IECONO1: The 27th Annual Conference of the IEEE Industrial Electronics Society

Operation of Unified Constant-frequency Integration Controlled Three-phase Active Power Filter in Unbalanced System

Taotao Jin, Chongming Qiao, 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: smedlev@ uci.edu

Abstract-In recent years, the power quality of the AC system has become a great concern due to the rapidly increased numbers of electronic equipment. In order to reduce harmonic contamination in power lines and improve the transmission efficiency, active power filter research became a hot topic. Many control methods for the Active Power Filter (APF) were proposed. The theory and experiments have demonstrated that Unified Constant-frequency Integration (UCI) controller features excellent performance, simple circuitry, and low cost control methods for three-phase APF under three-phase balanced conditions. In this paper, a three-phase APF working in an unbalanced condition with a UCI controller are studied. Analysis and simulation show that with UCI control sinusoid input current can be realized, whether the input voltages are balanced or unbalanced.

I. INTRODUCTION

The power quality of the AC system has become a great concern due to the rapidly increased numbers of electronic equipment. In order to reduce harmonic contamination in the power lines, two basic methods are used: a) a rectifier with power factor correction (PFC) is used to prevent the generation of harmonic current; b) an active power filter (APF) is used to eliminate harmonic current generated by other equipment.

Most of the three-phase APFs employ a boost converter as their power stage. The main distinction between different APFs is their control strategy. In recent years, many control methods were proposed, most reported control approaches used in APF need to sense the load currents and calculate harmonic and reactive components then use it as current reference to provide compensation. Those methods require fast and real-time calculation, therefore, a high-speed digital microprocessor and high performance A/D converters are necessary, yielding high cost, low reliability, and high complexity. Article [ I ] introduced a promising solution named Unified Constant-frequency Integration (UCI) controller based on one-cycle control and mains current sensing for a three-phase APF. The theory and experiment have proved that the UCI controller is a high performance and low cost solution under three-phase balanced conditions. In this paper, the three-phase APF working in the unbalanced power system with UCI controller is studied. Analysis, simulation and experiments have shown that UCI controlled APF realizes sinusoidal input current in either balanced or unbalanced power systems.

II. THE DIFFERENCE BETWEEN BALANCED AND UNBALANCED THREE-PHASE SYSTEM

h' / /

(c) Fig.1 The vector diagram of three-phase input voltage in balanced and unbalanced power system. (a) Three-phase balanced; (b) Three-phase unbalanced; (c) Decoupled three- phase unbalanced vector into non-zero components and zero components.

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IECON'OI: The 27th Annual Conference of the IEEE Industrial Electronics Society

negative vi, vi, v i , and zero sequence v: , v: , v:, In order to study the characteristics of UCI controlled APF

in an unbalanced system, it is important to understand the as drawn in Fig.1 (b). The vector sum Of the

Fig.2 The diagram of the three-phase APF with UCI controller

difference between a balanced and unbalanced three-phase positive and negative sequence components is zero, while the system. vector sum of the zero sequence components is non-zero.

Fig. l(a) and (b) show the vector diagram of three-phase Based on this characteristic, unbalanced three-phase voltages voltages in a balanced and unbalanced power system are decoupled into two parts-non-zero sequence respectively. The unbalanced three-phase input voltages components and zero sequence components as in Fig. 1 (c). v, , vb, V, can be decoupled into positive v,' , v;, V,' ,

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IECONO1: The 27th Annual Conference of the IEEE Industrial Electronics Society

111. REVIEW OF UCI CONTROLLER FOR APF WORKING IN THREE-PHASE BALANCED SYSTEM

Fig.2 shows the schematics of the three-phase APF system, which employs a three-phase Voltage Source Converter (VSC) and the UCI controller, where, i, , ib , i, represent the input currents of phase A, B, C respectively.

In order to realize the UCI controller, the Voltage Source Converter is operated in CCM mode and the driver signals to the two switches in each arm are set to be complementary. For example, the duty ratios of switches San ,sa, in phase A

are dun and 1 - d , respectively. Based on the inductor volt-second balance concept, a

steady state relationship that relates the input phase voltages, output voltage E via the switch duty ratios in CCM mode is shown as belbw: [:] = N(d) .E _ _ _ _ _ _ - _ _ - - - _ - - _ - (1)

where E is the output capacitor voltage of VSC, d is a vector function of duty ratios d , ,dun , etc, and N(d) is a linear

matrix equation of the duty ratios.

unity-power-factor, ie. For the three-phase APF, the control goal is to achieve

4 2 ) JTg = R e . ib _ _ - _ - - _ _ - - - _ - i:] where R, is the emulated resistance that reflects the real power of the load. Combination of the above two equations and elimination of input voltage vg yield the key equation

of UCI control: R, . i, = N ( d ) . V - - - - - - - _ - - - - - (3)

m

where R, is current sensing resistance and V, is given by c

Since V , + V , + V , = 0 , the relationship of phase

voltage v,, V , , V , , and output voltage E for the three-phase boost converter under CCM mode is as following [l]:

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The matrix in equation ( 5 ) is singular, so there are infinite numbers of solutions. With this characteristic, UCI control can be optimized for different situations. In article [l], vector operation was realized with UCI control. In this control, one line period is divided into six regions as depicted in Fig.3. In each region the duty ratio of the switch in the arm with dominant voltage is set to zero or one, and thus the other two duty ratios are solved by equation (5). For example, considering the region of 0-60" of the three-phase system shown in Fig.2, the duty ratio is set dbn = 1, ie. s,, is kept on

for the entire regions. Substituting d,, =l in t0 equation ( 5 ) and using the control goal, with equation (2) and (4), the following control key equation can be obtained.

Similarly, the control equations for the other five regions can be derived "I. These control equations can be realized by the one cycle control circuit that is composed of one integrator with reset along with some logic and linear components as

l i I I I I

I I I I

Fig.3 Three-phase voltage waveforms

shown in Fig.2. The operation waveforms of UCI controller are shown in Fig.4, where i, and i,, represent the currents from the

non-dominant phases selected by the input multiplex. In the beginning of each switching cycle, the clock pulse sets the two flip-flops. The currents ip and in from the input multiplex is linearly combined to form an input to each of the two comparators. At the other input of the two comparators is the value of V, minus the integrated value of Vm. Vm-VmdP is compared with R, . (2. ip + in ) in the upper comparator and

is compared with R, . ( i p + 2 - in) in the lower comparator as

depicted in Fig.2. When the two inputs of a comparator meet as depicted in Fig.4, the comparator changes its state, which

IECONO1: The 27th Annual Conference of the IEEE Industrial Electronics Society

s = 0.5 . T, A

I Fig4 The operation wavefimn of UCI controller

resets the correspondent Flip-Flop. As a result, the correspondent switch is turned off. In this process, the duty ratios d, and do are determined for the correspondent switch in each switching cycle. Implemeintation of equation (7) by one- cycle control results in the proposed controller.

IV. OPERATION CHAIUCTEIUSTIC OF UCI

CONDITION CONTROLLED THREE-PHASE APF IN UNBALANCED

As discussed in the previous section, equation ( 5 ) was derived under the assumption that V , + vb + V , = 0, however in an unbalanced three-phase system as shown in Fig.l(b), V , + V , + V , # 0, due to the presence of the zero sequence components. It is, therefore, the objective of this paper to examine the UCI controller under the unbalanced condition. With unbalanced three-phase voltages, the relationship established in equation ( 5 ) for the phase voltage V , , V , , V , , and

output voltage E needs be reevaluated. Because the switching frequency is much higher than the

line frequency (50 or 60Hz), the average node voltages for node A, B, C referring to the negative rail of bridge “N’ can be written as

V A N = ( l - d , , ) . E

VCN = ( l - d , , ) . E

vBN = (1 - d ). E _ _ _ _ _ _ _ _ _ _ _ _ _ _ (8) bn

According to equation (8), the three-phase APF circuit shown in Section I11 can be simplified to the average model in Fig.5. The average vector voltage at nodes A, B, C referring to the neutral point “0’ equal the phase vector voltages minus the voltage aciross the inductors La, L,, L, , which is given by

i CA, = i), - jwL i,, v,, = vb - jwL - i,, ------(9)

cc0 = +, - jwL a iLc

I I I I I I I

I I

I I I I

! I I I

I I

L-----------------J I I

FigSThe switching cycle average model for the power stage shown in Fig.1

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where L is inductance of the input inductors (assuming all the three APF inductor have same inductance), w is the line

angular frequency, and i,, , i,, , iLC are inductor current vectors. Because these inductors are operating at switching frequency and the impedance of La, L, ,L, are very small for 60Hz or 50Hz line frequency, the voltages across the inductors such as jwL . f,, are very small compared with the phase voltages and thus can be neglected. Therefore, equation (9) can be approximated as

. . .

VAO = vo +,, zz vb -_--_-_---_

vco = v,

v,, = CAN + v, vBo = VBN + v,, ---( 11)

vco = v, + vN,

(10)

The voltages at nodes A, H, C referring to neutral point I 1 “0” are given by

According to Fig. l(c), the three-phase unbalanced input

by: voltages include a zero sequence component, which is given

CO = f * (V , + Vb + V,) = *. (VA0 + VB0 + CCO) -----(12)

+, = -1. (VAN + vBN + vcN ) + CO -------( 13)

V,,-V0 = ~ A N - f . ( v A N + v B N + v C N ) = ~ a - v O

v,, -vo =vcN - $ . ( C A N +vBN +vcN)= v, -v,

where v0 is the zero sequence component. The combination of equation (1 1) and (12) yields

Substituting equation (13) and (10) into (12) results in

. . GBO -vo =vBN +VBN + G c N ) = cb -CO -(14)

Simplification of the above equations yields

IECONOl : The 27th Annual Conference of the IEEE Industrial Electronics Society

means that the capacitor on the DC bus of APF should be able to buff instant energy flowing in and out. The requirement depicts that the key of capacitor's selection is to calculate the value of the instant energy.

When an APF is working, two situations should be considered, the first one is the static state and the second one is the dynamic state. All of them are discussed below:

va -vo

In the time domain, it can be simplified as

[:; i ~ - ~ ] . [ r ~ ] = [ ~ ~ ~ ] _ _ _ _ _ _ _ _ _ _ _ (16)

where vanO vbno vcno are the non-zero sequence components. The combination of equation (8) and (16) yields the relationship between the duty ratios d,, d,, d,, , the

2 -1 -1 1) The static state: For three-phase balanced system, the current flowing

into APF can be decoupled into fundamental and harmonic -- -- 'CN ',no parts. Therefore, the there phases voltages can be expressed

as: V, = V . s ina yb = V.sirfo1-&/3)

phase voltages V, V, V, and DC rail voltage E as follows: = V ' sirfw+2n/3)

.. . voltage v, , v,, v, is replaced by vanO, vbnO,vcnO, which ca

indicates that duty ratios d,, , dbn d, only depend on DC rail I, =XI,, . s i n n - ( m + 2 n / 3 + p ) n=l

voltage E and the non-zero sequence component vane vbnO vcn0 . In an unbalanced system, the zero sequence input voltages do not influence the input current.

Supposing that UCI control is used under unbalanced system, considering Oo-6O0 region, duty ratio " dbn = 1 ", equation (17) can be simplified into:

Combine with UCI control key equation (7), the relation between input current and voltage can be derived as below:

Equation (19) can be continuously simplified into:

The equation shows that under an unbalanced system, the phase current will be linearly proportional to the non-zero

Then the instant power flowing into the DC capacitor can be expressed as below:

j? = -

V . I , (sin U X . sin n .(wt + cp) "=I

+ sin(m - 2x13). sin n . (wt - 2x13 + cp) + sin(m + 2 n / 3 ) . sin n . (m + 2x13 + 9))

v.z , = g- . (cos((n - 1)m + np) -cos(@ + 1)m + ncp)

, ,=I 2 2n 2 n 3 3

+ cos((n - l ) ( u - -) + ncp) - cos((n + l)(- --) + ncp)

2 n 2 n 3 3

+ cos((n - l)(m + -) + ncp) - cos((n + 1) (a + -) + ncp))

(21) ............................ Equation (21) depicts that only the 3rd, 6'h, 9Ih.. . harmonic

power can be found in the DC bus capacitor. Usually in a power system no even harmonic current exists, and the Sh, and 71h harmonic currents are the dominant parts. Therefore only the 6Ih power needs to be considered, which will be generated by the 5'h and 7'h harmonic currents.

sequence of the three-phase system vRn0 vbnO vcno ; therefore the three phase currents are expected to be sinusoidal.

Assuming the amplitude of the harmonic power is P,, the total power flows into or out of DC bus capacitor is achieved by integrating the half cycle of the 61h harmonic power as below: V. THE SELECTION OF CAPACITANCE ON DC BUS

(22)

If the DC bus voltage is U, and the largest voltage variation is Au, according to equation (22) the value of capacitor should be greater than

4 . s in6o~.dm =- 3 In order to get a good performance, the DC bus voltage

of a three-phase APF should be constant; therefore a feedback circuit is used, in order to avoid the interference between the control signal on the AC side and the DC side. The response speed of the DC controller is very low, which

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IECON'O1: The 27th Annual Conference of the IEEE Industrial Electronics Society

2. P6 cmin-s = 3 . (2. U . Au +

2) The dynamic state

Nonlinear

3-phase APF

Fig. 7 the curves of power changing (a) Load (b) Power system

Although all of the designs in this section are based on the three-phase balanced system, the result is sill applicable to the unbalanced system. -

Fig. 6 principle diagram of APF system VI. SIMULATION AND EXPERIMENT

Fig.6 shows a principle diagram of the APF system, which depicts that Pso,rc, = + Pcompensaror . In the load transient, the Power flow into tlhe load will experience a steep climbing like the curve in Fig.:! (a), but for power system the desirable transient of Psouse is exponential increasing or decreasing without overshot like the curve in Fig.7 (b). Since the two curves are different, the difference must be provided by APF's DC capacitor.

In fact the curves in Fig.7 (a) and (b) can be expressed in equation (24) and equation (25) respectively.

where z is the time constant.

capacitor can be expressed as below: Therefore the instant power flowing into the APF's DC

[eompensat o = O t I O

Assuming the transient lasts 32, the total power flows into the capacitor can be achieved by integrating the equation (26) as below:

- P,,,,) . (1 -$). dt

= ( E n i l i a / - Pfinal ) . * (2 + e-3 (27)

2 . ( e n i l i a , - 'final ) . r As in the discussion of the static state, according to

equation (27) the value of capacitor should be greater than

Simulation was conducted using Pspice9.2. The simulation conditions are: Software: Pspice9.2 Input AC voltage: va = 120V, vb = 40V, vc = 120V (RMS value) DC rail voltage: E = 440V Input inductance: L = 1.97mH Switch frequency: 50kHz Resistance of the nonlinear load: R = 78R Inductance of the nonlinear load: L = 42mH

%",\\ \ \

/

Fig.8 Vector relationship between input voltage V and its

none zero sequence component Vno

Assuming input current only follows the non-zero component of input voltage, according to vector diagram analysis in Fig.1 and the above simulation parameters, the phase difference between va and ia , vb and ib , V , and i , , should be -12.12', Oo, 12.12'' respectively, the amplitude of the non-zero component in v, , vb, V , should be 109.13v, 66 .67~ and 109.13~ (RMS value), which is shown in Fig.8.

,,. According to analysis in section 4, the input current will Since usually C,,,_q>>C,ln-s, the value of Cmln_d is used LU follow the non-zero component of input voltage vane, V b n O , vcn0 . The phase shift between voltage and current

select the DC bus capacitor.

in Fig. 9 verify the theory analysis.

0-7803-7 108-9/0 1/$10.00 (C):2001 IEEE 1544

IECON’O1: The 27th Annual Conference of the IEEE Industrial Electronics Society

W

)r In tm i5.I 2- 2% - 2 . 1

i U ( I C ) I ~ .n~I I (a~~Olnl~t~~I ) )

Fig.9 Simulation input three-phase voltage and current waveforms of APF with unbalanced input voltage-from top to bottom the voltage & current of Phase A, B, and C respectively

Using same parameters, an experiment was carried out. The result of the experiment is depicted in Fig. 10 and Fig. 1 1.

. ... , Reh ’ -- - 100 V S.Ooms, Fig.10 Experiment waveforms of APF with unbalanced input

voltage-phase comparison

Rev2 25omv 5.ooms Fig.11 Experiment waveforms of APF with unbalanced input voltage-amplitude comparison

In Fig.10 voltage and current waveforms of phase A, B, and C are listed from top to bottom respectively; In Fig.11

R1 is the voltage waveform of phase A, R2, R3, and R4 are the current waveform of phase A, B, and C respectively.

The waveforms in Fig.10 and Fig.11 show that the proposed control method performs normally in either balanced or unbalanced AC system.

VII. CONCLUSION

In this paper, the UCI controlled three-phase APF working under the three-phase unbalanced condition is studied. Theory analysis shows that under the unbalanced condition the input currents of the three-phese system will still be sinusoidal and they will follow the non-zero sequence component of input voltage. Then in order to design the APF system, the selection procedure for APF’s DC bus capacitor is discussed, which depicts that the value of DC bus capacitor is decided by DC bus voltage, the static harmonic power and the dynamic power flowing into the capacitor, A pspice simulation program and a lkVA experiment equipment were built up, all simulation and experiment results indicate that with UCI controller APF can eliminate system’s harmonic pollution either in balanced and unbalanced situation.

References:

[ I ] Chongming Qiao and Smedley, K.M. “Unified Constant- frequency Integration Control of Three-phase Active-Power- Filter with Vector Operation”: PESC’200 1, Vancouver, Canada, June, 2001.

[2]. A.V.Stankovic and T.A. Lip0 “A Novel Control Method for Input Output Harmonic Elimination of the PWM Boost Type Rectifier Under Unbalanced Operating Conditons”. APEC 2000, New Orleans, LA, USA, 6-10 Feb. 2000. p.413- 19 vol.1.

[3]. Chongming Qiao and Smedley, K.M. “Three-phase Active Power Filter with Unified Constant-frequency Control”. Published by IPEMC-2000 (Third International Power Electronics and Motion Control Conference), Augl5- 18, Beijing, China.

[4]. K. M Smedley and C. Qiao, “Unified Constant-frequency Integration Control of Three-phase Rectifiers, Inverters, and Active Power Filters for Unity Power Factor” US. Provisional Patent filed 911 999, Patent filed 812000, and approved 212001.

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