Setting directional overcurrent protection parameters using hybrid GA optimizer

Electric Power Systems Research 143 (2017) 400–408

Contents lists available at ScienceDirect

Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Setting directional overcurrent protection parameters using hybrid GA optimizer Fernando B. Bottura, Wellington M.S. Bernardes, Mário Oleskovicz, Eduardo N. Asada ∗ Department of Electrical and Computer Engineering, São Carlos School of Engineering, University of São Paulo, Brazil

a r t i c l e

i n f o

Article history: Received 16 May 2016 Received in revised form 14 September 2016 Accepted 18 September 2016 Keywords: Power system protection Directional overcurrent relay Genetic algorithms Linear programming Mixed non-linear programming

a b s t r a c t A Hybrid Genetic Algorithm (HGA) is proposed to solve the optimal coordination of Directional Overcurrent Relays (DORs) in meshed power transmission systems. In this research, the short circuit current direction os taken into account by the optimization model. By developing the problem oriented HGA, high-quality feasible coordination solutions for DORs have been obtained with good performance. The solutions provided by the HGA are compared with a selected set of classical mathematical programming solvers namely, AlphaECP, BARON 14, BONMIN, DICOPT, KNITRO and SBB which have been modeled with the General Algebraic Modelling System (GAMS). In order to validate the proposed DORs coordination method, a real meshed power system is considered. The proposed HGA provided high-quality coordination solutions, which represents 12.10% to 27.31% reduction on the average value of the performance function for all test cases when compared with the solutions provided by commercial solvers. © 2016 Elsevier B.V. All rights reserved.

1. Introduction In power systems operation, the protection system plays the critical role to keep the reliability and the operability of the system within highest levels. For this, the power protection is composed of various local and backup protection schemes to mitigate and minimize areas affected by short-circuits caused by natural or deliberate faults in the system. For technical reasons, the faults should be cleared by local protection rapidly and the area affected by the service interruption must be kept minimal. The overcurrent relay is a common solution for monitoring short-circuits currents and the Directional Overcurrent Relay (DOR) is indicated for meshed systems due to the possibility of identifying the direction of the fault currents [1]. Usually, the distance protection of transmission lines is set as the main protection system and the DORs are the backup devices. However, DOR can further improve the performance by optimizing its setting. The minimization of the affected area is correlated with the coordinated action of different type of relays, which should result in the isolation of the smallest part of the system under short-circuit situation.

∗ Corresponding author. E-mail addresses: [email protected] (F.B. Bottura), [email protected] (W.M.S. Bernardes), [email protected] (M. Oleskovicz), [email protected] (E.N. Asada). http://dx.doi.org/10.1016/j.epsr.2016.09.017 0378-7796/© 2016 Elsevier B.V. All rights reserved.

Concerning the directional overcurrent protection, various classical [2–4] and approximate computational methods [5–11] have been developed to improve the speed, coordination and selectivity by optimally adjusting the parameters of those relays. Therefore, the optimal setting of the relays is modeled as an optimization problem with nonlinear constraints and discrete variables. The performance index or expression that represents the quality of the relay setting is chosen for optimization, for instance the relay operation time can be used taking into account constraints imposed by the coordination, such as the operation of primary and backup relays, magnitude of short-circuits currents, system loading, priority among protection systems, etc. In this research, the main objective is to demonstrate and discuss the proposed DORs coordination algorithm. Thus, the prior operation of the distance protection of the transmission lines has not been included in the coordination constraints. However, it may be properly included modifying the time dial interval. The main parameters in DORs are the pickup current and the time dial, which defines the sensitivity of the relay for a given current as reference. These variables are represented as a continuous or discrete setting in the relays. Some classical optimization methods have been used for the optimal coordination. In [2], the Simplex algorithm is used to define the time dial and then the pickup current is calculated with the generalized reduced gradient method. In [3], the interior point Primal-Dual Predictor-Corrector algorithm is used as the solution method for the coordination of DORs taking into account definite

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

time relays as the backup units. Similarly to [4], the optimized settings of the DORs are obtained without the evaluation of a performance function; rather, specific rules are set to obtain feasible alternatives. For that method, the Time Multiplier Setting (TMS) defines a square area in the plane for each primary/backup relay pair. Depending on the pickup current values, the Coordination Time Interval (CTI) is represented by lines in this plane. All coordination constraints are satisfied by increasing gradually pickup current value and TMS in two distinct phases. Concerning the approximate methods, the population-based meta-heuristic algorithms are commonly used such as the derivations of Particle Swarm Optimization (PSO) [5,6] and Genetic Algorithms (GA) [7–9]. For those methods, some operational constraints are dealt with penalty factors. In [10,11] the time dial is calculated from the GA, some other approaches mix the dynamic search property from the meta-heuristics with the classical optimization methods which optimality conditions are applied, especially in cases where both time dial and pickup current are determined simultaneously [12,13]. In [14], the application of Teaching Learning-Based Optimization (TLBO) for the coordination of DORs in a meshed system is proposed, and a combination of the primary and backup relays is chosen based on a vector with LINKNET structure. In [15], the Multiple Embedded Crossover Particle Swarm Optimization (MECPSO) is proposed and the main characteristic is the velocity updating which increases the diversity of the swarm and widens the global search of the basic PSO. Considering the aforementioned coordination methodologies, this research presents a DOR coordination methodology using a Hybrid Genetic Algorithm (HGA) in order to obtain the Time Dial setting (TD) and the pickup current of the DORs installed in a real meshed system. The proposed HGA combines the calculation of the best TD obtained from linear programming model and the pickup current is defined by the GA. Although the general optimality is not ensured, in comparison with similar works, the results provided by the HGA present high quality due to the modeling of the problem which considers detailed representation of the system and real operation conditions provided by transmission utility. Important contributions to the method are the inclusion of the fault current angle and a better definition of search variables, based on operational limits and system characteristics, to improve the coordination solution quality. The DOR coordination methodology is tested using a real 138 kV transmission power system also modeled in CAPE (Computer-Aided Protection Engineering) software [16], in which the setting resulting from the proposed method is tested against CAPE embedded relay checking function. Additionally, the following contributions are also provided in this research: • Algorithm for setting main/backup DOR in meshed power systems; and • Case study with the proposed HGA in comparison with GAMS (General Algebraic Modeling System) solvers for the coordination of directional overcurrent protection. 2. DORs—coordination problem modeling The reliability in system protection demands at least two protection levels as in primary and backup protection scheme. Conprim sider Ti as the operation time of i-th primary relay and Tjback the operation time for the j-th backup relay. The coordination between the primary and backup pairs must respect the CTI, which is the required waiting time for the backup relay to produce a trip signal in case of its primary relay fails. The trigger time for the backup relay must be higher (slower operation time) than the primary relay prim stands for operactuation and this relation is shown in Eq. (1). Ti

401

ation time of i-th primary relay and Tjback is the operation time for the j-th backup relay. prim

Tjback − Ti

≥ CTI

(1)

In this work, the pickup current tap and TD of the relays comply with characteristics of commercial Siemens 7SJ64 relays (1A and 5A versions) [17]. The 1A version has its pickup current interval ranging from 0.1A to 4A in 0.01 regular steps, whereas the 5A version pick-up current interval ranges from 0.5A to 20A also with 0.01 regular steps. Thus, minimum Ipmin and maximum Ipmax settings values of pick-up current tap for each DOR installed in the test power system is calculated multiplying the associated CT (Current Transformer) ratio. The TD of both relay models varies from 0.05 to 3.2 in 0.01 regular steps. Both relays follow the normal inverse time curve defined by standard IEC 60255-3 [18], as shown in Eq. (2). T = 0.14 × TD/



ICC /Ip

0.02



−1

(2)

where Ip is the pick-up current and ICC is the short-circuit current measured by DOR. The direction of fault current is defined by the angle between the fault current and its phase voltage. Therefore, it represents an important input data for directional protection. For instance, the reverse direction of fault current does not activate the DOR, which exclude the affected relays from the coordination. This fact reduces the number of primary/backup pairs that really needs to be coordinated. Eq. (3) is added in the formulation to model the variation of the angle that defines the right direction, with min and max equal to −150◦ and 30◦ , respectively. min ≤ cc ≤ max

(3)

Finally, the DORs coordination problem is modeled as the minimization of the sum of all primary relay operation time. This optimization must consider all constraints concerning the TD and pickup current tap range, the system topology, and the rated values determined by the limits of the transmission lines. Eq. (4) depicts the optimization problem for the DORs coordination. min f (x) =



prim

Ti

(TDi , Icc , Ip i , ϒ i , A, B)

⎧ back prim Tj − Ti ≥ CTI ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ TDi ≤ TDi ≤ TDi ⎪ ⎪ ⎪ ⎪ Icap = min{ICB ; Isecc ; Iblock ; ICT ; Icond } ⎪ ⎪ ⎪ ⎪ ⎪ 20% ⎪ ⎨ Ip i ≥ Icap = 1.2 × Icap : i ∈ ˝k

s.t.

TDi ∈ DTDi

⎪ ⎪ ⎪ ⎪ ⎪ DTDi = (0.05; 0.06; 0.07; . . .; 3.19; 3.2) ⎪ ⎪ ⎪ ⎪ ⎪ Ip i ∈ DIp i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ DIpi = (Ip1 , Ip2 , . . ., IpNIP ) ⎪ ⎪ ⎩

[a] [b] [c] [d]

(4)

[e] [f ] [g] [h] [i]

Ip i = CTRi × ϒ i

where: i = 1, 2, . . ., r; j = 1, 2, . . ., r; r = number of relays; A, B − parameters of relay curve. For IEC normal inverse curve, A = 0.14 and prim − operation time of primary relay i; Tjback − operB = 0.02; Ti ation time of backup relay j; CTI − coordination time interval (0.3 s); ICC − short-circuit current measured by DOR; Icap − operating upper limit of the transmission line (normal condition); ICB − circuit breaker rated current; Isecc −circuit disconnector rated current; Iblock − rated current of the block coil; ICT − rated current of 20% − current limit of the transmission line the corresponding CT; Icap

402

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

considering safety factor. In this case, 20%; Icond − rated current of the TL k, m (conductor); k − DOR installed in TL k, m near the k bar; ϒ i − ith DOR pick-up current tap; and CTRi − is CT ratio of the ith DOR. The CAPE software was used for the system assessment using the short-circuit database provided by the Brazilian system operator (ONS) [19]. In this assessment three-phase short-circuits have been calculated within 1% distance of the primary relay (close-in fault). Therefore, it was to obtain the short-circuit currents  possible   for  primary relays ICC,p and their respective backup relays ICC,b . It is important to notice that the definition of primary and backup relays depends on the topological inspection of the system, which was carried out using an automatic procedure based on the strategy proposed in [20] and depicted in Section 3.

3.1. Definition of Primary/Backup (P/B) relays The definition of the relay pairs represents an important task prior to optimization and it defines the constraints of Eq. (1), therefore it also affects the final solution and consequently the optimization process. Moreover, a tool that automatically provides suitable DORs pairs for the analyzed electric network would save time to coordinate such devices. Thus, an algorithm to automate the P/B relays has been developed, leaving to the final user the acceptance of the possible pairs for the optimization. This issue has been solved based on ideas present in [20,23], by using an incidence matrix BR (NB rows × NR columns), where NB is the number of buses and NR is the number of DORs. Algorithm 1 depicts a set of functional instructions to find all P/B relays pairs. Algorithm 1.

Another version of hybrid solver that mixes classical optimization methods with metaheuristics can be found in [21]. In this paper, the analysis is further expanded with the use of Mixed Integer Nonlinear Programming solvers with the use of GAMS [22] interface. The solvers are AlphaECP, BARON 14, BONMIN, DICOPT, KNITRO and SBB. The relay setting is considered discrete and the proposed HGA is able to provide high-quality solutions due to the joint optimization solver. In the next section the techniques used for DORs coordination in this paper are shown.

Determination of P/B DORs.

3.2. Hybrid genetic algorithm optimizer

3. Techniques for DORs coordination

A Linear Programming (LP) stage, solved by the Simplex Method, and a GA stage provide the hybrid feature of the algorithm. The GA stage uses the LP which provides the optimal TD, and then defines the optimized pick-up current values that ensure the DORs coordination, as depicted in the flowchart of Fig. 1. The two main stages of the HGA (LP and GA) are highlighted in Fig. 1. The LP stage is initialized by randomly fixing the pick-up current tap values which are selected from the adjustment interval, complying with constraints c, d, g, h and i stated in Eq. (4). The picktap up currents taps Ipi are coded in sequential binary chromosome structure for the N-th DORs, as shown in Fig. 2.

Firstly, a method for achieving all pairs of relays is discussed and then, with the use of the model proposed in Section 2, the HGA optimizer and the Non-linear-mixed-integer programming solvers applied to the studied DORs coordination are presented.

3.2.1. LP stage The number of binary digits (ˇi ) are determined by the inequality proposed in Eq. (5), which will provide an adequate accuracy of

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

403

Fig. 1. Flowchart of the hybrid genetic algorithm optimization.

the pick-up current taps when considering the uniform step size value (ıi ) of the ith DOR.



2ˇi ≥

tap,max

Ipi

tap,min

− Ipi



+1

ıi tap,min

where Ipi

tap,max

and Ipi

(5)

are calculated using minimum and max-

imum pick-up current tap for the ith DOR, respectively, as well as constraints c, d, g, h and i described in Eq. (4). Therefore, since all C chromosomes have their pick-up current values randomly fixed, the LP stage calculates the TD that minimizes the sum of the primary relays operating time meeting the imposed constraints, i.e., considering the CTI and the TD interval of each DOR (b, e and f in Eq. (4)). The LP stage minimizes f (x), which is the sum of the primary DOR operation time calculated using the inverse time characteristic function (Eq. (2)). Thus, f (x) is given by Eq. (6). f (x) =

N

i=1



0.14 Icc /Ipi

0.02

−1

xi

(6)

where xi is the ith DOR (decision variable) and Icc is the primary relay close-in short-circuit. In LP stage, the Simplex Method may not find a feasible solution or even find an unbounded solution [24]. Thus, the respective chromosome must have its fitness value penalized by a factor MT , reducing its probability of surviving to next generations. The linprog function of the optimization toolbox from MATLAB® [25] has been used to perform the Simplex Method. Other successful use of

MATLAB® packages for power system protection research can be found in [26–28].

3.2.2. GA stage The GA starts by storing the optimum TD obtained from the LP stage in order to randomly initialize all chromosomes. The GA searches for the pick-up current taps that minimize the sum of the primary relays operation time, satisfying constraints a, c, d, g, h and i given by Eq. (4). The problem solved by GA has nonlinear objective function as in Eq. (7).

f (x) =

N

i=1

0.14

 Icc 0.02 yi

−1

(7)

TDi

where yi is the ith DOR pick-up current value (decision variable) and TDi is the ith time dial calculated by PL stage. Each chromosome must be evaluated by a fitness function Fit (x) in order to establish a criterion for its replication for the next generations. The fitness function is shown in Eq. (8). Fit (x) =

N

prim T i=1 i

+

LP

+

CTI

prim

(8)

where Ti is the operation time of the ith DOR, LP is the penalty factor from the LP stage and CTI is the penalty factor due to CTI violation (constraint a in Eq. (4)) after application of genetic operators.

Fig. 2. Example of the chromosome structure of the binary coded DOR pick-up current tap values.

404

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

To perform the fitness evaluation, the binary coded chromosome is mapped back to decimal representation using Eq. (9).

 Ipi = Ipmin + i

Ipmax − Ipmin i i 2ˇi − 1

 ˇi ×

2k bk

(9)

3.3. Tests with nonlinear-mixed-integer programming under GAMS interface In order to evaluate the performance of the hybrid method concerning the solution process, 6 nonlinear mixed integer programming solvers, most of them commercial, have been used in this research. The solvers are: BONMIN, DICOPT, KNITRO, AlphaECP, BARON, and SBB. They are used under GAMS modeling framework which works as unique modeling language for various different numerical solvers. Some details concerning each solver are given in next. The solver BONMIN (Basic Open-source Nonlinear Mixed INteger programming) features several algorithms based on branch and bound or branch and cut algorithms. The solver DICOPT (Discrete and Continuous OPTimizer) is based on an extension of outer-approximation algorithm for the equality relaxation strategy, and solves a series of NLP (Non-Linear Programming) and MIP (Mixed Integer Programming) subproblems to obtain solution with discrete variables [29]. In addition, the solver KNITRO, is designed to solve large scale nonlinear mixed integer problems and implements state-of-art interior point and active-sets methods [30]. The AlphaECP, based on the extended cutting plane (ECP) is described succinctly as an algorithm based on the extended cutting plane method, requiring only the solution of a mixed integer programming sub-problem in each iteration [29]. The solver BARON (Branch and Reduce Optimization Navigator) [29,31] implements deterministic global optimization algorithms of the branch-and-bound method which are promised to give global optimum under fairly general assumptions. Finally, the SBB (Simple Branch-and-Bound) solver [29,32] is based on a combination of the branch and bound method and some of the standard NLP solvers already supported by GAMS. Usually, the time dial for a relay is written as the sum of available dials for the relay. Each TDi is multiplied by a binary variable which will define the time dial for the relay. The same procedure is usually carried out when computing the pickup current settings [33]. In this paper, instead of using binary variable and considering equally spaced decimal values parameters of the relay, both TD and pick-up current tap (ϒ) are defined as integer variables and  divided by a scalar . Being TDZ =  5, 6, 7, 8, · · ·, 319, 320 and its scalar is equal to 100, therefore TD = T DZ /100 =

4. Simulation results

k=0

where bk represents the binary digits of the chromosome. After the fitness evaluation, the GA performs tournament selection, crossover and mutation over the chromosomes to build up the next generation. Since all DORs considered in this work have discrete values (restrictions e and f in Eq. (4)), both pickup current taps and TD are rounded off to the nearest feasible integer value before calculating the chromosome fitness. Subsequent iterations keep the same procedure as above by employing the new pick-up current taps referred to the new chromosomes population. The process continues until the value of the objective function, i.e., summation of primary relays operation time, remains unchanged or stabilizes  over a number of generations |(fi+1 (x) − fi (x))/fi (x) | < 10−4 or the maximum number of generations is reached. 10,000 generations have been set in this study.



strategy of discretization is easier for implementation, which decreases substantially the number of auxiliary variables.



0.05, 0.06, 0.07, 0.08, · · ·, 3.19, 3.20 . This

The system used for evaluation contains 22 DORs to be coordinated on 11 transmission lines (TLs) as shown in Fig. 3. It is a 138 kV transmission network which is a region within the Brazilian power system operated by ISA-CTEEP (Companhia de Transmissão de Energia Elétrica Paulista) transmission company. The minimization problem has 45 nonlinear constraints and 44 discrete variables. Using the CAPE software and the database of the test system provided by ONS [19], a short-circuit study has been carried out. In this study, the short-circuit currents for primary relays (ICC,p ) and short-circuit currents for its respective backup relays (ICC,b ) have been calculated. The set of primary relay (Rp ) and backup relay (Rb ) was defined in accordance with the main network configuration using the procedure described in Section 3. This definition also considers the minimum condition of relay operation, i.e., those relays P/B pairs which observe a low short-circuit current that may never produce a trip signal, resulting in a too long operation time that are not considered in the coordination process. In Table 1 all shortcircuit currents (module and respective angle) of the considered primary and backup relay pairs in coordination process are shown. Table 2 shows the rated currents of the TL elements discussed in Eq. (4) (constraints c and d). For each TL, the numbers in bold means that the component has the lowest value of the rated current which will limit the current in the bay. For example, TL1 is limited by its conductor, which rated current is 333A on both bays (1 and 2). On the other hand, TL10 is also limited by the conductor limit, however only by bay 19. The lowest current of TLs are observed for TL3, TL4, TL6 and TL7, and all of them are parallel lines (289A). The largest current operating limit is observed for TL1, TL2, TL5, TL8 and TL10. 20% is mostly determined by I Basically, Icap cond , followed by ICT (2 cases − TL9 and TL11). The HGA was performed with 50 chromosomes, 90% crossover rate and 0.3% mutation rate in order to achieve coordination among all 22 DORs. In Table 3 the TD and pick-up current tap (ϒ i ) values, calculated for HGA executions at the 3,500th generation, are shown. At this generation, the sum of the primary relays operation time f (x) tends to stabilize and all coordination constraints are satisfied achieving the stop criterion. The final value of f (x) found by the HGA at the 3,500th generation goes from 4.3882s to 4.4315s among all HGA executions, as listed in Table 3. AVER. and STDEV columns are the average and standard deviation, respectively. This data show that the HGA provides high quality feasible coordination solutions in all performed cases. It is also possible to observe in Table 3 that the TD setting values since 1st through 10th HGA execution are the same (STDEV equals to zero), remaining in the minimum allowed value (0.05), except TD17 and TD21 which are slightly higher (0.11 and 0.09, respectively) and represents 2 out of 22 relays (9.09% of the cases). These results can be explained due to the fact that TD is mainly calculated in the LP stage, which is always in search of the minimum feasible solution. Pick-up current taps (ϒ i ) calculated by the HGA are not similar in all 10 performed situations, showing a higher variation on its values when compared with the TD. This behavior is explained due to the different initial chromosome population and genetic operators’ actions that may lead to different final solutions, but near to the minimum coordination solution as mentioned before. One may also notice from Table 3 that 33% of the 1A version DORs have their 1A 1A pickup tap set in the range of 0.1A to 1A (ϒ 1 and ϒ31A ); 33.3% (ϒ 2 1A

and ϒ41A ) in the range of 1A to 2A; and the other 33.3% (ϒ 11 and 1A ) within the range of 2A to 4A. Regarding the 5A version DORs, ϒ13

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

405

Fig. 3. Real power transmission system: 11 TLs, 8 main buses, 22 DORs, several transformers and generators (some of them are distributed generators). 5A

5A

12.5% (ϒ 15 and ϒ 18 ) have their pickup taps set in the range of 0.5A 5A 5A 5A 5A 5A 5A 5A to 5A; 43.75% (ϒ 5 , ϒ 6 , ϒ 7 , ϒ 8 , ϒ 9 , ϒ 10 and ϒ 11 ) within 5A to 5A 5A 5A 5A 5A 10A; 31.25% (ϒ 12 , ϒ 14 , ϒ 16 , ϒ 20 and ϒ 22 ) in the range of 10A to 5A 5A 15A, and 12.5% (ϒ 17 and ϒ 21 ) within 15A to 20A. Moreover, it was verified from the optimization results that all coordination constraints are met at the first generations of the HGA. The fastest HGA execution achieves coordination among all DORs

at the 121st generation and the slowest HGA execution completes this process at the 740th generation. Subsequent generations seem to exclusively minimize f (x) keeping the coordination feasibility. Table 3 refers to DORs parameters also calculated by GAMS solvers used in this work. Firstly, AlphaECP (version 1.75.03) has found no solution after 167.23s, despite its ability to solve this type of problem. In the same way, DICOPT solver was not able to

Table 1 Short-Circuit Currents ICC,p for Primary Relays (Rp ) and short-circuit currents ICC,b for its respective backup relays (Rb ).

406

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

Table 2 Rated Current of TL Elements. ICB is the circuit breaker rated current; Isec is the circuit disconnector rated current; Iblock is the rated current of the block coil; ICT is the rated current of the corresponding CT; Icond is rated current of the TL; Icap is the current limit of the transmission line under normal operation; I20% cap is the current limit of the transmission line with safety factor of 20%. The values in bold are the current limitation imposed by the components which define Icap . TL

Bay/RDS

I CB (A)

I secc (A)

I block (A)

I CT (A)

I cond (A)

I cap (A)

20% Icap (A)

TL1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

1000 1000 1000 1000 1000 2000 2000 3150 1000 3150 1000 1600 1000 1600 2000 1600 2000 1000 1600 2000 1000 2000

600 600 600 600 600 2000 2000 800 600 800 600 500 600 500 2000 500 2000 600 500 2000 600 2000

630 630 630 630 1250 1250 1250 – 630 630 – – 400 400 – 630 – 630 630 – 630 1250

600 600 600 600 600 600 600 800 600 800 600 400 600 400 400 400 1600 300 400 400 300 400

333 333 333 333 289 860 860 289 333 333 289 289 289 289 860 333 380 333 333 860 333 860

333

402 402 402 402 346.8 346.8 446.8 348 399.6 400 348 346.8 348 346.8 400 400 360 361.6 400 400 360 360

TL2 TL3 TL4 TL5 TL6 TL7 TL8 TL9 TL10 TL11

find a feasible integer solution (4.91s), thus providing a nonlinear relaxed solution, which violates some of the constraints. Similar to the results obtained by AlphaECP, the settings found from DICOPT have been represented by ‘*’, due to the non-integer values. On the other hand, BARON 14 has reported a good result, without any infeasibility or errors after 8.59s. The majority of TD values (59.09%) were set in 0.05, and 22.72% were set in 0.06. Comparing the 1A version relays, 66.67% have ϒ values from 1 A to 2 A (R1 through R4), whereas 33.33% have ϒ values from 2 A to 4 A. No pickup taps were set from 0.1 A to 1 A, as it was observed in HGA

333 289 289 333 289 289 333 300 333 300

executions. Concerning the 5A version devices, 37.5% have their pickup taps set between 0.5 A to 5A; 18.75% in the range of 5A to 10A; 31.25% from 10 A to 15 A, and 12.5% within 15 A to 20 A. BONMIN solver was another one that provided a feasible solution, where DORs parameters are very similar to the ones given by the HGA. Among all solvers, BONMIM has been the one which achieved the lowest objective function (within 5.02s). The fifth solver KNITRO exceeded the maximum time of simulation, stopping at 360 s without a feasible solution. In this simulation, one constraint (R11–R14 pair) has not been satisfied, exceeding the CTI

Table 3 Time Dial and Pickup Tap of Relays R1– R22 (HGA and GAMS Solvers: AlphaECP (AE), BARON14 (B14), BONMIM (BM), DICOPT (DC) and KNITRO (KN)).

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

value. Finally, the sixth solver SBB has taken 104.96 s to achieve a solution. Among all solvers which provided a good quality solution, the SBB has provided the worst solution. Comparing all solvers (except SBB) which converge to a feasible solution, identical pickup tap values were obtained for relay R3 and for relays from R6 through R10, despite R3 being the only relay set with identical TDs values. Moreover, there is an interesting correlation between how many times the minimum TD (0.05) is set among all DORs (HGA = 22 times; BARON 14 = 13 times; BONMIN = 17 times; KNITRO = 14 times and; SBB = 2 times) and the value of f (x) in Table 3. The observed behavior reveals that lower values of f (x) may be reached when more relays are set with its minimum TD s. Although the HGA running time is higher than the BONMIN solver, an average of 33.4 min for the 8 performed cases at the 3,000th generation, the HGA can find different better feasible integer solutions in all performed tests. Moreover, since the coordination studies do not have the requirement to provide real-time response, the HGA running time is within acceptable values. The consideration of the current direction, represented by the constraint a of (4), results in better working of the search, since the currents with opposite direction to the settings of the relays do not need to be checked by the constraints. The numerical results have been obtained on i686 computer with a 3.40 GHz Intel® CoreTM i7-2600 microprocessor and 8 GB of memory running MS Windows 7 Professional Service Pack 1, for both HGA and GAMS solvers executions. Finally, from the results of Table 3 it is possible to verify the HGA was able to provide the set of parameters that represents a faster operating time for the DORs (f (x)) when compared with the feasible solutions provided by the GAMS solvers. All results have been tested against the CAPE built-in relay checking function.

5. Conclusions The optimized setting of DORs represents an important enhancement in power system protection. The optimized settings are based on mixed-integer nonlinear mathematical optimization, which has been solved by two approaches, the classical optimization methods and the approximate hybrid method, which combines positive features from both classical and approximated methods. The HGA obtained high-quality solutions which represent 12.10% and 27.31% reduction on the average value of the performance function for all test cases, when compared with the feasible integer solution given by BONMIN and SBB solvers, respectively. Comparing the best solution found by HGA and these solvers, 12.58% and 27.70% reduction have been reached in the study. The DICOPT and KNITRO solvers failed in finding the TD and current pick-up values that could provide coordination among the 22 modeled DORs. The difficulty in finding the solutions by classical algorithms is partially explained by the combinatorial nature of the problem in addition to the nonlinearity of the optimization model. Besides the solution quality, and ability in finding high quality solutions, the HGA has an important characteristic of presenting flexible structure to change the logic of the search process and also the feature of storing a set of feasible solutions which may be applied in the coordination problem, according to the desired protection strategy (policy).

Acknowledgements The authors are grateful to the São Paulo Research Foundation (FAPESP − Grant Number 2012/25292-1, 2014/27342-1) and to the ISA-CTEEP (PD-0068-0020/2011 − ANEEL) for supporting this research.

407

References [1] L. Hewitson, M. Brown, R. Balakrishnan, Practical Systems Protection, Elsevier-Newnes, 2004, pp. 288. [2] A.J. Urdaneta, R. Nadira, L.G.P. Jiménez, Optimal coordination of directional overcurrent relays in interconnected power systems, IEEE Trans. Power Deliv. 3 (July) (1988) 903–911. [3] A.J. Urdaneta, et al., Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays, Int. J. Electr. Power Energy Syst. 23 (2000) 819–825, http://dx.doi.org/10.1016/ S0142-0615(00)00097-1. [4] M. Ezzeddine, R. Kaczmarek, A novel method for optimal coordination of directional overcurrent relays considering their available discrete settings and several operation characteristics, Electr. Power Syst. Res. 81 (2011) 1475–1481, http://dx.doi.org/10.1016/j.epsr. 2011.02.014. [5] H. Leite, J. Barros, V. Miranda, The evolutionary algorithm EPSO to coordinate directional overcurrent relays, in: Proc: 10th IET International Conference on Developments in Power System Protection, Manchester, UK, 2010, pp. 1–5, http://dx.doi.org/10.1049/cp.2010.0318. [6] W.M.S. Bernardes, F.M.P. Santos, E.N. Asada, S.A. Souza, M.J. Ramos, Application of discrete PSO and evolutionary PSO to the coordination of directional overcurrent relays, in: Proc: 2013 17th International Conference on Intelligent System Applications to Power Systems (ISAP), Tokyo, Japan, 2013, pp. 1–6. [7] F.B. Bottura, W.M.S. Bernardes, M. Oleskovicz, E.N. Asada, M.J. Ramos, S.A. Souza, Coordination of directional overcurrent relays in meshed power systems using hybrid genetic algorithm optimization, in: Proc: 12th IET International Conference on Developments in Power System Protection (DPSP 2014), Copenhagen, Denmark, 2014, p. 12 (73-6). [8] F.B. Bottura, M. Oleskovicz, D.V. Coury, S.A. Souza, M.J. Ramos, Hybrid optimization algorithm for directional overcurrent relay coordination, in: Proc 2014 IEEE Power & Energy Society General Meeting, Washington, USA, 2014, pp. 1–5, http://dx.doi.org/10.1109/PESGM. 2014.6939826. [9] J.A. Sueiro, E. Diaz-Dorado, E. Míguez, J. Cidras, Coordination of directional overcurrent relay using evolutionary algorithm and linear programming, Int. J. Electr. Power Energy Syst. 42 (2012) 299–305, http://dx.doi.org/10.1016/j. ijepes.2012.03.036. [10] F. Razavi, H.A. Abyaneh, M. Al-Dabbagh, R. Mohammadi, H. Torkaman, A new comprehensive genetic algorithm method for optimal overcurrent relays coordination, Electr. Power Syst. Res. 78 (4) (2008) 713–720, http://dx.doi. org/10.1016/j.epsr. 2007.05.013. [11] P.P. Bedkar, R.S. Bhide, Optimum coordination of overcurrent relay using continuous genetic algorithm, Expert Syst. Appl. 9 (Sep. 2011) 11286–11292. [12] P.P. Bedkar, R.S. Bhide, Optimum coordination of directional overcurrent relays using the hybrid GA-NLP approach, IEEE Trans. Power Deliv. 26 (1) (2011) 109–119. [13] J. Sadeh, V. Aminotojari, M. Bashir, Optimal coordination of overcurrent and distance relays with hybrid genetic algorithm, Proc: 10th International Conference on Environment and Electrical Engineering (EEEIC−2011) (2011) 1–5, http://dx.doi.org/10.1109/EEEIC.2011.5874690. [14] M. Singh, B. Panigrahi, A. Abhyankar, Optimal coordination of directional over-current relays using teaching learning-based optimization (TLBO) algorithm, Int. J. Electr. Power Energy Syst. 50 (2013) 33–41, http://dx.doi.org/ 10.1016/j.ijepes.2013.02.011. [15] M. Farzinfar, M. Jazaeri, F. Razavi, A new approach for optimal coordination of distance and directional over-current relays using multiple embedded crossover PSO, Int. J. Electr. Power Energy Syst. 61 (2014) 620–628, http://dx. doi.org/10.1016/j.ijepes.2014.04.001. [16] Computer-Aided Protection Engineering-CAPE, Electrocon International Incorporated. [Online] Available: http://www.electrocon.com. (accessed: 18.02.16.). [17] Siemens AG (SIPROTEC), Multi-Functional Protection Relay with Local Control 7SJ62/63/64, firmware version 4.6, document number C53000-G1179-C147-1, (2007). [18] Electrical Relays—Part 3: Single Input Energizing Quantity Measuring Relays Whit Dependent or Independent Time, IEC, 1989, pp. 60255–60263. [19] Operador Nacional do Sistema-ONS. [Online] Available: http://www.ons.org. br/operacao/base dados curtoc referencia.aspx#dados. (accessed: 22.05.15.). [20] A.S. Braga, J.T. Saraiva, Coordination of overcurrent directional relays in meshed networks using the Simplex method, in Proc 8th Mediterranean Electrotechnical Conference, vol.3, pp. 1535–1538, (1996), 10.1109/MELCON.1996 551243. [21] A.S. Noghabi, J. Sadeh, H.R. Masshadi, Considering different network topologies in optimal overcurrent relay coordination using hybrid GA, IEEE Trans. Power Deliv. 24 (4) (2009) 1857–1863, http://dx.doi.org/10.1109/ TPWRD.2009.2029057. [22] The General Algebraic Modeling System (GAMS). Available: http://www. gams.com/, (accessed: 09.05.16.). [23] M. Damborg, R. Ramaswami, S.S. Venkata, J.M. Postforoosh, Computer aided transmission protection system design−part I: algorithms, IEEE Trans. Power Apparatus Syst. PAS-103 (1) (1984) 51–59, http://dx.doi.org/10.1109/TPAS. 1984.318576, ISSN 0018-9510. [24] S.S. Rao, Engineering Optimization Theory and Practice, 4th ed., John Wiley and Sons, Inc, Hoboken, New Jersey, 2009.

408

F.B. Bottura et al. / Electric Power Systems Research 143 (2017) 400–408

[25] The MathWorks, Inc., MATLAB and Optimization Toolbox Release 2012, Natick, Massachusetts, United States. [26] H. He, et al., Application of a SFCL for fault ride-through capability enhancement of DG in a microgrid system and relay protection coordination, IEEE Trans. Appl. Supercond. 26 (October (7)) (2016), http://dx.doi.org/10. 1109/TASC.2016.2599898. [27] S.S. Gokhale, V.S. Kale, An application of a tent map initiated Chaotic Firefly algorithm for optimal overcurrent relay coordination, Int. J. Electr. Power Energy Syst. 78 (2016) 336–342, http://dx.doi.org/10.1016/j.ijepes.2015.11. 087. [28] M.A.M. Ariff, B.C. Pal, A.K. Singh, Estimating dynamic model parameters for adaptive protection and control in power system, IEEE Trans. Power Syst. 30 (March (2)) (2015), http://dx.doi.org/10.1109/TPWRS. 2014.2331317. [29] The General Algebraic Modeling System (GAMS)−Solvers. Available: https:// www.gams.com/help/index.jsp?topic=%2Fgams.doc%2Fsolvers%2Findex. html. (accessed: 05.08.16.).

[30] Artelys Knitro Documentation Release 10.0.1, Artelys. Available: https:// www.artelys.com/downloads/pdf/composants-numeriques/knitro/Knitro 10 0 UserManual.pdf, (accessed: 09.05.16.). [31] N. Sahinidis, BARON user manual v. 15.6.5, The Optimization Firm, LLC, [Online], Jun 5, 2015. Available: http://www.minlp.com/downloads/docs/ baron%20manual.pdf, (accessed: 17.02.16.). [32] M.R. Bussieck, A.S. Drud, GAMS−SBB: a new solver for Mixed Integer Nonlinear Programming, talk, OR 2001, Section “Continuous Optimization”, 2001. Available: https://www.gams.com/presentations/or01/sbb.pdf, (accessed: 16.08.16.). [33] H.H. Zeineldin, E.F. El-Saadany, M.M.A. Salama, Optimal coordination of overcurrent relays using a modified particle swarm optimization, Electr. Power Syst. Res. 76 (11) (2006) 988–995, http://dx.doi.org/10.1016/j.epsr. 2005.12.001.