- Email: [email protected]
Application of cluster analysis for enhancing power consumption awareness in smart grids
Application of cluster analysis for enhancing power consumption awareness in smart grids
12
Guido Coletta*, Alfredo Vaccaro*, Domenico Villacci*, Ahmed F. Zobaa† *University of Sannio, Benevento, Italy, †Brunel University, Uxbridge, United Kingdom
1
Introduction
In recent years, transmission and distribution grids have been subjected to radical changes, which mainly affected their governance and operation criteria. The need for increasing the penetration of renewable power generators, the large-scale deployment of the liberalized electricity markets, and the difficulties in upgrading the grid infrastructure are some of the main challenges that should be faced by system operators. In this complex scenario, the role of grid users is drastically changing because they are evolving from passive customers, which were characterized by inelastic power demand profiles, to the so-called prosumers, which can play an active role by properly dispatching their generation units, modulating their power demand in response to price signals, and offering high-value services to grid operators. The increasing number of these new entities is expected to sensibly improve the efficiency and security of existing electrical grids by supporting their evolution to active, flexible, and self-healing systems composed of distributed and interactive resources. Thanks to these features, the development of new tools aimed at allowing the prosumers to optimally coordinate their consumption/production profiles in function of the grid state and the spot energy price has been recognized as one of the most important foundations of future smart grids. In this context, recent studies reported in the power system literature have demonstrated that in a smart grid domain, the prosumers, if supported by accurate and reliable information about their actual energy consumption, can achieve electric energy savings up to 5–10%, which mainly derive from the detection of load anomalies and the power demand adaption to the electricity price dynamic. These advanced functions, which are usually referred as demand-side management (DSM) and demand response (DR) techniques, allow smart grid operators to interact with the prosumers in order to modify the load profiles during severe grid contingencies, avoiding the need for activating large-scale load shedding plans while also allowing the prosumers to dynamically change their demand profiles according to optimal energy sourcing policies. Despite these benefits, the adoption of these functions in existing power systems is still at its infancy, and several open problems need to be fixed in order to
Application of Smart Grid Technologies. https://doi.org/10.1016/B978-0-12-803128-5.00012-X © 2018 Elsevier Inc. All rights reserved.
398
Application of Smart Grid Technologies
support their large-scale deployment. In particular, DSM and DR techniques frequently operate on data-rich but information-limited domains because the decisions that should be identified derive by the solution of complex optimization problems whose cost and constraints functions depend on a large quantity of uncorrelated and heterogeneous data (i.e., historical load profiles, spot prices, environmental variables, etc.). On the other hand, these decisions should be identified in computation times that should be fast enough for the information to be useful in a short-term operation horizon. Hence, the development of computing paradigms aimed at converting the power demand data into actionable information, allowing the prosumer to have a full understanding of the available information, represent a timely and relevant issue to address. In the light of this need, a promising research direction is the development of smart techniques for load profile analysis, which allows prosumers to detect irregular demand patterns such as unusual energy usage, decreasing efficiency, erroneous regulations, and load malfunctioning. This strategic information could enhance the energy efficiency, reduce the supplying costs, and increase the situational awareness of prosumers about their actual power demand. These features are extremely useful in complex energy systems, characterized by large and spatially distributed loads, where the sensor data streaming could not allow a full understanding of the actual energy usage [1, 2]. To address this issue, the adoption of principal component analysis (PCA) and data clustering techniques have been recognized as the most promising enabling methodologies for load pattern classification. In particular, in [3–5] the authors proposed a methodology based on cluster analysis for classifying the proper class of homogenous users, designing the most effective tariff paradigm for optimal energy sourcing. In [6] a similar technique based on PCA and hierarchical-based clustering techniques has been proposed to solve the same problem. Also, Ozgonenel et al. [7] compare the performances of Euclidean and Mahalanobis distances in k-mean-based clustering in the task of classifying electricity customers for fault detection, and in Almutairi et al. [8] a repeated k-mean clustering methodology, which improves the ability in consumer classification, is presented. According to these arguments, in this chapter the employment of selforganizing models based on clustering analysis for power consumption awareness in a smart grid domain is proposed. The main idea is to process the sensor data streaming for classifying the load profiles, correlating them with the endogenous measured variables, and identifying irregularities in energy consumption. The analysis of the statistical correlations between the power demand and the endogenous variables is performed by a fuzzy inference system, which computes the key performance indexes for each load profile class. These indexes are processed by an outlier detection technique, which identifies irregular load patterns originated from devices malfunctions, system faults or incorrect control settings. Experimental results obtained on a real case study are presented and discussed in order to emphasize the benefits deriving from the application of the proposed framework on complex load patterns.
Application of cluster analysis for enhancing power consumption awareness in smart grids
2
399
Mathematical preliminaries
2.1 Elements of cluster analysis The self-organizing models for load anomaly detection proposed in this chapter are based on a class of data-clustering techniques that aim to organize data in homogeneous clusters, characterized by high similarity degree. In this context, the main problem to solve is how to classify objects in homogeneous groups starting from multivariate observations, maximizing the similarity of the objects in the same cluster, and maximizing, at the same time, the difference between the different clusters.
2.1.1 Clustering techniques Among the different approaches that can be adopted for cluster formation, the topdown and the bottom-up paradigms are the most frequently adopted. The first one assumes that the cluster is generated starting from a single group containing all objects, then dividing it in smaller and more homogeneous ones until a termination criteria is satisfied. On the contrary, bottom-up processes associate objects starting from the situation that all of them initially represent distinct clusters. Another very common classification of data-clustering processes is between: l
l
Partitioning clustering Hierarchical clustering
Partitioning clustering techniques provide a division of data set into nonoverlapping sets. The cluster shapes are the product of predetermined criteria for group development and a cluster is evaluated by comparing each object with respect to a point representative of the cluster, namely the centroid. One of the most diffused partitioning clustering algorithms is represented by k-mean methodology. The mathematical formulation of the partitioning clustering can be expressed through the following definition: Definition 2.1 (Partitioning clustering). Let X ¼ {X1, X2, …, XN} a set of data. The partitioning clustering provides a subset C ¼ {C1, C2, …, Ck} such that:
X
¼
k [
Ci
i¼1
Ci \ Cj ¼ ∅ for i 6¼ j
Otherwise, hierarchical clustering is based on the inclusion of smaller clusters in bigger ones, hence allowing the presence of subclusters. The outcome of this algorithm is a hierarchy tree, namely the dendrogram, depicting correlations between different clusters levels. It can be noted that hierarchical clustering can be viewed as a
400
Application of Smart Grid Technologies
sequence of partitioning clusterings, and that one can obtain the latter by considering one of the levels of the dendrogram. The objective function followed by clustering algorithms’ points to highlighting the local structure of the data and maximizing the cluster dissimilarity. A further categorization concerns the possibility that an object belongs exclusively or not to a specific cluster. In the light of this need, three possibilities can be distinguished, leading to different clustering types: l
l
l
Exclusive clustering Overlapping (or nonexclusive) clustering Fuzzy clustering
It is worth observing that, in the first category, objects belong exclusively to a specific cluster while, in the second one, objects can belong simultaneously to more clusters. In many situations, instead, belonging to a cluster is not true, but there is a probability of belonging to different clusters. In this field of application, fuzzy or probabilistic clustering algorithms are very useful, allowing us to address these problems by considering each object belonging to each cluster with a membership degree between 0 and 1, subject to the constraint that the sum of them for each object must be 1. In a probabilistic sense, that is equal to saying that the sum of probabilities for each object must be 1. The last classification is between l
l
Partial clustering Complete clustering
A complete clustering assigns all objects to clusters while a partial one does not, allowing the addressing of data issues, that is, outliers, noise or out-of-interest data, among all.
2.1.2 Cluster classification After giving a classification of the clustering algorithms, let us provide now a classification of cluster types. It is possible to distinguish among five cluster typologies (i.e., well-separated, prototype-based, graph-based, density-based, and conceptual clusters). Well-separated is characterized by the propriety that the distance between points in different clusters is greater than the distance between any two points in the same cluster. Prototype-based is characterized by the propriety that the distance between each element in the cluster and the relative prototype is minimal with respect to the protothype of the other clusters. The prototype of the cluster is often a centroid (for continuous attributes data) or a medoid (for categorical attributes data). Graph-based is useful when data are represented by graphs. In such case a cluster is defined by a connected component, that is, a group of objects interconnected with each other, but that present has no connection with elements outside. Density-based is defined by a high-density data region surrounded by a low-density data region.
Application of cluster analysis for enhancing power consumption awareness in smart grids
401
Conceptual clusters is the most general cluster definition and includes all the previous. In particular, a cluster, in such a point of view, is simply defined as a group of objects that shares some proprieties. For example, a prototype-based cluster can be seen as the group of objects that shares the propriety to be the closest to the centroid.
2.1.3 k-Means The k-mean is an exclusive partitioning clustering technique based on prototype-based clusters and represents one of the simplest and popular approaches to cluster analysis. The k-mean technique allows grouping a data set into k predetermined clusters. Let us show the basic k-mean algorithm: the first step is to fix an initial set of k centroids and to assign each object of the dataset to the closest centroid. Then the centroids are updated by considering the objects of their relative clusters. The procedure repeats until the centroid does not change anymore. So, the algorithm can be summarized as follows: 1 Initialization of a number of cluster k and an initial centroid set C0; 2 while centroids change over a certain tolerance do 3 Assign elements to the closest cluster w.r.t. the ith-1 centroids; 4 Compute the ith centroid set on the basis of the associated objects; 5 end
The first question could be how to compute the distance between each object and the relative centroid. To answer this question, it is necessary to define appropriate metrics, that is, appropriate distances d(xi, xj), quantifying the affinity degree of couples of different objects (xi, xj). Formally, a generic distance or metric is defined as: Definition 2.2 (Metric). A metric (or distance) is defined as: dðx,yÞ ¼ ðjx yjp Þ1=p abiding by the following proprieties: 1. Nonnegativity d(x, y) 0 2. Symmetry d(x, y) ¼ d(x, y) 3. Triangle inequality d(x, y) d(x, z) + d(z, y) 4. Identity of indiscernible dðx,yÞ ¼ 0 , x ¼ y;
There exist miscellaneous distance definitions, for example: l
l
l
Manhattan distance (L1): d ¼ jx yj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Euclidean distance (L2): d ¼ ðx xÞ2 Mahalanobis distance: d ¼ (x, y)S1(x, y)
402
Application of Smart Grid Technologies
Formally, once the distance d is defined, the k-means procedure is formalized as: S ¼ argmin S
k X X
distðci , xÞ
(1)
i¼1 x2Si
where k is the number of clusters, x is an object, Si is the ith cluster and ci is the centroid of the ith cluster. For application domain addressed in this chapter, the most-used distances are the L1 and, among the others, L2. It could be demonstrated that for the Manhattan metric, the optimal ith centroid is the median of the object of the cluster. For the particular case of L2 metric: S ¼ argmin S
k X X
k x ci k22
(2)
i¼1 x2Si
with ci ¼
1 X x dimðSi Þ x2S
(3)
i
2.1.4
c-Means
c-Means is a fuzzy-based clustering technique extending the concepts introduced by the k-means algorithm. This approach consists of considering each object belonging to all the clusters with a certain confidence degree. 1 Initialization of a number of cluster k and an initial centroid set C0; 2 while centroids change over a certain tolerance do 3 Compute the fuzzy membership matrix, ω, w.r.t. the centroids; Compute the ith centroid set; 4 end
Formally, the c-means procedure is formalized as: S ¼ argmin S
k X n X
ωm i, j distðci , xj Þ
(4)
i¼1 j¼1
where n is the number of objects in the dataset and m > 1 is the fuzzifier coefficient indicating the cluster’s fuzziness by determining the belonging degree of each object to each cluster. In the limit of m ¼ 1 the weights ω tend to 0 or 1, representing the particular case of the k-means algorithm. Particularizing for the Euclidean metric, as for the previous section, the c-means algorithm can be formalized as: S ¼ argmin S
k X n X i¼1 j¼1
2 ωm i, j k xj ci k2
(5)
Application of cluster analysis for enhancing power consumption awareness in smart grids
403
with n X
ωm i, j xj
j¼1
ci ¼ X n ωm i, j
(6)
j¼1
and ωi, j ¼
1 k X k x i c j k2
(7)
k xi c k k 2 i¼1
3
Detecting load outliers by clustering analysis
The described techniques can play an important role in power consumption awareness by classifying load profiles, identifying the statistical correlations between these and the endogenous variables, and detecting irregular energy usage. In this context, the main idea is to properly classify the hourly demand and the environmental temperature profiles, and identifying their correlation by applying a fuzzy inference system. Fuzzy logic completely revises the classical set theory and the semantic concept of truth, turning upside down the traditional foundation of the classical set theory, because it allows the definition of a belonging degree of an object to a set, that is considering that object belongs to that set with a certain measure. According to this paradigm, an object can belong to more than one set. In the same way, the concept of truth is radically changed; in the classical meaning, for example, if A is true, it cannot be false and vice versa. In fuzzy logic, a statement is associated with a certain degree of truth. These features are particularly useful for the application under study, because they allow the obtaining of a reliable classification of the load and temperature profiles, and an effective assessment of their correlations. A generic fuzzy inference system can be organized into three different conceptual steps: (i) fuzzification, (ii) inference, and (iii) defuzzification. A graphic scheme of the above is provided in Fig. 2, and the overall architecture of the proposed framework is shown in Fig. 1. Analyzing these figures, it is worth nothing that the first step in applying the proposed framework is to obtain reference patterns for both the electrical and the environmental daily profiles by classifying the sensor data streaming generated by the power meter and the meteorological station. The distances between the measured and the reference profiles is then processed by a fuzzy inference system to discriminate the pattern regularity, namely to detect the so-called load and temperature anomalies. Starting from this estimation, and on the basis of heuristic experiences on thermostatic loads, it could be argued that a load anomaly induced by a temperature
404
Application of Smart Grid Technologies
anomaly could be considered as a regular load pattern, that is, during summer if the environmental temperature is extremely high, the load is expected to sensibly increase. On the contrary, a load anomaly that does not correspond to a temperature anomaly is a clear indication of an irregular load pattern. These straightforward heuristic rules have been translated in proper fuzzy rules, which represent the knowledge base of the proposed fuzzy inference system.
Power meter
Clustering
Data processing Fuzzy inference system
Meteo station
Clustering
Data processing
Fig. 1 Proposed algorithm.
Fuzzification HIGH
MIDDLE LOW
Defuzzification 1
Fuzzy rules
0.5 0
Fuzzification HIGH -10 MIDDLE LOW
Fig. 2 Fuzzy inference system.
-5
0
5
10
Application of cluster analysis for enhancing power consumption awareness in smart grids
4
405
Case study
In this section, the proposed framework has been applied in the task of detecting power demand irregularities for a large commercial user located in the south of Italy. The analyzed domain is characterized by complex demand patterns, mainly due to air conditioning, lighting, and medical and technological services, which changes considerably on the basis of the seasons and environmental conditions. The corresponding distribution of the yearly average power demands is reported in Fig. 3. As shown in Fig. 3, the air conditioning has a bearing of 42% on the total energy consumption. Further, lighting represents another relevant item in the energy computation because many wards need lighting for more than 12–14 h/day. Laundry and kitchen represent another big portion of the energy loads, even though they consist totally of thermal energy requirements. The electric system under analysis consists of a medium-voltage distribution network connected, by three power lines, to the user substation. In order to detect the demand irregularities for this complex user, the load profiles and the temperature measurements for 1 year of operation time, reported in Figs. 4 and 5, respectively, have been considered. Analyzing these figures, it is worth noting that the considered yearly profiles have been characterized by complex and heterogeneous patterns, which are characterized by extremely variable electrical and environmental dynamics. The proposed methodology can be conceptually divided into two main parts: the clustering-based classification of the load and temperature profiles, and the fuzzybased processing of the computed quantities. The first step consists in classifying the power meter and sensor acquisitions within predetermined clusters, through k-mean- and c-mean-based algorithms. The first are classified into 16 different clusters on the basis of the day (business day/holiday), the loading level (i.e., low and high load), and the season. Fig. 3 User energy consumptions.
Domestic hot water Laundry 13% 15%
Kitchen 12%
Lighting
2% Sterilization
16%
42% Heating and cooling
406
Application of Smart Grid Technologies
Fig. 4 One-year load profiles.
Environmental temperature (°C)
40
20
0 350
300
250
200
Day (n)
150
100
16 12 14
50
0
18 20
22 24
8 10 4 6 0 2 Time (h)
Fig. 5 One-year temperature profiles.
The results of this classification process are shown in Figs. 6–13, which depict the centroids identified by both k-mean and c-mean clustering techniques. Moreover, the temperature profiles are classified on the basis of the season and the day (hot, middle, and cold), as shown in Figs. 14–21, where, as for the active power load profiles, the cluster centroids for both k-mean and c-mean techniques are represented. The second conceptual step (i.e., the fuzzy-based outliers detection) computes the distance between each load and temperature profile and the corresponding centroid. When such distance is greater than a threshold value, the corresponding load profile is classified as an anomalous profile. In order to distinguish between endogenous or exogenous effects, the framework correlates demand and temperature profiles: if temperature and demand profiles are both anomalous the anomaly is classified as
Application of cluster analysis for enhancing power consumption awareness in smart grids 400
Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
407
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 6 Wintry load profiles: k-mean. (A) Business day; (B) holiday.
400
Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
(A)
0
5
10
15
20
25
Hour
Low load High load
350 300 250 200 150 100
(B)
0
5
10
15
20
25
Hour
Fig. 7 Spring load profiles: k-mean. (A) Business day; (B) holiday.
400
Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
0
5
10
(A)
15
20
Low load High load
350 300 250 200 150 100
25
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 8 Summer load profiles: k-mean. (A) Business day; (B) holiday. 400 Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
(A)
0
5
10
15 Hour
20
25
Low load High load
350 300 250 200 150 100
0
5
(B)
Fig. 9 Fall load profiles: k-mean. (A) Business day; (B) holiday.
10
15 Hour
20
25
408
Application of Smart Grid Technologies 400 Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load Mid-low load Mid-high load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 10 Wintry load profiles: c-mean. (A) Business day; (B) holiday. 400 Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load Mid-low load Mid-high load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 11 Spring load profiles: c-mean. (A) Business day; (B) holiday. 400 Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load Mid-low load Mid-high load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 12 Summer load profiles: c-mean. (A) Business day; (B) holiday. 400
Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
(A)
0
5
10
15 Hour
20
25
Low load Mid-low load Mid-high load High load
350 300 250 200 150 100
0
5
(B)
Fig. 13 Fall load profiles: c-mean. (A) Business day; (B) holiday.
10
15 Hour
20
25
Application of cluster analysis for enhancing power consumption awareness in smart grids 50 Environmental temperature (°C)
Environmental temperature (°C)
50
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
409
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 14 Wintry temperature profiles: k-mean. (A) Business day; (B) holiday. 50 Environmental temperature (°C)
Environmental temperature (°C)
50 Low temperature Mid temperature High temperature
40 30 20 10 0 -10
0
5
10
(A)
15
20
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
25
0
5
10
(B)
Hour
15
20
25
20
25
Hour
Fig. 15 Spring temperature profiles: k-mean. (A) Business day; (B) holiday. 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15 Hour
Fig. 16 Summer temperature profiles: k-mean. (A) Business day; (B) holiday. 50 Environmental temperature (°C)
Environmental temperature (°C)
50
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
(A)
0
5
10
15 Hour
20
25
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
(B)
0
5
10
15 Hour
Fig. 17 Fall temperature profiles: k-mean. (A) Business day; (B) holiday.
20
25
410
Application of Smart Grid Technologies 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 18 Wintry temperature profiles: c-mean. (A) Business day; (B) holiday. 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15
20
25
20
25
Hour
Fig. 19 Spring temperature profiles: c-mean. (A) Business day; (B) holiday. 50 Environmental temperature (°C)
Environmental temperature (°C)
50
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15 Hour
Fig. 20 Summer temperature profiles: c-mean. (A) Business day; (B) holiday. 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
(A)
0
5
10
15 Hour
20
25
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
(B)
0
5
10
15 Hour
Fig. 21 Fall temperature profiles: c-mean. (A) Business day; (B) holiday.
20
25
Application of cluster analysis for enhancing power consumption awareness in smart grids
411
exogenous while if only the absorption profile is anomalous, it is classified as endogenous, and the considered profile is detected as an outlier. The results of this process are summarized in Figs. 22–29, where, for each minimum and maximum temperature profile, the temperature and absorption anomalies have been highlighted by denoting them with circles and stars, respectively. Analyzing these results, it is possible to identify the days in which temperature and absorption outliers coexist in the system and, hence, it is possible to identify absorption anomalies that cannot be related to climatic events and that can be reasonably associated with other factors influencing system operation. Finally, the results of this application can be summarized in tabular format, allowing the performance comparison between k-mean and c-mean data clustering approaches (Tables 1–3). 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 Day (n)
40
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
(B)
0
5
10
15 Day (n)
20
25
Fig. 22 Wintry anomalies: k-mean. (A) Business day; (B) holiday. 50 Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15 Day (n)
20
25
Fig. 23 Spring anomalies: k-mean. (A) Business day; (B) holiday.
30 20 10 0 -10
(A)
50
Mean temperature Load anomalies Temperature anomalies
40
0
10
20
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
Fig. 24 Summer anomalies: k-mean. (A) Business day; (B) holiday.
15 Day (n)
20
25
412
Application of Smart Grid Technologies 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15
20
25
Day (n)
Fig. 25 Fall anomalies: k-mean. (A) Business day; (B) holiday. 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 Day (n)
40
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15 Day (n)
20
25
Fig. 26 Wintry anomalies: c-mean. (A) Business day; (B) holiday. 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15 Day (n)
20
25
Fig. 27 Spring anomalies: c-mean. (A) Business day; (B) holiday.
30 20 10 0 -10
(A)
50
Mean temperature Load anomalies Temperature anomalies
40
0
10
20
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
Fig. 28 Summer anomalies: c-mean. (A) Business day; (B) holiday.
15 Day (n)
20
25
50
Mean temperature Load anomalies Temperature anomalies
40
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
(A)
0
10
20
30 40 Day (n)
50
30 20 10 0 -10
60
(B)
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
15
20
25
Day (n)
Fig. 29 Fall anomalies: c-mean. (A) Business day; (B) holiday.
Table 1
Winter Spring Summer Fall
Table 2
Load anomalies k-Mean
c-Means
6 36 77 78 356 357 359 360 361 362 364 85 100 116 122 159 161 162 163 165 173 182 184 200 204 207 220 225 228 240 241 242 265 268 272 273 286 292 298 302 303 306 333 348 350
2 6 9 13 48 58 68 72 77 358 359 360 361 362 363 365 85 90 98 100 116 117 134 150 154 156 158 162 200 201 207 225 233 234 237 268 269 272 273 275 277 280 281 302 306 310 333 335 352
Temperature anomalies k-Mean
c-Means
Winter
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Spring
118 119 132 133 152 153 160 161 168 169 174 175 183 184 191 192 209 210 217 218 227 228 235 236 243 244 268 269 276 277 284 285 292 293 300 301
2 4 5 6 9 10 11 12 13 16 17 18 19 20 23 24 25 26 27 30 31 51 52 55 57 58 59 63 64 67 68 70 71 77 78 356 359 360 361 364 96 97 100 102 103 104 107 108 109 110 111 114 115 116 119 120 128 133 134 135 137 138 141 143 149 154 155 161 162 168 169
Summer
Fall
120 134 154 162 170 176 185 193 211 219 229 237
121 122 141 142 155 156 163 164 171 172 178 179 186 187 196 197 212 213 220 221 230 231 238 239
123 130 145 146 157 158 165 166 173 180 181 188 189 201 202 214 215 222 223 232 233 240 241
131 151 159 167
270 278 286 294 310
271 272 279 280 287 288 295 296 311 317
273 274 281 282 289 290 297 298 318 319
275 283 291 299
182 190 203 216 226 234 242
174 183 191 209 217 227 235 243 268 276 284 292 300
175 176 184 185 192 193 210 211 218 219 228 229 236 237 244 269 270 277 278 285 286 293 294 301 310
178 186 196 212 220 230 238
179 180 187 188 197 201 213 214 221 222 231 232 239 240
181 182 189 190 202 203 215 216 223 226 233 234 241 242
271 279 287 295 311
272 273 280 281 288 289 296 297 317 318
274 275 282 283 290 291 298 299 319
414
Application of Smart Grid Technologies
Table 3
Endogenous load anomalies
Winter Spring Summer Fall
5
k-Means
c-Means
6 77 78 356 357 359 360 361 362 364 85 100 116 200 204 207 225 265 302 303 306 333 348 350
48 72 358 362 363 365 85 90 98 117 150 156 158 200 207 225 302 306 333 335 352
Conclusion
The development of computing paradigms aimed at converting the power demand data into actionable information, allowing the prosumer to have a full understanding of the available information, represents a timely and relevant issue to address. In light of this need, this chapter analyzed the potential role of cluster analysis and fuzzybased programming for detecting irregular demand patterns, such as unusual energy usage, decreasing efficiency, erroneous regulations, and load malfunctioning. This strategic information could enhance the energy efficiency, reduce the supplying costs, and increase the situational awareness of prosumers about their actual power demand. Experimental results obtained on a real case study have been presented and discussed in order to assess the benefits deriving by the application of the proposed framework in the task of analyzing complex load patterns.
References [1] Y.-I. Kim, J.-M. Ko, J.-J. Song, H. Choi, Repeated clustering to improve the discrimination of typical daily load profile, J. Electr. Eng. Technol. 7 (3) (2012) 281–287. [2] S.-L. Yang, C. Shen, et al., A review of electric load classification in smart grid environment, Renew. Sustain. Energy Rev. 24 (2013) 103–110. [3] G. Chicco, R. Napoli, F. Piglione, Application of clustering algorithms and self organising maps to classify electricity customers, in: 2003 IEEE Bologna Power Tech Conference Proceedings, vol. 1, IEEE, 2003, p. 7. [4] G. Chicco, R. Napoli, F. Piglione, Comparisons among clustering techniques for electricity customer classification, IEEE Trans. Power Syst. 21 (2) (2006) 933–940. [5] G. Chicco, R. Napoli, F. Piglione, Load pattern clustering for short-term load forecasting of anomalous days, in: 2001 IEEE Porto Power Tech Proceedings, vol. 2, IEEE, 2001, p. 6. [6] Y. Li, Y. Cheng, L. Zhang, H. Huang, Application of multivariate statistical analysis to classify electricity customers, in: China International Conference on Electricity Distribution, 2008. CICED 2008, IEEE, 2008, pp. 1–6. [7] O. Ozgonenel, D.W.P. Thomas, T. Yalcin, I.N. Bertizlioglu, Detection of blackouts by using K-means clustering in a power system, in: 11th International Conference on Developments in Power Systems Protection, 2012. DPSP 2012, IET, 2012, pp. 1–6. [8] K. Anaparthi, B. Chaudhuri, N.F. Thornhill, B.C. Pal, Coherency identification in power systems through principal component analysis, IEEE Trans. Power Sys. 20 (3) (2005) 1658–1660.
12
Guido Coletta*, Alfredo Vaccaro*, Domenico Villacci*, Ahmed F. Zobaa† *University of Sannio, Benevento, Italy, †Brunel University, Uxbridge, United Kingdom
1
Introduction
In recent years, transmission and distribution grids have been subjected to radical changes, which mainly affected their governance and operation criteria. The need for increasing the penetration of renewable power generators, the large-scale deployment of the liberalized electricity markets, and the difficulties in upgrading the grid infrastructure are some of the main challenges that should be faced by system operators. In this complex scenario, the role of grid users is drastically changing because they are evolving from passive customers, which were characterized by inelastic power demand profiles, to the so-called prosumers, which can play an active role by properly dispatching their generation units, modulating their power demand in response to price signals, and offering high-value services to grid operators. The increasing number of these new entities is expected to sensibly improve the efficiency and security of existing electrical grids by supporting their evolution to active, flexible, and self-healing systems composed of distributed and interactive resources. Thanks to these features, the development of new tools aimed at allowing the prosumers to optimally coordinate their consumption/production profiles in function of the grid state and the spot energy price has been recognized as one of the most important foundations of future smart grids. In this context, recent studies reported in the power system literature have demonstrated that in a smart grid domain, the prosumers, if supported by accurate and reliable information about their actual energy consumption, can achieve electric energy savings up to 5–10%, which mainly derive from the detection of load anomalies and the power demand adaption to the electricity price dynamic. These advanced functions, which are usually referred as demand-side management (DSM) and demand response (DR) techniques, allow smart grid operators to interact with the prosumers in order to modify the load profiles during severe grid contingencies, avoiding the need for activating large-scale load shedding plans while also allowing the prosumers to dynamically change their demand profiles according to optimal energy sourcing policies. Despite these benefits, the adoption of these functions in existing power systems is still at its infancy, and several open problems need to be fixed in order to
Application of Smart Grid Technologies. https://doi.org/10.1016/B978-0-12-803128-5.00012-X © 2018 Elsevier Inc. All rights reserved.
398
Application of Smart Grid Technologies
support their large-scale deployment. In particular, DSM and DR techniques frequently operate on data-rich but information-limited domains because the decisions that should be identified derive by the solution of complex optimization problems whose cost and constraints functions depend on a large quantity of uncorrelated and heterogeneous data (i.e., historical load profiles, spot prices, environmental variables, etc.). On the other hand, these decisions should be identified in computation times that should be fast enough for the information to be useful in a short-term operation horizon. Hence, the development of computing paradigms aimed at converting the power demand data into actionable information, allowing the prosumer to have a full understanding of the available information, represent a timely and relevant issue to address. In the light of this need, a promising research direction is the development of smart techniques for load profile analysis, which allows prosumers to detect irregular demand patterns such as unusual energy usage, decreasing efficiency, erroneous regulations, and load malfunctioning. This strategic information could enhance the energy efficiency, reduce the supplying costs, and increase the situational awareness of prosumers about their actual power demand. These features are extremely useful in complex energy systems, characterized by large and spatially distributed loads, where the sensor data streaming could not allow a full understanding of the actual energy usage [1, 2]. To address this issue, the adoption of principal component analysis (PCA) and data clustering techniques have been recognized as the most promising enabling methodologies for load pattern classification. In particular, in [3–5] the authors proposed a methodology based on cluster analysis for classifying the proper class of homogenous users, designing the most effective tariff paradigm for optimal energy sourcing. In [6] a similar technique based on PCA and hierarchical-based clustering techniques has been proposed to solve the same problem. Also, Ozgonenel et al. [7] compare the performances of Euclidean and Mahalanobis distances in k-mean-based clustering in the task of classifying electricity customers for fault detection, and in Almutairi et al. [8] a repeated k-mean clustering methodology, which improves the ability in consumer classification, is presented. According to these arguments, in this chapter the employment of selforganizing models based on clustering analysis for power consumption awareness in a smart grid domain is proposed. The main idea is to process the sensor data streaming for classifying the load profiles, correlating them with the endogenous measured variables, and identifying irregularities in energy consumption. The analysis of the statistical correlations between the power demand and the endogenous variables is performed by a fuzzy inference system, which computes the key performance indexes for each load profile class. These indexes are processed by an outlier detection technique, which identifies irregular load patterns originated from devices malfunctions, system faults or incorrect control settings. Experimental results obtained on a real case study are presented and discussed in order to emphasize the benefits deriving from the application of the proposed framework on complex load patterns.
Application of cluster analysis for enhancing power consumption awareness in smart grids
2
399
Mathematical preliminaries
2.1 Elements of cluster analysis The self-organizing models for load anomaly detection proposed in this chapter are based on a class of data-clustering techniques that aim to organize data in homogeneous clusters, characterized by high similarity degree. In this context, the main problem to solve is how to classify objects in homogeneous groups starting from multivariate observations, maximizing the similarity of the objects in the same cluster, and maximizing, at the same time, the difference between the different clusters.
2.1.1 Clustering techniques Among the different approaches that can be adopted for cluster formation, the topdown and the bottom-up paradigms are the most frequently adopted. The first one assumes that the cluster is generated starting from a single group containing all objects, then dividing it in smaller and more homogeneous ones until a termination criteria is satisfied. On the contrary, bottom-up processes associate objects starting from the situation that all of them initially represent distinct clusters. Another very common classification of data-clustering processes is between: l
l
Partitioning clustering Hierarchical clustering
Partitioning clustering techniques provide a division of data set into nonoverlapping sets. The cluster shapes are the product of predetermined criteria for group development and a cluster is evaluated by comparing each object with respect to a point representative of the cluster, namely the centroid. One of the most diffused partitioning clustering algorithms is represented by k-mean methodology. The mathematical formulation of the partitioning clustering can be expressed through the following definition: Definition 2.1 (Partitioning clustering). Let X ¼ {X1, X2, …, XN} a set of data. The partitioning clustering provides a subset C ¼ {C1, C2, …, Ck} such that:
X
¼
k [
Ci
i¼1
Ci \ Cj ¼ ∅ for i 6¼ j
Otherwise, hierarchical clustering is based on the inclusion of smaller clusters in bigger ones, hence allowing the presence of subclusters. The outcome of this algorithm is a hierarchy tree, namely the dendrogram, depicting correlations between different clusters levels. It can be noted that hierarchical clustering can be viewed as a
400
Application of Smart Grid Technologies
sequence of partitioning clusterings, and that one can obtain the latter by considering one of the levels of the dendrogram. The objective function followed by clustering algorithms’ points to highlighting the local structure of the data and maximizing the cluster dissimilarity. A further categorization concerns the possibility that an object belongs exclusively or not to a specific cluster. In the light of this need, three possibilities can be distinguished, leading to different clustering types: l
l
l
Exclusive clustering Overlapping (or nonexclusive) clustering Fuzzy clustering
It is worth observing that, in the first category, objects belong exclusively to a specific cluster while, in the second one, objects can belong simultaneously to more clusters. In many situations, instead, belonging to a cluster is not true, but there is a probability of belonging to different clusters. In this field of application, fuzzy or probabilistic clustering algorithms are very useful, allowing us to address these problems by considering each object belonging to each cluster with a membership degree between 0 and 1, subject to the constraint that the sum of them for each object must be 1. In a probabilistic sense, that is equal to saying that the sum of probabilities for each object must be 1. The last classification is between l
l
Partial clustering Complete clustering
A complete clustering assigns all objects to clusters while a partial one does not, allowing the addressing of data issues, that is, outliers, noise or out-of-interest data, among all.
2.1.2 Cluster classification After giving a classification of the clustering algorithms, let us provide now a classification of cluster types. It is possible to distinguish among five cluster typologies (i.e., well-separated, prototype-based, graph-based, density-based, and conceptual clusters). Well-separated is characterized by the propriety that the distance between points in different clusters is greater than the distance between any two points in the same cluster. Prototype-based is characterized by the propriety that the distance between each element in the cluster and the relative prototype is minimal with respect to the protothype of the other clusters. The prototype of the cluster is often a centroid (for continuous attributes data) or a medoid (for categorical attributes data). Graph-based is useful when data are represented by graphs. In such case a cluster is defined by a connected component, that is, a group of objects interconnected with each other, but that present has no connection with elements outside. Density-based is defined by a high-density data region surrounded by a low-density data region.
Application of cluster analysis for enhancing power consumption awareness in smart grids
401
Conceptual clusters is the most general cluster definition and includes all the previous. In particular, a cluster, in such a point of view, is simply defined as a group of objects that shares some proprieties. For example, a prototype-based cluster can be seen as the group of objects that shares the propriety to be the closest to the centroid.
2.1.3 k-Means The k-mean is an exclusive partitioning clustering technique based on prototype-based clusters and represents one of the simplest and popular approaches to cluster analysis. The k-mean technique allows grouping a data set into k predetermined clusters. Let us show the basic k-mean algorithm: the first step is to fix an initial set of k centroids and to assign each object of the dataset to the closest centroid. Then the centroids are updated by considering the objects of their relative clusters. The procedure repeats until the centroid does not change anymore. So, the algorithm can be summarized as follows: 1 Initialization of a number of cluster k and an initial centroid set C0; 2 while centroids change over a certain tolerance do 3 Assign elements to the closest cluster w.r.t. the ith-1 centroids; 4 Compute the ith centroid set on the basis of the associated objects; 5 end
The first question could be how to compute the distance between each object and the relative centroid. To answer this question, it is necessary to define appropriate metrics, that is, appropriate distances d(xi, xj), quantifying the affinity degree of couples of different objects (xi, xj). Formally, a generic distance or metric is defined as: Definition 2.2 (Metric). A metric (or distance) is defined as: dðx,yÞ ¼ ðjx yjp Þ1=p abiding by the following proprieties: 1. Nonnegativity d(x, y) 0 2. Symmetry d(x, y) ¼ d(x, y) 3. Triangle inequality d(x, y) d(x, z) + d(z, y) 4. Identity of indiscernible dðx,yÞ ¼ 0 , x ¼ y;
There exist miscellaneous distance definitions, for example: l
l
l
Manhattan distance (L1): d ¼ jx yj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Euclidean distance (L2): d ¼ ðx xÞ2 Mahalanobis distance: d ¼ (x, y)S1(x, y)
402
Application of Smart Grid Technologies
Formally, once the distance d is defined, the k-means procedure is formalized as: S ¼ argmin S
k X X
distðci , xÞ
(1)
i¼1 x2Si
where k is the number of clusters, x is an object, Si is the ith cluster and ci is the centroid of the ith cluster. For application domain addressed in this chapter, the most-used distances are the L1 and, among the others, L2. It could be demonstrated that for the Manhattan metric, the optimal ith centroid is the median of the object of the cluster. For the particular case of L2 metric: S ¼ argmin S
k X X
k x ci k22
(2)
i¼1 x2Si
with ci ¼
1 X x dimðSi Þ x2S
(3)
i
2.1.4
c-Means
c-Means is a fuzzy-based clustering technique extending the concepts introduced by the k-means algorithm. This approach consists of considering each object belonging to all the clusters with a certain confidence degree. 1 Initialization of a number of cluster k and an initial centroid set C0; 2 while centroids change over a certain tolerance do 3 Compute the fuzzy membership matrix, ω, w.r.t. the centroids; Compute the ith centroid set; 4 end
Formally, the c-means procedure is formalized as: S ¼ argmin S
k X n X
ωm i, j distðci , xj Þ
(4)
i¼1 j¼1
where n is the number of objects in the dataset and m > 1 is the fuzzifier coefficient indicating the cluster’s fuzziness by determining the belonging degree of each object to each cluster. In the limit of m ¼ 1 the weights ω tend to 0 or 1, representing the particular case of the k-means algorithm. Particularizing for the Euclidean metric, as for the previous section, the c-means algorithm can be formalized as: S ¼ argmin S
k X n X i¼1 j¼1
2 ωm i, j k xj ci k2
(5)
Application of cluster analysis for enhancing power consumption awareness in smart grids
403
with n X
ωm i, j xj
j¼1
ci ¼ X n ωm i, j
(6)
j¼1
and ωi, j ¼
1 k X k x i c j k2
(7)
k xi c k k 2 i¼1
3
Detecting load outliers by clustering analysis
The described techniques can play an important role in power consumption awareness by classifying load profiles, identifying the statistical correlations between these and the endogenous variables, and detecting irregular energy usage. In this context, the main idea is to properly classify the hourly demand and the environmental temperature profiles, and identifying their correlation by applying a fuzzy inference system. Fuzzy logic completely revises the classical set theory and the semantic concept of truth, turning upside down the traditional foundation of the classical set theory, because it allows the definition of a belonging degree of an object to a set, that is considering that object belongs to that set with a certain measure. According to this paradigm, an object can belong to more than one set. In the same way, the concept of truth is radically changed; in the classical meaning, for example, if A is true, it cannot be false and vice versa. In fuzzy logic, a statement is associated with a certain degree of truth. These features are particularly useful for the application under study, because they allow the obtaining of a reliable classification of the load and temperature profiles, and an effective assessment of their correlations. A generic fuzzy inference system can be organized into three different conceptual steps: (i) fuzzification, (ii) inference, and (iii) defuzzification. A graphic scheme of the above is provided in Fig. 2, and the overall architecture of the proposed framework is shown in Fig. 1. Analyzing these figures, it is worth nothing that the first step in applying the proposed framework is to obtain reference patterns for both the electrical and the environmental daily profiles by classifying the sensor data streaming generated by the power meter and the meteorological station. The distances between the measured and the reference profiles is then processed by a fuzzy inference system to discriminate the pattern regularity, namely to detect the so-called load and temperature anomalies. Starting from this estimation, and on the basis of heuristic experiences on thermostatic loads, it could be argued that a load anomaly induced by a temperature
404
Application of Smart Grid Technologies
anomaly could be considered as a regular load pattern, that is, during summer if the environmental temperature is extremely high, the load is expected to sensibly increase. On the contrary, a load anomaly that does not correspond to a temperature anomaly is a clear indication of an irregular load pattern. These straightforward heuristic rules have been translated in proper fuzzy rules, which represent the knowledge base of the proposed fuzzy inference system.
Power meter
Clustering
Data processing Fuzzy inference system
Meteo station
Clustering
Data processing
Fig. 1 Proposed algorithm.
Fuzzification HIGH
MIDDLE LOW
Defuzzification 1
Fuzzy rules
0.5 0
Fuzzification HIGH -10 MIDDLE LOW
Fig. 2 Fuzzy inference system.
-5
0
5
10
Application of cluster analysis for enhancing power consumption awareness in smart grids
4
405
Case study
In this section, the proposed framework has been applied in the task of detecting power demand irregularities for a large commercial user located in the south of Italy. The analyzed domain is characterized by complex demand patterns, mainly due to air conditioning, lighting, and medical and technological services, which changes considerably on the basis of the seasons and environmental conditions. The corresponding distribution of the yearly average power demands is reported in Fig. 3. As shown in Fig. 3, the air conditioning has a bearing of 42% on the total energy consumption. Further, lighting represents another relevant item in the energy computation because many wards need lighting for more than 12–14 h/day. Laundry and kitchen represent another big portion of the energy loads, even though they consist totally of thermal energy requirements. The electric system under analysis consists of a medium-voltage distribution network connected, by three power lines, to the user substation. In order to detect the demand irregularities for this complex user, the load profiles and the temperature measurements for 1 year of operation time, reported in Figs. 4 and 5, respectively, have been considered. Analyzing these figures, it is worth noting that the considered yearly profiles have been characterized by complex and heterogeneous patterns, which are characterized by extremely variable electrical and environmental dynamics. The proposed methodology can be conceptually divided into two main parts: the clustering-based classification of the load and temperature profiles, and the fuzzybased processing of the computed quantities. The first step consists in classifying the power meter and sensor acquisitions within predetermined clusters, through k-mean- and c-mean-based algorithms. The first are classified into 16 different clusters on the basis of the day (business day/holiday), the loading level (i.e., low and high load), and the season. Fig. 3 User energy consumptions.
Domestic hot water Laundry 13% 15%
Kitchen 12%
Lighting
2% Sterilization
16%
42% Heating and cooling
406
Application of Smart Grid Technologies
Fig. 4 One-year load profiles.
Environmental temperature (°C)
40
20
0 350
300
250
200
Day (n)
150
100
16 12 14
50
0
18 20
22 24
8 10 4 6 0 2 Time (h)
Fig. 5 One-year temperature profiles.
The results of this classification process are shown in Figs. 6–13, which depict the centroids identified by both k-mean and c-mean clustering techniques. Moreover, the temperature profiles are classified on the basis of the season and the day (hot, middle, and cold), as shown in Figs. 14–21, where, as for the active power load profiles, the cluster centroids for both k-mean and c-mean techniques are represented. The second conceptual step (i.e., the fuzzy-based outliers detection) computes the distance between each load and temperature profile and the corresponding centroid. When such distance is greater than a threshold value, the corresponding load profile is classified as an anomalous profile. In order to distinguish between endogenous or exogenous effects, the framework correlates demand and temperature profiles: if temperature and demand profiles are both anomalous the anomaly is classified as
Application of cluster analysis for enhancing power consumption awareness in smart grids 400
Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
407
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 6 Wintry load profiles: k-mean. (A) Business day; (B) holiday.
400
Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
(A)
0
5
10
15
20
25
Hour
Low load High load
350 300 250 200 150 100
(B)
0
5
10
15
20
25
Hour
Fig. 7 Spring load profiles: k-mean. (A) Business day; (B) holiday.
400
Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
0
5
10
(A)
15
20
Low load High load
350 300 250 200 150 100
25
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 8 Summer load profiles: k-mean. (A) Business day; (B) holiday. 400 Low load High load
350
Active power demand (kW)
Active power demand (kW)
400
300 250 200 150 100
(A)
0
5
10
15 Hour
20
25
Low load High load
350 300 250 200 150 100
0
5
(B)
Fig. 9 Fall load profiles: k-mean. (A) Business day; (B) holiday.
10
15 Hour
20
25
408
Application of Smart Grid Technologies 400 Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load Mid-low load Mid-high load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 10 Wintry load profiles: c-mean. (A) Business day; (B) holiday. 400 Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load Mid-low load Mid-high load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 11 Spring load profiles: c-mean. (A) Business day; (B) holiday. 400 Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
0
5
10
(A)
15
20
300 250 200 150 100
25
Low load Mid-low load Mid-high load High load
350
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 12 Summer load profiles: c-mean. (A) Business day; (B) holiday. 400
Low load Mid-low load Mid-high load High load
350 300
Active power demand (kW)
Active power demand (kW)
400
250 200 150 100
(A)
0
5
10
15 Hour
20
25
Low load Mid-low load Mid-high load High load
350 300 250 200 150 100
0
5
(B)
Fig. 13 Fall load profiles: c-mean. (A) Business day; (B) holiday.
10
15 Hour
20
25
Application of cluster analysis for enhancing power consumption awareness in smart grids 50 Environmental temperature (°C)
Environmental temperature (°C)
50
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
409
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 14 Wintry temperature profiles: k-mean. (A) Business day; (B) holiday. 50 Environmental temperature (°C)
Environmental temperature (°C)
50 Low temperature Mid temperature High temperature
40 30 20 10 0 -10
0
5
10
(A)
15
20
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
25
0
5
10
(B)
Hour
15
20
25
20
25
Hour
Fig. 15 Spring temperature profiles: k-mean. (A) Business day; (B) holiday. 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15 Hour
Fig. 16 Summer temperature profiles: k-mean. (A) Business day; (B) holiday. 50 Environmental temperature (°C)
Environmental temperature (°C)
50
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
(A)
0
5
10
15 Hour
20
25
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
(B)
0
5
10
15 Hour
Fig. 17 Fall temperature profiles: k-mean. (A) Business day; (B) holiday.
20
25
410
Application of Smart Grid Technologies 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15
20
25
Hour
Fig. 18 Wintry temperature profiles: c-mean. (A) Business day; (B) holiday. 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15
20
25
20
25
Hour
Fig. 19 Spring temperature profiles: c-mean. (A) Business day; (B) holiday. 50 Environmental temperature (°C)
Environmental temperature (°C)
50
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
0
5
10
(A)
15
20
30 20 10 0 -10
25
Low temperature Mid temperature High temperature
40
0
5
10
(B)
Hour
15 Hour
Fig. 20 Summer temperature profiles: c-mean. (A) Business day; (B) holiday. 50
Low temperature Mid temperature High temperature
40
Environmental temperature (°C)
Environmental temperature (°C)
50
30 20 10 0 -10
(A)
0
5
10
15 Hour
20
25
Low temperature Mid temperature High temperature
40 30 20 10 0 -10
(B)
0
5
10
15 Hour
Fig. 21 Fall temperature profiles: c-mean. (A) Business day; (B) holiday.
20
25
Application of cluster analysis for enhancing power consumption awareness in smart grids
411
exogenous while if only the absorption profile is anomalous, it is classified as endogenous, and the considered profile is detected as an outlier. The results of this process are summarized in Figs. 22–29, where, for each minimum and maximum temperature profile, the temperature and absorption anomalies have been highlighted by denoting them with circles and stars, respectively. Analyzing these results, it is possible to identify the days in which temperature and absorption outliers coexist in the system and, hence, it is possible to identify absorption anomalies that cannot be related to climatic events and that can be reasonably associated with other factors influencing system operation. Finally, the results of this application can be summarized in tabular format, allowing the performance comparison between k-mean and c-mean data clustering approaches (Tables 1–3). 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 Day (n)
40
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
(B)
0
5
10
15 Day (n)
20
25
Fig. 22 Wintry anomalies: k-mean. (A) Business day; (B) holiday. 50 Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15 Day (n)
20
25
Fig. 23 Spring anomalies: k-mean. (A) Business day; (B) holiday.
30 20 10 0 -10
(A)
50
Mean temperature Load anomalies Temperature anomalies
40
0
10
20
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
Fig. 24 Summer anomalies: k-mean. (A) Business day; (B) holiday.
15 Day (n)
20
25
412
Application of Smart Grid Technologies 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15
20
25
Day (n)
Fig. 25 Fall anomalies: k-mean. (A) Business day; (B) holiday. 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 Day (n)
40
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15 Day (n)
20
25
Fig. 26 Wintry anomalies: c-mean. (A) Business day; (B) holiday. 50
Mean temperature Load anomalies Temperature anomalies
40 30 20 10 0 -10
0
10
20
(A)
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
15 Day (n)
20
25
Fig. 27 Spring anomalies: c-mean. (A) Business day; (B) holiday.
30 20 10 0 -10
(A)
50
Mean temperature Load anomalies Temperature anomalies
40
0
10
20
30 40 Day (n)
50
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
60
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
(B)
Fig. 28 Summer anomalies: c-mean. (A) Business day; (B) holiday.
15 Day (n)
20
25
50
Mean temperature Load anomalies Temperature anomalies
40
Environmental average temperature (°C)
Environmental average temperature (°C)
50
30 20 10 0 -10
(A)
0
10
20
30 40 Day (n)
50
30 20 10 0 -10
60
(B)
Mean temperature Load anomalies Temperature anomalies
40
0
5
10
15
20
25
Day (n)
Fig. 29 Fall anomalies: c-mean. (A) Business day; (B) holiday.
Table 1
Winter Spring Summer Fall
Table 2
Load anomalies k-Mean
c-Means
6 36 77 78 356 357 359 360 361 362 364 85 100 116 122 159 161 162 163 165 173 182 184 200 204 207 220 225 228 240 241 242 265 268 272 273 286 292 298 302 303 306 333 348 350
2 6 9 13 48 58 68 72 77 358 359 360 361 362 363 365 85 90 98 100 116 117 134 150 154 156 158 162 200 201 207 225 233 234 237 268 269 272 273 275 277 280 281 302 306 310 333 335 352
Temperature anomalies k-Mean
c-Means
Winter
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Spring
118 119 132 133 152 153 160 161 168 169 174 175 183 184 191 192 209 210 217 218 227 228 235 236 243 244 268 269 276 277 284 285 292 293 300 301
2 4 5 6 9 10 11 12 13 16 17 18 19 20 23 24 25 26 27 30 31 51 52 55 57 58 59 63 64 67 68 70 71 77 78 356 359 360 361 364 96 97 100 102 103 104 107 108 109 110 111 114 115 116 119 120 128 133 134 135 137 138 141 143 149 154 155 161 162 168 169
Summer
Fall
120 134 154 162 170 176 185 193 211 219 229 237
121 122 141 142 155 156 163 164 171 172 178 179 186 187 196 197 212 213 220 221 230 231 238 239
123 130 145 146 157 158 165 166 173 180 181 188 189 201 202 214 215 222 223 232 233 240 241
131 151 159 167
270 278 286 294 310
271 272 279 280 287 288 295 296 311 317
273 274 281 282 289 290 297 298 318 319
275 283 291 299
182 190 203 216 226 234 242
174 183 191 209 217 227 235 243 268 276 284 292 300
175 176 184 185 192 193 210 211 218 219 228 229 236 237 244 269 270 277 278 285 286 293 294 301 310
178 186 196 212 220 230 238
179 180 187 188 197 201 213 214 221 222 231 232 239 240
181 182 189 190 202 203 215 216 223 226 233 234 241 242
271 279 287 295 311
272 273 280 281 288 289 296 297 317 318
274 275 282 283 290 291 298 299 319
414
Application of Smart Grid Technologies
Table 3
Endogenous load anomalies
Winter Spring Summer Fall
5
k-Means
c-Means
6 77 78 356 357 359 360 361 362 364 85 100 116 200 204 207 225 265 302 303 306 333 348 350
48 72 358 362 363 365 85 90 98 117 150 156 158 200 207 225 302 306 333 335 352
Conclusion
The development of computing paradigms aimed at converting the power demand data into actionable information, allowing the prosumer to have a full understanding of the available information, represents a timely and relevant issue to address. In light of this need, this chapter analyzed the potential role of cluster analysis and fuzzybased programming for detecting irregular demand patterns, such as unusual energy usage, decreasing efficiency, erroneous regulations, and load malfunctioning. This strategic information could enhance the energy efficiency, reduce the supplying costs, and increase the situational awareness of prosumers about their actual power demand. Experimental results obtained on a real case study have been presented and discussed in order to assess the benefits deriving by the application of the proposed framework in the task of analyzing complex load patterns.
References [1] Y.-I. Kim, J.-M. Ko, J.-J. Song, H. Choi, Repeated clustering to improve the discrimination of typical daily load profile, J. Electr. Eng. Technol. 7 (3) (2012) 281–287. [2] S.-L. Yang, C. Shen, et al., A review of electric load classification in smart grid environment, Renew. Sustain. Energy Rev. 24 (2013) 103–110. [3] G. Chicco, R. Napoli, F. Piglione, Application of clustering algorithms and self organising maps to classify electricity customers, in: 2003 IEEE Bologna Power Tech Conference Proceedings, vol. 1, IEEE, 2003, p. 7. [4] G. Chicco, R. Napoli, F. Piglione, Comparisons among clustering techniques for electricity customer classification, IEEE Trans. Power Syst. 21 (2) (2006) 933–940. [5] G. Chicco, R. Napoli, F. Piglione, Load pattern clustering for short-term load forecasting of anomalous days, in: 2001 IEEE Porto Power Tech Proceedings, vol. 2, IEEE, 2001, p. 6. [6] Y. Li, Y. Cheng, L. Zhang, H. Huang, Application of multivariate statistical analysis to classify electricity customers, in: China International Conference on Electricity Distribution, 2008. CICED 2008, IEEE, 2008, pp. 1–6. [7] O. Ozgonenel, D.W.P. Thomas, T. Yalcin, I.N. Bertizlioglu, Detection of blackouts by using K-means clustering in a power system, in: 11th International Conference on Developments in Power Systems Protection, 2012. DPSP 2012, IET, 2012, pp. 1–6. [8] K. Anaparthi, B. Chaudhuri, N.F. Thornhill, B.C. Pal, Coherency identification in power systems through principal component analysis, IEEE Trans. Power Sys. 20 (3) (2005) 1658–1660.