A dynamic objective function for communication-based relaying: Increasing the controllability of relays settings considering N-1 contingencies

Electrical Power and Energy Systems 116 (2020) 105555

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A dynamic objective function for communication-based relaying: Increasing the controllability of relays settings considering N-1 contingencies Amin Yazdaninejadi, Vahid Talavat, Sajjad Golshannavaz

T

⁎

School of Electrical Engineering, University of Urmia, Urmia, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Dynamic mixed coordination Dual setting directional overcurrent relays Distance relays N-1 contingency

Considering different configurations of a protected network in relays coordination offers higher reliability, security, and sustainability. However, overcurrent relaying in N-1 contingency states stands as a complicated problem especially in interconnected sub-transmissions systems with distance relays. To overcome this challenge, the current paper proposes a coordination scheme in which dual setting directional overcurrent relays (DDOCRs) and low bandwidth communication links are jointly deployed instead of conventional DOCRs. By doing so, more flexibility and extensibility is provided in the coordination process. Moreover, in order to direct the relays settings toward optimal solutions, a new dynamic objective function is devised. This approach strengthens the controllability of relay settings in different conditions by pulling the variables towards the feasible region. The proposed formulation considers both standard and non-standard relay characteristics and demonstrates a nonlinear programming fashion which is solved by chaotic particle swarm optimization algorithm. Results approve that D-DOCRs in conjunction with distance relays can successfully maintain a proper coordination in N-1 contingency states, supported by the proposed dynamic approach.

1. Introduction Protective relay coordination is an important technical requirement for an effective protection scheme to guarantee selective, fast, and reliable isolation of faulty sections in power systems [1]. According to the study presented in [2] which addresses the NERC reliability standards, outages of any line or generator is considered as an N-1 contingency state. Previously, N-1 contingency states have been widely deployed in power energy system planning studies [3,4]. In a similar manner, a robust and successful protection scheme necessities adoption of N-1 states in relays coordination [5]. It is now a well-understood fact that optimal protection coordination of directional overcurrent relays (DOCRs) is a highly constrained optimization problem [1,6]. In sub-transmission systems, simultaneous deployment of both overcurrent and distance relays, as a common practice, increases the protection complexity and thus demands a strong coordination process. The aforementioned complexity stems from the fact that in such networks, three different coordination cases must be accounted for which include: (1) a distance relay with a distance relay, (2) a directional overcurrent relay (DOCR) with another DOCR, and (3) a DOCR with a distance relay. This complexity is further intensified when the aim is to have an assured protection for different configurations of the power systems which entails renewing of the protection ⁎

scheme. Directional overcurrent relaying, as a complicated problem, alone and beside distance relays is tackled in several literatures. Different optimization methods such as linear programming approaches in [6–8], heuristic algorithms in [9–12], and some hybrid algorithms in [13–15] are thoroughly investigated. Moreover, fuzzy logic is employed for coordinating overcurrent relays with time-current-voltage characteristics in [16]. Advantages of deploying different numeric relays are explored in [17,18]. Based on numeric DOCRs, different coordination strategies and adaptive protection coordination approaches are devised for overcurrent relaying in [19–23]. Numeric relays are based on the use of microprocessors and, in practice, their time-overcurrent protection units normally have fixed steps for current pickups and time multipliers lower than conventional relays. Moreover, in addition to conventional variables, some constant parameters can also be included in variables set which can offer more flexibility. What’s more, these relay can follow lookup tables which helps to yield arbitrary characteristics [24]. Moreover, the changes in network configuration ends in mal-operation of relays in protection process [5]. In [5] and [25], the protection coordination problem is tackled considering all possible network topologies. Although, the protection coordination metrics are improved in aforementioned studies, still, the miscoordination as an important issue remains a challenging concern in aggravating the

Corresponding author. E-mail address: [email protected] (S. Golshannavaz).

https://doi.org/10.1016/j.ijepes.2019.105555 Received 27 January 2019; Received in revised form 20 August 2019; Accepted 17 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. A typical power system, (a): main topology, (b): line 1 outage, (c): line 2 outage, (d): line 3 outage.

This issue not only is improved in the main configuration of the network but also is enhanced in N-1 contingency states. That is, the ongoing study puts forward an efficient protection coordination approach for combination of D-DOCRs and distance relays in sub-transmission systems considering N-1 contingency states. As mentioned earlier, how much the number of contingency states increases, the number of selectivity constraints is increased drastically which intensifies the complexity of relaying process, especially besides distance relays. This is while; each D-DOCR provides protection capabilities in both forward and reverse directions introducing two variables for time dial settings (TDS) and two variables for pickup currents (Ip) in optimization process. This feature of dual setting relays helps to relax the conventional selectivity constraints to lessen the complexity of optimization space. Therefore, the obtained relaxation in coordination process of D-DOCRs and distance relays can help to yield faster protection task and eliminate the miscoordination records. Another key point to remember is that numerical relays can follow various inverse-time characteristics. Therefore, besides the typical settings, some constant parameters of relays characteristics for overcurrent relays are also included in the coordination process of D-DOCRs and distance relays. Accordingly, relays characteristics parameters are treated as optimization variables which results in higher flexibility in the coordination process and hence lowers operation time in clearing faults. The proposed approach is modeled as a nonlinear programming problem and solved based on chaotic particle swarm optimization (CPSO) algorithm. Furthermore, to accomplish the complicated target, the evaluating part in optimization process is also improved by a dynamic objective function. This modification averts the possibility of getting trapped in local minima and strengthens the controllability of the relays settings. Detailed simulation studies are conducted on the IEEE 14-bus sub-transmission system to highlight the effectiveness of the proposed coordination approach against the conventional ones.

cascading outages. In [5], the overcurrent relays settings for a microgrid are obtained optimally considering all network topologies. However, the coordination problem is solved based on single fault location in mid-points of the lines. This approach depreciates accuracy of the protection coordination along with the protected line, particularly in far-end locations. Fast pace of technological advances in relays with communication capabilities has paved the way for robust communication-assisted protection schemes. Nowadays, communication-based protection schemes are so prevalent in different levels of power systems studies. The power system communication infrastructures and the cyber security are discussed in [26]. Moreover, cyber security of host-and network-based substations are enhanced in [27]. Various communicationbased protection schemes are presented for industrial networks in [28], for distribution networks in [29,30], and for transmission networks in [31]. In this context, communication-assisted dual setting DOCRs (DDOCRs) are realized to augment the protection system capabilities [32,33]. A single unit of these numeric relays covers both forward and reverse directions concurrently and deploys a low bandwidth communication link to transfer a simple blocking signal to avoid any possible miscoordination. Application of D-DOCR has been investigated in radial distribution systems [34], in meshed and DG-integrated distribution systems [23], and in islanded and grid-connected microgrid installations [35]. However, deployment of these relays besides distance relays has not been explored, yet. Such combination can provide further enhancements in relay coordination in meeting N-1 contingency states. Beside the technical features, as the related optimization process is aligned with high computation burden and a large search space, efficient optimization approaches should be devised. For instance, dynamic approaches could be deployed in optimization engines to avert the possibility of getting trapped in local minima and strengthening the controllability of the relays settings. This paper proposes a communication-assisted protection coordination approach that relies on a combination of D-DOCRs and distance relays for the protection of sub-transmission systems. Different combinations of D-DOCRs and distance relays are considered as primary and backup relays which requires an efficient and optimallytuned coordination process to overcome the miscoordination challenge.

2. Proposed method 2.1. Protection coordination considering N-1 contingencies In single contingency coordination process, the relays are adjusted 2

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coordination between R2rv and R1fw is maintained.

to operate in a sequence which is valid only for the main topology of the investigated power system. Power energy systems may experience changes in the network topology. Therefore, a robust protection scheme should satisfy the coordination task in N-1 contingency states. Though it is technically an acute need, it intensifies the complexity of the coordination process. To bring about a fruitful illustration of the case, Fig. 1(a) shows a simple test system to be explored. As can be seen, three network topologies are attainted based on single line outage contingencies in Fig. 1(b)–(d). If different network topologies are considered, pair relays experience different fault currents in different topologies and this in turn increases the number of constraints to be dealt. Therefore, a new protection scheme with simple optimization space could be supportive.

2.3. Joint communication-assisted D-DOCRs and distance relays The proposed mixed coordination of D-DOCRs and distance relays is presented in this subsection. Fig. 3 highlights the differences between the coordination of a conventional DOCR and the communication-assisted D-DOCR with distance relays, presented on an illustrative power system. In this figure, each relay set, identified by “S”, includes a distance relay and a DOCR. For a fault at point A and for the case of conventional DOCRs (Fig. 3a), the primary relays are (R1OC , R1Dis ) in S1 and (R6OC , R6Dis ) in S6. The backup relays are assigned as (R3OC , R3Dis ) in S3 and (R4OC , R4Dis ) in S4. Note that superscripts “OC” and “Dis” refer to overcurrent and distance relays, respectively. By referring to Fig. 3b, DDOCRs are deployed in conjunction with distance relays where different primary and backup relays are assigned. For the same fault, the Dis Dis OC primary relays are determined as (R1,OC fw , R1 ) in S1 and (R6, fw , R6 ) in Dis OC R R in S2 and in S3 and also S6. The backup relays are R2,OC 3 rv 5, rv in S5 and R4Dis in S4, respectively. In the conventional scheme, the first zone (Z1) of distance relay isolates the faults on 80–90% of the protected line. Moreover, no intentional time delay is considered. The second zone (Z2) protects the remainder of the line that is not seen by Z1. The third zone (Z3) not only covers the whole protected line but also protects the longest line leaving the ending bus. Coordination of Z2 and Z3 with the first zone is achieved by intentionally delaying the operation of relay for Z2 and Z3. In this way, a delay time of 15 to 30 cycles is considered for Z2 and a delay time of 20 cycles is deployed for Z3. This issue is further illustrated using the relay characteristics curves in Fig. 4(a). In combinatorial schemes, the coordination task is performed based on faults at four critical points. As can be seen, the first point covers near-end of the protected line. The second point accommodates the fault at the end of the second zone which corresponds to the backup distance relay. The third point relates to the fault at the beginning of the second zone of the primary distance relays. The last one is far-end fault point. If conventional DOCRs are deployed, see Fig. 4(a), coordination of two DOCRs (R1OC , R2OC ) must be fulfilled by satisfying the coordination time interval (CTI) at F1 and F4. Thus, to achieve the required CTI, there is a higher upward shift in time-inverse characteristics of R2OC which increases the relay operating time. On the other hand, by referring to Fig. 4(b) and in OC the case of D-DOCRs, instead of R2OC , R3,OC rv is the backup for R1 , represented in red. Accordingly, as shown in Fig. 4(b), the characteristic of R2OC can be shifted downward given that a blocking signal is sent to it once R1 operates. Thus, lower time-inverse characteristics could be achieved for forward sides of the relays. In the conventional scheme, for a fault at point F2, the second zone timing of R1Dis namely (TZ2 ) must be set at higher values than the operation time of R1OC and should satisfy the CTI constraint. Similarly, for a fault at F2, lower time-inverse characteristics could be achieved for R1,OC fw . Consequently, for a fault at F2, if D-DOCRs are deployed, maintaining the required CTI between the primary and backup relay pairs can be achieved with less operation time than the case with conventional DOCRs. If a fault occurs at the third critical point (F3), TZ2 of R1Dis must clear the fault. In the case of a failure, the backup relay R2OC isolates the fault after CTI. On the contrary, Fig. 4(b) presents the coordination between D-DOCRs and disOC OC tance relays. In this case, the following relay pairs (R1,OC fw , R3, rv ), (R1, fw , OC OC R2Dis ), (R1Dis , R3,OC R ) and ( , ) should be coordinated respectively for R 1, fw 3, rv rv Dis R and are asthe faults at F1, F2, F3, and F4. As can be seen, R1,OC 1 fw Dis signed as primary relays being backed up by R3,OC rv and R2 . In D-DOCRs, Dis R3,OC should be consistent with selectivity constraints at rv and TZ2 of R1 F3.

2.2. Operation of Communication-Assisted D-DOCRs The recently evolved D-DOCRs offer bidirectional protection capabilities in both forward (denoted by subscript “fw”) and (denoted by subscript “rv”) directions through a single unit. These functionalities are numerically provided without any increase in cumulative number of relays and thus making these relays an attractive choice in comparison to the conventional ones. In this context, the reverse side of each relay could be deployed as the backup unit for the next front line. The general representation of a conventional DOCR time-inverse characteristics can be expressed as follows.

⎛ t = TDS × ⎜ ⎜ ⎜ ⎝

α

() IF Ip

β

⎞ ⎟ ⎟ − 1⎟ ⎠

(1)

In (1), the coordination process is established based on TDS and Ip adjustments. In the case of D-DOCR, (TDSfw, Ipfw) and (TDSrv, Iprv) are involved in coordination process. Referring back to (1), α and β are the coefficients of time-inverse characteristics which are assumed to be constant in conventional standard coordination approach. In contradiction, numeric relays are capable of establishing non-standard timeinverse characteristics. In this case, not only TDS and Ip are variables in (1) that can be optimized, but also α and β are treated as optimization variables to define the optimal relay characteristic to be used. This feature provides higher flexibility in the coordination process which results in lower relay operation time for primary and backup units and averts miscoordination cases. Fig. 2 presents a protection scheme that relies on D-DOCR for a simple power system. For a fault at A, R1fw is assigned as the primary relay with the reverse side of R2 acting as its backup. A blocking signal should be transferred through a communication link to avoid mal-operation of the relays along the protected line. For the sake of clarity, consider the same fault at A. If R1fw cannot isolate the fault (due to a malfunction), both R2rv and R3fw are triggered by the fault currents. To avoid mal-operation of R3fw, R2 sends a blocking signal through a low bandwidth communication link to R3. Accordingly, protection

2.4. Enhancing the evaluation process: a dynamic objective function To transform the constrained problem in to an unconstrained one, usually different penalties are employed through the objective

Fig. 2. A typical power system. 3

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Fig. 3. Pair relays in protection task, (a): each relay set “S” contains a distance and a conventional DOCR, (b): each relay set “S” contains a distance and a D- DOCR.

F = {x ∈ Rn| uj (x ) ⩽ 0, j = 1, ...,Q, hj (x ) ⩽ 0, j = Q + 1, ...,P , yj (x ) ⩽ 0, j = P + 1, ...,J }

(5)

Accordingly, the proposed objective function is represented as follow:

OF = f (x ) + penalty1 + penalty2 + penalty3

(6)

Q

⎡ ⎤ penalty1 = [V1 (it )] × ⎢A ∑ (δj ωj Φ(dj (S ))) + PT⎥ δS ⎣ j=1 ⎦ ⎡ penalty2 = [V2 (it )] × ⎢A ⎣

⎡ penalty3 = [V3 (it )] × ⎢A ⎣

P

∑ j=Q+1

J

∑ j=P+1

(7)

⎤ (δj ωj Φ(dj (S ))) + PT⎥ δS ⎦

(8)

⎤ (δj ωj Φ(dj (S ))) + PT⎥ δS ⎦

(9)

where, A is severity factor, ωj is the weight factor for constraint j, dj (S ) is the measure of the degree of violation of constraint j introduced by solution S, Φ is the function of this measure, PT is the penalty threshold factor and V (it ) is an increasing function of the current iteration it in the range of (0,…,1). V (it ) is as follows: γ1 it ⎞ V1 (it ) = ⎛ ⎝ Maxit ⎠

Fig. 4. Combined coordination of (a): conventional DOCRs with distance relays, (b): D-DOCRs with distance relays.

it ⎞ V2 (it ) = ⎛ ⎝ Maxit ⎠

functions to steer the variables towards the optimal solutions. In this context, different statistic objective functions are presented in literature. Such objectives contain parameters to be set by the users in other to control the amount of penalty to be added when the constraints are violated. In this paper, dynamic penalties are considered through the objective function of the conducted study. As mentioned earlier, the proposed approach considers three sets of constraints in three different cases. Thereby, the problem can be considered within the following model:

minimize:z = f (x )

uj (x ) ⩽ 0; for j = 1, ...,Q ⎧ ⎪ Subject to: hj (x ) ⩽ 0; for j = Q + 1, ...,P ⎨ ⎪ yj (x ) ⩽ 0; for j = P + 1, ...,J ⎩

it ⎞ V3 (it ) = ⎛ ⎝ Maxit ⎠

(11)

γ3

(12)

where, γ1, γ2 , and γ3 are constant, Maxit is the total number of iterations and also:

(2)

1 if constraint j is violated δj = ⎧ ⎨ 0 otherwise ⎩

(13)

1 if S is feasible δs = ⎧ ⎨ ⎩ 0 otherwise

(14)

As mentioned earlier, recent trend in relays coordination process is based on advances in heuristic and intelligent optimization algorithms which calls the need for an efficient objective function. In the proposed penalty function approach, Φ measures the value of the penalties. In the earlier studies, the static term that measures the penalties varies through a quadratic function by any change in the negative part of discrimination time between any primary and backup relay [36]. Small violations are known as severe obstacle in obtaining reliable coordination [37] based on quadratic function. What’s more, increasing

(3)

where, u , h and y are the constraints with respect to each of the cases. The search space and feasible space, denoted by S and F, are defined by:

S = {x = (x1, x2 , ...,x n )T ∈ Rn : ln ⩽ x n ⩽ un , j = 1, ...,n}

(10)

γ2

(4) 4

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Table 3 Statistical analyses for results in first scenario. Parameters

Fault @ F1 F2

Minimum operation time of relays Maximum operation time of relays Mean of operation time of relays Variance of operation time of relays Sum of operation time of primary relays Sum of operation time of backup relays Total operation time of all relays in primary and backup process

0.254 0.331 0.773 0.869 0.455 0.547 0.022 0.018 13.641 16.415 35.719 35.236 352.758 s

F3

F4

0.533 0.9 0.701 0.01 21.042 50.104

0.338 1.495 0.687 0.041 20.613 115.713

Fig. 5. Shifting up respected penalty function.

previous ones are: (i) The proposed objective function provides different pressure on different violations. Moreover, to keep the optimization algorithm in road, it does not impose unusual pressure on the large violations. Accordingly, the shifting values in the proposed penalty methods, as shown in Fig. 5, help the optimization algorithm to pass from small miscoordinations. Furthermore, since three different coordination cases must be accounted in the relaying process, the shifted values are different for uj , hj and yj . Herein, uj shows the violation between two overcurrent relays in relays pair j. Likewise, hj and yj are considered for violations in two other cases which are illustrated in Fig. 5. That is, the case with huge number of small miscoordiantions can employ a big shifting value and the case with a few number of number of small miscoordiantions can employ a small shifting value. (ii) It has a dynamic feature. It is stated that by considering high degree of penalty, more pressure is imposed to attain feasibility. Consequently, the algorithm moves faster toward solution with lower violation, even if far from optimal. This is while; low degree of penalty results less emphasis on feasibility and the algorithm may trap in infeasible solutions [38]. The proposed objective function starts with low pressure and ends in high pressure. By doing so, initially the particles distribute vastly in search space. In continue, by updating particles in each loop, the objective function poses convenient pressure for converging algorithm. In coordination process, penalties are included for selectivity constraints which are violated. In the previous studies, the employed penalty terms are statics [23,36,37] or the employed dynamic behavior are associated with optimization algorithm which are applied on the whole of the objective function. This is while; in this paper, the proposed dynamic behavior is adopted for relays coordination and just applied on penalty terms. Moreover, the proposed dynamic penalty method behaves differently in different cases. As pointed earlier, the coordination combinations of D-DOCRs and distance relays has three cases. Therefore, the proposed dynamic penalty methods by employing different γ in (10), (11), and (12) considers different dynamic behavior

Table 1 Optimization variables in first scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Parameters

Relay no.

TDS

Ip(A)

TZ2 (s)

0.14 0.15 0.145 0.1 0.153 0.1 0.173 0.137 0.196 0.125 0.245 0.185 0.152 0.165 0.415

0.359 0.356 0.343 0.343 0.338 0.338 0.259 0.257 0.191 0.191 0.112 0.114 0.298 0.3 0.146

0.689 0.661 0.678 0.589 0.77 0.689 0.639 0.689 0.678 0.689 0.639 0.595 0.578 0.631 0.88

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Parameters TDS

Ip(A)

TZ2 (s)

0.27 0.399 0.125 0.286 0.148 0.45 0.227 0.401 0.208 0.402 0.4 0.434 0.525 0.34 0.413

0.146 0.147 0.147 0.344 0.344 0.123 0.123 0.185 0.185 0.075 0.075 0.032 0.032 0.108 0.108

0.587 0.849 0.789 0.84 0.9 0.679 0.57 0.732 0.619 0.664 0.698 0.823 0.533 0.765 0.9

the coefficients counts in quadratic function makes the optimization algorithm hard to converge. To overcome this issue, a new penalty method is proposed in [37] which employs a constant value for different violations through the penalty term. By doing so, the same pressure is created for both small and large miscoordiantions. Thereby, devising a proper Φ in the proposed dynamic objective function that can pass small violations and employ a proper pressure on small and large miscoordiantions is of interest. Here, Φ is inspired from those functions presented in [23] and [38]. This penalty term is a shifted logarithmic function which is depicted in Fig. 5. By doing so, advantages of proposed objective function with new penalty terms over

Table 2 Operation time of relays in second for different fault locations associated with first scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fault @

Relay no.

F1

F2

F3

F4

0.269 0.335 0.272 0.254 0.321 0.286 0.334 0.312 0.347 0.259 0.47 0.326 0.401 0.436 0.6

0.388 0.46 0.461 0.378 0.49 0.395 0.489 0.432 0.489 0.345 0.569 0.407 0.44 0.478 0.7

0.689 0.661 0.678 0.589 0.77 0.689 0.639 0.689 0.678 0.689 0.639 0.595 0.578 0.631 0.88

0.338 0.584 0.373 0.719 0.671 0.616 0.687 0.73 0.655 0.535 0.655 0.485 0.484 0.526 0.673

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

5

Fault @ F1

F2

F3

F4

0.565 0.564 0.281 0.504 0.436 0.673 0.48 0.651 0.519 0.593 0.631 0.593 0.626 0.53 0.773

0.618 0.699 0.331 0.589 0.52 0.713 0.499 0.779 0.577 0.645 0.68 0.65 0.701 0.624 0.869

0.587 0.849 0.789 0.84 0.9 0.679 0.57 0.732 0.619 0.664 0.698 0.823 0.533 0.765 0.9

0.705 0.806 1.495 0.667 0.756 0.748 0.521 0.887 0.674 0.693 0.729 0.744 0.771 0.704 0.982

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t fw, i, fa, c = TDSfw, i ×

⎛ ⎞ αfw, i ⎜ ⎟ ⎜ Isc, i, fa βfw,i ⎟ − 1⎟ ⎜ ⎛ Ip ⎞ , fw i ⎠ ⎝⎝ ⎠

⎞ ⎛ αrv, b ⎟ trv, b, fa, c = TDSrv, b × ⎜ ⎟ ⎜ Isc, b, fa βrv, b − 1⎟ ⎜ ⎛ Ip ⎞ ⎠ ⎝ ⎝ rv, b ⎠

(16)

(17)

Discrimination time (Δt ) is an important technical requirement for an efficient coordination process. By satisfying this constraint, coordination requirement of different pair relays is guaranteed. As clarOC OC ified, three different pair relays which include (Rfw , RrvOC ), (Rfw , RDis ) OC Dis and (R , Rrv ) should be satisfied. The coordination constraints, governing the operation of two D-DOCRs as the primary and backup, can be expressed as. OC

OC Δtb, fa OC = trvOC, b, fa − t fw , i, fa − CTI ⩾ 0, ∀ b

(18)

OC

uj = −Δtb, fa OC , j = 1, ...,P

(19)

P = B × Fa

(20)

In the second case, a D-DOCR acts as the primary relay and is backed up with a distance relay. In this case, the discrimination time is represented by (21). Here, the second zone of distance relay (TZ2 ) should be triggered CTI s following the operation time of D-DOCR. For the third case, the distance relay is the primary relay being backed up by a D-DOCR. For this case, (24) represents the discrimination time in which the operating time of D-DOCR exceeds the operation time of distance relay (TZ2 ) by CTI s. Dis

OC Δtb, fa OC = tbDis − t fw , i, fa − CTI ⩾ 0, ∀ b

(21)

Dis

Fig. 6. Discrimination time of relay pairs in different scenarios for (a): fault at F1, (b): fault at F2, (c): fault at F3, and (d): fault at F4.

hj = −Δtb, faOC , j = P + 1, ...,Q

(22)

Q=2×P

(23)

OC

Δtb, faDis = trvOC, b, fa − tbDis − CTI ⩾ 0, ∀ b for different cases.

(24)

OC

2.5. Proposed protection coordination scheme The main goal is to minimize the total operation time of all relays through optimal determination of the settings of D-DOCRs and also the second zone timing of distance relays. The proposed objective can be mathematically represented as follows: C

f (x ) =

⎡

Fa

I

B

⎤

I

⎣ fa = 1

i=1

b=1

⎦

i

(25)

J=3×P

(26)

Φ(d (Δt j )) =

⎧ if ⎨ if ⎩

Δt j > 0 Δt j < 0

0 log |Δt + 1| + vj

(27)

Besides the discrimination time constraints, TDS and Ip constraints should be considered for the inverse-time characteristics of D-DOCRs. Moreover, the second zone timing of distance relays (TZ2 ) should be settled within the corresponding limits which is expressed in (28)–(32).

OC OC ∑ ⎢ ∑ ( ∑ t fw , i, fa, c + ∑ trv, b, fa, c )⎥ + ∑ TZ 2, i c=1

yj = −Δtb, fa Dis, j = Q + 1, ...,J

(15)

where t fw and trv indicate the operation time of primary and backup relays, respectively. In (2), fa is the index of investigated fault, Fa represents the total number of faults to be analyzed, i is the primary relay index, I denotes the total number of relays, b is the backup relays index, B represents the total number of backup relays and pair relays, c is the index of network configuration, and C represents the total number of configurations to be analyzed. A set of constraints should be satisfied to assure reliable and fast isolation of faults. As clarified earlier, each communication-assisted DDOCRs provides protection in both forward and reverse directions. Considering a DOCR Ri , the forward and reverse time-current characteristics can be represented as follows.

TDSmin ⩽ TDSfw, i ⩽ TDSmax

(28)

TDSmin ⩽ TDSrv, b ⩽ TDSmax

(29)

Ipmin ⩽ Ipfw, i ⩽ Ipmax

(30)

Ipmin ⩽ Iprv, b ⩽ Ipmax

(31)

TZ 2min ⩽ TZ 2 j ⩽ TZ 2max

(32)

It should be noted that typically the coefficients of the inverse-time characteristic for D-DOCRs, namely α and β in (1), are not included as variables to be optimized in the protection coordination model. The proposed coordination strategy incorporates these parameters in the optimization problem to allow higher flexibility on the selection of the relay characteristic which would in turn contribute to achieving better 6

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Table 4 Optimization variables in second scenario. Relay no.

(37)

Parameters

3. Simulation results 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

TDSfw

(kA)

TDSrv

Iprv (A)

Tz2

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.105 0.1 0.125 0.1 0.1 0.1 0.147 0.1 0.169 0.1 0.244 0.185 0.143 0.134 0.257 0.13 0.258 0.1 0.17 0.1 0.297 0.158 0.238 0.107 0.281 0.281 0.304 0.367 0.205 0.263

0.105 0.1 0.125 0.1 0.1 0.1 0.147 0.1 0.169 0.1 0.244 0.185 0.143 0.134 0.257 0.13 0.258 0.1 0.17 0.1 0.297 0.158 0.238 0.107 0.281 0.281 0.304 0.367 0.205 0.263

0.359 0.356 0.343 0.343 0.338 0.338 0.259 0.257 0.191 0.191 0.112 0.114 0.298 0.3 0.2 0.187 0.201 0.147 0.47 0.344 0.168 0.123 0.252 0.252 0.102 0.102 0.032 0.044 0.147 0.147

0.52 0.518 0.49 0.477 0.432 0.507 0.489 0.52 0.578 0.52 0.515 0.595 0.578 0.515 0.37 0.406 0.35 0.406 0.383 0.375 0.36 0.394 0.41 0.358 0.429 0.42 0.551 0.465 0.477 0.551

3.1. System under study The proposed protection coordination scheme is tested on an IEEE 14-bus test system to determine the optimal coordination between communication-assisted D-DOCRs and distance relays. The system contains 14 buses, 15 lines, 3 transformers, and 5 generators. Each relay located at the two ends of a line contains one distance relay and a DDOCR. Hence, the proposed protection scheme includes 30 distance relays and 30 D-DOCRs. Detailed data on system parameters are provided in [39]. DIgSILENT Power Factory 14.3.1 is used to simulate the IEEE 14-bus test system. The short-circuit and load flow calculations are executed in this platform. CTI could be in the range of 0.2–0.5 s and in order to provide a fast protective scheme response, this parameter is set at 0.2 s. Concerning the coefficients of α and β, the minimum limits are set at 0.14 and 0.02, respectively. The maximum limits are assigned as 13.5 and 1, respectively. The minimum and maximum operation time of DOCRs should be adjusted to be within 0.1 and 2.5 sec, respectively. Moreover, TDS is bounded between 0.1 and 3 s whereas the minimum and maximum values of pickup currents (Ip) depend on the system short-circuit and load currents [23]. The deployed relays are numeric. Numerical relays can follow any characteristics by employing lookup table [24]. Therefore, the coordination process can be executed with continuous variables to obtain optimal characteristic. Afterward, relays can follow the obtained characteristics with lookup table. Four different scenarios are studied on the 14-bus test system where the proposed protection scheme is compared against the conventional one. First, distance relays and conventional DOCRs are coordinated based on the approach presented in [9]. Then, in the second case, conventional DOCRs are replaced with communication-assisted DDOCRs and the coordination is conducted considering fixed values of α and β. For the next case, the combination of distance relays and DDOCRs is evaluated considering non-standard inverse-time characteristics. For the last case, the coordination problem is solved considering N-1 contingency. In all of the investigated cases, the second zone timing variable (TZ2 ) of distance relays is kept within 0.2 and 0.9 s. C-PSO is one of the well-known optimization engines which is widely employed in power system problems [40,41]. On the other hand, overcurrent relaying beside distance relays stands as a non-convex optimization problem. Moreover, the primal PSO might be trapped into premature convergence especially for non-convex optimization [40]. Furthermore, in [40], it is also stated that C-PSO by using chaotic search can avoid

relay operation time. In this regard, constraints (33)–(36) are embedded within the proposed model. These constraints are for both the forward and reverse directions of DOCR.

α min ⩽ αfw, i ⩽ α max

(33)

α min ⩽ αrv, b ⩽ α max

(34)

βmin ⩽ βfw, i ⩽ βmax

(35)

βmin ⩽ βrv, b ⩽ βmax

(36)

what is more, the operation time of each D-DOCR should be preserved within the minimum and maximum permissible times, represented by (37).

Table 5 Operation time of relays in second for different fault locations associated with second scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fault @

Relay no.

F1

F2

F3

F4

0.192 0.223 0.188 0.254 0.21 0.286 0.193 0.228 0.177 0.207 0.192 0.176 0.264 0.264 0.145

0.277 0.307 0.318 0.378 0.32 0.395 0.282 0.315 0.25 0.276 0.232 0.22 0.289 0.29 0.169

0.52 0.518 0.49 0.477 0.432 0.507 0.489 0.52 0.578 0.52 0.515 0.595 0.578 0.515 0.37

0.241 0.389 0.258 0.719 0.438 0.615 0.396 0.533 0.335 0.428 0.267 0.263 0.319 0.319 0.162

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

7

Fault @ F1

F2

F3

F4

0.209 0.141 0.225 0.176 0.295 0.15 0.212 0.162 0.249 0.147 0.158 0.137 0.119 0.156 0.187

0.229 0.175 0.265 0.206 0.351 0.158 0.22 0.194 0.277 0.16 0.17 0.15 0.133 0.183 0.21

0.406 0.35 0.406 0.383 0.375 0.36 0.394 0.41 0.358 0.429 0.42 0.551 0.465 0.477 0.551

0.261 0.202 1.202 0.233 0.511 0.166 0.23 0.221 0.324 0.172 0.182 0.171 0.147 0.207 0.238

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this issue in non-convex problems. Therefore, in the conducted study, CPSO is chosen as the optimization tool. The coordination among DOCRs is performed in near-end and far-end points based on the proposed approach in [23]. The coordination process is performed for the case of bolted three phase faults. However, numerical relays provide comprehensive protection functions for feeder protection [32]. Therefore, the characteristic associated with single phase to ground fault is different from those that are considered for bolted three phase faults. Consequently, separate coordination process should be done to coordinate single phase to ground fault characteristics. In this case, although relays pairs experience different fault currents, but the proposed method would be the same.

Table 6 Statistical analyses for results in second scenario. Parameters

Fault @ F1

Minimum operation time of relays Maximum operation time of relays Mean of operation time of relays Variance of operation time of relays Sum of operation time of primary relays Sum of operation time of backup relays Total operation time of all relays in primary and backup process

F2

0.119 0.133 0.295 0.395 0.197 0.247 0.002 0.004 5.922 7.399 27.602 23.933 249.650 s

F3

F4

0.35 0.595 0.465 0.005 13.959 39.686

0.147 1.202 0.3383 0.045 10.149 95.262

1) Coordination of Distance Relays and Conventional DOCRs

Table 7 Optimization variables for the third scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

In this scenario, conventional DOCRs are deployed with one direction and only TDS, Ip, and TZ2 of all relays create the set of variables. The solution vector is presented in Table 1. These optimal relay settings end in operation time of relays which are reported in Table 2 for the faults F1, F2, F3, and F4. Moreover, a comprehensive statistical analyses for results in this scenario is performed in Table 3. This table presents minimum, maximum, mean, variance, and total operation time of relays in different fault locations. The total summation of the investigated cases is 352.758 s. Furthermore, discrimination time of relay pairs for these fault points are depicted in Fig. 6. As described, a proper protection scheme necessities satisfying the CTI constraints. However, as indicated in this figure, this is not the case for some of the relay pairs. This infeasible solution is recognized as uncoordinated cases where the backup relay may operate before the primary one. Thus, it is difficult to maintain adequate protection coordination with conventional DOCRs and distance relays.

Parameters

TDSfw

Ipfw

αfw

βfw

TDSrv

Iprv

αrv

βrv

Tz2 (s)

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.359 0.356 0.343 0.343 0.338 0.338 0.259 0.257 0.191 0.191 0.112 0.114 0.298 0.3 0.146 0.146 0.147 0.147 0.344 0.344 0.123 0.123 0.185 0.185 0.075 0.075 0.032 0.032 0.108 0.108

0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

0.037 0.043 0.036 0.049 0.041 0.055 0.037 0.044 0.034 0.04 0.037 0.034 0.051 0.051 0.028 0.04 0.028 0.043 0.034 0.056 0.029 0.041 0.032 0.048 0.029 0.031 0.027 0.024 0.03 0.036

0.1 0.1 0.1 0.1 0.1 0.1 0.104 0.1 0.125 0.1 0.168 0.109 0.1 0.1 3.2 3.2 3.2 0.1 3.179 0.1 3.2 0.127 3.2 1.716 1.942 1.466 1.068 0.215 2.66 0.197

0.359 0.356 0.343 0.343 0.338 0.338 0.259 0.257 0.191 0.191 0.112 0.114 0.298 0.3 0.2 0.146 0.147 0.147 0.344 0.344 0.123 0.123 0.185 0.185 0.075 0.102 0.032 0.032 0.118 0.108

0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.143 0.14 0.144 0.147 0.14 0.14 2.49 0.142 0.894 0.14 0.165 0.14 4.931 0.144 1.113 0.908 8.259 8.356 0.167 0.179 2.735 0.14

0.026 0.034 0.021 0.047 0.029 0.041 0.02 0.035 0.02 0.028 0.02 0.02 0.021 0.021 1 0.353 0.704 0.079 0.347 0.042 0.985 0.02 0.832 0.862 1 1 0.098 0.02 1 0.02

0.354 0.371 0.334 0.346 0.322 0.348 0.326 0.354 0.351 0.354 0.34 0.34 0.351 0.34 0.308 0.324 0.31 0.317 0.318 0.324 0.309 0.32 0.313 0.306 0.31 0.304 0.32 0.319 0.312 0.32

2) Coordination of Distance Relays and D-DOCRs based on Fixed α and β To overcome the miscoordination cases seen in the previous scenario, D-DOCRs rather than the conventional DOCRs are coordinated with distance relays. As elucidated earlier, application of D-DOCRs relaxes the optimization problem by making the coordination constraints to be independent. This opportunity is realized by introducing new set of variables, namely the reverse settings. The optimal solution vector consists of pervious set of variables and new set of variables is given in Table 4. The obtained operation times of relays are reflected in Table. 5 for the faults F1, F2, F3, and F4. Moreover, a comprehensive statistical analysis is also conducted in Table 6 for the results in this scenario. This table presents the minimum, maximum, mean, variance, and total operation time of relays in different fault locations. As can be seen, the sum of operation time is 249.650 s which shows a significant reduction. This analysis indicates that the minimum, maximum, and mean time of relays all together are diminished sensibly. Moreover, at different fault locations, discrimination time of relay pairs are portrayed in Fig. 6. As can be seen, the proposed approach not only eliminates the miscoordination cases but also can speed up the protection process.

Table 8 Operation Time of Relays in Second For Different Fault Locations Associated with Third Scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fault @

Relay no.

F1

F2

F3

F4

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.146 0.139 0.171 0.151 0.154 0.14 0.148 0.14 0.142 0.134 0.122 0.126 0.11 0.11 0.117

0.354 0.371 0.334 0.346 0.322 0.348 0.326 0.354 0.351 0.354 0.34 0.34 0.351 0.34 0.308

0.126 0.177 0.138 0.29 0.212 0.22 0.209 0.239 0.191 0.21 0.141 0.15 0.122 0.122 0.112

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Fault @ F1

F2

F3

F4

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.11 0.124 0.119 0.117 0.12 0.106 0.104 0.12 0.112 0.109 0.108 0.11 0.112 0.118 0.113

0.324 0.31 0.317 0.318 0.324 0.309 0.32 0.313 0.306 0.31 0.304 0.32 0.319 0.312 0.32

0.126 0.144 0.551 0.133 0.177 0.111 0.109 0.137 0.131 0.117 0.116 0.126 0.123 0.134 0.128

3) Coordination of Distance Relays and D-DOCRs based on Optimal α and β In this scenario, the proposed protection scheme is solved considering variable relay characteristics to obtain further improvements in protection metrics. As clarified before, D-DOCRs can follow both standard and non-standard time-inverse characteristics where more variables are included in the optimization problem. Thereby, the set of variables consists of TDSfw, TDSrv, Ipfw , Iprv , αfw, αrv, βfw , βrv , and TZ2 of all relays. These variables are optimally determined and are given in Table 7. Moreover, Table 8 reports the operation time of relays 8

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in four critical fault points. As can be seen, the proposed method yields fast response protection in clearing faults. Moreover, a comprehensive statistical analysis is also done and reported in Table 9 for the results in this scenario. This table gives the minimum, maximum, mean, variance, and total operation time of relays in different fault locations. As can be seen, the sum of operation time is 168.241 s which shows a remarkable reduction. This analysis indicates that the minimum, maximum and mean time of relays all together are reduced sensibly. Discrimination time of relay pairs are plotted in Fig. 6. Like pervious scenario, this figure reveals that the coordination process of all relays is accomplished, successfully. The comparison among these results indicates that the mixed D-DOCRs and distance relays performs better due to employing non-standard process.

Table 9 Statistical analyses for results in third scenario. Parameters

Fault @ F1

Minimum operation time of relays Maximum operation time of relays Mean of operation time of relays Variance of operation time of relays Sum of operation time of primary relays Sum of operation time of backup relays Total operation time of all relays in primary and backup process

F2

0.1 0.104 0.1 0.171 0.1 0.125 0 0 3 3.752 16.897 16.648 168.241 s

F3

F4

0.304 0.371 0.329 0 9.865 29.012

0.109 0.551 0.167 0.007 5.022 69.421

4) Coordination of Distance Relays and D-DOCRs based on Optimal α and β Considering N-1 Contingency

Table 10 Optimization variables for forth scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Parameters

TDSfw

Ipfw

αfw

βfw

TDSrv

Iprv

αrv

βrv

Tz2 (s)

1.369 0.582 0.542 0.558 0.546 0.561 1.072 1.213 0.547 0.552 0.556 0.554 0.6 0.543 0.596 0.545 0.541 1.205 0.611 0.59 0.69 0.627 0.582 0.539 0.549 0.605 0.582 0.962 0.593 0.549

0.356 0.356 0.343 0.343 0.338 0.338 0.257 0.257 0.191 0.191 0.112 0.112 0.298 0.298 0.146 0.146 0.147 0.147 0.344 0.344 0.123 0.123 0.185 0.185 0.075 0.075 0.032 0.032 0.108 0.108

0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

0.215 0.09 0.098 0.142 0.131 0.124 0.145 0.188 0.077 0.09 0.149 0.132 0.133 0.128 0.12 0.09 0.109 0.218 0.146 0.134 0.121 0.138 0.131 0.105 0.114 0.131 0.111 0.111 0.127 0.142

2.112 2.852 2.822 2.822 2.81 2.81 2.635 2.635 2.495 2.495 2.333 2.333 2.723 2.723 2.791 2.402 2.762 2.404 2.825 2.825 2.88 2.355 2.482 2.482 2.258 2.258 2.174 2.2 2.324 2.422

0.356 0.356 0.343 0.343 0.338 0.338 0.257 0.257 0.191 0.191 0.112 0.112 0.298 0.298 0.146 0.146 0.147 0.147 0.344 0.344 0.123 0.123 0.185 0.185 0.075 0.075 0.032 0.044 0.108 0.108

0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 1.28 0.14 0.14 0.14 0.14 0.14 4.674 0.372 0.764 0.14 0.404 0.14 7.735 0.14 3.13 0.44 1.012 0.14 0.14 0.54 0.527 0.703

0.292 0.521 0.342 0.723 0.504 0.532 0.307 0.442 1 0.317 0.172 0.215 0.293 0.292 1 0.508 0.522 1 0.485 0.718 1 0.24 1 0.672 0.47 0.129 0.123 0.331 0.41 0.489

0.556 0.522 0.509 0.474 0.343 0.566 0.429 0.566 0.466 0.566 0.537 0.525 0.509 0.537 0.324 0.346 0.326 0.338 0.382 0.346 0.325 0.341 0.333 0.345 0.449 0.365 0.476 0.425 0.454 0.476

As mentioned earlier, satisfying coordination task in N-1 contingency states is a complicated problem. Therefore, to verify effectiveness of the proposed approach, it is solved by considering different configurations of the network. Herein, for the sake of best performance, the set of the investigated variables is assumed to be the same with the third scenario. Moreover, the set of C consists of all network configurations. The obtained solution vector is presented in Table 10. To show effectiveness of the proposed approach, the operation time of relays are given in Table 11. Furthermore, proper statistical analysis is also done and reported in Table 12 for the results in this scenario. This table shows the minimum, maximum, mean, variance, and total operation time of relays in different fault locations. As can be seen, the sum of operation time is 293.2 s. This analysis indicates that compared with those results in the first scenario, the minimum, maximum and mean time of relays all together are reduced. Moreover, the discrimination time of relay pairs are depicted in Fig. 6 for these two configurations which endorse satisfying coordination tasks. Sometimes, in far-end fault points, the fault currents are in reverse direction with the corresponding backup relays [23]. Therefore, these fault points are not included in relays pairs and hence, there is not discrimination time among them. Thereby, some lines in Fig. 6 are not continuous. Due to the complexity of the problem, the total operation time of relays in the main configuration of the network is more than the obtained value in the third scenario. This is while; the proposed protection scheme has the best performance in each configuration of the network and clears the fault faster than the first scenario. Table. 13 is also considered to compare operation time of some primary and backup relays for the studied faults in all the scenarios, simultaneously. As can be seen, not only the operation time of primary and backup relays are diminished

Table 11 Operation time of relays in second for different fault locations associated with forth scenario. Relay no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fault @

Relay no.

F1

F2

F3

F4

0.17 0.259 0.179 0.169 0.146 0.227 0.226 0.227 0.226 0.225 0.113 0.117 0.205 0.194 0.113

0.229 0.473 0.255 0.534 0.336 0.524 0.522 0.617 0.449 0.495 0.169 0.188 0.255 0.24 0.13

0.556 0.522 0.509 0.474 0.343 0.566 0.429 0.566 0.466 0.566 0.537 0.525 0.509 0.537 0.324

0.274 0.366 0.322 0.266 0.237 0.325 0.356 0.337 0.328 0.309 0.143 0.153 0.229 0.215 0.137

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

9

Fault @ F1

F2

F3

F4

0.225 0.113 0.181 0.114 0.227 0.135 0.158 0.113 0.226 0.113 0.113 0.113 0.158 0.114 0.115

0.288 0.173 1.257 0.161 0.416 0.154 0.174 0.164 0.302 0.137 0.136 0.149 0.205 0.161 0.154

0.346 0.326 0.338 0.382 0.346 0.325 0.341 0.333 0.345 0.449 0.365 0.476 0.425 0.454 0.476

0.249 0.146 0.225 0.138 0.276 0.145 0.165 0.141 0.254 0.125 0.124 0.126 0.182 0.14 0.133

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Table 12 Statistical analyses for results in forth scenario. Parameters

Fault @ F1

Minimum operation time of relays Maximum operation time of relays Mean of operation time of relays Variance of operation time of relays Sum of operation time of primary relays Sum of operation time of backup relays Total operation time of all relays in primary and backup process in the MC 1 Main configure, 2Line 2–3 outage configure

F2

F3

F4

MC1

LC2

MC

LC

MC

LC

MC

LC

0.113 0.259 0.167 0.002 5.014 22.485 293.239 s

0.111 0.254 0.164 0.002 4.583 21.514

0.124 0.366 0.219 0.006 6.566 23.019

0.128 1.153 0.298 0.046 8.348 19.422

0.324 0.566 0.439 0.007 13.156 51.284

0.324 0.566 0.435 0.008 12.173 38.622

0.13 1.257 0.315 0.0519 9.447 137.895

0.123 0.358 0.209 0.006 5.852 70.570

Table 13 Comparing operation time and discrimination time of relays. Relays pair

For fault at F1 First scenario

(25, 16) (16, 17) (24, 21) (22, 23) (23, 30) Relays pair

(25, 16) (16, 17) (24, 21) (22, 23) (23, 30) Relays pair

(25, 16) (16, 17) (24, 21) (22, 23) (23, 30) Relays pair

(25, (16, (24, (22, (23,

16) 17) 21) 23) 30)

Second scenario

Third scenario

Forth scenario

tp

tb

Δt

tp

tb

Δt

tp

tb

Δt

tp

tb

Δt

0.565 0.564 0.673 0.651 0.773

0.693 0.704 0.673 0.521 0.888

−0.072 −0.06 −0.2 −0.33 −0.085

0.209 0.141 0.15 0.162 0.187

0.527 0.376 0.407 0.362 0.586

0.118 0.035 0.057 0 0.199

0.1 0.1 0.1 0.1 0.1

0.329 0.3 0.3 0.3 0.3

0.029 0 0 0 0

0.225 0.113 0.135 0.113 0.115

0.433 0.323 0.348 0.319 0.378

0.008 0.01 0.013 0.006 0.063

tb 0.665 0.586 0.62 0.57 0.637

Second scenario Δt −0.153 −0.313 −0.293 −0.409 −0.336

Third scenario tp 0.229 0.175 0.227 0.22 0.21

tb 0.429 0.685 0.427 0.42 0.41

Forth scenario Δt 0 0.31 0 0 0

tp 0.11 0.124 0.106 0.12 0.113

tb 0.31 0.324 0.306 0.32 0.313

Δt 0 0 0 0 0

tp 0.288 0.173 0.154 0.164 0.154

tb 0.488 0.373 0.354 0.364 0.354

Δt 0 0 0 0 0

tb 0.787 1.123 0.879 0.932 1.106

Δt

Second scenario tp

Δt

Third scenario tp tb

Δt

Forth scenario tp tb

Δt

0 0.074 0 0 0.006

0.406 0.35 0.36 0.41 0.551

tb 0.606 0.638 0.56 0.648 0.751

0 0.088 0 0.038 0

0.324 0.31 0.309 0.313 0.32

0.524 0.573 0.509 0.537 0.52

0 0.063 0 0.024 0

0.346 0.326 0.325 0.333 0.476

0.562 0.678 0.551 0.666 0.713

0.016 0.152 0.026 0.133 0.037

tb 0.831 1.189 0.948 1.162 1.182

Δt −0.074 0.183 0 0.075 0

Second scenario tp 0.261 0.202 0.166 0.221 0.238

tb 0.642 0.683 0.615 0.808 0.809

Δt 0.181 0.281 0.249 0.387 0.371

Third scenario tp tb 0.126 0.627 0.144 0.618 0.111 0.582 0.137 0.669 0.124 0.598

Δt 0.301 0.274 0.271 0.332 0.274

Forth scenario tp tb 0.249 0.583 0.146 0.712 0.145 0.613 0.141 0.839 0.133 0.822

Δt 0.134 0.366 0.268 0.498 0.489

For fault at F2 First scenario tp 0.618 0.699 0.713 0.779 0.773 For fault at F3 First scenario tp 0.587 0.849 0.679 0.732 0.9 For fault at F4 First scenario tp 0.705 0.806 0.748 0.887 0.982

coordination problem with proper and optimal inverse-time characteristics besides minimizing operation time of relays. In this case, one parameter may increase; though subsequent to dependence on other parameters, the operation time would decrease. For example, in this scenario, TDS corresponding to R1 in forward direction is 1.369 and the associated operation time is 0.17 s. This is while; in the first scenario, TDS is 0.14 and the associated operation time is 0.269 s. As can be seen, the operation time is lessened by contemplating optimal characteristics. Fig. 7. Comparison of the dynamic objective function versus the static one.

3.2. Exploring the effect of dynamic objective function

but also miscoordination problem is relaxed by employing the proposed method. Including additional parameters in the variable set facilities swiping the time current page with various type of inverse characteristics. Therefore, the optimization algorithm searches to settle down the

Here, in order to investigate performance of the proposed dynamic objective function via static one and also to select the best γ1, γ2 , and γ3, the third scenario is evaluated in different cases. These parameters are bounded within 1 and 3 with the step of 1 in different permutations. The obtained overall operation times, in different cases, are plotted in 10

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Fig. 8. Comparison of C-PSO with SA and conventional PSO.

Fig. 7. Each case is solved by C-PSO and the solutions are the best among a predetermined number of runs. In this figure, the case with static method is denoted with blue point. In the case of static method, by increasing the iteration numbers, the function Φ would not be changed. Therefore, the obtained value is more than the other cases. Among the other cases with dynamic penalties, the best response is attained with the parameters of γ1 = 2 , γ2 = 1, and γ3 = 1, indicated with yellow circle. Here, three different optimization platforms namely seeker algorithm (SA) [41], PSO, and C-PSO are evaluated to validate the performance of the proposed approach in obtaining near-optimal solutions. The coordination process executed with these algorithms in 20 different runs. Results, depicted in Fig. 8, demonstrates that C-PSO and SA algorithms contribute to similar solutions with less than 2.5% variations. Furthermore, it tackles the coordination problem better that conventional PSO. 4. Conclusions This paper proposed a novel protection scheme that relied on a combined coordination of communication-assisted D-DOCRs and distance relays for sub-transmission networks which can cover N-1 contingency states. To do so, an efficient multi-point optimal coordination approach was devised within which the complete protective and technical constraints were involved. It was shown that deployment of DDOCRs against the conventional DOCRs alters the coordination constraints such that a selective protection scheme without any miscoordination violation can be achieved. New dynamic penalty was employed through the objective function which resulted to better solutions. Moreover, the total operating times of primary and backup relays were reduced, remarkably. A remarkable reduction of relays total operating time was achieved by introducing non-standard inverse-time characteristics which can be explicitly applied in numeric D-DOCRs. Simulation results highlight the superior performance of the proposed protection scheme for sub-transmission systems. Declaration of Competing Interest The authors declared that there is no conflict of interest. References [1] Alipour M, Teimourzadeh S, Seyedi H. Improved group search optimization algorithm for coordination of directional overcurrent relays. Swarm Evol Comput 2015;23:40–9. [2] Commission UFER. Mandatory reliability standards for the bulk-power system. Order 2007;693:72. [3] Zhang H, Heydt GT, Vittal V, Quintero J. An improved network model for transmission expansion planning considering reactive power and network losses. IEEE Trans Power Syst 2013;28:3471–9. [4] Cova B, Losignore N, Marannino P, Montagna M. Contingency constrained optimal reactive power flow procedures for voltage control in planning and operation. IEEE Trans Power Syst 1995;10(2):602–8.

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[40] Lv X, Zhou D, Tang Y, Ma L. Transient stability preventive control of power systems using chaotic particle swarm optimization combined with two-stage support vector machine. Electr Pow Syst Res 2018;155:111–20. [41] Amraee T. Coordination of directional overcurrent relays using seeker algorithm. IEEE Trans Power Del 2012;27(3):1415–22.

coordination considering the priority of constraints. IEEE Trans Power Del 2011;26(3):1927–38. [38] Liu J, Teo KL, Wang X, Wu C. An exact penalty function-based differential search algorithm for constrained global optimization. Soft Comput 2015;20(4):1305–13. [39] Christie R. Power systems test case archive. IEEE 14 bus system, online; 2014 < http://www.ee.washington.edu/research/pstca/ > .

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