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Distributed Generators Placement for Loadability

Enhancement based on Reactive Power Margin

Tareq Aziz T. K. Saha N. Mithulananthan

School of Information Technology and Electrical Engineering, The University of Queensland,

Qld 4072, Australia

e-mail address: { taziz, saha, mithulan}@itee.uq.edu.au

Abstract This paper proposes a simple methodology for placing

two principal types of DG units - synchronous machine and

induction machine with an objective of enhancing loadability of

distribution system. The proposed methodology is based on the

concept of reactive power margin. Buses have been ranked based

on the reactive power margin and grouped as strong and

weak buses for finding suitable location of DG units. The effect

of size of DG unit on loadability is also examined along with grid

loss measure which leads to suitable size selection. The proposed

methodology is successfully applied to a modified 16 bus primary

distribution system using a commercially available analytical tool

and the results are verified using a research analytical software

tool.

Keywords- Grid integration, distributed generators, loadability,

suitable size, suitable location, reactive power margin.

I. INTRODUCTIONIn recent years, there has been a considerable increase of

penetration of renewable and non-renewable based distributedgeneration (DG) resources in distribution grids all over theworld. With the increased share of DG in power system,

allocation and sizing of DG has become the most importantconcerns for power system stability. Inappropriate selection oflocation and size of DG may lead to increased system loss andunacceptable voltage profile as have been found in severalstudies [1],[2]. Due to lack of new generation and increase indemand the existing infrastructure is already facing high gridloss and poor voltage profile. Moreover, it has been found thatradial distribution systems with a high resistance to reactanceratio causes a greater amount of loss and are more prone tovoltage instability [3]. However, in spite of all theseconstraints, maximizing loadability has been a good choice forthe distribution system operator who wants to optimize theirresources and maximize their profit in the current deregulatedmarket scenario.

Study on selecting proper location of DG unit is acomparatively new area, unlike selecting location for reactivepower compensators. The existing methodologies can beclassified into two main categories. The first category is basedon artificial intelligence techniques (e.g. genetic algorithm)[4],[5]. These techniques demand a large number ofcomputations resulting in slow convergence. On the otherhand, analytical methods with repetitive load flow stands asthe second category to decide the locations for DG in powersystem [6]-[8]. Ref. [6] and [7] however, optimizes only

location, keeping the size of DG constant using analyticalmethods. For example ref. [6] uses tangent vectors for rankingbuses and selects the best location for only one type of DG i.e.synchronous generator keeping its size constant. Ref. [8]optimizes both location and size but it considers DG as a realpower source without considering its reactive powercapability.

This paper proposes techniques to identify proper locationand size of two principal types of DG units (i.e. induction andsynchronous machine) for enhancing loadability. Dependingon chosen voltage stability index the buses of a primarydistribution system have been ranked first, which limits theirnumber for placing DG units resulting in reduced number ofload flow computations. Then based on those results alongwith loadability study a decision is made for placement of SGand IG in the system followed by determination of suitablesize of each DG unit on the selected buses. However, toachieve maximum system benefits in a deregulatedenvironment generator companies can work in collaborationwith the transmission and distribution companies to select thelocation of generators based on the proposed methodology.

This paper is organized as follows. Section II gives a briefintroduction to the distributed generators used in this paper.Then section III describes the static voltage stability indicesemployed to determine the location of placing DG units.Section IV describes the methodology for ranking the suitablelocation of buses for placing SG and IG along with fixing themaximum size of each type. Considering the practicalconstraints section V presents and describes the results forlocation and sizing of SG and IG in the test system along with asmall introduction to the test system. Section VI summarizesthe major contributions and conclusions.

II. DISTRIBUTED GENERATORS IN STUDYSynchronous generators connected to a distributionnetwork as DG units are mostly operated with constant active

power as their resource is not very volatile (bagasse basedCHP plant, gas turbines, solar thermal plants and internalcombustion engines). For SG, power factor control mode isusually adopted by the independent power producers as theirtarget is to maximize active power production [9]. So powerfactor control mode has been employed in this paper. Theactive and reactive power generation of a synchronousgenerator can be expressed as given in (1) and (2) [10].

This work was supported by the CSIRO Intelligent Grid Flagship

Collaboration Research Fund.

740978-1-4244-7397-7/10/$26.00 2010 IEEE IPEC 2010

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sincost

E

sX

qE

tIt

EG

P == (1)

sX

tE

tE

sX

qE

tIt

EG

Q

2

cossin == (2)

Where,t

E is the terminal voltage of the generator with per

unit system andfdi

adX

qE = represents the excitation voltage

due to field currentfdi . Here

sX and , respectively

represents synchronous reactance and internal rotor angle. Butfor a given real power output of a synchronous generator thereactive power generation is bounded by both armature andfield heating limits.

Because of the subtle nature of wind, induction generatorsare largely used in wind power plants [11]. Applications ofinduction generator are also found in micro turbines of smallhydro plants and internal combustion engines. In this paper,the squirrel cage rotor induction generator has been employed

which consumes reactive power from the system. With aterminal voltage

tE and rotor current

2I , the real and reactive

power generated by the induction generator is given by (3) and(4), respectively [12].

)*

2Re( I

tE

GP = (3)

)*

2Im( I

tE

GQ = (4)

Where

( ) ( )( )12222 ////2 ZjXsRjXjXsRjXE mmtI ++++= (5)

And111 jXRZ += (6)

Here, 1R =Stator resistance, 1X = Stator leakage reactance,

mX = Magnetizing reactance, 2R = Rotor resistance (referred

to stator), 2X = Rotor leakage reactance (referred to stator).

When an induction generator is placed on a bus, a portionof reactive power is usually locally supplied [13]. In this

paper, the capacitor size will be decided later depending on thegrid losses in presence of the induction generator.

III. STATIC VOLTAGE STABILITY AND INDICESOne of the principal factors of voltage collapse has been

identified as the increased load demand which is generally

accompanied by an increase in reactive power demand.Distance to collapse can be measured in terms of different

physical quantities such as loadability, reactive power reserveetc. Also, a number of performance indices have beendeveloped by the researchers to determine proximity tovoltage collapse [14].

A. Voltage Sensitivity FactorBased on the general concept, SF (sensitivity factor) index

for a system represented by ( ),zF can be defined as

d

dzSF = [15]. When SF becomes large, the system turns

insecure and ultimately collapses. Here the system voltagesare checked with respect to the change in loading which

results in a Voltage sensitivity factor (VSF) calculatedas

dP

dVVSF = . High sensitivity means even small changes

in loading causes large changes in voltage magnitude, whichindicates weakness of the bus.

B.Reactive Power MarginReactive power margin is measured as a distance between

the lowest MVAr point of Q-V curve and voltage axis asshown in Fig. 1 [16],[17]. The negative values of reactivesupply indicate the increasing reactive load. Thus reactive

power margin indicates how much further the loading on thatparticular bus can be increased before its loading limit is

expired and voltage collapse takes place. Reactive powermargins are used in [18] to evaluate voltage instabilityproblems for coherent bus groups. These margins are based onthe reactive reserves on generators, SVCs and synchronouscondensers that exhaust reserves in the process of computing aQ-V curve at any bus in a coherent group or voltage controlarea. In this study, this index is used to measure the strength ofthe buses of primary distribution system with a single feeder.The validity of this index in our study has been justified byanother index i.e. voltage sensitivity factor which has beenused earlier for the same purpose [6]. With the combinedresults from measurement of these two indices, themethodology described in section IV has been used to identifysuitable location and appropriate size of DG unit in the test

system.

Figure 1. Example Q-V curve and reactive power margin.

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IV. PROPOSED TECHNIQUESOverall procedure of the proposed approach can be

summarized in the following steps.

Step 1: Q-V curves are drawn for all buses to determine

reactive power margin of each bus. For a very largedistribution system Q-V curves can be drawn byconsidering the availability of primary resources.

Step 2: The buses are ranked in descending order of the valuesof reactive power margin to form a priority list interms of strength. Bus having the lowest reactive

power margin is the weakest bus. i.e. in an N bussystem the weakest bus (WB) can be defined asfollows:

inmN

Qinm

Qinm

Qinm

QMinWBarg

,...,arg

3,

arg2

,arg

1

whereinm

iQ

argis the reactive power margin of each

bus in MVAr.

Step 3: P-V curves are drawn to get VSF and loadability. All

the loads in the base case are presented as constant PQ

load and these are increased according to the followingrelation, keeping the power factor constant:

( )+= 10

PL

P

( )+= 10

QL

Q

Where0

P and0

Q represents the base case loading and

is the loading factor. However, the use of realisticload direction can be used to get a more practicalsolution in this static voltage stability study [19].

The weakest bus in an N bus system has

dP

NdV

dP

dV

dP

dV

dP

dVMaxWB ,......,3,2,1

Now from this result a ranking of buses based onstrength is decided and this list is used to verify resultsfound in step 2. Based on these index values twoseparate lists of buses weak bus and strong bus aremade. The above procedure reduces the solution spaceto these few buses in the list.

Step 4: Two different types of DG with increasing machine

sizes are placed on ranked buses. Locations for SG andIG are chosen individually with an objective ofincreased reactive power margin and loadability.

Step 5: Once the location for SG and IG has been fixed foreach bus in a priority list SG is placed and the size is

varied from minimum (0MW) to a higher value insmall steps until minimum grid loss is found byrunning repetitive load flow.

Step 6: Step 5 is now repeated with IG on preferred locations(derived from the first 4 steps) with the same targets.

Step 7: With an induction generator connected to the system,grid loss becomes greater than the base case valuewhen real power injection by the generator becomeszero due to lack of primary resources. So the minimum

compensator size is determined, which makes the gridloss with IG equal to base case grid loss.

V. SIMULATION RESULTS AND DISCUSSIONA. Test distribution System and Analytical Tool

In this study, the 16-bus distribution system as shown inFig. 2 is used. This system is a 23 kV balanced distribution

system with a total load of 28.7MW and 17.3MVAr,respectively. This system is a modified form of the one used in[20]. All the results presented in this paper were simulatedwith the DIgSILENT PowerFactory 14.0 [21], a commercialtool and also have been verified using a research analyticaltool PSAT [22].

B.Ranking of BusesBased on the proposed steps a ranking of buses from this

test system is made from the calculation of reactive powermargin and VSF of system buses. Figures 3 and 4 show thereactive power margin and VSF, respectively for all the load

buses. As can be seen from Fig. 3, bus 8 is the bus with thehighest margin of 150.35MVAr whereas bus 7 is the bus with

the lowest margin of 22.94MVAr. If we expand the concept ofthis index, it can be noted that when an amount of reactive

power equal to reactive power margin is drawn from that busby loads then it can experience collapse. For example if150.35MVAr of reactive power is drawn from only bus 8, withloads on all other buses remained unchanged, the system willexperience collapse though the total load at base conditioncounts to be only 17.3MVAr. So based on this comparisonindex, our study clearly defines bus 8 as the strongest bus and

bus 7 as the weakest bus.

Fig. 4 plots VSF of all load buses near to the point ofcollapse when maximum value of loadability or loading pointhas been reached (here this value is 2.615 times the base load).

Bus 7 comes out as the weakest bus while bus 8 stands out asthe strongest bus, even in terms of VSF. After closelyexamining these two plots together we can make a ranking of

buses based on their strengths.

Figure 2. Single line diagram of test system.

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Figure 3. Reactive power margin of load buses of the test system.

Figure 4. Voltage Sensitivity Factor of load buses of the test system.

Table I represents the first four weak buses whereas Table II

shows the first four strong buses. For example, in Table I busno. 7 stands out as the weakest bus with the lowest reactive

power margin (22.94MVAr) as well as the highest sensitivity

factor (0.038161 Volts p.u. /MW).

TABLEI.WEAK BUSES

Bus No. Reactive power

Margin (MVAr)

VSF

(Voltage p.u./MW)

7 22.94 0.038161

6 24.41 0.0361451 27.78 0.028193

4 32.54 0.026833

TABLEII.STRONG BUSES

Bus No. Reactive power

Margin (MVAr)

VSF

(Voltage p.u./ MW)

8 150.35 0.002927

10 78.22 0.005134

9 74.34 0.006029

14 65.97 0.008107

C.Determining Locations for SG and IGTo find the effect of DG units on reactive power margin,

IG and SG are placed separately on weak areas and theresulting reactive power margins are plotted in Figs. 5 and 6,respectively. The total system load was 28.7MW (i.e. around30MW) hence two machine sizes - 3MW (around 10% oftotal demand) and 6MW (around 20% of total demand) have

been chosen along with the base case with no DG (0MWrepresenting 0% penetration). To keep consistency forcomparison of results the same values of real power injection

Figure 5. Change in Reactive Power Margin in weak area with inclusion of

IG.

Figure 6. Change in Reactive Power Margin in weak area with inclusion of

SG.

have been assumed with SG too. SG used in this study isoperated in power factor control mode with a power factor of0.8 lagging.

These two plots clearly show that the inclusion of IG onthe weak buses does not improve the reactive power margin orstrength of these buses. For example, the reactive powermargin of weak buses like bus 7 remains unchanged around 23MVAr with the change in real power injection. But with the

inclusion of SG this margin and strength has greatly improvedwhich is more prominent with higher real power injection.Here it is observed that the reactive power margin of bus 7increases from 22.94MVAr to 29.74MVAr with an increase inreal power injection by the SG from 0MW to 6MW. So theincrease in reactive power margin indicates the growingstrength of the weak buses in the presence of the SG which isnot achievable with an IG on weak buses.

System loadability is clearly affected with the inclusion ofDG unit into the system. The results have been shown for DGwith increasing sizes: SG in Fig. 7 and IG in Fig. 8. With theincrease of size of SG, loadability improves in every case(greater than the base case loading margin = 2.615 p.u.). But,in this study, it has been found that the rate of increase of

loadability with respect to machine size is higher for weakbuses than strong buses. In a real scenario, this loadabilityimprovement with increasing machine size is limited by thethermal limit of the network components.

But as the size of the induction machine is increased theloadability decreases for almost every bus except the buses inthe strong area (as mentioned in Table II). The rate of increaseof loadability with IG is much lower than SG and after some

point it tends to decrease.

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Figure 10. Change in Grid losses and reactive power intake with Induction

machine size.

TABLEIV.SUITABLE SIZE OF INDUCTION GENERATOR

Bus

No.

Machine

Size

(MW)

Grid Loss (MW) Grid Loss

(MVAr)

(p.u.)

With

out IG

With IG With

out IG

With

IG

8 21 1.78 1.14 1.95 1.30 2.66

10 9 1.78 1.36 1.95 1.53 2.61

9 7.5 1.78 1.23 1.95 1.34 2.34

14 2.2 1.78 1.62 1.95 1.79 2.58

TABLEV.MINIMUM SIZE OF COMPENSATOR

Bus No. Induction

Machine

Size (MW)

Grid Loss (MW)

Compensat

or size

(MVAr)

With

out IG

With IG

(Real power

injection =0)

8 21 1.78 1.78 3

10 9 1.78 1.78 1.9

9 7.5 1.78 1.78 1.6

14 2.2 1.78 1.78 0.5

VI. CONCLUSIONSA methodology has been proposed based on Q-V curve to

determine the location of two major classes of DG -synchronous generator (SG) and induction generator (IG) -considering the reactive power issues of the system and thesemachines. Based on the result, it can be said that SG need to

be placed on weak bus whereas IG need to be placed on strongbus to enhance system loadability. It is interesting to note thatthe rate of improvement of loadability with SG on weak bus isgreater than the case where SG is placed at a strong bus. WithIG on strong bus loadability improves up to certain machinesize and then starts to decrease.

Once the locations have been fixed, lookup tables havebeen formed using the proposed methodology, which can beused to restrict the size of each type of DG in the system. At

suitable size of SG, reactive power intake of the system hasbeen found zero with minimum grid loss. However, in realityan independent power producer would go for the closest matchto the sizes mentioned in the market and deviations in grid lossand loadability due to this choice are within the tolerablerange.

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