An Identification Method for Transient Capacitive Current of ...
2009 Fifth International Conference on Information Assurance and Security
An Identification Method for Transient Capacitive Current of Distribution Network by ICMAC
Jianwen Zhao Yuanbin Hou School of Electrical and Control Engineering Xi’an University of Science and Technology Xi’an, China e-mail: [email protected] identification method of transient characters of single phase grounding fault is presented. Firstly, by normal BP network, transient capacitive current was identified, and then, a improved cerebellar model articulation controller network is given , by this new ICMAC network, transient capacitive current was identified as well as. Amounts of analyses and simulations show that, adopting ICMAC method, the occurring time of maximal amplitude of transient capacitive current and its free alternating component can be identified conveniently; while the relationship between capacitive current extremum and phase angle of fault phase voltage can also be found; identification speed and precision of this novel ICMAC network is higher than normal BP network’s.
Abstract—Capacitive current is an important influential ingredient for extinguishing electric arc, which comes into being when single phase ground fault occurs in resonance networks. In order to seize transient capacitive current’s characters, two identification methods are presented using back propagation (BP) neural network and novel improved cerebellar model articulation controller network (ICMAC) separately. With two methods, the maximal amplitude and the minimal amplitude of transient capacitive current can be identified, occurring time of transient capacitive current amplitude can be confirmed as well as. These methods were proved by simulation with Matlab, the simulating results indicate that this novel ICMAC network makes learning identification speed faster and identification precision higher than normal BP network, through adjusting learning factor dynamically. Effective identification of transient capacitive current’s characteristics provides evidences for further cure of capacitive current.
II.
ANALYSIS FOR TRANSIENT CAPACITIVE CURRENT OF SINGLE- PHASE GROUND FAULT Series transient current equivalent circuit of single-phase grounding fault is composed of L0 , C and R0 , in resonance network, where L0 is the equivalent inductance of threephase lines and power transformer; C is capacitance of electric network; R0 is equivalent resistance of zero sequence loop which include grounding resistance and arc canal resistance. If excitation of this series circuit is zero sequence sinusoidal voltage, u0 U fm sin(wt j ) , the transient capacitive current obtained is ic icos icst i I ( w f sin j sin w t - cos j cos w t )edt (1) cos cm f f w i I cm cos(wt j ) cst where icos is transient free alternating component, icst is steady-state main frequency component, I cm is magnitude of capacitive current ( I cm U fm wC ), U fm is magnitude of
Keywords- improved cerebellar model articulation controller; single-phase ground fault; BP network; transient capacitive current; identification.
I.
INTRODUCTION
While single-phase ground fault is happening along the running resonance distribution network, the inductive current of extinguishing coil will compensate the capacitive current which is a disaster to generate electric arc, and then affects power supply safety. So the research of capacitive current’s transient characters is important for suppressing electric arc, controlling complement of extinguishing coil, and etc. As a single-phase ground fault takes place at the distribution network, the grounding transient capacitive current is the nonlinear signal that contains an attenuating free alternating current and a steady-state main frequency current. For the complex nonlinear problems of power system, many researchers deliver artificial intelligence techniques to solve recent years, such as, faulty Line detection for distribution networks based on wavelet analysis [1]-[4], fault line detection based on rough set theory in indirectly grounding power system [5], [6], earth fault detection based on D-S evidence theory [7]-[9], and fault line detection based on fuzzy sets theory [10], [11]. All these are protection methods using steady-state characteristics of single-phase grounding fault. In this paper, the intelligent 978-0-7695-3744-3/09 $25.00 © 2009 IEEE DOI 10.1109/IAS.2009.227
phase voltage, w f is angular frequency of transient free
alternating component ( w f 1 L0C R0 2 L0 ), free 2
alternating cycle T f has a relationship T f 2p w f with w f , d is modulus decay of free alternating component ( d 1 Tc R0 2 L0 ), Tc is characteristic time. When the operation manner of system is steadiness, Tc is a constant. 315
Transient capacitive current consists of free alternating component and steady-state main frequency component, the bigger value of Tc is, the slower attenuation free alternating is, vice versa. It is obvious that transient capacitive current is a typical nonlinear signal.
network’s special feature is that association has local extensive ability, that is to say, Similar or close inputs produce alike output; six to one inputs produce almost isolated outputs. CMAC network is a kind of nonlinear mapping as a whole, but CMAC network is also a kind of linear mapping to each neure, it’s self-adapting (learning course) perform by linear model. In a word, CMAC network have characteristics of high learning speed, no local minimizing. CMAC network can be expressed as a mopping, f : S P , after received input vector S, CMAC system carries out hash coding, chooses number M of association unit, then produce an output vector P, this output vector is namely the weight value memories lay in association unit A*. Through supervisory learning, CMAC system train suitable nonlinear function. In the course of nonlinear learning, CMAC modifies weights continually, makes weights represent sampling value. Weight modifying equation of CMAC is (4).
III.
IDENTIFICATION OF TRANSIENT CAPACITIVE CURRENT USING BP NETWORK Artificial neural network (ANN) can approach any nonlinear course; using ANN to fit transient capacitive current of single-phase ground fault, more actual wave will be acquired. BP network is a multilayer feed forward network, adopting learning mode of least mean square error, is used broadly. “3-6-1 form” three layer BP network is build up to identify transient capacitive current. A 35kV distribution system is chosen as the simulation object, actual parameters of this system is as follow: threephase grounding capacitance C 4106 F , loop inductance L0 0.025H , loop resistance R0 20 . Through calculation using these parameters, we obtain I cm 36 A ， w 100p ， t c 0.0025s , d 1 t c 400 s-1 ,
ic & icp (A)
w0 1 L0 C 1000p ,
100
w f 1000p . It is obvious that
-100
free alternating angular frequency w0 is approximately equal to transient alternating angular frequency w f , this is cause of
ic ic p output of ANN
0
0
50
100
150
200
250
300
350
400
50
100
150
200 k
250
300
350
400
-3
x 10
e
4
1 L0C ? R0 2 L0 . After substituting all parameters above into equation (1), transient capacitive current of this 35kV system is expressed as icos 36.2(10sin j sin1000pt - cos j cos1000pt )e400t (2) icst 36.2 cos(100pt j) In order to identify capacitive current by BP network conveniently, sampling period is selected as 0.1ms, then equation (2) is changed into equation (3). icos 36.2(10sin j sin 0.1pk - cos j cos 0.1p k )e0.04 k (3) icst 36.2 cos(0.01pk j) Transient capacitive current was analyzed and identified with the “3-6-1 form” BP network above. Identification sample on different j is like icos and icst of equation (3). Through programming by M-file of MATLAB, the identification results about different j is illustrated by plot, the maximum of free alternating component and its occurring time are all be observed. The final identification results of transient capacitive current of 35kV system is shown as Fig.1-Fig.3, while j is equal to 0, p 4 , or p 2 . The curves are samples, the dots of curves are identification results, as Fig.1-fig.3 illustrates.
2
2
0
0
Figure 1. Identification results by BP network, j 0 . ic & icp (A)
400
ic ic p output of ANN
200 0 -200
6
0 x 10
50
100
150
200
250
300
350
400
50
100
150
200 k
250
300
350
400
-3
e
4 2 0
0
Figure 2. Identification results by BP network, j p 4 . ic & icp (A)
500
ic ic p output of ANN
0
-500
6
0 x 10
50
100
150
200
250
300
350
400
50
100
150
200 k
250
300
350
400
-3
e
4 2
IV.
IDENTIFICATION OF TRANSIENT CAPACITIVE CURRENT BY ICMAC NETWORK
0
0
Figure 3. Identification results by BP network, j p 2 .
A.
Learning of ICMAC Network CMAC network is a type of association one, for each output, only small parts of neures associate with it. CMAC
316
wn1 wn a (d wi )
error of ICMAC network is less than 4 106 , and does attenuate; the identification precise of ICMAC network is much higher than BP network’s; In addition, at the same station ICMAC network program is simpler than BP network, the ICMAC network works 20% faster than BP network. Let us consider the maximum value characteristics of transient capacitive current for now, according identification results of ICMAC network with high precise. As is shown in fig. 4 -Fig. 6. 1) If single phase grounding fault occurs at j 0 , fault phase voltage is passing zero point namely, transient free alternating current peak value reaches 24A at t 1ms ( k 10 )，transient capacitive peak value reaches 59A at
M
(4)
i 1
where wn is the nth time weight value, the nth time output of CMAC namely; d is input sample, the teaching
w M
signal also;
i 1
i
is the sum of weights about association
icos & icosp (A)
unit; a is learning coefficient . In normal CMAC networks, learning coefficient a is constant, the outputs of CMAC are given from regulating each memory weight of association unit. A improved cerebellar model articulation controller (ICMAC) is presented, learning coefficient a is established as dynamic value, and varies with learning times k and general learning times K, mathematically, k a b(1 ) (5) 1 K where b is a set constant, 0
An Identification Method for Transient Capacitive Current of Distribution Network by ICMAC
Jianwen Zhao Yuanbin Hou School of Electrical and Control Engineering Xi’an University of Science and Technology Xi’an, China e-mail: [email protected] identification method of transient characters of single phase grounding fault is presented. Firstly, by normal BP network, transient capacitive current was identified, and then, a improved cerebellar model articulation controller network is given , by this new ICMAC network, transient capacitive current was identified as well as. Amounts of analyses and simulations show that, adopting ICMAC method, the occurring time of maximal amplitude of transient capacitive current and its free alternating component can be identified conveniently; while the relationship between capacitive current extremum and phase angle of fault phase voltage can also be found; identification speed and precision of this novel ICMAC network is higher than normal BP network’s.
Abstract—Capacitive current is an important influential ingredient for extinguishing electric arc, which comes into being when single phase ground fault occurs in resonance networks. In order to seize transient capacitive current’s characters, two identification methods are presented using back propagation (BP) neural network and novel improved cerebellar model articulation controller network (ICMAC) separately. With two methods, the maximal amplitude and the minimal amplitude of transient capacitive current can be identified, occurring time of transient capacitive current amplitude can be confirmed as well as. These methods were proved by simulation with Matlab, the simulating results indicate that this novel ICMAC network makes learning identification speed faster and identification precision higher than normal BP network, through adjusting learning factor dynamically. Effective identification of transient capacitive current’s characteristics provides evidences for further cure of capacitive current.
II.
ANALYSIS FOR TRANSIENT CAPACITIVE CURRENT OF SINGLE- PHASE GROUND FAULT Series transient current equivalent circuit of single-phase grounding fault is composed of L0 , C and R0 , in resonance network, where L0 is the equivalent inductance of threephase lines and power transformer; C is capacitance of electric network; R0 is equivalent resistance of zero sequence loop which include grounding resistance and arc canal resistance. If excitation of this series circuit is zero sequence sinusoidal voltage, u0 U fm sin(wt j ) , the transient capacitive current obtained is ic icos icst i I ( w f sin j sin w t - cos j cos w t )edt (1) cos cm f f w i I cm cos(wt j ) cst where icos is transient free alternating component, icst is steady-state main frequency component, I cm is magnitude of capacitive current ( I cm U fm wC ), U fm is magnitude of
Keywords- improved cerebellar model articulation controller; single-phase ground fault; BP network; transient capacitive current; identification.
I.
INTRODUCTION
While single-phase ground fault is happening along the running resonance distribution network, the inductive current of extinguishing coil will compensate the capacitive current which is a disaster to generate electric arc, and then affects power supply safety. So the research of capacitive current’s transient characters is important for suppressing electric arc, controlling complement of extinguishing coil, and etc. As a single-phase ground fault takes place at the distribution network, the grounding transient capacitive current is the nonlinear signal that contains an attenuating free alternating current and a steady-state main frequency current. For the complex nonlinear problems of power system, many researchers deliver artificial intelligence techniques to solve recent years, such as, faulty Line detection for distribution networks based on wavelet analysis [1]-[4], fault line detection based on rough set theory in indirectly grounding power system [5], [6], earth fault detection based on D-S evidence theory [7]-[9], and fault line detection based on fuzzy sets theory [10], [11]. All these are protection methods using steady-state characteristics of single-phase grounding fault. In this paper, the intelligent 978-0-7695-3744-3/09 $25.00 © 2009 IEEE DOI 10.1109/IAS.2009.227
phase voltage, w f is angular frequency of transient free
alternating component ( w f 1 L0C R0 2 L0 ), free 2
alternating cycle T f has a relationship T f 2p w f with w f , d is modulus decay of free alternating component ( d 1 Tc R0 2 L0 ), Tc is characteristic time. When the operation manner of system is steadiness, Tc is a constant. 315
Transient capacitive current consists of free alternating component and steady-state main frequency component, the bigger value of Tc is, the slower attenuation free alternating is, vice versa. It is obvious that transient capacitive current is a typical nonlinear signal.
network’s special feature is that association has local extensive ability, that is to say, Similar or close inputs produce alike output; six to one inputs produce almost isolated outputs. CMAC network is a kind of nonlinear mapping as a whole, but CMAC network is also a kind of linear mapping to each neure, it’s self-adapting (learning course) perform by linear model. In a word, CMAC network have characteristics of high learning speed, no local minimizing. CMAC network can be expressed as a mopping, f : S P , after received input vector S, CMAC system carries out hash coding, chooses number M of association unit, then produce an output vector P, this output vector is namely the weight value memories lay in association unit A*. Through supervisory learning, CMAC system train suitable nonlinear function. In the course of nonlinear learning, CMAC modifies weights continually, makes weights represent sampling value. Weight modifying equation of CMAC is (4).
III.
IDENTIFICATION OF TRANSIENT CAPACITIVE CURRENT USING BP NETWORK Artificial neural network (ANN) can approach any nonlinear course; using ANN to fit transient capacitive current of single-phase ground fault, more actual wave will be acquired. BP network is a multilayer feed forward network, adopting learning mode of least mean square error, is used broadly. “3-6-1 form” three layer BP network is build up to identify transient capacitive current. A 35kV distribution system is chosen as the simulation object, actual parameters of this system is as follow: threephase grounding capacitance C 4106 F , loop inductance L0 0.025H , loop resistance R0 20 . Through calculation using these parameters, we obtain I cm 36 A ， w 100p ， t c 0.0025s , d 1 t c 400 s-1 ,
ic & icp (A)
w0 1 L0 C 1000p ,
100
w f 1000p . It is obvious that
-100
free alternating angular frequency w0 is approximately equal to transient alternating angular frequency w f , this is cause of
ic ic p output of ANN
0
0
50
100
150
200
250
300
350
400
50
100
150
200 k
250
300
350
400
-3
x 10
e
4
1 L0C ? R0 2 L0 . After substituting all parameters above into equation (1), transient capacitive current of this 35kV system is expressed as icos 36.2(10sin j sin1000pt - cos j cos1000pt )e400t (2) icst 36.2 cos(100pt j) In order to identify capacitive current by BP network conveniently, sampling period is selected as 0.1ms, then equation (2) is changed into equation (3). icos 36.2(10sin j sin 0.1pk - cos j cos 0.1p k )e0.04 k (3) icst 36.2 cos(0.01pk j) Transient capacitive current was analyzed and identified with the “3-6-1 form” BP network above. Identification sample on different j is like icos and icst of equation (3). Through programming by M-file of MATLAB, the identification results about different j is illustrated by plot, the maximum of free alternating component and its occurring time are all be observed. The final identification results of transient capacitive current of 35kV system is shown as Fig.1-Fig.3, while j is equal to 0, p 4 , or p 2 . The curves are samples, the dots of curves are identification results, as Fig.1-fig.3 illustrates.
2
2
0
0
Figure 1. Identification results by BP network, j 0 . ic & icp (A)
400
ic ic p output of ANN
200 0 -200
6
0 x 10
50
100
150
200
250
300
350
400
50
100
150
200 k
250
300
350
400
-3
e
4 2 0
0
Figure 2. Identification results by BP network, j p 4 . ic & icp (A)
500
ic ic p output of ANN
0
-500
6
0 x 10
50
100
150
200
250
300
350
400
50
100
150
200 k
250
300
350
400
-3
e
4 2
IV.
IDENTIFICATION OF TRANSIENT CAPACITIVE CURRENT BY ICMAC NETWORK
0
0
Figure 3. Identification results by BP network, j p 2 .
A.
Learning of ICMAC Network CMAC network is a type of association one, for each output, only small parts of neures associate with it. CMAC
316
wn1 wn a (d wi )
error of ICMAC network is less than 4 106 , and does attenuate; the identification precise of ICMAC network is much higher than BP network’s; In addition, at the same station ICMAC network program is simpler than BP network, the ICMAC network works 20% faster than BP network. Let us consider the maximum value characteristics of transient capacitive current for now, according identification results of ICMAC network with high precise. As is shown in fig. 4 -Fig. 6. 1) If single phase grounding fault occurs at j 0 , fault phase voltage is passing zero point namely, transient free alternating current peak value reaches 24A at t 1ms ( k 10 )，transient capacitive peak value reaches 59A at
M
(4)
i 1
where wn is the nth time weight value, the nth time output of CMAC namely; d is input sample, the teaching
w M
signal also;
i 1
i
is the sum of weights about association
icos & icosp (A)
unit; a is learning coefficient . In normal CMAC networks, learning coefficient a is constant, the outputs of CMAC are given from regulating each memory weight of association unit. A improved cerebellar model articulation controller (ICMAC) is presented, learning coefficient a is established as dynamic value, and varies with learning times k and general learning times K, mathematically, k a b(1 ) (5) 1 K where b is a set constant, 0
