Temporal Motifs in Smart Grid

Rucha Bhalchandra Joshi

1,2 a

, Annada Prasad Behera

1,2 b

and Subhankar Mishra

1,2 c

Machine Learning And Building (MLAB), School of Computer Sciences,

National Institute of Science Education and Research, Bhubaneswar - 752050, India

Homi Bhabha National Institute, Anushaktinagar, Mumbai - 400094, India

Keywords:

Smart Grid, Temporal Motifs, Complex Systems, Cyber-physical Systems.

Abstract:

A complex network can be characterized by patterns. Such frequently occurring signiﬁcant patterns are called

motifs and in a time dependent network, they are called temporal motifs. One of the temporal networks where

temporal motifs are observed and play a major role; is the Smart Grid. The energy consumption pattern across

the appliances, houses, communities and entire cities help energy utility companies and consumers plan their

electricity generation and consumption. The temporal motifs for the smart grid constitutes of the consumers

and producers and the edge or connection represents energy ﬂow between two participants of the network,

these connections last till the power is being consumed/generated. This paper formally deﬁnes the temporal

motifs for smart grid network and proposes a way to create such temporal motifs in the network. We also

discuss how the temporal motifs ﬁt into the hierarchical structure of power distribution system of Smart Grid.

1 INTRODUCTION

Many complex systems can be abstracted with the

help of networks. The entities participating in the sys-

tems are modeled as nodes and the relations by which

they are linked to each other are modeled as the edges

of a network graph. Abstractions help us study the

complex system such as food chain, citation network.

Time dependent systems can be abstracted as tem-

poral networks. Some notable examples of temporal

network are Facebook, Email as well as recent net-

works such as Bitcoin. Structure of the temporal net-

work changes with time. Since the edges in temporal

graphs depend on time, their presence is determined

only at a given time. To understand the behaviour of

the temporal network, it is essential to consider the

time of occurrence of temporal edges.

One such system is smart grid network. A smart

grid has various entities, such as producers, con-

sumers, transmitters of power, participating in the net-

work. The hierarchical structure of the smart grid

has been discussed by (Aggarwal et al., 2010; Mishra

et al., 2016) where the power distribution in the grid is

according to the voltage. (Rech and Harth, 2012) dis-

cussed the existence of the consumption sector of the

https://orcid.org/0000-0003-1214-7985

https://orcid.org/0000-0003-2377-8993

https://orcid.org/0000-0002-9910-7291

hierarchy wherein the lowermost layer consists of the

last links of distribution grid connecting consumers

to the main grid. A transformer supplies the power to

the consumers that are connected to it. So, the second

layer from the bottom consists of transformers. The

third layer is of substations that supply power to the

transformers in second layer. This hierarchy goes up

along with all the participating entities in the grid net-

work. Pattern of distribution of power consumption

over the period of time form motifs. These motifs de-

picts the behaviour of the participating entities.

In a smart grid, the meters can get the data pertain-

ing to each of the appliances used in the house that

consumes amount of electricity. Smart meter keeps

track of the consumption of each of the rooms or any

other infrastructure that consumes electricity. Hence,

at household level, the electricity consumption and

distribution is known with the help of smart meters.

The inferences about the usage of electricity at the

lowermost layer in a smart grid can be drawn by tak-

ing this consumption data into consideration.

Our contributions are as follows:

• We formally deﬁne temporal motifs that occur in

smart grid network.

• We show a method for constructing such Tempo-

ral Motifs in Smart Grid network.

• We discuss Temporal Motifs in Smart Grid with

overlapping window and ﬁtting the temporal mo-

122

Joshi, R., Behera, A. and Mishra, S.

Temporal Motifs in Smart Grid.

DOI: 10.5220/0009575301220127

In Proceedings of the 9th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2020), pages 122-127

ISBN: 978-989-758-418-3

tifs in the hierarchical structure of the smart grid.

The remainder of the paper is organized as follows:

Section 2 discusses the related work. We discuss the

background work in Section 3. Section 4 gives the de-

tailed explanation of our proposed model. We present

a case study and discussion of Temporal Motifs in

Smart Grid network are in Section 3 and 4 respec-

tively. We present the conclusions in Section 6.

2 RELATED WORK

Motifs (Milo et al., 2002) are the basic building

blocks of a complex network. They are recurring,

signiﬁcant patterns of interconnections. The network

motifs are deﬁned to study the structural design prin-

ciples of complex networks in various ﬁelds such as

biochemistry, neurobiology, ecology, engineering and

so on.

Motifs, deﬁned as the frequently occurring and

signiﬁcant patterns in time, can be used to character-

ize the time series data (Lin et al., 2003). Motifs in

temporal networks have been deﬁned in order to un-

derstand their role in the temporal networks such as

the network of emails, phone calls, social media etc.

(Paranjape et al., 2017). However, they only consider

the occurrence of the edges one at a time without any

duration attached to the existence of the edges.

Motif based pattern detection technique was pro-

posed to discover regular behaviour of smart meter

users (Funde et al., 2018). The model proposed by

(Funde et al., 2018) considers one appliance at a time

and detects the motifs formed by it. They develop

temporal association rule mining to ﬁnd the relation

between usage of energy by various appliances in a

particular time period. However, considering only

one appliance at a time does not tell a complete story

about the consumption pattern of the members of the

house.

3 BACKGROUND WORK

3.1 Temporal Graph and Motif

In a temporal graph G = (V, E) where V is set of ver-

tices and E is set of edges, the temporal edges are

represented as (u, v,t) where u, v ∈ V and a timestamp

t is associated with the edge. Temporal motif is a col-

lection of edges in a particular sequence that form a

particular structure in a given time window δ. Since

the timestamps are attached with each of the edges in

temporal network, the motif is the structure occurring

within time δ from the occurrence time of ﬁrst edge.

This time window of size δ is slid over the time as we

consider the next motif. When we consider the tem-

poral edges in smart grid, the edges occur at different

times but they last for a duration of time. Smart grid is

a speciﬁc application of temporal network where the

edges have a time of occurrence and it remains in the

network till the appliance that caused it to occur was

switched off or no longer draws any energy from the

meter. This differentiates our work from the previous

work as edges stay alive for a certain duration. We

say that an edge occurs at a given time when the appli-

ance corresponding to the node connecting the edge is

turned on. The smart meter captures the energy at par-

ticular time interval in a sequence, hence we have to

assign a window time to it rather than the actual start

time of the consumption. The energy consumption by

same appliance may vary at different times.

3.2 Topology of Smart Grid

Figure 1: Topology of Power Grid.

The power distribution grid is arranged according to

the voltage (Aggarwal et al., 2010). The various levels

of the hierarchy are connected using the voltage net-

works, here power plants are connected via high volt-

age networks and the level of household appliances is

connected using a voltage network. The smart grid

is deﬁned to consist of nodes N and interconnected

edges E; where nodes represent the actors and are

connected to #b other nodes (b is branching factor).

The levels of this hierarchy is denoted by L (Rech and

Harth, 2012).

4 SMART GRID TEMPORAL

MOTIFS

We propose a model (Figure 2) for creation of tem-

poral star motifs with associated symbol correspond-

ing to the energy consumption. We also show how

these motifs help to draw inferences from the hierar-

chy of the participants of a smart grid network. In

our proposed model the edges of the motifs have been

tagged with symbols associated with corresponding

energy consumption levels and time window. These

Temporal Motifs in Smart Grid

123

timestamps are indicatives of window frame num-

bers. They imply the order of occurrences of the motif

structures.

Figure 2: Overview of motif creation process for smart

grids.

Consider m

to be meter reading (total) at a given time

i. We consider a time series T = m

, m

, ..., m

. Each

consists of the values corresponding to internal dis-

tribution of energy among all the appliances utilizing

the energy at a given time i. Let A be the set of ap-

pliances. Let c

be the energy consumed by the j

appliance at time i. Therefore,

∑

j∈A

4.1 Motif Creation

A star motif is deﬁned as a graph of k nodes in to-

tal, out which one node (the center node) has k − 1

neighbors, which is the center node while all the other

nodes have only one neighbor each. An example of

star motif is shown in Fig. 3.

Figure 3: Example of a star motif. There are 5 nodes in

total. One center node and four neighbors to the center

node. The direction of the edges between the center node

and the neighboring nodes depends on the relationship be-

tween them.

Figure 4: Example of a static star motif in a house.

We consider a particular consumer where there are

various appliances in a house that contribute to over-

all consumption of energy in the house. All of which

are essentially connected to the main smart meter. We

create a star motif of these appliances along with the

smart meter. Fig 4 shows a star motif within a house

where we consider the smart meter in the house to be

the center node and all the appliances to be the rest

of the nodes which are only connected to the center

node. The nodes for the appliances that draw energy

from the meter are represented using an edge from

meter (center node) to the appliance (corresponding

neighboring node). For any other equipment that gen-

erates energy (e.g. solar panel), the edge goes from

the equipment to the center node.

4.2 Symbolic Representation

1. Data Preprocessing and Min-max Normaliza-

tion. Time series data preprocessing is done to

normalize the data. We consider smart meter data

which keeps track of consumption of each of the

appliance. We perform min-max normalization so

that the values after normalization lies between

[0, 1]. The normalized value y, of a data point x, is

given by

y =

(x − min)

(max − min)

where min is the minimum and max is the maxi-

mum data value in the dataset.

2. Piecewise Aggregate Approximation. On the

normalized data, we apply Piecewise Aggregate

Approximation (PAA) to discretize the data. By

selecting the right parameters in PAA, it can be

altered to suit the needs of the application at hand.

The normalized time series data is divided into w

windows. The average of values in every window

is calculated.

3. Matching Symbols to Energy Levels. After

PAA, we represent the energy consumption of

each of the appliance with a symbol. Number

of energy levels and their corresponding symbols

is another parameter that can be set according to

SMARTGREENS 2020 - 9th International Conference on Smart Cities and Green ICT Systems

124

Table 1: Description of variables associated with a temporal

edge in smart grid.

Variable Description

Supplier of power (any appli-

ance that produces or supplies

power)

Consumer of power (any appli-

ance that consumes power)

Timestamp of the time window

corresponding to the edge

Symbol corresponding to the

level of energy consumption as-

signed to the edge n the given

window

use case. The symbol values represent the lev-

els of energy consumption over normalized data.

The data values range between 0 and 1, so we de-

cide on number of symbol to be used and range

of each of energy consumption corresponding to

each symbol. The number of energy levels vary

application to application.

4.3 Symbol Assignments to Edges of a

Motif

The edges in static motif that we created in ﬁrst step,

for a house is assigned timestamps associated with the

time window in which we are determining the associ-

ated symbol. In the static motifs, edges are between

the main line and an appliance. The temporal edge

occurs in smart grid in the window in which an appli-

ance is turned on.

We deﬁne the temporal edge for grid network

as quadruple represented as (u, v, t

, x). Table 1 de-

scribes each component of the quadruple. We perform

the operations described in the previous steps on the

data, to get the symbols associated for each of the ap-

pliance in the same set of time windows. Then, for a

particular window, consider all the appliances along

with meter as nodes, while the energy production and

consumption among appliances determine the direc-

tions between the edges and the level of energy con-

sumption is given by the symbol associated with the

edge. The time window is in which we are determin-

ing the consumption level is given by the timestamp

corresponding to the time window.

The complete data of consumption in a grid can

be represented as the collection of the temporal edges

we deﬁned earlier.

Figure 5: Example of star motif in a house.

4.4 Temporal Motifs for Electric Grid

Network

As shown in Fig. 5, along with assignments of sym-

bols to the edges in static motif, note that this motif

structure occurs in a particular time duration, since

each of the symbols assigned to the edges represent

the level of consumption in a particular time period.

The motif helps us to look at the consumption and dis-

tribution of energy among all appliances in a time slot

in a house. The collection of such motifs over a time

windows of size δ is deﬁned to be a temporal motif

for energy consumption data.

5 CASE STUDY

We take an example to demonstrate the steps to cre-

ate Temporal Motifs in Smart Grid network. We take

a part of Pecan Street Dataport (Dataport, ) from 15

minute dataset. We consider a house with data-id 27,

which is located at New York. For this house, we

consider the consumption values for the time period

04:00:00 to 07.00.00 on 2019-05-01.

5.1 Motif Creation

Figure 6: Static Motif for house ID 27.

The underlying star motif for this house ID is shown

Temporal Motifs in Smart Grid

125

in Fig.6. This is derived based on the appliances used

in the house.

5.2 Symbolic Representation

1. Data Preprocesssing and Min-max Normaliza-

tion. Preprocessing and min-max normalization

of data is done according to formulas mentioned

in Section 1 to get the normalized data.

2. Piecewise Aggregate Approximation. Since the

data has a duration of 3 hours, with windows size

of 1 hour, the number of windows w = 3. For any

given time window there is a value attached to it

which is average of the values corresponding to

the timestamps in the window.

3. Matching Symbols to Energy Levels. We con-

sider 4 symbols a, b, c and d, they correspond to

four consumption levels. Very low consumption

is represented by a symbol a, b represents aver-

age energy consumption, c represents more than

average consumption of energy while very high

energy consumption is represented by symbol d.

We deﬁne the range for each of the symbols as

shown in Table.2.

Table 2: Range for each of the symbols.

Symbol Range

a 0 ≤ value < 0.25

b 0.25 ≤ value < 0.5

c 0.5 ≤ value < 0.75

d 0.75 ≤ value ≤ 1

5.3 Symbol Assignments to Edges of a

Motif

Each edge in the static motif created in Section 5.1

has a symbol that corresponds to the average of the

values of consumption on each edge in a window. The

symbols are assigned to the edges. An example of a

motif in House ID 27 for time window labelled t

for

duration on 1 hour is shown in Fig.7a.

5.4 Temporal Motifs for Electric Grid

Network

A sequence of motifs created in Section 5.3 may have

different symbols associated with their edges in dif-

ferent time windows, since the energy consumption

varies over time. Such a sequence is the temporal mo-

tif in a smart grid network. The ﬁnal temporal motif

with 3 time windows is shown in Fig.7. Increase in

(a) Motif at time t

(b) Motif at time t

Figure 7: Temporal Motifs in Smart Grid network.

consumption level is indicated by symbols inside up-

ward pointing triangles, whereas the decrease in con-

sumption is indicated by symbols inside triangles fac-

ing downward in the temporal motifs.

6 DISCUSSION

Overlapping Temporal Motifs

While we only consider the window for ﬁnding the

symbols associated with edges to be non-overlapping,

other possibilities to be considered are overlapping

window and the absolute consumption values. Con-

SMARTGREENS 2020 - 9th International Conference on Smart Cities and Green ICT Systems

126

sidering absolute values is too speciﬁc because the

consumption of energy on one day may not be exactly

the same as that on the next day. Hence assigning

symbols based on absolute values at a given time may

not help infer anything useful about the data. In a time

period, if the average data consumption is considered

then it gives the approximate consumption level of the

appliance.

Overlapping window can be considered if it is

needed for the application under consideration. We

slide the window over the time duration with some

predetermined time overlapping in two consecutive

windows. This would help in maintaining the infor-

mation related to continuity of the data to some extent

depending on how much the overlap is.

Fitting Temporal Motifs Into Smart Grid

Hierarchy

We propose this model for residential type of local-

ity. This is easily scalable to other types of localities

as well, such as industrial, commercial etc and can be

extended to ﬁt other hierarchical levels in the smart

grid as well as other complex networks. To study the

role that these motifs play in smart grid network, it

is essential that we consider the hierarchy of the par-

ticipants of the network. The hierarchy described in

(Rech and Harth, 2012) is discussed below to suit for

the requirement of our model.

• The very basic level in the hierarchy consists of

the appliances in a household. As discussed ear-

lier the motifs which are formed at this layer are

based on electricity consumption of each of the

appliances at various times.

• The layer above the layer of appliances is of

houses in a locality or a community residing at a

particular location. The motifs would consist of

the houses in the locality and the point of sup-

ply of electricity to all these houses as nodes.

The consumption of each of the houses at various

times would determine the edges and the direction

of the edges. These motifs can be deﬁned in sim-

ilar fashion as we did earlier by determining the

suitable parameter values.

• Similarly, the next layer consists of communities

which together form a city.

• More layers can be thought of and considered on

top of the previously mentioned layers so as to

build the model of motifs that will help enable us

to study and determine various aspects of a smart

grid network.

7 CONCLUSION

Temporal motifs play an important role in characteriz-

ing networks. The change in usage of power over time

helps to study the behaviour of the consumers. We

have formally deﬁned the Temporal Motifs in Smart

Grid network. We have also described the construc-

tion of such Temporal Motifs in Smart Grid network,

without overlapping windows, how to ﬁt them in the

hierarchical structure of the network. In future we

will use motifs to draw inferences about participants

of the grid network. We will also look at impact of

this model on the energy distribution policies.

ACKNOWLEDGEMENTS

This research was partially supported by

NRDMS/UG/S.Mishra/Odisha/E-01/2018

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