Power grid harmonic voltage measurement method based on test system transfer function

Abstract

This invention relates to a method for measuring grid harmonic voltage based on the transfer function of a test system, belonging to the field of power grid technology. This method detects the leakage current signal of capacitive devices in the power grid using a current sensor and constructs a functional relationship between the current sensor's output voltage and the grid harmonic voltage, thereby measuring the grid harmonic voltage based on the current sensor. Specifically, the amplitude-frequency and phase-frequency characteristics of the capacitive device, as well as the current transfer ratio and phase error of the current sensor, are obtained through frequency characteristic testing. Then, the transfer functions of the capacitive device and the current sensor are calculated separately. Combining the impedance transfer function of the capacitive device and the output transfer function of the current sensor, the transfer function of the test system is calculated to construct a functional relationship between the current sensor's output voltage and the grid harmonic voltage. This allows for convenient, fast, and accurate measurement of the grid harmonic voltage using a current sensor.

Description

Technical Field

[0001] This invention belongs to the field of power grid technology and relates to the measurement of power grid harmonic voltage, specifically to a method for measuring power grid harmonic voltage based on the transfer function of a test system. Background Technology

[0002] With the increasing proportion of new energy sources in the power grid and the integration of a large number of power electronic loads, the harmonic content of the power grid has increased. The integration of new energy sources such as wind and solar power, as well as high-power power electronic loads such as metal smelting, electric traction locomotives, and electric vehicle charging stations, seriously affect the power quality of the power grid. A smart, efficient, and clean intelligent grid is the inevitable trend for the future development of my country's power grid. Compared with the existing power grid, its advantages and advancements are mainly reflected in: the ability to acquire panoramic information about the power grid, timely detection and prediction of potential faults, and rapid isolation of faults when they occur, achieving self-recovery and avoiding large-scale power outages. Facing the ever-expanding scale of future intelligent grids, the lack of fault data and the scarcity of high-performance sensing equipment are major challenges to achieving intelligent grids. Wideband voltage, as an important state quantity characterizing transient fault information, makes the research on its sensing technology and the application analysis of sensing data crucial for building intelligent grids. If massive amounts of measured voltage data can be directly and accurately sensed and acquired, and then data mining and analysis can be performed, power grid security can be better strengthened and the intelligentization of equipment can be promoted. Therefore, accurate detection of power grid harmonic voltage is the foundation for power quality analysis and harmonic mitigation.

[0003] For measuring harmonic voltage in power grids, scholars both domestically and internationally have proposed numerous methods, including the transformer method, voltage divider method, equipment end-screen voltage divider method, CVT transfer function calculation method, and capacitive equipment leakage current method. Voltage dividers require available space for on-site installation, and the grounding of the voltage divider terminals is not isolated from the grounding of the measurement unit, making them primarily suitable for laboratory measurements and not for long-term harmonic voltage measurements. The end-screen voltage divider method utilizes the inherent capacitance of the capacitive equipment as a high-voltage capacitor, and connects a voltage-dividing capacitor in series at its end-screen grounding terminal as a low-voltage capacitor, forming a capacitive voltage divider to measure harmonic voltage. However, this method alters the primary wiring configuration of the equipment; an open circuit or poor contact in the end-screen can lead to equipment failure and even power grid outages.

[0004] Currently, voltage transformers are the most common devices for voltage measurement in power grid transmission lines and substations. While the technology is relatively mature, their capacity is limited, their dynamic range is small, and they are typically used to measure power frequency voltage signals. Furthermore, their large size makes them difficult to install on space-constrained transmission and distribution lines. In reality, the voltage signal range of the power grid varies greatly, ranging from 0 Hz (DC) to hundreds of megahertz. With the continuous advancement of ultra-high-voltage power grid construction in my country, the physical structure, operation mode, and dynamic characteristics of the power grid are undergoing profound changes. Conventional voltage monitoring devices struggle to accurately sense voltage state quantities in real time under these complex operating conditions, hindering the subsequent analysis and application of voltage sensing data. Simultaneously, the widespread application of distributed energy resources and power electronic devices during the development of smart grids may alter equipment structures and cause changes in power grid fault characteristics, increasing the difficulty of monitoring voltage state quantities at key nodes.

[0005] Electromagnetic voltage transformers (IVTs) are mainly used in power grids with voltage levels of 35kV and below. When the accuracy class is higher than 0.5, the response to voltage harmonics greater than 1kHz is poor. IVTs are rarely used in high-voltage power grids, and misoperation can lead to secondary side short circuits, causing malfunctions in protection devices or metering errors, affecting equipment and power grid operation safety. In power grids of 66kV and above, due to insulation requirements and cost advantages, capacitive voltage transformers (CVTs) are mainly used. To improve load-carrying capacity, the added compensating reactor has a center frequency of power frequency. The CVT is equivalent to a bandpass filter. The national standard for harmonics in public power grids, GB / T14549—1993, stipulates that it cannot be directly used for harmonic measurement. Therefore, the frequency characteristics of CVTs and their correction analysis have become a research hotspot. The CVT transfer function calculation method obtains the amplitude-frequency response curves at different voltage frequencies and corrects the measured harmonic voltages based on these response curves. However, due to the dispersion of stray capacitance within the CVT, the frequency and saturation characteristics of the compensating reactor and intermediate transformer core, and the differences in equipment, a large initial error limits the accuracy of the correction calculation. The grid voltage is measured based on the leakage current of capacitive devices. The grid voltage is reconstructed by integrating the leakage current. This method has no electrical connection to the high-voltage system and offers good safety. However, this method treats capacitive devices as pure capacitors, failing to consider the dielectric characteristics of capacitive devices. This means that the equivalent capacitance of capacitive devices varies significantly at different frequencies, leading to inconsistent equivalent voltage division ratios for different harmonic voltages. Furthermore, the numerous and densely packed key nodes requiring voltage measurement in smart grids pose new requirements for the size, cost, and ease of installation of voltage sensing equipment. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a method for measuring grid harmonic voltage by testing the transfer function of a test system. By calculating the transfer function relationship between voltage and current in the test system, the grid harmonic voltage can be calculated from the leakage current of the measured capacitor.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for measuring grid harmonic voltage based on the test system transfer function is proposed. This method detects the leakage current signal of capacitive equipment in the power grid using a current sensor and constructs a functional relationship between the output voltage of the current sensor and the grid harmonic voltage, thereby measuring the grid harmonic voltage based on the current sensor.

[0009] Specifically, firstly, a scatter plot of the dielectric characteristics of the capacitive device is obtained through frequency domain dielectric response testing. Then, the amplitude-frequency and phase-frequency characteristics of the capacitive device impedance under harmonic voltage are obtained from the scatter plot, and the impedance transfer function of the capacitive device is calculated based on the amplitude-frequency and phase-frequency characteristics of the capacitive device impedance. Next, a scatter plot of the frequency characteristics of the current sensor is obtained through frequency characteristic testing, and the current transfer ratio and phase error of the current sensor are obtained. The output transfer function of the current sensor is calculated based on the current transfer ratio and phase error of the current sensor. Finally, the transfer function of the test system is calculated by combining the impedance transfer function of the capacitive device and the output transfer function of the current sensor to construct the transfer function relationship between the current sensor output voltage and the grid harmonic voltage.

[0010] Furthermore, the amplitude-frequency response is expressed as:

[0011]

[0012] The phase frequency characteristic is expressed as:

[0013]

[0014] In the formula, C′ and C″ represent the real and imaginary parts of the complex capacitance of the capacitive device, respectively, n represents the harmonic voltage order, and ω1 represents the fundamental angular frequency;

[0015] The impedance transfer function of a capacitive device is then expressed as:

[0016] H1(s)=1 / (C′(s)s+C″(s)).

[0017] Furthermore, the current transfer ratio is expressed as:

[0018]

[0019] Phase error is expressed as:

[0020]

[0021] In the formula, M and L C and R C R represents the mutual inductance, self-inductance, and internal resistance of the current sensor coil, respectively. m C represents the amplification resistor value in the current sensor amplification circuit. f This indicates the value of the feedback capacitor in the amplifier circuit;

[0022] The output transfer function of the current sensor is then expressed as:

[0023]

[0024] In the formula, i 1n U represents the induced current flowing through the mutual inductance coil. mn This indicates the output voltage of the oscilloscope.

[0025] Furthermore, combining the impedance transfer function of the capacitive device and the output transfer function of the current sensor, the transfer function of the test system is expressed as follows:

[0026]

[0027] In the formula, This represents the nth harmonic voltage vector across the capacitive device. This indicates the output signal of the current sensor.

[0028] The beneficial effects of this invention are as follows: by constructing a functional relationship between the output voltage of the current sensor and the harmonic voltage of the power grid, the harmonic voltage of the power grid can be conveniently and quickly measured by the current sensor, and the measurement results are highly accurate.

[0029] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0030] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0031] Figure 1 A schematic diagram illustrating the principle of harmonic voltage reconstruction in a power grid;

[0032] Figure 2 A schematic diagram of the wiring for a test circuit of dielectric response of an oil-paper insulated capacitor;

[0033] Figure 3This is a schematic diagram showing the dielectric response test results of the impedance of an oil-paper insulated capacitor.

[0034] Figure 4 This is a scatter plot of the transfer curve of the transfer function.

[0035] Figure 5 This is a schematic diagram of a current sensor frequency characteristic test circuit.

[0036] Figure 6 This is a schematic diagram of the frequency characteristic test results of the current sensor;

[0037] Figure 7 A schematic diagram of the transfer coefficients of the test system;

[0038] Figure 8 This is a schematic diagram of odd harmonic voltage error. Detailed Implementation

[0039] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0040] Because the capacitive reactance of capacitors results in a much higher harmonic content in the leakage current than the voltage across the capacitor, measuring the leakage current signal using a current sensor is more accurate and easier than directly measuring high-voltage harmonic voltage. It is known that the dielectric properties of capacitors and the measurement error of current sensors affect harmonic voltage measurement; therefore, this invention considers the impedance transfer function of capacitive devices when measuring harmonic voltage at different frequencies. Simultaneously, a frequency-domain dielectric response meter is used to measure the dielectric properties of the capacitor within a specific frequency range. By testing the frequency characteristics of the current transducer, the output transfer function of the current transducer is obtained. Based on this, the transfer function relationship between the voltage and current of the measurement system is calculated, thus allowing the grid harmonic voltage to be obtained by measuring the leakage current of the capacitor. Figure 1 As shown.

[0041] Specifically, set The voltage across the capacitive device. Let H1 be the leakage current flowing through the capacitive device, then its transfer function can be expressed as:

[0042]

[0043] set up Let H2 be the output voltage of the current sensor, then its transfer function with respect to the leakage current can be expressed as:

[0044]

[0045] Combining equations (1) and (2), the transfer function H3 between the current sensor output voltage and the grid voltage can be obtained as follows:

[0046]

[0047] Among them, capacitive devices, due to the dielectric relaxation effect of their insulating medium, require analysis of their impedance transfer function H1 during harmonic voltage reconstruction; therefore, they cannot be simply regarded as pure capacitors. Similarly, current sensors, due to measurement errors in their coil parameters and circuit component parameters, require frequency characteristic testing and transfer function H2 analysis during voltage reconstruction.

[0048] Based on the above, in one embodiment of the present invention, an oil-paper insulated capacitor is selected as the object of study for the capacitive device of the reconfigurable voltage to analyze its impedance transfer function. This oil-paper insulated capacitor is composed of stacked and connected capacitor cores, with a capacitance of 300pF and a rated voltage of 50kV. The frequency domain dielectric spectrum of this capacitor is tested using a DIRANA dielectric response analyzer, with a test frequency range of 20Hz to 5kHz and a test voltage of 200V. The test circuit wiring is as follows. Figure 2 As shown.

[0049] The difference between the impedance of a capacitor and that of a pure capacitance model is as follows: Figure 3 As shown, its dielectric loss tangent decreases with increasing frequency. From the fundamental to the 50th harmonic, the tangent value changes from 0.0048 to 0.002, that is, the angle changes from 0.28° to 0.12°. According to equation (1) and Figure 3 From the dielectric parameters, the impedance transfer function of the capacitor can be obtained as shown in the following equation:

[0050] H1(s)=1 / (C′(s)s+C″(s))(4)

[0051] In the formula, C′ is the real part of the complex capacitor, and C″ is the imaginary part of the complex capacitor.

[0052] set up For the amplitude-frequency response of transfer function H1, For the phase frequency characteristic of the transfer function H1, we have:

[0053]

[0054]

[0055] In the formula, n represents the harmonic voltage order, and ω1 represents the fundamental angular frequency. For example... Figure 4 The figure shows the transfer curve of the transfer function. Figure 4 The scatter plot shows the amplitude-frequency response under the nth harmonic voltage. Phase frequency characteristics The amplitude-frequency response can be obtained from the scatter plot, therefore, the amplitude-frequency response can be obtained first from the scatter plot. Phase frequency characteristics Then, based on the amplitude-frequency characteristics Phase frequency characteristics Calculate the transfer function H1.

[0056] To ensure the accuracy of leakage current measurement, the frequency characteristics of the current sensor need to be calibrated. Specifically, this can be achieved by applying a constant amplitude voltage to the resistor at different frequencies and comparing it with the current measured by a current sensor that measures a fixed resistor, thus obtaining the output transfer function. Figure 5 The diagram shows a circuit for testing the frequency characteristics of a current sensor. R0 is a fixed resistor with a value of 1kΩ, and the signal generator output peak value is 1V. The frequency of the signal generator's voltage is changed and compared with the oscilloscope output voltage U. mn By comparison, the transfer ratio and phase error of the current sensor under different order harmonic voltages are obtained. The output transfer function based on the equivalent circuit of the current sensor can be expressed as:

[0057]

[0058] In the formula, i 1n This represents the induced current flowing through the mutual inductance coil, i.e., the secondary current; M, L C R C These represent the mutual inductance, self-inductance, and internal resistance of the coil, respectively. R m C represents the amplification resistor value in the current sensor amplification circuit. f This indicates the value of the feedback capacitor in the amplifier circuit to prevent self-oscillation.

[0059] The current transfer ratio and phase error of the current sensor under different harmonic voltages can be obtained by equation (7), as shown in the following equation:

[0060]

[0061]

[0062] In the formula, This indicates the current transfer ratio of the current sensor. This indicates the phase error of the current sensor. The frequency response test results of the current sensor are as follows: Figure 6 As shown, the current transfer ratio and phase error of the current sensor conform to equations (8) and (9). Therefore, it can be determined through... Figure 6 The scatter plot shown is obtained and Then, according to and Calculate the transfer function H2.

[0063] The transfer function H3 of the test system can be obtained from equations (3), (4) and (7), as shown below:

[0064]

[0065] In the formula, This represents the nth harmonic voltage vector across the high-voltage capacitor. This represents the output signal of the current sensor. The transfer coefficient of the test system is as follows: Figure 7 As shown in equation (10), the harmonic voltage across the capacitor is closely related to the output voltage of the current sensor. The voltage amplitude and phase shift of the test system are shown in the following equations:

[0066]

[0067]

[0068] Depend on Figure 1 As can be seen from equation (10), the harmonic voltage The relationship between the current sensor output voltage and the current sensor output signal is determined by the current sensor output signal. Combining equation (10), the amplitude and phase parameters of harmonic voltages of different orders can be calculated. In this embodiment, the fundamental frequency voltage and odd harmonic voltages with frequencies from 3rd to 49th are applied to the capacitor. The amplitude range of the odd harmonic voltage applied to the capacitor is 50 to 500V, and the voltage step is 50V. Taking the harmonic voltage on the capacitor measured by the high-voltage probe as a reference, the measurement error of the test system is analyzed, and the standard deviation of the relative error can be calculated by the following formula:

[0069]

[0070] In the formula, V Smn This represents the amplitude of the nth harmonic voltage measured by the calibration test system, in V. Cmn This represents the amplitude of the nth harmonic voltage measured by the high-voltage probe multiplied by 1000, where M represents the number of measurement points for each frequency. In this embodiment, there are 10 measurement points for each harmonic. The voltage errors for the 3rd to 49th odd harmonics are as follows: Figure 8 As shown, by Figure 8 It can be seen that E n The value range is 0 to 0.22%. The maximum absolute value of the phase error is less than 0.2°.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method of power system harmonic voltage measurement based on transfer function of a test system, characterized by: The method detects the leakage current signal of the capacitive device in the power grid through a current sensor, and constructs a transfer function relationship between the output voltage of the current sensor and the harmonic voltage of the power grid, so as to measure the harmonic voltage of the power grid based on the current sensor; Specifically, first, the dielectric characteristic scatter plot of the capacitive device is measured by frequency domain dielectric response test, then the amplitude-frequency characteristic and the phase-frequency characteristic of the impedance of the capacitive device under the harmonic voltage are obtained according to the scatter plot, and the impedance transfer function of the capacitive device is calculated according to the amplitude-frequency characteristic and the phase-frequency characteristic of the impedance of the capacitive device; the amplitude-frequency characteristic is expressed as: The phase-frequency characteristic is expressed as: wherein and Re and Xc represent the real and imaginary parts of the complex capacitance of the capacitive device, n n represents the order of the harmonic voltage, ω represents the fundamental angular frequency; and the impedance transfer function of the capacitive device is represented by: Then, the frequency characteristic scatter plot of the current sensor is measured by frequency characteristic test, and the current transfer ratio and the phase error of the current sensor are obtained, and the output transfer function of the current sensor is calculated based on the current transfer ratio and the phase error of the current sensor; The current transfer ratio is expressed as: The phase error is expressed as: wherein, , and represent mutual inductance, self-inductance and internal resistance of the current sensor coil, respectively, n represents a harmonic voltage order, represents a fundamental angular frequency, represents an amplification resistance value in the current sensor amplification circuit, represents a feedback capacitance value in the amplification circuit; The output transfer function of the current sensor is expressed as: wherein Iindisplays the induced current flowing through the mutual inductor, Voscdisplays the oscilloscope output voltage; Finally, the transfer function of the test system is calculated by combining the impedance transfer function of the capacitive device and the output transfer function of the current sensor, so as to construct the transfer function relationship between the output voltage of the current sensor and the harmonic voltage of the power grid.

2. The method of grid harmonic voltage measurement according to claim 1, characterized in that: The transfer function of the test system obtained by combining the impedance transfer function of the capacitive device and the output transfer function of the current sensor is expressed as: wherein represents the first n harmonic voltage vector, represents the current sensor output signal.

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