1. Introduction
The electric protection system plays an important safety function for the industrial installations. Its main purpose is to detect and clear the occurred faults rapidly and isolate only the faulted part of the system. The electric protection system performances are mainly depending on the type, setting and coordination of protective devices. A good electric protection design and setting improve the energy efficiency of the industrial installations in terms of ensure service continuity, decrease the outage time, prevents the devices damage, and lifetime extension. In this context, the nuclear event that has been occurred at the nuclear power plant of Forsmark in July 2006 it is mainly due to an incorrect tuning of a protective relay [1]. However, due to the complex topology of the modern interconnected power systems and the operation close to its limits, the setting and coordination of protective relays have become a very complex and tedious operation.
In order to ensure the reliability of the protective system, the tuning and coordination of protective relays require that the relays closes to the fault must trip faster than the others relays, in order to isolate only, the faulted part of the power system. Furthermore, each main relay has a backup relay acts after a certain time delay known as coordination time interval (CTI), giving the chance for the main relay to operate [2]. Therefore, the reliability and the efficiency of the protective relays depend greatly on theirs setting and coordination with the adjacent equipments [3].
In recent years, the optimal setting of protective relays has been reported in the literature based on various methods and techniques. The linear optimization of protective relays is proposed in [4-7] based on linear programming and simplex method. Furthermore, the non linear formulation of the optimal coordination of the overcurrent relays has been presented and solved using non linear optimization methods such as: random search technique [8], Genetic Algorithms and its variants [9-11], Differential Evolution method [12, 13], Seeker algorithm [14], Teaching learning-based optimization [15], and Hybrid methods [16, 17].
Based on the previous works in this field, it is clear that the overcurrent relay coordination problem is mainly modeled as continuous optimization problem, i.e. considering only the continuous decision variables. In addition, the relays characteristics and standards are usually chosen arbitrarily or by trial and error method. Furthermore, the violation constraint handling strategy was not presented in the most of the published papers.
On the other hand, the setting and coordination of protective relays is mainly based on the short circuit current seen by the relays. However, the short circuit current value seen by the relays can be varied according to various parameters such as: FACTS devices [18-20], current limiters, resistance faults, series compensation, wind turbines, and power system topology variation. In this case, the setting and coordination of protective relays must be recomputed.
In this chapter, the directional overcurrent relays (DOCR) setting and coordination problem is formulated as non-linear mixed integer constrained optimization problem considering various scenarios related to the power system topology and operation. The objective function of this optimization problem is the minimization of the operation time of the associated relays in the systems. Both real and integer decision variables are considered; where the real variables are the time dial setting (TDS), the pickup current (Ip), and the integer variables are the relay characteristics and standards. Where, these last are usually chosen arbitrarily or by trial and error method. To solve this constrained Mixed Integer optimization problem, an improved version of Biogeography-based optimization (BBO) able to manage the combinatory and constrained optimization problems is proposed. The BBO is validated on 3-bus, and 8-bus power systems test. Furthermore, an impact study of the fault resistance and the power system series compensation on the DOCR performances is presented. Various optimization scenarios are carried out considering the impact of resistance fault and power systems series compensation.
2. Overcurrent relays characteristics and standards
The overcurrent relays characteristics are divided on two types namely, independent and dependent tripping time characteristics. These characteristics could be used in the same time in the same relay.
2.1. Independent tripping time characteristic
In this type of characteristic, the tripping time of the relay is independent of the fault current value (see figure 1). This characteristic is easy to be set and understand, but their drawbacks are the relay tripping time is independent to the fault current, and sometimes the coordination is difficult to achieve with fuses. This type of characteristic is very used in France.
2.2. Dependent tripping time characteristic
Figure 2 presents the independent tripping time characteristic. From this figure, it is clear that the greater the fault current; the smaller the tripping time. This type of characteristic is widely used in Anglo-Saxons countries. Their advantages are: flexibility (various characteristic curves), small tripping time for large fault current, and the compatibility with the tipping curves of magneto-thermal circuit breakers and fuses. However, its setting is relatively difficult to achieve.
For each protective relay the operating time t is defined as follows [21, 22]:
where, t is the relay operating time (sec), TDS is time dial setting (sec), I_{F} is the fault current (A), Ip is pickup current (A), K_{CT} is ratio of the current transformer. The constants K, α and L depend to the characteristic curve of the relay.
Figure 3 depicts the impact of the TDS on the characteristic curve. From this figure, it is clear that when TDS increases, the curve moves from bottom to top, therefore the relay tripping time increases for the same fault current.
Figure 4 presents the impact of pickup current on the relay characteristic curve. From this figure, it is clear that when pickup current increases, the characteristic curve moves from left to right.
Table 1, presents the constants values of the overcurrent relay characteristic considering AREVA, IEC, and ANSI/IEEE standards [9].
3. Energy efficiency and protective relays coordination
The energy efficiency is a generic topic that deals with a large range of subjects such as building design, domestic appliances, vehicles, energy transmission and distribution systems, distributed and micro generation. In this chapter, an intelligent strategy is proposed to improve the energy transmission efficiency based on protective relay coordination. It is well known that the energy transmission efficiency requires that the electrical energy must be transmitted to the consumers with low cost, best quality (voltage and frequency), and in continuous manner. For doing so, the transmission grid must be well protected against various kinds of perturbations and contingences that have the negative impacts on energy transmission efficiency in terms of electricity cost increase due to the equipment renovation and maintenance, long time outage of the system, power quality degradation, and so on.
On the other hand, an appropriate design of electrical protective system can improve the energy transmission efficiency by rapid detection of any abnormal situation in the system and isolate only the faulted part, preventing the propagation of the fault and the total blackout of the system. To fulfill this purpose, the protective relays must be well tuned, selected and coordinated. An incorrect setting and coordination of protective relays can cause an extensive damage to the electrical components, outage of large part in the transmission system and may be the total blackout of the electrical grid.
However, the protective relays coordination in the interconnected power systems is very complex and must satisfy the various constraints related to the equipment protection, and coordination requirements.
In the electrical power system, there are several types of protection: namely distance protection mainly used in transmission networks, overcurrent protection used in distribution networks and differential protection for sensitive equipment such as electrical machines, buses, transformers and cables. Furthermore, in order to improve the electrical protection system reliability and efficiency, each electrical component in the system must be protected by two relays: main relay and backup relay; so that if the main relay fails; the backup relay trip after a predefined time delay.
On the other hand, the design and setting of electrical protection system represent a big challenge to the electrical engineers. Figure 5 depicts the main constraints and challenges related to this task. From this figure, it is clear that the protective relays setting requires the definition of pickup current, time dial, characteristic curve (e.g. Normal inverse, Very inverse, Extremely inverse,…etc.) and standard (e.g. AREVA, IEC, IEEE). Furthermore, these setting parameters must satisfy the equipment operation and relays coordination constraints. However, it should be noted that the protective relays setting is mainly based on the short circuit currents seen by the relays. However, several parameters have a great impact on the fault current seen by the relays and therefore on the protective relay efficiency and reliability. Some of these parameters are related to the control devices such as: FACTS devices, Series compensation, Faults current limiter, Wind turbine and the others parameters are related to the power system operation such as: power system operation near to its limits, power system topology variation, and fault resistance value. Therefore, it is clear that the setting and coordination of protective relays in the modern power systems become a difficult task with a big challenge.
4. Setting and coordination of overcurrent relays using heuristic optimization
The coordination of the overcurrent relays is formulated as a constrained optimization problem, where the optimization function and the constraints are presented as follows:
4.1. Objective function
The aim of this function is to minimize the total operating time of all DOCR relays in the system with respect to the coordination time constraint between the backup and primary relays.
where, t_{i} represents the operating time of the relay i, NR is represents the number of IDMT relays in the power system.
4.2. Optimization constraints
4.2.1. Coordination time interval
During the optimization procedure, the coordination between the primary and the backup relays must be satisfied the following constraint:
where, t_{backup} and t_{primary} are the operating time of the backup relay and the primary relay respectively, CTI is the minimum coordination time interval. For the electromechanical relays, the CTI is varied between 0,30 to 0,40 sec, while for the numerical relays it’s varied between 0,10 to 0,20 sec [15].
4.2.2. Time Dial Setting (TDS)
The TDS adjusts the time delay before the relay operates when the fault current reaches a value equal to, or greater than, the relay current setting Ip.
where, TDS_{min} and TDS_{max} are the minimum and the maximum limits of TDS respectively.
4.2.3. Pickup current (Ip)
The pickup current Ip represents the set point of the relay. During the optimization process IP is limited as follows:
where, Ip_{min} and Ip_{max} are the minimum and the maximum limits of Ip respectively.
4.2.4. Tripping time of the primary relays
In order to ensure a fast clearing of the fault, the tripping time of the primary relays must be limited as follows:
where, t_{primary_min} and t_{primary_max} are the minimum and the maximum limits of the tripping time of the primary relays.
4.2.5. Type of relays characteristics (RT)
The eight relays characteristics presented in table 1 are considered in the optimization process, and the coding of RT variable is presented in table 2. During the optimization process, the variable RT is limited as follows:
where, RT_{max} is the maximum limit of RT.
5. Biogeography-Based Optimization (BBO)
5.1. Principle
The Biogeography-based optimization (BBO) is a population based, stochastic optimization technique developed by Dan Simon in 2008, which deals with the geographical distribution principle of biological organisms [23].
A solution in BBO is called habitat, and its performance is assessed by Habitat Suitability Index (HSI) which is equivalent to the fitness in other population-based optimization algorithms like Genetic Algorithms (GAs). The decision variables that characterize habitability are called suitability index variables (SIVs). SIVs can be considered as the independent variables of the habitat and HSI calculation is carried out using these variables.
In BBO, the high HSI solutions represent habitats with many species, and low HSI solutions represent habitats with few species.
Figure 6, illustrates a model of species behavior in a single habitat. From figure 3, λ and µ represent the immigration and emigration rates respectively. Furthermore, it is clear that, when the habitat is empty (there are zero species), λ reaches its maximum value I, and µ is zero, and when the habitat reaches its maximum number of species (Smax), λ is zero and µ equals to its maximum value E.
The Ps(t) denotes the probability that a habitat contains exactly S species at time t, at time t+Δt the probability is computed as follows:
where, λs and μs are the immigration and emigration rates when there are S species in the habitat.
If time Δt is small enough so that the probability of more than one immigration or emigration can be ignored then taking the limit of equation (8) as Δt → 0 gives the following equation:
For k number of species in habitat, the emigration rate μk and the immigration λk are computed as follows:
where, E and I are the maximum emigration and immigration rates respectively, n is the total number of species in the habitat. If E=I:
The BBO is mainly based on two operators which are the migration and the mutation defined as follows [23].
5.2. Migration
In BBO, the migration is used to modify the existing solution based on other solutions with a probability of Pmod. If a given solution Si is selected to be modified, then its immigration rate λi is used to probabilistically decide whether or not to modify any SIV in that solution. After selecting any SIV of that solution for modification, emigration rates μ_{j} of other solutions Sj (Sj is j-th solution set other than Si, i.e. j ≠ i) are used to select which solutions among the population set will migrate randomly to chosen SIVs to the selected solution Si [23].
5.3. Mutation
Mutation rate of each set of solution can be calculated in terms of species count probability presented in (9) using the following equation [23]:
where, m_{max} is a user-defined parameter, Ps is the species count probability, and Pmax is the maximum species count probability
5.4. Improvements of the BBO base algorithm
As reported above, the optimal relay coordination problem is formulated as a mixed integer constrained optimization problem. For doing so, the following improvements are carried out on the base algorithm of BBO.
5.4.1. Mixed Integer coding of the solution
In order to solve the above combinatorial optimization problem, the BBO must be able to manage both real and integer decision variables. The real decision variables are represented by TDS and Ip as real decision variables and the integer variables are represented by the relay characteristic type (RT). This last, is usually chosen arbitrarily or by trial and error method.
Figure 7, illustrates the coding principle implemented in BBO for N relays. From this figure, it is clear that there are 2N real decision variables and N integer decision variables.
5.4.2. Constraints violation handling
During the optimization process, the coordination constraint presented in (3) could be violated. In this case, the penalty function presented in (14) is used to penalize the violated solutions.
where, F is the objective function presented in (1) without penalization; and PF is the penalty function defined as follows:
The Viol parameter is computed as follows:
6. Case studies and simulation results
During this study, the overcurrent relays parameters are limited as presented in table 3.
Decision Variable | Type | Minimum value | Maximum Value |
TDS | Real | 0.1 | 1.1 |
Ip | Real | 0.5 | 2 |
tprimary | Real | 0.05 | 1 |
RT | Integer | 1 | 8 |
6.1. Test systems
6.1.1. 3-bus test system
The 3-bus test system is presented in figure 8 has three generators, three buses, and six overcurrent relays. The detailed data of this system are presented in appendix.
6.1.2. 8-bus test system
The 8-bus system presented in figure 9 has two generators and with six buses, seventh lines and four loads. The power system study is compensated with Series capacitor located at middle of the transmission line 1-6. The series capacitor is installed in line 1-6. The 8-bus system has a link to another network, modeled by a short circuit power of 400 MVA. The transmission network consists of 14 numerical DOCRs relays. The detailed system data are given in the appendix.
6.2. Short circuit current computing methodology
The optimization of the overcurrent relays need, at first, the identification of the primary/backup (P/B) relay pairs for each faulted bus. After that, for each P/B relays pairs, the fault currents passing through the relays are calculated for a worst three phase faults applied near the bus as presented in figure 10.
6.3. Impact of resistance fault on the overcurrent relay performances
In this section, the impact of resistance fault value on the overcurrent relays performances is presented. The relays performances are measured by checking the violation of the constraints represented by the primary relays tripping time and the coordination time between the primary and backup relays. Three scenarios are considered in this study namely:
6.3.1. 3-bus test system
Table 4 presents the fault currents seen by the primary and backup relays in the 3-bus test system considering the resistance fault impact. Figures 11 and 12 present the evolution of fault currents seen by the primary and backup relays respectively with respect to the resistance fault value. From these figures, it is clear that the resistance fault has a great impact on the fault currents seen by the primary and backup relays, such a way, when the resistance value increases; the fault current decreases.
Table 5 presents the best overcurrent relays setting and coordination for the base case obtained by BBO. In this case the characteristic curves of the relays are fixed as IEC normal inverse (i.e. RT=2).
Table 6 presents the impact of resistance fault value on the tripping time of the primary relays. From this table, we can remark that the tripping time of the primary relays satisfy the constraint presented in (6) for R=0 ohms and R=50 ohms. But for R=100 ohms, the primary relays 1, 3, 4 and 6 violate this constraint and their tripping time exceeds the maximum limit fixed as 1s. From these results, we can conclude that when the resistance fault value increases the tripping time of the primary relays increases and may exceeds its maximum limit.
Another parameter used for the assessment of the impact of resistance fault on the overcurrent relays performances, which is the CTI between the P/B relays presented in table 7. From this table, we can remark that the resistance fault causes a miss of coordination between the primary relay N°4 and its backup N° 6 for R=50 ohms and R=100 ohms. The mines sign of the CTI means that the back relay trips before the primary relays. Thus, from the obtained results we can conclude that the resistance fault has a great impact on the relays performances and could cause a miss of coordination between the primary and the backup relays.
6.3.2. 8-bus test system
Table 8 presents the fault currents seen by the primary and backup relays in the 8-bus test system considering the fault resistance impact. Figures 13 and 14 depict respectively, the evolution of the fault currents seen by the primary and backup relays with respect to the resistance fault. From these figures, it is clear that the resistance fault has a great impact on the fault currents seen by the primary and backup relays, such a way, when the resistance value increases; the fault current decreases.
Table 9 presents the best overcurrent relays setting and coordination for the base case obtained by BBO. In this case the characteristic curves of the relays are fixed as IEC normal inverse (i.e. RT=2).
Table 10 presents the impact of the resistance fault value on the tripping time of the primary relays. From this table, we can observe that the tripping time of the primary relays satisfy the constraint presented in (6) for the base case only (i.e. R=0 ohms). For the case R=50 ohms the tripping time of 13 primary relays exceeds the maximum limit, and for R=100 ohms, all relays violated the tripping time limit fixed as 1s. From this result, we can conclude that the resistance fault has a negative impact on the overcurrent relays performances and causes the miss of coordination between the relays.
Another parameter used for the assessment of the resistance fault impact on the overcurrent relays performances which is the CTI between the primary and the backup relays presented in table 11. From this table, we can remark that the resistance fault causes four miss of coordination cases for R=50 ohms and nine miss of coordination cases for R=100 ohms. The mines sign of the CTI means that the back relay trips before the primary relays. Thus, from the obtained results we can conclude that the resistance fault has a great impact on the relays performances and causes the miss of coordination between the primary and the backup relays.
6.3.3. Impact of series compensation on overcurrent relay performances
In this section, the impact of series compensation on the overcurrent relays performances is presented. The relays performances are measured by checking the violation of the constraints represented by the primary relays tripping time and the CTI between the primary and backup relays. Three scenarios are considered in this study namely:
6.3.4. 3-bus test system
Table 12 presents the fault currents seen by the primary and backup relays in the 3-bus test system considering the series compensation of line 1-2. Figures 15 and 16 present the evolution of fault currents seen by the primary and backup relays respectively with respect to the series compensation ratio. From these figures, it is clear that the series compensation of line 1-2 has a great impact on the fault currents seen by the primary and backup relays, in such a way, when the compensation ratio increases; the impedance of the line decreases and therefore the fault current increases.
Table 13 presents the impact of the series compensation on the primary relays tripping time. From this table, we can observe that the tripping time of the primary relays for SC=35% and SC=70% satisfy the constraint presented in (6).
The CTI between the primary and the backup relays is presented in table 14. From this table, we can remark that the series compensation of line 1-2 causes a miss of coordination between the P/B relay pairs 3/1 and 6/2. Therefore, from the obtained results we can conclude that the series compensation of the power system has a great impact on the relays performances and causes a miss of coordination between the primary and the backup relays.
6.3.5. 8-bus test system
Table 15 presents the fault currents seen by the primary and backup relays in the 8-bus test system considering the series compensation of line 1-6. Figures 17 and 18 present the evolution of fault currents seen by the primary and backup relays with respect to the series compensation percent, respectively. From these figures, it is clear that the series compensation of line 1-6 has a great impact on the fault currents seen by the primary and backup relays, in such a way, when the series compensation ratio increases; the impedance of the line decreases and therefore the fault current increases.
Table 16 presents the impact of the series compensation on the primary relays tripping time. From this table, we can observe that the tripping time of the primary relays for SC=35% and SC=70% satisfy the constraint presented in (6).
The CTI between the primary and backup relays is presented in table 17. From this table, we can observe that the series compensation of line 1-6 causes a miss of coordination between the P/B relays pairs 2/7 and 12/14. Thus, from the obtained results we can conclude that the power system series compensation has a great impact on the relays performances and causes a miss of coordination between the primary and the backup relays.
6.4. Intelligent coordination of overcurrent relays
In this section, we present the best relays setting and coordination obtained by the proposed BBO considering the impact of resistance fault and power system series compensation. The objective of this optimization is to minimize the relays tripping time and eliminate the miss of coordinated problem caused by the resistance fault and the power system series compensation. As mentioned above, the proposed BBO is able to manage both real (TDS, and Ip) and discrete decision variables (RT).
6.4.1. Considering resistance fault
6.4.1.1. 3-bus test system
Table 18 presents the best relays setting and coordination considering the impact of resistance fault. From this table, it is clear that the proposed BBO can find the optimal TDS, Ip, and characteristic type that minimize the relays tripping time and satisfy all the constraints presented in tables 19 and 20. Therefore, we can conclude that the proposed algorithm is able to eliminate the miss coordination problem caused by the resistance fault.
6.4.1.2. 8-bus test system
Table 21 presents the best relays setting and coordination considering the impact of resistance fault. Table 22 presents the primary relays tripping time, and table 22 presents the CTI of the P/B pairs of relays. From table 23, we can remark that the primary relays tripping time is within it limits. From table 23, we can observe that the P/B pairs of relays are fully coordinated in the case of R=50 ohms. However, we observe two miss of coordination of P/B relays pairs: 7/13 and 14/1.
6.4.2. Considering series compensation
6.4.2.1. 3-bus test system
Table 24 presents the best relays setting and coordination considering the impact of the series compensation of line 1-2. Table 25 presents the primary relays tripping time. Table 26, presents the CTI of P/B relays. From these tables, we can observe that the proposed BBO find the best relays setting (TDS, Ip, characteristic curve) that minimize the relays tripping time and eliminate the miss of coordination caused by the impact of series compensation.
6.4.2.2. 8-bus test system
Table 27 presents the best relays setting and coordination considering the impact of the series compensation of line 1-6. Table 28 presents the primary relays tripping time. Table 29, presents the CTI of P/B relays. From these tables, we can observe that the proposed BBO find the best relays setting (TDS, Ip, characteristic curve) that minimize the tripping time and eliminate the miss of coordination caused by the impact of series compensation.
7. Conclusion
In this chapter, the overcurrent coordination problem in interconnected power systems has been formulated as non-linear constrained mixed integer optimization problem considering the impact of resistance fault and power system series compensation. The objective function is to minimize the total relays operating time with the optimal setting of real (TDS, and Ip) and integer (RT) decision variables. To solve this constrained mixed integer optimization problem, an improved Biogeography-based optimization (BBO) algorithm has been proposed. The BBO is validated on 3-bus, and 8-bus power test systems considering various scenarios related to the resistance fault and power system series compensation. The obtained results show that the resistance fault and the power system series compensation have a negative impact on the overcurrent relays performances in such a way increase the primary relays tripping time and cause the miss of coordination between the relays. Furthermore, it is concluded that the proposed BBO can solve, in almost the cases, the miss of coordination caused by the resistance fault the power system series compensation and therefore improve the energy efficiency of the power systems.
Appendix
Power systems test data
3-bus power system test data
Line | Vn (kV) | R (Ω) | X (Ω) | Y (S) | L (km) |
1 - 2 | 69 | 5.5 | 22.85 | 0,0000 | 50 |
1 - 3 | 69 | 4.4 | 18.00 | 0,0000 | 40 |
3 - 4 | 69 | 7.6 | 27.00 | 0,0000 | 60 |
8-bus power system test data