Series capacitor compensation for radial distribution networks (PDF ...

2011 IEEE PES Innovative Smart Grid Technologies – India

Series Capacitor Compensation for Radial Distribution Networks Sangeeta Das

D. Das

Department of Electrical Engineering Indian Institute of Technology Kharagpur 721302 [email protected]

Department of Electrical Engineering Indian Institute of Technology Kharagpur 721302 [email protected]

Abstract—Poor voltage regulation is a bane on our distribution system. This paper presents a technique of finding out the optimal values of compensation factors, of series capacitors, using genetic algorithm, placed in a radial distribution system. The voltage profile, active losses and the annual savings with series capacitors on different loading conditions (peak load, nominal load and light load) are discussed. The suggested method is optimized using genetic algorithm and is programmed using MATLAB software. Index Terms—Series capacitors, genetic algorithm, voltage profile, annual savings.

NOMENCLATURE • • • • • • • • • • •

Vi : voltage at the ith node Vi+1 : voltage at the (i+1)th node Zi : line impedance of the branch connecting ith and (i+1)th node and is equal to ri + jxi Pi : total real power load fed through the ith node Qi : total reactive power load fed through the ith node Pi+1 : total real power flow from(i+1)node Qi+1 : total reactive power flow (i+1)node Sl,i : total load at ith node and is equal to Pl,i + jQl,i Sl,( i+1): total load at (i+1)th node NB : total number of buses : current flowing in the branch connecting node Ii i and node i+1.

I.

INTRODUCTION

Poor voltage is one of the significant problems in distribution systems. Series capacitors tend to overcome this problem. When placed in a distribution system, they serve two main functions; to reduce the voltage drop and to reduce the active losses. Several papers [1 - 13] are available in the literature for the optimization of shunt capacitors in radial distribution systems but use of series capacitors in distribution 978-1-4673-0315-6/11/$26.00©2011 IEEE

systems remain untouched. The theory of series capacitors is very simple and is easily understood. The negative value of the capacitor reactance is used to cancel a major portion of the positive reactance of the line in a series connection. With the effective line impedance reduced, the voltage profile is greatly improved. At the same time, the active losses are reduced. A series capacitor regulates the voltage by directly offsetting the inductive reactance of the circuit to which it is applied [12]. A series capacitor can even be considered as a voltage regulator that provides for a voltage boost which is proportional to the magnitude of the current flowing through it. A series capacitor provides for a voltage rise which increases automatically and instantaneously as the load grows. The placement of series capacitors come with its own positive and negative side effects for both utility and customers. So certain precautions are to be taken and they are discussed in this paper. The basic objective of placing series capacitors on a distribution network is the voltage profile improvement along with minimization of active losses. For optimization of such a problem, the genetic algorithm (GA) optimization search technique is used. GA is a population based computerized search technique based on the mechanics of natural genetics and natural selection. It starts its search within the search space and finds out the most optimal value of the capacitor to be placed in the distribution network. GA is popular in solving optimization problems in different fields of applications mainly because of its robustness in finding optimal solution and ability to provide near optimal solution close to global minimum [11]. II.

METHODOLOGY

For series capacitors optimization, a load flow program for solving radial distribution network is necessary. The methodology for running the load flow under the general case where only a radial feeder is considered is discussed first. 1

2

3

4

5

s/s

First, that you have the correct template for your Pi + jQconfirm i Fig.1: five node sample distribution network


Later a general case is discussed. Figure 1 shows a 5 node sample radial distribution network and figure 2 shows the electrical equivalent of ith branch of fig. 1. V

can be placed depending on the descending order of the voltage drop in the entire network. X1

V i+1

X2

X3

X4

Zi Pi + jQi Xc

Pl,(i+1) + jQl,(i+1)

Fig.4. Sample radial distribution feeder with a series capacitor in branch 3

Fig. 2. Electrical equivalent of ith branch of fig. 1. From fig. 2, the following equations can be written, Pi+1 = Pi - (ri * (Pi2 + Qi2) / |Vi|2) - Pl,i+1 Qi+1 = Qi - (xi * (Pi2 + Qi2) / |Vi|2) - Ql,i+1 Ii = Pi - jQi / Vi* Vi+1 = Vi - IiZ i

(1) (2) (3) (4)

The following assumptions are considered for the load flow program: • V1: substation voltage • S1: substation power • S1 = P1 + j*Q1 • P1 = ∑NBj=2 Pl,i + active losses of the entire network • Q1 = ∑NBj=2 Ql,i + reactive losses of the entire network Note that node 1 is substation. After every iteration, the active and reactive power losses are added to the substation load. If the distribution system has a radial feeder along with lateral branches (fig 3) , then the same process of formulation applied to the main feeder can be repeated for the lateral by using the line flow equations mentioned from (1) to (4). 5

7

6

From fig. 4, the following equations can be written, X E = total inductive reactance from the source to the location of the series capacitor. XE =∑mj=1 xj where ‘m’ is the branch where the series capacitor is connected. X c = reactance of the series capacitor. We need to define a quantity ‘k’ called as the percent of compensation. ‘k’ is defined as k = (X C) / (X E) * 100(%) The compensation should lie in between 0 to 100%. The compensation should lie in between 0 to 100%. A value of ‘k’ greater than 100% means XC > XE is called overcompensation. The recommended practice is not to overcompensate. Overcompensation increases the risk of ferro resonance. Therefore, if overcompensation is considered, a careful review of the possible problems that might occur is recommended. After the insertion of the series capacitor, the load flow is made to run as before. IV.

1

2

3

4

In view of the above, main objective of the present work

8

are

s/s

9

10

11

12

Fig.3. Sample radial distribution feeder with lateral branches III.

OBJECTIVE FUNCTION

• to improve voltage profile • to reduce active losses • maximization of the annual energy cost savings. These goals are to be met satisfying a few constraints. • Losses after installing series capacitors should be less than losses before

• •

The voltage at the nodes must be within the voltage limits. The branches where the series capacitor is installed should not be over compensated.

PLACEMENT OF SERIES CAPACITORS

The series capacitor is placed in that branch of the network where the voltage drop is maximum. More than one capacitor

Hence the objective function for optimization can be stated mathematically as


Minimize F = sploss Subject to 0.0< k < 1.0 where sploss: total real power loss in a network, k: factor of compensation. The factor of compensation should lie in between 0.0(i.e. 0%) and 1(100%). The optimization is carried out for three different cases: a) Peak load : 100% of the loads. b) Nominal load: 60% of the peak loads. c) Light load : 40% of the peak loads. To run this objective, GA is used. Here the purpose of GA is to determine the optimal value of the capacitors to minimize the active losses .The fitness value i.e. sploss should be non negative. The compensation value should lie in between 0 & 1. The initials binary strings (chromosomes) are nothing but the factor of compensation. The factor of compensation for each capacitor is taken to be 10 bits thereby allowing the value of series capacitors to vary from 0 to 1023 kVAr. The 10 bits string is reduced to its decimal value lying in between 0 to 1 by using the equation ki = ki min + Di * (ki max – ki min) /(2λ – 1)

(5)

where ki min = minimum value of the factor of compensation i.e 0.0 k i max = maximum value of the factor of compensation i.e. 1.0 λi = length of the binary string (here the length of the binary string is assumed to be 10.) Di = binary value of the capacitor decoded to the decimal value pertaining to a particular population. V.

ALGORITHM

To satisfy the stated objective, the load flow is made to rum every time. The computer program is written and run on MATLAB 2010a software with 2.10 GHz clock. The procedure is considered as below: Step 1: • Form the initial binary strings (chromosomes) equal to the population size. Step 2: • • •

•

Evaluation of the fitness function: Convert the binary string into a decimal number. Use equation (5) to get a value in between 0.0 and 1.0. Run the load flow using the parameters obtained above to find out the power loss and the capacitor values. Arrange the capacitors values obtained in the ascending order of power loss.

Step 3: • Calculate the probability of each fitness obtained • Generate copies of the individuals based on their probability. These individuals are selected for mating in the mating pool. Step 4: • From the mating pool formed, select two parents. • Perform single point crossover and generate two offsprings. • Mutate these offsprings to bring out diversity in the new generation. Step 5: • Combine the present population with the offsprings generated. • Calculate the fitness value of each individual. • Select the best individuals for the next generation based on their fitness value keeping the population size intact. • Increase the generation count and move on to the next generation. In the present work, this process continues for the maximum generation set. This process was repeated for all the three types of loads. Following assumptions are taken in the above said algorithm: • An appropriate population size should be considered. Very small population size leads to premature convergence and very large size leads to unacceptably slow rate of convergence. Population size of about 60 was taken. • The crossover point and mutation point was randomly generated in between bit 5 to bit 7 for a 10 bit binary string for better optimized results. • The population size was kept constant at every generation. VI.

ANALYSIS

The above stated methodology was tested for a 10 node radial distribution system and for a 69 node lateral distribution system [6, 14]. The use of series capacitors was carried out at three places in each system. The systems were made to run for three load levels: peak (1.0), nominal (0.6) and light (0.4) load level. It has been found that with the use of series capacitors on three branches i.e branch 5, 3, 8 in a 10 node system, the voltage has improved from 0.837533 pu to 0.8774 pu at peak load level. The active losses have reduced from 783.6 kW to 722.19 kW for 100% loading in the network. At nominal load

2011 IEEE PES Innovative Smart Grid Technologies – India Load Level Peak Nominal Light

Load Level Peak Nominal Light

Compensation factors of Series Capacitors Branch 5 Branch 3 Branch 8 1.000 0.999 0.935 0.998 0.995 0.934 1.000 0.937 0.903

TABLE -1. Voltage magnitude (pu) Before After 0.873 0.877 0.909 0.929 0.941 0.954

Loss Reduction (kW) Before After 783.60 722.19 251.03 240.90 106.15 103.57

Annual Savings (Rs)

Compensation factors of Series Capacitors Branch 58 Branch 59 Branch 7 1.000 0.997 0.999 0.998 1.000 0.995 0.935 0.999 0.992

TABLE -2. Voltage magnitude (pu) Before After 0.909 0.947 0.948 0.969 0.966 0.979

Loss Reduction (kW) Before After 224.90 209.62 75.51 72.59 32.49 31.71

Annual Savings (Rs)

level, the voltage improved from 0.909 pu to 0.929 pu. And at light load level, the voltage improved to 0.954 pu. Similar observations were seen for the 69 node system [14]. The series capacitors were placed at branches 58, 59 and 7. The voltage improved from 0.909 pu to 0.947 pu at peak load level along with the reduction of losses from 224.9 kW to 209.62 kW. At nominal load level, the voltage improved from 0.948 pu to 0.969 pu. And at light load level, the voltage improved to 0.979 pu. With the use of series capacitors in the distribution system, there has been a significant improvement not only in the voltage profile but also in the reduction of losses. There has been savings in both the systems. The cost figures adopted are as follows: Ke = Rs 5/ kWhr Kc = Rs 400 /kVAr where Ke : cost of energy charges Kc : capacitor charges Peak hours in a year = 1000 hrs Nominal hours in a year = 6760 hrs Light load hours in a year = 1000 hrs Table 1 shows the values after placement of series capacitors for a 10 node system. Table 2 represents the values for a 69 node system after placement of series capacitor. Note that the reactive power delivered by the series capacitor depends on the current flowing through it. Rating of the series capacitor has been selected based on the reactive power delivered at the peak load level. However, reactance of series capacitor at any load level will remain unchanged and it was also observed during the optimization process. Therefore, for series capacitor optimization problem, one should optimize the value of compensation factor at each load level of series capacitor where it is connected. Considering all the three cases, annual cost savings a for 10 node system was found to be Rs.2,44,432 and for a 69 node system, it is Rs.87,978. VII. ISSUES The placement of series capacitors comes with its own positive and negative side effects for both utility and customers. With the use of series capacitors, the effective line impedance is reduced and the voltage profile is greatly improved. However, the series capacitors can become a problem when a fault occurs on the load side of a capacitor

2,44,431.9

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bank. So there is a requirement of a protective device. To eliminate these undesirable effects, it is necessary to completely bypass the capacitor during the occurrence of a fault. The bypass system will bypass the series capacitor in case of high current line faults downstream from the series capacitors. Overcompensation is to be avoided for the risk of ferro resonance. VIII. CONCLUSIONS GA has been successfully implemented for obtaining the optimized results of series capacitors. The positive effects provided by series compensation like improved voltage profile, reduced losses and annual cost savings were achieved. If the load varies frequently, then the series capacitor provides the best means as the voltage rises automatically as the load grows. Series capacitors have been placed applied on distribution circuits for over fifty years [12]. Many of these applications have been to reduce voltage variations associated with saw mills, rolling mills, crushers, mines and ski lifts. Motor starting is often one of the causes of the voltage variations. It is true that for high tension transmission lines, X/R ratio is high and series capacitors are suitable. But the examples considered for the present work also shows that the series capacitor improves the voltage and reduces the losses. Utilities may consider placement of series capacitors in a distribution system. It is true that the shunt capacitors reduce the losses, though not much they improve the voltage profile. But it has been seen here that the series capacitors improve the voltage, though not much they reduces the losses too. After placement of shunt capacitors, if the voltage is not improved to the acceptable limits, then series compensation would be more effective to raise the voltage levels. REFERENCES [1] J.J.Grainger and S.H.Lee, “Optimum Size and Location of Shunt Capacitors for Reduction of Losses on Distribution Feeders”, IEEE Transactions on Power Apparatus and Systems, vol. PAS-100, no. 3, pp 11051118, 1981. [2] J.V.Schmill, “Optimum size and location of shunt capacitors on distribution feeders”, IEEE Transactions on Power Apparatus and Systems, vol. 84, no. 9, pp. 825-832, 1965. [3] H.Duran,“Optimum number, Location, and Size of Shunt Capacitors in Radial Distribution Feeders: A dynamic programming approach”, IEEE

2011 IEEE PES Innovative Smart Grid Technologies – India Transactions on Power Apparatus and Systems, vol. PAS-87, no.9, pp. 17691774 , 1968. [4] N.E.Chang, “Locating shunt capacitors on primary feeder for voltage control and loss reduction”, IEEE Transactions on Power Apparatus and Systems, vol. PAS-88, no. 10, pp. 1574-1577,1969. [5] M.Ponnavaiko and K.S.Prakasa Rao, “Optimal choice of fixed and switched capacitors on radial distributors by the method of local variations”, IEEE Power Engineering Review, vol. PER-3, no. 6, pp. 35-36, 1983. [6] M.E.Baran and F.F.Wu, “Optimal sizing of capacitors placed on a radial distribution system”, IEEE Transactions on Power Delivery, vol. 4, no. 1, pp. 735-743, 1989. [7] M.E.Baran and F.F.Wu, “Optimal capacitor placement on radial distribution systems”, IEEE Transactions on Power delivery, vol. 4, no. 1, pp. 725-734, Jan 1989. [8] H.D.Chiang, J.C.Wang, O.Cockings and H.D.Shin, “Optimal capacitor placements in distribution systems. I. A new formulation and the overall problem”, IEEE Transactions on Power Delivery, vol. 5, no. 2, pp. 634-642, 1990. [9] Hsiao-Dong Chiang, Jin-Cheng Wang, Jianzhong Tong and G.Darling, “Optimal capacitor placement, replacement and control in large-scale unbalanced distribution systems: system solution algorithms and numerical studies”, IEEE Transactions on Power Systems, vol. 10, no. 1, pp. 363-369, 1995. [10] M.A.S.Masoum, M.Ladjevardi, A.Jafarian and E.F.Fuchs, “Optimal placement, replacement and sizing of capacitor Banks in distorted distribution networks by genetic algorithms”, IEEE Transactions on Power Delivery, vol. 19, no. 4, pp. 1794-1801, 2004. [11] D.Das, “Reactive power compensation for radial distribution networks using genetic algorithm”, Electrical Power and Energy Systems, vol. 24, pp. 573-581, 2002. [12]S.A.Miske, “Considerations for the application of series capacitors to radial power distribution circuits”, IEEE Transactions on Power Delivery , vol. 16, no. 2, pp. 306-318, 2001. [13] Y.G.Bae, “Analytical Method of Capacitor Allocation on Distribution Primary Feeders”, vol. PAS-97, no. 4, pp. 1232-1238, 1978. [14] M.Chakravorty and D.Das, “Voltage stability analysis of radial distribution networks”, International Journal of Electrical Power and Energy Systems, vol. 23, no. 2, pp. 129-135, Feb 2001.