5. SIMULATION AND EXPERIMENTAL RESULTS
To verify performance of the proposed active filter and its voltage balancing control
algorithm, simulation and experiment were conducted. In the simulation, the proposed algorithm
was simulated using Pspice program and numerical calculation. In hardware implementation, a 3level flying capacitor based active filter has been constructed using the Insulated Gate Bipolar
Transistors (IGBTs). The controller was designed based on a digital signal processor control
board (TMS320C32PCMA) along with a sinusoidal pulse-width modulation (SPWM). The
system’s specifications are as follows:
-
AC source
: vs = 220 V, f = 60 Hz,
-
Nonlinear load
: RL = 1 Ω, CL = 2 mF, and three-phase diode rectifier
-
Active filter
: Lf = 1 mH, Cdc = 8.2 mF, and Rf = 1mΩ, and fAF = 12 kHz
5.1 SIMULATION RESULTS
5.1.1 Control Algorithm
To discuss a control algorithm, the design procedures outlined were described in Chapter
4. The operating principle of the controller has been verified through the following simulation
steps.
Fig. 5.1 shows the source voltage and the current waveforms of a three-phase diode
rectifier. The rectifier is connected to 1 Ω resistor along with a capacitor of 2 mF. The load
current contains a lot of harmonic components in which are generated by the nonlinear load.
These currents, iLa, iLb, and iLc, are an example of the waveshape that activates the research
5. SIMULATION AND EXPERIMENTAL RESULTS
104
challenge for the active filter. To derive compensating references to the active filter, three-phase
vectors are transformed into α-β orthogonal coordinates. This transformation is useful for
determination of instantaneous reactive power.
Fig. 5.2 shows the derivation process of the compensating current references from the
instantaneous active and reactive powers. Since the instantaneous powers, pL and qL, are
decomposed into instantaneous real and imaginary powers, the ac components related to
harmonic current are filtered to be separated from the decomposed instantaneous power. Finally,
the compensating reference currents, iCa*, iCb* and iCc*, are derived from (4-6).
iLαα
iLββ
iLc
iLb
iLa
vsββ
vsαα
vbs
vas
vcs
Fig. 5.1 Calculation of source voltage and load current with α-β orthogonal coordinates.
5. SIMULATION AND EXPERIMENTAL RESULTS
105
iCa*
iCαα
iCββ
pC*
q C*
pL
qL
Fig. 5.2. Calculation of current commands from instantaneous reactive power.
Fig. 5.3 shows the compensated source voltage and current waveforms along with their
control signals. The generated control signals for the active filter create current references that
will cancel the harmonics in the load current. The current references are derived from the
calculation based on the instantaneous power theory. It is evident that the derived current
references are correct to ensure a dynamic identification of load harmonics. For simplification, a
switching frequency of 1 kHz was used to reduce a computer ruing time. However, in practice,
increasing the active filter operating frequency helps to get better compensating current
waveforms.
Fig. 5.4 shows the simulated waveforms of load currents of the diode-rectifier iLa, the
active filter iCa, and the ac source, ias. It was observed that the source current ias is purely
sinusoidal and the source voltage is almost distortion free. Thus, it indicates that the proposed
control algorithms perform very well under nonlinear load conditions.
5. SIMULATION AND EXPERIMENTAL RESULTS
106
ias
vas
A-leg upper switch gate signals
A-leg control signals
A-leg Modulation signals
Fig. 5.3. Compensated source voltage and current waveforms
and their control signals.
iLa
iCa
Uncompensated ias
Compensated ias
Fig. 5.4. Simulation results of a compensated source current.
5. SIMULATION AND EXPERIMENTAL RESULTS
107
5.1.2 Performance Evaluation
To evaluate the impact of an active filter, the compensated harmonic spectrum of ac
current was simulated under frequency domain, which is shown in Fig. 5.5. This indicates that
the harmonic current components of ias are dramatically reduced by the active filter. Furthermore,
in a three-phase system, the most significant harmonics were 5th (300 Hz) and 7th (420 Hz).
There are no triple harmonics like 3rd, 9th, 15th, etc. From Fig. 5.5, the total harmonic distortion
(THD) of the source current before and after compensating is summarized in Fig. 5.6. As a
result, the reduction of current harmonics was achieved from 29.94% to 2.0%.
Fig. 5.7 depicts the performance of the proposed controller with proportional-integral (PI)
gains. It is important to note that these simulations were for steady and transient state operations
with/ and without a controller for voltage balancing. Fig. 5.7(a) shows the simulation results of
overall operations with a controller. The only difference is in the first half period after start-up.
Fig. 5.7(b) shows a dynamic response of the controller associated with voltage balancing. It was
seen that some error was observed between iCa* and iCa. In spite, of them the active filter well
followed the current reference. Fig. 5.7(c) shows the voltage waveform of the active filter
without a PI controller. This result indicates that the voltage unbalance was observed to the flying
capacitor. Therefore, the effect of use of a PI voltage controller was major factor when the flying
capacitor was adapted to the active power applications.
5. SIMULATION AND EXPERIMENTAL RESULTS
108
The harmonic current components of ias are
dramatically reduced.
The active filter current, iCa,
compensates to ias.
A lot of the harmonic components
were observed to iLa.
Fig. 5.5. Compensated harmonic spectrum under frequency domain.
350
Ias
ILa
Ica
300
Current (A)
250
200
150
100
50
0
60
300
420
660
780
Frequency (Hz)
Fig. 5.6. THD comparison under active filtering.
5. SIMULATION AND EXPERIMENTAL RESULTS
109
ica
iLa
ica
ica*
iLa
ias
(a) Overall simulation results of the controller
ica
ica*
iLa
ica
(b) Dynamic responses of the controller with voltage balancing gains.
5. SIMULATION AND EXPERIMENTAL RESULTS
110
ica
ica*
iLa
iCa
(c) Dynamic responses of the controller without voltage balancing gains.
Fig. 5.7. Simulation results of an active filter with/and without a proportional-integral (PI)
voltage balancing controller.
5.1.3. Discussion
With various simulation works, a number of important observations were obtained
through the proposed active filter and its voltage balancing controller.
1) The voltage balancing controller absolutely contributes to make possible a successful
operation of the flying capacitor based active filter.
2) The proposed active filter along with a new phase-shifting controller reduced the
source current THD value.
3) The AF capacity is highly correlated with the THD of the load currents.
4) Simulation results were performed to develop some guidelines for active filter ratings
and size, by evaluating any desired level of cancellation.
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111
5.2 EXPERIMENTAL RESULTS
5.2.1. Test Descriptions
To demonstrate the effectiveness of the proposed control algorithm, a laboratory
prototype active filter using a 3-level flying capacitor converter was implemented. The
component values are identical to those used for the simulation as shown in Table 5.1. The threelevel voltage source converter used in the active filter was designed to compensate harmonics
control. This converter is connected to the dc capacitors and will cancel the harmonics from the
nonlinear load. The converter was implemented with an Insulated Gate Bipolar Transistors
(IGBTs). To realize the control algorithms shown in Fig. 4.9, a digital signal processor was used
to calculate the compensating current references. The algorithms are coded in the DSP board.
Table 5-1. System parameters of the experimental prototype
Source voltage
220 V
DC bus voltage
750 V
Source frequency
60 Hz
Switching frequency
12 KHz
Interface inductor
1 mH
DC capacitor
8200 µF
5.2.2. Experimental Verification
Fig. 5.8 shows the experimental results of the source voltage and the load currents
without an active filter. Since the three-phase rectifier, as a nonlinear load, is connected to ac
mains, the problem with nonlinear loads is their non-sinusoidal currents, iLa, iLb, and iLc. These
currents were observed with two short bursts of 2 – 3ms for each half cycle. They fed to the
power system so that it degrades power quality. In contrast, sinusoidal source currents shown in
Fig. 5.9 were obtained by using an active filter. With an active harmonic filter, the harmonic
distortion was significantly reduced. These experimental results are consistent with that of
simulation results in Chapter 4.
5. SIMULATION AND EXPERIMENTAL RESULTS
112
vas
500 V/div
iLa
50 A/div
iLb
50 A/div
iLa
50 A/div
5 ms/div
Fig. 5.8. Experimental results of the source voltage and the load currents
without an active filter.
vas
500 V/div
ias
50 A/div
ibs
50 A/div
ics
50 A/div
5 ms/div
Fig. 5.9. Experimental results of the source voltage and load currents
with an active filter.
5. SIMULATION AND EXPERIMENTAL RESULTS
113
Fig. 5.10 shows the compensated source voltage and current waveforms under high
impedance loads. The compensated source currents were nearly balanced, by injecting the
compensating harmonic components to the nonlinear load to improve power quality. However,
at the beginning of design stage, the active filter should be considered a certain level of
harmonics.
On the other hand, an active filter should be operated at any conditions to back up the
maximum harmonic compensation to the three-phase line. For example, even the only one phase
load current generates harmonics and two phase load currents are zero, (iLb = 0 A and iLc = 0 A),
as one of the worst operation cases, the active filter should operate with the only one phase load
current. Fig. 5.11 shows the compensated source voltage and current waveforms under
unbalanced load conditions. With the proposed controller, the active filter provides the maximum
current of 50 A to iLa.
vas
500 V/div
iLa
50 A/div
iLb
50 A/div
iLa
50 A/div
5 ms/div
Fig. 5.10. Compensated source voltage and current waveforms under high impedance load
conditions.
5. SIMULATION AND EXPERIMENTAL RESULTS
114
vas
500 V/div
iLa
50 A/div
iLb = 0 A
iLc = 0 A
50 A/div
50 A/div
5 ms/div
Fig. 5.11. Compensated source voltage and currents under unbalanced load conditions.
5.2.3 Dynamic Responses
To inspect a dynamic performance of the controller under transient states, the active filter
was tested under the load variation suddenly changes. Fig. 5.12 shows dc link voltage transitions
while the load suddenly linked to the main supply. The voltage across dc link capacitors slowly
decreases down to 720 V from 750 V. Its voltage drop comes from the inductors and main
devices.
On the other hand, Fig. 5.13 shows the dc capacitor voltage transition while the load
suddenly disconnected from the source. At this case, the voltage slowly increases up to 750 V
from 720 V. The rise of voltage depends on the capacitor capability. Even though the dc link
voltage takes 0.2 seconds to reach steady state, this is acceptable due to the fact that changes in
the flying capacitor are slowly decreasing by the PI gains of the voltage controller. The steady
state error is not exactly zero due to the window in the implementation of the voltage rising error.
If the error is within this window, the controller does not generate a correction signal.
5. SIMULATION AND EXPERIMENTAL RESULTS
115
vdc
200 V/div
iLa
50 A/div
0.1 s/div
Fig. 5.12 DC link voltage transitions while the load is suddenly connected to the source.
vdc
200 V/div
iLa
50 A/div
0.1 s/div
Fig. 5.13 DC link voltage transitions while the load is suddenly disconnected from the source.
5. SIMULATION AND EXPERIMENTAL RESULTS
116
Fig. 5.14 shows the soft-charging process of the dc link voltage. During the start-up, the
dc link voltage is slowly increasing with use of a current limiter such a magnetic circuit breaker
(MC). It is possible to make a charging balance between capacitors. In Fig. 5.14, the dc link
voltage reached the steady state value and stayed at its reference voltage. Thus, it indicates that
the proposed voltage controller is useful for the active filter applications.
vdc
200 V/div
iLa
50 A/div
0.1 s/div
Fig. 5.14. DC link voltage transitions during start-up.
5.3 CONCLUSION
The performance of a flying capacitor based active filter is highly dependant on the
voltage balancing between flying capacitors. Without voltage stabilization to the capacitor, it is
impossible to compensate harmonics that degrade the power quality. In this chapter, a new
voltage controller has been proposed and implemented for their voltage balancing in conjunction
with overall control algorithm. From the simulation and experiment, it is achieved that the
5. SIMULATION AND EXPERIMENTAL RESULTS
117
proposed controller can compensate the source current to be sinusoidal and balanced to maintain
the constant capacitor voltage. With relation to transient responses, the controller at transient and
steady state conditions was also characterized by the interaction between the control feasibility
and influences of the active filter.
In further work, a control scheme will be extensively analyzed and evaluated for the
static var applications.
5. SIMULATION AND EXPERIMENTAL RESULTS
118