Abstract:
An switching converter (APF) is a device that is connected in parallel to and cancels the reactive and harmonic currents from a group of nonlinear loads so that the resulting total current drawn from the ac source is sinusoidal. What is provided is an unified constant-frequency integration (UCI) APF control method based on one-cycle control. This method employs an integrator to control the pulse width of an ac-dc converter so that its current draw is precisely opposite to the reactive and harmonic current draw of the nonlinear loads. In contrast to previously proposed methods, there is no need to generate a current reference for the control of the converter current, thus no need for a multiplier, and no need to sense the ac line voltage, the APF current, or the nonlinear load current. Only one current sensor and one voltage sensor are used to sense the ac source current and the dc capacitor voltage. The control method features carrier free, constant switching frequency operation, minimum reactive and harmonic current generation, and simple analog circuitry. It provides a low cost and high performance solution for power quality control. This control method is generalized to control a family of converters that are suitable for APF applications.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to the field of active power filters and in particular to a control method based on one-cycle control. 
     2. Description of the Prior Art 
     In recent years, the usage of modem electronics equipment has been widely proliferating. This electronics equipment imposes nonlinear loads on the ac main or source that draw reactive and harmonic current in addition to active current. The reactive and harmonic current results in a low power factor, low efficiency, harmful electromagnetic interference to neighborhood appliances, as well as overheating of transformers. In order to solve these problems, many international agencies have proposed firm harmonic restrictions to electronic equipment. As a result, a vast number of power factor correction (PFC) techniques have been proposed to comply with these regulations. 
     Most techniques use a current shaper, whether in a two-stage multiple-switch configuration or a two-stage one-switch configuration, to shape the input current to a sinusoidal waveform. Since the current shaper is in the series path of the power, it requires high current and high voltage semiconductor devices and entails significant power losses. Therefore, PFC techniques are generally suitable for low to medium power applications. Furthermore, it is not convenient to insert a current shaper in existing electronic equipment, since significant redesign would be required. In high power applications, a parallel harmonic correction technique using an active power filter (APF) has been proposed and explored by many researchers. See, Fabiana Pottker and lov Barbi, “Power Factor Correction of Nonlinear Load Employing a Single Phase Active Power Filter: Control Strategy, Design Methodology and Experimentation” PESC 1997 Record 28 th  annual IEEE Power Electronics Specialists conference; D. A. Torrey, A Al-Zamel, “Single-phase active power filter for multiple nonlinear loads” IEEE Transactions on Power Electronics, Vol. 10, pp.263-271, May 1995; Simone Buso, Luigi Malesani, “Comparison of Current Control Techniques for Active Filter Applications” IEEE Trans on Industrial Electronics. Vol. 45. No. 5 October 1998; J.-C. Wu and H.-L. Jou “Simplified control method for the single-phase active power filter” IEE. Proc. Electr. power., Vol. 143, No. 3, May 1996; Hirofumi Akagi, “New trends in active filter for improving power quality” Proceeding of the 1996 International Conference on Power Electronics, Drives and Energy System for Industrial Growth; and J. Sebastian Tepper, Juan W. Dixon “A simple-frequency-independent method for calculating the reactive and harmonic current in a nonlinear load” IEEE Transaction on Industrial Electronics, Vol. 43, No. 6, December 1996. 
     An APF is a device that is connected in parallel to and cancels the reactive and harmonic currents from a group of nonlinear loads so that the resulting total current drawn from the ac source is sinusoidal. Ideally, the APF needs to generate just enough reactive and harmonic current to compensate the nonlinear loads in the line, thus it handles only a fraction of the total power to the load. Most APF control methods previously proposed need to sense the line voltage and the nonlinear load current, and then manipulate the information from these sensors to generate a current reference for the APF. Since the reference current has to reflect the load power of the nonlinear load, a multiplier is needed to scale the magnitude of the current reference. A control loop is necessary to control the converter to generate the reactive and harmonic current required by the nonlinear load. These functions are generally realized by a digital signal processing (DSP) chip with fast analog-to-digital (A/D) converters and high-speed calculations. The performance of these active power filters is based on three basic design criteria: the converter topologies, the control method used, and the method used to obtain the current reference. The complex circuitry results in high cost and unreliable systems, preventing this technique from practical applications. 
     What is needed is an API not subject to the inherent disadvantages of prior designs. 
     BRIEF SUMMARY OF THE INVENTION 
     The method of the invention is an unified constant-frequency integration (UCI) APF control method based on one-cycle control. It employs an integrator with reset as its core component to control the pulse width of an ac-dc converter so that its current draw is precisely opposite to the reactive and harmonic current draw of the nonlinear loads. The term, “reactive current”, shall be defined in this specificaiton and claims to include all current which is different in phase or at a different frequency from the AC source current, including the fundamental frequency, all harmonics and other nonlinear effects of the load. In contrast to all previously proposed methods, there is no need to generate a current reference for the control of the converter current, thus no need to sense the ac line voltage, the APF current, and the nonlinear load current. Only one current sensor and one voltage sensor (resister divider) are used to sense the ac source current and the voltage across the dc capacitor. The control method features constant switching frequency operation, minimum reactive and harmonic current generation, and simple analog circuitry. It provides a low cost and high performance solution for power quality control. 
     More specifically the invention is defined as a circuit comprising an AC source, a nonlinear load coupled to the AC source in which the nonlinear load has a reactive current drawn therefrom, and an active power filter coupled to the AC source in parallel with the nonlinear load. The active power filter is configured so that it has a current draw opposite to the reactive current draw of the nonlinear load and so that the reactive current draw of the nonlinear load is substantially cancelled out by the current draw of the active power filter. 
     The compensation of multiple nonlinear loads coupled to the AC source is included within the scope of the invention. In such a case, the active power filter is coupled to the AC source in parallel with each of the nonlinear loads. 
     The active power filter comprises a switched bridge circuit and a storage device coupled to the switched bridge circuit. In the illustrated embodiment the storage device is a capacitor, and the switched bridge circuit is a switched full wave-bridge. In another embodiment, the switched bridge circuit is a switched half wave-bridge, or a switched DC side directional boost circuit. 
     In all of the embodiments, the switched bridge circuit switches at a higher frequency than is characteristic of operation of the AC source and than the nonlinear load. The capacitor is configured to have a nearly constant voltage waveform across switching cycles. 
     The circuit further comprises an integrator with a reset circuit. The integrator has an input coupled to the active power filter. The integrator with the reset circuit has an output coupled to and controlling the switching of the active power filter. The integrator with the reset circuit is configured to control the switched bridge so that net current drawn from the AC source by the active power filter is equal to the fundamental active current drawn by the nonlinear load, and has substantially the same waveform and is in phase with the AC source. 
     In the illustrated embodiment, the active power filter comprises an AC to DC converter and a storage device coupled thereto having a control voltage, v c . The AC to DC converter is switched at a frequency characterized by a duty cycle, D. The nonlinear load and the active power filter are characterizable as an equivalent resistance, R e , which is coupled to the AC source. The AC source has a voltage, v s , and current, i s , and further comprises a sensing resistor, R s , which is coupled in series with the equivalent resistance, R e , and the AC source. The duty cycle, D, is controlled according to a control equation so that reactive and harmonic current of the nonlinear load is substantially cancelled. In one embodiment, such as a full wave bipolar converter, the control equation is 2Dv m =v m −R s *i s . where v m =R s v c /R e . In another embodiment, such as a full wave unipolar converter, a half wave converter, and a current source converter, the control equation is Dv m =v m −R s *i s  where v m =R s v c /R e . 
     The invention is also defined as a method of performing the above defined operations of the foregoing circuit, Namely, the invention can be defined as a method of filtering an AC source having a nonlinear load coupled to the AC source having a reactive current drawn therefrom by use of an active power filter coupled to the AC source in parallel with the nonlinear load comprising the steps of drawing reactive current with the nonlinear load, and drawing current with the active power filter opposite to the reactive current draw of the nonlinear load. As a result the reactive current draw of the nonlinear load is substantially cancelled out by the current draw of the active power filter. 
     The invention may be better visualized by turning to the drawings, wherein like elements are referenced by like numbers. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram which shows a shunt active power filter in parallel with a nonlinear load. 
     FIG.  2 ( a ) is a schematic of an equivalent circuit of FIG. 1 when 0&lt;t&lt;DT. 
     FIG.  2 ( b ) is a schematic of an equivalent circuit of FIG. 1 when DTs&lt;t&lt;Ts. 
     FIG.  2 ( c ) is a graph of the inductor current and voltage as a function of time of the circuit of FIG.  1 . 
     FIG. 3 is an equivalent circuit wherein a resistor, Re, is used to emulate a nonlinear load with an APF in parallel. 
     FIG. 4 is a schematic in partial block diagram form of an active power filter (APF) with an integration reset control according to the invention. 
     FIG. 5 is a schematic of a prototype circuit built to experimentally demonstrate the principles discussed in connection with the circuit of FIG.  4 . 
     FIG. 6 is a graph as a function of time of the performance of the circuit of FIG. 5 in which a diode rectifier with an RC load is the nonlinear load. The uppermost trace is line voltage, the second trace from the top is input current of the uncontrolled rectifier, the third trace from the top is in line current after compensation by the APF, and the fourth trace from the top is the current draw of the APF. 
     FIG. 7 is a graph as a function of time of the experimental results of the circuit of FIG. 5 in which the nonlinear load is a diode rectifier with RL load. The upper trace is the line voltage, second trace from the top is line current compensated by the APF, the third trace from the top is input current of uncontrolled rectifier, and the fourth trace from the top is current draw of the APF. 
     FIG. 8 is a graph as a function of time of the experimental results of proposed active power filter compensating multiple nonlinear loads, which consist of a diode rectifier with an RC filter and a diode rectifier with an RL load in parallel. The upper trace is the line voltage, second trace from the top is line current compensated by the APF, the third trace from the top is input current of uncontrolled rectifier, and the fourth trace from the top is current draw of the APF. 
     FIG. 9 is a graph as a function of time which shows the step response of an input AC current in which the active power filter compensates a diode rectifier with an RC load in the case where the load resistor, R, makes a step change. 
     FIG. 10 is a graph which shows the step response of input AC current in the active power filter when compensating a diode rectifier with an RL load when the load resistor, R, discontinuously changes from 120Ω to 60Ω at t=0. 
     FIG.  11 ( a ) is a schematic of a full-bridge voltage source converter operating in unipolar voltage mode in accordance with the invention. 
     FIG.  11 ( b ) is a schematic of a half bridge converter in accordance with the invention. 
     FIG. 12 is a graph of the simulation waveforms of the APF with a full bridge voltage source converter operating in unipolar voltage mode employing proposed control strategy as shown in FIG.  11 ( a ). 
     FIG. 13 is a graph of the simulation waveforms of the APF with a half bridge power stage as shown in FIG.  11 ( b ). 
     FIG. 14 is a schematic of a DC side APF or what is also called a shunt power factor correction circuit. 
     FIG. 15 is a schematic of a DC side APF bidirectional boost converter power stage or what is also called a shunt power factor correction circuit. 
     FIG. 16 is a graph of the simulation waveforms of the APF with a DC side APF operating with the control strategy of the invention. The upper trace is the line voltage. The second trace from the top is the line current after compensated by the APF. The third trace from the top is the output current of the APF. The fourth trace from the top is the current of the nonlinear loads. 
    
    
     The invention now having been illustrated in the foregoing drawings, the invention and its various embodiments as well as its generalization from the illustrated embodiment can be understood in the following detailed description. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     An Converter Topology 
     FIG. 1 shows a shunt active power filter  14  coupled to a power source  10  in parallel with a nonlinear load  12 . In reality, it is possible to have multiple nonlinear loads  12  in parallel. The power stage is composed of a current bidirectional H-bridge comprised of FET&#39;s  16   a - 16   d  and an energy storage capacitor  18  at the dc side. H-bridge  16   a - 16   d  is operated as a voltage-source converter that converts the dc voltage on energy storage capacitor  18  to an ac voltage to the line. H-bridge  16   a - 16   d  is controlled at the gates of Fets  16   a - 16   d  by logic or clock signals conventionally generated in accordance with the teachings set forth herein of the present invention. H-bridge  16   a - 16   d  can also be viewed as a boost converter from the viewpoint of dc capacitor  18 . The task of H-bridge  16   a - 16   d  is to provide the reactive and harmonic current required by the nonlinear load, 12  so that the net current draws from the ac source gives the fundamental active power used at nonlinear load  12 . 
     In order to realize a good compensation of the reactive and harmonic current to nonlinear load  12  at any point in one line cycle, the capacitor voltage must be greater than the peak of ac voltage. In the steady state, the capacitor voltage should be constant from one line cycle to another, since H-bridge  16   a - 16   d  only processes the reactive power. H-bridge  16   a - 16   d  is operated at switching frequency of f s . There are two switching states in each switching cycle, i.e. Fets  16   a  and  16   d  are on and Fets  16   b  and  16   c  are off during 0&lt;t&lt;DTs; and Fets  16   a  and  16   d  are off and Fets  16   b  and  16   c  are on during DTs&lt;t&lt;Ts, where t is time, Ts=1/fs is the switching period and D=T on /T s  is the duty ratio. 
     The equivalent circuits of the converter during 0&lt;t&lt;DT and DTs&lt;t&lt;Ts are shown in FIGS.  2 ( a ) and  2 ( b ). To simplify the analysis, it is assumed that: (1) the value of energy storage capacitor  18  is large enough so that its voltage Vc has a nearly constant waveform from one switching cycle to the next; and (2) the switching frequency fs is much higher than both the line frequency and the frequency of nonlinear load current. FIG.  2 ( c ) is a timing diagram of the waveforms in the circuit of FIGS.  2 ( a ) and  2 ( b ). Graph  48  is the current drawn by the APF as a function of time, and graph  50  is the voltage across the APF or inductor  20  as a function of time. According to the waveform in FIG.  2 ( c ), following equations are obtained. 
     During 0≦t≦t on                 i   L     =             v   s     +     v   c         L   c          t     +     I   0               (   1   )                                v   L   =v   s   +v   c   (2) 
     During t on ≦t≦T s                 i   L     =             v   s     -     v   c         L   c          t     +     I   P0               (   3   )                                v   L   =v   s   −v   c   (4) 
     Where v s  is the voltage on source  10 , v c  the voltage on capacitor  18 , L c  the inductance of inductor  20 , I 0 , the initial current, and I po  the peak current. In practice, the initial value I 0  and the peak value I po  of inductor current for each switching cycle can be different, i.e. I 0  may not be equal to I 1  and I po  may not be equal to I p1 , which are the currents during the second cycle. However, according to the assumption #(1) above, the waveform of the load current is assumed to be almost unchanged between switching cycles, i.e. I 0  equals I 1  and I po  equals I p1 . Using the voltage-second balance of an inductor in a one switch cycle in the steady state, 
     
       
         ( v   s   +v   c ) D= ( v   c   −v   s )(1 −D )  (5) 
       
     
     The relationship between energy storage capacitor voltage and the ac source voltage is                v   c     =       1     1   -     2      D         ·     v   s               (   6   )                                
     UCI Apf Control Method 
     The object of controlling H-bridge  16   a - 16   d  is to provide the reactive and harmonic current required by nonlinear load  12 , so that the net current draws from ac source  10  is the fundamental active power used at nonlinear load  12 . From the viewpoint of ac source  10 , nonlinear load  12  with an active power filter in parallel imposes a linear resistive load to the ac power system in the steady state. Therefore, an equivalent resistor R e  is used to emulate nonlinear load  12  with an active power filter in parallel for ac source  10  as shown in FIG.  3 . The control goal of APF is 
     
       
           v   s   =R   e   *i   s   (7) 
       
     
     Combination of equation (6) and (7) with a current sensing resistor  22 , R s  yields the following equation                    R   s       R   e            (     1   -     2      D       )     *     v   c       =       R   s     *     i   s               (   8   )             Let                           v   m     =         R   s       R   e            v   c               (   9   )                                
     Then the control goal of active power filter becomes 
      2 Dv   m   =v   m   −R   s   *i   s   (10) 
     In each switching cycle, if the duty ratio D is controlled to satisfy the equation (10), equation (7) is satisfied. In each line cycle, if the capacitor voltage is controlled to be constant from cycle to cycle, only the reactive power is processed in H-bridge  16   a - 16   d.  The net current drawn from ac source  10  is equal to the fundamental active current required by nonlinear load  12  and has the same waveform as and is in phase with the line voltage. The reactive and harmonic current of nonlinear load  12  is canceled from ac line current. 
     An one-cycle control based integrator with reset circuit is employed to realize equation (10) as shown in FIG.  4 . For examples of one-cycle control in other contexts, see K. M. Smedley and S. Cuk “One cycle control of switching converters” in IEEE PESC, 1991 Record, PP1173-1180; and Z. Lai. K. M. Smedley. “A General Constant Frequency Pulse-Width Modulator and Its Applications”. IEEE Transactions on Circuits and Systems I: Fundamental Theory And Applications, Vol. 45.(no. 4), IEEE, April, 1998, P386-96. Due to the assumption #(2) above, the v m  can be considered unchanged in one switching cycle, thus                  1     T   i              ∫   0     DT   s              v   m     ·                     ·   t             =       1     T   i            D   ·     T   s     ·     v   m                 (   11   )                                
     where T i  is an integration constant and T s  is switching period. 
     Let 
     
       
           T   i , =½ T   s ,                  1     T   i              ∫   0   DT            v   m     ·                     ·   t             =         1     T   i       ·   D   ·     T   s     ·     v   m       =       2   ·   D   ·     v   m       =       v   m     -       R   s     ·     i   s                     (   12   )                               
      
     
     is satisfied in each switching cycle. According to the above derivation, the active power filter with the proposed controller is shown in FIG.  4 . The control circuit contains a PI controller  24 , an integrator  26  with a reset switch  28 , a comparator  30 , and a clocked flip-flop  32  clocked by clock  36 . The capacitor voltage v c  is sensed from resistance divider  42 ,  44  and fed to PI controller  24  through subtraction node  40  with a reference voltage, V ref , and to generate an output of PI controller  24 , the error voltage v m . The input to integrator  26  is combined in a subtraction node  38  with R s  *I s  and provided to the input of comparator  30  with the other input of comparator  30  being the error voltage, v m . The object of PI controller  24  is to maintain the dc voltage of storage capacitor  18 . The switches  16   a  and  16   d,  which are protected by shunting diodes  46   a - 46   d  respectively, are turned on by the clock pulse. Integrator  26  integrates the error voltage v m , and the output of integrator  26  is compared with (v m −R s ·i s ). When the integrated is value reaches (v m −R s ·i s ), comparator  30  changes its output state and triggers flip/flop  32 , which in turn turns off switches  16   a  and  16   d , turns on switches  16   a  and  16   c  and resets integrator  26  by means of logic commands generated by driver  34  in response to flip-flop  32 . This process repeats in every switching cycle. The control goal of equation (10) is thus realized. 
     Experimental Verification 
     In order to verify the performance of the proposed control method, a single-phase active power filter prototype has been developed and tested in a 110V power system. The prototype circuit and component selection are shown in FIG. 5, which is set forth as an illustration and should not be considered as limiting the invention in any way. The power rating is 500 w and the switching frequency is 40 kHz. 
     Three kinds of different nonlinear loads were employed in the experimental tests. FIG. 6 is a graph shows the test results of the an active power filter compensating a diode rectifier with a RC load. The total harmonic distortion of the nonlinear load current considering up to the 20 th  harmonic component is 78.437%. After compensated by the active power filter, the total harmonic distortion of the AC source current is 8.54%. The uppermost trace  52  is line voltage, the second trace  54  from the top is input current of the uncontrolled rectifier, the third trace  56  from the top is in line current after compensation by the APF, and the fourth trace  58  from the top is the current draw of the APF. 
     FIG. 7 presents the results of the active power filter compensating a diode rectifier with RL load. The upper trace  60  is the line voltage, second trace  62  from the top is line current compensated by the APF, the third trace  64  from the top is input current of uncontrolled rectifier, and the fourth trace  66  from the top is current draw of the APF. The total harmonic distortion of nonlinear load current is 44.231%. After compensated by the active power filter of FIG. 5, the total harmonic distortion of the AC source current is 6.893%. The circuit of FIG. 5 is one implemented form of the circuit of FIG.  4  and like elements have been referenced by like numerals. 
     FIG. 8 shows the experimental results of the active power filter compensating multiple nonlinear loads, which consist of a diode rectifier with an RC filter and a diode rectifier with an RL load in parallel. The upper trace  68  is the line voltage, second trace  70  from the top is line current compensated by the APF, the third trace  72  from the top is input current of uncontrolled rectifier, and the fourth trace  74  from the top is current draw of the APF. The total harmonic distortion of total nonlinear load current is 36.33%. The total harmonic distortion of the AC source current compensated by the active power filter is 5.94%. Since the goal of control is to force the ac source current to follow the ac source voltage, the total harmonic distortion of the line current cannot be lower than that of the ac source voltage waveform. In the experiment above, the total harmonic distortion of AC source voltage is measured at 3.9%. 
     Trace  76  of FIG. 9 shows the step response of an input AC current of the active power filter when compensating a diode rectifier with an RC load when the load resistor, R. discontinuously changes from 450Ω to 200Ω at t=0. 
     Trace  78  of FIG. 10 shows the step response of input AC current in the active power filter when compensating a diode rectifier with an RL load when the load resistor, R, discontinuously changes from 120Ω to 60Ω at t=0. It is observed that the APF acts as a filter to smooth the step change of load currents and keep the input current sinusoid during the transient. This characteristic is advantageous for an AC source. 
     Generalization 
     The APF control method of the invention can be extended to other power stages of the active power filters as shown in FIGS.  11 ( a ),  11 ( b ), and FIG.  14 . In FIG.  11 ( a ), the power stage has the same topology as the circuit shown in FIG. 5, but with a different operation mode. In the circuit shown in FIG. 5, the full bridge power stage operates in a bipolar voltage and bipolar current mode, while the full bridge shown in FIG.  11 ( a ) operates in unipolar voltage and bipolar current mode. Two switches among the four operate at the line frequency while the other two switches operate at a high switching frequency, witch results in less switching loss. Table 1 below shows the switching states of switches  16   a - 16   b  in the mode of operation of FIG.  11 ( a ). In this operational mode, the relationship between V s  and V c  is          v   c     =       1     1   -   D       ·          v   s                                   
     and the control goal function becomes Dv m =v m −R s *i s . 
     FIG. 12 is a graph of the simulation waveforms of the APF with a full bridge voltage source converter operating in unipolar voltage mode employing proposed control strategy as shown in FIG.  11 ( a ). The upper trace  80  is the line voltage. The second trace  82  from the top is the line current after compensated by the APF. The third trace  84  from the top is the current of the nonlinear loads. The fourth trace  86  from the top is the current draw of the APF. 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Switches 
                 Vs &gt; 0 
                 Vs &lt; 0 
               
               
                   
                   
               
             
             
               
                   
                 Fet 16a 
                 Operating at f s  and in 
                 Off 
               
               
                   
                   
                 complementary mode 
               
               
                   
                   
                 with Fet 16b 
               
               
                   
                 Fet 16b 
                 Operating at f s   
                 On 
               
               
                   
                 Fet 16c 
                 Off 
                 Operating at f s  and in 
               
               
                   
                   
                   
                 complementary mode 
               
               
                   
                   
                   
                 with Fet 16d 
               
               
                   
                 Fet 16d 
                 on 
                 Operating at f s   
               
               
                   
                   
               
             
          
         
       
     
     FIG.  11 ( b ) is half bridge power stage and FIG. 13 is simulation waveforms under the UCI control. The circuit of FIG.  11 ( b ) use only two switches  16   a  and  16   b  and two corresponding capacitors  18   a  and  18   b.  However, the voltage stress on switches  16   a  and  16   b  is doubled compared to the full bridge switches, since each capacitor voltage in series should be higher than the peak of v s . Therefore, the half bridge power stage is suitable only for low voltage systems. 
     FIG. 13 is a graph of the simulation waveforms of the APF with a half bridge power stage as shown in FIG.  11 ( b ). The upper trace  88  is the line voltage. The second trace  90  from the top is the line current after compensated by the APF. The third trace  92  from the top is the output current of the APF. The fourth trace  94  from the top is the current of the nonlinear loads. The fifth and sixth traces  96  and  98  from the top are the capacitor voltages v c1  and v c2  respectively. 
     Furthermore, the proposed APF control strategy can be used in the DC side to compensate reactive and harmonic current in the DC side for the rectifier load as shown in FIG.  14 . The input ac voltage v s  is rectified by a diode bridge, generally denoted by reference numeral  100 . The rectified dc voltage is vg=|vs|. The bidirectional DC/DC converter  102  is controlled according to the invention in the manner similar to that described above to generate a current i p  that cancels the reactive and harmonic current of the load current i L  into the nonlinear load, which is generically represented by a load resistance  104 , a load capacitance  106 , and a DC-DC or DC-AC converter  108 . R s  is the source resistance and I g  the current from rectifier  100 . 
     FIG. 15 shows an example of DC side APF employing a two switch bidirectional boost converter  116  as the power stage. The switches  112 , S 1 , and  114 , S 2 , are turned on and off complementarily at a constant switching frequency. As a result, vcp=vg/(1−D) where v cp  is the voltage across capacitor  118 . The APF controller will realize the relation i g =v g /Re using a one-cycle control circuit as describe above, where Re is an emulated resistor. The control function is expressed as shown in Table 2. The configuration can be viewed as a shunt power factor correction circuit. FIG. 16 shows the simulated waveforms of DC side APF employing the UCI APF control. 
     From the simulation results, it is found that the DC active power filter has smaller power rate, smaller size and higher converting efficiency than that of PFC circuit. Because the DC power active filter only processes the reactive and harmonic currents that is much smaller than that of the boost converter used as a current shaper. In addition, the control strategy can be extended to three-phase systems. 
     Table 2 shows the APF control equations and the relationship of v c  and v s  of various power circuits. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Control Equations of Various Power Stages 
               
             
          
           
               
                   
                 Full-bridge 
                 Full-bridge 
                 Half-Bridge 
                 DC side 
               
               
                   
                 (FIG. 5 
                 (FIG. 11 (a) 
                 &lt;v c &gt; = &lt;v c1 &gt; = 
                 bidirectional 
               
               
                   
                 bipolar) 
                 unipolar) 
                 &lt;v c2 &gt; 
                 boost 
               
               
                   
                   
               
             
          
           
               
                 v c /v s   
                 1/(1 − 2D) 
                 1/(1 − D) 
                 1/(1 − D) 
                 1/(1 − D) 
               
               
                 Control 
                 2Dv m  = 
                 Dv m  = 
                 Dv m  = 
                 Dv m  = 
               
               
                 equation 
                 v m  − R s *i s   
                 v m  − R s *i s   
                 v m  − R s *i s   
                 v m  − R s *i s   
               
               
                   
               
               
                 &lt;v &gt;, &lt;v .&gt; and &lt;v &gt; are the homologous average values of v , v , and v  
               
             
          
         
       
     
     Conclusion 
     In its simplest terms the control method of the invention is based on one cycle control to realize an APF function given by: 
     
       
         
           i 
           s 
           =v 
           s 
           /R 
           e 
         
       
     
     where i s  is the source current, v s  the source voltage and R e  the equivalent resistance by which the source is loaded. Since i s =i L +i p , the current i p  generated by the APF will automatically cancel the reactive component of the nonlinear load current i L . 
     Every converter can be described by: 
     
       
           v   c   =v   s   M ( D ), 
       
     
     where M(D) is a function of the duty cycle D, which is called the conversion ratio. The idea of the invention is to combine the two equations above so that the circuit realizes the performance described by: 
     
       
           i   s   =[v   c   /M ( D )]/ R   e . 
       
     
     If a current sensing resistor, R s , is used to measure the source current, i s , then the circuit performance can also be described by: 
     
       
           R   s   i   s   =[R   s   v   c   /M ( D )]/ R   e . 
       
     
     The control circuit shown in FIG. 4 can be used with any converter. The control circuit is comprised of an integrator  26  having an input V 2  with a reset circuit  28  having its output coupled to the input of a comparator  30 . Comparator  30  has a second input V 1 . The output of comparator  30  is then coupled to the input of a clocked flip-flop  32  whose output is then used to control the switches in the converter according to the teachings of the invention. In the beginning of each switching cycle, a constant frequency clock  36  sets the flip-flop  32  that determines the beginning of the on-pulse. The integrator integrates its input v 2  until the integrated value reaches v 1 . Then the comparator  30  changes its state that resets the flip-flop  32 , which then terminates the on-pulse. This process repeats from cycle to cycle. As shown in FIG. 4 the voltage- or current-energy storage element, shown in the illustrated embodiment as a capacitor, but also meant to include an inductor, is fed back and compared to a reference voltage, v ref . The error, v e , will be processed by a compensator, e.g. a proportional integration (PI) compensator, or equivalently by a P compensator or proportional integration-differential (PID) compensator, to generate a low frequency signal, v m . This signal, v m , is used in the control block: 
     
       
           R   s   i   s   =v   m   /M ( D ) 
       
     
     to adjust the duty ratio, D, so that i s =v s /R e  is approximately realized. 
     For example, in the preferred embodiment of FIG. 1, v c =v s /[1−2D], so that M(D)=1/[1−2D]. The control condition then is expressed as R s i s =v m /M(D)=v m (1−2D), which can be rewritten as v m −R s i s =2 v m  D. The control of the invention is then realized if the signal, v m −R s i s , is connected to input V 1  of comparator  30  and the signal, 2 v m  D, is connected to input V 2  of integrator  26  of FIG.  4 . The result of this control will then be that i s  will be set to be approximated to v s /R e . 
     As a further example, in the unipolar embodiment where v c =v s /[1−D], so that M(D)=1/[1−D], the control condition then is expressed as R s i s =v m /M(D)=v m (1−D), which can be rewritten as v m −R s i s =v m D. The control of the invention is then realized if the signal, v m −R s i s , is connected to input V 1  of comparator  30  and the signal, v m  D, is connected to input V 2  of integrator  26  of FIG.  4 . The result of this control will then again be that i s  will be set to be approximated to v s /R e . 
     An unified constant-frequency integration (UCI) control of the active power filter is thus described above based on one-cycle control. This control method employs an integrator with reset as the component to control the duty ratio of an active power filter to realize net sinusoidal current draw from the ac source. Compared to previously proposed control methods, the UCI controller features simpler circuitry, no need for multipliers, no need for generating current references that reflect the reactive and harmonic portion of the load current, and no need to sense the load current and input voltage. Since the input current compensation is performed cycle by cycle, the compensated net current matches the input voltage closely, thus a unity power factor and low total harmonic distortion are achieved. Furthermore, since voltage across the energy storage capacitor is kept constant in the steady state, minimum current is generated by the APF to realize harmonic current cancellation. 
     Active power filters with UCI control can also damp the transient due to sudden changes in the load current. In the foregoing, the UCI control is used to control an active power filter employing a two level boost converter. Experimental result shows that the APF has excellent harmonic filtering capability demonstrated using many different nonlinear loads. This control method is applicable to most other APF topologies which are either parallel connected in the ac side or in the dc side. Active power filters with UCI controller provide a cost-effective and flexible solution for power quality control. Since the active power filter only processes the reactive and harmonic current, power losses and component rating should be lower compared to active power factor correcting methods. Due to the simplicity of the circuitry, it is very suitable for industrial production. For many existing nonlinear loads, unity power factor can be achieved by plugging an active filter to the ac inlet. 
     Many alterations and modifications may be made by those having ordinary skill in the art without departing from the spirit and scope of the invention. Therefore, it must be understood that the illustrated embodiment has been set forth only for the purposes of example and that it should not be taken as limiting the invention as defined by the following claims. 
     The words used in this specification to describe the invention and its various embodiments are to be understood not only in the sense of their commonly defined meanings, but to include by special definition in this specification structure, material or acts beyond the scope of the commonly defined meanings. Thus if an element can be understood in the context of this specification as including more than one meaning, then its use in a claim must be understood as being generic to all possible meanings supported by the specification and by the word itself. 
     The definitions of the words or elements of the following claims are, therefore, defined in this specification to include not only the combination of elements which are literally set forth, but all equivalent structure, material or acts for performing substantially the same function in substantially the same way to obtain substantially the same result. In this sense it is therefore contemplated that an equivalent substitution of two or more elements may be made for any one of the elements in the claims below or that a single element may be substituted for two or more elements in a claim. 
     Insubstantial changes from the claimed subject matter as viewed by a person with ordinary skill in the art, now known or later devised, are expressly contemplated as being equivalently within the scope of the claims. Therefore, obvious substitutions now or later known to one with ordinary skill in the art are defined to be within the scope of the defined elements. 
     The claims are thus to be understood to include what is specifically illustrated and described above, what is conceptionally equivalent, what can be obviously substituted and also what essentially incorporates the essential idea of the invention.