IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-20, NO.3, MAY/JUNE 1984 625 Instantaneous Reactive Power Compensators Comprising Switching Devices without Energy Storage Components HIROFUMI AKAGI, YOSHIHIRA KANAZAWA, AND AKIRA NABAE, MEMBER, IEEE quantities as the instantaneous space vectors. For simplicity, the three-phase voltages and currents excluding zero-phase sequence components will be considered in the following. In a-b-c coordinates, the a, b, and c axes are fixed on the same plane, apart from each other by 27r/3, as shown in Fig. 1. The instantaneous space vectors, ea and ia are set on the a axis, and their amplitude and (±,-) direction vary with the passage of time. In the same way, eb and ib are on the b axis, INTRODUCTION and ec and ic are on the c axis. These space vectors are easily TARIOUS TYPES of reactive power compensators has been transformed into a-3 coordinates as follows: V researched and developed to provide power factor correction [1] -[5] . Notably, the static reactive power compensator L[ed1] [1 -1/2 -1/2 comprising switching devices, which requires practically no en(1) 3 0 IefJ N3-\/ 2 JJeb vr3/172 ergy storage components such as capacitors or reactors, was ec proposed by Gyugyi and others [6] - [8]. However, it has been considered that the compensator can eliminate only the fundamental reactive power in steady states. The generalized control Pal [ipj [0 -1/2 -1/2 strategy including the compensation of the fundamental reac(2) tive power in transient states and the harmonic currents has J712 not yet been discussed in detail. L'ciJ In this paper, the instantaneous imaginary power, which is a new electrical quantity, is introduced in three-phase circuits. where the a and , axes are the orthogonal coordinates. NecesThen, the instantaneous reactive power is defined as a unique sarily, e, and iot are on the a axis, and ep and ig are on the,B value for arbitrary three-phase voltage and current waveforms axis. Their amplitude and (±,-) direction vary with the passage including all distorted waveforms, by using the abovementioned of time. Fig. 2 shows the instantaneous space vectors on the a-j3 coinstantaneous imaginary power. According to the theory deordinates. The conventional instantaneous power on the threeveloped in this paper, a new instantaneous reactive power compensator is proposed, comprising switching devices without en- phase circuit can be defined as follows; ergy storage components. This compensator can eliminate not p = eo - i + ep ff3 (3) only the fundamental reactive power in transient states but also some harmonic currents. For example, the harmonic currents having the frequencies of f ± 6f0 in a three-phase-to- where p is equal to the conventional equation: three-phase naturally commutated cycloconverter can be p = eaia + ebib + ecic eliminated, where f is the input frequency and f is the output frequency. The validity of the compensator is confirmed by In order to define the instantaneous reactive power, the experiments. authors introduce the instantaneous imaginary power space INSTANTANEOUS REACTIVE POWER THEORY vector defimed by Definition of Instantaneous Imaginary Power q =e., X i± X io. (4) +eg To deal with instantaneous voltages and currents in threephase circuits mathematically, it is adequate to express their As shown in Fig. 2, this space vector is the imaginary axis vecPaper IPCSD 83-46, approved by the Static Power Converter Committee of tor and is perpendicular to the real plane on the a-( coorthe IEEE Industry Applications Society for presentation at the 1983 Industry dinates, to be in compliance with the right-hand rule. Taking Applications Society Annual Meeting, Mexico City, Mexico, October 3-7. into consideration that eoe is parallel to i,, and e to i,, and Manuscript released for publication September 9, 1983. The authors are with the Faculty of Engineering, Technological University that eO, is perpendicular to ig and eg3 to io, the conventional instantaneous power, p and the instantaneous imaginary power q, of Nagaoka, Nagaoka 949-54, Niigata, Japan. Abstract-The conventional reactive power in single-phase or threephase circuits has been defined on the basis of the average value concept for sinusoidal voltage and current waveforms in steady states. The instantaneous reactive power in three-phase circuits is defined on the basis of the instantaneous value concept for arbitrary voltage and current waveforms, including transient states. A new instantaneous reactive power compensator comprising switching devices is proposed which requires practically no energy storage components. ia 0093-9994/84/0500-0625$01.00 i) 1984 IEEE Authorized licensed use limited to: BMS COLLEGE OF ENGINEERING. Downloaded on May 03,2010 at 06:54:21 UTC from IEEE Xplore. Restrictions apply. 1. NO. Conversely. The instantaneous real power in the three-phase circuit p is given as follows. are expressed by Both the physical meaning and reason for the naming of the instantaneous active and reactive currents are clarified in the following. They are given by the conventional definition as follows: [Pa] LI Fea e.e2 + e2 P ia< -ep+ q a-axis instantaneous active current: 13-axis ep 2 1q= e2 + 2P . which is the amplitude of q. axis and the 13 axis be Pa! and p.ep and its dimension is [W]. 3. or [var].2010 at 06:54:21 UTC from IEEE Xplore. using (7) and (8): lP ep i.ep 1oq e2 + e132 - 1-axis instantaneous reactive current: RELPLANE ea q. Restrictions apply. From (8) and (9) the following in is Accordingly.] a q -ep ea 1p 5 In (5) eaqai and eg -i.equations cause the dimension is not [W]. obviously mean instantaneous power e2 e2 because they are defined by the product of the instantaneous P Pa±p + ep2 eP2+e2 voltage in one axis and the instantaneous current in the same e. are laJ jea ep pP qqJ ea [-ep ea J (6) and eg in (6) is ep2 13-axis instantaneousractive power: Ppp e2 + e2 e2ep Note that the determinant with respect to a-13 The instantaneous currents on the coordinates. Let the instantaneous powers in the a. Oala ] Ler p eaia]l +[eaIq- ep i#qI (8) +ea2+2peP = Definition and Physical Meaning of Instantaneous Reactive Power Equation (5) is changed into the following equation: where a-axis instantaneous active power: Pap ea2 2 p2 P Lipl not zero. . zero. Instantaneous space vectors. q cannot be dealt with as a conventional electrical hand side are (9) always obtained: quantity.iaq + egpipq paeq + Ppq p as "instantaneous real power" to distinguish the conventional instantaneous power from the instantaneous imaginary power. 2. P [WI Fig. Hereinafter.626 P-AXIS IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. ia and ig divided into two kinds of instantaneous current compo- 13-axis instantaneous reactive power: p ea2 + 2 q. be. a-fl coordinates transformation.2 ~~~~~~P P ea +. Downloaded on May 03. [VA]. ea ti and ep 'a are not (9) e2 eg2 e 2+ epg2 instantaneous power because they are defined by the product of the instantaneous voltage in one axis and the instantaneous Note that the sum of the third and fourth terms of the rightcurrent not in the same axis but in the perpendicular axis. IA-20. Therefore. axis.p respectively. VOL. (10) p-e(ap + eig1p pap + Ppp the authors have named the conventional instantaneous power (11) 0=e. eaep q -e. So a new dimension must be introduced for q. Authorized licensed use limited to: BMS COLLEGE OF ENGINEERING. respectively: ia Lip O rea [- ep ea [P O ea epl e 01 Lq [-ep e _AS [api + [aq~ Li Lp qq (7) where Fig. a-axis instantaneous active current: ae-axis instantaneous reactive current: ip. p is the real power in the three-phase circuit. MAY/JUNE 1984 nents. The following relationship exists between the instantaneous imaginary power on the input side q and the instantaneous imaginary power on the output side q': ip Fig. qs(:01. 1ic 1e. Paqf' and ptqt are the instantaneous powers circulating between the static power converter and the load. As shown in this figure. Necessarily.. Pc is always zero. However. Ppq)p Instantaneous power flow. 3 shows a generalized instantaneous power flow in a static power converter system such as a three-phase-to-threephase cycloconverter. The instantaneous active and reactive currents are Assuming that there are neither energy storage components divided into the following two kinds of instantaneous currents. The second term is the instantaneous value of the harmonic currents which represents the ac component of the instantaneous real power. In addition. Accordingly.. 4 shows a basic compensation scheme of the instantaneous reactive power. nor losses in the static power converter. For this reason. the instantaneous com- pensating given by currents a-3S coordinates. be- + e2+ / a~ ep - (15) where p and are the dc and ac components of the instantaneous real power and qj and q are the dc and ac components of the instantaneous imaginary power. including zero-phase sequence components. there is no relation in the instantaneous reactive powers on the input and output sides. the following relation. Consequently. The first term of the righthand side of (15) is the instantaneous value of the conventional fundamental reactive current. The fourth term is the instantaneous value of the harmonic currents which represents the ac component of the instantaneous imaginary power. . pagp and pp coincides with the instantaneous real power in the three-phase circuit. 3. the displacement factor is unity not only in steady states but also in transient states. Therefore. Pc and qc are those on the compensator side. + ep2 ePe2+ep q Furthermore. pofp and ppp are named instantaneous active power. 2) The harmonic currents represented by the fourth term Authorized licensed use limited to: BMS COLLEGE OF ENGINEERING. ep --p ec . Equation (15) leads to the following essential conclusions.q cancel each other and make no contribution to the instantaneous power flow from the source to the load.O)P. which are caused by the instantaneous imaginary power on the load side. 2) The instantaneous powers. The third term is the instantaneous value of the conventional fundamental reactive current. p and q are those on the load side.respectively: ship exists: e e. concerning the ax axis instantaneous current on the q 0q'. Restrictions apply. cause Basic compensation scheme. the instantaneous real power coincides with three times the conventional active power per one phase. on the From (6). Note that the second and fourth terms include a conventional negative sequency component.Con. 1) The sum of the instantaneous powers. The instantaneous reactive power theory.: REACTIVE POWER COMPENSATORS 627 The basic principle of the compensator will now be considered. Fig. Note that the physical meaning of the instantaneous imaginary power defined in the three-phase circuit is quite different from that of the instantaneous reactive power in each phase. _ P P- Inspection of (10) and (11) leads to the following essential conclusions. The instantaneous reactive power compensator proposed in this paper eliminates the instantaneous reactive powers on the source side. the sum of the second and fourth terms is the instantaneous value of the conventional harmonic currents. 1) The instantaneous reactive power compensator eliminates both the third and fourth terms. SOURCE. Pafq and p. Where Ps and qs are the instantaneous real and imaginary powers on the source side.2010 at 06:54:21 UTC from IEEE Xplore. The compensator consists of only switching devices without energy storage components. CONTROL STRATEGY Fig.x _ 2 e. Paq and ppq on the input side. the instantaneous reactive powers. it is evident that both the instantaneous real power and the instantaneous imaginary power in a balanced sinusoidal three-phase circuit become constant. the instantaneous imaginary power is quite different in definition and physical meaning from the conventional reactive power based on the average value concept. is discussed in the Appendix. . the instantaneous imaginary power is numerically equal to three times the conventional reactive power per one phase. ica and i are L icp -. Paq and pq are named instantaneous reactive power. Downloaded on May 03. Therefore. La qc(l-f) C Fig. 4. 2+ep - Pe. r---q (14) e.AKAGI etal. are the instantaneous powers circulating between the source and the static power converter. load side. is turned on when iCa is equal to the lower limit of lCa* On the contrary. = ^-1/2 -1/2] Compensation Results of a Bridge Converter and a Cycloconverter Fig.' The 0.* are calculated instantaneously without any time delay by using the instantaneous voltages and currents on the load side. that is. 6 shows the control circuit of the compensator. 8 shows the responses to the step variation of the load resistance of the thyristor bridge converter in which the control delay angle is zero. EXPERIMENTAL RESULTS Instantaneous Reactive Power Compensator System Fig. IA-20. 10 shows the transient compensation results of a threephase-to-three-phase naturally commutated cycloconverter with a balanced load. Authorized licensed use limited to: BMS COLLEGE OF ENGINEERING. six power diodes. 7. Experimental system. The maximum switching frequency is set to about 30 kHz in the following experiments. Tr1 is turned off when iCa is equal to the upper limit of iCa*. Downloaded on May 03. The filter capacitors and reactors have the function of suppressing the harmonic currents caused by the switching operation of the power transistors.F dc capacitor.5-. Switching scheme of power transistors. a 5-. Fig. As shown in this figure. iCb. Fig.uF capacitors. 20 Hz and 80 Hz are eliminated because they are the harmonic currents caused by the ac component of the instantaneous imaginary power on the load side. and operational amplifiers. 2. the compensator has no devices except for the 5-pF capacitor on the dc side.4-mH reactors. The instantaneous reactive power compensator consists of six power transistors. The amplitude of the fundamental current of iS. Fig. output frequency f= 5 Hz The displacement factor on the source side is unity in the transient state. 9 shows the harmonic spectrum of iSa and ia in the steady state. output voltage ratio r = 0. [C] [ Fig-C 6. and three 2. The switching operation of the power transistors automatically forces the compensating currents iCa. 5.2010 at 06:54:21 UTC from IEEE Xplore. Fig.F filter capacitors. Restrictions apply. The references of the compensating currents iCa*. VOL.5-.628 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. NO. is smaller than that of ia because the fundamental reactive current of iSa is eliminated by the instantaneous reactive power compensator. the higher the switching frequency of the power transistors becomes. Fig. Now assume that the reference compensating current iCa* is positive. Accordingly. The transistor Tr. Although the harmonic currents of iSa are reduced considerably iSa is not purely sinusoidal. and icc to follow the reference compensating currents iCa*. Control circuit. the harmonic currents having the frequencies of f 6f0. MAY/JUNE 1984 can be eliminated by the compensator comprising switching devices without energy storage components. The displacement factor on the source side is unity not only in the steady state but also in the transient state. The operating conditions of the cycloconverter are as follows: input frequency f=50 Hz Tr Tr2 - Fig. iCb* and ic. 2 ci/2 Fig. Moreover. when the dc output current of the bridge converter is 10 A. Therefore the power circuit can be considered as a kind of three-phase current amplifier. and lCc*. The control circuit consists of several analog multipliers.F capacitor are not used as energy storage components but are necessary for the switching operation of the power transistors. This is due to the existence of the harmonic currents caused by the ac component of the instantaneous real power on the load side. three 0. the less the capacity of the capacitors and reactors. 6. 7 shows the switching scheme of the power transistors. 3.8. Fig. 5 shows the experimental system. 11 shows the harmonic spectrum of iSa and ia in the steady state. and the 5-. dividers. iCb*.4-mH filter reactors. Note that neither low-pass filters nor integrators exist in the control circuit. The loss in the compensator is about 20 W. . O 7-r''1A 200V ia ~eo I /f2 = 4 eA | 1 -1/2 1 /N2 1 /-1/2 ' Feal | eb (16) the e. the instantaneous imaginary power was introduced on the same basis as the conventional instantaneous real power in three-phase circuits. (4).uF dc capacitor VCd is (18) po = eo * io charged up to about 140 V. according to the theory of the instantaneous reactive power. the three independent quan140 V to 150 200 V at the instant that the compensator tities po. p. 5OHz/DIV 5OHz/DIV Fig.. : : rio |i =N I /2 1 1/NT I/Nr -1/2 -1/2 lial |ib (17) [ipg L 0 Vf/2 -v3/2_ j Buildup of the 5-.5A-_ EsS ~~~ ~~ia 50Hz/DIV _ 50Hz/DIV by the active power.. eb.B coordinates are given as follows: k . corresponding to the losses in the compensator. and q are given by comes into operation. t t Change of the Load d Compensation of cycloconverter. The instantaneous reactive power was defined.j VCd L 0 V3/2 --2VJLec J on Likewise. 9. while all the power transistors remain turned off. Compensation of bridge converter. Fig. the voltage across the 5-. and (18).5A- 7. i. It was verified by experiments that not only the fundamental reactive power in transient states but also the harmonic currents caused by the instantaneous imaginary power can be eliminated. was proposed. CONCLUSION In this paper. and the physical meaning was discussed in detail.: REACTIVE POWER COMPENSATORS 63A 629 17A Fig.AKAGI et al. eo and io converter. VCd builds up from power. 8.. The instantaneous space vectors ea. The compensator operates as a three-phase diode bridge which is defined by the instantaneous space vectors. The rms value of the line-to-line voltage is 100 V. are transformed into 0-a-. The instantaneous reactive power compensator comprising switching devices. 11. Lq L0 . APPENDIX DISCUSSION ON ZERO-PHASE SEQUENCE COMPONENTS It is possible to extend the instantaneous reactive power theory developed in this paper to the three-phase circuit including zero-phase sequence components [9]. and ig 0-a-. In (18) po has been named "instantaneous zero-phase sequence According to the experimental results. which requires practically no energy storage components.-. on the 0 axis: In this case. (19) |= |0 ea | ii| The reason why the capacitor voltage builds up is that the -ep e-J [igj switching operation of the power transistors is accompanied e . Note that the instantaneous real power [Po eo 10 on the compensator side Pc is held at zero and that the compensator has no devices except for the capacitor on the dc side.uF DC Capacitor Voltage The authors introduce another instantaneous power po. Restrictions apply.. and e.B coordinates as follows: Fig. Downloaded on May 03." From (3). the instantaneous space vectors io. 7. Authorized licensed use limited to: BMS COLLEGE OF ENGINEERING. Spectrum of is and i4. Spectrum of i& and i.2010 at 06:54:21 UTC from IEEE Xplore. 10. Inaba. He is now interested in the energy conversion and control development of rectifier and inverter technology at _ Tsurumi Works Engineering Department. I where 1aO = ibO = icO = iO/VI3 Let the a-. [3] L. IEEE/lASAnnu. 1977. He is engaged in research on ac drive systems and reactive power compensator systems. "Controllable static REFERENCES +4 | I/V N . VOL. Strycula. M. [5] 1. Japan. degree in electrical engineering from Niigata University. degree in electrical engineering from Nagoya Institute of Technology. respectively. and pc. 1980. because the sum of the instantaneous reactive powers is always zero. Akagi. on August 14. Harashima. Ind. degree from Waseda University. 137. -ep ea. Matsuura. from 1951 to 1970. Harumoto. Meeting. "Universal power distortion compensator of line commutated thyristor converter." IEEE Trans. 1375. Hirofumi Akagi was born in Okayama Prefecture. and W. Appl. MAY/JUNE 1984 E io ip = 0 ec. 1981. in 1964. he was involved in the research and development of power electronics. in Akim PcqJg ins~tantaneous zero-phase sequence power instantaneous active instantaneous reactive power The instantaneous reactive powers in each phase Paq. [8] Y. no. "Reduction of reactive power and balancing of supply currents for three-phase converter systems. and Ph. Appl. Downloaded on May 03." in Proc. 365. 917. Pbq. Since 1978. the following is obtained: Pa [eaiaO Jeaiap][ealaq] Kanazawa was born in Niigata Prefecture. "Active ac power filters.2 -1. Japan." in Proc. Ikeda. and the Dr. " in IEEE/IAS ISPCC. p. 5. Restrictions apply. e3 ° O 0 0 - Po O + - e0 0 ea e e 0 in the three-phase circuit which is represented by the sum of po and p. Kanazawa. Mr. and systems. Japan. p. he was a nonoccupied Lecturer of Waseda University. NO. (23) O~ -1 .. Iyf0 /3j2 ° 0 [iol 0_ 1 1/2 -V'3/2J Li"J 0 0 J3/2 |i ap| power compensators in electric supply system. IFAC.l _ 3q 0~~~~~~~ From (20). "High-frequency link power conversion. He is engaged in research on power electronics. W. Eng. on September 13. 0 ~in 1976 and 1979. Nabae. b-. Tsuboi. eo ° O 0 -ea Paq + Pbq + Pcq = 0. 1977. vol.D. Yoshihia |Pb |=| ebb0 |+| ebibP | + PPCJ eCibJ ecicp Lec + ebibq| ec i9J + = FPaol Pbo| LP oJ rPap 1 Paq |IPbpI| LPCP J |IPbq |- (22) 1947. 529." in Proc. vol. Hasegawa. 1938." in Proc. and K." in Proc. Tokyo. He received the B. especialy ac drive systems at the Heavy Apparatus Engineering Laboratory. IEEE/IA S ISPCC. Dr. and A. Ind. Hanke. in 1974 and the M. [2] H. Kanazawa is a member of the Institute of Electrical Engineers of Japan. Japan. IA-13. Japan. IA 20. Japan. 1978. the instantaneous currents on the a-b-c coordinates are divided in the following three components.S. 1972 to 1978. Japan. 387. Bose. Nabae. Yano. [6] L. and c-phase instantaneous powers be Pa. he has been an Assistant Professor at the Technological University of Nagaoka.. T.2010 at 06:54:21 UTC from IEEE Xplore. From Nabae (M'79) was born in Ehime Prefecture. C. K.S." presented at the IEEE/PES Winter Meeting. From t g_ 1970 to 1978. Achenbach. Y. JIEE IPEC-Tokyo. Pb. "Reactive power generation and control by thyristor circuits. [4] P. Niigata. He joined Toshiba Corporation in 1951. Tokyo. 858. Hochstetter. Espelage and B. Japan. Gyugyi and F.630 Inverse transformation of (19) gives IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. Akagi is a member of the Institute of Electrical Engineers of Japan.S. Gyugyi and E. IA-15. Y. that is. he was engaged in the research and . he has been a Professor at the Technological University of Nagaoka. 1976. 1977. respectively. p./2 L1/V -1. 1951. Takahashi and A. p.sq] Liaq] [iao] Al = L4cOJ ibO0| [iap]1 |Iibp| L'cp J + icq [icqJ (21) _ 1 instantaneous zero-phase sequen sequence curo-paen current active current instantaneous reactive current instantaneous Since 1979. Cibulika." IEEE Trans. Pcq make no contribution to the instantaneous power flow Authorized licensed use limited to: BMS COLLEGE OF ENGINEERING. F. degree from Tokyo University. [7] L. 3.P + O ea ep 01 O _O_ Op 1+. "Generalized theory of the instantaneous reactive power in three-phase circuits. [I] K. p. respectively: ial lb L 1/ -1/2 [I/V 1 ic INf1/ -1/2 --4/32 +±vf 1/. He was with Niitsu Techinical High School from 1964 to 1980. [9] H.S. Meeting. Japan. Also. He received the B. "New static var control using force-commutated inverters. Since 1980.1N/ -1/2 + 1/2 43/12 ||iaq -\ 3 2 1 i. p. "The high frequency base converter-A new approach to static high power conversion. IEEE/IA S Annu. Nagoya. Nabae is a member of the Institute of Electrical Engineers of Japan. Gyugyi. Japan. he has been an Assistant Professor at the Technological University of Nagaoka. 1924. By applying (21). Dr. 1977. 1983. on August 19. degrees in electrical engineering from Tokyo Institute of Technology. Japan. M. p. and H. Japan. He received the B.
Report "Instantaneous Reactive Power tors Comprising"