CN109975656B - High-resistance grounding fault detection method based on flexible direct-current power distribution network - Google Patents

Abstract

The invention discloses a high-resistance grounding fault detection method for a flexible direct-current power distribution network₁Component and to IMF₁Performing first-order difference operation to obtain a sudden change singular point, calculating an accumulated slope sum near the singular point, and comparing the slope sum value with a starting threshold value to distinguish a fault state from a normal state; next, the Prony algorithm is used to pair IMFs₁The components are subjected to parameter identification to obtain IMF₁And calculating the energy ratio of the characteristic frequency component to the direct current component, and further distinguishing different states through the difference of energy ratio values. Compared with the prior art, the method can adapt to accurate feature extraction in a strong noise environment, has self-adaptability in the feature extraction process, is convenient to apply, has high detection precision, can sharply judge the running state of the power distribution network system, and simultaneously improves the calculation speed.

Description

High-resistance grounding fault detection method based on flexible direct-current power distribution network

Technical Field

The invention belongs to the technical field of power grid fault detection, and particularly relates to a high-resistance grounding fault detection method for a flexible direct-current power distribution network.

Background

Recently, the number of direct current loads is increasing day by day, and when the traditional alternating current power distribution system is used for realizing the consumption of distributed energy and the power supply of the direct current loads, a large amount of power electronic current conversion equipment is needed, so that the investment cost is greatly increased. On the contrary, if the consumption of the distributed energy and the power supply of the direct current load are carried out through the direct current distribution system, a large amount of current conversion equipment can be saved, and the investment cost is reduced. In addition to the economic advantages, the dc distribution system has the following advantages compared to the conventional ac distribution system: improving power supply reliability, improving power quality and the like. Meanwhile, in recent years, the flexible commutation technology is gradually mature, and the rapid development of the direct-current power distribution network is promoted. Therefore, the flexible dc power distribution system becomes one of the mainstream trends of the future energy internet development.

A current relevant work

At present, the development of flexible direct current distribution system still faces a plurality of key technical problems and needs to be solved urgently, wherein including the accurate identification of operating condition, when High Impedance ground Fault (HIF) takes place, how to distinguish accurately with operating conditions such as Small Impedance ground Fault (SIF), Medium Impedance ground Fault (MIF), HIF, Load Switching state (Load Switching, LS) state, is one of the problems of restricting the development of flexible direct current distribution network. However, the damping value of the direct current line is very small in the practical situation, once the direct current line fails, the fault current can rapidly complete discharge within a few ms, so that the available fault data window is too short, the fault information is too little, and the conventional protection method cannot adapt to the rapid fault current discharge process, thereby failing; furthermore, since the fault current has no zero crossing point, the fault arc continues to exist, and higher requirements are put on the breaking capacity of the direct current circuit breaker. If the HIF is not eliminated in time, the harmfulness is huge, and further, voltage and current signals similar to the HIF are easily generated during normal load switching, so that how to accurately distinguish the HIF under the working conditions of the HIF, SIF, MIF, LS and the like in a flexible direct-current distribution network is worthy of deep research.

B problems of the existing high-resistance ground fault detection method

1) And (3) high-resistance fault feature extraction: the fixed basis functions result in insufficient feature characterization capability; the feature extraction process is not adaptive, and although the EMD algorithm is adaptive, the problems of modal aliasing, endpoint effect and the like are easy to occur; some feature components are not physically meaningful.

2) High-resistance fault detection criterion: the starting criterion of the existing HIF detection method is insensitive, and the distribution network system is judged to be in a normal state by mistake at the time; the starting criterion and the distinguishing criterion are not separately constructed, so that the HIF detection accuracy is low; the calculation is complex, and most of the criterion constructions have no physical significance.

3) The difficulty of fault detection of the direct-current power distribution network is as follows: after a fault occurs, the fault discharge process is fast, and the available fault information data window is short; the instantaneous discharge current is large, and the safe operation of the converter station is threatened; the fault current has no zero crossing point, which puts higher requirements on the breaking capacity of the direct current circuit breaker, and a feasible method is to judge the fault before the fault current rises to the maximum value.

The invention contributes to the following:

1) the feature extraction method comprises the following steps: adopting CEEMDAN (Complete empirical Mode decomposition with adaptive noise, CEEMDAN) to extract TZMC (Transient Zero Mode Current, TZMC) characteristic frequency component, eliminating the problems of EMD modal aliasing, end effect and the like, compared with EEMD, only adding paired white noise to the analyzed signal to realize accurate decomposition, and abandoning the problems that EEMD needs to manually set white noise intensity, adding times and the like when adding white noise; compared with WT, S-Transform and MM, the method does not need to set a basis function, the decomposition process has self-adaptive characteristic, and the transient characteristic information can be accurately extracted.

2) The detection criterion is as follows: for IMF₁The method comprises the steps that (Intrinsic Mode Function, IMF) components adopt first-order difference to obtain singular value points nq, HIF starting criteria are constructed by calculating cumulative slopes near nq and k, when k is larger than delta, the direct-current distribution network is judged to be in an abnormal operation state, and when k is smaller than delta, the direct-current distribution network is judged to be in a normal operation state. Further, by applying IMF₁The energy ratio of the Characteristic Frequency Component (CFC) and the direct current Component (DC) in the components is used for constructing a distinguishing criterion, and further distinguishing working conditions such as SIF, MIF and HIF. On the whole, the starting and distinguishing criteria of the structure of the invention respectively play their own roles, the judgment accuracy is high, and the invention has solid physical significance.

3) The solution is as follows: for the problem 3 existing in the direct-current power distribution network, the starting criterion constructed by the invention can be started when a plurality of sampling points are obtained, and the speed is high; the distinguishing criterion is to perform energy ratio operation on the characteristic frequency and the direct current component within 2ms, and the distinguishing criterion is also quick due to the fact that the direct current distribution network fault discharge current does not rise to the maximum value within 2ms as known by the existing literature. In addition, the method can accurately distinguish the working conditions of the HIF, MIF, SIF and LS of the direct current distribution network only through the zero-mode current data at the head end, double-end data volume is not needed, and the engineering practicability is high.

Disclosure of Invention

In order to achieve the purpose, the invention provides a high-resistance grounding fault detection method for a flexible direct current power distribution network, which is improved in that the method comprises the following steps:

step 1: extracting transient zero-mode current of the flexible direct-current power distribution network;

the flexible direct-current power distribution network adopts a direct-current side grounding mode, leads out a zero point position on a direct-current side by adopting a clamping resistor and is grounded through a high resistance; when a single-stage grounding fault occurs in the direct-current line, the fault current does not have a ground loop, the direct-current line current is still a rated value, the fault point only causes the change of a zero potential point of the system, the line voltage of a grounding electrode is changed into 0, the voltage of a non-grounding electrode is changed into 2 times of the original voltage, but the voltage difference between the two electrodes is unchanged, and the control system can still keep running;

transient zero-mode current i₀(t) is obtained by the following formula:

in the formula i_p(t)、i_n(t) the currents of the anode and the cathode of the flexible direct current distribution network are respectively, wherein t represents time;

i₀(t) the circulation directions of the positive electrode and the negative electrode are the same, and a loop is formed by passing through a grounding point; the structure of the direct current system zero mode network is related to the wiring mode of the transformer, the grounding mode of the neutral point and the grounding point position of the direct current system;

step 2: extracting the inherent modal function component by adopting a complementary set empirical mode decomposition algorithm, and specifically comprising the following steps of:

1) giving transient zero-mode currents i in pairs₀(t) adding white noise of the same size and opposite sign;

2) decomposing the transient zero-mode current added with the white noise by adopting an empirical mode decomposition method to obtain an inherent modal function component;

3) repeatedly adding different noises, and then carrying out empirical mode decomposition;

4) averaging all obtained inherent modal function components to obtain a final decomposition result;

wherein, the noise standard deviation is 0.02, and the maximum iteration number is 500;

the empirical mode decomposition comprises the following specific steps:

first find i₀(t) all the extreme points are interpolated by a cubic spline function curve, and i is fitted₀Upper envelope i of (t)_{0_max}(t); in the same way, obtaining the lower envelope line i_{0_min}(t); connecting the mean values of the upper envelope line and the lower envelope line in sequence to obtain a mean value line m₁(t)：

Reuse of i₀(t) subtracting m₁(t) to obtain h₁(t)：

h₁(t)＝i₀(t)-m₁(t)

H is to be₁(t) as original i₀(t), repeating the steps to obtain:

h₁₁(t)＝h₁(t)-m₁₁(t)

in the formula, m₁₁(t) is h₁(t) mean values of upper and lower envelope lines; if h₁₁(t) if the component is not the inherent modal function component, continuing to screen, repeating the method for k times to obtain data h screened for the k time_1k(t)：

h_1k(t)＝h_1(k-1)(t)-m_1(k)(t)

When h is generated_1k(t) meets the requirements for the screening termination criteria, then h_1k(t) is the 1 st order natural mode function component, denoted as c₁(t) that is

c₁(t)＝h_1k(t)

From i₀Subtracting c from (t)₁(t) obtaining the residual signal, i.e. the residual r₁(t)：

r₁(t)＝i₀(t)-c₁(t)

Will r is₁(t) treating as a new group i₀(t) repeating the modal decomposition process to obtain a total residual r_i(t)：

r_i(t)＝r_i-1(t)-c_i(t)，i＝2，3，…，n

To this end, i₀(t) may be determined from the n-th order normal mode function component and the residual r_n(t) constitution;

and step 3: carrying out parameter identification on the inherent modal function component;

performing parameter identification on the highest frequency component in the inherent modal function obtained by complementary set empirical mode decomposition by adopting a Pornia algorithm so as to accurately identify the characteristic frequency component in the highest frequency component in the inherent modal function and the parameter value of the direct current component, and further constructing a distinguishing criterion;

the Prony algorithm comprises the following specific steps:

1) the Porony algorithm hypothesis model consists of a combination of a series of exponential functions with arbitrary amplitude, phase, frequency and attenuation factors, i.e., the Porony algorithm consists of a set of attenuated sinusoidal components; the construction of the Prony algorithm model comprises the following steps:

in the formula, A_iIs the amplitude; theta_iIs the phase; alpha is alpha_iAs attenuation factor, α_i＜0，；f_iIs the oscillation frequency;

2) floor type

In each case having q₁A sum q of attenuated DC components₂The attenuation cosine component can be expressed as follows after the cosine is expanded by adopting an Euler formula:

3) let p be q₁+q₂Then the functional form of discrete time is:

wherein … x (N-1) is a model of the measured data x (0); b_mAnd z_mIs assumed to be complex, and

4) the method adopts the principle of minimum square error to approximate a real signal, and the formula of the principle of minimum square error is as follows:

therefore, the amplitude, the phase, the attenuation factor and the frequency of the characteristic frequency component and the direct current component can be obtained by adopting the Prony algorithm;

and 4, step 4: constructing a high-resistance grounding fault detection starting criterion to be distinguished from the normal state of the flexible direct-current power distribution network; by calculating i₀(t) at a singular value point n_qAccumulating the slope and k in the vicinity of delta t, setting a starting threshold delta, and judging when k is less than deltaDetermining the system to be in a normal operation state, otherwise, when k is larger than delta, judging the system to be in an abnormal operation state, and therefore, constructing a distinguishing criterion to further distinguish the following 3 states: small resistance ground fault, high resistance ground fault, load switching;

the singular value point n is obtained by processing the highest frequency component in the inherent modal function_qThe method specifically comprises the following steps:

1) to i₀(t) performing complementary set empirical mode decomposition to obtain the highest frequency component in the inherent mode function;

2) obtaining an extreme point of the highest frequency component in the inherent modal function;

3) calculating the amplitude difference between adjacent maximum points and minimum points, taking the absolute value, and calculating the interval;

4) positioning the position with the maximum absolute value of the extreme value difference and the minimum interval of the extreme values; since the singularities are usually instantaneous, the singular value point n_qThe extreme value interval is only one sampling interval in general, so that the position of the maximum value point at the minimum position of the extreme value interval is taken as a singular value point n_qThe position of (a);

and 5: constructing a high-resistance grounding fault detection distinguishing criterion;

i in power frequency period of 1/4 when earth fault or load switching occurs₀(t) as an original signal, constructing a distinguishing criterion by calculating the ratio of characteristic frequency component energy to direct current energy; the method specifically comprises the following steps:

1) characteristic frequency i_TAnd a direct current component i_BThe energy calculation formulas of (a) and (b) are respectively as follows:

in the formula: w_T、W_BAre respectively i_TAnd i_BEnergy of(ii) a n is the number of sampling points in the power frequency period of 1/4; Δ t is the sampling interval;

2) structure i_TAnd i_BThe energy ratio of (A) is:

during load switching, although transient zero-mode current in the flexible direct-current power distribution network is suddenly increased, the power supply structure of the flexible direct-current power distribution network is not essentially changed, so that no oscillation component is generated, namely, no characteristic frequency component i exists_TAt this time, only a direct current component exists in the transient zero-mode current; on the contrary, when a single-pole grounding fault occurs, the original balance state of the flexible direct-current power distribution network is broken, and therefore, a characteristic frequency component i is generated_T；

Based on this, the constructed distinguishing criterion 1 is: when detecting the absence of characteristic frequency components, i.e. W, in flexible DC distribution networks_TWhen R is equal to 0, R is calculated_ratioJudging the load to be switched normally when the load is 0; when R is_ratioWhen the resistance is more than or equal to 1, judging that the small resistance ground fault occurs; when R is more than or equal to 0.01_ratioIf the current is less than 1.00, judging the occurrence of a medium resistance grounding fault or a high resistance grounding fault;

to further distinguish whether the fault belongs to a medium-resistance ground fault or a high-resistance ground fault, R is required to be more than or equal to 0.01_ratioWhen the value is less than 1.00, further thinning is carried out, and the following definition is carried out: high resistance is defined as greater than 100 Ω and above; defining 1 omega-100 omega as middle resistance;

based on this, a discrimination criterion 2 is constructed: setting a threshold value epsilon, when epsilon is less than or equal to R_ratioIf the resistance is less than 1.00, the resistance is judged to be a medium resistance grounding fault, otherwise, R is more than or equal to 0.01_ratioIf the value is less than epsilon, the fault is judged to be a high-resistance grounding fault.

Compared with the prior art, the method can accurately reflect slight changes in the fault state and normal disturbance, can adapt to accurate feature extraction in a strong noise environment, and has adaptivity and convenient application in the feature extraction process; the detection precision is high, the running state of the power distribution network system can be sharply judged, and meanwhile, the calculation speed is improved.

Drawings

Fig. 1 is a VSC-based two-terminal dc power distribution system of the present invention.

FIG. 2 shows the zero mode current waveform under 4 operating conditions of the present invention.

FIG. 3 shows FFT analysis of various operating conditions according to the present invention.

FIG. 4 shows the TZMC and IMF thereof under various working conditions of the present invention₁And (4) components.

FIG. 5 shows the TZMC and its first order difference for each operating condition of the present invention.

FIG. 6 shows a detection process according to the present invention.

FIG. 7 is a diagram of noisy TZMC waveforms under various operating conditions of the present invention.

Detailed Description

The invention discloses a high-resistance grounding fault detection method for a flexible direct-current power distribution network, which comprises the following specific contents in an embodiment:

1 flexible direct current distribution network zero mode current extraction

As shown in fig. 1, in a two-terminal dc power distribution system based on a Voltage Source Converter (VSC), the present invention adopts a dc side grounding manner, and a zero point is led out at the dc side by using a clamping resistor and grounded through a high resistance. The common characteristic of these grounding modes is that the small current is grounded, when the single-stage grounding fault occurs on the direct current line, the fault current has no circuit to ground, and the direct current line current is still the rated value; the fault point only causes the change of the zero potential point of the system, the line voltage of the grounding electrode is changed into 0, the voltage of the non-grounding electrode is changed into 2 times of the original voltage, but the voltage difference between the two electrodes is not changed, and the control system can still keep running;

transient zero-mode current in a flexible direct-current distribution network contains abundant physical information, and high-resistance ground fault criteria can be constructed by analyzing the change rule of high-frequency components in the zero-mode current under the working conditions of high-resistance ground fault, small-resistance ground fault, load switching, normal operation and the like;

the TZMC in the flexible direct-current distribution network contains rich physical information, and can start by analyzing the change rule of high-frequency components in zero-mode current under the working conditions of HIF, SIF, LS, NC and the like, so that a high-resistance grounding fault criterion is constructed.

TZMC can be determined by the following formula:

in the formula i_p、i_nThe currents of the positive electrode and the negative electrode are respectively.

From i₀As can be seen, i of the DC system₀And i of the communication system₀Having similar properties, i₀The flow directions of the positive and negative electrodes are the same, and a loop must be formed through the grounding point. The structure of the zero-mode network of the direct current system is related to the wiring mode of the transformer, the grounding mode of the neutral point and the grounding point position of the direct current system.

Taking FIG. 1 as an example, i under SIF, 1000 Ω HIF, LS, NC 4 simulation conditions are given₀The waveform, as shown in fig. 2.

As can be seen from FIG. 2, when SIF occurs, i₀When the fault occurs, the sudden change characteristic is obvious and has strong oscillation trend i₀The waveform contains strong high frequency components, as shown in fig. 2 (a); in the occurrence of HIF, i₀Compared with the SIF working condition, the waveform has a less drastic change at the time of the fault, but it can also be seen that the time domain waveform has a certain high frequency content, as shown in fig. 2 (b); when the LS switching is not balanced, the balance between the positive pole and the negative pole of the direct current distribution network is broken, and at the moment, i appears₀However, since it is not a failure as compared with HIF, i₀No high frequency components appear in the waveform, as shown in fig. 2 (c); when the direct current distribution network is in NC, i cannot appear₀As shown in fig. 2 (d).

For i under the above 4 working conditions₀An FFT analysis was performed as in fig. 3. From the frequency domain, the specific gravity of the Characteristic Frequency Component (CFC) and the direct current component (DC) has a certain difference under the above 4 working conditions, and if the energy of the high frequency component and the direct current component can be accurately extracted, the HIF detection can be performed according to the ratio between the high frequency component and the direct current component.

2-feature IMF component extraction method

Extracting characteristic IMF components by adopting a CEEMDAN algorithm, wherein the completeness of a signal is ensured by adding white noise in pairs by adopting Complementary Ensemble Empirical Mode Decomposition (CEEMDAN). The complementary set empirical mode decomposition comprises the following specific steps:

step 1: giving transient zero-mode current signals i in pairs₀(t) adding white noise of the same size and opposite sign;

step 2: decomposing the zero-mode current signal added with the white noise by adopting an EMD decomposition method to obtain an IMF component;

step 3: repeatedly adding different noises, and then performing EMD decomposition;

step 4: all the obtained IMF components are averaged to obtain the final decomposition result.

Wherein, the noise standard deviation is 0.02, and the maximum iteration number is 500.

The EMD algorithm comprises the following specific steps:

first find i₀(t) all the extreme points are interpolated by a cubic spline function curve, and i is fitted₀Upper envelope i of (t)_{0_max}(t) of (d). In the same way, obtaining the lower envelope line i_{0_min}(t) of (d). Connecting the mean values of the upper envelope line and the lower envelope line in sequence to obtain a mean value line m₁(t)：

Reuse of i₀(t) subtracting m₁(t) to obtain h₁(t)：

h₁(t)＝i₀(t)-m₁(t) (3)

H is to be₁(t) as original i₀(t), repeating the steps to obtain:

h₁₁(t)＝h₁(t)-m₁₁(t) (4)

in the formula, m₁₁(t) is h₁(t) mean of upper and lower envelope curves. If h₁₁(t) if not IMF component, continuing the screening, repeating the above method k times to obtain the secondData h from k screens_1k(t)：

h_1k(t)＝h_1(k-1)(t)-m_1(k)(t) (5)

When h is generated_1k(t) meets the requirements for the screening termination criteria, then h_1k(t) is the 1 st order IMF component, denoted as c₁(t) that is

c₁(t)＝h_1k(t) (6)

From i₀Subtracting c from (t)₁(t) obtaining the residual signal, i.e. the residual r₁(t)：

r₁(t)＝i₀(t)-c₁(t) (7)

Will r is₁(t) treating as a new group i₀(t) repeating the modal decomposition process to obtain a total residual r_i(t)：

r_i(t)＝r_i-1(t)-c_i(t)，i＝2，3，…，n (8)

To this end, i₀(t) may be formed from the IMF component of order n and the residual r_n(t) is formed.

From the analysis, i was decomposed by CEEMDAN₀Of the plurality of IMF components obtained after (t), IMF₁Component is i₀(t) the highest frequency component, as known from the prior art, has the most sensitive reaction to the operating conditions of the DC distribution grid, and therefore, the IMF is used in the present invention₁Component is i₀(t) characteristic IMF component, and further analysis therewith.

FIG. 4 shows the TZMC and the respective IMF under various operating conditions₁Component waveforms, it can be seen that for SIF, MIF, HIF, IMF₁The components have obvious mutation at the initial moment of the fault and are accurately represented; for LS and NC, IMF thereof₁The components may better represent the trend of the TZMC, in general, the IMF for the high frequency components₁In other words, some characteristic information of fault and normal state can be accurately represented, and a foundation can be laid for the construction of the next accurate criterion。

3-feature IMF component parameter identification method

IMF obtained by decomposing CEEMDAN₁The components are subjected to parameter identification by using a Prony algorithm to accurately identify the IMF₁The characteristic frequency component and the parameter value of the direct current component, and then a distinguishing criterion is constructed.

The Prony's algorithm assumes that the model consists of a combination of a series of exponential functions with arbitrary amplitude, phase, frequency and attenuation factors, that is, consists of a set of attenuated sinusoidal components, i.e., a model with arbitrary amplitude, phase, frequency and attenuation factor

In the formula (10), A_iIs the amplitude; theta_iIs the phase (rad); alpha is alpha_iLess than 0, is attenuation factor; f. of_iIs the oscillation frequency (Hz).

In the formula (10), q is respectively₁A sum q of attenuated DC components₂And (3) attenuating cosine components, and expanding the cosine in the attenuated cosine components by using an Euler formula:

let p be q₁+q₂Then its function form of discrete time is:

as a model of the measurement data x (0), … x (N-1). More generally, b_mAnd z_mIs assumed to be complex, and

for approximating the analog signal to the true signal, the Prony algorithm uses the principle of least square error, i.e.

Thus, the amplitude, phase, attenuation factor, and frequency of the characteristic frequency component and the dc component can be obtained by the Prony algorithm.

4 high-resistance grounding fault detection criterion

4.1 starting criterion

To distinguish from the normal state, the calculation i is used₀(t) at a singular value point n_qAnd accumulating the slope and k in the nearby delta t, setting a starting threshold delta, judging that the system is in a normal operation state when k is less than delta, and judging that the system is in an abnormal operation state when k is more than delta, so that a distinguishing criterion needs to be established to further distinguish SIF, HIF and LS 3 states.

By applying to IMF₁The components are processed to obtain a singular value point n_qThe method comprises the following specific steps:

step 1: to i₀(t) performing improved complementary set empirical mode decomposition to obtain IMF₁；

Step 2: finding IMF₁Extreme points of the components;

step 3: calculating the amplitude difference between adjacent maximum points and minimum points, taking the absolute value, and calculating the interval;

step 4: and positioning the position where the absolute value of the extreme value difference is maximum and the distance between the extreme values is minimum. Since the singularities are usually instantaneous, the singular value point n_qThe extreme value interval is only one sampling interval in general, so that the position of the maximum value point at the minimum position of the extreme value interval is taken as a singular value point n_qThe position of (a).

The steps 2 to 4 can be simplified as follows: direct pair high frequency IMF after CEEMD decomposition₁The first order differential of the components is obtained, the module value is taken, the point with the maximum module value is i₀Singular value point n of (t)_qSpecifically, formula (15) is calculated, where n is a sampling point:

M_max＝max|IMF₁(n)-IMF₁(n-1)| (15)

calculating TZMC at singular value point n_qThe cumulative slope and k within the nearby Δ t, calculated as equation (16):

and m is the length of the intercepted data.

FIG. 5 shows the time domain TZMC and its first order difference waveform for various operating conditions.

As shown in fig. 5, when a ground fault occurs, as can be seen from fig. 5(a), 5(b) and 5(c), the time of the maximum value of the first-order difference waveform accurately corresponds to the time of the singular value of the TZMC waveform, at this time, the waveform transformation is most sensitive and severe near the time of the singular value, and the occurrence of the ground fault can be judged by calculating the cumulative slope and the k in the vicinity of the singular value; when in normal operation or load switching, as can be seen from fig. 5(d) and 5(e), for the TZMC, fig. 5(d) and 5(e) both show monotonically increasing or decreasing trend, and compared with the TZMC waveforms of fig. 5(a), 5(b) and 5(c), the singular values are not well determined, but the IMF defined by the present invention₁The components can accurately determine the maximum value moment, and further obtain the singular value moment of TZMC in figure 5(d) and figure 5(e), thereby calculating the corresponding accumulated slope and k value.

Further observation revealed that, when a ground fault occurs in fig. 5(a), 5(b), 5(c), the abrupt change of the TZMC waveform becomes relatively gentle with the increase of the ground resistance, and the numerical increment of the ordinate becomes gentle, which reflects that when the ground resistance value is increased in the actual distribution network, the value of the TZMC further decreases, and the abrupt change thereof becomes gentle; from fig. 5(d), fig. 5(e), it can be seen that its TZMC only shows a slow increase, not a sharp increase, when in NC or LS.

In conclusion, the TZMC waveforms of the NC, LS and ground fault 3 working conditions show different change characteristics, and based on the consideration, the invention calculates the singular value point n of the TZMC_qAnd (4) accumulating the slope and k nearby, and establishing a fault starting criterion by comparing the values of k.

Table 1 shows the cumulative slope k for each operating mode when n is 21And calculating the value. As can be seen from table 1, when a ground fault occurs, the value of k is gradually decreased as the ground resistance value increases, and is reflected in the actual TZMC waveform because n is attenuated as the ground resistance value increases_qThe amount of abrupt change in the neighborhood, and therefore, the k value in the neighborhood of the singular value will be reduced.

Table 1 k value range when n is 21

When the load is switched, when the input load power is increased, the k value is correspondingly increased, because large TZMC is generated during heavy load switching. By taking the data in the table 1 as reference and considering the interference factors and margins in the actual operation of the direct-current power distribution network in fig. 1, the starting threshold value delta is set to be 0.3. And when k is less than delta, the distribution network is judged to be in a normal operation state, otherwise, when k is more than delta, the distribution network is judged to be in an abnormal operation state.

4.2 differentiation criteria

I in power frequency period of 1/4 when earth fault or load switching occurs₀(t) as raw signal, constructing a discrimination criterion by calculating the ratio of CFC energy to DC energy.

Characteristic frequency i_TAnd a direct current component i_BEnergy calculation of formula (17), (18):

in the formula: w_T、W_BAre respectively i_TAnd i_BThe energy of (a); n is the number of sampling points in the power frequency period of 1/4; Δ t is the sampling interval.

2) Structure i_TAnd i_BIs as in formula (19):

the analysis shows that, although the TZMC in the distribution network is suddenly increased during the LS switching, the power supply structure of the TZMC is not changed essentially, so that no oscillation component is generated, namely, no characteristic frequency component i exists_TAt this time, the TZMC has only a direct current component; on the contrary, when the single-pole grounding fault occurs, the original balance state of the distribution network system is broken, and therefore, the characteristic frequency component i is generated_T。

Based on this, the differentiation criterion 1 constructed by the invention is as follows: when detecting the absence of CFC in TZMC, i.e. W_TWhen R is equal to 0, R is calculated_ratioJudging that the load is switched when the load is 0; when R is_ratioJudging the occurrence of SIF when the value is more than or equal to 1; when R is more than or equal to 0.01_ratioIf < 1.00, MIF or HIF is determined to occur.

To further distinguish whether the fault is MIF or HIF, it is necessary to set R to 0.01 ≦ R_ratioWhen the value is less than 1.00, further thinning is carried out, and the following definition is carried out: high resistance is defined as greater than 100 Ω and above; the resistance is defined as 1 Ω to 100 Ω.

Based on this, for the direct-current distribution network in fig. 1, through a large number of simulation experiments, a distinguishing criterion 2 is established: setting a threshold value epsilon, when epsilon is less than or equal to R_ratioIf less than 1.00, it is judged as MIF, otherwise, R is more than or equal to 0.01_ratioIf < ε, the sample was judged to be HIF. (after a lot of tests, for the dc distribution network system in fig. 1, the present invention takes ∈ 0.5).

Therefore, the constructed high-resistance grounding fault detection flow of the flexible direct current power distribution network is shown in fig. 6.

5 simulation verification

A two-terminal flexible direct current power distribution system as shown in fig. 1 was built in MATLAB with the parameters shown in table 2. The VSC converter station comprises 2 VSC converter stations, wherein a station 1 is controlled by constant active power, and a station 2 is controlled by constant direct-current voltage; the dc load is replaced by a dc resistance. In order to test the effectiveness of the method, the method is tested under the following working conditions respectively, specifically as follows:

TABLE 2 simulation parameters of DC systems

5.1 adding Strong noise

In order to test the adaptability of the method in a strong noise environment, Gaussian white noise with the signal-to-noise ratio of 1dB is added into the TZMC, the effectiveness of the method is tested, and the calculated data is shown in Table 3_ratio44.0 is more than 1, which accords with the criterion of the invention; similarly, when MIF occurs, R_ratioIf the ratio is 0.75, the ratio is 0.5 to 0.75 to 1, and MIF is judged to occur; upon occurrence of HIF, R_ratioIf the HIF is equal to 0.18, the HIF is judged to be accurate according to the criterion of the invention, and if the HIF is equal to 0.01 and is less than 0.18 and less than 0.5; when R is_ratioWhen the value is 0.0075, 0.0075 is less than 0.01, LS can be known according to the criterion of the invention, and the judgment is accurate. Therefore, the detection method has better adaptability. The TZMC of each working condition after adding 1dB strong noise is shown in fig. 7, and it can be seen that, in the fault working condition, as shown in fig. 7(a) and (b), as the transition resistance increases, the TZMC amplitude further decreases, and at this time, the noise has a greater influence on the TZMC, but the TZMC waveform can still be clearly identified; in comparison with NC, as shown in fig. 7(c) and (d), since LS and NC have small zero-mode current values, the influence of noise is large.

Meter 31 dB noise test

5.2 different fault location

In order to test the adaptability of the criterion of the invention at different fault positions, the operation conditions of SIF, MIF, HIF, LS and the like (the fault position of table 3 is 2 km) respectively occurring at the cable line 6km are simulated, and the calculation data are shown in table 4. Ratio R of CFC energy to DC energy when SIF occurs_ratio59.0 > 1; when 50 Ω ground fault occurs, R_ratioIf the ratio is 0.93, 0.5 is more than 0.93 and less than 1, and the MIF is judged to occur according to the criterion 2; as can be seen from Table 4, R occurs when 1000 Ω HIF occurs_ratio0.01 < 0.29 < 0.5, according toCriterion 2 can judge HIF to occur, which is consistent with the actual situation; when energy ratio R_ratioWhen 0.0009 is reached, 0.0009 < 0.01, and LS is judged as not a failure, and it is judged as correct as shown in table 4.

Test at 46 km of Table

5.3 short Window data

The length of the data window is directly related to the size of the data volume, and the longer the data window, the larger the data volume contained, whereas the shorter the data window, the less the data contained. To test the method's adaptability to the data window length, the test results of the post-failure TZMC waveform at 1ms window length are given, and are shown in table 5. For 1ms short window data, as shown in table 5, the method of the present invention can also accurately determine the operating condition. Further analysis shows that the shorter the data window is, the shorter the calculation time of the criterion of the invention is, and the more the operation condition can be judged quickly.

TABLE 51 ms data Window test

5.4 changing the current limiting inductance value

When the flexible direct current distribution network is practically applied, a current-limiting inductor L is usually connected in series at the head end of a power supply line₁To limit the short-circuit current level in the event of a fault, L₁The larger the value, the greater the limiting effect on the fault current, and conversely, L₁The smaller the limiting effect on the fault current. Since the present invention utilizes TZMC data, L₁To a certain extent, the fault zero-mode current waveform is influenced, and L is given for investigating the influence₁Calculated data at 0.2H are shown in table 6. As can be seen from Table 6, whenIncrease L₁Up to 0.2H (0.04H in tables 3, 4 and 5), R_ratioThe value can still accurately distinguish the operation conditions of SIF, MIF, HIF, LS and the like, and the judgment is correct.

TABLE 6 Current limiting inductance L₁Test at 0.2H

5.5 changing the interelectrode capacitance

Interelectrode capacitance C₁The value has strong influence on the voltage and current waveforms of the flexible direct current distribution network, and the value is proper C₁The value has direct effect on stabilizing DC waveform, and is used for investigating C₁The influence of the magnitude of the value on the process of the invention is given by C₁Test data at 3000uF, see table 7. In practical simulation, the fact that C is increased is found₁When the current is 3000uF, the positive and negative currents are smoother, the ripple phenomenon is less, and the quality of direct current voltage and current waveforms is better. As can be seen from the data in Table 7, the method of the present invention is not affected by the value of the interelectrode capacitance, and R is compared_ratioThe numerical value of (2) can accurately distinguish various working conditions.

TABLE 7 interelectrode capacitance C3000 uF test

Claims (1)

1. A high-resistance grounding fault detection method for a flexible direct-current power distribution network is characterized by comprising the following steps:

step 1: extracting transient zero-mode current of the flexible direct-current power distribution network;

the flexible direct-current power distribution network adopts a direct-current side grounding mode, leads out a zero point position on a direct-current side by adopting a clamping resistor and is grounded through a high resistance; when a single-stage grounding fault occurs in the direct-current line, the fault current does not have a ground loop, the direct-current line current is still a rated value, the fault point only causes the change of a zero potential point of the system, the line voltage of a grounding electrode is changed into 0, the voltage of a non-grounding electrode is changed into 2 times of the original voltage, but the voltage difference between the two electrodes is unchanged, and the control system can still keep running;

transient zero-mode current i₀(t) is obtained by the following formula:

in the formula i_p(t)、i_n(t) the currents of the anode and the cathode of the flexible direct current distribution network are respectively, wherein t represents time;

i₀(t) the circulation directions of the positive electrode and the negative electrode are the same, and a loop is formed by passing through a grounding point; the structure of the direct current system zero mode network is related to the wiring mode of the transformer, the grounding mode of the neutral point and the grounding point position of the direct current system;

step 2: extracting the inherent modal function component by adopting a complementary set empirical mode decomposition algorithm, and specifically comprising the following steps of:

1) giving transient zero-mode currents i in pairs₀(t) adding white noise of the same size and opposite sign;

2) decomposing the transient zero-mode current added with the white noise by adopting an empirical mode decomposition method to obtain an inherent modal function component;

3) repeatedly adding different noises, and then carrying out empirical mode decomposition;

4) averaging all obtained inherent modal function components to obtain a final decomposition result;

wherein, the noise standard deviation is 0.02, and the maximum iteration number is 500;

the empirical mode decomposition comprises the following specific steps:

first find i₀(t) all the extreme points are interpolated by a cubic spline function curve, and i is fitted₀Upper envelope i of (t)_{0_max}(t); in the same way, obtaining the lower envelope line i_{0_min}(t); connecting the mean values of the upper envelope line and the lower envelope line in sequence to obtain a mean value line m₁(t)：

Reuse of i₀(t) subtracting m₁(t) to obtain h₁(t)：

h₁(t)＝i₀(t)-m₁(t)

H is to be₁(t) as original i₀(t), repeating the steps to obtain:

h₁₁(t)＝h₁(t)-m₁₁(t)

in the formula, m₁₁(t) is h₁(t) mean values of upper and lower envelope lines; if h₁₁(t) if the component is not the inherent modal function component, continuing to screen, repeating the method for k times to obtain data h screened for the k time_1k(t)：

h_1k(t)＝h_1(k-1)(t)-m_1(k)(t)

When h is generated_1k(t) meets the requirements for the screening termination criteria, then h_1k(t) is the 1 st order natural mode function component, denoted as c₁(t) that is

c₁(t)＝h_1k(t)

From i₀Subtracting c from (t)₁(t) obtaining the residual signal, i.e. the residual r₁(t)：

r₁(t)＝i₀(t)-c₁(t)

Will r is₁(t) treating as a new group i₀(t) repeating the modal decomposition process to obtain a total residual r_i(t)：

r_i(t)＝r_i-1(t)-c_i(t)，i＝2，3，…，n

To this end, i₀(t) may be determined from the n-th order normal mode function component and the residual r_n(t) constitution;

and step 3: carrying out parameter identification on the inherent modal function component;

performing parameter identification on the highest frequency component in the inherent modal function obtained by complementary set empirical mode decomposition by adopting a Pornia algorithm so as to accurately identify the characteristic frequency component in the highest frequency component in the inherent modal function and the parameter value of the direct current component, and further constructing a distinguishing criterion;

the Prony algorithm comprises the following specific steps:

1) the Porony algorithm hypothesis model consists of a combination of a series of exponential functions with arbitrary amplitude, phase, frequency and attenuation factors, i.e., the Porony algorithm consists of a set of attenuated sinusoidal components; the construction of the Prony algorithm model comprises the following steps:

in the formula, A_iIs the amplitude; theta_iIs the phase; alpha is alpha_iAs attenuation factor, α_i＜0，；f_iIs the oscillation frequency;

2) floor type

In each case having q₁A sum q of attenuated DC components₂The attenuation cosine component can be expressed as follows after the cosine is expanded by adopting an Euler formula:

3) let p be q₁+q₂Then the functional form of discrete time is:

wherein … x (N-1) is a model of the measured data x (0); b_mAnd z_mIs assumed to be complex, and

4) the method adopts the principle of minimum square error to approximate a real signal, and the formula of the principle of minimum square error is as follows:

therefore, the amplitude, the phase, the attenuation factor and the frequency of the characteristic frequency component and the direct current component can be obtained by adopting the Prony algorithm;

and 4, step 4: constructing a high-resistance grounding fault detection starting criterion to be distinguished from the normal state of the flexible direct-current power distribution network; by calculating i₀(t) at a singular value point n_qAccumulating the slope and k in the nearby delta t, setting a starting threshold delta, judging that the system is in a normal operation state when k is less than delta, and judging that the system is in an abnormal operation state when k is more than delta, thereby constructing a distinguishing criterion and further distinguishing the following 3 states: small resistance ground fault, high resistance ground fault, load switching;

the singular value point n is obtained by processing the highest frequency component in the inherent modal function_qThe method specifically comprises the following steps:

1) to i₀(t) performing complementary set empirical mode decomposition to obtain the highest frequency component in the inherent mode function;

2) obtaining an extreme point of the highest frequency component in the inherent modal function;

3) calculating the amplitude difference between adjacent maximum points and minimum points, taking the absolute value, and calculating the interval;

4) positioning the position with the maximum absolute value of the extreme value difference and the minimum interval of the extreme values; since the singularities are usually instantaneous, the singular value point n_qThe extreme value interval is only one sampling interval in general, so that the position of the maximum value point at the minimum position of the extreme value interval is taken as a singular value point n_qThe position of (a);

and 5: constructing a high-resistance grounding fault detection distinguishing criterion;

i in power frequency period of 1/4 when earth fault or load switching occurs₀(t) as an original signal, constructing a distinguishing criterion by calculating the ratio of characteristic frequency component energy to direct current energy; the method specifically comprises the following steps:

1) characteristic frequency i_TAnd a direct current component i_BThe energy calculation formulas of (a) and (b) are respectively as follows:

in the formula: w_T、W_BAre respectively i_TAnd i_BThe energy of (a); n is the number of sampling points in the power frequency period of 1/4; Δ t is the sampling interval;

2) structure i_TAnd i_BThe energy ratio of (A) is:

during load switching, although transient zero-mode current in the flexible direct-current power distribution network is suddenly increased, the power supply structure of the flexible direct-current power distribution network is not essentially changed, so that no oscillation component is generated, namely, no characteristic frequency component i exists_TAt this time, only a direct current component exists in the transient zero-mode current; on the contrary, when a single-pole grounding fault occurs, the original balance state of the flexible direct-current power distribution network is broken, and therefore, a characteristic frequency component i is generated_T；

Based on this, the constructed distinguishing criterion 1 is: when detecting the absence of characteristic frequency components, i.e. W, in flexible DC distribution networks_TWhen R is equal to 0, R is calculated_ratioJudging the load to be switched normally when the load is 0; when R is_ratioWhen the resistance is more than or equal to 1, judging that the small resistance ground fault occurs; when R is more than or equal to 0.01_ratioWhen < 1.00, the judgment is madeA medium resistance ground fault or a high resistance ground fault occurs;

to further distinguish whether the fault belongs to a medium-resistance ground fault or a high-resistance ground fault, R is required to be more than or equal to 0.01_ratioWhen the value is less than 1.00, further thinning is carried out, and the following definition is carried out: high resistance is defined as greater than 100 Ω and above; defining 1 omega-100 omega as middle resistance;

based on this, a discrimination criterion 2 is constructed: setting a threshold value epsilon, when epsilon is less than or equal to R_ratioIf the resistance is less than 1.00, the resistance is judged to be a medium resistance grounding fault, otherwise, R is more than or equal to 0.01_ratioIf the value is less than epsilon, the fault is judged to be a high-resistance grounding fault.

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