NON-INTRUSIVE LOAD MONITORING FOR SMART GRIDS · 2020-07-11 · Non-Intrusive Load Monitoring has many published algorithms available, including both supervised methods that require

NON-INTRUSIVE LOAD MONITORING FOR SMART GRIDS

William SchneiderSr. Data ScientistDell [email protected]

Fernanda Campello de SouzaSr. Data ScientistDell [email protected]

Knowledge Sharing Article © 2018 Dell Inc. or its subsidiaries.

2018 Dell EMC Proven Professional Knowledge Sharing 2

Table of Contents Abstract ......................................................................................................................................................... 3

Introduction .................................................................................................................................................. 3

Data description ............................................................................................................................................ 4

Data exploration: aggregate energy consumption ....................................................................................... 7

Peak-period loads ......................................................................................................................................... 9

Demand forecasting .................................................................................................................................... 12

ARMA Model ........................................................................................................................................... 13

Baseline Model........................................................................................................................................ 14

Conclusion and future work ........................................................................................................................ 15

References .................................................................................................................................................. 17

Disclaimer: The views, processes or methodologies published in this article are those of the authors.

They do not necessarily reflect Dell EMC’s views, processes or methodologies.


Abstract

Electric power distribution systems have received increased attention in the past decade due to greater

availability of IoT devices, including two-way smart meters and edge gateways. This increased detail in

data provides utilities with deeoer visibility into the behavior of the grid to support challenges such as

demand response, where the utility must predict immediate demand since energy storage is limited.

Another active research effort in the delivery of electricity is non-intrusive load monitoring (NILM), in

which aggregate electricity usage data is used to determine the array of devices present. These two

efforts, one on a macro scale and another on a micro scale, could be merged into an approach which has

greater effectiveness. In this paper, we use the REFIT dataset to evaluate the potential of NILM

techniques to support demand response efforts through time-of-use pricing and macro-forecasting.

Additionally, we utilize unsupervised techniques to make the technique available to a much wider

customer base.

Introduction

The term Smart Grid refers to electric power distribution systems equipped with sensors along

transmission lines that can give real-time information on operation conditions and also enable two-way

communication between the utilities and customers. The increased availability of detailed operation

information in the smart grid allows for optimizing the process of energy generation and distribution,

improving reliability and promoting efficient use of the current infrastructure to meet a growing

demand for energy. More than half of utilities in the US are currently deploying smart grid infrastructure

to support an array of business challenges. The sensor devices market, in particular, is a growing one

that is expected to grow from USD 12.8 billion in 2017 to 20 billion by 2022 globally.

Since, in most situations, electricity cannot be stored in the amounts necessary to meet typical demand

gaps, its generation and distribution need to work as a just-in-time process, with more electricity

generated when demand increases. This creates challenges for utilities at times of peak demand,

sometimes forcing the use of more expensive and/or more polluting electricity generation methods, or

purchasing electricity from neighboring grids at a premium. In worst-case scenarios, it may result in

rolling or total blackouts. A potential benefit of smart grids is the capability to promote individual

behavioral changes in power consumption that can smooth overall energy demand, avoiding surges that

can increase costs and decrease reliability for all of a utility’s customers. This can be done through

increasing a customer’s visibility on their energy consumption at different times and offering incentives

for demand smoothing, such as time-of-use pricing programs.

The main device that enables this detailed visibility on electricity consumption is the smart meter, an

electricity meter that records aggregate consumption in short intervals (less than 1 hour) and transmits

this data to the utility, allowing for detailed monitoring of seasonality in consumption. In order to help

customers and utilities identify specific opportunities for savings, however, direct visibility into

consumption of specific devices would be useful. Smart meters can be deployed as a single meter for a

customer or in complex situations in order to measure specific devices. However, the field of Non-

Intrusive Load Monitoring (NILM) aims to disaggregate high-level aggregate measurements to

contributions of individual appliances, based on a single metering point (smart meter at main breaker


level). The latter promises to be a cheaper method of implementation and is therefore an active area of

research.

Non-Intrusive Load Monitoring has many published algorithms available, including both supervised

methods that require expensive labeled (disaggregated) data for training, as well as unsupervised

methods that, despite being generally less accurate than supervised methods, are of high interest due to

low setup cost and short training phase. In addition, NILM techniques differ in their data requirements:

energy, voltage, as well as frequency measurements. The methods most likely useful for smart grid

technology are those that are unsupervised and focused on low frequency monitoring, which can be

more reasonably expected to be available from multiple homes in a smart grid. Examples of this class of

NILM method can be found in (Kim, Marwah, Arlitt, Lyon, & Han, 2011), (Kolter & Jaakkola, 2012), (Zhao,

Stankovic, & Stankovic, 2016), among others.

In this paper we use the REFIT dataset (Murray, Stankovic, & Stankovic, 2017), which includes sub-

metering data for 20 houses in the Loughborough area of the UK in the period from July 2014 to July

2015, to evaluate the potential of NILM techniques in supporting smart grid analytics such as 1) When

do the peaks in electricity consumption in the grid occur (aggregated across houses)? 2) Are there

appliance loads during peak times with potential for deferred use (e.g. dishwashers, washers, dryers,

etc.)? Can we recommend discount offers or time-of-use pricing programs to create incentives for

customers to defer a portion of their electricity demand to times of lower overall demand? Which

customers show greater potential and should be targeted first? 3) Can we generate more accurate

demand forecasts at the grid level with the knowledge of individual consumer device make-up?

We analyze the points above based on baseline truth from the REFIT dataset, as well as run the same

analysis assuming inaccuracies on disaggregation results from NILM methodologies, in order to examine

the consistency of the results. The goal is to evaluate how accurate NILM results need to be to enable

this type of recommendation/customer relationship management, and what might be expected in terms

of grid reliability or other return on investment metrics.

Data description

The REFIT dataset contains 20 houses, each with 11 metering points: 2 mains, which combined give the

total apparent power drawn for the house, and 9 sub-metering points attached to 9 individual

appliances within the house (appliances differ between houses). The instantaneous active power

recordings are on average 8 seconds apart. We work with the cleaned dataset which re-aligns the

sensors when appliances move within a house and imputes values (Murray, Stankovic, & Stankovic,

2017).

Table 1 and Table 2 show additional information about the houses and appliances monitored. Houses 3,

11, and 21 from the REFIT dataset that affect the recording of total power consumption were removed

from the analysis due to issues and do not appear on the tables. House 9 was also removed because it

had too many gaps during our analysis period.


House Occupancy Dwelling Age

Number of Appliances

Dwelling Type Size

1 2 1975–1980 35 Detached 4 bed

2 4 — 15 Semi-detached

3 bed

4 2 1850–1899 33 Detached 4 bed

5 4 1878 44 Mid-terrace 4 bed

6 2 2005 49 Detached 4 bed

7 4 1965–1974 25 Detached 3 bed

8 2 1966 35 Detached 2 bed

10 4 1919–1944 31 Detached 3 bed

12 3 1991–1995 26 Detached 3 bed

13 4 post 2002 28 Detached 4 bed

15 1 1965–1974 19 Semi-detached

3 bed

16 6 1981–1990 48 Detached 5 bed

17 3 mid 60s 22 Detached 3 bed

18 2 1965–1974 34 Detached 3 bed

19 4 1945–1964 26 Semi-detached

3 bed

20 2 1965–1974 39 Detached 3 bed

Table 1: Information about houses from the REFIT dataset. Source: (Murray, Stankovic, & Stankovic, 2017)


House 1 2 4 5 6 7 8 10 12 13 15 16 17 18 19 20 Total

Television X X X X X X X X 2X 2X X X X X X X 18 Hi-Fi

X

X

2

Fridge-Freezer

X X X

X X

X 2X X X

10

Fridge X

X

X X

X X X 7 Freezer 2X

X

X 2X X 2X

X X X X 13

Microwave

X X X X

X X X X X

X X X X 13 Cooker Hood

X

1

Kettle

X X X X X X

X X X

X

X X 12 Toaster

X

X X X X

X

X

7

Misc Kitchen

2X

X

3 Washing Machine

X X 2X X X X X X

X X X X X X X 16

Washer Dryer

X

1 Tumble Dryer X

X

X X

X X

X

X 8

Dishwasher X X

X X X

X

X X X

X

X 11 Computer X

X X 2X

X

X X X X X

X 12

Router

0 Elec Heater X

2X

3

Lamp

X

1 Misc

X X

2

Table 2 Appliances monitored in each house from the REFIT dataset. Source: (Murray, Stankovic, & Stankovic, 2017), Table 3.

Since our objective is to simulate a small grid by assuming the REFIT houses are connected to the same

subnetwork we focused our analyses on a 3-month time frame where data from all houses are available,

from April to June 2014. To examine energy consumption over time for each home and for the entire

grid, we initially use the power readings within each 15-minute block to compute energy consumption

within that 15-minute block. For shortness we illustrate the energy consumption calculation in 1-minute

blocks on Table 3. The same logic was used to compute energy consumption in 15-minute blocks.


Read timestamp Aggregate

power read (W)

Time delta (seconds) Energy consumption (Wh)

4/1/2014 0:02:00 No Read

4/1/2014 0:02:01 180 1 0.05 4/1/2014 0:02:14 180 13 0.65 4/1/2014 0:02:15 180 1 0.05 4/1/2014 0:02:19 177 4 0.20 4/1/2014 0:02:28 180 9 0.45 4/1/2014 0:02:30 180 2 0.10 4/1/2014 0:02:33 180 3 0.15 4/1/2014 0:02:44 189 11 0.58 4/1/2014 0:02:47 189 3 0.16 4/1/2014 0:02:58 183 11 0.56 4/1/2014 0:03:00 No Read 2 0.10*

4/1/2014 0:03:01 177 * computed assuming the power for the last 2

seconds of the 1-minute block is 177 W (read at 0:03:01)

Total 60 seconds 3.04 Wh

Table 3: Example of energy consumption calculation in a 1-minute block, given apparent power reads within that minute.

We later leverage this initial 15-minute aggregation to produce hourly, daily, weekly, and monthly

aggregations to examine consumption patterns.

There are many gaps in the data that need to be filled to allow for an overall estimation of grid-level

power consumption at any given time. Some gaps are short, lasting just a few minutes, others are long,

lasting several days (up to 2 months in some cases). We handle these two types of gaps differently.

Shorter gaps (lasting less than 15 minutes), are filled by the energy consumption calculation illustrated

in Table 3. For longer gaps, we rely on averaging the closest prior and subsequent non-null data points

for the same house, appliance, time of day, and day of week.

Data exploration: aggregate energy consumption

In our analysis we assume the 17 selected houses from the REFIT dataset are connected to the same

subnetwork, forming a small grid. Although the REFIT houses were not chosen to fall on the same

subnetwork, they were all located at the same region of England and subject to the same weather

during the monitoring period, making the assumption of them being on a same subnetwork realistic in

that respect. To examine patterns in grid-level energy consumption, we add the total energy consumed

by all houses throughout the analysis period.


Figure 1 shows the average grid-level energy consumption in kWh, aggregated by day of week and hour

of day, for the 12-week period between April 6, 2014 – June 28, 2014, along with the standard error

margins. To ensure our data imputation process doesn’t create artificial seasonality patterns, we

removed periods with imputed reads from analysis. This means that 1-hour time periods for which at

least one of the houses had a gap longer than 15 minutes in the power reads was not considered when

computing average energy consumptions. We notice some patterns:

Average energy consumption is higher on weekends than on weekdays (which is expected in

cases where occupants must leave the house during weekdays for work and/or school

obligations).

Although patterns differ a bit from one weekday to the other, in general energy consumption

peaks during a 5-hour block in the evenings from about 4PM to 9PM, with a smaller peak in the

mornings, in the 3-hour block from about 5AM to 8AM (consistent with typical work/school

schedules).

Weekends also show two energy peaks, with an evening peak from about 4PM to 9PM (similar

to weekdays), and a morning peak from about 7AM to 11AM (a bit later than weekday morning

peaks). But energy consumption remains high in the middle of the day as well (albeit lower than

during the mornings and evenings.)

Figure 1: Average grid-level energy consumption in kWh, aggregated by day of week and hour of day, for the 12-week period between April 6, 2014 – June 28, 2014.

Based on these patterns, we define peak and off-peak hours as follows:

Peak hours: 5 - 8AM and 4 – 9PM on weekdays, 7AM - 9PM on weekends.

Off-peak hours: 12 - 5AM, 9AM – 4PM, and 9PM – 12AM on weekdays, 12 - 7AM and 9PM –

12AM on weekends.

Although the peak-hours analysis can also be done by day of the week, we chose to focus only on the

broader weekday/weekend distinction when evaluating potential for load deferral. This would result in

energy tariff rules that are simpler and easier for customers to remember.


Peak-period loads

Periods of peak consumption can bring increased risk to the grid, so we aim to find opportunities for

demand smoothing through incentives to change customer behavior. In this next section, we take a

closer look into energy consumption by different houses and appliances during grid-level consumption

peaks, singling out loads that customers could potentially defer to periods of lower grid-level demand.

Out of the appliances listed on Table 2, washing machine, washer dryer, tumble dryer, and dishwasher

stand out as potentially deferrable without having a big impact on lifestyle (no need to change meals or

leisure schedules, for example), so we look for opportunities to defer these loads to off-peak hours.

Figure 2 shows the total energy consumption (kWh) from April 6, 2014 – June 28, 2014 broken down by

appliance during peak and off-peak periods, for Houses 5, 6, and 7. Given there are only 9 sub-metering

points in each house, a good portion of the energy consumed cannot be attributed to an appliance and

is marked as unassigned. We can notice several opportunities for load deferral across the houses.

Houses 5 and 7 are good examples of load deferral candidates. They are among the top energy

consumers in the grid, have higher total consumption during peak periods than during off-peak periods,

and considerable (deferrable) consumption by dishwasher, tumble dryer, and washing machine during

peak periods.

Figure 2: Total energy consumption (kWh) from April 6, 2014 – June 28, 2014 by appliance during peak and off-peak periods, for Houses 5, 6, and 7.

Table 4 shows a summary of total and deferrable (dishwasher/washer/dryer) loads by house, during

peak and off-peak periods. In this table we also compute energy costs per house assuming two different

tariff schemes: a flat tariff of $0.2 per kWh, or a variable tariff of $0.35 per kWh in peak periods and

$0.05 per kWh in off-peak periods. When computing the energy cost for a house under flat tariff, we

assume the original load distribution between peak and off-peak periods is maintained, since the

customer would have no incentive to change habits. Under variable tariff, we examine two scenarios: 1)

the customer changes tariff scheme, but does not change behavior (no load deferral) or, 2) the customer

changes tariff scheme and defers the deferrable load (dishwasher/washer/dryer) to off-peak periods. In

the latter scenario, it is assumed that the customers’ behavior changes are incentivized by the potential


savings in the variable tariff scheme, but that they are also limited to deferral of loads that do not have a

big impact on leisure/meals/sleeping habits (i.e. only the previously deferrable load is moved).

In reality, customer behavior is difficult to predict. Some customers might place a higher value on

maintaining their current schedules and decide to forfeit the potential savings from load deferral, even

for tasks such as washing dishes and clothes. Others might be more cost-sensitive and decide to defer

even more of their total load to off-peak periods, going beyond dish/clothing washing. These nuances in

behavior should be examined through pilot programs in limited geographical regions and customer

surveys, to more accurately forecast the effect tariff incentives may have in the overall population

behavior. In the absence of supporting data on behavioral change, we aim to strike a balance in this

paper by making the (strong) assumption that the value placed on keeping dish/clothing washing

schedules is $0, so that customers would take advantage of any changes that bring savings (regardless of

the amount), and the (conservative) assumption that dish/clothing washing are the only activities that

customers would be willing to defer to off-peak periods.

Examining Table 4, we notice that Houses 5, 7, and 8 would benefit the most from a change to variable

tariff (higher cost savings), but Houses 5, 7, and 10 are the ones with higher deferrable loads during

peak periods (would bring more benefit to the grid if behavior changed). Note that Houses 12 and 13 do

not have enough deferrable load during peak periods to benefit from a variable tariff scheme, so in our

simulation we assume they would not switch tariffs nor change behavior. Given our assumptions,

making the variable tariff scheme available to this subnetwork would have the following effects from

the utility’s perspective:

Deferral of 847 kWh from peak to off-peak periods

o Total peak period load changes from 7,275.3 kWh to 6,428.2 kWh

o Total off-peak load changes from 6,796.0 kWh to 7,643 kWh

Decrease in revenue from $2,814.2 to $2,579.3 due to discounts given for customers using

more energy during off-peak periods.

The demand smoothing gains from deferring 847 kWh from (peak) periods where energy consumption

from other sources is still high, and hence reduces the chances of needing higher-cost energy generation

and/or suffering outages, would need to be balanced against the revenue reduction of $235 due to tariff

incentives. Given our assumptions that any cost savings would trigger costumer behavior changes, the

utility could make the tariff change much less extreme, 0.25/0.15 instead of 0.35/0.05 for example, and

still see the same amount of load deferral from peak periods while losing only $78.3 in revenue. In

reality, higher cost savings are likely to trigger more significant customer behavior changes overall and

promote more load deferrals. This tradeoff can be incorporated into the analysis once the relationship

between potential cost savings and propensity to defer loads is better understood for different

customer segments (through monitoring well designed surveys and pilot programs).


Table 4: Summary of total and potentially deferrable energy consumption, and costs under different tariff schemes, for all houses. Assumes there is sub-metering in place.

The load deferral and cost savings analysis in Table 4 assumes that we have direct measures of the

energy consumed by dishwashers, washers, and dryers. This is unlikely to be true for the majority of

houses. In reality, these loads would be disaggregated through some sort of NILM methodology, which

would produce estimates subject to accuracy limitations. Table 5 illustrates the potential impact of

disaggregation errors in load deferral and revenue loss estimates for the utility, as well as in estimates of

cost savings for customers. It assumes there is no sub-metering in place, and that the NILM

methodology overestimates deferrable loads by 20% (total peak and off-peak loads remain the same as

in Table 4, since they are measured by the main meter, but the breakdown between deferrable and non-

deferrable peak load changes). Since under our assumptions the inflated deferrable load estimates

would not cause a change in customer behavior patterns, the estimated load deferral would be inflated

by 20% as well (to 1016.4 kWh). The inflation on estimated revenue loss would be around 21% (to

$285.8). Table 6 shows the impact that varying deferrable load disaggregation errors would have in the

accuracy of estimations for total deferred load and total revenue loss, under a variable-tariff based

demand response program. Understanding how disaggregation inaccuracies impact estimated results of

demand response programs is essential to the program design phase, ensuring that decisions are made

taking into consideration the appropriate margin of error in estimated program impact to grid

operation.

Off-

Peak

Periods

house

Deferrable

load

(kWh)

Non-

Deferrable

load (kWh)

Total

load

(kWh)

Total

load

(kWh)

1 11.6 296.9 308.5 376.2 45% 1.7% 43.4% 136.9 126.8 123.3 13.6 yes 123.3

2 92.4 370.1 462.5 304.7 60% 12.0% 48.2% 153.4 177.1 149.4 4.1 yes 149.4

4 23.8 305.4 329.3 381.2 46% 3.4% 43.0% 142.1 134.3 127.2 14.9 yes 127.2

5 189.4 587.3 776.6 562.2 58% 14.1% 43.9% 267.8 299.9 243.1 24.6 yes 243.1

6 14.2 412.0 426.2 503.7 46% 1.5% 44.3% 186.0 174.3 170.1 15.9 yes 170.1

7 171.0 350.4 521.4 412.4 56% 18.3% 37.5% 186.8 203.1 151.8 35.0 yes 151.8

8 34.8 444.6 479.5 752.5 39% 2.8% 36.1% 246.4 205.4 195.0 51.4 yes 195.0

10 112.9 606.2 719.1 624.0 54% 8.4% 45.1% 268.6 282.9 249.0 19.6 yes 249.0

12 33.1 345.5 378.6 279.1 58% 5.0% 52.5% 131.5 146.5 136.5 -5.0 no 131.5

13 83.7 564.3 648.0 395.8 62% 8.0% 54.1% 208.8 246.6 221.5 -12.7 no 208.8

15 43.4 234.8 278.2 288.5 49% 7.7% 41.4% 113.3 111.8 98.8 14.6 yes 98.8

16 81.0 533.3 614.4 558.3 52% 6.9% 45.5% 234.5 242.9 218.6 15.9 yes 218.6

17 8.9 300.8 309.7 298.0 51% 1.5% 49.5% 121.5 123.3 120.6 0.9 yes 120.6

18 36.4 389.4 425.8 463.6 48% 4.1% 43.8% 177.9 172.2 161.3 16.6 yes 161.3

19 3.4 260.6 264.1 270.1 49% 0.6% 48.8% 106.8 105.9 104.9 1.9 yes 104.9

20 23.7 309.8 333.5 325.8 51% 3.6% 47.0% 131.9 133.0 125.9 6.0 yes 125.9

Total 963.9 6311.4 7275.3 6796.0 2814.2 2886.1 2597.0 217.3 2579.3

Total energy

cost

assuming

cheaper

option is

selected ($)

% of total load

during peak

periods if all

deferrable load

is moved to off-

peak

Total

energy

cost

under flat

tariff ($)

Total energy

cost under

variable tariff

without load

deferral ($)

Total energy

cost under

variable

tariff with

load deferral

($)

Potential

savings

from

switching

tariffs ($)

Likely to

switch

tariffs an

change

behavior?

Peak Periods % of total

load

during

peak

periods

% of total

load during

peak

periods that

is deferrable


Table 5: Summary of total and potentially deferrable energy consumption, and costs under different tariff schemes for all houses. Assumes there is no sub-metering and the NILM methodology overestimates deferrable loads by 20%.

Deferrable load

disaggregation error

Estimated Deferred

Load

Estimated Revenue

Loss

Estimated/Actual Deferred Load

Estimated/Actual Revenue Loss

-50% 278.21 121.91 33% 52%

-40% 447.47 140.52 53% 60%

-30% 528.25 163.00 62% 69%

-20% 603.72 185.64 71% 79%

-10% 762.34 209.55 90% 89%

0% 847.04 234.96 100% 100%

10% 931.74 260.38 110% 111%

20% 1016.45 285.79 120% 122%

30% 1101.15 311.20 130% 132%

40% 1185.85 336.61 140% 143%

50% 1270.56 362.02 150% 154%

Table 6: Impact of deferrable load disaggregation errors in accuracy of total deferred load and revenue loss estimations under a variable-tariff based demand response program.

Demand forecasting

We now turn to electric grid demand forecasting, or predicting future energy use on some relevant time

interval in advance. Better control over those forecasts translate into better control over incentives for

end customers. We argue that results from an energy disaggregation implementation can increase the

effectiveness of demand reduction incentives. First, in providing more accurate demand forecasts by

Off-

Peak

Periods

house

Deferrable

load

(kWh)

Non-

Deferrable

load

(kWh)

Total

load

(kWh)

Total

load

(kWh)

1 13.9 294.5 308.5 376.2 45% 2.0% 43.0% 136.9 126.8 122.6 14.3 yes 122.6

2 110.9 351.6 462.5 304.7 60% 14.5% 45.8% 153.4 177.1 143.8 9.6 yes 143.8

4 28.6 300.7 329.3 381.2 46% 4.0% 42.3% 142.1 134.3 125.7 16.4 yes 125.7

5 227.2 549.4 776.6 562.2 58% 17.0% 41.0% 267.8 299.9 231.8 36.0 yes 231.8

6 17.0 409.1 426.2 503.7 46% 1.8% 44.0% 186.0 174.3 169.2 16.7 yes 169.2

7 205.2 316.2 521.4 412.4 56% 22.0% 33.9% 186.8 203.1 141.5 45.2 yes 141.5

8 41.8 437.7 479.5 752.5 39% 3.4% 35.5% 246.4 205.4 192.9 53.5 yes 192.9

10 135.4 583.7 719.1 624.0 54% 10.1% 43.5% 268.6 282.9 242.3 26.4 yes 242.3

12 39.7 338.8 378.6 279.1 58% 6.0% 51.5% 131.5 146.5 134.5 -3.0 no 131.5

13 100.5 547.5 648.0 395.8 62% 9.6% 52.5% 208.8 246.6 216.4 -7.7 no 208.8

15 52.1 226.1 278.2 288.5 49% 9.2% 39.9% 113.3 111.8 96.2 17.2 yes 96.2

16 97.2 517.1 614.4 558.3 52% 8.3% 44.1% 234.5 242.9 213.8 20.8 yes 213.8

17 10.6 299.1 309.7 298.0 51% 1.8% 49.2% 121.5 123.3 120.1 1.4 yes 120.1

18 43.7 382.1 425.8 463.6 48% 4.9% 43.0% 177.9 172.2 159.1 18.8 yes 159.1

19 4.1 259.9 264.1 270.1 49% 0.8% 48.7% 106.8 105.9 104.7 2.1 yes 104.7

20 28.5 305.0 333.5 325.8 51% 4.3% 46.3% 131.9 133.0 124.5 7.4 yes 124.5

Total 1156.7 6118.6 7275.3 6796.0 2814.2 2886.1 2539.1 275.1 2528.5

Total

energy

cost

under flat

tariff ($)

Total energy

cost under

variable tariff

without load

deferral ($)

Total energy

cost under

variable tariff

with load

deferral ($)

Potential

savings

from

switching

tariffs ($)

Likely to

switch

tariffs an

change

behavior?

Total energy

cost

assuming

cheaper

option is

selected ($)

Peak Periods % of total

load

during

peak

periods

% of total

load during

peak

periods

that is

deferrable

% of total load

during peak

periods if all

deferrable

load is moved

to off-peak


including the low-level disaggregated appliances on the end customers’ level. Second, in providing a

more targeted offer which can prove more reliable in predicting the response to the offer.

Using our simulated grid aggregated to the hour, we build a demand forecasting model in two cases.

First, in the case where only aggregate data is known and used for the model. Second, when

disaggregation information is known. For the comparison, we use a simple demand forecasting model

based on ARMA to demonstrate the two cases. Using the 3-month period we have chosen, weekly

training data sets and single-day forecasting is chosen. This provides at least 11 different weeks of

model application for comparison.

ARMA Model

The ARMA model incorporates autocorrelations in a regression approach, parametrized by maximum

correlation factors 𝑝 and 𝑞. It is well known that electricity usage for residential customers has daily,

weekly, and yearly patterns, and any demand forecasting model must incorporate these patterns as a

first step. As is typical for the model, we compute the autocorrelations. For the 3-month period, Figure 3

shows the autocorrelation factor (ACF) for each house in the dataset. Vertical lighter bands in the image

correspond to relatively strong correlations for each multiple of 24 hour lags across houses. For some

houses, the correlation increases slightly at the 7-day lag, 168 hours. If the data is differenced by 24

hours, the correlation decreases significantly.

Figure 3: Heatmap of each house’s ACF for the three-month period.

For comparison, Figure 4 shows the partial autocorrelation factor (PACF) for the same data. Most of the

correlations here are not significant, except for one peak for house 8 at 24 hour lag. Most houses only

have a significant correlation for a one-hour lag.


Figure 4: Heatmap of the PACF for the three month period.

We set up our model to predict the future day, given a week of data. Due to the 24-hour correlation, we

difference the consumption over that time. With these correlation maps, we will vary the parameters

around 𝑝, 𝑞 ≤ 4.

Because the comparison involves data on the house level, each house’s aggregate consumption is

modeled separately, and then added together. In a real world scenario, this could be achieved using

edge compute devices which deal with limited data sets. The forecast results could be communicated

back to the core system.

Baseline Model

Applying the ARMA model to each house’s aggregate demand results in a baseline model for

comparison. Based on the correlation results shown above, we vary the parameters in a grid and, for

simplicity, we apply the same parameters for each house, though the coefficients of each model can

vary. With the differencing based on 24 hours, training sets provide very good fits. Figure 5 shows the fit

for one house (house 1). Note that it is possible for the prediction to be negative, which we will cap at

zero.


Figure 5: A typical fit to observed data for baseline model.

Table 7 shows average RSS values for each house’s model. Fitted values tend to be consistent over

houses. House 13 was observed to have some irregular features.

House ID Average RSS

1 0.010

2 0.020

4 0.004

5 0.089

6 0.037

7 0.030

8 0.021

10 0.058

12 0.006

13 0.109

15 0.001

16 0.020

17 0.010

18 0.006

19 0.002

20 0.017 Table 7: Average RSS values for each house’s model

Conclusion and future work

Our analysis shows that energy disaggregation has the potential to be beneficial to demand response

efforts for smart grid optimization through incentive programs and in demand response, even in the

presence of disaggregation errors. We also highlight the importance of understanding how these errors

affect the estimation of the program’s impact on grid operations, showing an example on how the errors

can be taken into account in the program design phase. We also argue the value of disaggregation

methods for improving consumption prediction. Future work will extend the modeling to incorporate

this data.


We are in an ongoing effort to implement NILM techniques and apply them to the REFIT dataset, to

better understand the potential impact of disaggregation errors in demand response analyses. This

paper evaluated the impact disaggregation errors would have on demand response analysis if the

assumption holds true that errors are, on average, uniform for all types of loads. But NILM techniques

often have a higher propensity of inaccurately disaggregating certain types of loads, and taking this into

account can provide better error estimates for the demand response analysis. Our current focus is on

NILM techniques that 1) are unsupervised, i.e. do not require pre-existing baseline truth from the

expensive individual monitoring of appliances for training, and 2) are focused on low frequency

monitoring, which can be more reasonably expected to be available from multiple homes in a smart

grid.


References

Kim, H., Marwah, M., Arlitt, M., Lyon, G., & Han, J. (2011). Unsupervised Disaggregation of Low

Frequency Power Measurements. Proceedings of the 2011 SIAM International Conference on

Data Mining, (pp. 747-758). Mesa, AZ, USA.

Kolter, J. Z., & Jaakkola, T. (2012). Approximate Inference in Additive Factorial HMMs with Application to

Energy Disaggregation. Proceedings of the 15th International Conference on Artificial Intelligence

and Statistics (AISTATS). La Palma, Canary Islands.

Murray, D., Stankovic, L., & Stankovic, V. (2017). An electrical load measurements dataset of United

Kingdom households from a two-year longitudinal study. Scientific Data, 4.

Zhao, B., Stankovic, L., & Stankovic, V. (2016). On a Training-Less Solution for Non-Intrusive Appliance

Load Monitoring Using Graph Signal Processing. IEEE Access, 4, 1784-1799.

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