SEVERAL interesting two-port power-conservative network

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1 704 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL 53, NO 3, MARCH 2006 Loss-Free Complex Impedance Network Elements Doron Shmilovitz, Member, IEEE Abstract The concept of loss-free complex impedance network elements (ie, elements with active and reactive impedance components and yet loss-free) is introduced Synthesis of such elements by means of switched-mode power converters with appropriate control has been demonstrated to be possible Some possible power processing-related applications of these elements are indicated, such as improved matching between ac sources and loads and VAR compensation It has further been demonstrated that loss-free complex impedance elements are suitable for modeling many power processing systems for the purpose of analysis as well as for design purposes Index Terms Active power factor correction, alternator, gyrator, loss-free resistor, low-harmonics rectifier, power conservative network, power sources, time-variable transformer, two-port power-conservative, VAR compensation Fig 1 Time-variable transformer coupling two subnetworks I INTRODUCTION SEVERAL interesting two-port power-conservative network elements have been introduced in recent years in the context of efficient power processing It has been found that switched-mode converters facilitate the synthesis of loss-free two-port network elements such as time-variable transformers [1] [8], gyrators [9], [10], and power sources [7], [9], [11] These circuits consist of loss-free elements (in principle) such as switches, inductors, capacitors, and transformers, implying no losses in the network Similarly to conventional transformers, time-variable transformers are two-port power-conservative network elements which couple two subnetworks and, as shown in Fig 1 The waveforms and component values within the subnetwork are scaled with respect to each other by a scaling factor defined by the transformer s transfer ratio However, the transfer ratio of time-variable transformers is tunable by means of a small-signal control voltage Time-variable transformer (TVT) is taken to refer to a conceptual network element whose transfer ratio is continuously (often, periodically) varied in a wide range at a relatively high rate In addition, TVTs have no saturation and thus may operate with dc waveforms Manuscript received March 21, 2005 This work was supported in part by the Israeli Ministry of National Infrastructure and Energy under Grant This paper was recommended by Associate Editor P K Rajan The author is with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel ( shmilo@engtauacil) Digital Object Identifier /TCSI (1) Fig 2 Symbolic representation of a gyrator Fig 3 LFR model as (a) a two-port element and (b) the power source characteristics The gyrator is defined by its admittance matrix [7], [9], [10] as follows: A gyrator is depicted schematically in Fig 2 Its characteristic property is that it converts a one-port network into, which is its dual with respect to the gyration conductance defined by Another member of this family of two-port loss-free network elements is the loss-free resistor (LFR) The LFR (introduced in [11]) is a two-port network consisting of an emulated resistance at the input port and a power source [7], [11] [13] at the output, as shown in Fig 3 The power source is defined as an element, which outputs a certain power regardless of the loads characteristics, the amount of which equals that of the power (2) (3) /$ IEEE

2 SHMILOVITZ: LOSS-FREE COMPLEX IMPEDANCE NETWORK ELEMENTS 705 Fig 4 LFCI having complex impedance input characteristics absorbed at the resistive input port The equations that describe the LFR model are (4) Fig 5 Rectification and VAR compensation by means of LFCI In principle, all of these network elements are power-conservative, ie, they do not generate nor dissipate power and they have no energy storage capability If they are to be employed for the purpose of processing a considerable amount of power, they must be realized by means of high-efficiency circuits Indeed, it has been established that all of these network elements can be realized by means of switched-mode converters with appropriate control (see [5] [8] and [10] [14]) In this paper, another two-port network element is introduced: theloss-freecompleximpedance(lfci), whichexhibitscomplex impedance characteristics at its input port(ie, active and reactive components) and power source characteristics at the output The synthesis of LFCI elements is discussed as well as its realization by means of switched-mode converters Possible applications of the LFCI are also indicated The concept is validated by simulation results II LFCI SYNTHESIS EMPLOYING AN LFR, A POWER-CONSERVATIVE COUPLING NETWORK, AND A STORAGE COMPONENT The LFCI is synthesized based on the LFR model, described in Fig 3 If the input port is augmented by reactive components such as capacitors and inductors, it would attain complex impedance characteristics (see Fig 4) As in the LFR, the instantaneous power absorbed by the emulated resistance component is transferred to the power source Such LFCI can be applied for the purpose of simultaneous VAR compensation and rectification, as shown in Fig 5, where the combination of emulated resistance and the power source may be modeling a switched-mode rectifier [7] and the capacitor C can be identified with a power factor correction capacitor Thus, both the LFCI and the inductive load consume currents that are phase-shifted with respect to the load, yet the ac source supplies only active power, thus minimizing the source rms current Since LFR elements can be realized by means of switchedmode converters [7], [11] [13], such direct realization of LFCI is, in principle, which is possible simply by adding a reactive element to the resistive emulating port of a switched-mode converter In many cases, it might not be feasible or practical to insert conventional reactive elements of the required value at the input (5) Fig 6 Capacitor synthesis by means of a gyrator and an inductor port, yet the reactive nature can be emulated by means of a TVT or a gyrator (depending on the nature of the physical storage component and that of the reactive component to be emulated) For instance, a gyrator ending with an inductor would exhibit capacitive characteristics at its input (see Fig 6) If a particular value of emulated capacitor is required at the input, the gyration conductance should be chosen accordingly as Though energy-conservative, the LFCI is not power-conservative (unlike the LFR), since its instantaneous input power differs from its instantaneous output power Since the coupling network (either a TVT or gyrator) has no storage capability, an energy storage component is always required in order to synthesize the reactive input behavior Fig 6 illustrates reactive input emulation by means of a coupling network (in this case, a gyrator) and a dedicated storage component (the inductor ) It should be noted that the dedicated storage element is connected to the coupling network output solely III LFCI SYNTHESIS EMPLOYING READILY EXISTING STORAGE COMPONENTS In some cases, large energy storage components do readily exist in the system When sufficiently large, these components may be regarded as sources (large inductors may be viewed as current sources whereas large capacitors might be viewed as voltage sources) Capacitors that store a large amount of energy (6)

3 706 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL 53, NO 3, MARCH 2006 Fig 7 LFR modeling of high-quality battery charging and voltage sources are quite common (such as dc bulk capacitors at rectifiers output) The dual-energy storing type (inductive) is not as common, yet inductive storage may also be found, such as in superconducting magnetic energy storage [14] While serving their initial storage function, these large storage components may also be used, at the same time, for the reactive component emulation, thus eliminating the need for a dedicated reactive component However, to be able to employ a readily existing storage component, it must be a large component (such as a large filter inductor or bulk capacitor) exhibiting either constant voltage or constant current, so that its initial functioning (energy storage) is not perturbed Let us consider, for example, the case of battery charging from an ac source by means of a switched-mode rectifier This is well modeled by an LFR [7] (see Fig 7) The input voltage and current are sinusoidal The input power, and thus the output power, are determined by the emulated resistance and by the input voltage as The resulting charging current is periodic with a frequency twice higher than that of the input voltage (or current) and an average value of It should be noted that the battery current is pulsating, as no filtering is involved The battery is a readily existing storage component that may be used for the generation of reactive current Since the primary source is a voltage source, a coupling network with programmed input current is required, and therefore a gyrator is used to reflect the constant voltage source as an ac current source (see Fig 8) This is facilitated by the proper programming of the gyration conductance The gyrator input current is actually the emulated capacitor current (Fig 6), resulting in The gyrator implies input current programming by means of the gyration ratio and the output voltage (7) (8) (9) (10) Fig 8 LFCI synthesis by means of an LFR and a gyrator where is the gyrator output voltage and is its input current Equations (9) and (10) yield the gyration conduction (11) Thus, in the example of battery charging from a sinusoidal voltage source, the gyrator will emulate a capacitor if its gyration ratio is controlled according to (12) Since both gyrators [9], [10] and LFRs [11] can be realized by means of switched-mode converters, efficient realization of LFCI with no dedicated storage component, like the one described in Fig 8, is possible IV SYNTHESIS OF MULTIPHASE LFCI The effect of reactive power in multiphase systems may be accomplished by the circulation of instantaneous power among the phases without any physical storage [15] This could be illustrated through recent definitions of reactive power (in particular, definitions of instantaneous reactive power ) [16] [19] LFCI synthesis in multiphase systems operating in steady state does not imply energy storage Therefore, it does not require any storage components Synthesis of multiphase reactive impedance with no energy storage components is illustrated in this section, where gyrator elements are chosen for coupling the input to the output This is valid only in balanced load situations Consider the multiphase system depicted in Fig 9 The source consists of ideal voltage sources having the same amplitude and angular frequency Each voltage source is phase shifted with respect to the following one in the sequence by

4 SHMILOVITZ: LOSS-FREE COMPLEX IMPEDANCE NETWORK ELEMENTS 707 Fig 9 Multiphase capacitive LFCI Under symmetrical loading (without loss of generality, linear load is treated herein), each phase is loaded by an identical LFCI load similar to the one depicted in Fig 4 Therefore, each phase supplies a sinusoidal current with equal amplitude and equal phase shift with respect to the phase voltage The load power equals the sum of power sources of the LFCI array regardless of the LFCI outputs interconnection (This is a property of power sources [7]) In this example, let us assume that each LFCI is of capacitive type, like the one depicted in Fig 5, consisting of an emulated input resistance and an emulated input capacitance, yielding (13) The phase voltage and current are defined as follows, where the rms values are adopted for the phasor magnitude notation: Fig 10 Multiphase LFCI synthesis by a gyrator array The gyrator array coupling network sets the following relation between input and output: (15) where is the vector of input currents to the gyrators, is the coupling matrix consisting of gyration conductances, and is the vector of the gyrators output voltages (16) In the scheme of Fig 10, the gyrator-based coupling network input currents are actually the phase s currents (17) (14) where is the phase number and is the number of phases Now, let us replace the LFCI array by a coupling network that contains no storage elements This may be accomplished either by an array of gyrators or an array of TVTs In many cases, the output exhibits voltage source characteristics, and, thus, the coupling network couples voltage sources at the input to a voltage source at the output Therefore, gyrators appear to be adequately suitable coupling elements Let us assume that the coupling network consists of gyrators, with each of them coupling a phase voltage to the gyrator s output voltage, as shown in Fig 10 Without loss of generality, let us assume that the gyrators outputs are all connected in parallel Let us denote the output voltage applied to the load by In this case, (15) reduces to This results in the gyration programming rule (18) (19) The existence of appropriate gyration conductance can be illustrated by two simple examples: charging of a battery load and energizing a resistive load

5 708 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL 53, NO 3, MARCH 2006 A Battery Load Suppose a battery is connected at the a-b terminals, whose voltage is This load dictates the output voltage (20) Substituting into (19) yields the time dependence of the gyration conductance (21) B Resistive Load Suppose that the output is loaded by a purely resistive load Since the coupling network does not have storage capability, the output power equals the input power on an instantaneous basis (22) The total power consumed by a multiphase balanced system is seen to be constant, and so is the load power Thus, the output voltage is also constant Substituting into (19) yields the gyration conductance V POSSIBLE APPLICATIONS OF LFCI ELEMENTS (23) (24) LFCI systems can be applied in power systems in cases in which ac voltage rectification is needed along with simultaneous generation (or consumption) of reactive power The LFCI model can be useful in describing and analyzing systems that contain rectifiers, resistive loads, and compensation components such as power factor correction filters and active filters Two such examples are given herein A LFCI Model for a High-Quality Rectifier With Reactive Power Compensation Capability Fig 11 shows a power system containing two loads that require compensation The third element, which can be modeled as LFCI, is capable of rectifying active power and compensating for the reactive power consumed by the other loads This is accomplished simply by emulating a certain degree of input capacitance without any physical capacitance [20] It should be noted that the value of the emulated capacitance is continuously tuned so that that optimal VAR compensation Fig 11 Rectification and VAR generation by means of LFCI is reached as loads 1 and 2 vary This is accomplished by means of control solely without any actual reactive components as in conventional solutions B Compensation for Source Output Impedance A second application example is the compensation for source output impedance Many of the ac voltage sources exhibit a significant output inductance (for instance, small generators operated at relatively high frequency such as onboard alternators in vehicles) The output impedance may represent the generator output inductance as well as the coupling network inductance (eg, transformers and transmission lines) Effective cancellation of this inductance would result in increased efficiency, increased load voltage, and, most importantly, increased overall power throughput This can be accomplished by a series-connected capacitor whose reactance cancels out with that of the source (see Fig 12) Like in the case of reactive power compensation, needs to be tunable in this case as well, since the output impedance it needs to compensate for varies with operational conditions In particular, in small generators, the frequency might vary in a quite wide range, resulting in a respective variation in the generator output impedance In most of the cases, using a physical capacitor in such an application is not practical because: 1) the capacitor value needs to be tuned in a wide range according to the variation of the source inductance and 2) the typical value of is a few tens of millihenrys and it has to carry large currents, making it impractical in terms of cost size and weight Thus, a switched-mode rectifier with compensation capability presents a promising solution A laboratory experiment was conducted in which a vehicle alternator was employed as an ac source Due to the application of a tunable series capacitor, the power throughput was increased by 27% The schematic diagram of this system is shown in Fig 13, however, the details of the experiment are beyond the scope of this paper

6 SHMILOVITZ: LOSS-FREE COMPLEX IMPEDANCE NETWORK ELEMENTS 709 Fig 12 Single-phase model of a generator with source impedance and a matched rectifier Fig 13 Optical matching of the three-phase alternator employing a three-phase LFCI VI LFCI REALIZATION Though it is possible to implement each of the coupling networks of Fig 8 (LFR and gyrator) by means of a switched-mode converter, it would be rather efficient to integrate both functions in one power stage Additionally, practical applications call for a controllable value of the emulated resistance and of the emulated input capacitance (depicted in Figs 9 and 12) Control of is necessary for balancing the power absorbed at the input with the power consumed by the load at the output [7] Thus, in orderto obtain the required phase shift between current and voltage at the LFCI, must be adjusted as varies Moreover, different amounts of reactive power may be required at the LFCI input for the purpose of VAR compensation, implying controllable If the LFCI is to operate with ac signals at its input, then the coupling network must accommodate bidirectional current conduction, voltage polarity, and bidirectional power flow Therefore, the commonly used high-quality rectifier topologies, which consist of a diode bridge rectifier at the front end followed by a unidirectional dc dc converter, do not apply To put it another way, if the circuit acquires complex impedance input characteristics, then the input power flow direction alters twice during a line cycle, but a diode bridge rectifier allows only unidirectional power flow In order to comply with voltage ratios during a complete line cycle, boosting topologies are considered as follows: (25) Some single-phase applicable topologies are depicted in Fig 14 The schemes shown in Fig 14(b) and (d) are the well-known full-bridge boost converter and the half-bridge Fig 14 Four suitable topologies for LFCI realization (a) Boost derived (b) Full-bridge (c) C uk derived (d) Half-bridge boost Fig 14(a) shows a variation of the half-bridge boost Fig 14(c) presents a topology introduced in [20], which may be viewed as variations of the C uk topology with an additional bias capacitor so as to levitate the ac voltage above zero level, creating a unipolar voltage at the C uk converter input Operation details of these topologies may be found in [21] Each of these topologies has been simulated by SPISE and by MATLAB and have been proven to be suitable for realization of the gyrator-based coupling network Some simulation results are presented in Fig 15 (for the single-phase case) VII SIMULATION RESULTS Fig 15 shows PSPICE simulation results obtained by simulating a circuit similar to the one in Fig 14(b), in which the LFCI compensates for the inductive power of a load connected in parallel This load comprises an inductor and a resistor connected in parallel H This load s current (denoted is seen to lag the applied voltage The full-bridge boost scheme of Fig 14(b) was employed along with a hysteretic controller, resulting in a constant current ripple (of the LFCI) and a varying switching frequency The inductive load consumes the complex power W VAR The switched-mode

7 710 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL 53, NO 3, MARCH 2006 Fig 15 Full-bridge-based LFCI simulation example (a) Schematic (b) Waveforms rectifier is tuned so as to consume 420 W but supply the 319 VAR (satisfied by the proper amplitude and leading phase of the converter input current ) The total reactive power supplied by the source is zero That can be seen by the source current, which is completely in phase with the source voltage VIII CONCLUSION The LFCI, which is a new two-port network element, was introduced in this paper In its single-phase version, this element belongs to the semi-power-conservative two-port network elements, as it requires a certain amount of storage capability, whereas, in a multiphase version, it is a power-conservative network element like the transformer, the gyrator, and the loss-free resistor This network element model may find applications in describing and modeling power-conditioning networks for the purpose of analysis and design REFERENCES [1] B D Anderson, D A Spaulding, and R W Newocomb, Time variable transformers, Proc IEEE, vol 53, no 6, pp , Jun 1965 [2] G W Wester and R D Middelbrook, Low-frequency characterization of switched Dc-Dc converters, IEEE Trans Circuit Theory, vol CT-9, no 5, pp , May 1973 [3] R W Newcomb, The semistate description of non linear time-variable circuits, IEEE Trans Circuits Syst, vol CAS-28, pp 62 71, Feb 1981 [4] S Jian, D M Mitchell, M F Greuel, P T Krein, and R M Bass, Averaged modeling of PWM converters operating in discontinuous conduction mode, IEEE Trans Power Electron, vol 16, no 4, pp , Jul 2001 [5] S R Sanders and G C Vergese, Synthesis of averaged circuit models for switched power converters, IEEE Trans Circuits Syst, vol 38, no 8, pp , Aug 1991 [6] D Czarkowski and M K Kazimierczuk, Static-and dynamic-circuit models of PWM buck-derived DC-DC convertors, in IEE Proc G, Circuits, Devices Syst, vol 139, Dec 1992, pp [7] R W Erickson and D Maksimovic, Fundamentals of Power Electronics, 2nd ed Norwell, MA: Kluwer, 2001 [8] D Shmilovitz, Time variable transformers operating at near unity transfer ratio and some possible applications, IEE Trans Power Appl, vol 151, no 2, pp , Mar 2004

8 SHMILOVITZ: LOSS-FREE COMPLEX IMPEDANCE NETWORK ELEMENTS 711 [9] S Singer, Canonical approach to energy processing network synthesis, IEEE Trans Circuits Syst, vol CAS-33, no 8, pp , Aug 1986 [10] M Ehsani, I Husain, and M O Bilgic, Power converters as natural gyrators, IEEE Trans Circuits Syst I, Fundam Theory Appl, vol 40, no 12, pp 946 9, Dec 1993 [11] S Singer, Realization of loss-free resistive elements, IEEE Trans Circuits Syst, vol 37, no 1, pp 54 60, Jan 1990 [12] J Sebastian, M M Hernando, A Fernandez, P J Villegas, and J Diaz, Input current shaper based on the series connection of a voltage source and a loss-free resistor, IEEE Trans Industry Appl, vol 37, no 2, pp , Mar/Apr 2001 [13] A Wang, Y Hongyi, and S Wang, Realization of source with internal loss-free resistive characteristic, IEEE Trans Circuits Syst I: Fundam Theory Appl, vol 48, no 7, pp , Jul 2001 [14] K M Smedley and R E Shafer, Experimental determination of electrical characteristics and circuit models of superconducting dipole magnets, Magnet, vol 30, pp , Sep 1994 [15] H Akagi, Y Kanazawa, and A Nabae, Instantaneous reactive power compensators comprising switching devices without energy storage components, IEEE Trans Ind Appl, vol IA-20, no 3, pp , May/Jun 1984 [16] Z Peng and J S Lai, Generalized instantaneous reactive power theory for three-phase power systems, IEEE Trans Instrum Meas, vol 45, no 1, pp , Feb 1996 [17] L S Czarnecki, On some misinterpretations of the instantaneous reactive power p-q theory, IEEE Trans Power Electron, vol 19, no 3, pp , May 2004 [18] A M Stankovic and H Lev-Ari, Frequency-domain observations on definitions of reactive power, IEEE Power Eng Rev, vol 20, no 6, pp 46 48, Jun 2000 [19] J Arrillaga, N R Watston, and S Chaen, Power Systems Quality Assessment New York: Wiley, 2000 [20] D Shmilovitz, D Czarkowski, Z Zabar, and S Y Yoo, A novel, single stage, unity power factor, rectifier/inverter for UPS applications, Proc IEEE Int Telecom Energy Conf, pp , Oct 1998 [21] D Shmilovitz, D Czarkowski, and Z Zabar, A novel switched rectifier for VAR compensation, Proc IEEE Int Symp Circuits Syst, vol 5, pp , 1999 Doron Shmilovitz (M 98) was born in Romania in 1963 He received the BSc, MSc, and PhD degrees from Tel Aviv University, Tel Aviv, Israel, in 1986, 1993, and 1997, respectively, all in electrical engineering From 1986 to 1990, he worked in Research and Development for the IAF, where he developed programmable electronic loads From 1997 to 1999, he was a Post-Ddoctoral Fellow with New York Polytechnic University, Brooklyn, NY, where he was involved with unity power factor bidirectional onboard chargers for EV Since 2000, he has been with the Faculty of Engineering, Tel Aviv University, where he established a power electronics research laboratory He is the author of over 50 conference and journal papers His research interests include the topology, dynamics, and control of switched-mode converters and power quality and power conversion for alternative energy sources and general circuit theory