Nonactive Current Definition and Compensation Using a Shunt Active Filter

Transcription

1 Nonative Current Definition and Compenation Uing a Shunt Ative Filter Yan Xu, Student Member, IEEE, John N. Chiaon, Senior Member, IEEE, Leon M. olbert, Senior Member, IEEE Abtrat hi paper preent a general definition of nonative urrent/power and the implementation for a hunt ompenation ytem. hi definition i univeral for different load, uh a non-periodi, unbalaned or ingle phae, and alo flexible in term of the ompenation reult. Unity power fator, pure inuoidal oure urrent, or zero non-ative power upply from the utility an be ahieved aording to different ompenation requirement. In addition, the orreponding urrent rating and energy torage requirement of the ompenation ytem are alo preented. Index erm ative filter, reative power, non-ative power, hunt ompenator, non-periodi urrent. I. INRODUCION onlinear load uh a ar furnae and power Neletroni onverter ontinue to be added to the power power grid at an inreaing rate. hey draw highly ditorted urrent from the utility a well a aue ditortion of the voltage. Mot power eletroni onverter generate harmoni omponent whoe frequenie are integer multiple of the ytem fundamental frequeny. However, in ome ae, uh a yloonverter, the line urrent may ontain both ub-harmoni (frequeny lower than fundamental frequeny) and uper-harmoni (frequeny higher than fundamental frequeny but not an integer multiple of it). hee waveform are onidered a nonperiodi although mathematially the urrent may till have a periodi waveform. In any event, the period of thee urrent i not equal to the period of the fundamental voltage [], [2]. An ar furnae i another example of a non-linear load that generate non-periodi urrent beaue it draw rapidly hanging power from the oure and the wave hape and amplitude are ontantly hanging. Voltage fliker and harmoni penetration problem aoiated with ar furnae have been reported in everal paper [3]-[5]. A tranient diturbane may alo be onidered a one kind of non-periodi urrent from the ompenation point of view. he diturbane may be aued by the udden addition of a large load to the ytem uh a tarting a motor, a fault, et. Y. Xu, J. N. Chiaon, and L. M. olbert, are with the Department of Eletrial and Computer Engineering, he Univerity of enneee, Knoxville, N USA ( yxu3@utk.edu, hiaon@utk.edu, tolbert@utk.edu). he definition and ompenation of non-inuoidal and non-periodi urrent and power ha been a oure of onern for ome time [6]-[]. However, mot of the previou effort have foued on the ompenation of periodi noninuoidal urrent intead of non-periodi urrent. he diverity of the feature of non-periodi urrent make their ompenation quite diffiult, and theoretially, their ompenation i very different than that for periodi ditorted urrent. However, from a pratial point of view, in both ae a ine wave with a ontant rm magnitude i preferred for the oure urrent after ompenation. Some previou paper by the author [], [2] elaborate a new definition of non-ative power/urrent. hi definition i applied to a ompenation ytem uing a onventional hunt ative filter. hi ompenator mut injet all of the non-ative omponent that are the differene between the deired oure urrent and the required load urrent. Baed on thi ompenation ytem, everal fator related to the definition itelf and the implementation are diued. hee fator inlude the averaging interval C, the oupling indutane L C, the DC link voltage v d, and the apaitane requirement C of the hunt ompenator. hey are determined by the harateriti of the load, the rating limit of the ompenator, and the deired ompenation reult. II. DEFINIION OF NON-ACIVE CURREN/POWER Intantaneou ative power i defined a the time rate of energy generation, tranfer, or utilization, where M i the phae number of the ytem: M i M p p v i. () i i he nonative urrent/power definition are baed on thi definition and an extenion of Fryze idea of nonative urrent/power []. he definition of intantaneou ative urrent i p (t) and nonative urrent i q (t) are: i p PL ( t ) 2 Vp ( t ) v i i( t) i q i p p i (2)

2 Utility Line where P L (t) i the average power of p(t) over the interval [t- C, t]: P t L t p(τ ) dτ, (3) and v p (t) and V p (t) are the intantaneou and rm value of the referene voltage: V P t t C C 2 v (τ ) dτ. (4) he definition are applied to a hunt ompenation ytem a hown in Fig.. he load urrent i l (t) i divided into i p (t) and i q (t), aording to the definition above. he ompenator provide the ompenation urrent i (t) i q (t), o that the utility need only to provide the oure urrent i (t) i p (t). Let C P t t PX p X ( τ ) dτ vs ( τ ) ix ( τ ) dτ, (5) t C t C where X S, L or C, o P S (t) and P C (t) are the ative power and the nonative power, repetively. hen and i S, p S Compenator C P + P P, (6) S C L PS PL, 0 a t. (7) P C i L, p L, p C Fig.. A hunt ompenator onfiguration. Load he hunt ompenator onit only of paive omponent (indutor and/or apaitor) and/or withing devie. Conequently, no external power oure i needed beaue it provide non-ative power only. Here the ompenator power lo i negleted. In (3) and (4), C i the averaging interval. heoretially, C an be hoen a any arbitrary value in the ae of nonperiodi urrent. However, it i deirable for the interval to be an integer multiple of the line frequeny period beaue of the deire that the oure urrent be inuoidal and have the ame frequeny a the oure voltage frequeny. In general, the period of the line voltage i not the ame a the period of the quai-periodi urrent i p (t). hu, different C will reult in quite different oure and ompenator urrent. C an be zero, one fundamental yle, one-half yle, or multiple yle, depending on the ompenation objetive and the paive omponent energy torage apaity. It wa hown in [2] that thi new definition ha the following feature: ) flexible to meet different ompenation objetive; 2) valid for non-inuoidal and non-periodi ytem; 3) valid for ingle phae and poly-phae ytem. able I illutrate that by hooing different voltage referene and time averaging interval, different oure urrent will reult. Beaue of it flexibility in regard to ompenation objetive, thi definition i quite uitable for analyzing the ompenation of non-periodi urrent. hi will be hown in Setion IV. ABLE I. PARAMEERS FOR DIFFEREN COMPENSAION OBJECIVES Compenation Objetive v P C Reulting Soure Current Single-phae or polyphae reative urrent Single-phae or polyphae reative urrent and harmoni urrent Intantaneou reative power for polyphae ytem Non-periodi diturbane urrent v /2 or Unity pf and inuoidal for inuoidal v v f /2 or Unity pf and inuoidal regardle of v ditortion v C 0 Intantaneouly unity pf for polyphae ytem v f n Redued amplitude and near ine wave with unity pf Subharmoni urrent v f n Pure ine wave or moothed ine wave with unity pf Stohati non-periodi urrent v f n Smoothed ine wave with unity pf III. SYSEM IMPLEMENAION AND CONROL hi definition i independent of the hunt ompenator ytem, i.e., the power eletroni baed ompenator ould be a normal inverter or a multilevel inverter; and the ontrol trategy ould be PWM or other. he definition give the referene urrent that the ompenator need to generate, aording to the ytem voltage, load urrent, ompenation requirement, and the rating limit of the ompenation ytem. In thi paper, a PWM inverter i ued. A hown in Fig. 2, L v v di dt. (8) herefore, (9) i the mathematial repreentation of the feedbak ontroller, and the ontrol blok diagram i hown in Fig. 3. K + K I v P i ) + v. (9) ( i he ytem voltage and load urrent i L are meaured and input to the non-ative urrent alulation blok, in whih the

3 Utility i S Inverter + v C v d L C withing ignal v d v d Control i L Fig. 2. Sytem Implementation. Load PI v C Fig. 3. Blok diagram of the ontroller. i L Nonative urrent alulation referene of the non-ative urrent that the ompenator need to generate i alulated aording to the definition preented in the previou etion. In the ontrol blok, the DC link voltage i regulated and the ompenator output voltage v C i alulated. he PWM pule ignal are then ued to generate the ontrol waveform v C. he onneting indutane L C between the ytem and the ompenator filter the ripple in the output urrent of the ompenator and provide the mehanim to ontrol by peifying v C.. IV. NON-ACIVE POWER COMPENSAION he ompenation ytem ha been imulated uing Simulink/MatLab. he definition i valid for ingle-phae or multiphae, inuoidal or non-inuoidal, periodi or nonperiodi, balaned or unbalaned ytem. Four different load are imulated, and the reult are hown in thi etion. A. hree-phae Harmoni Unbalaned Load In thi ae, load urrent ha harmoni and i not balaned in phae a, b, and, a hown in Fig. 4. he waveform to the left of the dahed line are oure urrent and neutral urrent before ompenation, whih i atually the ame a the load urrent. he oure urrent i ditorted by harmoni, and the neutral urrent i not zero. For ompenation of periodi urrent with fundamental period, hooing different C alone doe not hange the oure urrent harateriti. With referene to (3) and (4), the rm value of a periodi quantity doe not depend on the time averaging interval C if it i an integer multiple of /2. So, with C /2, the oure urrent and neutral urrent after ompenation are hown on the right ide of Fig. 4a and 4b. he non-ative omponent in the load urrent i ompletely ompenated, and the oure urrent now i purely inuoidal, in phae with the ytem voltage, and balaned. B. hree-phae Retifier Load A three-phae retifier i a typial non-linear load. he phae a urrent of a diode-baed retifier i hown in Fig. 5a. Baially, it i a periodi waveform whih an be deompoed into a Fourier erie a in the previou ae. However, the retifier urrent i not ontinuou, and the variation of the urrent with time (di/dt) of the non-ative urrent i very large (approahing infinity), a hown in Fig. 5. herefore, there are peial iue in the ompenation of a retifier load. In the ompenation of harmoni load in the previou (a) Load urrent phae a i La. (a) Soure urrent i S before and after ompenation (b) Soure urrent i S before and after ompenation. (b) Neutral urrent i N before and after ompenation Fig. 4. Simulation of harmoni unbalaned urrent ompenation. () Compenation urrent phae a a. Fig. 5. Simulation of retifier load ompenation.

4 (a) voltage phae a a and load urrent phae a i La. (a) Soure urrent i S ( C /2). (b) Soure urrent i S ( C /2). (b) Soure urrent i S ( C 2). Fig. 7. Simulation of tohati load ompenation. () Soure urrent i S ( C 2). (d) Soure urrent i S ( C 3). Fig. 6. Simulation of ingle-phae pule load ompenation. ubetion, the amplitude of v C i about the ame a, and a DC link voltage v d having a value equal to the peak value of will be enough to fulfill the ompenation tak. However, in retifier load ompenation, the high di/dt demand high v C, hene v d mut be muh greater than. In thi imulation, v d 2, and there are ignifiant overhoot in oure urrent (ee Fig. 5b). hee overhoot are due to the high di/dt and to a relatively mall value of v d. Inreaing v d an mitigate the overhoot, but alo aue higher power rating and urrent rating of the ompenator, i.e., a more expenive inverter. C. Single-phae Pule Load If a ingle-phae load i onneted to the three-phae utility, the ingle-phae urrent drawn from the ytem aue the unbalane of the ytem. Non-inuoidal load urrent, or individual high amplitude pule load urrent alo introdue high non-ative omponent to the ytem. In thi ae, the load urrent i a ingle-phae pule urrent, with a period of 3 ( i the fundamental period of the voltage). he poitive pule load urrent (red) our every 3 yle and ha a triangular hape a hown in Fig. 6a together with inuoidal ytem voltage (blue). In thi ae, the averaging interval C i a ritial fator to the ompenation. Fig. 6b, 6, and 6d how the three-phae oure urrent after ompenation where C i /2, 2, and 3, repetively. With the inreaing of C, ) i S i loer to a ine wave; 2) the three phae are more balaned; 3) i S i alway in phae with the voltage; 4) the magnitude of i S i dereaing. However, by inreaing C, the ompenator urrent i alo inreaing, and onequently, the apaitane rating and withing urrent rating mut inreae a well. Depending on the load harateriti, ompenator requirement, and the ompenation reult deired, a C an uually be hoen to meet all the objetive. In thi ae for example, C 2 ha a good oure urrent without too high of a ompenator rating. D. Stohati Load A tohati load i non-periodi, or theoretially, the period i infinity (a period muh larger than the fundamental period of the utility). In the latter ae, there are ubharmoni in the load, whoe frequenie are not an integer multiple of the fundamental frequeny. he nonative omponent in a tohati load annot be ompletely ompenated by hooing C a /2 or, or even everal time. In Fig. 7a, the waveform to the left of the dahed line are the oure urrent before ompenation (i.e., load urrent), and the right part are the oure urrent after ompenation, with C /2. here i till ignifiant non-ative omponent in i S, with variable peak value and non-inuoidal waveform hape. In Fig. 7b, i S i loer to a ine wave with le nonative omponent. Here a longer C mooth the oure urrent waveform. heoretially, i S ould be a pure ine wave if C goe to infinity, but in pratie, uh a C annot be implemented nor i it neeary. If C i large enough, inreaing C further will not typially improve the ompenation reult ignifiantly. For example, in thi ae hown in Fig. 7, the total harmoni ditortion (HD) of i S i 4% with C /2, and when C /2, the HD i only lightly maller than 4%. So there i no need to inreae C to a larger value a the mall dereae in HD i not worth the larger ot (higher rating of the ompenator and higher expene).

5 A. Averaging Interval, C V. DISCUSSION If there are only harmoni in the load urrent, a in Setion IV.A, C doe not hange the ompenation reult a long a it i an integral multiple of /2, where i the fundamental period of the ytem. Here the non-ative urrent i ompletely ompenated and a purely inuoidal, unity PF oure urrent i ahieved. However, in other ae, uh a in part B, C, and D of Setion IV, C ha ignifiant influene on the ompenation reult, and the power and energy torage rating of the ompenator omponent. With longer C, a better oure urrent will reult, but at the ot of higher power rating for the withe and apaitane. here i a tradeoff between better ompenation and higher ytem rating (i.e., ot). On the other hand, a longer C doe not neearily yield a better oure urrent waveform. For a peifi ytem, there i an appropriate C with whih the ompenation an be ahieved. For example, in part C of Setion IV, the pule load C depend on the period of the pule. B. Coupling Indutane, L C he indutane L C between the power ytem and the ompenator ould be the indutane of a tep-up tranformer or a oupling reator. It at a the filter of the ompenation urrent, whih ha high ripple ontent. If L C i too mall, it annot filter the ripple in the ompenation urrent ; and if L C i too large, the timeontant of the ytem will be o large that annot trak the referene, whih reult in inadequate operation of the ompenation ytem. L C i inverely proportional to the rm value of load urrent when the ripple in the oure urrent i limited to a peifi perentage (e.g. 5%): L K /, where K i a ontant. (0) I L C. DC Link Voltage, V d Rewrite (8) here: L v v di dt. For a given L C, the hange in urrent with time d /dt i determined by the voltage differene between v C and, o a fat urrent hange in require a large v C, whih in turn require a high voltage for the DC link of the inverter. Uually it i enough to have the DC link voltage higher than the peak value of the ytem voltage, but for ome appliation like the retifier load and the pule load in Setion IV, the DC link voltage i 3-5 time the ytem voltage to mitigate the overhoot of the oure urrent aued by the non-ative urrent not being able to trak the referene loely enough. D. DC Link Capaitane Rating C Aording to the definition in (7), the average power of the ompenator P C (t) over C i zero. However, the intantaneou power i not neearily zero. he ompenator generally ha a apaitor for energy torage, and thi apaitor operate in two mode: harge and diharge. Different apaitane value are required to fulfill different ompenation tak. he maximum energy tored in the apaitor i at the time t max when the apaitor goe from harge to diharge or vie vera. he minimum energy i zero at the time t min when v C 0, o that the maximum tored energy i t max E v i dt () t min he apaitane required of the ompenator i a funtion of the tored energy and voltage rating a C 2 E/(V d ) 2. VI. CONCLUSIONS A new definition of non-ative power/urrent wa preented. It ha been applied to a hunt non-ative power ompenation ytem, and the implementation of the ytem wa imulated. he imulation reult of everal different ae indiate that the definition i viable for different ytem inluding ingle-phae or poly-phae, inuoidal or non-inuoidal, periodi or non-periodi, balaned or unbalaned ytem. he definition i flexible in that it i appliable regardle of the onfiguration or the ontrol trategie of the ompenation ytem. VII. ACKNOWLEDGEMEN We would like to thank the National Siene Foundation for upporting thi work through ontrat NSF ECS VIII. REFERENCES [] H. Akagi, Y. Kanazawa, A. Nabae, Intantaneou Reative Power Compenator Compriing Swithing Devie without Energy Storage Component, IEEE ran. Ind. Appl., vol. 20, May/June 984, pp [2] L. Roetto, P. enti, Evaluation of Intantaneou Power erm in Multi-Phae Sytem: ehnique and Appliation to Power Conditioning Equipment, EEP, vol. 4, no. 6, Nov./De [3] F. Z. Peng, J. S. Lai, Reative Power and Harmonompenation Baed on the Generalized Intantaneou Reative Power heory for hree-phae Power Sytem, Proeeding of the 7th International Conferene on Harmoni and Quality of Power, La Vega, NV, Otober 6-8, 996, pp [4] L. M. olbert,. G. Habetler, Survey of Ative and Non-Ative Power Definition, IEEE International Power Eletroni Congre, Otober 5-9, 2000, Aapulo, Mexio, pp [5] F. Z. Peng, L. M. olbert, Z. Qian, Definition and Compenation of Non-Ative Current in Power Sytem, IEEE Power Eletroni Speialit Conferene, Cairn, Autralia, June 23-27, 2002, pp q

6 [6] G. Carpinelli, M. Di Manno, al., AC and DC Ar Furnae: A Comparion on Some Power Quality Apet, IEEE Power Engineering Soiety Summer Meeting, 999, pp [7] H. Akagi, Ative filter and Energy Storage Sytem Operated under Non-periodondition, IEEE Power Engineering Soiety Summer Meeting, Seattle, Wahington, July 5-20, 2000, pp [8] E. H. Watanabe, M. Arede, Compenation of Non-Periodurrent Uing the Intantaneou Power heory, IEEE Power Engineering Soiety Summer Meeting, Seattle, Wahington, July 5-20, 2000, pp [9] L. S. Czarneki, Non-Periodurrent: heir Propertie, Identifiation and Compenation Fundamental, IEEE Power Engineering Soiety Summer Meeting, Seattle, Wahington, July 5-20, 2000, pp [0] S. R. Mendi, M.. Bihop, J. F. Witte, Invetigation of Voltage Fliker in Eletri Ar Furnae Power Sytem, IEEE Indutry Appliation Magazine, vol. 2, no., Jan./Feb. 996, pp [] Y. Xu, L. M. olbert, F. Z. Peng, J. N. Chiaon, J. Chen, Compenation-baed Non-ative Power Definition, IEEE Power Eletroni Letter, vol., no. 2, June 2003, pp [2] L. M. olbert, Y. Xu, J. Chen, F. Z. Peng, J. N. Chiaon, Compenation of Irregular Current with Ative Filter, IEEE Power Engineering Soiety General Meeting, oronto, Canada, July 3-8, 2003, pp VIII. BIOGRAPHIES Yan Xu (S 2002) reeived the B.E. in Eletri Power Engineering from Shanghai Jiaotong Univerity, Shanghai, China and M.S. in Eletri Power Engineering from North China Eletri Power Univerity, Beijing, China. She worked in Anhui Eletri Power Company Ma anhan Branh, China from 995 to 998. She wa an engineer in the Power Dipath Department. She worked on the SCADA ytem and ontributed to everal SCADA projet in the ditribution and dipath enter. She preently i a Ph.D. tudent in Eletrial Engineering at he Univerity of enneee. Her reearh interet inlude non-ative power ompenation and priing, and it appliation in ditributed energy ytem. John N. Chiaon (S 982 M 984 SM 2003) reeived hi Bahelor' in Mathemati from the Univerity of Arizona, hi M.S. in Eletrial Engineering from Wahington State Univerity, and hi Ph.D. in Control from the Univerity of Minneota. Hi work in indutry tarted at Boeing Aeropae from 978 to 979 in the area of flight ontrol, guidane and navigation. From , he worked at Control Data in the area of CAD ytem, and from he worked at Honeywell Siene and ehnology Center in the area of inertial navigation. Hi latet tint in indutry wa from at ABB Daimler- Benz ranportation where he worked in the development of AC motor propulion ytem, real-time imulator, and the tability analyi of AC propulion ytem. Sine 999, he ha been on the faulty of Eletrial and Computer Engineering at he Univerity of enneee. He doe reearh in the area of the ontrol of eletri motor drive, multilevel onverter, hybrid eletri vehile a well a mathematial ytem theory. Dr. Chiaon i an aoiate editor of the IEEE ranation on Control Sytem ehnology. Leon M. olbert (S 989 M 99 SM 998) reeived the B.E.E., M.S., and Ph.D. in Eletrial Engineering from the Georgia Intitute of ehnology, Atlanta, Georgia He joined the Engineering Diviion of Lokheed Martin Energy Sytem in 99 and worked on everal eletrial ditribution projet at the three U.S. Department of Energy plant in Oak Ridge, N. In 997, he beame a reearh engineer in the Power Eletroni and Eletri Mahinery Reearh Center at the Oak Ridge National Laboratory. In 999, he wa appointed a an aitant profeor in the Department of Eletrial and Computer Engineering at the Univerity of enneee, Knoxville. He i an adjunt partiipant at the Oak Ridge National Laboratory and ondut joint reearh at the National ranportation Reearh Center (NRC). He doe reearh in the area of eletri power onverion for ditributed energy oure, motor drive, multilevel onverter, hybrid eletri vehile, and appliation of SiC power eletroni. Dr. olbert i a regitered Profeional Engineer in the tate of enneee. He i the reipient of a National Siene Foundation CAREER Award and the 200 IEEE Indutry Appliation Soiety Outtanding Young Member Award. He i an aoiate editor of the IEEE Power Eletroni Letter.