Proceedings of ICEE 2009 3rd International Conference on Energy and Environment, 7-8 December 2009, Malacca, Malaysia
Overcurrent Time Delay Determination Using Gain Scheduled PID Controllers Aidil Azwin Zainul ,Agileswari Ramasamy. Department of Electrical Communication Engineering Universiti Tenaga Nasional Putrajaya Malaysia.
[email protected]
source. We can say that the time delay gets bigger as the fault is further away from the source. The third issue is another problem where the type of fault will determine the level of fault current. If it is a three phase fault then the fault current will be higher while the fault current will be lower if it was a phase to phase or a single phase fault. This is an issue when it comes to the backup relay. Recent efforts have been used to ensure that the relay is more sensitive to load variations [1]. In this case, the setpoint current Is is changed according to the maximum demand of the day and also the presence of negative sequence components of the load current. Another effort made in [2] is to plainly use the negative sequence component to detect unbalanced faults and use conventional relay techniques to detect balanced faults. Some studies have also been done in using optimization methods to coordinate the overcurrent relays [3]. Another paper on optimization proposed that the two phase simplex method is used to determine the TMS of the relays [4]. In this paper we shall see how the PID controller coupled with gain scheduling is used to determine the time delay for an overcurrent relay. The PID values will be optimized using an objective function which is the operation time to be minimized and will be coupled with some constraints. The end result will be the same as optimizing the time dail setting of the overcurrent relays. Results are obtained using matlab. We shall also see in this paper how the use of gain scheduling used with PID controller will solve the distance of fault from voltage source.
Abstract— The inverse time overcurrent relay operation is based upon the current setpoint and also the time multiplier setting. Depending on the ratio of the value of the current and the setpoint current together with the value of the time multiplier setting, the amount of time delay for the trip command is determined using the inverse time characteristics. This would mean that the relay is not of the adaptive type and would possibly give a maltripping. This paper uses the concept of PID controller to determine the time delay for the overcurrent relay. Keywords- Gain scheduling, PID controller, Overcurrent relay, inverse time characteristic, Fault severity.
I.
INTRODUCTION
The inverse time characteristic has been used to determine the time delay for conventional overcurrent relays used today. The basic principle behind the time delay determination is the inverse time equation stated in (1).
Where Ifault represents the fault current, Is is the setpoint current, α depends on the relay characteristic of the relay and C depends on both the characteristic and the time multiplier setting of the relay. Analyzing the equation above, we can see that the relay time delay if connected to a power system would depend on the amount of fault current that the system would have in an event of a fault. The fault current of the system would then depend on three other factors. 1) The voltage level of the system. 2) The distance the fault is from the source of power. 3) Severity of fault. The first factor is usually not an issue in setting up the relay. The second and third issue is usually the problem. This is because the second issue is a random problem and with only one setting on the overcurrent relay, the relay time delay would then depend on the distance the fault is from the voltage
978-1-4244-5145-6/09/$26.00 ©2009 IEEE
Farrukh Hafiz Nagi Department of Mechanical Engineering Universiti Tenaga Nasional Putrajaya Malaysia
Izham Zainal Abidin Department of Electrical Power Engineering Universiti Tenaga Nasional Putrajaya Malaysia
II.
ELECTRICAL NETWORK MODEL
The function of the overcurrent relay is to react to a fault in the shortest time possible and to be as selective as possible in cutting of the supply such that only the faulty section of the system is isolated. The overcurrent relays are usually installed in a situation such that there will be one main relay and one backup relay. This is to ensure that if the main relay does not isolate the fault, the backup relay will isolate the fault. This is
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illustrated by fig. 1. Relay B would be the main relay if a fault were to occur in front of relay B. The relay located behind
relay B which is relay A is then considered as the backup relay.
Fig. 1: Testing circuit for main and backup relay coordination.
If the main relay were to isolate the fault then there would be a smaller disturbance to the power users compared to if the backup relay were to isolate the fault. If a fault were to occur in front of relay B then we could see that the relay B as the main relay will cut off the power supply to load B. The backup relay is set to trip only after a certain time delay the main relay has activated. This delay is typically around 0.5 seconds. This delay is to ensure that the main relay and it’s auxiliaries have sufficient time to react to the fault. If the backup relay were to trip before the main relay and the main relay is healthy, then this condition is considered as a mal tripping. Looking at figure 1 again if the relay A would trip for a fault in front of relay B then the supply at load A and B will trip. This is not desirable because there is no fault on the power line connecting the voltage source to load A. III.
From (4) we can see that the value of the time delay generated by the PID overcurrent relay is just the reciprocal of the PID response. Fig. 2 shows us how the PID controller with gain scheduling is used in order to determine the time delay for the overcurrent relay instead of using the inverse time characteristics. IV.
PID WITH GAIN SCHEDULLING OVERCURRENT RELAY
GAIN SCHEDULLING
The similar problem with the inverse time characteristic overcurrent relay relating to fault severity would be present if only 1 PID setting is used. Therefore a technique called gain scheduling is used in order to ensure that the time delay of the overcurrent relay does not vary much as the severity of the fault varies. In figure 2, we can see the blocks labeled as backup lookup table and main lookup table. These tables contain the PID constants Kp, Ki and Kd as the distance of fault varies. The distance of the fault is determined using the ratio
The PID controller is usually used as a speed or position controller for various mechanical systems. This method uses the difference between the setpoint parameter and the actual parameter as an input to the controller. In order to use the PID controller as an overcurrent controller, the input of the controller would be the ratio of the fault current and the setpoint current . Eq. (2) below shows how the response of the PID controller is given an error and (3) gives the relationship between the input of the PID controller, current setpoint and fault current.
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between the voltage at the relay and the nominal voltage of the system at each phase. This is explained using (5).
Fig. 2: Block diagram in simulink of gain schedulling PID controller used for overcurrent time delay determination TABLE I: VOLTAGE RATIO AT MAIN AND BACKUP RELAY AS THE FAULT DISTANCE FROM THE MAIN RELAY WAS VARIED
Main relay Distance Vratio 2.5 0.0689 5 0.1002 7.5 0.1294 10 0.1567 12.5 0.1823 15 0.2064 17.5 0.229 20 0.2504 22.5 0.2705 25 0.2896 30 0.3249 32.5 0.3412 35 0.3568 37.5 0.3716 40 0.3857 42.5 0.3992 45 0.412 47.5 0.4244 50 0.4681
varied. As we can see, the voltage ratio of the main relay is smaller than 0.5 while the voltage ratio of the backup relay is much bigger than 0.5. Referring to fig. 2, we can see a block called main or backup. This block has the function of choosing between the main and backup PID responses. This block will chose the main relay response if the voltage ratio is smaller than 0.5 and the backup relay if the ratio is bigger than 0.5.
Backup relay Distance Vratio 2.5 0.7595 5 0.7664 7.5 0.7735 10 0.7801 12.5 0.7864 15 0.7922 17.5 0.7977 20 0.803 22.5 0.8079 25 0.8126 30 0.8212 32.5 0.8252 35 0.8291 37.5 0.8327 40 0.8362 42.5 0.8395 45 0.8427 47.5 0.8457 50 0.8487
The values of the Kp, Ki and Kd had to be chosen for each values of the voltage ratio. This is where the explanation of why the distance interval of 2.5Km was chosen. If the distance interval was smaller, the voltage ratio will be smaller and in the event of a fault, the values of Kp, Ki and Kd will be varying rapidly with time. This will cause the time delay calculated by the PID controller to fluctuate. The time fluctuation will cause the relay to give a transient in the trip decision. The values of Kp, Ki and Kd was chosen using the simulink response optimization block. The following constraints were used for the main relay.
The voltage ratios were obtained by varying the distance from the main relay to fault from 2.5Km up till 50Km in intervals of 2.5 Km. TABLE I shows how the voltage ratio is as the distance between the fault and the main relay is
Eq. (6) tells us that we want the main relay to trip as soon as possible in this case, the relay has at most 0.2 seconds to trip in the event of a fault. In (7) we can see that the PID response will translate to an earlier trip, however it is used to ensure
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that the PID controller can cope with the transients of the fault current in the beginning of a fault. If the value was smaller, the optimization algorithm will not be able to find a feasible solution. This is one of the weaknesses of the PID controller used as an overcurrent relay.
5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5 50
The backup relay has to be coordinated such that the main relay is given sufficient time to trip. The backup relay can only activate after there is conformation that the main relay has failed. Eq. (8) shows us how the coordination between the main relay timing and the backup relay is related[4].
In equation 8, Δt is the minimum time that the backup relay must allow the main relay before it interferes the main relay. In our case, we would like the minimum time interval to be at least 0.5 seconds. Therefore the constraints of the backup relay could be defined by the equations below:
4.1499 4.1499 4.1499 4.1499 4.1499 4.1499 4.2189 4.2974 4.3756 4.4536 4.5313 4.6087 4.6859 4.7628 4.8396 4.9161 4.9923 5.0684 4.1499
0.2444 0.2444 0.2444 0.2444 0.2444 0.2444 0.2972 0.3483 0.3993 0.45 0.5006 0.5511 0.6014 0.6515 0.7015 0.7514 0.8011 0.8507 0.2444
-0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052 -0.0052
TABLE IIB: PID CONSTANT FOR BACKUP RELAY FOR DISTANCE OF FAULT FROM 2.5 TO 50KM.
Distance(Km) 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5 50
Simulating faults at every distance defined in table 2, the fault current is used as an input to the PID controller. The optimization block is then programmed with the constraints above for both main and backup relay. The optimization simulink diagram is shown in fig. 3 below:
Fig. 3: Optimization simulink block diagram for the main relay.
In fig. 3, we can see that the discrete PID controller will contain the constants that will be optimized. The block which has the label from workspace contains the values of fault current versus time. The block labeled signal constraints contain the optimization algorithm. The PID constants for every distance on the backup and main relay was obtained as shown in the TABLE II.
V.
Kd
Ki
Kd
2.5
4.1499
0.2444
-0.0052
Ki
Kd
0.3766 0.3766 0.3766 0.3766 0.3766 0.3766 0.3781 0.3851 0.3926 0.4003 0.4079 0.4155 0.4231 0.4306 0.4382 0.4457 0.4532 0.4606 0.4681 0.4755
0.4604 0.4604 0.4604 0.4604 0.4604 0.4604 0.4631 0.4755 0.489 0.5026 0.5162 0.5298 0.5433 0.5568 0.5702 0.5836 0.5969 0.6102 0.6235 0.6367
RESULTS AND DISCUSSION
The relay was then put to a similar test as the inverse time overcurrent relay was placed in. The setting of each relay is shown in table III. TABLE III:RELAY SETPOINT CURRENT FOR GAIN SCHEDULED PID RELAY
Relay Setpoint current(A) A 150 B 75 As seen from the TABLE III, the setpoint current was not changed from the previous IDMT setting. In this
TABLE IIA: PID CONSTANT FOR MAIN RELAY FOR DISTANCE OF FAULT FROM 2.5 TO 50KM.
Distance(Km)
Kd -0.0013 -0.0011 -0.0011 -0.0011 -0.0011 -0.0011 -0.0011 -0.0012 -0.0012 -0.0012 -0.0012 -0.0012 -0.0012 -0.0012 -0.0012 -0.0012 -0.0012 -0.0013 -0.0013 -0.0013
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experiment, the TDS was not set by the user. The time delay is not determined by the inverse time characteristic but the inverse of the PID response. The shortest delay on the main relay that this technique has is 86ms obtained from a double phase to ground fault 10Km from the main relay. The longest time delay for the main relay for this technique was 135ms recorded for a single phase fault 25Km from the relay. Looking at the coordination difference, the largest coordination difference was 738ms and the smallest coordination difference was 561ms. In other words, the largest and the smallest coordination difference were 238ms and 61ms away from the coordination constraints respectively. Concerning distance to fault variation, the largest in this technique was 77ms recorded during a single phase to ground fault. The smallest was 65ms recorded for a double phase to ground fault. A complete record of these results is shown in TABLE IV. VI.
Single phase fault Double phase to ground fault Phase to phase fault Three phase fault
CONCLUSION
Main relay timing
Backup relay timing
0.996 1.073 0.847 0.914
10Km 25Km 10Km 25Km
0.279 0.291 0.289 0.303
0.845 0.910 0.865 0.940
0.676 0.738 0.561 0.614 0.566 0.619 0.576 0.637
[1] Arturo Conde And Ernest Vazquez “Operation Logic Proposed For Time Overcurrent Relay” IEEE Transaction On Power Delivery, Vol. 22 No. 4 October 2007. [2] A.F. Elneweihi. E.O. Schweitzer III, and M.W. Feltis, “Negative Sequence Overcurrent Element Application and Coordination in Distribution Protection” Presented at the IEEE Power Eng. Soc. Summer Meeting, Seattle, WA, Jul. 12-16. 1992. [3] Hossien Askarian Abyaneh, Majid Al-Dabbagh, Hossien Kazemi Karegar Seyed Hesameddin Hossien Sadeghi “ A New Optimal Approach for Coordination of Overcurrent Relays in Interconnected Power System” IEEE Transactions On Power Delivery, Vol 18, No 2, April 2003. [4] Bijoy Chattopadhyay, M.S. Sachdev, T.S. Sidhu “An On-Line Relay Coordination Algorithm For Adaptive Protection Using Linear Programming Technique” IEEE Transactions On Power Delivery, Vol. 11, No 1, January 1996. [5] Hossien Askarian Abyane, Karim Faez, Hossien Kazemi Karager “ A New Method For Overcurrent Relay Using Neural Network and Fuzzy Logic” 1997 IEEE TENCON pp 407-409.
TABLE IV: TRIPPING TIME FOR MAIN AND BACKUP RELAY ON A GAIN SCHEDULED PID OVERCURRENT RELAY.
Distance to main relay
0.320 0.335 0.286 0.300
REFERENCES
The gain scheduling PID controller is suitable to be used as a time delay determination technique of an overcurrent relay in place of the inverse time overcurrent relay. This is due to the immunity the technique has to fault severity compared to an inverse time overcurrent relay. The ability of the gain scheduling PID controller to change its characteristic according to the fault current level and voltage level has obviously improved its capabilities in providing a more optimized operation of an overcurrent relay.
Fault Type
10Km 25Km 10Km 25Km
Coordination difference.
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