A Robust Non Linear Control Scheme for Single Phase Active Multi Level Rectifier Subject to Voltage Input Sags

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 single-phase 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 proportional-integral (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 1-kVA SPAMR using MATLAB/ Simulink and THD also analyzed.

Index TermsActive multilevel rectifier, generalized proportional-integral (GPI) controllers, robust nonlinear control,

sag compensation

1. 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 energy-inefficient. These problems have led to the generation pattern of standards and specifications such CFE recommendation as L0000-45 based on the IEEE 519, for the case of Mexico, created with the objective of reducing overall levels of distortion. Typical examples of non-linear 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

2. 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 non-controlled 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.

   1. 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]

      1. (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

      2. 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) (1-T): {-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)

      1. 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 dc-dc converter elevator.

      2. Dq Model

      C d V = 2i – i

      dt dc R

      According to the theoretical principle of single

      Then

      Vab= sgn(is)(1-T)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 steady-state variables are delayed 90

      ° 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 = (T-1 T U)T T-1TI

      s

      s

      dt

      1

      – V

      – V

      R dc

      (2.20)

      (2.13)

      C d Vdc = (T-1 Udq) T T-1I 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:

      T-1=TT

      Equation (2.21) takes the form

      C d Vdc =( Udq) T TT-1I dq – 1 V

      (2.22)

      dt s

      R dc

      (2.23)

      then:

      (2.15)

      Where TT-1 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

3. 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.

   1. 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 (tp-1)= p .

      obtaining a decade bandwidth a lower cutoff frequency

      v

      v

      p

      p

      v22 1 q fc=472Hz. Fig. 3.2 shows the non-linear 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(tp-1) 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

      1. 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 rule-lookup 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

         1. Rule Viewer

         2. Surface Viewer

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

   Simulink model of SPAMR

   (non linear load with GPI and Fuzzy controller)

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