Low-voltage flexible DC system fault detection method based on complex domain analysis

Abstract

The invention provides a low-voltage flexible DC system fault detection method based on complex domain analysis, and the method comprises the steps: obtaining and sampling a transient current signal in a low-voltage flexible DC system, fitting the transient current signal into a linear combination of a group of exponential functions, and obtaining a fitting exponential function; solving the fitting exponential function in a Z domain based on a Pade approximation method to obtain a complex index of the fitting exponential function; determining a fault threshold frequency according to the operation parameters of the low-voltage flexible DC system; the complex index is used as an analysis object, and the natural oscillation frequency of the low-voltage flexible direct-current system is obtained through formula calculation; and 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 outputting a fault detection result of the low-voltage flexible DC system in combination with a real part of a complex index. According to the method, the sensitivity to noise can be reduced, and meanwhile, the requirement of fault detection for speed is met.

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: 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; 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 the operating parameters of the low-voltage flexible direct current system; Step S4, taking the complex exponential as an analysis object and calculating the natural oscillation frequency of the low-voltage flexible direct current system through a formula. Step S5, taking the fault threshold frequency as the radius of the state circle, constructs a fault discrimination model based on the complex plane, compares the natural oscillation frequency with the fault threshold frequency in the fault discrimination model based on the complex plane, and outputs the fault detection result of the low-voltage flexible DC system in combination with the real part of the complex exponential.

[0006] The low-voltage flexible DC system fault detection method based on complex domain analysis provided by the application has the following beneficial effects: (1) In the low-voltage flexible DC system, the DC fault detection time should be limited within 2 ms in order 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, fully meeting the speed requirements of fault detection. And the application discriminates based on the complex exponential of the signal, which has an intuitive physical explanation.

[0007] (2) The application introduces a 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 in different noise environments, reducing the sensitivity of the criterion to noise.

[0008] (3) The 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 protection misoperation problem in multi-terminal systems. BRIEF DESCRIPTION OF DRAWINGS

[0009] Figure 1 is a schematic diagram of a simulation model; 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; Figure 3 is a schematic diagram of a second-order RLC series circuit; Figure 4 is a projection diagram of the complex exponential of the exponential function of the transient current under the load switching condition on the complex plane; Figure 5 is a schematic diagram of the fitting result of the exponential function of the transient current of the fault line; Figure 6 is a projection diagram of the complex exponential of the exponential function of the transient current of the fault line on the complex plane; Figure 7 is a schematic diagram of the fitting result of the exponential function of the transient current of the healthy line under the fault condition; Figure 8This 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

[0010] 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.

[0011] 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.

[0012] 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.

[0013] 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: 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.

[0014] The current in each DC line is monitored in real time by current sensors installed on each line. When a protection activation element (such as a current surge element) activates, the fault analysis program of this invention is started. The program extracts discrete currents within a very short data window after the transient occurs as analysis samples. To accurately describe the intrinsic physical characteristics of this transient process, this invention uses a model of a linear combination of nth-order exponential functions for fitting.

[0015] Specifically, fitting the exponential function Satisfy the following formula:

[0016] in, The fitting order is... For the first Each amplitude coefficient, For the first A complex index, For the response of a second-order RLC system, the time is typically taken as... This will allow you to obtain a sufficiently accurate fit.

[0017] Step S2: Solve the fitted exponential function in the Z-domain based on the Pad approximation method to obtain the complex exponent of the fitted exponential function.

[0018] Solving for nonlinear parameters directly in the time domain is computationally extremely difficult and time-consuming, making it unsuitable for relay protection applications requiring high-speed responses. Therefore, this invention employs an efficient solution algorithm based on Padre approximation in the Z-domain. This algorithm cleverly transforms the nonlinear fitting problem in the time domain into an algebraic problem in the Z-domain.

[0019] Step S2 specifically includes: Fit the exponential function The problem of solving the problem is transformed into the Z-domain, and the definition is... , To represent the period, fit an exponential function. Z-domain expression for:

[0020] in, As the independent variable, as independent variable The One extreme value, , The numerator coefficient, , , The coefficient is the denominator coefficient. By using the Pad approximation method, The coefficients of the series expansion match the coefficients of the transient current signal after Z-transformation, thus establishing a system of linear equations about the denominator coefficients. Solving the system of linear equations yields the denominator coefficients. Then, the following characteristic equations are constructed and solved to obtain... :

[0021] By solving the above characteristic equation, we can obtain The root, that is .

[0022] Finally, the fitting exponential function is calculated by the inverse relationship .

[0023] Step S3, determining the fault threshold frequency according to the operating parameters of the low-voltage flexible DC system.

[0024] Wherein, 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:

[0025] Wherein, 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.

[0026] The characteristic roots of the above linear differential equation directly determine the mode of transient response. Since the equivalent inductance of the loop at the time of fault is usually much smaller than the equivalent inductance of the system at the time of normal operation, the natural oscillation frequency at the time of fault will increase significantly, so the fault threshold frequency of the present application is set as: .

[0027] Step S4, taking the complex exponential as the analysis object, the natural oscillation frequency of the low-voltage flexible DC system is calculated by the formula.

[0028] Wherein, step S4 specifically includes: When the condition 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 exponential and the second complex exponential , the solution of which is a damped oscillation, and must be a pair of conjugate complex numbers, and satisfy:

[0029]

[0030]

[0031] wherein, is the damping coefficient, denotes the imaginary unit, is the damped oscillation angular frequency; the natural oscillation frequency is calculated as:

[0032] When the condition is satisfied, 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, which are the first complex exponential and the second complex exponential In this case, and will be two negative real numbers, and satisfy:

[0033]

[0034] the natural oscillation frequency is calculated as: .

[0035] Step S5, taking the fault threshold frequency as the state circle radius, constructs a fault discrimination model based on the complex plane, in which the natural oscillation frequency is compared with the fault threshold frequency, and the real part of the complex exponential is combined to output the fault detection result of the low-voltage flexible DC system.

[0036] wherein, step S5 specifically comprises: defining a state circle on the complex plane with the origin as the center and the fault threshold frequency as the radius, and then outputting the fault detection result of the low-voltage flexible DC system by the following steps: if , the characteristic 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.

[0037] The criterion can effectively distinguish high-frequency fault transients from low-frequency normal operations, for example, the complex exponential solved under the load switching condition is projected onto the complex plane, and the projection point will fall inside the state circle, so it is judged as a non-fault condition, as shown in Figure 4 .

[0038] In a multi-terminal low-voltage flexible DC system, a fault in one line will cause a change in the voltage of the entire system, thus all healthy lines will also exhibit transient responses. These healthy line responses may also contain high-frequency components, leading to… If the threshold is exceeded, if only the criteria are used... This could lead to misjudgments by the protection device. This invention, through further in-depth analysis of complex exponents... The physical meaning of complex exponents can be used to solve this problem. real part This represents the decay or growth rate of a transient process.

[0039] In this embodiment, in the criterion Based on this, if the conditional expression is further satisfied... If so, it is determined to be a faulty line in a convergent high-frequency transient state. for The real part, if it further satisfies the condition... If so, it is determined to be a healthy line affected by a fault that exhibits divergent high-frequency transients.

[0040] For the faulty line itself, its transient current is the process of the DC-side capacitor discharging through the fault point. This is a process of energy consumption and gradual decay, manifesting as convergent oscillation. Therefore, the complex exponential current obtained by fitting its current signal... In fact, the actual value must be negative. Its projection point must lie in the left half of the complex plane. By fitting and analyzing the transient current of the faulted line, its complex exponential projection point will be located outside the state circle and in the left half of the plane, such as... Figure 5 and Figure 6 As shown.

[0041] For a healthy line, its transient response is a process caused by a drop in the common bus voltage due to a remote fault, resulting in the line absorbing more power from its connected power source, exhibiting divergent oscillations. Therefore, the complex exponential function obtained by fitting its current signal... In fact, the part must be positive. Its projection point must be located in the right half of the complex plane. By fitting and analyzing the transient current of a healthy circuit under fault conditions, its complex exponential projection point will be located outside the state circle but in the right half of the plane, such as... Figure 7 and Figure 8 As shown.

[0042] like If the feature points on the complex plane are located inside or on the state circle, then the low-voltage flexible DC system is determined to be in a normal state.

[0043] Therefore, the final criterion of the application is a double criterion and a non-ambiguous geometric rule on the complex plane. The rule comprehensively considers the position of the complex exponential projection point relative to the state circle (internal and external relationship) and the half plane to which it belongs on the complex plane (left and right relationship), and can comprehensively and accurately diagnose the state of all lines of the system.

[0044] In summary, the low-voltage flexible DC system fault detection method based on complex domain analysis according to the above-mentioned embodiments has the following beneficial effects: (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 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, fully meeting the speed requirements of fault detection. And the application discriminates based on the complex exponential of the signal, which has an intuitive physical explanation.

[0045] (2) The 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 in different noise environments, reducing the sensitivity of the criterion to noise.

[0046] (3) The 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 protection misoperation problem in multi-terminal systems.

[0047] The above-mentioned embodiments only express several embodiments of the 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 application, some modifications and improvements can be made, which are all within the protection scope of the application. Therefore, the protection scope of the patent of the 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.

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, 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 the time.

3. The method for fault detection of low voltage flexible direct current system based on complex domain analysis according to claim 2, characterized in that, 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 ​ 4. The method for fault detection of low voltage flexible direct current system based on complex domain analysis according to claim 3, characterized in that, 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: 。 5. The method for fault detection of low voltage flexible direct current system based on complex domain analysis according to claim 4, characterized in that, 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 。 6. The low voltage flexible direct current system fault detection method based on complex domain analysis according to claim 5, 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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