ICMS’2014

INTERNATIONAL CONFERENCE OF MODELING AND SIMULATION 2014 Intelligent overcurrent relays setting based on mixed integer optimization and considering series compensation, fault resistance and relays characteristics Rabah BENABID

a

, Mohamed ZELLAGUI b , Mohamed BOUDOUR , Abdelaziz CHAGHI b

c

a

Electric Engineering Department, Nuclear Research Center of Birine, BP 180, 17200, Djelfa, Algeria b Electrical Engineering Department,University of Batna, Campus CUB, Research Center, 05000, Batna,Algeria c Electrical Engineering Department, USTHB, BP. 32, El Alia, Bab Ezzouar, 16111, Algiers - Algeria

ORAL SESSION Presented by : Rabah BENABID Keywords : Optimal relay coordination ; Overcurrent protection ; Non-linear constrained mixed integer optimization ; Short circuit analysis.

ABSTRACT The electric protection systems play an important role in the operation safety of the sensitive industries such as nuclear industry. Its main task is to detect and clear the occured faults rapidly and isolate only the faulted part of the system. However, due to the complex topology of the modern interconnected power systems, the coordination of the directional overcurrent relay has becomes a di¢ cult task. In this paper, the overcurrent coordination problem is formulated as non-linear mixed integer constrained optimization problem considering various scenarios related to the power system topology and operation such as : series compensation, faults resistance and relays characteristics and standards. The objective function of this optimization problem is the minimization of the operation time of the associated relays in the systems. Both real and integer decision variables are considered ; where the real variables are the time dial setting (TDS), the pickup current setting (IP), and the integer variables are the relay characteristics and standards. Where, these last are usually chosen arbitrarily or by trial and error method. To solve this constrained Mixed Integer optimization problem, an improved version of the particle swarm optimization (PSO) called Mixed Integer PSO (MIPSO) able to manage the combinatory and constrained optimization problems is proposed. The MIPSO is validated on 3-bus, and 8-bus power systems test. The obtained results show a high e¢ ciency of the proposed MIPSO to solve such complex optimization problem compared with PSO. c 2014 LESI. All right reserved.

1. Introduction Due to the operation of power systems near to their operating limits, any fault can trigger the cascading events and thus the blackout of the system. In this context, the nuclear event that has been occurred at the nuclear power plant of Forsmark in July Email : [email protected]

246

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2006 it is due to the incorrect tuning of a protective relay [1]. Therefore, the protective relays must be well tuned and coordinated to ensure the secure and safety operation of the power systems. The tuning and coordination of the overcurrent relay requires that the relays closes to the fault must trip faster than the others relays, in order to isolate, only, the faulted part of the power system. In order to ensure the reliability of the protective system ; each main relay has a backup relay act after a certain time delay known as coordination time interval (CTI), giving the chance for the main relay to operate [2]. Therefore, the reliability and the e¢ ciency of the overcurrent relays depend greatly on theirs setting and coordination with the adjacent equipments [3]. So, the overall protection is thus very complicated especially for the interconnected power systems. In recent years, many research e¤orts have been made to achieve the optimal optimum coordination of protective relays considering di¤erent problem formulations and methods. In [4-7], the optimal relay coordination is formulated as linear optimization problem and solved using linear optimization methods such as linear programming and simplex method. Furthermore, the non linear formulation of the optimal coordination of the overcurrent relays has been presented and solved using non linear optimization methods such as : random search technique [8], Genetic Algorithms and its variants [9-11], Di¤erential Evolution method [12, 13], Seeker algorithm [14], Teaching learning-based optimization [15], and Hybrid methods [16, 17]. From this previously published works, we notice that the overcurrent relay coordination problem is mainly modeled as continuous optimization problem, i.e. considering the continuous decision variables. The characteristics and the standards of the relays are chosen arbitrarily or by trial and error method. Furthermore, the violation constraint handling strategy is not reported in the most of the published papers. In the other hand, the Flexible AC transmission systems (FACTS) devices are widely installed in the power systems in order to increase the system transmission capacity and improve the power ‡ow control ‡exibility, and power system stability [18-20]. Unfortunately, these devices and other parameters such as resistance fault and power system topology modi…cation present a number of technical challenges in terms of setting protection relays due to their impact on the short-circuit current and therefore on the setting and coordination of the overcurrent relays. In this research paper, the overcurrent coordination problem is formulated as non-linear mixed integer constrained optimization problem considering various scenarios related to the power system topology and operation such as : series compensation, faults resistance and relays characteristics and standards. The objective function of this optimization problem is the minimization of the operation time of the associated relays in the systems. Both real and integer decision variables are considered ; where the real variables are the time dial setting (TDS), the pickup current setting (IP), and the integer variables are the relay characteristics and standards. Where, these last are usually chosen arbitrarily or by trial and error method. To solve this constrained mixed integer optimization problem, an improved version of the particle swarm optimization (PSO) called Mixed Integer PSO (MIPSO) able to manage the combinatory and constrained optimization problem is proposed. The MIPSO is validated on 3-bus, and 8-bus power systems test. The obtained results show a high e¢ ciency of the proposed MIPSO to solve such complex optimization problem compared with PSO. 247

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2. Optimal relay coordination : problem formulation and constraints The coordination of the IDMT relays is formulated as a constrained optimization problem, where the optimization function and the constraints are presented as follows : 2.1. Objective function The aim of this function is to minimize the total operating time of all DOCR relays in the system with respect to the coordination time constraint between the backup and primary relays.

F = M in

( NR X

)

(1)

(ti )

i=1

where, ti represents the operating time of the relay i, NR is represents the number of IDMT relays in the power system. For each protective relay the operating time t is de…ned as follows [21] :

t (s) = T DS

0 @

K IF KCT

IP

1

1

+ LA

(2)

where, t is relay operating time (sec), TDS is time dial setting (sec), IF is the fault current (A), IP is pickup current (A), KCT is ratio of the current transformer. The constant K, and L that depends of characteristic curve for IDMT directional overcurrent relay. Table 1, presents the overcurrent relay characteristic considering AREVA, IEC, and ANSI/IEEE standards [9]. Tab. 1. Overcurrent relays characteristics and standards. Type of characteristic Short time inverse Normal inverse Very inverse Extremely inverse Long time inverse Moderately Inverse Very Inverse Extremely inverse

Standard AREVA IEC IEC IEC AREVA ANSI/IEEE ANSI/IEEE ANSI/IEEE

K 0.05 0.14 13.5 80 120 0.0515 19.61 28.2

L 0.04 0 0.02 0 1 0 2 0 1 0 0.02 0.114 2 0.491 2 0.1217

2.2. Optimization constraints 2.2.1. Coordination time interval During the optimization procedure, the coordination between the primary and the backup relays must be veri…ed. In this paper, the coordination between the primary and the backup relays is ensured using the following constraint : tbackup

tprimary

(3)

CT I 248

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where, tbackup and tprimary are the operating time of the backup relay and the primary relay respectively, CTI is the minimum coordination time interval. For the electromechanical relays, the CTI is varied between 0,30 to 0,40 sec, while for the numerical relays it’s varied between 0,10 to 0,20 sec [15]. 2.2.2. Time dial setting (TDS) The TDS adjusts the time delay before the relay operates when the fault current reaches a value equal to, or greater than, the relay current setting IP . T DSmin

T DS

(4)

T DSmax

where, T DSmin and T DSmax are the minimum and the maximum limits of TDS respectively. 2.2.3. Pickup current (IP ) The pickup current IP represent the set point of the relay. During the optimization process IP is limited as follows : IP min

IP

(5)

IP max

where, IP min and IP max are the minimum and the maximum limits of IP respectively. 2.2.4. Tripping time of the primary relays In order to ensure a fast clearing of the fault, the tripping time of the primary relays must be limited as follows : where, tprimary min and tprimary max are the minimum and the maximum limits of the tripping time of the primary relays. 2.2.5. Type of relays characteristics (RT) The eight relays characteristics presented in table 1 are considered in the optimization process, and the coding of RT variable is presented in table 2. During the optimization process, the variable RT is limited as follows : 1

RT

(6)

RTmax

where, RTmax is the maximum limit of RT. Tab. 2. Coding of the relay characteristic (RT). Type of characteristic AREVA Short time inverse IEC Normal inverse IEC Very inverse IEC Extremely inverse AREVA Long time inverse ANSI/IEEE Moderately Inverse ANSI/IEEE Very Inverse ANSI/IEEE Extremely inverse 249

RT 1 2 3 4 5 6 7 8

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3. Optimization algorithm 3.1. Particle swarm optimization Particle Swarm Optimization (PSO) is population based stochastic optimization technique inspired from the social behavior of bird ‡ocking and …sh schooling. It was introduced …rstly by Eberhart and Kennedy in 1995 [30]. The PSO method is based on a population of particles. Each particle in the swarm memorizes its current position in the research space, its velocity, its best position pbest, and the best position found by the swarm gbest. The displacement of each particle in the research space is based on its position and its velocity [31] :

k+1 k xk+1 i;d = xi;d + vi;d

(7)

where, vik+1 , xki are the position of particle i in the iteration k +1 and k, respectively. The velocity of each particle in the swarm is de…ned as follows :

k+1 k vi;d = wvi;d + c1 rand1

pbesti;d

xki;d + c2 rand2

gbest

xki

(8)

where, c1 and c2 are the weighting factors, rand1 and rand2 are two uniform random numbers between zero and one. pbesti is the best solution of the particle i, gbest is the best solution in the swarm, and w is the weighting function de…ned as follows :

w = wmax

wmax wmax kmax

(9)

k

where, wmax and wmin are the maximum and the minimum values of the weighting function. kmax and k are the maximum number of iteration and the current iteration respectively. The algorithm of PSO is presented as follows : variables. – In this step the population is generated randomly between limits, where each particle has D variables. – Loop. – For each particle, evaluate the desired objective function in D variables. – Compare particle’s …tness with its pbesti, if the current value is better that pbesti, then the pbesti will take the value of the current solution, and pi is the current location of xi in D-dimensional. – Identify the particle in the neighborhood with the best success so far, and assign its index to the variable gbest. – Update the velocity and the position of the each particle according to the equation from (8) to (10). – If the stopping condition is satis…ed, exit loop. – End loop. 250

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Fig. 1. General ‡owchart of the PSO. 3.2. Proposed hybrid particle swarm optimization As reported above, the optimal coordination of overcurrent relays problem is usually modeled as constrained continuous mono-objective optimization problem. In this paper, a new formulation of the optimal relay coordination problem as a mixed integer constrained optimization problem is proposed. In order to solve this problem, a mixed integer version of the particle swarm optimization (MIPSO) is proposed. The MIPSO is ables to manage both real and integer decision variables, as well as to handle the constraints violation during the optimization process. The optimization problem has the TDS and the Ip as real decision variables and the relay characteristic type (RT) as an integer variable. This last is usually chosen arbitrarily or by trial and error method. Figure 2, presents the coding principle implemented in MIPSO for N relays. From this …gure, we can see that there are 2N real decision variables and N integer decision variables.

Fig. 2. Mixed integer coding of a solution in MIPSO. 3.3. Constraints violation handling During the optimization process, the coordination constraint presented in (3) could be violated. In this case, the penalty function presented in (11) is used to penalize the violated solutions. (10)

Fpenalyzed = F + P F

where, F is the objective function presented in (1) without penalization ; and PF is the penalty function de…ned as follows : 251

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PF =

NR X

(11)

V iol(i)

i=1

The Viol parameter is computed as follows : – Set Viol [1 : NR] = 0 – For each pair of primary relay i and backup relay j – If, ti –tj CTI – Viol(i) = Viol (i) + constant. 4. Case studies and simulation results 4.1. Methodology In order to evaluate the e¤ectiveness of the proposed MIPSO to solve the relay coordination problem modeled as mixed integer constrained mono-objective optimization problem ; two di¤erent power system ; namely 3-bus 6 relays and 8-bus 14 relays are used. The optimization of the overcurrent relays need, at …rst, the identi…cation of the primary/backup (P/B) relay pairs for each faulted bus. After that, for each P/B relays pairs, the fault currents passing through the relays are calculated for a worst three phase faults applied near the bus as presented in …gure 3.

Fig. 3. Presentation of near fault. In order to be more realistic, the optimal relay coordination is e¤ected considering the following three scenarios : – Scenario A : Optimal relay coordination for the original case. – Scenario B : Optimal relay coordination in the case of resistive three phase fault (RF=10 ). – Scenario C : Optimal relay coordination considering in the case of compensated power system with 70%. For scenarios A and B the relays characteristics are set to the IEC very inverse characteristics and the PSO and MIPSO parameters are presented in table 3 are chosen using trial and error method. Table 4, presents the decision variables limits that must be satis…ed during the optimization process. Tab. 3. PSO and MIPSO parameters. Number of population Number of generation Wmax /Wmin 500 5000 0.9/0.4 252

C1/C2 2/2

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Tab. 4. Limits of the optimization variables. Decision Variable Type TDS Real Ip Real tp Real RT Integer

Minimum value Maximum Value 0.1 1.1 0.5 2 0.05 1 1 8

4.2. 3-bus test system The 3-bus test system is presented in …gure 3 has three generators, three buses, and six overcurrent relays. The detailed data of this system are presented in appendix A. In the case of real-coded optimization, there are 12 real decision variables, and for the mixed integer optimization, there are 12 real decision variables and 6 integer variables. The computed short circuit current of the three scenarios are presented in table 5. Figure 5, presents the convergence characteristics of PSO and MIPSO for the three scenarios. From this …gure, we can the MIPSO has a better convergence characteristics and thus converge to the better result compared with the PSO. The best solutions given by PSO and MIPSO for scenarios A, B, and C are presented in tables 6, 7, and 8 respectively. From these tables, it is clear that MIPSO provides the best solution and also it is able to set the relays characteristics and standards. Tables 9 and 10 present respectively, the tripping time of the primary relays, as well as the time coordination between the primary and the backup relays. From this results, we can conclude that the constraints stated by equations (3) and (6) are satis…ed by PSO and MIPSO. Form these results obtained in the three scenarios A, B, and C, we can conclude that MIPSO provides the best results compared with PSO, and ensures an intelligent setting of the relays specially theirs characteristics and standards.

Fig. 4. Single line diagram of the 3-bus network. 253

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Tab. 5. Short circuit current of P/B relays of 3-bus test system. Three phase fault current (kA) PR BR Scenario A Scenario B N N PR BR PR 1 5 4.2336 0.6651 1.8120 2 4 2.7391 1.1056 1.3088 3 1 2.7929 1.1063 1.3252 4 6 3.1340 0.9223 1.4532 5 3 3.0325 0.9669 1.4318 6 2 4.1044 0.6864 1.7825

BR 0.2847 0.5283 0.5250 0.4277 0.4565 0.2981

Scenario C PR BR 4.9407 0.7086 2.9656 1.1419 3.6611 2.0942 3.0896 0.8683 3.0760 1.0216 4.4401 1.1530

Fig. 5. Convergence caracteristics of the three scenarios A, B, and C.

Tab. 6. Best relays coordination of scenario A. Relay N 1 2 3 4 5 6 F(s)

TDS 0.7608 0.6291 0.8861 0.1239 0.1144 0.1000

PSO Ip 0.5000 0.5000 0.5000 2.5000 2.5000 2.0041 0.4136

RT (…xed) TDS 2 0.3847 2 0.3410 2 0.4869 2 0.2722 2 1.1000 2 0.2648

254

proposed MIPSO Ip RT 2.5000 8 2.5000 8 2.5000 3 2.5000 3 1.8066 3 2.5000 8 0.3148

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Tab. 7. Best relays coordination of scenario B. Relay N 1 2 3 4 5 6 F(s)

TDS 0.1000 0.1000 0.1000 0.3094 0.1000 0.1000

PSO Ip 1.4888 .2015 1.7832 0.5000 1.2784 0.9401 0.3958

proposed MIPSO RT (…xed) TDS Ip RT 2 0.1581 2.5000 8 2 0.1740 2.5000 8 2 0.1766 2.5000 8 2 0.1175 2.5000 8 2 0.1924 2.5000 8 2 0.1039 2.5000 8 0.3

Tab. 8. Best relays coordination of scenario C. Relay N 1 2 3 4 5 6 F(s)

TDS 0.2590 0.2100 0.1841 0.8098 0.7893 0.4680

PSO Ip 2.5000 2.4024 2.5000 0.5000 0.5000 0.5032 0.5090

RT (…xed) TDS 2 0.6774 2 0.5490 2 1.1000 2 0.2645 2 0.5907 2 0.4074

proposed MIPSO Ip RT 2.5000 3 2.5000 3 2.5000 3 2.4999 3 2.5000 3 0.5000 2 0.3157

Tab. 9. Tipping time of the primary relays. Primary relay N

Scenario A PSO Proposed MIPSO 1 0.0733 0.0605 2 0.0625 0.0543 3 0.0863 0.0500 4 0.0841 0.0500 5 0.0527 0.0500 6 0.0549 0.0500 Violation 0 0

Scenario B PSO Proposed MIPSO 0.0700 0.0500 0.0515 0.0500 0.0768 0.0500 0.0880 0.0500 0.0500 0.0500 0.0595 0.0500 0 0

Scenario C PSO Proposed MIPSO 0.1095 0.0500 0.0950 0.0500 0.0698 0.0657 0.1072 0.0500 0.0697 0.0500 0.0578 0.0500 0 0

Tab. 10. P/B coordination time. P/B relay Scenario A pair N PSO Proposed MIPSO 1 0.2000 0.9908 2 0.2000 0.3540 3 0.2000 0.2000 4 0.2000 0.3507 5 0.2000 0.3711 6 0.2000 0.2000 Violation 0 0

Scenario B PSO Proposed MIPSO 0.2256 0.7368 0.2000 0.2549 0.2000 0.3655 0.2000 0.7826 0.2000 0.2224 0.2000 0.5935 0 0 255

Scenario C PSO Proposed MIPSO 0.2000 0.9103 0.2000 0.3216 0.2000 0.2138 0.2000 0.2156 0.2000 0.8013 0.2000 0.2829 0 0

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4.3. 8-bus test system The 8-bus system presented in …gure 6 has two generators and with six buses, seventh lines and fourth load. The power system study is compensated with Series capacitor located at middle of the transmission line 1-6. The series capacitor is installed in line 1-6. The 8-bus system has a link to another network, modeled by a short circuit power of 400 MVA. The transmission network consists of 14 numerical DOCRs relays. The detailed system data are given in the appendix A [3]. Since there are 14 relays, and each relay has two parameters to be optimized ; therefore the number of decision variables is 28 for the case of PSO and 42 for the case of MIPSO, whith 14 integer variables. The computed short circuit current of the three scenarios are presented in table 11. Figure 7, presents the convergence characteristics of PSO and MIPSO for the three scenarios. From this …gure, it is clear that the MIPSO has a better convergence characteristics and thus converge to the better result compared with the PSO. The best solutions given by PSO and MIPSO for scenarios A, B, and C are presented in tables 12, 13, and 14 respectively. From these tables, it is clear that MIPSO provides the best solution and also it is able to set the relays characteristics and standards. Tables 15 and 16 present respectively, the tripping time of the primary relays, as well as the time coordination between the primary and the backup relays. From these results, we can remark that the constraints stated by equations (3) and (6) are completely satis…ed by MIPSO, however the PSO fails to satisfy the time coordination constraints of relays 9 an 10 for scenario B, and relays 10 and 11 for scenario C. Therefore, it is clear that PSO fails to solve the relays coordination problem for 8-bus test system that has 28 decision variables. Form these results, we can conclude that MIPSO provides the best results compared with PSO, satisfy all the optimization constraints, and ensures an intelligent setting and coordination of the relays specially theirs characteristics and standards.

Fig. 6. Single line diagram of the 8-Bus network. 256

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Fig. 7. Convergence caracteristics of the thre scenarios A, B, and C.

Tab. 11. Short circuit current of P/B relays of 3-bus test system. PR N 1 2 2 3 4 5 6 6 7 7 8 8 9 10 11 12 12 13 14 14

BR N 6 1 7 2 3 4 5 14 5 13 7 9 10 11 12 13 14 8 1 9

Scenario A PR BR 3.2946 3.2946 6.1594 1.0094 6.1594 1.9164 3.7450 3.7450 3.9830 2.3214 2.5088 2.5088 6.2928 1.2325 6.2928 1.8182 5.2856 1.1843 5.2856 0.8525 6.2321 1.8105 6.2321 1.1894 2.5859 2.5859 4.0891 2.4289 3.9026 3.9026 6.1670 1.0084 6.1670 1.9145 3.0631 3.0631 5.2615 0.8621 5.2615 1.1499

Fault Current (kA) Scenario B PR BR 2.6571 2.6571 4.7993 0.7865 4.7993 1.4932 3.0518 3.0518 3.2314 1.8833 2.0265 2.0265 4.8981 0.9593 4.8981 1.4152 4.1021 0.9191 4.1021 0.6616 4.8584 1.4114 4.8584 0.9272 2.1000 2.1000 3.3195 1.9718 3.1653 3.1653 4.7957 0.7842 4.7957 1.4887 2.4682 2.4682 4.0854 0.6694 4.0854 0.8929 257

Scenario C PR BR 3.2646 3.2646 6.6124 0.4829 6.6124 2.9158 3.8692 3.8692 3.9662 2.3045 2.3821 2.3821 6.9768 0.9899 6.9768 2.7589 4.7174 0.9909 4.7174 0.4153 6.9111 2.7468 6.9111 0.9486 2.4681 2.4681 4.0812 2.4210 4.0429 4.0429 6.6200 0.4823 6.6200 2.9124 2.9912 2.9912 4.6861 0.4202 4.6861 0.9543

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Tab. 12. Best relays coordination of scenario A. Relay N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 F(s)

TDS 0.1000 0.2251 0.2353 1.1000 0.1000 1.1000 1.1000 0.1062 0.1000 0.5209 0.5881 1.1000 0.2713 0.1387

PSO Ip 2.5000 2.5000 2.5000 0.5000 2.5000 0.5000 0.5000 2.5000 1.5401 0.5000 0.5000 0.5000 0.5000 2.5000 3.7686

RT(…xed) 2 2 2 2 2 2 2 2 2 2 2 2 2 2

TDS 1.1000 1.1000 0.1000 0.1000 1.1000 0.3444 1.1000 0.1000 0.1000 1.1000 0.1739 1.1000 0.1000 0.3508

Proposed MIPSO Ip RT 0.5000 8 1.6990 8 2.5000 1 2.5000 3 0.5000 3 2.5000 8 0.5000 2 2.5000 2 2.5000 8 0.7410 8 0.5000 1 1.8431 8 2.5000 8 2.5000 8 2.7728

Tab. 13. Best relays coordination of scenario B. Relay N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 F(s)

TDS 0.1000 0.1538 0.8479 0.1000 0.1908 0.4961 0.1006 0.1000 0.3061 0.1000 0.1000 0.6503 0.1744 0.1000

PSO Ip 0.8814 2.5000 0.5000 2.5000 0.5000 0.5000 2.5000 2.5000 0.5000 0.5000 1.2865 0.5000 0.5000 2.5000 12.5489

RT(…xed) 2 2 2 2 2 2 2 2 2 2 2 2 2 2

258

TDS 0.5190 0.3723 0.1443 0.1081 0.1000 0.1790 0.1793 1.1000 1.1000 1.1000 1.1000 1.1000 0.1000 0.1000

Proposed MIPSO Ip RT 0.5000 8 2.5000 8 0.5000 1 2.3604 8 1.2140 8 2.5000 8 2.5000 8 0.5611 3 0.5000 3 0.5000 5 0.5000 7 1.8712 8 1.3650 8 2.5000 3 2.6257

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Tab. 14. Best relays coordination of scenario B. Relay N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 F(s)

TDS 0.1000 0.1762 0.8296 0.1000 0.2445 0.4882 0.2037 0.4605 0.1000 1.1000 0.1000 1.1000 0.1060 0.2206

PSO Ip 0.1000 2.5000 0.5000 2.1582 0.5000 0.5000 2.5000 0.5000 2.5000 0.5000 2.5000 0.5000 0.5000 2.5000 12.9414

RT(…xed) 2 2 2 2 2 2 2 2 2 2 2 2 2 2

TDS 0.1000 0.5413 0.5675 1.1000 0.1000 0.1000 1.1000 0.1917 0.1000 1.1000 0.1983 0.1822 0.2991 0.7615

Proposed MIPSO Ip RT 0.5000 1 2.5000 8 2.5000 8 0.5000 5 2.5000 8 2.5000 1 0.5000 2 2.5000 8 2.5000 8 0.7237 8 2.5000 8 0.5000 1 0.5000 8 2.5000 v 2.8422

Tab. 15. Tipping time of the primary relays of scenarios A, B, and C. Primary relay N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Violation

Scenario A PSO Proposed MIPSO 0.3006 0.1751 0.3280 0.2704 0.3799 0.3060 0.4613 0.1858 0.4244 0.2018 0.2887 0.1310 0.2282 0.2282 0.1528 0.1438 0.1422 0.0813 0.2126 0.1927 0.2518 0.3376 0.2947 0.2943 0.1493 0.1247 0.1541 0.1002 0 0

Scenario B PSO Proposed MIPSO 0.1168 0.0931 0.2967 0.2120 0.3081 0.2675 0.3078 0.1099 0.1621 0.0717 0.1682 0.0987 0.1467 0.0704 0.1902 0.0677 0.1637 0.1279 0.0506 0.3873 0.1459 0.5711 0.2253 0.4083 0.1203 0.0627 0.1465 0.0774 0 0 259

Scenario C PSO Proposed MIPSO 0.0515 0.2050 0.2373 0.1926 0.2365 0.2420 0.2028 0.3662 0.1751 0.2032 0.0987 0.2784 0.2548 0.2562 0.1099 0.0644 0.2611 0.0882 0.4499 0.1901 0.2353 0.1501 0.2742 0.3055 0.0598 0.0500 0.2779 0.2503 0 0

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Tab. 16. Tipping time of the primary relays of scenarios A, B, and C. P/B relay pair N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Violation

Scenario A PSO Proposed MIPSO 0.2607 0.2000 1.6505 0.3082 0.3189 0.3765 0.2000 0.2000 0.2000 0.2054 0.3216 0.2835 0.9919 0.7112 0.2396 0.4149 1.1581 0.6846 0.3718 2.5520 0.5337 0.5427 0.2000 0.2280 0.2000 0.2000 0.2000 0.2000 0.2193 0.2000 0.2000 1.2634 0.2000 0.2000 0.2000 0.2042 2.9363 0.6466 0.2141 0.2141 0 0

Scenario B PSO Proposed MIPSO 0.2000 0.2000 0.2000 0.2000 0.2000 0.2007 0.2000 0.2000 0.2000 0.2000 0.4057 0.2000 0.2000 0.2000 0.3637 0.5959 0.2401 0.2569 0.3749 0.8578 0.3466 0.3957 0.2000 0.5924 -0.0818 0.3255 0.2000 0.2330 0.2000 0.2000 0.2000 0.2000 0.2707 0.2142 0.3133 0.2000 0.4772 0.4717 0.2602 0.6347 0 0

Scenario C PSO Proposed MIPSO 0.2000 0.2013 0.2091 0.3032 0.2000 0.2263 0.2000 0.2000 0.2000 0.2000 0.2000 0.2300 0.3400 1.3715 0.3897 0.2754 0.2000 1.3885 0.3269 0.5486 0.3590 0.3811 0.8745 0.5576 0.4978 0.2000 -0.0051 0.2000 0.2190 0.2000 0.2000 0.2875 0.2000 0.2000 0.2000 0.2000 0.2617 0.3013 0.6963 0.3629 0 0

5. Conclusions In this paper, the overcurrent coordination problem in interconnected power systems has been formulated as non-linear mixed integer constrained optimization problem considering various scenarios related to the power system topology and operation such as : series compensation, faults resistance and relays characteristics and standards. The objective function is to minimize the total relays operating time with the optimal setting of real (TDS, and Ip) and integer (RT) decision variables. To solve this constrained mixed integer optimization problem, an improved version of the particle swarm optimization (PSO) called Mixed Integer PSO (MIPSO) has been proposed. This last is able to manage the combinatory and constrained optimization problem. The MIPSO is validated on 3-bus, and 8-bus power systems test and the obtained results are compared with the real coded PSO. The obtained results show that the MIPSO provides the best results for all simulations scenarios compared with the PSO. Furthermore, MIPSO satisfy all optimization constraints, however PSO fails to satisfy these constraints for scenario B and C of the 8-bus test system. Finally, we can conclude that MIPSO is more e¤ective than PSO in terms of objective function minimization, constraints satisfaction and thus ensures an intelligent setting and coordination of the overcurrent relays specially theirs characteristics and standards. 260

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Appendix A. Power systems test data A.1. 3-bus power system test data Tab. 17. Parameters Line Vn (kV) R ( ) X ( ) Y (S) 1 - 2 69 5.5 22.85 0,0000 1 - 3 69 4.4 18.00 0,0000 3 - 4 69 7.6 27.00 0,0000 Tab. 18. Parameters No. Bus Sn (MVA) Vn (kV) 1 1 100 69 2 2 25 69 3 3 50 50

L (km) 50 40 60

Xsc (%) 20 12 18

Tab. 19. Parameters Relay N Relay N 1 300/5 2 200/5 3 200/5 4 300/5 5 200/5 6 400/5 A.2. 8-bus power system test data Tab. 20. Line Vn (kV) R ( /km) 1 - 2 150 0,0040 1 - 3 150 0,0057 3 - 4 150 0,0050 4 - 5 150 0,0050 5 - 6 150 0,0045 2 - 6 150 0,0044 1 - 6 150 0,0050

Parameters X ( /km) 0,0500 0,0714 0,0563 0,0450 0,0409 0,050 0,0500

Y (S/km) 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000

L (km) 100 70 80 100 110 90 100

Tab. 21. Parameters No. No. Sn (MVA) Vn (kV) Xsc (%) 1 7 150 10 15 2 8 150 10 15 Tab. 22. Parameters No. Bus-Bus Sn (MVA) Vn.p (kV) Vn.s (kV) Xsc (%) 1 7-1 150 10 150 4 2 8-6 150 10 150 4 261

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Tab. 23. Parameters Relay No. In2 / In1 CT ration 1, 2, 4, 5, 6, 8, 10, 11, 12, 13 1200 / 5 240 3, 7, 9, 14 800 / 5 160

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