A novel approach for optimal allocation of fault current

21st Electrical Power Distribution Conference May 2016, Karaj- Alborz- Iran .

A novel approach for optimal allocation of fault current limiter in distribution system via combination of particle swarm optimization algorithm and genetic algorithm (PSOGA) Ali Mahmoudian

Mohsen Niasati

Faculty of Electrical Engineering, Semnan University Semnan, Iran [email protected]

Faculty of Electrical Engineering, Semnan University Semnan, Iran [email protected]

Abstract—Nowadays, power systems expansions are undeniable due to increase in power demands. This fact has caused the increase in short circuit level of power networks. So that, The occurrence of short circuit in such networks results in a large short circuit current throughout the system, which may exceed the rating of existing circuit breakers and damage power system equipments. There are some approaches to reduce and suppress this fault current such as power network reinforcement, equipment rating update, utilization of fault current limiter (FCLs) in power system and etc. Because of difficulty and non economic justification in some cases of power network reinforcement, the utilization of FCLs is effective way to limit and suppress fault currents. FCLs utilization have many benefits, such as power network reliability improvement, voltage stability and short circuit current limitation. But this effectiveness depends on rating, number and installation location of FCLs. In this paper, the authors providing a heuristic optimization algorithm that combined particle swarm optimization algorithm (PSO) and genetic algorithm (GA) so that has more effectiveness rather than both of PSO and GA to determine the optimal rating, number and location of FCLs to improve the power network reliability and fault current reduction. IEEE 30 bus system and IEEE 34 node system are considered to evaluate the effectiveness and feasibility of the proposed method. The objective functions considered for the optimal allocation are reliability of power system, economical impact and short circuit current reduction.

Keywords- Fault ;FCL; Reliability; Short circuit current; Distribution systems.

I.

INTRODUCTION

Nowadays, with the increasing demand for electric energy, Connection of distributed generation (DG) to the grid and the emergence of new technologies causes power systems have become greater and more complex, as a result the value of fault current increases in some cases, may exceed the ratings of

existing circuit breakers (CBs) and damage system equipment [1]. It is necessary to use circuit breakers with higher breaking current. This, in turn imposes heavy costs on the system. The problems of inadequate CB short-circuit ratings have become more serious when current CBs have the highest rating of the CB available in the market has been used. FCLs are elements that are placed in series with the network equipment to reduce the level of short circuit current during a fault. This equipment normally reveals little resistance against the flow of the current; however, after the short-circuit and in the initial moments after fault, their resistance suddenly increases which prevents raising the short circuit current [2, 3]. Limiters do not cause voltage sag and power loss in the steady state conditions of the system [4]. In addition to the short-circuit current limitation, studies have shown that the use of FCLs in power network allows the incensement in the transient stability of generators and consequently the global stability of the network [5-8]. Previous studies on FCL optimal allocation mainly focus on one objective function either fault reduction as in [911] or stability as in [7, 11]. References [12] and [13], hierarchical genetic algorithm (GA) combined with a micro GA was used to find the optimum locations of FCLs. In [10], authors used a search space reduction technique and GA to find the optimum number and locations of FCLs. Another approach has examined the Influence of fault type on the optimal location of superconducting fault current limiter in electrical power grid [8]. Eigen value analysis is also used to optimize resistive SFCL for multi-machine power system [14]. In this paper, in order to optimally allocate the FCLs in a power system, three objectives functions are considered. The objective functions considered in FCL placement problem are: (a) improving reliability; (b) economical use of FCLs and (c) minimizing the short-circuit current. The benchmark problems considered are modified IEEE-30 Bus and IEEE-34 Node.

In this paper, authors in order to reach optimal placement of FCLs propose PSOGA algorithm that combined particle swarm optimization (PSO) algorithm and genetic algorithm (GA). The proposed algorithm have better convergence rate than both of PSO and GA. II.

FAULT CURRENT CALCULATION AND FCL IMPEDANCE REDUCTION EFFECT

Albeit most power system faults are unsymmetrical, three phases symmetrical fault are used to specify the rating of circuit breakers due to it is the worst type of faults. For a balanced three-phase fault at bus i, the short-circuit current can be calculated by I isc 



Ei *Ib  Z ii



where I isc is the three-phase short-circuit current at bus i and Ei is the voltage before the fault at bus i. Commonly, Ei can be set as 1.0 p.u. Zii is the diagonal impedance of the impedance matrix (Zbus). Ib is the base current [10]. When adding a line with impedance Zb between buses j and k, each element of Zbus can be modified as [10]:



new old z xy  z xy 

(z xj  z xk )(z z

jj

jy

 z kk  2z

 z ky ) jk

 zb





old

where and Z Zbus, respectively.

xy



Figure 1. Thevenin equivalent when line is added between k and j buses.

Fig.2 represent the Thevenin equivalent circuit when an FCL with impedance Zfcl is installed on line between buses k and j and fired after the faults [10]. Therefore, the modification to the diagonal entries of Zbus after the FCL fired up at a branch between buses j and k is as following equation:

 

Znewxy



are the modified and old elements of

z ii  

(z ij  z ik )2 z

jj

 z kk  2z

jk

z p



In addition, the effect of inserting the impedance Zb series with the transmission line can be considered as a parallel impedance Zp with the network which can be obtained by the following equation:



z p  (z b ) / /(z b  z fcl )  

z b (z b  z fcl )  z fcl

(3)

Fig.1 represents the Thevenin equivalent by looking into the system from two existing buses when impedance Zb is added between them.

Figure 2. Thevenin equivalent circuit in the presence of FCL



III. UNDER STUDY NETWORKS INTRODUCE In this paper, there are two case studies that involve IEEE-30 buses system and IEEE-34 nodes system. These systems description are as follows. The IEEE-30 bus system has 6 generators, 21 load buses and 41 transmission lines [15]. The single line diagram of the system is depicted in Fig.3.

Installation of FCL in the power system can improve the network reliability. The addition of a new device in series with a system results in the weakening of the reliability of the system [17]. However, FCL lessens the failure rate of devices by decreasing the frequency of the excessive fault current [18, 19]. The improvement made by the FCL depends on its installation location. There are various reasons that cause a fault to fail in a protective equipment such as degraded operation, worn, arcing, and fault current [20]. Since optimal allocation of FCLs results in fault current reduction and it does not influence other failure rate terms, the main concern of the current paper is fault current.



0, k ,f  0, k ,f 0, k ,f



fault current worn

 0, k ,f degraded operation 

 0,k ,f arcing  ...

l ,k ,f  0,k ,f  0,k ,f

fault current

l ,k ,f 

 



Equation (6) represents the failure rate for failure event f at kth

Figure 3. Single line diagram of IEEE 30 buses system.

IEEE-34 nodes system is an actual feeder located in Arizona, with a nominal voltage of 24.9 kV. It is characterized by long and lightly loaded, two in-line regulators, an in-line transformer for short 4.16 kV section, unbalanced loading, and shunt capacitors [16]. The single line diagram of the system is depicted in Fig.4.

load after installing FCL in the lth line. 0, k ,f fault current is the failure rate that is only caused by fault current for failure event f at kth load when FCL does not exist in a network (l = 0). ηl,k,f is the fault current reduction efficiency of failure rate for failure event f at kth load when FCL is installed in the lth line[20]. 2) Estimation of system reliability There are various indices to evaluated system reliability such as system average interruption frequency index (SAIDI), Average service unavailability index (ASUI) and average energy not supplied (AENS). But all characteristics of a system cannot be considered by one of these system reliability indices. Therefore in this paper, weighted load reliability index (WLRI) which considers the effects of aforementioned indices is used to estimate the system reliability [20]. Equations (7) and (8) represent this index. 3

 Figure 4. Single line diagram of IEEE-34 Node system.

IV.

PROBLEM FORMULATION

The problem of FCL optimal allocation is a nonlinear optimization problem, and may include several objectives. This paper objective function is including reliability enhancement, the economical use of FCL and the short circuit current level reduction. These objective functions can describe as follows: A. Improvement of reliability 1) Influence of fault current limiter on system reliability

W LRI l ,k 

 w m R (m , l , k )  m 1





FCL circuit parameters for economical purposes [11]. These objective functions can be formulated as follows:



R (m , l , k ) 

 f  failure events l ,k ,f N k k  k 1 N k  f  failure events rl ,k ,f l ,k ,f N k k 8760 N k 1 k  f  failure events rl ,k ,f l ,k ,f pk k  k 1 N k



(m=1) N fcl



f2

(m=2)

(m=3)



 i 1 z i ,fcl  z fcl expected +pf (x )  z fcl expected

 

In (7) and (8), wm is the normalization factor for the value of mth reliability index, and Nk, rl,k,f , Pk are the number of customers, the repair time, and the amount of electric demand power, respectively.

f 3 (x ) 

N fcl  N fcl expected N fcl expected

z









where Zi,fcl and Nfcl are the impedance of the ith FCL and the number of fault current limiter used in the system, respectively. Zfclexpected and Nfclexpected are the expected impedance of FCLs and the expected number of FCLs injected in the system, respectively. pfz is penalty factor and is defined as follows:

This objective function is as follows: if z i ,fcl min  z i ,fcl  z i ,fcl max

RS (X ) f 1 (x )   RS (X  0)







i=1...N fcl



then pf z  0 else

pf z  max((z i ,fcl  z i ,fcl min ), ( z i ,fcl max  z i ,fcl ))

where:

K



RS (x ) 

w k W. LRI (X , k ) 



k 1

and

wk 

CIC of k th load point  average CIC of all types of customers

C. Fault current minimization In most papers, main objective of FCL utilization is fault current minimization [8, 10, and 22]. Despite the most power system faults are unsymmetrical; three phases symmetrical faults are used to specify the rating of circuit breakers because it is the worst type of faults. This objective can be formulated as follows:

 



X  [X 1 , X 2 ], X1  [sl1 , sl 2 ,..., sl n ], X 2  [z 1,fcl , z 2,fcl ,...z n ,fcl ]





where RS is an index that determine the effect of installation location of FCL on the system reliability. wk is a weighting factor which indicates the significance of kth load and is determined by considering customer interruption cost of each customer [21]. X is a 2n-dimensional vector which represents the location and impedance of FCLs. sli is either one or zero whose value indicates the clear existence or absence of FCL in ith line. RS(X=0) is the index of system reliability when there are not any FCLs in the power system. The lower WLRI, the greater is the system reliability. B. Economical aspects use of fault current limiter Although FCL is used to minimize the short circuit current and improve the system reliability; it is necessary to use the minimum possible number of FCLs with the smallest possible

f 4 (x )  I isc  (

Ei * I b )+pf I  Z ii



Zii is the diagonal impedance of the impedance matrix (Zbus) after inserting FCLs to the system. pfI is the penalty factor and is defined as follows: sc ,max if I sc j=1...Nb j Ij

pf I  0

(17)

sc ,max else pf I  500*( I sc ) j I j

V. PROPOSED ALGORITHM In this research, in order to optimally allocate the FCLs in a power system, PSOGA algorithm that combined particle swarm optimization algorithm (PSO) and genetic algorithm (GA) is used. This hybrid algorithm has all specification of PSO and GA algorithms and in each loop of algorithm both of them run. Convergence rate of this algorithm is better than that them. Results of next session reveal this asseveration.

VI. SIMULATION AND RESULS The multi-objective optimization problem discussed is applied to tow different case studies found in literature, namely IEEE30 Bus system and IEEE-34 Node system. For testing the effectiveness of PSOGA in the optimal placement of FCL problem, seven cases with different values of c1, c2, c3, and c4 are tested. The variations of control parameter values related to these cases are listed in Table I. In all cases, impedances of FCLs are considered to be continuous. Case no. 1 2 3 4 5 6 7

TABLE I. Parameter Variation C1 C2 C3 0 0.5 0.5 1 0 0 0 0 0 0.25 0.25 0.25 0.33 0.33 0.33 0 0.33 0.33 0.5 0 0

C4 0 0 1 0.25 0 0.33 0.5

GA PSO PSOGA

Tables 2 to 8 show GA, PSO and PSOGA algorithm results for seven considered cases. The suitable case must be selected on the basis of the network operator priority. However, in this paper, to verify which case is appropriate compared with the others, the WLRI for faults at the load point is checked, and small values are selected as a suitable case. The small values of WLRI mean to improve the system reliability.

Algorithm GA PSO PSOGA

PSOGA

Algorithm

A. IEEE-30 BUS SYSTEM Fig.3 illustrates the IEEE-30 Bus system. This system is previously described in Section 3. Before the injection of FCL to the network, system short circuit current is 2.9236p.u and weighted load reliability index (WLRI) is 0.7792.

TABLE II. Case.1 Algorithms Results Location ZFCL (P.U) WLRI of FCLs 1,29,31 0.98125,0.46497,0.24989 0.411 1,6,14 0.092692,0.0732,0.4745 0.384 18,39,40 0.20215,0.041852,0.3093 0.271

11,12,15,16 17,18,20,22,24 25,26,28,29,30 33,35,36,38,40

Algorithm GA PSO PSOGA

Algorithm GA PSO PSOGA

Algorithm Isc(P.U) GA 1.3711 1.3701 1.3688 PSO

Algorithm GA PSO

PSOGA

Algorithm GA

PSO

TABLE III. Case.2 Algorithms Results Location of ZFCL(P.U) WLRI FCLs 20,22,28,35,39 1.5494,0.79689,3.5529 0.079 3.4193,1.951 22,25,31,33 2.5581,2.0027,3.9142 0.08188 34,36,40 2.7594,1.1315 1.9357,1.7811 3.5*1023,26,28,30 1.3414,1.7766,1.0324 14 32,35,38,40 2.4268,2.4193,2.9352 2.0671,3.4393 TABLE IV. Case.3 Algorithms Results Location of ZFCL(P.U) FCLs 2,3,4,7,8,9 0.58731,2.0866,0.13969 11,12,13,14,15 3.9691,3.1762,2.9549 18,19,23,24,25,26 3.815,2.4043,1.6765 29,32,33 2.6797,0.9749,0.10835 0.4436,3.6476,2.7734 3.1355,0.86677,2.038 1,2,3,6,7,10 2.7649,1.9027,0.86479

Isc(P.U) 1.3704 1.3706

1.3587

WLRI

Isc (P.U)

0.13116

1.35

0.1069

1.36

PSOGA

1,3,5,7,8,9,10,16 18,19,20,21,23 25,26,29,31,33 34,38,41

2.0671,2.7193,3.6645 2.899,3.9131,2.6164 3.9783,1.1905,1.3286 4.4339,3.7775,0.8189 2.9731,3.2886,1.5435 1.465,2.5447,2.5773 3.5797,1.993,3.148 1.5942 1.6227,1.6561,4.1078 3.7884,2.3953,0.0035 2.2404,4.3152,3.7958 3.1,2.8826,1.9818 3.2171,1.3797,2.7608 1.2304,0.1772,3.2314 2.937

0.0887

TABLE V. Case.4 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 14,27,39 0.25535,0.58635,0.441 0.00417 36,37,41 0.4171,0.46756,0.69452 0.0748 9,14,41 0.01404,0.1368,0.0075 0.00215 TABLE VI. Case.5 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 6,18,30 2.0971,0.2399,0.471 0.003677 15,18,32 0.3222,0.00302,0.18263 0.0036 6,30 0.00006,0.34362 0.003106

TABLE VII. Case.6 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 7,8,15 0.4813,0.84914,0.51299 0.659 3,15,25 0.1433,0.4415,0.07094 0.618 4,13,32 0.06189,0.46984,0.423 0.481 TABLE VIII. Case.7 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 23,24,25,26 2.4627,0.2147,2.655 0.000326 27,30,33,34 3.2096,1.8584,2.7882 35,36,38,40 1.9162,0.2358,3.1385 2.1556,0.93163,2.7859 20,24,25,26 1.3589,3.3792,2.297 0.000383 28,29,30,32 4.755,2.0285,2.9474 33,34,41 1.8041,3.1147,0.15934 3.0428,2.9754 20,25,26,28 2.3894,3.4474,3.2474 0.000276 29,31,32,34 3.4568,3.5686,1.0754 35,36,38,41 2.088,0.14805,3.8238 2.3393,4.0821,2.334

1.34

Isc(P.U) 1.37 1.3652 1.3649

Isc(P.U) 1.3712 1.3686 1.365

Isc(P.U) 1.3715 1.3658 1.3621

Isc(P.U) 1.3682

1.3599

1.3501

As can be seen from these algorithms results, the Installation of FCL in network improve the power system reliability and mitigated the short circuit current peak and PSOGA algorithm results is better than PSO and GA. In cases 1, 3 and 6, because of considering a zero weight for reliability index (c1=0), WLRI values are great. Although, WLRI have small values in cases 2, 3 and 7, these cases are not useful from economical aspect because not considering corresponding weighting factors (c2, c3=0). In cases 4 and 5 with considering proper weighting factors for

objectives function, WLRI values has been reduced to an appropriate values and economical aspects is satisfied. B. IEEE-34 NODE SYSTEM Fig.4 illustrates the IEEE-34 Node system. This system is previously described in Section 3. Before the injection of FCL to the network, system short circuit current is 19.502p.u and weighted load reliability index (WLRI) is 0.341. Tables 9 to 15 show GA, PSO and PSOGA algorithm results for seven considered cases. Like IEEE-30 Bus system, the proper case must be selected on the basis of the network operator priority. However, in this paper, to verify which case is appropriate compared with the others, the WLRI for faults at the load point is checked, and small values are selected as an appropriate case. Algorithm GA PSO PSOGA

Algorithm GA PSO PSOGA

Algorithm GA

PSO

PSOGA

Algorithm GA PSO PSOGA

Algorithm GA PSO PSOGA

Algorithm GA PSO PSOGA

TABLE IX. Case.1 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 18,20,31 0.46783,0.47653,0.22853 0.332 21,28,29 0.4573,0.3711,0.23375 0.3121 25,26,31 0.33327,0.17121,0.1933 0.226 TABLE X. Case.2 Algorithms Results Location of FCLs ZFCL(P.U) WLRI 21,22,31,33 1.6429,3.6171 0.00374 2.2733,1.5231 2.586,3.0425 20,32 0.00375 2.1485,2.7491 20,22,27,28,30 0.00355 3.9042,2.72,2.7543 TABLE XI. Case.3 Algorithms Results Location of FCLs ZFCL(P.U) 2,3,6,7,12,17 2.4224,4.8418,0.13358 21,25,26,27 1.8863,0.2397,3.2458 28,29,30,33 2.8308,0.81341,0.85059 3.9667,4.2223,0.25236 0.51618,0.74557 1,4,11,20,23,25,27 2.9303,3.5177,1.4079 28,29,30,32 1.7161,2.882,0.58627 1.9601,0.65801,2.3609 1.7406,3.003 8,11,13,21,22 3.336,0.3819,0.2636 23,24,26,28 1.3927,3.0808,4.5798 1.5875,3.9707,4.0935

Algorithm GA PSO PSOGA

13.641 13.642 13.578

Isc(P.U) 13.642 13.642 13.641

Isc(P.U) 13.606

0.2732

13.623

0.209

13.413

TABLE XIII. Case.5 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 20,25,31 0.36444,0.5,0.4822 2.25*10-5 1,21,28 0.379,0.091,0.3044 2.24*10-5 1,20 0.33692,0.1424 2.81*10-6 TABLE XIV. Case.6 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 5,11,21 0.2475,0.30659,1.3905 0.239 1,9,12 0.22698,0.4247,0.0019 0.168 13,22,28 0.2674,0.00044,0.4674 0.138

It is observed that among the three evolutionary algorithms PSOGA most probably generates the solution which is better than other two algorithms.

REFERENCES

Isc(P.U) [3]

[4]

13.642 13.64 13.538

[5]

Isc(P.U)

[6]

13.641 13.621 13.44

CONCLUSION

In this paper, three evolutionary algorithms proposed and two case studies considered obtaining installation locations, impedance and the number of FCLs, simultaneously. These algorithms are PSO, GA and PSOGA. An adaptive penalty factors for violation of short circuit current limitation and FCLs impedance margins are considered in the cost functions.

[2]

Isc(P.U)

13.634 13.618 13.601

The installation of FCLs into a power system has a great effect to short circuit current suppression and system reliability improvement. However, how the installation of FCLs influence the reliability and short circuit current depend on the installation locations and their impedances.

[1]

13.641 13.638 13.621

Isc(P.U)

In cases 1, 3 and 6, because of considering a zero weight for reliability index (c1=0), WLRI values are great. While, WLRI have small values in cases 2, 3 and 7, these cases are not useful from economical point view rather than other cases. Cases 4 and 5 have good results and are suitable. As well as case 5 is more effective than case 4 from economical and reliability aspects. VII.

Isc(P.U)

WLRI 0.2896

TABLE XII. Case.4 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 1,5,10 0.4015,0.22502,0.037983 0.000112 1,5,12 0.5472,0.26657,0.031392 0.000166 9,16,25 0.28504,0.00275,0.3897 0.000103

TABLE XV. Case.7 Algorithms Results Location ZFCL(P.U) WLRI of FCLs 21,32 3.5612,0.017306 0.00269 11,14,22 1.233,0.01487,2.7129 0.00105 4,7,25,26 0.00265,3.2653,1.554 4.77*10-4 29,31,32 0.09647,3.2939,1.5313

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