Electrical Load Profile Analysis and Peak Load Assessment Using

Electrical Load Profile Analysis and Peak Load Assessment using Clustering Technique Desh Deepak Sharma, Student member, IEEE and S.N.Singh, Senior member, IEEE Electrical Engineering Department Indian Institute of Technology Kanpur Kanpur, India [email protected], [email protected]

Abstract—Load profile analysis in different regions is very useful to maximum power in early afternoon. In distribution system, level power utilities for managing the load requirements in economic and of current (i.e. load) is primary cause of power losses. If it is efficient manner. For the demand side management and grid possible to keep uniform electricity consumption level throughout operation, the variation in demand is to be known. In this paper, the day, then it is possible to reduce peak power loss and hence, classical k-means clustering approach is used for finding similar overall energy losses. Load shapes, load factor and loss factor can types of profiles of a practical system for demand variation analysis be related to overloading in distribution feeder, transformers and and energy loss estimation. For different zones, typical load profiles other equipment. Load shape with low load factor allows to based on similar consumption are obtained. Primarily, the load overloading and with high load factor care should be taken in factor represents feeder demand variation, and loss factor helps overloading. So, load shapes with different load factors conditions average energy loss estimation in distribution power system without are to be identified to find the limitations of use of overloads [2]. load flow studies. In this paper, a concept is proposed for analysis of electricity consumption pattern on different days in particular zones In electricity consumption data, there may be different types of based on cluster load factor and cluster loss factor. Normal and load shapes. So clustering algorithms are to be implemented to abnormal peak load requirements in cluster of similar types of identify and classify similar load profiles Classical k-means, fuzzy profile of days of different zones are identified. Cluster loss factor c-means, self organizing feature maps(SOFM), etc. are the helps in identifying the energy loss variation due to different load popular clustering algorithms implemented in load profiles data patterns. [8-11].In this paper, classical k-means clustering algorithm is selected for implementation on 05 zones of a 20 zones electricity Index Terms—k-means clustering algorithm, load shape, electricity consumption variation, load factor, peak load system. From literature, it is found that energy loss estimation is I. INTRODUCTION carried out based on the average daily load curve and the The very first step in managing electric load demand is to know measured monthly load profile of the system in [7], aggregate the general patterns of electricity consumption. Understanding the information (i.e. mean and variation) about the load curve data patterns helps the utilities to predict and anticipate possible bank in [6], and with defined load model while assigning demand variation which may occur. It is found that unit of statistical measures to the homogeneous and non-homogeneous electrical energy generated in a power system do not equal to the loads [16]. Loss formulas for clustered losses using fuzzy c- units delivered and consumed by end users. A gap between number (FCN) are presented based on weekday’s data of January electricity generation and electricity demand is to be identified 2000 [14]. Low voltage energy loss estimation is done considering and causes of the gap are to be analyzed. Distribution sector is the IP (irrigation pump-sets) non-heterogeneous loads [15]. There is weakest part of whole power system. With study of demand need to know the energy losses in distribution system of different variation analysis using load curves, it is possible to identify and regions at different intervals in a year or more, without reduce the distribution system losses and hence, the profit of considering the aggregate information. Clustering technique power utilities can be enhanced. Also, additional loading makes group of similar patterns and hence, it becomes easier to capacities of feeders, distribution transformers and other analyze energy loss estimation corresponding to different load equipment of distribution system can be known. In distribution patterns. power system, loss factor provides information of average energy In this paper, a method to relate the load factor and loss factor losses on distribution network in transmission of electricity to the to the clustered load profiles is proposed for peak-valley analysis. end customers [1]-[4],[12]. This concept aims to identify demand variation and maximum Electrical power consumptions of end users generally vary due demand requirement in different clusters of different regions. to behavior of customers, ambient conditions, etc. If load curves Cluster load factor and cluster loss factor terms are introduced for are available then load factor can represent the variation of a load defining the load factor and loss factor exclusively for similar type curve. Load factor can be improved by reducing peak load and of load profiles. Analysis of load profiles of different zones is hence, steady load curve is obtained [6]. Aging effects in feeders, done with values of cluster load factor and cluster loss factor. The transformers and other equipment of distribution power system relationship of range of loss factor of similar profiles to demand should be analyzed at different load factor conditions [2]. variation is shown. The proposed concept helps in identification Traditional economic cable curves are obtained using the of normal maximum demand and irregular maximum demand in relationship between the load factor and loss factor, and losses can cluster of similar load profiles. With proposed concept, it is also be computed with information of maximum demands. Economic possible to anticipate average consumption and average power cable curves are useful tools for choosing cables [6]. loss if similar types of electricity consumption occur in assumed days. The proposed approach is tested on a practical system. Different types of customers have different peak requirements at different period of time. Residential customers have maximum demand in evening hours while commercial customers may need 978-1-4799-6415-4/14/$31.00 ©2014 IEEE II. K-MEANS CLUSTERING ALGORITHM Let() is instantaneous demand, is the average demand Classical k-means algorithm is a partition based clustering and is the maximum demand in the designated period of algorithm which separates a set of n data objects into k clusters time , then load factor is defined as [7],[12]: based on similarity features[8]-[11]. Given a set of observations () = = = (5) ( , …………) where each observation is a d-dimensional real vector. This observation set is partitioned into k sets (k

= (11) =, (3) , Case 3:Load is steady: If the level of difference of peak load to Optimal values of centroids can be obtained with following off-peak load is negligible then again the value of the loss factor approaches the value of the load factor. expression = (12) ∑ = = ∑ (4) ∑ The interval of loss factor variation in relation to load factor can be computed as[7] Load data set consists of 24- dimension observation of load ≤ ≤ (13) profiles of different days of different zones[13]. The data set of year 2007 (ℛ) is considered for clustering purpose. In 1928, Buller and Woodrow found with actual electric system that the relationship between load factor and loss factor III. LOAD AND LOSS FACTORS should exist between two extremities of curve-1 and curve-2 as shown in Fig.1.An equation between load factor and loss factor Load factor is generally used to obtain the difference between with constant coefficient of 0.3 is developed[1],[3],[6]. average demand and maximum demand. So, it is a measure of uniformity or variance in electricity usage. A good load factor = 0.3( ) + 0.7( ) (14) indicates constant rate of electricity consumption. In ideal In1959, H.F. Hoebel modified the equation representing conditions, the value of load factor is 1.0 (or 100 %). relationship of loss factor and load factor with an exponent 1.6 as: = ( ). (15) V. CASE STUDIES Martin W. Gustafson et al. recommended modified equation An hourly load data of year 2007 of different zones are for relation of loss factor and load factor with 0.08 constant considered for testing the effectiveness of the proposed concept. coefficient in place of 0.3 and an exponent as 1.912 in place of 1.6 The data consist of 24-hours electricity consumption information as shown below[3],[6]. in kW of respective zones [13]. Authors of paper [8] find k-means clustering algorithm as the most stable algorithm out of other = algorithms and for given number of 05 clusters, the results are 0.08( ) + 0.92( ) (16) consistent. Thus, in this paper, k-means clustering algorithm is = ( ). (17) selected and implemented for clustering the load profile data with 5 clusters. Convergence of k-means clustering algorithm is A general empirical relationship between load factor and loss obtained with several run. Five groups of different days in factor is developed as [5],[12] different zones having similar consumption pattern are obtained =( ) + (1 − )( ) (18) for load profile analysis as average consumption, maximum consumption, variation in load curves etc. Centroid curves are mean load curves of the clusters and these are assumed as typical 1 load profiles (TLP) of the clusters. TLP of a cluster shows the Curve-1 behavior of consumption on the days of that cluster and the nature 0.5 Curve-2 of average consumption in a cluster. In this paper, only 5 zones Curve-3 are considered for showing results. Numbers of days in each 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 per unit loss factor loss per unit cluster are identified. The values of cluster load factor and cluster per unit load factor loss factor are calculated for each cluster. Day 01 is assumed for Figure 1. Load factor vs loss factor January 01, 2007.

IV. PROPOSED CONCEPT 1) Results of zone-1 In cluster 3, no morning peak occurs and the value of cluster In a region, the electricity demand can be different on different load factor is minimum as 0.5209 among all clusters and days. Using an appropriate clustering algorithm, the similar load corresponding range of cluster loss factor is 0.2713-0.5209 as profiles of different days of a region can be grouped, termed shown in Table I. Such type of electricity consumption behavior clusters. Average consumption and maximum consumption are occurs during summer after May 2007.In cluster 1 of this zone, different in different clusters. Mikić [16] demonstrated that loss the cluster load factor is maximum as 0.6745 and hence, variation factor depends not only on load factor but also on peak load and of electricity consumption is minimum. hence, there is difficulty in defining coefficient in (18). In x 104 different regions, the values of coefficients may be different in 4 TLP1 TLP2 (18) due to different load patterns of the regions. So selection of 3 TLP3 the coefficient of (18) has importance in estimation of energy. The TLP4 2 TLP5 load factor and loss factor are redefined and renamed for clustered load(kW) 1 load profiles of the region with information of number of days in a 1 2 4 6 8 10 12 14 16 18 20 22 24 cluster. The concept connects the similar electrical demand time(in hours) variation on different days to load factor and loss factor. Figure 2. Typical load profiles of 05 clusters(zone-1)

cluster 1 cluster 2 cluster4 3 cluster4 4 cluster 5 Cluster load factor is the ratio of the average load in a load x 104 x 104 x 10 x 10 x 104 profile cluster of a region to the normal peak load occurring in that 5 5 5 5 5 cluster. Similarly, cluster loss factor is the ratio of the mean power 4 4 4 4 4 loss to the peak power loss in a load profile cluster of a region. 3 3 3 3 3 Similar profiles are grouped in different clusters and these groups 2 2 2 2 2 1 1 1 1 1 of load curves can be analyzed based on cluster load factor and 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 cluster loss factor. Typical load shapes of the clusters have relation to the cluster load factor. Lesser value of cluster load Figure 3. Clustering results of zone-1(horizontal axis:time(in hours) and vertical axis:load(in kW) factor shows that load shapes in the cluster are such that electricity consumption has large variation and there may be a TABLE I. INFORMATION OF CLUSTER LOAD , CLUSTER large and only one peak. In the same way, for smaller values of LOSS FACTORS AND MAX. DEMAND(ZONE-1) cluster loss factor there might be large variation in power losses in Cluster cluster range of max. Day& time of max. distribution system. In this paper, irregular peak load is described no. (no. of LF cluster loss demand demand as sharp change in maximum demand of electricity, which occurs days) factor (kW) on a day for short duration of time while variation in electricity 01 (42) 0.6745 0.4550-0.6745 33749 March 19 (0800hr) consumption on this day is not significantly large. This is the dissimilar behavior of electricity consumption in the cluster. 02(129) 0.5754 0.3311-0.5754 27265 July 02 (1900hr) 03(111) 0.5209 0.2713-0.5209 43486 Aug 09 (1800hr) Main objectives of proposed concept are as following: 04 (27) 0.6198 0.3841-0.6198 45547 Feb 06 (0600hr) • Identification of similar load profiles, 05 (56) 0.6344 0.4025-0.6344 29028 March 08 (0800hr) • Finding the normal peak demand in similar load profile, • Identification of irregular peak demand, 2) Results of zone-2 • Estimation of average demand in similar load profiles and • Average energy loss in similar load profiles. In this zone, minimum value of cluster load factor is found in consumption can be verified with typical load profiles of cluster 1 as 0.6666 and corresponding range of cluster loss factor respective clusters as shown in Fig. 6. is 0.444-0.6666 as shown in Table II. With visual inspection of Figs 6 and 7, it is observed that cluster 1 have only evening peak 4) Results of zone-4 and variation in electricity consumption is highest. Most of the In this zone, there are some days where electricity electricity consumption patterns of cluster-1 occur during period consumption is sharply increased to some large value as compared of summer. Also cluster load factor and cluster loss factor are to average consumption (Fig.10). Such type of irregular variation maximum for cluster 3 and cluster 5.Variation in electricity affects the value of cluster load factor as maximum consumption consumption is less in clusters 3 and 5. is changed in large and average consumption in cluster is not x 105 changed significantly. Other days of cluster, excluding day of 3 TLP1 TLP2 irregular, the peak do not have sharp peak in electricity 2.5 TLP3 TLP4 2 consumption as seen in Fig. 9, such condition can be identified by TLP5 1.5 typical load profiles as shown in Fig.8. load(in kW) load(in

1 1 2 4 6 8 10 12 14 16 18 20 22 24 time(in hours) TABLE III. INFORMATION OF CLUSTER LOAD , CLUSTER LOSS FACTORS AND MAX. DEMAND(ZONE-3) Figure 4. Typical load profiles of 05 clusters(zone-2) Cluster no. cluster range of max. Day& time of max. 5 5 5 5 x 105 cluster 1 x 10 cluster 2 x 10 cluster 3 x 10 cluster 4 x 10 cluster 5 (no. of LF cluster loss demand demand 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 days) factor (kW) 2.5 2.5 2.5 2.5 2.5 01 (112) 0.7342 0.5390-0.7342 223741 March 30 (0800hr) 2 2 2 2 2 1.5 1.5 1.5 1.5 1.5 02(44) 0.7142 0.5101-0.7142 346909 Feb 06 (0800hr) 1 1 1 1 1 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 03(77) 0.7315 0.5350-0.7315 276396 March 09 (0800hr) Figure 5. Clustering results of zone-2(horizontal axis:time(in hours) and 04 (53) 0.6698 0.4486-0.7315 328719 Aug 08 (1600hr) vertical axis:load(in kW) 05 (79) 0.7073 0.5002-0.7073 263767 July 27 (1400hr)

TABLE II. INFORMATION OF CLUSTER LOAD , CLUSTER LOSS FACTORS AND MAX. DEMAND(ZONE-2) 1000 TLP1 TLP2 Cluster no. cluster range of max. Day& time of 800 TLP3 (no. of LF cluster loss demand max. demand 600 TLP4 days) factor (kW) TLP5 400 01 (57) 0.6666 0.4444-0.6666 304651 Aug 08 (1600hr) kW) load(in 200 1 2 4 6 8 10 12 14 16 18 20 22 24 02(74) 0.7141 0.5100-0.7141 240012 Aug 12(1800hr) time(in hours) 03(99) 0.7659 0.5865-0.7659 196617 May 27( 1600hr) Figure 8. Typical load profiles of 05 clusters(zone-4) 04 (52) 0.7031 0.4944-0.7031 321509 Feb 06 (0800hr) cluster1 cluster2 cluster3 cluster4 cluster5 05 (83) 0.7644 0.5844-0.7644 238476 Feb 28 (0800hr) 1200 1200 1200 1200 1000 1000 1000 1000 1000 750 750 750 750

5 500 500 500 500 500 x 10 TLP1 3 TLP2 250 250 250 250 2.5 TLP3 0 0 0 0 0 TLP4 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 2 TLP5 1.5

load(in kW) load(in Figure 9. Clustering results of zone-4(horizontal axis:time(in hours) and 1 1 2 4 6 8 10 12 14 16 18 20 22 24 vertical axis:load(in kW) time (in hours) Figure 6. Typical load profiles of 05 clusters(zone-3) 1200 1000 irregular peak cluster 1 cluster 2 cluster 4 cluster 4 800 5 5 cluster 3 5 x 10 x 10 x 105 x 105 x 10 3.5 3.5 3.5 3.5 3.5 600 3 3 3 3 3 load( in kW) 400 2.5 2.5 2.5 2.5 2.5 1 2 4 6 8 10 12 14 16 18 20 22 24 time( in hours) 2 2 2 2 2 1.5 1.5 1.5 1.5 1.5 Figure 10. Irregular peak is detected on Dec 16, 2007 at 2200hr 1 1 1 1 1 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 1 5 10 15 2024 In cluster 4 on day 350 (i.e Dec16, 2007), the maximum Figure 7. Clustering results of zone-3(horizontal axis:time(in hours) and consumption increases sharply to value 1104 kW at 2200hrs, vertical axis:load(in kW) which can be seen from Figs. 9 and10, Table IV. So value of 3) Results of zone-3 cluster load factor of cluster 4 is reduced to 0.5825 although typical load profile (TLP4) shows that variation in consumption of Minimum value of cluster load factor is 0.6698 and electricity in this group is not large (Fig.8). The value of cluster corresponding range of cluster loss factor is 0.4486-0.7315 in load factor is modified to 0.7226 with regular peak load 890kW cluster 4 which can be seen from Table III. During days of cluster of day 25(i.e Jan 25, 2007), while peak load of the day 350 is 4, the variation in consumption is large. Most of the days of assumed normal i.e. less than 890kW. Irregular peak of day 350 cluster 4 are in summer and consist of only evening peak, Fig. 6 is shown separately in Fig. 10. and 7. For clusters 1 and 3, the cluster load factor is approximately equal and maximum. Variation in electricity TABLE IV. INFORMATION OF CLUSTER LOAD , CLUSTER LOSS FACTORS except zone-4, one cluster is identified in which variation of AND MAX. DEMAND(ZONE-4) electricity consumption is large. This cluster of a zone has Cluster cluster range of max. Day& time of max. minimum value of cluster load factor. Days of this cluster of the no. (no. of LF cluster loss demand demand zone consist of large enhancement in consumption during evening days) factor (kW) hours compared to consumption during other time intervals of 01 (135) 0.6600 0.4356-0.6600 634 March 15 (2000hr) same days. In the zones except zone 4, most of the days of a cluster having minimum cluster load factor occur during summer 02(16) 0.7214 0.5205-0.7214 1057 Dec 17 (0900hr) (i.e after May).In zone -4, day of irregular peak load (Dec 16, 03(56) 0.7064 0.4991-0.7064 783 Nov 11 (0900hr) 2007) has been identified. Cluster loss factor finds the range of 04 (61) 0.5825 0.3393-0.5825 1104 Dec 16 (2200hr) coefficient for estimation of energy of the regions which may Modified : 0.7226 0.5221-0.7226 890 Jan 25 (2100hr) have different load patterns. The proposed concept helps the utilities in analysis and planning in finding the average 05 (97) 0.6498 0.4223-0.6498 740 Aug 25 (2100hr) consumption and estimation of energy for considered load patterns for the given days. For the load pattern of cluster -1 of 5) Results of zone-5 zone-1, the annual average consumption is 22764 kW and range of coefficient for energy estimation would be 0.4550-0.6745. In this zone, cluster 3 has minimum cluster load factor as 0.5053 among all clusters and corresponding range of cluster loss REFERENCES factor is 0.2553-0.5053 and given in Table V. Variation of [1] F.H.Buller and C.A.Woodrow, “Load factor-equivalent hour values electricity consumption on days of cluster 3 is higher compared to compared,” Electr.World,vol.92,no.2,pp.59-60,July14,1928. other days. In this zone also, such type of electricity consumption [2] V.M.Montsinger, “Effect of load power factor on operation of power pattern occur generally in summer. Cluster 2 consists of days on transforrmers by temperature,” Trans.AIEE, vol.59,no.11,pp.632- which the variation in electricity consumption is very less 636,Nov.1940. (Fig.12), value of cluster load factor of cluster 2 is largest (Table [3] M.W.Gustfson, J.S.Baylor and S.S.Mulnix, “The equivalent hours loss V). factor revisited,” IEEE Trans. On Power Systems, vol. 3,no.4,pp.1502- 15000 TLP1 1508,Nov.1988 TLP2 10000 TLP3 [4] M.W.Gustfson and J.S.Baylor, “Approximating the system losses equation,” TLP4 IEEE Trans. On Power Systems, vol. 4,no. 3,pp.850-855,Aug.1989. 5000 TLP5

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