In order to improve the reliability of busbar protection, a new fast busbar protection algorithm based on active power and extreme learning machine is proposed. By performing S-transformation on the fault voltage and current traveling wave, the active power amplitude within 0.1 ms after the fault is obtained. Simulate different fault types in the busbar area and build a bus fault feature vector sample set. The intelligent model of fault learning of extreme learning machine is established, and the sample set is used for training and testing to realize bus fault area identification. The simulation results show that the proposed busbar protection method can identify faults in the busbar area sensitively and reliably.
Busbar protection plays an important role in the power system and bears the responsibility of transmitting electrical energy [
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 [
In recent years, S-transformation and power theory have been more maturely used in power systems [
This paper draws on the direction traveling wave and power theory described in the literature [
{ Δ u ( x , t ) = Δ u + ( x − t v ) + Δ u − ( x + t v ) Δ i ( x , t ) = Δ i + ( x − t v ) + Δ i − ( x + t v ) v = 1 / L C (1)
where: t is the observation time, L and C are the inductance and capacitance of the line per unit length; Δ u + ( Δ u − ) , Δ i + ( Δ i − ) 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 ( k = 1 , 2 , 3 , 4 , 5 ) of each associated line of the bus bar is called an initial voltage and a current traveling wave. among them, the Δ u M is initial voltage traveling wave for bus M. Δ i k ( k = 1 , 2 , 3 , 4 ) is the current traveling wave measured for each line of the bus. Z c 1 ~ Z c 4 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 c m .
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 [
{ Δ i + = 1 2 [ Δ i + Δ u z c ] Δ i − = 1 2 [ Δ i − Δ u z c ] (2)
Δ u , Δ 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 [
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 min . Only the initial forward traveling wave is detected at each associated line R in the [ t 0 , t 0 + 2 d min / v ] time period, and there is no reverse traveling wave formed by the forward traveling wave reflection.
The Peterson equivalent circuit of bus m in case of point F1 fault is shown in
When S transforms, the traveling wave frequency is f = 50 ~ 100 kHz , when the super (extra) high-voltage transmission line wave impedance can be approximated as a real constant, it is equivalent to the resistance [
From the definition of the initial traveling wave complex power [
Δ S 1 = Δ u M Δ l 1 * (3)
when the internal F1 point of the busbar fails, the Peterson equivalent circuit of
Δ l 1 = Δ u M ( 1 / Z c 1 ) (4)
Since the line wave impedance is approximately a real constant, it is equivalent to the resistance [
Δ S ˜ 1 = Δ U ˙ M Δ I ˙ 1 ∗ = Δ U ˙ M × [ Δ U ˙ M * ( 1 / Z c 1 ) ] = Δ U M 2 × ( 1 / Z c 1 ) = P 1 + j Q 1 (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 = Δ U M 2 × ( 1 / Z c 1 ) (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 = Δ U M 2 / Z c i ( i = 1 , 2 , 3 , 4 , 5 ) .
Ideally, due to the internal fault of the bus, the wave impedance Z i ( i = 1 , 2 , 3 , 4 ) 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 ≈ P 2 ≈ P 3 ≈ P 4 , is greater than 0.
the bus bar, forming a forward wave Δ i 2 + formed by the reflection of the reverse traveling wave. Only the faulty line detects the reverse traveling wave during the [ t 0 , t 0 + 2 d dim / v ] time period.
In summary, when the bus line fails, the associated lines are in the [ t 0 , t 0 + 2 d dim / v ] 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 [ t 0 , t 0 + 2 d dim / v ] , the reverse traveling wave can only be detected on the faulty line.
When the F2 point on the L2 line fails, the Peterson equivalent circuit of the bus M is as shown in
As can be seen from
Δ I ˙ 2 = − Δ U ˙ M ( 1 / Z c 1 + 1 / Z c 3 + 1 / Z c 4 + j ω C m ) (7)
The complex power measured by the L2 fault line near the bus M-side protection unit IED2 can be obtained:
Δ S ˜ 2 = Δ U ˙ M Δ I ˙ 2 ∗ = Δ U ˙ M × [ − Δ U ˙ M * ( 1 / Z c 1 + 1 / Z c 3 + 1 / Z c 4 − j ω C m ) ] = − Δ U M 2 × ( 1 / Z c 1 + 1 / Z c 3 + 1 / Z c 4 ) + Δ U M 2 × j ω C m = P 2 + j Q 2 (8)
That is, when the busbar external fault occurs, the initial traveling wave active power of the faulty line is:
P 2 = − Δ U M 2 × ( 1 / Z c 1 + 1 / Z c 3 + 1 / Z c 4 ) (9)
For the non-faulty line connected to bus M, take L3 as an example. In
Δ I ˙ 3 = Δ U ˙ M ( 1 / Z c 3 ) (10)
The complex power measured by the M-side IED3 protection unit of the L3 line:
Δ S ˜ 3 = Δ U ˙ M Δ I ˙ 3 ∗ = Δ U ˙ M × [ Δ U ˙ M * ( 1 / Z c 3 ) ] = Δ U M 2 × ( 1 / Z c 3 ) = P 3 + j Q 3 (11)
P 3 = Δ U M 2 / Z c 3 (12)
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 = Δ U M 2 / Z c i ( i = 1 , 4 ) .
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 [
Set the continuous time signal to h ( t ) , then the continuous S transform of the time signal is defined as:
{ S ( τ , f ) = ∫ − ∞ ∞ h ( t ) g ( τ − t , f ) e − i 2 Π f t d t g ( τ − t , f ) = | f | 2 π e − ( τ − t ) 2 2 σ 2 (13)
τ 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, σ = 1 / | f | , g ( τ − t , f ) is a Gaussian window and is affected by frequency changes.
If h [ k T ] ( k = 0 , 1 , 2 , ⋯ , N − 1 ) is the signal h ( t ) 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 [ k T ] is:
h [ n N T ] = 1 N ∑ k = 0 N − 1 h [ k T ] e − j 2 Π k n N (14)
where n = 0 , 1 , ⋯ , N − 1
The discrete S transform of signal h ( t ) is:
{ S [ k T , n N T ] = ∑ r = 0 N − 1 H ( r + n N T ) e − 2 Π 2 r 2 n 2 e j 2 Π r k N , n 1 0 S [ k T , 0 ] = 1 N ∑ r = 0 N − 1 h ( r N T ) , n = 0 (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.
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 [
Δ i z = 4 Δ i α + Δ i β (16)
Δ u z = 4 Δ u α + Δ u β (17)
Among them, Δ u α , Δ i α are the voltage and current traveling wave α line mode components after decoupling treatment, Δ u β and Δ i β are the processed voltage and current traveling wave β line mode components.
In this paper, the method used in [
The combined modulus current Δ 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 Δ i 2 according to the above-mentioned S-transform principle, and one-dimensional complex vector [
Δ l 2 n ( t n , f z ) = Δ l 2 n ( t n , f z ) exp [ j θ 2 n ( t n , f z ) ] (18)
Δ l 2 g n ( t n , f Z ) , θ 2 g n ( t n , f Z ) are the amplitude of Δ l 2 g n ( t n , f Z ) , 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 Δ l 21 at the moment of t 1 , Δ l 2 g 1 ( t 1 , f Z ) obtained at the selected frequency f Z is the corresponding initial current traveling wave phasor at that time [
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 Δ U M · n 2 ( t n , f Z ) / Z c i , where i = 1 , 2 , 3 , 4 ; When the busbar is external, the initial traveling wave active power measured by the faulty line is Δ U M · n 2 ( t n , f Z ) / ( 1 / Z c 1 + 1 / Z c 3 + 1 / Z c 4 ) (assuming L2 line fault as an example), non-fault line active power is Δ U M g n ( t n , f Z ) / Z c i ( i = 1 , 3 , 4 ) .
The feedforward neural network is a kind of artificial neural network [
Extreme learning machine is an easy-to-use and effective single-hidden layer feedforward neural network SLFN learning algorithm [
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 [
Given N different training samples ( x i , t i ) , among them,
x i = [ x i 1 , x i 2 , ⋯ , x i n ] T ∈ R n t i = [ t i 1 , t i 2 , ⋯ , t i m ] T ∈ R M (19)
Given an excitation function g ( x ) , after that, the output containing L hidden layer nodes can be expressed as,
∑ i = 1 L β i g ( a i x j + b i ) = ∑ i = 1 L β i G ( a i , b i , x j ) = t i (20)
Among them, j = 1 , 2 , ⋯ , N ; a i = [ a i 1 , a i 2 , ⋯ , a i n ] 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; β i = [ β i 1 , β i 2 , ⋯ , β i m ] 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 ( a i , b i ) and map sample to the new fealure space through h ( x ) = [ G ( a 1 , b 1 , x ) , ⋯ , G ( a L , b L , x ) ] T . If the hidden layer matrix H is formed by the random fealure map h ( x ) , then:
H β = T (21)
Among it,
H = [ h ( x 1 ) ⋮ h ( x N ) ] = [ G ( a 1 , b 1 , x 1 ) ⋯ G ( a L , b L , x 1 ) ⋮ ⋱ ⋮ G ( a 1 , b 1 , x N ) ⋯ G ( a L , b L , x N ) ] ,
β = [ β 1 T ⋮ β L T ] L × m and T = [ t 1 T ⋮ t N T ] N × m
Sigmoid function is selected as the excitation function of hidden layer node g ( a i x j + b i ) = 1 1 + exp ( − a i x j + b i )
2) In the new feature space, the optimal output weight β ^ and β ^ = H + T are sought by least squares method by Equation (12), where H + is the Moore Penrose generalized inverse of H.
T-line line traveling wave protection R k ( k = 1 , 2 , 3 , 4 ) 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 ∇ P , among them:
∇ P m = [ ∇ P m 1 ∇ P m 2 ⋯ ∇ P m 5 ] 1 × 5
And ∇ P m i = [ P 1 P 2 ⋯ P 20 ] 1 × 20 ( m = 1 , 2 , 3 , 4 ; i = 1 , 2 , 3 , 4 ) , ∇ 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 ∇ 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
∇ P = [ ∇ P 11 ⋯ ∇ P ^ M 1 ∇ P 21 ⋯ ∇ P ^ M 2 ∇ P 31 ⋯ ∇ P ^ M 3 ] 1 × 15
The fault identification algorithm flow is shown in
The PSCAD/EMTDC electromagnetic transient simulation software is used to establish the 500 kVT connection line simulation model shown in
∇ P m = [ ∇ P m 1 ∇ P m 2 ⋯ ∇ P ^ m 5 ] 1 × 5 . Combine active power under different transition
resistances, different fault types and different initial angles of faults into fault eigenvectors ∇ 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 ∇ P = [ ∇ P 11 ⋯ ∇ P ^ M 1 ∇ P 21 ⋯ ∇ P ^ M 2 ∇ P 31 ⋯ ∇ P M 3 ] 1 × 15 .
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.
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
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%.
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
| Fault location | Transition resistance Ω | Fault initial angle | Fault distance | fault type | Decision result |
|---|---|---|---|---|---|
| Line, L1, L2, L3, L4 | 100 | 5 45 90 100 | Distance from bus M 80 km | Phase B short circuit to ground | External External External External |
| Busbar M | 300 | 5 45 90 100 | Phase B short circuit to ground | Internal Internal Internal Internal |
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.
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
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.
| Fault location | Transition resistance Ω | Fault initial angle/(˚) | Fault distance | fault type | Decision result |
|---|---|---|---|---|---|
| Line, L1, L2, L3, L4 | 0 200 500 800 | 45˚ | Distance from bus M 100 km | BC phase short to ground | External External External External |
| Bus M | 0 200 500 800 | 45˚ | Phase an earth fault | Internal Internal Internal Internal |
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
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.
| Fault location | Transition resistance/(˚) | Fault initial angle | Fault distance | Transition resistance Ω | Decision result |
|---|---|---|---|---|---|
| Line, L1, L2, L3, L4 | AG ABG BC ABC | 45˚ | Distance from bus M 20 km | 80 | External External External External |
| Bus M | AG ABG BC ABC | 45˚ | 200 | Internal Internal Internal Internal |
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.
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).
The authors declare no conflicts of interest regarding the publication of this paper.
Gilani, S.H.L., Dong, X.X. and Xu, H.Y. (2020) New Principle of Busbar Protection Based on Active Power and Extreme Learning Machine. Open Access Library Journal, 7: e6167. https://doi.org/10.4236/oalib.1106167