A low-voltage flexible direct-current system fault detection method based on complex domain analysis

Abstract

The application provides a low-voltage flexible DC system fault detection method based on complex domain analysis, comprising: acquiring and sampling a transient current signal in a low-voltage flexible DC system, fitting the transient current signal as a linear combination of a group of exponential functions, thereby obtaining a fitted exponential function; solving the fitted exponential function in the Z domain based on the Pad approximation method to obtain a complex exponential of the fitted exponential function; determining a fault threshold frequency according to an operating parameter of the low-voltage flexible DC system; taking the complex exponential as an analysis object, calculating a natural oscillation frequency of the low-voltage flexible DC system through a formula; taking the fault threshold frequency as a state circle radius, constructing a fault discrimination model based on a complex plane, comparing the natural oscillation frequency with the fault threshold frequency, and combining a real part of the complex exponential to output a fault detection result of the low-voltage flexible DC system. The application can reduce the sensitivity to noise and meet the speed requirement of fault detection.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of direct current system fault detection, and in particular to a low-voltage flexible direct current system fault detection method based on complex domain analysis. BACKGROUND

[0002] With the increasing penetration of distributed energy, low-voltage flexible direct current systems (LVDC) containing voltage source converters (VSC) have been widely researched and applied due to their inherent advantages in improving power quality, enabling flexible access to various energy sources, and enhancing system efficiency. However, the widespread use of voltage source converters has also brought serious protection challenges. Voltage source converters maintain DC voltage stability through large-capacity support capacitors on the DC side. Once a short-circuit fault occurs in the DC line, these capacitors will rapidly discharge through a very low impedance path, forming a fault current with a huge amplitude and a very high rise rate. This current not only causes permanent damage to power semiconductor devices such as freewheeling diodes in the converter, but also threatens the safe and stable operation of the entire system.

[0003] Therefore, the protection device of the low-voltage flexible direct current system must accurately detect the fault and take isolation measures within a very short time (usually less than 2ms). Existing fault detection methods can be broadly divided into time domain analysis and frequency domain analysis. Time domain analysis methods, such as traditional overcurrent protection and voltage differential protection, have fast response speed, but they are sensitive to noise and difficult to effectively distinguish transient disturbances, which can easily cause misoperation. Frequency domain analysis methods, such as wavelet transform, short-time Fourier transform, S-transform, and Hilbert-Huang transform, distinguish different transient processes by analyzing the characteristics of signals in the frequency domain, and have relatively strong identification ability. SUMMARY

[0004] In view of this, the present application provides a low-voltage flexible direct current system fault detection method based on complex domain analysis to reduce the sensitivity to noise while meeting the speed requirements of fault detection.

[0005] A low-voltage flexible direct current system fault detection method based on complex domain analysis, comprising:

[0006] Step S1, acquiring and sampling a transient current signal in the low-voltage flexible direct current system, fitting the transient current signal as a linear combination of a set of exponential functions, and obtaining a fitted exponential function;

[0007] Step S2, solving the fitted exponential function in the Z domain based on the Padé approximation method to obtain a complex exponential of the fitted exponential function;

[0008] Step S3, determining a fault threshold frequency according to the operating parameters of the low-voltage flexible direct current system;

[0009] Step S4, taking the complex index as an analysis object, obtaining the natural oscillation frequency of the low-voltage flexible DC system through formula calculation;

[0010] Step S5, taking the fault threshold frequency as a state circle radius, constructing a fault discrimination model based on a complex plane, comparing the natural oscillation frequency with the fault threshold frequency in the fault discrimination model based on the complex plane, and outputting a fault detection result of the low-voltage flexible DC system in combination with a real part of the complex index.

[0011] According to the low-voltage flexible DC system fault detection method based on complex domain analysis provided by the application, the following beneficial effects are achieved:

[0012] (1) In the low-voltage flexible DC system, the DC fault detection time should be limited within 2 ms, so as to reliably protect the entire system and the converter assembly. Unlike time-consuming and lengthy artificial intelligence algorithms, the application only needs to perform fast signal fitting and algebraic solving, the complexity of the core algorithm is effectively reduced, the calculation burden is small, and the detection can be completed within hundreds of microseconds, completely meeting the speed requirement of fault detection. And the application discriminates based on the complex index of the signal, which has an intuitive physical explanation.

[0013] (2) The application introduces a state circle on the complex plane as a criterion, which can directly identify the internal mode parameters of the system, rather than relying on signal energy, so that it can more reliably identify the real fault transient state under different noise environments, and reduce the sensitivity of the criterion to noise.

[0014] (3) The application can clearly distinguish between the convergent transient state of the fault line and the divergent transient state of the healthy line by analyzing the real part of the complex index, which fundamentally avoids the protection misoperation problem in the multi-terminal system. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a schematic diagram of a simulation model;

[0016] Figure 2 is a flowchart of the low-voltage flexible DC system fault detection method based on complex domain analysis provided by the embodiment of the application;

[0017] Figure 3 is a schematic diagram of a second-order RLC series circuit;

[0018] Figure 4 is a projection diagram of the complex index of the exponential function of the transient current under the load switching condition on the complex plane;

[0019] Figure 5 is a schematic diagram of the fitting result of the exponential function of the transient current of the fault line;

[0020] Figure 6 The projection of the complex exponent of the exponential function of the transient current of the faulted line onto the complex plane;

[0021] Figure 7 A schematic diagram showing the result of fitting the exponential function of the transient current of a healthy circuit under fault conditions;

[0022] Figure 8 This is the projection of the complex exponent of the exponential function of the transient current of a healthy circuit under fault conditions onto the complex plane. Detailed Implementation

[0023] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0024] This invention provides a fault detection method for low-voltage flexible DC systems based on complex domain analysis. This embodiment applies this method to... Figure 1 The simulation model shown illustrates a typical four-terminal flexible direct current transmission (VSC-MTDC) system topology, consisting of four voltage source converter stations (VSC1, VSC2, VSC3, VSC4) connected in a ring network via four DC lines (L12, L13, L34, L24). In the simulation model, VSC1, VSC2, and VSC3 obtain electrical energy from AC power sources and convert it into DC power for injection into the DC grid, while VSC2 acts as an inverter station to convert DC power back to AC power to supply local resistive loads. In the context of fault location research, this simulation model is primarily used to simulate the transient process of a short circuit or ground fault on a DC line (such as a point on L13) in a virtual environment, thereby generating high-fidelity voltage and current data to verify the accuracy, response speed, and reliability of specific fault location algorithms.

[0025] When a capacitor discharges and causes underdamped or overdamped oscillations, the mathematical expression of its transient current can be accurately described by a linear combination of exponential functions. This invention utilizes this characteristic for analysis.

[0026] Please see Figure 2 The fault detection method for low-voltage flexible DC systems based on complex domain analysis provided by this invention includes steps S1 to S5:

[0027] Step S1: Acquire and sample the transient current signal in the low-voltage flexible DC system, and fit the transient current signal into a linear combination of a set of exponential functions to obtain the fitted exponential function.

[0028] The current sensor installed on each DC line monitors the line current in real time. When the protection starting element (such as the current mutation element) acts, the fault analysis program of the application is started. The program will intercept the discrete current in a very short data window after the transient state occurs as an analysis sample. In order to accurately describe the internal physical characteristics of the transient process, the application adopts a model of linear combination of n-order exponential functions for fitting.

[0029] Specifically, the fitting exponential function satisfies the following formula:

[0030]

[0031] wherein, is the fitting order, is the amplitude coefficient of the th, is the complex exponential of the th, is the time. For the response of a two-order RLC system, usually can be obtained enough accurate fitting.

[0032] Step S2, solving the fitting exponential function in the Z domain based on the Pad approximation method, to obtain the complex exponential of the fitting exponential function.

[0033] Wherein, it is extremely difficult and time-consuming to solve the nonlinear parameters in the time domain directly, and it is not suitable for the relay protection field which requires high-speed response. Therefore, the application adopts a high-efficiency solving algorithm based on Pad approximation in the Z domain. The algorithm ingeniously converts the nonlinear fitting problem in the time domain into an algebraic problem in the Z domain.

[0034] Step S2 specifically includes:

[0035] The solving problem of the fitting exponential function is converted to the Z domain, and , represents a period, and the Z domain expression of the fitting exponential function is :

[0036]

[0037] wherein, is the independent variable, is the th pole value of the independent variable, , , is the numerator coefficient, , , is the denominator coefficient;

[0038] By Padé approximation method, the coefficients of the series expansion of are matched with the coefficients of the Z-transformed transient current signal, thereby establishing a linear equation system about the denominator coefficients, solving the linear equation system to obtain the denominator coefficients, and then constructing and solving the following characteristic equation to obtain :

[0039]

[0040] By solving the above characteristic equation, the roots of , i.e. , are obtained.

[0041] Finally, the complex exponent of the fitted exponential function is calculated by the inverse relationship .

[0042] Step S3, determining the fault threshold frequency according to the operating parameters of the low-voltage flexible DC system.

[0043] In the low-voltage flexible DC system with VSC, at the initial stage of short-circuit fault, the large-capacity support capacitor on the DC side of the VSC will discharge quickly to the fault point through the fault line. The physical model of the fault loop of the low-voltage flexible DC system can be equivalent to a second-order RLC series circuit, which can be referred to in Figure 3 . The second-order RLC series circuit satisfies the following linear differential equation:

[0044]

[0045] where is the fault current, is the equivalent capacitance on the DC bus side, and are the equivalent inductance and resistance of the line, respectively, is the fault resistance, denotes differentiation.

[0046] The characteristic roots of the above linear differential equation directly determine the mode of transient response. Since the equivalent inductance of the loop at fault is usually much smaller than the equivalent inductance of the system at normal operation, the natural oscillation frequency at fault will increase significantly, so the fault threshold frequency of the present application is set as:

[0047] .

[0048] Step S4, taking the complex exponent as the analysis object, and calculating the natural oscillation frequency of the low-voltage flexible DC system by the formula.

[0049] wherein step S4 specifically comprises:

[0050] When the condition formula is met, the low-voltage flexible DC system is in an under-damped state, and the linear differential equation of the second-order RLC series circuit has two conjugate complex roots, the first complex index and the second complex index , and the solution is in the form of a decaying oscillation, and must be a pair of conjugate complex numbers, and satisfy:

[0051]

[0052]

[0053]

[0054] wherein, is the decay coefficient, represents an imaginary number, is the damped oscillation angular frequency;

[0055] then the calculation formula of the natural oscillation frequency is:

[0056]

[0057] When the condition formula is met, the low-voltage flexible DC system is in an over-damped state, and the linear differential equation of the second-order RLC series circuit has two unequal negative real roots, the first complex index and the second complex index , and in this case, and will be two negative real numbers, and satisfy:

[0058]

[0059]

[0060] then the calculation formula of the natural oscillation frequency is:

[0061] .

[0062] Step S5, taking the fault threshold frequency as the state circle radius, constructs a fault discrimination model based on a complex plane, in which the natural oscillation frequency and the fault threshold frequency are compared, and the real part of the complex index is combined to output the fault detection result of the low-voltage flexible DC system.

[0063] wherein, step S5 specifically comprises:

[0064] A state circle with the origin as the center and the fault threshold frequency as the radius is defined on the complex plane, and then the following steps are adopted to output the fault detection result of the low-voltage flexible DC system:

[0065] If , the feature point on the complex plane is located outside the state circle, it is determined that the low-voltage flexible DC system is in a fault state.

[0066] The criterion can effectively distinguish the high-frequency fault transient state from the low-frequency normal operation, for example, the complex index obtained by solving under the load switching condition is projected to the complex plane, and the projection point will fall within the state circle, so as to be judged as a non-fault condition, as shown in Figure 4

[0067] In a multi-terminal low-voltage flexible DC system, the voltage of the entire system will change when a line fault occurs, so all healthy lines will also have transient responses. These healthy line responses may also contain high-frequency components, causing to exceed the threshold, and if only the criterion is used, it may lead to misjudgment of the protection device. The present application solves this problem by further analyzing the physical meaning of the complex index . The real part of the complex index represents the decay or growth rate of the transient process.

[0068] In this embodiment, on the basis of the criterion , if the condition formula is further met, it is determined that the fault line is a convergent high-frequency transient state, is the real part of , and if the condition formula is further met, it is determined that the healthy line affected by the fault is a divergent high-frequency transient state.

[0069] For the fault line itself, the transient current is the process of discharging the DC side capacitor through the fault point, which is a process of energy consumption and gradual decay, showing convergent oscillation. Therefore, the complex index obtained by fitting the current signal is necessarily negative in the real part. Its projection point is necessarily located in the left half of the complex plane. The complex index projection point of the transient current of the fault line will be located outside the state circle and in the left half of the complex plane, as shown in Figure 5 and Figure 6 .

[0070] ​​For healthy lines, its transient response is the process that the voltage of the common bus decreases due to the remote fault point, so that the line absorbs more power from the power supply side connected to it, which is manifested as divergent oscillation. Therefore, the complex exponential obtained by fitting the current signal of the line is , the real part of which must be positive. Its projection point must be located in the right half plane of the complex plane. By fitting and analyzing the transient current of the healthy line under fault conditions, the projection point of the complex exponential will be located outside the state circle but in the right half plane, as shown in Figure 7 and Figure 8 .

[0071] If , the characteristic point on the complex plane is located inside or on the state circle, it is determined that the low-voltage flexible DC system is in a normal state.

[0072] Therefore, the final criterion of the present application is a double criterion and a non-ambiguous geometric rule on the complex plane. The rule comprehensively considers the position of the projection point of the complex exponential relative to the state circle (inside-out relationship) and the half plane it belongs to on the complex plane (left-right relationship), and can comprehensively and accurately diagnose the state of all lines of the system.

[0073] In summary, the low-voltage flexible DC system fault detection method based on complex domain analysis according to the above embodiment has the following beneficial effects:

[0074] (1) In the low-voltage flexible DC system, the DC fault detection time should be limited within 2ms in order to reliably protect the entire system and the converter components. Unlike time-consuming and lengthy artificial intelligence algorithms, the present application only needs to perform fast signal fitting and algebraic solving, the complexity of the core algorithm is effectively reduced, the calculation burden is small, and the detection can be completed within hundreds of microseconds, fully meeting the speed requirements of fault detection. And the present application discriminates based on the complex exponential of the signal, which has an intuitive physical explanation.

[0075] (2) The present application introduces the state circle on the complex plane as a criterion, which can directly identify the intrinsic mode parameters of the system, rather than relying on signal energy, so that it can more reliably identify the real fault transient under different noise environments, reducing the sensitivity of the criterion to noise.

[0076] (3) The present application can clearly distinguish between convergent transients of fault lines and divergent transients of healthy lines by analyzing the real part of the complex exponential, which fundamentally avoids the problem of protection misoperation in multi-terminal systems.

[0077] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are within the scope of protection of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for fault detection of a low voltage flexible direct current system based on complex domain analysis, characterized in that, The method comprises the following steps: Step S1, acquiring and sampling a transient current signal in a low-voltage flexible direct current system, fitting the transient current signal into a linear combination of a group of exponential functions, and obtaining a fitted exponential function; Step S2, solving the fitted exponential function in the Z domain based on the Padé approximation method to obtain a complex exponential of the fitted exponential function; Step S3, determining a fault threshold frequency according to an operating parameter of the low-voltage flexible direct current system; Step S4, taking the complex exponential as an analysis object, and calculating a natural oscillation frequency of the low-voltage flexible direct current system through a formula; Step S5, taking the fault threshold frequency as a state circle radius, constructing a fault discrimination model based on a complex plane, comparing the natural oscillation frequency with the fault threshold frequency in the fault discrimination model based on the complex plane, and outputting a fault detection result of the low-voltage flexible direct current system in combination with a real part of the complex exponential; In step S1, the exponential function is fitted satisfies the following equation: wherein, is the order of the fit, is the amplitude coefficient, is the complex exponential, is the complex exponential, is the complex exponential, is time; Step S2 specifically comprises: The problem of solving the exponential function is converted to the Z domain, and the definition , is given, where T represents the period, then the Z domain expression of the exponential function is ​ wherein is an argument, is an argument the first pole value, , is a numerator coefficient, , , is a denominator coefficient; By the Padé approximation method, the coefficients of the series expansion of are matched with the coefficients of the Z-transformed transient current signal, thereby establishing a system of linear equations with respect to the denominator coefficients, which are solved to obtain the denominator coefficients, and then the following characteristic equation is constructed and solved to obtain : Finally, the complex exponential of the fitting exponential function is computed by the inverse relation ​ Step S3 specifically comprises: The physical model of a fault loop of the low-voltage flexible direct current system is equivalent to a second-order RLC series circuit, and the second-order RLC series circuit satisfies the following linear differential equation: wherein is the fault current, is the DC bus side equivalent capacitance, and are the equivalent inductance and resistance of the line, respectively, is the fault resistance, denotes the differential; Fault threshold frequency Is: ； Step S4 specifically comprises: When the condition is satisfied, the low-voltage flexible direct-current system is in an under-damped state, the linear differential equation of the second-order RLC series circuit has two conjugate complex roots, respectively, a first complex index and a second complex index , and satisfies: wherein is the attenuation coefficient, denotes the imaginary unit, is the damped oscillation angular frequency; The natural oscillation frequency is calculated by the formula When the condition is satisfied, the low-voltage flexible direct current system is in an over-damped state, the linear differential equation of the second-order RLC series circuit has two unequal negative real roots, respectively, a first complex exponential and a second complex exponential , and satisfies: The natural oscillation frequency is calculated by the formula 。 2. The method for fault detection of low voltage flexible direct current system based on complex domain analysis according to claim 1, characterized in that, Step S5 specifically comprises: A state circle is defined on the complex plane with the origin as the center and the fault threshold frequency as the radius Then the following steps are adopted to output the fault detection result of the low-voltage flexible DC system: If , the feature point on the complex plane is located outside the state circle, it is determined that the low-voltage flexible DC system is in a fault state; if further condition is met, it is determined that the fault line of convergent high-frequency transient state, is the real part of , if further condition is met, it is determined that the healthy line affected by the fault of divergent high-frequency transient state; If , the characteristic point on the complex plane is located inside or on the state circle, it is determined that the low-voltage flexible direct-current system is in a normal state.

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