Keywords

1 Introduction

With the advancement of smart grid and information technology, the research and application of the principle of multi-terminal longitudinal differential protection has received extensive attention [1,2,3,4]. The device of the multi-terminal longitudinal differential protection needs to obtain remote sampling data. These data transmission paths are different, and there will be time errors due to link blockage during transmission, so data at different collection points need to have accurate synchronization processing methods, which can ensure the synchronization of data and the accuracy of fault calculation and discrimination [5]. Data synchronization includes synchronous sampling and data window synchronization. Generally, intelligent multi-terminal longitudinal differential protection usually adopts data acquisition based on satellite and high-precision clock synchronization, and data transmission adopts high-speed optical fiber wide-area self-healing network. After adopting methods such as synchronous pulse sampling and resampling, the delay error of the data in the transformer and the sampling link can be effectively compensated, but the delay error caused by the data in the transmission link requires an effective method to realize the data window synchronization. Synchronization methods include data time-scaling method, link fixed delay compensation method, etc. [6,7,8,9,10]. Literature [11] proposed a fault current fundamental wave zero-crossing point identification method to solve the difficulty of protection data synchronization, and pointed out the huge cost of multi-terminal and wide-area differential protection data synchronization technology; Literature [12] analyzed the shortcomings of multiple synchronization clock methods, and proposed a network-wide time synchronization scheme based on sparse phasor measurement unit PMU; Literature [13] proposed a network sampling synchronization method based on an external reference clock source; Literature [14] proposed a data synchronization method based on clock difference to solve the problem of inconsistent data synchronization between two-way channel routing in a self-healing ring network.

According to the requirements of the specification, the relay protection device should not rely on the external time synchronization system to realize the protection function, so the data time stamping method is usually not adopted. The link fixed delay compensation method usually first measures the rated delay value of the data transmission link, and then compensates the delay error between the data according to the fixed delay value to achieve synchronization. The disadvantage is that the link delay has some uncertainties, so the delay compensation method has errors.

For the protection of the multi-terminal longitudinal differential principle, it is necessary to obtain remote sampling values to judge the fault interval. The data transmission distance is so long and the link segments are much more than we expected. During the data transmission process, link congestion and routing self-healing reconstruction may occur due to data storms. Therefore, the uncertainty of the transmission delay of the data will cause a large phase difference, calculation error and even a wrong operation of the protection [15, 16]. For the new wide-area differential protection that needs to adaptively construct the protection range according to the grid network topology, the end points and data links of the protection are not fixed, and the transmission delay of the data at each end is more uncertain. It is necessary to eliminate delay errors to ensure that the data between each end is synchronized. For UHV systems, the transmission distance is longer, the data communication volume is larger, and the data link is more complicated. The endpoints and normal communication links that constitute the multi-terminal longitudinal differential principle protection are fixed, but the end points of the wide area differential protection and the normal communication link may not be fixed. The possibility of a large delay error between the sampled data at each end is higher, and the possibility of the protection device's erroneous action is also higher.

This paper proposes a self-healing synchronization algorithm for relay protection data based on wavelet transform to calculate sudden changes. Aiming at the delay of current sampling data in the transmission process due to communication link problems in the power system, it is assumed that the sudden changes of multi-terminal faults are accurately collected. Under the premise, according to the characteristics of the waveform mutation of the sampled data during the short-circuit fault, the value of each sampled data is calculated. At the moment of the fault sudden change, the time difference is compensated by this, the sampling data synchronization is realized, and the application of the algorithm in the multi-terminal system is studied.

2 Mutation Algorithm and Data Delay Error

2.1 The Method of Calculating the Abrupt Change by Wavelet Transform

After the line fails, the waveform has abrupt and singularity. The traditional Fourier transform analysis method and the time domain analysis method will produce large errors, and the wavelet analysis has a good ability to detect the sudden change of the signal.

Let Ψ(x) be the basis wavelet, fw (a, b) represents the continuous wavelet transform of the signal f (x) ∈ L2(R), which can be expressed as

$$\begin{array}{c}{f}_{\mathrm{w}}(a,b)=\frac{1}{\sqrt{a}}{\int }_{-\infty }^{+\infty } f(x){\Psi }^{*}\left(\frac{x-b}{a}\right)=\langle f(x),{\Psi }_{a,b}(x)\rangle \end{array}$$
(1)

In the formula: a is the expansion factor; b is the translation factor; Ψa,b(x) is the wavelet function that selects the basis wavelet Ψ(x) corresponding to a and b.

The modulus maximum point of the wavelet transform corresponds to the current fault time one-to-one. The wavelet modulus maximum point indicates that the signal has the largest rate of change at this point.

2.2 The Impact of Data Delay on the Performance of Longitudinal Differential Drotection

The multi-terminal system has m-side power supply and multi-terminal longitudinal differential protection. The differential current Id and braking current Ir of each branch in the protection area can be expressed as

$$\left\{\begin{array}{c}{\mathrm{I}}_{\mathrm{d}}=\left|{\sum}_{\mathrm{j}=1}^{\mathrm{m}} {\mathrm{I}}_{\mathrm{j}}\right|\\ {\mathrm{I}}_{\mathrm{r}}={\sum}_{\mathrm{j}=1}^{\mathrm{m}} \left|{\mathrm{I}}_{\mathrm{j}}\right|\end{array}\right.$$
(2)

In the formula, Ä°j is the current phasor of branch j.

In normal system operation and out-of-area faults, the differential current is 0 under ideal conditions, and the actual value is the unbalanced current caused by measurement errors and other factors, while the braking current is relatively large; when the system has an area fault, the differential current is the sum of the fault currents provided by each branch, the differential current value is larger, and the protection should satisfy the action equation for reliable action. The differential protection action equation can be expressed as

$$ \left\{ {\begin{array}{*{20}l} {{\text{I}}_{{\text{d}}} \geqslant {\text{k}}_{{\text{r}}} {\text{I}}_{{\text{r}}} } \hfill \\ {{\text{I}}_{{\text{d}}} \geqslant {\text{I}}_{{{\text{op}}}} } \hfill \\ \end{array} } \right. $$
(3)

Where: kr is the braking coefficient; Iop is the starting current.

The multi-terminal longitudinal differential protection uses the optical fiber network to transmit the sampled signal. The signal propagation speed in the optical fiber is about 2/3 of the speed of light in vacuum, the signal delay is about 5 μm/km, and the signal is converted, processed, and relayed. Additional delays are also generated in links such as relays and switches.

For multi-terminal longitudinal differential protection that needs to collect large-scale multi-point data, it is easy to sample data from each branch. But due to long data link transmission distance, channel congestion, data packet loss, route switching, etc. Loss of synchronization results in a phase difference. The relationship between the delay time difference between data ΔtER and the phase difference ΔφER can be expressed as

$$\Delta {\mathrm{\varphi }}_{\mathrm{ER}}={\upomega }_{\mathrm{N}}\Delta {\mathrm{t}}_{\mathrm{ER}}$$
(4)

In the formula, ωN is the power frequency angular velocity. In normal operation or an out-of-zone fault, the phase error of the two current phasors with the amplitude of Im due to the delay error, the unbalanced differential current and the braking current are

$$\left\{\begin{array}{l}{\mathrm{I}}_{\mathrm{d}}=2{\mathrm{I}}_{\mathrm{m}}sin\left(\Delta {\mathrm{t}}_{\mathrm{ER}}/2\right)\\ {\mathrm{I}}_{\mathrm{r}}=2{\mathrm{I}}_{\mathrm{m}}\end{array}\right.$$
(5)

In the case of an out-of-zone fault, the differential protection action Eq. (3) can be expressed as

$$ \frac{{{\text{I}}_{{\text{d}}} }}{{{\text{I}}_{{\text{r}}} }} = \sin (\Delta {\text{t}}_{{{\text{ER}}}} /2) \geqslant{\text{k}}_{{\text{r}}} $$
(6)

In the case of an area fault, the delay error will also bring errors to the calculation of the differential current. The differential current and the braking current are

$$\left\{\begin{array}{l}{\mathrm{I}}_{\mathrm{d}}=2{\mathrm{I}}_{\mathrm{m}}cos\left(\Delta {\mathrm{t}}_{\mathrm{ER}}/2\right)\\ {\mathrm{I}}_{\mathrm{r}}=2{\mathrm{I}}_{\mathrm{m}}\end{array}\right.$$
(7)

In the event of a fault in the area, the differential protection action Eq. (3) can be expressed as

$$ \frac{{{\text{I}}_{{\text{d}}} }}{{{\text{I}}_{{\text{r}}} }} = \cos (\Delta {\text{t}}_{{{\text{En}}}} /2) \geqslant {\text{k}}_{{\text{r}}} $$
(8)

Table 1 shows the delay error, phase error, and the ratio of the internal and external differential current Id to the braking current Ir of the two current phasors whose amplitudes are both Im when the fault occurs outside and inside the area.

It can be seen from Table 1 that with the increase of the delay error, the ratio shows a decreasing and increasing trend when the internal and external faults occur, and they are equal when the delay error reaches 5 ms. There is an intersection, so the delay error will bring obvious errors to the differential current calculation, and the protection device may cause the protection to malfunction or refuse to operate due to the loss of synchronization of the sampling data.

Table 1. Phase error and ratio of differential/braking current of different time delay error
Full size table

For a double-ended line, the currents at each end are Ä°1 and Ä°2 respectively. If the differential current Id and the braking current Ir are

$$\left\{\begin{array}{c}{\mathrm{I}}_{\mathrm{d}}=\left|{\dot{\mathrm{I}}}_{1}+{\dot{\mathrm{I}}}_{2}\right|\\ {\mathrm{I}}_{\mathrm{r}}=\left|{\dot{\mathrm{I}}}_{1}-{\dot{\mathrm{I}}}_{2}\right|\end{array}\right.$$
(9)

Then the actual action equations when the fault occurs outside the zone and the zone are respectively

$$ \begin{aligned} \frac{{{\text{I}}_{{\text{d}}} }}{{{\text{I}}_{{\text{r}}} }} = & \,\tan (\Delta {\text{t}}_{{{\text{ER}}}} /2) \geqslant {\text{k}}_{{\text{r}}} \\ \frac{{{\text{I}}_{{\text{d}}} }}{{{\text{I}}_{{\text{r}}} }} = & \,\arctan (\Delta {\text{t}}_{{{\text{ER}}}} /2) \geqslant {\text{k}}_{{\text{r}}} \\ \end{aligned} $$
(10)

Since the value of the tangent function is greater than the sine, it is more prone to malfunction when using this action equation in the case of an out-of-zone fault.

3 Principle of Self-healing Synchronization Algorithm for Mutation Data

In order to eliminate the influence of the delay error of the sampled value in the data link on the protection device, this paper proposes a data self-healing synchronization algorithm based on wavelet transform to calculate the moment of sudden change. The principle is that when a short-circuit fault occurs in the power system, after the protection device receives the sampling the data, first calculate the failure mutation time of each data mutation amount, and according to the data failure mutation time, compensate the transmission time error between each sampling value, realize the synchronization of the failure data sequence, and use the resynchronized sampling value to calculate the failure differential current and braking current value, realize the principle of multi-side differential and wide-area differential protection.

For m-terminal longitudinal differential protection, the received data includes m-terminal sampling data, and a fault occurs at time n, and the protection device actually receives the current data sequence at terminal j at time n as ij(kj), j = 1, 2,…, M, as shown in Fig. 1, the data transmission delay is

$$\Delta {\mathrm{t}}_{\mathrm{j}}={\mathrm{k}}_{\mathrm{j}}-\mathrm{n}$$
(11)

In the formula: n is the time when the fault occurs; kj is the mutation moment actually received by the protection.

By calculating the time of the sudden change of the data at each end, the time difference between the accepted current sequence ii(ki) and ij(kj) at the i-end can be calculated, as shown in Fig. 1, the time difference Δtji can be expressed as

$$\Delta {\mathrm{t}}_{\mathrm{ji}}={\mathrm{k}}_{\mathrm{j}}-{\mathrm{k}}_{\mathrm{i}}$$
(12)

By compensating the time difference Δtji between the sequence ii(ki) and ij(kj), a new i-terminal current sequence ii(n + Δtji) is obtained. Similarly, the current sequence of the other terminals after compensation is calculated, and then it is compared with the j-terminal current sequence ij(kj). Calculate the differential current, as shown in Fig. 1, the m-terminal longitudinal differential current is

$${\mathrm{i}}_{\mathrm{d}}(\mathrm{n})=\left|{\sum}_{\mathrm{i}\ne \mathrm{j}}^{\mathrm{M}-1} {\mathrm{i}}_{\mathrm{i}}\left(\mathrm{n}+\Delta {\mathrm{t}}_{\mathrm{ji}}\right)+{\mathrm{i}}_{\mathrm{j}}(\mathrm{n})\right|$$
(13)
Fig. 1.
figure 1

Schematic of mutation data synchronization algorithm

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By calculating the moment of sudden change in the current sequence at each end, the time difference caused by the delay of the transmission link is compensated, the additional phase error of the current sequence at each end is eliminated, the current sequence at each end can be resynchronized, and the protection device can correctly calculate the post-fault differential current, judge the fault section, avoid the wrong operation of the protection device due to the delay error of the data transmission link.

When the system is running normally, the electrical quantity at each end does not produce a sudden change, and the sudden change method cannot be used to achieve synchronization. At this time, the phase difference of the current at each end constituting the differential protection is small, and the fixed delay compensation method and the waveform zero-crossing point detection can be used to achieve data synchronization.

4 Simulation Verification of Self-healing Synchronization Algorithm for Mutation Data

Use PSCAD to establish a 500 kV multi-terminal power grid system simulation model, as shown in Fig. 2, simulate the internal and external short-circuit faults under various operating conditions in the system, collect fault current signals at each end of the system, write simulation programs, and simulate sampling data is transmitted to the protection device through the optical fiber communication channel, random delay errors are generated due to factors such as channel distance, congestion, route self-healing or reconstruction, which causes the sampling data received by the protection device to lose synchronization, and this paper proposes wavelet transform to calculate the sudden change amount data self-healing synchronization algorithm resynchronizes and corrects the data to ensure that the protection device correctly judges the fault zone.

Fig. 2.
figure 2

PSCAD simulation principle of multi-terminal power system

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4.1 External Fault Simulation Analysis

When the external fault point F1 in Fig. 2 is short-circuited, the multi-terminal longitudinal differential protection device receives the current at each end through the communication channel. For the convenience of observation, the A-phase current on each side is selected for analysis. As shown in Fig. 3(a), from the current waveform, the currents on each side that should have abrupt changes at the time of the fault are obviously out of synchronization. After eliminating the influence of the distributed capacitance of the line through current compensation and eliminating the influence of the non-periodic component in the sampled data, the phase A current on each side is shown in Fig. 3(b). It can be seen from Fig. 3 (a) and (b) that there is a significant phase difference between the short-circuit currents of phase A at each end, and a large differential current will be generated when an external fault occurs. The following calculation methods need to be used to calculate the differential current and braking current

$$\left\{\begin{array}{l}{\mathrm{I}}_{\mathrm{d}}=\left|{\dot{\mathrm{I}}}_{1}+{\dot{\mathrm{I}}}_{2}+{\dot{\mathrm{I}}}_{3}\right|\\ {\mathrm{I}}_{\mathrm{r}}=\left|{\mathrm{I}}_{1}\right|+\left|{\mathrm{I}}_{2}\right|+\left|{\mathrm{I}}_{3}\right|\end{array}\right.$$
(14)

Using the sudden change data self-healing synchronization algorithm proposed in this paper, the sampled data on each side can be resynchronized according to the sudden change time. After synchronization, the short-circuit current of each endpoint and the calculated differential current phase A waveform are shown in Fig. 3.

As shown in (c), it can be seen that the short-circuit current at each end after resynchronization eliminates the phase difference and only has a small differential current. Perform simulation programming on the differential current Id and braking current Ir of the multi-terminal longitudinal differential protection, calculate the effective value of the differential current Id and braking current Ir, and draw the braking curve, as shown in Fig. 3(d), including From the moment when the first fault mutation occurs on one side of the line, to the last side mutation.

Sampling data several cycles after the time, where the arrow is the direction of the order of data change over time. It can be seen from Fig. 3(d) that from the moment of the first sudden change to the sudden change on each side, the differential current action characteristic is in the action zone, indicating that in the event of an external fault, the data is out of synchronization or due to factors such as communication congestion. Part of the data is lost, guarantee.

The protective device may malfunction due to too much error in the calculated value of the differential current. The differential current action characteristic after the external fault synchronization is always in the braking zone, indicating that the out-of-synchronization data of the external fault has been resynchronized.

Fig. 3.
figure 3

Simulation analysis of external faults

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4.2 Ixternal Fault Simulation Analysis

When the internal fault point F2 in Fig. 2 is short-circuited, the protection device receives currents from each end point through the communication channel, and the phase A currents on each side are shown in Fig. 4(a). Obviously out of sync at the moment of sudden change in current on each side.

Phenomenon, after compensating the distributed capacitive current of the line and eliminating the influence of the non-periodic component, the phase A current on each side is shown in Fig. 4(b).

After using the sudden change data self-healing synchronization algorithm proposed in this paper to realize data resynchronization, the short-circuit current and differential current waveform diagram of each end point are shown in Fig. 4(c). It can be seen from Fig. 4(c) that the short-circuit current of each terminal after resynchronization eliminates the phase difference, and the differential current can accurately reflect the fault current.

Fig. 4.
figure 4

Simulation analysis of internal faults

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There is an obvious phase difference in the short-circuit current of phase A at each end. The calculated differential current is greatly reduced, and the braking current is relatively large. The effective value of the current is calculated and the braking curve is drawn, as shown in Fig. 4(d). The sequence direction of the time change, and the differential current action characteristic is in the action zone, indicating that the internal fault out-of-synchronization data can ensure the correct action of the protection device after resynchronization and correction.

Figure 4(d) includes data from the moment of the first fault mutation on one side of the line to a few cycles after the last moment of mutation; the differential current action characteristic is in the braking zone, indicating that in the event of an internal fault, Using the failure sampling data that is out of synchronization or partly lost, the protection device may decrease the sensitivity of the action or even refuse to move due to the significant reduction in the calculated value of the differential current.

It can be seen from the simulation analysis that the synchronization of the sampled value is very important for the multi-terminal longitudinal differential protection. When there is a large phase error between the sampled values, it may cause errors in the calculation of the differential current and lead to protection. Misoperation or refusal of operation due to wrong judgment of the fault zone. This paper proposes a multi-terminal longitudinal differential protection mutation data synchronization algorithm based on wavelet transform that can effectively correct the transmission phase error of the sampled data, and automatically realize the multi-side sampled data. The re-synchronization ensures the accuracy of the calculation of the differential current of the multi-terminal longitudinal differential protection and the correctness of the fault interval judgment, and improves the reliability of the multi-terminal longitudinal differential protection and wide-area differential protection.

5 Conclusion

Using the sampling data of the fault current at each end, due to the complexity of the transmission link and the communication problem, and the characteristics of different sudden changes, a multi-terminal longitudinal differential protection based on wavelet transform to calculate sudden change data self-healing synchronization algorithm is proposed. Realize the resynchronization of the sampled data at each end that has lost synchronization, and ensure that the protection device correctly judges the fault interval, thereby improving the reliability of the multi-terminal longitudinal differential protection and the wide-area differential protection. The principle analysis and simulation verification prove the correctness and effectiveness of the algorithm.

This algorithm is not only suitable for multi-terminal longitudinal differential protection based on steady-state components, but also suitable for longitudinal differential protection based on transient components of sampled values. For the wide-area differential principle protection and remote backup protection center based on wide-area information, the use of mutation data self-healing synchronization algorithms or other data synchronization algorithms is even more important to ensure the reliability of protection actions.