Home Energy Management Systems: A Review Of Modelling and ... · Home Energy Management Systems: A...

Home Energy Management Systems: A Review OfModelling and Complexity

Marc Beaudina,b, Hamidreza Zareipoura,c

aDepartment of Electrical and Computer Engineering, University of Calgary, 2500

University Dr. NW, Calgary AB T2N 1N4

bE-mail: [email protected], Phone: +1 (347)-669-4319

cE-mail: [email protected], Phone: +1 (403)-210-9516

Abstract

The increasing demand for electricity and the emergence of smart grids havepresented new opportunities for home energy management systems (HEMS) indemand response markets. HEMS are demand response tools that shift andcurtail demand to improve the energy consumption and production profile ofa dwelling on behalf of a consumer. HEMS usually create optimal consump-tion and production schedules by considering multiple objectives such as energycosts, environmental concerns, load profiles, and consumer comfort.

The existing literature has presented several methods, such as mathemat-ical optimization, model predictive control, and heuristic control, for creatinge�cient operation schedules and for making good consumption and productiondecisions. However, the e↵ectiveness of the methods in the existing literaturecan be di�cult to compare due to diversity in modelling parameters, such asappliance models, timing parameters, and objectives.

The present paper provides a comparative analysis of the literature on HEMS,with a focus on modelling approaches and their impact on HEMS operations andoutcomes. In particular, we discuss a set of HEMS challenges such as forecastuncertainty, modelling device heterogeneity, multi-objective scheduling, compu-tational limitations, timing considerations, and modelling consumer well-being.

The presented work is organized to allow a reader to understand and com-pare the important considerations, approaches, nomenclature, and results inprominent and new literary works without delving deeply into each one.

Keywords: Home energy management system, appliance models, householddevice models, smart home, optimal residential energy management, net-zerohomes, home energy scheduling, smart grid

1. Introduction

Society is concerned about the potential consequences of greenhouse gasemissions, and is becoming increasingly aware of how energy consumption is re-lated to climate change. Furthermore, the cost of energy is rising due to growing

Preprint submitted to Elsevier December 22, 2014

demand and limited supply. In particular, the cost of electricity has increasedsince the deregulation of the power industry in many regions [1]. The electric-ity sector is facing challenges in expanding power generation and transmissioninfrastructure. The debates over high voltage transmission lines in Alberta arean example [2]. In addition, it is increasingly di�cult to add electric generationunits, as thermal generation produce CO2 emissions, nuclear power has issueswith nuclear proliferation and plant meltdown, and new hydro dams are di�cultto place because the optimal sites are already used.

As a result, improved demand response is being considered an importantelement of the portfolio of solutions to the society’s energy crisis [3], consid-ering the capabilities of the smart grids [3, 4]. Demand response has gainedsome penetration within the electricity market, and is defined as “intentionalelectricity consumption pattern modifications by end-use customers that are in-tended to alter the timing, level of instantaneous demand, or total electricityconsumption” according to [5].

However, due to the lack of the necessary electricity grid communicationinfrastructure [6] and incentive system to allow proper consumer participation,shifts in consumer behavior are minimal. Since billing is based on a monthlyaverage rate aggregated over a large number of customers [7] rather than re-flective of the fluctuations in power pool prices, residential consumers do notbenefit from changing their energy demand at critical times. Several alternativepricing schemes such as time-of-use [8–10], real-time-pricing [5, 7, 8, 11], incre-mental block rates [12], critical peak pricing [5, 7, 8], and demand charges [7]have been evaluated to address electricity pricing issues. However, electricityprices are not the only drivers that a↵ect demand response participation rates,i.e., residential consumers do not want to spend time to analyze consumptiondecisions and micro-manage household devices to save money.

Thus, implementation of smart technologies increases the responsiveness ofresidential electricity consumers [8, 13]. For example, demand reductions dur-ing the peak period are larger by 22% in time-of-use pricing, and by 10-27% incritical peak pricing when additional technology is included in the the pricing ex-periment [8]. Based on the data in [8], the price elasticity of demand increasesby 47%-113% when smart technologies are included. The responsiveness in-creases in the presence of smart technology because specialized technology, suchas a residential energy management system (HEMS), is in a better position thanhumans to evaluate the uncertainties of prices, demand, and external variables,and to plan for an appropriate response without human intervention.

Briefly, a HEMS is a demand response tool that shifts and curtails demandto improve the energy consumption and production profile of a house accordingto electricity price and consumer comfort. The HEMS can communicate withhousehold devices and the utility, as needed, and receive external information(e.g., solar power production, electricity prices, etc.) to improve the energyconsumption and production schedule of household devices. The HEMS findsthe optimal operation schedule by using a scheduling algorithm, and dispatchessignals appropriately. One such scheduling algorithm is the MWA found in [14].

The literature has not yet converged on a single term to describe a unit

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that improves the energy consumption and production pattern by managingdevices or appliances in a home. While the names used to describe these systemsare inconsistent across the literature, the names “Energy management system”(EMS), “Home energy management system” (HEMS), and “Residential energymanagement system” (REMS) are used with higher frequency, as shown in Table1.

A HEMS could reduce operational cost of electricity by 23.1% (mean of 25references in Table 2), or reduce residential peak demand by 29.6% (mean of 18references in Table 2). In addition, according to [64], other advantages of us-ing HEMS include minimization of energy wastage, reduce household occupantintervention, be eco-friendly, and improve resident well-being.

There are numerous survey and review papers on HEMS and smart gridsecurity [76, 77], communications infrastructure [64, 75, 78, 79], building controlarchitecture [80], smart grids [79, 81], and demand response [7, 8, 81], as wellas general scheduling, optimization, and modelling approaches [82–86]. Someworks also partially survey the HEMS literature [87, 88]. However, this paperfocuses on the reviewing the modelling and complexity framework in HEMS.

In this paper, we review the current state of residential energy schedul-ing within the literature, and bring new discussions to contextualize modellingoptimal scheduling of residential energy operations. We summarize the cur-rent state, challenges, and approaches of modelling household device, multipleobjectives of the occupants, uncertainty pertinent to residential energy con-sumption (e.g., electricity prices, weather forecasts, occupant behaviour), andinfrastructure implications. In addition, we expand on the previous discussionson describing the implications and impacts of computational limitations on res-idential energy scheduling models.

There are two major contributions associated with this work. First, we pro-vide an in-depth review of the modelling approaches for HEMS. This can act asa rapid reference to improve access to the pertinent literary works, and avoid du-plication of research. Second, we summarize the computational considerationsassociated with modelling HEMS. This may be useful for helping HEMS imple-mentation and research as it gives insight on the trade-o↵s between schedulingoptimality and complexity.

The remainder of this work is described as follows: In Section 2, we describethe challenges associated to HEMS, with a focus on modelling. In Section 3, wediscuss the modelling approaches used for HEMS in the literature. In Section4, we discuss complexity and computational considerations for HEMS models.Finally, we conclude our work in Section 5.

2. Understanding the challenges of home energy management sys-tems

2.1. Diversity of residential electrical devices

There is a multitude of electrical devices in each household, and there is sig-nificant diversity in the ownership rates of di↵erent devices, as shown in Table 3.

3

Table 1: Names for HEMS in literatureName ReferencesActive Demand-side management sys-tem

[15]

Central hub controller [16]Controller [17–19]Demand-side control unit [20]Demand-side management system [21]Energy box [22, 23]Energy consumption control unit [24]Energy consumption scheduler [25, 26]Energy management controller [27]Energy Management System [5, 28–33]Energy scheduler [12]ESTIA [34]Expert and predictive system [35]Gateway System [7]Home automation system [36, 37]Home energy controller [38]Home Energy Management device [39, 40]Home energy management system [41–44]Home energy management unit [45]Home Gateway [46]Load Manager Household [47–49]MavHome [50, 51]Optimized Energy Management Sys-tem

[52]

Power scheduler [53]Residential Energy Management Sys-tem

[14, 54–57]

Residential Energy System [58]Scheduler [9, 59]Smart Energy Management System [60]Smart home controller [61]Smart scheduler [62]Smart scheduling device [63]

4

Table 2: E�ciency of HEMS

Ref. CostReduction

PeakReduction

Tari↵ structure

[62] 4.2-11% real-time pricing, feed-in tari↵s, netsale;

[63] 18-22% 20-25% real-time pricing[41] 25-28% time-of-use pricing[16] 20% 50% real-time pricing[65] 24-27% real-time pricing[28] 15.86% real-time pricing[34] >10.9% real-time pricing[61] 7% time-of-use pricing[60] 20% real-time pricing[17] 12% real-time pricing[53] 16-23%[59] 30-40% real-time pricing[66] 7.8%[52] 38%[67] 57-60% 25.5-61.2% Flat rates, real-time pricing[23] 5-38% real-time pricing[29] 21.70% real-time pricing[38] 26-30%[45] 20-80% real-time pricing[12] 1.3-25% inclining block rates[25] 18% 17%a quadratic cost[26] 37.% 38.1%a quadratic cost[18] 30%[68] 7.2-42%[69] 18% time-of-use pricing[70] <49.7% time-of-use pricing, peak demand

charge[57] 17.7-20.1% time-of-use pricing[24] 15.7% 25.5%a inclining block rates, real-time pricing[71] 25% time-of-use pricing[72] 50-90%[73] 16-34.8% real-time pricing[40] 12-50% real-time pricing[74] >12% 35-40% time-of-use pricing[33] 23.7% 31.3%a inclining block rates, real time pricing[75] 42%Mean 23.1% 29.6%

aDenotes Peak to average ratio reduction

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For example, 45.6% of Canadian households do not own a portable stereo, while42.3% of households own one, 9.7% own two, and 2.3% own three or more. Fur-ther, there is a significant heterogeneity in the power consumption/productionand quantity of use of di↵erent devices, as evidenced by [89]. Factors that con-tribute to the diversity and the energy consumption pattern of devices includedwelling characteristics, lifestyle, a✏uence, and occupancy. Here, we explicitlychoose to use the word device rather than appliance to include energy storageunits, electric vehicles, and energy producers under the scope of the HEMS.

Thus, it is important for the HEMS to be flexible in its architecture, suchthat each HEMS can coordinate the schedule of multiple unique devices. Indeed,within the literature, the devices considered within HEMS vary considerably.

Table 4 presents a literature histogram illustrating the frequency of appear-ance of certain devices considered in HEMS. Although this literature reviewis not necessarily a representative sample of the entire field, it is clear thatsome devices have been selected as better candidates for modelling of demandresponse. Devices limited to a single author include the following: Instant wa-ter heater [90], Video recorder [68], Vacuum Cleaner [92], Toaster [41], Radio[68], Co↵ee maker[68], Cooker hood [41], Hair dryer[41], Phone [41], Printer[68],Purifier[92], Evap cooling [62, 63], furnace fan [62, 63], heat pump [62, 63].

Particularly, space heaters, water heaters, air conditioners, refrigerators, en-ergy storage, plug-in hybrid electric vehicles (PHEV) or electric vehicles (EV),clothes washers, dishwashers, renewable energy generation (PV/Wind), clothesdryers, lighting, freezers and ovens appear at the top of the list. This is logical,as the energy consumption of these devices coincides with the largest contrib-utors to residential load, as shown in Table 5. It should be noted that energystorage devices, such as batteries, PV panels, and residential wind turbines arenot common within homes, but are often included in HEMS models as aspira-tional goals for future environmentally-friendly homes.

2.2. The multi-objective nature of the residential setting

While the purpose of HEMS in the literature is consistent, that is, to bettermanage consumption of energy, the objectives assigned to these systems can varysignificantly. In this section, we group HEMS into various classes of objectivesfound in the literature, as shown in Table 6: cost, well-being, consumptionpattern, and emissions. These are further described as follows:

• Costs include any financial expenditures associated with the managementof energy. Although the cost of energy consumption is the predominantfactor, a HEMS may also include device start-up costs [21], rewards andpenalties for following a desired profile [20, 22], battery deterioration [32],and the cost of carbon tax [43]. Cost is the easiest objective to measure,as monetary values for these di↵erent components are readily available.

• Well-being pertains to consumer lifestyle, and is considered as an impor-tant objective to maintain when managing energy consumption. Lossesin the quality of service rendered by energy delivery bestow inconvenience

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Table 3: Device ownership rates in Canada (Percentage)

Quantity owned 0 1 2 3 4+Air conditioning [89] 47.7 52.3Computer [89] 18.5 52.3 20.2 6.2 2.8Digitally versatile disc (DVD)player [89]

15.0 60.4 19.4 4.0 1.2

Electric heating [89] 60.3 39.7Freezer [89] 38.1 55.2 6.1 0.5 0.0Home theatre system [89] 73.5 23.6 2.9Portable stereo [89] 45.6 42.3 9.7 2.3Radio [68] 4.0 96.0Co↵ee maker [68] 4.0 96.0Printer [68] 59.0 41.0Refrigerator [89] 0 71.7 26.8 1.6Stereo [89] 37.0 55.2 6.6 1.2Telephones (electric) [89] 6.3 31.5 30.5 17.9 13.8Television [89] 0.7 36.5 35.6 17.7 9.4Video game console [89] 64.7 24.8 8.0 1.7 0.9Videocassette recorder (VCR)ownership [89]

25.5 60.4 11.9 1.7 0.5

Energy star AC [89] 43.9 56.1Electric Stove [89] 9.5 90.5Microwave oven [89] 5.4 94.6Dishwasher [89] 35.1 64.9Electric dryer [89] 25.7 74.3Clothes washer [89] 10.1 89.9Electric hot water heater [89] 56.0 44.0Video recorder [89] 88.8 11.2Quantity owned 0 1-5 6-10 11-20 20+Incandescent [89] 10.7 17.6 24.0 26.8 20.9Compact fluorescent light (CFL)[89]

37.9 22.2 19.4 15.1 5.4

Halogen [89] 69.2 15.0 8.0 5.2 2.5Fluorescent [89] 57.6 27.2 9.5 4.3 1.3

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Table 4: Histogram of devices considered in the residential setting in the literature (Referencesin square brackets)

212019181716151413121110987654321

[62][63][22][14][54][16][34][21][90][36][37][39][23][30][69][9][70][57][73][74][91]

[62][63][92][14][54][41][16][65][90][93][47][48][49][30][69][9][70][57][73][94][91]

[62][63][22][41][16][65][34][61][37][93][60][17][39][52][67][30][57][73][32][95]

[62][63][92][41][16][21][61][90][47][48][49][96][68][57][72][74][91]

[62][63][22][16][20][97][52][67][23][98][18][19][69][57][32][40]

[14][54][41][65][61][93][67][29][38][9][70][35][57][71][40][91]

[62][63][92][41][16][65][21][61][90][67][15][68][57][74][91]

[62][63][41][16][65][21][61][90][15][68][57][91]

[62][63][14][54][16][20][23][69][9][70][35][74]

[62][63][16][65][21][90][93][15][68][57]

[62][63][92][41][16][90][93][52][67][68]

[62][63][90][47][48][49][96][68][72][91]

[62][63][92][41][16][65][61][90][68][91]

[62][63][92][41][61][52][68]

[14][54][16][69][9][70]

[99][100][98][18][19]

[62][63][92][41][68]

[92][41][61][74]

[62][63][41][68]

[62][63][61][90]

[62][63][52]

[62][63]

[62][63]

[62][63]

Spaceheater

Water

heater

Air

conditioner

Refrigerator

Battery/E

nergy

storage

PHEV/E

V

Clothes

washer

Dishw

asher

PV/W

ind

Clothes

dryer

Lights

Freezer

Oven

Television

Poo

lpump

µ-C

HP

Microwave

Iron

Com

puter

Well/water

pump

Fan

Evapcooling

Furnacefan

Heatpump

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Table 5: Energy consumption in a typical Canadian dwelling in 2007

Device Annual energy consumptionSpace heatinga 19.3 MWh [101]Water heatingb 5.5 MWh [101]Air conditioning 0.6 MWh [101]Refrigerator 597 kWh [101]Clothes washer 400 kWhc [102]Dishwasher 350 kWh [102]Clothes dryer 964 kWhc [101, 102]Lighting 1277 kWh [101]Freezer 470 kWh [101]Oven/Stove 717 kWh [101]Vehicles 3.6 MWhd [101]

a100% of Canadian households have space heating: 44.5% of Canadians usednatural gas heating, and 17.4% used other sources [89]

b99.6% of Canadian households have water heating: 51.4% uses natural gasheating, and 4.5% uses other sources [89]

cEnergy for hot water requirements included in this quantity.dBased on the average car travelling a distance of 17899 km in a year [101]

using an electric vehicle with the specifications based on the Nissan Leaf 2013.Fuel economy of 0.2 kWh/km [103], for a total of 9.8 kWh per day.

upon the consumer. Modelling of well-being is further described in Section3.2.

• Load profiling is the third class of objectives. It evaluates the desirability ofthe load profile to some party, such as reducing peak demand for the utility[38], or reducing grid dependence for the consumer [15]. Several loadprofile objectives consider the following: shedding requirement deviation[95], target consumption [27], load shifts and cuts[98], peak shaving [18],and self-consumption [15].

• Emissions are the final class of objectives, generally referring to the green-house gas emissions associated with the consumption of electricity. Theseemissions may be directly associated with consuming electricity based onthe grid emissions intensity, usually measured in grams of CO2 equivalentper kWh of electricity consumed. However, it is also possible to mea-sure emissions by inferring the indirect impact of certain actions, such asnot fulling charging a PHEV or controlling the use of a micro-combinedheating and power (µ-CHP) unit.

2.3. Uncertainty of future consumption

In addition to the diversity of devices and objectives to consider, there is alsoa significant degree of uncertainty pertinent to households. These uncertainties

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Table 6: Objectives considered in HEMS literature

Objectives ReferencesCost [19, 20, 25, 26, 28,

35, 41, 42, 57, 59,63, 71, 74, 92, 94,104]

Well-being [37, 62]Consumption [15, 27, 38, 52, 53,

75, 91, 95, 98]Cost and well-being [9, 14, 17, 21–24,

29, 31–34, 36, 39,40, 47–50, 54, 58,60, 61, 65–67, 69,70, 73, 90, 97, 100,105, 106]

Cost and consumption pattern [18]Consumption and well-being [93]Cost, consumption, emissions [16]Cost, well-being, emissions, con-sumption

[43]

include PV/wind power production, occupancy, energy consumption behaviour,and weather conditions [14].

In order for HEMS to schedule household devices, it often incorporates fore-casts of these uncertainties. Methods of forecasting include neural networks,support vector machines, usage of experts, and fuzzy logic [107]. The accu-racy of a forecast strongly depends on the forecasting system, the forecastingmethod, and the method for measuring error.

In Table 7, we illustrate a limited sample of the success of forecasts pertinentto HEMS. Briefly, we describe forecast methodologies and error measurementmethods for electricity prices, residential electricity demand, and heat demand.Other works have attempted to forecast 24-hour wind speed [108], solar power[109, 110], residential demand [111, 112], water demand [113], and occupantbehavior [50]. However, it should be noted that we focus our work on review-ing how HEMS literature addresses uncertainty in the modelling, rather thanforecasting methodologies.

In Table 7, the mean absolute percentage error (MAPE), mean bias error(MBE), mean squared error (MSE), root mean squared error (RMSE), andcoe�cient of variance (CV) are used as di↵erent methods for evaluating errors.

Many works on HEMS focus solely on scheduling, and assume that forecastswill either be available either through an external source, or be addressed by adi↵erent component of the HEMS. In this case, these works will either assumethat forecasts are accurate [10, 70, 73], or arbitrarily inject forecast errors intothe data to simulate errors in forecasts [14, 20, 23, 29, 54, 62]. Thus, it is

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Table 7: Illustration of uncertainties, forecasting technique, and measurement of error

Uncertain vari-able

Forecast methodology Error measurement

24-hour electricityprices [28]

Auto-regressive integratedmoving-average (ARIMA)

95% certainty bounds

24-hour electricityprice [12]

Auto-regressive forecast-ing

MAPE: 13%

Next-hour electric-ity price [107]

Linear regression CV: 26 to 40%MBE: -0.13 to 0.15%MAPE: 24 to 32%

Feed-forward neural net-works

CV: 24 to 40%MBE: -0.08 to 2.05%MAPE: 21 to 31%

Support Vector Regres-sion


Least squares support vec-tor machine


Hierarchal Mixtures ofExperts


Fuzzy-C Means with feedforward neural networks


24-hour demand[114]

Holt-Winters MAPE: 40% (1 house)MAPE: 5% (160 house)

Seasonal Naive MAPE: 49% (1 house)MAPE: 6% (160 house)

24-hour demand[44]

Artificial Neural Network+ Wavelet transformation

MAPE: 7 to 13%RMSE: 15 to 34 W

Artificial Neural Network+ Wavelet transformation+ Error correction

MAPE: 5 to 9%RMSE: 7 to 32 W

24-hours heat de-mand [99]

Neural networks MAPE: 26%

24-hour heat de-mand [19]

Neural networks MAPE: 17%

24-hours HVACstate [39, 115]

Kalman state prediction MSE: 0.01 to 0.15 �C2

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necessary for HEMS to account for uncertainty in forecasts in its schedulingprocess, as described in Section 3.4.

2.4. Infrastructure challenges

For a HEMS to function e↵ectively, it requires access to certain information(e.g., weather forecasts and electricity prices), and the ability to send propersignals to the correct recipient (e.g., loads and the utility). However, the currentelectricity grid has limited functionality in communicating with HEMS. Thus,a smarter electricity infrastructure, called a smart grid, is envisioned to enablethe deployment of HEMS by adding a communications layer to the grid [75,116]. Some of the communications standards described in [77, 78] include WiFi,WiMax, 3G, digital subscriber line (DSL), Ethernet, Zigbee, Optical fibers, andprogrammable logic controller (PLC).

Within a home, the HEMS and the devices must be able to communicatevia control and information signals to optimize the consumption and produc-tion schedule. Di↵erent communications standards have been envisioned withinthe home area network, such as HomePlug (IEEE P1901), Ethernet (IEEE802.3), X10 (X10 standard), Insteon (X10 standard), ITU G.hn (G.hn), Z-Wave (Zensys, IEEE 802.15.4) WiFi (IEEE 802.11, IEEE 802.15.4), ONE-NET(Open-source) 6LowPAN (IEEE 802.15.4), ZigBee (IEEE 802.15.4), and EnO-cean (EnOcean standard) [64].

Thus, for HEMS to function e↵ectively, devices require the ability to broad-cast vital information about their state and energy requirements, as well as actbased on signals received from the HEMS. Devices with these improved capabil-ities are called smart appliances or smart devices [21, 77, 106, 117]. While it isassumed in the literature that the HEMS directly controls the device, it is not anecessity. For example, the control of smart devices may be centralized [72, 96],or the HEMS may simply be providing the necessary information for a smartdevice to create its own independent schedule. The work in [70] investigates thevalue of coordinating devices; thus in the uncoordinated scenario, each devicecould, in theory, schedule itself.

However, an increase in communications between smart devices, HEMS,and the electricity grid implies a higher installation and operational costs [7], aswell as larger information security concerns [76–78]. The financial impact andsecurity requirements vary depending on whether specific information is sentfrom the grid to the house, from the house to the grid, or both. Thus, it wouldbe advantageous to install the minimum communications infrastructure to meetthe functional requirements of the HEMS. However, the minimum infrastructurerequirement is strongly dependent on electricity tari↵ structures and systemarchitecture.

In Section 3.5, we outline communication infrastructure requirements forsensitivity, direction and quantity of information flow, based on the mathemat-ical HEMS model.

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3. Modelling Considerations for home energy management systems

3.1. Modelling demand response of devices

In order for HEMS to flexibly include new loads in a coordinated schedule,several issues need to be addressed. Beyond the infrastructure and communi-cation challenges associated with the dynamic inclusion of new devices, such asrecognizing one’s PHEV returning home, the modelling and control of a multi-tude of devices can be a significant barrier to the deployment of HEMS.

Since each device has unique characteristics, it can be di�cult for the HEMSto intuitively develop a model that represents each device, although some workshave attempted to [9, 14, 16, 54, 70, 73]. Thus, many works in the literaturehave attempted to simplify the modelling complexity by creating limited re-sponse classes for all devices. By using response classes, devices are classifiedby their general demand response behaviour, and thus require significantly lessinformation for modelling. In general, the works that distinguishe responseclasses model groups of devices with characteristics as described in Table 8. Weprovide descriptive names for each response class based on the names found inthe literature; however, as of 2014, there is very little convergence concerninghow to name each response class. The response classes include uncontrollableloads, curtailable loads, uninterruptible loads, interruptible loads, regulatingloads, and energy storage.

While most of the works that use mathematical optimization formulate de-vices with the characteristics listed in Table 8, there is a high level of disagree-ment concerning which devices belong to each response class. For example, theworks [12, 15, 25, 61, 74, 75, 91, 93] state that refrigerators are uncontrollableloads, while they are considered uninterruptible loads in [62, 63, 68], interrupt-ible loads in [22, 24], and regulating loads in [21, 47–49, 67, 90]. This may beexplained by the fact that refrigerators have relatively short cycling character-istics (20 to 45 minutes) and thus may be perceived as an uncontrollable loadat an hourly resolution, while being controllable at the minute resolution. Twoother plausible explanations might be that the authors in the aforementionedworks disagree on acceptable levels of inconvenience for occupants to accept fromrefrigerator operations, and the benefit of additional investment in the demandresponse infrastructure to allow demand response of refrigerators. Several otherdevices that are categorized in at least three di↵erent response classes in theliterature include space heaters, air conditioners, ovens/stoves, water heaters,clothes dryers, and freezers.

3.2. Modelling of well-being

Well-being pertains to the lifestyle of the consumers, and is considered animportant objective to maintain when managing energy consumption. Whenthere is a loss in the quality of service rendered by energy delivery, then incon-venience is bestowed upon the consumer.

Di↵erent names have been used to describe this, such as frustration [62],unsatisfied services [36], disutility [97], inconvenience [90], discomfort [66], valueof energy services [70], and service loss [34].

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Table 8: Response classes of devices

Responseclass

Used in... Commonnames

Description Form

Uncon-trollableloads

[12, 15, 20–22, 24, 33, 35,38, 41, 53, 62,63, 65, 74, 75,91–93, 97]

Non-deferrableloads;non-shiftableloads;must-run loads;essential loads;

Loads that cannot or should not be altered bythe HEMS because they provide a necessaryor high value to the occupants of the house.This can also include uncontrollable genera-tion from sources such as PV and wind. Ex-amples often include television and essentiallighting.

None

Curtail-able loads

[55, 67, 68] Price-responsiveloads

Loads whose energy consumption can be cur-tailed without any temporal consequences.Curtailable loads are often a function of elec-tricity price. For example, when lighting isdimmed due to electricity price, consumersdo not increase light consumption at a laterperiod to make-up for reduced energy con-sumption

None

Uninter-ruptibleloads

[12, 15, 21,22, 24, 32, 33,36, 37, 39, 53,55, 57, 59, 62,63, 65, 68,74, 75, 90–93, 106]

Burst loads;non-preemptiveloads;deferrable loads;shiftable loads;time-shiftableloads.

Loads that must run through a complete setof operations before completing their task.Uninterruptible loads are generally modelledsuch that they consume a fix quantity ofpower for a specific quantity of consecutivetime steps. Some examples include dishwash-ers, clothes washers and clothes dryers.

Integerpro-gram-ming

Inter-ruptibleloads

[12, 20, 22,24, 25, 27, 32,33, 39, 41, 53,59, 62, 63, 65,67, 74, 75, 91,97],

Preemptiveloads;Deferrable loads;Shiftable loads;Controllableloads;power-shiftableappliances.

Loads that can be interrupted and resumeoperation at a later time with little or noconsequence. Interruptible loads are com-monly modelled such that they consume afixed quantity of power for a specific quantityof time steps. Some examples include PHEV.

Integerpro-gram-ming

Regulatingloads

[21, 22, 27,32, 34, 36, 37,39, 40, 47–49,55, 67, 90, 93,97]

Thermostaticallycontrolled loads;Permanent ser-vices;controllable dy-namicload;Regular loads;Thermal loads

Load that must maintain a device’s energystate in proximity of a desired state. Reg-ulating loads require power input to controlan energy state often modelled with Newton’sLaw of Cooling. They usually have operatinglimits or penalties for deviating from the de-sired energy state in order to maintain theoccupants’ well-being. Examples include airconditioning, space heating and energy stor-age.

Linearpro-gram-ming

Energystorage

[20, 22, 32,35, 57, 58, 63,67, 97]

Battery Loads that can be used to store and dispenseenergy when needed. Often modelled alongwith regulating loads.

Linearpro-gram-ming

14

It can be complex to infer the inconvenience incurred to the consumer as aresult of a shifted load because inconvenience is not time-invariant, and popu-lations are heterogeneous. For example, in thermal comfort applications, idealtemperature, as well as the discomfort accrued from a deviation from the idealtemperature, will change with respect to di↵erent people, and with respect totime [118, 119].

The modelling of well-being varies depending on the source of the literature.However, most models of inconvenience can be classed into two categories: in-convenience due to timing, and inconvenience due to undesirable energy states.In the former case, a penalty is attributed to delays in the use of devices due toload shifting, such as washing machines and dryers [12, 21, 22, 24, 33, 62]. Inthe latter case, a penalty is attributed to deviations from an ideal energy state,such as the temperature of a house [17, 23, 34, 66]. Models of well-being aresummarized in Table 9. Note that some formulations are based on increasingvalue [70], others on minimizing penalties [32]; we standardize everything topenalties. Typical penalty functions are described as follows:

• Bounded values penalties imply that the load must be served between twoboundary values. For state-dependent device models, this may includeminimum and maximum permissible dwelling temperature [73]. For time-dependent device models, this may include earliest and latest permissibledevice activation times [16].

• Linear deviation penalty is proportional to the distance from the idealstate or time. For state-dependent device models, the penalty function islinear with respect to an ideal state, such as the ideal dwelling temperature[34]. For time-dependent device models, the penalty function is linearwith respect to an ideal activation time [33], such as the time to start awashing machine. In mathematical optimization problems, if the penaltyforms an absolute value function, then it implies that it must be at leasta mixed integer linear program (MILP) if applied to a state-dependentdevice model.

• Quadratic deviation penalty is quadratic with respect to the deviationfrom the ideal operation of a device, such as in [34] and [93]. Note thatin mathematical optimization problem for state-dependent device mod-els, this implies at least quadratic programming (QP) if the penalty isincluded within the objective, and quadratically constrained quadraticprogramming (QCQP) if it is part of the set of constraints.

• Binary penalty attributes a value to an energy service if it is rendered, orpenalizes a non-rendered service. For example, in [70], if dwelling tem-perature is within ±1�C of the desired temperature, then the task ofheating is considered successful. Otherwise, it is unsuccesful. In math-ematical optimization problems, a binary penalty requires mixed integerlinear programming (MILP) or integer programming (IP) if applied to astate-dependent model.

15

Table 9: Modelling of well-being in the literature

Penalty function State-dependentmodel references

Time-dependentmodel references

Bounded values [73], [100], [66], [120],[104], [16], [65], [61], [36],[37], [47], [48], [49]

[16, 21, 24, 27, 40, 59, 106]

Linear deviation penalty [32, 34, 36, 37, 60, 67, 73] [22, 32, 33, 36]Quadratic deviationpenalty

[34, 39, 40, 67] [93]

Binary penalty [9], [70], [10], [14], [54]Linear penalty for unde-livered services

[9], [70], [10], [14], [54],[17]

Exponential deviationpenalty

[12]

Other penalty structure [22, 23, 67] [62]

• Linear penalty for undelivered services can be used when a value is at-tributed to external modifiers of a device’s energy state. For example, hotwater usage and electric vehicle battery usage can be modelled this way.In reality, the consumer does not care about the temperature of the watertank, nor the state of charge of the electric vehicle, but rather that thereis hot water and battery power for them to use. As such, a penalty forundelivered services may be reasonable [70].

• Exponential deviation penalty functions can also be used to penalize de-viations, such as in [12]. If this were applied to state-dependent devicemodels, then it would require non-linear programming (NLP) to solve.However, exponential deviation penalties may be appropriate for time-dependent device models as the value of time is typically evaluated on anexponential basis in traditional economics.

• Other penalty structures may be used if deemed appropriate. For exam-ple, [22] creates a penalty function based on the maximum temperaturedeviation from ideal in a dwelling.

It should be noted that although these penalty functions were presentedin the context of a consumer’s well-being, these can also be applied to otherobjectives. For example, [40] uses a bounded cost objective, and [20] uses lin-ear deviation penalties to model cost penalties for deviating from forecastedproduction of electricity.

3.3. Modelling multi-objectivity

In order to ensure that the scheduling problem can concurrently considermultiple objectives, multi-objective optimization is often used. The work in[85] elaborates on multi-objective optimization theory and applications, and

16

further describes the types of multi-objective optimization formulation. A multi-objective optimization is formulated as follows:

minx2X

f(x) (1)

where, f(x) denotes the objective function vector as a function of its variablesx, and X denotes the feasible design space. When it is possible to state thedecision-maker’s trade-o↵ between various objectives before solving the opti-mization problem, then it is considered an a priori approach. When this is notpossible, then it is considered a posteriori approach.

Table 10 summarizes the multi-objective optimization methods used in HEMSliterature. In 32 of the 35 cases within Table 10, a priori approaches are pre-sented, while posteriori approaches are used in [58, 93, 105]. The a priorimethods may be preferable as they allow consumer preferences to be definedonce at the outset, and do not require ongoing inputs from the consumer. Themethods with higher prominence in the literature in Table 10 are summarizedas follows:

• Weighted sum adds a scalar weight to each objective, such that the newobjective function is the sum of all the objectives. This is the simplestmethod for addressing multi-objective problems, but requires the value ofobjective to be linearly scalable. In HEMS applications, this is the mostcommon method for addressing scheduling problems, such as weighing thetrade-o↵ between cost, comfort and convenience in [23].

• Bounded objective methods change all but one objective into constraintswithin an acceptable range. For example, well-being can be accounted forby setting acceptable temperature limits for thermal comfort, such as in[73]. Bounded objective is the second most common method for addressingmultiple objectives.

• Physical programming requires a more in-depth understanding of the sys-tem, and uses functions to realistically model the trade-o↵s between thevarious objectives. For example, it may be possible to know the value ofdiscomfort accrued by a household occupant as a function of temperature.Note that in the case where the trade-o↵ functions are linear with respectto the other objectives, it is analogous to weighted sum.

• Pareto fronts are planes that describe the trade-o↵s between the variousobjectives, and are a posteriori methods for allowing a decision-makerto select the best solution after seeing the portfolio of Pareto optimalsolutions. For example, the authors in [58] and [105] display the trade-o↵sbetween the objectives to allow decision-makers to choose the best resultsfor themselves.

17

Table 10: Techniques used for addressing multi-objective optimization problems

Technique Frequency ReferencesWeighted sum 14 [9, 12, 14, 16, 22–24, 29, 34, 40,

54, 69, 70, 73]Bounded objectives 9 [17, 39, 55, 65, 66, 73, 90, 100,

106]Physical programming 7 [31–33, 62, 67, 93, 97]Pareto front 2 [58, 105]Goal programming 1 [61]Weighted min-max 1 [60]Constraint satisfaction problem 1 [36]Technique for Order Preferenceby Similarity to Ideal Solution(TOPSIS)

1 [43]

3.4. Modelling for uncertainty

As forecasts are never fully accurate, several strategies have been developedto address uncertainty. In Table 11, we present various approaches to addressinguncertainty in HEMS, separated by their forecasting requirements.

One method for addressing uncertainty in the future is to simply not usepredicted data. For example, in [41, 47–49, 68, 96], forecasts are not used sincethe control systems are dependent solely on past and present data in order tomake real-time solutions based on heuristics. Alternatively, in [25, 26, 121],uncertainties in price are removed by iteratively gaming price and load quantitybetween the consumers and the utility until a known price is reached. However,the heuristics imperfectly model the optimal schedule, and game-theory is notuseful for reducing uncertainty in non-human-generated data, such as weather,wind speed, and insolation.

Thus, incorporating uncertainty into the scheduling process has the potentialto improve scheduling e�ciency. Model predictive control is the most commonmethod for addressing forecast errors, and is an open-loop online control systemthat approximates the desired solution by reducing the impact of the undesireddynamic properties of the system. According to [122], model predictive control isa methodology rather than a single technique. We elaborate on model predictivecontrol further, and distinguish it from online scheduling.

Some works incorporate uncertainty into the scheduling model. The mostprominent works feature stochastic optimization, robust optimization, stochas-tic fuzzy optimization, chance constrained optimization, and stochastic dynamicprogramming. Optimization under uncertainty is well described in the literature[86, 123–125], but we briefly describe each as follows:

• Robust optimization recognizes that the uncertain parameters have a boundedrange and distribution, and focuses on minimizing the impact of the worst-case scenario. For example, if the objective were to reduce the cost of elec-tricity, a robust optimization problem would minimize the upper-bound

18

that a consumer would pay. While robust optimization may not be themost cost-e↵ective solution over a long period of time (i.e., some schol-ars may argue that minimizing expected costs best achieves this), robustoptimization is well-suited to risk-adverse consumers. From a modellingperspective, it has been shown that the robust counterpart to a linearprogramming problem becomes a second-order conic problem, which iscomputationally tractable [126], and further that polynomially-solvableinteger problems remain polynomially solvable [127]. Thus, robust opti-mization is practical for implementing in HEMS since the added complex-ity of including uncertainty can be limited in many cases, as described in[128].

• Chance-constrained optimization recognizes that the uncertainty has arange and distribution, and focuses on minimizing the worst-case scenariowith a confidence interval, say ↵. Other names for chance-constrained op-timization include probabilistically constrained optimization, and optimiza-tion under value-at-risk. Unlike robust optimization, chance-constrainedoptimization can use unbounded distributions of uncertainty since it onlyneeds to cover the majority of cases (i.e., with ↵ certainty). For exam-ple, [31] minimizes costs while ensuring that the probability of outage isbelow ↵. However, the current description of chance-constrained opti-mization does not quantify the undesired impact for the 5% value-at-risk,so a common solution for addressing the shape of the 5% tail is to in-clude a measure of expected shortfall, under optimization with conditionalvalue-at-risk. The most common method of evaluating the conditionalvalue-at-risk is to include the variance of the distribution of the solution.

• Stochastic optimization problems recognize that some decisions need tobe made at a given time, while some can be made at a later time pe-riod as more information becomes available. This is achieved by creatinga probabilistic scenario tree that is representative of the system. Evenif the stochastic tree were able to accurately represent the uncertaintyin the scheduling problem, the inclusion of schedule corrections due toeach set of future information through recourse variables, as shown in Fig.1, shows that the number of variables grows exponentially with respectto the number of recourse stages. This causes the described multi-stagestochastic optimization to su↵er greatly from the curse of dimensional-ity [129], making it undesirable for HEMS. Thus, a two-stage stochasticoptimization approach is more common. The non-anticipatory nature ofstochastic programs separate here-and-now variables that are required fordecision-making from the wait-and-see variables that do not need to befixed until a later time when certain information is realized [124, 129]. Itis assumed that the wait-and-see variables can be fixed at a later time byusing an approach such as rolling horizon scheduling.

• Stochastic dynamic programming relies on finite state-space models to op-timize the objective based on the cost of memoryless state transition. From

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Table 11: Addressing uncertainty with HEMS

Not using forecastsHeuristic real-time scheduling [41, 47–49, 68, 96]Online scheduling [21, 131]Using point-forecastsGame theory [25, 26, 121]Model predictive control [12, 14, 16, 19, 20, 25, 26, 34, 39, 40, 54,

95, 132–134]Day-ahead scheduling with real-timeadjustments

[132, 135]

Incorporating the uncertaintywithin the modelModel predictive control [23, 28, 136]Stochastic optimization [65, 134, 136]Robust optimization [9, 24, 28, 65, 137]Fuzzy programming [60]Chance constrained optimization [31, 138]Stochastic dynamic programming [23, 59]Other methods [139]

any given state, there is a finite set of actions that can be taken, whichresults in certain probabilities of transitioning to other states, which pro-duces a cost or a reward for the transition. These problems can be solvedby starting from the final time step, and recursively finding the optimalpath back to the initial state. Stochastic dynamic programming is an ex-tension of Markov chains, and thus is often called the Markov decisionprocess. Since the size of the problem grows significantly with respectto the number of states, stochastic dynamic programs can be NP-hard,although problems can often be set-up to be solved or approximated inpolynomial time [130], which is desirable for HEMS. However, the finitestate representation of stochastic dynamic programming may lead to aninaccurate model of the system.

• Fuzzy programming is an extension of fuzzy logic, where truth values cantake any value between 0 and 1 rather than being limited by the two binaryoptions. Thus, multi-valued logic describes reasoning rather than fixedexact values [123]. By applying non-crisp values to forecasts in order toencompass general future behaviours, the HEMS can make rapid decisionsto approximate the optimal schedule of residential devices based on a givenlevel of confidence in the fuzzy parameters. In [60], the fuzzy parametersinclude electricity prices and outdoor temperature.

Scheduling under uncertainty has not yet fully penetrated the HEMS litera-ture as of 2014. However, optimization under uncertainty is not new to demand-side management, and a literature review is available in [140] on demand-

20

response in micro-grids.While some methods incorporate the uncertainty within the mathematical

model, other methods rely on updating algorithms to reduce the impact of un-certainty, such online scheduling algorithms and model predictive control. FromTable 11, we see that model predictive control is the most common approachfor addressing uncertainty used within the HEMS literature at the present time,thus, we elaborate on this technique further, and di↵erentiate it from onlinescheduling, as follows:

• Model Predictive Control : Residential electricity demand is highly inter-mittent and variable, which makes it very di�cult to predict. Whilestochastic optimization approaches can reduce scheduling errors by ac-counting for the distribution of possible outcomes, they generally do notaccount for new information as it becomes available (e.g., electricity price,improved weather forecast, and changes in demand). One potential ex-ception is the exhaustive use of multi-stage stochastic optimization withrecourse; however, this is computationally intractable even for small prob-lems. In order to reduce scheduling ine�ciencies, model predictive control(MPC) has been used.

MPC is often used by planners to sequentially make short-term decisionsover a long horizon. For example, a HEMS scheduler could optimize thestate-of-charge of an energy storage system in a dwelling that containsrooftop PV panels [20]. While MPC is typically used with deterministicpoint-forecasts, it is a general methodology that can also work in con-junction with stochastic optimization approaches. By using time seriesmodelling, MPC generally schedules over a planning horizon, T , waits fora predefined period, updates its forecasts, and repeats this process. Inother words, MPC has the capability to receive new data and periodi-cally update its schedule by sequentially solving the problem. Since theerrors for proximal forecasts are small compared to distal forecasts, it isassumed that the schedules for the first few steps are near optimal. Thus,the schedule is committed for a short period before the next schedulinginstance. However, MPC is a greedy algorithm, since it uses locally opti-mal solutions at each stage, in the hope of finding a global solution. Asa result, is important to ensure that the planning horizon is su�cientlylong to avoid myopic optimization. One example of the consequence of agreedy algorithm that results in myopic optimization in HEMS is energystorage systems being fully discharged at the end of a planning horizon[14].

To evaluate the e↵ectiveness of MPC, the results are often compared toa perfect-knowledge o✏ine counterpart, where the HEMS schedules de-vices with all future inputs known. Thus, the o✏ine scheduling problemrepresents the best-case scenario. When exploiting the structure of MPC,the complexity of the problem grows at a rate of O(T (n+m)3) instead ofO(T 3(n+m)3) [141]. Thus, even with perfect knowledge of future inputs,

21

MPC may still be a e↵ective strategy since solving the o✏ine problem mayrequire excessive computational burden due to the increase in horizon, T .

More information on model-predictive control can be found in [122, 142,143]. Within the scheduling literature, the terms rolling horizon [54], re-ceding horizon, online scheduling, and model predictive control are some-times used interchangeably, depending on the scientific community.

• Online scheduling: While some may refer online scheduling to model pre-dictive control, it should be noted, however, that the use of the termsonline algorithm or online optimization may be ambiguous in the liter-ature, as these terms may also represent a di↵erent class of schedulingproblems, described in [84]. Online scheduling is applied to HEMS ap-plications in [131] and [21], where online scheduling is used to minimizepeak load in a house. Typically, “online scheduling” and “online optimiza-tion” algorithms sequentially process inputs without having any a prioriknowledge of upcoming inputs. In other words, each input, often called atask or a job, is revealed at an instance in time, and the online schedulermust find the best way to include it into the plan. The uncertainty isnot modelled, and the scheduler must find a way to include new itemsappearing in the queue. Tetris is a classical online scheduling problem.Because future inputs are unknown, the online scheduler may create sub-optimal schedules. To evaluate online scheduling, the algorithm comparesits worst-case performance to the o✏ine optimal schedule using a regretfunction or a competitive ratio.

Although both online scheduling and MPC can both include new infor-mation in its scheduling algorithm, it is important to distinguish them.

3.5. Communications infrastructure requirements inferred based on modellingIn this section, we discuss information requirements between the grid and

the HEMS, grouping them by direction (grid-to-house or house-to-grid) andfrequency, and discuss issues regarding vulnerability [76, 77, 91] and volume ofinformation.

Except in direct load control, which will be discussed further, informationsent from the utility (i.e., grid-to-house) is used to inform households on how toimprove their electricity consumption [12]. This information can be broadcastwith a single signal to multiple houses, as it is non-specific. Thus, cost iskept manageable, and information can be retrieved by each household on an as-needed basis, such as from the internet. As this information is publicly available,the security risk associated with interception or attack is minimal. The impactof interception is negligible since this information is publicly available, while anattack would simply cause misinformation to the HEMS, which could result insuboptimal operations.

Conversely, information sent from the household to the utility (house-to-grid) is highly sensitive [76], and needs to be secured as it provides very specificinformation about the household’s behaviour to the electricity grid. An inter-ception of this signal can, for example, allow a thief to know when a house is

22

Table 12: Information flow and frequency

Informationflow

Grid-to-house House-to-grid

Minimal Flat rates, feed-in tari↵ rates,time-of-use rates, inclining blockrates, declining block rates, gridgreenhouse gas emissions inten-sity

Electricity bill, consumption,well-being parameters

Dynamic Dynamic pricing, variable peakpricing rates, critical days,marginal emissions rates, directload control signals, dynamicforecasts (e.g., wind, solar,weather)

Dynamic load prediction, directload control overrides

vacant [76]. Since the consumption of each house is unique, each house needs tosend a separate signal to the electricity grid. Thus, the system must be designedto process at least as many simultaneous signals as there are houses.

Depending on the frequency of information between the electricity grid andhouseholds, the required communication infrastructure can vary significantly.We group the requirements as “minimal”, and “dynamic”. When informationrequirements are minimal, changes may occur monthly or seasonally, so commu-nication infrastructure requirements are lower. For example, if the time-of-userates change seasonally [144], the utility can send a letter or e-mail to eachcustomer to advise them to reprogram their HEMS with new parameters.

Finally, when signals are dynamically updated, it may be desirable to avoiddirect human intervention. Thus, the communication infrastructure betweenthe HEMS and the utility would need to be automated. In this case, it may beimportant to ensure that a reliable, secure, communication network is availablefor the transmission of information. For example, the 24-hour-ahead electricityprice forecast from the electricity grid may need to be frequently updated dueto information about unplanned outages and spot market [12, 14]. In Table 12,we describe the frequency and nature of information flow between the householdand the electricity grid. Note that in general, the utility broadcasts pricing andforecast information, while the house sends information on consumption [12, 14].

The HEMS modelling requirements are dependent on the market and com-munication infrastructure. In a case where information from the grid is minimalor unnecessary, the HEMS only needs to communicate with the devices in thehouse. When frequent or dynamic signals are sent from the grid, then the HEMScan passively receive information from the grid, either through the internet, orthrough broad wireless signals. Finally, when active bi-directional communica-tion is required between the HEMS and the utility, such as in game theoreticapproaches [25, 26, 121], the HEMS must be designed to send information fre-quently, securely, and with an e↵ective communication protocol. In addition,

23

Table 13: Inferred minimum communications requirements based solely on price and loadinformation signals. Grid to house communications requirements on the vertical axis, andHouse to grid communications on the horizontal axis.

Minimal DynamicMinimal [9, 35, 40, 52, 53, 61, 69–71]Dynamic [12, 14, 16, 17, 20, 21, 23, 24, 29,

32–34, 36, 37, 39, 43, 58–60, 62,65, 73, 90]

[22, 25–28, 31, 40, 63, 67, 92, 93,97]

Table 14: Density and direction of DLC schemes

Dense DLC scheme Sparse DLC schemeBi-directional [66, 93–95, 100] [40, 47–49, 72]Unidirectional [68]

the HEMS may need to consider the reliability of the signals transmitted [31].Thus, from the HEMS models presented in the literature, it should be possibleto infer the necessary communication infrastructure requirements. In Table 13,we illustrate the required communications capabilities based solely on price andload signals (i.e., other information requirements, such as weather forecasts, areignored for evaluating communications infrastructure). Note that there are nocases where households send signals to the utility without receiving signals.

For the remainder of this section, we elaborate on the communications in-frastructures in direct load control (DLC) schemes. In DLC schemes, a centralcontroller is able to directly control loads within a house. While price signals aregeneral signals, the density of information transmission may be much higher, asthe central controller may require information about consumer preference anddevice energy states to send unique signals to each household, or to each device.It should also be noted that DLC models also have a higher risk of intractability,especially if the central controller uses optimization to directly control each de-vice, since the size of the problem may become very big if the central controllercontrols a large number of devices or houses.

We consider the signals that the central controller sends to the household.If the central controller sends customized signals to each house, we designatethem as dense DLC signals, whereas if the utility sends a single signal to con-trol devices, then we consider them sparse DLC signals. Conversely, when thehouseholds need to send signals back to the utility, then the DLC scheme isbidirectional. However, if the households does not require to send signals backto the central controller, then it is considered a unidirectional DLC scheme. InTable 14, we describe the DLC scheme by direction and density of signals. Notethat the literature sampled in this table is limited as it is not the focus of thepresent work. However, it can be seen that the majority of the DLC schemes inthe literature is envisioned to include bi-directional communication.

24

4. Complexity and the Scheduling Process

4.1. Adressing complexity in models

The goal of a HEMS is to control the electricity profile within a home areanetwork (HAN) on behalf of a consumer. However, this is not an easy task, aseach device connected to the HAN exhibits unique behaviour, and measurementsand forecasts are not exact. To simplify the scheduling process, models are usedto approximate the optimal schedule of devices within the household; however,there is a trade-o↵ between optimality and complexity. Three approaches aregenerally used to schedule residential energy consumption: mathematical opti-mization, meta-heuristic searches, and heuristic methods. We summarize theapproaches used in literature to address the scheduling process in Table 15.

Mathematical optimization approaches systematically choose input valuessuch that an optimal schedule is attained.

• Linear programming problems are the simplest form of mathematical op-timization, where the objective and constraints are a�ne functions. Theycan be solved in polynomial-time, but may not be su�ciently accurate inrepresenting the household energy system.

• Quadratic programming problems are also relatively simple, as the onlydi↵erence from a linear program is the quadratic objective. If the objectiveis positive definite, then the problem can be solved in polynomial time.However, if it is indefinite, then it is an NP-hard problem.

• Convex programming problems have a convex objective function, linearequality constraints, and concave inequality constraints. This form ofoptimization problem is more complex than the previous two; however, itis guaranteed to converge if a solution exists.

• Dynamic programming problems break large complex problems into smallersub-problems, and recursively solve the problems by storing sub-problemsolutions. In HEMS applications, variables are typically confined to dis-crete values only.

• Mixed integer linear programming problems include integer variables, andalthough non-linear, are NP-complete in complexity. These problems al-low discontinuities in modelling for additional flexibility, such as binaryvariables, but require algorithms such as branch-and-bound to solve.

• Mixed integer non-linear programming and non-linear programming prob-lems can be very di�cult to solve, and may not guarantee that a solutionis found if it exists.

As some of these optimization methods are computationally expensive anddi�cult to solve, meta-heuristic and heuristic methods are often used to find theoptimal schedule. Meta-heuristic searches make few or no assumptions aboutthe problem being optimized. Many meta-heuristic algorithms, such as evo-lutionary algorithms and genetic algorithms, use large population sizes that

25

Table 15: Energy management scheduling approaches

Mathematical Optimization ReferencesLinear programming [12, 17, 20, 25, 28, 34, 37, 52, 62, 63, 66,

73]Quadratic programming [31, 38–40, 67, 97]Convex programming [26, 32]Dynamic programming [23, 59, 66]Mixed integer linear programming [14, 16, 18, 19, 21, 22, 24, 27, 35, 40, 54,

55, 61, 65, 74, 75, 91, 93, 100, 106]Mixed integer non-linear programming [92]Meta-heuristic search ReferencesImmune clonal selection programming [60]Genetic algorithm [29, 33, 95]Tabu search [36]Particle swarm optimization [9, 69, 70]Evolutionary algorithms [58, 105]Heuristic scheduling ReferencesMix of optimization and heuristics [21, 22, 73, 93]Backtracking-based scheduling [53]State-queueing model [96]Artificial neural networks [15]Markov decision processes [45]Constraint optimization by broadcast-ing

[145]

Technique for Order of Preference bySimilarity to Ideal Solution (TOPSIS)

[43]

Other heuristic methods [41, 47–49, 68, 71, 72, 90, 94]

travel semi-randomly within a search space until they converge near a solu-tion. By searching over a large set of feasible solutions, meta-heuristics canoften find good solutions with less computational e↵ort than their mathemat-ical optimization counterparts. Thus, they are useful approaches for solvingoptimization problems.

Heuristics are knowledge-based techniques to approximate solutions basedon certain prescribed rules. Heuristic approaches to energy scheduling requireexperience and knowledge of the energy systems in the home. Provided thatthe heuristic approaches are well-designed, they are useful for significantly re-ducing the computational burden of a scheduling algorithm, while adequatelyapproximating the optimal schedule. For example, a simple heuristic approachis to charge a battery when the price of electricity is below a threshold, and todischarge the battery when the price rises above a di↵erent threshold.

26

Table 16: Number of time steps in HEMS scheduling problems in the literature

Resolution SchedulingHorizon

Numberof timesteps inschedulingproblem

References

– – 1 [47–49, 68, 72, 73, 94, 96]7.5m 7.5m to 1h 1-8 [95]20m 6h40m 20 [53]6m 2h 20 [36]1h 24h 24 [9, 12, 15, 17, 20, 23–26, 28, 29,

31, 34, 39, 40, 42, 43, 52, 57–59,61–63, 67, 69–71, 90, 92, 93, 97,99, 120, 145]

30m 1h to 24h 2-48 [14]30m 24h 48 [44]1h 48h 48 [23]1m 1h 60 [39, 40]5m 6h 72 [66]15m 24h 96 [16, 22, 32, 60, 73–75, 91, 104]– – 100 [21]12m 24h 120 [33]6m 24h 240 [18, 19, 98, 100]5m 24h 288 [65]3m-10m 24h 144-480 [106]1h 8760h 8760 [35]

4.2. Growth of the problem size

4.2.1. Growth of problem size due to timing parametersThe size of a scheduling problem is dependent on the time resolution and the

scheduling horizon. Multiplied together, these variables determine the numberof time steps in a scheduling problem, as illustrated in Table 16.

Based on the formulation in the works cited in Table 16, we see that thenumber of variables, n, and constraints, m, both increase linearly with respect tothe number of time steps, all else being equal . This is as a result of variables thatare associated with each specific time step, such as power input from devices.Each variable also adds a set of constraints, such as power limits from devicesat a given time step. The rate that n and m grow with respect to T varies withrespect to the quantity of devices controlled by the HEMS, and the complexityof device models and tari↵ structures.

Also from the works referenced in Table 16, there is an o↵set of number ofvariables nT0 and the number of constraints mT0 required simply for creatingthe optimization problem. These constraints and variables are independent ofthe number of time steps. Typically, these constraints include summations over

27

time, or functions strongly coupled with the objective function.For example, if the optimization problem required the sum of the energy

consumption of a device over the scheduling horizon, incrementing the number oftime steps in the problem by one would not require a new summation constraint.It would simply require the constraint to include one more time step. Further,adding a new variable for the total energy consumption would not be required.

As a result, we can formulate the relation between T , n, and m using para-metric equations:

n = nT0 + cTnT (2)

m = mT0 + cTmT, (3)

where, nT0 and mT0 are the number of variables and constraints when there isa scheduling horizon of zero time steps, respectively, and cTn and cTm are thelinear growth rate of variables and constraints with respect to the number oftime steps, respectively.

However, it should be noted that n and m do not necessarily have to varylinearly with respect to T . For example, in a non-deterministic model, such asmulti-stage stochastic optimization with recourse, where the number of stagesis dependent on T , the number of stochastic variables grows exponentially withrespect to T . As illustrated in Fig. 1, the number of variables required doublesfor each incremental time step due to the uncertainty model. Alternatively,network time-dependencies also cause the number of constraints to grow super-linearly with respect to T . Despite the possibility of super-linear growth of nand m with respect to T , we have not found any real examples within the HEMSliterature.

4.2.2. Growth of problem size due to number of devicesThe size of the problem increases with the number of devices considered by

the HEMS.Assuming that each device has identical modelling topologies, a similar linear

relation can generally be found between the number of devices D, and theproblem sizes n and m, since each incremental device requires the additionof new variables and constraints. As a result, we can formulate the relationbetween D, n, and m, with the following parametric equations:

n = nD0 + cDnD (4)

m = mD0 + cDmD, (5)

where, nD0 and mD0 are the number of variables and constraints when thereis zero devices controlled by the HEMS, respectively, and cDn and cDm are thelinear growth rate of variables and constraints with respect to the number ofdevices, respectively.

As with T , it is possible for the problem to grow super-linearly with respectto the number of devices, such as in a network problem. As illustrated in 2,

28

x1

x11

x12

x111

x112

x121

x122

x1111

x1121

x1112

x1122

x1211

x1221

x1212

x1222

T = 1 T = 2 T = 3 T = 4

Figure 1: Illustration of how problem size can grow super linearly with respect to number ofscheduling time steps, T , with stochastic optimization with recourse

29

some constraints could increase at a rate m / D(D� 1)/2 if the constraints aredependent on the number of interactions in a network of devices. However, thissurvey of the HEMS literature has not yielded any such cases.

x1 x1 x2

x1 x2

x3

x1 x2

x3 x4

D = 1 0 connections

D = 20+1 = 1 connection

D = 30+1+2 = 3 connection

D = 40+1+2+3 = 6 connection

Figure 2: Illustration of how the complexity of deterministic scheduling problems could growwith respect to the number of devices, D, in network problems

It should be noted that when the device models are diverse, as described inSection 2.1 and 3.1, the size of the problem may not grow linearly with respectto the number of devices.

4.2.3. Growth of problem size due to number of time steps and devicesSince n and m are linearly dependent on D and T separately, we can re-write

(2)-(5) as a bilinear function as follows:

n = n0 + cTnT + cDnD + cnTD (6)

m = m0 + cTmT + cDnD + cmTD, (7)

where n0 and m0 are the number of variables and constraints that act as theskeleton of the optimization problem; cTn and cTm are the number of variablesand constraints added for each incremental time step to the problem (inde-pendent of number of devices); cDn and cDm are the number of variables andconstraints added for each incremental device to the problem (independent ofnumber of time steps); and, cn and cm are the variable and constraint growth

30

Table 17: Example of problem size growth parameters from the linear programming model in[12] due to number of time steps and number of devices.

Coe�cient Sourcem0 = 1 due to objectivecTm = 3 from IBR tari↵ structure and hourly load limitscDm = 2 from device power limitscm = 1 from device operationsn0 = 0cTn = 2 from IBR tari↵ structurecDn = 0cn = 1 from device power draw at each time step.

Table 18: Rescheduling interval used in the literature

ReschedulingInterval

Reference

1m [35, 39, 47–49, 68, 72]5m [54, 65]6m [18, 19, 100]7.5m [95]15m [16, 94]1h [12, 20, 23–25, 28, 34, 40, 59, 99]0.5h–24h [14]

coe�cients that are dependent on both D and T . In all cases in the reviewedliterature, m > n, which is logical because each new variable should be con-strained in some fashion. For example, in [12], where inclining block rate (IBR)tari↵s are used based on total hourly consumption, the problem size growth pa-rameters are summarized in Table 17. Thus, with these parameters, as well asinformation about the form of the optimization problem (i.e., linear program-ming in this case), it is possible to gain a better appreciation of the growthin computational time as a function of the number of devices and time stepsconsidered by an optimization model.

4.3. Computational considerations

For residential applications, HEMS have limited computational capability,and has a limited quantity of time for producing the necessary operational de-cisions. The quantity of time for making scheduling decisions is related to theinterval before the next round of decisions, as shown in Table 18. Other possi-ble factors that contribute to the time pressure for operational decisions includedeadlines for communicating information to the utility, or game-theoretic ap-proaches where the consumer must iteratively propose full schedules for eachtime step [12]. Thus, it is important to size and model the problem such thatoperational decisions can be made in a timely manner.

31

Table 19: Consequences of reducing model complexity

Technique Modevalue

Consequence

Reducing theschedulingresolution

1h Intermittency and variability in demand is not capturedwithin the model, which leads to suboptimal operation. Forexample, in [146], the maximum power consumption usinga 10-minute time resolution is 6 times higher than a 1-hourtime resolution. However, it was shown in [106] that therescheduling interval can be increased from 3 to 10 minuteswith little consequence.

Reducingschedulinghorizon

24h If reduced too far, it can lead to myopic optimization. It issuggested in [34] that we need up to a 13-hour horizon.

Lengtheningthereschedul-ing interval

1h When forecast errors are large, the scheduling algorithmbenefits more from frequent rescheduling [14].

Reducingnumber ofdevices co-ordinated byHEMS

1a Under certain incentive systems, uncoordinated loads cansynchronously consume power, which can lead to undesir-able demand peaks. For example, [70] shows that there maybe up to a 49.7% loss of value from lack of coordination.

Modifyingthe modelstructure

MILP,MPC

Creating a less complex model can reduce the modellingaccuracy and lead to suboptimal or infeasible operations.For example, the works in [34, 39, 40, 54] use multiple hori-zons for capturing high resolution data with a long planninghorizon by reducing the model complexity.

aThe mean number of devices coordinated by HEMS is higher than 1; however,the mode is low due to the numerous works focusing on controlling a singledevices.

Without consequence, it is sometimes possible to leverage the characteristicsof the HEMS model to reduce the computational complexity of the problem.For example, the block tridiagonal structure of MPC models implies that thecomplexity of the problem can be reduced from O(T 3(n+m)3) to O(T (n+m)3)[141]. In a second example, in Time-Of-Use pricing schemes, devices can bescheduled independently [70], which can separate a large problem into smallersubproblems.

However, when the model structure cannot be further leveraged, and thecomputational complexity needs to be further reduced, the model must be com-promised. As discussed in [54], methods to reduce the computational complexityof HEMS algorithms are described in Table 19. However, each of these methodscan negatively impact the operation schedule.

Based on the previous literature survey, Table 19 summarizes that the mostfrequent models of HEMS use a 1-hour time resolution, 24-hour planning hori-

32

zon, 1-hour rescheduling interval, using model predictive control to solve a mixedinteger linear programming problem. However, the works in [14, 34, 54, 146]suggest that these may not necessarily the most suitable parameters for resi-dential energy scheduling. As such, it is important to use proper parameters inorder to have a balance between the scheduling horizon, rescheduling interval,and time resolution.

5. Conclusion

In this paper, we have reviewed the methods employed in the literaturefor modelling di↵erent aspects of residential energy management. We presentthe challenges concerning modelling frameworks, and discuss the computationalconsiderations associated with HEMS. Based on this review, it is clear thatmany di↵erent modelling approaches are explored in the HEMS literature toaccount for household devices, uncertainty, various objectives, and schedulingmethodologies. Thus, we make two recommendations.

While some of the diverse modelling approaches may exist for finding newmethods for improving energy scheduling in the residential setting, it is clearthat there is very little convergence in establishing a common baseline for eval-uating new methods. As a result, it can be di�cult to compare the e↵ectivenessof various approaches in HEMS, as illustrated in Table 2. Thus, it is recom-mended that a baseline be created for evaluating HEMS, equivalent to the IEEE14, 30, and 118 bus systems used for evaluating power flow. This may allowa common baseline method for modelling well-being and household devices, aswell as providing common time-series data such as device consumption pattern,occupancy patterns, and roof-top PV generation.

In addition, given the limited computational capacities of home energy man-agement systems to manage diverse quantities of devices in a volatile householdsetting that may require higher resolution data, it is recommended that measuresof complexity and tractability are included, in order to provide a fair comparisonof the trade-o↵s between optimal scheduling and computational considerations.

6. Acknowledgements

The authors would like to thank Dr. Ana Nikolic for helping in the editingand proof-reading of the manuscript.

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