Protective systems continuously monitor the electrical status of power system
components and de-energize them (for instance by tripping a circuit breaker)
as speedily as possible when they are the site of a serious disturbance such
as a short-circuit fault. Directional over-current relays (DOCRs) are used as
the main protection and or back-up for the protection of transmission lines.
The main reason for applying back-up protection is to ensure in the event of
failure or non-availability of the main protection the fault will be cleared
after a certain time delay known as Coordination Time Interval (CTI). Therefore
all of the protective relays must be coordinated well with each other. The problem
of coordinating protective relays is the process of finding suitable relay settings
such that the relay closest to the fault would operates faster than other relays
(Al-Odienat, 2006; Tumay et al.,
In systems that are protected by DOCRs, Time Dial Setting (TDS) and the pickup
current (Ip) setting for directional over-current relays, must be calculated
exactly such that the coordination all relays with each other is met (Zeineldin
et al., 2006; El-Arroudi et al., 2005).
There are different factors that may affect on protective relay settings and
disturb the selectivity and coordination of these relays. An important one of
these factors is transmission line series compensation. Series capacitor (SC)
is commonly installed on transmission line to increase loadability of the line,
enhance system stability, improve load sharing on parallel paths and reduce
line losses (Jazaeri et al., 2011; Moravej
et al., 2011; Sidhu and Khederzadeh, 2006;
Samimi and Golkar, 2012). Despite the beneficial effects
of SCs, their presence in the fault loop affects the voltage and current signals
at the relaying point and it can disturb the selectivity and original coordination
of relays. Therefore it is necessary to carefully carry out a study to determine
new setting of DOCRs. Basically, to determine the settings of DOCRs, two different
approaches are used; conventional approach such as trial and error approach
(Abdelaziz et al., 2002) and optimization techniques.
But nowadays because of the complexity of power systems, the optimization techniques,
with respect to their inherent advantages, has higher accuracy than conventional
methods of relay coordination.
In literature at first, in uncompensated systems, for optimal coordination
of over-current relays, due to the complexity of nonlinear optimization technique
the traditional optimal coordination has been performed using linear programming
approach including simplex, two phase simplex methods (Urdaneta
et al., 1988; Chattopadhyay et al., 1996).
It should be noted that due to simplification of these methods the solution
obtained in this way would not be optimal.
Recently, the optimization methods are used to solve the DOCRs coordination
problem as a complex and non-convex optimization problem. Genetic Algorithm
(GA) and Evolutionary Algorithm (EA) are proposed to calculate the optimal solution
for relay setting (Razavi et al., 2008; So
and Li, 2000). Noghabi et al. (2009) and
Bedekar and Bhide (2011) reported the problem of determining
the optimum settings of DOCRs is formulated as a Nonlinear Programming Problem
(NLPP) and hybrid GA approach is proposed to find the optimum solution.
PSO algorithm which is one of the capable heuristic techniques to solve constrained
optimization problems, has been recently adopted due to its superiority over
other Evolutionary Algorithm (EA) regarding its memory and computational time
requirements as it relies on very simple mathematical operations, also it requires
very few lines of computer code to implement (Kennedy and
Eberhart, 1995; Yap et al., 2011; Gao
et al., 2009; Minhat et al., 2008).
The optimal coordination of over current relays (Zeineldin
et al., 2006; Mansour et al., 2007)
has been done by methods based on PSO Algorithm.
It should be noted that all of the aforementioned references in above have
presented some methods for optimal relays coordination in uncompensated systems.
In literature only different problems faced by protective relays in series compensated
lines and some of the solution to these problems are researched and published
but the relays coordination problem is not discussed (Marttila,
1992; Jena and Pradhan, 2010). Moravej
et al. (2011) have proposed a new approach for optimal coordination
of distance relays in compensated systems which have a combined protection scheme
with over-current relays.
In this study a new approach for the optimal coordination of directional over-current relays in series compensated system, as a constrained nonlinear optimization problem, is proposed. In other word, a systematic method for formulation of the problem of determining optimum settings of DOCRs is presented.
The Modified Adaptive Particle Swarm Optimization (MAPSO) is employed to solve the proposed optimization problem that has low sensitivity with respect to both its adjustable parameters and initial point.
FORMULATION OF THE PROBLEM
A typical inverse time over-current relay consists of two units: (i) an instantaneous
unit and (ii) a time-delay unit. The time-delay unit has two values to be set,
the pickup current value (Ip) and the Time Dial Setting (TDS). The pickup current
value (Ip), is the minimum current value for which the relay operates and the
TDS adjusts time-delay before a relay whenever the fault current reaches a value
equal to or greater than the pickup current (Ip). This section presents the
over-current relays coordination problem.
DOCRs coordination problem: In the coordination problem of DOCRs, the aim is to determine the TDS and Ip of each relays, so that the overall operating time of the primary relays is minimized. Therefore the objective function can be stated as follows:
where, Tik indicates the operation time of DOCRi for a fault in
zone K and Wi is a coefficient which depends upon the probability
of a given fault occurring in each protection zone. Since the lines are of approximately
equal length Wi is usually set to 1 (Urdaneta
et al., 1996).
Relay characteristics: The over-current relays employed in this paper are considered as digital (numerical) and directional with standard IDMT characteristics (Inverse Definite Minimum Time) that comply with the IEC255-3 standard and have their tripping direction away from the bus:
where, TDSi and Ipi are the time dial setting and pickup current setting of the ith relay, respectively and Ii is the short circuit current passing through ith relay. However it can be shown that the proposed method can be easily applied to a system with combination of DOCRs with different characteristics (e.g., Very inverse, extremely inverse, etc.).
The constraints, that make the optimization problem infeasible, can be stated as follows:
Selectivity constraints for primary-backup relays: The requirement of selectivity dictates that when a fault occurs, the area isolated by the protective relay must be as small as possible, with only the primary protection relay operating.
In addition, the failure possibility of a protective relay must be considered. In this situation, another relay must operate as backup protection. In order to satisfy the requirement of selectivity, the following constraint must be added:
where,TiFi, TjFi are the operating time of ith primary relay (Tiprimary) and jth back-up relay (TFiback-up) respectively for the near-end fault Fi as shown in Fig. 1.
The Coordination Time Interval (CTI) is the minimum time gap in operation between the primary and its backup relay. CTI depends upon type of relays, speed of the circuit breaker and a safety margin which is usually selected between 0.2 and 0.5 sec.
|| Primary and backup relays
Bounds on relay settings: The limits on the relay parameter can be presented as follows:
The minimum pickup current setting of the relay is the maximum value between
the minimum available current setting ()
and maximum local current ()
passes through it. In similar, the maximum pickup current setting is chosen
minimum value between ()
on the relay and minimum fault current ()
which passes through it (Noghabi et al., 2009).
Limits on primary operation time:
This constraint imposes constraint on each term of objective function to lie
between 0.05 and 1 sec.
MODIFIED ADAPTIVE PARTICLE SWARM OPTIMIZATION (MAPSO)
Particle swarm optimization (PSO) is a population based search method that
introduced by Kennedy and Eberhart as a modern heuristic optimizer (Kennedy
and Eberhart, 1995).
During last decade many studies focused on this method and almost all of them
strongly confirmed the abilities of this newly proposed optimization technique,
abilities such as fast convergence, finding global optimum, simple programming
and adaptability with constrained problems (Kennedy and
Eberhart, 1995; Gao et al., 2011; Yap
et al., 2011).
In PSO, the feasible solution, called particles, share their information with each other and run toward best trajectory to find optimum solution in an iterative process. A velocity vector is defined for each particle and particle position depends on this velocity. In each iteration, the velocity and position of particles are updated:
where, Vi, iter and Xi, iter represent the velocity vector
and the position vector of ith particle at each iteration, respectively
are personal best position of ith particle and global best position of swarm
until iteration iter, respectively w is inertia weight factor which controls
the global and local exploration capabilities of particles; the constants c1,
c2 represent the learning rate or the acceleration term that pulls
each particle towards Pbest and Gbest positions. r1
and r1 are two random numbers between 0 and 1. In this study, a specific
kind of tree topology for the PSO is used that each level of the tree has only
one node or one particle. In this topology, each particle can move up and down
by any number of levels in each iteration and so the hierarchy is updated in
one iteration (Amjady and Soleymanpour, 2010; Sutha
and Kamaraj, 2008).
To enhance the efficiency of the PSO and to control the local search and convergence
to the global optimum solution, some modifications are proposed by Chaturvedi
et al. (2008) and Ratnaweera et al. (2004).
In this study, to deal with the complicated problem of relays coordination,
the Modified Adaptive Particle Swarm Optimization (MAPSO) is employed which
has presented by Amjady and Soleymanpour (2010) and
has the following new modification.
||The split-up of the cognitive part into the best and not-best
||Personal best position exchanging
||New velocity limiter
Therefore, in this study, due to some advantages of the MAPSO such as robustness,
good exploration capability and convergence behavior, the proposed coordination
problem is solved using MAPSO.
DOCRs COORDINATION IN THE SERIES COMPENSATED SYSTEMS
Series compensation increases power transfer capability and improves power system stability. Figure 2 shows the single line of a simplified compensated system which the SC is considered in the middle of a line. The capacitive reactance XSC is typically from 25 to 75% of the line inductive reactance XL. On the other hand the degree of compensation of the line, C, is stated as:
The typical protective bypass system consists of a metal oxide varistor (MOV),
bypass gap, damping reactor and bypass circuit breaker. The varistor provides
overvoltage protection of the series capacitor during power system faults. The
bypass gap is controlled to spark over in the event of excess varistor energy.
The bypass breaker closes automatically in the case of prolonged gap conduction
or other platform contingencies. The breaker also allows the operator to insert
or bypass the series capacitor. The damping reactor limits the capacitor discharge
resulting from gap flashover or bypass breaker closure (Fig. 3)
Therefore in normal operation, the overvoltage protection does not operate and the SC equivalent impedance is a pure capacitive reactance. In this case MOVs will be untriggered and the equivalent impedance of SC bank is equal to:
|| The single line of a simplified series compensated system
|| Configuration of a series capacitor
During high fault current, the conduction of MOVs increase and the equivalent
impedance of SC according to Goldsworthy model (Goldsworthy,
1987) is obtained as:
where, RMOV is related to conduction of the MOV. The bypass gap
operates when the energy absorbed by the MOV is greater than the preset value.
In the bypass gap operation mode, the equivalent impedance of SC bank is the
inductive reactance of the damping reactor (Sidhu and Khederzadeh,
Series Capacitors (SCs) and their protective bypass systems, in spite of their beneficial effects on the power system performance, cause some problems for protective relays and may leads to mis-coordination. Therefore the relays coordination in series compensated systems is considered to be one of the most difficult tasks.
In this study a critical phenomenon of compensated system that influence the performance of DOCRs, is described in the following:
||This phenomenon should be considered in the relay coordination
|| Flowchart of the proposed method for optimal relay coordination
As stated earlier, the coordination problem of DOCRs is a function of short circuit current level. In other words, the operating time of DOCRs depend on fault current through it. It is apparent that due to presence of SC in the line, the short circuit current passing through the main and backup relays for near-end fault (Fi) will be changed. Therefore in this paper with considering the series compensation the Short circuit analyses are performed and new coordination problem is solved for computing the related optimum setting of the relays.
Figure 4 shows the summary of the proposed method to solve the coordination problem of DOCRs using MAPSO. This method is used for both uncompensated and compensated systems. At first, in order to consideration of related constraints, the short circuit currents for the faults close to the circuit breaker of the main over-current relays are calculated. Short circuit analyses are performed for different fault impedances to find the worst case. In the last resort the MAPSO algorithm is run and the optimum relay settings are obtained.
SIMULATION AND RESULTS
In order to consider the impact of series compensation on the protective relay settings, the coordination formulation corresponding to the compensated and uncompensated systems was tested successfully for various systems, out of which one is presented in this study and effectiveness of used MAPSO is evaluated. For this purpose, two scenarios are examined for related test case as follows:
||Scenario A: optimal relay coordination in the uncompensated
This scenario is considered as the base original system without series capacitor (SC) and the optimal settings of DOCRs is calculated.
||Scenario B: optimal relay coordination in the compensated
In this scenario, test case is compensated by series capacitor. Then the optimal coordination problem is solved and the obtained results are compared with those obtained from Scenarios A.
The selected test system is the 8-bus study network. For obtaining the optimum
results, at first, the Primary /Backup (P/B) relay pairs are identified which
in two scenarios are the same. After that, for each P/B relay pairs, the short
circuit current passing through the relays for near-end fault is calculated.
The three phase faults, as worst fault, are applied at the near-end of each
relay. It should be noted that the short circuit analysis are done for each
scenario. The best solution of the MAPSO algorithm, among 25 trail runs is calculated,
since the MAPSO begins from a random initial point (step 1 of the step by step
algorithm). Also the parameters of the MAPSO, according to Amjady
and Soleymanpour (2010), have been set based on trial and error and the
best values are selected.
Test case: 8- bus system: The proposed method for optimal coordination
directional over-current relays, in compensated and uncompensated systems, is
applied to this test case separately. The 8- bus system, as shown in Fig.
5, is compensated with series capacitor located at middle of the line 1-6.
The degree of compensation is assumed to be 65 percent (C = 65%). The system
data are given in Table 1-4 (Zeineldin
et al., 2006). The 8-bus system has a link to another network, modeled
by a short circuit power of 400 MVA. The transmission network consist of 14
DOCRs with IEC standard inverse type characteristic which their location are
indicated in Fig. 5.
|| Line characteristics of 8-buses system
|| Generators data of 8-buses system
|| Transformers data of 8-buses system
|| Loads data of 8-buses system
||Single line diagram of series compensated 8-bus system
In both scenarios A and B, for DOCRs, TDS values can range continuously from 0.1 to 1.1 and CTI is assumed to be 0.2 sec.
Table 5 corresponding to scenario A, shows the primary/backup (P/B) pairs and corresponding fault currents for the faults exactly close to the circuit breaker of the main over-current relays.
Similarly, due to presence of the SC in scenario B, the short circuit analyses are performed and the obtained results are shown in Table 5.
It is apparent from Table 5 that the fault current passing through the main relays is increased in scenario B in comparison to scenario A. Due to the presence of SC in scenario B, the net fault impedance for all faults behind SC is reduced and the fault current is increased. In other word the presence of SC in a system will change the normal power flow as well as the short circuit current all over the relays.
The relays 7 and 14 are located in the series compensated line 1-6 and have a contrary manner than other relays (Fig. 5).
Table 6 shows the obtained optimal values of the decision variables in both scenarios (i.e. Ipi, TDSi).
It can be observed from the results presented in Table 6 that, the optimal values of Ipi and TDSi are the typical setting used in DOCRs protection scheme. The objective function value has been calculated as the sum of the operating time of each relay for the fault in its primary zone of protection. As noted earlier, the operating time of DOCRs is a function of fault current level. Therefore due to increase in fault current in the presence of SC, the optimal value of objective function in scenario B is less than scenario A.
|| P/B Relay pairs and the near-end fault currents in 8-buses
system (scenario A and B).
|| Optimal relay settings in 8-buses system using MAPSO
The operating time of the primary and backup relays for both scenarios, corresponding to primary/backup (P/B) pairs, is shown in Table 7. It can be seen that the coordination between relays (with respect to related constraints and minimum CTI of 0.2 s) is maintained in all cases.
The following observation can be found in Table 7 for two scenarios A and B.
|| Operating time of primary and backup relays
In scenario A, the relay 1 will take 0.439 s to operate for fault corresponding to P/B No. 1, whereas it will operate in 1.098 s and 1.368 s for faults corresponding to P/B No. 2, 19, respectively. The similar description can be derived from Table 7 for scenario B.
This is desirable, because for fault corresponding to P/B No. 1, relay 1 is primary relay and hence it is first to operate, whereas for fault P/B No. 2 and 19, relay 1 is backup relay and should operate after related primary relays. Similar description can be given for operating time of each relay for different fault points.
The comparison of two scenarios shows that, due to presence of SC and increase in the fault current level in the section B, the operating time of each P/B relays in this scenario is lower than those in the scenario A. But the operating time of primary relays 7 and 14, that are located in series compensated line, are become less in scenario B.
Also it can be seen from Table 7 that, in scenario A, the time taken by relay 1 (backup for relay 14) to operate for fault corresponding to P/B No. 19 is 1.368 seconds. It is because small amount of fault current flows through relay 1 and major amount of fault current flows through relay 9 (other backup for relay 14). Similar description can be given for operating time of other relays not only in scenario A but also in scenario B.
In this study, the optimal coordination problem of directional over-current relays has been presented firstly. Then with considering the effect of series capacitor on the relays setting, a new method for optimal coordination of directional over-current relays, in series compensated systems, has been proposed.
In this study the presented coordination problems as nonlinear problems have been solved using the MAPSO and the optimum results are obtained. As expected, on comparison, the best solution found in series compensated systems, due to increase in the fault currents level is computed lower than that in uncompensated systems.
The second author would like to thank the office of gifted students at Semnan University for financial support.