UNIVERSIDADE ESTADUAL DE CAMPINAS
SISTEMA DE BIBLIOTECAS DA UNICAMP
REPOSITÓRIO DA PRODUÇÃO CIENTIFICA E INTELECTUAL DA UNICAMP
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https://ieeexplore.ieee.org/document/8503057
DOI: 10.1049/joe.2018.0262
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©2018 by Institution of Engineering and Technology. All rights reserved.
DIRETORIA DE TRATAMENTO DA INFORMAÇÃO Cidade Universitária Zeferino Vaz Barão Geraldo
The Journal of Engineering
The 14th International Conference on Developments in Power System
Protection (DPSP 2018)
Increasing sensitivity for transformer
protection using incremental differential
eISSN 2051-3305 Received on 4th May 2018 Accepted on 23rd May 2018 E-First on 3rd September 2018 doi: 10.1049/joe.2018.0262 www.ietdl.org
Fabiano Magrin
1, Maria Cristina Tavares
21Academic Department of Electrical Engineering, Federal University of Technology, Brazil 2Department of Systems and Energy, University of Campinas, Brazil
E-mail: fgsmagrin@gmail.com
Abstract: This study presents a new protection element that can increase transformer differential sensitivity. The new element,
called incremental differential, takes the differential currents, operation and restraint currents and, using a new mathematical approach, it can be more sensitive than the standard differential. The study presents the mathematical calculation and how the incremental differential handles with the errors involved in the differential protection. It also presents the algorithm response for some fault cases, always comparing the element to the standard differential algorithm. As the new element is simple in a mathematical concept, the protection element was developed inside a commercial relay just using the manufacturer programming language and the users’ available programming area. The contributions of this work are the method to increase sensitivity using the same variables already available in differential relays, and the possibility to use the algorithm in a field installed relay.
1 Introduction
One crucial factor when protecting power transformer is that the protection relay elements do not work in the concept of avoiding the damage before it happens as in transmission lines, but they work to minimise the damage and, consequently, in the reduction of the costs involved in the repairing. Also, the protection needs to be fast to avoid extreme cases as fire caused by internal faults. Transformer fault statistical data [1–5] along the year shows that the number of internal faults is considerable and the differential element cannot handle internal faults involving few turns [6–10]. These faults are usually detected by the gas relays and they are also not adequate to detected faults with few turns or, if they can detect, they are not fast enough. As can be verified in [11, 12], at the best situation the gas relays can operate in 50 ms.
Based on that and trying to use, if possible, the same relays already installed in the field, this paper presents a new protection element, called incremental differential that can be obtained from the operation and restraint currents. The use of the same relay can reduce costs associated to relay exchange. The cost is not just the relay acquisition, but the engineering associated with it, the field labour and the eventual system being off-service. Although the new element can be implemented in a field relay, the equipment must accomplish some requirements as it must be available to the user analogue and digital data, and allow the user to make mathematical and Boolean operations. Fortunately, some relays in the market have these features for a long time.
In the following sections, the incremental differential, how it can handle transformer protection errors and also the results for some transformer faults will be presented. To present the results, the new element implemented in a commercial relay was connected to a real-time digital simulator. Also, the element is compared to a commercial differential relay that was also connected to the simulator allowing the comparison between standard differential and the proposed incremental differential.
2 Incremental differential principles
As mentioned before, the new element was developed based on the operation and restraint currents. The relay used to program the algorithm was not a transformer protection relay but instead a line protection relay model SEL-421. This equipment was used due to its available mathematical and Boolean tools. As the relay does not
have the differential currents, they were calculated using the same principles as the transformer relay to be compared, in this case the SEL-787 [13], as shown in the following equations:
IOP=
∑
k = 1 n I˙k (1) IRT=∑
k = 1 n I˙k (2)Analysing an external fault based on the equation, it is expected a significant increase in the restraint current (IRT) but not in the operation current (IOP). For an internal fault, it is expected an increase for both currents. How much these currents increase depends on the fault location and on the transformer surrounding system. For an internal fault which involves very few turns, the very low increase in the operation current promote a non-operation of the differential element. It is important to remember that the traditional differential has always a minimum pick-up, and also the slopes. It is interesting in the differential element that the slope setting is its own desensitisation and, for a transformer, many errors are involved such as current transformers (CTs) mismatch, CTs errors and transformer tap. All these facts promote a non-sensitive element.
During the operation of the transformer without fault, the restraint current is always much higher than the operation current. As the new algorithm wants to work just with the incremental quantities avoiding errors associated to the load current, the first step of the element is to subtract the actual current from the current measured in the previous cycle according to the following equations:
ΔIOP= IOP− IOP−1cycle= IOPf lt− IOPpre (3)
ΔIRT= IRT− IRT−1cycle= IRTf lt− IRTpre (4)
These equations eliminate any difference existing in the operation current due to external errors as mentioned above, but also from internal errors of the relay. Also, the restraint current does not
operate anymore with high values but close to the axis origin, valid for both currents.
To avoid the slopes settings, as mentioned, as they desensitise the protection, we will analyse the way of the incremental operation and restraint currents behave for internal and external faults.
2.1 External faults
Below is the mathematical analysis of an external fault for the incremental restraint current
IRTpre= I˙1+ I˙2 (5)
IRTf lt= x ∗ I˙1+ y ∗ I˙2 (6) where x and y are, respectively, the increasing factors of the high (I1) and low (I2) sides currents.
Applying (5) and (6) to (4)
ΔIRT= x ∗ I˙1 + y ∗ I˙2− I˙1− I˙2 ΔIRT= x − 1 ∗ I˙1 + y − 1 ∗ I˙2
Considering that the high side and low side currents have the same value, in per unit, during the pre-fault
I˙1 = I˙2
ΔIRT− x + y − 2 ∗ I˙1 ΔIRT− x + y − 2 ∗ Iload
(7)
Equation (7) shows the response of the incremental restraint current for an external fault in relation to the increase of the high and low sides currents of the transformer. If there is no CT problem, x and y have the tendency to be the same.
Making the same analysis for the incremental operation current
IOPpre= I˙1+ I˙2 (8)
Considering that the high side current has the opposite direction of the low side current, (8) can be rewritten as
IOPpre= I1− I2 (9)
IOPf lt= x ∗ I˙1+ y ∗ I˙2
IOPf lt= x ∗ I
1− y ∗ I2
(10)
Applying (9) and (10) to (3) and leaving, for a moment, the absolute operator out of the equations
ΔIOP= x ∗ I1− y ∗ I2− I1+ I2 ΔIOP= x − 1 ∗ I1− y − 1 ∗ I2
Again, considering that the high side and low side have the same current during the pre-fault
ΔIOP= x − y ∗ I1 (11)
Applying again the absolute operator to (11)
ΔIOP= x − y ∗ Iload (12)
As mentioned before, for an external fault, x and y are quite the same which means that (12) shows that the incremental operation current is almost zero for an external fault.
Table 1 exemplify the behaviour of (7) and (12) for different possibilities of external fault. Depending on the CTs errors, x and y will be different even for an external fault without any saturation.
From Table 1 it is possible to notice that the incremental restraint current tends to increase substantially while the incremental operation current tends to stay close to zero.
2.2 Internal faults
Analysing the restraint element, it is possible to notice that there is no mathematical modification in the incremental element, so only the operation element needs to be analysed. Equation (9) is still valid as it is applied to the current during pre-fault, although currents during the internal fault will change. It assumes that both currents, high and low sides, have the same direction
IOPf lt= x ∗ I˙1+ y ∗ I˙2 = x ∗ I1+ y ∗ I2 (13) Applying (9) and (13) to (3) and leaving, for a moment, the absolute operator out of the equations
ΔIOP= x ∗ I1+ y ∗ I2− I1+ I2 ΔIOP= x − 1 ∗ I1+ y + 1 ∗ I2
Again, considering that the high side and low side have the same current during the pre-fault
ΔIOP= x + y ∗ Iload (14)
In this case, as all elements in (14) are positive, neglecting the absolute operator has no effect.
Analysing (7) and (14) it is possible to verify that the incremental operation current is always twice the load current higher than the incremental restraint current.
Table 2 exemplifies the behaviour of (7) and (14).
Comparing Tables 1 and 2 it is clear that directions of the two operators are quite different when an internal or external fault happens.
Table 1 External faults
x y ΔIRT ΔI0P
2 2 2 0
5 5 8 0
1.9 2 1.9 0.1
4.9 5 7.9 0.1
Table 2 Internal faults
x y ΔIRT ΔI0P
2 2 2 4
5 5 8 10
1.9 2 1.9 3.9
Transforming this analysis into a mathematical form, the new algorithm needs a second calculation part.
One way to represent the two operators is by a line equation and knowing that the initial point is always in the axis origins, the slope of the incremental element can be calculated as presented in the following equation:
y = m ∗ x + basb = 0 m = ΔΔIIOP
RT
(15)
m in (15) is associated with line inclination.
Table 3 shows the calculation of m for the same values presented in Tables 1 and 2.
Based on the above analysis, the new characteristic transformer protection is depicted in Fig. 1.
As the directions of the incremental differential currents are quite different, it is necessary just to compare the line slope to adjust the new setting.
3 Analysis of the element considering errors
In the previous section, it was presented the base math for the algorithm and this section presents how the element handles the errors involved in the transformer protection. At the end, it will be possible to have a setting for the m variable.
Looking into the SEL-787 instruction manual [13], the manufacturer has some typical calculation to determine the slopes. For the first slope, which is usually in the load region the CT error is around 3% and [14] also specifies the same value for CT error
under load condition. Also, the manual says that the following errors must be considered:
• Excitation current (typically 1–4%)
• No-load tap changer (NLTC) (typically ± 5%) • Load tap changer (typically ± 10%)
• Relay accuracy (±5% or ± 0.02·Inom, whichever is largest.) Considering the worst case, the maximum error according to the manufacturer is 17% when using a NLTC, which gives a slope of 9.3%. The setting suggested by the manufacturer is 15%. However, many transformers work with a load tap-charger and, in the worst case, one set of CTs can have 3% error in one direction while the other group can have an opposite error. In this matter, the maximum error is 25% which gives a slope of 14.3%. Looking at this value, it is possible to say that this error is too close to the slope proposed by the manufacturer. Nevertheless, the practice experience shows that this setting, 15%, has an adequate response.
Considering that the CT error can increase to about 10% during faults, the setting proposed by the manufacturer is 50% for slope 2.
Table 4 shows the results for m calculation. The value m is calculated considering two situations, an external fault and an internal fault with the same current at both sides. A 5 pu current was used for both sides.
Analysing Table 4, it is possible to verify that m is always small for external faults. The errors need to go for unreal values like 50% in each set of CTs, considering them in opposite direction, for m to reach values as large as 0.50. We can conclude that m will properly represent CTs’ mean errors. Looking at internal faults, m has the
Table 3 m evaluation
x y m (external fault) m (internal fault)
2 2 0 2
5 5 0 1.25
1.9 2 0.05 2.05
4.9 5 0.01 1.25
Fig. 1 Incremental differential characteristic
Table 4 Incremental element calculus for different errors
Excitation, % CT, % Tap, % Relay, % Total error, % m (internal fault) m (external fault)
4 3 5 5 17 1.23 0.09 4 ± 3 5 5 20 1.22 0.11 4 3 10 5 22 1.22 0.12 4 ± 3 10 5 25 1.22 0.14 4 10 10 5 29 1.23 0.18 4 ± 10 10 5 39 1.22 0.23
tendency to stay very high and decrease as the errors increase. That enables an establishment of m for internal faults as 1.0.
Based on these facts, any value between 0.5 and 1.0 will give the incremental differential element a very good result as will be presented in the results section.
Also, m-values above 1.0 can be used. The variable m will be close to 1.0 just in cases when one side of the transformer is open and there is no load at the transformer, which is the case of transformer energisation. For values lower than 1.0, during inrush the element must be blocked by harmonic elements as it is used today in the differential protection. More information about this case can be found in [15]. If values above 1.0 are used, the incremental element is already immune to inrush situations, which gives a very good advantage over the differential element and it turns the incremental differential a good additional element to work in parallel to the standard differential.
4 New element
The incremental element was developed inside the SEL-421 relay [16]. As this relay is not a differential relay, it has no differential currents. It forced the implementation to be from the restraint and operation currents calculation until the entire new element. The protection and automation users’ areas of the relay was used.
The differential currents could be calculated for each phase, as it was done in [15], but for programming simplification and to analyse the element sensitivity, it was decided to develop a positive incremental differential element. The positive differential element needs to be developed just for one phase, reducing the code, and allowing its use for fault in the three phases.
Below are the few lines necessary to calculate the positive restraint and operation currents.
PMV21 is the compensated positive current for one side of the transformer. AMV015 has the same functionality as the TAP compensation in the SEL-787.
PMV22 is the same but for the second winding of the transformer.
PMV23 and PMV24 are used to rotate the positive angle, both sides of the transformer, in order to set the W input of the relay as the reference. It was done mainly for measurements purposes.
PMV25 and PMV26 are the real and imaginary parts of the phasorial sum, operation current, considering the transformer angle compensation.
PMV27 is the operation current itself. PMV28 is the restraint current.
# POSITIV SEQUENCE DIFFERENTIAL CURRENTS PMV21 : = IA1WFM * AMV015 PMV22 : = IA1XFM * AMV016 PMV23 : = IA1WFA - IA1WFA PMV24 : = IA1XFA - IA1WFA PMV25 : = PMV21 + PMV22 * COS(PMV24 + AMV005) PMV26 : = PMV22 * SIN(PMV24 + AMV005) PMV27 : = SQRT(PMV25 * PMV25 + PMV26 * PMV26) PMV28 : = PMV21 + PMV22
The programming of the entire incremental differential element can be reproduced and found in [15].
5 Results
To test the new protection element, the element was implemented inside the SEL-421, and the relay was connected to a real-time digital simulator, as shown in Fig. 2. All system data can be found in detail in [17, 18]. As a comparison base, another transformer differential relay was used, the SEL-787, also connected to the simulator. Both equipments received the same currents. The relays were connected to protect one of the two 230/69 kV transformers between buses B4 and B8.
All kind of faults, internal and external, were applied to the protection zone. Also, internal faults were applied to the transformer, as turn-to-ground and turn-to-turn faults. The SEL-787 settings are shown in Table 5. The relay has two differential elements, one element which works with harmonic restraint and a second which works with harmonic blocking, and both were enabled. The new incremental differential element has only two settings, a minimum operation value and the slope value (m), they were set to 0.05 and to 1.02 pu, respectively. As the relay used in the simulation is not a transformer relay, as mentioned before, any element was not used to block the incremental differential during inrush. The above slope setting, m, already provides inrush immunity.
The main test results are presented in the next section.
Fig. 2 Power system
Table 5 SEL-787 settings
Setting description Value
minimum operation 0.5 pu
slope 1 15%
transition to slope 2 6.0 pu
slope 2 35%
second harmonic 15%
fourth harmonic 10%
5.1 External fault and inrush
Both elements had a satisfactory result for external fault and for inrush. In Fig. 3, it is possible to see the relay currents at both sides of the transformer. Analysing the digital signals, it is clear that there was no operation from both protection elements. Hence, the differential and the incremental differential had no problem to handle this line-to-line (BC) fault.
In Fig. 4, it is possible to see the inrush currents at the high side of the transformer. At the low side, there are no currents. Looking at the digital signals, it is possible to see the circuit breaker, CB, status, DJw1 and DJw2, and that the differential relay blocked the differential element using the second and fourth harmonic algorithm, bit HB2. The incremental differential did not trip even without any specific algorithm for inrush condition.
5.2 Internal faults at 230 kV side
The high voltage side of the transformer has a wye connection and it is solidly grounded. At this side the differential could operate for turn-to-ground faults until 5%, less than that, the element could not detect the faults. For inter-turn faults, the response of the differential element was the same.
The incremental differential could see faults until 2% for turn-to-ground and for inter-turn faults. Fig. 5 shows the response for both elements for a 2% inter-turn fault. It is possible to observe that the currents at both sides of the transformer did not change much. There is a DC value at the high side, but it is possible to verify that the steady-state current value is almost the same as the pre-fault. The incremental element could detect the fault after 1 cycle of fault inception and trip after half cycle, as the function has a half cycle
Fig. 3 External fault
Fig. 4 Inrush
DJw1 – CB status for winding 1 (high side); DJw2 – CB status for winding 2 (low side); 87B – restraint element with harmonic blocking; 87R – restraint element with harmonic restraint; 87U – unrestraint differential; HB2 – second and fourth harmonic blocking; HB5 – fifth harmonic blocking; Dfi1p – incremental differential pick-up; Dfi1t – incremental differential trip
time delay. The 2% turn-to-ground response was identical and will not be presented here.
5.3 Internal faults at 69 kV side
The low side of the transformer is connected in delta. The same internal faults were applied to this side and the differential element could cover only the first and last 30% of the winding for turn-to-ground faults. This means that 40% of the winding is not protected by this element. The most difficult fault location is exactly the middle of the winding.
The incremental differential could protect the entire winding and issued the trip signal always at the same speed. Fig. 6 shows a turn-to-ground fault at 31% of the winding. It can be observed that the phase differential did not trip while the incremental differential had a very fast response to the event. It is also possible to verify in Fig. 6 that again the faults currents did not change much when compared to the pre-fault currents.
6 Conclusions
The paper presented a new protection algorithm for power transformers protection. First it was presented how the new incremental differential behaves when exposed to internal and external faults. The algorithm uses the same quantities used by a regular differential protection, it means, the restraint and operation currents. The new algorithm only uses a different mathematical
approach to increase sensitivity for internal fault. The principle also makes the incremental differential less suitable for external faults.
In this matter, the paper also presented how the algorithm handles the errors involved in a transformer protection and how to avoid inrush phenomenon.
Due to its simplicity, the new element could be programmed inside a commercial relay programming area, allowing a comparison between the proposed algorithm and a commercial differential transformer protection relay through the use of a real-time simulator. The tests were performed in a real power system of Brazil Interconnected System.
During the simulations, the algorithm proved to be immune to external faults and to inrush currents. Also, the element could operate until 2% for turn-to-ground and inter-turn faults. The element also could operate for turn-to-ground faults in the middle of the delta winding.
We propose the use of the incremental element as a complementary protection function to the differential element. The new element was not conceived to work alone, as it was not designed to cover faults during transformer energisation.
7 Acknowledgments
The researcher thanks the CNPq and FAPESP agencies for the financial support.
Fig. 5 2% Inter-turn fault – 230 kV side
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