Digital Simulation of Predictive Current Control of Inverter with Future Reference Consideration using MATLAB

IJSTE - International Journal of Science Technology & Engineering | Volume 1 | Issue 12 | June 2015 ISSN (online): 2349-784X

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269

Digital Simulation of Predictive Current Control

of Inverter with Future Reference Consideration

using MATLAB

Arya Jyoti Deo Bibhu Prasad Panigrahi

PG Scholar Department of Electrical Engineering

Department of Electrical Engineering

Indira Gandhi Institute of Technology, Sarang,

Dhenkanal, India

Indira Gandhi Institute of Technology, Sarang,

Dhenkanal, India

Abstract

This paper presents the current control of two level voltage source inverter (VSI) designed in a discretized model using model

predictive control (MPC) technique. MPC basically deals with the minimization of cost function of the system. Cost function is a

measure of error between the measured value and the reference taken. But if the sampling time of the discretized model is quite

large then a delay will be observed during the application of the control technique. The delay compensation is done with the

consideration of future reference value in the cost function formulation. The optimized voltage vector obtained by this method

results in a output load current with reduced ripple content. The simulation results obtained without and with delay compensation

are discussed.

Keywords: Cost function, Delay Compensation, Inverter, Load, Predictive Controller

________________________________________________________________________________________________________

I. INTRODUCTION

Predictive control is not a specific algorithm rather an approach for the control design. According to the mode of control it can be

classified in various ways. Control scheme[4] like dead beat control deals with the minimization of error where as the hysteresis

control decides whether the evaluated variable is within the tolerance band or not. The control scheme discussed in this paper is

model predictive control which basically deals with the minimization of the cost function of the system. In this method the model

of the system is used to predict the future value of the variable up to a predicted horizon in time and the optimum sequence is

obtained. According to receding horizon strategy, the controller used in MPC applies only the first element of the sequence. But

the optimization problem is solved for every sampling instant with the comparison between the measured and the new sequence

of optimized data available after each of the sampling instant. For proper operation, all possible switching sates are evaluated and

the corresponding optimal value is stored to be applied next [2]. If the sampling time taken is more, then the calculation time is

quite significant. Hence there will be a delay between the instant of current measurement and the instant of new switching state

application. This results in an oscillation of the load current around its reference with the increase in the ripple content of the

measured current. The reduction in the ripple can be obtained by compensating the delay observed by evaluating the cost

function using the future values of the reference currents.

II. CONVERTER MODEL

The three phase two level voltage source inverter circuit model used is shown in figure-1. The switches Sy , y=1,2,6 are operated in complementary mode and the voltage signal takes a value of 1 if switches of the upper leg are ON, otherwise the

signal value is 0.

Depending on the switching signals the output phase to neutral voltages of the inverter can be described as:

)4(

)3(

)2(

dccN

dbbN

daaN

VSV

VSV

VSV

Digital Simulation of Predictive Current Control of Inverter with Future Reference Consideration using MATLAB (IJSTE/ Volume 1 / Issue 12 / 045)


270

Fig. 1: Circuit Model of Two-Level Inverter

The output voltage vector of the VSI can be defined as:

)5()(3

2 2 cNbNaN VVVV

Where the unitary vector =1



271

)10()()()1()1( kEkVL

Tk

L

RTk ssp

where Ip represents the predicted value of the load current for the (k+1)

th instant, when load current I(k) is applied at k

th instant.

The term V(k) and )( k represents the voltage and estimated value of back emf vector at kth instant. The load back emf can be calculated by the following equation.

)11()1()()()1()1(

kT

LRk

T

LkVk

ss

where )1( k is the estimated value of )1( k . As the frequency of the load back emf is quite less than the sampling

frequency so it can be assumed that )( k = )1( k .

V. DELAY COMPENSATION

If the difference between the calculation time and the sampling time Ts is quite significant then there will be a delay for the

application of optimized switching state. During the evaluation of the optimized cast function the old switching state will

continue to apply.This delay can be compensated by estimating the load current value, using the optimum voltage vector [1] as:

)12(11 kVL

Tk

L

RTk ss

Where 1 k is the estimated value of load current at (k+1)th instant obtained by using the current value at kth instant, k and the optimum vector at k

th instant.Using this estimated value of current the prediction process is repeated with the load shifted

by one step forward in time domain. The estimated current for the next instant is

)13(1112

kV

L

Tk

L

RTk ss

Where 1kV is the voltage vector at (k+1)th instant. Then the modified cost function is evaluated on the basis of future error considering the future values of the measured and

reference current as follows:

)14()2()2()2()2( ____ kikikikic prefpref

Where )2(_ ki ref and )2(_ ki ref are the values of the reference current at (k+2)th

instant calculated by using

Lagranzes extrapolation formula as follows;

15231862 kikikiki refrefrefref The switching state that minimizes the modified cost function is selected and stored to be applied in the next sampling instant.

VI. SIMULATION RESULTS

The MATLAB/Simulink model [2] used for the predictive current control of the VSI is shown in Figure 3.

Fig. 3: Simulink Block Diagram for Simulation of Predictive Current Control

The output phase currents are compared with their corresponding reference currents for two cases. In the first case no delay

compensation is applied .In the second case delay compensation is done by estimating the load current for (k+1)th

instant and

using this value to predict the optimum vector. Hence the load model is made to be shifted by one step forward in time domain.



272

Fig. 4 (a)

Fig. 4 (b)



273

Fig. 4 (c)

Fig. 4: Comparison of Simulation Result Of Output Current With Reference Current Without And With Delay Compensation (A) For Phase A

(B) For Phase B (C) For Phase C.

Fig. 5: Comparison of Simulation Result of Measured Load Current in Two Phase Co-Ordinate System without and With Delay Compensation



274

VII. APPENDIX

System Parameters:

DC link voltage: Vd= 600 V; Sampling period, Ts=50s; Resistance: R=10; Load Inductance: L=10mH; Back emf: E=100V;

ACKNOWLEDGMENT

This work is completed successfully by the constant support from Prof. Bibhu Prasad Panigrahi, Head of the Department and all

faculty members of Electrical Engineering Department, Indira Gandhi institute of technology, Sarang, India.

REFERENCES

[1] J. Rodriguez, P. Cortes, Predictive control of power converters and electrical drives,1st edition, John Willey & Sons,Inc.,2012 [2] J. Rodriguez, J. Pontt, C. Silva, Predictive current control of voltage source inverter. IEEE Transactions on Industrial Electronics,vol.54, no. 1, pp. 495-

503, February 2007.

[3] P. Cortes, J. Rodriguez, D.E. Quevedo, and C. Silva, Predictive current control strategy with imposed load current spectrum, IEEE Transactions on Industrial Electronics, vol. 23 ,no. 2, pp. 612-618, March 2008.

[4] J. A. Rossiter, Model based predictive control: a practical approach, 1st edition, CRC Press, 2005. [5] N. Mohan, T. M. Undeland, and W.P. Robbins, Power electronics, 3rd edition, John Willey & Sons,Inc.,2003 [6] H. Abu-Rub, J. Guzinski, Z. Krzeminski, and H. Toliyat, Predictive current control of voltage source inverters, IEEE Transactions on Industrial

Electronics, vol. 51 ,no. 3, pp. 585-593, June 2004.

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Digital Simulation of Predictive Current Control of Inverter with Future Reference Consideration using MATLAB