Unified Constant-frequency Integration Control of Active Power Filters

Luowei Zhou and Keyue M. Smedley Department of Electrical and Computer Engineering

University of California, Irvine, CA 92697 Tel: (949) 824-6710, Fax: (949) 824-3203

Email: smedley @ uci .edu

ABSTRACT An active power filter (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 main is sinusoidal. This paper presents a Unified Constant-frequency Integration (UCI) APF control method based on one-cycle control. This method 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. 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 main 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. Detailed analysis and design were conducted using a two-level ac- dc boost topology. A prototype was developed to demonstrate the performance of the proposed APF. This control method is generalized to control a family of converters that are suitable for APF applications. All findings are supported by experiments and simulation.

1. Introduction In recent years, the usage of modern electronic equipment has been increasing rapidly. These electronics equipment impose nonlinear loads to the ac main that draw reactive and harmonic current in addition to active current. The reactive and harmonic current lead to low power factor, low efficiency, harmful electromagnetic interference to neighborhood appliance, 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, vest numbers of power factor correction (PFC) techniques have been proposed in compliance 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 processes all the power and thus requires high current and high voltage semiconductor devices and involves significant power losses. Therefore, PFC techniques are generally suitable for low to medium power applications.

0-7803-5864-3/00/$10.00 0 2000 IEEE

Furthermore, it is not convenient to insert a current shaper to existing electronic equipment, since significant redesign would be required. An alternative parallel harmonic correction technique, shunt active power filter (APF), has been explored by many researchers ['-I6]. The shunt APF was considered to be the most basic configuration for APF[11*[217[31. 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 main 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. The performance of these active power largely depends on the inverter topologies and the PWM control method. The commonly used inverter topologies for APF applications include both voltage and current type inverters, where the voltage type inverters are reported more cost effective than their counterparts[']. In order to control the inverter to produce a current that is equal to the amplitude and opposite in direction of the reactive current of the nonlinear load, a current reference was required. Many articles have been published that focus on obtaining the current reference for three phase or single phase APF'31.[41.'51,[61,[71,[*1. Typical control methods are linear current control, digital deadbeat control, hysteresis controlrg1. In addition, ada tive predictive filterIgl'[lll, neural network

for obtain the control reference and for the control loop itself typically require several high precision analog multipliers or a high speed DSP chip with fast A/D, which results in complex circuitry and sensitivity to the component parameters. Some indirect control methods were reported that sense the line current and force it to follow the line voltage, In these methods, calculation of the current reference is no longer necessary, which greatly simplifies the control circuitry. However precision multipliers are still

controller[121' P 13] were reported. Most proposed methods

required to scale the current according to the load leve1[WW1.[W

This paper presents a Unified Constant-frequency Integration (UCI) APF control method based on one- cycle c ~ n t r o l [ ~ ~ " ~ ~ ~ This method 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. In contrast to all

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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 main 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. Detailed analysis and design were conducted using a two-level ac-dc boost topology. A prototype was developed to demonstrate the performance of the proposed APF. This control method is generalized to control a family of converters that are suitable for APF applications. All findings are supported by experiments and simulation.

This paper is organized as following: A boost inverter topology and its switching mode for single- phase APF are described in Section 2. The proposed UCI APF control method is detailed in Section 3. A prototype was developed to demonstrate the performance of the proposed APF with the UCI control method. The experimental results are provided in Section 4. This control method is used to control a family of inverters and the simulating results are given in Section 5 . Section 6 gives a conclusion.

- I - I -

2. Inverter topology

I @vs +IL ITYI

'i: Fig. 1 shows a shunt active power filter in parallel with a nonlinear load

Fig 1 shows a shunt active power filter in parallel with a nonlinear load. In reality, it is possible to have multiple nonlinear loads in parallel. The power stage is composed of a current bi-directional H-bridge and an energy storage capacitor at the dc side. This H-bridge is operated as a voltage-source inverter that converts the dc voltage on the energy storage capacitor to an ac voltage to the line. This H-bridge can also be viewed as a boost converter from the viewpoint of the dc capacitor. The task of the H-bridge is to provide the reactive and harmonic current required by the nonlinear load, so that the net current draws from the ac main gives the fundamental active power used at the nonlinear load. In order to realize a good compensation of the reactive and harmonic current to the nonlinear load 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 the H-bridge only process the reactive power. The H-bridge is operated at switching frequency of fs. There are two switching states in each switching cycle, i.e. MI, M3 are on and MZ, M4 are off during O<t<DT, and MI, M3 are off and Mz, M4 are on during DTs<t<Ts, where Ts = l/fs is the switching period and D = To,,/Ts is the duty ratio. The equivalent circuits of the inverter during O<tcDT and DTs<t<Ts are shown in Fig 2. To simplify the analysis, it is assumed that (1) the value of the energy storage capacitor C is large enough so that its voltage Vc is nearly constant in one switching cycle. (2) The switching frequency fs is much higher than both the line frequency and the frequency of nonlinear load current. According to the waveform in Fig.2, following equations are obtained.

I 1 I

Ode DT, equivalent circuit (b) DTset<Ts equivalent circuit

V S V C % vc-vs

(c) inductor current and voltage Hg. 2. the inverter equivalent model and inductor current and voltage waveform

During 0 I t I to,

VL = v, + vc During to, I t 5 T,

(2)

(3)

VL = v, - v, In practice, the initial value Io and the peak value

I , , of inductor current for each switching cycle can

be different, i.e. Io may not be equal to I , and I , , may not be equal to I , , . However, according to the assumption (2), load current is assumed to be almost unchanged in one switching cycle, i.e. Io equals I ,

(4)

407

and I , , equals I , , . Using the voltage--second

balance of inductor in one switch cycle in the steady state,

The relationship between energy storage capacitor voltage and the ac source voltage is

(v, + v, )D = (v, - vs )(1- 0) (5)

3. Proposed UCI APF control method

Fig. 3. The equivalent resistor Re is used to emulate the nonlinear load with an APF

The control object of the H-bridge is to provide the reactive and harmonic current required by the nonlinear load, so that the net current draws from the ac main is the fundamental active power used at the nonlinear load. From the viewpoint of the ac main, the nonlinear load with an active power filter in parallel imposes a linear resistive load to the ac power system in steady state. Therefore, an equivalent resistor R, is used to emulate the nonlinear load with an active power filter in parallel for ac main as shown in Fig3.The control goal of APF is

Combination of equation (6) and (7) with a current sensing resistor R, yields the following equation

v, = R, *is (7)

R "(1 - 2 0 ) * v , = R , * is (8) Re

R S Let v, = -v, Re

(9)

Then the control goal of active power filter becomes

In each switching cycle if the duty ratio D is controlled to satisfy the equation (lo), 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 the H-bridge. The net current drawn from the ac main is equal to the fundamental active current required by the nonlinear load that has the same waveform as and in phase with line voltage. The reactive and harmonic current of nonlinear load is canceled from ac line current. The one-cycle control based integrator with reset circuit is employed to realize equation (10) as shown in Fig. 4. Due to the

2Dv, = v, - R , * is (10)

assumption (2), the V, can be considered unchanged in one switching cycle, thus . DT.

where Ti is integration constant and T, is switching period.

Let 1 q. = -T , , 2

1 1 - Jv, .d.t =- D 1; v, =2. D. v, =v, -4 ai, ( 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, an integrator with a reset switch, a comparator, and a flip-flop. The capacitor voltage V, is sensed and fed to the PI controller, at the output of PI controller the error voltage v, is obtained. The goal of the PI controller is to maintain the dc voltage of the storage capacitor. The switches MI, M4 are turned on when the clock pulse comes. The integrator integrates the error voltage V, , and the output of integrator is compared

with (vm - R, is). When the integrated value

reaches (vm - R, is) , the comparator output changes its state that triggers the flip/flop, which in turn turns off switches MI, Mq, turns on switches Mz, M3 and resets the integrator. This process repeats in every switching cycle. The control goal of equation (10) is realized.

T i Q K

Fig. 4. the proposed active power filter with integration reset control

4. 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 llOV power system. The prototype circuit and component selection are shown in Fig 5 . The power rating is 500w and the switching frequency is 40kHz. Three kinds of different nonlinear loads are employed in the experimental tests. Fig. 6 shows the test results of the

408

proposed active power filter compensating a diode rectifier with a RC load. The total harmonic distortion (THD) of the nonlinear load current considering up to 2 0 ~ component is 78.437%. After compensated by proposed active power filter, the THD of AC mains current is 8.54%. Fig.7 presents the results of the active power filter compensating a diode rectifier with RL load. The THD of nonlinear load current is 44.231%. After compensated by active power filter, the THD of the AC mains current is 6.893%. Fig.8 shows 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 THD of total nonlinear load current is 36.33%. The THD of the AC mains current compensated by active power filter is 5.94%. Since the goal of the proposed control force the ac mains current to follow the ac mains voltage, the THD of the line current can not be lower than that of the ac mains voltage waveform. In the experiment, the THD of AC mains voltage is measured 3.9%. Fig. 9 shows the step response of input AC current of the proposed active power filter compensating a diode rectifier with an RC load when the load resistor R step changes from 450 Q to 2WQ. Fig. 10 shows the step response of input AC current in the proposed active power filter compensating a diode rectifier with an RL load when the load resistor R step changes from 120Q to 60Q. 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 AC main.

Fig. 6, The experimental results of the proposed APF power filter compensating a diode rectifier with RC load. The upper trace is the line voltage in 5OOv/div. The second trace is the input current of uncontrolled rectifier in 5Aldiv. The third trace is line current compensated by proposed APF in 5Ndiv. The bottom trace is current draw of the proposed AF'F in 5Aldiv.

-

Fig. 7, The experimental results of the proposed APF power filter compensating a diode rectifier with RL load. The upper trace is the line voltage in 5OOv/div. The second trace is line current compensated by proposed APF in ZNdiv, The third trace is input current of uncontrolled rectifier in 2Aldiv. The bottom trace is current draw of the proposed APF in 2Aldiv

Fig. 5 Prototype circuit of proposed active power filter

Fig. 8, The experimental results of proposed active power filter compensating multiple nonlinear loads, The upper trace is the line voltage in 5OOv/div. The second trace is total current of multiple nonlinear loads; The third trace is the line current after compensated by proposed APF in 5Ndiv. The bottom trace is current draw of the proposed APF in 5Ndiv

409

becomes Dv, = v, - R , * is . Table 1 switches states of unipolar operation mode of Fie. 9 (a)

switc hes MI

Fig.9 The variation waveform of input AC current whilein RC load the R step changes from 450 a to 200 a,

v,,O v,<o

complementary off operating at f, and in

Fig IO. The variation waveform of input AC current while in RL load the R step changes from 120 a to 60 a.

5. Generalization

Q--J+q---

Wg.11 three power circuits of active power filter (a) Full-bridge voltage source inverteroperating in unipolar voltage mode. (b) Half bridge inverter.(c) Current source inverter

The proposed APF control method can be extended to other power stages of active power filters as shown in Fig 11 and Fig.14. In Fig 11 (a), the power stage has the same topology as the experiment 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 bipolar voltage, bipolar current mode, while the full bridge shown in Fig.11 (a) operates in unipolar voltage, bipolar current mode. Two switches among the four operate in line frequency while the other two switches in high switching frequency, witch results to less switching loss. Table.1 shows the switching states of switches MI -M4. In this operation mode, the relationship between V, and V, is

V , = -. I and the control goal function 1 1 - D

I mode with M2. M2 I operating at f, on

operating at f, and 1: 1:; 1 i; c o 7 1 mode with M+ o eratin at f,

Fig 10 shows the simulation waveforms of APF with the UCI control operating in unipolar voltage mode. Fig l l (b) is half bridge power stage and Fig 13 is simulation waveforms under the UCI control. This circuit use only two switches and two capacitors. However, the voltage stress of switches is doubled compared to the full bridge switches, since each capacitor voltage in series should be higher than the peak of v,, Therefore, the half bridge power stage is suitable only for low voltage system. Furthermore, the proposed APF control strategy can be used in the DC side to compensate reactive and harmonic current in DC side for the rectifier load as shown in Fig. 14. The input ac voltage vs is rectified by a diode bridge. The rectified dc voltage vg=Ivsl. The bidirectional DCDC converter is controlled to generate a current ip that cancels the reactive and harmonic current of the load current iL. Fig.15 shows an example of DC side APF employing two switch bidirectional boost converter as the power stage. The switches S1 and S2 are turned on and off complementary at a constant switching frequency. As a result, vcp=vg/(l-d). The APF controller will realize ig=vg/Re using the one-cycle control circuit, 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 proposed control strategy can be extend to three-phase systems, the three phase active power filter with UCI APF control will be presented and discussed in detail in the future. Table 2 .shows the APF control equations and the relationship of v, and v, of various power circuits.

410

1-1119 a .

Qn ." ................................................................................................................... I

Full-bridge Full-bridge (Fig.5 (Fig9 (a)

, iimi

Half-Bridge DC side <vc>=<vc~.> bidmtio

. .

Control equation

.- . b h I- & la h la Iy k&

ll9 I11W

Fig.12 simulation waveform of APF with full bridge voltage source inverter operating in unipolar voltage mode employing proposed control strategy, The upper trace is the line voltage. The second trace is the line current after compensated by proposed APF, The third trace is current of nonlinear loads. The bottom trace is current draw of the proposed APF

.................

................................................................................................................. , . WCTJ mr

2Dvm=vm- DVm=Vm- Dv,=v,- DVm=Vm- R,*i, R,*i, R,*i. R,*i,

a -11.1

. I(U1 m ..........

.m............................................................-.........................-..........................._I 1m1 . w, ^

, . - - 1(p+ . _r ...................................... . . . . ( h U I I I I I l M t h l

1- I *D:q . qt)n.0:9

Fig 13 Simulation waveform of APF with half bridge power stage employing proposed control strategy, The upper trace is the line voltage. The second trace is the line current after compensated by proposed APF, The third trace is output current of the proposed APF: The fourth trace is current of nonlinear loads. The bottom traces are capacitor voltage vcl and vc2

Fig. 14 DC side active power filter or called shunt power factor correction circuit

I bipolar) I uni-plar) I =<v& I nboost VJV, I ll(l-2D) I U(l-D) I l/(l-D) I l/(l-D)

DC-DC or DC--AC

Fig. 15 an example of DC side active power filter-Bidirection boost converter power stage or called shunt power factor correction circuit

Fig 16 Simulation waveform of APF with DC side APF employing proposed control strategy, The upper trace is the line voltage. The second trace is the line current after compensated by proposed APF, The third trace is output current of the proposed APF The fourth trace is current of nonlinear loads. The bottom traces are capacitor voltage V,.

6. . Concluskm A Unified Constant-frequency Integration (UCI) control of active power filter is proposed based on one- cycle control. This control method employs an integrator with reset as its core component to control the duty ratio of an active power filter to realize net sinusoidal current draw from the ac main. Compared to previously proposed control methods, the UCI controller features simpler circuitry: no need for multipliers, no need for generating current reference that reflects the reactive and harmonic portion of the load current, 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 THD 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 this paper, the UCI control is used to control an active power filter employing a two level boost inverter. A prototype of 500w has been

41 1

developed and tested. Experimental result shows that the new APF has excellent harmonic filtering capability demonstrated using many different nonlinear loads. This control method is applicable to most other APF topologies 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.

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