KANG, Yong Cheol (1 Jinheung Dubblepark, 829-4 Hoseong-dong 1-ga, Deokjin-gu, Jeonju-si, Jeonbuk 561-740, 07-1206, KR)
ZHENG, Tai Ying (606 Dormitary, Jeonbuk National Univ.Deokjin-dong 1ga, Deokjin-gu, Jeonju-si, Jeonbuk 561-756, KR)
KIM, Yong Kyun (3-805, Hyundai Apt.961, Dogok-dong, Gangnam-gu, Seoul 135-270, KR)
KANG, Yong Cheol (1 Jinheung Dubblepark, 829-4 Hoseong-dong 1-ga, Deokjin-gu, Jeonju-si, Jeonbuk 561-740, 07-1206, KR)
ZHENG, Tai Ying (606 Dormitary, Jeonbuk National Univ.Deokjin-dong 1ga, Deokjin-gu, Jeonju-si, Jeonbuk 561-756, KR)
Claims
[1] A method of compensating for errors of a measuring current transformer in consideration of hysteresis characteristics of a core, the method comprising: a first step of measuring secondary current at predetermined time intervals, and calculating a secondary voltage based on a value of the secondary current; a second step of calculating magnetic flux based on the secondary voltage, and calculating a reference value for selecting magnetic flux-magnetizing current relationship information and secondary voltage-core loss current relationship information based on the calculated magnetic flux; a third step of selecting the magnetic flux-magnetizing current relationship information and the secondary voltage-core loss current relationship information, which correspond to the reference value, from among a plurality of pieces of magnetic flux-magnetizing current relationship information and a plurality of pieces of secondary voltage-core loss current relationship information, which are obtained based on the hysteresis characteristics of the core; a fourth step of calculating a value of the magnetizing current for the magnetic flux based on the magnetic flux and the magnetic flux-magnetizing current relationship information selected at the third step; a fifth step of calculating a value of core loss current for the secondary voltage based on the secondary voltage and the secondary voltage-core loss current relationship information selected at the third step; and a sixth step of calculating exciting current based on the values of the magnetizing current and the core loss current, and calculating compensation current based on the values of the exciting current and the secondary current.
[2] A method of compensating for errors of a measuring current transformer in consideration of hysteresis characteristics of a core, the method comprising: a first step of measuring secondary current at predetermined time intervals, and calculating a secondary voltage based on a value of the secondary current; a second step of calculating magnetic flux based on the secondary voltage, and calculating a reference value for selecting magnetic flux-magnetizing current relationship information and secondary voltage-core loss current relationship information based on the calculated magnetic flux; a third step of determining whether a previously stored reference value exists; a fourth step of, if, as a result of the determination at the third step, it is determined that the previously stored reference value exists, determining whether a difference between the reference value calculated at the second step and the previously stored reference value falls within a predetermined error range; a fifth step of, if, as a result of the determination at the fourth step, it is determined that the difference falls within the predetermined error range, obtaining a value of magnetizing current for the magnetic flux based on the magnetic flux and the previously stored magnetic flux-magnetizing current relationship information; a sixth step of calculating a value of core loss current for the secondary voltage based on the secondary voltage and the previously stored secondary voltage-core loss current relationship information; and a seventh step of calculating exciting current based on the values of the magnetizing current and the core loss current, and calculating compensation current based on the values of the exciting current and the secondary current.
[3] The method according to claim 2, wherein, if, as a result of the determination at the third step, it is determined that no previously stored reference value exists, or if, as a result of the determination at the fourth step, the difference does not fall within the predetermined error range, the fifth step comprises, before obtaining the value of the magnetizing current for the magnetic flux: a step 5-1 of storing the reference value; and a step 5-2 of selecting magnetic flux-magnetizing current relationship information and secondary voltage-core loss current relationship information, which correspond to the reference value calculated at the second step, from among the plurality of pieces of magnetic flux-magnetizing current relationship information and the plurality of pieces of secondary voltage-core loss current relationship information, which are obtained based on the hysteresis characteristics of the core, and storing the magnetic flux-magnetizing current relationship information and the secondary voltage-core loss current relationship information.
[4] The method according to any of claims 1 to 3, wherein the reference value is a maximum value or an average of the magnetic flux in a single period, which is calculated at the second step.
[5] The method according to claim 1 or 3, wherein the obtaining the plurality of pieces of magnetic flux-magnetizing current relationship information based on the hysteresis characteristics of the core comprises: a first step of selecting an arbitrary first point and a second point, at which a magnitude of magnetic flux is identical to that at the first point but a magnitude of the exciting current is different from that at the second point, from a measured single magnetic flux-exciting current curve; a second step of calculating a midpoint on a straight line, which connects the two points selected at the first step; a third step of performing the first and second steps for all points on the magnetic flux-exciting current curve, and obtaining a magnetic flux-magnetizing current curve by connecting calculated midpoints; and a fourth step of obtaining a plurality of magnetic flux-magnetizing current curves by repeating the above steps for remaining measured magnetic flux-exciting current curves. [6] The method according to claim 1 or 3, wherein the obtaining the plurality of pieces of secondary voltage-core loss current relationship information based on the hysteresis characteristics of the core comprises: a first step of calculating the core loss current based on the exciting current obtained based on the magnetic flux-exciting current curve and the magnetizing current obtained based on the magnetic flux-magnetizing current curve; a second step of obtaining a secondary voltage-core loss current curve using the core loss current and the secondary voltage; and a third step of obtaining a plurality of secondary voltage-core loss current curves by repeating the above steps for remaining magnetic flux-exciting current curves and magnetic flux-magnetizing current curves. |
Description
METHOD OF COMPENSATING FOR ERRORS OF MEASURING CURRENT TRANSFORMER IN CONSIDERATION OF HYSTERESIS CHARACTERISTICS OF CORE
Technical Field
[1] The present invention relates, in general, to a method of compensating for the errors of a measuring current transformer in consideration of the hysteresis characteristics of a core, and, more particularly, to a method of compensating for the errors of a measuring current transformer, which compensates for the errors of the measuring current transformer in consideration of the hysteresis characteristics of a core in such a way that a hysteresis loop, which shows the relationship between magnetic flux and exciting current, is not used as it is, but a magnetic flux-magnetizing current curve and a secondary voltage-core loss current curve are estimated based on a magnetic flux- exciting current curve, and the errors of the current transformer are compensated for based on the estimated magnetic flux-magnetizing current curve and secondary voltage-core loss current curve, thereby more easily and accurately compensating for errors.
[2]
Background Art
[3] Current Transformers (CTs) have a purpose of reducing the magnitude of primary current, and then supplying the primary current to equipment such as a measuring instrument or a protective relay. Based on the material of core, current transformers are divided according to the types thereof into a core current transformer which uses iron, an air-core current transformer which uses an air core, and an air-gap current transformer which uses a core having air gaps therein. In a current transformer, which has been generally used, iron is used as a core in order to maximize magnetic flux linkage between primary current and secondary current.
[4] In the normal state, a measuring current transformer must transform current and then input the transformed current to a measuring instrument. Here, in order to accurately recognize the operational state of a system, very accurate data about primary current must be obtained. However, a current transformer which operates in a low current region has a disadvantage in that large errors occur due to the material or configuration of a core. The errors of a core current transformer are mainly caused by exciting current generated due to the hysteresis characteristics of the core. Although methods of using a core having high permeability and of increasing the cross section of a core were used in the prior art in order to decrease the errors, the prior art methods have dis-
advantages in that the cost of producing a current transformer and the size of the current transformer are increased, so that the ability to solve the problems of hysteresis is limited because of the non-linear characteristics of the core.
[5] With regard to a method of compensating for the errors of a core current transformer, there is a method of compensating for exciting current based on the state of load by connecting an analog circuit to the secondary side of the core current transformer. However, in this method, the non-linear characteristics of the exciting current are not considered, so that there are limitations in the ability to compensate for errors, and the core current transformer may be damaged when overcurrent is formed in a transient state.
[6] With regard to another method of improving the accuracy of a current transformer, a digital compensation method of decreasing the errors of a core current transformer has been proposed. This method obtains compensation current by estimating exciting current using a hysteresis loop, which shows the relationship between magnetic flux and the exciting current, and adding the estimated exciting current to measured secondary current. This method enables the hysteresis characteristics of the core to be directly compensated for, so that the accuracy of a current transformer can be improved. However, in the case in which Direct Current (DC) offset components or harmonics are included in primary current, there is a disadvantage in that large errors occur.
[7] In order to solve the problems of the digital compensation method, Korean Patent
Registration No. 10-0561712-0000 discloses a method of compensating for errors, which can decrease the errors of a measuring current transformer, compared to a method using an existing hysteresis loop, by employing core resistance and a magnetic flux-magnetizing current curve. Although this method has an advantage in that errors can be more simply and accurately compensated for because a magnetic flux- magnetizing current curve can be approximated to a single line or a curve function in a period of decreased magnetic flux, has problems in that it is difficult to approximate the magnetic flux-magnetizing current curve to a single curve function and in that a plurality of curve functions is required, because the curve has a loop form instead of a single curve in a period of great magnetic flux.
[8]
Disclosure of Invention Technical Problem
[9] Accordingly, the present invention has been made keeping in mind the above problems occurring in the prior art, and an object of the present invention is to provide a method of compensating for the errors of a measuring current transformer, which
compensates for the errors of the measuring current transformer in consideration of the hysteresis characteristics of a core in such a way that a hysteresis loop, which shows the relationship between magnetic flux and exciting current, is not used as it is, but a magnetic flux-magnetizing current curve and a secondary voltage-core loss current curve are estimated based on a magnetic flux-exciting current curve, and the errors of the current transformer are compensated for based on the estimated magnetic flux- magnetizing current curve and secondary voltage-core loss current curve, thereby more easily and accurately compensating for errors.
[10]
Technical Solution
[11] In order to accomplish the above object, the present invention provides a method of compensating for the errors of a measuring current transformer in consideration of the hysteresis characteristics of a core, the method including a first step of measuring secondary current at predetermined time intervals, and calculating a secondary voltage based on the value of the secondary current; a second step of calculating magnetic flux based on the secondary voltage, and calculating a reference value for selecting magnetic flux-magnetizing current relationship information and secondary voltage- core loss current relationship information based on the calculated magnetic flux; a third step of selecting the magnetic flux-magnetizing current relationship information and the secondary voltage-core loss current relationship information, which correspond to the reference value, from among a plurality of pieces of magnetic flux-magnetizing current relationship information and a plurality of pieces of secondary voltage-core loss current relationship information, which are obtained based on the hysteresis characteristics of the core; a fourth step of calculating the value of the magnetizing current for the magnetic flux based on the magnetic flux and the magnetic flux-magnetizing current relationship information selected at the third step; a fifth step of calculating the value of core loss current for the secondary voltage based on the secondary voltage and the secondary voltage-core loss current relationship information selected at the third step; and a sixth step of calculating exciting current based on the values of the magnetizing current and the core loss current, and calculating compensation current based on the values of the exciting current and the secondary current.
[12] Further, in order to accomplish the above object, the present invention provides a method of compensating for the errors of a measuring current transformer in consideration of the hysteresis characteristics of a core, the method including a first step of measuring secondary current at predetermined time intervals, and calculating a secondary voltage based on the value of the secondary current; a second step of calculating magnetic flux based on the secondary voltage, and calculating a reference
value for selecting magnetic flux-magnetizing current relationship information and secondary voltage-core loss current relationship information based on the calculated magnetic flux; a third step of determining whether a previously stored reference value exists; a fourth step of, if, as the result of the determination at the third step, it is determined that the previously stored reference value exists, determining whether a difference between the reference value calculated at the second step and the previously stored reference value falls within a predetermined error range; a fifth step of, if, as the result of the determination at the fourth step, it is determined that the difference falls within the predetermined error range, obtaining the value of magnetizing current for the magnetic flux based on the magnetic flux and the previously stored magnetic flux- magnetizing current relationship information; a sixth step of calculating the value of core loss current for the secondary voltage based on the secondary voltage and the previously stored secondary voltage-core loss current relationship information; and a seventh step of calculating exciting current based on the values of the magnetizing current and the core loss current, and calculating compensation current based on the values of the exciting current and the secondary current.
[13] Here, if, as the result of the determination at the third step, it is determined that no previously stored reference value exists, or if, as the result of the determination at the fourth step, the difference does not fall within the predetermined error range, the fifth step includes, before obtaining the value of the magnetizing current for the magnetic flux: a step 5-1 of storing the reference value; and a step 5-2 of selecting magnetic flux-magnetizing current relationship information and secondary voltage-core loss current relationship information, which correspond to the reference value calculated at the second step, from among the plurality of pieces of magnetic flux-magnetizing current relationship information and the plurality of pieces of secondary voltage-core loss current relationship information, which are obtained based on the hysteresis characteristics of the core, and storing the magnetic flux-magnetizing current relationship information and the secondary voltage-core loss current relationship information.
[14] Further, the reference value is the maximum value or the average of the magnetic flux in a single period, which is calculated at the second step.
[15] Meanwhile, the obtaining the plurality of pieces of magnetic flux-magnetizing current relationship information based on the hysteresis characteristics of the core includes a first step of selecting an arbitrary first point and a second point, at which the magnitude of magnetic flux is identical to that at the first point but the magnitude of the exciting current is different from that at the second point, from a measured single magnetic flux-exciting current curve; a second step of calculating a midpoint on a straight line, which connects the two points selected at the first step; a third step of performing the first and second steps for all points on the magnetic flux-exciting
current curve, and obtaining a magnetic flux-magnetizing current curve by connecting calculated midpoints; and a fourth step of obtaining a plurality of magnetic flux- magnetizing current curves by repeating the above steps for remaining measured magnetic flux-exciting current curves.
[16] Further, the obtaining the plurality of pieces of secondary voltage-core loss current relationship information based on the hysteresis characteristics of the core includes a first step of calculating the core loss current based on the exciting current obtained based on the magnetic flux-exciting current curve and the magnetizing current obtained based on the magnetic flux-magnetizing current curve; a second step of obtaining a secondary voltage-core loss current curve using the core loss current and the secondary voltage; and a third step of obtaining a plurality of secondary voltage- core loss current curves by repeating the above steps for remaining magnetic flux- exciting current curves and magnetic flux-magnetizing current curves.
[17]
Advantageous Effects
[18] As described above, since the method of compensating for the errors of a measuring current transformer in consideration of the hysteresis characteristics of a core according to the present invention estimates the intermediate curve of a hysteresis loop, which shows the relationship between magnetic flux and exciting current, as a magnetic flux-magnetizing current curve, so that there are advantages in that the errors of a measuring current transformer can be compensated for using a simple method, and in that a measuring current transformer having high accuracy can be produced.
[19]
Brief Description of the Drawings
[20] The above and other objects, features and other advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:
[21] FIG. 1 is an equivalent circuit in which conversion with regard to a secondary side is performed on a measuring current transformer according to a preferred embodiment of the present invention;
[22] FIG. 2 is a graph showing the wave forms of the respective exciting current, core loss current, and magnetizing current of the measuring current transformer in a single period according to the preferred embodiment of the present invention;
[23] FIG. 3 is a graph showing the magnetic flux-exciting current curve of the measuring current transformer and a magnetic flux-magnetizing current curve estimated based on the magnetic flux-exciting current curve according to a preferred embodiment of the present invention;
[24] FIG. 4 is a graph showing a secondary voltage-core loss current curve estimated based on the magnetic flux-exciting current curve of the measuring current transformer according to a preferred embodiment of the present invention;
[25] FIGS. 5 to 7 are graphs showing respective hysteresis loops based on variation in the current of the measuring current transformer, and magnetic flux-magnetizing current curves and secondary voltage-core loss current curves estimated based on the respective hysteresis loops according to a preferred embodiment of the present invention;
[26] FIG. 8 is a flowchart showing a method of compensating for the errors of the measuring current transformer according to a preferred embodiment of the present invention;
[27] FIG. 9 shows a system model for verifying the performance of the method of compensating for the errors of the measuring current transformer according to a preferred embodiment of the present invention;
[28] FIGS. 10 to 13 are graphs showing results in the case in which the primary current of the current transformer corresponds to 5% of rated current in the system model of FIG. 9; and
[29] FIGS. 14 to 17 are graphs showing results in the case in which the primary current of the current transformer corresponds to 100% of rated current in the system model of FIG. 9.
[30]
Mode for the Invention
[31] The above-described objects, features, and advantages of the present invention will be clearly understood through the embodiments of the present invention below with reference to the attached drawings. Therefore, those skilled in the art will easily grasp the technical spirit of the present invention.
[32] Further, it should be noted that, in the following description, when it is determined that the detailed descriptions of well-known techniques related to the present invention would obscure the gist of the present invention, they are omitted.
[33] The preferred embodiments of the present invention will be described in detail with reference to the attached drawings below.
[34] FIG. 1 is an equivalent circuit in which conversion with regard to a secondary side is performed on a measuring current transformer according to a preferred embodiment of the present invention.
[35] In the equivalent circuit, reference character I 1 indicates primary current converted with regard to a secondary side, reference character i 2 indicates secondary current, reference character i 0 indicates exciting current, reference character i c indicates core loss current, and reference character R c indicates core loss resistance. Reference
character i m indicates magnetizing current, and reference character L m indicates magnetizing inductance. The relationship between core loss resistance and magnetizing inductance is shown using the non-linear relationship between magnetic flux and magnetizing current. Reference character R b indicates the secondary load of the current transformer, and reference character V 2 indicates secondary voltage.
[36] The exciting current i 0 may be divided into the magnetizing current i m and the core loss current i c , and can be expressed as the following Equation 1.
[37]
[38] i o (t)= i m (t)+ i c (t)
(1) [39] [40] FIG. 2 is a graph showing the wave forms of the respective exciting current i 0 , core loss current i c , and magnetizing current i m in a single period. A solid line indicates the exciting current, a dotted line indicates the core loss current, and a dashed line indicates the magnetizing current. [41] The primary current converted into the secondary side can be expressed using a sum of measured secondary current and exciting current, and is expressed as the following
Equation 2. [42]
(2)
[44]
[45] The errors of the measuring current transformer occur due to the exciting current.
Therefore, if the exciting current is accurately estimated and then the measured secondary current is compensated for by the exciting current, the primary current can be accurately obtained, and the accuracy of the core current transformer can be improved.
[46]
[47] FIG. 3 is shows a process of estimating a magnetic flux-exciting current curve according to a preferred embodiment of the present invention. The curve, indicated by the solid line in FIG. 3, is a curve indicating the relationship between the magnetic flux and the exciting current λ-i 0 of the core, and shows the hysteresis characteristics of the core.
[48] In FIG. 3, a point A is located on a descending hysteresis curve, and a point B is located on an ascending hysteresis curve. Further, the points A and B have a relationship in which the magnitudes of the magnetic flux thereof are the same but the
magnitudes of the exciting current thereof are different from each other. In the present invention, the midpoint between the points A and B is taken as indicating the magnetizing current i m . That is, when it is assumed that the coordinates of the respective points A and B are (i A , λ) and (i B , λ), the magnetizing current is determined using the following Equation 3.
[49]
[50]
( /*)
2
(3)
[51]
[52] The magnetizing current can be calculated using all of the points located on the hysteresis loop as in the Equation 3, and a magnetic flux-magnetizing current curve used in the present invention can be obtained by plotting the magnitudes of the calculated magnetizing current and magnetic flux in coordinates. The dotted line in the middle of FIG. 3 indicates a magnetic flux-magnetizing current curve estimated using this method.
[53]
[54] FIG. 4 shows a secondary voltage-core loss current curve obtained based on the hysteresis loop and the estimated magnetic flux-magnetizing current curve. The core loss current can be obtained using the following Equation 4 based on the Equations 1 and 3.
[55]
[56] . = . . = . ( » α + JB) _ (J λ- JB) l c l 0 " l m l A ~ j j
(4) [57]
[58] Since the secondary voltage can be obtained based on the measured secondary current using the formula
V ,= R l 2
, a secondary voltage-core loss current curve can be obtained by plotting the calculated core loss current and secondary current in coordinates, as shown in FIG. 4.
[59]
[60] FIGS. 5 to 7 show a plurality of magnetic flux-magnetizing current curves and secondary voltage-core loss current curves estimated based on the respective hysteresis
loops of FIG. 2 through the above-described process.
[61] FIG. 5 shows hysteresis curves which indicate the relationship λ-i 0 between the magnetic flux and the exciting current of the core. The innermost loop indicates the case in which the primary current corresponds to 5% of rated current, and the outermost loop indicates the case in which the primary current corresponds to 120% of the rated current. A plurality of magnetic flux-magnetizing current curves and a plurality of secondary voltage-core loss current curves, which are estimated based on the hysteresis loops shown in FIG. 5, are shown in FIGS. 6 and 7, respectively.
[62]
[63] FIG. 8 is a flowchart showing the method of compensating for the errors of the measuring current transformer according to a preferred embodiment of the present invention.
[64] First, the secondary current i 2 is measured at predetermined time intervals at step
S601, and the secondary voltage V 2 is calculated based on the values of the secondary current at step S602. The magnetic flux λ can be obtained based on the secondary voltage using the following Equation 5 at step S603.
[65]
[66]
KO= fr V 2 {t)dt+%{ 1 0 ) t n
(5)
[67]
[68] where λ(t 0 ) indicates initial magnetic flux, and can be obtained using the characteristic in which the average of λ(t) in a single period is 0.
[69] The maximum value of the magnetic flux X 103x is obtained using variation in the values of the magnetic flux in a single period, which are obtained at step S603, at step S604. In this step, in order to obtain the maximum value of the magnetic flux, the values of the magnetic flux in at least a single period must be obtained. Therefore, when the present invention is initially performed, the steps S601 to S603 are repeated until the values of the magnetic flux are obtained in at least a single period. After the values of the magnetic flux are obtained in at least a single period, the maximum value of the magnetic flux can be obtained using the value of the magnetic flux at a current time point and the values of the magnetic flux in a previous single period from the current time point.
[70] As shown in FIGS. 6 and 7, since the respective maximum values of the magnetic flux λ max differ in the respective curves, an optimized magnetic flux-magnetizing current curve and an optimized secondary voltage-core loss current curve can be
selected using the maximum values of the magnetic flux λ max at steps S608 and S609. Although only a method of using the maximum value of the magnetic flux λ max in order to select an optimized magnetic flux-magnetizing current curve has been described as an example in the present embodiment, the present invention is not limited thereto. It will be clearly understood by those skilled in the art that an optimized magnetic flux- magnetizing current curve can be selected using various references, such as the average magnetic flux X ms in a single period, which enable the characteristics of the respective curves to be distinguished therebetween, as well as using the maximum value of the magnetic flux λ max .
[71] Further, as described at steps S605 to S607, the maximum value of the magnetic flux λ max obtained at a previous execution stage is stored, and the maximum value of magnetic flux X 103x calculated at a current stage is compared with the maximum value of the magnetic flux λ max stored at the previous stage at step S606. The maximum value of the magnetic flux λ rms is stored only when the difference in the maximum values of the magnetic flux λ rms does not fall within a predetermined error range, and then a new magnetic flux-magnetizing current curve and a new secondary voltage-core loss current curve are selected based on the stored maximum value of the magnetic flux. Otherwise, the curve selected at the previous stage is used without change. Accordingly, when errors are compensated for, unnecessary calculations are reduced and the speed of calculation can be improved. However, in the state where the current transformer is initially operated, since the maximum value of magnetic flux λ max at a previous stage has not been stored, steps S607 to S609 should be executed, as in the case in which the maximum value of the magnetic flux λ max does not fall within the predetermined error range. The error range can be appropriately selected by the user of the present invention according to necessity, and is determined by considering elements such as the accuracy required from the present current transformer and the speed of calculation required to compensate for errors.
[72] The magnetizing current i m and the core loss current i c are obtained using a magnetic flux-magnetizing current curve and a secondary voltage-core loss current curve, which are determined at steps S608 and S609, at steps S610 and S611. The exciting current i 0 is obtained using the sum of the magnetizing current and the core loss current at step S612, and a primary current value I 1 ' can be very accurately estimated based on the exciting current value and a previously measured secondary current value at step S613. The estimated primary current value is applied to the measuring current transformer at step S614, and the errors of the measuring current transformer can be effectively compensated for by performing the above-described process repeatedly.
[73] FIGS. 9 to 13 shows results in which the performance of the method of compensating for the errors of the measuring current transformer according to the present invention is
verified using an Electromagnetic Transients Program (EMTP).
[74] As shown in FIG. 9, in order to verify the performance of the proposed method of compensating for the errors of the measuring current transformer, a 154 kV two-bus transmission system is simulated, and the two buses are connected by a transmission line 50 km long. The frequency of the system is 60 Hz, and the system is simulated using the EMTP. 64-sample data are used for a period, and a primary Resistor- Capacitor (RC) filter for preventing overlapping, which has a cut-off frequency of 1,920 Hz, is used as a low pass filter.
[75] In order to measure the current of the system, a current transformer is simulated beside the buses. A measuring current transformer having a current transform ratio of 100/5 A and a saturation point of 0.02 Vs and 2.047 A is used, and is modeled using 96 elements in EMTP. The hysteresis characteristics are simulated using Hysteresis Data (HYSDAT), which is the auxiliary program of the EMTP, and an overcurrent constant is set to 2. With regard to the secondary load of the current transformer, the pure resistance load is used and simulated by 12.5 VA (0.5 ω).
[76] FIGS. 10 to 13 show the results in the case in which the primary current of the current transformer corresponds to 5% of rated current. In FIG. 10, a solid line indicates primary current appropriate to the current transform ratio, a dashed line indicates measured secondary current, and a dotted line indicates compensation current. FIGS. 11 and 12 show enlarged views in order to clearly indicate the results to which a compensating algorithm is applied. Although errors corresponding to the magnitude of the exciting current occur between the measured secondary current (indicated by the dashed line in FIG. 12) and the primary current (shown in FIG. 11), little difference exists between the compensation current (indicated by a solid line in FIG. 12) and the primary current. In FIG. 13, the dotted line indicates the core loss current, the dashed line indicates the magnetizing current, and the solid line indicates the exciting current. The values thereof are estimated by applying the compensating algorithm. The sum of the estimated core loss current value and magnetizing current value is equal to the estimated exciting current value.
[77] FIGS. 14 to 17 show results in the case in which the primary current of the current transformer corresponds to rated current (100%).
[78] The following Table 1 shows simulation results of respective cases in which the primary current of the current transformer corresponds to 5%, 20%, 100%, and 120% of the rated current. It can be seen that current errors and phase errors are decreased after the compensating algorithm is applied.
[79]
[80] Table 1
[Table 1] [Table ]
[81] [82] Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims.
[83]