Microgrids Real-Time Pricing Based on Clustering Techniques - MDPI

energies Article

Microgrids Real-Time Pricing Based on Clustering Techniques Hao Liu 1 1 2

*

ID

, Nadali Mahmoudi 2 and Kui Chen 2, *

Jiangsu Province Laboratory of Mining Electric and Automation, China University of Mining and Technology, Xuzhou 221000, China; [email protected] Ernst & Young, Brisbane QLD 4000, Australia; [email protected] Correspondence: [email protected]; Tel.: +86-158-6217-8271

Received: 1 May 2018; Accepted: 21 May 2018; Published: 30 May 2018







Abstract: Microgrids are widely spreading in electricity markets worldwide. Besides the security and reliability concerns for these microgrids, their operators need to address consumers’ pricing. Considering the growth of smart grids and smart meter facilities, it is expected that microgrids will have some level of flexibility to determine real-time pricing for at least some consumers. As such, the key challenge is finding an optimal pricing model for consumers. This paper, accordingly, proposes a new pricing scheme in which microgrids are able to deploy clustering techniques in order to understand their consumers’ load profiles and then assign real-time prices based on their load profile patterns. An improved weighted fuzzy average k-means is proposed to cluster load curve of consumers in an optimal number of clusters, through which the load profile of each cluster is determined. Having obtained the load profile of each cluster, real-time prices are given to each cluster, which is the best price given to all consumers in that cluster. Keywords: clustering technique; improved weighted fuzzy average k-means; microgrids; pattern-based pricing; smart grids

1. Introduction 1.1. Background, Motivations and Aims Microgrids are expected to play a key role in future electricity markets, either as islanded or connected to the main grid. Microgrid operators are then responsible for delivering energy to consumers while meeting technical and economic criteria. One key issue for microgrid operator is determining proper pricing tariffs for consumers. One way is deploying the traditional flat prices for all consumers, which is deemed to be an inefficient pricing in electricity markets. An alternative is to define various price tariffs like time of use or even real-time prices. To this end microgrid operators need to understand their consumers’ characteristics so as they can assign optimal pricing schemes to various consumers. Clustering techniques are known as a suitable method for load profiling according to load patterns of consumers, which help find the key characteristics of consumers. Consumers are clustered in various groups per their load pattern similarities. These techniques are indeed used for load profiling of consumers, where several applications such as future investments and planning are some. This paper aims at determining optimal pricing schemes for microgrid considering load profile of consumers. To this end, an improved WFA k-means is proposed to accurately cluster consumers in several groups. These techniques cluster consumers based on their load similarities in each time interval for the entire day. Further, a similarity index, i.e., clustering dispersion indicator, is used to find the optimal number of clusters, which delivers the clusters with most similarities, but most Energies 2018, 11, 1388; doi:10.3390/en11061388

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difference with other clusters. Having the best cluster numbers, a load profile for each cluster is identified. This load profile is then used as a representative profile (RP) for all consumers in the given cluster. After that, microgrid operator deploys these representative profiles to determine price schemes for the consumers in each cluster. 1.2. Literature Review and Contributions Research on microgrids has received a great deal of attention in recent years. An overview of microgrids control and energy management is given in [1]. A new model for plug-in or plug-out microgrids is presented in [2], where a hybrid interactive communication optimization solution is developed for optimal power dispatch of multiple microgrids. Technical issues of microgrids are addressed in several papers such as [3–7]. In terms of economic aspects of microgrids, studies such as energy scheduling by microgrids [8,9] and renewable energy in microgrids [10,11] are presented. Optimal renewable energy integration in microgrids is addressed in [12]. Authors in [13] proposes a new model for enabling demand response by microgrids. A chance-constrained approach is used in [14] in order to model microgrid scheduling. Although several papers address the economic modelling of microgrids, they mainly focus on the high-level and wholesale modelling of these grids and pay less attention on how to offer optimal prices to consumers. This is indeed an area this paper contributes over the existing studies. In regards to clustering applications in power systems, most studies consider these techniques for load profiling [15–19]. These papers mostly use the basic clustering techniques such as k-means or the heuristic methods to classify load curves of consumers in several groups. Some drawbacks that these traditional clustering techniques have include randomly selecting the initial cluster centers which affect the final clustering result. Further, they mostly use the Euclidean distance measure for the computation of distance between data, which is not the accurate method for this purpose. This is the second area of our contributions. Overall, this paper contributes over the existing studies in following aspects. 1.

2.

This paper proposes a clustering-based pricing scheme for microgrids through which a microgrid operator can assign proper price tariffs on its consumers based on the load curves clustered in distinctive classes. As for clustering techniques, this paper applies an improved weighted fuzzy average k-means to overcome the drawbacks of the traditional k-means techniques.

The rest of the paper is in the following order. Section 2 describes the methodology framework, including the two-step framework, the clustering process and the procedure to achieve representative profiles (RPs) of consumers. Numerical results are presented in Section 3, where the case study is defined and several results are presented and then the scenarios for pricing schemes by microgrid operators are discussed. Conclusions are finally given in Section 4. 2. Methodology Framework The proposed pricing scheme is provided in two steps. The first step accounts for consumers’ load clustering and deriving the representative load profile of each cluster. Then, in the second step, the microgrid operator deploys the outcome of the first step in order to design its proper pricing according to its requirements. Figure 1 illustrates the proposed two-step pricing scheme.

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Figure Figure 1. 1. The proposed two-step two-step pricing pricing scheme. scheme.

Each step step is is discussed discussed in in detail detail in in following following subsections. subsections. Each 2.1. Clustering Process Process 2.1. The load load clustering clustering procedure procedure includes includes four four steps steps as as follows. follows. The first step accounts accounts for for the the The selection of the proper data, e.g., load profiles of consumers in similar voltage levels, areas and within selection of the proper data, e.g., profiles of consumers in similar voltage levels, areas and within distinctivenetwork networklocation. location.Once Oncethe the data collected, next ensures processing. In aa distinctive data is is collected, thethe next stepstep ensures datadata processing. In this this phase, outliers theare data are identified and removed. Step 3 load includes curve clustering, phase, outliers in the in data identified and removed. Step 3 includes curveload clustering, where the where theclustering proposed technique clustering is technique is carried out on consumers’ and then using the proposed carried out on consumers’ load profileload andprofile then using the adequacy adequacy such measures such CDI, the best number are of clusters chosen. Lastly, the representative measures as CDI, theas best number of clusters chosen. are Lastly, the representative profile (RP) profile of is each cluster isby determined identifying the relevant center ofcluster. the relevant are of each (RP) cluster determined identifyingbythe center of the RPs arecluster. indeedRPs useful indeed useful to represent the further distinctive actions, pricing schemer here, which can be carried to represent the further distinctive actions, pricing schemer here, which can be carried out on the out on the consumers in each cluster. consumers in each cluster. This paper proposes fuzzy average (IWFA) k-means as follows. The This paper proposes the theimproved improvedweighted weighted fuzzy average (IWFA) k-means as follows. traditional k-means hashas thethe following procedure. According are The traditional k-means following procedure. Accordingthe theEuclidean Euclideandistance, distance, the the data are clustered in in several several classes. classes. The data in each cluster have common features but different from other other clustered clusters. It starts with an initial clustering and defines initial clusters, then iterates the approach approach until until clusters. reach aa final final minimum minimum difference differencein inthreshold thresholdof ofthe thetwo twoconsecutive consecutiveiterations. iterations. reach One issue issue in in k-means k-means clustering clustering to to be be considered considered is is the the simple simple averaging averaging method method which which is is used used One for cluster centers. Medians have shown better performance than averages, although they may for cluster centers. Medians have shown better performance than averages, although they may remove remove good To points. To overcome thisa issue, a type fuzzy averaging is employed that puts the good points. overcome this issue, type of fuzzyofaveraging is employed that puts the center center prototype among the more densely situated points [2,9]. prototype among the more densely situated points [2,9]. Consider {l(1),…, l(p)} as a set of p numbers. The algorithm initially considers the sample mean µ(0) and variance σ2 to start the process, to determine the weighted fuzzy average. Considering a vector of L with H components, the cluster center is calculated as follows:

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Consider {l(1) , . . . , l(p) } as a set of p numbers. The algorithm initially considers the sample mean µ(0) and variance σ2 to start the process, to determine the weighted fuzzy average. Considering a vector of L with H components, the cluster center is calculated as follows: ( p)

 (r ) w( p,h)

(r +1)

= exp−

µ( p,h) =

(r )

lh − µ(h)



2σ2



for h = 1, . . . , H

∑( p=1,P) w( p,h) X( p,h) (r )

for h = 1, . . . , N

(1)

(2)

This algorithm computes σ2 on several iterations and then uses it as a fixed number. This could lead to a sufficiently close WFA. Further, using the Euclidean distance in the traditional k-means does not have proper accuracy. To resolve this issue, a new distance computation method is applied which ensure having more similar load curves in each cluster. To this end, the distance is computed using Equation (3), which weights the components of load curves based on their variance distinction. v u u1 ( p) (k) d(l , r ) = t H

H

∑

h =1

σh2 σ

2

(k) 2

( p)

(lh − rh )

(3)

Moreover, since the traditional k-means uses initial cluster centers randomly, the accuracy of load clustering is jeopardized. As such, the following equation is used to compute the initial cluster centers. (0)

rkh = a + b ×

k−1 K−1

for h = 1, . . . , N

and k = 1, . . . , K

(4)

The method is iterated for different a and b to find the optimal outcome for clustering load curves. There are several adequacy measures such as CDI, which allow us to determine the optimal number of clusters. Indeed, as the number of cluster declines, lower similarities in each cluster are witnessed. Extremely, for cluster number equals to 1, all load curves are grouped in one cluster, which has the lowest accuracy. On the other hand, increasing the number of clusters leads to more accurate clusters with a high level of similarity in each cluster. Ultimately, when the number of clusters is equal to the number of load curves, each cluster will have one load curve, which has the highest accuracy. However, this is obviously not the optimal number as we use clustering techniques to decrease the computational burden of large datasets. As such, CDI is used where the knee of the curve, which shows values of adequacy measure versus different number of clusters, is equal to the best number of classes. CDI is determined as follows. Depending on the distance between the load curves in the same cluster and (inversely) the distance between other cluster centers, CDI is given below. r CDI =

1 K

∑kK=1 q

h

1 2n(k)

1 2K

(k)

∑nn=1 d2 (l (n) , L(k) )

∑kK=1 d2 (r (k) , R)

i (5)

This metric assesses the similarities of the load curves in the same class and (inversely) on the inter-distance among the class representative load curves. In order to calculate the CDI [20,21], the following distances are defined. 1.

The distance between two load curves (e.g., between two hours l(i) and l(j) , of the set L(k) ) is defined as: v u u 1 H (i ) ( j) 2 (i ) ( j ) d(l , l ) = t ∑ (lh − lh ) (6) H h =1 where H is the number of intervals of each load curve.

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2. The distance between a cluster center r(k) and the subset L(k) is:

2.

The distance between a cluster center r(k) and the subset L(k) is: v () u1 (k) 1 n𝑑 (𝑟2( )(, k𝑙)( )()m) 𝑑 𝑟 (k,)𝐿 (k) = u t ( ) d (r , L ) = 𝑛 ( k ) ∑ d (r , l ) n m =1 ( )

( )

(7) (7)

(k) where the number of curves load curves incluster. k-th cluster. where n(k) isntheisnumber of load in k-th

The overall overall clustering clustering procedure The procedure based based on on the theimproved improvedWFA WFAk-means k-meansisisillustrated illustratedininFigure Figure2.2.

Figure 2. 2. The The procedure procedure of of the the proposed proposed improved improved WFA WFA k-means. k-means. Figure

2.2. Microgrid Microgrid Pricing Pricing Scheme Scheme 2.2. Havingobtained obtainedthe the RPs from clustering the microgrid can design itspricing properschemes pricing Having RPs from clustering step,step, the microgrid can design its proper schemes in step 2. To this end, the operator seeks to maximize its profit (or minimizes its cost). A in step 2. To this end, the operator seeks to maximize its profit (or minimizes its cost). A comprehensive comprehensive framework for thiscan pricing scheme can be complicated, the operator has to framework for this pricing scheme be complicated, where the operatorwhere has to consider the energy consider the energy that it buys from the upstream grid, which might be uncertain, and then sell it to that it buys from the upstream grid, which might be uncertain, and then sell it to consumers considering consumers considering the proposed pricing scheme in athis paper.mathematical This leads to a complex the proposed pricing scheme in this paper. This leads to complex optimization, mathematical optimization, which is usually solved through a typical stochastic programming which is usually solved through a typical stochastic programming approach [9,22–25]. Please note approach [9,22–25]. Please note that this comprehensive framework is not the focus of our current

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Normalized load Normalized load

that this comprehensive is not the focus of our current work,various where pricing our main aim is work, where our main aimframework is to develop clustering techniques to facilitate schemes work, whereclustering our main techniques aim is to develop clustering techniques to facilitate various pricing schemes to develop facilitate various pricing conditions, schemes and options for wholesale microgrid and options for microgrid operators.toDepending on the network peak demand, and optionsDepending for microgrid Depending on the network conditions, peak demand, wholesale operators. onoperators. the network conditions, demand, wholesale the market prices, and the distributed energy resourcespeak which a microgrid has, itmarket could prices, decide and on the market prices, and resources the distributed energy resources which adecide microgridthe has, it could decide on the distributed energy a microgrid has,could it could optimal pricing schemes. optimal pricing schemes. The which load curve clustering alleviate toondetermine customer-targeted optimal pricing schemes.could The load curve clustering could alleviate to determine customer-targeted The load curve clustering to determine customer-targeted pricing schemes. For example, pricing schemes. For example, alleviate those customers having a similar pattern as the wholesale prices pricing schemes. For example, those customers having a similar pattern as the wholesale prices those customers a similar pattern as the wholesale be targeted for real-time would be targetedhaving for real-time pricing or other schemes suchprices as ToUwould with high pricing during peak would be targeted for real-time pricing or other schemes such as ToU with high pricing during peak pricing or other as ToU with pricing wholesale prices.toIn present our future wholesale prices.schemes In our such future work, wehigh intend to during furtherpeak develop this work a wholesale prices. In our future work, we intend to further develop this work to present a work, we intend to further develop this work to present a comprehensive model for microgrid comprehensive model for microgrid energy scheduling. comprehensive model for microgrid energy scheduling. energy scheduling. 3. Numerical Results 3. 3. Numerical Numerical Results Results In order to implement the proposed approach, 75 customers in a distribution level are chosen. In to the proposed approach, 75 in level are In order order to implement implement proposed approach, 75 customers customers inaa distribution distribution arechosen. chosen. The data was provided by a the Tehran distribution network service provider, but in anlevel agreement for The data was provided by a Tehran distribution network service provider, but in an agreement for The data was provided by a Tehran distribution network service provider, but in an agreement confidential feeders. Figure 3 shows the normalized load curve of these customers and Figurefor 4 confidential feeders. Figure 33shows the load of these customers and 4 confidential Figure shows the normalized normalized load curve curve thesecurves customers and Figure Figure represents thefeeders. total curve of these profiles. As can be seen, variousofload exist which make4 represents the total curve of these profiles. As can be seen, various load curves exist which make represents the total curve of these profiles. can be seen, various exist which determining a single price tariffs difficult andAsinefficient. Further, theload totalcurves load illustrates thatmake the determining aa single price tariffs difficult and inefficient. Further, the total load illustrates that the determining single price tariffs difficult and inefficient. Further, the total load illustrates that customers impose a peak load around noon and another peak load in the evening. If the pricingthe is customers impose aa peak load noon and another peak load in the If the pricing is customers impose peak load around around noon another peak load the evening. evening. thesame pricing defined based on the load profile in Figure 4, and the noon peak could beinreduced but at Ifthe timeis defined based on the load profile in Figure 4, the noon peak could be reduced but at the same time defined based on the load profile in Figure 4, However, the noon peak could be clustering reduced but at the samebring time there could be risk of worsening evening peak. the following results could there could be risk of worsening evening peak. However, the following clustering results could bring there could be risk of worsening evening peak. However, the following clustering results could bring an advantage to the microgrid to define smart pricing schemes. an an advantage advantage to to the the microgrid microgrid to to define define smart smart pricing pricing schemes. schemes. 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 hours hours

Normalzied load Normalzied load

Figure Figure3.3.Load Loadcurve curveofofall allconsumers. consumers. Figure 3. Load curve of all consumers. 35 35 30 30 25 25 20 20 15 15 10 10 5 5 0 0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 hours hours Figure 4. Total load curve of all consumers. Figure 4. Total load curve of all consumers. Figure 4. Total load curve of all consumers.

The improved WFA k-means is applied to the given load curves and a range of cluster numbers The improved WFA k-means is applied to the given load curves and a range of cluster numbers between 1 and 20 clusters are obtained. In order to determine the optimal number of clusters, the CDI between 1 and 20 clusters are obtained. In order to determine the optimal number of clusters, the CDI

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The improved k-means is applied to the given load curves and a range of cluster numbers Energies 2018, 11, x FORWFA PEER REVIEW 7 of 12 measure is applied for each cluster number and its values are calculated. Then, the CDI values are between 1 and 20 clusters are obtained. In order to determine the optimal number of clusters, the CDI plotted against the number of clusters, as given in Figure 5. As can be seen, the CDI values decrease measure is is applied applied for for each each cluster cluster number number and and its itsvalues values are arecalculated. calculated. Then, Then, the the CDI CDI values values are are measure as the number of clusters increases, which means the load profiles have more similarities in each plottedagainst againstthe thenumber numberofofclusters, clusters,asasgiven given Figure can seen, CDI values decrease plotted inin Figure 5. 5. AsAs can bebe seen, thethe CDI values decrease as cluster, but more dissimilarities compared with other clusters. As mentioned earlier, it is proven that as the number of clusters increases, which means theprofiles load profiles havesimilarities more similarities each the number of clusters increases, which means the load have more in each in cluster, the knee of this curve represents the optimal number of clusters. As such, according to Figure 5, this cluster, more dissimilarities compared with other As clusters. As mentioned it isthat proven that but morebut dissimilarities compared with other clusters. mentioned earlier, it earlier, is proven the knee number is equal to three clusters. thethis knee of this curve represents the optimal clusters. As such, to according Figure 5, this of curve represents the optimal number ofnumber clusters.ofAs such, according Figure 5,tothis number is number is equal to three clusters. equal to three clusters. 3

CDI Values CDI Values

2.5 3 2.5 2

1.5 2 1.5 1

0.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0 Number of clusters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Number of clusters Figure 5. CDI versus the number of clusters. Figure 5. CDI versus the number of clusters. Figure 5. CDI versus the number of clusters.

Having obtained the number of clusters, load curves in each cluster are identified. Sixty customers are clustered innumber class 1, of while the number of load curves in clusters 2 and 3Sixty are customers 5 and 10, Having load curves in each cluster identified. Havingobtained obtainedthethe numberclusters, of clusters, load curves in eachare cluster are identified. Sixty respectively. Figures provide load curves in each cluster. As can2 and be seen, 1 accounts for are clustered inclustered class6–8 1, while the 1, number of load curves clusters 3 arecluster 52and respectively. customers are in class while the number of in load curves in clusters and10, 3 are 5 and 10, those customers which have two peak periods around noon and in the evening. Further, their peak Figures 6–8 provide load in each Aseach can be seen, As cluster for those customers respectively. Figures 6–8curves provide load cluster. curves in cluster. can 1beaccounts seen, cluster 1 accounts for load is have around 40% ofperiods the maximum load of allincustomers. Note that, these customers have a very which two peak around noon and the evening. Further, their peak load is around 40% those customers which have two peak periods around noon and in the evening. Further, their peak short of medium between the two peak periods, while other periods have oflow load of thetime loadofofload all maximum customers. Note these customers very short time medium load ismaximum around 40% the load ofthat, all customers. Note have that, athese customers have a very consumption. load two peak periods, while have low load other consumption. shortbetween time ofthe medium load between theother two periods peak periods, while periods have low load Custer 2 2involves those customers which havehave a peak load during the working hours. These Custer involves those customers which a peak load during the working hours. consumption. customers are indeed some some commercial customers which have lowlow consumption. Their peak isis TheseCuster customers are indeed commercial customers which have consumption. Their peak 2 involves those customers which have a peak load during the working hours. These indeed 50% of the maximum load of all customers. indeed 50% are of the maximum of all customers. customers indeed some load commercial customers which have low consumption. Their peak is Cluster 33represents those customers with high highconsumption consumptionamong amongall allclusters. clusters.Further, Further, can Cluster represents those customers with it it can be indeed 50% of the maximum load of all customers. be seen that these customers have a higher load around noon, while the second peak, which is lower seen that these higher loadwith around while theamong second all peak, whichFurther, is loweritthan Cluster 3 customers represents have thoseacustomers highnoon, consumption clusters. can than the noon peak load, happens inevening. the evening. the noon peak load, happens in the be seen that these customers have a higher load around noon, while the second peak, which is lower than the noon peak load, happens in the evening. 0.6

Normalized load Normalized load

0.5 0.6 0.4 0.5 0.3 0.4 0.2 0.3

0

hours

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.1 0.2

hours Figure 6. Load curves of consumers in cluster 1. Figure 6. Load curves of consumers in cluster 1. Figure 6. Load curves of consumers in cluster 1.

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0.4 0.4 0.5 0.3 0.3 0.4 0.2 0.2 0.3 0.1 0.1 0.2 0 0.10

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424

Normalized load load Normalized load Normalized

0.6

0.5 0.5 0.6

hours hours

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

Normalized laod laod Normalized laod Normalized

1.2 1.2

hours Figure 7. Load curves of consumers in cluster 2. Figure 7. Load curves of consumers in cluster 2. Figure 7. Load curves of consumers in cluster 2. Figure 7. Load curves of consumers in cluster 2.

1 1.21 0.8 1 0.8 0.6 0.8 0.6 0.4 0.6 0.4 0.2 0.4 0.2 0 0.20 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 hours 0 hours 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 Figure 8. Load curves of hours consumers in cluster 3. Figure Figure 8. Load Load curves curves of of consumers consumers in cluster 3.

Having the load curves Figure in each8. cluster, the center of eachincluster Load curves of consumers cluster can 3. be determined. The center Having the load load curves curves in in each eachcluster, cluster,the thecenter centerofofeach each clustercan can determined. The center Having the bebe determined. center of of each cluster provides the representative profile (RP) of thecluster relevant cluster. Figure 9 The delivers the of each cluster provides the representative profile (RP) of the relevant cluster. Figure 9 delivers the eachof cluster provides the The representative profile of the relevant cluster. Figure 9 delivers thecluster, RPs of Having the clusters. load curves in each cluster, the(RP) center ofthe each cluster can be determined. The center RPs the given RPs indeed clearly confirm discussion of load curves in each RPs of theclusters. given clusters. The RPs indeed clearly confirm the discussion ofcurves load curves incluster, each cluster, the given The RPs indeed clearly confirm the discussion of load in each given of eachincluster thethe representative profile (RP) of the3 relevant Figure delivers the given Figuresprovides 5–8. Thus, microgrid could target cluster to reducecluster. both their noon9 and evening given in Figures 5–8. Thus, the microgrid could target cluster 3 to reduce both noon their noon and evening in Figures 5–8. Thus, the microgrid could target cluster 3 to reduce both their and evening peak RPs the given clusters. The RPs indeed clearlyfor confirm the discussion peakofload, whereas cluster 2 could be targeted noon peak clipping. of load curves in each cluster, peak whereas cluster 2 could be targeted for noon peak clipping. load, load, whereas 2 could targeted for noon peak clipping. given in Figurescluster 5–8. Thus, thebe microgrid could target cluster 3 to reduce both their noon and evening peak load, whereas cluster 2 could be targeted forCluster noon 2peak clipping. Cluster 1 Cluster 3

Normalized load load Normalized load Normalized

Cluster 1

Cluster 2

Cluster 3

0.8 0.8 Cluster 1 Cluster 2 Cluster 3 0.7 0.7 0.6 0.8 0.6 0.5 0.7 0.5 0.4 0.6 0.4 0.3 0.5 0.3 0.2 0.4 0.2 0.1 0.3 0.1 0.20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 hours 0 hours 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Figure 9. Representative Patterns hours (RPs) of all clusters. Figure 9. Representative Patterns (RPs) of all clusters. Figure 9. Representative Patterns (RPs) of all clusters.

Considering the representative profiles obtained through load clustering, the microgrid operator Figure 9. Representative Patterns (RPs) of all clusters. is now able to define proper pricing schemes. Following scenarios are some cases that the microgrid operator can consider.

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Considering the representative profiles obtained through load clustering, the microgrid operator Energies 9 of 12 is now 2018, able 11, to 1388 define proper pricing schemes. Following scenarios are some cases that the microgrid operator can consider. If the customers are inelastic, the microgrid can uses the RPs to determine optimal time of use If the customers are inelastic, the microgrid can uses the RPs to determine optimal time of use tariffs. This allows the operator to achieve a higher revenue by charging consumers according to their tariffs. This allows the operator to achieve a higher revenue by charging consumers according to representative load profile. As an example, Figure 10 provides the normalized time of use tariffs for their representative load profile. As an example, Figure 10 provides the normalized time of use tariffs each cluster. Note that the prices can be scaled up based on the actual prices that the microgrid for each cluster. Note that the prices can be scaled up based on the actual prices that the microgrid operator determines based on its optimization procedure. operator determines based on its optimization procedure. 1.2

Normalized price

1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324 hours

Figure10. 10. A Atypical typicaltime timeof ofuse usetariff tariff for for each each cluster. cluster. Figure

In In case case that that all all customers customers have have smart smart meters meters with with the the ability ability of of real-time real-time pricing, pricing, this this type type of of pricing scheme can be easily determined based on RPs. That is, considering real-time prices which pricing scheme can be easily determined based on That is, considering real-time prices which have have similar similar patterns patterns to to the the RPs RPs of of each each cluster cluster will will help help the theoperator operator to toincrease increase its its revenue revenue of of selling selling energy energy to to consumers. consumers. To To this end, the real-time price patterns can exactly follow the RPs in Figure 9. If If some some consumers consumers are are elastic elastic to to prices, prices, they they may may reduce reduce their their load load during during peak peak prices. prices. This This load load can can be be shifted shifted to to off-peak off-peak periods periods or or even curtailed curtailed without without recovery recovery in off-peak periods. periods. The The load load shifting shifting program program is is dependent dependent on the elasticity of consumers. This program is defined as follows. ()

( ) = 24( ) + ∑ ( 0,(i))× × ( )− ( ) , D D (i ) = D0 (i ) + ∑i=1 E(i, j) × × [ρ( ()j) − ρ0 ( j)], i = 1, 2, · · · , 24 0 ( j )⋯ ,24 =ρ1,2,

(8) (8)

where, is the the initial initial demand demand of where, D0((i)) is of consumers consumers before before demand demand response. response. D((i)) is is the the demand demand after after conducting the demand response program. ( ) is the initial price of consumers before demand conducting the demand response program. ρ0 (i ) is the initial price of consumers before demand response. is the the new new pricing pricing model model for for load load reduction reduction programs. programs. The response. ρ((i)) is The elasticity elasticity of of consumers consumers between between the the i-th i-th and and j-th j-th hours hours is is defined defined as: as: () ( , ) = ρ0 ( j ) × E(i, j) = ( )× D0 (i ) ( , ) 0, if ( ( 0, ifif E(i, ,j))≤ 0,

() ∂D (i ) () ∂ρ( j) =

(9) (9)

(10) i=j (10) j) ≥ 0, if of i 6=consumers j Note that cross elasticity is defined Eas(i,the elasticity to the price in other periods, whileNote self-elasticity the sensitivity of consumers to the price in the relevant that crossiselasticity is defined as the elasticity of consumers to theperiod. price in other periods, By carrying out the given program, and depending on the consumers’ elasticity, while self-elasticity is the sensitivity of consumers to the price in the relevant period. the microgrid operator can shiftout thethe load fromprogram, peak hours, around noon which coincides system By carrying given and particularly depending on the consumers’ elasticity, thethe microgrid peak as shown in Figure 4, to off-peak e.g., early morning. However, program operator can shift the load from peak periods, hours, particularly around noon whichthis coincides therequires system apeak deepasunderstanding of the characteristics of consumers. Although detailed studies are required for shown in Figure 4, to off-peak periods, e.g., early morning. However, this program requires this purpose, one key solution is using the RPs derived from load clustering in step 1, i.e., Figure 9. a deep understanding of the characteristics of consumers. Although detailed studies are required for Considering the following for the from givenload demand response programs can be9. this purpose,this onefigure, key solution is using findings the RPs derived clustering in step 1, i.e., Figure interpreted. First, consumers in cluster 1 are the most suitable customers for implementing the given Considering this figure, the following findings for the given demand response programs can be interpreted. First, consumers in cluster 1 are the most suitable customers for implementing the given demand response program. This is due to the following reasons. As can be seen from Figure 9,

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these consumers have the highest consumption among all clusters. As such, it would be easier to achieve the targeted load reduction during peak hours if these consumers are considered as the priority. Second, these consumers are high consuming residential customers which their peak consumption coincides with the system peak. Therefore, these consumers might be in a category that has family members staying at home during the day, and using their electric appliances in this period, which indicate the high possibility of achieving load reduction from them. Cluster 2 has the lowest load reduction capability due to following reasons. First, these consumers are more likely small to medium commercial customers, which have low ability to shift their load to other periods. Further, their consumption compared to cluster 1 is low, which shows lower priority for these consumers to carry out demand response. Lastly, cluster 3 has also low demand response potential. Although their peak load coincides the system peak load, these consumers peak is less than 20% of the maximum load of all consumers. That is, these consumers are expected to have the low share of shift-able loads compared to consumers in cluster 3. As a result, it can be highlighted that the proposed approach helps microgrid operators better identify the consumers having demand response potential. First, this approach helps classify consumers and then identifying their features such as their type (residential, commercial, etc.), their consumption level (high, low, medium), their coincidental peak load with the system peak, and other relevant features. Moreover, identifying proper consumers from a large number of consumers for suitable demand response programs is not a practical approach. Thus, deploying clustering techniques to group these consumers in a reasonable number of classes would facilitate this for the microgrid operator. 4. Conclusions This paper presents a new model for pricing by microgrid operators in which the operator uses clustering techniques to classify consumers load curves into a specific number if clusters, which help identify their representative profiles (RPs) and also reduce the size of data on which the operator has to work. Having this RPs, the operator can identify the consumers’ type in each cluster, and other features such as their consumption level and whether their peak load coincides the system peak. This helps the operator to decide best pricing schemes such as real-time pricing and time of use tariffs for consumers, as well as to define possible demand response and load reduction programs for consumers to reduce its system peak load. The proposed model is applied on 75 load curves of consumers and the results are obtained. Optimal numbers of clusters are defined, which shows distinctive consumers in three clusters. Each cluster’s RP represents its consumers’ characteristics. While clusters 1 and 3 include residential consumers with high and low consumption, respectively, cluster 2 includes low energy consuming commercial consumers. Considering these RPs’ various pricing models and typical time of use tariffs are suggested. Further, the clusters are prioritized for demand response actions to reduce the peak load of the microgrid during the noon. This work can be extended to consider a comprehensive model which takes into account energy purchasing from the wholesale market and then selling it through the defined pricing scheme to consumers by the microgrid operator. Author Contributions: Conceptualization, H.L. and N.M.; Methodology, H.L. and N.M.; Validation, H.L. and N.M.; Formal Analysis, H.L. and N.M.; Data Curation, K.C.; Writing-Original Draft Preparation, H.L., N.M. and K.C.; Writing-Review & Editing, H.L. Acknowledgments: Jiangsu Province Laboratory of Mining Electric and Automation gives the support of working places and experiment places. The paper is Nadali’s work, not Ernst & Young view. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclatures (r )

µ(h)

The hth component of weighted fuzzy average in the rth iteration

σ2

Variance of WFA k-means Variance of the hth component of load profiles

σh2

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σ2 a b l ( p)

Average variance Adjusting parameter Adjusting parameter The pth input curve The hth component of pth input curve

( p)

lh r (k) rh

(k)

Centeriod of the kth cluster The hth component of centeriod of the kth cluster

rkh

(0)

The hth component of initial centeriod of the kth cluster

w( p,n)

The hth component of computed weight of the pth curve in the rth iteration

(r )

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