Fixed/switched type shunt capacitor planning of distribution systems by considering customer load patterns and simplified feeder model

Fixed/switched type shunt capacitor planning of distribution systems by considering customer load patterns and simplified feeder model

M.Y.Cho Y.W.Chen

Indexing terms: Distribution jeeder, Reactive power compensation, Capacitor operation strategy, Simplified feeder model, Customer load patterns

Abstract: A shunt capacitor planning strategy to reduce system resistive losses and improve voltage profile for distribution feeders has been proposed. The objective function consists of peak load loss, energy loss and shunt capacitor cost, while operational constraints such as bus voltage profile and real shunt capacitor size are considered throughout the overall solution procedure. A three-phase load flow program, which accounts for the mutual coupling effect between conductors, unbalanced loading among phases, and feeders with multiple lateral branches, is applied to enhance the computer simulation. The simplified feeder model has been developed to derive the equivalent circuit of minor lateral branches so that the data processing work for the feeder configuration can be reduced efficiently. Besides, the customer load patterns as well as the feeder load curve for various seasons are derived so that the section load behaviour can be estimated more realistically. According to the reactive load duration curve of the feeders studied, the capacitor operation strategy by considering both fixed and switched shunt capacitors is developed to determine the proper size, location and switching time of capacitors to enhance the system operation efficiency. Two practical feeders in the Taipower (Taiwan Power) distribution system are selected for demonstration to show the effectiveness of the proposed method. Capacitors with optimal size are installed according to the schemes derived by computer analysis. Field tests are then performed and the energy loss reduction as well as the improvement of power quality of the test feeders can be justified.

0 IEE, 1997 IEE Proceedings online no. 19971387 Paper first received 17th July 1996 and in revised form 24th March 1997 M.Y. Cho is with the Department of Electrical Engineering, National Koahsiung Institute of Technology, Kaohsiung, Taiwan, Republic of China Y.W. Chen is with the Taiwan Power Company, Taipei, Taiwan, Republic of China

1 Introduction

Capacitor planning of distribution systems provides the strategy of reactive power compensation so that the real power loss can be reduced and both the system voltage profile and the power factor can be improved [I]. The SVC (static VAr compensator), which uses the power electronic technique for adaptive reactive power compensation, has been applied in the industrial power system to compensate for large changes in reactive power demand (such as with a rolling mill in a steel plant), but it is still not cost-justified in distribution systems. On the other hand, shunt capacitor banks have been verified to have satisfactory cost benefits and are widely used for passive reactive power compensation in distribution systems.

Up to now, many capacitor planning methodologies have been proposed by homogeneous reactive power load distribution and uniform conductor size along the feeder [2-41. Recently, J.J. Grainger et al. [5-8] have given more practical consideration to the distribution system by normalising the different sizes of the primary feeder with uniform conductor size to derive the equivalent feeder [5], and also consider the feeder with lateral configuration [6-81. A decomposition through isolated subproblems has been developed to optimally solve the reactive power compensation in radial distribution feeders with distorted substation voltage [9]. Variables such as the size and installation location for both fixed and switched type capacitors, and the operation time period for switched type capacitors are all taken into account. The initial values for the state variables are assumed and proceed to solve the nonlinear equations iteratively until all variables converge to the final solution. Inspection of these papers reveals that the load estimation for each feeder section is not accurate because the differences between various load customers and the weather conditions in various seasons have been ignored. By contrast, in Taipower distribution systems the feeder comprises a more complicated structure of lateral branches and several types of load customers for each section of the feeder. Work on processing feeder configuration data (such as manually simplifying the configuration of minor lateral branches, summation of transformer loading, and the length and the size of feeder conductors of each section branch) from the feeder map is very time-consuming. For this reason, it is necessary to develop a more efficient and practical method to calculate the reactive power compensation

533 IEE Proc-Cener. Transm. Distrib., Vol. 144, No. 6 , November 1997

in the Taipower distribution system so that distribution engineers can determine the optimum locations and sizes of shunt capacitors to be installed.

In this paper, a simplified feeder model has been derived to accurately represent the equivalent circuit of the minor lateral branches of distribution feeders. While the feeder configuration is based on the major feeder branches for installing the shunt capacitors, the efficiency of the data processing for minor lateral branches can be enhanced. The following actions are then proposed to achieve the reactive power compensation more practically: 1. Several typical load patterns of residential, commercial and industrial customers are identified to simulate the variation of daily reactive power demand at each load bus according to the load demand and load composition. 2. An objective function consisting of peak loss, energy loss and fixedlswitched type capacitor cost as well as the operation constraints of bus voltage profile and real capacitor size are formulated with a nonlinear programming technique. 3. A three-phase load flow program which considers mutual coupling among conductors and imbalance phase loading is then developed to calculate the system power losses accurately to enhance the simulation results. By the above procedures, a practical capacitor planning strategy is derived in this paper to solve the requirements of fixed and switched capacitors to fit the reactive power demand of the study feeders. During the solution procedure, the load duration curve obtained from the daily load curve of the feeder under study is applied to decide the proper operation time period of the switched capacitors. Also, the sensitivity index of system loss is solved by three-phase load flow to determine the proper capacitor installation location. The optimum solution for capacitor planning is achieved when the total cost defined in the objective function is minimised and the operation constraints are satisfied.

athematical modelling of distribution feeders

The mathematical modelling of distribution feeder components affects the accuracy of computer simulation for shunt capacitor planning. Detailed models of the line conductor, including the mutual coupling effect, distribution transformers and voltage regulators [lo, 111 are considered in this paper. Because the shunt capacitors for reactive power compensation have been designed to be installed along the major branches of a feeder, the equivalent circuit models of minor lateral branches are derived so that the load characteristics, transformer core loss, line conductor impedance and transformer leakage impedance can be simplified significantly. The daily load profile of the study feeder is determined by the field test to represent the reactive power variation and the daily load duration curve for capacitor planning.

2. I patterns To represent the load behaviour more accurately, typical load patterns of specific customers residing along the feeders should be derived. In this study, six

Derivation of customer daily load

534

typical daily load patterns of selected customers for each season are determined to support the load evaluation of the hourly section loading. These are: one type of residential load; two types of commercial load; two types of industrial load; and one type of entertainmentileisure load customers. The power recorders are installed at each venue to collect the energy consumption during each 5 min time interval over 1 year. Figs. 1, 2 and 3, respectively, show the typical daily load curves of the residential, commercial and industrial customers on weekdayslweekends during the summer season. The peak loading of residential customers in Fig. 1 is at 11 pm. It is noted that the daily loading of commercial customers can be approximately divided into two levels, and the peak loadings of commercial customer types I and I1 occur from 10 am to 10 pm and from 7 pm to 5 am, respectively. For industrial customers, the load behaviour on weekdays and at weekends is quite different. For the type I1 industrial customer, the daily loading varies little due to the 24h continuous operation of its processes. The detailed procedure for deriving these and other customer load patterns can be seen in [l 11.

1 3 5 7 9 11 13 15 17 19 21 23 h

Fig. 1 -+-weekday -H- weekend

Daily load pattern of residential customer

01 I I I I I I I I I I I

1 3 5 7 9 11 13 15 17 19 21 23 h

Daily load pattern of commercial customers Fig. 2 -+-weekday I -W- weekend I -A- weekday I1 -X- weekend IT

A Taipower feeder usually serves a mixture of these types of customers at suburban and rural areas. The feeder daily load curves on weekdays and at weekends are quite different due to the significant load variation of main industrial customers. The hourly reactive power in a feeder’s daily load curve is then sorted in descending order to derive the daily load duration curves. The base loading, peak loading and corresponding time interval in the load duration curve

IEE Proc -Cener Trnnsm Distrib , VoI 144, No 6, November 1997

are then used to calculate the optimum VAr compensation by both fixed and switched capacitors.

01 I I , I I I , I I , I

1 3 5 7 9 11 13 15 17 19 21 23 h

Daily loud pattern of industrial customers Fig. 3 -+-weekday I -W- weekend I -A- weekday TI -X- weekend I1

2.2 Estimation of hourly section loading The estimation of hourly section loading directly reflects the load variation of the feeder sections and affects the accuracy of the capacitor planning strategy by computer simulation. It is not easy to calculate feeder section loading because the customer load characteristics and the load composition of the feeder sections are difficult to obtain. This paper presents a systematic method to calculate the hourly power loading of each feeder section by the derived customer load patterns stated above, load composition and customer billing data of a feeder. The percentage of each load customer and the power consumption of each feeder section are identified by field investigation according to the feeder circuit diagram and load distribution diagram. The 24h P, Q loading for feeder section i and customer j is determined by eqns. 1 and 2, respectively. According to the customer load pattern, the P, Q loading at hour t of customer j on feeder section i can be obtained by eqn. 3. Consequently, the hourly feeder section loading is computed by eqn. 4:

24

(P, Q ) i , t o t = C ( P , Q ) t x PTi

(P, Q)?,t,t = (P, &)$ , to t x PTtj%

(1)

(2)

t=l

b

(4) j=l

where: (P, (P, Q);,,,, is the 24h load of section i PT:h is the electricity percentage of section i P T l h is the electricity percentage of section i, customer

(P, e>$,, is the 24h load of section i customer j LDP6 is the load (p.u.) of customerj at hour t X24LDP,j is the 24h load (P.u.) of customer j (P , Q)1 is the P, Q load of section i, customer j at hour t.

is the P, Q load of section i at hour t

.i

2.3 Derivation of simplified lateral branch model The feeder in a distribution system often consists of voluminous customers with different load patterns, distribution transformers, and primary and secondary line conductors. It becomes very tedious for data collection and preparation. Because the capacitors for reactive power compensation are designed to be installed along the major feeder branches in the Taipower distribution system, it is necessary to represent the minor lateral branches by equivalent circuits to simplify distribution loss analysis and capacitor planning as shown in Figs. 4 and 5. For this lateral branch, a three-phase load flow program is executed to obtain total high tension line loss PLossl + jQLossl, total low tension line loss PLOss2 + jQLoss2, total transformer copper loss P,,,oss + J'QcuLoSs,

and core loss PcRLoss + jQcRLoss, respectively. The equivalent impedance of a high-tension line, RI, XI, a transformer winding, R,, X,, and a secondary feeder, R3, X3, are then solved by eqns. 5-11:

PLossi + ~ Q L O S S ~

I11 1, R1 + j X 1 =

PCULOSS + jQcULoss n

i=l

R2 + jx, = PCULOSS + ~ Q G U L O S S

I11 l2 PCRLOSS + ~ Q C R L O S S

n

~ ( P C R L O S S ~ + ~ Q C R L O S S ~ ) 2= 1

PCRLOSS + ~ Q C R L O S S

v2 I,= (

IL = I1 - IC

P L O S S ~ + ~ Q L O S S Z R3 +jx3 =

lILI2 PTOTAL L O A D + ~ Q T O T A L LOAD

n

i=l

Lot eral bronc h H.T. customer

A t r . 1 A t r . 2 tr.N "y"3OOkVA"y" A50kVA 1 850 kVA

load 1 load2 0 . 0 h

load N

I primary feeder

Fig. 4 Original feeder lateral branch configuration

where PLossl + jQLossl is the high tension lateral conductor loss PLoss2 + jQLoSs2 is the low tension lateral conductor loss PcuLossi + jQcuLossi is the copper loss of transformer i

535 IEE Proc-Gener. Trunsm. Distrib., Vol. 144, No. 6, November 1997

PcRLOssl + jQCRLOSSz is the core loss of transformer i P T o T A L LOAD + jQ,OTAL LOAD is the total load demand PLOAD2 + jQLOADl is the load demand at bus i 1, is the high tension lateral load current 1, is the low tension lateral load current 2, is the transformer core loss current. The total loads of the lateral branches are lumped together by eqn. 12. The resulting equivalent circuit of the lateral branch is represented in Fig. 5 .

primary feeder 0 R2

a core Loss i x3

total load

Fig.5 SimpliJed equivalent circuit of lateral brunch in one phase

3 Formulation of capacitor planning problem

In this study, both fixed and switched capacitors are considered to compensate the reactive power flow along the feeder. The fixed capacitors are determined according to the base loading and supply the reactive power all the time, while the switched capacitors are installed and switched on and off to supply the reactive power according to the feeder load duration curve.

Table 1: Cost coefficients in objective function

K, ($/kW-year) K, ($/kWh) K, ($/kVAr-year)

110.6 0.04 0.36

3. I Fixed capacitor planning The objective of capacitor planning is to find the optimum capacitor size, installation location and switched time period along the feeder so that (i) the real power loss during peak load period, (ii) the total energy loss over the study period and (iii) the capacitors’ equivalent installation cost can be minimised while the operation constraints are met. The objective function for the fixed capacitors is therefore expressed as eqn. 13. The coefficients in the equation are summarised in Table 1. Here, the coefficient K, is approximated by taking the fixed capacitor cost divided by its expectation lifetime, which is assumed to be 10 years in this study.

Minimize F = KpPLts + K,EL,,, + K,Q, ymzn - Iv,lI Alv,l 5 V y a z - 1x1

4

H(sz - P Q ~ ) = o (13) p= 1

Qz 2 0

where: Kp is the annual cost of per unit power loss ($lkW-

Ke is the cost of per unit energy loss ($lkWh) K, is the annual cost of per unit fixed capacitor ($1 kVAr-year) P& is the system peak power loss with fixed capacitors El,,, is the total system energy loss Q, is the total installed capacitor rating VImm, Vzmax are the lower and upper voltage limits V, is the bus voltage before compensation AV, is the bus voltage change after compensation

The hourly power loss can be expressed as a function of capacitor rating as shown in eqn. 14, and the energy loss is defined as the summation of the hourly real power loss during the period under study in eqn. 15:

Year)

n n

z = l j=1 r

T &ss = 1 p,,ss( t )dt (15)

where: PLoss is the system hourly power loss n is the total number of phase buses e,, €lo are the bus current angles after compensation eyi, Ovj are the bus voltage angles after compensation Q , Qj are the installed capacitor ratings at buses i, j Ici, Icj are the bus load injection currents after compensation Vci, Vcj are the bus voltage magnitudes after compensation VRi, VRj are the capacitor rated voltages PIoss(t) is the system power loss during hour t.

With respect to the constraints in this paper, the bus voltage limit can be simplified by the voltage variation after reactive power compensation, A Vi, which is related to the capacitor injection current and may be expressed as

\

From the viewpoint of practical implementation, the capacitor’s rating in the objective function is confined to be the actual discrete size.

3.2 Switched capacitor planning The objective function of reactive power planning by including the switched capacitors is expressed as eqn. 17, where NT is the duration over which the switched capacitor is committed. It is noted that the energy losses are calculated separately according to the

IEE Proc -Gene7 Transm Distrib , Vol 144, No 6, November 1997 536

operation of the switched capacitor. Also, the coefficient K,, is set to be twice the value of K, due to the installation of the timer device:

N T 24

t=l t=NT+l

(17) where Et$(t) is the total system energy loss with the switched capacitor 'off period E&(t) is the total system energy loss with the switched capacitor 'on' period K,, is the annual cost of the per unit switched capacitor ($/kVAr-year) Pl;& is the system peak power loss with fixed and switched capacitors.

4 Capacitor planning strategy

4.7 Sensitivity index The solution procedure for the optimisation of capacitor planning will become very complicated and difficult to solve if all the variables (size, location and switched time of the capacitors) are considered simultaneously. In this paper, the sensitivity index is applied to select the locations where the capacitors should be installed to achieve the largest loss reduction. The sensitivity index is obtained by placing one unit capacitor (300kVAr) at each bus along the feeder and examining the amount of real power loss reduction as in eqn. 14. The bus with the largest loss reduction is selected for the capacitor installation.

Since the daily load curves of the distribution feeders differ from each other and vary over a wide range, a capacitor planning strategy is proposed in this paper to properly compensate for reactive power flow over a daily load curve. The proposed method is divided into two solution stages. The first stage is to solve the size and location of fixed capacitors according to the base load of the reactive power curve, and the second stage is to determine the size, location and committed time of the switched capacitors according to the reactive power duration curve.

4.2 Procedure of fixed capacitor planning Step I : Derive the reactive power load duration curve by the typical load curve. Step 2: Based on the minimum reactive power load, (LDC),,,, the possible alternatives of capacitor ratings may be determined. Because three types of real capacitor rating - 300, 600 and 1200kVAr - are considered

for reactive power compensation in the Taipower system, the required compensated rating will be the multiples of 300 kVAr,

From the (LDC),, and N obtained, possible alternatives for fixed capacitor ratings are obtained as shown in Table 2. For instance, if 3.5 5 N I: 4.5, then 1200kVAr capacitor rating will be required for reactive power load compensation. The alternative with two sets of (600, 600) kVAr or with three sets of (600, 300, 300) kVAr can be selected. Step 3: For each alternative in Table 2, three-phase load flow is executed to calculate the sensitivity index of system loss to determine the installation location for each set of fixed capacitors. Step 4: Compute the total system cost for each alternative and select the one with the lowest cost.

4.3 Procedure of switched capacitor planning Step I : Apply a sensitivity index to select the installation location for each switched capacitor. Step 2: Add one unit set capacitor and calculate the cost change of the objective function, Acost and the corresponding switched time duration. If Acost < 0, go to next step, else repeat the process of reactive power compensation. Step 3: Calculate the total system cost TOTAL- COST(k) for the kth set capacitor during the time period obtained in step 2. If the change in total cost is larger than zero, return to step 1 for further compensation, else stop the compensation process, and the size, location and switched time of the switched capacitors are obtained.

5 Numerical results

In this paper, two Taipower distribution feeders which serve the mixture of industrial, residential commercial and leisure customers are selected for computer simulation to demonstrate the effectiveness of the proposed method. The simplified lateral branches have been derived, and are included in each bus of major feeder branches. Table 3 shows the data for feeders LY37 and BX33. The number of major line segments for feeders LY37 and BX33 are simplified to be ten and eight, respectively. The load composition is determined by the field survey, and the feeder load curves are solved by the field measurement [l 13. There are two types of commercial and industrial load customers, and one cus-

Table 2: Feasible alternatives for fixed capacitor planning

N Total rating (kVAr) One set (kVAr) Two sets (kVAr) Three sets (kVAr)

N < 0.5

0.55 N e 1.5

1 .51 N c 2 . 5

2.5 5 N < 3.5

3.5 5 N < 4.5

4.5 5 N e 5.5

5.5 5 N e 6.5

6.5 5 N e 7.5

0

300

600 -

1200 1500

1800

2100

0

300

600 -

1200 -

-

-

- - (300, 300)

(600, 300)

(600,600)

(1 200, 300)

(1 200, 600)

-

- - -

(300, 300,300) (600,300,300)

(600, 600, 300)

(600, 600, 600) (1200, 300, 300)

(1200,600, 300)

IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. 6, November 1997 531

Table 3: Data for feeders LY37 and BX33

Feeder Section

LY37 1

2

3

4

5

6

7

8

9

10

BX33 1

2

3

4

5

6

7

8

Conductor size

500xIpe

477AL

477AL

477AL

477AL

477AL

477AL

477AL

477AL

477AL

500xIpe

477AL

477AL

477AL

477AL

477AL

477AL

477AL

Length (m)

1830

780

630

I010

2320

950

270

770

810

890

370

340

390

1020

770

310

590

410

Load composition (%)

Residential Commercial I Commercial II Industrial I Industrial II Culture

80 0

60 20

50 20

50 0

70 0

40 0

0 0 60 0

40 0

30 0

20

0

30

10

20

0

10

0

0 0 0 20

0

0

20

0

20

0 10

20

0

0

0 0 0

0

0 0

0

0

20

10

10

10

50

20

0

10

50

100

60

50

80

100

90

50

0

10

0

0

0

0 0

0 0

30

0

10

40

0 0

0

50

20

0

20

20

30

50

10

40

60

0 0

0

0 0

0

0

0

Table 4: Capacitor installation and corresponding operation strategies

Operation time Location busilength (m)

Feeder Time period Type Size

LY37 fixed 600 28/8640 -

weekday 600 16/6080 summer 300 10/3360

switched 1200 12/4400

fixed

weekend summer

switched

fixed

weekday nonsummer

switched

fixed

weekend nonsummer

switched

600

600

300

600

600

600

300

1200

600

600

300 -

28/8640

1616080

1013360

2/960

2818640

16/6080

1013360

12/4400

2818640

16/6080

10/3360 -

- - BX33 fixed

weekday switched 1200 18/5760

summer 1200 12/2760

600 611320

- - weekend fixed summer switched - -

- - fixed weekday nonsummer switched 1200 1815760

1200 12/2760

fixed - - weekend n ~ r m ” r switched 600 U720

-

8-12, 13-22

-

18-2 1

-

8-20

-

8-12, 13-18

8-12, 13-17

9-17

8-12, 13-18 8-12, 13-17

-

8-12, 13-17

538 IEE Proc -Gener Transm Dzstrzb , Vol 144, No 6, November 1997

Table 5: Results of cost saving by proposed method for test feeders, $

0.90-

Feeder LY37 BX33

Time Period Summer Nonsummer Summer Nonsummer

peak loss cost 17033 14621 10295 7802

Without energy loss cost 35446 32489 9569 8657

compensation capacitor cost 0 0 0 0

total cost ( i) 52479 47110 19864 16459

peak loss cost 12080 10931 6415 4957

With energy loss cost 25598 23174 6606 5819

compensation capacitor cost 1227 1227 1674 1339

total cost (i i) 38905 35332 14695 12115

Net saving (i)-(ii) 13574 11778 5169 4344

Annual cost saving 25352 9513

tomer type for both residential and leisure loads in the feeders under study. By performing the computer simulation, the optimum size, location and switched times of the shunt capacitors are calculated and the resulting cost saving and improvement of power quality are determined.

Table 4 shows the capacitors installed and the corresponding operation strategies for feeders LY37 and BX33. For feeder LY37 during weekdays in summer there are three fixed capacitors with ratings of 600, 600 and 300kVAr installed at buses 28, 16 and 10, respectively, to obtain the reactive power compensation for the minimum reactive power load. The length meas- ured from the substation outlet also shows the location to install the capacitor efficiently for the field test. Moreover, one switched capacitor with 1200kVAr rating is installed at bus 12 to compensate the reactive power from 8 to 12am and from 13 to 22pm. Since the base loading of the reactive power load pattern in each different time period was varied consistently, all the operation strategies for the fixed capacitor are equal. For feeder BX33 in summer, there is a set of three switched capacitors with 1200, 1200 and 600kVAr rating installed at buses 18, 12 and 6, respectively, to compensate reactive power levels for different time periods. Because the base loading of the reactive power of feeder BX33 is very small during summer weekends, no fixed capacitors are required.

To verify the effectiveness of the proposed strategy, several power meters are installed at the selected load bus along the major feeder branches to measure the variation of power consumption, voltage profile and power factor of the tested feeders over one year. Table 5 shows the cost saving obtained by the proposed method over a I year period. The equivalent cost of peak loss and energy loss as well as the capacitor cost are considered. The total costs of feeder LY37 during the summer and nonsummer seasons are reduced from $52 479 to $38 905 and from $47 110 to $35 332, respectively, which means that cost savings of $13 574 and $1 1778 have been obtained. The annual cost savings of feeders LY37 and BX33 are $25 352 and $9513. Fig. 6 shows the daily power loss of the feeder LY37 without and with compensation during the summer season A significant loss reduction has been achieved by the proposed reactive power compensation. Figs. 7 and 8 represent the daily power factor and bus voltage, respectively, of feeder LY37. It is found that both the average power factor and the voltage profile

have been improved from 0.89 to 0.99 and from 0.923p.u. to 0.978p.u., respectively.

2 L 6 8 10 12 1L 16 18 20 22 2L h

Fig.6 W without compensation 0 with compensation -+- loss reduction

Result of dudypoiver loss of jeeder LY37

0.96 I ' O 0 h

0.80 o.8LL 2 L 6 8 10 12 1L 16 18 20 22 2 L

h Fig. 7 Result of power factor of feeder L Y37 -+- without compensation -.- with compensation

0.88l I

1 2 3 L 5 6 7 8 9 1 0 1 1 bus no.

Fig.8 -+- without compensation -m- with compensation

Result of bus voltage offeeder LY37 ut peuk loading

IEE PuoccGener. Transm. Distrib., Vol. 144, No. 6 , November 1997 539

6 Conclusion

This paper has developed a systematic procedure for feeder capacitor planning to improve the feeder power quality for distribution systems. More precise modelling of distribution systems has been derived so that the mutual coupling effect between phase conductors, feeder configuration with different laterals and three- phase imbalance loading are all included in the three- phase load flow analysis to enhance the accuracy of the proposed reactive power compensation strategy. The simplified feeder modelling technique based on three- phase load flow has also been developed and applied to derive the equivalent circuits of minor lateral branches in the feeder to simplify the procedure of data preparation. The objective function, which consists of peak power loss, energy loss and capacitor cost, and the constraints of bus voltage profile and practical discrete capacitor size, are formulated as the quadratic function of capacitor rating at each bus. The customer load patterns and feeder load curves derived by the field test are applied to estimate the hourly section loading accurately.

In the first stage of the solution procedure, the size and installation location of fixed type capacitors are determined according to the base reactive power load. The size, installation location and commitment time of switched type capacitors are then solved to properly compensate the reactive power duration curve. During the problem solution process, a sensitivity index is applied to determine the installation location where the lowest real power loss can result from reactive power compensation.

To verify the effectiveness of the proposed reactive power compensation, two practical Taipower distribution feeders have been selected for computer simulation. It is found that the energy loss and operation cost can be significantly reduced and the power quality can also be improved. It is concluded that the proposed method does provide better capacitor

planning for distribution engineers to enhance the operation efficiency of distribution systems by improved reactive power compensation.

7 Acknowledgments

The authors gratefully thank the Business Department of Taipower Company for providing valuable data and excellent discussion. The financial support for this work from National Science Council, contract NSC 86- 2213-E-151-003, is also highly appreciated.

8

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2

3

4

5

6

7

8

9

10

11

References

MILLER, T.J.E.: ‘Reactive power control in electric system’ (John Wiley & Sons, Inc., New York, 1982, 1st edn.) BARAN, M.E., and WU, F.F.: ‘Optimal capacitor placement on radial distribution systems’, IEEE Trans., 1989, P D 4 , (l), pp. 725-734 BARAN, M.E., and WU, F.F.: ‘Optimal sizes of capacitors placed on a radial distribution systems’, IEEE Trans., 1989, PD-

CHEN, C.S., SHU, C.T., and YAN, Y.H.: ‘Optimal distribution capacitor placement considering mutual coupling effect of conductors’, IEEE Trans., 1995, PD-10, (2), pp. 987-994 GRAINGER, J.J., and LEE, S.H.: ‘Optimum size and location of shunt capacitors for reduction of losses on distribution feeders’, IEEE Trans., 1981, PAS-100, (3) , pp. 1105-1118 GRAINGER, J.J., and CIVANLAR, S.: ‘Volt/VAr control on distribution system with lateral branches using shunt capacitors and voltage regulators. Part I: The overall problem’, IEEE Trans., 1985, PAS-104, (l l) , pp. 3278-3283 CIVANLAR, S., and GRAINGER, J.J.: ‘Volt/VAr control on distribution system with lateral branches using shunt capacitors and voltage regulators. Part 11: The solution method’, IEEE Trans., 1985, PAS-104, ( l l ) , pp. 3284-3290 CIVANLAR, S., and GRAINGER, J.J.: ‘Volt/VAr control on distribution system with lateral branches using shunt capacitors and voltage regulators. Part 111: The numerical results’, IEEE Trans., 1985, PAS-104, ( l l ) , pp. 3291-3297 WU, Z.Q., and LO, K.L.: ‘Optimal choice of fixed and switched caoacitors in radial distributors with distorted substation voltaee’.

4, (l), pp. 735-738

I k E Proc -Gener Transm Distrib , 1995, 142, (I), pp 24-28 CHEN C S , HWANG, J C , CHO M Y , and CHEN, Y W ‘Development of simplified loss models for distribution system analysis’, IEEE Trans.,, PD-9, (3) , pp. 1545-1551 CHEN, C.S., HWANG, J.C., TZENG, Y.M., and CHO, M.Y.: ‘Determination of customer load characteristics by load survey system’, IEEE Trans., 1996, PD-11, (3), pp. 1430-1437

540 IEE ProcGener. Transm. Distrib., Vol. 144, No. 6, November 1997

Documents

Fixed/switched type shunt capacitor planning of distribution systems by considering customer load patterns and simplified feeder model