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<n). Each set represents a cluster of data. All clusters have means such where = () is the energy supplied to the system in that sum of Euclidean distance of observations (associated to duration of time . respective cluster) to mean is minimum. Let () is instantaneous power loss, is the average power The objective is defined to find points, which are close to loss and is the power loss during maximum demand in the centroids of different clusters, as designated period of time , then loss factor is defined as [7],[12]: () = = = (6) ℱ=∑∑ − (1) : where = () is the energy losses in the system in duration of time . where (, …………)∈ℛ are k clusters with unknown centroids. Power losses are proportional to square of demand [6],[7],[12] The objective function (1) can be further written as as () ≅ [()] (7) ℱ=∑ ∑ − (2) For available hourly or 15-min interval load profile data, the load factor and loss factor are defined as[6],[7],[12]: 1, if is associated to cluster − where = 0, otherwise ∑ () = (8) Following steps of k- means algorithm is realized while the ∑[()] = (9) objective function is minimized. () 1. Initialize centroids ( , …………) randomly where () is the electricity demand at -hour or -time interval. 2. Select optimal values of for fixed values of Three cases are considered to describe the relation between (, …………) load factor and loss factor[5],[12]. 3. Choose new optimal values of (, …………) Case 1: Off-peak load is zero: In this case, load factor becomes 4. Repeat steps (2) and (3) until convergence with new equal to load factor. values of (, …………) = (10) Award equal to 1 while the distance of to -th centroid is minimum among the distances to other centroids. Case 2: Very short lasting peak: If peak occurs for very short Mathematically, it can be described in following way duration of time then the value of loss factor approaches the value of load factor squared. = (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.