Fundamental wave zero sequence current detection method based on time domain CPT theory

Abstract

The invention belongs to the technical field of power system measurement and control, and relates to a fundamental wave zero-sequence current detection method based on a time domain CPT theory, which comprises the following steps: obtaining a time domain current signal and a voltage signal based on an actual power grid; based on the time domain current signal and the voltage signal, obtaining a physical quantity based on a CPT theory; the physical quantities based on the CPT theory comprise homologous voltage, active power, reactive power and basic apparent power; calculating the physical quantity based on the CPT theory to obtain a fundamental current effective value, a fundamental current voltage phase angle difference and a fundamental current phase; substituting the physical quantity, the voltage signal, the fundamental current effective value and the fundamental current phase based on the CPT theory into a zero-sequence current calculation formula to obtain fundamental zero-sequence current information; the fundamental wave zero-sequence current information comprises a fundamental wave zero-sequence current instantaneous value and a fundamental wave zero-sequence current effective value and amplitude; therefore, fundamental wave zero-sequence current detection which works stably under the conditions of harmonic distortion and three-phase imbalance is realized.

Description

Technical Field

[0001] This invention relates to the field of power system measurement and control technology, and specifically discloses a fundamental zero-sequence current detection method based on time-domain CPT theory. Background Technology

[0002] With the large-scale integration of distributed generation (DG), power electronic interface loads, and renewable energy, distribution networks exhibit a dual characteristic of "high proportion of new energy + high penetration of power electronics." This leads to problems such as three-phase load asymmetry and the superposition of harmonics and interharmonics, making zero-sequence current more common and significantly time-varying in low-voltage distribution networks and microgrid scenarios. The fundamental zero-sequence current not only relates to neutral line heating, losses, and protection settings, but also involves the operational safety of the distribution transformer neutral point, power quality evaluation, and the robustness of source-grid-load coordinated control. Therefore, rapid, reliable, and low-cost online detection of this current has significant engineering value.

[0003] There are two main types of existing detection paths: (1) methods based on frequency domain decomposition, such as performing FFT / DFT on three-phase voltage and current, extracting the fundamental component, and then calculating the zero sequence; (2) methods based on coordinate transformation and phase-locked loop (PLL), such as Park transformation / synchronous rotating coordinate system decoupling, and then estimating the zero sequence quantity from the synchronous phasor. The above methods can achieve good results under steady-state and near-sinusoidal conditions, but they expose multiple limitations under the background of high voltage and high humidity.

[0004] High computational and latency costs: FFT / DFT and dq transforms require long observation windows and numerous multiply-accumulate operations. Window effects and frequency drift can introduce amplitude / phase deviations, which are not suitable for scenarios with high instantaneous requirements.

[0005] Strong synchronicity dependence: PLL phase-locked loops are quite sensitive to harmonics and negative sequence. Under non-ideal waveforms, phase locking and tracking speed are limited, which further affects the accuracy and stability of zero-sequence estimation.

[0006] Insufficient adaptability to imbalance / distortion: Traditional power theories mostly assume a sinusoidal balanced system; although control theories such as PQ (instantaneous reactive power) can be calculated in the time domain, their ability to suppress the coupling of "reactive power-distortion-imbalance" is limited, and distortion components are easily mixed into reactive power / reactive power measurement, thus affecting the purity of the fundamental zero sequence extraction.

[0007] Conservative Power Theory (CPT) is a power theory framework centered on homogeneous quantities. It emphasizes the energy consistency decomposition of voltage and current in the time domain to achieve a clear distinction between active and non-active power (including distortion). CPT exhibits good theoretical consistency and explanatory power under unbalanced and non-sinusoidal conditions, and has been applied in power quality analysis and active power filtering control. However, publicly available CPT applications mostly focus on harmonic / interharmonic processing and non-active power decomposition.

[0008] In summary, existing technologies lack low-complexity methods for the rapid and robust extraction of fundamental zero-sequence current under conditions of imbalance and distortion; schemes relying on FFT / DFT, dq, and PLL struggle to balance instantaneity and robustness, and have high hardware and debugging costs; and metering, control, and power quality management lack a unified time-domain theoretical foundation to connect the application process.

[0009] In view of this, this invention proposes a fundamental zero-sequence current detection method based on time-domain CPT theory. This fundamental zero-sequence current detection technology possesses instantaneous performance and low computational complexity, and can operate stably under harmonic distortion and three-phase imbalance conditions. The technology requires minimal data, which can be obtained from commonly used energy meters, and can be integrated into energy meters, making it highly applicable and easy to implement. Furthermore, the proposed fundamental zero-sequence current detection method can share a unified theoretical framework with the control strategy of the distribution network, enabling consistency of models and parameters across metering, analysis, control, and governance, facilitating large-scale engineering deployment in low-voltage distribution networks and microgrids. Summary of the Invention

[0010] The purpose of this invention is to provide a fundamental zero-sequence current detection method based on time-domain CPT theory, addressing the problem of providing a fundamental zero-sequence current detection method with instantaneous performance and low computational complexity based on time-domain theory, achieving stable fundamental zero-sequence current detection under harmonic distortion and three-phase imbalance conditions; the specific solution is as follows: This includes: obtaining time-domain current and voltage signals based on an actual power grid (assuming sinusoidal voltage and a 120° phase difference between voltage phases); obtaining physical quantities based on CPT theory based on the time-domain current and voltage signals; physical quantities based on CPT theory include source voltage, active power, reactive power, and basic apparent power; calculating the fundamental current RMS value, fundamental current-voltage phase angle difference, and fundamental current phase based on the CPT theory; substituting the CPT-based physical quantities, voltage RMS and instantaneous values, fundamental current RMS value, and fundamental current phase into the zero-sequence current calculation formula to obtain fundamental zero-sequence current information; fundamental zero-sequence current information includes the fundamental zero-sequence current instantaneous value, as well as the fundamental zero-sequence current RMS value and amplitude.

[0011] Furthermore, based on power grid standards, voltage signals are obtained, including: by collecting actual current information from the power grid, three-phase time-domain current signals and three-phase time-domain voltage signals are obtained.

[0012] Furthermore, the time-domain current signal includes the A-phase time-domain current signal. B-phase time-domain current signal and C-phase time-domain current signal The voltage signal includes the A-phase time-domain voltage signal. B-phase time-domain voltage signal and C-phase time-domain voltage signal .

[0013] Furthermore, based on the time-domain current and voltage signals, physical quantities based on CPT theory are obtained, including: calculating the active power of the three phases based on the time-domain current and voltage signals; processing the voltage signals based on CPT theory to obtain the three-phase common source voltages; calculating the three-phase reactive power based on the common source voltages and time-domain current signals; and calculating the basic apparent power of the three phases based on the active and reactive power.

[0014] Furthermore, based on CPT theory, the voltage signal is processed to obtain the three-phase common-source voltages, including: performing periodic mean-based integration on the product of the voltage signal and the current signal to obtain the inner product operator; performing cumulative integration on the voltage signal to obtain the integration operator; extracting the periodic mean of the voltage signal to obtain the mean operator of the voltage signal; and substituting the integration operator and the mean operator into the common-source integration operator to obtain the common-source voltages.

[0015] Furthermore, the active power is: ; in, This represents the active power of phase X; X represents the three-phase variable, including phases A, B, and C; T represents the fundamental period. This represents the integral over time t over one fundamental period; t represents the time variable. This represents the voltage signal of phase X; This represents the time-domain current signal of phase X; The voltages from the same source are: ; in, ω represents the common source voltage of phase X; ω represents the angular velocity of the fundamental wave. This represents the voltage signal of phase X; τ represents the time variable distinct from t. Reactive power is: ; in, This represents the reactive power of phase X; The basic apparent power is: ; in, This represents the basic apparent power of phase X.

[0016] Furthermore, the physical quantities based on CPT theory are calculated to obtain the effective value of the fundamental current, the phase angle difference between the fundamental current and voltage, and the phase of the fundamental current. This includes: calculating the effective value of the three-phase fundamental current based on active power, reactive power, effective voltage value, and effective value of the same source voltage; calculating the phase angle difference between the three-phase fundamental current and voltage based on active power and reactive power; and calculating the phase of the three-phase fundamental current based on the voltage phase and the phase angle difference between the fundamental current and voltage.

[0017] Furthermore, the effective value of the fundamental current is: ; in, This represents the effective value of the fundamental current in phase X; This represents the active power of phase X; This represents the effective voltage value of phase X; This represents the effective value of the common-source voltage of phase X; This represents the reactive power of phase X; The phase angle difference between the fundamental current and voltage is: ; in, This represents the phase angle difference between the fundamental current and voltage of phase X; Represents the arcsine function; This represents the reactive power of phase X; This represents the basic apparent power of phase X; The phase of the fundamental current is: ; in, This indicates the phase of the fundamental current in phase X; This indicates the voltage phase of phase X.

[0018] Furthermore, by substituting the physical quantities based on CPT theory, the effective value of the fundamental current, the phase of the fundamental current, the effective value of the voltage, and the instantaneous value into the zero-sequence current calculation formula, the fundamental zero-sequence current information is obtained, including: calculating the instantaneous value of the fundamental zero-sequence current using the active power, reactive power, effective value and instantaneous value of the voltage, as well as the effective value and instantaneous value of the same source voltage of the three phases; and calculating the effective value and amplitude of the fundamental zero-sequence current using the effective value and phase of the fundamental current of the three phases.

[0019] Furthermore, the effective value of the fundamental zero-sequence current is: ; in, This represents the effective value of the fundamental zero-sequence current; This represents the effective value of the fundamental current in phase A; This represents the effective value of the fundamental current in phase B; denoted by , represents the effective value of the fundamental current in phase C; cos represents the cosine function. This represents the phase difference between the fundamental currents of phases A and B; This represents the phase difference between the fundamental currents of phases A and C; This represents the phase difference between the fundamental currents of phases B and C; The fundamental zero-sequence current amplitude is: ; in, Indicates the amplitude of the fundamental zero-sequence current; The instantaneous value of the fundamental zero-sequence current is: ; in, This represents the instantaneous value of the fundamental zero-sequence current; This represents the instantaneous value of phase x voltage. This represents the instantaneous value of the same source voltage as x. This represents the active power of phase X; This represents the effective voltage value of phase X; This represents the effective value of the common-source voltage of phase X; This represents the reactive power of phase X.

[0020] The present invention has the following advantages and beneficial effects: This invention presents a fundamental zero-sequence current detection method based on time-domain CPT theory, which features strong instantaneous performance and requires no additional components. Because it eliminates the need for Fourier decomposition and coordinate system transformation, the data requirements are low, and data can be obtained using common energy meters, resulting in lower hardware costs. Furthermore, it only requires data analysis of the detected voltage and current within each phase, and does not require a phase-locked loop to synchronously obtain inter-phase information across all three phases.

[0021] Due to the inherent instantaneous nature of time-domain theory, the fundamental zero-sequence current detection method provided by this invention can be applied to the control field. For new power systems with a large number of new energy sources, CPT theory can serve as a control theory, allowing metering, control, and power quality management to be within the same theoretical framework, thus better aligning with other engineering applications.

[0022] The fundamental zero-sequence current detection method based on time-domain CPT theory provided by this invention can adapt to load conditions with harmonic distortion and three-phase imbalance, and has greater universality than traditional power theory and commonly used control theory PQ theory (instantaneous reactive power theory). Therefore, it can be used in low-voltage distribution networks and microgrid scenarios with distributed power generation and renewable energy integration. Attached Figure Description

[0023] Figure 1 An exemplary flowchart of a fundamental zero-sequence current detection method based on time-domain CPT theory provided by the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0025] Existing technologies for calculating zero-sequence current in unbalanced problems often employ a simplified method using idealized current phase, which introduces errors. Statistical analysis based on actual power grid measurements reveals that, in reality, three-phase imbalance is primarily caused by the load, and the current phase deviates significantly from the idealized 120°. Methods that deduce the current phase based on the current-voltage phase difference are based on traditional power theory or PQ theory requiring coordinate axis transformation. Therefore, in harmonic environments, the fundamental component cannot be directly extracted and additional processing (such as adding Fourier decomposition) is required.

[0026] For fundamental current extraction, frequency domain methods based on Fourier analysis are used. However, this approach has a large time delay (10 cycles), high hardware requirements (large computational load), and is not suitable for large-scale application (high cost). Furthermore, it cannot be used in fields such as control (due to the excessive time delay). For new energy power generation, control requirements are high, so time domain theory is often used. This leads to the problem of different theoretical foundations being adopted in different fields.

[0027] Considering future development trends such as grid connection of new energy sources and distributed power generation, it would be better to adopt a unified power theory foundation for control and metering theories. The CPT theory used in this invention has the same active power metering as the national standard, while the non-active power part has been further decomposed, thus exhibiting good compatibility and promising future prospects for control applications. Furthermore, as it is a time-domain method, it can be used simultaneously in control and power metering fields, with lower hardware requirements and less computational complexity.

[0028] This invention provides a fundamental zero-sequence current detection method based on time-domain CPT theory, such as... Figure 1 As shown, it includes the following: Based on a real power grid (assuming sinusoidal voltage and an ideal 120° phase difference between voltage phases), time-domain current and voltage signals are obtained, including: By collecting actual current information from the power grid, three-phase time-domain current and voltage signals are obtained. The time-domain current signal includes the A-phase time-domain current signal. B-phase time-domain current signal and C-phase time-domain current signal The time-domain voltage signal includes the A-phase time-domain voltage signal. B-phase time-domain voltage signal and C-phase time-domain voltage signal .

[0029] Based on time-domain current and voltage signals, physical quantities based on CPT theory are obtained; these physical quantities include co-source voltage, active power, reactive power, and fundamental apparent power, including: The active power of the three phases is calculated based on the time-domain current and voltage signals. The active power is: ; in, This represents the active power of phase X; X represents the three-phase variable, including phases A, B, and C; T represents the fundamental period. This represents the integral over time t over one fundamental period; t represents the time variable. This represents the voltage signal of phase X; This represents the time-domain current signal of phase X.

[0030] Based on CPT theory, voltage signals are processed to obtain the three-phase common-source voltages, including: The inner product operator is obtained by periodically integrating the product of the voltage and current signals; the inner product operator is: ; in, Represents the inner product operator; It can be related to voltage; It can be related to current; Indicates a voltage signal; This represents a current signal.

[0031] By performing cumulative integration on the voltage signal, we obtain the integration operator; the integration operator is: ; in, Represents the integral operator; the signal before the indefinite integral is The indefinite integral becomes τ represents a time variable distinct from t.

[0032] Periodic mean extraction is performed on the voltage signal to obtain the mean operator of the voltage signal; the mean operator is: ; in, The averaging operator for voltage signals.

[0033] Substituting the integration operator and the averaging operator into the same-source integration operator, we obtain the same-source voltage. The same-source integral is: homogeneous integrals , ω is the angular velocity.

[0034] After substitution, the three-phase source voltages are: ; in, ω represents the common source voltage of phase X; ω represents the angular velocity of the fundamental wave. τ represents the voltage signal of phase X; τ represents the time variable distinct from t.

[0035] Based on the source voltage and time-domain current signal, calculate the reactive power of the three phases; the reactive power is: ; in, This represents the reactive power of phase X.

[0036] Based on active and reactive power, the basic apparent power of the three phases is calculated. This basic apparent power differs from the apparent power in the original CPT theory. Compared to the original CPT theory, the basic apparent power in this invention eliminates the distorted power calculated from the empty current in the CPT theory, allowing this application to obtain more accurate fundamental zero-sequence current information using fewer parameters. The basic apparent power is: ; in, This represents the basic apparent power of phase X. In this application context, basic apparent power refers to the apparent power of the fundamental frequency (in certain situations, it may not necessarily refer to the apparent power of the fundamental frequency, such as in cases of voltage source distortion, where the basic apparent power differs from the apparent power of the fundamental frequency). Similarly, the reactive power in this invention also differs from the traditional definition. The reactive power in this invention, based on CPT theory, actually refers to the reactive power of the fundamental frequency (again, in the context of this invention, it corresponds to the reactive power of the fundamental frequency in traditional power theory; in cases such as voltage source distortion, it differs from the reactive power of the fundamental frequency).

[0037] Taking phase A as an example, the calculation method for the other two phases is the same: reactive power Active power Basic apparent power: .

[0038] Calculations are performed on physical quantities based on CPT theory to obtain the effective value of the fundamental current, the phase angle difference between the fundamental current and voltage, and the phase of the fundamental current, including: Based on active power, reactive power, RMS voltage, and RMS voltage from the same source, calculate the RMS value of the fundamental current in the three phases. The RMS value of the fundamental current is: ; in, This represents the effective value of the fundamental current in phase X; This represents the active power of phase X; This represents the effective voltage value of phase X; This represents the effective value of the common-source voltage of phase X; This represents the reactive power of phase X.

[0039] Based on the fundamental apparent power and reactive power, calculate the phase angle difference between the fundamental current and voltage of the three phases; the phase angle difference between the fundamental current and voltage is: ; in, The phase angle difference between the fundamental current and voltage of phase X is represented by arcsin; arcsin represents the arcsine function. This represents the reactive power of phase X; This represents the basic apparent power of phase X.

[0040] Based on the voltage phase and the phase angle difference between the fundamental current and voltage, the fundamental current phase of the three phases is calculated; the fundamental current phase is: ; in, This indicates the phase of the fundamental current in phase X; This indicates the voltage phase of phase X.

[0041] For example, to find the phase of the fundamental current of phase A. , ,in, Given the voltage phase, the phases of the fundamental currents of the other two phases can be calculated similarly. and .

[0042] Substituting the physical quantities based on CPT theory, the effective value of the fundamental current, the phase of the fundamental current, the effective value of the voltage, and the instantaneous value into the zero-sequence current calculation formula, the fundamental zero-sequence current information is obtained. This information includes the instantaneous value of the fundamental zero-sequence current, as well as its effective value and amplitude, including: The effective value of the fundamental zero-sequence current is calculated using the effective values ​​and phases of the three-phase fundamental currents. The effective value of the fundamental zero-sequence current is: ; in, This represents the effective value of the fundamental zero-sequence current; This represents the effective value of the fundamental current in phase A; This represents the effective value of the fundamental current in phase B; denoted by , represents the effective value of the fundamental current in phase C; cos represents the cosine function. This represents the phase difference between the fundamental currents of phases A and B; This represents the phase difference between the fundamental currents of phases A and C; This represents the phase difference between the fundamental currents of phases B and C. , , .

[0043] Calculate the fundamental zero-sequence current amplitude based on the effective value of the zero-sequence current; the fundamental zero-sequence current amplitude is: ; in, This represents the amplitude of the fundamental zero-sequence current.

[0044] The instantaneous value of the fundamental zero-sequence current is calculated using the active power, reactive power, RMS and instantaneous voltage values ​​of the three phases, as well as the RMS and instantaneous voltage values ​​of the same source voltage. The instantaneous value of the fundamental zero-sequence current is: ; in, This represents the instantaneous value of the fundamental zero-sequence current; This represents the instantaneous value of phase x voltage. This represents the instantaneous value of the same source voltage as x. This represents the active power of phase X; This represents the effective voltage value of phase X; This represents the effective value of the common-source voltage of phase X; This represents the reactive power of phase X.

[0045] Example 1 Signal Acquisition Without phase-locked loops, it obtains actual, complete instantaneous information of three-phase current and voltage, excluding phase, without Fourier decomposition processing. Therefore, it consists of three sets of independent time-domain signals between phases, but the ABC phase sequence must be distinguished to obtain... and the corresponding .

[0046] The power supply voltage is provided by the power grid. In reality, the harmonics and three-phase imbalance of the power grid mainly originate from the load. Therefore, it is acceptable to consider the power supply as having ideal three-phase phases and a sinusoidal waveform.

[0047] To demonstrate the effect, a specific example is given: The three-phase amplitudes are unequal, and the three-phase phases differ by 120°. The expression for this sinusoidal voltage signal is as follows: ; ; .

[0048] With DC bias, the expressions for harmonic interference and three-phase unbalanced current are: ; ; .

[0049] CPT theoretical physical quantity calculation (taking phase A as an example, the other two phases are similar), T=0.02: Active power: ; ; .

[0050] Reactive power: In CPT theory, the voltage of the same source is defined as: ; ; ; .

[0051] The corresponding reactive power is: ; ; .

[0052] Define a fundamental apparent power S (the apparent power defined by CPT theory itself includes the distortion power D calculated from the empty current), and define a new fundamental apparent power here. Based on the already calculated CPT theory , Calculate the basic apparent power It is 4.50, and similarly we can obtain For 1.00 and It is 1.50.

[0053] Fundamental current phase solution 1) Calculate the phase angle difference between the fundamental current and voltage. Current-voltage phase difference: The results are respectively .

[0054] Calculate the phase of the fundamental current: The result is .

[0055] Solving for the fundamental zero-sequence current: Solving for the fundamental current: Substitute The effective values ​​of the fundamental currents of the three phases were obtained. .

[0056] Substituting into the complete formula for solving the effective value of the fundamental zero-sequence current: The effective value of the fundamental zero-sequence current can then be calculated to be 1.32. Regarding the amplitude... The value is 1.87.

[0057] The instantaneous value of the fundamental zero-sequence current is: ; The result is: ; ; in, This represents the instantaneous value of the fundamental zero-sequence current; This represents the instantaneous value of phase x voltage. This represents the instantaneous value of the same source voltage as x.

[0058] The actual results are: fundamental zero-sequence current RMS value 1.3217, amplitude 1.86916, instantaneous value The error based on the patented method comes from rounding during the calculation process.

[0059] This invention simplifies some of the theoretically required parameters by solving for the fundamental zero-sequence current, based on the definition of CPT theory, thereby achieving a fundamental zero-sequence current solution with less hardware requirements and lower delay, and can be used extensively in power grids at low cost.

[0060] No FFT and dq transformation required: The measured voltage is replaced by an "ideal fundamental three-phase voltage reference", and the fundamental phase angle and zero-sequence current are directly calculated in the time domain with the help of the same source quantity (CPT), which significantly reduces the amount of computation and delay.

[0061] The application of CPT in unbalanced / distorted scenarios has been expanded from "harmonic / interharmonic detection" to "fundamental zero-sequence current detection," and it explicitly distinguishes between reactive power from the same source and distortion components, thereby improving the robustness of phase angle calculation.

[0062] Compatible with the same theoretical framework for metering and control: CPT connects the theoretical foundations of metering, governance and control, which facilitates large-scale deployment in low-voltage distribution networks / microgrids, improves data utilization and reduces hardware usage costs.

[0063] The original CPT theory does not consider the neutral current (which is equal to three times the zero-sequence current), so it is not involved in the solution of the neutral current. Furthermore, the original theory does not involve the decomposition of sequence components for unbalance analysis, so it does not show or involve the calculation of zero-sequence current, and cannot be directly used for the calculation of three-phase current unbalance in my country. Its application here expands the application scenario of the theory itself.

[0064] In engineering, traditional frequency domain methods based on Fourier decomposition have high hardware requirements, necessitating CPUs for Fourier decomposition, resulting in long latency (10 cycles). This is detrimental to control and large-scale application (high hardware requirements, and the difficulty in handling interharmonic problems necessitates additional algorithms to increase computational complexity). They are often used in power quality analysis or mitigation where real-time performance is not critical. Traditional power theory ignores harmonic distortion (the method used in power grids) in its calculations. and believe The calculated S and Q both contain harmonics.

[0065] This invention uses a fundamental zero-sequence current calculation method based on CPT theory. On the one hand, it can be used to extract fundamental zero-sequence current information in real time and calculate three-phase imbalance in real time. It is relatively inexpensive and simple to calculate (only involving addition, subtraction, multiplication, division, and integration). On the other hand, it can be used in the control field (because its theoretical basis is time-domain CPT theory). Therefore, for power grids with new energy access, control, power quality analysis, and electricity metering can be under a unified theoretical framework.

[0066] In the past, zero-sequence current calculations often employed idealized three-phase current phase angles in engineering practice (limited by phase-locked loops, the three-phase current phase angles could not be measured synchronously), resulting in significant errors. This application, however, uses a method based on CPT theory. By idealizing the voltage phase angle (the supply voltage is provided by the power grid; in reality, harmonics and three-phase imbalances in the power grid mainly originate from the load, so this idealization is acceptable), it calculates the current phase angle difference by only calculating the product of current and voltage, thus providing a more accurate calculation. Furthermore, the CPT-based method uses reactive power... and basic apparent power The calculation can eliminate harmonic interference (because of the existence of common source variables, the non-active part is distinguished into distortion and reactive Q), therefore, in the calculation Compared to the traditional Q / S, the current phase calculated based on CPT theory is the true one with only the fundamental wave.

[0067] Simulation results (comparison of several methods for determining the fundamental zero-sequence current in the time domain): I. Data Generation: 40,000 sets of current vector data, each set containing three vectors: A, B, and C. Instantaneous value expression form It involves changing three pieces of information: amplitude, phase, and frequency.

[0068] Each vector has a fundamental frequency of 50Hz and a fundamental frequency vector amplitude of 0-100, rounded to the nearest integer.

[0069] Data phases for groups 1-10000: A(-30,0), B(-150,-120), C(-270,-240), all at 50Hz.

[0070] The phase of data groups 10001-20000: A(-15,15), B(-135,-105), C(-255,-225) are all 50Hz.

[0071] Data sets 20001-30000: Phase: A(-30,0), B(-150,-120), C(-270,-240), fundamental frequency 50Hz, harmonics of fundamental frequency multiples 3, 5, 7, 9, 11, 13, with amplitudes of 12%, 7%, 9%, 5%, 7%, 3% of the fundamental frequency amplitude, respectively.

[0072] Data sets 30001-40000 have the following phases: A(-15,15), B(-135,-105), C(-255,-225). The fundamental frequency is 50Hz, and the fundamental frequency multiples are 3, 5, 7, 9, 11, and 13. The harmonic amplitudes are 12%, 7%, 9%, 5%, 7%, and 3 percent of the fundamental frequency amplitude, respectively.

[0073] In addition, the 20,000-40,000 data sets include interharmonics ([1.5,3.7,5.5,7.5,8.3,11.2]) that are difficult to handle by frequency domain detection methods based on FFT transformation, with amplitude ratios (compared to the fundamental frequency) of [0.05,0.04,0.03,0.04,0.03,0.02]).

[0074] The voltage is a 50Hz sinusoidal voltage with a phase difference of 120° between the three phases and an amplitude of 1.

[0075] II. Methods Used In reality, due to the cost of phase-locked loops (PLLs), power grids often lack data on the phase angles of the currents between the three phases. Therefore, when calculating zero-sequence current, idealized phase angles are often used for the current phase, or the current phase angle information is approximated by calculating the phase angle. Thus, the time-domain detection methods for zero-sequence current can be divided into: 1. Simplified models of idealized phases; 2. Calculation models that obtain the current phase angle by calculating the current-voltage phase difference. Here, we will conduct a theoretical analysis and comparison of active power based on traditional theory, reactive power based on traditional power theory, and the method based on CPT theory proposed in this article.

[0076] The main difference between the different methods lies in solving for the current phase. Therefore, the main explanation is the process of solving for the current phase using different methods, as follows: Theoretical phase angle (simplified model): Theoretical phase angle: A commonly used engineering method. Solve for the zero-sequence current, neglecting harmonic effects and the phase shift of the actual current.

[0077] The phase angle is calculated (by inverting the current-voltage phase difference through power, thus obtaining the current phase). The zero-sequence current is obtained. This includes: Traditional P: Solved using active power from traditional power theory. ,in This refers to the apparent power of phase A in traditional power theory, which is equal to the effective value of the phase A current multiplied by the effective value of the phase A voltage. The other two phases are calculated similarly. Traditional power theory can eliminate harmonics, but it cannot distinguish between the phase lead and lag of current and voltage, and it cannot identify capacitive scenarios.

[0078] Traditional Q: Calculated using reactive power calculation methods in traditional power theory. ,in In traditional power theory, the apparent power of phase A is defined as the effective value of the phase A current multiplied by the effective value of the phase A voltage. , The active power of phase A is the reactive power calculated according to traditional power theory. Including harmonics, the calculations for the other two phases are similar. Traditional Q cannot eliminate the influence of harmonics and obtain the fundamental zero-sequence current in scenarios involving harmonic and unbalanced coupling.

[0079] Improved CPT Theory: This paper presents a fundamental zero-sequence current detection method based on an improved CPT theory.

[0080] By comparing the errors of different methods using the generated data, the comparison result is the average deviation rate for every 10,000 data sets: .

[0081] Table 1: Comparison of Zero-Sequence Current Detection Methods

[0082] Table 2. Analysis of Error Sources in the Time-Domain Method for Fundamental Zero-Sequence Current Detection (Based on Sinusoidal Voltage and a 120° Phase Difference Between Voltage Phases)

[0083] Compared to frequency domain methods based on FFT, CPT-based methods overcome the following drawbacks (delay, hardware and algorithm costs, difficulty in handling interharmonics, etc.): (1). Spectrum leakage and fence effect (the core defect of the essence is that it is difficult to deal with interharmonic problems. However, the verification of this application just happens to include interharmonics, which can prove that the method proposed in this invention can easily deal with interharmonic problems.) When the signal period is not an integer multiple of the window length, performing an FFT will result in energy from one frequency point spreading to other frequencies across the entire spectrum. When detecting the fundamental (50Hz) component, interference from neighboring frequencies will be introduced, leading to inaccurate calculated amplitude and phase. The spectrum calculated by the FFT is discrete. If the actual signal frequency falls exactly between two discrete spectral lines, the FFT cannot accurately estimate its amplitude and phase, and can only approximate it using adjacent spectral lines, inevitably introducing error.

[0084] The widespread use of power electronic equipment has introduced a large number of interharmonics. If the frequency of the interharmonics is close to the fundamental frequency, spectral leakage will cause the fundamental frequency and interharmonics to interfere with each other, resulting in serious distortion of the extraction of fundamental frequency parameters.

[0085] (2) The contradiction between frequency resolution and real-time performance (According to engineering requirements, FFT requires at least 10 cycles, so it is difficult to adapt to scenarios with high real-time requirements, especially in places with many control requirements such as new energy grid connection. However, CPT theory, as a time-domain method, has a real-time calculation process.) To improve resolution, the number of sampling points N must be increased or the sampling rate fs must be decreased. Increasing N requires a longer data window, meaning a longer signal acquisition time is needed for a single FFT calculation. This reduces the system's response speed, and for relay protection requiring rapid fault clearing, the delay is unacceptable. Decreasing fs may violate the Nyquist sampling theorem, causing frequency aliasing. Within a limited, short data window (e.g., 1-2 power frequency cycles), the frequency resolution is very low, which exacerbates the picket fence effect and spectral leakage, making it difficult to meet the requirements of high-precision measurements.

[0086] (3) The accuracy of calculation is greatly affected by the window function and synchronous sampling, which leads to increased hardware costs. In engineering, window function interpolation algorithms are often used to suppress leakage and improve accuracy (CPT is theoretically simple to implement and does not require complex windowing algorithms).

[0087] Increased complexity: This increases the complexity of the algorithm, and different window functions have different main lobe widths and side lobe attenuation characteristics, which need to be selected and weighed according to specific applications, resulting in a lack of universality.

[0088] Hardware synchronization is required: the ideal approach is to achieve strict synchronous sampling (i.e., ensure that the sampling frequency is an integer multiple of the signal's fundamental frequency), but this requires expensive hardware phase-locked loop circuits, which increases costs.

[0089] (4) Delay and computational efficiency: FFT analysis requires waiting for a complete data window to be acquired before calculation can begin, and a result is only obtained at the end of the data window. To obtain the fundamental component, it first needs to calculate all frequency components in the signal, and then extract the information of the 50Hz spectral line from thousands of spectral lines, while discarding the other 99.9% of the calculation results. For relay protection requiring fast action, time-domain methods can provide near real-time feedback, while FFT requires waiting for a data window, resulting in a slow response speed. In terms of computational load, when only a few frequencies such as the fundamental wave are of concern, the computational load of the time domain is much less than that of FFT, which calculates the entire spectrum.

[0090] CPT theory overcomes the shortcomings of existing time-domain methods based on traditional power theory: Unable to adapt to harmonic and unbalanced environments: Traditional Fryze power theory and PQ theory, commonly used in control applications, lack corresponding power definitions and are unsuitable for the superimposed imbalances and distortions in low-voltage distribution networks. Furthermore, they suffer from unclear power definitions and current distortion. Therefore, traditional power theory is often used for electricity metering in power grids, while PQ theory is primarily used in control applications. Neither method can achieve universal applicability from control to metering. Additionally, they typically require the use of phase-locked loops (PLLs) or low-pass filters, which introduces overall time delays. When the grid voltage experiences distortion, drops, or imbalance, the tracking performance of the PLL deteriorates, leading to instability in the foundation of the entire detection system and severe distortion of the calculated power components.

[0091] CPT theory, because it directly processes instantaneous values, naturally does not require complex coordinate transformations using a PLL, nor does it require a low-pass filter to extract power components. CPT's related calculations are performed point-by-point in the time domain, which inherently makes the method fast. Furthermore, CPT theory can provide a universal tool for future applications in large-scale renewable energy grid-connected systems, distributed power sources, and small microgrids.

[0092] With the development trend of power systems integrating new energy sources and distributed power generation, the fundamental zero-sequence current detection method based on CPT theory has a promising application prospect. In summary, this invention proposes a fundamental zero-sequence current detection method based on improved Conservative Power Theory (CPT). This method systematically applies Conservative Power Theory to low-voltage distribution networks for the first time, providing a unified physical and algorithmic framework for key issues such as analysis, protection, and metering, demonstrating significant synergistic advantages in complex power environments. This framework enables the same core algorithm to achieve accurate calculation of neutral line losses with low hardware cost (solving the dependence of FFT frequency domain methods on high-performance hardware and synchronous sampling), and to complete zero-sequence current detection at near-zero latency, meeting the stringent speed requirements of relay protection and control fields (overcoming the latency bottleneck caused by the data window limitation of traditional frequency domain algorithms).

[0093] Meanwhile, the CPT-based detection method proposed in this invention does not rely on the ideal voltage amplitude balance and current sinusoidal assumption, enabling stable operation under complex conditions commonly encountered in low-voltage distribution networks, such as three-phase imbalance and harmonic distortion. Its physical essence based on power conservation endows the algorithm with natural immunity to current waveform distortion. Compared with traditional PQ theory and Fryze power theory, this method, based on CPT, exhibits higher robustness and accuracy in extracting real fault characteristics, calculating power components, and distinguishing harmonics.

[0094] Furthermore, in real-time calculation and monitoring of fundamental zero-sequence current, the CPT method eliminates the need for expensive high-performance harmonic analyzers or high-sampling-rate synchronous ADCs. Relying solely on existing low-cost smart meters or embedded acquisition terminals, it accurately separates the fundamental and harmonic power components through simple time-domain operations, significantly reducing system implementation costs. For ground fault protection scenarios with extremely high delay requirements, the CPT method can complete zero-sequence current detection and judgment within milliseconds, significantly improving the speed and reliability of distribution protection and breaking through the time response limit of frequency-domain algorithms.

[0095] Therefore, this invention is not only a simple detection method, but also, based on the scalable and unified analysis framework of CPT theory, it can be applied to tasks that traditionally rely on different theoretical models and are difficult to coordinate, from power quality monitoring and rapid fault isolation to fine energy efficiency management. It enables algorithm sharing and data interoperability, significantly improving the economy, reliability and coordination of distribution automation systems, and providing a new theoretical foundation and implementation path for the safe, efficient and intelligent operation of new power systems.

[0096] The above are merely preferred embodiments of the present invention and are not intended to limit the present 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 detecting fundamental zero-sequence current based on time-domain CPT theory, characterized in that, include: Based on the actual power grid, time-domain current and voltage signals are obtained; Based on time-domain current and voltage signals, physical quantities based on CPT theory are obtained; Physical quantities based on CPT theory include co-source voltage, active power, reactive power, and basic apparent power. The effective value of the fundamental current, the phase angle difference between the fundamental current and voltage, and the phase of the fundamental current are calculated based on the CPT theory. Substituting the physical quantities based on CPT theory, the effective and instantaneous values ​​of voltage, the effective value of fundamental current, and the phase of fundamental current into the zero-sequence current calculation formula, the fundamental zero-sequence current information is obtained; the fundamental zero-sequence current information includes the instantaneous value of fundamental zero-sequence current as well as the effective value and amplitude of fundamental zero-sequence current.

2. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 1, characterized in that, Based on the actual power grid, time-domain current and voltage signals are obtained, including: By collecting actual current information from the power grid, three-phase time-domain current signals are obtained; the time-domain current signals include the A-phase time-domain current signal. B-phase time-domain current signal and C-phase time-domain current signal ; By collecting actual voltage information from the power grid, three-phase time-domain voltage signals are obtained; the time-domain voltage signals include the A-phase time-domain voltage signal. B-phase time-domain voltage signal and C-phase time-domain voltage signal .

3. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 1, characterized in that, Physical quantities based on CPT theory are obtained from time-domain current and voltage signals, including: The active power of the three phases is calculated using time-domain current and voltage signals. The voltage signal is processed based on CPT theory to obtain the three-phase common source voltage; The reactive power of the three phases is calculated using the same source voltage and time-domain current signals. Calculate the basic apparent power of the three phases using active power and reactive power.

4. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 3, characterized in that, Based on CPT theory, voltage signals are processed to obtain the three-phase common-source voltages, including: The inner product operator is obtained by periodically integrating the product of the voltage and current signals. By performing cumulative integration on the voltage signal, the integration operator is obtained; Periodic mean extraction is performed on the voltage signal to obtain the mean operator of the voltage signal; Substituting the integral operator and the mean operator into the same-source integral operator yields the same-source voltage.

5. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 3, characterized in that, Active power is: ； in, This represents the active power of phase X; X represents the three-phase variable, including phases A, B, and C; T represents the fundamental period. This represents the integral over time t over one fundamental period; t represents the time variable. This represents the voltage signal of phase X; This represents the time-domain current signal of phase X; The voltages from the same source are: ； in, ω represents the voltage originating from the same source in phase X; ω represents the angular velocity of the voltage. This represents the voltage signal of phase X; τ represents the time variable distinct from t. Reactive power is: ； in, This represents the reactive power of phase X; The basic apparent power is: ； in, This represents the basic apparent power of phase X.

6. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 1, characterized in that, Calculations are performed on physical quantities based on CPT theory to obtain the effective value of the fundamental current, the phase angle difference between the fundamental current and voltage, and the phase of the fundamental current, including: Calculate the fundamental current RMS value of the three phases based on active power, reactive power, RMS voltage and RMS voltage from the same source. Calculate the phase angle difference between the fundamental current and voltage of the three phases based on the basic apparent power and reactive power; The fundamental current phase of the three phases is calculated based on the voltage phase and the phase angle difference between the fundamental current and voltage.

7. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 6, characterized in that... The effective value of the fundamental current is: ; in, This represents the effective value of the fundamental current in phase X; This represents the active power of phase X; This represents the effective voltage value of phase X; This represents the effective value of the common-source voltage of phase X; This represents the reactive power of phase X; The phase angle difference between the fundamental current and voltage is: ； in, This represents the phase angle difference between the fundamental current and voltage of phase X; Represents the arcsine function; This represents the reactive power of phase X; This represents the basic apparent power of phase X; The phase of the fundamental current is: ； in, This indicates the phase of the fundamental current in phase X; This indicates the voltage phase of phase X.

8. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 1, characterized in that, Substituting the physical quantities based on CPT theory, the effective value of the fundamental current, the phase of the fundamental current, the effective value of the voltage, and the instantaneous value into the zero-sequence current calculation formula, the fundamental zero-sequence current information is obtained, including: The instantaneous value of the fundamental zero-sequence current is calculated using the active power, reactive power, effective and instantaneous voltage values ​​of the three phases, as well as the effective and instantaneous voltage values ​​of the same source. The effective value and amplitude of the fundamental zero-sequence current are calculated using the effective value and phase of the three-phase fundamental current.

9. The fundamental zero-sequence current detection method based on time-domain CPT theory according to claim 8, characterized in that, The effective value of the fundamental zero-sequence current is: ； in, This represents the effective value of the fundamental zero-sequence current; This represents the effective value of the fundamental current in phase A; This represents the effective value of the fundamental current in phase B; denoted by , represents the effective value of the fundamental current in phase C; cos represents the cosine function. This represents the phase difference between the fundamental currents of phases A and B; This represents the phase difference between the fundamental currents of phases A and C; This represents the phase difference between the fundamental currents of phases B and C; The fundamental zero-sequence current amplitude is: ； in, Indicates the amplitude of the fundamental zero-sequence current; The instantaneous value of the fundamental zero-sequence current is: ； in, This represents the instantaneous value of the fundamental zero-sequence current; This represents the instantaneous value of phase x voltage. This represents the instantaneous value of the same source voltage as x. This represents the active power of phase X; This represents the effective voltage value of phase X; This represents the effective value of the common-source voltage of phase X; This represents the reactive power of phase X.

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