The conventional graphical representation of the instantaneous compensation power flow for singlephase active power filters(APFs) simply represents the active power flow and the reactive power flow which flowing between the power source and the active filter / the load. But, this method does not provide the information about the rectification mode and the compensation mode of APFs, especially, the loss for each mode was not considered at all. This is very important to understand the compensation operation characteristics of APFs. Therefore, this paper proposes the graphical representation of the instantaneous compensation power flow for singlephase APFs considering the instantaneous rectification mode and the instantaneous inversion mode. Three cases are verified in this paper  without compensation, with compensation of the active power ‘p’ and the fundamental reactive power ‘q’, and with compensation of only the distorted power ‘h’. To ensure the validity of the proposed approach, PSIM simulation is achieved. As a result, we could confirm that the proposed approach was easy to explain the instantaneous compensation power flow considering the instantaneous rectification mode and the instantaneous inversion mode of APFs, also, Total Harmonic Distortion(THD)/Power Factor (P.F) and Fast Fourier Transform(FFT) analysis were compared for each case.
1. Introduction
Power factor improvement and harmonics suppression are important issue to obtain the high power quality of the power system because the modern industrial devices contain the sensitive devices. Active power filters(APFs)
[1

11]
have been accepting as an efficient device for compensating the harmonics and reactive power of nonlinear loads such as thyristor controlled rectifiers or variable speed drives. In order to compensate the harmonics and reactive power using APFs, APFs should be operated to the instantaneous rectification mode and the instantaneous inversion mode during the compensation operation. Also, the compensation performance of APFs are directly decided by the generated instantaneous compensation power
[12

17]
. But the conventional of graphical representation of the compensation power flow
[12

15]
for APFs is only presents the active power and reactive power flows for APFs compensation operation.
This method can not present the rectification mode which is charging the compensation energy and the compensation mode which is discharging the compensation energy. Furthermore, the loss for each mode was not considered at all, also the distortion power flow can not describe. Therefore, if the instantaneous compensation power which flowing between APFs and AC power source can be illustrate in graph, then, it can be easily understood the compensation operation of APFs.
This paper briefly discusses the graphical representation of the instantaneous compensation power flow which could be practicable to understand the harmonics and reactive power compensation for singlephase APFs in both case of behaving in the instantaneous rectification mode and the instantaneous rectification inversion mode. The instantaneous compensation power can be decomposed into the active component, the fundamental reactive component and the distorted component. Compensation operation modes of singlephase APFs are represented by each decomposed power components. Distorted and reactive powers of nonlinear loads can be independently controlled by singlephase active power filters, and its instantaneous power flows of before and after compensation can be illustrated in graph.
To ensure the validity of the proposed approach, computer simulation was performed. Three case verifications  without compensation, with compensation (active power ‘p’ and fundamental reactive power ‘q’), and with compensation (only distorted power ‘h’) were achieved in this paper. As a result, we could confirm that the proposed approach can illustrate more exquisitely and more significantly the instantaneous compensation power flow of singlephase APFs considering the instantaneous rectification mode and the instantaneous inversion mode. Finally, THD / P.F and FFT results for each case is compared and discussed.
2. Compensation Operation of SinglePhase Active Power Filters
Fig. 1 (a)
shows the equivalent circuit of singlephase active power filters during the compensation operation, where ‘s’, ‘p’ and ‘n’ respectively denote the instantaneous apparent power, the instantaneous active power and the instantaneous nonactive power.
Equivalent circuit of singlephase active power filters (APFs) (‘(+)’ : rectification mode, ‘()’ : inversion mode)
With two operation modes  the rectification and the inversion modes as shown in
Figs. 1(b)
and
Fig. 1(c)
, singlephase active power filters generate the instantaneous compensation power ‘n’ (that is, the nonactive power) to AC power source.
‘(+)’ denotes that singlephase active power filters operate as the rectification mode and ‘()’ denotes the inversion mode. ‘J’ and ‘y’ refer the compensation current source of singlephase active power filters and equivalent admittance of singlephase active power filters. Also, i
_{c}
denotes the compensation current which generated from the current source ‘J’ of singlephase active power filters.
Fig. 2
shows the waveforms of compensation current i
_{c}
and power ‘n’ while i
_{L}
means the nonlinear loads current. The instantaneous compensation current i
_{c}
is generally composed of the fundamental reactive current i
_{r}
and the harmonic current i
_{h}
. First of all, for the rectification mode in interval (I, III) as shown in
Figs. 2
and
Fig. 3
, the instantaneous nonactive power (+)n is transferred from the AC power source to APFs. In the same time, ()n is transferred from singlephase active power filters to the AC power source for the inversion mode in interval(II, IV).
Waveforms of the compensation current and power: (a) Load current i_{L} and source voltage ‘v’; (b) compensation current i_{c}; (c) Compensation power ‘n’
Operation quadrants of singlephase APFs according to i_{c}
3. Graphical Representation of the Instantaneous Compensation Power Flow
The instantaneous apparent power (supply power) ‘s’ is expressed in terms of two components the instantaneous active power ‘p’, the instantaneous nonactive power ‘n’, and their instantaneous values fulfill the following relation.
Also, the instantaneous compensation current i
_{c}
calculated by using the instantaneous load current i
_{L}
described as (2), and i
_{c}
is formulated by (3). As shown in
Fig. 2(b)
, the instantaneous compensation current i
_{c}
is divided into (+) i
_{c}
for rectification and ()i
_{c}
for inversion.
The instantaneous load current i
_{L}
without DC offset component :
The instantaneous compensation current i
_{c}
:
where (+) i
_{c }
; interval I ( 0 <ωt<ωt
_{1}
) : rectification mode interval III(ωt
_{2}
<ωt<ωt
_{3}
): rectification mode

(−) ic; interval II (ωt1<ωt<ωt2): inversion mode

interval IV (ωt3<ωt<ωt4): inversion mode
As mentioned above, (+)i
_{c}
, the first term of (4) refers the instantaneous compensation current of the rectification mode and it has the same polarity compared with ‘v’. And reversely, () i
_{c}
, the second term of (4) refers the instantaneous compensation current of the inversion mode and it has the reverse polarity compared with ‘v’. This means that the instantaneous compensation power ‘n’ which flowing between the AC power source and singlephase active power filters can be formulated by (5).
where (+) n ; interval I ( 0 <ωt<ωt
_{1}
) : rectification mode interval III (ωt
_{2}
< ωt<ωt
_{3}
) : rectification mode

() n ; interval II (ωt1<ωt<ωt2): inversion mode

interval IV (ωt3<ωt<ωt4): inversion mode
Now, let’s consider the loss w
_{o}
of singlephase active power filters such as DC energy chargedischarge loss, switching loss and input LC filter loss of PWM converter. During singlephase active power filter works, singlephase active power filters produce the compensation loss w
_{o}
for each operation mode. Singlephase active power filters loss can be classified into two losses in (6) that is (+)w
_{o}
for rectification mode and ()w
_{o }
for inversion mode respectively. But, generally, it is very difficult to know that the individual w
_{o}
for each operation mode as mentioned above.
where (+)w
_{o}
; interval I ( 0 <ωt<ωt
_{1}
) : rectification mode interval III (ωt
_{2}
< ωt<ωt
_{3}
) : rectification mode

()wo; interval II (ωt1<ωt<ωt2): inversion mode

interval IV (ωt3<ωt<ωt4): inversion mode
But, we already know that the DC capacitor voltage of singlephase voltage source type active power filters should be controlled to constant voltage level, while the DC reactor current of the current source types should be controlled to constant current level, because of build up of the compensation energy.
Fig. 4
shows the compensation current and power waveforms considering the DC energy build up. The DC side energy control of singlephase active power filters aim at the DC energy build up for compensation. In order to build up of the DC capacitor voltage in case of the voltage source APFs, The current i
_{0}
in phase with source voltage ‘v’ is added to i
_{c}
as shown in
Fig. 4(a)
. The current i
_{0}
is calculated by multiplying the unity ‘v’ by the DC voltage error (PI controller output) defined as the difference between the DC voltage reference and the DC capacitor voltage. Note that the DC energy build up compensation current i
_{0}
and power ‘p
_{o}
’ are always the active components.
Compensation waveforms considering the DC energy build up: (a) Compensation current i_{C} ; (b) compensation power p_{0}
The loss w
_{o}
in (6) can be represented by ‘p
_{o}
’ in
Fig. 4(b)
. This means that w
_{o}
is nearly equivalent to p
_{o}
because the loss of the ideal APFs goes to zero, hence the DC energy build up of singlephase active power filters does not need. The power p
_{o}
can be divided into two parts; (+)p
_{o}
for the rectification mode and ()p
_{o}
for the inversion mode respectively. Unlike ‘n’ in
Fig. 4(b)
, note that ()p
_{o}
does not keep the reverse polarity compared with ‘v’ over the inversion mode. That is, this means that p
_{o}
still places in the inversion interval (II or IV) though it is positive.
The resultant instantaneous compensation power n’ considering the DC energy build up can be expressed by (7)(11).
As mentioned above, ()p
_{o}
means that p
_{o}
still places in the inversion interval(II or IV) though it is positive.
Hence;
4. Simulation and Verification
In order to obtain the proposed instantaneous compensation power flow diagram of singlephase APFs, computer simulation using a PSIM simulation software was done as shown in
Fig. 5
. The power theory for the compensation current calculation was based on the general Fourier Series Method.
Table 1
shows the simulation parameters. As shown in
Table 1
, the AC source voltage (155V/60Hz) supplies to the nonlinear thyristor loads. Voltage source type singlephase active power filter serve as the compensator of the reactive and distorted power generated from thyristor loads. To build up of DC capacitor voltage, PI controller is used, and Hysteresis Current Control(HCC) is applied to control of the compensation current i
_{c}
’. Three cases  without compensation, with compensation (active power ‘p’ and fundamental reactive power ‘q’) and with compensation (only distorted power ‘h’) are verified and the power quality of each case is compared in this paper.
PSIM simulation model
Simulation parameters
 4.1 Without compensation
Fig. 6
shows the instantaneous compensation power flow by the graphical representation for no compensation, and
Fig. 7
shows the simulated results.
The instantaneous compensation power flow diagram for no compensation
Simulated results for no compensation
As shown in
Fig. 7(a)
, waveform of i
_{s}
is distorted and lagged in comparison with the phase of AC source voltage v’.
Fig. 7(b)
shows that the instantaneous apparent power ‘s’ can be decomposed into the active power ‘p’, the fundamental reactive power ‘q’ and the distorted power ‘h’. The active power ‘p’ f lows toward the one side direction while the ‘q’ and ‘h’ flow to the bidirection.
As shown
Fig. 6
, during no operation of singlephase APFs, the power ‘n’ flowing between AC power source and singlephase active power filters are zero, and ‘s’ is directly transferred to the nonlinear loads. But, if singlephase APFs operate, the compensation power appears between singlephase APFs and AC power source. Graphical representation in
Fig. 6
is useful for describing the compensation power flow and the operation of singlephase active power filters.
The instantaneous compensation power flow diagram for ‘q’ and ‘h’ compensation
Simulated results for fundamental reactive power ‘q’ and distorted power ‘h’ compensation.
 4.2 With compensation (‘q’ and ‘h’)
Fig. 8
shows the instantaneous compensation power flow diagram, in case that the instantaneous compensation power component (fundamental reactive power ‘q’ and distorted power ‘h’) is simultaneously compensated by singlephase APF considering the DC voltage build up.
Fig. 9
shows the simulated results for ‘q’ and ‘h’ compensation.
Fig. 9(a)
shows the AC source voltage ‘v’ and current i
_{s}
. As compared with
Fig. 7(a)
, the waveform of is is nearly sinusoidal and in phase with ‘v’. Also,
Fig. 9(b)
shows the decomposed source powers. As expected, we can know that only ‘p’ remains in AC power source while the supply power ‘s’ is still supplied to the load side. This means that the P.F and THD of AC power source is improved.
FFT results of i_{L} and i_{s} for ‘q’ and ‘h’ compensation (xaxis: 100Hz, yaxis: 10A/div.)
THD and each harmonics levels of current for ‘q’ and ‘h’ compensation
THD and each harmonics levels of current for ‘q’ and ‘h’ compensation
As the FFT results shown in
Fig. 10
, a nonlinear thyristor load generates
i_{L}
with large 3rd harmonic content. As given in
Table 2
, the 3rd harmonic component of
i_{L}
reaches to 20% for the 60Hz fundamental component. After harmonics compensation is achieved, with respect to the source current
i_{s}
, the 3rd component of
i_{s}
is reduced to 2% for the 1st component as given in
Table 2
. These means that highly distorted
i_{s}
is changed into a sinusoidal waveform by compensation operation of the proposed system. As a result, the THD of
i_{s}
is improved, also the unity power factor (P.F) is obtained.
Fig. 11
shows the simulated results of the instantaneous compensation power and current for
Fig. 9
. Waveforms of
Figs. 11(a)

(b)
follow the compensation principle in
Fig. 4
. First of all, the compensation reference for the DC voltage build up should be recalculated as (i
_{c}
’ = i
_{c}
+ i
_{0}
) in
Fig. 11(a)
because i
_{0}
is added to i
_{c}
. As shown in
Fig.11(b)
, the instantaneous compensation power n’= p
_{o}
+(q+h) = p
_{o}
+ n flows between singlephase APFs and AC power source.
The compensation power ‘n’ is calculated by using ‘q’ and ‘h while p
_{o}
serves as the DC energy build up compensation power. Actually, ‘n’ reciprocates between singlephase APFs and AC power source. The proposed approach represents very well ‘q’ and ‘h’ for the rectification and inversion modes.
Simulated results of the compensation current and power
Fig. 11(c)
shows the comparison result of the calculated n’ and the actual ‘n’. Because the calculated compensation reference power ‘n’ is seriously distorted, the actual compensation power ‘n’ can not follow in the suddenly changed point. As a result, the spikes periodically remain in the compensated source current i
_{s}
as shown in
Fig. 9(a)
.
 4.3 With compensation(‘h’)
Fig. 12
shows the instantaneous compensation power flow diagram in case that singlephase APFs control only ‘h’ component. Because only ‘h’ is controlled by singlephase APFs, ‘p’ and ‘q’ remain in AC power source as shown in
Fig. 13(b)
, while the supply power ‘s’ is still supplied to the load side. In this case, the AC source voltage ‘v’ and current i
_{s}
presented in
Fig. 13(a)
.
The instantaneous compensation power flow diagram for only distorted power ‘h’ compensation
Simulated results for only distorted power ‘h’ compensation
THD and each harmonics levels of current for only ‘h’ compensation
THD and each harmonics levels of current for only ‘h’ compensation
FFT results of i_{L} and i_{s} for only ‘h’ compensation (xaxis: 100Hz, yaxis: 10A/div.)
Simulated results of the compensation current and power
Fig. 14
shows the FFT results for only distorted power ‘h’ compensation. As compared with
Fig.10
, it can be seen that there is a difference in the 60Hz fundamental component of the compensated
i_{s}
. Firstly, in case that only the distorted power is compensated, the 60Hz fundamental component in the compensated
i_{s}
is larger than in case of the two components compensation, because the 60Hz fundamental reactive component remains in the compensated supply current
i_{s}
. With respect to the THD and P.F of the compensated
i_{s}
, we can know that THD is 2% and P.F is 0.95.
Fig. 15
shows the simulated results of the compensation power n’ and current i
_{c}
’. The operation principle is nearly similar as compared with ‘q’ and ‘h’ compensation in
Fig.11
.
5. Conclusion
This paper deals with the graphical method to present the instantaneous compensation power flow of singlephase active power filters (APFs) considering the rectification and inversion modes. The following conclusions can be derived from the results of this study. Compared with the conventional method, the proposed method is useful to illustrate the compensation principle of singlephase APFs by the graphical method. The equivalent circuit of singlephase APFs is obtained into the rectification and inversion modes in order to suit proposed approach. In case that the reactive and harmonic powers of nonlinear loads are simultaneously or independently controlled by singlephase APFs, and we could verified that the proposed approach was easy to explain the instantaneous compensation power flow. With respect to power quality such as the THD and P.F, in case that the distorted and fundamental reactive power are compensated, unity power factor was achieved, and in case that only the distorted power is compensated, THD was reduced to 2%.
BIO
YoungGook Jung He was born in Gwangju, Korea, in 1963. He received the B.S., the M.S. and Ph.D. degrees in electrical engineering from Chonnam National University, Gwangju, Korea, in 1986, 1988 and 1996, respectively. He is currently an Associate Professor in the Department of Electrical Engineering, Daebul University, YoungamGeun, Chonnam, Korea. His current research interests include Zsource converters and their applications, random PWM schemes, active power filters, power quality problems and solutions. Dr. Jung received several Prize Paper Awards from the KIEE and KIPE of Korea
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