A STATISTICAL ANALYSIS OF LOSS
FACTOR: A CASE STUDY IN
APEPDCL-KAKINADA
G.SAILAJA1
GMR Institute of Technology 1
Email:Sailu140186@gmail.com
M.SAISESHA2
Vishnu Institute of Technology for women
T.S.L.V.AYYARAO3
3
GMR Institute of Technology
Abstract— Given that the total amount of losses in a distribution system is known, with a reliable methodology
for the technical loss calculation, the non-technical losses can be obtained by subtraction. A usual method of calculation technical losses in the electric utilities uses two important factors: load factor and the loss factor. The load factor is usually obtained with energy and demand measurements, whereas, to compute the loss factor it is necessary the learning of demand and energy loss, which are not, in general, prone of direct measurements. In this work, a statistical analysis of this relationship using the curves of a sampling of consumers in a specific company is presented. These curves will be summarized in different bands of coefficient k. Then, it will be possible determine where each group of consumer has its major concentration of points
keywords— constant coefficient k, load curves, load factor ,loss factor.
I. INTRODUCTION
The availability of an adequate amount of electricity and better utilization of it is essential for the growth and development of the country. The demand for electrical energy has outstripped the availability causing widespread shortages in different areas. The distribution network is a crucial network, which delivers electrical energy directly to the doorsteps of the consumer. In India the distribution networks are contributing to a loss of 15% against total system loss of 21%. Hence, the search for loss minimum reconfiguration of distribution networks has always been the concern of electric power utilities.
Each electric utility has its owner method to determine the characteristics of its consumers. Thus, it is through of these measurements that will be possible determining the effect of consumers in different aspects, for example, their influence on the energy losses. The updating of the load curves by measurement campaigns using customer samplings make easier the determination of some parameters, and consequently the loss calculation. Losses
in distribution systems are divided in technical (inherent of the system) and non-technical losses, also called commercial loss (associated, mainly, to the electricity theft). Given that the total amount of losses in a distribution system is known, with a reliable methodology for the technical loss calculation, the non-technical losses can be obtained by subtraction.
In the past few years, several methods have been presented in the literature [1-7], that enable the utility engineer to calculate distribution and transmission demand and energy losses from computer simulations, sampling techniques, load flows, and regression analyses. These techniques yield the value of the losses as well as equations to enable their calculation. These equations are generally in the form of a quadratic equation with losses
presented as a function of the load. It is possible, however, to quickly approximate the system losses equation in parabolic form from data readily available to the engineer basic transformer data and the system's hourly loads. This approximation is adequate in a variety of applications, particularly rate analyses and cost-of-service studies, for which losses are used by the utility engineer.
Losses in distribution system divided into two categories 1. Technical losses
2.Commercial loss
Technical losses
HT network because of high current flowing through LT network. Low line losses result in low cost per unit to the consumer. For a country as whole low line losses means better utilization of sources of energy
COMMERCIAL LOSSES
These losses are major part in our Indian system mainly occur due to pilferage of energy, which has become a social evil in all parts of the country. This can be reduced by properly educating people apart from taking administrative methods.
Many factors play a role in the creation and reporting of losses on an electric system. The technical losses include those caused by current and resistance, hysteresis, eddy currents, and dielectric losses (corona). Commercial losses mainly due to electricity theft. These losses are obtained if total system losses are known by subtracting technical losses from the total system losses. A usual method of calculation of technical losses in the electric utilities uses two important factors: load factor (LF) and the loss factor (
L
SF
). The load factor isusually obtained with energy and demand measurements, whereas compute the loss factor it is necessary the learning of demand and energy loss, which are not, in general, prone of direct measurements. Therefore, it is needed to determine the relationship between these factors. Generally it is used the expression that relates both factors, through the coefficient k, whose value is recommended to be between 0.04 and 0.3. For these areas, many utility engineers have calculated losses by applying the old standard empirical equivalent hours loss factor equation and using a value of 0.3 for the constant coefficient.
2.This project uses extensive analysis of a variety of load curves and statistical evaluation techniques to determine appropriate value k for a wide range of utilities. These curves will be summarized in different ranges of k .For k equal to 0.2, 0.4, 0.6 and0.8, and also the k equal 0and 1 curves were presented. In this project an analysis with real life load curves is presented, determining new values for coefficient k. Further it is presented case studies in Brazilian electric utility and in HT network and LT network in APEPDCLKAKINADA division in order to determine the relationship between load and loss factor. And also loss factor and energy loss are estimated.
Statistical analysis has been proposed in this project to obtain the relationship between load factor and loss factor using the curves of a sampling of consumers in aspecific company. This project uses extensive analysis of a variety of load curves and statistical evaluation techniques to determine appropriate value k for a wide range of utilities. These curves will be summarized in different ranges of k .For k equal to 0.2, 0.4, 0.6 and0.8, and also the k equal 0and 1 curves were presented. In this project an analysis with real time load curves is presented, determining new values for coefficient K.
The Relationship between the Load and Loss factor
A statistical analysis of loss factor to determine the energy losses in the electric utilities uses two important factors: load factor (
LF
) and the loss factor (L
SF
). The load factor is usually obtained with energy and demand measurements, whereas, to compute the loss factor it is necessary the learning of demand and energy loss, which are not, in general, prone of direct measurements. Therefore, it is needed to determine the relationship between these factors. The following section describes the procedure to estimate the loss factorThe loss factor is defined as the ratio of the average power loss over a period of time to the peak load power loss in that same period. Historically this value has been calculated from an empirical equation originally derived by Buller and Woodrow [10]-[11].
LF
K
F
L
S
+
LF
2
1
K
……….(1) Where k is a constantLoad Factor
LF
: Ratio between the average power
Daverage
and the maximum demand
D
max
,in a period of time.
T
dt
t
D
D
D
D
T
average
0max max
1
………(2)
Where
D
t
dt
T
0
T
D
E
LF
max
………(3)Equation (4.3) is the most common form for determining the load factor, because energy (E) and maximum demand
D
max
are obtained through measurements at the substation and supply points of consumers.Loss Factor
L
F
S : Ratio between the average power losses
L
average
and the losses during peak load
L
max
in a period of the time.
T
dt
t
L
L
L
L
F
L
T
average S
0max max
1
………(4)
Where
Tt
L
0
is the instantaneous demand that represents the energy supplied to the system (E) during the period of the time T. Thus, it is obtained
T
L
e
F
L
Smax
………(5)Nonetheless, Equation(5) is not viable for loss factor calculation, because the power and energy losses are not obtained from direct measurements. Their estimations are based on previous knowledge of their own loss factors.
Acknowledging that loads present nearly constant power factor, and expressing both the demand and energy in p.u.
of their respective maximum values, it is computed the following relationship between losses and demand:
2
t
D
t
L
………(6)Thus the loss factor can be expressed in relation to the demand
T
dt
t
D
D
F
L
T
S
0max
2
1
………(7)
T
D
i
D
LF
T
i
max 1
………..(8)When hourly measurements are available, the integral of expressions (2) and (4) can be substituted by summations, as in (8) and (9): The load factor was calculated from the hourly load data using Equation(8) The equivalent hours loss factor was calculated from the hourly Equation(9)
………(10
Equation(10) was obtained from Equation(1) and represents the k from the real load curves. Constant coefficient
k to be determined by putting the calculated values of equivalent hours loss factor and load factor in Equation(10).
II. SAMPLINGOFCONSUMERS
Usually for tariff calculations, companies make measurement campaigns and then obtain characteristic curves for consumers separated by groups, e.g. tariff groups. A measurement campaign for the APEPDCL electric utilities aimed at reviewing the electric tariffs, in which the companies obtained typical load curves for the consumers according to each tariff group.
In APEPDCL has determined many roles to EPDCL distribution companies [1]. \ Some of them are:
• The utilities should maintain permanent service of load characterization of their consumer units and transformer
loading.
• The sampling definition should have a consolidate statistical base to the determination of quantity and locality of measure points.
• The acceptable error level of the sampling of each stratification should be in maximum at 20%, with reliable level of 95%.
• Utilities need to characterize the load curve:
o Carry out measurements in entire universe of transformation and of consumer units equal or more than 69 kV;
o Use the available information on unit consumer electronic meters, and when be necessary, by complementary mensuration;
o Consider Weekday, Saturday and Sunday; o Consider the several segments of consumer units, according to tariff genre, classes of consumer units and consumed bands to billing goals;
o Measurement performed in consumer units and in transformations must be represented by typical load
0 5 10 15 20
0 20 40 60 hours Po w e r i n M W
0 5 10 15 20
0 20 40 60 hours Po w e r i n M W
0 5 10 15 20
0 50 100 hours Po w e r i n M W
0 5 10 15 20
0 10 20 30 40 50 hours Po w e r i n M W
0 5 10 15 20
0 50 100 150 hours Po w e r i n M W
0 5 10 15 20
0 10 20 30 40 hours Po w e r i n M W
0 5 10 15 20
0 20 40 60 hours Po w e r i n M W
0 5 10 15 20
0 10 20 30 40 50 hours Po w e r i n M W
0 5 10 15 20
0 50 100 hours Po w e r i n M W
curves, according to specific consumed bands. The figures from 1 to 10 represent some of these bands. • Annually, the company should present a simplified one phase diagram of its power flow system in maximum loading (of last 12 months) including the losses in each voltage level.
• APEPPDCL can request to the company: the data, methodologies and results of the measurements and of measurement campaign when it is needed. The load profile of the consumer classes were obtained, and in the following figures (1 to 10) are showed the average load curves of the sampling used in this work. Each figure has an average curve of Weekday, Sunday and Saturday. These curves represent the main consumer classes and voltage levels of APEPDCL Systems.
l
III. RESULTSANDANALYSIS
A statistical analysis of loss factor to determine the energy loss in a distribution company explained in chapter 4 is applied with two different case studies carried out from
1.APEPDCL
In this work an analysis made on different areas of the APEPDCL-Kakinada Division. The daily load curves data of different consumer groups are presented in Appendix-A. The Fig. 5.5 & 5.6 shows Domestic, Commercial, the average load curves of the sampling used in this work. Each figure has an average curve of weekday, and Sunday. The Fig. 5.7 shows the localization of the points of relationship between load and loss factor, for all curves of the sampling of consumers. From Fig.5.7 it is noticed that al points are inserted between the k equal 0 and 1 curves. Fig.5.8 shows the relationship between load and loss factors for different ranges of k. For example k=0.2, 0.4, 0.6, 0.8 and also k equal to 0and 1.Unlike in Fig.5.7 shows the relationship between load and loss factors for all points of the sampling. To obtain average load and loss factors from Domestic, Commercial, Typical load curves are calculated using 4.8 and4.9 and are tabulated in Table 5.4.Table 5.5 shows percentage of each group for different values of k perceptually in which band each group has its more and less concentration of points with the proposed algorithm implemented in MATLAB by using load curves data given in Appendix-A .Note that only two classes HT Industrial LT agricultural do not have their majority of points in the range k equal to 0.2.Other classes like Domestic, Commercial
and
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
load factor
lo
s
s
f
a
c
to
r
Fig 6.2 :loss factor Vs load factor
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
load factor
lo
ss f
a
ct
o
r
CONCLUSIONS
In this thesis a statistical analysis of the relationship between load and loss factor considering the application for APEPDCL Kakinada division was presented. The technical loss and consequently non technical loss calculations have been big challenge of the majority of utilities in developing countries. A loss calculation methodology which uses the loss factor is used by utility engineers, defined this factor with precision was important to obtain both losses. The loss factor calculation can be obtained by two ways presented in Eq 4.1 and 4.9.The second way, by 4.9, need the knowing of consumer load curves, but normally these companies do not have the specific load curve of each their consumers. From the analysis it is important to determine specific coefficients k of their consumers Eq 4.1 was used.
The company analyzed is present in different regions of the APEPDCL Kakinada division, and then its areas of concession can be considered as different distribution companies. Some areas present more rural consumers, mean while others present more industrial consumers. Therefore in each of these regions a coefficient k can be used.
References
[1] “A Statistical Analysis of Loss Factor to Determine the Energy Losses”, M. E.de Oliveira, Student Member, IEEE, D. F. A. Boson, and A. Padilha-Feltrin, 2008.
[2] O. M. Mikic, “Variance-Based Energy Loss Computation in Low Voltage Distribution Networks,” IEEE Trans. Power Systems, vol. 22, no. 1, pp. 179- 187, Feb 2007.
[3] R. Taleski and D. Rajicic, “Energy summation method for energy loss computation in radial distribution networks,” IEEE Trans. Power Syst., vol. 11, no. 2, pp. 1104–1111, May 1996.
[4] A. L. Shenkman, “Energy loss computation by using statistical techniques IEEE Trans. Power Del., vol. 5, no. 1, pp. 254–258, Jan. 1990.
