OPTIMAL CAPACITOR PLACEMENT AND SIZING IN DISTRIBUTION SYSTEMS USING POWER LOSS INDEX

Indian Streams Research Journal

KEYWORDS:

Optimal capacitor placement, Maximum loadability index (MLI), Energy efficiency, Reconfiguration of distributed generation.

I.INTRODUCTION

The delivery of power from sources to the consumer points is always accompanied with power losses. It has been reported in literature review that power losses occurring in distribution networks account for as much as 13% of the generated energy [1]. Such non-negligible amount of power losses has a direct impact on the financial results and the overall efficiency of distribution utilities is reduced [1].

The aim of this paper is to examine the effect of optimal size and location of capacitor to improve the loadability (i.e. MLI) and energy efficiency of the existing power distribution systems. MLI gives an estimate of additional load as a factor of the existing load that may be connected at the candidate node before reaching the system voltage collapse. The value of MLI computed is a function of source voltage or sending end node voltage.

Losses can be reduced by series or shunt compensation of capacitor installation so as to locally supply a considerable portion of the reactive power demanded by the consumers and thereby reducing the reactive component of branch currents. The installation of shunt capacitors provides supplementary benefits, such as voltage profile improvement, the power factor improvement and enhanced stability of the distribution system.

This paper is organized as follows. An overview of the operation of smart distribution system is discussed in section II. The procedure for the estimation of maximum loadability limit of radial distribution systems is discussed in section III. The mathematical formulation of capacitor placement and sizing is described in section IV. The simulation results obtained for IEEE 15-bus radial distribution system are

Abstract:

An energy efficient power distribution network can provide cost effective and collaborative platform for supporting present and future smart distribution system requirements. Energy efficiency in distribution systems is achieved through optimal capacitor placement and sizing. The main objective of this paper is to estimate the maximum loadability margin in radial distribution systems for optimal capacitor placement and sizing. The work also aims to achieve reduction in system power loss and improvement in voltage profile. The optimal location for capacitor placement is determined based on Power Loss Index (PLI). The proposed work is implemented in benchmark IEEE 15-bus radial distribution system and results are analyzed. Simulation programs for the work have been developed in MATLAB. The simultaneous improvement in loadability limit and power loss reduction enhances energy efficiency in distribution systems by releasing power demand and feeder capacity.

OPTIMAL CAPACITOR PLACEMENT AND SIZING IN DISTRIBUTION SYSTEMS USING POWER LOSS INDEX

1 2 3V.SUGANTHI , S.MAHALAKSHMI , S.KALYANI

1 2 3UG student, UG student, Professor,Department of Electrical & Electronics Engineering,

Kamaraj College of Engineering & Technology, Virudhunagar .

ORIGINAL ARTICLE

ISSN:-2230-7850METHODS ENRICHING POWER & ENERGY DEVELOPMENTS (MEPED'13)

thApril 12 , 2013

detailed in section V. Finally, important conclusions are drawn in section VI.

II. SMART DISTRIBUTION SYSTEM

A distribution system is a complex network, and the designed configuration has direct bearing on its operation and performance. Distribution systems act as mediator between generation and consumption, and usually operate on the verge of its loadability limit, so as to supply as many consumers as possible. Therefore, under critical loading condition, the chances of voltage collapse in the area with high load and low voltage profile increases. In most cases, the incidence of unexpected voltage collapse has been experienced due to rapid growth in power demands of certain industrial loads When such collapse occurs, some industrial loads are disconnected through automatic cut-off switches resulting in severe interruptions. The smart distribution systems are capable of predicting the critical loading conditions and also providing the preventive measures in advance. The selection of optimal size and location of capacitor is associated with reactive components of branch current. It has been identified that by installing the capacitor of optimum size at appropriate location, the system loadability can be increased and a significant reduction in the system losses can be achieved.

III. ESTIMATION OF MAXIMUM LOADABILITY

To determine the expression for the estimation of maximum loadability, a simple two-bus radial distribution system as shown in Fig. 1 is considered.

The phasor diagram of equivalent radial distribution system between two nodes is shown in Fig. 2.

OPTIMAL CAPACITOR PLACEMENT AND SIZING IN DISTRIBUTION.............

2

Fig. 1 Single line representat ion of IEEE 2-Bus

Radial Distribution system

ns - sending node nr - receiving node Vi-1 - sending end voltage Vi - receiving end voltage Ii - branch current. ri - resistance of the branch xi - reactance of the branch Pi+jQ i - load at receiving end

Fig. 2 Phasor diagram of the distribution system

From the phasor diagram ,

Further re-arranging, as in equation (5) and writing in generalized form with respect to the ith node, for the network having 'n' no. of nodes, the receiving end node voltage equation is obtained as under:

As in equation (6) mathematically the voltage solution does not exist when the term Y2 becomes negative. Therefore the solution exists when,

The possible solution, as in equation (7) at particular load defines loadability limit at that node. In order to determine the maximum loadability, the existing load (P + jQ ) is replaced by the term {MLIi * (P + i i i

jQ )}while the load power factor is assumed constant. Further, modifying, as in equation as quadratic i

equation by equating it to zero, the MLI is calculated as under:i

3

iiii rIVVOA +==- qycoscos1 (1)

iiii xIVVAB +==- qysinsin1 (2)

.2222

1 OBABOAVi =+=-

22 )sin()cos( iiiiii xIVrIV +++= qq (3)

On solving equ (3),

])[(222

222222

1i

iiiiiiiiii

V

QPxrQxPrVV

+++++=-

(4)

Where,

.sin

.cos

q

q

iii

iii

IVQ

IVP

=

=

i

iii

V

QPI

2

122)( +

=

Re-arranging the equ(4),

)tan1(cos

)tan1(cos22

2222

2222221

qq

qq

++

++++=-

ii

iiiiiiii

Ix

IrQxPrVV

(5)

.)])((

)}(2

[{)(2

2

12222

22

12

12

YXQPxr

QxPrV

QxPrV

V

iiii

iiiii

iiiii

i

±=++

-+-±+-= --

(6)

Here,

)(2

21

iiiii QxPr

VX +-=-

2

122222

21 )])(()}(

2[{ iiiiiiii

i QPxrQxPrV

Y ++-+-=-

.0))(()}(2

{ 222222

1 ³++-+--iiiiiiii

i QPxrQxPrV

(7)


Using equation (8), the MLI can be estimated at different loading conditions. To illustrate the estimation of MLI, a lossy distribution system is considered. The sending end voltage, load power factor, the line resistance and reactance is assumed to be |1.0| p.u, 0.8, 2.8Ù and 2.2Ù respectively. The value of MLI reaches to '1', indicating that additional load leads to voltage collapse. The network loadability limit when MLI=1.000 is found to be 8.496MVA, which is called as critical loading limit. The fourth column of Table 1 gives the additional load, which is obtained by taking the difference of individual MVA load from the critical load value i.e. 8.496. The additional load indicates the extra load, which can be connected to the receiving end node of the sample system without the cause of voltage collapse of the system.

IV. MATHEMATICAL FORMULATION FOR CAPACITOR PLACEMENT AND SIZING

The problem of optimal capacitor placement requires determination of the location, sizes and number of capacitors to be installed, subject to the certain operational constraints, in a distribution system to achieve the maximum benefits.

A. Calculation of Capacitor Size

The total active power loss for a distribution system with branches is given by,

Where, Ii and ri are the current magnitude and resistance respectively of the branch 'i'. Separating the real and reactive components of current the power loss can be expressed as:

4

2

222221

)(2

]))(()([

iiii

iiiiiiiiii

QrPx

QPxrQxPrVMLI

+

++++-=

-

(8)

å==

n

i iiL rITP1

2 (9)


Where, TPLa is power loss due to active components of current and TPLr is power loss due to reactive components of current. The placement of the capacitor aims to maximize the system loss reduction and the mathematical equations are obtained as follows:

If a capacitor of current Ick is placed at a node k, the total real power loss of the system is given by equation (12)

(12)

Here 'b' is the branch segments in radial path from source to candidate nodes.

The total loss reduction ÄTPLk can be expressed by equation (13) as:

The capacitor current Ick that provides the maximum loss saving can be obtained from by taking the first derivative of equation (13) with respect to Ick,

Solving equation (14), the capacitor current for maximum loss saving is given by equation (15) as:

It is assumed that there is no significant improvement in the node voltage Vk after capacitor placement, due to change in active component of load current, at respective nodes. Therefore, the size of capacitor at candidate node can be calculated as:

The size of capacitor calculated, as in equation (16), may differ at each node. The placement of these sizes of capacitor at respective node does not guarantee to improve the required parameters uniformly.

B. Calculation of Power Loss Index

The network when compensated by Qck (i.e. optimal capacitor size calculated, as in (16) releases the feeder KVAR capacity and reduces resultant power loss). The power loss reduction in the compensated network varies from minimum to maximum value, and is calculated for each ith node using equation (17) given below:

ÄTPLi = TPLi (Base) - TPLi (compensated, Qck ) (17)

Based on the loss reduction, the power loss index PLI (i.e. normalized value in (0 1) range) can be

5

åå- -+=

n

i

n

iiriiaiL rIrITP

1 1

22 (10)

Therefore,

LrLaL TPTPTP += (11)

åå å == ¹+++=

n

i iai

n

jbi

n

jbi iriickriL rIrIrIITP1

2

)( )(

22)(

åå ==--=D

k

jbi ick

k

jbi irickLk rIrIITP)(

2

)(2 (13)

0)(2)(

)()(=+-=

Dåå ==

k

jbi ick

k

jbi irick

Lk rIrII

TP

d

d(14)

)(

)(

)(

å

å

=

=-=

k

jbi i

k

jbi iri

ck

r

rII (15)

kckck VIQ = (16)


obtained, in respect to the candidate node, using equation (18):

Using power loss index, the reduction in active power loss is calculated which in turn is used in determining the selection criterion for optimal capacitor placement. The optimal location for the capacitor placement is identified as the node having the maximum PLI.

V. SIMULATION RESULTS AND DISCUSSION

The proposed work is simulated in a benchmark standard IEEE 15-bus radial distribution system, whose single line diagram is shown in Fig. 3. The bus data and branch data of the test system are taken from [2] and the substation voltage is maintained at 1.0p.u. The distribution system is assumed to be balanced and operating under constant power load model. Initially by assuming flat voltage profile as 1p.u. and line power loss as zero the load flow program is run. The base case load flow solution obtained by Newton Raphson method for the IEEE 15-node distribution system is shown in Table 2.

The maximum loadability limit calculated for each bus using equation (8) is shown in Table 3. The system MVA load is varied at bus 7 and the values of node voltage and MLI evaluated are tabulated in Table 4. It has been observed that the small variation in load in 7th bus after 6.628MVA leads to sudden shutdown of the system due to voltage collapse which has been highlighted in the Table 4. It results in the severe interruptions while supplying power. Therefore, to operate the system under such critical loading conditions, especially when power demand is growing, the loadability limit has to improve. This can be achieved by optimal capacitor placement. Capacitor placement at suitable location proves to improve the maximum loadability limit by locally supplying reactive power demand and reducing the line power loss.

6

minmax

min

LL

LLii

TPTP

TPTPPLI

D-D

D-D= (18)

Fig. 3 IEEE 15 bus distribution system


The optimum capacitor size in KVAr to be installed at respective nodes computed using equation (16) is shown in Table 5. The network becomes reconfigured by placement of capacitor with suitable size at various nodes. In order to analyze the performance of the reconfigured network, the percentage measure of average voltage profile improvement and average reduction in total real power loss attained with respect to base case solution after placing the capacitor of calculated size (Qck) at the respective nodes is detailed in Table 5. Fig. 4 shows the voltage profile improvement and power loss reduction with respect to capacitor placed at respective nodes. It is observed from Fig. 4 and Table 5 that maximum voltage profile and

7

Table 2 Base case load flow solution BusNo. Voltage(pu) Ploss(pu) Qloss(pu)

1 1.0000 0.5094 0.4693 2 0.9273 0.5064 0.4664 3 0.8899 0.4358 0.3978 4 0.8785 0.4922 0.4526 5 0.8774 0.5039 0.4640 6 0.9029 0.4955 0.4569 7 0.9006 0.4953 0.4568 8 0.8965 0.4396 0.4076 9 0.9159 0.4534 0.4174

10 0.9147 0.5055 0.4658 11 0.8748 0.4908 0.4520 12 0.8599 0.4100 0.3792 13 0.8585 0.5023 0.4629 14 0.8667 0.4175 0.3828 15 0.8758 0.4919 0.4524

Table 3 Estimated MLI values

Bus

No

1 2 3 4 5

MLI - 252.32 26.791 79.444 252.32

Bus

No

6 7 8 9 10

MLI 79.444 79.444 26.791 26.791 252.32

Bus

No

11 12 13 14 15

MLI 79.444 26.791 252.32 26.791 79.444

Table 4 Voltage & MLI variation at 7 bus

Load in MVA

Voltage (pu)

MLI A dditional Load(MVA)

2.5 0.8064 2.6513 4.1280

3 0.7843 2.2094 3.6280

3.5 0.7606 1.8938 3.1280

4 0.7350 1.6571 2.6280

4.5 0.7067 1.4730 2.1280

5 0.6749 1.3257 1.6280

5.5 0.6376 1.2051 1.1280

6 0.5906 1.1047 0.6280

6.5 0.5148 1.0197 0.1280

6.628 0.4552 1.0000 0

7 No solution 0.9469 -0.3720


maximum power loss reduction occurs when a capacitor of size 708.8937 KVAr is installed at 14th bus.

The optimal capacitor placement can also be determined using the power loss index calculated using equation (18) for various capacitor sizes calculated as shown in Table 6. Fig. 5 shows the variation of PLI (power loss index) and Qck (size of the capacitor) in every node of the network system. The node having maximum value of PLI is identified as the suitable candidate node for the capacitor placement. It is observed from Table 6 and Fig. 5 that node 12 has a maximum PLI value of 1.000.

8

Table 5 Dete rmination of capacitor size

Bus No. C apaci tor Size (KVAr)

Voltage Profi le

Improvement (%)

Real Power Loss Reduction (% )

2 43.1839 0.0573 0.5427

3 714.0000 1.4600 12.742 4 143.0000 0.3400 3.1313

5 142.8261 0.3493 3.1120 6 485.4295 0.8313 7.7680

7 531.6006 0.9267 8.2413 8 375.8294 0.6827 6.7913

9 104.6100 0.1620 1.6267 10 118.0891 0.1900 1.8120

11 103.3249 0.2533 2.4547 12 496.5955 1.3387 12.1613

13 466.0855 1.2840 11.0287

14 708.8937 1.7373 14.988 15 373.9869 0.8947 7.7160

Fig. 4 Average Voltage Profile Improvement and Power Loss Reduction after Capacitor Placement


From the above simulation results, voltage improvement is found to be maximum at 14th bus and then at 3rd bus. The maximum capacitor size needed to be installed at 3rd bus is of size 714 KVAr. Based on PLI value, the first priority for the capacitor placement is given to 12th node with sizing 496.5955 KVAr followed by the consecutive capacitor placement at 14th, 8th, 9th, 3rd nodes and so on. Hence, based on the estimation of PLI, the capacitor placement problem is found to be optimized, achieving a significant improvement in system voltage profile and reduction in system loss, thereby enhancing overall efficiency of the system.

VI. CONCLUSION

This paper has proposed an efficient method for the optimal location and sizing of capacitors in radial distribution systems. The paper has also presented a conventional method for the determination of maximum loadability limit and power loss index. The results presented has clearly indicated that a considerable improvement in power loss reduction and voltage profiles is achieved by optimal capacitor placement and sizing. The future scope of work will focus on the inclusion of cost savings in capacitor installation.

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Table 6 Variation of PLI &Qck at all the buses

Bus No. Qck (MVAr) PLI

2 0.0432 0.4269

3 0.7140 0.8017

4 0.1430 0.5053

5 0.1428 0.3710

6 0.4854 0.2899

7 0.5316 0.2553

8 0.3758 0.8648

9 0.1046 0.8589

10 0.1181 0.3947

11 0.1033 0.5398

12 0.4966 1.0000

13 0.4661 0

14 0.7089 0.8760

15 0.3740 0.3445

2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bus No

PLI&

Qck

Qck

PLI

Fig. 5 Variation of PLI &Qck at all the buses


REFERENCES

[1] H.M. Khodr, F.G. Olsina, P.M. De Oliveira-De Jesus, J.M. Yusta, Maximum Savings Approach for Location and Sizing of Capacitors in Distribution Systems, Electric Power Systems Research, Vol. 78, 2008, pp. 1192-1203.[2] D.das, D.P. Kothari, A.Kalam, “A simple and efficient method for load flow solution of radial distribution networks”, Int. Journal of Electrical power & energy systems, vol. 17, No. 5, pp. 335-346, 1995.[3]Ikbal Ali, Mini S. Thomas, Pawan Kumar, “Optimal capacitor placement in smart distribution systems to improve its maximum loadability and energy efficiency”, Int. Journal of Engineering, Science and Technology, Vol. 3, No. 8, 2011, pp. 271-284.[4] Mesut E. Baran and Felix F.Wu, “Optimal sizing of capacitors placed on a radial distribution system,” IEEE Transactions on power delivery, Vol. 4,No. 1, January 1989.[5]A.M.Sharaf, S.T.Ibrahim, “Optimal capacitor placement in distribution networks” Electric power system research 3T (1996) 181-187,PO Box 4400,university of new Brunswick, Frederiction, N.B, Canada E3B 5A3.

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OPTIMAL CAPACITOR PLACEMENT AND SIZING IN DISTRIBUTION SYSTEMS USING POWER LOSS INDEX

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