Electrical Power and Energy Systems 33 (2011) 1243–1250

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Effect of load models on assessment of energy losses in distributed generationplanning

Kejun Qian a,⇑, Chengke Zhou a, Malcolm Allan a, Yue Yuan b

a School of Engineering and Computing, Glasgow Caledonian University, G4 0BA Glasgow, UKb College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 June 2010Received in revised form 21 December 2010Accepted 12 April 2011Available online 18 May 2011

Keywords:Distributed generationLoad modelEnergy lossesVoltage profileLoad forecasting

0142-0615/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijepes.2011.04.003

⇑ Corresponding author. Address: School of EngineeCaledonian University, 70 Cowcaddens Road, G4 0BA331 8919.

E-mail address: Kejun.Qian@gcu.ac.uk (K. Qian).

Distributed Generation (DG) is gaining in significance due to the keen public awareness of the environ-mental impacts of electric power generation and significant advances in several generation technologieswhich are much more environmentally friendly (wind power generation, micro-turbines, fuel cells, andphotovoltaic) than conventional coal, oil and gas-fired plants. Accurate assessment of energy losses whenDG is connected is gaining in significance due to the developments in the electricity market place, such asincreasing competition, real time pricing and spot pricing. However, inappropriate modelling can giverise to misleading results. This paper presents an investigation into the effect of load models on the pre-dicted energy losses in DG planning. Following a brief introduction the paper proposes a detailed voltagedependent load model, for DG planning use, which considers three categories of loads: residential, indus-trial and commercial. The paper proposes a methodology to study the effect of load models on the assess-ment of energy losses based on time series simulations to take into account both the variations ofrenewable generation and load demand. A comparative study of energy losses between the use of a tra-ditional constant load model and the voltage dependent load model and at various load levels is carriedout using a 38-node example power system. Simulations presented in the paper indicate that the loadmodel to be adopted can significantly affect the results of DG planning.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The load in a distribution system generally consists of threemain types, i.e., residential, commercial and industrial load, withtheir proportion in the total load demand varying with time, e.g.,hourly, daily and seasonally. The nature of these three types ofloads is such that their active and reactive power components re-spond differently to variations in the voltage and frequency ofthe system [1,2]. System planners need to understand the exactnature of load sensitivity of voltage in order to precisely quantifythe economic benefits of installing DG. Korunovic et al. [3] studiedthe static load characteristics of a medium-voltage distributionnetwork by conducting field measurements and concluded thatsteady-state distribution load can be modelled as exponential volt-age-dependent model in a relatively wide voltage range, from 0.96to 1.1 of the nominal voltage with errors less than 5%.

The variation in the actual power demand with voltage has be-come more prominent in recent years as increasing penetration of

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ring and Computing, GlasgowGlasgow, UK. Tel.: +44 141

renewable DGs, such as intermittent wind, has made voltageprofiles on the distribution feeders more dynamic. The connectionof DG to distribution networks near load centre could change mag-nitude and direction of network power flows. This would impacton network operation and planning practices of distribution com-panies with both technical and economic implications. Investiga-tions have therefore been carried out into DG planning indistribution systems in recent years [4–13], among which powersystem losses reduction due to the introduction of DG in distribu-tion systems attracts much attention [10–13]. Most of these inves-tigations focused on assessing the power loss reductions broughtabout by DG and utilised a constant load model in the power flowanalysis, that is, the load power was considered to be independentof variations in feeder voltage. In general, the regulator sets a losstarget for each of the UK distribution network operator (DNO).DNOs are rewarded if their real losses are lower than the loss tar-get. Otherwise, the DNOs are economically penalised. Although atpresent the economic incentives to reduce losses are on the DNOs,it is possible that DNOs will pass part of the reward to DG ownersfor assisting reducing network losses in the future [12]. However,an accurate quantification of energy losses associated with DG lar-gely depends on the load models employed in the power flow algo-rithms. Therefore, the load models will have a direct consequenceon DNO’s profit.

1 2 4 6 8 10 120.70

Month

Loa

dde

man

d,p.

u.

3 5 7 9 11

0.75

0.80

0.85

0.90

0.95

1.00

1.05

Fig. 2. Monthly load level of the studied system.

2 6 10 14 20 240.4

0.6

0.8

1.0

1.2 Typical winter load

Typical summer load

Time of day, h

Loa

d de

man

d, p

.u.

4 8 12 16 18 22

Fig. 3. Normalised load profiles in winter and summer of the studied system.

6 10 16 20 240.2

0.4

0.6

0.8

1.0

222 4 8 12 14 18

Residential

CommercialIndustrial

Time of day, h

Nor

mal

ised

load

, p.u

.

Fig. 4. Normalised load patterns for the three load classes [22].

1244 K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250

Frantz et al. [14] highlighted that the load model can signifi-cantly affect the predicted system performance. A detailed volt-age-dependent load model was adopted in an optimal capacitorinstallation/switching study by Rizy et al. [15] in a distribution sys-tem where the authors demonstrated that the detailed load modelaccurately predicted that the active power injection increased withthe voltage increase whilst the constant load model failed to do so.Singh and Misra [16] performed a comparative study of real andreactive power loss, real and reactive power intake at the mainsubstation and MVA support provided by installing DG resourcesfor different type of load models. The authors in [16] highlightedthat load models can significantly affect the optimal location andsizing of DG resources in distribution system and they alsointegrated the detailed load models in DG planning using multi-objective optimisation [17]. Qian et al. [18] carried out a study ofthe effect of load models on the assessment of power losses whena high penetration level of DGs is integrated in LV distribution sys-tems. These studies successfully accounted for load models in DGplanning, however, only catered for a single load level and failedto take into account the variations in renewable DG power outputand making them impossible to determine the actual impact ofvariable forms of renewable DGs. As renewable DG is highly vari-able power source. At any instant in time its export will alter theexisting power flows and bus voltages in the direct path from theconnected bus to the substation. Subsequently, the voltage andvoltage-dependent load at all buses will change at each time in-stant. Therefore, with a high penetration level of renewable energygeneration, a single power flow solution can no longer describe thepossible system states in a representative way.

The focus of the present paper is to evaluate the significance ofload models on assessment of energy losses in a distribution sys-tem with high penetration level of DG, using a 38-bus examplepower system as a vehicle. In order to capture the effects thatthe variability of both demand and renewable DGs has on the per-formance of distribution systems, this paper proposes a methodol-ogy based on time series simulations to assess the energy losses ofdistribution systems with high penetration level of renewable DGs.

2. System modelling and simulation

2.1. The example system

The example system shown in Fig. 1 [19] will be used for thestudy. The voltage rating of the radial system is 11 kV. DGs are tobe connected to the system as embedded generations, instead ofbeing connected directly to the Grid Supply Point (GSP, definedas the point of supply from the national transmission system tothe local system of the distribution network operator or non-embedded customers [20]). Details of the system can be found inTable A1 in Appendix A.

Simulations are carried out for a calendar year to analyse theimpact of load models on distribution losses under different sce-narios. The computation of energy losses is on a half-hourly basis

Fig. 1. 38-node radial distribution system [19].

which requires half-hourly demand data; however, the 38-nodesample system does not provide half hourly load data. As a result,the data given in Table A1 is assumed to be the peak load and loadsfor the rest of time are obtained by assuming the same load varia-tion as real historical data in Figs. 2 and 3. The power demand ateach of the 38 nodes arising from each of the residential, industrialand commercial sectors are assumed to follow the pattern shownin Fig. 4, with detailed figures in Table A2. Power system simula-tion was carried out using the ‘Interactive Power Systems Analysis’(IPSA) software [21].

2.2. Components of load power demand

Fig. 2 shows the typical annual load profile in the UK. The dailydemand profile varies over the seasons of a year as given in Fig. 3where the peak demand occurred on 23rd January 2008, and theminimum demand occurred on 22nd June 2008 [22]. Fig. 4

Table 1Typical load types and exponent values [24].

Load type Residential Commercial Industrial

npr nqr npc nqc npi nqi

Summer Day 0.72 2.96 1.25 3.50 0.18 6.00Night 0.92 4.04 0.99 3.95 0.18 6.00

Winter Day 1.04 4.19 1.50 3.15 0.18 6.00Night 1.30 4.38 1.51 3.40 0.18 6.00

Constant impedance 2.0 2.0 2.0 2.0 2.0 2.0Constant current 1.0 1.0 1.0 1.0 1.0 1.0Constant power 0.0 0.0 0.0 0.0 0.0 0.0

Note: subscripts r, c, i represent residential, commercial and industrial load,respectively.

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,0000

0.2

0.4

0.6

0.8

1.0

Number of hours

Win

d po

wer

out

put,

p.u.

Fig. 5. Wind power output [22].

K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250 1245

illustrates the three components of the typical load pattern, i.e. res-idential, industrial and commercial. The magnitudes are norma-lised by the daily peak power demand [23].

2.3. Voltage-dependent load model

In conventional load flow analysis, it was assumed that activeand reactive power loads are constant values, regardless of themagnitude of voltages in the same bus. Due to the voltage-dependence of distribution load, in this paper, practical voltage-dependent load models, i.e., residential, commercial and industrialgiven in [24] has been adopted. A voltage dependent load model isa static load model that represents the power relationship tovoltage as an exponential equation, which can be mathematicallyexpressed as,

PL ¼ PL0Vnp ð1Þ

Q L ¼ Q L0Vnq ð2Þ

where np and nq are active and reactive power exponents, respec-tively. PL and QL are the values of real and reactive powers, whilePL0 and QL0 are the values of active and reactive powers at nominalvoltages, respectively. V is the voltage magnitude at a load node.Eqs. (1) and (2) neglect the frequency-dependence of distributionload, due to the fact that the range of frequency variation is rela-tively narrow.

Common values for exponents of static loads are given in Table 1[25] in order to evaluate the effects of various load models on DGplanning. For practical application, the evaluation of coefficients np

and nq requires field measurement and parameter estimationtechniques.

It is assumed in the studied system that each load node consistsof three components of load consumption. The proportion of eachload type in the total load is varying across the time scale, asshown in Table A2. Let a, b, and c are the percentages of residential,commercial and industrial load at each load node respectively (a, b,and c is determined by the values shown in Table A2), the voltagedependent load model can therefore be expressed as follows,

PL ¼ aPL0Vnpr þ bPL0Vnpc þ cPL0Vnpi ð3Þ

Q L ¼ aQL0Vnqr þ bQ L0Vnqc þ cQ L0Vnqi ð4Þ

2.4. Distributed generation model

In this paper, wind generators are considered in the simulationas the DG sources.

The power produced by wind turbines was estimated using thecharacteristics provided by the manufacturers, taking into accountthe half-hourly wind speed data. Fig. 5 shows the wind power out-

put during a whole year [23]. A wind farm is simulated as a singlewind power unit with installed capacity equal to the total windfarm capacity.

It is now common that wind turbines use doubly-fed, variablespeed induction generators with an IGBT converter in the rotor cir-cuit, which enables the DG to operate at any desired power output[25]. Therefore DGs with capability of controlling reactive power(leading/lagging power factors) and those operating at unity powerfactor are both considered in the paper.

2.5. Scenarios

In this study, it is assumed that a single DG (aggregated DGs) isconnected to one of the load nodes on the distribution feeder. Thestudy will take into account various DG penetration levels (pene-tration level is defined as the ratio of the amount of DG power in-jected into the network to the total feeder load), DG location, andreactive power control strategies of DG. DG penetration level isgradually increased from 0% (base case, i.e. without DG) to 40%,which is the long term target set in Scotland, UK for 2020. Accord-ing to the current Grid Code requirements in the UK, any mediumor large wind farms must provide a reactive power capability of0.95 lead/lag at its Grid Entry Point [26] (GEP, defined as a pointat which a Generating Unit directly connected to the National Elec-tricity Transmission System, or connects to distribution systems[20]); therefore there are three particular situations to be studiedfor energy loss analysis of the studied system where the DG atthe GEP is represented by a virtual power plant which can providea reactive power capability of 0.95 leading, unity and 0.95 lagging,while the voltage at the GEP should be within the operating limits.

3. Methodology

In order to estimate the effect of load models on the assessmentof energy losses in a distribution system with high penetration ofDGs, a methodology is developed to compute annual energy lossesbased on time series simulation. The single power flow problem inconventional load flow analysis is expanded to multiple simula-tions with individual values for each time step. In order to accountfor the variability of daily load profile and wind power output, themethod calculates system losses for every half hourly period dur-ing a calendar year. This requires running the load flow for eachtime interval (half an hour), allowing for consideration of the de-tailed load model and DG power output during that time interval.The impact of load models on energy losses are measured as thedifference between losses with traditional constant load modeland the proposed detailed load model in the considered scenariosof DG penetration.

1246 K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250

The complete procedure of the developed approach is shown inFig. 6.

In order to quantify the impacts of load models on the results ofenergy loss reductions due to the presence of DG during a wholeyear, two indices are developed.

3.1. Voltage profile

Network losses largely depend on the voltage profile when thesystem load is represented by a voltage dependent model. In orderto quantify the changes in voltage profile, due to the introductionof DGs, across the network during a period of time, it is necessaryto develop an index of voltage profile.

The proposed voltage index quantifies the improvement in thevoltage magnitude in a simple manner with the inclusion of DG.It is defined as the difference between actual voltage profile andthe nominal voltage (1.0 p.u.).

Since the simulation will be carried out on a half-hourly basis,the proposed voltage profile index is developed allowing for con-sideration of time-varying voltage magnitude and load demandat each time interval, shown as below,

Kvolt ¼Pnb

i¼1

Pncj¼1jVij � V0jnbnc

� 100% ð5Þ

where Kvolt is the voltage index, nb is the number of load nodes inthe studied system, nc is the number of time intervals (half-hourly),Vij and V0 are voltage magnitudes for actual and nominal voltage(1.0 p.u.), respectively, at bus i at time instant j. This index shouldbe used only after making sure that voltage magnitude at each loadnode is within its allowable minimum and maximum limits, typi-cally between 0.94 p.u. and 1.06 p.u., reflecting the UK practice.Therefore, the less the voltage index, the better the voltage profile.

3.2. Energy losses

Annual energy losses index is defined as the ratio of the totalenergy losses to the total energy demand on the feeder on an an-nual energy basis, which can be expressed as below,

KLoss ¼Pnc

j¼1PLossjPnb

i¼1

Pncj¼1PLij

� 100% ð6Þ

where KLoss is the energy losses index, PLossj is the system energylosses at time instant j. While DG may reduce energy losses byreducing power flows, it can increase losses at a high penetration

Fig. 6. Flowchart of the developed methodology.

level due to the reverse power flow along the lines. The lower theenergy loss index, the better the benefits in terms of power lossreduction due to DG.

4. Results and analysis

In this section, results are presented with the proposed ap-proach to evaluate the effect the load models have on the resultsof the energy losses calculation.

As assumed in this study, a single DG will be installed alter-nately on various nodes along the feeder. The DG penetration levelwill gradually increase from 0% to 40%. DGs are modelled withthree power factors: 0.95 leading, unity and 0.95 lagging,respectively.

4.1. Impact of load models on energy losses with various DGpenetration levels

Table 2 summaries the results obtained for various DG penetra-tion levels, using an example in which a single DG (operating at0.95 lagging power factor) is located at node 14 of the studied fee-der. The load models ‘Const.’ and ‘Volt.’ are abbreviations of theconstant and voltage dependent load model, respectively.

It can be observed from Table 2 that when DG is connected tothe feeder with a low penetration level (630%), both the voltageprofile and the energy loss indices decrease with the increase inDG penetration level until they reach a minimum level. Once theminimum level is reached, the voltage index begins to increasedue to the voltage improvement by DG, while energy loss indexcontinues to decrease. It should be noted voltage at each busshould be maintained within ±6% of the nominal voltage(1.0 p.u.). Therefore, the voltage index improvement listed in Table2 due to the DGs indicates a significant impact on voltage profile.

Fig. 7 shows the difference in energy losses (extracted from Ta-ble 2) when the two load models are employed.

It can be observed from Fig. 7 that when a low penetration levelof DG connected to the studied system, simulation with constantload model produces conservative results, i.e., the energy loss in-dex KLoss with constant load model is greater than that with voltagedependent load model. However, as DG penetration level increasesto a higher level, simulation with constant load model starts toshow optimistic results. The reason is that although DG can im-prove system voltage profile with a low penetration level, the volt-age magnitudes at all feeder nodes except the root node are stillless than 1.0 p.u., leading to lower power consumption when volt-age-dependent load is adopted. As DG penetration increases to acritical level, the load demand resulting from voltage improvementdue to the DG exceeds the constant load. The increase in loadwould in turn lower partly the energy loss reduction brought by

Table 2Simulation results for various DG penetration levels.

DG penetration (%) Load model Voltage indexKvolt (%)

Loss index KLoss (%)

0 Const. 4.425 4.972Volt. 3.942 4.523

10 Const. 3.152 3.941Volt. 2.780 3.595

20 Const. 2.426 2.968Volt. 2.196 2.727

30 Const. 2.125 2.043Volt. 2.019 1.878

40 Const. 2.143 1.616Volt. 2.196 1.638

1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

20Simulation resultsCurve fittingSimulation resultsCurve fitting

Dif

fere

nce

in e

nerg

y lo

sses

bet

wee

n th

e tw

o lo

ad m

odel

s K

loss, %

Voltage index Kvolt, %

Fig. 8. Correlation between the voltage index and the difference in energy lossesindex by using the two load models in power flow analysis.

0

1.0

2.0

3.0

4.0With constant load modelWith voltage-dependent load modelWith constant load modelWith voltage-dependent load modelWith lt d d t l d d l

0.95 leading unity 0.95 lagging

DG operating power factor

Ene

rgy

loss

inde

x, %

0.5

1.5

2.5

3.5

4.5

Fig. 9. Differences in energy losses index between employing constant and voltagedependent load models with various DG operating power factors.

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

20% 30% 40%10%

DG penetration level

Ene

rgy

loss

inde

x, %

With constant load modelWith voltage-dependent load modelWith constant load modelWith voltage-dependent load model

4.0

Fig. 7. Differences in energy losses index between employing constant and voltagedependent load models.

K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250 1247

DG, hence, an optimistic result due to the constant load model. Insuch a case, if the DNO chooses to reward the DG owners to helpreducing power losses, DNO will pay more than actual benefitsbrought by DG if constant load model is employed in the energyloss analysis. This would not be revealed if proper load model inenergy loss assessment was not taken into account.

The critical penetration level between conservative and opti-mistic results due to constant load model for wind power genera-tion is 32.5% for the studied system. However, it may vary amongvarious power systems depending on the system topology and loadmodel parameters.

Another phenomenon has also been observed in Fig. 7. The dif-ference in energy loss index in absolute value monotonically de-creases when the DG penetration level is less than 30%. This isdue to the fact that, at the base case (without DG), the voltage pro-file of the studied system is less than 1.0 p.u., making the actualload appear to be less than the nominal load demand due to thevoltage dependence of load. As DG penetration level increases,the voltage profile increases and brings a rise in load demand(within the studied penetration level from 0% to 30% in this case,the greater the DG penetration, the closer the load to the nominalload), consequently lower value of difference in simulation resultsbetween voltage-dependent load and constant load models is ob-served (simulation with constant load model always uses nominalload, which is based on nominal voltage).

Since the difference in energy losses between using the twoload models is caused by the deviation in voltage from its nominalvalue due to DG, it is necessary to understand to what extent thevariation in voltage can affect energy losses from a mathematicalpoint of view.

It is defined in this paper that the difference in energy losses(DKLoss) between using constant load and voltage-dependent loadmodels, is determined by,

DKLoss ¼KLoss-con � KLoss-vol

KLoss-con� 100% ð7Þ

where DKLoss is the difference in energy losses between using con-stant load and voltage-dependent load models. KLoss-con and KLoss-vol

are energy losses calculated with constant load and voltage-depen-dent load model, respectively. A positive symbol of DKLoss indicatesthat simulation results calculated with constant load model isgreater than that with voltage dependent load model.

The correlation between the voltage index and the difference inenergy losses by using the two load models is quantified in Fig. 8.Regression analysis is performed in order to obtain a mathematicalcorrelation for energy losses. It is found that correlation between

the voltage index (absolute value) and the difference in energy lossindex (absolute value) by using the two load models can be best fitby a linear function.

Fig. 8 reveals that: (1) the difference in energy losses betweenthe constant load model and the voltage-dependent load modelsincrease monotonically with the increase in voltage index; (2) a1% variation in voltage index due to the connection of DG (operat-ing at 0.95 lagging power factor) to the studied system will resultin 3.58% energy losses difference, between adopting constant loadand voltage-dependent load models in power flow analysis.

4.2. Impact of load models on energy losses with various reactivepower control strategies

Although utilities favour and even require DGs to operate at lag-ging power factor (DG supplies reactive power to utility grid), var-ious DGs are likely to operate at unity or leading power factors.Energy losses are calculated for all scenarios in which DGs operatewith power factors in the range of 0.95 lagging to 0.95 leading (DGdraws reactive power from utility grid) as shown in Fig. 9. In orderto study the difference in energy losses between the constant loadmodel and the voltage-dependent load model when various reac-tive power control strategies of DG are employed, the penetrationlevel of DG is fixed at 20%. Table 3 shows the simulation resultsassociated with various DG operating power factors.

It can be observed from Table 3 that both voltage and energyloss indices decrease as the DG reactive control strategy movesfrom leading power factor through unity to lagging power factor.

2.0

3.0

With constant load modelWith voltage-dependent load modelWith constant load modelWith voltage-dependent load model

rgy

loss

inde

x, %

1.5

2.5

3.5

4.0

4.5

Table 3Simulation results for various DG operating power factors.

DG power factor Load model Voltage index Kvolt (%) Loss index KLoss (%)

0.95 Leading Const. 3.965 4.078Volt. 3.421 3.507

Unity Const. 3.354 3.474Volt. 3.057 3.089

0.95 Lagging Const. 2.426 2.968Volt. 2.196 2.727

1248 K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250

This interprets that among the above three reactive power controlstrategies, DG can most benefit distribution system when it oper-ates at lagging power factor, i.e., supplying reactive power topower systems.

Fig. 9 shows the difference in energy losses between using con-stant load and voltage-dependent load models with various DGoperating power factors.

As shown in Fig. 9 the study reveals that: (1) the DG operatingpower factor can play a vital role in line-loss reduction, (2) energylosses index exhibits lower value under lagging power factor con-ditions and decreases as the power factor moves from leadingthrough unity to lagging for both the constant load and voltage-dependent load models.

Fig. 10 shows the variation of the difference (DKLoss) in energylosses between the two load models with various power factorsas well as DG penetration levels. Fig. 10 reveals that (1) the differ-ence in energy loss results (DKLoss) between using constant loadand voltage-dependent load models monotonically increases whenthe power factor moves from lagging through unity to leading. Thereason is that the consumption of reactive power by DG (at leadingpower factor) degrades the network’s power factor and results ingreater voltage drop, and therefore a greater difference in energylosses between employing constant load model and voltage-dependent load model in power flow analysis, (2) DKLoss decreasesas DG penetration level increases for the three operating powerfactors. The rate of decrease in DKLoss shows a greatest value whenDG is operating at lagging power factor.

0

1.0

0.95 leading unity 0.95 lagging

DG operating power factorvariable

Ene

0.5

Fig. 11. Differences in energy losses index between employing constant and

4.3. Impact of load models on energy losses with variable DG operatingpower factor

Since both the wind power output and system load profile varywith time, in this paper, another reactive power control strategy isproposed to vary the power factors of DG units in different time

-5

0

5

10

15

20

Dif

fere

nce

in e

nerg

y lo

ss in

dex

betw

een

two

load

mod

els

Klo

ss ,

%

20% 30% 40%10%

DG penetration level

0.95 lagging p.f.Unity p.f.0.95 leading p.f.

Fig. 10. Differences in energy losses index between employing constant andvoltage dependent load models with various DG operating power factors.

periods. This is a strategy to tune renewable DG units to supplyreactive power during peak hours and to consume reactive powerduring off-peak hours.

Fig. 11 shows the difference in energy losses between the con-stant and voltage dependent load models associated with theaforementioned variable reactive power control strategy versuskeeping a constant power factor across the studied time scale.The first three cases assume that DG is working at each time inter-val (half hourly) with a constant power factor equals to 0.95 lead-ing, unity and 0.95 lagging, respectively. In these three cases, DG ismodelled as PQ node. In the fourth case it is assumed that the DGsupplies reactive power during peak hours and consumes it duringoff-peak hours. In this case, DG is modelled as a PV node maintain-ing the voltage at the reference value set by the network operator.

It can be seen from Fig. 11 that the variable power factor has abeneficial effect on energy losses.

4.4. Impact of load models on energy losses with various DG locations

Consider now the case when DG, operating at 0.95 laggingpower factor with a penetration level of 20%, is moved to down-stream (e.g., node No. 18) and upstream (e.g., node No. 5) alongthe feeder. The difference in energy losses between employing con-stant load and voltage-dependent load models at various loadnodes has been studied. Fig. 12 shows the difference in energylosses index between the two load models by installing a singleDG alternately at all load nodes along the main feeder.

voltage dependent load models with various DG operating power factors.

3 5 7 9 11 13 15 170

1

2

3

4

5

2 4 6 8 10 12 14 16 18

Ene

rgy

loss

inde

x K

Los

s, %

Node no. where DG is located

With constant load modelWith voltage-dependent load modelWith constant load modelWith voltage-dependent load model

Fig. 12. Energy loss index by installing a single DG alternately at various locationsalong the feeder.

Table A1System and load parameters for 38-node system.

Branch parameters Loads on to-node

F T R/p.u. X/p.u. PL0/p.u. QL0/p.u.

1 2 0.000574 0.000293 0.1 0.062 3 0.00307 0.001564 0.09 0.043 4 0.002279 0.001161 0.12 0.084 5 0.002373 0.001209 0.06 0.035 6 0.0051 0.004402 0.06 0.026 7 0.001166 0.003853 0.2 0.17 8 0.00443 0.001464 0.2 0.18 9 0.006413 0.004608 0.06 0.029 10 0.006501 0.004608 0.06 0.02

10 11 0.001224 0.000405 0.045 0.0311 12 0.002331 0.000771 0.06 0.03512 13 0.009141 0.007192 0.06 0.03513 14 0.003372 0.004439 0.12 0.0814 15 0.00368 0.003275 0.06 0.0115 16 0.004647 0.003394 0.06 0.0216 17 0.008026 0.010716 0.06 0.0217 18 0.004558 0.003574 0.09 0.04

2 19 0.001021 0.000974 0.09 0.0419 20 0.009366 0.00844 0.09 0.0420 21 0.00255 0.002979 0.09 0.0421 22 0.004414 0.005836 0.09 0.04

3 23 0.002809 0.00192 0.09 0.0523 24 0.005592 0.004415 0.42 0.224 25 0.005579 0.004366 0.42 0.2

6 26 0.001264 0.000644 0.06 0.02526 27 0.00177 0.000901 0.06 0.02527 28 0.006594 0.005814 0.06 0.0228 29 0.005007 0.004362 0.12 0.0729 30 0.00316 0.00161 0.2 0.630 31 0.006067 0.005996 0.15 0.0731 32 0.001933 0.002253 0.21 0.132 33 0.002123 0.003301 0.06 0.04

8 34 0.012453 0.012453 0.0 0.09 35 0.012453 0.012453 0.0 0.0

12 36 0.012453 0.012453 0.0 0.018 37 0.003113 0.003113 0.0 0.025 38 0.003113 0.003113 0.0 0.0

F: from node, T: to node, R: resistance, X: reactance, PL0, QL0: real and reactive powerload at nominal voltage.

K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250 1249

It can be seen from Fig. 12 that (1) losses start to decrease whenthe distance between DG location and Grid Supply Point (GSP, nodeNo. 1) increases until it reaches a minimum value (at node No. 14).Once the minimum value is reached, energy losses begin to in-crease slowly as DG location moves to the direction of feederend. This is because when DG location is moving towards theGSP, the transmission of DG power to distant load centre increasesthe system losses. When DG is moving towards the load centre(feeder end), losses may also increase due to reversed power flowalong the feeder (i.e., from load centre where DG is located to thedistribution substation). However, there is a location where DGcould benefit most to the system in terms of power loss reduction.In this case, locating DG at node 14 results in the least networklosses. (2) The difference in energy losses between employingconstant load and voltage-dependent load models has a maximumvalue at node No. 2 (the node next to the GSP). This is becausewhen DG is located at node No. 2, the system has the lowest volt-age profile compared to the case that DG is located at other poten-tial locations. As a result, simulation with voltage-dependent loadmodel for DG at node No. 2 resulted in the largest difference in en-ergy loss index between the two load models.

5. Conclusions

In this paper, the effect of load models on the assessment of en-ergy losses in DG planning is investigated. The paper comes to thefollowing conclusions:

(1) The real and reactive power injection by installation of DGcould significantly affect the system voltage profile. In afuture distribution system with high penetration level of dis-tributed generation, where the quantification of DNOs andDG owners’ benefits largely depends on the models of powerflow analysis, the assumption of a constant power loadmodel is no longer appropriate.

(2) It has been established in this paper that DG planning basedon constant power load models could lead to either conser-vative or optimistic results, depending on the DG penetra-tion level and load model parameters. Simulation resultsshow that for the scenario with 1% variation in voltage pro-file, there is 3.58% of total losses difference between employ-ing constant load and voltage dependent load models.

(3) There are many factors that can affect the difference in sim-ulation results between constant and voltage-dependentload models. In this paper, the impact of DG penetrationlevel, DG location and DG reactive power control strategieson the difference of simulation results between the two loadmodels have been studied. The constant load model wouldresult in conservative results when DG penetration is atlow level, while optimistic results at higher penetrationlevel. Meanwhile, the less the distance between DG locationto the Grid Supply Point, the greater the difference in energylosses between using constant and voltage-dependent load

Table A2Load compositions of the case study during a day.

Hour 1 2 3 4 5 6

Residential 0.66 0.63 0.60 0.58 0.60 0Commercial 0.17 0.17 0.18 0.20 0.23 0Industrial 0.17 0.20 0.22 0.22 0.17 0

13 14 15 16 17 1

Residential 0.14 0.14 0.15 0.18 0.20 0Commercial 0.37 0.39 0.46 0.41 0.44 0Industrial 0.49 0.47 0.39 0.41 0.36 0

models. With respect to the reactive power control strate-gies, DG operating at leading power factor (DG draws reac-tive power from the utility grid) is more sensitive to loadmodels than that at lagging power factors. A variable powerfactor control strategy is proposed to reduce the sensitivityof energy losses to the load model.

Appendix A

See Tables A1 and A2.

7 8 9 10 11 12

.55 0.30 0.11 0.10 0.11 0.12 0.17

.15 0.14 0.32 0.34 0.33 0.37 0.46

.30 0.56 0.57 0.56 0.56 0.51 0.37

8 19 20 21 22 23 24

.33 0.60 0.7 0.74 0.76 0.75 0.71

.47 0.30 0.23 0.19 0.15 0.15 0.16

.20 0.10 0.06 0.07 0.09 0.10 0.13

1250 K. Qian et al. / Electrical Power and Energy Systems 33 (2011) 1243–1250

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