[ieee 2012 china international conference on electricity distribution (ciced) - shanghai, china...

C I C I C I C I CCCC E D E D E D E D 5th International Conference on Electricity Distribution Shanghai, 5-6 Sept 2012

Paper FP0147

Paper No. FP0147 1/4

OPTIMAL CAPACITOR PLACEMENT FOR DISTRIBUTION

FEEDER MAXIMUM SAVINGS

Meng Zhang

National Grid - USA

[email protected]

ABSTRACT

This paper illustrates the process used for capacitor

placement on an existing radial distribution feeder with an

objective of reducing the downstream power loss while

minimizing total cost. The Loss Sensitivity Factors are

used to determine the candidate buses for capacitor

placement and an experimental methodology is used to

find the exact optimal capacitors locations and capacitors

sizes. The method is tested on an existing 13.2kV feeder.

Simulation is done using CYME and results are presented.

Keywords: Optimal Capacitor Placement, Maximum Loss

Savings

INTRODUCTION

The increase in power demand exposes loading capacity

challenges to the existing power systems. To meet the load

demand, systems are sometimes required to upgrade the

existing cables and transformers to have more capacity or

to expand by increasing the number of feeders. However,

this may not be easily achieved by many utilities due to

various constraints. Radial distribution systems typically

spread over large areas and suffer a significant portion of

total power losses. Therefore, minimizing system loss can

also provide more capacity for the substation and feeders

and relieve loading issues. In addition, the heat dissipated

due to power loss increases the temperature of the

associated electric components and can result in insulation

failure. By minimizing the power losses, the system may

acquire longer life span and have greater reliability [3].

The loss minimization in distribution systems is very

essential to improve the overall efficiency and profit of

power delivery. The utility companies in practice usually

reduce these losses by placing capacitor banks on

distribution primary feeders. Advantages with capacitor

bank placement include improving feeder voltage profile,

improving power factor, reducing power losses and

increasing feeder capacity. It is therefore of utility

companies’ great interest and benefit to optimize capacitor

placement to reduce power loss and maximize net profit.

A considerable amount of research work was done on the

subject of optimal capacitor placement. M. Damodar Reddy

[1] used fuzzy logic to include heuristics and engineering

judgments into the capacitor allocation optimization

process to compensate for any lack of certainty in the data,

and proposed using Real Coded Genetic Algorithm

(RCGA) to find the optimal capacitor sizes. R. Srinivasa

Rao [2] took into account that the commercially available

capacitors were discrete and proposed using Loss

Sensitivity Factors to find candidate locations and using

Plant Growth Simulation Algorithm (PGSA) to estimate the

required level of capacitive compensation. In

Mahmoodianfard’s paper [3], the cost of capacitor

placement, the cost of power losses and the bus voltage

profiles were considered in the optimization problem.

In those studies however, distance between each capacitor

and that between station and each capacitor were usually

not considered. In this project, capacitor placement

optimization problem is to minimize power losses, taking

into account the minimum distance constraint, along with

other constraints including bus voltage limits, “kW loss

saved/kVar installed” criteria and available discrete

capacitor sizes. “Loss Sensitivity Factors” are used to

decide the sequence in which buses are to be considered for

placement. Only 600kVar and 900kVar capacitors are used

in the project as is the case of the utility company’s

practice. Three different options are discussed and an

optimal solution is proposed based on minimizing the total

of energy loss cost and capacitor placement cost. The

project is performed on a real feeder (Watt St 23052

13.2kV) and simulation is performed on CYME.

OBJECTIVE

The objective of the project is to reduce the energy losses

on the feeder while minimizing the total cost, and at the

same time the bus voltage should be maintained within

minimum and maximum limits, the cumulative “kW loss

saving/ kVar installed” ratio with each new capacitor

installed should satisfy the minimal value that is decided by

the utility company and the distance of each capacitor from

the station and that between each capacitor should also

satisfy certain design criteria. Thus the optimal capacitor

placement problem can be expressed as:

min f=min (COST)

s.t maxmin VVV ≤≤

.

01.0

1

, ≥∆

∑=

i

j

C

j

lossT

Q

P


Paper FP0147


,1000. ftCSta i ≥− ftCC ji 1500≥− ,

i=1, 2…n, j=1, 2… i, ij ≠

Where COST is the objective function and can be written

as:

)(1

,

C

ii

n

i

cfLossTp QKKPKCOST ++/= ∑=

Where

pK : Equivalent annual cost per unit of power loss in

$/kW

cfK : Fixed cost for capacitor installation in $

iK : Capacitor purchase rate in $/kVar

C

iQ : Size of the thi capacitor in kVar

ALGORITHM

Consider the simplified one-line diagram of a feeder in

Figure 1. From the one-line, it can be derived that the real

power loss and reactive power loss between bus i and bus

i+1 are:

1,2

22

)1,(

1,2

22

)1,(

)(

)(

++

++

⋅+

=

⋅+

=

ii

i

ii

iilineloss

ii

i

ii

iilineloss

XV

QPQ

RV

QPP

Then the real and reactive power flowing out of bus i+1 are

)1,(11 +++ −−= iilinelossLiii PPPP

)1,(11 +++ −−= iilinelossLiii QQQQ

Where iP and iQ are the real and reactive power flowing

out of bus i, and LiP and LiQ are the real and reactive loads

at bus i. 1, +iiR and 1, +iiX are the resistance and reactance

of the line section between buses i and i+1.

The Loss Sensitivity Factors ( efflineloss QP ∂∂ / ) were

introduced by R. Srinivasa Rao [2] to determine the

sequence in which the candidate buses are to be considered

for capacitors placement.

Consider a distribution line as given below:

Real power loss in the line is given by [ ] [ ]kRIk ∗2 which

can be expressed as

[ ][ ]kR

qV

qQqPqP

effeff

lineloss 2

22 )][][(][

+=

Similarly the reactive power loss can be expressed as

[ ] [ ]kXqV

qQqPqQ

effeff

lineloss 2

22

][

)][][( +=

Where

][qPeff = Total effective real power supplied beyond bus

“q”.

][qQeff = Total effective reactive power supplied beyond

bus “q”.

Then, Loss Sensitivity Factors can be expressed as

[ ]

[ ]2

2

][

][2

][

][2

qV

kXqQ

Q

Q

qV

kRqQ

Q

P

eff

eff

lineloss

eff

eff

lineloss

∗∗=

∂

∂

∗∗=

∂

∂

The Loss Sensitivity Factors

eff

lineloss

Q

P

∂

∂are calculated from

base case load flow. They are used to identify the most

suitable buses for capacitors placements and to decide in

which sequence they are to be considered. The larger the

Loss Sensitivity Factor of a bus, the more suitable the bus is

for capacitor placement.

Buses that are within 1000ft from the substation are

excluded from Loss Sensitivity Factors calculation, since

those buses are too close to the substation for capacitors

placements. The remaining buses form the modified vector

b_lsf. Loss Sensitivity Factors are calculated of those buses

in vector b_lsf and elements are rearranged in descending

order based on the calculated Loss Sensitivity Factor.


Paper FP0147


A capacitor is first placed at the first bus in the vector as

that is the most suitable bus based on Loss Sensitivity

Factors. Load flow is then performed and downstream

power loss at the station is calculated. Then move the

capacitor to the second bus in the vector. Repeat these steps

for the first ten buses in vector b_lsf. Bus b_lsf[k] which

results in the minimum downstream power loss at the

station is decided as the location for the first capacitor bank.

Then revise the candidate buses and remove those that are

within 1500ft from b_lsf[k]. Then repeat these steps until

no more capacitor banks are needed. The restrictions can

be all candidate buses are within 1500ft away from the

buses with capacitors, some bus voltages are above

1.05p.u, or cumulative 01.0,

<installed

savedloss

Q

Pfor any

additional capacitor banks.

The complete optimal capacitor placement process in this

project can be simplified into following steps:

Step 1 Perform load flow analysis on base case using

CYME.

Step 2 Filter the buses based on the constraints and save the

buses for Loss Sensitivity Factors calculation in vector

b_lsf.

Step 3 Rearrange the buses in b_lsf in descending order

based on the calculated Loss Sensitivity Factors.

Step 4 Place the first capacitor at the candidate buses in

b_lsf one at a time and calculate the corresponding

downstream power loss at the station.

Step 5 Identify the optimal bus which results in the

minimum downstream power loss.

Step 6 Revise vector b_lsf and remove buses within 1500ft

from the optimal bus found in step 4.

Step 7 Repeat steps 4 to 6 until no more capacitors are

needed.

Step 8 Record the total real power loss on the feeder after

all the capacitors are placed.

SIMULATION & RESULTS

The project works on Watt St 23052 13.2kV feeder in

Schenectady, Central New York State. Total of 1260 line

sections are modeled in CYME including primary and

secondary, overhead and underground. The primary side of

the feeder is 13.2 kV with some step-down 4.16kV areas.

And the feeder runs mostly overhead.

In the project, only overhead primary three phase sections

over 1000ft away from the substation are considered for

capacitors placement. Applying these constraints, a vector

containing 233 buses is formed from the base case for Loss

Sensitivity Factors calculation.

The complete simulation is done using CYME.

CAP200_13.2 and CAP300_13.2 are chosen from CYME

capacitor library for the 600kVar and 900kVar capacitors

since those are the sizes National Grid uses on 13.2kV

feeders. Load Flow function is used to provide buses

voltages, real power loss on each section and the total real

power loss at the station.

Three options are studied: Option 1, only use 600kVar

capacitors; Option 2, only use 900kVar capacitors; Option

3, use both 600kVar and 900kVar capacitors. A

comparison among the three options regarding total real

loss saving and costs is shown in the table below.

The assumptions used in the cost calculation are:

1. Energy rate K=$0.06/kWhr

2. Installation of each capacitor is $11,000/location

3. Purchase rate of capacitor is $3.0/kVar

4. The calculation is for a year, 365 days period.

Table 1. Net Annual Saving for the Three Options

It is observed from the table that Option 2 has the

maximum net annual saving, which is minimum annual cost

including capacitor placement and energy lost cost.

Therefore, option 2 to install 3 900kVar capacitor banks is

the optimal solution for this feeder. The image below shows

the feeder in GIS (Geographic Image System) with the

black dots indicating the locations of the three capacitors in

the optimal option.


Paper FP0147


CONCLUSIONS

In this project, exhaust experiment method along with Loss

Sensitivity Factors to find the optimal capacitors placement

on a real feeder is presented. Loss Sensitivity Factors are

calculated to decide candidate buses and thus reduce the

exhaust experiment sizes. Exhaust experiment is used to

identify optimal location and size for each capacitor.

Three options for capacitors placements are proposed.

Based on the net annual dollar saving, Option 2 installing

three 900kVar capacitors is recommended.

It should be pointed that system is assumed to be balanced

in this project, while in reality unbalanced system requires

different algorithm and further study is needed. It should

also be noticed that the final recommendation relies heavily

on all the cost assumptions made, including cost for

capacitor placement and cost for energy loss. When those

costs in practice are different from the assumptions made,

the recommendation could be different.

REFERENCES

[1] Damodar Reddy, M; Veera Reddy, V.C, 2008,

"Optimal capacitor placement using fuzzy and real

coded generic algorithm for maximum savings",

Journal of Theoretical and Applied Information

Technology, 2005-2008, 219-226

[2] Srinivasa Rao, R; Narasimham, S.V.L, 2008, “Optimal

capacitor placement in a radial distribution system

using plant growth simulation algorithm”, World

Academy of Science, Engineering and Technology 45,

715-722

[3] Forough Mahmoodianfard, Hossein Askarian Abyaneh,

HamidReza Salehi, 2010, “Optimal capacitor

placement for loss reduction”, Modern Electric Power

Systems, Wroclaw, Poland

[4] Shikha Gupta, Gursewak Singh Brar, 2011, “An

efficient approach for capacitor sizing and location on

a radial distribution system using artificial intelligence

technique”, Journal of Engineering Research and

Studies, Vol. II, Issue II

BIOGRAPHY

Meng Zhang received a B.S in Electrical Engineering

from University of New Orleans in 2009 and an M.S in

Electrical Engineering with a concentration in Power

System from Northeastern University in 2011. She is a

distribution and sub-transmission planning engineer at

National Grid USA since 2010.

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