Outage Management in Residential Demand Response Programs

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Outage Management in Residential DemandResponse Programs

Mohammad Rastegar, Student Member, IEEE, and Mahmud Fotuhi-Firuzabad, Fellow, IEEE

Abstract—This paper proposes a novel optimization basedhome load control (HLC) to manage the operation periods ofresponsive electrical appliances, determine several recommendedoperation periods for nonresponsive appliances, and schedulethe charge/discharge cycling of plug-in hybrid electric vehicle(PHEV) considering various customer preferences. The customerpreferences are in the format of payment cost, interruption cost,and different operational constraints. The projected algorithmis online, in which household appliances are initially scheduledbased on the payment cost, and when the home load is inter-rupted, the scheduling will be updated to minimize customerinterruption cost. Due to vehicle to home capability of PHEV,the home outage can be managed through solving the proposedoptimization problem. Several realistic case studies are carriedout to examine the performance of the suggested method. In addi-tion, the impacts of common electricity tariffs on the HLC resultsare investigated. The results reveal that employing the proposedHLC program benefits not only the customers by reducing theirpayment and interruption costs, but also utility companies bydecreasing the peak load of the aggregate load demand.

Index Terms—Home load control, interruption cost, outagemanagement, payment cost, plug-in hybrid electric vehicle.

NOMENCLATURE

Sets and Indices

a Denotes an appliance.A Set of appliances.t Denotes a period.T Set of periods.j Denotes a nonresponsive appliance.J Set of nonresponsive appliances.k Denotes a responsive appliance whose consumption

level is controlled.K Set of responsive appliances whose consumption

level is controlled.m Denotes an on/off controlled responsive appliance

which can operate interruptedly.M Set of on/off controlled responsive appliances which

can operate interruptedly.n Denotes an on/off controlled responsive appliance

which should operate uninterruptedly.

Manuscript received June 20, 2014; accepted July 4, 2014.Paper no. TSG-00629-2014.

The authors are with the Center of Excellence in Power system Controland Management, Electrical Engineering Department, Sharif University ofTechnology, Tehran 11365-11155, Iran (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.2014.2338794

N Set of on/off controlled responsive appliances whichshould operate uninterruptedly.

Variables and Functions

ch(t) Charging rate of PHEV at period t [kWh].Cost Total cost function [ � c/day].dch(t) Discharging rate of PHEV at period t [kWh].E(t) Total energy consumption at period t [kWh].E•(t) Energy consumption level of appliance (•) at

period t [kWh].I•(t) Binary indicator of appliance (•) status at period

t, where 1 means on and 0 means off.Idcha (t) Binary indicator of supplying appliance a at period

t by PHEV, where 1 means supplying by PHEV.IC Interruption cost function.IC(t) Customer interruption cost at period t.LEa(t) Lost energy of appliance a at period t.NRE(t) Energy consumption of nonresponsive appliances

at period t.PC Payment cost function.PC(t) Customer payment cost at period t.PHE(t) Energy consumption of PHEV at period t [kWh].RE(t) Energy consumption of responsive appliances at

period t [kWh].y•(t) Startup binary indicator of appliance (•) where 1

means becoming on at period t.z•(t) Shutdown binary indicator of appliance (•) where

1 means becoming off at period t.

Constants

b• Beginning period of allowable operation interval ofappliance (•).

c PHEV arrival period to home.cap Capacity of PHEV battery [kWh].chmax Maximum charging rate of PHEV battery

[kWh/period].dchmax Maximum discharging rate of PHEV battery

[kWh/period].Dk Maximum deviation from the maximum value of

energy consumption of appliance k over the periods[kWh].

e• End period of allowable operation interval of appli-ance (•).

E• Energy consumption of appliance (•) at eachperiod [kWh].

Edesk (t) Desired energy consumption level of appliance k

at period t [kWh].

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Emaxk (t) Maximum energy consumption level of appliance

k at period t [kWh].Emin

k (t) Minimum energy consumption level of appliancek at period t [kWh].

Eout PHEV electrical energy consumption in out-of-home interval [kWh].

g PHEV departure period from home.Iout(t) Binary indicator of PHEV, where 1 means PHEV

came back home.NP Number of periods in scheduling horizon.O(t) Binary indicator of home load interruption at

period t, where 1 means home is on outage and0, vice versa.

PHE0 Initial charging level of PHEV battery [kWh].PHEf Final charging level of PHEV battery [kWh].s Switching time [period].U• Number of required operation periods for appliance

(•).ηch AC to DC conversion efficiency for PHEV battery.ηdch DC to AC conversion efficiency for PHEV battery.λ(t) Tariff at period t [ � c].μ• Value of lost energy of appliance (•) [ � c/kWh].

Abbreviations

DR Demand response.HLC Home load control.PHEV Plug-in hybrid electric vehicle.VOLL Value of lost load.V2H Vehicle to home.

I. INTRODUCTION

A. Motivation and Problem Description

DR IS ONE of the prominent programs to realize smartdistribution grid. In the price-based DR, a well-designed

time-varying pricing can be an effective tool for reducing strainon electricity infrastructure, improving energy efficiency, andsaving customer’s money [1], [2]. Recent developments haveshaped DR in various countries, with increasing focus on pro-grams requiring deliberate and informed demand decisions byresidential customers [3]. Experiments show that residentialcustomers can conclusively reduce peak-period energy use inresponse to time differentiated prices, which may lead to lowerpayment cost [4].

The main obstacle to implement DR for residential cus-tomers is the low level of demand side participation [5].Lack of customer’s sufficient knowledge about the mannerof response to the received prices is the main reason of lowparticipation level of customers. New devices such as smartmeters and in-home displays are being introduced into themarket place that would allow customers to know where theirpower is going and what they can do to control usage, lowertheir bills, and help to reduce the carbon footprint [6], [7].However, these devices are not quite enough for the properimplementation of DR programs due to impatience of resi-dential customers to consecutively track the received data andrespond to them. The solution is to design an automatic DRprogram, namely HLC, by which the household appliances

and facilities are scheduled in an optimal manner with mini-mum customer’s intervention. Customer’s preferences shouldbe properly incorporated in the HLC process to encouragethem to actively participate in such programs.

Household appliances are generally classified into twogroups; responsive and nonresponsive [5]. The operation timeof responsive appliances unlike nonresponsive ones can beshifted while is sensitive to time-varying prices.

PHEV technology is an emerging paradigm and a promis-ing solution to some environmental and economical problems.However, utilities are becoming concerned about the overloadsthat may take place in distribution systems due to multipledomestic PHEV charging activities. This issue subsequentlyleads to the higher payment cost, which is also unpleas-ant from the customer’s viewpoint [8], [9]. Accordingly, itseems necessary to incorporate charge scheduling of PHEVsin the HLC program. On the other hand, with the possi-bility of discharging the PHEV battery, an opportunity isprovided to supply the household load at the time of highprice tariffs. This capability is called V2H which conse-quently saves the customer’s money and makes the load profileflatter.

B. Literature Review

Several papers published in recent years have focused onthe modeling, formulation, and results of HLC. To begin with,Du and Lu [10] represent a novel appliance commitment algo-rithm that schedules the load of thermostatically controlledhousehold based on the price and consumption forecasts. Inthis algorithm, time-varying temperature range is specifiedas the user comfort. Reference [11] presents the develop-ment of a home energy management algorithm for controllinghousehold power-intensive appliances including space-coolingunits, water heaters, clothes dryer, and electric vehicles.Koutitas [12] proposes two load control algorithms to changethe operation states of the flexible smart devices to mini-mize both the customer and utility costs. Tsui and Chan [13]try to propose a mathematical model in the format of con-vex programming instead of mixed integer programming todetermine the on/off status of appliances. In addition, [14]mathematically formulates the optimization based HLC con-sists of a set of solar photovoltaic modules, a small windturbine, an energy storage system, an electric vehicle, and aset of controllable appliances. The objective is to minimizeenergy costs in the format of mixed integer linear program-ming from the consumer’s perspective. Samadi et al. [15]propose a novel optimization-based real-time residential loadmanagement algorithm that takes into account load uncertaintyin order to minimize the energy payment for each user. Inthis algorithm, as the demand information of the appliances isgradually revealed over time, the operation schedule of con-trollable appliances is updated accordingly. All of the reviewedpapers conclude that their proposed algorithms reduce thepayment cost as well as the peak load or peak to aver-age ratio. In addition, they consider the customer comfortas an objective function or operational constraints in theirformulations.


RASTEGAR AND FOTUHI-FIRUZABAD: OUTAGE MANAGEMENT IN RESIDENTIAL DEMAND RESPONSE PROGRAMS 3

C. Paper Contribution

To the best of authors’ knowledge, none of the previ-ous researches addresses the customer interruption cost inthe HLC process. Moreover, almost all literatures incorpo-rate the uncontrolled appliances consumptions as fix inputs intheir scheduling programs. However, the preferred operationperiods for nonresponsive appliances can be reported to thecustomer.

In this paper, the procedure and problem formulation ofa novel day-ahead HLC program are proposed to optimallyschedule electrical appliances and a PHEV to minimize thecustomer payment and interruption costs for the next day.Almost all the customers are frequently concerned abouttheir electricity payment cost. Furthermore, in the case ofany electricity service interruptions, customers’ convenienceis inevitably jeopardized as a matter of useless appliances.Therefore, to maximize customer comfort, this paper mini-mizes the customer interruption cost as well as payment costthrough HLC procedure considering operational constraints. Inaddition to the energy consumption of responsive appliancesat each period and charge/discharge scheduling of PHEV,the proposed method in this paper determines several pre-ferred operation periods of nonresponsive appliances. As theoccurrence time of home load interruption is uncertain, HLCshould be effectuated online, i.e., the operation time of appli-ances is firstly scheduled based on the payment cost and thenis rescheduled at the time of interruption occurrence basedon the interruption cost. The V2H capability might bringmore benefits due to supplying load during the high-tariff andinterruption periods.

The impact of HLC at a sample household with commonelectrical appliances and a PHEV is probed in various casesto present informative aspects of the proposed method. Inaddition, the impacts of different time-varying tariffs includ-ing time of use (TOU), inclining block rate (IBR), andcombination of them are investigated on the HLC results.

II. HOUSEHOLD LOAD CLASSIFICATION

In this paper, household electrical loads are classified intotwo main categories of responsive loads such as washers anddryers, and nonresponsive loads such as vacuum cleaner andpersonal computer.

Responsive appliances can be divided into two groups.1) A number of responsive appliances can be controlled in

on/off status. For instance, a washing machine has def-inite electricity consumption in each operation periodand operation periods can be determined by HLC. Inthe set of on/off controlled appliances, some appliancesshould operate uninterruptedly while others can operatein separate periods. For example, if operation time of adishwasher is 60 min, this time should be embedded inthe predetermined allowable interval without any inter-ruption. On the other side, clothes dryer can operate inseparate periods in the allowable interval.

2) The electricity consumption level of some responsiveappliances can be controlled at each period. For exam-ple, the energy consumption level of heating/cooling

system in winter/summer days should be in a definiteinterval at each period to provide proper home tem-perature. HLC can determine the consumption level ofheating/cooling system such that not only guarantees thecustomer comfort but also decreases the customer cost.

In the set of nonresponsive appliances, the recommendedoperation periods are proposed to the customer by HLC. Forexample, if a customer wants to use computer for 3 h between8 A.M. and 10 P.M., HLC will propose him several 3-h periodsas the preferred operation periods during 8 A.M. to 10 P.M.The customer has an authority to turn the nonresponsive appli-ances on during each of the proposed periods based on hispreferences.

III. ONLINE HLC PROCEDURE

In the proposed HLC program, we try to address all thecustomer concerns about the load management. The mostimportant concern that each customer notices at the first glanceis payment cost. Consequently, as the first step of HLC proce-dure, household appliances are scheduled based on minimizingthe payment cost. Payment cost is the product of tariff andelectrical energy consumption at each period. Therefore, min-imizing this cost may result in shifting the energy consumptionfrom high tariff to low tariff periods. In addition to the changein operation scheduling of appliances, the presence of PHEVin HLC leads to a decrease in the cost of supplying load.The reason for this is that PHEV battery can be charged atlow tariff periods and discharged at high tariff ones to supplyhousehold loads.

If the home load is not interrupted, the objective of HLCwill be minimizing the payment cost. If a home load out-age is occurred, the cost of buying the electricity from thegrid will be zero and interruption cost will be the customer’sconcern during the home outage time. The outage occur-rence affects the scheduled operation periods of appliancesand PHEV charging/discharging periods. Subsequently, thescheduling is updated based on minimizing the interruptioncost at the time of outage occurrence. Customer interruptioncost is the product of VOLL and the amount of lost energy.VOLL is determined by the customer and may be different forvarious appliances. In the case of home outage occurrence, thescheduling horizon is the outage time duration, which is esti-mated by the HLC performer. The more accurate the outageduration is estimated, the more the scheduling is optimal. Theload interruption duration is estimated based on the availablehistorical data. If the home load interruption did not finishbefore the estimated time, the scheduling would be updatedbased on the interruption cost for another period and, thiscontinues until the end of home load interruption.

At the end time of home load interruption, HLC is updatedagain based on the payment cost for remaining periods of theday considering the updated statuses of appliances and PHEVat that time. It should be noted that, other customer preferencesare incorporated as constraints in the HLC procedure.

The above procedures are modeled and formulated in theoptimization problem in the next section.



IV. HLC PROBLEM FORMULATION

As described before, to encourage customer to participatein DR programs, customer costs should be considered in theHLC. In a smart home with electrical appliances and a PHEVwith the V2H capability, payment and interruption are thecustomer’s costs. These costs are formulated in the follow-ing subsections to be incorporated in the objective function ofthe optimization problem.

A. Payment Cost

Payment cost is the function of tariff and total electricalenergy consumption at each period. This is mathematicallyformulated as

PC =∑

t∈T

PC(t) (1a)

PC(t) = λ(t)E(t). (1b)

T is the set of scheduling periods in next day and λ(t) isdetermined based on the type of price-based DR programs inwhich the customer participates.

In recent years, the TOU energy price is researched by manyscholars and also implemented by lots of utilities [16], [17].Also, many utilities such as Pacific Gas & Electric (PGE),San Diego Gas & Electric, and the Southern California Edisoncompanies have used IBR pricing for years [18], [19].

Mathematical formulation of the three-level TOU tariff, IBRtariff, and their combination are, respectively, shown in

λTOU(t) =⎧⎨

⎩

λ1 if t ∈ T1λ2 if t ∈ T2λ3 if t ∈ T3

(2)

λIBR(t) ={

α 0 ≤ E(t) ≤ γ

β E(t) > γ(3)

λTOU&IBR(t) =

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

⎧⎨

⎩

α1 t ∈ T1α2 t ∈ T2α3 t ∈ T3

0 ≤ E(t) ≤ γ

⎧⎨

⎩

β1 t ∈ T1β2 t ∈ T2β3 t ∈ T3

E(t) > γ

(4)

where, in (2) and (4), T1, T2, and T3 are, respectively, the setof off-peak, mid-peak, and on-peak tariff periods during a day.So, T1

⋃T2

⋃T3 = T . In (2), λ1, λ2, and λ3 are, respectively,

tariffs at off-peak, mid-peak and on-peak periods during a day.So, λ1 ≤ λ2 ≤ λ3. In (3), α and ββ are the price of energyconsumption lower and higher than the threshold γ (kWh)at each period, respectively. In (4), {α1, β1}, {α2, β2}, and{α3, β3} are, respectively, the price rates of off-peak, mid-peak,and on-peak periods. So, α1 ≤ α2 ≤ α3 and β1 ≤ β2 ≤ β3.Energy consumption more than the predetermined thresholdvalue, γ , is calculated by price βq,∀q ∈ {1, 2, 3} and theelectrical consumption lower than or equal to γ is calculatedby price αq,∀q ∈ {1, 2, 3}. αq is clearly lower than βq.

B. Interruption Cost

Customer interruption cost is the summation of the productof appliances’ VOLL and the amount of energy lost at each

period. This is formulated in

IC =∑

t∈T

IC(t) (5a)

IC(t) =∑

a∈A

μaLEa(t) (5b)

where, μa is the VOLL of appliance a, determined by the cus-tomer, and LEa(t) is the lost energy of appliance a at period t.LEa(t) will be zero if appliance a is supplied by the gridor PHEV.

C. Objective Function and Constraints

As described in the HLC procedure, the objective func-tion before and after the load interruption interval is paymentcost and during that is interruption cost. So, the objectivefunction is

min Cost =∑

t∈T

[O(t)IC(t) + (1 − O(t))PC(t)]. (6)

O(t) is the binary indicator of home outage at period t.When a household load interruption occurs, the objective func-tion is minimizing interruption cost during the outage time;otherwise, payment cost will be minimized. Payment and inter-ruption costs were, respectively, formulated in (1) and (5a).

Energy consumption at period t consists of energy con-sumption of nonresponsive appliances (NRE(t)), energy con-sumption of responsive appliances (RE(t)), and PHEV energyconsumption (PHE(t)). This is mathematically explained in

E(t) = NRE(t) + RE(t) + PHE(t). (7)

E(t) is the amount of energy purchased from the grid,which may be capped to a maximum value due to technicalconstraints.

Energy consumption of nonresponsive appliances is formu-lated as

NRE(t) =∑

j∈J

Ej(t) (8)

where

Ej(t) = Ij(t)Ej. (9)

Ij(t) is one of the decision binary variable of HLC wherebythe preferred operation periods of nonresponsive appliancesare reported. Each nonresponsive appliance has a definite oper-ation time. For example, a vacuum cleaner (VC) should be onfor 30 min to do its task properly. Therefore, the operationtime of vacuum cleaner is 30 min and this time should bethroughout its allowable operation interval ([bVC, eVC]). Sincewe want to recommend several 30-min intervals to the cus-tomer, the determined operation time is exposed by factor f inthe formulation. So

∑

t∈[bj,ej]

Ij(t) = f Uj. (10)

It is assumed that the operation periods of nonresponsiveappliances should be consecutive. Therefore

t+Uj−1∑

h=t

Ij(h) ≥ Ujyj(t), ∀t ≤ NP − Uj + 1. (11)



The relations between yj(t) and zj(t), which are the startupand shutdown indicators, and Ij(t) are according to

zj(t) + yj(t) ≤ 1 (12)

yj(t) − zj(t) = Ij(t) − Ij(t − 1). (13)

K is the set of responsive appliances whose consumptionlevel is controlled. In addition, M and N are considered asthe sets of on/off controlled responsive appliances; in set M,appliances can operate interruptedly while, in set N, appliancesshould uninterruptedly operate. Equation (14) illustrates thetotal energy consumption of responsive appliances at period t

RE(t) =∑

m∈M

Em(t) +∑

n∈N

En(t) +∑

k∈K

Ek(t) (14)

where

Em(t) = Im(t)Em (15)

En(t) = In(t)En. (16)

For on/off controlled appliances, the energy consumptionper each operation period is fixed and operation periods(Im(t) and In(t)) are determined by solving the problem.For appliances in set K, the energy consumption level ateach period (Ek(t)) is resulted by solving HLC problem.Equations (17)–(22) are the operational constraints related toresponsive appliances

∑

t∈[bm,em]

Im(t) = Um, ∀m (17)

∑

t∈[bn,en]

In(t) = Un, ∀n (18)

t+Un−1∑

h=t

In(h) ≥ Unyn(t), ∀t ≤ NP − Un + 1, ∀n (19)

zn(t) + yn(t) ≤ 1, ∀n (20)

yn(t) − zn(t) = In(t) − In(t − 1), ∀n (21)

Emink (t) ≤ Ek(t) ≤ Emax

k (t), ∀k. (22)

Equations (17) and (18) guarantee the required oper-ation periods for proper operation of responsive appli-ances. Equation (19) warrants the uninterruptible operationof responsive appliances in set N. The relation betweenstartup/shutdown indicators and the status of appliance n ispresented in (20) and (21). The energy consumption level ofappliance k is limited in (22).

Consider that heating/cooling system is one of the mem-bers of set K (set of responsive appliances whose consumptionlevel is controlled). It is assumed that, in addition to (22)that determines minimum and maximum level for the energyconsumption, the customer can determine desired energy con-sumption level (Edes

k (t)) for heating/cooling systems accordingto desired room temperature. Providing customer comfort, thesummation of deviation from the desired value of energyconsumption is capped to a definite value (Dk). This ispresented in

∑

t∈T

∣∣∣Edesk (t) − Ek(t)

∣∣∣ ≤ Dk , ∀k. (23)

The desired value can be determined based on the his-torical home temperature profile and energy consumption ofheating/cooling systems [10].

According to (24), PHE(t) consists of charging and dis-charging components, which are divided or multiplied by theconversion efficiencies

PHE(t) = 1

ηchch(t) − ηdchdch(t) (24)

where, the minus sign of the discharged energy (dch(t)) showsV2H capability of PHEV.

PHEV is out of home in a predetermined interval, i.e.,[g, c

].

During this interval, PHEV consumes the determined electri-cal energy, Eout. Since ch(t) and dch(t) are, respectively, theamount of in-home charging and discharging, they would bezero during the out-of-home interval.

Before the departure period, g, the PHEV owner usuallyexpects to have a fully charged battery. So

g−1∑

t=1

(ch(t) − dch(t)) + PHE0 = cap. (25)

Discharging energy should be lower than the PHEV batterycharge state as presented in

dch(t) ≤ PHE0 +t−1∑

h=1

(ch(h) − dch(h)) − Iout(t)Eout (26)

where, Iout(t) is a binary variable which is 1 after the arrivalperiod of PHEV, i.e., period c. The right hand side of (26)shows the state of PHEV battery charge at each period.

As another constraint related to PHEV, the charging anddischarging rates are restricted to a maximum level by

ch(t) ≤ chmax (27)

dch(t) ≤ dchmax. (28)

In (29), the battery charge level at the end of schedulinghorizon is enforced to be PHEf

∑

t∈T

(ch(t) − dch(t)) − Iout(NP)Eout + PHE0 = PHEf . (29)

Also, charge state of battery should not exceed the PHEVbattery capacity. So

PHE0 +t−1∑

h=1

(ch(h) − dch(h)) − Iout(t)Eout ≤ cap. (30)

Up to here, payment cost, the household electrical energyconsumption, and related constraints have been entirely mod-eled and formulated. Interruption cost and the associatedoperational constraints are described below to complete theoptimization formulation.

As presented in (5), IC(t) is the function of lost energy ofappliances in each period and the value of lost energy. Thelost energy of appliance a during the load interruption time,at period t, is calculated by

LEa(t) = Ea(t)[(1 − Idcha (t)) + s(1 − Idch

a (t − 1))Idcha (t)]O(t).

(31)



Idcha (t) is one of the decision binary variables, where 1

means that appliance a is supplied by discharging PHEV atperiod t during the outage, and s is the time of switching fromthe grid to PHEV for supplying load. s is given in terms ofperiod. According to (31), if appliance a is not supplied byPHEV at period t-1 and is supplied by PHEV at period t, i.e.,Idcha (t − 1) = 0 and Idch

a (t) = 1, so, LEa(t) = Ea(t)s. If PHEVsupplies appliance a at both periods t and t-1, LEa(t) willbe zero.

The summation of Ea(t) Idcha (t) over all the appliances is

the amount of discharged energy of PHEV at period t duringthe outage time. This is mathematically presented in

∑

a∈A

Idcha (t)Ea(t) = dch(t). (32)

Considering V2H capability, PHEV can supply the appli-ances which have been scheduled to be on during the outagetime. So

Idcha (t) ≤ Ia(t). (33)

Interruption cost is minimized during the home load inter-ruption considering the value of lost energy of each applianceand operational constraints of PHEV mentioned before. Thisleads to outage management through HLC Program.

The proposed problem is in the mixed-integer programming(MIP) format since various high-performance solvers are avail-able to deal with them. We use the CPLEX solver 11.2.0 forsolving the proposed model.

V. NUMERICAL STUDY

This section analyzes the proposed HLC formulationthrough different case studies. The designed cases are simpleenough to deeply investigate different aspects of the pro-pounded HLC. In the following, after describing the variousrequired assumptions, we probe three cases.

1) Case 1: A home without HLC.2) Case 2: Case 1 with HLC and without load interruption.3) Case 3: Case 2 with load interruption.In these cases, TOU is assumed as the incorporated tariff.

The impact of IBR pricing, and combination of TOU and IBRtariffs are also investigated on the results of HLC at the endof this section. The results are probed from the customer andutility points of view by, respectively, reporting total cost andpeak load.

A. Assumptions

HLC is solved for the next day (24 h). The schedulingperiod is considered 10 min. Therefore, number of periods(NP) is 144 periods. The given home has typical electricalappliances whose data for a typical day are separately foundin Tables I and II.

Tables I and II outline the energy consumption per oper-ation period (Ea), the number of operation periods (Ua), thebeginning (ba), and the end periods (ea) of allowable operationinterval for each appliance. For nonresponsive appliances, f isassumed 3.

TABLE INONRESPONSIVE APPLIANCES DATA [20]

TABLE IION/OFF CONTROLLED RESPONSIVE APPLIANCES DATA [20]

TABLE IIIMAXIMUM AND MINIMUM ENERGY CONSUMPTION FOR

HEATING SYSTEM

TABLE IVPHEV DATA

In addition to the mentioned appliances in Tables I and II,heating system is assumed as the responsive appliance whoseconsumption level is controlled. Based on the standard temper-ature for a room in a typical winter day according to customerrequest, Emax

Heating(t) and EminHeating(t) for different periods are

assumed as Table III.Desired energy consumption of heating system (Edes

Heating(t))to provide proper room temperature at period t is assumed tobe equal to Emax

Heating(t). DHeating, which is the deviation fromEmax

Heating(t), is assumed to be 0.36 kWh for the day. Also, valueof lost energy of appliance a (μa) is assumed 20 � c/kWh forall appliances.

PHEV specifications in the smart home are outlined inTable IV.

According to Table IV, out of home interval of PHEVis [49, 96] in which in-home PHEV charging/discharging isnot possible. Since the final charging level of a PHEV ina day is the initial charging level of the next day, in thispaper PHEf and PHE0 are assumed to be the same and equalto 3.9 kWh.

Related parameters associated with the introduced three-level TOU tariff are reported in Table V.

In addition to the customer costs, peak load is reportedin the following case studies. Although the customer doesnot concern about the peak load issue, it is an impor-tant factor for the operator of distribution system for futuredecision-making.



TABLE VTOU TARIFF PARAMETERS

Fig. 1. Household load in Case 1.

B. Case 1

In this case, the household load of a typical home withaforementioned appliances and a PHEV is modeled. Theoperation periods of the appliances should be placed in thedetermined allowable operation intervals. The consumptionlevel of heating system is assumed to be at its maximumvalue (desired value). Also, it is assumed that PHEV is chargedwith its maximum rate of charging from the plug-in time. Theplug-in time is supposed to be the arrival period of PHEV(period 96) and PHEV is initially assumed fully charged inthis case (PHE0 = cap). V2H is not possible in this uncon-trolled case. A sample result of appliance consumption isdrawn in Fig. 1.

If the customer consumes according to Fig. 1 and the tar-iff is abovementioned TOU tariff, payment cost for electricalenergy consumption in a day will be � c 173.99 and the peakload will be 4.435 kW. The previous studies on the house-hold load, [8] and [21], have shown that the usual peak loadof the residential customer is near 2.5 kW. Higher peak loadin Case 1 than the literatures is due to coinciding PHEVcharging periods and the peak of household consumption inthis case.

If a home load interruption happened, interruption costwould be imposed to the customer. For example, assume that ahome outage is occurred during periods 115–126. During thisinterval, according to the sample consumption in Fig. 1, tele-vision and personal computer are on, respectively, for ten andsix periods. In addition, heating system consumes 0.03 kWhduring these periods. Consequently, customer interruption costwill be � c 38.36 based on μa = 20 � c/kWh.

C. Case 2

In this case, a smart home with the aforementioned appli-ances and a PHEV is considered to probe the results ofapplication of the proposed HLC. The scheduling horizonis a day, 144 periods. It is assumed that, in this case, theload is not interrupted during the day. Therefore, the objec-tive function is only minimizing payment cost during theday. The output of applying HLC is operation schedules for

TABLE VIOPERATION PERIODS OF APPLIANCES IN CASE 2 WITHOUT V2H

TABLE VIIOPERATION PERIODS OF APPLIANCES IN CASE 2 WITH V2H

TABLE VIIIENERGY CONSUMPTION OF HEATING SYSTEM IN CASE 2 WITHOUT V2H

TABLE IXENERGY CONSUMPTION OF HEATING SYSTEM IN CASE 2 WITH V2H

responsive appliances, recommended operation periods fornonresponsive appliances, and charging/discharging schedulefor PHEV.

The operation/preferred operation periods of appliances,extracted from solving the problem with and without consid-ering V2H are, respectively, shown in Tables VI and VII. Inaddition, consumption levels of heating system in these twomodes are presented in Tables VIII and IX.

The results certify that all appliances operate/preferablyoperate in allowable intervals mentioned in Tables I and II.Also, the consumption levels of heating system inTables VIII and IX are in the mentioned range in Table III.With or without V2H, the operation periods of appliancesand the consumption level of heating system are generallyin the possible lowest tariff periods among their allowableoperation intervals. For example, allowable operation intervalof coffee maker includes low and medium tariff periods; butoperation periods of coffee maker resulted from HLC are lowtariff periods, periods 41 and 42. PHEV charging/discharginglevels in Case 2 are reported in Figs. 2 and 3. In thesefigures, the PHEV charging/discharging is illustrated as thepositive/negative load.



Fig. 2. PHEV charging in Case 2 without V2H.

Fig. 3. PHEV charging/discharging in Case 2 with V2H.

According to Fig. 2, in the mode without V2H, PHEVis charged at periods 1–17 to fully charge the PHEV bat-tery before the departure time (period 49). These periods areexpectedly low tariff periods. In this mode, at the arrival periodof PHEV (period 96), the battery charge level is 2.8 kWh;so, PHEV is charged in the late periods of the day to reachexpected 3.9 kWh charge level. According to Fig. 3, in themode with V2H, PHEV is expectedly charged during low tar-iff periods and discharged during high tariff ones. This leadsto lower payment cost for the customer. The resulted paymentcost without and with V2H are, respectively, � c 135.32 and� c 132.98. In comparison to Case 1, payment cost is descendedin this case. In the mode without V2H, the reduced cost is justthe result of controlling the operation periods of appliancesand charge scheduling of PHEV. Considering V2H capability,supplying the household load by PHEV in high tariff periodsalso leads to cost decrement.

The household loads with and without V2H are depicted inFig. 4. In this figure, nonresponsive appliances, i.e., vacuumcleaner, television, and personal computer were, respectively,assumed to be on at periods 140–142, 127–144, and 133–144,without V2H. In addition, in the mode with V2H, these non-responsive appliances were, respectively, assumed to be on atperiods 142–144, 127–144, and 133–144.

The peak load in Case 2 without V2H is 3.4 kW, which islower than the previous case due to shifting consumption frommedium and high consumption periods to lower ones. In themode with V2H, PHEV is discharged in high tariff periodsto more benefit the customer, and recharged instead in lowertariff periods to provide required charge of the battery at theend of the day. This leads to the peak load of 3.8 kW, which,


TABLE XENERGY CONSUMPTION OF HEATING SYSTEM DURING THE HOME

OUTAGE

although it is lower than that of Case 1, is higher than themode without V2H.

D. Case 3

In this case, it is assumed that the household load is inter-rupted at period 115. The home outage duration is estimated2 h, 12 periods, based on the previous database. In addition,it is assumed that the home outage finishes at the predictedperiod, period 126. The result of HLC before period 114is the same as Case 2. At period 115 the HLC is updatedbased on interruption cost during periods 115–126. Afterperiod 126, the scheduling is again determined based on thepayment cost.

Since the value of lost load of appliances, 20� c/kWh, islarger than tariff prices, PHEV tries to supply the applianceswhich have been scheduled to be on based on the payment costduring the load interruption interval. As reported in Case 2with V2H, clothes dryer has been scheduled to be on at peri-ods 121 and 125 which are coincides with the householdload interruption. In addition, consumption levels of heat-ing system have been scheduled to be 0.025 and 0.030 kWhat, respectively, periods 115–120 and 121–126. Other appli-ances have been scheduled to be off during these periods.The result of Case 2 showed that the state of PHEV batterycharge is 1.627 kWh at period 114. As the discharging rateof PHEV is capped to 0.233 kWh, considering the efficiency,near 0.205 kWh energy can be supplied by PHEV during eachperiod of home outage interval. Also, s is assumed 0.05 ofperiod in this case.

The result of solving HLC problem during the load inter-ruption shows that clothes dryer is supplied by PHEV inprescheduled periods, i.e., 121 and 125, and consumptionlevels of heating system are as presented in Table X.

Interruption cost will be equal to � c 1.2. The comparisonbetween this cost and the interruption cost presented in Case 1( � c 38.36), certifies the effective roll of V2H in home outagemanagement.



TABLE XIOPERATION PERIODS OF APPLIANCES IN CASE 3 AFTER OUTAGE


HLC is effectuated again after the home load interruptionto achieve the optimal solution for remaining periods in theday. The PHEV battery charge level after the home outage,at period 127, is 0.888 kWh. This charge level is assumedas the initial charging level of PHEV for the new schedulinghorizon. The new scheduling horizon is periods 127 to 144.It should be noted that, washing machine, dishwasher, andcoffee maker have done their tasks before home outage occur-rence; so they are omitted from the new HLC. In addition,clothes dryer has operated two periods before period 127;so, its required operation periods for proper operation are 3.Another update is required for the allowable deviation of heat-ing system (Dheating) according to abovementioned schedulesbefore period 127. It is updated to 0.095 kWh for the remain-ing periods in this case. Considering these constraints andother operational constraints of PHEV, HLC program resultsin the appliance operation periods as Table XI.

Energy consumption of heating system after the load inter-ruption is 0.025 kWh at each period.

The household load is illustrated in Fig. 5 based on thereported solution of HLC in Case 3.

According to Fig. 5, before the home load interruption, thehousehold load is the same as Case 2. The peak load is 3.36kW, which is expectedly lower than the peak load in Case 1.Payment cost is � c 137.782 for a day. This shows that, althoughthe load interruption changes the primary optimal schedul-ing, the outage management prohibits the high increment inpayment cost compared with Case 2.

E. Impacts of Different Pricings on HLC Results

In this subsection, impacts of incorporating TOU tariff, IBRtariff, and combination of them in HLC on the payment costand the household load are investigated. In these studies, theload interruption is not considered but V2H capability is takeninto account.

In defined IBR tariff in (3), α is assumed 0.9 of the averagetariff in specified TOU tariff in Table V, and β is set to 1.4

TABLE XIIIBR+TOU TARIFF DATA

Fig. 6. Household loads incorporating different pricings.

TABLE XIIIHLC RESULTS INCORPORATING DIFFERENT TARIFFS

of α value. According to Table V, average tariff is � c 12.312.So, α = � c 11.081 and β = � c 14.774.

In the defined tariff in (4) which is the combination of TOUand IBR tariffs, α1, α2, and α3 are, respectively, set 0.9 ofλ1, λ2, and λ3 during T1, T2, and T3. Also, β1, β2, and β3will be set 1.4 of α1, α2, and α3, respectively. γ is assumed0.5 kWh which is equal to 3 kW load. These parameters areconcluded in Table XII.

Household load incorporating TOU tariff was presentedbefore, in Fig. 4. Loads by incorporating IBR tariff andcombination of IBR and TOU tariffs are presented in Fig. 6.

Payment cost and peak load resulted from applying HLCare presented in Table XIII.

The results show that the load is distributed during the dayby incorporating IBR pricing, due to higher tariffs for the con-sumption beyond the threshold. In addition, incorporating IBRmakes peak load limit to the threshold.

Due to low value of α1, the consumption is shifted to theseperiods in the case of considering the combination of IBRand TOU tariffs. Consequently, payment cost and the peakload are, respectively, decreased 10.5% and 21% compared tothe case with TOU application.

VI. CONCLUSION

This paper proposes a novel online HLC to determine opti-mal operation scheduling of electrical appliances and a PHEV,considering entire customer preferences and operational con-straints. Customer’s concerns about payment and interruptioncosts are addressed in this paper. V2H capability of PHEVis also employed in the HLC procedure to manage the homeoutage. Outputs of the HLC problem are energy consumption



of responsive appliances at each period, preferred operationperiods of nonresponsive appliances, and charge/dischargescheduling of PHEV. The results show that employing HLCprogram lowers payment cost about 22% by controlling theoperation periods of appliances. In addition, V2H capabilityof PHEV lowers payment cost as well as interruption cost ofthe customer. The results verify that the peak load is descendedin case of applying HLC. In addition, the impacts of incorpo-rating different familiar household tariffs on HLC results showthat applying IBR to TOU tariff not only makes payment costlower, but also limits the peak load. The results also show thatthe savings of up to � c 55 per day on payment cost and 1.5 kWon household peak demand can be achieved by applying IBRtariff, while maintaining the customer’s satisfaction.

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Mohammad Rastegar (S’12) received the B.S. and M.S. degrees in electricalengineering from the Sharif University of Technology, Tehran, Iran, in 2009and 2011, respectively, where he is currently pursuing the Ph.D. degree fromthe Electrical Engineering Department.

His current research interests include power system reliability, smart grid,and residential demand response programs.

Mahmud Fotuhi-Firuzabad (F’14) received the B.Sc. and M.Sc. degrees inelectrical engineering from the Sharif University of Technology, Tehran, Iran,and the University of Tehran, Tehran, in 1986 and 1989, respectively, andthe M.Sc. and Ph.D. degrees in electrical engineering from the University ofSaskatchewan, Saskatoon, SK, Canada, in 1993 and 1997, respectively.

He is currently a Professor and Head of the Electrical EngineeringDepartment, Sharif University of Technology.

Dr. Fotuhi-Firuzabad is a member of the Center of Excellence in PowerSystem Control and Management. He serves as an Editor of the IEEETRANSACTIONS ON SMART GRID and the Guest Editor-in-Chief of a specialissue (Microgrids) of the IEEE TRANSACTIONS ON SMART GRID.

http://www.ieso.ca/imoweb/siteshared/tou_rates.asp

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Outage Management in Residential Demand Response Programs