Beni Mohammad

Rahmatullah Hammamian

Reza Haghifam

Sadegh Amani

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 C I R E D 22nd International Conference on Electricity Distribution Stockholm, 10-13 June 2013 
 
Paper 1113 
 
 
CIRED2013 Session 6 Paper No  1113      
ESTIMATION OF CUSTOMERS DAMAGE FUNCTION BY QUESTIONNAIRE METHOD 
 
 
 Sadegh Amani Beni Mohammad-Reza Haghifam Rahmatullah Hammamian 
 Tarbiat Modares University – Iran Tarbiat Modares University – Iran ChaharMahal Va Bakhtiari Electrical 
                                                                                                                                                         Distribution CO.-Iran 
 s.amanibeni@modares.ac.ir haghifam@modares.ac.ir hammamian@chpedc.ir 
 
ABSTRACT 
Financial compensation of customer interruption costs and 
its determination is the important issue in the new 
deregulated and restructured power system environment.  
Usually utility pay interruption costs of customers. The 
standard way to describe interruption costs is customer 
damage function (CDF) that determines relationship 
between interruption duration and its customer economic 
losses. This paper present a practical method to estimate 
CDF for domestic customers. Proposed method has been 
applied to estimation of CDF in a distribution network.  
INTRODUCTION 
Electric service interruption is unpleasant event and has 
various social, economic and psychological effects on the 
society. Customers and retailers contract for supply of 
electric service. In the contracts usually financial 
compensation of interruption is considered. Also utilities or 
wire companies are responsible for interruption to retailers 
and/or customers. From economic view, main challenge in 
this matter is determination of interruption cost. From 
reliability viewpoint customer interruption cost is important 
for utility because utilities with customer interruption and 
supply costs of electric service optimizes their costs and 
select best plan for expansion. Figure 1 show that if the 
utility invests correspond to “R*” the total cost of service 
reliability is in optimal point of investment in reliability. 
 
Figure 1. Valuing Reliability Benefits and Costs 
Customers’ economic losses as a result of reliability and 
power-quality problems can be summarized by what is 
called CDF. CDF explains relationship between interruption 
duration and its Customer economic losses and has key role 
in interruption cost determination. This idea was first 
suggested in 1994 by Goel and Billinton. They described 
the customer damage function as a simple linear equation 
relating average interruption cost to the duration of an 
interruption. They used data collected from customers to 
describe this function. In 1995, Keane and Sullivan 
suggested a more general form of the CDF – that could be 
used to predict interruption cost values from a number of 
variables that have been shown in interruption cost surveys 
to influence customer interruption costs. CDF is function of 
interruption attributes, customer characteristics, 
environmental attributes that Interruption attributes are 
factors such as interruption duration, season, time of day, 
and day of the week during which the interruption occurs. 
Customer characteristics include factors such as: customer 
type, customer size, business hours, household family 
structure, presence of interruption-sensitive equipment, and 
presence of back-up equipment. Environmental attributes 
include: temperature, humidity, storm frequency, and other 
external/climate conditions [1]. 
CDF determination is important issue in interruption cost 
evaluation. Many researches determined CDF from some 
methods for example in Ref. [2] discrete CDF for some 
sector of customer in Canada has been reported. CDF also is 
used in system studies as input [3,4]. 
The interruption cost determination has many difficulties in 
economic theories and techniques of calculation. It possible 
that the interruption cost is reported with various result 
dependent to many factors. Reference [5] includes a 
bibliography of many researches on the subject of 
interruption cost evaluation. Based on literature review, 
methods of determined interruption cost can be classified as 
follows: 
macroeconomic indicators based methods 
Interruption cost can be determined by dividing gross 
national product (GNP) by total power consumption [6]. 
This method is simple and inexpensive, but has very 
Unrealistic. 
Case study based methods 
In this method interruption cost estimate after a major event 
[7]. Result of this method is more accurate but major 
Interruption rarely occurs and method is expensive. 
Market based method 
Interruption costs are determined using data gathering on 
purchases of backup generation and subscriptions to 
interruptible rate options. Like the macroeconomic method, 
these data are relatively inexpensive to acquire [7]. 
 C I R E D 22nd International Conference on Electricity Distribution Stockholm, 10-13 June 2013 
 
Paper 1113 
 
 
CIRED2013 Session 6 Paper No  1113      
Customer survey based method 
In this method customer survey is used. Usually in this 
method interruption cost are calculated by questionnaire 
method. In this method willingness to pay (WTP) and 
Willingness to accept (WTA) are important that defined 
bellow [8]: 
WTP: An approach to determine how many the consumers 
are willing to pay to avoid an outage. 
WTP: An approach to determine how many the consumers 
would be willing to accept in compensation for an outage 
that has occurred. 
PROPOSED METHOD FOR DETERMINATION 
OF CDF FOR DOMESTIC CUSTOMERS BASED 
ON QUESTIONNAIRE 
CDF can be determined by interruption cost results. 
Proposed method uses from questionnaire to determination 
of WTP and WTA for customers, then CDF should be 
determined. Outage cost (OC) can be calculated from 
equation 1:  
2
WTP WTA
OC

                                               (1) 
In the designed questionnaire WTA and WTP is asked for 
outage duration: 30min and 2,4,8,16,24 hours and WTP is 
average of two parts, one is normalized WTP for 30min and 
2,4,8,16,24 hours, another is maximum WTP for avoid of 
one hour interruption in day and night. With two part for 
WTA, this term can be had more accuracy. All of WTP and 
WTA normalized per hour. Usually The System Average 
Interruption Duration Index (SAIDI) that is the average 
outage duration for each customer served is less than 10 
hours and it is suitable to estimate CDF for 10 hours, but 
CDF is estimated for 16 and 24 hours to eliminate 
sensitivity of estimated CDF to other duration of 
interruption. Method described in figure 2. In questionnaire 
can be ask about other data such as existence of backup 
generator, reaction to service interruption, equipment that is 
important to work in interruption time and etc for additional 
analyses. 
This method should be done every 3-5 years and applied for 
similar customers that classified in some categories. It is 
possible that estimate CDF in seasons but it is more 
expensive. With regard to CDF should have reasonable 
value for any interruption duration, “a” and “b” defined. 
Considering “a” obtained from macroeconomic indicators 
based methods. Parameter of “c” and “g” determined by 
expert in CDF issue and is more than one. These parameters 
determine OCmax calculated by equation 2: 
( )
max
2
g a b
OC

                                               (2) 
In statistics, reliability refers to the consistency of a 
measure. The reliability coefficient of Cronbach’s Alpha 
used to estimate the reliability of the questions [9, 10]. 
 
Figure 2. Proposed method for determination CDF 
 C I R E D 22nd International Conference on Electricity Distribution Stockholm, 10-13 June 2013 
 
Paper 1113 
 
 
CIRED2013 Session 6 Paper No  1113      
CASE STUDY 
In a small area, proposed algorithm has been implemented. 
Questionnaires distributed between 40 Customers of Imam 
Khomeini street, Ben County, ChaharMahal Va Bakhtiary, 
Iran and 35 ones completed and returned. These customers  
were, single phase, 25 A. in this study Cronbach’s Alpha is 
equal to 0.53 Table 1 shows OC in 30min and 2,4,8,16,24 
hours in May 2012 as gathered and processed data. 
Table 1. OC($/kW) in 30min and 2,4,8,16,24 hours in 
May 2012 
Oc(0.5) Oc(2) Oc(4) Oc(8) Oc(16) Oc(24) 
0.8 3.63 7.28 11.91 22.69 34.46 
1.21 5.62 10.67 19.29 38.63 57.73 
0.79 3.29 6.94 12.11 22.67 36.91 
0.78 3.74 6.35 12.15 23.08 34.34 
1.09 4.64 8.79 16.87 33.38 48.84 
0.79 3.59 6.91 12.35 23.21 34.61 
1.09 5.22 9.32 16.92 32.82 51.32 
0.96 4.04 8.64 14.76 30.44 45.47 
1.15 4.89 9.93 17.76 34.09 51.69 
0.82 3.74 7.18 12.59 26.04 35.98 
0.55 2.54 4.92 8.76 16.72 25.32 
0.71 3.62 5.9 10.77 22.02 32.93 
0.54 3.13 5.25 8.17 14.38 24.46 
0.59 2.52 5.26 9.33 18.68 25 
1.04 4.38 8.31 16.1 31.38 46.39 
0.81 3.94 7.18 12.51 24.01 36.6 
0.53 2.49 4.75 7.91 14.97 23.09 
0.9 4.58 7.27 13.61 26.25 42.12 
0.68 3.67 6.29 10.1 21.43 29.6 
0.95 4.45 7.94 14.35 27.99 42.47 
0.62 3.33 5.16 9.81 18.13 27.81 
0.5 2.41 4.12 7.8 13.96 22.28 
0.88 4.16 7.36 13.64 27.56 40.44 
0.91 4.61 7.47 13.52 27.33 42.32 
0.98 4.48 8.49 14.89 29.25 44.34 
0.87 4.4 7 13.41 24.85 37.97 
0.66 3.34 5.52 10.15 19.63 27.81 
1.02 4.57 8.46 16.3 32.46 46.09 
0.46 2.48 4.57 6.64 14.59 21.1 
0.75 3.87 6.4 11.41 21.95 33 
0.79 3.36 7.08 12.44 22.89 37.39 
0.9 3.98 7.77 13.91 26.61 42.53 
0.54 3.13 5.06 8.39 16.08 24.92 
0.72 3.26 5.83 10.69 20.04 33.74 
0.74 3.63 6.92 11.51 22.2 33.3 
From [11] Iran GDP in 2009 equal to 331.01 B$ and from 
[12] total consumption in of 2009 electric energy is 
165.177GWh, then “a” is 2.0039. For “g” equal to 1, 2 and 
3 and “b” equal to 1, 10, 50, 100 and 200 OCmax calculated 
and presented in table 2. (“D” is 0.02$) 
Table 2. OCmax($/kW) for “g” equal to 1,2 and 3 and 
“b” equal to 1, 10, 50 ,100 and 200 
g 
OCmax 
1 2 3 
OCmax(b=200) 3.001955 6.003909 9.005864 
OCmax(b=100) 2.001955 4.003909 6.005864 
OCmax(b=50) 1.501955 3.003909 4.505864 
OCmax(b=10) 1.101955 2.203909 3.305864 
OCmax(b=1) 1.011955 2.023909 3.035864 
 
Regarding to Tables 1 and 2 and proposed algorithm, 
average of OCs is presented in table 3. 
Table 3. OCmax($/kW) for OCmax equal to 2.2, 2.02, 2, 
1.5, 1.1, 1.01 and greater than 2.2 
Ocma\h 0.5 2 4 8 16 24 
>2.2 0.81 3.8 6.92 12.4 24 36.48 
2.2 0.78 3.42 6.56 12 23.68 35.76 
2.02 0.74 3.3 6.28 11.52 22.4 34.32 
2 0.74 3.3 6.28 11.36 22.4 34.32 
1.5 0.61 2.5 5.12 9.6 19.52 28.8 
1.1 0.52 0 4.12 7.76 15.2 23.76 
1.01 0.48 0 0 7.44 14.56 22.08 
 
Figure 3. CDF for OCmax equal to 2.2, 2.02, 2, 1.5, 1.1, 
1.01 and more than 2.2 
From figure3 is seen that for OCmax less than 1.1 zero 
points appear. Also for OCmax more than 2, diagrams near 
together. Sensitivity analysis of diagrams and parameters 
help to select appropriate parameters 
For complete proposed algorithm steps with table 3 data 
CDF curves is estimated in linear, quadric and cubic 
functions for OCmax=2.2 and based on Sig(significant) 
index on Analysis of Variance (ANOVA) one function is 
selected. All the information presented in [13], the major 
interest of the researcher will most likely be focused on the 
value located in the "Sig." column. If the number (or 
numbers) found in this column is (are) less than the critical 
value (alpha) set by the experimenter, then the effect is said 
to be significant. Since this value is usually set at .05, any 
value less than this will result in significant effects, while 
any value greater than this value will result in 
nonsignificant effects. Sig of 3 way of curve estimation is 
presented in table 4. 
Table 4. Sig for linear, quadric and cubic function 
 item Sig 
Linear t .000 
 Constance .141 
Quadric t .000 
 t^2 .865 
 Constance .300 
Cubic t .000 
 t^2 .119 
 t^3 .120 
 Constance .731 
 C I R E D 22nd International Conference on Electricity Distribution Stockholm, 10-13 June 2013 
 
Paper 1113 
 
 
CIRED2013 Session 6 Paper No  1113      
Figure 4 shows estimated curves of CDF. 
 
Figure 4. Estimated curves of CDF. 
Based on Sig index, cubic function is selected for CDF. It is 
important that cubic and quadric function after of 24 hours 
goes to left side and it is possible that estimated CDF after 
24 hours be incorrect. 
CONCLUSION 
In this paper, a new algorithm based on interruption cost 
determination methods is proposed to estimate domestic 
CDF. Because of relation between domestic CDF and 
welfare of costumers that couldn’t convert to monetary 
equivalent, this method uses some benchmarks including 
“a”,”b” and “g”. 
Curve estimation is an important step in this paper that 
implemented with regard to Sig index. Finally in a case 
study, domestic CDF has been estimated. 
Although domestic CDF estimation is difficult but proposed 
method with benchmarks and statistics tools make it easier 
and reasonable. 
FUTURE WORK 
This project aims to propose practical and reasonable 
method for domestic CDF estimation and implementation of 
it in case study. In future work authors will use from more 
statistics tools specially statistics test and other tools for 
more accurate domestic CDF estimation. Consequently will 
be using from feedback control for evaluating results. 
Acknowledgments 
The authors acknowledge ChaharMahal Va Bakhtiari 
Electrical Distribution CO support. 
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ESTIMATION OF CUSTOMERS DAMAGE FUNCTION BY QUESTIONNAIRE METHOD

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ESTIMATION OF CUSTOMERS DAMAGE FUNCTION BY QUESTIONNAIRE METHOD

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