Direct current power distribution network t-connection line current differential protection method based on frequency domain bandwidth

Abstract

The application discloses a DC power distribution network T connection line current differential protection method based on a frequency domain bandwidth, which comprises the following steps: 1, decoupling the DC power distribution bipolar line by using phase-mode transformation, selecting a mode network for bipolar fault, and decoupling the capacitor between lines by using frequency domain transformation to establish a complex frequency domain network for analyzing differential current; 2, based on the complex frequency domain network, establishing a frequency response expression of differential current, and analyzing the amplitude-frequency characteristics of differential current according to the expression to obtain the distribution range of differential current spectrum under different fault types; 3, according to the amplitude-frequency characteristics of differential current, calculating the 3-dB bandwidth corresponding to the maximum amplitude attenuation to a specified proportion; and 4, comparing the calculated 3-dB bandwidth with a preset bandwidth threshold. The method has the advantages that the bandwidth can stably represent the system characteristics and improve the reliability of fault discrimination.

Description

Technical Field

[0001] This invention relates to the field of power system relay protection technology, and more specifically, to a method for differential protection of T-connected line current in DC distribution networks based on frequency domain bandwidth. Background Technology

[0002] Currently, driven by the "dual-carbon" strategic goal, large-scale integration of distributed generation has become an important trend in the development of new power systems. Compared with traditional AC distribution systems, DC distribution networks have advantages such as low transmission losses, high power quality, flexible control, and adaptability to the intermittency and volatility of distributed generation, and are widely used in urban distribution networks, industrial parks, data centers, and new energy microgrids. As the scale of photovoltaic, energy storage, and flexible DC equipment integration continues to expand, the network structure of DC distribution systems is becoming increasingly complex. To meet the flexible integration needs of distributed generation, the T-type integration method has become an important form of distributed generation integration into DC distribution networks due to its simple structure, convenient expansion, and lower construction costs.

[0003] However, the introduction of T-junctions alters the radial topology of traditional DC distribution networks, significantly changing fault current propagation paths, energy distribution patterns, and transient response characteristics, thus posing new challenges to system protection. Particularly during bipolar short-circuit faults, a low-impedance path forms between the positive and negative poles of the DC line, causing a rapid voltage drop. Multiple converters and distributed power sources simultaneously inject large-value fault currents into the fault point. Since DC systems widely employ power electronic devices for energy conversion, and these devices typically have low overcurrent tolerance, failure to promptly disconnect the fault current can lead to device damage, equipment shutdown, or even system-wide cascading failures. Therefore, establishing a fast, reliable, and applicable fault identification and protection mechanism suitable for complex topologies is crucial for ensuring the safe and stable operation of DC distribution systems.

[0004] Existing DC line protection methods mainly include current amplitude protection, voltage change rate protection, traveling wave protection, and differential protection. Among them, differential protection has advantages such as good selectivity and fast response speed, and is considered an important development direction for DC line protection. However, in DC distribution networks containing T-junction branches, existing differential protection methods still have the following technical problems:

[0005] T-junctions alter the distribution of fault current, causing it to split among multiple branches. This weakens the current amplitude characteristics relied upon by traditional differential protection, reducing protection sensitivity. Furthermore, the transient process of a bipolar short-circuit fault is extremely short-lived, leading to rapid decay of fault characteristics. Traditional time-domain protection methods struggle to extract stable and reliable fault criteria within this short timeframe, impacting protection response speed. With the increasing number of distributed power sources and flexible converters, multiple power sources simultaneously feed fault current to the fault point. Differences in transient responses generated by different control strategies result in dispersed fault characteristics, reducing the reliability of traditional protection methods. Simultaneously, reflection and refraction occur when the fault transient current propagates to the T-junction, causing variations in the propagation characteristics of different frequency components. This redistributes the fault current spectrum energy, affecting the performance of traditional protection methods based on fixed-frequency characteristics. Different fault locations correspond to different line propagation paths and attenuation processes, resulting in significant locational correlation in the fault current spectrum characteristics, increasing the difficulty of protection setting. Under short-line and multi-branch structures, the fault transient enters the attenuation phase before fully unfolding, leading to insufficient effective information within the traditional frequency domain analysis window and affecting fault identification accuracy. When a fault occurs near a T-junction, transient components from different directions may cause spectral reconstruction at the protection measurement point, rendering the characteristic laws upon which traditional protection relies ineffective. Existing research mainly focuses on the amplitude, polarity changes, and local frequency energy characteristics of the fault current, while insufficient research is conducted on the spectral bandwidth expansion law after a fault occurs and its correlation with characteristics within and outside the fault zone. The effective information contained in the initial stage of a fault has not been fully explored. Especially in DC distribution systems with T-junction branches, the fault transient spectral bandwidth not only reflects the fault energy release process but is also closely related to the fault location, topology, and fault current propagation path. Current protection methods have not established an effective correlation mechanism between the fault spectral bandwidth and the discrimination between faults within and outside the line zone, making it difficult to simultaneously meet the requirements of protection operation speed, reliability, sensitivity, and adaptability. Summary of the Invention

[0006] The main objective of this invention is to provide a method for differential protection of T-connected line current in DC distribution networks based on frequency domain bandwidth, so as to solve at least one technical problem in the prior art.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for differential protection of T-connected line current in a DC distribution network based on frequency domain bandwidth is provided, comprising:

[0008] Step 1: Line decoupling and complex frequency domain network modeling: Decouple the bipolar DC distribution line using phase mode transformation, select a single-mode network for bipolar faults, and decouple the capacitance between the lines using frequency domain transformation to establish a complex frequency domain network for analyzing differential current.

[0009] Step 2: Frequency response function construction and spectrum characteristic analysis: Based on the complex frequency domain network, establish the frequency response expression of the differential current, and analyze the amplitude-frequency characteristics of the differential current accordingly to obtain the distribution range of the differential current spectrum under different fault types;

[0010] Step 3: 3-dB bandwidth feature extraction: Based on the amplitude-frequency characteristics of the differential current, calculate the 3-dB bandwidth corresponding to the differential current signal when the maximum amplitude attenuates to a specified ratio, and use it as a feature quantity characterizing the spectrum distribution range.

[0011] Step 4: Protection Criterion Construction and Fault Identification: Compare the 3-dB bandwidth calculated in Step 3 with the preset bandwidth threshold. If the 3-dB bandwidth is less than the preset bandwidth threshold, it is determined that an inter-pole fault has occurred within the zone, and a trip command is executed. If the 3-dB bandwidth is greater than or equal to the preset bandwidth threshold, it is determined that an external fault has occurred, and the protection does not operate.

[0012] Preferably, phase mode transformation is used to decouple the bipolar DC distribution line, specifically using the following transformation matrix:

[0013]

[0014] Where, x p x n For the positive and negative electrical quantities in the phase domain, x0 and x1 represent the zero and line-mode components, respectively.

[0015] Preferably, the complex frequency domain network includes: a complex frequency domain equivalent one-mode network constructed based on the node admittance matrix during intra-area faults, which includes the equivalent inductance, resistance, capacitance of MMC and the equivalent capacitance of T-connected branches; and a complex frequency domain equivalent one-mode network constructed based on the node admittance matrix during extra-area faults, which includes the line unit parameters and the equivalent capacitance of T-connected branches.

[0016] Preferably, the frequency response expression of the differential current is established using a complex frequency domain network, and its amplitude-frequency characteristics are analyzed accordingly. The admittance matrix of the fault network nodes in the region is as follows:

[0017]

[0018] In the formula, Let k represent the node voltages of node a, node b, and node m, respectively. These represent the node currents injected into node k, node a, node b, and node m, respectively. These represent the node self-admittances corresponding to injected node k, node a, node b, and node m, respectively. Indicates the admittance of the series branch of the line. This represents the admittance corresponding to the line's distributed capacitance to ground;

[0019] in,

[0020]

[0021] In the formula, The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; represents the fault transition resistance; s represents the Laplace operator.

[0022] Preferably, the differential current expression in the complex frequency domain of the fault within the zone is:

[0023]

[0024] In the formula, This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; Let k and m represent the node voltages, respectively.

[0025] make The frequency domain response is:

[0026]

[0027] In the formula, Let k and m represent the node voltages, respectively. This is the equivalent resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; This refers to the capacitors of the MMC submodule and the equivalent capacitance on the DC side.

[0028] Preferably, the admittance matrix of the faulty network nodes outside the region is:

[0029]

[0030] In the formula, Let k represent the node voltages of node a, node b, and node m, respectively. These represent the node currents injected into node k, node a, node b, and node m, respectively. These represent the node self-admittances corresponding to injected node k, node a, node b, and node m, respectively. Indicates the admittance of the series branch of the line. This represents the admittance corresponding to the line's distributed capacitance to ground;

[0031] in,

[0032]

[0033] In the formula, The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; represents the fault transition resistance; s represents the Laplace operator.

[0034] Preferably, the differential current expression in the complex frequency domain of an external fault is:

[0035]

[0036] make The frequency domain response is:

[0037]

[0038] In the formula, These represent the node voltages at nodes a and b, respectively. The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This is the equivalent distributed capacitance of the line; This represents the equivalent capacitance to ground of the T-connected branch.

[0039] Preferably, the 3-dB bandwidth is analyzed and calculated when faults occur inside or outside the protection zone to construct a protection criterion. To quantitatively characterize the differences in the aforementioned spectral distribution range, the 3-dB bandwidth is introduced as a criterion feature. The 3-dB bandwidth refers to the bandwidth at which the signal amplitude decays to its maximum value in the amplitude-frequency response curve of the system or signal. The bandwidth corresponding to a multiple of 1;

[0040] During an in-zone fault, the peak differential current is:

[0041]

[0042] In the formula, Let k and m represent the node voltages, respectively. This is the equivalent resistance after MMC conversion;

[0043] When an external fault occurs, the peak differential current is:

[0044]

[0045] In the formula, These represent the node voltages at nodes a and b, respectively. This is the equivalent series resistance per unit length of the line.

[0046] Preferably, based on the differential current frequency response function and its peak value expression, the 3-dB bandwidth corresponding to the fault differential current inside and outside the fault zone is calculated:

[0047]

[0048]

[0049] in, , for , The difference between characteristic roots; The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; This indicates the fault transition resistance.

[0050] The technical solution of this invention has the following technical effects:

[0051] (1) This invention constructs protection criteria based on the system frequency response mechanism, transforms the fault identification problem into a frequency response bandwidth characteristic identification problem, and breaks through the limitations of traditional differential protection which mainly relies on current amplitude, polarity or fixed frequency band energy characteristics, providing a new analysis and implementation approach for fault protection of DC distribution networks with T-connection branches.

[0052] (2) By establishing a complex frequency domain model involving line resistance, inductance, capacitance and MMC equivalent inductance, the quantitative relationship between differential current frequency response characteristics and system parameters is revealed, which provides clear physical mechanism support for protection criteria and improves the interpretability and theoretical rigor of protection actions.

[0053] (3) This invention discovers that the differential current frequency response functions corresponding to faults within and outside the fault zone differ fundamentally in the 3-dB bandwidth. Specifically, the frequency response energy corresponding to faults within the fault zone is mainly concentrated within a limited frequency range, exhibiting a clear narrowband characteristic; while faults outside the fault zone are affected by the line impedance network and the frequency selectivity of the external system, resulting in a wider frequency response coverage and exhibiting broadband characteristics. Utilizing this difference to construct protection criteria can effectively distinguish between faults within and outside the fault zone.

[0054] (4) Since the 3-dB bandwidth reflects the overall distribution range of frequency response rather than a specific frequency point or fixed frequency band energy, the protection criterion does not depend on the specific peak position of the spectrum. Even if the fault spectrum shifts with the fault location, operating mode and system parameters, it can still maintain a stable fault discrimination capability and improve the protection adaptability.

[0055] (5) The frequency response characteristics of the differential current and the line parameters (resistance, inductance, capacitance) are analyzed. Even when these parameters change, the bandwidth can still stably characterize the system characteristics, thereby improving the reliability of fault diagnosis. The proposed protection method can withstand a 50Ω transition resistance and is not affected by 20dB white noise.

[0056] (6) The bandwidth criterion proposed in this invention essentially reflects the attenuation law of the system frequency response. Its characteristic formation process is determined by the line structure and fault location, rather than by the absolute amplitude of the fault current. Therefore, it has strong robustness to the transition resistance. It can still maintain reliable operation under the condition of 50Ω transition resistance, which improves the ability to identify high-resistance faults.

[0057] (7) Since the extraction process of the 3-dB bandwidth is based on the overall trend of frequency response change, while random noise mainly manifests as local spectral disturbances, this invention can effectively reduce the impact of noise on the protection results. It can still accurately identify faults under 20dB white noise conditions, thus improving the anti-interference capability in engineering application environments. Attached Figure Description

[0058] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0059] Figure 1 A simplified topology diagram of a DC distribution system including T-connected branches is shown, based on the frequency domain bandwidth-based differential protection method for DC distribution network T-connected line current according to the present invention.

[0060] Figure 2 It shows Figure 1 An equivalent one-mode network view of the faulted line within the area in the frequency domain bandwidth-based differential protection method for T-connected line current in DC distribution network.

[0061] Figure 3 It shows Figure 1 An equivalent one-mode network view of the faulted line outside the zone in the DC distribution network T-connection line current differential protection method based on frequency domain bandwidth.

[0062] Figure 4 It shows Figure 1 The equivalent one-mode complex frequency domain network view of the faulted line in the area of ​​the DC distribution network T-connection line current differential protection method based on frequency domain bandwidth.

[0063] Figure 5 It shows Figure 1 An equivalent one-mode complex frequency domain network view of the faulted line outside the zone in the DC distribution network T-connection line current differential protection method based on frequency domain bandwidth.

[0064] Figure 6 It shows Figure 1 A spectrum view of the inter-pole fault differential current in the DC distribution network based on frequency domain bandwidth differential protection method for T-connected line current.

[0065] Figure 7 It shows Figure 1 The spectrum view of the differential current of the inter-pole fault in the DC distribution network based on frequency domain bandwidth. Detailed Implementation

[0066] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0067] like Figures 1 to 7As shown, this embodiment of the invention provides a method for differential protection of T-connected DC distribution lines based on frequency domain bandwidth, including: Step 1: Line decoupling and complex frequency domain network modeling: Decoupling the bipolar DC distribution lines is performed using phase mode transformation. A single-mode network is selected for bipolar faults, and the capacitance between lines is decoupled using frequency domain transformation to establish a complex frequency domain network for analyzing the differential current; Step 2: Frequency response function construction and spectral characteristic analysis: Based on the complex frequency domain network, the frequency response expression of the differential current is established, and the amplitude-frequency characteristics of the differential current are analyzed accordingly to obtain the differential current spectrum under different fault types. Distribution range; Step 3: 3-dB bandwidth feature extraction: Based on the amplitude-frequency characteristics of the differential current, calculate the 3-dB bandwidth corresponding to the differential current signal when the maximum amplitude attenuates to a specified proportion, as a feature quantity characterizing the spectrum distribution range; Step 4: Protection criterion construction and fault identification: Compare the 3-dB bandwidth calculated in Step 3 with a preset bandwidth threshold. If the 3-dB bandwidth is less than the preset bandwidth threshold, it is determined that an inter-pole fault has occurred within the zone, and a trip command is executed; if the 3-dB bandwidth is greater than or equal to the preset bandwidth threshold, it is determined that an external fault has occurred, and the protection does not operate.

[0068] This invention analyzes the relationship between the frequency response characteristics of differential current and line parameters (resistance, inductance, capacitance, and MMC equivalent inductance), revealing a fundamental difference between in-zone and out-of-zone faults in the 3-dB bandwidth. In-zone faults exhibit narrow-band characteristics, while out-of-zone faults exhibit wide-band characteristics. Based on this, a bandwidth criterion is constructed to achieve rapid fault identification. The frequency response is obtained through phase mode transformation and complex frequency domain modeling. The proposed protection method can withstand a 50Ω transition resistance and is unaffected by 20dB white noise. By exploring the transient frequency spectrum bandwidth characteristics and their variation patterns of faults, rapid fault identification and accurate differentiation are achieved, thereby improving the fault protection performance and power supply reliability of DC distribution systems.

[0069] This invention utilizes phase-mode transformation to decouple bipolar DC power distribution lines, and selects a single-mode network for bipolar fault analysis; it uses frequency domain transformation to decouple inter-line capacitances and establishes a complex frequency domain network for analysis; it uses the complex frequency domain network to establish the frequency response expression of the differential current and analyzes its amplitude-frequency characteristics accordingly; it analyzes and calculates the 3-dB bandwidth for faults inside and outside the zone, and constructs a protection criterion. If the bandwidth is less than the threshold, it is determined that an inter-pole fault has occurred inside the zone; otherwise, it is determined that an fault has occurred outside the zone.

[0070] Phase mode transformation is used to decouple the DC distribution bipolar lines when faults occur inside and outside the fault zone. The phase mode transformation matrix is ​​as follows:

[0071]

[0072] Where, x p x nFor the positive and negative electrical quantities in the phase domain, x0 and x1 represent the zero and line-mode components, respectively.

[0073] The analog network of faulty lines inside and outside the area is Figure 2 As shown: Equivalent one-mode network of the faulty line within the area. Figure 3 For faulty lines outside the area, the equivalent one-mode network is included. , and These represent the resistance, inductance, and capacitance values ​​per unit length of the circuit. This is the equivalent capacitance of the T-connected branch.

[0074] This invention utilizes frequency domain transformation to decouple inter-line capacitances and establishes a complex frequency domain network for analysis. The equivalent one-mode complex frequency domain network of the line under fault conditions inside and outside the fault zone is as follows: Figure 4 As shown: The equivalent one-mode complex frequency domain network of the faulty line within the area. Figure 5 As shown, the faulty line outside the area is equivalent to a one-mode complex frequency domain network.

[0075] This invention utilizes a complex frequency domain network to establish the frequency response expression of the differential current, and analyzes its amplitude-frequency characteristics accordingly. The admittance matrix of the fault network nodes within the region is as follows:

[0076]

[0077] In the formula, Let k represent the node voltages of node a, node b, and node m, respectively. These represent the node currents injected into node k, node a, node b, and node m, respectively. These represent the node self-admittances corresponding to injected node k, node a, node b, and node m, respectively. Indicates the admittance of the series branch of the line. This represents the admittance corresponding to the line's distributed capacitance to ground.

[0078] in,

[0079]

[0080] In the formula, The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; represents the fault transition resistance; s represents the Laplace operator.

[0081] The differential current expression in the complex frequency domain of the fault within the zone is:

[0082]

[0083] In the formula, This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; Let k and m represent the node voltages, respectively.

[0084] make The frequency domain response is:

[0085]

[0086] In the formula, Let k and m represent the node voltages, respectively. This is the equivalent resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; This refers to the capacitors of the MMC submodule and the equivalent capacitance on the DC side.

[0087] Similarly, the admittance matrix of the faulty network nodes outside the region is:

[0088]

[0089] In the formula, Let k represent the node voltages of node a, node b, and node m, respectively. These represent the node currents injected into node k, node a, node b, and node m, respectively. These represent the node self-admittances corresponding to injected node k, node a, node b, and node m, respectively. Indicates the admittance of the series branch of the line. This represents the admittance corresponding to the line's distributed capacitance to ground.

[0090] in,

[0091]

[0092] In the formula, The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; represents the fault transition resistance; s represents the Laplace operator.

[0093] The differential current expression in the complex frequency domain of an external fault is:

[0094]

[0095] make The frequency domain response is:

[0096]

[0097] In the formula, These represent the node voltages at nodes a and b, respectively. The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This is the equivalent distributed capacitance of the line; This represents the equivalent capacitance to ground of the T-connected branch.

[0098] As can be seen from the above frequency response expression, the amplitude of the differential current is a function of frequency, and its amplitude exhibits a significant non-uniform distribution characteristic as it changes with frequency. When the interaction between inductive and capacitive reactance reaches a certain equilibrium, the system has a characteristic frequency, causing the differential current amplitude to reach its maximum value near this frequency. When the frequency deviates from this characteristic frequency, the amplitude gradually decreases, resulting in a concentrated distribution characteristic of the differential current's frequency response within a certain frequency range. The introduction of the T-connected branch capacitor alters the system's equivalent capacitive reactance distribution, thus affecting the variation of the reactance term in the differential current's frequency response function. This further leads to changes in its characteristic frequency and spectral distribution range, easily resulting in multiple characteristic frequencies in the frequency response, thus causing the spectral distribution to exhibit dispersed characteristics. For energy criteria based on fixed frequency band divisions, the discrimination result will shift with changes in system parameters, leading to a decrease in the adaptability and stability of the criterion.

[0099] This invention analyzes and calculates the 3-dB bandwidth when there are faults inside or outside the calculation area, and constructs protection criteria.

[0100] To quantitatively characterize the differences in the aforementioned spectral distribution ranges, a 3-dB bandwidth is introduced as a criterion feature. The 3-dB bandwidth refers to the bandwidth at which the signal amplitude decays to its maximum value in the amplitude-frequency response curve of a system or signal. The bandwidth corresponding to a multiple of 1.

[0101] During an in-zone fault, the peak differential current is:

[0102]

[0103] In the formula, Let k and m represent the node voltages, respectively. This is the equivalent resistance after MMC conversion.

[0104] When an external fault occurs, the peak differential current is:

[0105]

[0106] In the formula, These represent the node voltages at nodes a and b, respectively. This is the equivalent series resistance per unit length of the line.

[0107] Based on the differential current frequency response function and its peak value expression, the 3-dB bandwidth corresponding to the fault differential current inside and outside the fault zone is calculated:

[0108]

[0109]

[0110] in, , for , The difference between characteristic roots; The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; This indicates the fault transition resistance.

[0111] The variation in the spectral characteristics of the system differential current is closely related to the circuit parameters, with the bandwidth primarily influenced by the equivalent inductance, resistance, and capacitance parameters. In medium-voltage DC distribution networks, the parameters of each component exhibit significant differences in magnitude. Typically, the equivalent inductance of the MMC converter is 2-3 orders of magnitude larger than the line unit inductance. Simultaneously, the equivalent capacitance of the MMC converter, even when connected in parallel with the equivalent capacitance of the T-connected branch and the line unit-to-ground capacitance, still significantly dominates, generally being 3-4 orders of magnitude larger than the line-side capacitance. In contrast, there is no significant order of magnitude difference between the equivalent resistance of the MMC converter and the line unit resistance. Therefore, when the fault occurs within the line protection zone, the frequency response function corresponding to the differential current has a lower cutoff frequency, resulting in a smaller 3-dB bandwidth. Conversely, when the fault occurs outside the protection zone, due to changes in the system equivalent parameters, the cutoff frequency of the frequency response function increases, corresponding to a larger 3-dB bandwidth. This difference stems from the influence of the system equivalent parameters on the pole distribution of the frequency response function. Within the system parameter range corresponding to this embodiment, the 3-dB bandwidth threshold is selected as 1000Hz.

[0112] In summary, specifically:

[0113] Based on the phase mode transformation, the DC distribution bipolar lines for faults occurring inside and outside the fault zone are decoupled respectively, and a one-mode network of the fault lines inside and outside the fault zone is established. The phase mode transformation matrix is:

[0114]

[0115] Where, x p x n For the positive and negative electrical quantities in the phase domain, x0 and x1 represent the zero and line-mode components, respectively.

[0116] Frequency domain transformation is used to decouple the capacitance between lines, establishing a complex frequency domain network. The frequency response expression of the differential current is then established using this complex frequency domain network, and its amplitude-frequency characteristics are analyzed accordingly. The expression for the differential current in the complex frequency domain under fault conditions within the fault zone is as follows:

[0117]

[0118] In the formula, Let k and m represent the node voltages, respectively. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; This refers to the capacitors of the MMC submodule and the equivalent capacitance on the DC side.

[0119] make The frequency domain response is:

[0120]

[0121] In the formula, Let k and m represent the node voltages, respectively. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; This refers to the capacitors of the MMC submodule and the equivalent capacitance on the DC side.

[0122] Similarly, the expression for the differential current in the complex frequency domain under an external fault is:

[0123]

[0124] In the formula, These represent the node voltages at nodes a and b, respectively. This represents the admittance corresponding to the line's distributed capacitance to ground; This represents the equivalent capacitance to ground of the T-connected branch.

[0125] make The frequency domain response is:

[0126]

[0127] In the formula, These represent the node voltages at nodes a and b, respectively. The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This is the equivalent distributed capacitance of the line; This represents the equivalent capacitance to ground of the T-connected branch.

[0128] As can be seen from the above frequency response expression, the amplitude of the differential current is a function of frequency, and its amplitude exhibits a significant non-uniform distribution characteristic as it changes with frequency. When the interaction between inductive and capacitive reactance reaches a certain equilibrium, the system has a characteristic frequency, causing the differential current amplitude to reach its maximum value near this frequency. When the frequency deviates from this characteristic frequency, the amplitude gradually decreases, resulting in a concentrated distribution characteristic of the differential current's frequency response within a certain frequency range. The introduction of the T-connected branch capacitor alters the system's equivalent capacitive reactance distribution, thus affecting the variation of the reactance term in the differential current's frequency response function. This further leads to changes in its characteristic frequency and spectral distribution range, easily resulting in multiple characteristic frequencies in the frequency response, thus causing the spectral distribution to exhibit dispersed characteristics. For energy criteria based on fixed frequency band divisions, the discrimination result will shift with changes in system parameters, leading to a decrease in the adaptability and stability of the criterion.

[0129] The 3-dB bandwidth was analyzed and calculated for faults inside and outside the designated area to construct protection criteria. To quantitatively characterize the differences in the aforementioned spectral distribution range, 3-dB bandwidth was introduced as a criterion feature. 3-dB bandwidth refers to the bandwidth at which the signal amplitude decays to its maximum value in the amplitude-frequency response curve of the system or signal. The bandwidth corresponding to a multiple of 1.

[0130] During an in-zone fault, the peak differential current is:

[0131]

[0132] In the formula, Let k and m represent the node voltages, respectively. Equivalent resistance after MMC conversion

[0133] When an external fault occurs, the peak differential current is:

[0134]

[0135] In the formula, These represent the node voltages at nodes a and b, respectively. Equivalent series resistance per unit length of the line

[0136] Based on the differential current frequency response function and its peak value expression, the 3-dB bandwidth corresponding to the fault differential current inside and outside the fault zone is calculated:

[0137]

[0138]

[0139] in, , for , The difference between characteristic roots; The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; This indicates the fault transition resistance.

[0140] When a fault occurs within the line protection zone, the frequency response function corresponding to the differential current has a lower cutoff frequency, resulting in a smaller 3-dB bandwidth. However, when the fault occurs outside the protection zone, due to changes in the system's equivalent parameters, the cutoff frequency of the frequency response function increases, resulting in a larger 3-dB bandwidth. This difference stems from the influence of the system's equivalent parameters on the pole distribution of the frequency response function. Within the system parameter range corresponding to this embodiment, the 3-dB bandwidth threshold is selected as 1000Hz.

[0141] This invention discloses a method for differential protection of T-connected line current in DC distribution networks based on frequency domain bandwidth: Figure 1 A simplified topology diagram of a DC power distribution system including T-connected branches.

[0142] When an inter-pole fault occurs within the line zone, the 3-dB bandwidth of the differential current is mainly related to the equivalent inductance, resistance, and capacitance of the MMC converter. When an inter-pole fault occurs outside the line zone, the bandwidth of the differential current is mainly related to the equivalent capacitance, inductance, and resistance of the line, as well as the equivalent inductance of the T-connected branch. The two are different in magnitude. Therefore, there are significant differences in the differential current-based criteria for inter-pole faults within and outside the line zone.

[0143] The above characteristics indicate that there is a significant difference in the 3-dB frequency domain bandwidth of the fault time difference flow between the area and outside the area, which can be used to form a protection criterion.

[0144] To verify the application performance of the proposed protection method, a simulation platform was built on the PSCAD platform. Figure 1 A simplified topology diagram of a DC power distribution system including T-junction branches. Signal acquisition is installed at both ends K and M, with a sampling frequency of 10kHz.

[0145] The proposed protection process steps are as follows:

[0146] 1) Decouple the DC distribution bipolar line and each capacitor by using phase mode transformation and frequency domain transformation, and calculate the complex frequency domain expression of the differential current inside and outside the region;

[0147] 2) Establish the frequency response expression of the differential current using a complex frequency domain network, and analyze its amplitude-frequency characteristics accordingly;

[0148] 3) Analyze and calculate the 3-dB bandwidth when there is a fault inside or outside the zone, and construct a protection criterion. If the bandwidth is less than the threshold, it is determined that an inter-pole fault has occurred inside the zone; otherwise, it is determined that the fault is outside the zone.

[0149] Simulation tests were conducted using PSCAD / EMTDC to verify the relay protection performance at different fault locations.

[0150] Figure 6 and 7The results of the differential current spectrum diagram for faults between poles inside and outside the protection zone are shown. When the fault is inside the protection zone, the 3-dB bandwidth of the differential current signal is 160.37Hz, which is greater than the threshold of 1000Hz, so the protection criterion is correct. When the fault is outside the protection zone, the 3-dB bandwidth of the differential current signal is 4351.67Hz, which is less than the threshold of 1000Hz, so the protection does not operate.

[0151] The above results were correctly identified.

[0152] This invention elevates the fault criterion from statistical characteristics of signal energy to structural characteristics of the system's frequency response. Based on a complex frequency domain network, the differential current frequency response function is derived, thereby obtaining a 3-dB bandwidth. Essentially, this bandwidth is a structural characteristic parameter of the system's frequency response function. This bandwidth originates from the analytical expression of the differential current and is determined by the line parameters (R, L, C) and the MMC equivalent inductance, belonging to the system's intrinsic characteristics. The bandwidth in this application is an analytical quantity determined by the system transfer function, not a statistical quantity obtained through signal decomposition. The prerequisites for implementing the 3-dB bandwidth criterion in this application are: phase-mode transformation decoupling, construction of a single-mode network, establishment of a complex frequency domain model, derivation of the differential current analytical expression, obtaining the frequency response function, and calculation of the 3-dB bandwidth. The 3-dB bandwidth is derived based on complete system modeling, not through direct signal processing.

[0153] Unlike existing DC distribution network protection methods that primarily rely on current amplitude, current direction, traveling wave characteristics, or fixed frequency band energy characteristics, this invention starts from the system frequency response mechanism, establishes a complex frequency domain network model including line resistance, inductance, capacitance, and MMC equivalent inductance, derives the frequency response expression of the differential current, and utilizes the 3-dB bandwidth of the frequency response to construct a fault criterion, achieving rapid identification of bipolar faults in DC distribution networks with T-connected branches. This method transforms the traditional protection approach based on local signal characteristics into one based on the overall frequency domain structure characteristics of the system, elevating the fault identification object from a simple fault current signal to the network frequency response characteristics under fault conditions. It theoretically constructs a mapping relationship between "network structure—frequency response bandwidth—fault region," providing a new technical approach for DC distribution network protection.

[0154] This invention, through complex frequency domain analysis, reveals a fundamental difference in the differential current frequency response function between in-zone and out-of-zone faults within a 3-dB bandwidth. Under in-zone fault conditions, the system frequency response energy is primarily concentrated within a finite frequency range, exhibiting a distinctly narrowband characteristic. Under out-of-zone fault conditions, the fault current passes through more line parameters and network nodes, resulting in a wider frequency response coverage and broadband characteristics. The bandwidth criterion constructed based on this principle does not depend on the absolute amplitude of the fault current, the location of the spectral peak, or fixed frequency band divisions; instead, it utilizes the overall distribution characteristics of the frequency response to achieve fault identification. Therefore, even with changes in system operation, fluctuations in distributed power output, alterations in line parameters, or spectral shifts, the proposed criterion maintains stable fault identification capabilities, significantly improving the adaptability and robustness of the protection method.

[0155] Furthermore, this invention introduces MMC dynamic characteristics into the differential protection frequency response analysis process for the first time, enabling the frequency response function to simultaneously reflect the combined effects of line parameters, converter parameters, and network topology. Since the 3-dB bandwidth is essentially determined by the distribution of system poles and zeros, which are in turn influenced by both network topology and parameter distribution, the bandwidth characteristic proposed in this invention actually reflects the inherent structural properties of the system under fault conditions. Compared to traditional protection methods that rely on instantaneous sampled values ​​or local frequency components, this invention utilizes the overall structure of the system frequency response for fault discrimination, exhibiting stronger physical interpretability and higher theoretical completeness.

[0156] Furthermore, the bandwidth criterion proposed in this invention is derived from the overall attenuation law of the system's frequency response, rather than the local characteristics of a specific frequency point or band. Therefore, it effectively avoids the protection performance degradation caused by frequency drift, band mismatch, and parameter changes. Since the bandwidth characteristics reflect the spectral distribution range rather than the magnitude of the spectral amplitude, it maintains a high identification capability even under high-impedance fault conditions. Simultaneously, random noise mainly affects local frequency components and is unlikely to alter the overall system frequency response bandwidth. Therefore, this invention exhibits excellent noise immunity, having been verified to withstand 50Ω transition resistance and 20dB white noise interference, thus improving protection reliability in engineering application environments.

[0157] This invention also transforms the T-connection branch structure, traditionally considered a disadvantage in protection systems, into usable discriminative information. In traditional protection methods, T-connections lead to fault current shunting, spectral distortion, and difficulties in protection setting. However, this invention utilizes the impact of the T-connection structure on frequency response bandwidth to establish fault criteria. This transforms network topology changes from merely constraints in protection design into crucial evidence for fault identification, achieving a technological shift from "eliminating topology influences" to "utilizing topology characteristics." This concept breaks through the traditional design paradigm of DC line protection and possesses strong innovation.

[0158] In summary, this invention not only proposes a novel bipolar fault protection method but also establishes for the first time the intrinsic relationship between the differential current frequency response bandwidth and the fault region, realizing the transformation from amplitude criteria to structural criteria, from local signal criteria to system characteristic criteria, and from time-domain analysis to frequency-domain structural analysis. The proposed method has clear physical mechanism support, excellent resistance to parameter fluctuations, good resistance to transition resistance, and noise immunity, and has the potential for further application in multi-terminal DC distribution networks, complex T-connection networks, and high-proportion renewable energy access scenarios.

[0159] As can be seen from the above description, the embodiments of the present invention achieve the following technical effects:

[0160] Analyzing the relationship between the differential current frequency response characteristics and line parameters (resistance, inductance, capacitance, and MMC equivalent inductance), we found a fundamental difference in the 3-dB bandwidth between faults within and outside the fault zone. Faults within the zone exhibit narrow-band characteristics, while faults outside the zone exhibit wide-band characteristics. Based on this, a bandwidth criterion is constructed to achieve rapid fault identification. The frequency response is obtained through phase mode transformation and complex frequency domain modeling. Since the 3-dB bandwidth reflects the overall distribution range of the frequency response, its essence is determined by the system frequency response function and does not depend on fixed frequency band division. Therefore, even if the spectrum changes, the bandwidth can still stably characterize the system characteristics, thereby improving the reliability of fault identification. The proposed protection method can withstand a 50Ω transition resistance and is unaffected by 20dB white noise.

[0161] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for differential protection of T-connected line current in DC distribution network based on frequency domain bandwidth, characterized in that, include: Step 1: Line decoupling and complex frequency domain network modeling: Decouple the bipolar DC distribution line using phase mode transformation, select a single-mode network for bipolar faults, and decouple the capacitance between the lines using frequency domain transformation to establish a complex frequency domain network for analyzing differential current. Step 2: Frequency response function construction and spectrum characteristic analysis: Based on the complex frequency domain network, establish the frequency response expression of the differential current, and analyze the amplitude-frequency characteristics of the differential current accordingly to obtain the distribution range of the differential current spectrum under different fault types; Step 3: 3-dB bandwidth feature extraction: Based on the amplitude-frequency characteristics of the differential current, calculate the 3-dB bandwidth corresponding to the differential current signal when the maximum amplitude attenuates to a specified ratio, and use it as a feature quantity characterizing the spectrum distribution range. Step 4: Protection criterion construction and fault identification: Compare the 3-dB bandwidth calculated in Step 3 with the preset bandwidth threshold. If the 3-dB bandwidth is less than the preset bandwidth threshold, it is determined that an inter-pole fault has occurred in the zone, and a trip command is executed. If the 3-dB bandwidth is greater than or equal to the preset bandwidth threshold, it is determined to be an external fault, and the protection will not operate.

2. The differential protection method for T-connected line current in DC distribution network based on frequency domain bandwidth as described in claim 1, characterized in that, In step 1, the bipolar DC power distribution line is decoupled using phase mode transformation, specifically using the following transformation matrix: ； Where, x p x n For the positive and negative electrical quantities in the phase domain, x0 and x1 represent the zero and line-mode components, respectively.

3. The method for differential protection of T-connected DC distribution network current based on frequency domain bandwidth as described in claim 1, characterized in that, In step 1, the complex frequency domain network includes: a complex frequency domain equivalent one-mode network constructed based on the node admittance matrix for faults within the region, which includes the equivalent inductance, resistance, capacitance of MMC and the equivalent capacitance of T-connected branches; and a complex frequency domain equivalent one-mode network constructed based on the node admittance matrix for faults outside the region, which includes the line unit parameters and the equivalent capacitance of T-connected branches.

4. The method for differential protection of T-connected DC distribution network current based on frequency domain bandwidth as described in claim 1, characterized in that, The frequency response expression of the differential current is established using a complex frequency domain network, and its amplitude-frequency characteristics are analyzed accordingly. The admittance matrix of the fault network nodes in the region is as follows: ； In the formula, Let k represent the node voltages of node a, node b, and node m, respectively. These represent the node currents injected into node k, node a, node b, and node m, respectively. These represent the node self-admittances corresponding to injected node k, node a, node b, and node m, respectively. Indicates the admittance of the series branch of the line. This represents the admittance corresponding to the line's distributed capacitance to ground; in, ； In the formula, The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; represents the fault transition resistance; s represents the Laplace operator.

5. The method for differential protection of T-connected DC distribution network current based on frequency domain bandwidth as described in claim 1, characterized in that, The differential current expression in the complex frequency domain of the fault within the zone is: ； In the formula, This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; Let k and m represent the node voltages, respectively. make The frequency domain response is: ； In the formula, Let k and m represent the node voltages, respectively. This is the equivalent resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; This refers to the capacitors of the MMC submodule and the equivalent capacitance on the DC side.

6. The method for differential protection of T-connected line current in DC distribution network based on frequency domain bandwidth as described in claim 1, characterized in that, The admittance matrix of the faulty network nodes outside the region is: ； In the formula, Let k represent the node voltages of node a, node b, and node m, respectively. These represent the node currents injected into node k, node a, node b, and node m, respectively. These represent the node self-admittances corresponding to injected node k, node a, node b, and node m, respectively. Indicates the admittance of the series branch of the line. This represents the admittance corresponding to the line's distributed capacitance to ground; in, ； In the formula, The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; represents the fault transition resistance; s represents the Laplace operator.

7. The method for differential protection of T-connected DC distribution network current based on frequency domain bandwidth as described in claim 1, characterized in that, The differential current expression in the complex frequency domain of an external fault is: ； make The frequency domain response is: ； In the formula, These represent the node voltages at nodes a and b, respectively. The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This is the equivalent distributed capacitance of the line; This represents the equivalent capacitance to ground of the T-connected branch.

8. The method for differential protection of T-connected DC distribution network current based on frequency domain bandwidth as described in claim 1, characterized in that, The 3-dB bandwidth was analyzed and calculated for faults inside and outside the protection zone to construct protection criteria. To quantitatively characterize the differences in the aforementioned spectral distribution range, the 3-dB bandwidth was introduced as a criterion feature. The 3-dB bandwidth refers to the bandwidth at which the signal amplitude decays to its maximum value in the amplitude-frequency response curve of the system or signal. The bandwidth corresponding to a multiple of 1; During an in-zone fault, the peak differential current is: ； In the formula, Let k and m represent the node voltages, respectively. This is the equivalent resistance after MMC conversion; When an external fault occurs, the peak differential current is: ； In the formula, These represent the node voltages at nodes a and b, respectively. This is the equivalent series resistance per unit length of the line.

9. The method for differential protection of T-connected DC distribution network current based on frequency domain bandwidth as described in claim 1, characterized in that, Based on the differential current frequency response function and its peak value expression, the 3-dB bandwidth corresponding to the fault differential current inside and outside the fault zone is calculated: ； ； in, , for , The difference between characteristic roots; The equivalent series resistance per unit length of the line; The equivalent series inductance per unit length of the line; This refers to the series impedance of the line. This is the equivalent distributed capacitance of the line; This represents the equivalent admittance of the MMC converter station converted to the DC side. This is the equivalent damping resistance after MMC conversion; The equivalent inductance after conversion of the MMC bridge arm inductance; For the MMC submodule capacitors and DC-side equivalent capacitance; This represents the equivalent capacitance to ground of the T-connected branch; This indicates the fault transition resistance.

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