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New Principle of Busbar Protection Based on Active Power and Extreme Learning Machine ()

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*Open Access Library Journal*,

**7**, 1-18. doi: 10.4236/oalib.1106167.

1. Introduction

Busbar protection plays an important role in the power system and bears the responsibility of transmitting electrical energy [1] [2]. When a fault occurs on the bus, if it cannot be processed in time, it will inevitably affect the stable operation of the power system and even cause the regional power system to collapse [3]. In order to prevent the serious consequences of the busbar fault, special busbar protection should be set to timely and correctly interrupt the faulty busbar short-circuit current. The protection device should operate quickly and reliably to shorten the fault removal time and ensure the stable operation of the power grid [4] [5]. In order to prevent the serious consequences of busbar faults, special busbar protection should be set to timely and correctly interrupt all busbar short-circuit currents, which puts higher requirements on the performance of busbar protection.

The protection of power frequency in busbar protection is the most widely used in current differential protection, but it may be misjudged due to problems such as TA error and TA saturation [6], and the action speed is slow, and it is protected in the super/extra high voltage grid. Performance does not meet system operating requirements. Although transient protection can achieve rapid protection, there is still a small initial angle [7]. The literature [8] defines the transient traveling wave power. The wavelet transform method is used to identify and compare the transient traveling wave power polarity of each line. According to the polarity characteristics of the traveling wave power of all lines in the fault, the busbar area is discriminated. External failure, but did not solve the effect of small initial angle of failure. In [9], the directional traveling wave on each outgoing line in a specific time period after the fault is integrated, and the busbar fault is established by analyzing the magnitude of the forward and backward traveling wave integral ratio.

In recent years, S-transformation and power theory have been more maturely used in power systems [10] [11] [12]. In [10], the fault direction identification is realized by using the S-transformed power difference between the active power and the busbar. Reference [11] uses the S-transform reactive power to detect the fault direction when the amplitude of the reactive power is outside the busbar.

This paper draws on the direction traveling wave and power theory described in the literature [10] [11] [12], combined with the application of S transform in power system [13] [14] [15], calculates the voltage and current traveling wave S transform active for a period of time after each fault of the busbar line. Power is combined with the limit learning machine to achieve faults inside and outside the busbar.

2. Fault Current Traveling Wave Characteristics Analysis

2.1. The Basic Theory of Fault Traveling Waves

Figure 1 shows the busbar of the 500 kV substation, L1 - L4 are the four lines connected by the busbar M, and R1 - R4 are the traveling wave protection units installed at the M end of the corresponding bus near the bus. When the fault occurs at the F2 on the line L2, The wave propagates from the fault point along the line to both sides and deflection occurs at the discontinuity of the wave impedance. For any point on the line from the fault point x, the transient voltage and current at this point are obtained [9]:

$\{\begin{array}{l}\Delta u\left(x,t\right)=\Delta {u}_{+}\left(x-tv\right)+\Delta {u}_{-}\left(x+tv\right)\\ \Delta i\left(x,t\right)=\Delta {i}_{+}\left(x-tv\right)+\Delta {i}_{-}\left(x+tv\right)\\ v=1/\sqrt{LC}\end{array}$ (1)

Figure 1. Sketch map of 500 kV busbar system.

where: t is the observation time, L and C are the inductance and capacitance of the line per unit length; $\Delta {u}_{+}\left(\Delta {u}_{-}\right),\Delta {i}_{+}\left(\Delta {i}_{-}\right)$ are the forward (reverse) traveling waves of voltage and current propagating along the positive (reverse) direction of X.

According to the traveling wave propagation theory, the time when the initial traveling wave reaches the bus bar M is ${t}_{0}$, the traveling wave is deflected and reflected for the second time to reach the bus bar. The moment is ${t}_{1}$, so in ${t}_{0}~{t}_{1}$ time period, the fault traveling wave obtained by the protection unit ${R}_{k}\left(k=1,2,3,4,5\right)$ of each associated line of the bus bar is called an initial voltage and a current traveling wave. among them, the $\Delta {u}_{M}$ is initial voltage traveling wave for bus M. $\Delta {i}_{k}\left(k=1,2,3,4\right)$ is the current traveling wave measured for each line of the bus. ${Z}_{c1}~{Z}_{c4}$ are the wave impedances of the associated lines L1 to L5 of the bus bar, and the equivalent impedance of the bus line M to the ground stray capacitance is ${Z}_{cm}$.

2.2. Analysis of Fault Current Traveling Wave Propagation Process

2.2.1. Characteristics of Current Traveling Wave in Busbar Internal Fault

The analysis shows that the transient voltage and current at any point on the line are superposition of the forward and reverse traveling waves. The current forward and reverse traveling waves obtained by Equation (1) are [9]:

$\{\begin{array}{l}\Delta {i}_{+}=\frac{1}{2}\left[\Delta i+\frac{{\Delta}_{u}}{{z}_{c}}\right]\\ \Delta {i}_{-}=\frac{1}{2}\left[\Delta i-\frac{{\Delta}_{u}}{{z}_{c}}\right]\end{array}$ (2)

${\Delta}_{u}$, ${\Delta}_{t}$ are the voltage and current fault components measured for each line R, and ${Z}_{c}$ is the line wave impedance.

It can be seen from the propagation characteristics of the traveling wave that the traveling wave at the fault point and the bus bar will be deflected [9]. Referring to Figure 1, the positive direction of the traveling wave is defined as the bus line pointing to the line. When the internal fault of the bus line occurs, the traveling mode of the traveling wave is as shown in Figure 2, among them, $\Delta {i}_{{n}^{+}}\left(n=1,2,3,4,5\right)$ is the forward traveling wave of the nth associated line.

When an internal fault occurs in the busbar, each outgoing line is a transmission line with evenly distributed parameter characteristics, and the wave impedance does not deflect on the line. Let the length of the shortest line L among the associated lines be ${d}_{\mathrm{min}}$. Only the initial forward traveling wave is detected at each associated line R in the $\left[{t}_{0},{t}_{0}+2{d}_{\mathrm{min}}/v\right]$ time period, and there is no reverse traveling wave formed by the forward traveling wave reflection.

2.2.2. Initial Traveling Wave Power Distribution in Case of Internal Fault of Bus M

The Peterson equivalent circuit of bus m in case of point F1 fault is shown in Figure 3, where $\Delta {\stackrel{\dot{}}{u}}_{m}$ is the traveling wave vector of the initial voltage of bus M measured, and $\Delta {\stackrel{\dot{}}{I}}_{k}\left(k=1,2,3,4,5\right)$ is the traveling wave vector of the current measured by the M terminal protection unit of each line connected to the bus. The wave impedances of lines ${\text{L}}_{1}~{\text{L}}_{5}$ are ${Z}_{c1}~{Z}_{c5}$ and ${Z}_{cm}$ are equivalent impedances of stray capacitance of bus m to ground.

When S transforms, the traveling wave frequency is $f=50~100\text{\hspace{0.17em}}\text{kHz}$, when the super (extra) high-voltage transmission line wave impedance can be approximated as a real constant, it is equivalent to the resistance [15] in the Peterson equivalent circuit, and the bus-to-ground equivalent capacitance impedance ${Z}_{cm}=1/j\omega {C}_{m}=1/j2\pi f{C}_{m}$ is imaginary (f is corresponding traveling frequency).

Figure 2. Propagation of fault traveling wave in fault of bus.

Figure 3. Equivalent circuit based on Peterson principle for busbar internal fault.

From the definition of the initial traveling wave complex power [15], taking the L1 line as an example, the initial traveling wave complex power of the M-side of the near-busbar of the line can be obtained as:

$\Delta {S}_{1}=\Delta {u}_{M}\Delta {l}_{1}^{*}$ (3)

when the internal F1 point of the busbar fails, the Peterson equivalent circuit of Figure 3 shows:

$\Delta {l}_{1}=\Delta {u}_{M}\left(1/{Z}_{c1}\right)$ (4)

Since the line wave impedance is approximately a real constant, it is equivalent to the resistance [16] - [19] in the equivalent circuit, and the complex power measured by the M1 IED1 protection unit of the L1 line can be obtained:

$\begin{array}{c}\Delta {\stackrel{\u02dc}{S}}_{1}=\Delta {\stackrel{\dot{}}{U}}_{M}\Delta {\stackrel{\dot{}}{I}}_{1}^{\ast}=\Delta {\stackrel{\dot{}}{U}}_{M}\times \left[\Delta {\stackrel{\dot{}}{U}}_{M}^{*}\left(1/{Z}_{c1}\right)\right]\\ =\Delta {U}_{M}^{2}\times \left(1/{Z}_{c1}\right)={P}_{1}+j{Q}_{1}\end{array}$ (5)

In the middle: ${P}_{1}$ is the initial traveling wave active power of the line, and ${Q}_{1}$ is the initial traveling wave reactive power of the line, when the busbar internal fault occurs:

${P}_{1}=\Delta {U}_{M}^{2}\times \left(1/{Z}_{c1}\right)$ (6)

Similarly, the initial traveling wave active power measured by the M-side protection unit of other lines connected to the busbar can be derived: ${P}_{i}=\Delta {U}_{M}^{2}/{Z}_{ci}\left(i=1,2,3,4,5\right)$.

Ideally, due to the internal fault of the bus, the wave impedance ${Z}_{i}\left(i=1,2,3,4\right)$ of each line is almost the same. According to formula (5), the initial traveling wave active power measured by all associated lines of the bus is basically the same, that is ${P}_{1}\approx {P}_{2}\approx {P}_{3}\approx {P}_{4}$, is greater than 0.

2.2.3. Current Traveling Wave Characteristics of Busbar External Fault

Figure 4 shows the propagation of forward and reverse traveling waves when line L2 fails. Among them, $\Delta {i}_{n\text{+}}\left(n=1,2,3,4\right)$ is the forward traveling wave of each associated line, $\Delta {i}_{2-}$ is the reverse traveling wave of the line L2, since the reverse traveling wave of the line L2 forms a buckling reflection when reaching

Figure 4. Propagation of fault traveling wave in fault of bus.

the bus bar, forming a forward wave $\Delta {i}_{2\text{+}}$ formed by the reflection of the reverse traveling wave. Only the faulty line detects the reverse traveling wave during the $\left[{t}_{0},{t}_{0}+2{d}_{\mathrm{dim}}/v\right]$ time period.

In summary, when the bus line fails, the associated lines are in the $\left[{t}_{0},{t}_{0}+2{d}_{\mathrm{dim}}/v\right]$ time period, only the forward traveling wave is detected; when the bus area outside the fault occurs, when an out-of-bus fault occurs within the time period $\left[{t}_{0},{t}_{0}+2{d}_{\mathrm{dim}}/v\right]$, the reverse traveling wave can only be detected on the faulty line.

2.2.4. Initial Traveling Wave Power Distribution When Bus M External Fault

When the F2 point on the L2 line fails, the Peterson equivalent circuit of the bus M is as shown in Figure 5.

As can be seen from Figure 5:

$\Delta {\stackrel{\dot{}}{I}}_{2}=-\Delta {\stackrel{\dot{}}{U}}_{M}\left(1/{Z}_{c1}+1/{Z}_{c3}+1/{Z}_{c4}+j\omega {C}_{m}\right)$ (7)

The complex power measured by the L2 fault line near the bus M-side protection unit IED2 can be obtained:

$\begin{array}{c}\Delta {\stackrel{\u02dc}{S}}_{2}=\Delta {\stackrel{\dot{}}{U}}_{M}\Delta {\stackrel{\dot{}}{I}}_{2}^{\ast}\\ =\Delta {\stackrel{\dot{}}{U}}_{M}\times \left[-\Delta {\stackrel{\dot{}}{U}}_{M}^{*}\left(1/{Z}_{c1}+1/{Z}_{c3}+1/{Z}_{c4}-j\omega {C}_{m}\right)\right]\\ =-\Delta {U}_{M}^{2}\times \left(1/{Z}_{c1}+1/{Z}_{c3}+1/{Z}_{c4}\right)+\Delta {U}_{M}^{2}\times j\omega {C}_{m}\\ ={P}_{2}+j{Q}_{2}\end{array}$ (8)

That is, when the busbar external fault occurs, the initial traveling wave active power of the faulty line is:

${P}_{2}=-\Delta {U}_{M}^{2}\times \left(1/{Z}_{c1}+1/{Z}_{c3}+1/{Z}_{c4}\right)$ (9)

For the non-faulty line connected to bus M, take L3 as an example. In Figure 5:

$\Delta {\stackrel{\dot{}}{I}}_{3}=\Delta {\stackrel{\dot{}}{U}}_{M}\left(1/{Z}_{c3}\right)$ (10)

The complex power measured by the M-side IED3 protection unit of the L3 line:

$\begin{array}{c}\Delta {\stackrel{\u02dc}{S}}_{3}=\Delta {\stackrel{\dot{}}{U}}_{M}\Delta {\stackrel{\dot{}}{I}}_{3}^{\ast}=\Delta {\stackrel{\dot{}}{U}}_{M}\times \left[\Delta {\stackrel{\dot{}}{U}}_{M}^{*}\left(1/{Z}_{c3}\right)\right]\\ =\Delta {U}_{M}^{2}\times \left(1/{Z}_{c3}\right)={P}_{3}+j{Q}_{3}\end{array}$ (11)

${P}_{3}=\Delta {U}_{M}^{2}/{Z}_{c3}$ (12)

Figure 5. Equivalent circuit based on Peterson principle for busbar external fault.

Similarly, the initial traveling wave active power measured by the M-side protection unit of other non-faulty lines connected to the busbar can be obtained: ${P}_{i}=\Delta {U}_{M}^{2}/{Z}_{ci}\left(i=1,4\right)$.

3. Calculate the Initial Traveling Wave Active Power Based on the S Transform

3.1. Basic Principle of S Transform

S transform is a reversible local time-frequency analysis method, which avoids the selection of window function and improves the fixed window width defects. At the same time, the feature quantity extracted by S transform is not sensitive to noise [17].

Set the continuous time signal to $h\left(t\right)$, then the continuous S transform of the time signal is defined as:

$\{\begin{array}{l}S\left(\tau ,f\right)={\displaystyle \underset{-\infty}{\overset{\infty}{\int}}h\left(t\right)g\left(\tau -t,f\right){\text{e}}^{-i2\Pi ft}\text{d}t}\\ g\left(\tau -t,f\right)=\frac{\left|f\right|}{\sqrt{2\pi}}{\text{e}}^{-\frac{{\left(\tau -t\right)}^{2}}{2{\sigma}^{2}}}\end{array}$ (13)

$\tau $ is the parameter that controls the position of the Gaussian window on the time axis, f is the continuous frequency, t is the time, i is the imaginary number, $\sigma =1/\left|f\right|$, $g\left(\tau -t,f\right)$ is a Gaussian window and is affected by frequency changes.

If $h\left[kT\right]\left(k=0,1,2,\cdots ,N-1\right)$ is the signal $h\left(t\right)$ discrete time series obtained by sampling, T is the sampling interval and N is the number of sampling points. The discrete Fourier transform function of $h\left[kT\right]$ is:

$h\left[\frac{n}{NT}\right]=\frac{1}{N}{\displaystyle \underset{k=0}{\overset{N-1}{\sum}}h\left[kT\right]{\text{e}}^{-j\frac{2\Pi kn}{N}}}$ (14)

where $n=0,1,\cdots ,N-1$

The discrete S transform of signal $h\left(t\right)$ is:

$\{\begin{array}{l}S\left[kT,\frac{n}{NT}\right]={\displaystyle \underset{r=0}{\overset{N-1}{\sum}}H\left(\frac{r+n}{NT}\right){\text{e}}^{-\frac{2{\Pi}^{2}{r}^{2}}{{n}^{2}}}{\text{e}}^{j\frac{2\Pi rk}{N}},{n}^{1}0}\\ S\left[kT,0\right]=\frac{1}{N}{\displaystyle \underset{r=0}{\overset{N-1}{\sum}}h\left(\frac{r}{NT}\right),n=0}\end{array}$ (15)

A complex time-frequency matrix is obtained by S transform, which reflects the time domain and frequency domain characteristics of the signal and the amplitude information of the traveling wave in the time domain.

3.2. Calculation of Initial Traveling Wave Active Power

For a three-phase transmission system, there is a coupling between each phase voltage and each phase current, which is generally decoupled by phase-mode transformation. In this paper, the combined modulus method is used to transform the phase mode to reflect various fault types [17]:

$\Delta {i}_{z}=4\Delta {i}_{\alpha}+\Delta {i}_{\beta}$ (16)

$\Delta {u}_{z}=4\Delta {u}_{\alpha}+\Delta {u}_{\beta}$ (17)

Among them, $\Delta {u}_{\alpha},\Delta {i}_{\alpha}$ are the voltage and current traveling wave α line mode components after decoupling treatment, $\Delta {u}_{\beta}$ and $\Delta {i}_{\beta}$ are the processed voltage and current traveling wave β line mode components.

In this paper, the method used in [18] [19] is used to perform discrete S-transformation on the transformed combined modulus fault voltage and current traveling wave modulus, and extract the phasor corresponding to 20 sampling points of the single-frequency initial traveling wave.

The combined modulus current $\Delta {i}_{2}$ obtained by the IED2 protection unit after a three-phase short circuit occurs at point F2 on line L2 as an example, discrete S-transform principle $\Delta {i}_{2}$ according to the above-mentioned S-transform principle, and one-dimensional complex vector [18] [19] is obtained on selected frequency ${f}_{Z}$, which can be expressed as:

$\Delta {l}_{2n}\left({t}_{n},{f}_{z}\right)=\Delta {l}_{2n}\left({t}_{n},{f}_{z}\right)\mathrm{exp}\left[j{\theta}_{2n}\left({t}_{n},{f}_{z}\right)\right]$ (18)

$\Delta {l}_{2gn}\left({t}_{{}^{n}},{f}_{Z}\right),{\theta}_{2gn}\left({t}_{n},{f}_{Z}\right)$ are the amplitude of $\Delta {l}_{2gn}\left({t}_{n},{f}_{Z}\right)$, where n is the sampling point n and ${t}_{n}$ is the sampling time of the sampling point n.

After the fault occurs, the transient traveling wave reaches the bus M after a period of time and propagates on the bus associated line. The L2 line near-bus M-side protection unit IED2 captures the initial traveling wave, if the amplitude of the line is $\Delta {l}_{21}$ at the moment of ${t}_{1}$, $\Delta {l}_{2g1}\left({t}_{1},{f}_{Z}\right)$ obtained at the selected frequency ${f}_{Z}$ is the corresponding initial current traveling wave phasor at that time [18] [19]. Similarly, the initial voltage traveling wave phasor $\Delta {U}_{M1}\left({t}_{1},{f}_{Z}\right)$ measured by bus M at time ${t}_{1}$ can be obtained. The other non-faulty line associated with the bus is near the bus end at the selected frequency ${f}_{Z}$. The phasors corresponding to the 20 initial sampling points of the initial current traveling wave are $\Delta {l}_{1n}\left({t}_{n},{f}_{Z}\right)\Delta {l}_{3n}\left({t}_{n},{f}_{Z}\right)$ and $\Delta {l}_{4n}\left({t}_{n},{f}_{Z}\right)\left(n=1,2,\cdots ,20\right)$.

Under the selected S-transform single frequency, using the phasor corresponding to each sampling point of the initial traveling wave obtained by the above-mentioned derivation, the active power corresponding to 20 sampling points of the initial traveling wave of each associated line in the occurrence of the out-of-area fault of the bus M can be calculated.

Based on the above analysis, when the busbar is internally generated, the initial traveling wave active power measured by each associated line of the busbar is $\Delta {U}_{M\xb7n}^{2}\left({t}_{n},{f}_{Z}\right)/{Z}_{ci}$, where $i=1,2,3,4$ ; When the busbar is external, the initial traveling wave active power measured by the faulty line is $\Delta {U}_{M\xb7n}^{2}\left({t}_{n},{f}_{Z}\right)/\left(1/{Z}_{c1}+1/{Z}_{c3}+1/{Z}_{c4}\right)$ (assuming L2 line fault as an example), non-fault line active power is $\Delta {U}_{Mgn}\left({t}_{n},{f}_{Z}\right)/{Z}_{ci}\left(i=1,3,4\right)$.

4. Extreme Learning Machine

The feedforward neural network is a kind of artificial neural network [20]. In this neural network, each neuron starts from the input layer, receives the input of the previous stage, and inputs it to the next stage until the output layer. There is no feedback throughout the network, and a directed acyclic graph can be used. The feedforward neural network is the earliest proposed artificial neural network and the simplest type of artificial neural network. According to the number of layers of the feedforward neural network, it can be divided into a single layer feedforward neural network and a multilayer feedforward neural network. Among them, common feedforward neural networks include BP neural network [20], radial basis function (RBF) neural network [20] and extreme learning machine (ELM) neural network [20].

Extreme learning machine is an easy-to-use and effective single-hidden layer feedforward neural network SLFN learning algorithm [20]. The network consists of input layer, hidden layer and output layer, input layer and hidden layer and hidden layer. Among them, the input layer has n neurons, corresponding to n input variables; the hidden layer has 1 neuron; the output layer has m neurons, corresponding to m output variables. Figure 6 is a block diagram of a single hidden layer ELM network.

ELM only needs to set the number of hidden layer neurons in the network. It does not need to adjust the input weight of the network and the bias of the hidden element during the execution of the algorithm. Compared with the traditional neural network [21] [22], it changes. The BP neural network is based on the gradient descent learning idea. It does not need to iteratively update the network parameters. It changes the SVM learning performance and relies on the parameter adjustment. It has the advantages of fast learning speed and good generalization performance, and only produces the unique optimal solution.

Given N different training samples $\left({x}_{i},{t}_{i}\right)$, among them,

$\begin{array}{l}{x}_{i}={\left[{x}_{i1},{x}_{i2},\cdots ,{x}_{in}\right]}^{\text{T}}\in {R}^{n}\\ {t}_{i}={\left[{t}_{i1},{t}_{i2},\cdots ,{t}_{im}\right]}^{\text{T}}\in {R}^{M}\end{array}$ (19)

Given an excitation function $g\left(x\right)$, after that, the output containing L hidden layer nodes can be expressed as,

$\underset{i=1}{\overset{L}{\sum}}{\beta}_{i}g\left({a}_{i}{x}_{j}+{b}_{i}\right)={\displaystyle \underset{i=1}{\overset{L}{\sum}}{\beta}_{i}G}}\left({a}_{i},{b}_{i},{x}_{j}\right)={t}_{i$ (20)

Figure 6. ELM network structure.

Among them, $j=1,2,\cdots ,N$ ; ${a}_{i}={\left[{a}_{i1},{a}_{i2},\cdots ,{a}_{in}\right]}^{\text{T}}$ is the input weight of the input node and the i-th hidden layer node; ${b}_{i}$ is the neuron offset for the i-th hidden layer node; ${\beta}_{i}={\left[{\beta}_{i1},{\beta}_{i2},\cdots ,{\beta}_{im}\right]}^{\text{T}}$ is the output weight of the i-th hidden layer node and the output node.

The algorithm steps are as follows:

1) Randomly selected $\left({a}_{i},{b}_{i}\right)$ and map sample to the new fealure space through $h\left(x\right)={\left[G\left({a}_{1},{b}_{1},x\right),\cdots ,G\left({a}_{L},{b}_{L},x\right)\right]}^{\text{T}}$. If the hidden layer matrix H is formed by the random fealure map $h\left(x\right)$, then:

$H\beta =T$ (21)

Among it,

$H=\left[\begin{array}{c}h\left({x}_{1}\right)\\ \vdots \\ h\left({x}_{N}\right)\end{array}\right]=\left[\begin{array}{ccc}G\left({a}_{1},{b}_{1},{x}_{1}\right)& \cdots & G\left({a}_{L},{b}_{L},{x}_{1}\right)\\ \vdots & \ddots & \vdots \\ G\left({a}_{1},{b}_{1},{x}_{N}\right)& \cdots & G\left({a}_{L},{b}_{L},{x}_{N}\right)\end{array}\right]$,

$\beta ={\left[\begin{array}{c}{\beta}_{1}^{\text{T}}\\ \vdots \\ {\beta}_{L}^{\text{T}}\end{array}\right]}_{L\times m}$ and $T={\left[\begin{array}{c}{t}_{1}^{\text{T}}\\ \vdots \\ {t}_{N}^{\text{T}}\end{array}\right]}_{N\times m}$

Sigmoid function is selected as the excitation function of hidden layer node $g\left({a}_{i}{x}_{j}+{b}_{i}\right)=\frac{1}{1+\mathrm{exp}\left(-{a}_{i}{x}_{j}+{b}_{i}\right)}$

2) In the new feature space, the optimal output weight $\stackrel{^}{\beta}$ and $\stackrel{^}{\beta}={H}^{+}T$ are sought by least squares method by Equation (12), where ${H}^{\text{+}}$ is the Moore Penrose generalized inverse of H.

5. Bus Fault Area Identification Method

T-line line traveling wave protection ${R}_{k}\left(k=1,2,3,4\right)$ unit after fault detected voltage and current traveling wave is S-transformed and the S-transform single frequency is selected to be 60 kHz. Select different transition resistances, different fault types and different initial angles of the fault to simulate the faults of the bus and the associated line. The out-of-area lines are simulated according to the same fault and different fault distances are set as simulation conditions. Bus internal fault and external fault constitute active power vector $\nabla P$, among them:

$\nabla {P}_{m}={\left[\nabla {P}_{m1}\nabla {P}_{m2}\cdots \nabla {P}_{m5}\right]}_{1\times 5}$

And $\nabla {P}_{mi}={\left[{P}_{1}{P}_{2}\cdots {P}_{20}\right]}_{1\times 20}\left(m=1,2,3,4;i=1,2,3,4\right)$, $\nabla P$ indicates bus fault data, The initial traveling wave active power vector of the fault in the busbar is combined into a bus fault characteristic vector $\nabla P$. In this way, the bus fault feature is characterized, and the fault region label is used as the sample data of the extreme learning machine, wherein

$\nabla P={\left[\nabla {P}_{11}\cdots \nabla {\stackrel{^}{P}}_{M1}\nabla {P}_{21}\cdots \nabla {\stackrel{^}{P}}_{M2}\nabla {P}_{31}\cdots \nabla {\stackrel{^}{P}}_{M3}\right]}_{1\times 15}$

The fault identification algorithm flow is shown in Figure 7.

Figure 7. Flow chart of fault branch identification algorithm.

6. Simulation and Experiment

The PSCAD/EMTDC electromagnetic transient simulation software is used to establish the 500 kVT connection line simulation model shown in Figure 1. The line model uses a frequency-dependent distributed parameter model that can accurately reflect transient and harmonic responses. The line type uses TOWER: 3H5 tower. The simulation sampling frequency is 200 kHz, and the lengths of each branch are L_{1} = 230 km, L_{2} = 250 km, L_{3} = 300 km, and L_{4} = 210 km. Select the S-transform single frequency to calculate the fault active power under different conditions of different transition resistances, different fault types and different initial angles of the fault, and form the active power vector

$\nabla {P}_{m}={\left[\nabla {P}_{m1}\nabla {P}_{m2}\cdots \nabla {\stackrel{^}{P}}_{m5}\right]}_{1\times 5}$. Combine active power under different transition

resistances, different fault types and different initial angles of faults into fault eigenvectors $\nabla P$. In order to characterize the fault characteristics in the busbar area, the sample set required by the extreme learning machine is established

accordingly, wherein $\nabla P={\left[\nabla {P}_{11}\cdots \nabla {\stackrel{^}{P}}_{M1}\nabla {P}_{21}\cdots \nabla {\stackrel{^}{P}}_{M2}\nabla {P}_{31}\cdots \nabla {P}_{M3}\right]}_{1\times 15}$.

6.1. Sample Data

In order to verify the effectiveness and reliability of the algorithm, this paper chooses to carry out simulation experiments in the busbar area and outside under different fault types, different transition resistances, and different initial angles of faults.

The training samples of the extreme learning machine are composed of the active power of each line in the associated line of the busbar and the internal fault of the busbar. The random fault samples of the bus-line associated line are 96 fault eigenvectors obtained by simulating three different faults for the four branches outside the zone under different fault conditions. At the same time, in order to improve the reliability of the algorithm, different fault distances are set in the fault.

6.2. Extreme Learning Machine Intelligent Fault Recognition Model Establishment and Training Sample Test Analysis

The fault characteristic training sample is input into the limit learning machine for training, and a trained extreme learning machine bus fault recognition model is obtained. Among them, the optimal number of neurons in the hidden layer of the extreme learning machine obtained by the trial and error method is 35.

The fault characteristic training samples are input into the trained extreme learning machine intelligent fault recognition model for testing, and the comparison of the predicted results is shown in Figure 8.

It can be seen from the above figure that the test sample data in the extreme learning machine fault intelligent recognition model has a correct rate of 100%.

6.3. Test Sample Test Analysis

6.3.1. Different Fault Initial Angle Test

The fault characteristic test samples of different initial angles of the faults are input into the intelligent learning model of the limit learning machine busbar fault area for testing. The comparison of the prediction results is shown in Figure 9, wherein Table 1 is the simulation verification result corresponding to the fault condition.

Figure 8. Comparison of training set prediction results.

Figure 9. Comparison of test set prediction results.

Table 1. Test results of protection algorithm under different inception angles for external fault of bus.

It can be seen from the above chart that the accuracy of the test results in the extreme learning machine fault intelligent identification model is 100%, and the faults in the zone can be identified when different types of faults occur in the busbar area, so the protection algorithm is not affected by the initial angle of the fault.

6.3.2. Analysis of Different Transition Resistance Tests

The fault characteristic test samples of different transition resistances in the area and outside are input into the intelligent learning model of the limit learning machine busbar fault area for testing. The comparison of the prediction results is shown in Figure 10 and Table 2 is the simulation verification result corresponding to the fault condition.

It can be seen from the above chart that the test sample data in the extreme learning machine intelligent fault identification model test results in a correct rate of 100%, in the occurrence of different transition resistance faults within the busbar area and outside can accurately identify the faults inside and outside the area, so the fault identification algorithm is not The effect of the transition resistance.

Figure 10. Comparison of training set prediction results.

Table 2. Test results of protection algorithm under different transition resistance in case of external fault of bus.

6.3.3. Testing of Different Fault Types

The fault characteristic test samples tested by different fault types in the area and outside are input into the intelligent learning model of the limit learning machine bus fault area for testing. The comparison of the predicted results is shown in Figure 11, wherein Table 3 is the simulation verification result corresponding to the fault condition.

It can be seen from the above chart that the test sample data has a correct rate of 100% in the test of the intelligent learning model of the extreme learning machine, and can accurately identify the faults in the area and outside under different fault types, so the protection algorithm is basically not affected by the fault type.

Based on the above analysis, the proposed algorithm is not affected by the initial angle of the fault, the transition resistance and the type of fault, and can reliably identify the fault area.

Figure 11. Comparison of training set prediction results.

Table 3. Test results of protection algorithm under different fault types in case of external fault of bus.

7. Conclusions

This paper proposes a new fast bus protection algorithm based on the combination of active power and extreme learning machine. By performing S-transformation on the fault voltage and current traveling wave, the active power amplitude within 0.1 ms after the fault is utilized. The feasibility of the fault identification method is verified by a large number of simulation experiments. The theoretical and simulation results show that:

1) The algorithm identifies the fault area by establishing the intelligent identification model of the bus fault area. In the simulation analysis under various working conditions, the fault can quickly and accurately identify the fault area, which basically overcomes the influence of transition resistance and initial angle of fault.

2) The protection algorithm only uses the information of the initial traveling wave of the voltage and current, the criterion is simple, the setting is easy, the required data window is short, and the communication volume is small.

3) Compared with the traditional bus fault region identification algorithm, the algorithm shows better performance in motion speed and fault identification accuracy.

Acknowledgements

This research was supported by Project Supported by Sichuan Science and Technology Department Project (2017JY0338, 2019YJ0477, 2018GZDZX0043, 2018JY 0386); Artificial Intelligence Key Laboratory of Sichuan Province (2019RYY01); Enterprise Informatization and Internet of Things Measurement and Control Technology Sichuan University Key Laboratory Project (2018WZY01); Sichuan Institute of Science and Technology Sichuan Academician (Expert) Workstation Project (2018YSGZZ04); Science and Technology Project Funding of State Grid Corporation of China (Contract No.521997180016).

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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