Power transmission line parameter test system and test method

Abstract

The invention discloses a power transmission line parameter test system and test method, and relates to the field of power transmission line testing, and the key points of the technical scheme are that the test system comprises a test power supply module, a self-adaptive interference suppression module and a line parameter test module which are connected in sequence; the test power supply module is used for outputting voltage values of different test frequencies; the adaptive interference suppression module is used for enabling a test power supply module to effectively inject single frequency into the line parameter test module every time so as to reduce electromagnetic induction current and capacitance coupling voltage in the line parameter test module; and the line parameter test module is used for being connected with each phase of a direct-current or alternating-current power transmission line. The problem that inductive interference generated by an operation line adjacent to a to-be-tested power transmission line cannot be suppressed in the prior art is solved.

Description

Technical Field

[0001] The present invention relates to the field of power transmission line testing, and more specifically, to a power transmission line parameter testing system and a testing method. Background Art

[0002] Transmission line parameters are essential data for power system flow calculation, relay protection setting, overvoltage calculation, system operation mode selection, etc. They are mainly obtained by actual measurement after the construction or reconstruction of transmission lines. During the line parameter test, interference sources such as space charged particles, adjacent charged lines, and communication carrier signals will generate interference signals on the measured line under the action of electromagnetic and electrostatic induction. Among them, static electricity and electromagnetic induction interference of adjacent charged lines are the main factors. Usually, the power frequency variable phase method, different frequency method, incremental method, interference method and harmonic wave method are used to effectively eliminate the influence of most interference on the test. However, the length of UHV transmission lines for cross-regional power transmission can reach hundreds to thousands of kilometers, and they usually share transmission corridors with ultra-UHV transmission lines. The voltage and current induced on the transmission line to be tested can reach thousands to hundreds of thousands of volts and tens of amperes respectively, which will have a serious impact on the safety of test personnel and equipment. Interference suppression measures must be taken before testing.

[0003] The interference of the transmission line to be tested is mainly divided into electrostatic component, power frequency component and high frequency component. The electrostatic component is mainly generated by the mutual capacitance charging between the adjacent live AC and DC transmission lines, the power frequency component is generated by the mutual inductance coupling between the adjacent live AC lines, and the high frequency component is generated by the high-order harmonics of the adjacent live AC and DC lines through the mutual inductance coupling between the lines. In actual measurement, it mainly manifests as DC component, power frequency component, 3k harmonic component, and 12k harmonic component (12-pulse rectification is mostly used in DC projects). At present, the induced voltage and current of AC and DC lines can be determined by simulation calculation or actual measurement methods. However, during the line parameter test, due to the safety of power grid operation and power supply guarantee, it is difficult to shut down the adjacent lines to reduce the interference to the transmission line to be tested. Therefore, the simulation calculation or actual measurement methods proposed by the current related technologies cannot effectively suppress the influence of the induced voltage and induced current generated by the adjacent lines on the line parameter test process, so it is impossible to guarantee the safety of the transmission line parameter test work and the accuracy of the parameter test results. Summary of the invention

[0004] The purpose of the present invention is to provide a transmission line parameter testing system and a testing method, which solves the problem that the related art cannot suppress the inductive interference generated by the running lines adjacent to the transmission line to be tested.

[0005] In a first aspect of the present invention, a transmission line parameter test system is provided, the test system comprising a test power supply module, an adaptive interference suppression module and a line parameter test module connected in sequence;

[0006] The test power supply module is used to output voltage values ​​of different test frequencies;

[0007] The adaptive interference suppression module is used to enable the test power supply module to effectively inject a single frequency into the line parameter test module each time, so as to reduce the electromagnetic induction current and capacitive coupling voltage in the line parameter test module;

[0008] The line parameter test module is used to connect to each phase of a DC or AC power transmission line.

[0009] In one implementation, the adaptive interference suppression module has an input terminal, an output terminal and a ground terminal, and the adaptive interference suppression module includes a first resistor, an inductor, a second resistor and a capacitor;

[0010] The first resistor is used to reduce the inductive interference current of the DC or AC transmission line to the ground loop and the electromagnetic induction current of the loop between each phase of the DC or AC transmission line at the same frequency as the test power module;

[0011] The capacitor is connected in parallel with the inductor to form a low impedance path of the line capacitance coupling interference voltage frequency different from the test power injection frequency, so as to reduce the electromagnetic induction voltage generated by the capacitance coupling voltage of the DC or AC transmission line;

[0012] The second resistor is used to control the bandwidth range of same-frequency intercommunication and different-frequency blocking;

[0013] Among them, one end of the first resistor is used as an input end, the other end of the first resistor is connected to a node where the inductor, the second resistor and the capacitor are connected in parallel as an output end, and another node where the first inductor, the second resistor and the capacitor are connected in parallel is used as a ground end.

[0014] In one implementation, when the transmission line for parameter testing is a DC transmission line, the test power supply module is a two-phase symmetrical frequency modulation test power supply, the number of the adaptive interference suppression modules is two, and the number of the line parameter test modules is two;

[0015] A DC transmission line parameter test system is constructed by a two-phase symmetrical frequency modulation test power supply, two adaptive interference suppression modules and two line parameter test modules.

[0016] In one implementation, when the transmission line for parameter test is an AC transmission line, the test power supply module is a three-phase symmetrical frequency modulation test power supply, the number of the adaptive interference suppression modules is three, and the number of the line parameter test modules is three;

[0017] An AC transmission line parameter test system is constructed by a three-phase symmetrical frequency-modulated test power supply, three adaptive interference suppression modules and three line parameter test modules.

[0018] A second aspect of the present invention provides a transmission line parameter testing method, which is applied to a transmission line parameter testing system provided in the first aspect of the present invention, and the testing method comprises:

[0019] Obtain the test frequency range and withstand voltage of the test power module;

[0020] Calculate the product range of the inductance and capacitance of the adaptive interference suppression module under the test frequency range, select the capacitance value of the capacitor according to the withstand voltage, and determine the inductance value of the inductor according to the product range and the capacitance value of the capacitor;

[0021] Determining the quality factor and angular frequency of the adaptive interference suppression module according to the frequency response function and transfer function of the adaptive interference suppression module;

[0022] The resistance values ​​of the first resistor and the second resistor are determined according to the quality factor and the angular frequency.

[0023] In one implementation, the inductance value of the inductor changes only with the test frequency of the test power supply.

[0024] In one implementation, the process of controlling the inductance value of the inductor to change only with the test frequency of the test power supply is specifically as follows:

[0025] The test power module deflects the voltage phase by 180 degrees through an inverter, isolates the inductance control loop from the test power module through impedance transformation, connects the voltage signal after impedance transformation to the middle coil connector of the inductor, and the reverse flux controlled inductance value tested by the test power module changes only linearly with the test frequency.

[0026] In one implementation, the formula for calculating the product range is: Where, f represents the test frequency, L f C1 represents the inductance of the inductor, and C2 represents the capacitance of the capacitor.

[0027] In one implementation, the frequency response function is expressed as: Where τ1 = L f / R2,τ2=R1*C1,L f C1 represents the inductance of the inductor, and C2 represents the capacitance of the capacitor.

[0028] In one implementation, the expression of the transfer function is: Among them, ω p represents the angular frequency, Q p represents the quality factor, s represents a complex variable, Q p =ω p / 2Re(G(jω)), G(jω) represents the frequency response function, Im represents the complex imaginary part, and Re represents the complex real part.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] In a transmission line parameter test system provided by the present invention, the test system includes a test power supply module, an adaptive interference suppression module and a line parameter test module; the test power supply module is used to output voltage values ​​of different test frequencies; the adaptive interference suppression module is used to enable the test power supply module to effectively inject a single frequency into the line parameter test module each time to reduce the electromagnetic induction current and capacitive coupling voltage in the line parameter test module; the line parameter test module is used to connect with each phase of a DC or AC transmission line; currently, the test frequency of the test power supply module is injected into the line parameter test module at a single frequency, and the adaptive interference suppression module provided in this embodiment can ensure that the test power supply module effectively injects a single frequency into the line parameter test loop each time, clamps the electromagnetic induction current and capacitive coupling voltage amplitudes in the line parameter test loop that are different from the test power injection frequency, improves the test accuracy of the line parameter test at a single frequency and ensures the safety of the test power supply module and the tester. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0032] Figure 1 A schematic diagram of the structure of a power transmission line parameter testing system provided by an embodiment of the present invention applied to a DC transmission line;

[0033] Figure 2 A schematic diagram of the structure of a power transmission line parameter testing system provided by an embodiment of the present invention applied to an AC transmission line;

[0034] Figure 3 A schematic diagram of the circuit structure of an adaptive interference suppression module provided in an embodiment of the present invention;

[0035] Figure 4 A schematic diagram showing that the inductance of the adaptive interference suppression module provided by an embodiment of the present invention can be adjusted according to the frequency;

[0036] Figure 5 A schematic diagram showing how the inductance of an adaptive interference suppression module provided in an embodiment of the present invention varies with frequency;

[0037] Figure 6 A curve diagram of the transfer function of the adaptive interference suppression module provided in an embodiment of the present invention.

[0038] Marks and corresponding parts names in the attached drawings:

[0039] L f , inductor; R1, first resistor; R2, second resistor; C1, capacitor. DETAILED DESCRIPTION

[0040] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0041] It should be noted that the terms "include" or "may include" used in various embodiments of the present application indicate the presence of the function, operation or element applied for, and do not limit the addition of one or more functions, operations or elements. In addition, as used in various embodiments of the present application, the terms "include", "have" and their cognates are only intended to indicate specific features, numbers, steps, operations, elements, components or a combination of the foregoing items, and should not be understood as first excluding the presence of one or more other features, numbers, steps, operations, elements, components or a combination of the foregoing items or the possibility of adding one or more features, numbers, steps, operations, elements, components or a combination of the foregoing items.

[0042] In various embodiments of the present application, the expression "or" or "at least one of B or / and C" includes any combination or all combinations of the words listed at the same time. For example, the expression "B or C" or "at least one of B or / and C" may include B, may include C, or may include both B and C.

[0043] In addition, terms such as "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0044] Please refer to Figure 1 and Figure 2 , Figure 1 A schematic diagram of the structure of a power transmission line parameter testing system provided by an embodiment of the present invention applied to a DC transmission line; Figure 2 A schematic diagram of a transmission line parameter testing system provided by an embodiment of the present invention applied to an AC transmission line is shown in FIG. Figure 1 and Figure 2As shown, the test system includes a test power supply module, an adaptive interference suppression module and a line parameter test module which are connected in sequence; the test power supply module is used to output voltage values ​​of different test frequencies; the adaptive interference suppression module is used to enable the test power supply module to effectively inject a single frequency into the line parameter test module each time to reduce the electromagnetic induction current and capacitive coupling voltage in the line parameter test module; the line parameter test module is used to be connected to each phase of a DC or AC transmission line.

[0045] In this embodiment, Figure 1 and Figure 2 The dotted box in the figure is the adaptive interference suppression module provided in this embodiment. It should be understood that the test power supply module and the line parameter test module described in this embodiment are both components of the existing test system, that is, they are well-known technologies, such as Figure 1 The right part of the dashed box in the middle. It should also be noted that, in view of the simulation calculation or actual measurement methods provided by the current relevant technologies to determine the induced voltage and induced current of the UHV AC and DC lines to be tested, the induced voltage and current methods in the power industry standards DL_T 1583-2016 and DL / T 1566-2016 can be used to test the DC and AC transmission lines respectively, and the induced voltage and current at the head end of the transmission line to be tested under the two states of open circuit and short circuit can be measured. The frequency response of the test instrument should cover [0-2500Hz] in order to obtain the high-frequency components of the induced voltage and current.

[0046] like Figure 3 As shown, Figure 3 The circuit structure diagram of the adaptive interference suppression module provided in the embodiment of the present invention is as follows. The adaptive interference suppression module has an input terminal, an output terminal and a ground terminal. The adaptive interference suppression module includes a first resistor R1, an inductor L f , a second resistor R2 and a capacitor C1; the first resistor R1 is used to reduce the inductive interference current of the DC or AC transmission line to the ground loop with the same frequency as the test power module and the electromagnetic induction current of the loop between the phases of the DC or AC transmission line; the capacitor C1 is connected in parallel with the inductor to form a low-impedance path with a line capacitance-coupled interference voltage frequency different from the test power injection frequency, so as to reduce the electromagnetic induction voltage generated by the capacitance-coupled voltage of the DC or AC transmission line; the second resistor R2 is used to control the bandwidth range of the same frequency intercommunication and different frequency blocking; wherein, one end of the first resistor R1 is used as the input end, and the other end of the first resistor R1 is connected to the inductor L f A node connected in parallel with the second resistor R2 and the capacitor C1 is connected as an output terminal, and the inductor L f Another node where the second resistor R2 and the capacitor C1 are connected in parallel serves as a ground terminal.

[0047] In this embodiment, the first resistor R1 in the adaptive interference suppression module is a series resistor, which reduces the line-to-ground loop induction interference current and the two-pole line loop electromagnetic induction interference current of the same frequency as the test power supply; the capacitor C1 is a parallel capacitor, and the inductor L f It is connected in parallel and changes with the frequency to form a low impedance path of line capacitance coupling interference voltage frequency different from the test power injection frequency, thereby reducing the line capacitance coupling interference voltage; the second resistor R2 is a parallel resistor, which serves as a quality factor for adjusting the peak value of the resonance peak impedance, controls the bandwidth range of co-frequency intercommunication and heterodyne blocking, and improves the test accuracy of line parameters.

[0048] like Figure 1 As shown, when the transmission line for parameter test is a DC transmission line, the test power supply module is a two-phase symmetrical frequency modulation test power supply, the number of the adaptive interference suppression modules is two, and the number of the line parameter test modules is two; a DC transmission line parameter test system is constructed by a two-phase symmetrical frequency modulation test power supply, two adaptive interference suppression modules and two line parameter test modules.

[0049] Specifically, in Figure 1 In the test mode, the influence of induced voltage and current must be considered at the same time, which is the most complicated case of interference suppression (the other test mode is when the ends of poles I and II are open and not grounded, and only the influence of induced voltage needs to be considered).

[0050] like Figure 2 As shown, when the transmission line for parameter test is an AC transmission line, the test power supply module is a three-phase symmetrical frequency modulation test power supply, the number of the adaptive interference suppression modules is three, and the number of the line parameter test modules is three; an AC transmission line parameter test system is constructed by a three-phase symmetrical frequency modulation test power supply, three adaptive interference suppression modules and three line parameter test modules.

[0051] As an implementation mode, the test frequency of the test power module is defined in this embodiment as being within the range of 30 Hz to 2500 Hz, and may of course be 30 Hz to 3000 Hz, and this embodiment does not impose any specific limitation.

[0052] In summary, in a transmission line parameter test system provided in an embodiment of the present invention, the test system includes a test power supply module, an adaptive interference suppression module and a line parameter test module; the test power supply module is used to output voltage values ​​of different test frequencies; the adaptive interference suppression module is used to enable the test power supply module to effectively inject a single frequency into the line parameter test module each time to reduce the electromagnetic induction current and capacitive coupling voltage in the line parameter test module; the line parameter test module is used to connect to each phase of a DC or AC transmission line; at present, the test frequency of the test power supply module is injected into the line parameter test module at a single frequency, and the adaptive interference suppression module provided in this embodiment can ensure that the test power supply module effectively injects a single frequency into the line parameter test loop each time, clamps the electromagnetic induction current and capacitive coupling voltage amplitudes in the line parameter test loop that are different from the test power injection frequency, improves the test accuracy of the line parameter test at a single frequency and ensures the safety of the test power supply module and the tester.

[0053] The embodiment of the present invention further provides a transmission line parameter testing method, which is applied to a transmission line parameter testing system as described in the above embodiment, and the testing method includes:

[0054] Obtain the test frequency range and withstand voltage of the test power supply module; calculate the product range of the inductance and capacitance of the adaptive interference suppression module under the test frequency range, select the capacitance value of the capacitor according to the withstand voltage, and determine the inductance value of the inductor according to the product range and the capacitance value of the capacitor; determine the quality factor and angular frequency of the adaptive interference suppression module according to the frequency response function and transfer function of the adaptive interference suppression module; determine the resistance values ​​of the first resistor and the second resistor according to the quality factor and the angular frequency.

[0055] Specifically, before testing the parameters, it should be noted that the inductance value of the inductor of the adaptive interference suppression module only changes with the test frequency of the test power supply.

[0056] like Figure 4 and 5 As shown, the specific implementation of the change in the inductance value of the inductor is as follows: the test power supply module deflects the voltage phase by 180 degrees through the inverter, isolates the inductance control loop from the test power supply module through impedance transformation, connects the voltage signal after impedance transformation to the middle coil connector of the inductor, and the inductance value controlled by the reverse flux tested by the test power supply module changes linearly only with the test frequency.

[0057] like Figure 3 As shown, the parameters of each component in the interference suppression module are calculated and configured. The specific calculation process is as follows:

[0058] 1. According to formula 1, calculate the inductance L at the initial frequency of 30Hz fThe product range of capacitor C1 and the inductor L should be reasonably selected according to the withstand voltage. f The inductance value and the capacitance value of capacitor C1.

[0059] Where, f represents the test frequency, L f C1 represents the inductance of the inductor, and C2 represents the capacitance of the capacitor.

[0060] 2. The frequency response function G(jω) of the adaptive interference suppression module is shown in Formula 2, where τ1 = L f / R2,τ2=R1*C1.

[0061]

[0062] The transfer function H(s) of the adaptive interference suppression module is shown in Formula 3:

[0063] Among them, ω p represents the angular frequency, Q p represents the quality factor, s represents a complex variable, Q p =ω p / 2Re(G(jω)), G(jω) represents the frequency response function, Im represents the complex imaginary part, and Re represents the complex real part.

[0064] Taking the test frequency of 30Hz to 2500Hz as an example, it is necessary to pass the adaptive interference suppression loop as the frequency changes, such as Figure 6 As shown, according to formulas 1 to 3, the parameters must satisfy ω p / Q p Less than the frequency step, the 1 / 1.414 gain at -3dB needs to meet the power supply current capacity requirement, that is, the inductor L is obtained f , the values ​​of the first resistor R1, the second resistor R2 and the capacitor C1.

[0065] Based on the parameter values ​​of the components of the adaptive interference suppression module determined in the above embodiments, the influence of the induced interference generated by the adjacent lines of the corresponding voltage level on the transmission line to be tested can be suppressed, thereby solving the problem that the related technology cannot suppress the induced interference generated by the operating lines adjacent to the transmission line to be tested.

[0066] In summary, in a transmission line parameter testing method provided by the present invention, the testing process is implemented by the transmission line parameter testing system described in the above embodiment, and the testing system includes a test power supply module, an adaptive interference suppression module and a line parameter testing module; the test power supply module is used to output voltage values ​​of different test frequencies; the adaptive interference suppression module is used to enable the test power supply module to effectively inject a single frequency into the line parameter testing module each time to reduce the electromagnetic induction current and capacitive coupling voltage in the line parameter testing module; the line parameter testing module is used to connect to each phase of a DC or AC transmission line; at present, the test frequency of the test power supply module is injected into the line parameter testing module at a single frequency, and the adaptive interference suppression module provided in this embodiment can ensure that the test power supply module effectively injects a single frequency into the line parameter testing loop each time, clamps the electromagnetic induction current and capacitive coupling voltage amplitude in the line parameter testing loop that are different from the test power injection frequency, improves the test accuracy of the line parameter test at a single frequency and ensures the safety of the test power supply module and the tester.

[0067] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A transmission line parameter testing system, characterized in that: The test system includes a test power supply module, an adaptive interference suppression module and a line parameter test module which are connected in sequence; The test power supply module is used to output voltage values ​​of different test frequencies; The adaptive interference suppression module is used to enable the test power supply module to effectively inject a single frequency into the line parameter test module each time, so as to reduce the electromagnetic induction current and capacitive coupling voltage in the line parameter test module; The line parameter testing module is used to connect to each phase of a DC or AC transmission line.

2. A transmission line parameter testing system according to claim 1, characterized in that: The adaptive interference suppression module has an input terminal, an output terminal and a ground terminal, and the adaptive interference suppression module includes a first resistor, an inductor, a second resistor and a capacitor; The first resistor is used to reduce the inductive interference current of the DC or AC transmission line to the ground loop and the electromagnetic induction current of the loop between each phase of the DC or AC transmission line at the same frequency as the test power module; The capacitor is connected in parallel with the inductor to form a low impedance path of the line capacitance coupling interference voltage frequency different from the test power injection frequency, so as to reduce the electromagnetic induction voltage generated by the capacitance coupling voltage of the DC or AC transmission line; The second resistor is used to control the bandwidth range of same-frequency intercommunication and different-frequency blocking; Among them, one end of the first resistor is used as an input end, the other end of the first resistor is connected to a node where the inductor, the second resistor and the capacitor are connected in parallel as an output end, and another node where the first inductor, the second resistor and the capacitor are connected in parallel is used as a ground end.

3. A transmission line parameter testing system according to claim 2, characterized in that: When the transmission line for parameter test is a DC transmission line, the test power supply module is a two-phase symmetrical frequency modulation test power supply, the number of the adaptive interference suppression modules is two, and the number of the line parameter test modules is two; A DC transmission line parameter test system is constructed by a two-phase symmetrical frequency modulation test power supply, two adaptive interference suppression modules and two line parameter test modules.

4. A transmission line parameter testing system according to claim 2, characterized in that: When the transmission line for parameter test is an AC transmission line, the test power supply module is a three-phase symmetrical frequency modulation test power supply, the number of the adaptive interference suppression modules is three, and the number of the line parameter test modules is three; An AC transmission line parameter test system is constructed by a three-phase symmetrical frequency modulation test power supply, three adaptive interference suppression modules and three line parameter test modules.

5. A transmission line parameter testing method, applied to a transmission line parameter testing system as claimed in any one of claims 1 to 4, characterized in that: Test methods include: Obtain the test frequency range and withstand voltage of the test power module; Calculate the product range of the inductance and capacitance of the adaptive interference suppression module under the test frequency range, select the capacitance value of the capacitor according to the withstand voltage, and determine the inductance value of the inductor according to the product range and the capacitance value of the capacitor; Determining the quality factor and angular frequency of the adaptive interference suppression module according to the frequency response function and transfer function of the adaptive interference suppression module; The resistance values ​​of the first resistor and the second resistor are determined according to the quality factor and the angular frequency.

6. A transmission line parameter testing method according to claim 5, characterized in that: The inductance value of the inductor changes only with the test frequency of the test power supply.

7. A transmission line parameter testing method according to claim 6, characterized in that: The process of controlling the inductance value of the inductor to change only with the test frequency of the test power supply is specifically as follows: The test power module deflects the voltage phase by 180 degrees through an inverter, isolates the inductance control loop from the test power module through impedance transformation, connects the voltage signal after impedance transformation to the middle coil connector of the inductor, and the reverse flux controlled inductance value tested by the test power module changes only linearly with the test frequency.

8. A transmission line parameter testing method according to claim 5, characterized in that: The formula for calculating the product range is: Where, f represents the test frequency, L f C1 represents the inductance of the inductor, and C2 represents the capacitance of the capacitor.

9. A transmission line parameter testing method according to claim 5, characterized in that: The expression of the frequency response function is: Where τ1=L f / R2,τ2=R1*C1,L f C1 represents the inductance of the inductor, and C2 represents the capacitance of the capacitor.

10. A transmission line parameter testing method according to claim 5, characterized in that: The expression of the transfer function is: Among them, ω p represents the angular frequency, Q p represents the quality factor, s represents a complex variable, Q p =ω p / 2Re(G(jω)), G(jω) represents the frequency response function, Im represents the complex imaginary part, and Re represents the complex real part.

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