The 6th PSU-UNS International Conference on Engineering and Technology (ICET-2013), Novi Sad, Serbia, May 15-17, 2013

University of Novi Sad, Faculty of Technical Sciences

Abstract: Distribution power grid load modeling is com-prised out of knowing its qualitative and quantitative prop-erties, in terms of active and reactive power consumption, but also properties such as load dependency to voltage and frequency. Determination of load-to-voltage dependency is not sufficiently explored and documented. Main reasons for that are lack of robust procedure and relatively large num-ber of experiments that need to be performed out in the field. This paper presents a robust procedure for deter-mining load-to-voltage dependency with relatively small number of experiments needed. The procedure is verified in a real distribution power grid.

Keywords: Load-to-Voltage Dependency, Load Modeling, Voltage Reduction, Distribution Power Grid

1. INTRODUCTION

Modern power distribution utilities (PDU), which are more and more present on electrical energy markets, are forced to operate on borders of their technical limitations. What definitely contributes to that is the fact that they often get very challenging demands to fulfill. Some of the chal-lenges they need to cope with are tied to real-time operation where, with minimal investments, state of the system needs to be estimated, optimal power flows and voltages need to be achieved, peak load shaving needs to be fast and effi-cient, etc. Likewise, in simulation, it is very important to have good system state estimation, especially for states far from normal ones. It is clear that abilities of the existing Supervisory Control and Data Acquisition (SCADA) sys-tems are no longer sufficient to realize such challenging demands required from PDUs. The application of relatively new Smart Grid Concept (SGC) [1], which encompasses Distribution Management System (DMS) [2], can make them achievable. The DMS includes many of its advanced applications for analysis, control and planning of distribu-tion network (DN). When tightly integrated with the exist-ing SCADA systems, and constantly increasing number of Intelligent Electronic Devices (IED – AMI, MDM, etc.), once challenging demands will become PDU common prac-tices. Thereby, the quality of SGC and DMS applications does not depend only on quality of DMS calculations, but also on the quality and quantity of data about DN (collected in real-time and in non real-time). Among data collected in

non real-time, the most critical for the quality of results, but at the same time the most unreliable, are data about power consumption (loads). In accordance to constantly increasing demands required from PDU, the demands set for DMS power applications and DMS load modeling are also be-coming higher. It is not enough to model load with constant power consumption. The load must be modeled with de-pendency to number of parameters, such as: 1) temperature; 2) considered moment in time, day and season; 3) instanta-neous voltage; 4) coincidence factor; and finally 5) decay effect (how much time passed from last voltage change, i.e. what can be expected in future after voltage has been changed and stays on value different from nominal one). The load model must take into account decay effect in order to be able to predict its behavior in case something like de-scribed happens with voltage. Model of power consumption dependent on temperature is shown in many papers [3,4]. Relatively simple procedure for determining normalized daily load profiles (NDLP) of characteristic customer types in characteristic days and seasons is shown in [5]. Papers which contain information about load-to-voltage dependen-cy of tangible customer types are rare [4], but even rarer are the ones that depict precise procedures for their experimen-tal determination [6]. Determination of load-to-voltage de-pendency for each individual customer may be technically feasible, but definitely not economically justifiable. This paper offers practically applicable procedure for load-to-voltage dependency determination by performing relatively small number of in-field experiments. Applicability of pro-cedure is fully verified in scope of DMS project realized for one of the North American PDU.

After the Introduction, basic concepts of load modeling and procedure for determining value of load-to-voltage de-pendency are given in part 2. An example of application of this procedure is given in part 3. Procedure verification is presented in part 4. Conclusion and references are given in parts 5 and 6, respectively.

2. LOAD MODELING

The model of power consumption, referenced in this pa-per, is based on following terms and definitions: Load – a group of individual consumers which are of dif-

ferent consumer types, such as: constant current, power or impedance, or constant energy, time or power. Each

A METHOD FOR LOAD-TO-VOLTAGE DEPENDENCY DETERMINATION

Goran S. Švenda, Jovan M. Lukić University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia*

*Authors to correspondence should be addressed via email: svenda@uns.ac.rs, jovanluk@uns.ac.rs

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consumer has its own characteristics which can be com-pared to some others’, and by which loads can be classi-fied into classes. Load quantifier – maximal or average value of consumer's

power consumption, or consumed electrical energy on a daily, monthly, yearly basis [5]. Normalized daily load profile (NDLP) – daily load profile

divided by a Load quantifier. Similar loads – all consumers which in the same manner

change value of their consumption depending on current time, type of a current day and season, changes in temper-ature and voltage, and for which the effects of those changes last equally long. Characteristic load – consumer defined with two NDLP

(for active and reactive power, or for current module and power factor), load quantifiers, and with coefficients which depict dependency of temperature and voltage (load coefficients). It is usually defined for residential-, commercial-, agricultural- and industrial-type of consum-ers. For more precise determination of power consump-tion, each type can be further divided into subtypes, such as: residential loads with locally or remotely provided heat-ing, settlements with-, or without hot water provided, etc. Characteristic day – a day which represents all similar

days, i.e. days in which all similar consumers can be de-scribed with their unique Load quantifier, and common Characteristic load. Usually is defined separately for work day, Saturday and Sunday, as well as for holidays. If one wants to be even more accurate, every characteristic day can be further divided into subtypes, such as: type work-day into subtypes Monday through Friday; type holiday into subtypes New Year, Christmas, etc. Characteristic season – time period in which characteristic

load, in every characteristic season, describes well enough power consumption of a consumer. Usually it is defined to match with calendar seasons (spring, summer, fall, win-ter), but also it often can be defined for each month sepa-rately, then to match duration of heating season, periods when particular industry is work- or break mode, etc.

In accordance with previously defined terms and defini-tions, pre-estimated value of active and reactive powers for a moment t, can be defined as:

quant.rr )()( XtxtX , },{ QPX , (1)

where pr(t) and qr(t) represent values of active and reactive

powers in moment t – values obtained by having available NDLP, in [p.u.], and Pquant and Pquant load quantifiers, in

[kW]. Pre-estimated values are defined for rated voltage Vr(t).

Of course, for more accurate calculations, one cannot disregard the fact that most consumers are not always sup-plied with nominal voltage, and that change in supplied voltage changes amount of power consumed by consumer. It is also very clear that dependency of a complex DN con-sumer, such as dependency on voltage supplied, cannot be formulated analytically. However, it can be appropriately determined by performing relatively small number of expe-riments. That particular dependency is referred to as load-to-voltage dependency, and is defined by the following rela-tion:

11

11

/100][

/100][

iii

iiiX VVV

XXXB

i, },{ QPX , (2)

where Pi, Qi, Vi and Pi–1, Qi–1, Vi–1 represent values of ac-

tive-, reactive power and voltage obtained in moments i and i–1, respectively; BP i and BQ i represent active and reactive

load-to-voltage dependency. Statistically, expected values of coefficients BP and BQ can be determined by having

available sufficiently large number of samples from a popu-lation. The procedure for experimental determination of coefficients is presented in section three of this paper.

Estimation of active P(t,V) and reactive Q(t,V) power in a moment t, for voltage value V(t), is defined by relations:

)](1[)(),( r tVBtXVtX X , },{ QPX , (3)

rr /100])([)( VVtVtV , (4)

where subscript r indicates pre-estimated variables which are realized for nominal voltage supplied Vr(t), relation (1).

3. EXPERIMENTS

The proposed procedure has been verified on a large North American DN. The network supplies around 1.5 mil-lion of customers and has around 1300 medium voltage feeders. During year 2011 two experiments have been rea-lized: 1) winter, 15-17 February, consumer types Residen-tial and Commercial, and 2) summer, 4-8 August, consumer types Residential, Commercial and Industrial. Experiments encompassed 9 medium voltage feeders (groups of 3 feed-ers are dominantly supplying residential, commercial and industrial load). During experiments, voltage was changed by 1.4% and 2.8% from actual. This is depicted in Fig. 1

Fig. 1. Pattern for voltage changes during experiments

Data capture, on a 30 second interval, and during the entire experiment, was simultaneously obtained for the active power, reactive power and voltage. By specially designed program code paired measurements were ana-lyzed and further processed in order to obtain representa-tive samples from the entire population. The samples do not include influences of disturbances that occurred dur-ing the experiment. Some of the disturbances worth men-tioning are as follows: short circuit events, switching events, capacitor banks closing or tripping, large custom-ers connecting to- and disconnecting from the grid. After representative population samples had been obtained, pairs of relations (3) were formed for each moment in time for which pairs of points (A,B), (C,D), (E,F) in Fig. 1 can be determined. Next step was to replace known values in those pairs of relations: measured ),( VtP , cal-

culated ν , and value read from the NDLP of the con-

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sume Pr(t). Analogous procedure was done for the reac-

tive power Q. Solving of system of two equations by unknown BP (BQ), the value of load coefficient is ob-

tained. That value becomes candidate for statistical processing to find expected value and its standard devia-tion.

The results of statistical processing are depicted in Fig. 2, where histograms and probability density functions (PDF) of load coefficients for February time frame and Commercial type of load are given.

Fig. 2. Load Coefficients – Expected value

Table 1. Load Coefficients, as random variable

Feeder BP P

Febr

uary

Com Res Ind Com Res Ind 1 1.20 1.65 / 0.58 0.82 / 2 1.37 1.64 / 0.57 0.96 / 3 1.28 1.21 / 0.56 0.72 / 1.27 1.56 / 0.57 0.88 /

Aug

ust

Com Res Ind Com Res Ind 1 0.85 0.94 1.26 0.47 0.58 0.82 2 0.66 0.87 1.26 0.38 0.55 0.85 3 0.67 0.86 1.07 0.37 0.56 0.82 0.77 0.92 1.19 0.44 0.57 0.83

Expected values of load coefficients and their standard deviations are presented in Table 1. They are obtained by processing data from experiments performed in two differ-ent seasons, for three types of loads, for each feeder and aggregately.

4. PROCEDURE VERIFICATION

Verification of the proposed procedure for determining load coefficients is done with following steps:

1. Assessment of pre-estimated feeder head load, based on power flow calculation for pre-estimated load Pr(t) and

Qr(t), depicted by relation (1), obtained for nominal vol-

tage value of V(t)=Vr=123.5 V.

2. Correction of pre-estimated load values, based on meas-ured voltage V(t) on feeder heads, and utilizing relations (3) and (4). Corrected values are called estimated values.

3. Estimated and measured load values comparison.

As an example of the proposed procedure, Fig.3 illu-strates values of measured and estimated active powers, for one of the feeders that supplies dominantly commercial type of consumers. Fig.3a illustrates: pre-estimated active power (black dashed line), estimated active power (red solid line) and measured active power (blue solid line). Fig.3b illu-

strates measured, unusually large changes of voltage V(t) on feeder head busbar (orange solid line) and nominal voltage Vr(t) (orange dashed line). Examples in Fig. 4 and Fig. 5 are

obtained on feeders which dominantly supply residential and industrial type of load, respectively.

0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Bp [%/%]

Density Commercial (average)PDF Commercial 1 PDF Commercial 2 PDF Commercial 3 PDF

a) Load profile, measured and estimated active power

b) Voltage changes

Fig. 3. Verification (feeder Com1, February 22. 2011.)

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It is also interesting to discuss results in terms of error

which describes deviation of estimated from measured power. The error is calculated by following relation:

measmeasest /100)( kkkk PPPP , (5)

where k goes from 1 through number of readings for meas-ured active power.

Table 2 depicts the expected values of relative differ-ences between calculated (estimated) and measured values of active powers ΔP and standard deviations of those values ΔP The values are calculated by following relations:

N

kkP

NP

1

1, (6)

N

kkP PP

Nσ

1

22 ][1

. (7)

Table 2. Expected value of relative error and its standard deviation

Feeder ΔP ΔP

Febr

uary

Com Res Ind Com Res Ind

1 –0.07 0.63 –0.07 0.63 –0.07 0.63 2 –0.35 0.60 –0.35 0.60 –0.35 0.60 3 0.08 0.53 0.08 0.53 0.08 0.53 –0.08 0.45 –0.08 0.45 –0.08 0.45

Aug

ust

Com Res Ind Com Res Ind 1 –0.10 –0.35 –0.10 –0.35 –0.10 –0.352 –0.14 –0.24 –0.14 –0.24 –0.14 –0.243 –0.13 –0.25 –0.13 –0.25 –0.13 –0.25 –0.14 –0.32 –0.14 –0.32 –0.14 –0.32

Table 3 depicts absolute expected values of relative differ-ences between calculated (estimated) and measured values of active powers |ΔP| and standard deviations of those val-ues |ΔP|. The values are calculated by following relations:

N

kkP

NP

1

1, (8)

N

kkP

PPN

σ1

22 ][1

. (9)

Table 3. Expected absolute value of relative error and its standard deviation

Feeder |ΔP| |ΔP|

Febr

uary

Com Res Ind Com Res Ind

1 0.98 2.60 0.98 2.60 0.98 2.602 1.87 2.92 1.87 2.92 1.87 2.92 3 1.21 1.85 1.21 1.85 1.21 1.85 1.38 2.5 1.38 2.5 1.38 2.5

Aug

ust

Com Res Ind Com Res Ind 1 0.77 1.29 0.77 1.29 0.77 1.29 2 0.76 1.19 0.76 1.19 0.76 1.19 3 0.78 1.22 0.78 1.22 0.78 1.22 0.79 1.26 0.79 1.26 0.79 1.26

5. CONCLUSION

This paper presents very simple, but at the same time robust procedure for experimental determination of load-to-voltage dependency, i.e. load coefficients. Additionally, their application in terms of estimation of large area load is given. Application of the procedure, as well as its verifica-tion is done in real USA distribution network.

When information about load coefficients becomes

a) Load profile, measured and estimated active power

b) Voltage changes

Fig. 5. Verification (feeder Ind1, August 10. 2011.)

a) Load profile, measured and estimated active power

b) Voltage changes

Fig. 4. Verification (feeder Res1, August 10. 2011.)

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available, one can take further steps in terms of forming more complex model of loads, model which encompasses coincidence factor change effects, as well as voltage change effects which decays in time.

6. REFERENCES

[1] R.G.Pratt, et all, The Smart Grid – An Estimation of the Energy and CO2 Benefits; Pacific Northwest National Laboratory, USA, 2010.

[2] D.S.Popović, Power Application – A Cherry on the Top of the DMS Cake, DA/DSM DistribuTECH Europe 2000, Vienna, Austria, October 10-12, 2000, Specialist Track 3, Session 3, Paper 2.

[3] C.E.Asbury, Weather load model for electric demand and energy forecasting; IEEE Trans. on PAS, Vol. PAS-94, No.4, July 1975.

[4] R.F.Preiss, V.J.Warnock, Impact of voltage reduction on energy and demand; IEEE Trans. on PAS, Vol. PAS-97, No.5, September/October 1978.

[5] S.Kuzmanović, G.S.Švenda, Z.Ovcin, Practical Statis-tical Methods in Distribution Load Estimation; 20-th In-ternational Conference on Electricity Distribution – CIRED, Prague, 8-11 June 2009, Session No.4, Paper 0585.

[6] J.C.Erickson, S.R.Gilligan, The effects of voltage reduc-tion on distribution circuit loads; IEEE Trans. on PAS, Vol. PAS-101, No.7, July 1982.

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