec-trical engineering from the Syed Baber Ali Schoolof Science and Engineering, Lahore University ofManagement Sciences (LUMS), Lahore, Pakistan, in2013. He is currently pursuing the Ph.D. degree fromthe Singapore University of Technology and Design,Singapore.

From 2013 to 2014, he was a Research Assistantat LUMS under the supervision of Dr. N. Ul Hassan.His current research interests include demandresponse management in smart grids, renewable

energy integration in existing power grids, and storage in electrical vehicles.

Chau Yuen (S’04–M’06–SM’12) received theB.Eng. and Ph.D. degrees in electrical and electronicengineering from Nanyang Technological University,Singapore, in 2000 and 2004, respectively.

He was a Post-Doctoral Fellow with LucentTechnologies Bell Laboratories, Murray Hill, NY,USA, in 2005. He was a Visiting Assistant Professorat Hong Kong Polytechnic University, Hong Kong,in 2008. From 2006 to 2010, he was a SeniorResearch Engineer at the Institute for InfocommResearch, Singapore. He has been an Assistant

Professor at the Singapore University of Technology and Design, Singapore,since 2010.

Dr. Yuen was the recipient of the IEEE Asia-Pacific Outstanding YoungResearcher Award in 2012. He serves as an Associate Editor for the IEEETRANSACTIONS ON VEHICULAR TECHNOLOGY.

Wayes Tushar (S’06–M’13) received the B.Sc.degree in electrical and electronic engineeringfrom the Bangladesh University of Engineeringand Technology, Dhaka, Bangladesh, and the Ph.D.degree in engineering from Australian NationalUniversity, Canberra, ACT, Australia, in 2007 and2013, respectively.

He is currently a Post-Doctoral Research Fellowwith the Singapore University of Technology andDesign, Singapore. He was a Visiting Researcherat National Information and Communication

Technology Australia (NICTA), Canberra, in 2013. He was a Visiting StudentResearch Collaborator at the School of Engineering and Applied Science,Princeton University, Princeton, NJ, USA, in 2011. His current researchinterests include the signal processing for distributed networks, game theory,and energy management for smart grids.

Mr. Tushar was the recipient of the Best Paper Award in the AustralianCommunications Theory Workshop, 2012, and the IEEE InternationalConference on Communications, 2013.