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CHAPTER 4
FUZZY LOGIC BASED PWM TECHNIQUE FOR
UNBALANCED VOLTAGE CONDITION
The electric power distribution systems are unbalanced due to
untransposed distribution lines and unbalanced loads. Also the loads on the
power system vary from time to time. Hence there is the need to design an
active power filter, which is capable of maintaining the THD limit within the
IEEE norms under variable load conditions. This chapter presents a fuzzy
logic based PWM current control technique which performs well under
unbalanced and variable load conditions since the controller do not need an
accurate mathematical model; it can work with imprecise inputs and can
handle nonlinearity. The performance of the controller is tested for
unbalanced voltage and changing load condition. Also, a fuzzy logic-based
controller is developed to control the DC voltage of the capacitor.
4.1
PROPOSED CONTROL STRATEGY
The schematic diagram of the proposed fuzzy logic based Shunt
Active Filter is shown in Figure 4.1.
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Figure 4.1 Schematic diagram of Shunt Active Filter
The active power filter consists of three principal parts, namely, the
voltage source inverter, DC energy storage device (Cf) and coupling
inductance (Lf). The inverter is used to charge and to discharge the capacitor
in order to provide the required compensation current, the capacitor is used to
store energy and the inductance is used to smoothen the ripple of the
harmonic current injected by active power filter. The AC supply provides the
required active power and the capacitor of active power filter provides the
reactive power for the load.
In the proposed work, a fuzzy-logic based PWM control technique
is used to generate the gating signals. Switching signals obtained, after proper
amplification and isolation are given to the switching devices of the PWM
converter. The DC link capacitor voltage is maintained constant by a fuzzy
logic controller.
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The proposed fuzzy logic based intelligent control offer a very
satisfactory performance, without the need of a detailed mathematical model
of the system.
4.1.1
Development of Fuzzy Based Current Controller
Figure 4.2 Schematic diagram of fuzzy controller
The block diagram representation of the proposed FLC is shown in
Figure 4.2. The FLC has two input signals, namely, current error and change
in current error. Five membership functions are assigned for both input and
output. Figure 4.3 shows the membership functions for input and output
variables. Triangular membership function is used to represent the input and
output variables. With two input variables and with five labels for each
variable there are 25 input label pairs. The rule table relating each of the 25
input pairs to the respective output label is given in Table 4.1.
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Figure 4.3
Membership functions for input and output variables for
Current Control
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Table 4.1 Fuzzy Rule Base for current Control
e
NL
NM
EZ
PM
PL
NL
PB
PM
PM
PM
PB
NM
PB
PM
PL
PM
PB
EZ
PVB
PM
PVL
PM
PVL
PM
PB
PM
PL
PM
PB
PL
PB
PM
PM
PM
PB
de
4.1.2
Fuzzy Logic Based Voltage Control
The DC side of the inverter is connected to a capacitor. The DC
capacitor provides a constant DC voltage and the real power necessary to
cover the losses of the system. In the steady state, the real power supplied by
the source should be equal to the real power demand of the load plus a small
power to compensate the losses in the active filter. Thus, the DC capacitor
voltage is maintained at a reference value. A fuzzy logic controller is applied
to maintain the constant voltage across the capacitor by minimizing the error
between the capacitor voltage and the reference voltage.
To design the FLC, variables which can represent the dynamic
performance of the system to be controlled should be chosen as the inputs to
the controller. The error (e) and the rate of error (de) are taken as controller
inputs and the real power (Preg) requirement for voltage regulation is taken as
the output of the FLC. The input and output variables are represented by
seven linguistic variables, namely, NL(Negative Large), NM (Negative
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Medium), NS (Negative Small), ZE (Zero), PS (Positive Small), PM (Positive
Medium) and PL (Positive large). Membership functions of the input and
output variables are shown in Figure 4.4. The fuzzy IF-THEN rules formed
for controlling the DC voltage are given in Table 4.2.
Figure 4.4
Membership functions for the input and output variables
for Voltage Control
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Table 4.2 Fuzzy Rule Base for voltage control
e
NL
NM
NS
ZE
PS
PM
PL
NL
NL
NL
NL
NL
NM
NS
ZE
NM
NL
NL
NL
NM
NS
ZE
PS
NS
NL
NL
NM
NS
ZE
PS
PM
ZE
NL
NM
NS
ZE
PS
PM
PL
PS
NM
NS
ZE
PS
PM
PL
PL
PM
NS
ZE
PS
PM
PL
PL
PL
PL
NL
NM
NS
ZE
PS
PM
PL
de
4.2
SIMULATION RESULTS
This section presents the details of the simulation carried out on a
test system connected with a fuzzy logic-based shunt active filter. The test
system used in the previous chapters is used here also (Figure 4.5). The
proposed control strategy is incorporated in the shunt active filter. The values
of the circuit elements used in the simulation are given in Table 4.3.
MATLAB/SIMULINK is used to simulate the test system and the proposed
shunt active filter. The active filter performance is evaluated under steady
state and transient system conditions. The comprehensive simulation results
are presented below.
Figure 4.5 Test System
Table 4.3 System Parameters
Parameter
Supply phase to phase voltage,
frequency
Specification
415 V (rms), 50 Hz
Line Parameters (Rs, Ls)
1
Load Resistance (R1,R2)
70 , 50
Load Inductance (L1,L2)
37 mH, 3mH
Load I Power rating
7kw and 1160VAr
Load II Power rating
5kw and 940VAr
Filter coupling Inductance (Lf)
3 mH, 0.5
Inverter DC bus capacitor
1mF
Vdc (reference)
700V
Sampling Time
2x10-6 sec
Switching Frequency
16 kHz
,
1mH
Load II
Load I
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A.
Ideal Source Voltage Condition
First the system is simulated without the active filter. In this case,
the circuit breaker 1 is closed and circuit breaker 2 is opened. The three phase
load current waveform without any filter with ideal source voltage is shown in
Figure 4.6 (a). Figure 4.6(b) shows the harmonic spectrum of the distorted
waveform. The total harmonic distortion of the distorted line current is
26.34%. From the harmonic spectrum, it is evident that, the supply current is
distorted due to the dominancy of fifth and seventh harmonic spectral
components.
a) Distorted three phase line current
b) Harmonic Spectrum of the line current
Figure 4.6
Distorted line current and harmonic spectrum caused by
three phase uncontrolled rectifier
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Next, an active filter with the proposed control strategy is connected
in parallel with the load. The fuzzy logic controller is used to maintain the
voltage across the DC side capacitor constant. Figure 4.7 shows the source
current along with the frequency spectrum in the presence of the active power
filter with the proposed control scheme. The THD of current in Phase A, B
and C has reduced to 3.87%, 3.89% and 3.39%. It shows that the THD has
been very much reduced after connecting the filter. The performance of the
active filter with the proposed controller is found to be excellent, and the
source current is practically sinusoidal and it is in phase with the supply
voltage as shown in Figure 4.8.
Figure 4.7
Harmonic
Technique
current
filtering
with
proposed
Control
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Figure 4.8 Waveform of Source voltage and Current in Phase A
Figure 4.9
DC bus voltage maintenance-Performance comparison of PI
and Fuzzy control
The fuzzy-logic controller is used to maintain constant DC voltage
across the capacitor. The performance the fuzzy controller is compared with
the PI controller which is given in Figure 4.9. It is observed that the DC bus
voltage is exactly maintained at the reference value by the fuzzy logic
controller, whereas some deviations are present with the PI controller. The
performance comparison is made between PI and Fuzzy controller and it is
given in table 4.4.
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Table 4.4 Performance Comparison between PI and Fuzzy
S.No
Parameters
1
Settling time
2
Rise time
2
Overshoot
PI
0.04 sec
0.015sec
21%
Fuzzy
0.01 sec
0.005sed
11%
Case B: Unbalanced Source Voltage
In this case, the source voltage is made unbalanced from 0.6 sec to
0.7 sec as shown in Figure 4.10 (a). The unbalance is due to the voltage
deviation in phase A. In the absence of the filter, the load current THD is
35.66 % after 0.6 sec. The load current and its harmonic spectrum are shown
in Figure 4.10 (b) and 4.10 (c) respectively. The high value of THD is due to
the dominancy of the 3rd, 5th and 7th spectral content of the load current. The
current waveform and its harmonic spectrum with general p-q and modified
p-q theory along with proposed control strategy are given in Figure 4.11.
Since
the
compensation
current
references
have
negative-sequence
component, the three phase compensated source current is not sinusoidal with
general p-q theory. The THD value of source current after compensation is
3.09% upto 0.6 sec and 7.5% after 0.6 sec in phase A with p-q theory. From
the result it is clear that the general p-q theory is not suitable for unbalanced
source voltage conditions.
But the modified p-q theory reduces the THD value to 2.4 % upto
0.6 sec and 2.5% after 0.6 sec in phase A and also the compensated three
phase source current is balanced and sinusoidal. The summary of source
currents and their THD for general and modified p-q theory is given in table
IV. The proposed control technique along with modified p-q theory has
performed well under the unbalanced source voltage conditions.
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Figure 4.10 Distorted line current and harmonic spectrum under
unbalanced source voltage condition
Figure 4.11 Harmonic current filtering under unbalanced supply with
proposed Technique
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Case C. Under Varying Load Condition
To observe the transient characteristics of the proposed control
strategy, a step change in load current was applied. For this, the load I is
connected to the source upto 0.3 sec through circuit breaker I after that CB1
disconnects the load I from the source and CB2 connects the load II to the
source. Figure 4.12 (a) and (b) show the source current without filter and with
Shunt Active Filter respectively. The transient behavior of the proposed
technique is compared with the conventional fixed hysteresis control as
shown in Figure 4.12 (c). The proposed technique has good time response
since it can predict the crossover point in each half switching period based on
the instantaneous current reference signal.
Figure 4.12 Load and Source current waveform during step change in
load
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4.3
CONCLUSION
This chapter has presented a fuzzy logic based PWM current control
technique for developing the active filter for three-phase systems and also a
fuzzy logic controller is applied to maintain the constant voltage across the
capacitor by minimizing the error between the capacitor voltage and the
reference voltage. The performance of the proposed current control technique
is good for both unbalanced and varying load conditions since the controller
does not depend on the system parameter. Further the proposed controller has
good time response and it can compensate the harmonics present in the source
within half a cycle of the fundamental frequency. The simulation results show
that the proposed technique is effective in current harmonic filtering and can
keep the THD value within the IEEE standard.