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 Total Downloads : 235
 Authors : Harisha B, K. Rama
 Paper ID : IJERTV2IS100887
 Volume & Issue : Volume 02, Issue 10 (October 2013)
 Published (First Online): 29102013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Robust Non Linear Control Scheme for Single Phase Active Multi Level Rectifier Subject to Voltage Input Sags
Harisha B K. Rama
M. Tech (EPS), Assistant Professor,
Department of EEE, Department of EEE,
St. Martins Engineering College, St. Martins Engineering College, Hyderabad, Andhra Pradesh Hyderabad, Andhra Pradesh
Abstract
In this paper, a robust nonlinear controller is proposed for the singlephase active multilevel rectifier (SPAMR) subject to voltage input sags. The controlling scheme is based on the input output model of the rectifier system combined with exact linearization achieved via Fuzzy and generalized proportionalintegral (GPI) control. The fuzzy plus GPI controller provides enhanced robustness for the SPAMR against unexpected voltage sags and load changes. The main contribution of this paper resides on avoiding the need for voltage sags detection algorithms while improving the dynamic response of the SPAMR. Simulation results obtained on a 1kVA SPAMR using MATLAB/ Simulink and THD also analyzed.
Index TermsActive multilevel rectifier, generalized proportionalintegral (GPI) controllers, robust nonlinear control,
sag compensation

Introduction
In recent years, the harmonic pollution in power systems due to loads not Linear has become a serious problem. As a result of the current injection distorted grid, power quality has been diminished, the above is seen reflected in problems such as voltage distorted in the common connection point under power factor on sensitive loads malfunction[2], failure critical loads, among others, making the use of energyinefficient. These problems have led to the generation pattern of standards and specifications such CFE recommendation as L000045 based on the IEEE 519, for the case of Mexico, created with the objective of reducing overall levels of distortion. Typical examples of nonlinear loads are energy conversion systems, where the controlled rectifiers filtering capacitors, one of the most common causes of harmonic distortion found in both the industrial and domestic applications.
At present a variety of processes require power generation Direct current (DC) from a source of alternating current (ac), this transformation is usually achieved through a rectifying circuit, which is constituted by a diode bridge does not controlled and a capacitor as filter element as shown in Fig 1. Although
the advantages of this system, among which are simplicity and low cost, important to mention the problems it creates, such as voltage sag, increased harmonic distortion current and low power factor.
Fig.1. Basic Circuit rectification

Single Phase Active Multilevel Rectifier
The problems associated with rectification systems exposed to this point, is Own uncontrolled rectifier circuit. Furthermore, the active rectifier circuits possess the ability to reduce these problems. Specifically, the Single Phase active multilevel converter (SPAMR) shown in Figure2 is capable of correcting factor regulate power and dc voltage given by the sum of the voltages across each capacitor, i.e, Vdc= Vc1+ Vc2
Figure 2. Single Phase Active Multilevel Rectifier (SPAMR)
This topology consists of a noncontrolled diode bridge, an inductor elevator two capacitors and two bidirectional switches. Appropriately switching the switches, it is possible to regulate the dc voltage at the desired operating point, keeping the free input current harmonics and high power factor. These features make this system an element that efficiently leverages the power provided by the mains without deteriorating the
quality thereof as proven in research work in general are discussed in the next section.
In the literature there have been several
control schemes for the SPAMR, between which the main feature is the power factor correction, decreasing harmonic distortion in the input current and dc voltage regulation.

Analysis Of Single Phase Active Multilevel Rectifier
2.2.3 Mode 3 [T1 Closed, T2 Open]
(2.2)
2.2 Modes of Operation
In the third mode of operation the capacitors
and loaded when the current input is positive and
SPAMR behavior can be divided into four modes, which depend on the state of the switches and. Figure
negative, respectively. Similarly voltages and increase in value according to the sign of the input current. The
2.2 shows the equivalent circuits. Each mode of
and the equation describing its behavior is:
operation offers different characteristics, so that the switching of the switches can increase or decrease the input current and load or unload voltages in the
(2.3)
capacitors. Such features can reduce distortion input current and dc voltage desired operating point.
2.2.1 Mode 1[T1 Open, T2 Open]
the level of to maintain a
2.2.4 Mode 4 [T1 Closed, T2 Closed]
The latter mode of operation is the absolute value of the input current increases because the voltage
Because the lifting frames of the circuit, the absolute
between terminals ab circuit equals zero. The equation
value decreases and the voltage at both capacitors
that describes the behavior is
increase its value. The circuit corresponding to this
mode of operation shown in Figure equation describing its behavior is
2.2.2 Mode 2[T1 Open, T2 Closed]

(a) and the
(2.1)
(2.4)
Based on the above analysis, is presented in Table 2.1, it shows the level of voltage between terminals ab of the SPAMR for each mode depending on the sign of the input current
Is
T1
T2
Vab
Positive values
0
0
Vc1+Vc2
0
1
Vc1
1
0
Vc2
1
1
0
Negative values
0
0
(Vc1+Vc2)
0
1
Vc2
1
0
Vc1
1
1
0
Is
T1
T2
Vab
Positive values
0
0
Vc1+Vc2
0
1
Vc1
1
0
Vc2
1
1
0
Negative values
0
0
(Vc1+Vc2)
0
1
Vc2
1
0
Vc1
1
1
0
In the second mode of operation the capacitor is charged and the voltage increases value when the input current is positive. Moreover, the capacitor and
charged voltage increases in value current is negative. The equation behavior
when the input describes their
Table 2.1.Voltage between terminals ab of the SPAMR

Mathematical Model
The differential equations describing the dynamics of the SPAMR are given by
i = Vdc
(2.8)
R R
Then
(2.5)
Finally, we define the switching function nd obtain the dynamic model of SPAMR represented by: = sgn (iS) (1T): {1, 0, +1} where is obtained using the
technique of pulse width
(SPWM).
modulation sinusoidal
Ls d is
dt
=[
Rs r
] [ is
1
1
] + [ ]Vs
C d Vdc
dt
2r 1/R
Vdc
0
(2.9)
2.3.1 Simplification at Three Levels
(2.6)

Average Model
The state equations in (2.9) do not represent a
useful model of the SPAMR because the switching
In order to obtain a model to derive the control algorithm proposed in this thesis, it is assumed that the
function is provided within the set of discrete {1,0,+1} Causing the is bilinear model (solid parts). Therefore,
switches simultaneously switched i.e. T1=T2=T. Thus use two of the four operating modes SPAMR thus, the voltage generated between terminals ab is three levels as shown in Table2.2.
the dynamical model obtained in previous section is
considered as a average (The average pattern obtained by averaging the dynamic model by switching period under assumption that the switching frequency is infinite) model assuming switching to a high frequency and redefining it as a continuous function u: R {1,
+1} sufficiently differentiable.
Thus, the average model SPAMR is:
Ls is
Ls is
IS
T1
T2
VAB
POSITIVE
0
0
VC1+VC2
1
1
0
NEGATIVE
0
0
(VC1+VC2)
1
1
0
IS
T1
T2
VAB
POSITIVE
0
0
VC1+VC2
1
1
0
NEGATIVE
0
0
(VC1+VC2)
1
1
0
d
0
0
dt =[Rs u
] [ is ] +
1]V
Table 2.2. Voltage between terminals ab of the SPAMR when T1=T2=T
C d Vdc
dt
2u 1/R
Vdc [ s
(2.10)
Moreover, it is considered that the load resistors are equal, i.e.R1=R2=R, Likewise, the capacitors C1=C2=C. In this way we obtain the state as
On the other hand, the GPI has been widely applied to obtain dc dc converters satisfactory results. Based on this background, 2.10) is mapped to a framework of synchronous reference
the sum of Vc1 and Vc2 adding the effect of the
resistance and inductor associated with the SPAMR model can be rewritten as
(2.7)
through dq transformation phase. Thus the average pattern SPAMR contains only dc signals so that it can be seen as a dcdc converter elevator.

Dq Model
C d V = 2i – i
dt dc R
According to the theoretical principle of single
Then
Vab= sgn(is)(1T)Vdc
phase dq transformation , is generated orthogonal imaginary circuit, this imaginar circuit is composed of
the same components the a tual circuit with the difference that all steadystate variables are delayed 90
Â° from their counterparts in the real circuit. Thus, you get a frame of reference stationary and applying the transformation matrix:
(2.18)
(2.11)
Now, using the vectors and in (2.10), the dc voltage equation can be rewritten in vec or form as:
Variables are obtained in the dq synchronous reference
frame where grid frequency is in rad /s.
The SPAMR, the real and imaginary signals are
C d Vdc= UT I
s
s
dt
1
– V
– V
R dc
s(2.19)
(2.12)
Using the above vectors in the model (2.10), the equation of the input current can be rewritten in vector form as:
Observation: The above equation implies that adding imaginary product to Voltage equation in the model (2.10), the dc component doubles its value while the voltage ripple disappears due to cancellation between the components of actual signals ac and imaginary.
Applying a transformation matrix T (2.19) yields:
L I
L I
d
sdt s
= – Rs
Is Vdc
U + Vs
C d Vdc = (T1 T U)T T1TI
s
s
dt
1
– V
– V
R dc
(2.20)
(2.13)
C d Vdc = (T1 Udq) T T1I dq – 1 V
Applying the transformation matrix T has:
dc
dc
T [Ls d is] = T[ RsIs V U + Vs]
dt
Vdc
(2.14)
dt s R dc
using matrix properties:
(2.21)
Transforming the left side of the above equation, taking the derivative of matrix product TIs:
T1=TT
Equation (2.21) takes the form
C d Vdc =( Udq) T TT1I dq – 1 V
(2.22)
dt s
R dc
(2.23)
then:
(2.15)
Where TT1 represents an identity matrix; thus, the equation for the dc voltage is rewritten as
C d Vdc =( Udq) T I dq – 1 V
dt s
R dc
(2.24)
(2.16)
Substituting (2.16) in (2.14) yields the equation of the
Finally the complete model of the SPAMR in the dq synchronous reference frame is
input current under dq synchronous reference:
L d i d = wL i – R id + vd – v ud
sdt s
s s s s s dc
L d i q = wL id – R i + v – v
ud
sdt s
s s s s s dc
L d d = L d + Vd – R d – Udq V
(2.17)
(2.25)
d 1 d d
sdt s
Where
s d s s d dc
C vdc – vdc + is u d R
+ is u



Control Objectives
The control objectives are

Stabilize the dc voltage at the desired operating point.

Reduce the THD of the input current.

Correct the power factor.
which must be met even in the presence of disturbances in the input source, and considering an unknown current demand.
As concluded in the previous chapter, the control objectives are met using the schemes proposed, but the performance thereof is to shocks poor, therefore, is the task of GPI provide robustness to the system, for it is used system model in the presence of disturbances.

Nonlinear Control & GPI
Similarly to the previous section, the controller is implemented using nonlinear GPI is obtained for the current loop and using again the same outer loop voltage.
3.3.1. Current Loop
Using the control law in the perturbed model, the closed loop dynamics output vector is reduced to an integrator
(3.1)
Figure 3.1 GPI current controllers for SPARM
From the diagram in Figure 3.1, the transfer functions for each output taking 1 as a disturbance are
(3.5)
Nominal control input v*=0 because y*is constant and the characteristic polynomial
(3.6)
Has a fully assignable pole arbitrarily. Then, selecting the coefficients
(3.7)
as follows, kc23= 3000 kc22=1000 kc21=60 and kc20= 1 It
v vd
releases the loopCurrent about switching frequency,
Where V =[ 12] And (tp1)= p .
obtaining a decade bandwidth a lower cutoff frequency
v
v
p
p
v22 1 q fc=472Hz. Fig. 3.2 shows the nonlinear control scheme
Defining the error control signals and outputs as
(3.2)
Where V* = Y. * the error dynamics is given by
(3.3)
Assuming 1(tp1) disturbance is well approximated by
using the controller GPI auxiliary inputs.
Fig.3.2. Block diagram of nonlinear control scheme & GPI for the SPAMR
a polynomial of second order (p 1=2), GPI controller third order
(3.4)
the system provides robustness with respect to

Fuzzy Plus GPI in Voltage Loop
Fuzzy logic and generalized proportional integral (GPI) controllers are use in SPAMR for sag mitigation. A simulation study of the SPAMR with GPI is studied. The Fuzzy rules and the inference
perturbations in the input voltage.
The block diagram o is shown in Fig. 3.1.
mechanism of the fuzzy logic controller (FLC) are evaluated by using conventional rulelookup tables that
encode the control knowledge in a rules form. The
performance assessment of the studied position controllers is based on dynamic response and error integral criteria. The results obtained from the FLC are not only superior in the output voltage, but also much better in reducing the total harmonic distortion
Fig.3.3Block diagram of nonlinear control scheme Fuzzy & GPI for the SPAMR

Rule Viewer

Surface Viewer


Simulink model of SPAMR (non linear load with GPI controller)
Simulink model of SPAMR
(non linear load with GPI and Fuzzy controller)

Simulation Results
Two types of tests were proposed
to validate the
Simulation results of SPAMR with GPI
(non linear load)
nonlinear control scheme ability to achieve the control objectives. The first one is concerned with the quality of the steadystate behavior and the second one is the

output voltage (b) input current (c) input voltage
ability to compensate voltage sags without using
detection algorithms. The performance of the scheme on the entire operation range was also tested. For this purpose, an ac mains voltage sag was induced at the same time of several load changes.
Simulation results of SPAMR Fuzzy and GPI
(non linear load)

output voltage (b) input current (c) input voltage

THD of Non Linear Load With GPI Controller
THD of Non Linear Load With Fuzzy Plus GPI Controller
Conclusion
A nonlinear control scheme for an SPAMR has been proposed. The main motivations for this proposal were to provide to the SPAMR with the capability to work well in the operation range while exhibiting a good dynamic behavior. At the same time, this approach enjoys added robustness properties with respect to ac mains voltage perturbations and dynamical load changes while eliminating the need for a sag detection
algorithm. This is, particularly, relevant from a power electronics viewpoint. It is important to mention that the controller parameters, both, in the simulations and in the experimental tests, were kept to be the same.
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