A standard repetitive controller (RC) is theoretically able to replace a bank of resonant controllers in harmonic signals tracking applications. However, the traditional RC has some drawbacks such as a poor dynamic response and a complex structure to compensate grid frequency deviations for an effective unified power quality conditioner (UPQC) control scheme. In order to solve these problems, an improved RC with an outstanding dynamic response and a simplified grid frequency adaptive scheme is proposed for UPQC control systems in this paper. The control strategy developed for the UPQC has delay time, i.e., onesixth of a fundamental period (T
_{p}
/6), repetitive controllers. As a result, the UPQC system can provide a fast dynamic response along with good compensation performance under both nonlinear and unbalanced loads. Furthermore, to guarantee the excellent performance of the UPQC under grid frequency deviations, a grid frequency adaptive scheme was developed for the RC using a simple first order Padé’s approximation. When compared with other approaches, the proposed control method is simpler in structure and requires little computing time. Moreover, the entire control strategy can be easily implemented with a lowcost DSP. The effectiveness of the proposed control method is verified through various experimental tests.
I. INTRODUCTION
In recent decades, the intensive use of power electronics devices and nonlinear loads such as diode rectifiers, adjustable speed motor drives, and switching power supplies has led to the injection of many harmonic currents into power distribution systems. Harmonic currents have various severe effects on power systems such as voltage distortions, increased losses and heat in networks, malfunctions of electronic equipment, and degraded power quality in networks. Therefore, the installation of power filters and power custom devices to improve power quality has become a mandatory requirement for both network operators and end users.
Various kinds of compensating devices have been proposed and developed in the literature. These devices include passive filters, shunt active power filters (APFs)
[1]
,
[2]
, and hybrid APFs
[3]
, which mitigate current harmonics, and series APFs
[4]
and dynamic voltage restorers
[5]
, which deal with voltage distortions and voltage sag compensation.
Recently, the unified power quality conditioner (UPQC), which is composed of shunt and series APFs, has been developed as an advanced and powerful compensation device to simultaneously deal with current and voltage related problems. Most of the previous UPQC control methods involve voltage sag/harmonic detectors and voltage/current controllers to provide different power quality improvement functions
[6]

[10]
. To avoid complex control schemes and hardware, many researchers have tried to implement UPQCs without harmonic extractors through advanced control schemes such as hysteresis controllers
[11]

[14]
, artificial neural network and particle swarm optimizationbased controllers
[15]
,
[16]
, and proportionalintegral (PI) plus resonant controllers
[17]
. Among these methods, the resonant control approach offers the best control performance thanks to its effectiveness in tracking harmonic signals. However, since each resonant controller effectively tracks only one specific frequency signal, a large number of resonant controllers are needed to regulate all of the concerned harmonic components. This makes the whole control scheme complex and bulky.
To simplify the complexity of multiple resonant controllers, the repetitive controller (RC) is one of the promising solutions. A single RC can replace a bank of resonant controllers to simultaneously compensate a large number of harmonic components. The RC has been widely applied to various power converter applications such as UPSs
[19]

[21]
, active power filters
[22]
, and gridconnected inverters
[23]
. Despite the effectiveness of the RC in harmonic compensation/rejection, the traditional RC regularly suffers from two main shortcomings: a poor dynamic response, which is due to a long delay time, i.e., one fundamental period; and deteriorated performance under system frequency variations, e.g., grid frequency deviations. To resolve the slow transient response of the traditional RC, a number of control approaches have been introduced where the RC is designed to compensate only the (6
n
±1)th (
n
= 1, 2, 3…) harmonics, which reduces the time delay by six times
[24]

[27]
. However, under unbalanced load conditions, the performance of these RCs is diminished because they can only deal with (6
n
±1)th (
n
= 1, 2, 3…) harmonic components, which is suitable for threephase nonlinear loads.
On the other hand, to maintain the same performance of the RC despite grid frequency deviations, two main approaches have been introduced: adjusting the sampling period of the control system so that the number of delay samples,
N
, can be maintained as an integer value
[28]
,
[29]
; or approximating the fraction delay term so that the RC can be accurately implemented even though
N
is a noninteger number
[30]

[35]
. The first solution is simple and easy to implement. However, it does not guarantee a good performance when the grid frequency variations increase. Furthermore, in the case where the sampling period is changed, the whole control system needs to be redesigned. The second solution, approximating the fraction delay term, can be achieved by a first order low pass filter (LPF)
[30]
, a finite impulse response (FIR) filter
[31]
, Linear interpolation
[32]
, and Lagrange interpolation
[33]

[35]
. A LPF with a variable cutoff frequency is simple to implement. However, this method cannot ensure a good performance of the RC in the case of grid frequency variations because finding the relationship between the cutoff frequency of the LPF and the grid frequency deviation is quite challenging. On the other hand, FIR filters and Lagrange interpolation with adjustable coefficients are more complicated, consume long computational time and require high order FIR filters to guarantee an accurate approximation. Unfortunately, with a complex control system the RC is no longer simple compared to other control techniques.
In order to solve the above mentioned problems in the traditional RC, i.e., a poor dynamic response due to a long delay time and complexity in terms of compensating grid frequency deviations, this paper introduces a modified RC and the grid frequency adaptive method to implement a versatile UPQC control system. To overcome the slow dynamic response of the traditional RC, a new RC was developed with a reduced delay time, i.e., onesixth of a fundamental period (
T_{p}
/6), so that the UPQC system can achieve approximately six times faster response than that of the traditional RC. In addition, by combining two RCs, the UPQC is able to achieve good performance under both nonlinear and unbalanced load conditions. Moreover, a simple grid frequency adaptive scheme is developed by using a first orderPadé’s approximation to maintain the same UPQC performance in spite of grid frequency deviations. Thanks to the simple control structure and reduced computation time of the Padé’s approximation, the proposed control strategy is significantly simplified compared to other grid frequency adaptive algorithms. The proposed control algorithm can be easily implemented with lowcost DSPs such as TMS320F2812 of Texas Instruments. Finally, its feasibility is verified through various experimental tests.
II. PROPOSED CONTROL STRATEGY FOR THE UPQC
Fig. 1
shows the configuration of a threephase UPQC connected with a utility grid and loads. The UPQC consists of two voltage source inverters connected backtoback through a common DClink capacitor, where one inverter is a shunt APF and the other inverter is a series APF. The series APF is connected in series between the supply and the load through a series transformer. Meanwhile, the shunt APF is connected in parallel with the loads through an inductor
L_{sh}
. An
LC
(
L_{f}
,
C_{f}
) filter is connected at the AC output voltage of the series APF to eliminate highfrequency switching noises. In
Fig. 1
, in order to deal with voltage and current related problems, the conventional control strategies require voltage sag/harmonic detectors and current/voltage controllers that must be designed properly to achieve good performance. As a consequence, a complex control system is often needed to fulfill the control objectives.
System configuration and traditional control strategy for UPQC.
To overcome the complexity of the conventional control approaches and to enhance the control performance of the UPQC, an improved control strategy is suggested where modified RCs are used, as shown in
Fig. 2
. It can be seen in this figure that the RC voltage controller is designed in the series APF to compensate the load voltage to be sinusoidal despite voltage distortions at the supply side. Meanwhile, a PI2RC current controller is developed in the shunt APF, so that the supply current is compensated to be balanced and sinusoidal in spite of current distortions/imbalances. The operating principles of the voltage and current controllers are explained in detail in the following sections.
Proposed control strategy for UPQC.
 A. Current Controller for the Shunt APF
If nonlinear loads are used in a system, as given in
Fig. 2
, the load current is composed of the fundamental component (
i
_{L1}
) and harmonic components (
i_{Lh}
) as follows:
In order to compensate the supply current (
i_{S}
) to be sinusoidal and inphase with the supply voltage (
v_{S}
), the traditional control methods regularly involve harmonic detection and current regulation stages
[6]
,
[7]
. In this paper, a simplified control method is used wherein the supply current reference
is directly generated to be sinusoidal and inphase with the supply voltage:
where
is the amplitude of the supply current reference, which is determined by the outer DClink voltage control loop.
This control method does not use a harmonic detector. Thus, the control performance of the shunt APF relies solely upon the current regulator. To achieve good compensation performance with the simplified current controller, this paper develops an advanced current controller with the aid of a PI controller and a modified RC. The traditional RC has characteristics similar to those of a bank of resonant controllers. It is able to simultaneously track a large number of harmonic currents/voltages
[19]
. A block diagram of the traditional RC is illustrated in
Fig. 3
and the transfer functions of the PI controller and the RC in the continuous time domain are expressed in (3) and (4), respectively.
where
K_{p}
and
K_{i}
are the proportional and integral gains of the PI controller, respectively,
T_{d}
is the time delay of the RC,
Q(s)
is the filter transfer function, and
K_{r}
is the RC gain.
Block diagram of the traditional RC.
Since the time delay
T_{d}
in (4) is selected to be the same as the fundamental period (
T_{p}
) of the supply voltage, the RC can compensate all of the harmonics (odd and even). However, it has a poor dynamic performance due to its long time delay
[19]
. To overcome this time delay problem,
T_{d}
is reduced six times to be
T_{d}
=
T_{p}
/ 6. Although the dynamic response is significantly improve, this solution is only effective with the (6
n
±1)th (
n
=1, 2, 3…) harmonic components
[24]
,
[25]
. Therefore, to achieve a fast transient response and effectiveness of the controller under abnormal load conditions, an enhanced current controller with two RCs that have a delay time of
T_{d}
=
T_{p}
/ 6 is suggested. The block diagram of the proposed PI2RC current controller is shown in
Fig. 4
, and the transfer functions of the two RCs, RC1 and RC2, are follows:
Block diagram of the proposed PI2RC current controller.
Fig. 5
presents the frequency response in (5) and (6) with a fundamental frequency of 50 Hz. In
Fig. 5
(a), the RC1 designed in the
dq
reference frame provides a high peak gain at the 6
n
th (
n
= 1, 2, 3…) harmonic orders, i.e., 300 Hz, 600 Hz, 900 Hz, and so on. Therefore, RC1 can effectively compensate (6
n
± 1)th (
n
= 1, 2, 3…) harmonics. Meanwhile, in
Fig. 5
(b), RC2 is designed to produce a high peak gain at the (6
n
3)th (
n
= 1, 2, 3…) (triplen) harmonic orders, (i.e., 150 Hz, 450 Hz, 750 Hz, and so on). Therefore, it is able to compensate the (6
n
3)th (
n
= 1, 2, 3…) harmonics. As a result, a combination of two RCs is sufficient to track all of the odd harmonics. Compared to the oddharmonic RC developed in
[21]
, the proposed RC provides a faster dynamic response due to the reduced time delay.
Frequency response of (a) RC1 and (b) RC2.
 B. Voltage Controller for the Series APF
Assume that the voltage available at the supply bus (
v_{S}
) is distorted and includes fundamental (
v
_{s1}
) and harmonic components (
v_{Sh}
) as follows:
Similar to the control of the shunt APF, a simple approach is used to determine the reference voltage for the series APF so that the reference load voltage is directly generated in the
dq
reference frame without a voltage sag detector or a harmonic detector as follows:
where
is the magnitude of the load voltage, which is a predetermined value. By generating the reference load voltage as in (8), the load voltage is always made to be sinusoidal with a predetermined constant magnitude of
.
In order to properly control the load voltage to follow (8), the proposed voltage controller is designed in the
dq
reference frame using a RC and a supply voltage feedforward loop. In fact, the harmonic voltages in (7) in a threephase system are mainly composed of the (6
n
±1)th (
n
= 1, 2, 3...) harmonic orders. Hence, only these harmonics are considered and compensated in the voltage controller of the series APF. As a result, RC1, with the transfer function given in (5), is adopted for the voltage controller of the series APF. In addition, by adding a supply voltage feedforward loop in the series APF control scheme in
Fig. 6
, the UPQC can effectively deal voltage sags without any additional voltage controllers.
Block diagram of the control scheme for the series APF.
III. FREQUENCY ADAPTIVE SCHEME FOR THE RC
For digital implementation, the transfer function of the PI controller and the RC in (3) and (5) are transformed into the discrete time domain by using the backward Euler discretization method as (9) and (10), respectively.
where
N
=
T_{p}
/ (6
T_{s}
) is the number of delay samples, which is an integer,
T_{s}
is the sampling period, and
z^{k}
is the phase lead term to compensate the phase lag caused by the plant
G_{P}(z)
.
As mentioned earlier, in practical systems, the grid frequency is not always constant, but may have small variations around its nominal value. For instance, with a nominal frequency of 50 Hz, power systems are regularly allowed to operate continuously with frequency deviations within the range from 49.550.5 Hz
[36]
. Then, if the grid frequency is different from the design frequency of the RC, the effectiveness of the RC is significantly diminished.
In order to maintain good performance of the RC despite frequency variations, a frequencyadaptive scheme is developed by using Padé’s approximation, and it is applied to the RC as shown in
Fig. 7
. Compared to the previous frequency adaptive schemes such as the FIR filter
[31]
, Linear or Lagrange interpolation
[23]

[35]
, Padé’s approximation is much simpler in structure, and it requires less computation. The other methods regularly need a high order function for an accurate approximation. However, a first or second order is sufficient with Padé’s approximation
[37]
.
Block diagram of the RC with frequency adaptive scheme.
To adapt to grid frequency variations, the proposed controller is composed of two parts: a phaselocked loop (PLL) and a fraction delay approximation algorithm. When the grid frequency changes, the grid frequency (
ω_{p}
) can be precisely detected through the PLL, whose algorithm is explained in
[38]
. Then, a fundamental period (
T_{p}
) is determined as
T_{p}
= 2
π
/
ω_{p}
and the number of delay samples,
N
, of the RC can be calculated as
N
=
T_{p}
/ (6
T_{s}
). Based on the number of delay samples
N
, the proposed RC can be implemented as (10). However, if N is a noninteger number due to grid frequency changes, the RC cannot be directly implemented in digital implementation. In order to solve this problem, the delay function
in (5) and (6) is modified as:
where
N_{i}
+
N_{fr}
=
N
, with
N_{i}
and
N_{fr}
being the integer and fractional parts of
N
, respectively.
Since
N_{i}
is an integer, the term is
can be easily implemented in the
z
domain as
z
^{Ni}
. Meanwhile, since
N_{fr}
is a fractional number,
cannot be directly implemented in the zdomain. Therefore,
is approximated by using a firstorder Padé’s approximation
[37]
:
Transferring
C(s)
into the zdomain by using backward Euler discretization, the delay function
C(z)
is described as:
Finally, the transfer function of the proposed RC in the
z
domain with the frequencyadaptive scheme is described as:
In order to investigate the effect of frequency variations on RCs,
Fig. 8
shows the frequency responses nearby the 6
^{th}
harmonics 300Hz at a nominal grid frequency of 50Hz for different kinds of RCs. These include the RC without a frequency adaptive scheme, the RC developed in
[30]
, the RC without fraction delay approximation, and the proposed frequency RC. In this figure, it is assumed that the actual grid frequency is changed to 49.5 Hz from the nominal grid frequency, 50 Hz, and the 6
^{th}
harmonic frequency is changed from 300 Hz (sixth of 50Hz) to 297 Hz (sixth of 49.5Hz). From
Fig. 8
, for the RC without a frequency adaptive scheme, the peak gain at 297 Hz is significantly reduced to 30 dB compared to the original peak gain (55 dB) because the peak gain remains at 300 Hz without compensation. Similarly, the peak gains of the other methods, except the proposed RC, also are not located at the changed frequency, 297 Hz. Therefore, the effectiveness of the RCs is dramatically degraded when the grid deviates from its nominal value (50 Hz). In contrast, the proposed RC with the frequency adaptive scheme has exactly the peak gain at the sixth of 49.5 Hz, so that the proposed control scheme can maintain a good performance regardless of grid frequency deviations.
Frequency response of RC with different frequency adaptive techniques.
IV. DESIGN OF REPETITIVE CONTROLLERS
 A. Design of the RC for the Series APF
In order to design the RC in (14), three components are considered: the filter
Q(z)
, the phase lead term
z^{k}
, and the RC controller gain
K_{r}
. Among these three components, the filter
Q(z)
, that is used to improve the system stability by reducing the peak gain of the RC at a high frequency range, has to be determined first. Afterward, the phase lead term
z^{k}
is designed to compensate the phase lag caused by the control plant to achieve better harmonic compensation performance of the RC. Finally, the controller gain of the RC,
K_{r}
is chosen based on the system stability condition in (17).
1) Selection of the filter Q(z): Q(z)
is used to improve system stability by reducing the peak gain of the RC at the high frequency range. There are two popular methods that have been used in previous studies to employ
Q(z)
: a closed unity gain
Q(z)
=0.95, and a zerophase LPF
Q
(
z
) = (
z
+ 2 +
z
^{1}
) / 4
[20]
,
[21]
. In this study, these two types of
Q(z)
are adopted, and the frequency responses of the RC for both types of
Q(z)
are plotted in
Fig. 9
in order to determine a suitable
Q(z)
for the RC. In
Fig. 9
(a), when
Q(z)
=0.95, the RC provides a high gain over the entire frequency range. As a result, the system becomes unstable due to the high gain at the high frequency region. In contrast, in
Fig. 9
(b), with
Q
(
z
) = (
z
+ 2 +
z
^{1}
) / 4, the gain of the RC is high at the low order harmonics. However, it reduces to significantly less than 0 dB at the high frequency range (higher than 2 kHz). It is wellknown that a low peak gain at the high frequency range can ensure a robust system. Furthermore, in contrast to the typical first order LPF, the zerophase LPF does not shift to the original position of the RC peak gain. Therefore, the use of this zerophase LPF does not affect the RC accuracy. Thus,
Q
(
z
) = (
z
+ 2 +
z
^{1}
) / 4 was chosen for this study.
Frequency response of the openloop transfer function of the PIRC controller with Q(z)=0.95 and (b) Q(z) = (z + 2 + z^{1}) / 4.
2) Determination of the Phase Lead Term z^{k}
: Because the control plant
G_{p}(z)
commonly acts a lowpass filter, which introduces some phase lag, a phase lead term
z^{k}
is needed to compensate the phase lag of
G_{p}(z)
, and k is selected to minimize the phase displacement of
G_{p}
(
z
)
z^{k}
, where the transfer function of inductor
L_{sh}
in the continuous and discrete time domains are given as:
Fig. 10
shows the frequency response of
G_{p}
(
z
)
z^{k}
with different values of
k
. From
Fig. 10
,
k
=5 is selected because it provides a minimum phase displacement near the dominant harmonics, such as the 5
^{th}
, 7
^{th}
, 11
^{th}
and 13
^{th}
, and the system stability is guaranteed up to the 37
^{th}
harmonic component at a frequency of 1.85 kHz. According to
[20]
, the phase displacement of
G_{p}
(
z
)
z^{k}
should not exceed the limitation [90°;90°] in order to ensure that the system is stable. Furthermore, to remove the effect of the delay time due to the digital control in the experimental implementation,
k
=6 is used.
Phase lag compensation with different values of k.
3) Determination of the Controller Gain K_{r}
: In order to investigate the stability condition of the RC and to determine the controller gain
K_{r}
, the tracking error of the RC with respect to the reference value is derived from
Fig. 3
as:
Let
H
(
z
) =
Q
(
z
) −
K_{r}z^{k}G_{p}
(
z
). Based on the small gain theorem
[19]
, the repetitive control system is sufficiently stable if the vector
H
(
e^{jωTs}
) is located within the unity circle. Consequently, the stability condition of the repetitive control system is given as:
ω
∈[0,
π
/
T_{s}
]; where
π
/
T_{s}
is the Nyquist frequency.
The loci of the vector
H
(
e^{jωTs}
) are plotted in
Fig. 11
with respect to different values of
K_{r}
and the controller gain
K_{r}
is selected based on the stability condition given in (17). It can be observed that the vector
H
(
e^{jωTs}
) is located inside the unity circle, i.e., the system is stable if
K_{r}
is less than 1.2. In fact, a large
K_{r}
offers a better steadystate performance as well as a faster response. However, it also limits the stability margin of the system. Therefore, in order to guarantee a sufficient stability margin,
K_{r}
=0.8 is selected.
Loci of the vector H(e^{jωTs}).
 B. Design of the RC for the Series APF
The design of the RC for the series APF is similar to that of the shunt APF. In terms of the filter
Q(z)
, the zero phaseshift LPF
Q
(
z
)= (
z
+ 2 +
z
^{1}
) / 4 is also selected.
The next step is to determine the phase lead term
z^{k}
to compensate the phase lag caused by
G_{p}(z)
. The plant of the series APF is the
LC
filter with the transfer functions in continuous and discrete time domains defined as;
The frequency response of
G_{p}
(
z
)
z^{k}
is illustrated in
Fig. 12
with different values of
k
. From
Fig. 12
,
k
=3 is chosen. This can minimize the phase displacement of
G_{p}
(
z
)
z^{k}
. Moreover, to remove the impact of the delay time due to the digital control,
k
=4 is selected in practice implementation.
Phase lag compensation with different values of k.
Similar to
Fig. 11
, the controller gain
K_{r}
for the RC in the series APF is also determined based on the loci of the vector
H
(
e^{jωTs}
) as shown in
Fig. 13
. From
Fig. 13
,
K_{r}
=1 is selected.
Loci of the vector H(e^{jωTs}).
V. EXPERIMENTAL RESULTS
In order to validate the effectiveness of the proposed control strategy, an experimental system was built in the laboratory as shown in
Fig. 14
. The system parameters for the whole system are given in the Appendix. The control strategy is implemented using a 32bit fixedpoint DSP (TMS320F2812 of Texas Instruments). The sampling and switching frequencies are set to 9 kHz so that
N
= 30 at a nominal grid frequency of 50 Hz. The supply voltage is generated by a Programmable AC Power Source (Chroma 61704), and a threephase diode rectifier is used as the nonlinear load. The total harmonic distortion (THD) values of the load voltage and the supply current are measured by a power analyzer (HIOKI 3193). The supply voltage
v_{Sa}
is programmed to have a total harmonic distortion (THD) of 8.61%, and the load current
i_{La}
is distorted due to a nonlinear load with a high THD of 25.2% that is caused by the threephase diode rectifier.
Experimental platform of threephase UPQC.
 A. SteadyState Performance of the Voltage and Current Harmonic Compensation
Fig. 15
shows the harmonic compensation performance of the UPQC by using the traditional PI controller in
Fig. 15
(a), which is one of the traditional controllers; the PI controller plus multiple resonant controllers in
Fig. 15
(b), which is one of the advanced controllers; and the proposed control strategy in
Fig. 15
(c). As shown in
Fig. 15
(a), by using only the PI controller, harmonic compensation cannot be achieved. The load voltage and the supply current are far from sinusoidal waveforms. On the other hand, even though the load voltage and the supply current are effectively compensated through the PI controller plus multiple resonant controllers and the proposed control methods in
Fig. 15
(b) and
15
(c), respectively, they have a small difference in their performance. As investigated in the RC characteristic, one single RC can simultaneously compensate a large number of harmonic components. Meanwhile, due to the long computation time of the resonant controller, the control method in
[17]
can add three resonant controllers with the maximum harmonic order up to the 19
^{th}
order. For this reason, the proposed control algorithm provides a better control performance compared to the PI controller plus multiple resonant controllers with lower values for the THD of the load voltage and supply current as shown in
Table I
. In addition, from
Table I
, the proposed control method needs a much shorter computation time compared to the multiple resonant controller solution. Therefore, the proposed control algorithm is simpler and more effective compared to the other control methods. These results verify the effectiveness of the proposed control strategy for voltage and current harmonics compensation.
Steadystate performance of the UPQC by using (a) PI controller, (b) PI3R controller, and (c) Proposed controller.
COMPARISON OF THE HARMONIC COMPENSATION PERFORMANCE AND CALCULATION TIME OF THE DIFFERENT CONTROL STRATEGIES
COMPARISON OF THE HARMONIC COMPENSATION PERFORMANCE AND CALCULATION TIME OF THE DIFFERENT CONTROL STRATEGIES
 B. Dynamic Response of the Current Harmonics Compensation under Load Changes
To demonstrate the fast dynamic response of the proposed control method for the UPQC under load variations, an experimental test on the UPQC with a load change is carried out. In this test, the supply voltage is the same as that in the steady state test, while the nonlinear load current has a step change from 70% load to the full load condition. The experimental results are shown in
Fig. 16
, where the load voltage, supply current, load current, and DClink voltage are plotted. From
Fig. 16
(a), it can be observed that the dynamic response of the traditional RC is very poor when the load changes. Even after a long period of time, about 160ms, the supply current has not settled down into the new steadystate condition (sinusoidal waveform). In contrast, by using the proposed RC, the supply current reaches the new steadystate condition in a short time, about 20ms. These results clearly verify the fast transient characteristic of the proposed RC. In
Fig. 16
, even though the DClink voltage does not recover quickly, the voltage reduction is very small (only 10 V), and it has no effect on the operation of the UPQC.
Dynamic response of the UPQC under load current change with (a) the traditional RC and (b) the proposed RC.
 C. Performance of the Proposed Control Strategy under Unbalanced and Nonlinear Loads
Fig. 17
(a) shows experimental result of the UPQC by using the RC introduced in
[24]
under nonlinear and unbalanced load condition, where a singlephase diode rectifier is connected between phases “a” and “b” to create an unbalanced load condition. In
Fig. 17
(a), it can be observed that both the load voltage and the supply currents cannot be compensated to be sinusoidal because the RC developed in
[24]
only tracks the (6
n
± 1)th (
n
= 1, 2, 3…) harmonics. As a result, the RC cannot deal with the triplen harmonics generated by the unbalanced load. Therefore, the RC in
[24]
cannot provide good harmonic compensation performance under unbalanced and nonlinear loads. In contrast, as presented in
Fig. 17
(b), by using the proposed control algorithm, the load voltage and the supply currents are effectively compensated to be sinusoidal and balanced even though the load currents are distorted and unbalanced. This is because the proposed current controller is developed to track the (6
n
3)th (
n
= 1, 2, 3…) (triplen) along with the (6
n
± 1)th (
n
= 1, 2, 3…) harmonics with two RCs. As a result, it can effectively compensate all odd harmonic currents generated by loads. These results verify the feasibility of the proposed control strategy. It can effectively compensate harmonic currents generated from unbalanced load and nonlinear loads.
Experimental results of the UPQC under nonlinear and unbalanced load conditions using (a) the RC deveoped in [24] and (b) the proposed RC.
 D. Performance of the Voltage and Current Harmonic Compensation under Grid Frequency Deviations
In
Figs. 15

17
, the UPQC with the proposed control strategy was shown to provide good compensation performance at a nominal grid frequency of 50 Hz. However, in practice, the grid frequency is not always constant, but may have small variations around the nominal value.
Fig. 18
shows the effects of grid frequency deviations without the frequencyadaptive scheme. The performance of the UPQC at a grid frequencies of 49.5 Hz and 50.5 Hz are shown in
Figs. 18
(a) and
18
(b), respectively. As can be seen, under the condition where the frequencyadaptive scheme is not adopted, the performance of the UPQC significantly deteriorates when the grid frequency deviates from the nominal frequency of 50Hz. In contrast, as shown in
Fig. 19
, thanks to the effectiveness of the frequencyadaptive scheme, the compensating performance of the UPQC does not deteriorate despite the grid frequency deviations. The load voltage and the supply current are still compensated to be sinusoidal with very low THD values.
Experimental results of UPQC without adaptivefrequency scheme at (a) 49.5 Hz, (b) 50.5 Hz.
Experimental results of UPQC with adaptivefrequency scheme at (a) 49.5 Hz, (b) 50.5 Hz.
Table II
shows a summary of the THD values for the load voltage and the supply current both with and without the frequencyadaptive scheme. As indicated in
Table II
, under grid frequency changes, the good performance of the UPQC is difficult to maintain without the frequencyadaptive scheme. In contrast, under the proposed frequencyadaptive scheme, the THD values of the load voltage and the supply current are kept extremely low. They are less than 1% and 2%, respectively, and are completely compliant with the IEEE 5191992 standards [39].
PERFORMANCE OF THE UPQCWITH AND WITHOUT THE FREQUENCYADAPTIVE SCHEME
PERFORMANCE OF THE UPQCWITH AND WITHOUT THE FREQUENCYADAPTIVE SCHEME
VI. CONCLUSION
In this paper, a simplified UPQC control system was proposed by using a modified RC which has a fast transient response and grid frequency adaptive capability along with excellent steadystate performance. The UPQC with the proposed control approach is able to effectively compensate both the load voltage and the supply current to be sinusoidal regardless of voltage distortions in the supply side and nonlinear/unbalanced loads. In addition, owing to the frequencyadaptive scheme in the RC, an excellent compensation performance of the UPQC is maintained in spite of grid frequency deviations. The whole control strategy was implemented using a TMS320F2812 DSP and the effectiveness of the proposed control method was verified through experimental results. They show that he load voltage and the supply current are compensated to be sinusoidal, with THD values of less than 1% and 2%, respectively, in all test cases. Despite its simplified controller configuration, the proposed control method provides a better control performance compared to other control strategies.
Acknowledgements
This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF20100025483).
BIO
QuocNam Trinh was born in Vietnam, in 1985. He received his B.S. degree in Power Engineering from the Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2008, and his Ph.D. degree in Electrical Engineering from the University of Ulsan, Ulsan, Korea, in 2014. Since August 2014, he has been with the Energy Research Institute @ NTU, Nanyang Technological University, Singapore, as a Postdoctoral Research Fellow. His current research interests include active power filters, harmonic compensation, distributed generation, and gridconnected inverters.
HongHee Lee received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Seoul National University, Seoul, Korea, in 1980, 1982, and 1990, respectively. From 1994 to 1995, he was a Visiting Professor at Texas A&M University, College Station, TX, USA. He has been a Professor in the School of Electrical Engineering, Department of Electrical Engineering, University of Ulsan, Ulsan, Korea, since 1985. He is also the Director of the Networkbased Automation Research Center (NARC), University of Ulsan, which is sponsored by the Ministry of Trade, Industry and Energy, Korea. His current research interests include power electronics, networkbased motor control, and renewable energy. Dr. Lee is a member of the Institute of Electrical and Electronics Engineers (IEEE), the Korean Institute of Power Electronics (KIPE), the Korean Institute of Electrical Engineers (KIEE), and the Institute of Control, Robotics and Systems (ICROS).
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