INTRODUCTION
One of the electrical system adapter structures is back to back inverter. According
to the controlling structure, back to back inverters might have different operations
in compensation. For example, they can operate as shunt and series active filters
to simultaneously compensate the load current, harmonics and voltage oscillations.
This is called unified power quality conditioner (Akagi et
al., 1984; Aredes and Watanabe, 1995).
The duty of UPQC is decreasing the disturbances which effect the operation of the sensitive load. UPQC is able to compensate the swell, sag and unbalanced voltage, current and voltage harmonics and reactive power, through shunt and series voltage source inverters. Voltage source inverter has to generate sinusoidal voltage with the frequency, amplitude and the phase determined by the control system. As shown in Fig. 1, in order to clear the switching oscillation, a passive filter is applied at the output of each inverter. At the output of shunt inverter, high pass second order LC or first order RC filter is allocated and at the output of series inverter, low pass second order LC or resonance filter is allocated.
UPQC controller provides the compensation voltage (v*_{f}) through the UPQC series inverter and provides conditioning current (i*_{f}) through the shunt inverter by instantaneous sampling of load current and source voltage and current. Resulted reference current are compared with shunt inverter output current (i_{fa}, i_{fb} and i_{fc}), in a hysteresis type PWM current controller. Then, the required controlling pulses are generated. Required compensation current is generated by inverter applying these signals to the inverter. Resulted reference voltages are compared with a triangular wave form and required controlling pulses are generated to be applied to series voltage source inverter switches.
In this study, a suitable controlling method has been selected to simulation and the rating of series and shunt inverters has been calculated through loading calculations of these inverters applying phasor diagram to increase the design accuracy.
MATERIALS AND METHODS
This study is consisted of three main parts: selecting the controlling method, controller design, series and shunt inverters loading. The controller design section has three subsections: shunt inverter control, DC link control and series inverter control. Theses parts have discussed and finally the simulation results have been introduced.
Selecting the controlling method: UPQC is vastly studied by several
researches as an infinite method for power quality conditioning (Akagi
and Fujita, 1995; Peng et al., 1998; Fujita
and Akagi, 1998; Chen et al., 2000; Hu and
Chen, 2000). Different UPQC controlling methods can be classified in three following
classes: timedomain controlling method, frequencydomain controlling method
and new techniques. Furrier method is one of the methods can be named as frequencydomain
methods. The methods such as PQ theory, instantaneous reactive power, algorithms
based on the synchronous dq reference frame, instantaneous power balance method,
balanced energy method, synchronous detection algorithm, direct detection algorithm
and notch filter based controlling method are some can be mentioned for timedomain
methods. Dead beat control, space vector modulation and wavelet conversion are
some of the new techniques (Mariun et al., 2004).
Three general standards considered to select the controlling method are load characteristics, required accuracy and application facility. All methods end in to similar results when the reference signal is calculated under balanced and sinusoidal conditions where each ends in to different results under unbalanced and non sinusoidal conditions. Dead beat controlling method presents the best operation among the others but more expense should be paid for its calculations.
Among the introduced methods the reference frame methods seem to be more appropriate. The fact is that it needs sinusoidal and balanced voltage and is not sensitive to voltage distortions and is relatively simple. In result, the response time of the control system shortens. So it’s prior to utilize the synchronous reference frame theory in UPQC controlling circuit.
CONTROLLER DESIGN
The control system of proposed system is shown in Fig. 1 which is comprised of three following parts:
• 
Shunt inverter control 
• 
DC link voltage control 
• 
Series inverter control 
Shunt inverter control: Figure 2 shows the UPQC shunt
inverter controlling block diagram using synchronous reference frame theory
where the sensitive load currents are i_{la}, i_{lb} and i_{lc}.
The measured currents of load are transferred into dq0 frame using sinusoidal functions through dq0 synchronous reference frame conversion. The sinusoidal functions are obtained through the grid voltage using PLL. Here, the currents are divided into AC and DC components.
The active part of current is i_{d} and i_{q} is the reactive
one. AC and DC elements can be derived by a low pass filter. Controlling algorithm
corrects the system’s power factor and compensates the all current harmonic
components by generating the reference current as Eq. 2:

Fig. 1: 
Overall configuration and control of proposed system 

Fig. 2: 
Shunt inverter control block diagram 
Here, system’s current are:
Switching losses and the power received from the DC link capacitors through the series inverter can decrease the average value of DC bus voltage. Other distortions such as unbalance conditions and sudden changes in load current can result in oscillations in DC bus voltage.
In order to track the error between the measured and desired capacitor voltage
values, a PI controller is applied. The resulted controlling signal is applied
to current control system in shunt voltage source inverter which stabilizes
the DC capacitor voltage by receiving required power from the grid. Δi_{dc},
the output of PI controller is added to the q component of reference current
and so the reference current would be as Eq. 4:
As shown in Fig. 4, the reference current is transferred into abc frame through reverse conversion of synchronous reference frame. Resulted reference current (i*_{fa}, i*_{fb} and i*_{fc}) are compared with the output current of shunt inverter (i_{fa}, i_{fb} and i_{fc}) in PWM. Now, the current controller and the required controlling pulses are generated. Required compensation current is generated by inverter applying these signals to shunt inverter’s power switch gates.
DC link voltage control: A PI controller is used to track the error
exists between the measured and desired values of capacitor voltage in order
to control the DC link voltage as Fig. 3 (Ghosh
and Ledwich, 2001).
This signal is applied to current control system in shunt voltage source inverter
in a way that the DC capacitor voltage is stabilized by receiving the required
active power from the grid. Correct regulation of proportional controller’s
parameter plays an important role in DC voltage control system’s response.
Too much increase in proportional gain leads to instability in control system
and too much reduction decreases the responding speed of control system. Integral
gain of controller corrects the steady state error of the voltage control system.

Fig. 3: 
DC link voltage control block diagram 

Fig. 4: 
Series inverter control block diagram 
If this gain value is selected large, the resulted error in steady state is corrected faster and too much increase in its value ends in overshoot in system response.
Series inverter control: Sinusoidal voltage controlling strategy of
load is generally proposed to control the series part of UPQC. Here, the series
part of UPQC is controlled in a way that it compensates the whole voltage distortions
and maintains load voltage 3phase balanced sinusoidal. In order to reach this,
the synchronous reference frame theory is applied (Hu and
Chen, 2000).
In this method the desired value of load phase voltage in d axis and q axis is compared with the load voltage and the result is considered as the reference signal.
The controlling circuit of series inverter is shown in Fig. 4. SPWM method is used to optimize the response of series inverter.
SERIES AND SHUNT INVERTERS LOADING
Generally, the injected voltage has the same phase with the source voltage
when there is balanced voltage source. So, series inverter usually consumes
active power. If there is (same phase) injection, UPQC is compensated with the
least voltage (Basu et al., 2007). Following figures
explain the UPQC operation in system’s main frequency.
The index 1 presents the variable related to the situation faced before the
voltage drop occurrence and index 2 presents the situation faced after the voltage
drop occurrence. V_{L} is the voltage of load and V_{o} is the
load nominal value in pu V_{S} is the source voltage and I_{S}
is the source current. I_{L} presents the load current which has the
power factor of cosφ. I_{o} is the nominal value of load current
in p.u and I_{C} is the current injected by shunt inverter.

Fig. 5: 
Phasor diagram of shunt and series inverters loading 
When the voltage and current of the system have the same phases, the transferring
power of series inverter is completely active because of the operation of shunt
inverter (Basu et al., 2007). As it is obvious
in Fig. 5, shunt inverter current increases by voltage drop
occurrence. The reason is the consumption of active power by series inverter
through shunt inverter. When the voltage drops in grid, the series inverter
should compensate voltage drop to maintain the voltage in desired value. This
injected voltage and source current have the same phases. So, the series inverter
just transfers the active power.
As it’s obvious in Fig. 5, the shunt inverter receives
active power from the grid in addition to reactive power injection, as voltage
drops. This power is the one that series inverter requires to inject to the
grid in order to compensate voltage drop and it is obtained from the shunt inverter
through the DC link.
According to the vector diagrams of Fig. 5 following term can be mentioned for each phase:
For load current it can be mentioned that:
Assuming that, the UPQC has no losses it can be noted that the electrical power of load side would not change passing the UPQC and will have the same value in the source side.
As voltage drops V_{S2} is less than V_{S1} (V_{S2}<V_{S1}). If x is the voltage drop value in pu:

Fig. 6: 
Comparison of VA loading for series inverter of UPQC at different
power factor and p.u voltage sag values 
Following relation should be valid to have the constant active power in both load and source sides:
where, I_{S2} can be expressed as follow:
So, the nominal power of series inverter (S_{seinv.}) is as follow:
The current injected by shunt inverter in p.u is:
So, the nominal power of shunt inverter (S_{shinv.}) is:
Adding the nominal powers of series and shunt inverters, the nominal power of UPQC is obtained.
Results shown in Fig. 6 present that the loading of series
inverter is similar during low voltage drops for different power factors and
is the function of load power factor in high voltage drops.

Fig. 7: 
Comparison of VA loading for shunt inverter of UPQC at different
power factor and p.u voltage sag values 
If the power factor is high the loading ratio of series inverter is high too.
Finally, the maximum loading occurs for unit power factor.
Results shown in Fig. 7 present that in shunt inverter, voltage drop value is the function of power factor and if the power factor is low, the loading is high which seems logical. This is because of the fact that if power factor is low, the shunt inverter should inject more current to compensate the power factor. For high values of voltage drop, the loading of the shunt inverter greatly increases which is because of the fact that series inverter requires more current to compensate the voltage drop. This current is provided by shunt inverter.
RESULTS AND DISCUSSION
In this study, power circuit is modeled as a 3phase 3wire system with a non linear load comprised of RC load which is connected to grid through 3phase diode bridge. Circuit parameters used in simulation are shown in Table 1.
The simulated load is a RC diode nonlinear 3phase load which imposes a non sinusoidal current to grid with more than 40% THD. Load current is shown in Fig. 8.
In Fig. 9 the source current, injected current and total
harmonic distortion before and after being compensated by shunt inverter are
shown. Shunt inverter is activated in 0.04 sec of operation. Immediately, the
source current is corrected. The results shown in Fig. 9 present
that the shunt part has been able to correct the source current appropriately.
Also, the THD of load current is reduced to 5 from 40% of source current.

Fig. 8: 
Nonlinear load current (A) 
Table 1: 
Circuit parameters 

Figure 10 shows the source side voltage, load side voltage
and the voltage injected by the series inverter to simulate swell and sag of
the voltage. As shown in Fig. 10 the voltage distortions imposed to load from
the grid are properly compensated by series inverter. In this simulation, series
inverter operates at 0.02 sec and voltage source faces with 100 V voltage sag.
A voltage swell with 50 V voltage peak occurs in 0.08 sec. Simulation results
show that the load voltage is constant during the operation of UPQC series inverter.
DC link voltage is shown in Fig. 11. In this simulation,
series and shunt inverters start to operate at 0.02 sec. As it is seen, capacitor
voltage is decreasing until this moment. By operating shunt inverter, the capacitor
voltage increases and reaches to the reference value (600 V). At 0.04 sec of
operation voltage sag with 100 V amplitude occurs in source voltage. The average
value of capacitor voltage drops about 10 V occurring this voltage sag and faces
with small oscillations in lower values. At 0.08 sec of operation voltage swell
with about 50 V amplitude occurs at 0.08 sec of operation. The average value
of capacitor increases about 15 V occurring this swell and faces with small
oscillations in voltages around 600 V. Figure 11 shows the
exact operation of control loop of DC link capacitor voltage.

Fig. 9: 
(a) Source current, (b) Injected current and (c) Source current
THD, before and after compensation 

Fig. 10: 
(a) Source voltage, (b) Injected voltage and (c) load voltage,
before and after compensation 

Fig. 12: 
Power factor correction 
RL load with 6
kW active power and 6 kVAR reactive power is applied in simulation to study
how reactive power is compensated by shunt inverter. Simulation results show that the phase difference between voltage and current
is cleared by shunt inverter operation. In other words, UPQC compensates the
reactive power with 0.7 power factor and so there is unit power factor in source
side of system. Actually, by operating UPQC, required reactive power is provided
via., UPQC.
Figure 12 shows the load current and voltage. As it is shown,
load current phase leads voltage phase initially. At 0.06 sec of operation and
operating shunt inverter the phase difference between voltage and current gets
zero.
Comparison of this study results with related studies, indicates that the proposed system compensates voltage and current distortions accurately and the response time of the control system is relatively low and also the proposed control system is simply applicable.
CONCLUSION
In this study Unified Power Quality Conditioner (UPQC) is designed and simulated through synchronous reference frame theory. Simulation results show the proposed system’s ability in voltage distortion, reactive power and current harmonics compensation. PI controller balances the power between series and shunt inverters by stabilizing DC link voltage.
Loading of shunt and series inverters are being operated through phasor method which greatly assists the proper designation of inverters. The operation of proposed system is analyzed using MATLAB/SIMULINK software. Simulation results confirm the correct operation of the proposed system.