62 CHAPTER 3 SHUNT ACTIVE FILTER USING AI TECHNIQUES 3.1 INTRODUCTION This chapter will deal in the details of Voltage Source Inverter (VSI) based Shunt Active Filter, its elementary compensation principle, design parameters and the mathematical modeling using Synchronous Reference Frame theory and the different types of controller proposed to maintain the DC link voltage. The schematic diagram of Shunt Active Filter is presented in Fig 3.1.It consists of three phase supply, three phase non-linear load, R-L filter, and shunt connected VSI Active Filter. Fig 3.1 Schematic Diagram of Shunt Active Filter The shunt connected VSI active power filter, with a self-controlled DC bus (capacitor on the DC side) has a topology similar to that of static compensator (STATCOM) used for reactive power compensation. The Shunt Active Filter injects a harmonic currents with the same amplitude as that of the load into the ac system but with opposite phase displacement. In this case the Shunt Active Filter operates as a current source injecting the harmonic component generated by the load but with a phase-shifted of 180[8,11,17,18,29].
Transcript
62
CHAPTER 3
SHUNT ACTIVE FILTER USING AI TECHNIQUES
3.1 INTRODUCTION
This chapter will deal in the details of Voltage Source Inverter (VSI) based Shunt
Active Filter, its elementary compensation principle, design parameters and the
mathematical modeling using Synchronous Reference Frame theory and the different
types of controller proposed to maintain the DC link voltage. The schematic diagram
of Shunt Active Filter is presented in Fig 3.1.It consists of three phase supply, three
phase non-linear load, R-L filter, and shunt connected VSI Active Filter.
Fig 3.1 Schematic Diagram of Shunt Active Filter
The shunt connected VSI active power filter, with a self-controlled DC bus (capacitor
on the DC side) has a topology similar to that of static compensator (STATCOM) used
for reactive power compensation. The Shunt Active Filter injects a harmonic currents
with the same amplitude as that of the load into the ac system but with opposite phase
displacement. In this case the Shunt Active Filter operates as a current source injecting
the harmonic component generated by the load but with a phase-shifted of
180 [8,11,17,18,29].
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3.2 MATHEMATICAL MODELING OF SHUNT ACTIVE FILTER
The analytical behavior of Shunt Active Filter can be successfully performed by
modeling the three phase source with Active Filter connected in parallel to the
distribution load.
The Shunt Active Filter with Voltage Source Inverter shown in Fig 3.2, is modeled in
the stationary reference frame abc [72,59,13,14,19]
[
]
[
]
[
]
[
] (3.1)
Fig 3.2 Shunt Active Filter with Voltage Source Inverter
The active filter of can be modeled in the rotating dq reference frame from (1) with the
aim of reducing control complexity if compared with the control using the stationary
abc reference frame model.
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In order to convert quantities from abc to an arbitrary rotating dq0 reference frame, the
transformation matrix is necessary and is given below
√
[
√
⁄ √
⁄ √
⁄ ]
(3.2)
A Phase Locked Loop (PLL) scheme is used to determine the angle for the dq
reference frame orientation such that and √ ⁄ , assuming the supply
voltage
(3.3)
In steady-state conditions the fundamental component of dqo quantities is constant.
Thus harmonics on the inverter can be imposed by separating the constant current
component from the oscillating component. This oscillating component with reverse
phase is the reference of the controller.
The dynamical model of the system in dqo reference frame obtained is from equations
(3.1) and (3.2) [72, 4] results in,
[
]
[
]
(3.4)
Where and are the switching state functions of the system in dq reference
frame and is the supply angular frequency. Expanding the first and second rows of
equation (3.4)
(3.5)
(3.6)
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Let and are the right side terms of the equations (3.5) and (3.6), therefore
(3.7)
(3.8)
The terms and are the respective outputs of the two current PI controllers:
∫ (3.9)
∫ (3.10)
where - and
- are the current errors
Using equation (3.7) and (3.8) the switching state functions are
(3.11)
(3.12)
The terms
and
are known as compensation parts which may be
added or not to the output of PI controllers.
The third equation of the model (3.4) is given by
(3.13)
This equation can be rewritten as:
(3.14)
In order to control the DC voltage, a PI controller is used
∫ (3.15)
Where is the voltage error. The control effort is given by equation
(3.16)
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Assuming that the current loop is ideal, the following properties hold
(3.17)
Assuming the supply voltage is given by equation (3.3) the transformation of and
[38]to dq coordinates yields √ and . As a result
and
√ .The control effort can be approximated by
√
(3.18)
The instantaneous active power is .In order to maintain the DC-link voltage
the DC, d axis current in (3.18) must be added to because the current does not
contribute for the active power to maintain the DC link voltage.
3.3 SYNCHRONOUS REFERENCE FRAME CONTROL THEORY
The synchronous reference frame theory or d-q theory is based on time-domain
reference signal estimation techniques. It can perform the operation in steady-state or
transient state for voltage and current waveforms. Synchronous reference frame
method is utilized to extract the harmonic content of the load and thus allows to
control the active filters in real-time system [24].
It is basically the transformation of coordinates from a three-phase abc stationary
coordinate system to the dq0 rotating coordinate system. This transformation is made
of two steps:
(i) First step is the transformation from the three phase stationary coordinate system to
the two phase α − β stationary coordinate system;
(ii) Second step is the transformation from α − β stationary coordinate system to the d-
q rotating coordinate system.
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Fig 3.3 shows the transformation of three phase quantities ua , ub and uc in abc
stationary reference frame to a two axis system with α axis in line with axis a . In a-b-
c, stationary axes (the axis abc are fixed) are separated from each other by 120°
From the relationships in projections and unchanged magnitude of formed vectors, the
transformation matrix is obtained as
[
√
√
]
(3.19)
The last row is used to obtain the zero sequence component of a three phase quantity.
The second step is to convert two axis stationary to two axis rotating frame
transformation as shown in Figure 3.3, and the rotating axis d is with the speed of ω
with respect to axis α. Therefore the transformation matrix is obtained as
[
] (3.20)
Fig 3.3 Reference Frame Transformations
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Through this transformation, the ac component in α − β plane at speed of ω is
transformed to DC component. The two steps are combined together to form a
complete d-q transformation and the whole transformation matrix is obtained as
[
⁄
⁄
⁄ ]
(3.21)
3.4 D-Q TRANSFORMATION BASED HARMONIC DETECTION
Rotating reference frame d-q transformations are used for extracting fundamental and
harmonic currents. This theory transforms the corresponding fundamental current or
harmonics to become DC components and other untargeted frequency components
still to ac component in the frame. Therefore, these components can be filtered out by
low pass filtering (LPF). After an inverse d-q transformation in the respective frame,
the unfiltered DC components are transformed back to corresponding harmonic. A
targeted frequency component can then be separated from other frequency
components in harmonic load currents. This process can be explained by Fig 3-4
.
Fig 3.4 D-Q Transformation Procedure
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3.5 PLL SYNCHRONISATION
Phase-Locked Loop (PLL) is a technique that is used to obtain an accurate
synchronization to the grid [60, 47] The PLL circuit provides the rotation speed
(rad/sec) to the rotating reference frame [24]. The block diagram of Synchronous
Frame-PLL (SF-PLL) is illustrated in Fig 3.5. It explains that the instantaneous phase
angle θ is detected by synchronizing the PLL rotating reference frame to the utility
voltage vector. Utility voltage vector sets the direct or quadrature axis reference
voltage vd or vq to zero by PI controller resulting in the reference being locked to the
utility voltage vector phase angle, the voltage frequency f and amplitude vm. The
amplitude, phase and frequency values provided by SRF-PLL are not individual-phase
but average information. Under ideal condition i.e distorted or unbalance utility
conditions, SF-PLL with a high bandwidth can yield a fast and precise detection of the
phase and amplitude of the utility voltage vector. In case the utility voltage is distorted
with high-order harmonics, the SF-PLL can still operate with reduced bandwidth but
at the cost of the PLL response speed reduction in order to reject and cancel out the
effect of these harmonics on the output [73, 54]. SRF-PLL may not be applied to
single phase systems in a straightforward manner. However, it provides a useful
structure for single-phase PLLs as long as the 90-degree-shifted orthogonal
component of the single phase input signal is created [109].
Fig 3.5 Block Diagram of Synchronous Frame-PLL
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3.6 ROLE OF DC CAPACITOR
The DC side capacitor plays the following important role:
(i) it maintains a DC voltage with small ripple in steady state, and
(ii) It serves as an energy storage element to supply real power difference
between load and source during the transient period.
[
] [
] [
]
Thus, the DC capacitor voltage can be maintained at a reference value. However,
when the load condition changes the DC capacitor can be used to compensate the real
power balance between the source and the load. In order to keep satisfactory operation
of the active filter, the peak value of the reference current is adjusted proportionally
according to the change in the real power drawn from the source. Thus charging and
discharging of the capacitor compensates the real power consumed by the load. If the
DC capacitor voltage is recovered and attains the reference voltage, the real power
supplied by the source is supposed to be equal to that consumed by the load again.
Thus, in this fashion the peak value or the reference source current can be obtained by
regulating the average voltage of the DC capacitor. The real/reactive power injection
may result in the ripple voltage of the DC capacitor. A low pass filter is generally used
to filter these ripples, which introduce a finite delay.
3.7 CONTROL STARTEGY OF SHUNT ACTIVE FILTER
Synchronous Reference Frame Theory was introduced in [132] is used to generate the
pulses for the semiconductor switches which support the maximum filter current
introduced to the main side. The three phase currents (ia,,ib,ic) , load currents (iLa, iLb,
iLc), the PCC voltages (vsa, vsb, vsc) and DC bus voltage (vDC) of active filter are sensed
as feedback signals. Load currents are transformed into synchronously rotating
reference frame d axis and q axis by using cos and sin where is derived from
three phase PLL circuit. Synchronous Reference Frame control of Shunt Active Filter
is shown in Fig 3.6.
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The d-axis and q-axis currents consist of fundamental and harmonic components as
iii daddLd (3.22)
iii qaqdLq (3.23)
Fig 3.6 Synchronous Reference Frame Control Strategy of Active Filters [144]
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3.7.1 PI Controller
The PI controller consists of proportional term and integral term. Proportional value
determines the reaction to the current error; the Integral determines the reaction based
on the sum of recent errors. The reference currents for the control of active filter are
generated according to the equation (30). The output of PI controller at the DC bus
voltage of active filter is considered as the current (iloss) for meeting its losses.
vkvvkii ndeidndendepdnlossnloss )()1()()1()()(
(3.23)
where, vv ndede )1( is the error between the reference(vDC*) and sensed (vDC) DC
voltage at the nth sampling instant. Kpd and Kid are the proportional and the integral
gains of the DC bus voltage PI controller.
The reference source current is therefore expressed as,
iii lossddd
* (3.24)
Similarly PI controller is used to regulate reactive power
vkvvkii nteiqntentepqnqrsnqr )()1()()1()()(
(3.25)
The reference supply quadrature axis current is as
iii qrqdq
* (3.26)
where, vvv nsnte )(
*
)( denotes the error between reference (vs*) and actual(vs(n))
terminal voltage amplitudes at the n sampling instant. Kpq and Kiq are the proportional
and the integral gains of the PI controller [144].
3.7.2 Switching Signal
The switching signals for the PWM converter are obtained by comparing the actual
source currents (isa, isb, and isc) with the reference current templates (isa*, isb*, and isc*)
in the hysteresis current controller. Switching signals so obtained, after proper
amplification and isolation, are given to switching devices of the PWM converter [89].
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3.8 INTELLIGENT CONTROLLER SCHEME
Recent research works investigate and improve active power compensation by
developing new advanced control methods. Intelligent control is a class
of control techniques that use various AI computing approaches like fuzzy logic,
neural network, evolutionary computation genetic algorithm etc. Artificial Intelligence
techniques are the recent trends used for the enhancement of power quality .The
fuzzy-logic based controllers are also used for the control circuit design of active
filters. Fuzzy logic serves to represent uncertain and imprecise knowledge of the
system, whereas fuzzy control allows taking a decision even if we can’t estimate
inputs/ outputs only from uncertain predicates [133,145,150]. Artificial-intelligence
(AI) techniques, particularly the NNs, are having a significant impact on power-
electronics applications. Neural-network-based controllers provide fast dynamic
response while maintaining the stability of the converter system over a wide operating
range and are considered as a new tool to design control circuits for power quality
devices [181].To maintain the DC link voltage of Shunt Active Filter constant the DC
side capacitor voltage is compared with a reference value. The obtained error e
(=VDCref-VDC) and the change of error signal ce(n)=e(n)-e(n-1) at the nth sampling
instant act as inputs to implement the fuzzy control algorithm and neural network The
output of these intelligent controller takes care of the active power demand of load and
the losses in the system.
3.8.1 Design of Fuzzy Logic Controller
The key issue of harmonic reduction and reactive power compensation by fuzzy
control can be implemented by computing the active power using fuzzy logic
controller. Fig 3.7 shows the block diagram of implemented fuzzy logic control
scheme of Shunt Active Filter.
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Fig 3.7 Block Diagram of Implemented Fuzzy Logic Control Scheme of Shunt Active
Filter
The fuzzy control rule design involves defining rules that relate the input variables to
the output model properties. As FLC is independent of the system model, the design is
mainly based on the intuitive feeling for, and experience of, the process. To design the
FLC, it is common to use the output error (e) and the rate of error (e’) as controller
inputs One input is difference between the DC capacitor voltage and reference voltage
termed as error ‘e’ and second input is the rate of change of error ‘ce’. The triangular
shaped membership functions are considered for the input variables error ‘e’ (v*DC-
vDC), change in error ‘ce’ (de/dt) and output. Fig 3.8 shows the shapes of input/output
variables and the assignment of fuzzy control rules. Three membership functions
namely SN (small negative),S (small), SP (small positive), ZE (zero), are selected for
input variables and PS (positive small), NS (negative small) and Z (zero) are chosen
for output variables. Firstly all three variables are normalized with in the membership
function range. In the second stage, the fuzzy variables are processed by an interface
which executes 9 control rules. As both inputs have three subsets, a fuzzy rule base
formulated for the present application is shown in Fig 3. In third stage as
defuzzification and denormalization, the fuzzy variables are converted back to crisp
variables. Hence output is representing the active power losses.
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The fuzzy controller is characterized as follows:
• Three fuzzy sets for each input and output.
• Triangular membership functions for simplicity.
• Fuzzification using continuous universe of discourse.
• Implication using Mamdani's 'min' operator.
• Defuzzification using the ‘centroid’ method.
Fig 3.8 Input/ Output Variables and Fuzzy Control Rules
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3.8.2 Design of ANN Controller
Conventionally PI controllers are used to maintain the DC capacitor voltage constant.
The presented research work implements ANN by replacing the PI controller.
Artificial Neural Network has the ability to learn from experience in order to improve
their performance and to adapt themselves to changes in the environment. Structure of
ANN is the neuron which consists basically of a summer and an activation function as
shown in Fig 3.9.
The Feed Forward Back propagation (FFBP) algorithm is one of the most widely used
techniques in Artificial Neural Network (ANN). The term “feed forward” indicates
that the network has links that extend in only one direction. Feed Forward allows
signal to travel one way only; from input to output. There is no feedback (loops) i.e.
the output of any layer does not affect that same layer. Feed forward ANNs tends to be
straight networks that associate inputs with outputs as shown in Fig 3.10
Fig 3.9 Basic Structure of ANN
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Fig 3.10 A Typical Feedforward Neural Network
Except during training, there are no backward links in a feedforward network; all links
proceed from input nodes toward output nodes.
To train a neural network to perform some task, weights of each unit are adjusted in
such a way that the error between the desired output and the actual output is reduced.
This process requires that the neural network compute the error derivative of the
weights (EW).The back propagation algorithm is the most widely used method for
determining the EW.
3.8.2.1 The Back Propagation Algorithm
In the back propagation algorithm, each iteration of training involves the following
steps [66].
1) Training data is fed through the network in a forward direction, producing results
at the output layer. This is done by computing the weighting sum coming into the unit
and then applying the sigmoid function.
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The 'x' vector is the activation of the previous layer.
( →
→) (3.27)
=
(3.28)
The 'w' vector denotes the weights linking the neuron unit to the previous neuron
layer.
2)Squared error of the network is calculated at the output nodes based on known
target information, and the necessary changes to the weights that lead into the output
layer are determined based upon this error calculation,
( →)
∑
(3.29)
't' denotes a target value in the target vector, and 'o' denotes the activation of a unit in
the output layer.
3) To calculate the error term of each output unit, indicated below as 'delta'.
∑ (3.30)
The error term is related to the partial derivative of each weight with respect to the
network error.
4) Calculate the error term of each of the hidden units.
∑ (3.31)
The hidden unit error term depends on the error terms calculated for the output units.
5) Compute the weight deltas. ' ' here is the learning rate. A low learning rate can
ensure more stable convergence. A high learning rate can speed up convergence in
some cases.
(3.32)
'x' denotes the unit that's connected to the unit downstream by the weight 'w'
6) The final step is to add the weight deltas to each of the weights. This method
involves recomputing the network error before the next weight layer error terms are
computed.
(3.33)
Once finished, proceed back to step 1.
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These networks are characterized by their topology, the way in which they
communicate with their environment, the manner in which they are trained, and their
ability to process in formation. ANNs are being used to solve AI problems without
necessarily creating a model of a real dynamic system. To reduce the current
harmonics in the supply voltage a multilayer feedforward- type ANN-based controller
is designed. This network is designed with three layers, the input layer with 1, the
hidden layer with 30, and the output layer with 1 neuron, respectively. The neural
network is trained by specifying the input data (difference between the VDC reference
voltage and VDC voltage) and target data (representing active power loss) ,’tansig’
transfer functions between layers, 'trainlm’ and 1000 the number of epochs.
3.8.3 Particle Swarm Optimization Technique
PSO algorithm will search for the optimal parameters for PI parameters for
maintaining the DC link voltage (Kpv,Kiv) The objective function W is defined as
∫
(3.34)
where error is defined the difference between reference DC voltage and capacitor
voltage.
The problem formulations adopts the Integral of time square error (ITSE criteria) of
DC link voltage as the objective function, to determine the PI control parameters for
getting a minimum THD of the source current. The PSO searching method will try to
search the best controller parameters until the minimum W is achieved. It means that
the controller parameters from the searching process provide the best performance of
the vo response.
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ALGORITHM
For each particle
Initialize particle
END
Do
For each particle
Calculate fitness value
If the fitness value is better than the best personal fitness value in history, set current
value as a new best personal fitness value
End
Choose the particle with the best fitness value of all the particles, and if that fitness
value is better than current global best, set as a global best fitness value
For each particle
Calculate particle velocity according velocity change equation
Update particle position according position change equation
End
While maximum iterations or minimum error criteria is not attained
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3.9 HYSTERESIS CONTROLLER
The active filter is comprised of three-phase IGBT based VSI bridge to allow
independent current control. The upper device and the lower device in one phase leg
of VSI are switched in complementary manner. Hysteresis controllers are commonly
used and easy to implement, because it is able to achieve a very fast dynamic response
[116]. Hysteresis control schemes are based on a nonlinear feedback loop with two-
level hysteresis comparators. One disadvantage is that it is difficult to limit the
minimum and maximum switching frequencies in order to have a good tracking of the
reference current.
Fig.3.11 Hysteresis Controller
Hysteresis current control is utilized independently for each phase and directly
generates the switching signals for three-phase voltage source inverter. An error signal
e(t) is the difference between the desired current iref (t) and the actual current iactual (t) . If
the error current exceeds the upper limit of the hysteresis band, the upper switch of the
inverter arm is turned OFF and the lower switch is turned ON. These current errors are
given to hysteresis current controller as shown in Fig 3.11
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{
} (3.35)
Here the hysteresis band limit hb=0.2. The interface inductor between inverter and
Point of common coupling suppresses the harmonics caused by the switching
operation of the inverter.
3.10 SYSTEM CONFIGURATION
An Active Filter is composed of three-phase source, a linear and nonlinear load, a
voltage source inverter with DC energy source, and a controller. All these components
are modeled separately, integrated and then solved to simulate the system. Three-
phase source is supplied by a sinusoidal balanced three-phase 415 V amplitude having
50 Hz frequency, with a source inductance of 2mH and a source resistance of 0.2Ω.
The system data and the parameters selected for simulation studies are given in Table
3.1.Three phase nonlinear load is considered for simulating different operating on
source and load side. Three phase three wire Shunt Active Filter developed in
MATLAB using Power System Blockset toolbox is shown in Fig. 3.12.
Fig 3.12 MATLAB Based Simulation Model of Three Phase Three Wire Shunt Active
Filter
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3.10.1 Design Parameters of Shunt Active Filter
A three-leg voltage source converter (VSC) is used as a active filter and it has six
insulated-gate bipolar transistors (IGBTs), three interface inductors, and one dc
capacitor. The line to line voltage (VL-L) of the VSC is considered as 415V. The ac
inductor and the dc capacitor selection are as below.
(i) DC Capacitor Voltage
The minimum dc bus voltage should be greater than twice of the peak of the phase
voltage of the system [3.21]. The dc bus voltage is calculated as
= √ (√ ) (3.36)
where, m is the modulation index and is considered as 1. Thus Vdc is obtained as
677.60 for VLL of 415Vand it is selected as 750V.
(ii) DC Bus Capacitor
The value of dc capacitor (Cdc) depends on the instantaneous energy available to the
active filter during transients [17]. The principle of energy conservation is applied as,
[
] (3.37)
where, Vdc is the reference dc voltage and Vdc1 is the minimum voltage level of dc bus,
a is the over loading factor, V is the phase voltage, I is the phase current and t is time
by which the dc bus voltage is to be recovered.
Considering, a 2.5% (19 V) reduction in dc bus voltage during transients,
Vdc= 750 V, Vdc1= 731 V, V= 239.60V, I= respective phase current for nonlinear load
1 and nonlinear load 2 considered in Chapter 3, t= 350 μ s, a= 1.2, the calculated value
of Cdc is approximated to 2200μ F.
(iii) AC Inductor
The selection of the ac inductance (Lf) depends on the current ripple, switching
frequency fs, dc bus voltage (Vdc) and the Lf is given as,
(√ ) (3.38)
where m is the modulation index and a is the over-load factor. Considering =
5%, fs= 10 kHz, m =1, Vdc = 750V, a=1.2, the Lf value is calculated and round off
value of Lf of 10mH and 5mH is selected for nonlinear load 1 and nonlinear load 2.
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Table 3.1 Parameters of the System Considered for Shunt Active Filter
Source voltage and frequency 415 V (L-L) and 50Hz
Source Resistance and Inductance 0.2 ohms and 2 mH
Three phase non linear
Load 1
Balanced Load :–
5 ohms and 30e-3 H
Three phase full rectifier drawing
12 A of current
Unbalanced Load:-
Phase a -15 ohms
Phase b -5 ohms and 30e-3 H
Phasec-5 ohms and 30e-3 H
Three phase full rectifier drawing
12 A of current
Three phase nonlinear load 2 Phase a -25 ohms
Phase b -10 ohms and 80e-3 H
Phasec-10 ohms and 80e-3 H
Three phase full rectifier drawing
12 A of current
DC Link voltage 2200e-6 F
Active Filter Inductance for
linear load 1
10mH
Active Filter Inductance for linear
load 2
5mH
Reference voltage 750 V
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3.11 SIMULATION RESULTS
In this section, dynamic performance of the three-phase three-wire Shunt Active Filter
is evaluated through MATLAB considering the system under balanced and
unbalanced non-linear load with different operating conditions. Since due to nonlinear
load current harmonics are introduced in the source current therefore, Shunt Active
Filter is assessed for harmonic cancellation in source current, reactive power
compensation and load balancing .The Steady state performance is analyzed by the
FFT analysis of source current where Shunt Active Filter is appraised by directing the
active power loss in DC capacitor through PI controller, Fuzzy controller, Artificial
Neural Network control and PSO technique.
3.11.1 Transient Performance of Balanced and Unbalanced Nonlinear Load
without Active Filter
The three phase nonlinear load connected to three phase supply draws harmonics and
reactive power component from the AC Mains. This leads to distorted source current.
Fig 3.13 shows switching performance of three phase three wire with balanced
nonlinear current without filtering. Initially linear load is connected to the three phase
supply. At time 0.3s balanced nonlinear load is connected to the system as shown in
Fig 3.13. Hence source current is same as the load current without compensation.
Fig 3.14 shows the performance of three phase three wire Shunt Active Filter with
unbalanced load. Initially unbalanced linear load is connected to the three phase
supply drawing nonlinear current from the source. Hence the source current is also
unbalanced and nonlinear due to the addition of nonlinear unbalanced load.
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Fig 3.13 The Performance of Three Phase Three Wire System with Balanced
Nonlinear Load
87
Fig 3.14The Performance of Three Phase Three Wire System with Unbalanced
Nonlinear Load
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3.11.2 Transient Performance of Balanced and Unbalanced Nonlinear Load with
Shunt Active Filter under Different Operating Conditions.
Synchronous Reference Frame Theory is used to generate compensating current which
adds up in the load current to get sinusoidal source current. The reference source
currents are derived from the sensed PCC voltages (vsa, vsb, vsc.), load currents (iLa, iLb,
iLc) and the DC bus voltage of active filter (vDC). A hysteresis current controller is
used over the reference (iLa*, iLb*, iLc*) and sensed (iLa, iLb, iLc) load currents to
generate the gating signals for the IGBTs of the VSC. The DC capacitor voltage is
responsible for active power loss. Hence the difference between the DC bus voltage
and the reference DC voltage is given to the PI controller to maintain the DC bus
voltage constant equal to 750V.
In Synchronous Reference Frame Theory abc stationary co-ordinates are converted to
dq rotating reference frame. PLL synchronization of source voltage is must to
determine the synchronizing angle. Fig 3.15 shows the PLL synchronized waveform
of source voltage. The direct axis and quadrature axis load current so obtained by
making use of the synchronizing angle is shown in Fig 3.16
Fig 3.15 PLL Synchronized Waveform of Source Voltage.
89
Fig 3.16 Direct Axis and Quadrature Axis Load Current
The performance of three-phase shunt active filter is demonstrated for the transient
and steady state and results are validated by MATLAB simulation for total harmonic
deduction, reactive power compensation along with power factor correction. The
model is analyzed under varying loads in different operating conditions.
3.11.2.1 Transient Performance of Shunt Active Filter under Balanced Source
Balanced Load Condition
The transient performance of the Shunt Active Filter under balanced source balanced
load condition is shown in Fig.3.17.Initially balanced linear load is connected to the
three phase sinusoidal source. Active Filter is activated at time t=0.1s.Due to linear
balanced load source current is also sinusoidal and balanced. A non-linear load is
connected at 0.3 sec. Nonlinearity of current can be seen in the load current whereas
the source current is observed as sinusoidal due to the filtering action provided by the
Active Filter. This verifies the proper compensation. The source voltage, source
current, load current, compensating current are depicted in Fig. 3.17.
The VSI inverter is composed of IGBT/Diodes switch. Thus the charging of DC
capacitor, connected at the DC side of VSI initiates charging as soon as the three
90
phase supply is connected to the system. When the Active Filter is switched ON at
time t=0.1s by providing the gate pulses to IGBT’s of the VSI DC capacitor activates
to reach the reference value of 750V as shown in Fig 3.18. At time t=0.3s nonlinear
load is connected at the distribution side and it is observed that the DC bus voltage of
Active Filter is able to maintain close to the reference value under all disturbances.
Fig 3.17.The Transient Performance of Shunt Active Filter under Balanced Source
Balanced Load Condition
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Fig. 3.18 The Charging of DC Capacitor of Shunt Active Filter under Balanced Source
Balanced Load Condition
3.11.2.2 Transient Performance of Shunt Active Filter under Unbalanced Source
Balanced Load Condition
The transient performance of the Shunt Active Filter under unbalanced source
