Finding the location of switched capacitor banks in distribution systems based on wavelet transform

Transcription

1 UPEC00 3t Aug - 3rd Sept 00 Finding the location of witched capacitor bank in ditribution ytem baed on wavelet tranform Bahram nohad Shahid Chamran Univerity in Ahvaz bahramnohad@yahoo.com Mehrdad keramatzadeh Shahid Chamran Univerity in Ahvaz mdkeramatzadeh@yahoo.com Mohen aniei Shahid Chamran Univerity in Ahvaz mohen.aniei@gmail.com Abtract- In thi paper, a method i propoed for determining the exact location of witched capacitor bank in ditribution ytem. The method conit of two tep. In the firt tep, the technique i baed on meaurement of voltage and current tranient created by capacitor witching. The hypothei tate that: The lope of voltage and current tranient wave form created by capacitor witching immediately before and after the witching intant will have oppoite polarity for monitoring the location at line and branche feeding the capacitor and identical polarity for monitoring the location at other part of the power network. Wavelet tranform technique are ued to determine the exact witching intant effectively. Simulation i done by EMTP. In the econd tep, uing the exiting capacitor witching tranient data, a method baed on linear circuit theory i ued to etimate the exact ditance of witched capacitor bank from the monitoring location and it i imulated with Matlab Software. The method i valid for both wye and delta configured capacitor bank. Thi propoed method i applied to the IEEE 37-bu ditribution ytem. Index Term--Capacitor witching, Power quality monitoring, wavelet tranform, Electromagnetic Magnetic Tranient Program (EMTP I. INTRODUCTION Capacitor bank are widely ued in both tranmiion and ditribution ytem to provide reactive power, increae ytem capacity, voltage upport, and reduce power loe. Several technique have been propoed to determine the relative location of witched capacitor. Some of paper invetigated the diturbance energy flow during the tranient period and the polarity of the initial peak of the diturbance power to find out the relative location of the witched capacitor bank. The technique require a proviion that the diturbance energy mut be greater than or equal to a certain percentage of the peak excurion of the diturbance energy. If thi condition i atified, the technique ubequently compare polaritie of final value of diturbance energy and power. Unfortunately, the technique require three-phae voltage and current waveform and aume contant teadytate intantaneou power. Furthermore, thee paper do not provide a theoretical analyi of it method. In [], kyeon decribe two fundamental ignature of hunt capacitor bank witching tranient phenomena from which one can accurately determine the relative location of an energized capacitor bank and whether it i uptream or downtream from the monitoring location. Mathematical analyi of a capacitor bank energizing prove that the energized capacitor bank affect only the uptream reactive power flow and at the energizing intant, the gradient (time derivative of voltage and current waveform meaured uptream from the capacitor location will have oppoite ign. The revere i true in that at the energizing intant, gradient of voltage and current waveform meaured downtream from the ame capacitor location will have equal ign. Thu, we can preciely determine the relative location of the witched capacitor bank by imply evaluating power factor change and the ign of voltage and current waveform gradient at the witching intant. The efficacy of our practical direction-finding technique i demontrated analytically and by way of timedomain imulation model and actual data. In thi paper, a method i propoed for finding the location of hunt witched capacitor bank and determining the exact location of witched capacitor bank in ditribution ytem. The method conit of two tep. In the firt tep, the technique i baed on meaurement of voltage and current tranient created by capacitor witching. The hypothei tate that: The lope of voltage and current tranient wave form created by capacitor witching immediately before and after the witching intant will have oppoite polarity for monitoring location at line and branche which feed the capacitor and identical polarity for monitoring location at other part of the power network. Wavelet tranform technique are ued to determine the exact witching intant effectively. The time intant i ued to extract the tranient portion of data, the fractional cycle i right after the capacitor energizing, and the teady-tate data before and after the witching operation. The teady-tate data are conidered to be one or two cycle of voltage and current right before witching and two or three cycle after witching. Thereafter, the two propoed algorithm are applied to thee extracted data to determine the relative location of the capacitor bank. In the econd tep, a method baed on linear circuit theory i ued to etimate the exact ditance of witched capacitor bank from monitoring location uing exiting capacitor witching tranient data. The method i valid for both wye and delta configured capacitor bank. In [,3] imulation i done by PSCAD and the IEEE-3 bu ditribution ytem i imulated that i o mall, but in thi paper imulation i done by EMTP and then the efficacy of the propoed algorithm i validated uing the IEEE 37-bu ditribution ytem.

2 II. WAVEET TRANSFORM The wavelet tranform [4] repreent a ignal via time-cale bai function that are dilated and tranlated verion of a mother wavelet (t. A wavelet function (t i a normalized ( (t = zero average function, centered in the neighborhood of t=0. A family of thee bai function i obtained by caling and tranlating with S and u, repectively: t u ( t = ( ( Then, the wavelet tranform of a ignal f(t at cale and poition u i computed by correlating f(t with a wavelet (t a preented below: wf u, =< f, >= + f ( t t u * ( ( u, dt ( where * denote complex conjugate. Dilation by the cale i inverely proportional to frequency and repreent the periodic (harmonic nature of the ignal. Thi i an important characteritic of the wavelet tranform that enable timefrequency localization of the ignal ince the mother wavelet can be conidered to be a window function. The wavelet coefficient wf(u, meaure the imilarity between the dilated and tranlated mother wavelet and the target ignal at time (u and cale (. It hould be noted that the Pareval theorem can be ued to obtain the wavelet tranform in the frequency domain: wf + u, = f ( w π ( u, ( w dw Combined with the characteritic of the analytic wavelet tranform, which will be detailed in Section II-A, (3 preent an efficient method to obtain the wavelet coefficient. In eence, the wavelet tranform provide good time reolution at high dilation (low frequencie but good high-frequency reolution acrifice it time reolution due to the Heienberg uncertainty principle. The time ( t reolution of the wavelet tranform are Δ and frequency ( Δ w Δ t = Δt Δ w = Δw / where ubcript indicate the mother and wavelet. Thu, two modal component in time cannot be identified unle they are more than Δt apart. Similarly, two ditinct pectral component cannot be dicriminated unle they are more than Δ w apart. A. Analytic Wavelet Tranform An analytic wavelet can be contructed by the frequency modulation of a real and ymmetric window g(t (i.e., ( t = g( t exp( jηt. The Fourier tranform of (t i then ( g( w η t. Thu, ( w = 0 = > (3 for w<0 if g ( w = 0 for w η. Hence, i analytic. Specifically, a Gabor wavelet i a repreentative of an analytic wavelet tranform and i obtained from a Gauian window: t g( t = exp( (4 4 δ ( δ Π The Fourier tranform of thi window i then computed a follow: δ w 4 g( w = (4δ Π exp( (5 Thu, if δ η >>, g ( w 0 for w > η Hence, Gabor wavelet are conidered to be analytic. The Fourier tranform of Ψ i a dilation of Ψ (w by a u,, and can be obtained jmu u. ( w = Ψ( w e. Thu, the AWT of f (t (. e., wf ( u, i i the invere Fourier tranform of the frequency function obtained by multiplying (w by Ψ (w. Thu, given the Fourier tranform of the choen analytic wavelet tranform, computational complexity can be reduced. Thi i becaue the Fourier and invere Fourier tranform of the ignal f (t at each cale can be calculated efficiently via fat Fourier tranform (FFT. In practice, thi i a ignificant benefit of the propoed method becaue it can be eaily implemented in the exiting monitoring device. An analytic wavelet tranform define a local time--frequency energy denity called a calogram: Ρ f ( u, wf ( u, (6 w = Note that we focu on the intantaneou frequency w (u defined a η / ( u. Thi i related to the ridge of the normalized calogram Ρw f ( u,. B. SWITCHED-CAPACITOR OCATION TECHNIQUE The wavelet tranform i efficient for the analyi of nontationary and fat tranient wideband ignal, uch a fat tranient caued by the witching of hunt capacitor. The wavelet tranform i a mapping of a time ignal to the timecale joint repreentation. Uing wavelet tranform, all ignal information i preerved. The wavelet tranform provide multireolution ignal analyi with hifted and dilated window. Generally, the wavelet tranform decompoe the ignal into hifted and dilated verion of mother wavelet. There are many type of mother wavelet ued in ignal decompoition, uch a Haar, Daubichie (db, Coiflet (coif, and Symmlet (ym. The choice of the mother wavelet play a ignificant role in detecting and localizing different type of tranient. The choice of the mother wavelet depend on the particular application; For hort and fat tranient diturbance, uch a the cae in thi tudy, db4 and db6 are recommended, while for low tranient diturbance, db8 and db0 are particularly good. III. PROBEM DESCRIPTION The problem i to find the exact location of witched capacitor bank with analyzing capacitor witching tranient meaured by Power Quality Monitoring device (PQM. Thi algorithm ha two tep. f

3 A. Finding Direction of Switched Capacitor Bank The hypothei i a follow: the lope of voltage and current tranient waveform created by capacitor witching immediately before and after the witching intant will have oppoite polarity for monitoring location at line and branche which feed the capacitor and identical polarity for monitoring location at other part of the power network. By the propoed method one can determine the branch containing witched capacitor bank in a real ditribution ytem and find the bu that contain capacitor bank. Variou Simulation reult how that the method i valid in all normal, back-toback, and abnormal witching of wye-and delta-configured capacitor bank. To prove the hypothei let u ue a imple network illutrated at Fig., with the tate equation a hown in (. Although a more complicated network could be ued to prove thi fact, the implification doe not limit the validity of the hypothei for complicated ditribution network. Simulation i done by EMTP. V C Fig.. A imple network to prove the hypothei R, I = V, C R C C + V 0 The value of V SC in (7, i conidered contant ince the power ytem fundamental frequency i ubtantially lower than a typical capacitor witching frequency. By conidering a typical ditribution ytem the value of element in Fig. a well a initial condition can be determined and then (7 can be olved. By olving (7, the trace of current and voltage are a hown in Fig. for branche which feed the capacitor and other part of the power network. (a SC (b (7 The trace illutrated in Fig., confirm the hypothei ince for PQM which i located in the branch which feed the capacitor bank, the lope of tranient current and voltage have oppoite polarity. And for PQM which i located in the other branche the lop of current and voltage have identical polarity. It i poible to expand the hypothei to a method applicable in real ditribution ytem which have many branche. Fig. 3 how a typical feeder in a ditribution ytem, with ome lateral connected to it. Fig. 3: A typical ditribution ytem According to the hypothei, when the capacitor i witched on, immediately after the witching intant, the lope of the voltage and current with the direction a hown in Fig. 4, in branche (, (3, and (7 will have oppoite polarity and in other branche will have identical polarity. Thi i becaue branche (, (3 and (7 are feeding the capacitor bank and other branche are not. The concept of the hypothei i not complicated. Since when a capacitor with no initial charge i witched on it act a hort circuit and therefore the impedance of the branch containing witched capacitor decreae. So the current of the line and branche which feed the capacitor bank will increae. A a reult according to the circuit theory the current of all other line and branche will decreae. Anyway meaured voltage will decreae becaue of hort circuit at capacitor location. Thu, by meauring the lope of tranient voltage and current and verifying the ign of calculated lope, one can determine if the capacitor bank i located at branche which feed capacitor. Conidering all poible condition of capacitor witching, the following general index i propoed to quantify the current change. + + VI = t t t t D ( V V ( I I (8 Where I - t, I + t, are the intantaneou current of each branch - and V t, V + t are the intantaneou voltage immediately before and after the witching intant a hown in Fig.. B. Ditance Etimation of Switched Capacitor Bank After determining the direction of the witched capacitor bank, the exact location of the capacitor bank hould be determined. In thi ection, thi method i ued and incorporated a real ditribution ytem. Fig. 3 and Fig. 4 how a typical ditribution ytem and it equivalent circuit repectively. (c (d Fig.. Voltage and current waveform recorded from power quality monitor which are uptream (a and b, and down tream (c and d from the witched capacitor bank. Fig.4. the equivalent circuit of the ditribution ytem, hown in fig.3 According to [3]:

4 + V ( t 7 + V ( t V ( t d 7 u = th (9 7 = (0 + th V ( t d 7 = K, K = ( + u V ( t V ( t Where V( i the aplace tranform of voltage at bu 3, V c (t - ci the intantaneou ource voltage before the witching, V(t - and V(t + are intantaneou voltage meaured at bu 3 immediately before and after the witching intant t, a illutrated in Fig.. u i the line inductance per unit length for branch (7, which i known d 7. d 7 i the ditance between monitoring location and the witched capacitor location. Uing (9 and (0, ( i obtained. In ( u i known. V(t - and V(t + can be determined from voltage tranient waveform (Fig... For finding th one can conider only the inductance of main feeder from bu (3 to the ource, without conidering lateral. Thi implification doe not make any error in real ditribution ytem. Thu by uing (, the exact ditance between monitoring location and the witched capacitor bank (d 7 in ditribution ytem can be determined. Where V( i the aplace tranform of voltage at bu 3, V c (t - ci the intantaneou ource voltage before the witching, V(t - and V(t + are intantaneou voltage meaured at bu 3 immediately before and after the witching intant t, a illutrated in Fig.. u i the line inductance per unit length for branch (7, which i known d 7. d 7 i the ditance between monitoring location and the witched capacitor location. Uing (9 and (0, ( i obtained. In ( u i known. V(t - and V(t + can be determined from voltage tranient waveform (Fig... For finding th one can conider only the inductance of main feeder from bu (3 to the ource, without conidering lateral. Thi implification doe not make any error in real ditribution ytem. Thu by uing (, the exact ditance between monitoring location and the witched capacitor bank (d 7 in ditribution ytem can be determined. IV. SIMUATION RESUTS In thi ection, a cae tudy will be done to how the efficacy of the propoed method in order to determine the exact location of a witched capacitor bank. The IEEE 37-bu ditribution ytem i ued for imulation purpoe. In thi ytem modeled in EMTP oftware, a 50µƒ hunt capacitor bank located on bu 73 i witched on (Fig. 5 - Appendix. The ditance between thi capacitor bank and the monitoring location at bu 70 i mile. In thi cae, a 9 µƒ fixed capacitor i alo connected to the bu 73. When the capacitor bank on bu 73 i witched on, there will be an interaction between the witched and fixed capacitor bank. Thi effect i called back to back capacitor witching and will increae the frequency of capacitor witching tranient. So in thi cae tudy, the effect of back to back capacitor witching i taken into account. Power-quality monitoring device (PQM are located on bue 70, 703, 704, 709, 7, 70 and 734. So the voltage of thee bue a well a branch current with the direction hown in Fig. 5 are meaured. Switching intant i detected by wavelet tranform technique and i calculated. A. Cae With no Back-to-Back Capacitor Switching In the IEEE 37-bu ditribution ytem modeled in EMTP oftware, a 50 µƒ capacitor bank i witched on at bu 73 (Fig. 5. Suppoe that the fixed capacitor bank doe not exit in the ytem. Table I illutrate the reult of thi cae tudy. TABE I Simulation Reult of Calculation DVI For Cae A. A -0.9 A 0.03 A B B B 0.09 C C C 0.00 A A A B B B C C C A A 0.04 A B B B 0.05 C C 0.75 C A 0.35 A 0.09 A B B B C 0.53 C 0.67 C A A 0.34 A B B B C C C A A A B B B C C 0.3 C A 0.33 A A B B B 0.00 C C 0.05 C A A A B B B C 0.34 C C 0.79 A A A B 0.58 B B C 0.07 C 0.3 C A A 0.80 A B 0.6 B B 0.07 C C 0.99 C A A A 0.00 B B B C 0.6 C C 0.40 A A B B C 0.9 C 0.0 B. Cae With Back-to-Back Capacitor Switching In thi cae, a 9 µƒ fixed capacitor i alo connected to the bu 73. When the capacitor bank on bu 73 i witched on, there i an interaction between the fixed and witched capacitor bank. Thi effect i called back-to-back capacitor witching. Back-to-back capacitor witching phenomena increae the frequency of capacitor witching tranient. Thu, in thi cae, the effect of back-to-back capacitor

5 witching i taken into account. Table II illutrate the reult of thi tudy. TABE II Simulation Reult of Calculation DVI for Cae B. A A 0.48 A B B B 0.05 C C C A -0.7 A 0.34 A B B B C C 0.8 C 0.05 A A 0.43 A B B B C C 0.4 C 0.8 A 0.04 A A B B B C 0.59 C C A 0.0 A 0.47 A B B B C C 0.3 C 0.3 A A A B B B C C 0.34 C A 0.0 A A B B B 0.06 C 0.90 C C A 0.33 A A B B B C 0.8 C 0.8 C A 0.07 A 0.8 A B 0.6 B B 0.04 C C C A 0.06 A A B B B C 0.54 C C A A 0.03 A B B B 0.0 C C 0.63 C A 0.03 A 0.00 B B C 0.46 C A hown in Table I and II, at branche (, (, and (3 which are feeding the witched capacitor, ha negative ign for all phae and poitive for other branche. On the other hand, at branch (3, ha the greatet value. Thi reult wa expected ince thi branch i the nearet branch to the witched capacitor bank and thu voltage and current change in thi branch i the greatet. Reult how that uing the propoed method, it i poible to determine the exact branch that contain witched capacitor bank. Back-to-back capacitor witching doe not affect the accuracy of the method. Thi technique i teted uing many imulation with different capacitor poition and the reult are concluive. Simulation reult how that changing location, ize, and type of capacitor bank connection doe not affect the reult efficacy. So the method i general and can be ued in any condition of capacitor witching. Baed on the technique explained in ection III-B, the ditance of the witched capacitor bank from monitoring location at bu 73, will be determined. Since (5 i right for the ditribution ytem (Fig. 5, (0 can be ued. Table III how the reult calculated for phae A. TABE III: Simulation Reult for Ditance Etimation V a(t -,t + k d etimated(mi D real(mi Error.73, Accordingly, with thi algorithm the location of witched capacitor bank can be exactly determined. The Error in thi cae tudy i only 3.3 percent which i acceptable. Thi technique i teted through different imulation and the reult are concluive. Simulation reult howed that other condition uch a different capacitor ize, location, and type of capacitor bank connection doe not affect the reult accuracy. V. CONCUSION Thi paper propoe an algorithm to find the exact location of witched capacitor bank in ditribution ytem. It i baed on the meaurement and analyi of intantaneou voltage and current waveform. The method doe not require any circuit and load data. Two cae tudie are done in order to validate the method. The effect of back to back capacitor witching i imulated, which imulation reult how that it doe not affect the validity of reult. The technique i proved and i imulated for a cae in the IEEE 37-bu ditribution ytem. VI. REFERENCES [] Kyeon Hur, and Surya Santoo, On Two Fundamental Signature for Determining the Relative ocation of Switched Capacitor Bank, IEEE Tranaction on Power Delivery, vol. 3, no., April 008. [] H. Khani, M. Moallem, and S. Sadri, On Tracking and Finding the ocation of Switched Capacitor Bank in Ditribution Sytem, IEEE T&D Aia 009. [3] H. Khani, M. Moallem, and S. Sadri, A Novel Algorithm for Determining the Exact ocation of Switched Capacitor Bank in Ditribution Sytem, IEEE T&D Aia 009. [4] Kyeon Hur, Surya Santoo, Etimation of Sytem Damping ParameterUing Analytic Wavelet Tranform, IEEE TRANSACTIONS ON POWER DEIVERY, VO. 4, NO. 3, JUY 009. Appendix Fig5 : The IEEE 37-bu ditribution ytem