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Characteristic analysis of zero-mode inrush current of high-impedance transformer
Electrical Power and Energy Systems 117 (2020) 105716
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Characteristic analysis of zero-mode inrush current of high-impedance transformer
T
⁎
Wenbin Caoa, , Xianggen Yina, Zhe Zhanga, Yuanlin Pana, Yuxue Wangb, Xiangyuan Yina a b
State Key Laboratory of Advanced Electromagnetic Engineering and Technology (HUST), Wuhan 430074, China Power Dispatching Control Center of Guangdong Power Grid, Guangzhou 510000, China
A R T I C LE I N FO
A B S T R A C T
Keywords: High-impedance transformer Winding arrangement Hollow inductance Saturated mutual inductance Zero-mode inrush current
In recent years, zero-sequence overcurrent protection misoperated frequently when the high-impedance transformers are energized without load. This paper studies the characteristics of zero-mode inrush current of the high-impedance transformers, including amplitude and attenuation. Firstly, the corresponding relation of “winding arrangement – flux distribution – equivalent circuit parameters” of transformer was clarified. On the basis of analyzing single-phase and three-phase inrush current, the analytical expression and equivalent circuit of zero-mode inrush current were proposed. Then, according to the different winding arrangement, the different parameters of hollow inductance, self-leakage inductance and saturated mutual inductance of the high-impedance transformers and ordinary transformer were explained and calculated. Further, based on the different parameters and analytical expression, the zero-mode inrush current characteristics of high-impedance transformers were analyzed. The correctness of characteristic analysis of high-impedance zero-mode inrush current was verified via digital simulations and dynamic physical simulations tests.
1. Introduction There will be a large inrush current during the transient voltage recovery process after transformer energization or external fault removal. This is due to that the flux linkage cannot be mutated, and free aperiodic component will be generated. In this process, the transformer iron core will intermittently enter saturation, and the magnetizing inductance will be sharply reduced, resulting in large inrush current. At present, there have been extensive discussions on the generation mechanism of magnetizing inrush currents (including sympathetic inrush current), discrimination between inrush current and fault current, their influences on transformer differential protection and related countermeasures [1–6]. However, in the energization process of transformer, there may appear the operation of zero-sequence protection (a type of backup protection) while no operation of transformer differential protection. This phenomenon is related to the zero-sequence component caused by the unbalanced magnetizing inrush current of the transformer, which for a long time in the past has not been prominent enough to arouse people’s attention. The zero-mode inrush current is the sum of the instantaneous values of three-phase primary inrush current. Different from the zero-sequence current generated by the fault, the fundamental reason for the zeromode inrush current generated by the transformer lies in the non-linear ⁎
characteristics of the iron core saturation and the inconsistency of the saturation degree among the three-phase iron cores. This kind of zeromode inrush current that is similar to inrush current has no unified waveform shape, which has long been found [7], but its formation mechanism is unknown. Ref. [8] qualitatively explained that under different remanences and closing angles of the transformer, three-phase asymmetric inrush currents with different harmonic contents would be generated, leading to the generation of zero-mode current, and the simulation waveform of zero-mode inrush current was given. Refs. [9,10] simulated and analyzed the characteristics of zero-mode inrush current and its influence on zero-sequence protection of main transformer, lines and bus. However, the above papers did not carry out mechanism and analytical analysis for the zero-mode inrush current. In recent years, the power grid capacity has been increasing gradually [11–13]. In order to limit the short-circuit current, new highimpedance transformers have been widely used [14,15]. However, when the high-impedance transformer (especially the high-impedance transformer with built-in high-voltage winding) is energized, the zerosequence overcurrent protection of the busbar (segment) breaker or even its upper level line frequently misoperated, which seriously endangers the operation safety of the power grid. Through the analysis of on-site recorded waveform, it could be known that the three-phase primary winding inrush current presented a large unbalanced feature,
Corresponding author. E-mail address: [email protected] (W. Cao).
https://doi.org/10.1016/j.ijepes.2019.105716 Received 16 April 2019; Received in revised form 27 September 2019; Accepted 18 November 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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2.2. The equivalent circuit of transformer and the analytical analysis of single-phase magnetizing inrush current
and the initial value of the zero-sequence component of the inrush current was large. After attenuating for a period of time (the set time of zero-sequence overcurrent protection), its value is still greater than the setting value, which directly led to the misoperation of the zero-sequence overcurrent protection. Strictly speaking, the zero-sequence current is the fundamental frequency component of the zero-mode inrush current, which differs in concept and often used without distinction. While a zero-sequence current is specific to a particular frequency, a zero-mode inrush current is the sum of the instantaneous values of the three-phase currents, which has richer frequency content. In order to accurately grasp its mechanism and further put forward countermeasures, the zero-mode inrush current should be directly analyzed. Compared with the ordinary transformer, the winding arrangement of high-impedance transformers have changed, which may affect the amplitude and attenuation of their zero-mode inrush currents. The three-phase primary winding inrush currents of the misoperated transformer are seriously unbalanced, the initial value of the zero-mode inrush current is large, and its fundamental frequency component (zerosequence current) remains at a high level after the setting time, which causes the zero-sequence protection misoperation. There is currently no simulation model for simulating high-impedance transformer inrush currents. There is also no physical model and physical tests for highimpedance transformers. Therefore, it is urgent to further understand and study the zero-mode inrush characteristics of high-impedance transformers comprehensively.
The zero-mode inrush current is the sum of the instantaneous values of the three-phase inrush current, and the single-phase inrush current is the basis for deriving the three-phase inrush current and the zero-mode inrush current. Therefore, the correspondence between the flux distribution and the equivalent circuit parameters is analyzed firstly, and the physical process and mathematical analytical expression of singlephase magnetizing inrush current are obtained to further analyze the zero-mode inrush current characteristics of the transformer. Generally, when analyzing the generation mechanism of inrush current or studying the factors affecting inrush current, the magnetizing inductance will be linearized [15], that is, the magnetizing inductance is considered as a constant value. This method is effective in understanding the generation mechanism of inrush current or analyzing the influence of external factors (such as system impedance, initial fault current angle, etc.) on inrush current, but not useful in analyzing the influence of different winding arrangement on inrush current. The main difference of winding arrangement is mainly manifested by the difference of magnetizing inductance after saturation (called “saturated mutual inductance”). However, linearization treatment will assume that the magnetizing inductance is a constant value, which is basically a large unsaturated inductance value. The difference of saturated mutual inductance caused by different winding arrangement has little influence on the unsaturated inductance. The impact of winding arrangement on inrush characteristics cannot be well explained by simple inductance linearization. Therefore, the saturated magnetizing characteristics of the core are considered in this paper. As shown in Fig. 2, the iron core magnetizing characteristic curve can be equivalent to two straight lines according to IEC hypothesis. The main flux linkage passing the core is composed of two parts: the flux linkage generated when the iron core is replaced with air, (i.e., ψH = LHi), and the flux linkage generated by the iron core magnetization, (i.e., ψF = μ0WSJ = LFi). J is the magnetization. When the iron core is fully saturated, J = JSat. S is the cross-sectional area of the core; W is the number of winding turns. According to the equivalent magnetizing characteristic curve, when the iron core is not saturated, LF=∞; when the iron core is saturated, LF = 0. When B < BSat, the magnetic field intensity is small (i.e., H = 0), and the magnetic density is BJ = μ0J. BJ is called “unsaturated core magnetic density”. J∈(−JSat, JSat). JSat is the saturated magnetization. When B > BSat, the magnetization curve is represented by a straight line, and the slope is μ0, and the magnetic density is B = μ0JSat + μ0H. The flux linkage pass through the iron core is ψI (i.e., ψI = WSB).
2. Mechanism and analytical analysis of zero-mode inrush current When a YYΔ-connected three-winding transformer is energized on the high-voltage (HV) winding, not only the HV winding will generate inrush current, but also the low-voltage (LV) delta winding will generate circulating current. At this time, the three-winding transformer is equivalent to a double-winding transformer. The transformer equivalent circuit can reflect transformer flux distribution in the form of concentrated parameters, so it is more convenient to analyze the inrush current by using the transformer equivalent circuit. 2.1. Winding arrangement of transformer and its flux distribution As shown in Fig. 1, the flux generated by the current flowing through the HV winding (winding 1) is called the “total magnetic flux”. The magnetic flux interlinked in the LV winding (winding 2) is called “mutual flux”, which consists of the “mutual main flux” passing through iron core and the “mutual-leakage flux” passing through the air gap. The flux generated by the HV winding that does not interlink with the LV winding is called the “self-leakage flux”. As can be seen from Fig. 1, winding 2 is closer to the iron core, with smaller air gap area, whereas winding 1 is far from the iron core, with large air gap area. Under the same magnetic density, less flux can pass through winding 2 as compared with winding 1. Therefore, the winding arrangement determines the flux distribution status. If the winding arrangement position changes, the corresponding flux distribution will change accordingly.
Fig. 1. Magnetic flux distribution of windings.
Fig. 2. Magnetizing characteristic curve. 2
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Fig. 3. The closing circuit of single-phase transformer and equivalent circuit.
⎧ when B < BSat , ψI = μ0 WSJ ⎨ ⎩ when B > BSat , ψI = μ0 WSJSat + LH i
Fig. 4. Y0/△-connected three-phase transformer equivalent circuit.
dψ ri + = Us sin(ωt + α ) dt
2.3. The analytical analysis of zero-mode inrush current On the basis of single-phase inrush current, three-phase inrush current and zero-mode inrush current are further deduced. The Y0/ △-connected three-phase transformer equivalent circuit is shown in Fig. 4. After simplifying the three-phase voltage differential equation, the following equation is obtained:
(2)
ψ = ψs + ψσ + ψK + ψI = (Ls + Lσ + LK ) i + ψI = (Ls + Lσ + LK ) i + WSBI
(3)
where, r is the total resistance of the closing circuit, and ψ is the total flux linkage, including the system flux linkage ψs(i.e., ψs = Lsi), the selfleakage flux linkage ψσ(i.e., ψσ = Lσi), the mutual leakage flux linkage ψK(i.e., ψK = LKi) and the core flux linkage ψI(i.e., ψI = WSBI). BI is the core magnetic density. The above illustrates the linear correspondence between the inductance and the flux linkage. The larger the flux which passes through the winding is, the larger the corresponding inductance is. The corresponding inductance in the equivalent circuit will change as the winding arrangement changes. According to (2), the total flux linkage is:
Us [cos α − cos(ωt + α )] + ψr − r ω
0
uB = (Ls + uC = (Ls +
Us [cos α − cos(ωt + α )] + ψr ω
(4)
ea + eb + ec = −3LσD
ψ − μ0 WSJSat i= Ls + Lσ + Mair
(5)
(Ls0 + Lσ )
ωψr − ωμ0 WSJSat ⎤ Us ⎡ cos α − cos(ωt + α ) + ⎥ ⎢ Us ωL ⎣ ⎦
+ ec
(10)
diD dt
(11)
di 0 di = LσD D dt dt
(12)
Because the initial current is zero, there is: (6)
i0 = (7)
LσD iD Ls0 + Lσ
(13)
iD is also a zero-mode current. According to the theory of self and mutual inductance, the total flux linkage of phase A is:
When ψ < μ0WSJSat and B < BSat, the working point is on the ordinate as shown in Fig. 2, where H is zero and i is zero. According to (5) and (7), the magnetizing current of the single-phase transformer is:
i=
+ ea + eb
All electrical quantities have been calculated to the HV side. After adding the three equations of (10) and taking the relationship of “iA + iB + iC = 3i0” into account, (12) is obtained:
According to (1) and (3):
ψ = (Ls + Lσ + Mair ) i + μ0 WSJSat
di 0 dt di + (Ls0 − Ls ) dt0 di + (Ls0 − Ls ) dt0
+ (Ls0 − Ls )
where, Ls and Ls0 are line positive-sequence inductance and zero-sequence inductance respectively. Lσ is the self-leakage inductance of the primary winding. LσD is the self-leakage inductance of the secondary winding. ea, eb and ec are the induced back electromotive force. iD is the circulating current of secondary delta winding, which satisfies (11).
Where, ψr is the iron core remanence (i.e.,ψr = WSBr) and Br is the remanence density. In order to simplify the analysis, the resistance is not counted, which means the attenuation of the flux linkage is not considered. So (4) becomes (5):
ψ=
diA dt di Lσ ) dtB di Lσ ) dtC
uA = (Ls + Lσ )
t
∫ idt
(9)
It can be seen from (9) that when the external conditions are the same, the amplitude of the inrush current is determined only by the denominator L. Note that L here is the value when the iron core is saturated, which is much smaller than the unsaturated inductance. When the iron core enters saturation, the iron core inductance decreases sharply from a maximum value, of which the value is similar to the “self-leakage inductance” and “saturated mutual inductance” of the windings. Therefore, the inrush current is sensitive to the changes of the latter two.
LK and LH are mutual inductance on the magnetizing branch which correspond to the saturated mutual flux passing through the air (both the air gap and the core replaced with air). Therefore, let the saturated mutual inductance be Mair = LH + LK. The closing circuit of singlephase transformer and its equivalent circuit are shown in Fig. 3. The parameters of the equivalent circuit correspond to the flux distribution. It can be seen from the above that when the core is saturated (i.e., LF = 0), the self-inductance of HV winding is L11 = Lσ + Mair, which also known as the HV winding hollow inductance Lair. When the transformer is energized, the differential equation is as shown in (2) and (3):
ψ=
Us ⎡ B − BSat ⎤ cos α − cos(ωt + α ) + r ⎥ ωL ⎢ Bs ⎣ ⎦
i= (1)
ψA = (Ls + Lσ + Mair ) iA + Mair iD + (Ls0 − Ls ) i 0 + μ0 WSJA
(14)
where, Lσ + Mair = Lair, JA is not necessarily a saturated value. Because in the case of iD, although JA does not reach the saturated value, iA is not zero. By substituting (5) and (13) into (14) and referring to (8) and (9), we obtain:
(8)
where, L = Ls + Lσ + Mair, Us = ωWSBs, BSat = μ0JSat, ψr = WSBr. (9) is got from (8): 3
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iA =
BrA − μ0 JA ⎤ Us ⎡ − ci 0 cos α − cos(ωt + α ) + ⎥ Bs ωL ⎢ ⎦ ⎣
(15)
There is similar situation for the inrush current of phase B and phase C:
iB =
BrB − μ0 JB ⎤ Us ⎡ − ci 0 cos(α − 120°) − cos(ωt + α − 120°) + ⎥ Bs ωL ⎢ ⎦ ⎣ (16)
iC =
BrC − μ0 JC ⎤ Us ⎡ − ci 0 cos(α − 240°) − cos(ωt + α − 240°) + ⎥ ⎢ Bm ωL ⎣ ⎦ (17)
where L = Ls + Lσ + Mair is the self-inductance of the primary loop circuit, which is the same as L in (8), and c is:
c=
Mair (Ls0 + Lσ ) + LσD (Ls0 − Ls ) LLσD
Fig. 5. Three-phase magnetic density schematic diagram.
⎧ Bs [cos α − cos(ωt + α )] + BrA ⎪ ⎪ BSat BJA (t ) = BSat ⎨ ⎪ −BSat ⎪ − BSat ⎩
(18)
According to (15), (16) and (17): C
1 U 1 ⎛ 3i 0 = × s × ∑ Br − μ 0 1+c ωL Bs ⎜ A ⎝
C
∑ J ⎞⎟ A
⎠
ωBs ⎡ ⎣
Mair (Ls 0 + Lσ ) LσD
(20)
⎧ Bs [cos(α − 240°) − cos(ωt + α − 240°)] + BrC |BJC (t )| ⩽ ⎪ ⎪ BSat BJC (t ) = BSat BJC (t ) > BSat ⎨ ⎪ −BSat BJC (t ) < ⎪ − B Sat ⎩
C
+ Ls0 + Lσ + Mair ⎤ ⎦
According to (20), the zero-mode inrush current is determined by multiple parameters. The parameters in the denominator reflect the difference between different kinds of transformers. The amplitude of the zero-mode inrush current depends on the initial remanence of the three-phase iron core and the unbalance of the magnetization, which are represented by the molecules in (20). When the sum of the initial remanence is zero and three-phase iron core are not saturated (i.e., the three-phase magnetization is symmetrical), the zero-mode inrush current will be zero According to (13) and (20), the total current of the magnetizing branch is: C
i∑ m (t ) = 3i 0 (t ) + 3iD (t ) =
(24) The image description of (24) is shown in Fig. 5. The three-phase total magnetic density B(t) is a three-phase symmetrical sinusoidal waveform in the figure, and the three-phase unsaturated core magnetic density BJ(t) is the value of the solid line which is in the blue area. The key to calculating the zero-mode inrush current is to calculate the sum of the three-phase unsaturated core magnetic density BJ(t).
C
Us ⎜⎛∑ Br − ∑ BJ (t ) ⎟⎞ A ⎠ ⎝A ωBs ⎡Mair + ⎣
LσD (Ls 0 + Lσ ) ⎤ LσD + (Ls 0 + Lσ ) ⎦
2.4. The equivalent circuit of zero-mode inrush current (21)
According to (21), zero-mode equivalent circuit of transformer is potted shown as Fig. 6. Mair is on the common magnetizing branch, Lσ, Ls0 and LσD are connected in parallel. In actual situation, due to the effect of resistance loss, the threephase core will gradually drop out of saturation, so that the saturation unbalance will be continuously reduced, and the zero-mode equivalent voltage will gradually attenuate to zero. The attenuation process of the
According to the physical meaning of BJ(t) = μ0J(t), the “unsaturated core magnetic density” is defined:
BJ (t ) =
⎧ B (t ) BSat ⎨ − ⎩ BSat
BJA (t ) <
⎧ Bs [cos(α − 120°) − cos(ωt + α − 120°)] + BrB |BJB (t )| ⩽ ⎪ ⎪ BSat BJB (t ) = BSat BJB (t ) > BSat ⎨ ⎪ −BSat BJB (t ) < ⎪ − B Sat ⎩
Us ⎛⎜∑ Br − ∑ BJ (t ) ⎞⎟ A ⎠ ⎝A
3i 0 (t ) =
BJA (t ) > BSat
(19)
According to (18) (19), and BJ(t) = μ0J(t): C
|BJA (t )| ⩽
|BJ (t )| ⩽ BSat BJ (t ) > BSat BJ (t ) < − BSat
(22)
According to (5), “system total magnetic density” is defined:
B (t ) =
ψ (t ) = Bs [cos α − cos(ωt + α )] + Br WS
(23)
According to (22) and (23), three-phase BJ(t):
Fig. 6. The equivalent circuit of zero-mode inrush current. 4
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the failure rate decreases and the reliability is better. T-Lse is simple in structure design, but the additional serial inductance increases the difficulty of operation and maintenance, so its reliability is not as good as the T-Hin [16,17]. The difference of the three types of transformers lies only in the winding arrangement. Therefore, it is necessary to compare and analyze the parameter differences of three kinds of transformers taking the winding arrangement into account. At present, there are few studies on the inrush current characteristics of high-impedance transformers. Traditional analytical methods are used in Ref. [15] to study the inrush currents characteristics of T-Hin. In Ref. [18], statistical analysis was conducted based on the inrush current tests data of 21 groups of T-Hin with closing failure, and results showed that T-Hin had large inrush current, small attenuation time constant, and high rate of zero-mode current. However, there have been no research works on the differences in parameters and characteristics analysis of zero-mode inrush among T-Hin, T-Lse and T-Ord. In terms of the number of misoperation accidents, the misoperation accidents occurred during the energization of T-Hin are far more than that of T-Lse and T-Ord with the same iron core and wiring, while it remains unknown that whether T-Lse and TOrd have the potential for misoperation. Therefore, the zero-mode inrush current characteristics considering the difference in parameters between the two kinds of high-impedance transformers will be studied and compared with the zero-mode inrush current of T-Ord.
total magnetic density B(t) of each phase can be described as follow. When the iron core is unsaturated, the magnetizing inductance is very large, which is considered as infinite, and the attenuation time constant (τ = L/R) is also very large. In a short time, it can be considered that the magnetic density does not attenuate, that is, when B(t) enters the blue “non-attenuation region” in Fig. 5, it does not attenuate. In contrast, when the core is saturated, the total inductance of the system is small, which is the slope of the broken line in Fig. 5. The attenuation time constant is τ = L/R, namely, in Fig. 5, when B(t) enters the gray area, it will attenuate with the attenuation time constant τ. In conclusion, the attenuation process of the total magnetic density B(t) of each phase will follow the cycle of “saturation-unsaturation” and “attenuation-unattenuation” of the iron core, and the length of attenuation time in each cycle will also change with the saturation degree. Finally, the aperiodic components will attenuate to zero, and B(t) will all remain in the “unattenuated region” for steady running. At this time, the sum of symmetric unsaturated iron core magnetic densities BJ(t) of threephases will be zero, the zero-mode equivalent voltage will be zero, and the zero-mode inrush current will disappear.
3. The differences in winding arrangement and parameter of highimpedance transformers 3.1. Two kinds of high-impedance transformers
3.2. Short-circuit inductance and self-leakage inductance of HV and LV winding
Generally, the H-M impedance of the high-impedance is standard impedance (the same as ordinary transformer), and H-L impedance and M-L impedance are high impedance [16]. At present, there are two commonly used high-impedance transformers, one is the high-impedance transformer with built-in HV windings (which is called T-Hin for short), and the other is the high-impedance transformer with inductance connected in series at low-voltage winding (T-Lse for short). For T-Hin, the HV winding is placed close to the iron core and the winding arrangement from inside to outside is iron core–HV–MV–TV–LV, as shown in Fig. 7(b) (“TV” means the tap-changing windings). For T-Lse, series inductances are directly connected in the LV delta windings of the ordinary transformer (T-Ord for short) so as to improve the H-L impedance and the M−L impedance of the transformer, as shown in Fig. 7(c). The T-Hin increases the impedance by changing the winding arrangement without additional equipment, so
This part first calculates the different parameters of the three kinds of transformers through the equivalent circuit and the original parameters, and then explains the essential reasons of the different parameters based on the corresponding relationship of “winding arrangement – flux distribution – equivalent circuit parameters” in the last section. The actual transformer (capacity: 240/240/80 MVA; voltage: 220/ 115/10.5 kV) which caused misoperation is selected to analyze the difference in parameters of three kinds of transformers, as shown in Table 1. The larger the diameter of the winding coil is, the larger the hollow inductance is. The HV winding of T-Hin is on the inside and its Lair is smaller. It is well known that the short-circuit impedance of a transformer is essentially the leakage inductance between the two windings of the transformer, more precisely the sum of the self-leakage inductances of the two windings. For double-winding transformers, the magnetizing branch is very large when the iron core is unsaturated, and the leakage inductance could be ignored. Therefore, the short-circuit impedance obtained from the short-circuit test is evenly distributed to HV and LV windings to form the T-type equivalent circuit, or the total short circuit impedance is distributed to secondary winding, forming Γ-type equivalent circuit. However, when analyzing the amplitude of inrush current, the magnetizing mutual impedance is small when the iron core is saturated, and the self-leakage impedance on both sides cannot be ignored. Therefore, Table 1 Parameters comparison of different kinds of transformers. Parameters Short-circuit inductance at rated gear (%) No-load loss (kW) No-load current (%) Hollow inductance of HV Xair = ωLair (%)
Fig. 7. Winding arrangement of several kinds of transformer.
H-M H-L M−L
T-Hin
T-Lse
T-Ord
13.65(14) 36.41(36) 20.64(22) 96.53 0.067 21
15.03(14) 38.83(36) 21.29(22) 95 0.06 34
14.17(14) 25.12(23) 8.47(9) 103.4 0.05 34
Note: The values in parentheses are the design values. 5
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inductance. Considering the complexity of the actual winding, the formula cannot be used to calculate the exact value, but it can be used for comparison between different kinds of transformers. The hollow inductances are generally measured by the manufacturer and recorded in the factory test report. The hollow inductor of the winding is measured when the iron core is not inserted. Ignore the difference in wire diameters of different types of transformers, as shown in Fig. 8. Compared with T-Ord and T-Lse, the HV winding coil of T-Hin has a smaller diameter. According to (25), its Lair is also smaller. This conclusion is consistent with the relationship of the actual hollow inductance parameters shown in Table 1. While Lair = Lσ + Mair, and Lσ is almost the same, it can be seen that the difference of T-Hin lies in the saturated mutual inductance Mair, which is smaller than that of T-Ord and T-Lse. Based on the above analysis, the comparison relationship of different transformers are: Lσ(Ord)≈Lσ(Hin)≈Lσ(Lse); Mair(Ord) = Mair(Lse)＞Mair(Hin); LσD(Ord)＜ LσD(Hin) = LσD(Lse). According to the zero-mode inrush current expression in (20), the zero-mode inrush current expressions for T-Lse and T-Hin are:
Table 2 Equivalent self-leakage inductance of HV and LV windings. Percentage of impedance %
Inside
Outside
T-Hin T-Lse T-Ord
H:14.7(14) L:22.5(22) L:9.7(9)
L:21.7(22) H:16.3(14) H:15.4(14)
Note: The values in parentheses are the design values.
C
3i 0(Lse) (t ) = ωBm ⎡ ⎣
Fig. 8. The winding arrangement and the space flux distributions of the HV and LV windings.
C
Um ⎜⎛∑ Br − μ0 ∑ J (t ) ⎟⎞ A ⎠ ⎝A Mair (Lse) (Ls0 + Lσ (Lse) ) Lσ D(Lse) ↑
(26) C
it is necessary to clarify the value of the self-leakage inductance of the two windings, which is related to the winding arrangement. According to the short-circuit tests data, the self-leakage inductance of each side is calculated as shown in Table 2. The self-leakage inductances of the HV primary winding of the three kinds of transformers are approximately equal; the self-leakage inductances of the LV secondary winding of T-Hin and T-Lse are approximately equal. The winding arrangement and the space flux distributions of the HV and LV windings are shown in Fig. 8.
ωBm ⎡ ⎣
Mair (Hin) ↓ (Ls0 + Lσ (Hin) ) LσD (Hin) ↑
↑↑ + Ls0 + Lσ (Hin) + Mair (Hin) ↓⎤ ⎦ (27)
The red arrow in the above formula indicates the comparison of two high-impedance transformer parameters compared with the ordinary transformer parameters. By comparison of (20) (26) and (27), based on the fact that the zero-mode equivalent voltages of the three transformers are substantially equal when the attenuation of the inrush current is not considered (or at the start of the inrush current), it is known that the zero-mode inrush current of T-Hin is the largest, that of T-Lse is the second, and that of T-Ord is the smallest. According to the zero-mode equivalent circuit shown in Fig. 6, it can be intuitively judged that the zero-mode voltage generated by the imbalance is in the common branch. On the one hand, the secondary self-leak inductance of T-Hin is larger than that of T-Ord, the current flowing to the primary winding will be larger. On the other hand, the saturated mutual inductance of THin is smaller than that of T-Ord and T-Lse, and the total current will be larger. In short, there are two factors that cause the amplitude of the zero-mode inrush current to be larger, which are the large value of the secondary leakage inductance LσD and the small value of the saturated mutual inductance Mair. Therefore, based on the above two factors, the zero-mode inrush current of T-Hin will be larger than that of T-Ord and T-Lse. Compared with T-Ord, T-Lse has larger secondary self-leakage inductance, so the zero-mode inrush current of the T-Lse also larger than that of T-Ord.
4.1. Amplitude analysis of zero-mode inrush current of high-impedance transformer The difficulty in analyzing the transient inrush current characteristics of transformer lies in the non-linearity of magnetizing branch inductance. In order to facilitate the analysis of the difference in inrush current characteristics between high-impedance transformer and ordinary transformer, the two-section linear model of transformer magnetizing characteristic curve is adopted, as shown in Fig. 2. The twosection linear model divides the transformer magnetizing characteristic curve into the saturated region and the unsaturated region, where the cut-off point is the inflection point of the magnetizing curve, and the corresponding flux value is φSat. When the transformer flux is greater than φSat, i.e., when the transformer iron core is saturated, a straight line can be used to approximate the transformer magnetizing curve, and the slope of such line is the hollow inductance of the winding coil. When the transformer generates a large inrush current, the iron core reaches deep saturation and it can be approximated as air, and the inductance of winding coil is hollow inductance as the winding coil is full of air. The expression of the hollow inductance Lair is (25) [19]:
μ0 πND 2 4d
C
Um ⎛⎜∑ Br − μ0 ∑ J (t ) ⎞⎟ A ⎠ ⎝A
3i 0(Hin) (t ) =
4. Characteristic analysis of zero-mode inrush current of highimpedance transformer
Lair =
↑
+ Ls0 + Lσ (Lse) + Mair (Lse) ⎤ ⎦
4.2. Attenuation analysis of zero-mode inrush current of high-impedance transformer The recorded data of inrush currents of the three types of transformers with the same capacity and voltage level were observed, and it was found that all of them attenuated very slowly. Based on this, this paper further studies the relative attenuation speeds of inrush currents of T-Hin, T-Lse and T-Ord using attenuation time constant (τ = Lair/R). The inrush process is a nonlinear transient process, which cannot be accurately analyzed using the attenuation time constant. However, when the inrush current is large, the magnetizing characteristic curve is
(25)
where: μ0 is the permeability, D is the winding coil diameter, and d is the wire diameter. (25) is the decisive formula of the hollow 6
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almost linear when it crosses the inflection point and enters the deep saturation region, and using the attenuation time constant for analysis is feasible in such case. The magnetizing inductance in unsaturated region is very large, which can be approximately considered not attenuated. Therefore, the overall attenuation of the inrush current can be indirectly measured by the attenuation time constant in the saturated region. The expression of the air-core coil resistance R is as follows:
R=
4ρπND d2
Table 3 Distribution of inductance of each side of three kinds of transformer during noload closing. Equivalent circuit
Parameters
T-Hin
T-Lse
T-Ord
Lσ LσD Mair
0.14pu 0.22pu 0.07pu
0.14pu 0.22pu 0.2pu
0.14pu 0.09pu 0.2pu
(28)
where, ρ is the wire resistivity. Assuming that the external system parameters of the transformer are the same, the attenuation time constants when the core is extremely saturated can be obtained according to (25) and (28):
τ=
μ Dd Lair = 0 R 16ρ
(29)
According to (29), compared with T-Lse and T-Ord, the HV winding coil diameter D of T-Hin is smaller, its attenuation time constant upon deep saturation of iron core is slightly smaller, and its attenuation is slightly faster. T-Lse and T-Ord have the same diameter and attenuation speed. Although the zero-mode inrush current of T-Hin attenuates slightly faster, its amplitude is large, and it remains at a high level when it attenuates to the setting time of protection, so that misoperation occurs, as shown in Fig. 9. According to [18], the average values of the hollow inductance Lair, the resistance R and the attenuation time constant τ of T-Hin (model 220 kV/240MVA) respectively are 0.1358 H, 0.1784 Ω and 0.7635 s, and that of T-Ord respectively are 0.2159 H, 0.2685 Ω and 0.8125 s, which are consistent with the conclusions of this paper.
Fig. 10. Simulation and recorded waveform of three-phase inrush current.
5. Digital simulation of zero-mode inrush current of highimpedance transformer 5.1. Simulation modeling and parameters determination for high-impedance transformer Fig. 11. Simulation and recorded waveform of zero-mode inrush current and zero-sequence current RMS.
As different kinds of transformers have different winding arrangement, their self-leakage inductances at HV side and LV side are obviously different. By default, the PSCAD transformer simulation model takes half of the input short-circuit leakage inductance as the selfleakage inductance on both sides, which is not in line with the actual situation. In this paper, a kind of transformation method is adopted, in which the simulated magnetizing branch is placed on the HV side, the HV self-leakage impedance is added on the system side, and the actual LV self-leakage inductance is taken as the short-circuit impedance to be input in the transformer simulation model. The “core inductance” of transformer model is the saturated mutual inductance Mair, which is the value of the hollow inductance minus the primary self-leakage inductance. The specific values of the three transformer parameters are shown in Table 3. The above parameters are respectively input into the improved transformer simulation model of this paper, and the current transformer transient simulation model is considered in the simulation [20].
Under the same external factors, the simulation of the three-phase primary inrush current, zero-mode current and zero-sequence current RMS is shown in Fig. 10 and Fig. 11. The simulated waveform and the on-site recorded waveform agree well. The improved simulation model in this paper can be used to study the inrush current characteristics of high-impedance transformers. 5.2. Simulation comparison of zero-mode inrush current of high-impedance transformer In addition to the winding arrangement concerned in this paper, the factors affecting the inrush current characteristics include remanence, closing angle, system impedance, neutral point grounding, etc. The influence of above factors on the inrush current characteristics has been extensively discussed [2,21]. Therefore, when analyzing the inrush current characteristics of the three kinds of transformers, these factors are no longer considered. Under the same external conditions, the comparison of the zero-mode inrush currents and zero-sequence currents RMS of the three kinds of transformers is shown in Fig. 12. As shown in Fig. 12, the zero-mode inrush current and zero-sequence current RMS of T-Hin are the largest, followed by T-Lse and TOrd. By observing the attenuation trends of them, their attenuation are all slow, in which the T-Hin is slightly faster, while T-Lse is basically the same as the T-Ord. The simulation results are consistent with the conclusion of mechanism analysis. Compared with T-Lse and T-Ord,
Fig. 9. The attenuation of zero-sequence current RMS. 7
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Fig. 12. Simulation waveform of zero-mode inrush current and zero-sequence inrush current RMS.
the initial value of the zero-sequence current of T-Hin is much larger. Even though the zero-sequence current of T-Hin attenuates slightly faster than that of T-Lse and T-Ord, it still remains at a high level when the attenuation reaches the setting time, thus leading to the zero-sequence protection misoperation.
Fig. 13. Dynamic physical simulation tests.
6. Dynamic physical simulation tests of zero-mode inrush current of high-impedance transformer In order to further verify the theoretical and simulation results of the zero-mode inrush current characteristics of the high-impedance transformer, we designed and manufactured several transformer physical models with the same structure as the actual transformers for dynamic physical simulation tests. Taking the transformer that caused the protection misoperation in the field as the prototype, referring to the parameters of the two high-impedance transformers and ordinary transformers shown in Table 1, we designed and manufactured transformer physical models on the basis of ensuring that the main parameters such as the percentage of short-circuit inductance are as equal as possible. The capacity of the physical model transformer is: 20/20/6.67 kVA; the voltage is: 0.8/0.4182/0.0382 kV. The specific parameters are shown in Table 4. Wherein, the T-Lse is formed by a T-Ord with inductance connected in series at LV delta winding, as shown in Fig. 7. In the dynamic physical simulation laboratory of Huazhong University of Science and Technology, the zero-mode inrush current tests of T-Hin, T-Lse and T-Ord are carried out to compare the zeromode inrush current characteristics of the three kinds of transformers. Fig. 13 is a picture of the field test, which includes three types of transformers, a high-voltage grid analog screen and a switch controller. In order to eliminate interference from other factors, the three kinds of transformers are guaranteed to be opened at a uniform angle (phase A: 180°) without load to ensure the same remanence status and then closed at a uniform angle (phase A: 0°) to ensure the same magnetic bias. The zero-mode inrush currents and zero-sequence currents RMS of the three kinds of transformers obtained are shown in Fig. 14. As can be seen from Fig. 14, the zero-mode current and zero-sequence current
Fig. 14. Dynamic physical simulation waveform of zero-mode inrush current and zero-sequence inrush current RMS.
RMS of T-Hin are the largest, and that of T-Lse are the second, the smallest is that of T-Ord. and attenuation of T-Hin is slightly faster than the other. The correctness of the conclusions of the theory and simulation is verified. 7. Summary In order to find out the causes of protection misoperation and further propose countermeasures, this paper focuses on the zero-mode inrush current characteristics of high-impedance transformers. The main work and conclusions of this paper are as follows:
Table 4 Parameters comparison of different kinds of transformers. Parameters Short-circuit inductance at rated gear (%)
H-M H-L M−L
No-load loss (kW) No-load current (%) Hollow inductance of HV Xair = ωLair (%)
T-Hin
T-Lse
T-Ord
13.37 37.22 29.17 122 2.82 14.33
13.24 39.37 28.98 119 2.28 17.28
13.24 22.27 11.88 119 2.28 17.28
(1) The corresponding relation of “winding arrangement – flux distribution – equivalent circuit parameters” of transformer was clarified. On the basis of analyzing single-phase and three-phase inrush current, the analytical expression and equivalent circuit of zeromode inrush current were proposed. (2) According to the different winding arrangement, the different parameters of hollow inductance, self-leakage inductance and saturated mutual inductance of T-Ord, T-Hin and T-Lse were explained and calculated. Compared with T-Ord, T-Hin and T-Lse 8
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respectively increase the leakage inductance by increasing the leakage magnetic area and the series inductance. Their primary selfleakage inductance is basically equal; the HV winding of T-Hin is built-in, its hollow inductance and saturated mutual inductance are both reduced. (3) According to the analytical expression of zero-mode inrush current and the different parameters of three kinds of transformers, the zero-mode inrush current characteristics of high-impedance transformer are analyzed. The zero-mode inrush current and zero-sequence current RMS of T-Hin are the largest, followed by T-Lse and T-Ord. The attenuation of T-Hin is slightly faster. Compared with T-Lse and T-Ord, the initial value of the zero-sequence current of THin is much larger. Even though the zero-sequence current RMS of T-Hin attenuates slightly faster than that of T-Lse and T-Ord, it still remains at a high level when the attenuation reaches the setting time, thus leading to the zero-sequence protection misoperation. (4) High-impedance transformer digital simulation models and physical models that can reflect the differences in structure and parameters are constructed respectively. Both digital simulation and dynamic physical simulation tests verify the correctness of the zeromode inrush current characteristics of high-impedance transformers.
[2] Qi X, Yin X, Zhang Z, et al. The research on transformer sympathetic inrush current and its identification method. IEEJ Trans Electr Electron Eng 2016;4(11):442–50. [3] Wu Q, Ji T, Li M, et al. Using mathematical morphology to discriminate between internal fault and inrush current of transformers. IET Gener Transm Distrib 2016;10(1):73–80. [4] Dashti H, Davarpanah M, Sanaye-Pasand M, et al. Discriminating transformer large inrush currents from fault currents. Int J Electr Power Energy Syst 2016;75:74–82. [5] Ahmed AA, Abdelsalam HA. Mitigation of transformer-energizing inrush current using grid-connected photovoltaic system. Int J Electr Power Energy Syst 2016;79:312–21. [6] Samantaray SR, Dash PK. Decision Tree based discrimination between inrush currents and internal faults in power transformer. Int J Electr Power Energy Syst 2011;33(4):1043–8. [7] Xu C. Analysis of the zero-sequence inrush current waveform for 500 kV transformer. Power Syst Protect Control 1983;11(3):13–21. [8] Du J, Liu S, Wang B. Study on principle of zero-sequence component caused by transformer inrush phenomenon. Electric Appl 2007;26(1):27–31. [9] Du J, Zhang J, Hu P. Analysis of influence of transformer and inrush current on zero-sequence protection. Electric Appl 2009;28(1):42–6. [10] Fang Y, Xu X, Zhu B. Influence of transformer inrush on zero-sequence current protection. Electr Power Autom Equip 2008;28(9):115–8. [11] Hou K, Shao G, Wang H, et al. Research on practical power system stability analysis algorithm based on modified SVM. Protect Control Modern Power Syst 2018;3(1):1–7. [12] He Y, Chen Y, Yang Z, et al. A review on the influence of intelligent power consumption technologies on the utilization rate of distribution network equipment. Protect Control Modern Power Syst 2018;3(1):1–7. [13] Rodriguez P, Rouzbehi K. Multi-terminal DC grids: challenges and prospects. J Mod Power Syst Clean Energy 2017;5(4):515–23. [14] Guo Q, Wang J, Zheng F, et al. An application of inrush current suppression technology based on CNN in switching operation of high-voltage built-in high-impedance transformer. IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia) 2018;2018:511–6. [15] Li X, Luo L, Xie J, et al. Impact of inrush current characteristics of high-voltage built-in high-impedance transformer on relay. Autom Electr Power Syst 2016;40(11):108–14. [16] Fu J. Comparison on different design schemes of 220 kV high-impedance transformer. Transformer 2017;54(2):1–7. [17] Li H. Design of 220kV on-load-tap-changing high impedance transformer with three windings. Transformer 2009;46(5):1–7. [18] Li Y, Shu Z, Wang R, et al. Calculation and analysis of magnetizing inrush current of high impedance transformer with built-in high voltage winding. Transformer 2017;54(8):1–5. [19] Zhang J. Formation mechanism of transformer magnetizing inrush current and simulation model of current transformer. Zhejiang University 2005. [20] Yin X, Zhang Z, Qi X, et al. Modeling and analysis for practical CT based on transient test and parameter identification. CSEE J Power Energy Syst 2016;2(4):51–7. [21] Cong W, Wang W, Xiao J, et al. Transformer inrush current restraining scheme based on switching voltage amplitude controlling method. Autom Electr Power Syst 2017;41(8):159–65.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This paper is supported by the national key research and development plan of China (2016YFB0900600) and Guangdong Power Grid Science &Technology Project (GDKJXM20162461). References [1] Zhang A, Ji T, Li M, et al. An identification method based on mathematical morphology for sympathetic inrush. IEEE Trans Power Delivery 2018;33(1):12–21.
9
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Characteristic analysis of zero-mode inrush current of high-impedance transformer
T
⁎
Wenbin Caoa, , Xianggen Yina, Zhe Zhanga, Yuanlin Pana, Yuxue Wangb, Xiangyuan Yina a b
State Key Laboratory of Advanced Electromagnetic Engineering and Technology (HUST), Wuhan 430074, China Power Dispatching Control Center of Guangdong Power Grid, Guangzhou 510000, China
A R T I C LE I N FO
A B S T R A C T
Keywords: High-impedance transformer Winding arrangement Hollow inductance Saturated mutual inductance Zero-mode inrush current
In recent years, zero-sequence overcurrent protection misoperated frequently when the high-impedance transformers are energized without load. This paper studies the characteristics of zero-mode inrush current of the high-impedance transformers, including amplitude and attenuation. Firstly, the corresponding relation of “winding arrangement – flux distribution – equivalent circuit parameters” of transformer was clarified. On the basis of analyzing single-phase and three-phase inrush current, the analytical expression and equivalent circuit of zero-mode inrush current were proposed. Then, according to the different winding arrangement, the different parameters of hollow inductance, self-leakage inductance and saturated mutual inductance of the high-impedance transformers and ordinary transformer were explained and calculated. Further, based on the different parameters and analytical expression, the zero-mode inrush current characteristics of high-impedance transformers were analyzed. The correctness of characteristic analysis of high-impedance zero-mode inrush current was verified via digital simulations and dynamic physical simulations tests.
1. Introduction There will be a large inrush current during the transient voltage recovery process after transformer energization or external fault removal. This is due to that the flux linkage cannot be mutated, and free aperiodic component will be generated. In this process, the transformer iron core will intermittently enter saturation, and the magnetizing inductance will be sharply reduced, resulting in large inrush current. At present, there have been extensive discussions on the generation mechanism of magnetizing inrush currents (including sympathetic inrush current), discrimination between inrush current and fault current, their influences on transformer differential protection and related countermeasures [1–6]. However, in the energization process of transformer, there may appear the operation of zero-sequence protection (a type of backup protection) while no operation of transformer differential protection. This phenomenon is related to the zero-sequence component caused by the unbalanced magnetizing inrush current of the transformer, which for a long time in the past has not been prominent enough to arouse people’s attention. The zero-mode inrush current is the sum of the instantaneous values of three-phase primary inrush current. Different from the zero-sequence current generated by the fault, the fundamental reason for the zeromode inrush current generated by the transformer lies in the non-linear ⁎
characteristics of the iron core saturation and the inconsistency of the saturation degree among the three-phase iron cores. This kind of zeromode inrush current that is similar to inrush current has no unified waveform shape, which has long been found [7], but its formation mechanism is unknown. Ref. [8] qualitatively explained that under different remanences and closing angles of the transformer, three-phase asymmetric inrush currents with different harmonic contents would be generated, leading to the generation of zero-mode current, and the simulation waveform of zero-mode inrush current was given. Refs. [9,10] simulated and analyzed the characteristics of zero-mode inrush current and its influence on zero-sequence protection of main transformer, lines and bus. However, the above papers did not carry out mechanism and analytical analysis for the zero-mode inrush current. In recent years, the power grid capacity has been increasing gradually [11–13]. In order to limit the short-circuit current, new highimpedance transformers have been widely used [14,15]. However, when the high-impedance transformer (especially the high-impedance transformer with built-in high-voltage winding) is energized, the zerosequence overcurrent protection of the busbar (segment) breaker or even its upper level line frequently misoperated, which seriously endangers the operation safety of the power grid. Through the analysis of on-site recorded waveform, it could be known that the three-phase primary winding inrush current presented a large unbalanced feature,
Corresponding author. E-mail address: [email protected] (W. Cao).
https://doi.org/10.1016/j.ijepes.2019.105716 Received 16 April 2019; Received in revised form 27 September 2019; Accepted 18 November 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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2.2. The equivalent circuit of transformer and the analytical analysis of single-phase magnetizing inrush current
and the initial value of the zero-sequence component of the inrush current was large. After attenuating for a period of time (the set time of zero-sequence overcurrent protection), its value is still greater than the setting value, which directly led to the misoperation of the zero-sequence overcurrent protection. Strictly speaking, the zero-sequence current is the fundamental frequency component of the zero-mode inrush current, which differs in concept and often used without distinction. While a zero-sequence current is specific to a particular frequency, a zero-mode inrush current is the sum of the instantaneous values of the three-phase currents, which has richer frequency content. In order to accurately grasp its mechanism and further put forward countermeasures, the zero-mode inrush current should be directly analyzed. Compared with the ordinary transformer, the winding arrangement of high-impedance transformers have changed, which may affect the amplitude and attenuation of their zero-mode inrush currents. The three-phase primary winding inrush currents of the misoperated transformer are seriously unbalanced, the initial value of the zero-mode inrush current is large, and its fundamental frequency component (zerosequence current) remains at a high level after the setting time, which causes the zero-sequence protection misoperation. There is currently no simulation model for simulating high-impedance transformer inrush currents. There is also no physical model and physical tests for highimpedance transformers. Therefore, it is urgent to further understand and study the zero-mode inrush characteristics of high-impedance transformers comprehensively.
The zero-mode inrush current is the sum of the instantaneous values of the three-phase inrush current, and the single-phase inrush current is the basis for deriving the three-phase inrush current and the zero-mode inrush current. Therefore, the correspondence between the flux distribution and the equivalent circuit parameters is analyzed firstly, and the physical process and mathematical analytical expression of singlephase magnetizing inrush current are obtained to further analyze the zero-mode inrush current characteristics of the transformer. Generally, when analyzing the generation mechanism of inrush current or studying the factors affecting inrush current, the magnetizing inductance will be linearized [15], that is, the magnetizing inductance is considered as a constant value. This method is effective in understanding the generation mechanism of inrush current or analyzing the influence of external factors (such as system impedance, initial fault current angle, etc.) on inrush current, but not useful in analyzing the influence of different winding arrangement on inrush current. The main difference of winding arrangement is mainly manifested by the difference of magnetizing inductance after saturation (called “saturated mutual inductance”). However, linearization treatment will assume that the magnetizing inductance is a constant value, which is basically a large unsaturated inductance value. The difference of saturated mutual inductance caused by different winding arrangement has little influence on the unsaturated inductance. The impact of winding arrangement on inrush characteristics cannot be well explained by simple inductance linearization. Therefore, the saturated magnetizing characteristics of the core are considered in this paper. As shown in Fig. 2, the iron core magnetizing characteristic curve can be equivalent to two straight lines according to IEC hypothesis. The main flux linkage passing the core is composed of two parts: the flux linkage generated when the iron core is replaced with air, (i.e., ψH = LHi), and the flux linkage generated by the iron core magnetization, (i.e., ψF = μ0WSJ = LFi). J is the magnetization. When the iron core is fully saturated, J = JSat. S is the cross-sectional area of the core; W is the number of winding turns. According to the equivalent magnetizing characteristic curve, when the iron core is not saturated, LF=∞; when the iron core is saturated, LF = 0. When B < BSat, the magnetic field intensity is small (i.e., H = 0), and the magnetic density is BJ = μ0J. BJ is called “unsaturated core magnetic density”. J∈(−JSat, JSat). JSat is the saturated magnetization. When B > BSat, the magnetization curve is represented by a straight line, and the slope is μ0, and the magnetic density is B = μ0JSat + μ0H. The flux linkage pass through the iron core is ψI (i.e., ψI = WSB).
2. Mechanism and analytical analysis of zero-mode inrush current When a YYΔ-connected three-winding transformer is energized on the high-voltage (HV) winding, not only the HV winding will generate inrush current, but also the low-voltage (LV) delta winding will generate circulating current. At this time, the three-winding transformer is equivalent to a double-winding transformer. The transformer equivalent circuit can reflect transformer flux distribution in the form of concentrated parameters, so it is more convenient to analyze the inrush current by using the transformer equivalent circuit. 2.1. Winding arrangement of transformer and its flux distribution As shown in Fig. 1, the flux generated by the current flowing through the HV winding (winding 1) is called the “total magnetic flux”. The magnetic flux interlinked in the LV winding (winding 2) is called “mutual flux”, which consists of the “mutual main flux” passing through iron core and the “mutual-leakage flux” passing through the air gap. The flux generated by the HV winding that does not interlink with the LV winding is called the “self-leakage flux”. As can be seen from Fig. 1, winding 2 is closer to the iron core, with smaller air gap area, whereas winding 1 is far from the iron core, with large air gap area. Under the same magnetic density, less flux can pass through winding 2 as compared with winding 1. Therefore, the winding arrangement determines the flux distribution status. If the winding arrangement position changes, the corresponding flux distribution will change accordingly.
Fig. 1. Magnetic flux distribution of windings.
Fig. 2. Magnetizing characteristic curve. 2
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Fig. 3. The closing circuit of single-phase transformer and equivalent circuit.
⎧ when B < BSat , ψI = μ0 WSJ ⎨ ⎩ when B > BSat , ψI = μ0 WSJSat + LH i
Fig. 4. Y0/△-connected three-phase transformer equivalent circuit.
dψ ri + = Us sin(ωt + α ) dt
2.3. The analytical analysis of zero-mode inrush current On the basis of single-phase inrush current, three-phase inrush current and zero-mode inrush current are further deduced. The Y0/ △-connected three-phase transformer equivalent circuit is shown in Fig. 4. After simplifying the three-phase voltage differential equation, the following equation is obtained:
(2)
ψ = ψs + ψσ + ψK + ψI = (Ls + Lσ + LK ) i + ψI = (Ls + Lσ + LK ) i + WSBI
(3)
where, r is the total resistance of the closing circuit, and ψ is the total flux linkage, including the system flux linkage ψs(i.e., ψs = Lsi), the selfleakage flux linkage ψσ(i.e., ψσ = Lσi), the mutual leakage flux linkage ψK(i.e., ψK = LKi) and the core flux linkage ψI(i.e., ψI = WSBI). BI is the core magnetic density. The above illustrates the linear correspondence between the inductance and the flux linkage. The larger the flux which passes through the winding is, the larger the corresponding inductance is. The corresponding inductance in the equivalent circuit will change as the winding arrangement changes. According to (2), the total flux linkage is:
Us [cos α − cos(ωt + α )] + ψr − r ω
0
uB = (Ls + uC = (Ls +
Us [cos α − cos(ωt + α )] + ψr ω
(4)
ea + eb + ec = −3LσD
ψ − μ0 WSJSat i= Ls + Lσ + Mair
(5)
(Ls0 + Lσ )
ωψr − ωμ0 WSJSat ⎤ Us ⎡ cos α − cos(ωt + α ) + ⎥ ⎢ Us ωL ⎣ ⎦
+ ec
(10)
diD dt
(11)
di 0 di = LσD D dt dt
(12)
Because the initial current is zero, there is: (6)
i0 = (7)
LσD iD Ls0 + Lσ
(13)
iD is also a zero-mode current. According to the theory of self and mutual inductance, the total flux linkage of phase A is:
When ψ < μ0WSJSat and B < BSat, the working point is on the ordinate as shown in Fig. 2, where H is zero and i is zero. According to (5) and (7), the magnetizing current of the single-phase transformer is:
i=
+ ea + eb
All electrical quantities have been calculated to the HV side. After adding the three equations of (10) and taking the relationship of “iA + iB + iC = 3i0” into account, (12) is obtained:
According to (1) and (3):
ψ = (Ls + Lσ + Mair ) i + μ0 WSJSat
di 0 dt di + (Ls0 − Ls ) dt0 di + (Ls0 − Ls ) dt0
+ (Ls0 − Ls )
where, Ls and Ls0 are line positive-sequence inductance and zero-sequence inductance respectively. Lσ is the self-leakage inductance of the primary winding. LσD is the self-leakage inductance of the secondary winding. ea, eb and ec are the induced back electromotive force. iD is the circulating current of secondary delta winding, which satisfies (11).
Where, ψr is the iron core remanence (i.e.,ψr = WSBr) and Br is the remanence density. In order to simplify the analysis, the resistance is not counted, which means the attenuation of the flux linkage is not considered. So (4) becomes (5):
ψ=
diA dt di Lσ ) dtB di Lσ ) dtC
uA = (Ls + Lσ )
t
∫ idt
(9)
It can be seen from (9) that when the external conditions are the same, the amplitude of the inrush current is determined only by the denominator L. Note that L here is the value when the iron core is saturated, which is much smaller than the unsaturated inductance. When the iron core enters saturation, the iron core inductance decreases sharply from a maximum value, of which the value is similar to the “self-leakage inductance” and “saturated mutual inductance” of the windings. Therefore, the inrush current is sensitive to the changes of the latter two.
LK and LH are mutual inductance on the magnetizing branch which correspond to the saturated mutual flux passing through the air (both the air gap and the core replaced with air). Therefore, let the saturated mutual inductance be Mair = LH + LK. The closing circuit of singlephase transformer and its equivalent circuit are shown in Fig. 3. The parameters of the equivalent circuit correspond to the flux distribution. It can be seen from the above that when the core is saturated (i.e., LF = 0), the self-inductance of HV winding is L11 = Lσ + Mair, which also known as the HV winding hollow inductance Lair. When the transformer is energized, the differential equation is as shown in (2) and (3):
ψ=
Us ⎡ B − BSat ⎤ cos α − cos(ωt + α ) + r ⎥ ωL ⎢ Bs ⎣ ⎦
i= (1)
ψA = (Ls + Lσ + Mair ) iA + Mair iD + (Ls0 − Ls ) i 0 + μ0 WSJA
(14)
where, Lσ + Mair = Lair, JA is not necessarily a saturated value. Because in the case of iD, although JA does not reach the saturated value, iA is not zero. By substituting (5) and (13) into (14) and referring to (8) and (9), we obtain:
(8)
where, L = Ls + Lσ + Mair, Us = ωWSBs, BSat = μ0JSat, ψr = WSBr. (9) is got from (8): 3
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iA =
BrA − μ0 JA ⎤ Us ⎡ − ci 0 cos α − cos(ωt + α ) + ⎥ Bs ωL ⎢ ⎦ ⎣
(15)
There is similar situation for the inrush current of phase B and phase C:
iB =
BrB − μ0 JB ⎤ Us ⎡ − ci 0 cos(α − 120°) − cos(ωt + α − 120°) + ⎥ Bs ωL ⎢ ⎦ ⎣ (16)
iC =
BrC − μ0 JC ⎤ Us ⎡ − ci 0 cos(α − 240°) − cos(ωt + α − 240°) + ⎥ ⎢ Bm ωL ⎣ ⎦ (17)
where L = Ls + Lσ + Mair is the self-inductance of the primary loop circuit, which is the same as L in (8), and c is:
c=
Mair (Ls0 + Lσ ) + LσD (Ls0 − Ls ) LLσD
Fig. 5. Three-phase magnetic density schematic diagram.
⎧ Bs [cos α − cos(ωt + α )] + BrA ⎪ ⎪ BSat BJA (t ) = BSat ⎨ ⎪ −BSat ⎪ − BSat ⎩
(18)
According to (15), (16) and (17): C
1 U 1 ⎛ 3i 0 = × s × ∑ Br − μ 0 1+c ωL Bs ⎜ A ⎝
C
∑ J ⎞⎟ A
⎠
ωBs ⎡ ⎣
Mair (Ls 0 + Lσ ) LσD
(20)
⎧ Bs [cos(α − 240°) − cos(ωt + α − 240°)] + BrC |BJC (t )| ⩽ ⎪ ⎪ BSat BJC (t ) = BSat BJC (t ) > BSat ⎨ ⎪ −BSat BJC (t ) < ⎪ − B Sat ⎩
C
+ Ls0 + Lσ + Mair ⎤ ⎦
According to (20), the zero-mode inrush current is determined by multiple parameters. The parameters in the denominator reflect the difference between different kinds of transformers. The amplitude of the zero-mode inrush current depends on the initial remanence of the three-phase iron core and the unbalance of the magnetization, which are represented by the molecules in (20). When the sum of the initial remanence is zero and three-phase iron core are not saturated (i.e., the three-phase magnetization is symmetrical), the zero-mode inrush current will be zero According to (13) and (20), the total current of the magnetizing branch is: C
i∑ m (t ) = 3i 0 (t ) + 3iD (t ) =
(24) The image description of (24) is shown in Fig. 5. The three-phase total magnetic density B(t) is a three-phase symmetrical sinusoidal waveform in the figure, and the three-phase unsaturated core magnetic density BJ(t) is the value of the solid line which is in the blue area. The key to calculating the zero-mode inrush current is to calculate the sum of the three-phase unsaturated core magnetic density BJ(t).
C
Us ⎜⎛∑ Br − ∑ BJ (t ) ⎟⎞ A ⎠ ⎝A ωBs ⎡Mair + ⎣
LσD (Ls 0 + Lσ ) ⎤ LσD + (Ls 0 + Lσ ) ⎦
2.4. The equivalent circuit of zero-mode inrush current (21)
According to (21), zero-mode equivalent circuit of transformer is potted shown as Fig. 6. Mair is on the common magnetizing branch, Lσ, Ls0 and LσD are connected in parallel. In actual situation, due to the effect of resistance loss, the threephase core will gradually drop out of saturation, so that the saturation unbalance will be continuously reduced, and the zero-mode equivalent voltage will gradually attenuate to zero. The attenuation process of the
According to the physical meaning of BJ(t) = μ0J(t), the “unsaturated core magnetic density” is defined:
BJ (t ) =
⎧ B (t ) BSat ⎨ − ⎩ BSat
BJA (t ) <
⎧ Bs [cos(α − 120°) − cos(ωt + α − 120°)] + BrB |BJB (t )| ⩽ ⎪ ⎪ BSat BJB (t ) = BSat BJB (t ) > BSat ⎨ ⎪ −BSat BJB (t ) < ⎪ − B Sat ⎩
Us ⎛⎜∑ Br − ∑ BJ (t ) ⎞⎟ A ⎠ ⎝A
3i 0 (t ) =
BJA (t ) > BSat
(19)
According to (18) (19), and BJ(t) = μ0J(t): C
|BJA (t )| ⩽
|BJ (t )| ⩽ BSat BJ (t ) > BSat BJ (t ) < − BSat
(22)
According to (5), “system total magnetic density” is defined:
B (t ) =
ψ (t ) = Bs [cos α − cos(ωt + α )] + Br WS
(23)
According to (22) and (23), three-phase BJ(t):
Fig. 6. The equivalent circuit of zero-mode inrush current. 4
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the failure rate decreases and the reliability is better. T-Lse is simple in structure design, but the additional serial inductance increases the difficulty of operation and maintenance, so its reliability is not as good as the T-Hin [16,17]. The difference of the three types of transformers lies only in the winding arrangement. Therefore, it is necessary to compare and analyze the parameter differences of three kinds of transformers taking the winding arrangement into account. At present, there are few studies on the inrush current characteristics of high-impedance transformers. Traditional analytical methods are used in Ref. [15] to study the inrush currents characteristics of T-Hin. In Ref. [18], statistical analysis was conducted based on the inrush current tests data of 21 groups of T-Hin with closing failure, and results showed that T-Hin had large inrush current, small attenuation time constant, and high rate of zero-mode current. However, there have been no research works on the differences in parameters and characteristics analysis of zero-mode inrush among T-Hin, T-Lse and T-Ord. In terms of the number of misoperation accidents, the misoperation accidents occurred during the energization of T-Hin are far more than that of T-Lse and T-Ord with the same iron core and wiring, while it remains unknown that whether T-Lse and TOrd have the potential for misoperation. Therefore, the zero-mode inrush current characteristics considering the difference in parameters between the two kinds of high-impedance transformers will be studied and compared with the zero-mode inrush current of T-Ord.
total magnetic density B(t) of each phase can be described as follow. When the iron core is unsaturated, the magnetizing inductance is very large, which is considered as infinite, and the attenuation time constant (τ = L/R) is also very large. In a short time, it can be considered that the magnetic density does not attenuate, that is, when B(t) enters the blue “non-attenuation region” in Fig. 5, it does not attenuate. In contrast, when the core is saturated, the total inductance of the system is small, which is the slope of the broken line in Fig. 5. The attenuation time constant is τ = L/R, namely, in Fig. 5, when B(t) enters the gray area, it will attenuate with the attenuation time constant τ. In conclusion, the attenuation process of the total magnetic density B(t) of each phase will follow the cycle of “saturation-unsaturation” and “attenuation-unattenuation” of the iron core, and the length of attenuation time in each cycle will also change with the saturation degree. Finally, the aperiodic components will attenuate to zero, and B(t) will all remain in the “unattenuated region” for steady running. At this time, the sum of symmetric unsaturated iron core magnetic densities BJ(t) of threephases will be zero, the zero-mode equivalent voltage will be zero, and the zero-mode inrush current will disappear.
3. The differences in winding arrangement and parameter of highimpedance transformers 3.1. Two kinds of high-impedance transformers
3.2. Short-circuit inductance and self-leakage inductance of HV and LV winding
Generally, the H-M impedance of the high-impedance is standard impedance (the same as ordinary transformer), and H-L impedance and M-L impedance are high impedance [16]. At present, there are two commonly used high-impedance transformers, one is the high-impedance transformer with built-in HV windings (which is called T-Hin for short), and the other is the high-impedance transformer with inductance connected in series at low-voltage winding (T-Lse for short). For T-Hin, the HV winding is placed close to the iron core and the winding arrangement from inside to outside is iron core–HV–MV–TV–LV, as shown in Fig. 7(b) (“TV” means the tap-changing windings). For T-Lse, series inductances are directly connected in the LV delta windings of the ordinary transformer (T-Ord for short) so as to improve the H-L impedance and the M−L impedance of the transformer, as shown in Fig. 7(c). The T-Hin increases the impedance by changing the winding arrangement without additional equipment, so
This part first calculates the different parameters of the three kinds of transformers through the equivalent circuit and the original parameters, and then explains the essential reasons of the different parameters based on the corresponding relationship of “winding arrangement – flux distribution – equivalent circuit parameters” in the last section. The actual transformer (capacity: 240/240/80 MVA; voltage: 220/ 115/10.5 kV) which caused misoperation is selected to analyze the difference in parameters of three kinds of transformers, as shown in Table 1. The larger the diameter of the winding coil is, the larger the hollow inductance is. The HV winding of T-Hin is on the inside and its Lair is smaller. It is well known that the short-circuit impedance of a transformer is essentially the leakage inductance between the two windings of the transformer, more precisely the sum of the self-leakage inductances of the two windings. For double-winding transformers, the magnetizing branch is very large when the iron core is unsaturated, and the leakage inductance could be ignored. Therefore, the short-circuit impedance obtained from the short-circuit test is evenly distributed to HV and LV windings to form the T-type equivalent circuit, or the total short circuit impedance is distributed to secondary winding, forming Γ-type equivalent circuit. However, when analyzing the amplitude of inrush current, the magnetizing mutual impedance is small when the iron core is saturated, and the self-leakage impedance on both sides cannot be ignored. Therefore, Table 1 Parameters comparison of different kinds of transformers. Parameters Short-circuit inductance at rated gear (%) No-load loss (kW) No-load current (%) Hollow inductance of HV Xair = ωLair (%)
Fig. 7. Winding arrangement of several kinds of transformer.
H-M H-L M−L
T-Hin
T-Lse
T-Ord
13.65(14) 36.41(36) 20.64(22) 96.53 0.067 21
15.03(14) 38.83(36) 21.29(22) 95 0.06 34
14.17(14) 25.12(23) 8.47(9) 103.4 0.05 34
Note: The values in parentheses are the design values. 5
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inductance. Considering the complexity of the actual winding, the formula cannot be used to calculate the exact value, but it can be used for comparison between different kinds of transformers. The hollow inductances are generally measured by the manufacturer and recorded in the factory test report. The hollow inductor of the winding is measured when the iron core is not inserted. Ignore the difference in wire diameters of different types of transformers, as shown in Fig. 8. Compared with T-Ord and T-Lse, the HV winding coil of T-Hin has a smaller diameter. According to (25), its Lair is also smaller. This conclusion is consistent with the relationship of the actual hollow inductance parameters shown in Table 1. While Lair = Lσ + Mair, and Lσ is almost the same, it can be seen that the difference of T-Hin lies in the saturated mutual inductance Mair, which is smaller than that of T-Ord and T-Lse. Based on the above analysis, the comparison relationship of different transformers are: Lσ(Ord)≈Lσ(Hin)≈Lσ(Lse); Mair(Ord) = Mair(Lse)＞Mair(Hin); LσD(Ord)＜ LσD(Hin) = LσD(Lse). According to the zero-mode inrush current expression in (20), the zero-mode inrush current expressions for T-Lse and T-Hin are:
Table 2 Equivalent self-leakage inductance of HV and LV windings. Percentage of impedance %
Inside
Outside
T-Hin T-Lse T-Ord
H:14.7(14) L:22.5(22) L:9.7(9)
L:21.7(22) H:16.3(14) H:15.4(14)
Note: The values in parentheses are the design values.
C
3i 0(Lse) (t ) = ωBm ⎡ ⎣
Fig. 8. The winding arrangement and the space flux distributions of the HV and LV windings.
C
Um ⎜⎛∑ Br − μ0 ∑ J (t ) ⎟⎞ A ⎠ ⎝A Mair (Lse) (Ls0 + Lσ (Lse) ) Lσ D(Lse) ↑
(26) C
it is necessary to clarify the value of the self-leakage inductance of the two windings, which is related to the winding arrangement. According to the short-circuit tests data, the self-leakage inductance of each side is calculated as shown in Table 2. The self-leakage inductances of the HV primary winding of the three kinds of transformers are approximately equal; the self-leakage inductances of the LV secondary winding of T-Hin and T-Lse are approximately equal. The winding arrangement and the space flux distributions of the HV and LV windings are shown in Fig. 8.
ωBm ⎡ ⎣
Mair (Hin) ↓ (Ls0 + Lσ (Hin) ) LσD (Hin) ↑
↑↑ + Ls0 + Lσ (Hin) + Mair (Hin) ↓⎤ ⎦ (27)
The red arrow in the above formula indicates the comparison of two high-impedance transformer parameters compared with the ordinary transformer parameters. By comparison of (20) (26) and (27), based on the fact that the zero-mode equivalent voltages of the three transformers are substantially equal when the attenuation of the inrush current is not considered (or at the start of the inrush current), it is known that the zero-mode inrush current of T-Hin is the largest, that of T-Lse is the second, and that of T-Ord is the smallest. According to the zero-mode equivalent circuit shown in Fig. 6, it can be intuitively judged that the zero-mode voltage generated by the imbalance is in the common branch. On the one hand, the secondary self-leak inductance of T-Hin is larger than that of T-Ord, the current flowing to the primary winding will be larger. On the other hand, the saturated mutual inductance of THin is smaller than that of T-Ord and T-Lse, and the total current will be larger. In short, there are two factors that cause the amplitude of the zero-mode inrush current to be larger, which are the large value of the secondary leakage inductance LσD and the small value of the saturated mutual inductance Mair. Therefore, based on the above two factors, the zero-mode inrush current of T-Hin will be larger than that of T-Ord and T-Lse. Compared with T-Ord, T-Lse has larger secondary self-leakage inductance, so the zero-mode inrush current of the T-Lse also larger than that of T-Ord.
4.1. Amplitude analysis of zero-mode inrush current of high-impedance transformer The difficulty in analyzing the transient inrush current characteristics of transformer lies in the non-linearity of magnetizing branch inductance. In order to facilitate the analysis of the difference in inrush current characteristics between high-impedance transformer and ordinary transformer, the two-section linear model of transformer magnetizing characteristic curve is adopted, as shown in Fig. 2. The twosection linear model divides the transformer magnetizing characteristic curve into the saturated region and the unsaturated region, where the cut-off point is the inflection point of the magnetizing curve, and the corresponding flux value is φSat. When the transformer flux is greater than φSat, i.e., when the transformer iron core is saturated, a straight line can be used to approximate the transformer magnetizing curve, and the slope of such line is the hollow inductance of the winding coil. When the transformer generates a large inrush current, the iron core reaches deep saturation and it can be approximated as air, and the inductance of winding coil is hollow inductance as the winding coil is full of air. The expression of the hollow inductance Lair is (25) [19]:
μ0 πND 2 4d
C
Um ⎛⎜∑ Br − μ0 ∑ J (t ) ⎞⎟ A ⎠ ⎝A
3i 0(Hin) (t ) =
4. Characteristic analysis of zero-mode inrush current of highimpedance transformer
Lair =
↑
+ Ls0 + Lσ (Lse) + Mair (Lse) ⎤ ⎦
4.2. Attenuation analysis of zero-mode inrush current of high-impedance transformer The recorded data of inrush currents of the three types of transformers with the same capacity and voltage level were observed, and it was found that all of them attenuated very slowly. Based on this, this paper further studies the relative attenuation speeds of inrush currents of T-Hin, T-Lse and T-Ord using attenuation time constant (τ = Lair/R). The inrush process is a nonlinear transient process, which cannot be accurately analyzed using the attenuation time constant. However, when the inrush current is large, the magnetizing characteristic curve is
(25)
where: μ0 is the permeability, D is the winding coil diameter, and d is the wire diameter. (25) is the decisive formula of the hollow 6
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almost linear when it crosses the inflection point and enters the deep saturation region, and using the attenuation time constant for analysis is feasible in such case. The magnetizing inductance in unsaturated region is very large, which can be approximately considered not attenuated. Therefore, the overall attenuation of the inrush current can be indirectly measured by the attenuation time constant in the saturated region. The expression of the air-core coil resistance R is as follows:
R=
4ρπND d2
Table 3 Distribution of inductance of each side of three kinds of transformer during noload closing. Equivalent circuit
Parameters
T-Hin
T-Lse
T-Ord
Lσ LσD Mair
0.14pu 0.22pu 0.07pu
0.14pu 0.22pu 0.2pu
0.14pu 0.09pu 0.2pu
(28)
where, ρ is the wire resistivity. Assuming that the external system parameters of the transformer are the same, the attenuation time constants when the core is extremely saturated can be obtained according to (25) and (28):
τ=
μ Dd Lair = 0 R 16ρ
(29)
According to (29), compared with T-Lse and T-Ord, the HV winding coil diameter D of T-Hin is smaller, its attenuation time constant upon deep saturation of iron core is slightly smaller, and its attenuation is slightly faster. T-Lse and T-Ord have the same diameter and attenuation speed. Although the zero-mode inrush current of T-Hin attenuates slightly faster, its amplitude is large, and it remains at a high level when it attenuates to the setting time of protection, so that misoperation occurs, as shown in Fig. 9. According to [18], the average values of the hollow inductance Lair, the resistance R and the attenuation time constant τ of T-Hin (model 220 kV/240MVA) respectively are 0.1358 H, 0.1784 Ω and 0.7635 s, and that of T-Ord respectively are 0.2159 H, 0.2685 Ω and 0.8125 s, which are consistent with the conclusions of this paper.
Fig. 10. Simulation and recorded waveform of three-phase inrush current.
5. Digital simulation of zero-mode inrush current of highimpedance transformer 5.1. Simulation modeling and parameters determination for high-impedance transformer Fig. 11. Simulation and recorded waveform of zero-mode inrush current and zero-sequence current RMS.
As different kinds of transformers have different winding arrangement, their self-leakage inductances at HV side and LV side are obviously different. By default, the PSCAD transformer simulation model takes half of the input short-circuit leakage inductance as the selfleakage inductance on both sides, which is not in line with the actual situation. In this paper, a kind of transformation method is adopted, in which the simulated magnetizing branch is placed on the HV side, the HV self-leakage impedance is added on the system side, and the actual LV self-leakage inductance is taken as the short-circuit impedance to be input in the transformer simulation model. The “core inductance” of transformer model is the saturated mutual inductance Mair, which is the value of the hollow inductance minus the primary self-leakage inductance. The specific values of the three transformer parameters are shown in Table 3. The above parameters are respectively input into the improved transformer simulation model of this paper, and the current transformer transient simulation model is considered in the simulation [20].
Under the same external factors, the simulation of the three-phase primary inrush current, zero-mode current and zero-sequence current RMS is shown in Fig. 10 and Fig. 11. The simulated waveform and the on-site recorded waveform agree well. The improved simulation model in this paper can be used to study the inrush current characteristics of high-impedance transformers. 5.2. Simulation comparison of zero-mode inrush current of high-impedance transformer In addition to the winding arrangement concerned in this paper, the factors affecting the inrush current characteristics include remanence, closing angle, system impedance, neutral point grounding, etc. The influence of above factors on the inrush current characteristics has been extensively discussed [2,21]. Therefore, when analyzing the inrush current characteristics of the three kinds of transformers, these factors are no longer considered. Under the same external conditions, the comparison of the zero-mode inrush currents and zero-sequence currents RMS of the three kinds of transformers is shown in Fig. 12. As shown in Fig. 12, the zero-mode inrush current and zero-sequence current RMS of T-Hin are the largest, followed by T-Lse and TOrd. By observing the attenuation trends of them, their attenuation are all slow, in which the T-Hin is slightly faster, while T-Lse is basically the same as the T-Ord. The simulation results are consistent with the conclusion of mechanism analysis. Compared with T-Lse and T-Ord,
Fig. 9. The attenuation of zero-sequence current RMS. 7
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Fig. 12. Simulation waveform of zero-mode inrush current and zero-sequence inrush current RMS.
the initial value of the zero-sequence current of T-Hin is much larger. Even though the zero-sequence current of T-Hin attenuates slightly faster than that of T-Lse and T-Ord, it still remains at a high level when the attenuation reaches the setting time, thus leading to the zero-sequence protection misoperation.
Fig. 13. Dynamic physical simulation tests.
6. Dynamic physical simulation tests of zero-mode inrush current of high-impedance transformer In order to further verify the theoretical and simulation results of the zero-mode inrush current characteristics of the high-impedance transformer, we designed and manufactured several transformer physical models with the same structure as the actual transformers for dynamic physical simulation tests. Taking the transformer that caused the protection misoperation in the field as the prototype, referring to the parameters of the two high-impedance transformers and ordinary transformers shown in Table 1, we designed and manufactured transformer physical models on the basis of ensuring that the main parameters such as the percentage of short-circuit inductance are as equal as possible. The capacity of the physical model transformer is: 20/20/6.67 kVA; the voltage is: 0.8/0.4182/0.0382 kV. The specific parameters are shown in Table 4. Wherein, the T-Lse is formed by a T-Ord with inductance connected in series at LV delta winding, as shown in Fig. 7. In the dynamic physical simulation laboratory of Huazhong University of Science and Technology, the zero-mode inrush current tests of T-Hin, T-Lse and T-Ord are carried out to compare the zeromode inrush current characteristics of the three kinds of transformers. Fig. 13 is a picture of the field test, which includes three types of transformers, a high-voltage grid analog screen and a switch controller. In order to eliminate interference from other factors, the three kinds of transformers are guaranteed to be opened at a uniform angle (phase A: 180°) without load to ensure the same remanence status and then closed at a uniform angle (phase A: 0°) to ensure the same magnetic bias. The zero-mode inrush currents and zero-sequence currents RMS of the three kinds of transformers obtained are shown in Fig. 14. As can be seen from Fig. 14, the zero-mode current and zero-sequence current
Fig. 14. Dynamic physical simulation waveform of zero-mode inrush current and zero-sequence inrush current RMS.
RMS of T-Hin are the largest, and that of T-Lse are the second, the smallest is that of T-Ord. and attenuation of T-Hin is slightly faster than the other. The correctness of the conclusions of the theory and simulation is verified. 7. Summary In order to find out the causes of protection misoperation and further propose countermeasures, this paper focuses on the zero-mode inrush current characteristics of high-impedance transformers. The main work and conclusions of this paper are as follows:
Table 4 Parameters comparison of different kinds of transformers. Parameters Short-circuit inductance at rated gear (%)
H-M H-L M−L
No-load loss (kW) No-load current (%) Hollow inductance of HV Xair = ωLair (%)
T-Hin
T-Lse
T-Ord
13.37 37.22 29.17 122 2.82 14.33
13.24 39.37 28.98 119 2.28 17.28
13.24 22.27 11.88 119 2.28 17.28
(1) The corresponding relation of “winding arrangement – flux distribution – equivalent circuit parameters” of transformer was clarified. On the basis of analyzing single-phase and three-phase inrush current, the analytical expression and equivalent circuit of zeromode inrush current were proposed. (2) According to the different winding arrangement, the different parameters of hollow inductance, self-leakage inductance and saturated mutual inductance of T-Ord, T-Hin and T-Lse were explained and calculated. Compared with T-Ord, T-Hin and T-Lse 8
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respectively increase the leakage inductance by increasing the leakage magnetic area and the series inductance. Their primary selfleakage inductance is basically equal; the HV winding of T-Hin is built-in, its hollow inductance and saturated mutual inductance are both reduced. (3) According to the analytical expression of zero-mode inrush current and the different parameters of three kinds of transformers, the zero-mode inrush current characteristics of high-impedance transformer are analyzed. The zero-mode inrush current and zero-sequence current RMS of T-Hin are the largest, followed by T-Lse and T-Ord. The attenuation of T-Hin is slightly faster. Compared with T-Lse and T-Ord, the initial value of the zero-sequence current of THin is much larger. Even though the zero-sequence current RMS of T-Hin attenuates slightly faster than that of T-Lse and T-Ord, it still remains at a high level when the attenuation reaches the setting time, thus leading to the zero-sequence protection misoperation. (4) High-impedance transformer digital simulation models and physical models that can reflect the differences in structure and parameters are constructed respectively. Both digital simulation and dynamic physical simulation tests verify the correctness of the zeromode inrush current characteristics of high-impedance transformers.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This paper is supported by the national key research and development plan of China (2016YFB0900600) and Guangdong Power Grid Science &Technology Project (GDKJXM20162461). References [1] Zhang A, Ji T, Li M, et al. An identification method based on mathematical morphology for sympathetic inrush. IEEE Trans Power Delivery 2018;33(1):12–21.
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