Estimation of Conservation Voltage Reduction Factors Using ... - MDPI

energies Article

Estimation of Conservation Voltage Reduction Factors Using Measurement Data of KEPCO System Kwan-Shik Shim 1 , Seok-Il Go 1 , Sang-Yun Yun 1 Chang-Hoon Shin 2 and Seon-Ju Ahn 1, * 1

2

*

ID

, Joon-Ho Choi 1 , Won Nam-Koong 2 ,

Department of Electrical Engineering, Chonnam National University, Gwangju 61186, Korea; [email protected] (K.-S.S.); [email protected] (S.-I.G.); [email protected] (S.-Y.Y.); [email protected] (J.-H.C.) Energy System Group Energy New Business Laboratory, Korea Electric Power Research Institute, Daejeon 34056, Korea; [email protected] (W.N.-K.); [email protected] (C.-H.S.) Correspondence: [email protected]; Tel.: +82-62-530-1738; Fax: +82-62-530-1749

Received: 21 November 2017; Accepted: 11 December 2017; Published: 15 December 2017

Abstract: This paper describes a method to estimate conservation voltage reduction (CVR) factors using data measured in power distribution systems. A direct method is proposed to estimate CVR factors using only data measured at the moment of the transformer tap change. The mean absolute deviation (MAD) direct method is proposed to consider direct methods and load variations. The proposed methods do not necessitate intentional tap changes for testing purposes. Instead, the voltage and load changes that occur when the tap changes, for voltage regulation purposes, are measured and utilized in the CVR factor calculation. The proposed methods were tested using data obtained from the Korea Electric Power Corporation (KEPCO) system, and the results revealed that CVR factors for both active power and reactive power could be estimated using data measured in power distribution systems. Results of the CVR factor estimation for the active power revealed that the highest CVR factors occurred in winter, during which a large quantity of heating loads exist. In addition, the estimated CVR factors for the reactive power were higher than the estimated CVR factors for the active power because reactive power is more sensitive to voltage changes. Keywords: conservation voltage reduction; CVR factor; distribution system; estimation; load; measurement

1. Introduction To support the sustainable growth of humanity, new technologies are being developed to solve real world problems such as energy depletion and environmental pollution. In the field of electrical power, which can be directly or indirectly related to these problems, new technologies such as smart grids are being developed [1,2]. Recently, nations worldwide have experienced electric energy shortages, which result from environmental problems and rapid economic growth. Consequently, the construction of new power generation and transmission facilities has been delayed because of these economic and environmental problems. Power companies have the tendency to operate their systems at peak load because of the electric energy shortage, and voltage reduction is performed to reduce the load demand at this peak [3–5]. This voltage reduction can be accomplished by reducing the bus voltage, which is achieved through adjusting the taps of power transformers. If the bus voltage decreases, then the voltage-dependent load demand also decreases. This causes the demand power to decrease. Generally, voltage reduction methods are classified into three types: conservation voltage reduction (CVR), emergency voltage reduction (EVR), and routine voltage reduction (RVR) [6]. However, CVR has been mainly used to reduce the demand load through voltage reduction. Energies 2017, 10, 2148; doi:10.3390/en10122148

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Distribution voltage reduction was first carried out by the Pacific Gas and Electric (PG & E) company in 1948 to reduce the peak load [7]. Afterwards, it was mainly used to decrease demand loads because energy saving became a social issue due to the 1970s oil shock. After PG & E tested the impact of voltage reduction in 1975, the California Power Commission asked power companies to test nominal voltage drops and implement constant voltage reductions. Since then, power companies have constantly tested distribution voltage reduction and proven its impact. In particular, the Independent Electrical System Operator (IESO), located in Ontario, Canada, performs distribution voltage reduction every 18 months to analyze the effects of power load reductions caused by voltage reduction and to check emergency measures [8]. The US Department of Energy (DOE) reported that the voltage being supplied to more than 90% of normal homes and shopping centers is higher than the required level. Therefore, appropriate voltage reduction can effectively ensure energy saving and stable operation of systems at peak load. The Korea Electric Power Corporation (KEPCO) also adjusts the taps of power transformers for voltage reduction when operational reserves are insufficient. When rolling blackouts occurred in 15 September 2011, taps of power transformers were adjusted to secure reserves of approximately 1000 MW. Since then, KEPCO has performed voltage reductions when reserve shortages occur at peak load during winter and summer. One study in the literature [9] describes the results of estimating the CVR of power distribution units using GridLAB-D, which was developed at the Pacific Northwest National Laboratory (PNNL). Another paper from the literature [10] also describes the effect of adjusting the distribution voltage in smartgrid environments. In one study [11], CVR factors were estimated by applying supply curves, and the energy saving costs were subsequently calculated. In another study [12], energy saving by voltage reduction and its economic implications were evaluated. Some researchers [13] described a volt/var control method and CVR, while others [14] proposed a method to estimate the CVR factors by applying a voltage control technique that inhibits the occurrence of low voltage during distribution voltage reduction. KEPCO performed voltage reduction from the summer of 2012 to the spring of 2013 to analyze its effects. The results from analyzing the energy saving and voltage reduction effects in the KEPCO system using the Substation Operating Results Management System (SOMAS) data are described in the study by Nam et al. [15]. Although the CVR factors vary with the type of load and the season, the typical values reported in the previous studies range from 0.3 to 0.9 [16]. This paper introduces and describes a method to estimate CVR factors using measurement data from power distribution systems and presents the results of applying this method to the KEPCO system. The percentages of voltage and load changes are calculated from data obtained at the moment of abrupt voltage changes due to tap changes in the transformers of the power distribution system. Then, the ratio of the voltage change percentage and load change percentage is calculated to estimate CVR factors. In addition, the MAD is used to calculate load variations, which are reflected in the calculation of the load change percentage and utilizes to estimate CVR factors. The average of the CVR factors obtained by filtering the voltage and load changes and the estimated CVR factors are used to calculate the representative CVR factor of each distribution line. As a result of evaluating the CVR factor of the KEPCO system, the CVR factor was estimated to be the largest during winter, with heavy heating loads. Additionally, the CRV factor was estimated to be the smallest during summer, when a large amount of air conditioners is being used. Because reactive power is sensitive to voltage changes, CVR factors for the reactive power were found to be much higher than those for the active power. The composition of this paper is as follows. Section 2 describes the CVR factor estimation method. Section 3 gives the data measurements of the KEPCO distribution system. Section 4 presents the results of estimating CVR factors of the KEPCO distribution system. Finally, conclusions of the study are provided in Section 5.

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2. Conservation Voltage Reduction (CVR) Factor Estimation Method 2.1. Definition of CVR Factors In power distribution systems, loads are always subject to change. To quantitatively identify the effects of voltage reduction, the reduction of demand loads with respect to voltage changes needs to be estimated. The CVR factor is defined as the percentage of load reduction with respect to the percentage of voltage change, and is a quantitative indicator of demand load reductions with respect to voltage changes. Therefore, CVR factors are quantitative indicators that can be used to independently identify the effects of voltage reduction. CVR factors for the active and reactive powers can be expressed using the voltage and load change percentages as follows: -

-

The active power CVR factor CVPP =

%∆P %∆V

(1)

CVPQ =

%∆Q %∆V

(2)

The reactive power CVR factor

where %∆V is the percentage of the voltage change, and %∆P and %∆Q are the percentage variations of the active and reactive demand loads, respectively. 2.2. Direct Method In previous research studies, change of the demand load was calculated from the measured load when the voltage reduction was applied, and the estimated load assuming the voltage reduction was not applied. Therefore, the accuracy of the CVR factor depends on the accuracy of the load estimation. If the load variations are large, it is difficult to accurately estimate the demand loads; subsequently, large errors occur in calculating the CVR factor. We propose a new method, named the direct method, to calculate the CVR factor by calculating voltage and load changes directly from measured data. In other words, it is a method through which CVR factors can be estimated using only measured values without requiring the estimation of demand loads. The voltage and load change percentages required in the calculation of CVR factors from measured values can be expressed as follows: %∆V =

Va f t − Vpre ∆V × 100 = × 100 % Vmean Vmean

(3)

%∆P =

Pa f t − Ppre ∆P × 100 = × 100 % Pmean Pmean

(4)

Q a f t − Q pre ∆Q × 100 = × 100 % Qmean Qmean

(5)

%∆Q =

where Vpre and Vaft are the voltages measured before and after performing the voltage adjustment, respectively, and Vmean is the mean voltage. Ppre and Paft are the active power loads measured before and after performing the voltage adjustment, respectively, and Pmean is the mean active power load. Qpre and Qaft are the reactive power measured before and after performing the voltage adjustment, respectively, and Qmean is the mean reactive power load. The variables with subscript ‘pre’ and ‘aft’ represent the single data point immediately prior to and after the voltage reduction, respectively, and the variables with subscript ‘mean’ refers to the average value of the two single point data. The proposed method does not need to perform intentional tap changes for testing purposes. Instead, the voltage and load changes that occur when the tap changes, for voltage regulation purposes,

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are measured measured and and utilized utilized in in the the CVR CVR factor factor calculation. calculation. Typical Typical voltages voltages and and loads loads before before and and after after are changing the transformer taps are shown in Figure 1. changing the transformer taps are shown in Figure 1.

load

voltage and load(pu)

Ppre

voltage

Vpre

Vaft Paft

time (sec) Figure 1. Voltage Voltage and and load load before before and and after after changing changing the the taps. taps.

2.3. Filtering 2.3. The transformer transformer tap tap changes changes up up to to 10 times a day, although it it depends depends on the load characteristics The day, although characteristics of the thedistribution distributionlines. lines. Therefore, measurement the voltage and load changes can be of Therefore, measurement data data of theofvoltage and load changes can be obtained obtained as many times as the number of tap changes. The representative value of the CVR factor as many times as the number of tap changes. The representative value of the CVR factor over a period over a period of time a(for example, a month orbe a season) canas befollows: calculated as follows: of time (for example, month or a season) can calculated

1 nn CVR mean  1  CVR i CVRmean = n ∑ CVRi  1 i n i =1

(6) (6)

Estimating CVR factors in power distribution systems requires sensitive mathematical calculations. Estimating CVR factors in power distribution systems requires sensitive mathematical calculations. For example, the voltage variation by one tap adjustment of a transformer is approximately 1%, and For example, the voltage variation by one tap adjustment of a transformer is approximately 1%, and the the range of typical CVR factor values is very small, ranging from 0.5 to 1.0. The filtering method range of typical CVR factor values is very small, ranging from 0.5 to 1.0. The filtering method directly directly influences the CVR factor estimation results. Thus, appropriate filtering is the most important influences the CVR factor estimation results. Thus, appropriate filtering is the most important part in part in estimating CVR factors. The representative CVR factor is calculated only using valid cases estimating CVR factors. The representative CVR factor is calculated only using valid cases that satisfy that satisfy the following filtering rules. the following filtering rules. When the taps of transformers change, voltages and loads also change accordingly. Ideally, When the taps of transformers change, voltages and loads also change accordingly. Ideally, when the voltage decreases, the loads also decrease; when the voltage increases, the loads also when the voltage decreases, the loads also decrease; when the voltage increases, the loads also increase. increase. However, in some cases, the direction of the load change was opposite of the direction of However, in some cases, the direction of the load change was opposite of the direction of the voltage the voltage change; thus, the calculated CVR factor values were negative. In those cases, it can be change; thus,that the the calculated factorofvalues were In those cases, it of canthe be load considered considered naturalCVR increase the load is negative. larger than the decrease due tothat the the natural increase of the load is larger than the decrease of the load due to the voltage reduction. voltage reduction. Therefore, it is reasonable to exclude these cases when calculating the Therefore, it is reasonable exclude these cases the representative CVR factor value. representative CVR factortovalue. Only cases in when whichcalculating the measured voltage and the measured load Only cases in which the measured voltage and the measured load change were in the same direction change were in the same direction were chosen when calculating the CVR factor. were chosen when calculating the CVR factor. V  0, P  0 (7) ∆V (7) V> 0, 0, ∆P P >  00 (8) ∆V < 0, (OLTC) ∆P < 0 have 17 tap positions, which means that (8) In the KEPCO system, on-load tap changers one tap change produces a voltage variation of approximately 1.25%. Thus, load changes that can In the KEPCO system, on-load tap changers (OLTC) have 17 tap positions, which means that one occur in response to one tap change are limited. Therefore, very large load change percentages and tap change produces a voltage variation of approximately 1.25%. Thus, load changes that can occur small voltage change percentages calculated from the measured data are excluded.

0.2  %ΔP  2.0

(9)

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in response to one tap change are limited. Therefore, very large load change percentages and small voltage change percentages calculated from the measured data are excluded. 0.2 < %∆P < 2.0

(9)

%∆V > 0.5

(10)

Under a normal load, CVR factors consist of values ranging from 0.2 to 1.5%. Therefore, estimated CVR factors that are too high or too low are excluded. 0.2 < CVR < 2.0

(11)

Although the filtering criteria described in Equations (9)–(11) were chosen basically based on the intuition and engineering judgment, it can be applied to different system with minor modifications. For example, if the OLTC has 33 tap positions, then the parameter values of Equations (9) and (10) should be halved. The fine-tuning of the parameters would increase the accuracy of the CVR factor estimation, but it is left as a future work. 2.4. Mean Absolute Deviation (MAD) Direct Method The direct method directly calculates the load change percentage from measured loads. Thus, the variation of load regardless of the voltage reduction affects calculated CVR factors. The MAD direct method is proposed to take into account the effect of natural variation in load. The load variations that occur right before tap changes is calculated and reflected in the calculation of the load change percentage. Load variation before tap changes can be calculated using MAD. This term refers to the average of the absolute deviations of each measured value from the mean. If n measured values are represented as P1 , P2 , . . . , Pn and the average value is Pm , the MAD can be expressed as follows: PMAD =

1 n | Pi − Pm | n i∑ =1

(12)

The MAD percentage right before tap changes (%PMAD ) is expressed as follows: %PMAD =

PMAD × 100 [%] Pm

(13)

The maximum and minimum load change percentages caused only by voltage reduction can be calculated as follows: -

The minimum load change percentage %∆Pmin = %∆P − %PMAD

-

(14)

The maximum load change percentage %∆Pmax = %∆P + %PMAD

(15)

Figure 2 shows the MAD, the maximum load change percentage, and the minimum load change percentage.

%  Pmin  %  P  % PMAD

-

(14)

The maximum load change percentage %  Pmax  %  P  % PMAD

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Figure 2 shows the MAD, the maximum load change percentage, and the minimum load change percentage.

Figure 2. Percentage load variation andmean meanabsolute absolute deviation direct method. Figure 2. Percentage load variation and deviationofofthe the direct method.

The maximum and minimum load change percentages can be used to estimate the minimum and maximum CVR values as follows: -

-

The minimum CVR factor CVRmin =

%∆Pmin %∆V

(16)

CVRmax =

%∆Pmax %∆V

(17)

The maximum CVR factor

If the calculated load changes, ∆Pmin and ∆Pmax , satisfy the filtering rules in Equations (7)–(9) and the calculated CVR factors, CVRmin and CVRmax , satisfy the rule in Equation (11), the CVR factor can be calculated from Equation (18). However, if any of the above values does not satisfy the filtering rule, it is excluded from the CVR factor calculation. CVR MAD =

CVRmin + CVRmax 2

(18)

3. Measurement of Distribution System Data in the Korea Electric Power Corporation (KEPCO) System 3.1. Acquisition of Distribution Line Data To estimate the CVR factor of each distribution line, a data acquisition system (DAS) was installed on the distribution lines, and the long-term voltage and load data were acquired from this system. The DAS used a sampling rate of 1 sample per second (sps). The sampling rate depends on the purpose of the data. For example, a very fast sampling rate is required for power quality analysis or protection. On the contrary, for the voltage regulation in a distribution system, an average value of several minutes is enough. The data sampling rate required for CVR factor estimation also varies depending on the method of analysis and scale of the load of the system. If the size of load is small and the sampling rate is low, it is not possible to accurately capture the load change at the moment of voltage reduction. Therefore, to estimate the CVR factor for a small load like a distribution line, a sampling rate, sufficiently faster than that used for the usual voltage regulation, is required. In this study, data of the voltage, active power, and reactive power of the distribution lines connected to the Chimsan substation were acquired. The results of using this data in the CVR factor calculation are described in this chapter. The loads from this substation possess characteristics of residential and commercial areas. Figure 3 shows the DAS and distribution lines of the Chimsan substation. Table 1 shows the data acquisition line of the Chimsan substation and the data acquisition date.

In this study, data of the voltage, active power, and reactive power of the distribution lines connected to the Chimsan substation were acquired. The results of using this data in the CVR factor calculation are described in this chapter. The loads from this substation possess characteristics of residential and commercial areas. Figure 3 shows the DAS and distribution lines of the Chimsan substation. Energies 2017, Table 10, 21481 shows the data acquisition line of the Chimsan substation and the data acquisition 7 of 16 date.

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Configuration of Chimsan substation. Table Figure 1. Data3. acquisition line and date of the Chimsan substation. Figure 3. Configuration of the the Chimsan substation.

Month

Data Acquisition Period

2016.09

2016.09.12–2016.09.28

Acquisition Data Value

Month

Data Acquisition Period

V, P, Q Acquisition Data Value

2016.102016.092016.09.29–2016.10.28 2016.09.12–2016.09.28

V,V, P, Q P, Q

2016.09.29–2016.10.28 2016.112016.102016.11.18–2016.12.13

P, Q V,V, P, Q

2016.11

2017.02

D/L Name Bookgong, Daebang, Gosung, Nowoon, Samgong D/L Name Bookgong, Daebang, Gosung, Bookgong, Daebang, Gosung, Nowoon, Samgong Nowoon, Samgong Bookgong, Daebang, Gosung,Gosung, Bookgong, Daebang, Nowoon, Samgong Nowoon, Samgong Bookgong, Daebang, Gosung, Bookgong, Daebang, Gosung, Nowoon, Samgong Bookgong, Daebang, Gosung, Nowoon, Samgong Nowoon, Samgong Bookgong, Daebang, Bookgong, Daebang, Gosung,Gosung, Nowoon, Samgong Nowoon, Samgong

Table 1. Data acquisition line and date of the Chimsan substation.

2016.11.18–2016.12.13

2017.02.17–2017.03.17

2017.02

2017.02.17–2017.03.17

2017.062017.062017.06.01–2017.06.30 2017.06.01–2017.06.30

V, P, Q

V, P, Q V, P, Q

V,V, P, Q P, Q

3.2.Voltage Voltageand andLoad Loadofofthe theChimsan ChimsanSubstation Substation 3.2. Figure44shows showsthe theload loadand andvoltage voltageofofthe theBookgong Bookgongdistribution distributionline line(D/L) (D/L)of ofthe theChimsan Chimsan Figure substation,which whichwere weremeasured measuredatataasampling samplingrate rateofof11sps. sps.The Thenormalized normalizedvoltage voltageand andload loadvalues values substation, areshown shownininFigure Figure4,4,where wherethe thegreen greenline linerepresents representsload loadvalues valuesand andthe theblue blueline linerepresents representsvoltage voltage are values.Voltages Voltagesbefore beforeand andafter afterthe thetap tapchange, change,which whichare areindicated indicatedwith withcircles, circles,show showaasignificant significant values. change.When Whenthe thevoltage voltagechanges, changes,the thedirect directmethod methodcan canbe beapplied appliedto tothe themeasured measureddata datato toestimate estimate change. theCVR CVRfactors. factors. the

Figure Figure4.4.Load Loadand andvoltage voltageofofthe theBookgong Bookgongdistribution distributionline line(D/L): (D/L):trend trendover overseveral severalminutes. minutes.

Figure 55 shows shows an 4 around thethe tap tap change. As shown in thein figure, Figure an enlarged enlargedversion versionofofFigure Figure 4 around change. As shown the voltagevoltage and load atdata the moment of the tap change can be acquired from the distribution systems. figure, anddata load at the moment of the tap change can be acquired from the distribution Therefore, CVR factors be estimated from the measured active and reactive powerpower data of the systems. Therefore, CVRcan factors can be estimated from the measured active and reactive data distribution systems under normal operating conditions, devoid of any intentional voltage reduction test.

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of the distribution systems under normal operating conditions, devoid of any intentional voltage reduction test. Energies 2017, 10, 2148 8 of 16

Figure 5. Load and voltage of the Bookgong D/L: details at the moment of tap change. Figure 5. Load and voltage of the Bookgong D/L: details at the moment of tap change.

3.3. Data Processing

3.3. Data Processing

The amount of data acquired over a long period of time using a DAS for distribution lines can

The amount data acquired over a long period of time using a DAS distribution lines can be very large. of Performing iterative calculations on a large amount of data can for require a considerable be very large.ofPerforming calculations on a large amount ofwere datastored can require a considerable amount computationiterative time. Therefore, data acquired using the DAS in a binary format so that it could be quickly called by the calculation program. In this binary files were amount of computation time. Therefore, data acquired using the DASstudy, werethese stored in a binary format called to perform calculations thethe CVR factors. so that it could be quickly calledofby calculation program. In this study, these binary files were Several factors could beofused verify the acquired data. In this study, only measurement errors called to perform calculations the to CVR factors. and data leakage were verified. No measurement errors were found in the acquired data because Several factors could be used to verify the acquired data. In this study, only measurement errors none of the data was significantly different from the standard deviation. However, leakage was found and data leakage were verified. No measurement errors were found in the acquired data because none in the measured data because there were many parts in the data where timestamps were missing. of the dataApproximately was significantly different from the standard deviation. However, leakage found 60 data leakage cases occurred in 86,400 samples acquired during was a single day.in the measured data because there were many parts in the data where timestamps were missing. The leakage rate of the data acquired by the DAS was 0.07%. Because the leakage did not Approximately 60 itdata leakage cases occurred in 86,400 of samples a leaked single day. continuously occur, did not significantly affect the estimation the CVRacquired factors. Induring addition, The leakage ratereplaced of the data acquired theofDAS was before 0.07%.and Because theloss. leakage did not continuously data were by the average by value the data after the Fornot the DAS used in this study, voltage, active power, the reactive power data are stored occur, it did significantly affect thethe estimation of the CVRand factors. In addition, leaked data were in separate files with their own timestamp. Since voltage and load data immediately before and after replaced by the average value of the data before and after the loss. the voltage reduction are used, time synchronization between voltage and load data is very For the DAS used in this study, the voltage, active power, and the reactive power data are stored important. If two measured data sets are not synchronized, the calculated CVR factor will contain a in separate files with their own timestamp. Since voltage and load data immediately before and after serious error. Therefore, time values had to be synchronized between the voltage and load data. In the voltage reduction are used, time synchronization between voltage and load data is very important. this study, the direct method was applied to the data after the preprocessing to check for time If twosynchronization measured data sets are synchronized, the calculated factorBecause will contain a serious between thenot voltage and load data and correct it ifCVR necessary. there was a error. very Therefore, time values had to be synchronized between the voltage and load data. In this study, large quantity of data, this time synchronization required a large amount of computation time. the direct method was applied data of after preprocessing to check for time synchronization Therefore, when storing datato in the the DAS the the distribution lines, time synchronization must always between the voltage and load data and correct it if necessary. Because there was a very large quantity be performed. of data, this time synchronization required a large amount of computation time. Therefore, when 4. Estimation CVRofFactors of the KEPCO System storing data in theof DAS the distribution lines, time synchronization must always be performed. CVR factors were estimated by applying the direct method to the data acquired in the DAS

4. Estimation of each CVRdistribution Factors ofline theofKEPCO System installed on the Chimsan substation. Data before and after tap changes were extracted from each distribution line of the Chimsan substation. Voltage and load change percentages CVR factors were estimated by applying the direct method to the data acquired in the DAS were calculated when signs of the extracted voltage and load changes were the same. In addition, installed on each distribution line of the Chimsan substation. Data before and after tap changes were CVR factors were calculated when the calculated values met the filtering conditions. CVR factors of extracted from each lines distribution line of the Chimsan substation. Voltage percentages the distribution were estimated by calculating the average of valuesand that load were change within the CVR were filtering calculated when signs of the extracted voltage and load changes were the same. In addition, range. The filtering conditions shown in Table 2 were applied. CVR factors were calculated when the calculated values met the filtering conditions. CVR factors of the distribution lines were estimated by calculating the average of values that were within the CVR filtering range. The filtering conditions shown in Table 2 were applied.

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Table 2. Filtering conditions for estimating the load of CVR factors. Filtering Term voltage and load variation percent voltage variation percent load variation CVR range

Range

Description

∆V > 0, ∆P > 0 ∆V < 0, ∆P < 0 0.5 < %∆V < 1.5 0.2 < %∆P < 2.0 0.2 < CVR < 2.0

voltage drop voltage rising voltage load -

Table 3 summarizes the CVR factor calculated from the data measured from all D/Ls of the Chimsan substation by using the direct method. In the table, “CVRp ” represents average CVR factors, and “No” refers to the number of times that the filtering conditions were met. For example, filtering conditions were satisfied a total of 88 times in the Bookgong D/L measurement data during September 2016, and the representative CVR factor of this month was calculated to be 0.827. On the other hand, filtering conditions were not satisfied with regard to the measured data of the Nowoon D/L during June 2017, so CVR factors could not be estimated. Table 3. CVR factors for the active power of the Chimsan substation (direct method). 2016.09 D/L Bookgong Daebang Gosung Nowoon Samgong Mean

2016.10

2016.11

2017.02

2017.06

CVRp

No

CVRp

No

CVRp

No

CVRp

No

CVRp

No

0.827 0.803 0.918 0.828 0.829 0.841

88 48 64 45 48 -

0.723 0.921 0.785 0.833 0.829 0.818

115 45 73 47 54 -

0.885 0.834 0.681 0.836 0.939 0.835

110 58 40 70 51 -

0.843 0.890 0.943 0.905 0.885 0.893

179 101 124 83 85 -

0.734 0.881 0.820 0.878 0.828

265 127 185 114 -

Mean 0.802 0.866 0.829 0.851 0.872 0.842

The Chimsan substation supplies electricity to metropolitan areas. The DAS data are acquired from D/Ls that feed both commercial and residential areas, which makes it difficult to distinguish the characteristics of the CVR factor between commercial and residential loads. The average CVR factors were estimated to be in the range of 0.802–0.872 for all D/Ls of the Chimsan substation. The lowest mean CVR factor (0.802) was found in the Bookgong D/L, and the highest mean CVR factor (0.872) was found in the Samgong D/L. However, the estimated CVR factors were almost the same because D/Ls of the Chimsan substation are located in the same area and have similar load characteristics. CVR factors were estimated by applying the MAD direct method to the data measured from all D/Ls of the Chimsan substation, and the mean CVR factor was calculated from these values. The filtering conditions of the MAD direct method are presented in Table 4. Table 4. Filtering conditions for estimating CVR factor of load (MAD). Filtering Term voltage and load variation percent voltage variation MAD percent load variation MAD CVR range

Range

Description

∆V > 0, ∆P > 0 ∆V < 0, ∆P < 0 0.5 < %∆V < 1.5 0.2 < %∆PMAD < 2.0 0.2 < CVR MAD < 2.0

voltage drop voltage rising voltage load -

Table 5 lists CVR factors estimated by applying the MAD direct method to the DAS data acquired from the Chimsan substation. The CVR factors of the Nowoon D/L during June 2017 are not listed in the table because they could not be calculated due to a lack of data.

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Table 5. CVR factors for the active power of the Chimsan substation (MAD direct method). Table 5. CVR factors for the active power of the Chimsan substation (MAD direct method).

D/L D/L

Bookgong Daebang Bookgong Daebang Gosung Gosung Nowoon Nowoon Samgong Samgong Mean Mean

2016.09 2016.09 No CVR p CVR No 0.707 32 p 0.764 3219 0.707 0.764 0.790 1914 0.790 14 0.750 3333 0.750 0.646 4141 0.646 0.731 0.731 - -

2016.10 2016.10 No CVR p CVR No 0.689 40 p 0.722 40 31 0.689 0.722 0.773 31 21 0.773 21 0.799 15 15 0.799 0.646 27 27 0.646 0.726 0.726 - -

2016.11 2016.11 No CVR p CVR No 0.766 45 p 0.761 45 30 0.766 0.761 0.821 30 42 0.821 42 0.763 71 71 0.763 0.761 25 25 0.761 0.774 0.774 - -

2017.02 2017.02 No CVR p CVR No 0.757 66 p 0.800 66 46 0.757 0.800 0.774 46 22 0.774 22 0.789 35 35 0.789 0.810 37 37 0.810 0.786 0.786 - -

2017.06 2017.06 No CVR p CVR No 0.684 81 p 0.768 81 64 0.684 0.768 0.760 64 59 0.760 59 - - 0.764 57 57 0.764 0.744 0.744 - -

Mean Mean

0.721

0.763 0.721 0.763 0.784 0.784 0.775 0.775 0.725 0.725 0.754 0.754

CVR factors were estimated be range in theofrange of 0.721–0.784 forofall of the Chimsan CVR factors were estimated to be to in the 0.721–0.784 for all D/Ls theD/Ls Chimsan substation. In themethod, MAD direct method, lowest factor was found in the and Bookgong Insubstation. the MAD direct the lowest CVRthe factor wasCVR also found in thealso Bookgong D/L, almost D/L, all and CVR almost all other factors wereofsimilar to those of the direct method. The MAD direct method other factors wereCVR similar to those the direct method. The MAD direct method produced lower produced lower than CVR the factor values than Since the direct Since many of the under-estimated cases CVR factor values direct method. manymethod. of the under-estimated cases have already been have already been filtered the filtering (5)method and (6),filtering the MAD direct method filtered by the filtering rule of by Equations (5) andrule (6), of theEquations MAD direct conditions apply filtering conditions apply more to the over-estimated cases. Consequently, the MAD direct method more to the over-estimated cases. Consequently, the MAD direct method produces lower values than produces lower values than the direct method. introduction of MAD direct would help the direct method. The introduction of MAD directThe method would help prevent themethod overestimation of prevent thevoltage overestimation the effect of reduction.of the effect of voltage reduction. 4.1. of of Estimated CVR Factors 4.1.Seasonal SeasonalTrend Trend Estimated CVR Factors CVR CVRfactors factorsofofeach eachseason seasonwere wereestimated estimatedtotoanalyze analyzethe theeffect effectofofvoltage voltagereduction reductionbybyseason. season. The data measured atat each D/L The data measured each D/Lofofthe theChimsan Chimsansubstation substationcan canbebeclassified classifiedbybyseason seasonasasfollows. follows.

September2016: 2016:Early Earlyfall fall September October2016: 2016:Fall Fall October November 2016: Early winter November 2016: Early winter February 2017: Winter February 2017: Winter June 2017: Early summer June 2017: Early summer Figure 6 shows CVR factor values estimated by applying the direct method to the data measured 6 shows CVR factorcategorized values estimated by applying directaverage methodCVR to thefactors data measured for Figure each D/L, and are further by season. Figure the 7 shows of all D/Ls for each D/L, are further categorized season. Figure 7 shows average CVRand factors of allwith D/Ls classified byand season. CVR factors were by estimated to be high in early winter winter, the classified by season. CVR factors were estimated to be high in early winter and winter, with the exception of the CVR factor of the Gosung D/L. The highest CVR factors were found in February exception of the factor of the Gosung D/L. The highest CVR factors were found in February 2017, 2017, which is CVR considered winter. which is considered winter.

-

-

Figure CVR factors each D/Lclassified classifiedbybyseason. season. Figure 6. 6. CVR factors of of each D/L

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1111 ofof 1616 11 11 of of 16 16

Figure CVR factors of all D/Lsclassified classifiedby byseason. season. Figure 7. Average CVR factors D/Ls classified by season. Figure 7.Average Average CVR factors of all D/Ls classified by season. Figure 7. 7. Average CVR factors ofof allall D/Ls

Figure shows CVR factor values estimated direct method. Figure by season seasonby byapplying applyingthe theMAD MAD direct method. Figure8 88shows showsCVR CVRfactor factorvalues values estimated estimated by by season by applying the MAD direct method. Figure 8 shows CVR factor values estimated by season by applying the MAD direct method. CVR values were estimated to be high in (February 2017). CVR values were winter (November2016) 2016)and andwinter winter (February 2017). CVR values wereestimated estimatedto tobe behigh high in in early early winter winter (November (November 2016) and winter (February 2017). CVRFigure values were estimated to bevalues high in early winter (November 2016) and winter (February 2017). 9 shows the mean CVR of all D/Ls by season, which were calculated using CVR values Figure 9 shows season,which whichwere werecalculated calculated using CVR values Figure 9 showsthe themean meanCVR CVRvalues valuesof of all all D/Ls by season, using CVR values Figure 9 showsfrom the mean CVR values ofdirect all D/Ls by season, whichthe were calculated using CVR values estimated applying the MAD method. In were also estimatedfrom fromapplying applyingthe theMAD MAD direct direct method. In this case, highest CVR factors were also estimated In this this case, case,the thehighest highestCVR CVRfactors factors were also estimated from applying the MAD direct method. In this case,ofthe highest CVR factors were also found found winter (February 2017), followed by CVR 2016), as seen found in winter(February (February2017), 2017),followed followed by factors early winter (November 2016), as as seen found inin winter CVR factors factorsof ofearly earlywinter winter(November (November 2016), seen in winter (February 2017), followed by CVR factors of early winter (November 2016), as seen in the direct method case. in the direct method case. in in thethe direct method case. direct method case.

Figure 8. factors estimated by applying the MAD direct method, classified Figure 8. CVR CVR factors estimated applyingthe theMAD MADdirect directmethod, method,classified classified by by season. season. Figure 8. CVR factors estimated byby applying by season. Figure 8. CVR factors estimated by applying the MAD direct method, classified by season.

Figure 9. CVR factors estimated applying the MAD direct method, classified Figure 9. Average Average CVR factors estimated by applyingthe theMAD MADdirect directmethod, method, classified classified by by season. season. Figure 9. Average CVR factors estimated byby applying season.

Figure 9. Average CVR factors estimated by applying the MAD direct method, classified by season.

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When data by Whenanalyzing analyzing data byseason, season,CVR CVRfactors factorsofof ofearly earlywinter winterand andwinter winterwere werefound foundtoto tobe behigher higher When analyzing data by season, CVR factors early winter and winter were found be higher than those of summer and fall. This is because many resistive loads such as heaters are used in thanthose thoseof ofsummer summerand andfall. fall.This isisbecause becausemany manyresistive resistiveloads loadssuch suchas asheaters heatersare areused usedin inthe the than the winter. Therefore, the largest voltage reduction effect is observed in winter when taking season winter. Therefore, the largest voltage reduction effect is observed in winter when taking season into winter. Therefore, the largest voltage reduction effect is observed in winter when taking season into into account. account. account. 4.2. of of thethe Estimated CVR Factors 4.2.Time TimeTrend Trend Estimated CVR Factors 4.2. Time Trend of the Estimated CVR Factors Figure the mean CVR factors ofof allall D/Ls Figure10 10shows shows the mean CVR factors D/Lsof ofthe theChimsan Chimsansubstation substationby bytime. time.The TheCVR CVR Figure 10 shows the mean CVR factors of all D/Ls of the Chimsan substation by time. The CVR factors estimated using both the direct method and MAD direct method were higher during the dawn factors estimated using both the direct method and MAD direct method were higher during the dawn factors estimated using both the direct method and MAD direct method were higher during the dawn and time than was andevening evening timeperiods periods thanthose thoseduring duringthe thedaytime. daytime.This Thischaracteristic characteristic wasdue duetoto tolarger largerheating heating and evening time periods than those during the daytime. This characteristic was due larger heating loads at dawn and night. loadsat atdawn dawnand andnight. night. loads

Figure 10. Average CVR factors of all D/Lsby bytime. time. Figure 10. Average CVR factors D/Ls by time. Figure 10. Average CVR factors ofof allall D/Ls

4.3.Statistical StatisticalVerification Verificationofofthe theEstimated EstimatedCVR CVRFactors Factors 4.3. 4.3. Statistical Verification of the Estimated CVR Factors Estimating the the CVR CVR factors factors for for voltage voltage reduction reduction requires requires sensitive sensitive numerical numerical calculations. calculations. Estimating Estimating the CVR factors for voltage reduction requires sensitive numerical calculations. In this In this study, many CVR factors were estimated from the DAS data of each D/L. Then, theirmean mean In thismany study,CVR many CVR were factors were estimated from thedata DAS eachThen, D/L. Then, their study, factors estimated from the DAS ofdata eachofD/L. their mean was was calculated to determine the representative CVR factor of each D/L. Figures 11 and 12 illustrate was calculated to determine the representative factor of each D/L. Figures1111and and1212illustrate illustrate calculated to determine the representative CVRCVR factor of each D/L. Figures distributiondiagrams diagramsof ofthe theCVR CVRfactor factorvalues valuesof ofthe theBookgong Bookgongand andGosung GosungD/L, D/L,respectively, respectively,which which distribution distribution diagrams of the CVR factor values of the Bookgong and Gosung D/L, respectively, which are estimated by the direct method and the MAD direct method. areestimated estimatedby bythe thedirect directmethod methodand andthe theMAD MADdirect directmethod. method. are

Figure 11. Distribution of the CVR factors estimated the Bookgong D/L. Figure 11. Distribution ofof the CVR factors estimated atatat the Bookgong D/L. Figure 11. Distribution the CVR factors estimated the Bookgong D/L.

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Figure12. 12.Distribution Distributionofofthe theCVR CVRfactors factorsestimated estimatedatatthe theGosung GosungD/L. D/L. Figure

When the the distribution distribution of a normal distribution curve, the When of the theestimated estimatedCVR CVRfactors factorspresents presents a normal distribution curve, estimated CVRs can be considered accurate. The CVR factors of the Bookgong D/L show a normal the estimated CVRs can be considered accurate. The CVR factors of the Bookgong D/L show a distribution curve. However, CVR factor values of values the Gosung possess a wide range normal distribution curve. However, CVR factor of theD/L Gosung D/L possess a distribution; wide range thus, they dothus, not show a normal distribution curve. All CVR factors calculated the MAD direct distribution; they do not show a normal distribution curve. All CVR factorsfrom calculated from the method produced normal distribution curves. Therefore, CVR factors estimated using the MAD MAD direct method produced normal distribution curves. Therefore, CVR factors estimated using the direct method are considered more reliable. MAD direct method are considered more reliable. 4.4.Estimation EstimationofofCVR CVR Factors Factors for for Reactive ReactivePower Power 4.4. CVRfactors factorsof ofthe thereactive reactivepower powerwere wereestimated estimatedby byapplying applyingthe thedirect directmethod methodand andthe theMAD MAD CVR direct method to the reactive power data acquired from the DAS installed in each distribution line of direct method to the reactive power data acquired from the DAS installed in each distribution line the Chimsan substation. Table 6 lists the filtering conditions used to estimate CVR factors of the of the Chimsan substation. Table 6 lists the filtering conditions used to estimate CVR factors of the reactivepower. power. reactive Table6.6.Filtering Filteringconditions conditionsfor forestimating estimatingCVR CVRfactors factorsofofthe thereactive reactiveload. load. Table

Filtering Term

Filtering Term

voltage and load variation

voltage and load variation

percent voltage variation percent voltage variation percent load variation percent load variation CVR range CVR range

MAD percent load variation

MAD percent load range variation MAD CVR MAD CVR range

Range Description Description V  0, Q  0 voltage drop ∆V > 0,∆Q V >0,0 Q  0 voltage drop voltage rising ∆V < 0, ∆Q < 0 voltage rising 0.5 < % voltage 0.5 < %∆V 1.5V  1.5 voltage 0.2  %  Q  30.0 reactive load 0.2 < %∆Q < 30.0 reactive load 0.2 < CVR < 30.0 0.2MAD  CVR  30.0 MAD 0.2 < %∆Q MAD < 30.0 reactive load 0.2  %QMAD  30.0 reactive load 0.2 < CVR MAD < 30.0 0.2  CVRMAD  30.0 Range

Table 7 summarizes the mean CVR factors calculated by applying the direct method to the reactive Table 7 summarizes the mean CVR factors calculated by applying the direct method to the power data measured in all D/Ls of the Chimsan substation. Table 8 lists the mean reactive power CVR reactive power data measured in all D/Ls of the Chimsan substation. Table 8 lists the mean reactive values calculated by applying the MAD direct method. In the two tables, “CVRq ” represents average power CVR values calculated by applying the MAD direct method. In the two tables, “CVRq” reactive power CVR factors, and “No” represents the number of times that the filtering conditions represents average reactive power CVR factors, and “No” represents the number of times that the were satisfied. Additionally, “NaN” signifies that the CVR factor could not be calculated because the filtering conditions were satisfied. Additionally, “NaN” signifies that the CVR factor could not be filtering condition was not satisfied. calculated because the filtering condition was not satisfied.

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Table 7. CVR factor of the reactive power of the Chimsan substation (direct method). EnergiesD/L 2017, 10, 2148 2016.09

CVRq

2016.10 No

CVRq

2016.11

No

CVRq

2017.02

No

CVRq

2017.06

No

CVRq

No

Bookgong 12.006 83 13.365 91 18.068 28 19.528 33 11.316 193 Table 7. CVR factor of the reactive power of the Chimsan substation (direct method). Daebang 7.454 74 8.175 90 8.159 94 7.723 148 7.526 207 Gosung D/L

Nowoon

NaN 2016.09 7.898 CVR q

No4

NaN 2016.10 NaN CVR q

No-

NaN 2016.11 6.664 CVR q

7 No

5.684 2017.02 6 3.764 CVR q

4 No

11.308 2017.06 113 NaN CVR q

No-

14 of 16 Mean

14.857 7.807 11.308 Mean

-

Samgong 9.849 8357 13.365 8.981 78 11.981 15 9.309 116 11.316 9.961 159 14.857 10.016 Bookgong 12.006 91 18.068 28 19.528 33 193 Daebang 7.454 74 8.175 90 8.159 94 7.723 148 7.526 207 7.807 Mean 9.770 10.174 12.736 12.187 9.601 10.997 Gosung NaN NaN NaN 5.684 6 11.308 113 11.308 Nowoon 7.898 4 NaN 6.664 7 3.764 4 NaN Table 9.849 8. CVR factor reactive of the Chimsan substation116 (MAD9.961 direct method). Samgong 57 of the 8.981 78power 11.981 15 9.309 159 10.016 Mean 9.770 10.174 12.736 12.187 9.601 10.997

D/L

2016.09

2016.10

2016.11

2017.02

2017.06

Noof the CVR q No No substation CVRq No direct CVRqmethod). No Table 8.CVR CVRqfactor reactive power CVR of theq Chimsan (MAD

Bookgong 12.053 80 2016.09 Daebang 8.228 63 D/L CVRq No Gosung NaN Bookgong 12.053 80 Nowoon 8.322 631 Daebang 8.228 Gosung NaN Samgong 10.659 -44 Nowoon 8.322 1 mean 10.313 44Samgong 10.659 mean

10.313

-

mean

13.317 88 2016.10 8.590 77 CVRq No NaN 13.317 88 NaN 778.590 NaN -64 9.883 NaN 10.597 649.883

18.725 25 2016.11 8.896 80 CVRq No NaN 18.725 25 8.777 802 8.896 NaN 12.563 12 8.777 2 13.395 1212.563

19.756 24 2017.02 7.870 129 CVRq No NaN 19.756 24 NaN 1297.870 NaN -96 9.775 NaN 12.467 9.775 96

11.673 159 2017.06 7.364 166 CVRq No 12.009 78 11.673 159 NaN 1667.364 12.009 10.644 78 117 NaN 9.894 10.644 117

15.105 8.190 Mean 12.009 15.105 8.190 12.009 10.705 11.502 10.705

10.597

13.395

12.467

9.894

11.502

-

-

-

-

The highest CVR factor (14.857) was estimated in the Bookgong D/L, and the lowest CVR factor (7.807) was observed in the Daebang D/L. Similar results were obtained from the MAD direct method, The highest CVR factor (14.857) was estimated in the Bookgong D/L, and the lowest CVR factor as shown in Table 8. This suggests that the largest reactive power control effect could be obtained in (7.807) was observed in the Daebang D/L. Similar results were obtained from the MAD direct method, the Bookgong D/L through voltage reduction. as shown in Table 8. This suggests that the largest reactive power control effect could be obtained in CVR factors of the reactive power are much higher than those of the active power. This can be the Bookgong D/L through voltage reduction. attributed to the fact that the reactive power is more sensitive to voltage changes than the active CVR factors of the reactive power are much higher than those of the active power. This can be power. attributed to the fact that the reactive power is more sensitive to voltage changes than the active power. In the Gosung D/L and Nowoon D/L, CVR factors for the reactive power could not be calculated In the Gosung D/L and Nowoon D/L, CVR factors for the reactive power could not be calculated in most cases. Figures 13 and 14 demonstrate larger images of the voltage and load values of the in most cases. Figures 13 and 14 demonstrate larger images of the voltage and load values of the Bookgong D/L and the Nowoon D/L during voltage changes measured in June 2017. Whereas reactive Bookgong D/L and the Nowoon D/L during voltage changes measured in June 2017. Whereas reactive power changes before and after tap changes are prominent in the Bookgong D/L data, reactive power power changes before and after tap changes are prominent in the Bookgong D/L data, reactive power changes caused by voltage changes are difficult to identify in the Nowoon D/L data. Thus, CVR changes caused by voltage changes are difficult to identify in the Nowoon D/L data. Thus, CVR factors could not be estimated. factors could not be estimated.

Figure Figure13. 13.Voltages Voltagesand andloads loadsofofthe theBookgong BookgongD/L. D/L.

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Figure14. 14. Voltages Voltagesand andloads loadsof ofthe theNowoon NowoonD/L. D/L. Figure

4.5. Summary Summary of of the the CVR CVR Factor Factor Estimation Estimation 4.5. CVR factors factorswere wereestimated estimatedtotobebeininthe therange rangeofof0.802–0.872 0.802–0.872 when applying direct method CVR when applying thethe direct method to to the measured at D/Ls of Chimsan the Chimsan substation. When applying the MAD method, the datadata measured at D/Ls of the substation. When applying the MAD directdirect method, CVR CVR factors were estimated berange in theofrange of 0.721–0.784. Similar mean CVRs were calculated factors were estimated to be intothe 0.721–0.784. Similar mean CVRs were calculated because because D/Ls of the substation Chimsan substation located theand same thusload have similar load D/Ls of the Chimsan are locatedare in the same in area, thusarea, haveand similar characteristics. characteristics. Lower factors were estimated when using the when MADcompared direct method when Lower CVR factors wereCVR estimated when using the MAD direct method with results compared with results obtained using the direct method. obtained using the direct method. When classifying classifying results results by by season, season, high high CVR CVR factors factors were were estimated estimated in When in early early winter winter and and winter. winter. When classifying by time, high CVR factors were estimated in the evening and at dawn. This can be be When classifying by time, high CVR factors were estimated in the evening and at dawn. This can attributed to the large amount of heat loads are used in the winter and in the evening. attributed to the large amount of heat loads are used in the winter and in the evening. Anotherfinding findingisisthat thatthe theCVR CVRfactors factors reactive power were much higher those of Another ofof thethe reactive power were much higher thanthan those of the the active power. This is because reactive power is more sensitive to voltage changes. When applying active power. This is because reactive power is more sensitive to voltage changes. When applying the the direct method the reactive data measured atofD/Ls of the Chimsan substation, CVR direct method to thetoreactive powerpower data measured at D/Ls the Chimsan substation, CVR factors factors were estimated in theofrange of 7.807–14.857. thehand, otherwhen hand,applying when applying the direct MAD were estimated to be in to theberange 7.807–14.857. On the On other the MAD direct method to theCVR data,factors CVR factors were estimated berange in theof range of 8.190–15.105. method to the data, were estimated to be intothe 8.190–15.105. 5. Conclusions Conclusions 5. This This paper paper described described aa method method to to estimate estimate CVR CVR factors factors using using data data measured measured from from power power distribution distribution systems systems and and presented presentedthe theresults resultsof ofits itsapplication applicationto tothe theKEPCO KEPCOsystem. system. Voltage percentages were calculated fromfrom data data acquired at the at moment at which Voltageand andload loadchange change percentages were calculated acquired the moment at large voltage changeschanges occurredoccurred due to tap changes transformers of the distribution system. The ratio which large voltage due to tap in changes in transformers of the distribution system. of theratio voltage change percentage and load change percentage calculated tocalculated estimate CVR factors. The of the voltage change percentage and load change was percentage was to estimate CVR factors. addition, MADwas direct method was used to calculate the loadwere variations, which In addition, theInMAD directthe method used to calculate the load variations, which incorporated were the calculation percentage loadtochanges order to estimate CVR factors. The in the incorporated calculation ofinpercentage load of changes in order estimateinCVR factors. The mean of the CVR mean of thefound CVR factors was found afterchanges filteringand voltage changes and load changes. factors was after filtering voltage load changes. The results results of of estimating estimating CVR CVR factors factors of of the the KEPCO KEPCO system system revealed revealed that that the the highest highest mean mean CVR CVR The factors were were found found during during winter, winter, which which has has high high heating heating load. load. The The lowest lowest mean mean CVR CVR factors factors were were factors found in in the the summer, summer, which which has has high high constant constant power power load. load. Because Because reactive reactive power power is is sensitive sensitive to to found voltage changes, changes, CVR CVR factors factors of of the the reactive reactive power power were were found found to to be be much much higher higher than than those those of of the the voltage active power. power. active By testing the direct method and MAD direct method in the KEPCO system, we can confirm that CVR factors of both active and reactive power can be accurately estimated using data acquired from power distribution systems.

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By testing the direct method and MAD direct method in the KEPCO system, we can confirm that CVR factors of both active and reactive power can be accurately estimated using data acquired from power distribution systems. Acknowledgments: This work was supported by KEPCO Research Institute grant funded by Korea Electric Power Corporation (R16DA11). Author Contributions: Kwan-Shik Shim prepared the manuscript and implemented the theory and simulations. Seon-Ju Ahn supervised the study and discussed the results. Seok-Il Go and Won Nam-Koong analyzed the data. Joon-Ho Choi, Sang-Yun Yun, and Chang-Hoon Shin discussed the results and commented on the manuscript. All authors read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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